diff options
Diffstat (limited to 'REORG.TODO/sysdeps/ieee754')
961 files changed, 105820 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/Makefile b/REORG.TODO/sysdeps/ieee754/Makefile new file mode 100644 index 0000000000..5c7fc3fc52 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/Makefile @@ -0,0 +1,4 @@ +ifeq ($(subdir),math) +sysdep_headers += ieee754.h +endif + diff --git a/REORG.TODO/sysdeps/ieee754/bits/huge_val.h b/REORG.TODO/sysdeps/ieee754/bits/huge_val.h new file mode 100644 index 0000000000..fb3ba69c44 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/bits/huge_val.h @@ -0,0 +1,53 @@ +/* `HUGE_VAL' constant for IEEE 754 machines (where it is infinity). + Used by <stdlib.h> and <math.h> functions for overflow. + Copyright (C) 1992-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_H +# error "Never use <bits/huge_val.h> directly; include <math.h> instead." +#endif + +/* IEEE positive infinity (-HUGE_VAL is negative infinity). */ + +#if __GNUC_PREREQ(3,3) +# define HUGE_VAL (__builtin_huge_val()) +#elif __GNUC_PREREQ(2,96) +# define HUGE_VAL (__extension__ 0x1.0p2047) +#elif defined __GNUC__ + +# define HUGE_VAL \ + (__extension__ \ + ((union { unsigned __l __attribute__((__mode__(__DI__))); double __d; }) \ + { __l: 0x7ff0000000000000ULL }).__d) + +#else /* not GCC */ + +# include <endian.h> + +typedef union { unsigned char __c[8]; double __d; } __huge_val_t; + +# if __BYTE_ORDER == __BIG_ENDIAN +# define __HUGE_VAL_bytes { 0x7f, 0xf0, 0, 0, 0, 0, 0, 0 } +# endif +# if __BYTE_ORDER == __LITTLE_ENDIAN +# define __HUGE_VAL_bytes { 0, 0, 0, 0, 0, 0, 0xf0, 0x7f } +# endif + +static __huge_val_t __huge_val = { __HUGE_VAL_bytes }; +# define HUGE_VAL (__huge_val.__d) + +#endif /* GCC. */ diff --git a/REORG.TODO/sysdeps/ieee754/bits/huge_valf.h b/REORG.TODO/sysdeps/ieee754/bits/huge_valf.h new file mode 100644 index 0000000000..f24bcf452f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/bits/huge_valf.h @@ -0,0 +1,51 @@ +/* `HUGE_VALF' constant for IEEE 754 machines (where it is infinity). + Used by <stdlib.h> and <math.h> functions for overflow. + Copyright (C) 1992-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_H +# error "Never use <bits/huge_valf.h> directly; include <math.h> instead." +#endif + +/* IEEE positive infinity (-HUGE_VAL is negative infinity). */ + +#if __GNUC_PREREQ(3,3) +# define HUGE_VALF (__builtin_huge_valf()) +#elif __GNUC_PREREQ(2,96) +# define HUGE_VALF (__extension__ 0x1.0p255f) +#elif defined __GNUC__ + +# define HUGE_VALF \ + (__extension__ \ + ((union { unsigned __l __attribute__((__mode__(__SI__))); float __d; }) \ + { __l: 0x7f800000UL }).__d) + +#else /* not GCC */ + +typedef union { unsigned char __c[4]; float __f; } __huge_valf_t; + +# if __BYTE_ORDER == __BIG_ENDIAN +# define __HUGE_VALF_bytes { 0x7f, 0x80, 0, 0 } +# endif +# if __BYTE_ORDER == __LITTLE_ENDIAN +# define __HUGE_VALF_bytes { 0, 0, 0x80, 0x7f } +# endif + +static __huge_valf_t __huge_valf = { __HUGE_VALF_bytes }; +# define HUGE_VALF (__huge_valf.__f) + +#endif /* GCC. */ diff --git a/REORG.TODO/sysdeps/ieee754/bits/inf.h b/REORG.TODO/sysdeps/ieee754/bits/inf.h new file mode 100644 index 0000000000..eee0f2ea88 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/bits/inf.h @@ -0,0 +1,29 @@ +/* `INFINITY' constant for IEEE 754 machines. + Copyright (C) 2004-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_H +# error "Never use <bits/inf.h> directly; include <math.h> instead." +#endif + +/* IEEE positive infinity. */ + +#if __GNUC_PREREQ(3,3) +# define INFINITY (__builtin_inff()) +#else +# define INFINITY HUGE_VALF +#endif diff --git a/REORG.TODO/sysdeps/ieee754/bits/nan.h b/REORG.TODO/sysdeps/ieee754/bits/nan.h new file mode 100644 index 0000000000..b6e14f5873 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/bits/nan.h @@ -0,0 +1,52 @@ +/* `NAN' constant for IEEE 754 machines. + Copyright (C) 1992-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_H +# error "Never use <bits/nan.h> directly; include <math.h> instead." +#endif + + +/* IEEE Not A Number. */ + +#if __GNUC_PREREQ(3,3) + +# define NAN (__builtin_nanf ("")) + +#elif defined __GNUC__ + +# define NAN \ + (__extension__ \ + ((union { unsigned __l __attribute__ ((__mode__ (__SI__))); float __d; }) \ + { __l: 0x7fc00000UL }).__d) + +#else + +# include <endian.h> + +# if __BYTE_ORDER == __BIG_ENDIAN +# define __qnan_bytes { 0x7f, 0xc0, 0, 0 } +# endif +# if __BYTE_ORDER == __LITTLE_ENDIAN +# define __qnan_bytes { 0, 0, 0xc0, 0x7f } +# endif + +static union { unsigned char __c[4]; float __d; } __qnan_union + __attribute__ ((__unused__)) = { __qnan_bytes }; +# define NAN (__qnan_union.__d) + +#endif /* GCC. */ diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/Makefile b/REORG.TODO/sysdeps/ieee754/dbl-64/Makefile new file mode 100644 index 0000000000..5557c75b45 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/Makefile @@ -0,0 +1,6 @@ +ifeq ($(subdir),math) +# branred depends on precise IEEE double rounding +CFLAGS-branred.c = $(config-cflags-nofma) +CFLAGS-e_sqrt.c = $(config-cflags-nofma) +CFLAGS-e_pow.c = $(config-cflags-nofma) +endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/MathLib.h b/REORG.TODO/sysdeps/ieee754/dbl-64/MathLib.h new file mode 100644 index 0000000000..ffda70a413 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/MathLib.h @@ -0,0 +1,100 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/********************************************************************/ +/* Ultimate math functions. Each function computes the exact */ +/* theoretical value of its argument rounded to nearest or even. */ +/* */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round nearest mode of IEEE 754 standard. */ +/********************************************************************/ + +#ifndef UMATH_LIB +#define UMATH_LIB +/********************************************************************/ +/* Function changes the precision mode to IEEE 754 double precision */ +/* and the rounding mode to nearest or even. */ +/* It returns the original status of these modes. */ +/* See further explanations of usage in DPChange.h */ +/********************************************************************/ +unsigned short Init_Lib (void); + +/********************************************************************/ +/* Function that changes the precision and rounding modes to the */ +/* specified by the argument received. See further explanations in */ +/* DPChange.h */ +/********************************************************************/ +void Exit_Lib (unsigned short); + + +/* The asin() function calculates the arc sine of its argument. */ +/* The function returns the arc sine in radians */ +/* (between -PI/2 and PI/2). */ +/* If the argument is greater than 1 or less than -1 it returns */ +/* a NaN. */ +double uasin (double); + + +/* The acos() function calculates the arc cosine of its argument. */ +/* The function returns the arc cosine in radians */ +/* (between -PI/2 and PI/2). */ +/* If the argument is greater than 1 or less than -1 it returns */ +/* a NaN. */ +double uacos (double); + +/* The atan() function calculates the arctanget of its argument. */ +/* The function returns the arc tangent in radians */ +/* (between -PI/2 and PI/2). */ +double uatan (double); + + +/* The uatan2() function calculates the arc tangent of the two arguments x */ +/* and y (x is the right argument and y is the left one).The signs of both */ +/* arguments are used to determine the quadrant of the result. */ +/* The function returns the result in radians, which is between -PI and PI */ +double uatan2 (double, double); + +/* Compute log(x). The base of log is e (natural logarithm) */ +double ulog (double); + +/* Compute e raised to the power of argument x. */ +double uexp (double); + +/* Compute sin(x). The argument x is assumed to be given in radians.*/ +double usin (double); + +/* Compute cos(x). The argument x is assumed to be given in radians.*/ +double ucos (double); + +/* Compute tan(x). The argument x is assumed to be given in radians.*/ +double utan (double); + +/* Compute the square root of non-negative argument x. */ +/* If x is negative the returned value is NaN. */ +double usqrt (double); + +/* Compute x raised to the power of y, where x is the left argument */ +/* and y is the right argument. The function returns a NaN if x<0. */ +/* If x equals zero it returns -inf */ +double upow (double, double); + +/* Computing x mod y, where x is the left argument and y is the */ +/* right one. */ +double uremainder (double, double); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/asincos.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/asincos.tbl new file mode 100644 index 0000000000..5e7670c3b1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/asincos.tbl @@ -0,0 +1,5168 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/***************************************************************************/ +/* Table for arcsin() and arccos() FUNCTIONS */ +/***************************************************************************/ + +#ifdef BIG_ENDI +static const union {int4 i[5136];double x[2568];} asncs = { .i = { +/**/ 0x3FC04000, 0x00000000, +/**/ 0x3FF02169, 0x88994424, +/**/ 0x3FB0A6A2, 0xB799B115, +/**/ 0x3FC6EF15, 0xD57409A0, +/**/ 0x3FAA141E, 0xAF52EAA0, +/**/ 0x3FB75591, 0xABBBE261, +/**/ 0x3FA72B51, 0xD206D88F, +/**/ 0x3C96B595, 0x5BB33E7D, +/**/ 0x3FC04B41, 0xA03E2700, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF7E9677, 0x66BBDC7C, +/**/ 0x3FC0C000, 0x00000000, +/**/ 0x3FF02386, 0xF9E23A56, +/**/ 0x3FB1308C, 0x60FD0235, +/**/ 0x3FC7099F, 0x14D16B02, +/**/ 0x3FAAFED6, 0x27C01EE1, +/**/ 0x3FB79C6F, 0xDBCD5F98, +/**/ 0x3FA8144A, 0x4084DAAC, +/**/ 0xBC87C092, 0x38D8505E, +/**/ 0x3FC0CC55, 0x56C9F380, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF7C7906, 0x1DC5AA24, +/**/ 0x3FC14000, 0x00000000, +/**/ 0x3FF025B5, 0xB27141F6, +/**/ 0x3FB1BB18, 0x04CE7400, +/**/ 0x3FC72514, 0x72907342, +/**/ 0x3FABEC60, 0x0BF4222C, +/**/ 0x3FB7E610, 0x75B3736C, +/**/ 0x3FA9024C, 0x5199C343, +/**/ 0xBC8AE84C, 0x06B56F60, +/**/ 0x3FC14D7A, 0x3DEFA070, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF7A4A4D, 0x8EBE0A5C, +/**/ 0x3FC1C000, 0x00000000, +/**/ 0x3FF027F5, 0xC6DE8F57, +/**/ 0x3FB2464B, 0x345751E1, +/**/ 0x3FC74178, 0xCF026805, +/**/ 0x3FACDCD8, 0x40A9E0D6, +/**/ 0x3FB83282, 0xEB1D9C38, +/**/ 0x3FA9F590, 0xD7BE707B, +/**/ 0xBCAB9768, 0x03A2A6D6, +/**/ 0x3FC1CEB0, 0xE03B4870, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF780A39, 0x2170A943, +/**/ 0x3FC24000, 0x00000000, +/**/ 0x3FF02A47, 0x4C759796, +/**/ 0x3FB2D22B, 0x92771935, +/**/ 0x3FC75ECF, 0x26ABA06D, +/**/ 0x3FADD05B, 0x486A1932, +/**/ 0x3FB881D7, 0x5AF971D5, +/**/ 0x3FAAEE52, 0x831AEE0C, +/**/ 0x3CA13F57, 0xAD1B1BEF, +/**/ 0x3FC24FF9, 0xC8E09330, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF75B8B3, 0x8A68699B, +/**/ 0x3FC2C000, 0x00000000, +/**/ 0x3FF02CAA, 0x59374E09, +/**/ 0x3FB35EBE, 0xD44E8BEA, +/**/ 0x3FC77D1A, 0x92E4BE8A, +/**/ 0x3FAEC706, 0x4A6C34FD, +/**/ 0x3FB8D41E, 0x972F6E07, +/**/ 0x3FABECCD, 0xF9845F69, +/**/ 0x3C8BA1FA, 0x945C4185, +/**/ 0x3FC2D155, 0x83C058B0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF7355A6, 0xC8B1F774, +/**/ 0x3FC34000, 0x00000000, +/**/ 0x3FF02F1F, 0x03DC7745, +/**/ 0x3FB3EC0A, 0xC1EE9F61, +/**/ 0x3FC79C5E, 0x4A82E6D2, +/**/ 0x3FAFC0F7, 0x19B1EF72, +/**/ 0x3FB9296A, 0x2AA943E5, +/**/ 0x3FACF141, 0xEF8B9DE7, +/**/ 0xBC834081, 0x083C8716, +/**/ 0x3FC352C4, 0x9D6E5610, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF70E0FC, 0x2388BB30, +/**/ 0x3FC3C000, 0x00000000, +/**/ 0x3FF031A5, 0x63D81251, +/**/ 0x3FB47A15, 0x370B721F, +/**/ 0x3FC7BC9D, 0xA28731E5, +/**/ 0x3FB05F26, 0x1E305BE9, +/**/ 0x3FB981CC, 0x5FA50FBD, +/**/ 0x3FADFBEF, 0x42AC4083, +/**/ 0x3CA20ACB, 0xA8E107C7, +/**/ 0x3FC3D447, 0xA336F5E0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF6CB538, 0x4FDB5D5C, +/**/ 0x3FC44000, 0x00000000, +/**/ 0x3FF0343D, 0x9159D86F, +/**/ 0x3FB508E4, 0x23B3747C, +/**/ 0x3FC7DDDC, 0x0ED597CB, +/**/ 0x3FB0DF92, 0x79ADF104, +/**/ 0x3FB9DD58, 0x4658D945, +/**/ 0x3FAF0D19, 0x14ACA06B, +/**/ 0xBCA4E10D, 0xDF636EFE, +/**/ 0x3FC455DF, 0x23252C00, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF6784DD, 0x4C4F221A, +/**/ 0x3FC4C000, 0x00000000, +/**/ 0x3FF036E7, 0xA550D410, +/**/ 0x3FB5987D, 0x8D0AF1E7, +/**/ 0x3FC8001D, 0x22F39726, +/**/ 0x3FB161D0, 0xA1116D73, +/**/ 0x3FBA3C21, 0xBBEA1528, +/**/ 0x3FB01282, 0x74202FF6, +/**/ 0x3CAA0611, 0xD10866E2, +/**/ 0x3FC4D78B, 0xAC086560, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF6230B5, 0x5E57DF8A, +/**/ 0x3FC54000, 0x00000000, +/**/ 0x3FF039A3, 0xB96E0F8A, +/**/ 0x3FB628E7, 0x8E0C29F6, +/**/ 0x3FC82364, 0x92CEDE01, +/**/ 0x3FB1E5F0, 0xFB7B5D84, +/**/ 0x3FBA9E3D, 0x71BD08EE, +/**/ 0x3FB0A1FD, 0x5F7FFAB4, +/**/ 0xBC90F980, 0xEF04F6E7, +/**/ 0x3FC5594D, 0xCD7A8DC0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF59711A, 0x47C1D879, +/**/ 0x3FC5C000, 0x00000000, +/**/ 0x3FF03C71, 0xE8275C12, +/**/ 0x3FB6BA28, 0x584C2A23, +/**/ 0x3FC847B6, 0x338C3D4B, +/**/ 0x3FB26C04, 0x59A55DD8, +/**/ 0x3FBB03C0, 0xF5202D6A, +/**/ 0x3FB13522, 0x9C6466A4, +/**/ 0x3C983C9A, 0x2A268973, +/**/ 0x3FC5DB26, 0x17E62A20, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF4C70BE, 0xC51F7008, +/**/ 0x3FC64000, 0x00000000, +/**/ 0x3FF03F52, 0x4CBA31A9, +/**/ 0x3FB74C46, 0x34C49ADE, +/**/ 0x3FC86D15, 0xFC5F33CC, +/**/ 0x3FB2F41B, 0xFA419D7C, +/**/ 0x3FBB6CC2, 0xB757E82A, +/**/ 0x3FB1CC18, 0xDA4D5C39, +/**/ 0xBCA862D4, 0x2DFB224D, +/**/ 0x3FC65D15, 0x1C8C8AF0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF25B668, 0xB9CADBBF, +/**/ 0x3FC6C000, 0x00000000, +/**/ 0x3FF04245, 0x032EA88F, +/**/ 0x3FB7DF47, 0x84A2B473, +/**/ 0x3FC89388, 0x076A60F5, +/**/ 0x3FB37E49, 0x8E8394C1, +/**/ 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0x41226106, 0x04D6F19C, +/**/ 0x3CABCCF5, 0x15E5252C, +/**/ 0x3FF1EE3F, 0xFF35681A, +/**/ 0x40026000, 0x00000000, +/**/ 0x3F593B59, 0x9CAD4CE9, +/**/ 0x3FECF000, 0x00000000, +/**/ 0x4002BD54, 0x664A8350, +/**/ 0x40173EFF, 0x945190A0, +/**/ 0x403EFA80, 0xC7CC5224, +/**/ 0x406958AA, 0x896F1658, +/**/ 0x40973450, 0x4FD54E04, +/**/ 0x40C6BF55, 0x4CD60C4A, +/**/ 0x40F75EBE, 0x3EFFD07C, +/**/ 0x4128D03C, 0x9E2E6981, +/**/ 0xBC987CEE, 0xC8A488FF, +/**/ 0x3FF2135F, 0x8F597306, +/**/ 0x4002C000, 0x00000000, +/**/ 0xBF555CCD, 0xABE583FE, +/**/ 0x3FED1000, 0x00000000, +/**/ 0x40031D52, 0x2A40EA5C, +/**/ 0x4018C6B3, 0x52B4947D, +/**/ 0x404131AE, 0x5D01146E, +/**/ 0x406D54FB, 0x0163E71C, +/**/ 0x409BFE8A, 0xEF3ED15B, +/**/ 0x40CC9C28, 0xA33A6B00, +/**/ 0x40FEA523, 0x1456E1A6, +/**/ 0x4130F60F, 0xFC8790DB, +/**/ 0x3CAC104F, 0x6FABCA41, +/**/ 0x3FF23939, 0x30D87C68, +/**/ 0x40032000, 0x00000000, +/**/ 0xBF556EAD, 0xF8AD1CF9, +/**/ 0x3FED3000, 0x00000000, +/**/ 0x400383C4, 0xC053C623, +/**/ 0x401A7A81, 0x6ADBFF2C, +/**/ 0x40432C5B, 0xE219A24E, +/**/ 0x40711484, 0x30F4B8D8, +/**/ 0x40A10659, 0xBC59423E, +/**/ 0x40D22C09, 0x3D537AE5, +/**/ 0x410454A2, 0xA4B7D930, +/**/ 0x41378151, 0xC151F3C3, +/**/ 0xBCA2F226, 0x779E9951, +/**/ 0x3FF25FD9, 0x254E3F9C, +/**/ 0x40038000, 0x00000000, +/**/ 0x3F5E2602, 0x9E311A8B, +/**/ 0x3FED5000, 0x00000000, +/**/ 0x4003F16A, 0xA2F65F8C, +/**/ 0x401C61AF, 0x36C0308E, +/**/ 0x40457C82, 0x5337FF7D, +/**/ 0x407407A3, 0x7FB84BA9, +/**/ 0x40A4E476, 0x4C74DEA7, +/**/ 0x40D75638, 0xDF1C2124, +/**/ 0x410B5320, 0xA2556E94, +/**/ 0x414087CD, 0x7D68ABBE, +/**/ 0xBCACD58C, 0x73A87AB9, +/**/ 0x3FF2874D, 0x10017B06, +/**/ 0x40040000, 0x00000000, +/**/ 0xBF7D2ABA, 0x1340E849, +/**/ 0x3FED7000, 0x00000000, +/**/ 0x40046722, 0x7BA9A810, +/**/ 0x401E851F, 0xCBC74735, +/**/ 0x40483596, 0xF3879985, +/**/ 0x4077AAEB, 0xCD297F00, +/**/ 0x40A9E3C8, 0x31669F50, +/**/ 0x40DE5420, 0xB7CBB664, +/**/ 0x41129F7B, 0xB75100A0, +/**/ 0x4147A1C1, 0x51D127BF, +/**/ 0x3CAC647E, 0x46D9C78F, +/**/ 0x3FF2AFA4, 0x304962AE, +/**/ 0x40046000, 0x00000000, +/**/ 0x3F6C89EE, 0xA6A041C9, +/**/ 0x3FED9000, 0x00000000, +/**/ 0x4004E5F2, 0x7A99A835, +/**/ 0x402077E5, 0x15B0232D, +/**/ 0x404B70C1, 0xEE468866, +/**/ 0x407C334A, 0x43A041C3, +/**/ 0x40B036D1, 0x53D2C164, +/**/ 0x40E3F7B1, 0x10CCEDBE, +/**/ 0x4119C160, 0xF6C2E560, +/**/ 0x415131DD, 0x6D21D20F, +/**/ 0x41878683, 0x2EC50766, +/**/ 0xBCA95596, 0xD1134ECC, +/**/ 0x3FF2D8EF, 0xA8F4B028, +/**/ 0x4004E000, 0x00000000, +/**/ 0x3F67C9EA, 0x66A0D2C7, +/**/ 0x3FEDB000, 0x00000000, +/**/ 0x40056F11, 0xD6373B90, +/**/ 0x4021D7AC, 0xC3747DF3, +/**/ 0x404F4EF3, 0x6A014D6F, +/**/ 0x4080F4C4, 0x505C454B, +/**/ 0x40B48D16, 0x214975C5, +/**/ 0x40EAACFD, 0xF57BFAC6, +/**/ 0x41222235, 0x5225A6ED, +/**/ 0x41598643, 0xACBA67AB, +/**/ 0x419267B9, 0xDE5D19B9, +/**/ 0xBCAEF63C, 0x42C92439, +/**/ 0x3FF30342, 0xD86BED76, +/**/ 0x40056000, 0x00000000, +/**/ 0x3F7E23AC, 0x6E771F48, +/**/ 0x3FEDD000, 0x00000000, +/**/ 0x400603F5, 0x3D2D8CF1, +/**/ 0x40236A84, 0xEF4A10FA, +/**/ 0x4051FDF3, 0x4EA265AF, +/**/ 0x408499B5, 0xD944F636, +/**/ 0x40BA64B8, 0x37F73BAC, +/**/ 0x40F21B9F, 0x259B27FC, +/**/ 0x412A0669, 0x265D5B9F, +/**/ 0x41635D8E, 0x3DC806E2, +/**/ 0x419D8657, 0x36AD8B00, +/**/ 0x3CA4CEEB, 0x3FFCDCA3, +/**/ 0x3FF32EB3, 0xC69D2D10, +/**/ 0x40060000, 0x00000000, +/**/ 0x3F5FA9E9, 0x6C678625, +/**/ 0x3FEDF000, 0x00000000, +/**/ 0x4006A65F, 0x5FCDF915, +/**/ 0x40253B6E, 0x68321BDA, +/**/ 0x4054D949, 0x706E8DA9, +/**/ 0x408950EF, 0x4A70D2D7, +/**/ 0x40C13319, 0x1F15E14E, +/**/ 0x40F907B1, 0x846A9BD5, +/**/ 0x4133139C, 0x17C39016, +/**/ 0x416E1DA3, 0xBC86F11B, +/**/ 0x41A8597F, 0xD9F86F3B, +/**/ 0x3C32D4F8, 0x7D0D5190, +/**/ 0x3FF35B5B, 0xAFA88354, +/**/ 0x4006A000, 0x00000000, +/**/ 0x3F697D7F, 0x37E455FD, +/**/ 0x3FEE1000, 0x00000000, +/**/ 0x40075877, 0x41D1DBF9, +/**/ 0x402758A8, 0xF5852184, +/**/ 0x405861EE, 0x65C0F467, +/**/ 0x408F83C0, 0xD2D91276, +/**/ 0x40C6CA7C, 0x43EC3B0E, +/**/ 0x4101A722, 0x718322C8, +/**/ 0x413CA4C6, 0x9533D806, +/**/ 0x417812B7, 0xE9899583, +/**/ 0x41B4B875, 0x85EE8B86, +/**/ 0xBC99DEFB, 0xD1AEEED1, +/**/ 0x3FF38957, 0xB510476E, +/**/ 0x40076000, 0x00000000, +/**/ 0xBF6E22F8, 0xB8901BF9, +/**/ 0x3FEE3000, 0x00000000, +/**/ 0x40081CE6, 0xE1C37E57, +/**/ 0x4029D4F3, 0xD3DC9910, +/**/ 0x405CD074, 0xE3095065, +/**/ 0x4093E764, 0xC5C38224, +/**/ 0x40CEC5AE, 0x3CAE1F31, +/**/ 0x41097A50, 0xC0645F38, +/**/ 0x41461866, 0xD8A7F25E, +/**/ 0x4183DAF5, 0x8C2F04A3, +/**/ 0x41C2450E, 0xA9143C1F, +/**/ 0x3C7D25BE, 0x9FD995BC, +/**/ 0x3FF3B8C9, 0xC35D33E6, +/**/ 0x40082000, 0x00000000, +/**/ 0xBF58C8F1, 0xE40D49E0, +/**/ 0x3FEE5000, 0x00000000, +/**/ 0x4008F706, 0x285640BB, +/**/ 0x402CC96B, 0x3B2B7CD1, +/**/ 0x40613ADF, 0xC5341328, +/**/ 0x4099908D, 0x16E928A9, +/**/ 0x40D53986, 0x7CC08A3C, +/**/ 0x4112DFC5, 0x31DD3E45, +/**/ 0x41519499, 0xE2A13787, +/**/ 0x4190F943, 0xF94424AD, +/**/ 0x41D0C6BC, 0xCDCD49BE, +/**/ 0xBC9E2458, 0x6D41701D, +/**/ 0x3FF3E9D9, 0xC088BD28, +/**/ 0x40090000, 0x00000000, +/**/ 0xBF71F3AF, 0x537E8A00, +/**/ 0x3FEE7000, 0x00000000, +/**/ 0x4009EB18, 0x6562D1E0, +/**/ 0x40302C31, 0x75651223, +/**/ 0x4064E431, 0x336E41C7, +/**/ 0x40A0BCA6, 0xA065DA69, +/**/ 0x40DE034D, 0x917AF357, +/**/ 0x411CD2C1, 0x4168FB0F, +/**/ 0x415CFEB6, 0x15BB794D, +/**/ 0x419E3EE1, 0x6EFFD5E5, +/**/ 0x41E024E7, 0x1ACB4D9C, +/**/ 0xBC9C29C8, 0xD93F153F, +/**/ 0x3FF41CB7, 0x2183E810, +/**/ 0x4009E000, 0x00000000, +/**/ 0x3F7630CA, 0xC5A3C038, +/**/ 0x3FEE9000, 0x00000000, +/**/ 0x400AFEA6, 0xA364196F, +/**/ 0x403258F3, 0x0B19A2EB, +/**/ 0x4069BDA5, 0x2520AC75, +/**/ 0x40A669BC, 0x8F67EDEA, +/**/ 0x40E5D78C, 0xC026C9F8, +/**/ 0x4126CCB4, 0x1E3B36C2, +/**/ 0x4168EDE4, 0xBF45C805, +/**/ 0x41AC2F6A, 0x8AC89E76, +/**/ 0x41F0675E, 0x4CA9EB55, +/**/ 0x42336AC1, 0x0D13E3DF, +/**/ 0x3C9B1D74, 0xF2DE93A6, +/**/ 0x3FF4519B, 0x155FB22E, +/**/ 0x400B0000, 0x00000000, +/**/ 0xBF4595C9, 0xBE690E67, +/**/ 0x3FEEB000, 0x00000000, +/**/ 0x400C3908, 0x4BD1C065, +/**/ 0x40350D88, 0x26C39FFD, +/**/ 0x4070296B, 0x69D3E79E, +/**/ 0x40AED279, 0xD7FEEA5D, +/**/ 0x40F072A8, 0xFD5BD547, +/**/ 0x4132CDB9, 0x4A08BB38, +/**/ 0x41768482, 0x536BED06, +/**/ 0x41BBE1FF, 0x2F10E88D, +/**/ 0x4201C966, 0xABDBBDAC, +/**/ 0x42471011, 0x02E62DDA, +/**/ 0xBCA0855D, 0x3E907E71, +/**/ 0x3FF488CB, 0x8FA73920, +/**/ 0x400C4000, 0x00000000, +/**/ 0xBF6BDED0, 0xB8FE6DDF, +/**/ 0x3FEED000, 0x00000000, +/**/ 0x400DA439, 0x12AAF9A9, +/**/ 0x40387D46, 0x62F25109, +/**/ 0x4074C339, 0x3F133A3F, +/**/ 0x40B5E143, 0x662036F9, +/**/ 0x40F9CF04, 0x74467831, +/**/ 0x41404E10, 0x576C6FA8, +/**/ 0x41859489, 0xFF4F8E88, +/**/ 0x41CD88D2, 0xB44962A9, +/**/ 0x4214D838, 0x97A288F3, +/**/ 0x425DE10B, 0x6CF738B3, +/**/ 0xBC8E9EA7, 0x5F7263CC, +/**/ 0x3FF4C29F, 0xAA786F36, +/**/ 0x400DA000, 0x00000000, +/**/ 0x3F60E44A, 0xABE6A2AD, +/**/ 0x3FEEF000, 0x00000000, +/**/ 0x400F4E35, 0xC169B52F, +/**/ 0x403CF773, 0x29E8699C, +/**/ 0x407B6D37, 0xFC1818D6, +/**/ 0x40C02655, 0x1386790A, +/**/ 0x41054A1F, 0x4FF79D1E, +/**/ 0x414E104A, 0x7DB0265A, +/**/ 0x41963C39, 0xE5C8114B, +/**/ 0x41E10156, 0xF52A87DB, +/**/ 0x422ADD76, 0x2E9E7ABE, +/**/ 0x427586AB, 0x6EC81361, +/**/ 0x3C935690, 0xE395EEA6, +/**/ 0x3FF4FF86, 0x2E5965A2, +/**/ 0x400F4000, 0x00000000, +/**/ 0x3F7C6B82, 0xD36A5E70 } }; + +#else +#ifdef LITTLE_ENDI +static const union {int4 i[5136];double x[2568];} asncs = { .i = { +/**/ 0x00000000, 0x3FC04000, +/**/ 0x88994424, 0x3FF02169, +/**/ 0xB799B115, 0x3FB0A6A2, +/**/ 0xD57409A0, 0x3FC6EF15, +/**/ 0xAF52EAA0, 0x3FAA141E, +/**/ 0xABBBE261, 0x3FB75591, +/**/ 0xD206D88F, 0x3FA72B51, +/**/ 0x5BB33E7D, 0x3C96B595, +/**/ 0xA03E2700, 0x3FC04B41, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x66BBDC7C, 0xBF7E9677, +/**/ 0x00000000, 0x3FC0C000, +/**/ 0xF9E23A56, 0x3FF02386, +/**/ 0x60FD0235, 0x3FB1308C, +/**/ 0x14D16B02, 0x3FC7099F, +/**/ 0x27C01EE1, 0x3FAAFED6, +/**/ 0xDBCD5F98, 0x3FB79C6F, +/**/ 0x4084DAAC, 0x3FA8144A, +/**/ 0x38D8505E, 0xBC87C092, +/**/ 0x56C9F380, 0x3FC0CC55, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x1DC5AA24, 0xBF7C7906, +/**/ 0x00000000, 0x3FC14000, +/**/ 0xB27141F6, 0x3FF025B5, +/**/ 0x04CE7400, 0x3FB1BB18, +/**/ 0x72907342, 0x3FC72514, +/**/ 0x0BF4222C, 0x3FABEC60, +/**/ 0x75B3736C, 0x3FB7E610, +/**/ 0x5199C343, 0x3FA9024C, +/**/ 0x06B56F60, 0xBC8AE84C, +/**/ 0x3DEFA070, 0x3FC14D7A, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x8EBE0A5C, 0xBF7A4A4D, +/**/ 0x00000000, 0x3FC1C000, +/**/ 0xC6DE8F57, 0x3FF027F5, +/**/ 0x345751E1, 0x3FB2464B, +/**/ 0xCF026805, 0x3FC74178, +/**/ 0x40A9E0D6, 0x3FACDCD8, +/**/ 0xEB1D9C38, 0x3FB83282, +/**/ 0xD7BE707B, 0x3FA9F590, +/**/ 0x03A2A6D6, 0xBCAB9768, +/**/ 0xE03B4870, 0x3FC1CEB0, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x2170A943, 0xBF780A39, +/**/ 0x00000000, 0x3FC24000, +/**/ 0x4C759796, 0x3FF02A47, +/**/ 0x92771935, 0x3FB2D22B, +/**/ 0x26ABA06D, 0x3FC75ECF, +/**/ 0x486A1932, 0x3FADD05B, +/**/ 0x5AF971D5, 0x3FB881D7, +/**/ 0x831AEE0C, 0x3FAAEE52, +/**/ 0xAD1B1BEF, 0x3CA13F57, +/**/ 0xC8E09330, 0x3FC24FF9, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x8A68699B, 0xBF75B8B3, +/**/ 0x00000000, 0x3FC2C000, +/**/ 0x59374E09, 0x3FF02CAA, +/**/ 0xD44E8BEA, 0x3FB35EBE, +/**/ 0x92E4BE8A, 0x3FC77D1A, +/**/ 0x4A6C34FD, 0x3FAEC706, +/**/ 0x972F6E07, 0x3FB8D41E, +/**/ 0xF9845F69, 0x3FABECCD, +/**/ 0x945C4185, 0x3C8BA1FA, +/**/ 0x83C058B0, 0x3FC2D155, +/**/ 0x00000000, 0x3FF04000, +/**/ 0xC8B1F774, 0xBF7355A6, +/**/ 0x00000000, 0x3FC34000, +/**/ 0x03DC7745, 0x3FF02F1F, +/**/ 0xC1EE9F61, 0x3FB3EC0A, +/**/ 0x4A82E6D2, 0x3FC79C5E, +/**/ 0x19B1EF72, 0x3FAFC0F7, +/**/ 0x2AA943E5, 0x3FB9296A, +/**/ 0xEF8B9DE7, 0x3FACF141, +/**/ 0x083C8716, 0xBC834081, +/**/ 0x9D6E5610, 0x3FC352C4, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x2388BB30, 0xBF70E0FC, +/**/ 0x00000000, 0x3FC3C000, +/**/ 0x63D81251, 0x3FF031A5, +/**/ 0x370B721F, 0x3FB47A15, +/**/ 0xA28731E5, 0x3FC7BC9D, +/**/ 0x1E305BE9, 0x3FB05F26, +/**/ 0x5FA50FBD, 0x3FB981CC, +/**/ 0x42AC4083, 0x3FADFBEF, +/**/ 0xA8E107C7, 0x3CA20ACB, +/**/ 0xA336F5E0, 0x3FC3D447, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x4FDB5D5C, 0xBF6CB538, +/**/ 0x00000000, 0x3FC44000, +/**/ 0x9159D86F, 0x3FF0343D, +/**/ 0x23B3747C, 0x3FB508E4, +/**/ 0x0ED597CB, 0x3FC7DDDC, +/**/ 0x79ADF104, 0x3FB0DF92, +/**/ 0x4658D945, 0x3FB9DD58, +/**/ 0x14ACA06B, 0x3FAF0D19, +/**/ 0xDF636EFE, 0xBCA4E10D, +/**/ 0x23252C00, 0x3FC455DF, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x4C4F221A, 0xBF6784DD, +/**/ 0x00000000, 0x3FC4C000, +/**/ 0xA550D410, 0x3FF036E7, +/**/ 0x8D0AF1E7, 0x3FB5987D, +/**/ 0x22F39726, 0x3FC8001D, +/**/ 0xA1116D73, 0x3FB161D0, +/**/ 0xBBEA1528, 0x3FBA3C21, +/**/ 0x74202FF6, 0x3FB01282, +/**/ 0xD10866E2, 0x3CAA0611, +/**/ 0xAC086560, 0x3FC4D78B, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x5E57DF8A, 0xBF6230B5, +/**/ 0x00000000, 0x3FC54000, +/**/ 0xB96E0F8A, 0x3FF039A3, +/**/ 0x8E0C29F6, 0x3FB628E7, +/**/ 0x92CEDE01, 0x3FC82364, +/**/ 0xFB7B5D84, 0x3FB1E5F0, +/**/ 0x71BD08EE, 0x3FBA9E3D, +/**/ 0x5F7FFAB4, 0x3FB0A1FD, +/**/ 0xEF04F6E7, 0xBC90F980, +/**/ 0xCD7A8DC0, 0x3FC5594D, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x47C1D879, 0xBF59711A, +/**/ 0x00000000, 0x3FC5C000, +/**/ 0xE8275C12, 0x3FF03C71, +/**/ 0x584C2A23, 0x3FB6BA28, +/**/ 0x338C3D4B, 0x3FC847B6, +/**/ 0x59A55DD8, 0x3FB26C04, +/**/ 0xF5202D6A, 0x3FBB03C0, +/**/ 0x9C6466A4, 0x3FB13522, +/**/ 0x2A268973, 0x3C983C9A, +/**/ 0x17E62A20, 0x3FC5DB26, +/**/ 0x00000000, 0x3FF04000, +/**/ 0xC51F7008, 0xBF4C70BE, +/**/ 0x00000000, 0x3FC64000, +/**/ 0x4CBA31A9, 0x3FF03F52, +/**/ 0x34C49ADE, 0x3FB74C46, +/**/ 0xFC5F33CC, 0x3FC86D15, +/**/ 0xFA419D7C, 0x3FB2F41B, +/**/ 0xB757E82A, 0x3FBB6CC2, +/**/ 0xDA4D5C39, 0x3FB1CC18, +/**/ 0x2DFB224D, 0xBCA862D4, +/**/ 0x1C8C8AF0, 0x3FC65D15, +/**/ 0x00000000, 0x3FF04000, +/**/ 0xB9CADBBF, 0xBF25B668, +/**/ 0x00000000, 0x3FC6C000, +/**/ 0x032EA88F, 0x3FF04245, +/**/ 0x84A2B473, 0x3FB7DF47, +/**/ 0x076A60F5, 0x3FC89388, +/**/ 0x8E8394C1, 0x3FB37E49, +/**/ 0x160F3472, 0x3FBBD95A, +/**/ 0x39844810, 0x3FB26708, +/**/ 0x698BC8EA, 0x3C994228, +/**/ 0x6D8C14A0, 0x3FC6DF1B, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x754477AC, 0x3F422819, +/**/ 0x00000000, 0x3FC74000, +/**/ 0x285A8CEB, 0x3FF0454A, +/**/ 0xC21B9224, 0x3FB87332, +/**/ 0x92A93402, 0x3FC8BB10, +/**/ 0x3ED3F586, 0x3FB40A9F, +/**/ 0x643217C8, 0x3FBC499F, +/**/ 0x5D29A16B, 0x3FB3061A, +/**/ 0x3DF9F2D7, 0xBCA3B2DF, +/**/ 0x9DE6A160, 0x3FC76139, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x6A33AB4B, 0x3F5528A1, +/**/ 0x00000000, 0x3FC7C000, +/**/ 0xD9E48D58, 0x3FF04861, +/**/ 0x81461BF6, 0x3FB9080E, +/**/ 0x00E32FFA, 0x3FC8E3B4, +/**/ 0xAFB1F2A5, 0x3FB4992F, +/**/ 0xF33705D5, 0x3FBCBDAB, +/**/ 0x7E23EE89, 0x3FB3A97A, +/**/ 0xCCE44C41, 0x3C7AAD12, +/**/ 0x4187FAE0, 0x3FC7E370, +/**/ 0x00000000, 0x3FF04000, +/**/ 0xC91AAF11, 0x3F60C3B3, +/**/ 0x00000000, 0x3FC84000, +/**/ 0x36478509, 0x3FF04B8C, +/**/ 0x70FAC1B4, 0x3FB99DE1, +/**/ 0xDAA92166, 0x3FC90D76, +/**/ 0x06C416A6, 0x3FB52A0E, +/**/ 0x1CDCA344, 0x3FBD359A, +/**/ 0x7EFD4CA0, 0x3FB45155, +/**/ 0x35A8895D, 0x3C396CA5, +/**/ 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0xD86A7BFF, 0x4060E864, +/**/ 0x515F5BD6, 0x408B95CC, +/**/ 0xD070B4A1, 0x40B8180C, +/**/ 0xC9B24D80, 0x40E60D2C, +/**/ 0xAA392CAF, 0x4114DBF6, +/**/ 0xF5844C55, 0xBCA89BD0, +/**/ 0xDBFAF236, 0x3FF1A603, +/**/ 0x00000000, 0x4001C000, +/**/ 0xB37285FC, 0xBF4E66E4, +/**/ 0x00000000, 0x3FECB000, +/**/ 0x1757F6B1, 0x40020E3D, +/**/ 0xAE890640, 0x40149CE9, +/**/ 0xD6174F60, 0x403972D4, +/**/ 0x8C82DF92, 0x40634079, +/**/ 0xACAB5569, 0x40904BE6, +/**/ 0xB362E75A, 0x40BD8A99, +/**/ 0x389374DC, 0x40EC0ED7, +/**/ 0xCA5E9653, 0x411B8ADF, +/**/ 0x4A1E3E49, 0xBC80CBC7, +/**/ 0x704F5D26, 0x3FF1C9CF, +/**/ 0x00000000, 0x40020000, +/**/ 0xAFED62A2, 0x3F7C7A2E, +/**/ 0x00000000, 0x3FECD000, +/**/ 0x6B3395AA, 0x40026327, +/**/ 0x33FB1467, 0x4015DD66, +/**/ 0xDCF3437C, 0x403C0610, +/**/ 0xC9D7C47A, 0x406607CE, +/**/ 0xA330DC5C, 0x409360FB, +/**/ 0x38A3194B, 0x40C240B4, +/**/ 0xBAA6A879, 0x40F20437, +/**/ 0x04D6F19C, 0x41226106, +/**/ 0x15E5252C, 0x3CABCCF5, +/**/ 0xFF35681A, 0x3FF1EE3F, +/**/ 0x00000000, 0x40026000, +/**/ 0x9CAD4CE9, 0x3F593B59, +/**/ 0x00000000, 0x3FECF000, +/**/ 0x664A8350, 0x4002BD54, +/**/ 0x945190A0, 0x40173EFF, +/**/ 0xC7CC5224, 0x403EFA80, +/**/ 0x896F1658, 0x406958AA, +/**/ 0x4FD54E04, 0x40973450, +/**/ 0x4CD60C4A, 0x40C6BF55, +/**/ 0x3EFFD07C, 0x40F75EBE, +/**/ 0x9E2E6981, 0x4128D03C, +/**/ 0xC8A488FF, 0xBC987CEE, +/**/ 0x8F597306, 0x3FF2135F, +/**/ 0x00000000, 0x4002C000, +/**/ 0xABE583FE, 0xBF555CCD, +/**/ 0x00000000, 0x3FED1000, +/**/ 0x2A40EA5C, 0x40031D52, +/**/ 0x52B4947D, 0x4018C6B3, +/**/ 0x5D01146E, 0x404131AE, +/**/ 0x0163E71C, 0x406D54FB, +/**/ 0xEF3ED15B, 0x409BFE8A, +/**/ 0xA33A6B00, 0x40CC9C28, +/**/ 0x1456E1A6, 0x40FEA523, +/**/ 0xFC8790DB, 0x4130F60F, +/**/ 0x6FABCA41, 0x3CAC104F, +/**/ 0x30D87C68, 0x3FF23939, +/**/ 0x00000000, 0x40032000, +/**/ 0xF8AD1CF9, 0xBF556EAD, +/**/ 0x00000000, 0x3FED3000, +/**/ 0xC053C623, 0x400383C4, +/**/ 0x6ADBFF2C, 0x401A7A81, +/**/ 0xE219A24E, 0x40432C5B, +/**/ 0x30F4B8D8, 0x40711484, +/**/ 0xBC59423E, 0x40A10659, +/**/ 0x3D537AE5, 0x40D22C09, +/**/ 0xA4B7D930, 0x410454A2, +/**/ 0xC151F3C3, 0x41378151, +/**/ 0x779E9951, 0xBCA2F226, +/**/ 0x254E3F9C, 0x3FF25FD9, +/**/ 0x00000000, 0x40038000, +/**/ 0x9E311A8B, 0x3F5E2602, +/**/ 0x00000000, 0x3FED5000, +/**/ 0xA2F65F8C, 0x4003F16A, +/**/ 0x36C0308E, 0x401C61AF, +/**/ 0x5337FF7D, 0x40457C82, +/**/ 0x7FB84BA9, 0x407407A3, +/**/ 0x4C74DEA7, 0x40A4E476, +/**/ 0xDF1C2124, 0x40D75638, +/**/ 0xA2556E94, 0x410B5320, +/**/ 0x7D68ABBE, 0x414087CD, +/**/ 0x73A87AB9, 0xBCACD58C, +/**/ 0x10017B06, 0x3FF2874D, +/**/ 0x00000000, 0x40040000, +/**/ 0x1340E849, 0xBF7D2ABA, +/**/ 0x00000000, 0x3FED7000, +/**/ 0x7BA9A810, 0x40046722, +/**/ 0xCBC74735, 0x401E851F, +/**/ 0xF3879985, 0x40483596, +/**/ 0xCD297F00, 0x4077AAEB, +/**/ 0x31669F50, 0x40A9E3C8, +/**/ 0xB7CBB664, 0x40DE5420, +/**/ 0xB75100A0, 0x41129F7B, +/**/ 0x51D127BF, 0x4147A1C1, +/**/ 0x46D9C78F, 0x3CAC647E, +/**/ 0x304962AE, 0x3FF2AFA4, +/**/ 0x00000000, 0x40046000, +/**/ 0xA6A041C9, 0x3F6C89EE, +/**/ 0x00000000, 0x3FED9000, +/**/ 0x7A99A835, 0x4004E5F2, +/**/ 0x15B0232D, 0x402077E5, +/**/ 0xEE468866, 0x404B70C1, +/**/ 0x43A041C3, 0x407C334A, +/**/ 0x53D2C164, 0x40B036D1, +/**/ 0x10CCEDBE, 0x40E3F7B1, +/**/ 0xF6C2E560, 0x4119C160, +/**/ 0x6D21D20F, 0x415131DD, +/**/ 0x2EC50766, 0x41878683, +/**/ 0xD1134ECC, 0xBCA95596, +/**/ 0xA8F4B028, 0x3FF2D8EF, +/**/ 0x00000000, 0x4004E000, +/**/ 0x66A0D2C7, 0x3F67C9EA, +/**/ 0x00000000, 0x3FEDB000, +/**/ 0xD6373B90, 0x40056F11, +/**/ 0xC3747DF3, 0x4021D7AC, +/**/ 0x6A014D6F, 0x404F4EF3, +/**/ 0x505C454B, 0x4080F4C4, +/**/ 0x214975C5, 0x40B48D16, +/**/ 0xF57BFAC6, 0x40EAACFD, +/**/ 0x5225A6ED, 0x41222235, +/**/ 0xACBA67AB, 0x41598643, +/**/ 0xDE5D19B9, 0x419267B9, +/**/ 0x42C92439, 0xBCAEF63C, +/**/ 0xD86BED76, 0x3FF30342, +/**/ 0x00000000, 0x40056000, +/**/ 0x6E771F48, 0x3F7E23AC, +/**/ 0x00000000, 0x3FEDD000, +/**/ 0x3D2D8CF1, 0x400603F5, +/**/ 0xEF4A10FA, 0x40236A84, +/**/ 0x4EA265AF, 0x4051FDF3, +/**/ 0xD944F636, 0x408499B5, +/**/ 0x37F73BAC, 0x40BA64B8, +/**/ 0x259B27FC, 0x40F21B9F, +/**/ 0x265D5B9F, 0x412A0669, +/**/ 0x3DC806E2, 0x41635D8E, +/**/ 0x36AD8B00, 0x419D8657, +/**/ 0x3FFCDCA3, 0x3CA4CEEB, +/**/ 0xC69D2D10, 0x3FF32EB3, +/**/ 0x00000000, 0x40060000, +/**/ 0x6C678625, 0x3F5FA9E9, +/**/ 0x00000000, 0x3FEDF000, +/**/ 0x5FCDF915, 0x4006A65F, +/**/ 0x68321BDA, 0x40253B6E, +/**/ 0x706E8DA9, 0x4054D949, +/**/ 0x4A70D2D7, 0x408950EF, +/**/ 0x1F15E14E, 0x40C13319, +/**/ 0x846A9BD5, 0x40F907B1, +/**/ 0x17C39016, 0x4133139C, +/**/ 0xBC86F11B, 0x416E1DA3, +/**/ 0xD9F86F3B, 0x41A8597F, +/**/ 0x7D0D5190, 0x3C32D4F8, +/**/ 0xAFA88354, 0x3FF35B5B, +/**/ 0x00000000, 0x4006A000, +/**/ 0x37E455FD, 0x3F697D7F, +/**/ 0x00000000, 0x3FEE1000, +/**/ 0x41D1DBF9, 0x40075877, +/**/ 0xF5852184, 0x402758A8, +/**/ 0x65C0F467, 0x405861EE, +/**/ 0xD2D91276, 0x408F83C0, +/**/ 0x43EC3B0E, 0x40C6CA7C, +/**/ 0x718322C8, 0x4101A722, +/**/ 0x9533D806, 0x413CA4C6, +/**/ 0xE9899583, 0x417812B7, +/**/ 0x85EE8B86, 0x41B4B875, +/**/ 0xD1AEEED1, 0xBC99DEFB, +/**/ 0xB510476E, 0x3FF38957, +/**/ 0x00000000, 0x40076000, +/**/ 0xB8901BF9, 0xBF6E22F8, +/**/ 0x00000000, 0x3FEE3000, +/**/ 0xE1C37E57, 0x40081CE6, +/**/ 0xD3DC9910, 0x4029D4F3, +/**/ 0xE3095065, 0x405CD074, +/**/ 0xC5C38224, 0x4093E764, +/**/ 0x3CAE1F31, 0x40CEC5AE, +/**/ 0xC0645F38, 0x41097A50, +/**/ 0xD8A7F25E, 0x41461866, +/**/ 0x8C2F04A3, 0x4183DAF5, +/**/ 0xA9143C1F, 0x41C2450E, +/**/ 0x9FD995BC, 0x3C7D25BE, +/**/ 0xC35D33E6, 0x3FF3B8C9, +/**/ 0x00000000, 0x40082000, +/**/ 0xE40D49E0, 0xBF58C8F1, +/**/ 0x00000000, 0x3FEE5000, +/**/ 0x285640BB, 0x4008F706, +/**/ 0x3B2B7CD1, 0x402CC96B, +/**/ 0xC5341328, 0x40613ADF, +/**/ 0x16E928A9, 0x4099908D, +/**/ 0x7CC08A3C, 0x40D53986, +/**/ 0x31DD3E45, 0x4112DFC5, +/**/ 0xE2A13787, 0x41519499, +/**/ 0xF94424AD, 0x4190F943, +/**/ 0xCDCD49BE, 0x41D0C6BC, +/**/ 0x6D41701D, 0xBC9E2458, +/**/ 0xC088BD28, 0x3FF3E9D9, +/**/ 0x00000000, 0x40090000, +/**/ 0x537E8A00, 0xBF71F3AF, +/**/ 0x00000000, 0x3FEE7000, +/**/ 0x6562D1E0, 0x4009EB18, +/**/ 0x75651223, 0x40302C31, +/**/ 0x336E41C7, 0x4064E431, +/**/ 0xA065DA69, 0x40A0BCA6, +/**/ 0x917AF357, 0x40DE034D, +/**/ 0x4168FB0F, 0x411CD2C1, +/**/ 0x15BB794D, 0x415CFEB6, +/**/ 0x6EFFD5E5, 0x419E3EE1, +/**/ 0x1ACB4D9C, 0x41E024E7, +/**/ 0xD93F153F, 0xBC9C29C8, +/**/ 0x2183E810, 0x3FF41CB7, +/**/ 0x00000000, 0x4009E000, +/**/ 0xC5A3C038, 0x3F7630CA, +/**/ 0x00000000, 0x3FEE9000, +/**/ 0xA364196F, 0x400AFEA6, +/**/ 0x0B19A2EB, 0x403258F3, +/**/ 0x2520AC75, 0x4069BDA5, +/**/ 0x8F67EDEA, 0x40A669BC, +/**/ 0xC026C9F8, 0x40E5D78C, +/**/ 0x1E3B36C2, 0x4126CCB4, +/**/ 0xBF45C805, 0x4168EDE4, +/**/ 0x8AC89E76, 0x41AC2F6A, +/**/ 0x4CA9EB55, 0x41F0675E, +/**/ 0x0D13E3DF, 0x42336AC1, +/**/ 0xF2DE93A6, 0x3C9B1D74, +/**/ 0x155FB22E, 0x3FF4519B, +/**/ 0x00000000, 0x400B0000, +/**/ 0xBE690E67, 0xBF4595C9, +/**/ 0x00000000, 0x3FEEB000, +/**/ 0x4BD1C065, 0x400C3908, +/**/ 0x26C39FFD, 0x40350D88, +/**/ 0x69D3E79E, 0x4070296B, +/**/ 0xD7FEEA5D, 0x40AED279, +/**/ 0xFD5BD547, 0x40F072A8, +/**/ 0x4A08BB38, 0x4132CDB9, +/**/ 0x536BED06, 0x41768482, +/**/ 0x2F10E88D, 0x41BBE1FF, +/**/ 0xABDBBDAC, 0x4201C966, +/**/ 0x02E62DDA, 0x42471011, +/**/ 0x3E907E71, 0xBCA0855D, +/**/ 0x8FA73920, 0x3FF488CB, +/**/ 0x00000000, 0x400C4000, +/**/ 0xB8FE6DDF, 0xBF6BDED0, +/**/ 0x00000000, 0x3FEED000, +/**/ 0x12AAF9A9, 0x400DA439, +/**/ 0x62F25109, 0x40387D46, +/**/ 0x3F133A3F, 0x4074C339, +/**/ 0x662036F9, 0x40B5E143, +/**/ 0x74467831, 0x40F9CF04, +/**/ 0x576C6FA8, 0x41404E10, +/**/ 0xFF4F8E88, 0x41859489, +/**/ 0xB44962A9, 0x41CD88D2, +/**/ 0x97A288F3, 0x4214D838, +/**/ 0x6CF738B3, 0x425DE10B, +/**/ 0x5F7263CC, 0xBC8E9EA7, +/**/ 0xAA786F36, 0x3FF4C29F, +/**/ 0x00000000, 0x400DA000, +/**/ 0xABE6A2AD, 0x3F60E44A, +/**/ 0x00000000, 0x3FEEF000, +/**/ 0xC169B52F, 0x400F4E35, +/**/ 0x29E8699C, 0x403CF773, +/**/ 0xFC1818D6, 0x407B6D37, +/**/ 0x1386790A, 0x40C02655, +/**/ 0x4FF79D1E, 0x41054A1F, +/**/ 0x7DB0265A, 0x414E104A, +/**/ 0xE5C8114B, 0x41963C39, +/**/ 0xF52A87DB, 0x41E10156, +/**/ 0x2E9E7ABE, 0x422ADD76, +/**/ 0x6EC81361, 0x427586AB, +/**/ 0xE395EEA6, 0x3C935690, +/**/ 0x2E5965A2, 0x3FF4FF86, +/**/ 0x00000000, 0x400F4000, +/**/ 0xD36A5E70, 0x3F7C6B82 } }; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/atnat.h b/REORG.TODO/sysdeps/ieee754/dbl-64/atnat.h new file mode 100644 index 0000000000..3ba064ae59 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/atnat.h @@ -0,0 +1,154 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: atnat.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ +#ifndef ATNAT_H +#define ATNAT_H + +#define M 4 + +#ifdef BIG_ENDI + static const number + /* polynomial I */ +/**/ d3 = {{0xbfd55555, 0x55555555} }, /* -0.333... */ +/**/ d5 = {{0x3fc99999, 0x999997fd} }, /* 0.199... */ +/**/ d7 = {{0xbfc24924, 0x923f7603} }, /* -0.142... */ +/**/ d9 = {{0x3fbc71c6, 0xe5129a3b} }, /* 0.111... */ +/**/ d11 = {{0xbfb74580, 0x22b13c25} }, /* -0.090... */ +/**/ d13 = {{0x3fb375f0, 0x8b31cbce} }, /* 0.076... */ + /* polynomial II */ +/**/ f3 = {{0xbfd55555, 0x55555555} }, /* -1/3 */ +/**/ ff3 = {{0xbc755555, 0x55555555} }, /* -1/3-f3 */ +/**/ f5 = {{0x3fc99999, 0x9999999a} }, /* 1/5 */ +/**/ ff5 = {{0xbc699999, 0x9999999a} }, /* 1/5-f5 */ +/**/ f7 = {{0xbfc24924, 0x92492492} }, /* -1/7 */ +/**/ ff7 = {{0xbc624924, 0x92492492} }, /* -1/7-f7 */ +/**/ f9 = {{0x3fbc71c7, 0x1c71c71c} }, /* 1/9 */ +/**/ ff9 = {{0x3c5c71c7, 0x1c71c71c} }, /* 1/9-f9 */ +/**/ f11 = {{0xbfb745d1, 0x745d1746} }, /* -1/11 */ +/**/ f13 = {{0x3fb3b13b, 0x13b13b14} }, /* 1/13 */ +/**/ f15 = {{0xbfb11111, 0x11111111} }, /* -1/15 */ +/**/ f17 = {{0x3fae1e1e, 0x1e1e1e1e} }, /* 1/17 */ +/**/ f19 = {{0xbfaaf286, 0xbca1af28} }, /* -1/19 */ + /* constants */ +/**/ a = {{0x3e4bb67a, 0x00000000} }, /* 1.290e-8 */ +/**/ b = {{0x3fb00000, 0x00000000} }, /* 1/16 */ +/**/ c = {{0x3ff00000, 0x00000000} }, /* 1 */ +/**/ d = {{0x40300000, 0x00000000} }, /* 16 */ +/**/ e = {{0x43349ff2, 0x00000000} }, /* 5.805e15 */ +/**/ hpi = {{0x3ff921fb, 0x54442d18} }, /* pi/2 */ +/**/ mhpi = {{0xbff921fb, 0x54442d18} }, /* -pi/2 */ +/**/ hpi1 = {{0x3c91a626, 0x33145c07} }, /* pi/2-hpi */ +/**/ u1 = {{0x3c2d3382, 0x00000000} }, /* 7.915e-19 */ +/**/ u21 = {{0x3c6dffc0, 0x00000000} }, /* 1.301e-17 */ +/**/ u22 = {{0x3c527bd0, 0x00000000} }, /* 4.008e-18 */ +/**/ u23 = {{0x3c3cd057, 0x00000000} }, /* 1.562e-18 */ +/**/ u24 = {{0x3c329cdf, 0x00000000} }, /* 1.009e-18 */ +/**/ u31 = {{0x3c3a1edf, 0x00000000} }, /* 1.416e-18 */ +/**/ u32 = {{0x3c33f0e1, 0x00000000} }, /* 1.081e-18 */ +/**/ u4 = {{0x3bf955e4, 0x00000000} }, /* 8.584e-20 */ +/**/ u5 = {{0x3aaef2d1, 0x00000000} }, /* 5e-26 */ +/**/ u6 = {{0x3a98c56d, 0x00000000} }, /* 2.001e-26 */ +/**/ u7 = {{0x3a9375de, 0x00000000} }, /* 1.572e-26 */ +/**/ u8 = {{0x3a6eeb36, 0x00000000} }, /* 3.122e-27 */ +/**/ u9[M] ={{{0x38c1aa5b, 0x00000000} }, /* 2.658e-35 */ +/**/ {{0x35c1aa4d, 0x00000000} }, /* 9.443e-50 */ +/**/ {{0x32c1aa88, 0x00000000} }, /* 3.355e-64 */ +/**/ {{0x11c1aa56, 0x00000000} }};/* 3.818e-223 */ + +#else +#ifdef LITTLE_ENDI + static const number + /* polynomial I */ +/**/ d3 = {{0x55555555, 0xbfd55555} }, /* -0.333... */ +/**/ d5 = {{0x999997fd, 0x3fc99999} }, /* 0.199... */ +/**/ d7 = {{0x923f7603, 0xbfc24924} }, /* -0.142... */ +/**/ d9 = {{0xe5129a3b, 0x3fbc71c6} }, /* 0.111... */ +/**/ d11 = {{0x22b13c25, 0xbfb74580} }, /* -0.090... */ +/**/ d13 = {{0x8b31cbce, 0x3fb375f0} }, /* 0.076... */ + /* polynomial II */ +/**/ f3 = {{0x55555555, 0xbfd55555} }, /* -1/3 */ +/**/ ff3 = {{0x55555555, 0xbc755555} }, /* -1/3-f3 */ +/**/ f5 = {{0x9999999a, 0x3fc99999} }, /* 1/5 */ +/**/ ff5 = {{0x9999999a, 0xbc699999} }, /* 1/5-f5 */ +/**/ f7 = {{0x92492492, 0xbfc24924} }, /* -1/7 */ +/**/ ff7 = {{0x92492492, 0xbc624924} }, /* -1/7-f7 */ +/**/ f9 = {{0x1c71c71c, 0x3fbc71c7} }, /* 1/9 */ +/**/ ff9 = {{0x1c71c71c, 0x3c5c71c7} }, /* 1/9-f9 */ +/**/ f11 = {{0x745d1746, 0xbfb745d1} }, /* -1/11 */ +/**/ f13 = {{0x13b13b14, 0x3fb3b13b} }, /* 1/13 */ +/**/ f15 = {{0x11111111, 0xbfb11111} }, /* -1/15 */ +/**/ f17 = {{0x1e1e1e1e, 0x3fae1e1e} }, /* 1/17 */ +/**/ f19 = {{0xbca1af28, 0xbfaaf286} }, /* -1/19 */ + /* constants */ +/**/ a = {{0x00000000, 0x3e4bb67a} }, /* 1.290e-8 */ +/**/ b = {{0x00000000, 0x3fb00000} }, /* 1/16 */ +/**/ c = {{0x00000000, 0x3ff00000} }, /* 1 */ +/**/ d = {{0x00000000, 0x40300000} }, /* 16 */ +/**/ e = {{0x00000000, 0x43349ff2} }, /* 5.805e15 */ +/**/ hpi = {{0x54442d18, 0x3ff921fb} }, /* pi/2 */ +/**/ mhpi = {{0x54442d18, 0xbff921fb} }, /* -pi/2 */ +/**/ hpi1 = {{0x33145c07, 0x3c91a626} }, /* pi/2-hpi */ +/**/ u1 = {{0x00000000, 0x3c2d3382} }, /* 7.915e-19 */ +/**/ u21 = {{0x00000000, 0x3c6dffc0} }, /* 1.301e-17 */ +/**/ u22 = {{0x00000000, 0x3c527bd0} }, /* 4.008e-18 */ +/**/ u23 = {{0x00000000, 0x3c3cd057} }, /* 1.562e-18 */ +/**/ u24 = {{0x00000000, 0x3c329cdf} }, /* 1.009e-18 */ +/**/ u31 = {{0x00000000, 0x3c3a1edf} }, /* 1.416e-18 */ +/**/ u32 = {{0x00000000, 0x3c33f0e1} }, /* 1.081e-18 */ +/**/ u4 = {{0x00000000, 0x3bf955e4} }, /* 8.584e-20 */ +/**/ u5 = {{0x00000000, 0x3aaef2d1} }, /* 5e-26 */ +/**/ u6 = {{0x00000000, 0x3a98c56d} }, /* 2.001e-26 */ +/**/ u7 = {{0x00000000, 0x3a9375de} }, /* 1.572e-26 */ +/**/ u8 = {{0x00000000, 0x3a6eeb36} }, /* 3.122e-27 */ +/**/ u9[M] ={{{0x00000000, 0x38c1aa5b} }, /* 2.658e-35 */ +/**/ {{0x00000000, 0x35c1aa4d} }, /* 9.443e-50 */ +/**/ {{0x00000000, 0x32c1aa88} }, /* 3.355e-64 */ +/**/ {{0x00000000, 0x11c1aa56} }};/* 3.818e-223 */ + +#endif +#endif + +#define A a.d +#define B b.d +#define C c.d +#define D d.d +#define E e.d +#define HPI hpi.d +#define MHPI mhpi.d +#define HPI1 hpi1.d +#define U1 u1.d +#define U21 u21.d +#define U22 u22.d +#define U23 u23.d +#define U24 u24.d +#define U31 u31.d +#define U32 u32.d +#define U4 u4.d +#define U5 u5.d +#define U6 u6.d +#define U7 u7.d +#define U8 u8.d + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/atnat2.h b/REORG.TODO/sysdeps/ieee754/dbl-64/atnat2.h new file mode 100644 index 0000000000..27033b6ceb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/atnat2.h @@ -0,0 +1,161 @@ + +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: atnat2.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + + + +#ifndef ATNAT2_H +#define ATNAT2_H + + +#define MM 5 +#ifdef BIG_ENDI + + static const number + /* polynomial I */ +/**/ d3 = {{0xbfd55555, 0x55555555} }, /* -0.333... */ +/**/ d5 = {{0x3fc99999, 0x999997fd} }, /* 0.199... */ +/**/ d7 = {{0xbfc24924, 0x923f7603} }, /* -0.142... */ +/**/ d9 = {{0x3fbc71c6, 0xe5129a3b} }, /* 0.111... */ +/**/ d11 = {{0xbfb74580, 0x22b13c25} }, /* -0.090... */ +/**/ d13 = {{0x3fb375f0, 0x8b31cbce} }, /* 0.076... */ + /* polynomial II */ +/**/ f3 = {{0xbfd55555, 0x55555555} }, /* -1/3 */ +/**/ ff3 = {{0xbc755555, 0x55555555} }, /* -1/3-f3 */ +/**/ f5 = {{0x3fc99999, 0x9999999a} }, /* 1/5 */ +/**/ ff5 = {{0xbc699999, 0x9999999a} }, /* 1/5-f5 */ +/**/ f7 = {{0xbfc24924, 0x92492492} }, /* -1/7 */ +/**/ ff7 = {{0xbc624924, 0x92492492} }, /* -1/7-f7 */ +/**/ f9 = {{0x3fbc71c7, 0x1c71c71c} }, /* 1/9 */ +/**/ ff9 = {{0x3c5c71c7, 0x1c71c71c} }, /* 1/9-f9 */ +/**/ f11 = {{0xbfb745d1, 0x745d1746} }, /* -1/11 */ +/**/ f13 = {{0x3fb3b13b, 0x13b13b14} }, /* 1/13 */ +/**/ f15 = {{0xbfb11111, 0x11111111} }, /* -1/15 */ +/**/ f17 = {{0x3fae1e1e, 0x1e1e1e1e} }, /* 1/17 */ +/**/ f19 = {{0xbfaaf286, 0xbca1af28} }, /* -1/19 */ + /* constants */ +/**/ inv16 = {{0x3fb00000, 0x00000000} }, /* 1/16 */ +/**/ opi = {{0x400921fb, 0x54442d18} }, /* pi */ +/**/ opi1 = {{0x3ca1a626, 0x33145c07} }, /* pi-opi */ +/**/ mopi = {{0xc00921fb, 0x54442d18} }, /* -pi */ +/**/ hpi = {{0x3ff921fb, 0x54442d18} }, /* pi/2 */ +/**/ hpi1 = {{0x3c91a626, 0x33145c07} }, /* pi/2-hpi */ +/**/ mhpi = {{0xbff921fb, 0x54442d18} }, /* -pi/2 */ +/**/ qpi = {{0x3fe921fb, 0x54442d18} }, /* pi/4 */ +/**/ mqpi = {{0xbfe921fb, 0x54442d18} }, /* -pi/4 */ +/**/ tqpi = {{0x4002d97c, 0x7f3321d2} }, /* 3pi/4 */ +/**/ mtqpi = {{0xc002d97c, 0x7f3321d2} }, /* -3pi/4 */ +/**/ u1 = {{0x3c314c2a, 0x00000000} }, /* 9.377e-19 */ +/**/ u2 = {{0x3bf955e4, 0x00000000} }, /* 8.584e-20 */ +/**/ u3 = {{0x3bf955e4, 0x00000000} }, /* 8.584e-20 */ +/**/ u4 = {{0x3bf955e4, 0x00000000} }, /* 8.584e-20 */ +/**/ u5 = {{0x3aaef2d1, 0x00000000} }, /* 5e-26 */ +/**/ u6 = {{0x3a6eeb36, 0x00000000} }, /* 3.122e-27 */ +/**/ u7 = {{0x3a6eeb36, 0x00000000} }, /* 3.122e-27 */ +/**/ u8 = {{0x3a6eeb36, 0x00000000} }, /* 3.122e-27 */ +/**/ u91 = {{0x3c6dffc0, 0x00000000} }, /* 1.301e-17 */ +/**/ u92 = {{0x3c527bd0, 0x00000000} }, /* 4.008e-18 */ +/**/ u93 = {{0x3c3cd057, 0x00000000} }, /* 1.562e-18 */ +/**/ u94 = {{0x3c329cdf, 0x00000000} }, /* 1.009e-18 */ +/**/ ua1 = {{0x3c3a1edf, 0x00000000} }, /* 1.416e-18 */ +/**/ ua2 = {{0x3c33f0e1, 0x00000000} }, /* 1.081e-18 */ +/**/ ub = {{0x3a98c56d, 0x00000000} }, /* 2.001e-26 */ +/**/ uc = {{0x3a9375de, 0x00000000} }, /* 1.572e-26 */ +/**/ ud[MM] ={{{0x38c6eddf, 0x00000000} }, /* 3.450e-35 */ +/**/ {{0x35c6ef60, 0x00000000} }, /* 1.226e-49 */ +/**/ {{0x32c6ed2f, 0x00000000} }, /* 4.354e-64 */ +/**/ {{0x23c6eee8, 0x00000000} }, /* 2.465e-136 */ +/**/ {{0x11c6ed16, 0x00000000} }},/* 4.955e-223 */ +/**/ ue = {{0x38900e9d, 0x00000000} }, /* 3.02e-36 */ +/**/ two500 = {{0x5f300000, 0x00000000} }, /* 2**500 */ +/**/ twom500 = {{0x20b00000, 0x00000000} }; /* 2**(-500) */ + +#else +#ifdef LITTLE_ENDI + + static const number + /* polynomial I */ +/**/ d3 = {{0x55555555, 0xbfd55555} }, /* -0.333... */ +/**/ d5 = {{0x999997fd, 0x3fc99999} }, /* 0.199... */ +/**/ d7 = {{0x923f7603, 0xbfc24924} }, /* -0.142... */ +/**/ d9 = {{0xe5129a3b, 0x3fbc71c6} }, /* 0.111... */ +/**/ d11 = {{0x22b13c25, 0xbfb74580} }, /* -0.090... */ +/**/ d13 = {{0x8b31cbce, 0x3fb375f0} }, /* 0.076... */ + /* polynomial II */ +/**/ f3 = {{0x55555555, 0xbfd55555} }, /* -1/3 */ +/**/ ff3 = {{0x55555555, 0xbc755555} }, /* -1/3-f3 */ +/**/ f5 = {{0x9999999a, 0x3fc99999} }, /* 1/5 */ +/**/ ff5 = {{0x9999999a, 0xbc699999} }, /* 1/5-f5 */ +/**/ f7 = {{0x92492492, 0xbfc24924} }, /* -1/7 */ +/**/ ff7 = {{0x92492492, 0xbc624924} }, /* -1/7-f7 */ +/**/ f9 = {{0x1c71c71c, 0x3fbc71c7} }, /* 1/9 */ +/**/ ff9 = {{0x1c71c71c, 0x3c5c71c7} }, /* 1/9-f9 */ +/**/ f11 = {{0x745d1746, 0xbfb745d1} }, /* -1/11 */ +/**/ f13 = {{0x13b13b14, 0x3fb3b13b} }, /* 1/13 */ +/**/ f15 = {{0x11111111, 0xbfb11111} }, /* -1/15 */ +/**/ f17 = {{0x1e1e1e1e, 0x3fae1e1e} }, /* 1/17 */ +/**/ f19 = {{0xbca1af28, 0xbfaaf286} }, /* -1/19 */ + /* constants */ +/**/ inv16 = {{0x00000000, 0x3fb00000} }, /* 1/16 */ +/**/ opi = {{0x54442d18, 0x400921fb} }, /* pi */ +/**/ opi1 = {{0x33145c07, 0x3ca1a626} }, /* pi-opi */ +/**/ mopi = {{0x54442d18, 0xc00921fb} }, /* -pi */ +/**/ hpi = {{0x54442d18, 0x3ff921fb} }, /* pi/2 */ +/**/ hpi1 = {{0x33145c07, 0x3c91a626} }, /* pi/2-hpi */ +/**/ mhpi = {{0x54442d18, 0xbff921fb} }, /* -pi/2 */ +/**/ qpi = {{0x54442d18, 0x3fe921fb} }, /* pi/4 */ +/**/ mqpi = {{0x54442d18, 0xbfe921fb} }, /* -pi/4 */ +/**/ tqpi = {{0x7f3321d2, 0x4002d97c} }, /* 3pi/4 */ +/**/ mtqpi = {{0x7f3321d2, 0xc002d97c} }, /* -3pi/4 */ +/**/ u1 = {{0x00000000, 0x3c314c2a} }, /* 9.377e-19 */ +/**/ u2 = {{0x00000000, 0x3bf955e4} }, /* 8.584e-20 */ +/**/ u3 = {{0x00000000, 0x3bf955e4} }, /* 8.584e-20 */ +/**/ u4 = {{0x00000000, 0x3bf955e4} }, /* 8.584e-20 */ +/**/ u5 = {{0x00000000, 0x3aaef2d1} }, /* 5e-26 */ +/**/ u6 = {{0x00000000, 0x3a6eeb36} }, /* 3.122e-27 */ +/**/ u7 = {{0x00000000, 0x3a6eeb36} }, /* 3.122e-27 */ +/**/ u8 = {{0x00000000, 0x3a6eeb36} }, /* 3.122e-27 */ +/**/ u91 = {{0x00000000, 0x3c6dffc0} }, /* 1.301e-17 */ +/**/ u92 = {{0x00000000, 0x3c527bd0} }, /* 4.008e-18 */ +/**/ u93 = {{0x00000000, 0x3c3cd057} }, /* 1.562e-18 */ +/**/ u94 = {{0x00000000, 0x3c329cdf} }, /* 1.009e-18 */ +/**/ ua1 = {{0x00000000, 0x3c3a1edf} }, /* 1.416e-18 */ +/**/ ua2 = {{0x00000000, 0x3c33f0e1} }, /* 1.081e-18 */ +/**/ ub = {{0x00000000, 0x3a98c56d} }, /* 2.001e-26 */ +/**/ uc = {{0x00000000, 0x3a9375de} }, /* 1.572e-26 */ +/**/ ud[MM] ={{{0x00000000, 0x38c6eddf} }, /* 3.450e-35 */ +/**/ {{0x00000000, 0x35c6ef60} }, /* 1.226e-49 */ +/**/ {{0x00000000, 0x32c6ed2f} }, /* 4.354e-64 */ +/**/ {{0x00000000, 0x23c6eee8} }, /* 2.465e-136 */ +/**/ {{0x00000000, 0x11c6ed16} }},/* 4.955e-223 */ +/**/ ue = {{0x00000000, 0x38900e9d} }, /* 3.02e-36 */ +/**/ two500 = {{0x00000000, 0x5f300000} }, /* 2**500 */ +/**/ twom500 = {{0x00000000, 0x20b00000} }; /* 2**(-500) */ + +#endif +#endif + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/branred.c b/REORG.TODO/sysdeps/ieee754/dbl-64/branred.c new file mode 100644 index 0000000000..30ae9c79e2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/branred.c @@ -0,0 +1,144 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*******************************************************************/ +/* */ +/* MODULE_NAME: branred.c */ +/* */ +/* FUNCTIONS: branred */ +/* */ +/* FILES NEEDED: branred.h mydefs.h endian.h mpa.h */ +/* mha.c */ +/* */ +/* Routine branred() performs range reduction of a double number */ +/* x into Double length number a+aa,such that */ +/* x=n*pi/2+(a+aa), abs(a+aa)<pi/4, n=0,+-1,+-2,.... */ +/* Routine returns the integer (n mod 4) of the above description */ +/* of x. */ +/*******************************************************************/ + +#include "endian.h" +#include "mydefs.h" +#include "branred.h" +#include <math.h> +#include <math_private.h> + +#ifndef SECTION +# define SECTION +#endif + + +/*******************************************************************/ +/* Routine branred() performs range reduction of a double number */ +/* x into Double length number a+aa,such that */ +/* x=n*pi/2+(a+aa), abs(a+aa)<pi/4, n=0,+-1,+-2,.... */ +/* Routine return integer (n mod 4) */ +/*******************************************************************/ +int +SECTION +__branred(double x, double *a, double *aa) +{ + int i,k; + mynumber u,gor; + double r[6],s,t,sum,b,bb,sum1,sum2,b1,bb1,b2,bb2,x1,x2,t1,t2; + + x*=tm600.x; + t=x*split; /* split x to two numbers */ + x1=t-(t-x); + x2=x-x1; + sum=0; + u.x = x1; + k = (u.i[HIGH_HALF]>>20)&2047; + k = (k-450)/24; + if (k<0) + k=0; + gor.x = t576.x; + gor.i[HIGH_HALF] -= ((k*24)<<20); + for (i=0;i<6;i++) + { r[i] = x1*toverp[k+i]*gor.x; gor.x *= tm24.x; } + for (i=0;i<3;i++) { + s=(r[i]+big.x)-big.x; + sum+=s; + r[i]-=s; + } + t=0; + for (i=0;i<6;i++) + t+=r[5-i]; + bb=(((((r[0]-t)+r[1])+r[2])+r[3])+r[4])+r[5]; + s=(t+big.x)-big.x; + sum+=s; + t-=s; + b=t+bb; + bb=(t-b)+bb; + s=(sum+big1.x)-big1.x; + sum-=s; + b1=b; + bb1=bb; + sum1=sum; + sum=0; + + u.x = x2; + k = (u.i[HIGH_HALF]>>20)&2047; + k = (k-450)/24; + if (k<0) + k=0; + gor.x = t576.x; + gor.i[HIGH_HALF] -= ((k*24)<<20); + for (i=0;i<6;i++) + { r[i] = x2*toverp[k+i]*gor.x; gor.x *= tm24.x; } + for (i=0;i<3;i++) { + s=(r[i]+big.x)-big.x; + sum+=s; + r[i]-=s; + } + t=0; + for (i=0;i<6;i++) + t+=r[5-i]; + bb=(((((r[0]-t)+r[1])+r[2])+r[3])+r[4])+r[5]; + s=(t+big.x)-big.x; + sum+=s; + t-=s; + b=t+bb; + bb=(t-b)+bb; + s=(sum+big1.x)-big1.x; + sum-=s; + + b2=b; + bb2=bb; + sum2=sum; + + sum=sum1+sum2; + b=b1+b2; + bb = (fabs(b1)>fabs(b2))? (b1-b)+b2 : (b2-b)+b1; + if (b > 0.5) + {b-=1.0; sum+=1.0;} + else if (b < -0.5) + {b+=1.0; sum-=1.0;} + s=b+(bb+bb1+bb2); + t=((b-s)+bb)+(bb1+bb2); + b=s*split; + t1=b-(b-s); + t2=s-t1; + b=s*hp0.x; + bb=(((t1*mp1.x-b)+t1*mp2.x)+t2*mp1.x)+(t2*mp2.x+s*hp1.x+t*hp0.x); + s=b+bb; + t=(b-s)+bb; + *a=s; + *aa=t; + return ((int) sum)&3; /* return quater of unit circle */ +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/branred.h b/REORG.TODO/sysdeps/ieee754/dbl-64/branred.h new file mode 100644 index 0000000000..c3fd7dd27b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/branred.h @@ -0,0 +1,80 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/************************************************************************/ +/* MODULE_NAME: branred.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + +#ifndef BRANRED_H +#define BRANRED_H + +#include <dla.h> + +#ifdef BIG_ENDI +static const mynumber + +/**/ t576 = {{0x63f00000, 0x00000000}}, /* 2 ^ 576 */ +/**/ tm600 = {{0x1a700000, 0x00000000}}, /* 2 ^- 600 */ +/**/ tm24 = {{0x3e700000, 0x00000000}}, /* 2 ^- 24 */ +/**/ big = {{0x43380000, 0x00000000}}, /* 6755399441055744 */ +/**/ big1 = {{0x43580000, 0x00000000}}, /* 27021597764222976 */ +/**/ hp0 = {{0x3FF921FB, 0x54442D18}} ,/* 1.5707963267948966 */ +/**/ hp1 = {{0x3C91A626, 0x33145C07}} ,/* 6.123233995736766e-17 */ +/**/ mp1 = {{0x3FF921FB, 0x58000000}}, /* 1.5707963407039642 */ +/**/ mp2 = {{0xBE4DDE97, 0x40000000}}; /*-1.3909067675399456e-08 */ + +#else +#ifdef LITTLE_ENDI +static const mynumber + +/**/ t576 = {{0x00000000, 0x63f00000}}, /* 2 ^ 576 */ +/**/ tm600 = {{0x00000000, 0x1a700000}}, /* 2 ^- 600 */ +/**/ tm24 = {{0x00000000, 0x3e700000}}, /* 2 ^- 24 */ +/**/ big = {{0x00000000, 0x43380000}}, /* 6755399441055744 */ +/**/ big1 = {{0x00000000, 0x43580000}}, /* 27021597764222976 */ +/**/ hp0 = {{0x54442D18, 0x3FF921FB}}, /* 1.5707963267948966 */ +/**/ hp1 = {{0x33145C07, 0x3C91A626}}, /* 6.123233995736766e-17 */ +/**/ mp1 = {{0x58000000, 0x3FF921FB}}, /* 1.5707963407039642 */ +/**/ mp2 = {{0x40000000, 0xBE4DDE97}}; /*-1.3909067675399456e-08 */ + +#endif +#endif + +static const double toverp[75] = { /* 2/ PI base 24*/ + 10680707.0, 7228996.0, 1387004.0, 2578385.0, 16069853.0, + 12639074.0, 9804092.0, 4427841.0, 16666979.0, 11263675.0, + 12935607.0, 2387514.0, 4345298.0, 14681673.0, 3074569.0, + 13734428.0, 16653803.0, 1880361.0, 10960616.0, 8533493.0, + 3062596.0, 8710556.0, 7349940.0, 6258241.0, 3772886.0, + 3769171.0, 3798172.0, 8675211.0, 12450088.0, 3874808.0, + 9961438.0, 366607.0, 15675153.0, 9132554.0, 7151469.0, + 3571407.0, 2607881.0, 12013382.0, 4155038.0, 6285869.0, + 7677882.0, 13102053.0, 15825725.0, 473591.0, 9065106.0, + 15363067.0, 6271263.0, 9264392.0, 5636912.0, 4652155.0, + 7056368.0, 13614112.0, 10155062.0, 1944035.0, 9527646.0, + 15080200.0, 6658437.0, 6231200.0, 6832269.0, 16767104.0, + 5075751.0, 3212806.0, 1398474.0, 7579849.0, 6349435.0, + 12618859.0, 4703257.0, 12806093.0, 14477321.0, 2786137.0, + 12875403.0, 9837734.0, 14528324.0, 13719321.0, 343717.0 }; + +static const double split = CN; /* 2^27 + 1 */ + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/dbl2mpn.c b/REORG.TODO/sysdeps/ieee754/dbl-64/dbl2mpn.c new file mode 100644 index 0000000000..8294dc26ed --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/dbl2mpn.c @@ -0,0 +1,107 @@ +/* Copyright (C) 1993-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include "longlong.h" +#include <ieee754.h> +#include <float.h> +#include <stdlib.h> + +/* Convert a `double' in IEEE754 standard double-precision format to a + multi-precision integer representing the significand scaled up by its + number of bits (52 for double) and an integral power of two (MPN frexp). */ + +mp_size_t +__mpn_extract_double (mp_ptr res_ptr, mp_size_t size, + int *expt, int *is_neg, + double value) +{ + union ieee754_double u; + u.d = value; + + *is_neg = u.ieee.negative; + *expt = (int) u.ieee.exponent - IEEE754_DOUBLE_BIAS; + +#if BITS_PER_MP_LIMB == 32 + res_ptr[0] = u.ieee.mantissa1; /* Low-order 32 bits of fraction. */ + res_ptr[1] = u.ieee.mantissa0; /* High-order 20 bits. */ + # define N 2 +#elif BITS_PER_MP_LIMB == 64 + /* Hopefully the compiler will combine the two bitfield extracts + and this composition into just the original quadword extract. */ + res_ptr[0] = ((mp_limb_t) u.ieee.mantissa0 << 32) | u.ieee.mantissa1; + # define N 1 +#else + # error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif +/* The format does not fill the last limb. There are some zeros. */ +#define NUM_LEADING_ZEROS (BITS_PER_MP_LIMB \ + - (DBL_MANT_DIG - ((N - 1) * BITS_PER_MP_LIMB))) + + if (u.ieee.exponent == 0) + { + /* A biased exponent of zero is a special case. + Either it is a zero or it is a denormal number. */ + if (res_ptr[0] == 0 && res_ptr[N - 1] == 0) /* Assumes N<=2. */ + /* It's zero. */ + *expt = 0; + else + { + /* It is a denormal number, meaning it has no implicit leading + one bit, and its exponent is in fact the format minimum. */ + int cnt; + + if (res_ptr[N - 1] != 0) + { + count_leading_zeros (cnt, res_ptr[N - 1]); + cnt -= NUM_LEADING_ZEROS; +#if N == 2 + res_ptr[N - 1] = res_ptr[1] << cnt + | (N - 1) + * (res_ptr[0] >> (BITS_PER_MP_LIMB - cnt)); + res_ptr[0] <<= cnt; +#else + res_ptr[N - 1] <<= cnt; +#endif + *expt = DBL_MIN_EXP - 1 - cnt; + } + else + { + count_leading_zeros (cnt, res_ptr[0]); + if (cnt >= NUM_LEADING_ZEROS) + { + res_ptr[N - 1] = res_ptr[0] << (cnt - NUM_LEADING_ZEROS); + res_ptr[0] = 0; + } + else + { + res_ptr[N - 1] = res_ptr[0] >> (NUM_LEADING_ZEROS - cnt); + res_ptr[0] <<= BITS_PER_MP_LIMB - (NUM_LEADING_ZEROS - cnt); + } + *expt = DBL_MIN_EXP - 1 + - (BITS_PER_MP_LIMB - NUM_LEADING_ZEROS) - cnt; + } + } + } + else + /* Add the implicit leading one bit for a normalized number. */ + res_ptr[N - 1] |= (mp_limb_t) 1 << (DBL_MANT_DIG - 1 + - ((N - 1) * BITS_PER_MP_LIMB)); + + return N; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/dla.h b/REORG.TODO/sysdeps/ieee754/dbl-64/dla.h new file mode 100644 index 0000000000..88e8ffb1ca --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/dla.h @@ -0,0 +1,183 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +#include <math.h> + +/***********************************************************************/ +/*MODULE_NAME: dla.h */ +/* */ +/* This file holds C language macros for 'Double Length Floating Point */ +/* Arithmetic'. The macros are based on the paper: */ +/* T.J.Dekker, "A floating-point Technique for extending the */ +/* Available Precision", Number. Math. 18, 224-242 (1971). */ +/* A Double-Length number is defined by a pair (r,s), of IEEE double */ +/* precision floating point numbers that satisfy, */ +/* */ +/* abs(s) <= abs(r+s)*2**(-53)/(1+2**(-53)). */ +/* */ +/* The computer arithmetic assumed is IEEE double precision in */ +/* round to nearest mode. All variables in the macros must be of type */ +/* IEEE double. */ +/***********************************************************************/ + +/* CN = 1+2**27 = '41a0000002000000' IEEE double format. Use it to split a + double for better accuracy. */ +#define CN 134217729.0 + + +/* Exact addition of two single-length floating point numbers, Dekker. */ +/* The macro produces a double-length number (z,zz) that satisfies */ +/* z+zz = x+y exactly. */ + +#define EADD(x,y,z,zz) \ + z=(x)+(y); zz=(fabs(x)>fabs(y)) ? (((x)-(z))+(y)) : (((y)-(z))+(x)); + + +/* Exact subtraction of two single-length floating point numbers, Dekker. */ +/* The macro produces a double-length number (z,zz) that satisfies */ +/* z+zz = x-y exactly. */ + +#define ESUB(x,y,z,zz) \ + z=(x)-(y); zz=(fabs(x)>fabs(y)) ? (((x)-(z))-(y)) : ((x)-((y)+(z))); + + +#ifdef __FP_FAST_FMA +# define DLA_FMS(x, y, z) __builtin_fma (x, y, -(z)) +#endif + +/* Exact multiplication of two single-length floating point numbers, */ +/* Veltkamp. The macro produces a double-length number (z,zz) that */ +/* satisfies z+zz = x*y exactly. p,hx,tx,hy,ty are temporary */ +/* storage variables of type double. */ + +#ifdef DLA_FMS +# define EMULV(x, y, z, zz, p, hx, tx, hy, ty) \ + z = x * y; zz = DLA_FMS (x, y, z); +#else +# define EMULV(x, y, z, zz, p, hx, tx, hy, ty) \ + p = CN * (x); hx = ((x) - p) + p; tx = (x) - hx; \ + p = CN * (y); hy = ((y) - p) + p; ty = (y) - hy; \ + z = (x) * (y); zz = (((hx * hy - z) + hx * ty) + tx * hy) + tx * ty; +#endif + + +/* Exact multiplication of two single-length floating point numbers, Dekker. */ +/* The macro produces a nearly double-length number (z,zz) (see Dekker) */ +/* that satisfies z+zz = x*y exactly. p,hx,tx,hy,ty,q are temporary */ +/* storage variables of type double. */ + +#ifdef DLA_FMS +# define MUL12(x,y,z,zz,p,hx,tx,hy,ty,q) \ + EMULV(x,y,z,zz,p,hx,tx,hy,ty) +#else +# define MUL12(x,y,z,zz,p,hx,tx,hy,ty,q) \ + p=CN*(x); hx=((x)-p)+p; tx=(x)-hx; \ + p=CN*(y); hy=((y)-p)+p; ty=(y)-hy; \ + p=hx*hy; q=hx*ty+tx*hy; z=p+q; zz=((p-z)+q)+tx*ty; +#endif + + +/* Double-length addition, Dekker. The macro produces a double-length */ +/* number (z,zz) which satisfies approximately z+zz = x+xx + y+yy. */ +/* An error bound: (abs(x+xx)+abs(y+yy))*4.94e-32. (x,xx), (y,yy) */ +/* are assumed to be double-length numbers. r,s are temporary */ +/* storage variables of type double. */ + +#define ADD2(x, xx, y, yy, z, zz, r, s) \ + r = (x) + (y); s = (fabs (x) > fabs (y)) ? \ + (((((x) - r) + (y)) + (yy)) + (xx)) : \ + (((((y) - r) + (x)) + (xx)) + (yy)); \ + z = r + s; zz = (r - z) + s; + + +/* Double-length subtraction, Dekker. The macro produces a double-length */ +/* number (z,zz) which satisfies approximately z+zz = x+xx - (y+yy). */ +/* An error bound: (abs(x+xx)+abs(y+yy))*4.94e-32. (x,xx), (y,yy) */ +/* are assumed to be double-length numbers. r,s are temporary */ +/* storage variables of type double. */ + +#define SUB2(x, xx, y, yy, z, zz, r, s) \ + r = (x) - (y); s = (fabs (x) > fabs (y)) ? \ + (((((x) - r) - (y)) - (yy)) + (xx)) : \ + ((((x) - ((y) + r)) + (xx)) - (yy)); \ + z = r + s; zz = (r - z) + s; + + +/* Double-length multiplication, Dekker. The macro produces a double-length */ +/* number (z,zz) which satisfies approximately z+zz = (x+xx)*(y+yy). */ +/* An error bound: abs((x+xx)*(y+yy))*1.24e-31. (x,xx), (y,yy) */ +/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc are */ +/* temporary storage variables of type double. */ + +#define MUL2(x, xx, y, yy, z, zz, p, hx, tx, hy, ty, q, c, cc) \ + MUL12 (x, y, c, cc, p, hx, tx, hy, ty, q) \ + cc = ((x) * (yy) + (xx) * (y)) + cc; z = c + cc; zz = (c - z) + cc; + + +/* Double-length division, Dekker. The macro produces a double-length */ +/* number (z,zz) which satisfies approximately z+zz = (x+xx)/(y+yy). */ +/* An error bound: abs((x+xx)/(y+yy))*1.50e-31. (x,xx), (y,yy) */ +/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc,u,uu */ +/* are temporary storage variables of type double. */ + +#define DIV2(x,xx,y,yy,z,zz,p,hx,tx,hy,ty,q,c,cc,u,uu) \ + c=(x)/(y); MUL12(c,y,u,uu,p,hx,tx,hy,ty,q) \ + cc=(((((x)-u)-uu)+(xx))-c*(yy))/(y); z=c+cc; zz=(c-z)+cc; + + +/* Double-length addition, slower but more accurate than ADD2. */ +/* The macro produces a double-length */ +/* number (z,zz) which satisfies approximately z+zz = (x+xx)+(y+yy). */ +/* An error bound: abs(x+xx + y+yy)*1.50e-31. (x,xx), (y,yy) */ +/* are assumed to be double-length numbers. r,rr,s,ss,u,uu,w */ +/* are temporary storage variables of type double. */ + +#define ADD2A(x, xx, y, yy, z, zz, r, rr, s, ss, u, uu, w) \ + r = (x) + (y); \ + if (fabs (x) > fabs (y)) { rr = ((x) - r) + (y); s = (rr + (yy)) + (xx); } \ + else { rr = ((y) - r) + (x); s = (rr + (xx)) + (yy); } \ + if (rr != 0.0) { \ + z = r + s; zz = (r - z) + s; } \ + else { \ + ss = (fabs (xx) > fabs (yy)) ? (((xx) - s) + (yy)) : (((yy) - s) + (xx));\ + u = r + s; \ + uu = (fabs (r) > fabs (s)) ? ((r - u) + s) : ((s - u) + r); \ + w = uu + ss; z = u + w; \ + zz = (fabs (u) > fabs (w)) ? ((u - z) + w) : ((w - z) + u); } + + +/* Double-length subtraction, slower but more accurate than SUB2. */ +/* The macro produces a double-length */ +/* number (z,zz) which satisfies approximately z+zz = (x+xx)-(y+yy). */ +/* An error bound: abs(x+xx - (y+yy))*1.50e-31. (x,xx), (y,yy) */ +/* are assumed to be double-length numbers. r,rr,s,ss,u,uu,w */ +/* are temporary storage variables of type double. */ + +#define SUB2A(x, xx, y, yy, z, zz, r, rr, s, ss, u, uu, w) \ + r = (x) - (y); \ + if (fabs (x) > fabs (y)) { rr = ((x) - r) - (y); s = (rr - (yy)) + (xx); } \ + else { rr = (x) - ((y) + r); s = (rr + (xx)) - (yy); } \ + if (rr != 0.0) { \ + z = r + s; zz = (r - z) + s; } \ + else { \ + ss = (fabs (xx) > fabs (yy)) ? (((xx) - s) - (yy)) : ((xx) - ((yy) + s)); \ + u = r + s; \ + uu = (fabs (r) > fabs (s)) ? ((r - u) + s) : ((s - u) + r); \ + w = uu + ss; z = u + w; \ + zz = (fabs (u) > fabs (w)) ? ((u - z) + w) : ((w - z) + u); } diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/doasin.c b/REORG.TODO/sysdeps/ieee754/dbl-64/doasin.c new file mode 100644 index 0000000000..7c2f3c3dc2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/doasin.c @@ -0,0 +1,84 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/**********************************************************************/ +/* MODULE_NAME: doasin.c */ +/* */ +/* FUNCTION: doasin */ +/* */ +/* FILES NEEDED:endian.h mydefs.h dla.h doasin.h */ +/* mpa.c */ +/* */ +/* Compute arcsin(x,dx,v) of double-length number (x+dx) the result */ +/* stored in v where v= v[0]+v[1] =arcsin(x+dx) */ +/**********************************************************************/ + +#include "endian.h" +#include "mydefs.h" +#include <dla.h> +#include <math_private.h> + +#ifndef SECTION +# define SECTION +#endif + +/********************************************************************/ +/* Compute arcsin(x,dx,v) of double-length number (x+dx) the result */ +/* stored in v where v= v[0]+v[1] =arcsin(x+dx) */ +/********************************************************************/ +void +SECTION +__doasin(double x, double dx, double v[]) { + +#include "doasin.h" + + static const double + d5 = 0.22372159090911789889975459505194491E-01, + d6 = 0.17352764422456822913014975683014622E-01, + d7 = 0.13964843843786693521653681033981614E-01, + d8 = 0.11551791438485242609036067259086589E-01, + d9 = 0.97622386568166960207425666787248914E-02, + d10 = 0.83638737193775788576092749009744976E-02, + d11 = 0.79470250400727425881446981833568758E-02; + + double xx,p,pp,u,uu,r,s; + double tc,tcc; +#ifndef DLA_FMS + double hx,tx,hy,ty,tp,tq; +#endif + + +/* Taylor series for arcsin for Double-Length numbers */ + xx = x*x+2.0*x*dx; + p = ((((((d11*xx+d10)*xx+d9)*xx+d8)*xx+d7)*xx+d6)*xx+d5)*xx; + pp = 0; + + MUL2(x,dx,x,dx,u,uu,tp,hx,tx,hy,ty,tq,tc,tcc); + ADD2(p,pp,c4.x,cc4.x,p,pp,r,s); + MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc); + ADD2(p,pp,c3.x,cc3.x,p,pp,r,s); + MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc); + ADD2(p,pp,c2.x,cc2.x,p,pp,r,s); + MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc); + ADD2(p,pp,c1.x,cc1.x,p,pp,r,s); + MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc); + MUL2(p,pp,x,dx,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc); + ADD2(p,pp,x,dx,p,pp,r,s); + v[0]=p; + v[1]=pp; /* arcsin(x+dx)=v[0]+v[1] */ +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/doasin.h b/REORG.TODO/sysdeps/ieee754/dbl-64/doasin.h new file mode 100644 index 0000000000..c6b64597fb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/doasin.h @@ -0,0 +1,63 @@ + +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: doasin.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + + + +#ifndef DOASIN_H +#define DOASIN_H + +#ifdef BIG_ENDI + + static const mynumber +/**/ c1 = {{0x3FC55555, 0x55555555}}, /* 0.16666666666666666 */ +/**/ cc1 = {{0x3C655555, 0x55775389}}, /* 9.2518585419753846e-18 */ +/**/ c2 = {{0x3FB33333, 0x33333333}}, /* 0.074999999999999997 */ +/**/ cc2 = {{0x3C499993, 0x63F1A115}}, /* 2.7755472886508899e-18 */ +/**/ c3 = {{0x3FA6DB6D, 0xB6DB6DB7}}, /* 0.044642857142857144 */ +/**/ cc3 = {{0xBC320FC0, 0x3D5CF0C5}}, /* -9.7911734574147224e-19 */ +/**/ c4 = {{0x3F9F1C71, 0xC71C71C5}}, /* 0.030381944444444437 */ +/**/ cc4 = {{0xBC02B240, 0xFF23ED1E}}; /* -1.2669108566898312e-19 */ + +#else +#ifdef LITTLE_ENDI + + static const mynumber +/**/ c1 = {{0x55555555, 0x3FC55555}}, /* 0.16666666666666666 */ +/**/ cc1 = {{0x55775389, 0x3C655555}}, /* 9.2518585419753846e-18 */ +/**/ c2 = {{0x33333333, 0x3FB33333}}, /* 0.074999999999999997 */ +/**/ cc2 = {{0x63F1A115, 0x3C499993}}, /* 2.7755472886508899e-18 */ +/**/ c3 = {{0xB6DB6DB7, 0x3FA6DB6D}}, /* 0.044642857142857144 */ +/**/ cc3 = {{0x3D5CF0C5, 0xBC320FC0}}, /* -9.7911734574147224e-19 */ +/**/ c4 = {{0xC71C71C5, 0x3F9F1C71}}, /* 0.030381944444444437 */ +/**/ cc4 = {{0xFF23ED1E, 0xBC02B240}}; /* -1.2669108566898312e-19 */ + + +#endif +#endif + + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/dosincos.c b/REORG.TODO/sysdeps/ieee754/dbl-64/dosincos.c new file mode 100644 index 0000000000..372872b42b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/dosincos.c @@ -0,0 +1,223 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/********************************************************************/ +/* */ +/* MODULE_NAME: dosincos.c */ +/* */ +/* */ +/* FUNCTIONS: dubsin */ +/* dubcos */ +/* docos */ +/* FILES NEEDED: endian.h mydefs.h dla.h dosincos.h */ +/* sincos.tbl */ +/* */ +/* Routines compute sin() and cos() as Double-Length numbers */ +/********************************************************************/ + + + +#include "endian.h" +#include "mydefs.h" +#include <dla.h> +#include "dosincos.h" +#include <math_private.h> + +#ifndef SECTION +# define SECTION +#endif + +extern const union +{ + int4 i[880]; + double x[440]; +} __sincostab attribute_hidden; + +/***********************************************************************/ +/* Routine receive Double-Length number (x+dx) and computing sin(x+dx) */ +/* as Double-Length number and store it at array v .It computes it by */ +/* arithmetic action on Double-Length numbers */ +/*(x+dx) between 0 and PI/4 */ +/***********************************************************************/ + +void +SECTION +__dubsin (double x, double dx, double v[]) +{ + double r, s, c, cc, d, dd, d2, dd2, e, ee, + sn, ssn, cs, ccs, ds, dss, dc, dcc; +#ifndef DLA_FMS + double p, hx, tx, hy, ty, q; +#endif + mynumber u; + int4 k; + + u.x = x + big.x; + k = u.i[LOW_HALF] << 2; + x = x - (u.x - big.x); + d = x + dx; + dd = (x - d) + dx; + /* sin(x+dx)=sin(Xi+t)=sin(Xi)*cos(t) + cos(Xi)sin(t) where t ->0 */ + MUL2 (d, dd, d, dd, d2, dd2, p, hx, tx, hy, ty, q, c, cc); + sn = __sincostab.x[k]; /* */ + ssn = __sincostab.x[k + 1]; /* sin(Xi) and cos(Xi) */ + cs = __sincostab.x[k + 2]; /* */ + ccs = __sincostab.x[k + 3]; /* */ + /* Taylor series for sin ds=sin(t) */ + MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, d, dd, ds, dss, r, s); + + /* Taylor series for cos dc=cos(t) */ + MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + + MUL2 (cs, ccs, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc); + MUL2 (dc, dcc, sn, ssn, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + SUB2 (e, ee, dc, dcc, e, ee, r, s); + ADD2 (e, ee, sn, ssn, e, ee, r, s); /* e+ee=sin(x+dx) */ + + v[0] = e; + v[1] = ee; +} +/**********************************************************************/ +/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */ +/* as Double-Length number and store it in array v .It computes it by */ +/* arithmetic action on Double-Length numbers */ +/*(x+dx) between 0 and PI/4 */ +/**********************************************************************/ + +void +SECTION +__dubcos (double x, double dx, double v[]) +{ + double r, s, c, cc, d, dd, d2, dd2, e, ee, + sn, ssn, cs, ccs, ds, dss, dc, dcc; +#ifndef DLA_FMS + double p, hx, tx, hy, ty, q; +#endif + mynumber u; + int4 k; + u.x = x + big.x; + k = u.i[LOW_HALF] << 2; + x = x - (u.x - big.x); + d = x + dx; + dd = (x - d) + dx; /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */ + MUL2 (d, dd, d, dd, d2, dd2, p, hx, tx, hy, ty, q, c, cc); + sn = __sincostab.x[k]; /* */ + ssn = __sincostab.x[k + 1]; /* sin(Xi) and cos(Xi) */ + cs = __sincostab.x[k + 2]; /* */ + ccs = __sincostab.x[k + 3]; /* */ + MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, d, dd, ds, dss, r, s); + + MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + + MUL2 (cs, ccs, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc); + MUL2 (dc, dcc, sn, ssn, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + + MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, d, dd, ds, dss, r, s); + MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + MUL2 (sn, ssn, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc); + MUL2 (dc, dcc, cs, ccs, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (e, ee, dc, dcc, e, ee, r, s); + SUB2 (cs, ccs, e, ee, e, ee, r, s); + + v[0] = e; + v[1] = ee; +} +/**********************************************************************/ +/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */ +/* as Double-Length number and store it in array v */ +/**********************************************************************/ +void +SECTION +__docos (double x, double dx, double v[]) +{ + double y, yy, p, w[2]; + if (x > 0) + { + y = x; yy = dx; + } + else + { + y = -x; yy = -dx; + } + if (y < 0.5 * hp0.x) /* y< PI/4 */ + { + __dubcos (y, yy, w); v[0] = w[0]; v[1] = w[1]; + } + else if (y < 1.5 * hp0.x) /* y< 3/4 * PI */ + { + p = hp0.x - y; /* p = PI/2 - y */ + yy = hp1.x - yy; + y = p + yy; + yy = (p - y) + yy; + if (y > 0) + { + __dubsin (y, yy, w); v[0] = w[0]; v[1] = w[1]; + } + /* cos(x) = sin ( 90 - x ) */ + else + { + __dubsin (-y, -yy, w); v[0] = -w[0]; v[1] = -w[1]; + } + } + else /* y>= 3/4 * PI */ + { + p = 2.0 * hp0.x - y; /* p = PI- y */ + yy = 2.0 * hp1.x - yy; + y = p + yy; + yy = (p - y) + yy; + __dubcos (y, yy, w); + v[0] = -w[0]; + v[1] = -w[1]; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/dosincos.h b/REORG.TODO/sysdeps/ieee754/dbl-64/dosincos.h new file mode 100644 index 0000000000..9fda3d77cc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/dosincos.h @@ -0,0 +1,80 @@ + +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: dosincos.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + + + +#ifndef DOSINCOS_H +#define DOSINCOS_H + + +#ifdef BIG_ENDI +static const mynumber +/**/ s3 = {{0xBFC55555, 0x55555555}},/* -0.16666666666666666 */ +/**/ ss3 = {{0xBC6553AA, 0xE77EE482}},/* -9.2490366677784492e-18 */ +/**/ s5 = {{0x3F811111, 0x11110F15}},/* 0.008333333333332452 */ +/**/ ss5 = {{0xBC21AC06, 0xDA488820}},/* -4.7899996586987931e-19 */ +/**/ s7 = {{0xBF2A019F, 0x5816C78D}},/* -0.00019841261022928957 */ +/**/ ss7 = {{0x3BCDCEC9, 0x6A18BF2A}},/* 1.2624077757871259e-20 */ +/**/ c2 = {{0x3FE00000, 0x00000000}},/* 0.5 */ +/**/ cc2 = {{0xBA282FD8, 0x00000000}},/* -1.5264073330037701e-28 */ +/**/ c4 = {{0xBFA55555, 0x55555555}},/* -0.041666666666666664 */ +/**/ cc4 = {{0xBC4554BC, 0x2FFF257E}},/* -2.312711276085743e-18 */ +/**/ c6 = {{0x3F56C16C, 0x16C16A96}},/* 0.0013888888888888055 */ +/**/ cc6 = {{0xBBD2E846, 0xE6346F14}},/* -1.6015133010194884e-20 */ +/**/ c8 = {{0xBEFA019F, 0x821D5987}},/* -2.480157866754367e-05 */ +/**/ cc8 = {{0x3B7AB71E, 0x72FFE5CC}},/* 3.5357416224857556e-22 */ + +/**/ big = {{0x42c80000, 0x00000000}}, /* 52776558133248 */ + +/**/ hp0 = {{0x3FF921FB, 0x54442D18}}, /* PI / 2 */ +/**/ hp1 = {{0x3C91A626, 0x33145C07}}; /* 6.123233995736766e-17 */ +#else +#ifdef LITTLE_ENDI +static const mynumber +/**/ s3 = {{0x55555555, 0xBFC55555}},/* -0.16666666666666666 */ +/**/ ss3 = {{0xE77EE482, 0xBC6553AA}},/* -9.2490366677784492e-18 */ +/**/ s5 = {{0x11110F15, 0x3F811111}},/* 0.008333333333332452 */ +/**/ ss5 = {{0xDA488820, 0xBC21AC06}},/* -4.7899996586987931e-19 */ +/**/ s7 = {{0x5816C78D, 0xBF2A019F}},/* -0.00019841261022928957 */ +/**/ ss7 = {{0x6A18BF2A, 0x3BCDCEC9}},/* 1.2624077757871259e-20 */ +/**/ c2 = {{0x00000000, 0x3FE00000}},/* 0.5 */ +/**/ cc2 = {{0x00000000, 0xBA282FD8}},/* -1.5264073330037701e-28 */ +/**/ c4 = {{0x55555555, 0xBFA55555}},/* -0.041666666666666664 */ +/**/ cc4 = {{0x2FFF257E, 0xBC4554BC}},/* -2.312711276085743e-18 */ +/**/ c6 = {{0x16C16A96, 0x3F56C16C}},/* 0.0013888888888888055 */ +/**/ cc6 = {{0xE6346F14, 0xBBD2E846}},/* -1.6015133010194884e-20 */ +/**/ c8 = {{0x821D5987, 0xBEFA019F}},/* -2.480157866754367e-05 */ +/**/ cc8 = {{0x72FFE5CC, 0x3B7AB71E}},/* 3.5357416224857556e-22 */ + +/**/ big = {{0x00000000, 0x42c80000}}, /* 52776558133248 */ + +/**/ hp0 = {{0x54442D18, 0x3FF921FB}}, /* PI / 2 */ +/**/ hp1 = {{0x33145C07, 0x3C91A626}}; /* 6.123233995736766e-17 */ +#endif +#endif + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_acos.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_acos.c new file mode 100644 index 0000000000..8f7cd89249 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_acos.c @@ -0,0 +1 @@ +/* In e_asin.c */ diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_acosh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_acosh.c new file mode 100644 index 0000000000..c1f3590f75 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_acosh.c @@ -0,0 +1,69 @@ +/* @(#)e_acosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include <math.h> +#include <math_private.h> + +static const double + one = 1.0, + ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + +double +__ieee754_acosh (double x) +{ + double t; + int32_t hx; + u_int32_t lx; + EXTRACT_WORDS (hx, lx, x); + if (hx < 0x3ff00000) /* x < 1 */ + { + return (x - x) / (x - x); + } + else if (hx >= 0x41b00000) /* x > 2**28 */ + { + if (hx >= 0x7ff00000) /* x is inf of NaN */ + { + return x + x; + } + else + return __ieee754_log (x) + ln2; /* acosh(huge)=log(2x) */ + } + else if (((hx - 0x3ff00000) | lx) == 0) + { + return 0.0; /* acosh(1) = 0 */ + } + else if (hx > 0x40000000) /* 2**28 > x > 2 */ + { + t = x * x; + return __ieee754_log (2.0 * x - one / (x + __ieee754_sqrt (t - one))); + } + else /* 1<x<2 */ + { + t = x - one; + return __log1p (t + __ieee754_sqrt (2.0 * t + t * t)); + } +} +strong_alias (__ieee754_acosh, __acosh_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_asin.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_asin.c new file mode 100644 index 0000000000..9808f3981c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_asin.c @@ -0,0 +1,647 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/******************************************************************/ +/* MODULE_NAME:uasncs.c */ +/* */ +/* FUNCTIONS: uasin */ +/* uacos */ +/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */ +/* doasin.c sincos32.c dosincos.c mpa.c */ +/* sincos.tbl asincos.tbl powtwo.tbl root.tbl */ +/* */ +/* Ultimate asin/acos routines. Given an IEEE double machine */ +/* number x, compute the correctly rounded value of */ +/* arcsin(x)or arccos(x) according to the function called. */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/******************************************************************/ +#include "endian.h" +#include "mydefs.h" +#include "asincos.tbl" +#include "root.tbl" +#include "powtwo.tbl" +#include "MathLib.h" +#include "uasncs.h" +#include <float.h> +#include <math.h> +#include <math_private.h> + +#ifndef SECTION +# define SECTION +#endif + +void __doasin(double x, double dx, double w[]); +void __dubsin(double x, double dx, double v[]); +void __dubcos(double x, double dx, double v[]); +void __docos(double x, double dx, double v[]); +double __sin32(double x, double res, double res1); +double __cos32(double x, double res, double res1); + +/***************************************************************************/ +/* An ultimate asin routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of arcsin(x) */ +/***************************************************************************/ +double +SECTION +__ieee754_asin(double x){ + double x1,x2,xx,s1,s2,res1,p,t,res,r,cor,cc,y,c,z,w[2]; + mynumber u,v; + int4 k,m,n; + + u.x = x; + m = u.i[HIGH_HALF]; + k = 0x7fffffff&m; /* no sign */ + + if (k < 0x3e500000) + { + math_check_force_underflow (x); + return x; /* for x->0 => sin(x)=x */ + } + /*----------------------2^-26 <= |x| < 2^ -3 -----------------*/ + else + if (k < 0x3fc00000) { + x2 = x*x; + t = (((((f6*x2 + f5)*x2 + f4)*x2 + f3)*x2 + f2)*x2 + f1)*(x2*x); + res = x+t; /* res=arcsin(x) according to Taylor series */ + cor = (x-res)+t; + if (res == res+1.025*cor) return res; + else { + x1 = x+big; + xx = x*x; + x1 -= big; + x2 = x - x1; + p = x1*x1*x1; + s1 = a1.x*p; + s2 = ((((((c7*xx + c6)*xx + c5)*xx + c4)*xx + c3)*xx + c2)*xx*xx*x + + ((a1.x+a2.x)*x2*x2+ 0.5*x1*x)*x2) + a2.x*p; + res1 = x+s1; + s2 = ((x-res1)+s1)+s2; + res = res1+s2; + cor = (res1-res)+s2; + if (res == res+1.00014*cor) return res; + else { + __doasin(x,0,w); + if (w[0]==(w[0]+1.00000001*w[1])) return w[0]; + else { + y=fabs(x); + res=fabs(w[0]); + res1=fabs(w[0]+1.1*w[1]); + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } + } + /*---------------------0.125 <= |x| < 0.5 -----------------------------*/ + else if (k < 0x3fe00000) { + if (k<0x3fd00000) n = 11*((k&0x000fffff)>>15); + else n = 11*((k&0x000fffff)>>14)+352; + if (m>0) xx = x - asncs.x[n]; + else xx = -x - asncs.x[n]; + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+xx*(asncs.x[n+5] + +xx*asncs.x[n+6]))))+asncs.x[n+7]; + t+=p; + res =asncs.x[n+8] +t; + cor = (asncs.x[n+8]-res)+t; + if (res == res+1.05*cor) return (m>0)?res:-res; + else { + r=asncs.x[n+8]+xx*asncs.x[n+9]; + t=((asncs.x[n+8]-r)+xx*asncs.x[n+9])+(p+xx*asncs.x[n+10]); + res = r+t; + cor = (r-res)+t; + if (res == res+1.0005*cor) return (m>0)?res:-res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __dubsin(res,z,w); + z=(w[0]-fabs(x))+w[1]; + if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1); + else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1); + else { + y=fabs(x); + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } + } /* else if (k < 0x3fe00000) */ + /*-------------------- 0.5 <= |x| < 0.75 -----------------------------*/ + else + if (k < 0x3fe80000) { + n = 1056+((k&0x000fe000)>>11)*3; + if (m>0) xx = x - asncs.x[n]; + else xx = -x - asncs.x[n]; + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+xx*(asncs.x[n+5] + +xx*(asncs.x[n+6]+xx*asncs.x[n+7])))))+asncs.x[n+8]; + t+=p; + res =asncs.x[n+9] +t; + cor = (asncs.x[n+9]-res)+t; + if (res == res+1.01*cor) return (m>0)?res:-res; + else { + r=asncs.x[n+9]+xx*asncs.x[n+10]; + t=((asncs.x[n+9]-r)+xx*asncs.x[n+10])+(p+xx*asncs.x[n+11]); + res = r+t; + cor = (r-res)+t; + if (res == res+1.0005*cor) return (m>0)?res:-res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __dubsin(res,z,w); + z=(w[0]-fabs(x))+w[1]; + if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1); + else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1); + else { + y=fabs(x); + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } + } /* else if (k < 0x3fe80000) */ + /*--------------------- 0.75 <= |x|< 0.921875 ----------------------*/ + else + if (k < 0x3fed8000) { + n = 992+((k&0x000fe000)>>13)*13; + if (m>0) xx = x - asncs.x[n]; + else xx = -x - asncs.x[n]; + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+xx*(asncs.x[n+5] + +xx*(asncs.x[n+6]+xx*(asncs.x[n+7]+xx*asncs.x[n+8]))))))+asncs.x[n+9]; + t+=p; + res =asncs.x[n+10] +t; + cor = (asncs.x[n+10]-res)+t; + if (res == res+1.01*cor) return (m>0)?res:-res; + else { + r=asncs.x[n+10]+xx*asncs.x[n+11]; + t=((asncs.x[n+10]-r)+xx*asncs.x[n+11])+(p+xx*asncs.x[n+12]); + res = r+t; + cor = (r-res)+t; + if (res == res+1.0008*cor) return (m>0)?res:-res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + y=hp0.x-res; + z=((hp0.x-y)-res)+(hp1.x-z); + __dubcos(y,z,w); + z=(w[0]-fabs(x))+w[1]; + if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1); + else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1); + else { + y=fabs(x); + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } + } /* else if (k < 0x3fed8000) */ + /*-------------------0.921875 <= |x| < 0.953125 ------------------------*/ + else + if (k < 0x3fee8000) { + n = 884+((k&0x000fe000)>>13)*14; + if (m>0) xx = x - asncs.x[n]; + else xx = -x - asncs.x[n]; + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*(asncs.x[n+6] + +xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+ + xx*asncs.x[n+9])))))))+asncs.x[n+10]; + t+=p; + res =asncs.x[n+11] +t; + cor = (asncs.x[n+11]-res)+t; + if (res == res+1.01*cor) return (m>0)?res:-res; + else { + r=asncs.x[n+11]+xx*asncs.x[n+12]; + t=((asncs.x[n+11]-r)+xx*asncs.x[n+12])+(p+xx*asncs.x[n+13]); + res = r+t; + cor = (r-res)+t; + if (res == res+1.0007*cor) return (m>0)?res:-res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + y=(hp0.x-res)-z; + z=y+hp1.x; + y=(y-z)+hp1.x; + __dubcos(z,y,w); + z=(w[0]-fabs(x))+w[1]; + if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1); + else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1); + else { + y=fabs(x); + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } + } /* else if (k < 0x3fee8000) */ + + /*--------------------0.953125 <= |x| < 0.96875 ------------------------*/ + else + if (k < 0x3fef0000) { + n = 768+((k&0x000fe000)>>13)*15; + if (m>0) xx = x - asncs.x[n]; + else xx = -x - asncs.x[n]; + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*(asncs.x[n+6] + +xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+ + xx*(asncs.x[n+9]+xx*asncs.x[n+10]))))))))+asncs.x[n+11]; + t+=p; + res =asncs.x[n+12] +t; + cor = (asncs.x[n+12]-res)+t; + if (res == res+1.01*cor) return (m>0)?res:-res; + else { + r=asncs.x[n+12]+xx*asncs.x[n+13]; + t=((asncs.x[n+12]-r)+xx*asncs.x[n+13])+(p+xx*asncs.x[n+14]); + res = r+t; + cor = (r-res)+t; + if (res == res+1.0007*cor) return (m>0)?res:-res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + y=(hp0.x-res)-z; + z=y+hp1.x; + y=(y-z)+hp1.x; + __dubcos(z,y,w); + z=(w[0]-fabs(x))+w[1]; + if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1); + else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1); + else { + y=fabs(x); + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } + } /* else if (k < 0x3fef0000) */ + /*--------------------0.96875 <= |x| < 1 --------------------------------*/ + else + if (k<0x3ff00000) { + z = 0.5*((m>0)?(1.0-x):(1.0+x)); + v.x=z; + k=v.i[HIGH_HALF]; + t=inroot[(k&0x001fffff)>>14]*powtwo[511-(k>>21)]; + r=1.0-t*t*z; + t = t*(rt0+r*(rt1+r*(rt2+r*rt3))); + c=t*z; + t=c*(1.5-0.5*t*c); + y=(c+t24)-t24; + cc = (z-y*y)/(t+y); + p=(((((f6*z+f5)*z+f4)*z+f3)*z+f2)*z+f1)*z; + cor = (hp1.x - 2.0*cc)-2.0*(y+cc)*p; + res1 = hp0.x - 2.0*y; + res =res1 + cor; + if (res == res+1.003*((res1-res)+cor)) return (m>0)?res:-res; + else { + c=y+cc; + cc=(y-c)+cc; + __doasin(c,cc,w); + res1=hp0.x-2.0*w[0]; + cor=((hp0.x-res1)-2.0*w[0])+(hp1.x-2.0*w[1]); + res = res1+cor; + cor = (res1-res)+cor; + if (res==(res+1.0000001*cor)) return (m>0)?res:-res; + else { + y=fabs(x); + res1=res+1.1*cor; + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } /* else if (k < 0x3ff00000) */ + /*---------------------------- |x|>=1 -------------------------------*/ + else if (k==0x3ff00000 && u.i[LOW_HALF]==0) return (m>0)?hp0.x:-hp0.x; + else + if (k>0x7ff00000 || (k == 0x7ff00000 && u.i[LOW_HALF] != 0)) return x + x; + else { + u.i[HIGH_HALF]=0x7ff00000; + v.i[HIGH_HALF]=0x7ff00000; + u.i[LOW_HALF]=0; + v.i[LOW_HALF]=0; + return u.x/v.x; /* NaN */ + } +} +#ifndef __ieee754_asin +strong_alias (__ieee754_asin, __asin_finite) +#endif + +/*******************************************************************/ +/* */ +/* End of arcsine, below is arccosine */ +/* */ +/*******************************************************************/ + +double +SECTION +__ieee754_acos(double x) +{ + double x1,x2,xx,s1,s2,res1,p,t,res,r,cor,cc,y,c,z,w[2],eps; + mynumber u,v; + int4 k,m,n; + u.x = x; + m = u.i[HIGH_HALF]; + k = 0x7fffffff&m; + /*------------------- |x|<2.77556*10^-17 ----------------------*/ + if (k < 0x3c880000) return hp0.x; + + /*----------------- 2.77556*10^-17 <= |x| < 2^-3 --------------*/ + else + if (k < 0x3fc00000) { + x2 = x*x; + t = (((((f6*x2 + f5)*x2 + f4)*x2 + f3)*x2 + f2)*x2 + f1)*(x2*x); + r=hp0.x-x; + cor=(((hp0.x-r)-x)+hp1.x)-t; + res = r+cor; + cor = (r-res)+cor; + if (res == res+1.004*cor) return res; + else { + x1 = x+big; + xx = x*x; + x1 -= big; + x2 = x - x1; + p = x1*x1*x1; + s1 = a1.x*p; + s2 = ((((((c7*xx + c6)*xx + c5)*xx + c4)*xx + c3)*xx + c2)*xx*xx*x + + ((a1.x+a2.x)*x2*x2+ 0.5*x1*x)*x2) + a2.x*p; + res1 = x+s1; + s2 = ((x-res1)+s1)+s2; + r=hp0.x-res1; + cor=(((hp0.x-r)-res1)+hp1.x)-s2; + res = r+cor; + cor = (r-res)+cor; + if (res == res+1.00004*cor) return res; + else { + __doasin(x,0,w); + r=hp0.x-w[0]; + cor=((hp0.x-r)-w[0])+(hp1.x-w[1]); + res=r+cor; + cor=(r-res)+cor; + if (res ==(res +1.00000001*cor)) return res; + else { + res1=res+1.1*cor; + return __cos32(x,res,res1); + } + } + } + } /* else if (k < 0x3fc00000) */ + /*---------------------- 0.125 <= |x| < 0.5 --------------------*/ + else + if (k < 0x3fe00000) { + if (k<0x3fd00000) n = 11*((k&0x000fffff)>>15); + else n = 11*((k&0x000fffff)>>14)+352; + if (m>0) xx = x - asncs.x[n]; + else xx = -x - asncs.x[n]; + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*asncs.x[n+6]))))+asncs.x[n+7]; + t+=p; + y = (m>0)?(hp0.x-asncs.x[n+8]):(hp0.x+asncs.x[n+8]); + t = (m>0)?(hp1.x-t):(hp1.x+t); + res = y+t; + if (res == res+1.02*((y-res)+t)) return res; + else { + r=asncs.x[n+8]+xx*asncs.x[n+9]; + t=((asncs.x[n+8]-r)+xx*asncs.x[n+9])+(p+xx*asncs.x[n+10]); + if (m>0) + {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; } + else + {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); } + res = p+t; + cor = (p-res)+t; + if (res == (res+1.0002*cor)) return res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __docos(res,z,w); + z=(w[0]-x)+w[1]; + if (z>1.0e-27) return max(res,res1); + else if (z<-1.0e-27) return min(res,res1); + else return __cos32(x,res,res1); + } + } + } /* else if (k < 0x3fe00000) */ + + /*--------------------------- 0.5 <= |x| < 0.75 ---------------------*/ + else + if (k < 0x3fe80000) { + n = 1056+((k&0x000fe000)>>11)*3; + if (m>0) {xx = x - asncs.x[n]; eps=1.04; } + else {xx = -x - asncs.x[n]; eps=1.02; } + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*(asncs.x[n+6]+ + xx*asncs.x[n+7])))))+asncs.x[n+8]; + t+=p; + y = (m>0)?(hp0.x-asncs.x[n+9]):(hp0.x+asncs.x[n+9]); + t = (m>0)?(hp1.x-t):(hp1.x+t); + res = y+t; + if (res == res+eps*((y-res)+t)) return res; + else { + r=asncs.x[n+9]+xx*asncs.x[n+10]; + t=((asncs.x[n+9]-r)+xx*asncs.x[n+10])+(p+xx*asncs.x[n+11]); + if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0004; } + else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0002; } + res = p+t; + cor = (p-res)+t; + if (res == (res+eps*cor)) return res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __docos(res,z,w); + z=(w[0]-x)+w[1]; + if (z>1.0e-27) return max(res,res1); + else if (z<-1.0e-27) return min(res,res1); + else return __cos32(x,res,res1); + } + } + } /* else if (k < 0x3fe80000) */ + +/*------------------------- 0.75 <= |x| < 0.921875 -------------*/ + else + if (k < 0x3fed8000) { + n = 992+((k&0x000fe000)>>13)*13; + if (m>0) {xx = x - asncs.x[n]; eps = 1.04; } + else {xx = -x - asncs.x[n]; eps = 1.01; } + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*(asncs.x[n+6]+xx*(asncs.x[n+7]+ + xx*asncs.x[n+8]))))))+asncs.x[n+9]; + t+=p; + y = (m>0)?(hp0.x-asncs.x[n+10]):(hp0.x+asncs.x[n+10]); + t = (m>0)?(hp1.x-t):(hp1.x+t); + res = y+t; + if (res == res+eps*((y-res)+t)) return res; + else { + r=asncs.x[n+10]+xx*asncs.x[n+11]; + t=((asncs.x[n+10]-r)+xx*asncs.x[n+11])+(p+xx*asncs.x[n+12]); + if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0032; } + else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0008; } + res = p+t; + cor = (p-res)+t; + if (res == (res+eps*cor)) return res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __docos(res,z,w); + z=(w[0]-x)+w[1]; + if (z>1.0e-27) return max(res,res1); + else if (z<-1.0e-27) return min(res,res1); + else return __cos32(x,res,res1); + } + } + } /* else if (k < 0x3fed8000) */ + +/*-------------------0.921875 <= |x| < 0.953125 ------------------*/ + else + if (k < 0x3fee8000) { + n = 884+((k&0x000fe000)>>13)*14; + if (m>0) {xx = x - asncs.x[n]; eps=1.04; } + else {xx = -x - asncs.x[n]; eps =1.005; } + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*(asncs.x[n+6] + +xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+ + xx*asncs.x[n+9])))))))+asncs.x[n+10]; + t+=p; + y = (m>0)?(hp0.x-asncs.x[n+11]):(hp0.x+asncs.x[n+11]); + t = (m>0)?(hp1.x-t):(hp1.x+t); + res = y+t; + if (res == res+eps*((y-res)+t)) return res; + else { + r=asncs.x[n+11]+xx*asncs.x[n+12]; + t=((asncs.x[n+11]-r)+xx*asncs.x[n+12])+(p+xx*asncs.x[n+13]); + if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0030; } + else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0005; } + res = p+t; + cor = (p-res)+t; + if (res == (res+eps*cor)) return res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __docos(res,z,w); + z=(w[0]-x)+w[1]; + if (z>1.0e-27) return max(res,res1); + else if (z<-1.0e-27) return min(res,res1); + else return __cos32(x,res,res1); + } + } + } /* else if (k < 0x3fee8000) */ + + /*--------------------0.953125 <= |x| < 0.96875 ----------------*/ + else + if (k < 0x3fef0000) { + n = 768+((k&0x000fe000)>>13)*15; + if (m>0) {xx = x - asncs.x[n]; eps=1.04; } + else {xx = -x - asncs.x[n]; eps=1.005;} + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*(asncs.x[n+6] + +xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+xx*(asncs.x[n+9]+ + xx*asncs.x[n+10]))))))))+asncs.x[n+11]; + t+=p; + y = (m>0)?(hp0.x-asncs.x[n+12]):(hp0.x+asncs.x[n+12]); + t = (m>0)?(hp1.x-t):(hp1.x+t); + res = y+t; + if (res == res+eps*((y-res)+t)) return res; + else { + r=asncs.x[n+12]+xx*asncs.x[n+13]; + t=((asncs.x[n+12]-r)+xx*asncs.x[n+13])+(p+xx*asncs.x[n+14]); + if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0030; } + else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0005; } + res = p+t; + cor = (p-res)+t; + if (res == (res+eps*cor)) return res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __docos(res,z,w); + z=(w[0]-x)+w[1]; + if (z>1.0e-27) return max(res,res1); + else if (z<-1.0e-27) return min(res,res1); + else return __cos32(x,res,res1); + } + } + } /* else if (k < 0x3fef0000) */ + /*-----------------0.96875 <= |x| < 1 ---------------------------*/ + + else + if (k<0x3ff00000) { + z = 0.5*((m>0)?(1.0-x):(1.0+x)); + v.x=z; + k=v.i[HIGH_HALF]; + t=inroot[(k&0x001fffff)>>14]*powtwo[511-(k>>21)]; + r=1.0-t*t*z; + t = t*(rt0+r*(rt1+r*(rt2+r*rt3))); + c=t*z; + t=c*(1.5-0.5*t*c); + y = (t27*c+c)-t27*c; + cc = (z-y*y)/(t+y); + p=(((((f6*z+f5)*z+f4)*z+f3)*z+f2)*z+f1)*z; + if (m<0) { + cor = (hp1.x - cc)-(y+cc)*p; + res1 = hp0.x - y; + res =res1 + cor; + if (res == res+1.002*((res1-res)+cor)) return (res+res); + else { + c=y+cc; + cc=(y-c)+cc; + __doasin(c,cc,w); + res1=hp0.x-w[0]; + cor=((hp0.x-res1)-w[0])+(hp1.x-w[1]); + res = res1+cor; + cor = (res1-res)+cor; + if (res==(res+1.000001*cor)) return (res+res); + else { + res=res+res; + res1=res+1.2*cor; + return __cos32(x,res,res1); + } + } + } + else { + cor = cc+p*(y+cc); + res = y + cor; + if (res == res+1.03*((y-res)+cor)) return (res+res); + else { + c=y+cc; + cc=(y-c)+cc; + __doasin(c,cc,w); + res = w[0]; + cor=w[1]; + if (res==(res+1.000001*cor)) return (res+res); + else { + res=res+res; + res1=res+1.2*cor; + return __cos32(x,res,res1); + } + } + } + } /* else if (k < 0x3ff00000) */ + + /*---------------------------- |x|>=1 -----------------------*/ + else + if (k==0x3ff00000 && u.i[LOW_HALF]==0) return (m>0)?0:2.0*hp0.x; + else + if (k>0x7ff00000 || (k == 0x7ff00000 && u.i[LOW_HALF] != 0)) return x + x; + else { + u.i[HIGH_HALF]=0x7ff00000; + v.i[HIGH_HALF]=0x7ff00000; + u.i[LOW_HALF]=0; + v.i[LOW_HALF]=0; + return u.x/v.x; + } +} +#ifndef __ieee754_acos +strong_alias (__ieee754_acos, __acos_finite) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_atan2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_atan2.c new file mode 100644 index 0000000000..3c9d964b9b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_atan2.c @@ -0,0 +1,620 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/************************************************************************/ +/* MODULE_NAME: atnat2.c */ +/* */ +/* FUNCTIONS: uatan2 */ +/* atan2Mp */ +/* signArctan2 */ +/* normalized */ +/* */ +/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat2.h */ +/* mpatan.c mpatan2.c mpsqrt.c */ +/* uatan.tbl */ +/* */ +/* An ultimate atan2() routine. Given two IEEE double machine numbers y,*/ +/* x it computes the correctly rounded (to nearest) value of atan2(y,x).*/ +/* */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/************************************************************************/ + +#include <dla.h> +#include "mpa.h" +#include "MathLib.h" +#include "uatan.tbl" +#include "atnat2.h" +#include <fenv.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <stap-probe.h> + +#ifndef SECTION +# define SECTION +#endif + +/************************************************************************/ +/* An ultimate atan2 routine. Given two IEEE double machine numbers y,x */ +/* it computes the correctly rounded (to nearest) value of atan2(y,x). */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/************************************************************************/ +static double atan2Mp (double, double, const int[]); + /* Fix the sign and return after stage 1 or stage 2 */ +static double +signArctan2 (double y, double z) +{ + return __copysign (z, y); +} + +static double normalized (double, double, double, double); +void __mpatan2 (mp_no *, mp_no *, mp_no *, int); + +double +SECTION +__ieee754_atan2 (double y, double x) +{ + int i, de, ux, dx, uy, dy; + static const int pr[MM] = { 6, 8, 10, 20, 32 }; + double ax, ay, u, du, u9, ua, v, vv, dv, t1, t2, t3, t7, t8, + z, zz, cor, s1, ss1, s2, ss2; +#ifndef DLA_FMS + double t4, t5, t6; +#endif + number num; + + static const int ep = 59768832, /* 57*16**5 */ + em = -59768832; /* -57*16**5 */ + + /* x=NaN or y=NaN */ + num.d = x; + ux = num.i[HIGH_HALF]; + dx = num.i[LOW_HALF]; + if ((ux & 0x7ff00000) == 0x7ff00000) + { + if (((ux & 0x000fffff) | dx) != 0x00000000) + return x + y; + } + num.d = y; + uy = num.i[HIGH_HALF]; + dy = num.i[LOW_HALF]; + if ((uy & 0x7ff00000) == 0x7ff00000) + { + if (((uy & 0x000fffff) | dy) != 0x00000000) + return y + y; + } + + /* y=+-0 */ + if (uy == 0x00000000) + { + if (dy == 0x00000000) + { + if ((ux & 0x80000000) == 0x00000000) + return 0; + else + return opi.d; + } + } + else if (uy == 0x80000000) + { + if (dy == 0x00000000) + { + if ((ux & 0x80000000) == 0x00000000) + return -0.0; + else + return mopi.d; + } + } + + /* x=+-0 */ + if (x == 0) + { + if ((uy & 0x80000000) == 0x00000000) + return hpi.d; + else + return mhpi.d; + } + + /* x=+-INF */ + if (ux == 0x7ff00000) + { + if (dx == 0x00000000) + { + if (uy == 0x7ff00000) + { + if (dy == 0x00000000) + return qpi.d; + } + else if (uy == 0xfff00000) + { + if (dy == 0x00000000) + return mqpi.d; + } + else + { + if ((uy & 0x80000000) == 0x00000000) + return 0; + else + return -0.0; + } + } + } + else if (ux == 0xfff00000) + { + if (dx == 0x00000000) + { + if (uy == 0x7ff00000) + { + if (dy == 0x00000000) + return tqpi.d; + } + else if (uy == 0xfff00000) + { + if (dy == 0x00000000) + return mtqpi.d; + } + else + { + if ((uy & 0x80000000) == 0x00000000) + return opi.d; + else + return mopi.d; + } + } + } + + /* y=+-INF */ + if (uy == 0x7ff00000) + { + if (dy == 0x00000000) + return hpi.d; + } + else if (uy == 0xfff00000) + { + if (dy == 0x00000000) + return mhpi.d; + } + + SET_RESTORE_ROUND (FE_TONEAREST); + /* either x/y or y/x is very close to zero */ + ax = (x < 0) ? -x : x; + ay = (y < 0) ? -y : y; + de = (uy & 0x7ff00000) - (ux & 0x7ff00000); + if (de >= ep) + { + return ((y > 0) ? hpi.d : mhpi.d); + } + else if (de <= em) + { + if (x > 0) + { + double ret; + if ((z = ay / ax) < TWOM1022) + ret = normalized (ax, ay, y, z); + else + ret = signArctan2 (y, z); + if (fabs (ret) < DBL_MIN) + { + double vret = ret ? ret : DBL_MIN; + double force_underflow = vret * vret; + math_force_eval (force_underflow); + } + return ret; + } + else + { + return ((y > 0) ? opi.d : mopi.d); + } + } + + /* if either x or y is extremely close to zero, scale abs(x), abs(y). */ + if (ax < twom500.d || ay < twom500.d) + { + ax *= two500.d; + ay *= two500.d; + } + + /* Likewise for large x and y. */ + if (ax > two500.d || ay > two500.d) + { + ax *= twom500.d; + ay *= twom500.d; + } + + /* x,y which are neither special nor extreme */ + if (ay < ax) + { + u = ay / ax; + EMULV (ax, u, v, vv, t1, t2, t3, t4, t5); + du = ((ay - v) - vv) / ax; + } + else + { + u = ax / ay; + EMULV (ay, u, v, vv, t1, t2, t3, t4, t5); + du = ((ax - v) - vv) / ay; + } + + if (x > 0) + { + /* (i) x>0, abs(y)< abs(x): atan(ay/ax) */ + if (ay < ax) + { + if (u < inv16.d) + { + v = u * u; + + zz = du + u * v * (d3.d + + v * (d5.d + + v * (d7.d + + v * (d9.d + + v * (d11.d + + v * d13.d))))); + + if ((z = u + (zz - u1.d * u)) == u + (zz + u1.d * u)) + return signArctan2 (y, z); + + MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8); + s1 = v * (f11.d + v * (f13.d + + v * (f15.d + v * (f17.d + v * f19.d)))); + ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (u, du, s2, ss2, s1, ss1, t1, t2); + + if ((z = s1 + (ss1 - u5.d * s1)) == s1 + (ss1 + u5.d * s1)) + return signArctan2 (y, z); + + return atan2Mp (x, y, pr); + } + + i = (TWO52 + TWO8 * u) - TWO52; + i -= 16; + t3 = u - cij[i][0].d; + EADD (t3, du, v, dv); + t1 = cij[i][1].d; + t2 = cij[i][2].d; + zz = v * t2 + (dv * t2 + + v * v * (cij[i][3].d + + v * (cij[i][4].d + + v * (cij[i][5].d + + v * cij[i][6].d)))); + if (i < 112) + { + if (i < 48) + u9 = u91.d; /* u < 1/4 */ + else + u9 = u92.d; + } /* 1/4 <= u < 1/2 */ + else + { + if (i < 176) + u9 = u93.d; /* 1/2 <= u < 3/4 */ + else + u9 = u94.d; + } /* 3/4 <= u <= 1 */ + if ((z = t1 + (zz - u9 * t1)) == t1 + (zz + u9 * t1)) + return signArctan2 (y, z); + + t1 = u - hij[i][0].d; + EADD (t1, du, v, vv); + s1 = v * (hij[i][11].d + + v * (hij[i][12].d + + v * (hij[i][13].d + + v * (hij[i][14].d + + v * hij[i][15].d)))); + ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + + if ((z = s2 + (ss2 - ub.d * s2)) == s2 + (ss2 + ub.d * s2)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); + } + + /* (ii) x>0, abs(x)<=abs(y): pi/2-atan(ax/ay) */ + if (u < inv16.d) + { + v = u * u; + zz = u * v * (d3.d + + v * (d5.d + + v * (d7.d + + v * (d9.d + + v * (d11.d + + v * d13.d))))); + ESUB (hpi.d, u, t2, cor); + t3 = ((hpi1.d + cor) - du) - zz; + if ((z = t2 + (t3 - u2.d)) == t2 + (t3 + u2.d)) + return signArctan2 (y, z); + + MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8); + s1 = v * (f11.d + + v * (f13.d + + v * (f15.d + v * (f17.d + v * f19.d)))); + ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (u, du, s2, ss2, s1, ss1, t1, t2); + SUB2 (hpi.d, hpi1.d, s1, ss1, s2, ss2, t1, t2); + + if ((z = s2 + (ss2 - u6.d)) == s2 + (ss2 + u6.d)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); + } + + i = (TWO52 + TWO8 * u) - TWO52; + i -= 16; + v = (u - cij[i][0].d) + du; + + zz = hpi1.d - v * (cij[i][2].d + + v * (cij[i][3].d + + v * (cij[i][4].d + + v * (cij[i][5].d + + v * cij[i][6].d)))); + t1 = hpi.d - cij[i][1].d; + if (i < 112) + ua = ua1.d; /* w < 1/2 */ + else + ua = ua2.d; /* w >= 1/2 */ + if ((z = t1 + (zz - ua)) == t1 + (zz + ua)) + return signArctan2 (y, z); + + t1 = u - hij[i][0].d; + EADD (t1, du, v, vv); + + s1 = v * (hij[i][11].d + + v * (hij[i][12].d + + v * (hij[i][13].d + + v * (hij[i][14].d + + v * hij[i][15].d)))); + + ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + SUB2 (hpi.d, hpi1.d, s2, ss2, s1, ss1, t1, t2); + + if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); + } + + /* (iii) x<0, abs(x)< abs(y): pi/2+atan(ax/ay) */ + if (ax < ay) + { + if (u < inv16.d) + { + v = u * u; + zz = u * v * (d3.d + + v * (d5.d + + v * (d7.d + + v * (d9.d + + v * (d11.d + v * d13.d))))); + EADD (hpi.d, u, t2, cor); + t3 = ((hpi1.d + cor) + du) + zz; + if ((z = t2 + (t3 - u3.d)) == t2 + (t3 + u3.d)) + return signArctan2 (y, z); + + MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8); + s1 = v * (f11.d + + v * (f13.d + v * (f15.d + v * (f17.d + v * f19.d)))); + ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (u, du, s2, ss2, s1, ss1, t1, t2); + ADD2 (hpi.d, hpi1.d, s1, ss1, s2, ss2, t1, t2); + + if ((z = s2 + (ss2 - u7.d)) == s2 + (ss2 + u7.d)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); + } + + i = (TWO52 + TWO8 * u) - TWO52; + i -= 16; + v = (u - cij[i][0].d) + du; + zz = hpi1.d + v * (cij[i][2].d + + v * (cij[i][3].d + + v * (cij[i][4].d + + v * (cij[i][5].d + + v * cij[i][6].d)))); + t1 = hpi.d + cij[i][1].d; + if (i < 112) + ua = ua1.d; /* w < 1/2 */ + else + ua = ua2.d; /* w >= 1/2 */ + if ((z = t1 + (zz - ua)) == t1 + (zz + ua)) + return signArctan2 (y, z); + + t1 = u - hij[i][0].d; + EADD (t1, du, v, vv); + s1 = v * (hij[i][11].d + + v * (hij[i][12].d + + v * (hij[i][13].d + + v * (hij[i][14].d + + v * hij[i][15].d)))); + ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + ADD2 (hpi.d, hpi1.d, s2, ss2, s1, ss1, t1, t2); + + if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); + } + + /* (iv) x<0, abs(y)<=abs(x): pi-atan(ax/ay) */ + if (u < inv16.d) + { + v = u * u; + zz = u * v * (d3.d + + v * (d5.d + + v * (d7.d + + v * (d9.d + v * (d11.d + v * d13.d))))); + ESUB (opi.d, u, t2, cor); + t3 = ((opi1.d + cor) - du) - zz; + if ((z = t2 + (t3 - u4.d)) == t2 + (t3 + u4.d)) + return signArctan2 (y, z); + + MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8); + s1 = v * (f11.d + v * (f13.d + v * (f15.d + v * (f17.d + v * f19.d)))); + ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (u, du, s2, ss2, s1, ss1, t1, t2); + SUB2 (opi.d, opi1.d, s1, ss1, s2, ss2, t1, t2); + + if ((z = s2 + (ss2 - u8.d)) == s2 + (ss2 + u8.d)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); + } + + i = (TWO52 + TWO8 * u) - TWO52; + i -= 16; + v = (u - cij[i][0].d) + du; + zz = opi1.d - v * (cij[i][2].d + + v * (cij[i][3].d + + v * (cij[i][4].d + + v * (cij[i][5].d + v * cij[i][6].d)))); + t1 = opi.d - cij[i][1].d; + if (i < 112) + ua = ua1.d; /* w < 1/2 */ + else + ua = ua2.d; /* w >= 1/2 */ + if ((z = t1 + (zz - ua)) == t1 + (zz + ua)) + return signArctan2 (y, z); + + t1 = u - hij[i][0].d; + + EADD (t1, du, v, vv); + + s1 = v * (hij[i][11].d + + v * (hij[i][12].d + + v * (hij[i][13].d + + v * (hij[i][14].d + v * hij[i][15].d)))); + + ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + SUB2 (opi.d, opi1.d, s2, ss2, s1, ss1, t1, t2); + + if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); +} + +#ifndef __ieee754_atan2 +strong_alias (__ieee754_atan2, __atan2_finite) +#endif + +/* Treat the Denormalized case */ +static double +SECTION +normalized (double ax, double ay, double y, double z) +{ + int p; + mp_no mpx, mpy, mpz, mperr, mpz2, mpt1; + p = 6; + __dbl_mp (ax, &mpx, p); + __dbl_mp (ay, &mpy, p); + __dvd (&mpy, &mpx, &mpz, p); + __dbl_mp (ue.d, &mpt1, p); + __mul (&mpz, &mpt1, &mperr, p); + __sub (&mpz, &mperr, &mpz2, p); + __mp_dbl (&mpz2, &z, p); + return signArctan2 (y, z); +} + +/* Stage 3: Perform a multi-Precision computation */ +static double +SECTION +atan2Mp (double x, double y, const int pr[]) +{ + double z1, z2; + int i, p; + mp_no mpx, mpy, mpz, mpz1, mpz2, mperr, mpt1; + for (i = 0; i < MM; i++) + { + p = pr[i]; + __dbl_mp (x, &mpx, p); + __dbl_mp (y, &mpy, p); + __mpatan2 (&mpy, &mpx, &mpz, p); + __dbl_mp (ud[i].d, &mpt1, p); + __mul (&mpz, &mpt1, &mperr, p); + __add (&mpz, &mperr, &mpz1, p); + __sub (&mpz, &mperr, &mpz2, p); + __mp_dbl (&mpz1, &z1, p); + __mp_dbl (&mpz2, &z2, p); + if (z1 == z2) + { + LIBC_PROBE (slowatan2, 4, &p, &x, &y, &z1); + return z1; + } + } + LIBC_PROBE (slowatan2_inexact, 4, &p, &x, &y, &z1); + return z1; /*if impossible to do exact computing */ +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_atanh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_atanh.c new file mode 100644 index 0000000000..a9d19a0472 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_atanh.c @@ -0,0 +1,74 @@ +/* Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@gmail.com>, 2011. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + + +/* __ieee754_atanh(x) + Method : + 1.Reduced x to positive by atanh(-x) = -atanh(x) + 2.For x>=0.5 + 1 2x x + atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + 2 1 - x 1 - x + + For x<0.5 + atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) + + Special cases: + atanh(x) is NaN if |x| > 1 with signal; + atanh(NaN) is that NaN with no signal; + atanh(+-1) is +-INF with signal. + + */ + +#include <float.h> +#include <inttypes.h> +#include <math.h> +#include <math_private.h> + +static const double huge = 1e300; + +double +__ieee754_atanh (double x) +{ + double xa = fabs (x); + double t; + if (isless (xa, 0.5)) + { + if (__glibc_unlikely (xa < 0x1.0p-28)) + { + math_force_eval (huge + x); + math_check_force_underflow (x); + return x; + } + + t = xa + xa; + t = 0.5 * __log1p (t + t * xa / (1.0 - xa)); + } + else if (__glibc_likely (isless (xa, 1.0))) + t = 0.5 * __log1p ((xa + xa) / (1.0 - xa)); + else + { + if (isgreater (xa, 1.0)) + return (x - x) / (x - x); + + return x / 0.0; + } + + return __copysign (t, x); +} +strong_alias (__ieee754_atanh, __atanh_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_cosh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_cosh.c new file mode 100644 index 0000000000..52a5d5007d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_cosh.c @@ -0,0 +1,88 @@ +/* Optimized by Ulrich Drepper <drepper@gmail.com>, 2011 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : cosh(x) := ------------------- + * 2 + * 22 <= x <= lnovft : cosh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + +#include <math.h> +#include <math_private.h> + +static const double one = 1.0, half = 0.5, huge = 1.0e300; + +double +__ieee754_cosh (double x) +{ + double t, w; + int32_t ix; + u_int32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD (ix, x); + ix &= 0x7fffffff; + + /* |x| in [0,22] */ + if (ix < 0x40360000) + { + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if (ix < 0x3fd62e43) + { + if (ix < 0x3c800000) + return one; /* cosh(tiny) = 1 */ + t = __expm1 (fabs (x)); + w = one + t; + return one + (t * t) / (w + w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + t = __ieee754_exp (fabs (x)); + return half * t + half / t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862e42) + return half * __ieee754_exp (fabs (x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD (lx, x); + if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (u_int32_t) 0x8fb9f87d))) + { + w = __ieee754_exp (half * fabs (x)); + t = half * w; + return t * w; + } + + /* x is INF or NaN */ + if (ix >= 0x7ff00000) + return x * x; + + /* |x| > overflowthresold, cosh(x) overflow */ + return math_narrow_eval (huge * huge); +} +strong_alias (__ieee754_cosh, __cosh_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp.c new file mode 100644 index 0000000000..6757a14ce1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp.c @@ -0,0 +1,361 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/***************************************************************************/ +/* MODULE_NAME:uexp.c */ +/* */ +/* FUNCTION:uexp */ +/* exp1 */ +/* */ +/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h uexp.h */ +/* mpa.c mpexp.x slowexp.c */ +/* */ +/* An ultimate exp routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of e^x */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/***************************************************************************/ + +#include <math.h> +#include "endian.h" +#include "uexp.h" +#include "mydefs.h" +#include "MathLib.h" +#include "uexp.tbl" +#include <math_private.h> +#include <fenv.h> +#include <float.h> + +#ifndef SECTION +# define SECTION +#endif + +double __slowexp (double); + +/* An ultimate exp routine. Given an IEEE double machine number x it computes + the correctly rounded (to nearest) value of e^x. */ +double +SECTION +__ieee754_exp (double x) +{ + double bexp, t, eps, del, base, y, al, bet, res, rem, cor; + mynumber junk1, junk2, binexp = {{0, 0}}; + int4 i, j, m, n, ex; + double retval; + + { + SET_RESTORE_ROUND (FE_TONEAREST); + + junk1.x = x; + m = junk1.i[HIGH_HALF]; + n = m & hugeint; + + if (n > smallint && n < bigint) + { + y = x * log2e.x + three51.x; + bexp = y - three51.x; /* multiply the result by 2**bexp */ + + junk1.x = y; + + eps = bexp * ln_two2.x; /* x = bexp*ln(2) + t - eps */ + t = x - bexp * ln_two1.x; + + y = t + three33.x; + base = y - three33.x; /* t rounded to a multiple of 2**-18 */ + junk2.x = y; + del = (t - base) - eps; /* x = bexp*ln(2) + base + del */ + eps = del + del * del * (p3.x * del + p2.x); + + binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 1023) << 20; + + i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356; + j = (junk2.i[LOW_HALF] & 511) << 1; + + al = coar.x[i] * fine.x[j]; + bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j]) + + coar.x[i + 1] * fine.x[j + 1]); + + rem = (bet + bet * eps) + al * eps; + res = al + rem; + cor = (al - res) + rem; + if (res == (res + cor * err_0)) + { + retval = res * binexp.x; + goto ret; + } + else + { + retval = __slowexp (x); + goto ret; + } /*if error is over bound */ + } + + if (n <= smallint) + { + retval = 1.0; + goto ret; + } + + if (n >= badint) + { + if (n > infint) + { + retval = x + x; + goto ret; + } /* x is NaN */ + if (n < infint) + { + if (x > 0) + goto ret_huge; + else + goto ret_tiny; + } + /* x is finite, cause either overflow or underflow */ + if (junk1.i[LOW_HALF] != 0) + { + retval = x + x; + goto ret; + } /* x is NaN */ + retval = (x > 0) ? inf.x : zero; /* |x| = inf; return either inf or 0 */ + goto ret; + } + + y = x * log2e.x + three51.x; + bexp = y - three51.x; + junk1.x = y; + eps = bexp * ln_two2.x; + t = x - bexp * ln_two1.x; + y = t + three33.x; + base = y - three33.x; + junk2.x = y; + del = (t - base) - eps; + eps = del + del * del * (p3.x * del + p2.x); + i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356; + j = (junk2.i[LOW_HALF] & 511) << 1; + al = coar.x[i] * fine.x[j]; + bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j]) + + coar.x[i + 1] * fine.x[j + 1]); + rem = (bet + bet * eps) + al * eps; + res = al + rem; + cor = (al - res) + rem; + if (m >> 31) + { + ex = junk1.i[LOW_HALF]; + if (res < 1.0) + { + res += res; + cor += cor; + ex -= 1; + } + if (ex >= -1022) + { + binexp.i[HIGH_HALF] = (1023 + ex) << 20; + if (res == (res + cor * err_0)) + { + retval = res * binexp.x; + goto ret; + } + else + { + retval = __slowexp (x); + goto check_uflow_ret; + } /*if error is over bound */ + } + ex = -(1022 + ex); + binexp.i[HIGH_HALF] = (1023 - ex) << 20; + res *= binexp.x; + cor *= binexp.x; + eps = 1.0000000001 + err_0 * binexp.x; + t = 1.0 + res; + y = ((1.0 - t) + res) + cor; + res = t + y; + cor = (t - res) + y; + if (res == (res + eps * cor)) + { + binexp.i[HIGH_HALF] = 0x00100000; + retval = (res - 1.0) * binexp.x; + goto check_uflow_ret; + } + else + { + retval = __slowexp (x); + goto check_uflow_ret; + } /* if error is over bound */ + check_uflow_ret: + if (retval < DBL_MIN) + { + double force_underflow = tiny * tiny; + math_force_eval (force_underflow); + } + if (retval == 0) + goto ret_tiny; + goto ret; + } + else + { + binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 767) << 20; + if (res == (res + cor * err_0)) + retval = res * binexp.x * t256.x; + else + retval = __slowexp (x); + if (isinf (retval)) + goto ret_huge; + else + goto ret; + } + } +ret: + return retval; + + ret_huge: + return hhuge * hhuge; + + ret_tiny: + return tiny * tiny; +} +#ifndef __ieee754_exp +strong_alias (__ieee754_exp, __exp_finite) +#endif + +/* Compute e^(x+xx). The routine also receives bound of error of previous + calculation. If after computing exp the error exceeds the allowed bounds, + the routine returns a non-positive number. Otherwise it returns the + computed result, which is always positive. */ +double +SECTION +__exp1 (double x, double xx, double error) +{ + double bexp, t, eps, del, base, y, al, bet, res, rem, cor; + mynumber junk1, junk2, binexp = {{0, 0}}; + int4 i, j, m, n, ex; + + junk1.x = x; + m = junk1.i[HIGH_HALF]; + n = m & hugeint; /* no sign */ + + if (n > smallint && n < bigint) + { + y = x * log2e.x + three51.x; + bexp = y - three51.x; /* multiply the result by 2**bexp */ + + junk1.x = y; + + eps = bexp * ln_two2.x; /* x = bexp*ln(2) + t - eps */ + t = x - bexp * ln_two1.x; + + y = t + three33.x; + base = y - three33.x; /* t rounded to a multiple of 2**-18 */ + junk2.x = y; + del = (t - base) + (xx - eps); /* x = bexp*ln(2) + base + del */ + eps = del + del * del * (p3.x * del + p2.x); + + binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 1023) << 20; + + i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356; + j = (junk2.i[LOW_HALF] & 511) << 1; + + al = coar.x[i] * fine.x[j]; + bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j]) + + coar.x[i + 1] * fine.x[j + 1]); + + rem = (bet + bet * eps) + al * eps; + res = al + rem; + cor = (al - res) + rem; + if (res == (res + cor * (1.0 + error + err_1))) + return res * binexp.x; + else + return -10.0; + } + + if (n <= smallint) + return 1.0; /* if x->0 e^x=1 */ + + if (n >= badint) + { + if (n > infint) + return (zero / zero); /* x is NaN, return invalid */ + if (n < infint) + return ((x > 0) ? (hhuge * hhuge) : (tiny * tiny)); + /* x is finite, cause either overflow or underflow */ + if (junk1.i[LOW_HALF] != 0) + return (zero / zero); /* x is NaN */ + return ((x > 0) ? inf.x : zero); /* |x| = inf; return either inf or 0 */ + } + + y = x * log2e.x + three51.x; + bexp = y - three51.x; + junk1.x = y; + eps = bexp * ln_two2.x; + t = x - bexp * ln_two1.x; + y = t + three33.x; + base = y - three33.x; + junk2.x = y; + del = (t - base) + (xx - eps); + eps = del + del * del * (p3.x * del + p2.x); + i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356; + j = (junk2.i[LOW_HALF] & 511) << 1; + al = coar.x[i] * fine.x[j]; + bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j]) + + coar.x[i + 1] * fine.x[j + 1]); + rem = (bet + bet * eps) + al * eps; + res = al + rem; + cor = (al - res) + rem; + if (m >> 31) + { + ex = junk1.i[LOW_HALF]; + if (res < 1.0) + { + res += res; + cor += cor; + ex -= 1; + } + if (ex >= -1022) + { + binexp.i[HIGH_HALF] = (1023 + ex) << 20; + if (res == (res + cor * (1.0 + error + err_1))) + return res * binexp.x; + else + return -10.0; + } + ex = -(1022 + ex); + binexp.i[HIGH_HALF] = (1023 - ex) << 20; + res *= binexp.x; + cor *= binexp.x; + eps = 1.00000000001 + (error + err_1) * binexp.x; + t = 1.0 + res; + y = ((1.0 - t) + res) + cor; + res = t + y; + cor = (t - res) + y; + if (res == (res + eps * cor)) + { + binexp.i[HIGH_HALF] = 0x00100000; + return (res - 1.0) * binexp.x; + } + else + return -10.0; + } + else + { + binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 767) << 20; + if (res == (res + cor * (1.0 + error + err_1))) + return res * binexp.x * t256.x; + else + return -10.0; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp10.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp10.c new file mode 100644 index 0000000000..6c8783e405 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp10.c @@ -0,0 +1,50 @@ +/* Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +static const double log10_high = 0x2.4d7637p0; +static const double log10_low = 0x7.6aaa2b05ba95cp-28; + +double +__ieee754_exp10 (double arg) +{ + int32_t lx; + double arg_high, arg_low; + double exp_high, exp_low; + + if (!isfinite (arg)) + return __ieee754_exp (arg); + if (arg < DBL_MIN_10_EXP - DBL_DIG - 10) + return DBL_MIN * DBL_MIN; + else if (arg > DBL_MAX_10_EXP + 1) + return DBL_MAX * DBL_MAX; + else if (fabs (arg) < 0x1p-56) + return 1.0; + + GET_LOW_WORD (lx, arg); + lx &= 0xf8000000; + arg_high = arg; + SET_LOW_WORD (arg_high, lx); + arg_low = arg - arg_high; + exp_high = arg_high * log10_high; + exp_low = arg_high * log10_low + arg_low * M_LN10; + return __ieee754_exp (exp_high) * __ieee754_exp (exp_low); +} +strong_alias (__ieee754_exp10, __exp10_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp2.c new file mode 100644 index 0000000000..9efda23f06 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp2.c @@ -0,0 +1,133 @@ +/* Double-precision floating point 2^x. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* The basic design here is from + Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical + Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft., + 17 (1), March 1991, pp. 26-45. + It has been slightly modified to compute 2^x instead of e^x. + */ +#include <stdlib.h> +#include <float.h> +#include <ieee754.h> +#include <math.h> +#include <fenv.h> +#include <inttypes.h> +#include <math_private.h> + +#include "t_exp2.h" + +static const double TWO1023 = 8.988465674311579539e+307; +static const double TWOM1000 = 9.3326361850321887899e-302; + +double +__ieee754_exp2 (double x) +{ + static const double himark = (double) DBL_MAX_EXP; + static const double lomark = (double) (DBL_MIN_EXP - DBL_MANT_DIG - 1); + + /* Check for usual case. */ + if (__glibc_likely (isless (x, himark))) + { + /* Exceptional cases: */ + if (__glibc_unlikely (!isgreaterequal (x, lomark))) + { + if (isinf (x)) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TWOM1000 * TWOM1000; + } + + static const double THREEp42 = 13194139533312.0; + int tval, unsafe; + double rx, x22, result; + union ieee754_double ex2_u, scale_u; + + if (fabs (x) < DBL_EPSILON / 4.0) + return 1.0 + x; + + { + SET_RESTORE_ROUND_NOEX (FE_TONEAREST); + + /* 1. Argument reduction. + Choose integers ex, -256 <= t < 256, and some real + -1/1024 <= x1 <= 1024 so that + x = ex + t/512 + x1. + + First, calculate rx = ex + t/512. */ + rx = x + THREEp42; + rx -= THREEp42; + x -= rx; /* Compute x=x1. */ + /* Compute tval = (ex*512 + t)+256. + Now, t = (tval mod 512)-256 and ex=tval/512 [that's mod, NOT %; + and /-round-to-nearest not the usual c integer /]. */ + tval = (int) (rx * 512.0 + 256.0); + + /* 2. Adjust for accurate table entry. + Find e so that + x = ex + t/512 + e + x2 + where -1e6 < e < 1e6, and + (double)(2^(t/512+e)) + is accurate to one part in 2^-64. */ + + /* 'tval & 511' is the same as 'tval%512' except that it's always + positive. + Compute x = x2. */ + x -= exp2_deltatable[tval & 511]; + + /* 3. Compute ex2 = 2^(t/512+e+ex). */ + ex2_u.d = exp2_accuratetable[tval & 511]; + tval >>= 9; + /* x2 is an integer multiple of 2^-54; avoid intermediate + underflow from the calculation of x22 * x. */ + unsafe = abs (tval) >= -DBL_MIN_EXP - 56; + ex2_u.ieee.exponent += tval >> unsafe; + scale_u.d = 1.0; + scale_u.ieee.exponent += tval - (tval >> unsafe); + + /* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial, + with maximum error in [-2^-10-2^-30,2^-10+2^-30] + less than 10^-19. */ + + x22 = (((.0096181293647031180 + * x + .055504110254308625) + * x + .240226506959100583) + * x + .69314718055994495) * ex2_u.d; + math_opt_barrier (x22); + } + + /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */ + result = x22 * x + ex2_u.d; + + if (!unsafe) + return result; + else + { + result *= scale_u.d; + math_check_force_underflow_nonneg (result); + return result; + } + } + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO1023 * x; +} +strong_alias (__ieee754_exp2, __exp2_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_fmod.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_fmod.c new file mode 100644 index 0000000000..e82b302200 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_fmod.c @@ -0,0 +1,173 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __ieee754_fmod(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include <math.h> +#include <math_private.h> + +static const double one = 1.0, Zero[] = { 0.0, -0.0, }; + +double +__ieee754_fmod (double x, double y) +{ + int32_t n, hx, hy, hz, ix, iy, sx, i; + u_int32_t lx, ly, lz; + + EXTRACT_WORDS (hx, lx, x); + EXTRACT_WORDS (hy, ly, y); + sx = hx & 0x80000000; /* sign of x */ + hx ^= sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if ((hy | ly) == 0 || (hx >= 0x7ff00000) || /* y=0,or x not finite */ + ((hy | ((ly | -ly) >> 31)) > 0x7ff00000)) /* or y is NaN */ + return (x * y) / (x * y); + if (hx <= hy) + { + if ((hx < hy) || (lx < ly)) + return x; /* |x|<|y| return x */ + if (lx == ly) + return Zero[(u_int32_t) sx >> 31]; /* |x|=|y| return x*0*/ + } + + /* determine ix = ilogb(x) */ + if (__glibc_unlikely (hx < 0x00100000)) /* subnormal x */ + { + if (hx == 0) + { + for (ix = -1043, i = lx; i > 0; i <<= 1) + ix -= 1; + } + else + { + for (ix = -1022, i = (hx << 11); i > 0; i <<= 1) + ix -= 1; + } + } + else + ix = (hx >> 20) - 1023; + + /* determine iy = ilogb(y) */ + if (__glibc_unlikely (hy < 0x00100000)) /* subnormal y */ + { + if (hy == 0) + { + for (iy = -1043, i = ly; i > 0; i <<= 1) + iy -= 1; + } + else + { + for (iy = -1022, i = (hy << 11); i > 0; i <<= 1) + iy -= 1; + } + } + else + iy = (hy >> 20) - 1023; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if (__glibc_likely (ix >= -1022)) + hx = 0x00100000 | (0x000fffff & hx); + else /* subnormal x, shift x to normal */ + { + n = -1022 - ix; + if (n <= 31) + { + hx = (hx << n) | (lx >> (32 - n)); + lx <<= n; + } + else + { + hx = lx << (n - 32); + lx = 0; + } + } + if (__glibc_likely (iy >= -1022)) + hy = 0x00100000 | (0x000fffff & hy); + else /* subnormal y, shift y to normal */ + { + n = -1022 - iy; + if (n <= 31) + { + hy = (hy << n) | (ly >> (32 - n)); + ly <<= n; + } + else + { + hy = ly << (n - 32); + ly = 0; + } + } + + /* fix point fmod */ + n = ix - iy; + while (n--) + { + hz = hx - hy; lz = lx - ly; if (lx < ly) + hz -= 1; + if (hz < 0) + { + hx = hx + hx + (lx >> 31); lx = lx + lx; + } + else + { + if ((hz | lz) == 0) /* return sign(x)*0 */ + return Zero[(u_int32_t) sx >> 31]; + hx = hz + hz + (lz >> 31); lx = lz + lz; + } + } + hz = hx - hy; lz = lx - ly; if (lx < ly) + hz -= 1; + if (hz >= 0) + { + hx = hz; lx = lz; + } + + /* convert back to floating value and restore the sign */ + if ((hx | lx) == 0) /* return sign(x)*0 */ + return Zero[(u_int32_t) sx >> 31]; + while (hx < 0x00100000) /* normalize x */ + { + hx = hx + hx + (lx >> 31); lx = lx + lx; + iy -= 1; + } + if (__glibc_likely (iy >= -1022)) /* normalize output */ + { + hx = ((hx - 0x00100000) | ((iy + 1023) << 20)); + INSERT_WORDS (x, hx | sx, lx); + } + else /* subnormal output */ + { + n = -1022 - iy; + if (n <= 20) + { + lx = (lx >> n) | ((u_int32_t) hx << (32 - n)); + hx >>= n; + } + else if (n <= 31) + { + lx = (hx << (32 - n)) | (lx >> n); hx = sx; + } + else + { + lx = hx >> (n - 32); hx = sx; + } + INSERT_WORDS (x, hx | sx, lx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} +strong_alias (__ieee754_fmod, __fmod_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_gamma_r.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_gamma_r.c new file mode 100644 index 0000000000..818fa94766 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_gamma_r.c @@ -0,0 +1,220 @@ +/* Implementation of gamma function according to ISO C. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const double gamma_coeff[] = + { + 0x1.5555555555555p-4, + -0xb.60b60b60b60b8p-12, + 0x3.4034034034034p-12, + -0x2.7027027027028p-12, + 0x3.72a3c5631fe46p-12, + -0x7.daac36664f1f4p-12, + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 184, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static double +gamma_positive (double x, int *exp2_adj) +{ + int local_signgam; + if (x < 0.5) + { + *exp2_adj = 0; + return __ieee754_exp (__ieee754_lgamma_r (x + 1, &local_signgam)) / x; + } + else if (x <= 1.5) + { + *exp2_adj = 0; + return __ieee754_exp (__ieee754_lgamma_r (x, &local_signgam)); + } + else if (x < 6.5) + { + /* Adjust into the range for using exp (lgamma). */ + *exp2_adj = 0; + double n = __ceil (x - 1.5); + double x_adj = x - n; + double eps; + double prod = __gamma_product (x_adj, 0, n, &eps); + return (__ieee754_exp (__ieee754_lgamma_r (x_adj, &local_signgam)) + * prod * (1.0 + eps)); + } + else + { + double eps = 0; + double x_eps = 0; + double x_adj = x; + double prod = 1; + if (x < 12.0) + { + /* Adjust into the range for applying Stirling's + approximation. */ + double n = __ceil (12.0 - x); + x_adj = math_narrow_eval (x + n); + x_eps = (x - (x_adj - n)); + prod = __gamma_product (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + double exp_adj = -eps; + double x_adj_int = __round (x_adj); + double x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + double x_adj_mant = __frexp (x_adj, &x_adj_log2); + if (x_adj_mant < M_SQRT1_2) + { + x_adj_log2--; + x_adj_mant *= 2.0; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + double ret = (__ieee754_pow (x_adj_mant, x_adj) + * __ieee754_exp2 (x_adj_log2 * x_adj_frac) + * __ieee754_exp (-x_adj) + * __ieee754_sqrt (2 * M_PI / x_adj) + / prod); + exp_adj += x_eps * __ieee754_log (x_adj); + double bsum = gamma_coeff[NCOEFF - 1]; + double x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1 (exp_adj); + } +} + +double +__ieee754_gamma_r (double x, int *signgamp) +{ + int32_t hx; + u_int32_t lx; + double ret; + + EXTRACT_WORDS (hx, lx, x); + + if (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 0)) + { + /* Return value for x == 0 is Inf with divide by zero exception. */ + *signgamp = 0; + return 1.0 / x; + } + if (__builtin_expect (hx < 0, 0) + && (u_int32_t) hx < 0xfff00000 && __rint (x) == x) + { + /* Return value for integer x < 0 is NaN with invalid exception. */ + *signgamp = 0; + return (x - x) / (x - x); + } + if (__glibc_unlikely ((unsigned int) hx == 0xfff00000 && lx == 0)) + { + /* x == -Inf. According to ISO this is NaN. */ + *signgamp = 0; + return x - x; + } + if (__glibc_unlikely ((hx & 0x7ff00000) == 0x7ff00000)) + { + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ + *signgamp = 0; + return x + x; + } + + if (x >= 172.0) + { + /* Overflow. */ + *signgamp = 0; + ret = math_narrow_eval (DBL_MAX * DBL_MAX); + return ret; + } + else + { + SET_RESTORE_ROUND (FE_TONEAREST); + if (x > 0.0) + { + *signgamp = 0; + int exp2_adj; + double tret = gamma_positive (x, &exp2_adj); + ret = __scalbn (tret, exp2_adj); + } + else if (x >= -DBL_EPSILON / 4.0) + { + *signgamp = 0; + ret = 1.0 / x; + } + else + { + double tx = __trunc (x); + *signgamp = (tx == 2.0 * __trunc (tx / 2.0)) ? -1 : 1; + if (x <= -184.0) + /* Underflow. */ + ret = DBL_MIN * DBL_MIN; + else + { + double frac = tx - x; + if (frac > 0.5) + frac = 1.0 - frac; + double sinpix = (frac <= 0.25 + ? __sin (M_PI * frac) + : __cos (M_PI * (0.5 - frac))); + int exp2_adj; + double tret = M_PI / (-x * sinpix + * gamma_positive (-x, &exp2_adj)); + ret = __scalbn (tret, -exp2_adj); + math_check_force_underflow_nonneg (ret); + } + } + ret = math_narrow_eval (ret); + } + if (isinf (ret) && x != 0) + { + if (*signgamp < 0) + { + ret = math_narrow_eval (-__copysign (DBL_MAX, ret) * DBL_MAX); + ret = -ret; + } + else + ret = math_narrow_eval (__copysign (DBL_MAX, ret) * DBL_MAX); + return ret; + } + else if (ret == 0) + { + if (*signgamp < 0) + { + ret = math_narrow_eval (-__copysign (DBL_MIN, ret) * DBL_MIN); + ret = -ret; + } + else + ret = math_narrow_eval (__copysign (DBL_MIN, ret) * DBL_MIN); + return ret; + } + else + return ret; +} +strong_alias (__ieee754_gamma_r, __gamma_r_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_hypot.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_hypot.c new file mode 100644 index 0000000000..76eb408348 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_hypot.c @@ -0,0 +1,161 @@ +/* @(#)e_hypot.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_hypot(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 32 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * y1= y with lower 32 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include <math.h> +#include <math_private.h> + +double +__ieee754_hypot (double x, double y) +{ + double a, b, t1, t2, y1, y2, w; + int32_t j, k, ha, hb; + + GET_HIGH_WORD (ha, x); + ha &= 0x7fffffff; + GET_HIGH_WORD (hb, y); + hb &= 0x7fffffff; + if (hb > ha) + { + a = y; b = x; j = ha; ha = hb; hb = j; + } + else + { + a = x; b = y; + } + SET_HIGH_WORD (a, ha); /* a <- |a| */ + SET_HIGH_WORD (b, hb); /* b <- |b| */ + if ((ha - hb) > 0x3c00000) + { + return a + b; + } /* x/y > 2**60 */ + k = 0; + if (__glibc_unlikely (ha > 0x5f300000)) /* a>2**500 */ + { + if (ha >= 0x7ff00000) /* Inf or NaN */ + { + u_int32_t low; + w = a + b; /* for sNaN */ + if (issignaling (a) || issignaling (b)) + return w; + GET_LOW_WORD (low, a); + if (((ha & 0xfffff) | low) == 0) + w = a; + GET_LOW_WORD (low, b); + if (((hb ^ 0x7ff00000) | low) == 0) + w = b; + return w; + } + /* scale a and b by 2**-600 */ + ha -= 0x25800000; hb -= 0x25800000; k += 600; + SET_HIGH_WORD (a, ha); + SET_HIGH_WORD (b, hb); + } + if (__builtin_expect (hb < 0x23d00000, 0)) /* b < 2**-450 */ + { + if (hb <= 0x000fffff) /* subnormal b or 0 */ + { + u_int32_t low; + GET_LOW_WORD (low, b); + if ((hb | low) == 0) + return a; + t1 = 0; + SET_HIGH_WORD (t1, 0x7fd00000); /* t1=2^1022 */ + b *= t1; + a *= t1; + k -= 1022; + GET_HIGH_WORD (ha, a); + GET_HIGH_WORD (hb, b); + if (hb > ha) + { + t1 = a; + a = b; + b = t1; + j = ha; + ha = hb; + hb = j; + } + } + else /* scale a and b by 2^600 */ + { + ha += 0x25800000; /* a *= 2^600 */ + hb += 0x25800000; /* b *= 2^600 */ + k -= 600; + SET_HIGH_WORD (a, ha); + SET_HIGH_WORD (b, hb); + } + } + /* medium size a and b */ + w = a - b; + if (w > b) + { + t1 = 0; + SET_HIGH_WORD (t1, ha); + t2 = a - t1; + w = __ieee754_sqrt (t1 * t1 - (b * (-b) - t2 * (a + t1))); + } + else + { + a = a + a; + y1 = 0; + SET_HIGH_WORD (y1, hb); + y2 = b - y1; + t1 = 0; + SET_HIGH_WORD (t1, ha + 0x00100000); + t2 = a - t1; + w = __ieee754_sqrt (t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b))); + } + if (k != 0) + { + u_int32_t high; + t1 = 1.0; + GET_HIGH_WORD (high, t1); + SET_HIGH_WORD (t1, high + (k << 20)); + w *= t1; + math_check_force_underflow_nonneg (w); + return w; + } + else + return w; +} +strong_alias (__ieee754_hypot, __hypot_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_ilogb.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_ilogb.c new file mode 100644 index 0000000000..1e338a59c1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_ilogb.c @@ -0,0 +1,63 @@ +/* @(#)s_ilogb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_ilogb.c,v 1.9 1995/05/10 20:47:28 jtc Exp $"; +#endif + +/* ilogb(double x) + * return the binary exponent of non-zero x + * ilogb(0) = FP_ILOGB0 + * ilogb(NaN) = FP_ILOGBNAN (no signal is raised) + * ilogb(+-Inf) = INT_MAX (no signal is raised) + */ + +#include <limits.h> +#include <math.h> +#include <math_private.h> + +int +__ieee754_ilogb (double x) +{ + int32_t hx, lx, ix; + + GET_HIGH_WORD (hx, x); + hx &= 0x7fffffff; + if (hx < 0x00100000) + { + GET_LOW_WORD (lx, x); + if ((hx | lx) == 0) + return FP_ILOGB0; /* ilogb(0) = FP_ILOGB0 */ + else /* subnormal x */ + if (hx == 0) + { + for (ix = -1043; lx > 0; lx <<= 1) + ix -= 1; + } + else + { + for (ix = -1022, hx <<= 11; hx > 0; hx <<= 1) + ix -= 1; + } + return ix; + } + else if (hx < 0x7ff00000) + return (hx >> 20) - 1023; + else if (FP_ILOGBNAN != INT_MAX) + { + /* ISO C99 requires ilogb(+-Inf) == INT_MAX. */ + GET_LOW_WORD (lx, x); + if (((hx ^ 0x7ff00000) | lx) == 0) + return INT_MAX; + } + return FP_ILOGBNAN; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_j0.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_j0.c new file mode 100644 index 0000000000..4b440cf0d0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_j0.c @@ -0,0 +1,458 @@ +/* @(#)e_j0.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26, + for performance improvement on pipelined processors. + */ + +/* __ieee754_j0(x), __ieee754_y0(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j0(x): + * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... + * 2. Reduce x to |x| since j0(x)=j0(-x), and + * for x in (0,2) + * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; + * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) + * for x in (2,inf) + * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * as follow: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (cos(x) + sin(x)) + * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j0(nan)= nan + * j0(0) = 1 + * j0(inf) = 0 + * + * Method -- y0(x): + * 1. For x<2. + * Since + * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) + * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. + * We use the following function to approximate y0, + * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 + * where + * U(z) = u00 + u01*z + ... + u06*z^6 + * V(z) = 1 + v01*z + ... + v04*z^4 + * with absolute approximation error bounded by 2**-72. + * Note: For tiny x, U/V = u0 and j0(x)~1, hence + * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) + * 2. For x>=2. + * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * by the method mentioned above. + * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. + */ + +#include <math.h> +#include <math_private.h> + +static double pzero (double), qzero (double); + +static const double + huge = 1e300, + one = 1.0, + invsqrtpi = 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ + tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +/* R0/S0 on [0, 2.00] */ + R[] = { 0.0, 0.0, 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ + -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ + 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ + -4.61832688532103189199e-09 }, /* 0xBE33D5E7, 0x73D63FCE */ + S[] = { 0.0, 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ + 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ + 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ + 1.16614003333790000205e-09 }; /* 0x3E1408BC, 0xF4745D8F */ + +static const double zero = 0.0; + +double +__ieee754_j0 (double x) +{ + double z, s, c, ss, cc, r, u, v, r1, r2, s1, s2, z2, z4; + int32_t hx, ix; + + GET_HIGH_WORD (hx, x); + ix = hx & 0x7fffffff; + if (ix >= 0x7ff00000) + return one / (x * x); + x = fabs (x); + if (ix >= 0x40000000) /* |x| >= 2.0 */ + { + __sincos (x, &s, &c); + ss = s - c; + cc = s + c; + if (ix < 0x7fe00000) /* make sure x+x not overflow */ + { + z = -__cos (x + x); + if ((s * c) < zero) + cc = z / ss; + else + ss = z / cc; + } + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if (ix > 0x48000000) + z = (invsqrtpi * cc) / __ieee754_sqrt (x); + else + { + u = pzero (x); v = qzero (x); + z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrt (x); + } + return z; + } + if (ix < 0x3f200000) /* |x| < 2**-13 */ + { + math_force_eval (huge + x); /* raise inexact if x != 0 */ + if (ix < 0x3e400000) + return one; /* |x|<2**-27 */ + else + return one - 0.25 * x * x; + } + z = x * x; + r1 = z * R[2]; z2 = z * z; + r2 = R[3] + z * R[4]; z4 = z2 * z2; + r = r1 + z2 * r2 + z4 * R[5]; + s1 = one + z * S[1]; + s2 = S[2] + z * S[3]; + s = s1 + z2 * s2 + z4 * S[4]; + if (ix < 0x3FF00000) /* |x| < 1.00 */ + { + return one + z * (-0.25 + (r / s)); + } + else + { + u = 0.5 * x; + return ((one + u) * (one - u) + z * (r / s)); + } +} +strong_alias (__ieee754_j0, __j0_finite) + +static const double +U[] = { -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ + 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ + -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ + 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ + -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ + 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ + -3.98205194132103398453e-11 }, /* 0xBDC5E43D, 0x693FB3C8 */ +V[] = { 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ + 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ + 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ + 4.41110311332675467403e-10 }; /* 0x3DFE5018, 0x3BD6D9EF */ + +double +__ieee754_y0 (double x) +{ + double z, s, c, ss, cc, u, v, z2, z4, z6, u1, u2, u3, v1, v2; + int32_t hx, ix, lx; + + EXTRACT_WORDS (hx, lx, x); + ix = 0x7fffffff & hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0, y0(0) is -inf. */ + if (ix >= 0x7ff00000) + return one / (x + x * x); + if ((ix | lx) == 0) + return -1 / zero; /* -inf and divide by zero exception. */ + if (hx < 0) + return zero / (zero * x); + if (ix >= 0x40000000) /* |x| >= 2.0 */ + { /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + __sincos (x, &s, &c); + ss = s - c; + cc = s + c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if (ix < 0x7fe00000) /* make sure x+x not overflow */ + { + z = -__cos (x + x); + if ((s * c) < zero) + cc = z / ss; + else + ss = z / cc; + } + if (ix > 0x48000000) + z = (invsqrtpi * ss) / __ieee754_sqrt (x); + else + { + u = pzero (x); v = qzero (x); + z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrt (x); + } + return z; + } + if (ix <= 0x3e400000) /* x < 2**-27 */ + { + return (U[0] + tpi * __ieee754_log (x)); + } + z = x * x; + u1 = U[0] + z * U[1]; z2 = z * z; + u2 = U[2] + z * U[3]; z4 = z2 * z2; + u3 = U[4] + z * U[5]; z6 = z4 * z2; + u = u1 + z2 * u2 + z4 * u3 + z6 * U[6]; + v1 = one + z * V[0]; + v2 = V[1] + z * V[2]; + v = v1 + z2 * v2 + z4 * V[3]; + return (u / v + tpi * (__ieee754_j0 (x) * __ieee754_log (x))); +} +strong_alias (__ieee754_y0, __y0_finite) + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ + -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ + -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ + -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ + -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ +}; +static const double pS8[5] = { + 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ + 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ + 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ + 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ + 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ +}; + +static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ + -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ + -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ + -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ + -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ + -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ +}; +static const double pS5[5] = { + 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ + 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ + 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ + 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ + 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ +}; + +static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ + -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ + -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ + -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ + -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ + -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ +}; +static const double pS3[5] = { + 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ + 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ + 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ + 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ + 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ +}; + +static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ + -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ + -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ + -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ + -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ + -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ +}; +static const double pS2[5] = { + 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ + 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ + 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ + 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ + 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ +}; + +static double +pzero (double x) +{ + const double *p, *q; + double z, r, s, z2, z4, r1, r2, r3, s1, s2, s3; + int32_t ix; + GET_HIGH_WORD (ix, x); + ix &= 0x7fffffff; + /* ix >= 0x40000000 for all calls to this function. */ + if (ix >= 0x41b00000) + { + return one; + } + else if (ix >= 0x40200000) + { + p = pR8; q = pS8; + } + else if (ix >= 0x40122E8B) + { + p = pR5; q = pS5; + } + else if (ix >= 0x4006DB6D) + { + p = pR3; q = pS3; + } + else + { + p = pR2; q = pS2; + } + z = one / (x * x); + r1 = p[0] + z * p[1]; z2 = z * z; + r2 = p[2] + z * p[3]; z4 = z2 * z2; + r3 = p[4] + z * p[5]; + r = r1 + z2 * r2 + z4 * r3; + s1 = one + z * q[0]; + s2 = q[1] + z * q[2]; + s3 = q[3] + z * q[4]; + s = s1 + z2 * s2 + z4 * s3; + return one + r / s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ + 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ + 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ + 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ + 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ +}; +static const double qS8[6] = { + 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ + 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ + 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ + 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ + 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ + -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ +}; + +static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ + 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ + 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ + 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ + 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ + 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ +}; +static const double qS5[6] = { + 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ + 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ + 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ + 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ + 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ + -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ +}; + +static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ + 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ + 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ + 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ + 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ + 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ +}; +static const double qS3[6] = { + 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ + 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ + 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ + 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ + 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ + -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ +}; + +static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ + 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ + 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ + 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ + 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ + 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ +}; +static const double qS2[6] = { + 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ + 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ + 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ + 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ + 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ + -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ +}; + +static double +qzero (double x) +{ + const double *p, *q; + double s, r, z, z2, z4, z6, r1, r2, r3, s1, s2, s3; + int32_t ix; + GET_HIGH_WORD (ix, x); + ix &= 0x7fffffff; + /* ix >= 0x40000000 for all calls to this function. */ + if (ix >= 0x41b00000) + { + return -.125 / x; + } + else if (ix >= 0x40200000) + { + p = qR8; q = qS8; + } + else if (ix >= 0x40122E8B) + { + p = qR5; q = qS5; + } + else if (ix >= 0x4006DB6D) + { + p = qR3; q = qS3; + } + else + { + p = qR2; q = qS2; + } + z = one / (x * x); + r1 = p[0] + z * p[1]; z2 = z * z; + r2 = p[2] + z * p[3]; z4 = z2 * z2; + r3 = p[4] + z * p[5]; z6 = z4 * z2; + r = r1 + z2 * r2 + z4 * r3; + s1 = one + z * q[0]; + s2 = q[1] + z * q[2]; + s3 = q[3] + z * q[4]; + s = s1 + z2 * s2 + z4 * s3 + z6 * q[5]; + return (-.125 + r / s) / x; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_j1.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_j1.c new file mode 100644 index 0000000000..eb446fd102 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_j1.c @@ -0,0 +1,466 @@ +/* @(#)e_j1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26, + for performance improvement on pipelined processors. + */ + +/* __ieee754_j1(x), __ieee754_y1(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j1(x): + * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... + * 2. Reduce x to |x| since j1(x)=-j1(-x), and + * for x in (0,2) + * j1(x) = x/2 + x*z*R0/S0, where z = x*x; + * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) + * for x in (2,inf) + * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * as follow: + * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (sin(x) + cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j1(nan)= nan + * j1(0) = 0 + * j1(inf) = 0 + * + * Method -- y1(x): + * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN + * 2. For x<2. + * Since + * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) + * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. + * We use the following function to approximate y1, + * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 + * where for x in [0,2] (abs err less than 2**-65.89) + * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 + * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 + * Note: For tiny x, 1/x dominate y1 and hence + * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) + * 3. For x>=2. + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * by method mentioned above. + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static double pone (double), qone (double); + +static const double + huge = 1e300, + one = 1.0, + invsqrtpi = 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ + tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +/* R0/S0 on [0,2] */ + R[] = { -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ + 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ + -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ + 4.96727999609584448412e-08 }, /* 0x3E6AAAFA, 0x46CA0BD9 */ + S[] = { 0.0, 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ + 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ + 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ + 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ + 1.23542274426137913908e-11 }; /* 0x3DAB2ACF, 0xCFB97ED8 */ + +static const double zero = 0.0; + +double +__ieee754_j1 (double x) +{ + double z, s, c, ss, cc, r, u, v, y, r1, r2, s1, s2, s3, z2, z4; + int32_t hx, ix; + + GET_HIGH_WORD (hx, x); + ix = hx & 0x7fffffff; + if (__glibc_unlikely (ix >= 0x7ff00000)) + return one / x; + y = fabs (x); + if (ix >= 0x40000000) /* |x| >= 2.0 */ + { + __sincos (y, &s, &c); + ss = -s - c; + cc = s - c; + if (ix < 0x7fe00000) /* make sure y+y not overflow */ + { + z = __cos (y + y); + if ((s * c) > zero) + cc = z / ss; + else + ss = z / cc; + } + /* + * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) + * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) + */ + if (ix > 0x48000000) + z = (invsqrtpi * cc) / __ieee754_sqrt (y); + else + { + u = pone (y); v = qone (y); + z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrt (y); + } + if (hx < 0) + return -z; + else + return z; + } + if (__glibc_unlikely (ix < 0x3e400000)) /* |x|<2**-27 */ + { + if (huge + x > one) /* inexact if x!=0 necessary */ + { + double ret = math_narrow_eval (0.5 * x); + math_check_force_underflow (ret); + if (ret == 0 && x != 0) + __set_errno (ERANGE); + return ret; + } + } + z = x * x; + r1 = z * R[0]; z2 = z * z; + r2 = R[1] + z * R[2]; z4 = z2 * z2; + r = r1 + z2 * r2 + z4 * R[3]; + r *= x; + s1 = one + z * S[1]; + s2 = S[2] + z * S[3]; + s3 = S[4] + z * S[5]; + s = s1 + z2 * s2 + z4 * s3; + return (x * 0.5 + r / s); +} +strong_alias (__ieee754_j1, __j1_finite) + +static const double U0[5] = { + -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ + 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ + -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ + 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ + -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ +}; +static const double V0[5] = { + 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ + 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ + 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ + 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ + 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ +}; + +double +__ieee754_y1 (double x) +{ + double z, s, c, ss, cc, u, v, u1, u2, v1, v2, v3, z2, z4; + int32_t hx, ix, lx; + + EXTRACT_WORDS (hx, lx, x); + ix = 0x7fffffff & hx; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if (__glibc_unlikely (ix >= 0x7ff00000)) + return one / (x + x * x); + if (__glibc_unlikely ((ix | lx) == 0)) + return -1 / zero; /* -inf and divide by zero exception. */ + /* -inf and overflow exception. */; + if (__glibc_unlikely (hx < 0)) + return zero / (zero * x); + if (ix >= 0x40000000) /* |x| >= 2.0 */ + { + __sincos (x, &s, &c); + ss = -s - c; + cc = s - c; + if (ix < 0x7fe00000) /* make sure x+x not overflow */ + { + z = __cos (x + x); + if ((s * c) > zero) + cc = z / ss; + else + ss = z / cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if (ix > 0x48000000) + z = (invsqrtpi * ss) / __ieee754_sqrt (x); + else + { + u = pone (x); v = qone (x); + z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrt (x); + } + return z; + } + if (__glibc_unlikely (ix <= 0x3c900000)) /* x < 2**-54 */ + { + z = -tpi / x; + if (isinf (z)) + __set_errno (ERANGE); + return z; + } + z = x * x; + u1 = U0[0] + z * U0[1]; z2 = z * z; + u2 = U0[2] + z * U0[3]; z4 = z2 * z2; + u = u1 + z2 * u2 + z4 * U0[4]; + v1 = one + z * V0[0]; + v2 = V0[1] + z * V0[2]; + v3 = V0[3] + z * V0[4]; + v = v1 + z2 * v2 + z4 * v3; + return (x * (u / v) + tpi * (__ieee754_j1 (x) * __ieee754_log (x) - one / x)); +} +strong_alias (__ieee754_y1, __y1_finite) + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ + 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ + 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ + 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ + 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ +}; +static const double ps8[5] = { + 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ + 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ + 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ + 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ + 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ +}; + +static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ + 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ + 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ + 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ + 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ + 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ +}; +static const double ps5[5] = { + 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ + 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ + 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ + 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ + 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ +}; + +static const double pr3[6] = { + 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ + 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ + 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ + 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ + 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ + 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ +}; +static const double ps3[5] = { + 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ + 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ + 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ + 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ + 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ +}; + +static const double pr2[6] = { /* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ + 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ + 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ + 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ + 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ + 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ +}; +static const double ps2[5] = { + 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ + 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ + 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ + 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ + 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ +}; + +static double +pone (double x) +{ + const double *p, *q; + double z, r, s, r1, r2, r3, s1, s2, s3, z2, z4; + int32_t ix; + GET_HIGH_WORD (ix, x); + ix &= 0x7fffffff; + /* ix >= 0x40000000 for all calls to this function. */ + if (ix >= 0x41b00000) + { + return one; + } + else if (ix >= 0x40200000) + { + p = pr8; q = ps8; + } + else if (ix >= 0x40122E8B) + { + p = pr5; q = ps5; + } + else if (ix >= 0x4006DB6D) + { + p = pr3; q = ps3; + } + else + { + p = pr2; q = ps2; + } + z = one / (x * x); + r1 = p[0] + z * p[1]; z2 = z * z; + r2 = p[2] + z * p[3]; z4 = z2 * z2; + r3 = p[4] + z * p[5]; + r = r1 + z2 * r2 + z4 * r3; + s1 = one + z * q[0]; + s2 = q[1] + z * q[2]; + s3 = q[3] + z * q[4]; + s = s1 + z2 * s2 + z4 * s3; + return one + r / s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ + -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ + -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ + -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ + -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ +}; +static const double qs8[6] = { + 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ + 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ + 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ + 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ + 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ + -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ +}; + +static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ + -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ + -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ + -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ + -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ + -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ +}; +static const double qs5[6] = { + 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ + 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ + 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ + 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ + 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ + -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ +}; + +static const double qr3[6] = { + -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ + -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ + -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ + -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ + -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ + -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ +}; +static const double qs3[6] = { + 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ + 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ + 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ + 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ + 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ + -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ +}; + +static const double qr2[6] = { /* for x in [2.8570,2]=1/[0.3499,0.5] */ + -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ + -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ + -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ + -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ + -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ + -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ +}; +static const double qs2[6] = { + 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ + 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ + 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ + 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ + 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ + -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ +}; + +static double +qone (double x) +{ + const double *p, *q; + double s, r, z, r1, r2, r3, s1, s2, s3, z2, z4, z6; + int32_t ix; + GET_HIGH_WORD (ix, x); + ix &= 0x7fffffff; + /* ix >= 0x40000000 for all calls to this function. */ + if (ix >= 0x41b00000) + { + return .375 / x; + } + else if (ix >= 0x40200000) + { + p = qr8; q = qs8; + } + else if (ix >= 0x40122E8B) + { + p = qr5; q = qs5; + } + else if (ix >= 0x4006DB6D) + { + p = qr3; q = qs3; + } + else + { + p = qr2; q = qs2; + } + z = one / (x * x); + r1 = p[0] + z * p[1]; z2 = z * z; + r2 = p[2] + z * p[3]; z4 = z2 * z2; + r3 = p[4] + z * p[5]; z6 = z4 * z2; + r = r1 + z2 * r2 + z4 * r3; + s1 = one + z * q[0]; + s2 = q[1] + z * q[2]; + s3 = q[3] + z * q[4]; + s = s1 + z2 * s2 + z4 * s3 + z6 * q[5]; + return (.375 + r / s) / x; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_jn.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_jn.c new file mode 100644 index 0000000000..3fecf82f10 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_jn.c @@ -0,0 +1,347 @@ +/* @(#)e_jn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __ieee754_jn(n, x), __ieee754_yn(n, x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with overflow signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for n<x, forward recursion us used starting + * from values of j0(x) and j1(x). + * for n>x, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const double + invsqrtpi = 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ + two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ + one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ + +static const double zero = 0.00000000000000000000e+00; + +double +__ieee754_jn (int n, double x) +{ + int32_t i, hx, ix, lx, sgn; + double a, b, temp, di, ret; + double z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + EXTRACT_WORDS (hx, lx, x); + ix = 0x7fffffff & hx; + /* if J(n,NaN) is NaN */ + if (__glibc_unlikely ((ix | ((u_int32_t) (lx | -lx)) >> 31) > 0x7ff00000)) + return x + x; + if (n < 0) + { + n = -n; + x = -x; + hx ^= 0x80000000; + } + if (n == 0) + return (__ieee754_j0 (x)); + if (n == 1) + return (__ieee754_j1 (x)); + sgn = (n & 1) & (hx >> 31); /* even n -- 0, odd n -- sign(x) */ + x = fabs (x); + { + SET_RESTORE_ROUND (FE_TONEAREST); + if (__glibc_unlikely ((ix | lx) == 0 || ix >= 0x7ff00000)) + /* if x is 0 or inf */ + return sgn == 1 ? -zero : zero; + else if ((double) n <= x) + { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + if (ix >= 0x52D00000) /* x > 2**302 */ + { /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + double s; + double c; + __sincos (x, &s, &c); + switch (n & 3) + { + case 0: temp = c + s; break; + case 1: temp = -c + s; break; + case 2: temp = -c - s; break; + case 3: temp = c - s; break; + } + b = invsqrtpi * temp / __ieee754_sqrt (x); + } + else + { + a = __ieee754_j0 (x); + b = __ieee754_j1 (x); + for (i = 1; i < n; i++) + { + temp = b; + b = b * ((double) (i + i) / x) - a; /* avoid underflow */ + a = temp; + } + } + } + else + { + if (ix < 0x3e100000) /* x < 2**-29 */ + { /* x is tiny, return the first Taylor expansion of J(n,x) + * J(n,x) = 1/n!*(x/2)^n - ... + */ + if (n > 33) /* underflow */ + b = zero; + else + { + temp = x * 0.5; b = temp; + for (a = one, i = 2; i <= n; i++) + { + a *= (double) i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b / a; + } + } + else + { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + double t, v; + double q0, q1, h, tmp; int32_t k, m; + w = (n + n) / (double) x; h = 2.0 / (double) x; + q0 = w; z = w + h; q1 = w * z - 1.0; k = 1; + while (q1 < 1.0e9) + { + k += 1; z += h; + tmp = z * q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n + n; + for (t = zero, i = 2 * (n + k); i >= m; i -= 2) + t = one / (i / x - t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two / x; + tmp = tmp * __ieee754_log (fabs (v * tmp)); + if (tmp < 7.09782712893383973096e+02) + { + for (i = n - 1, di = (double) (i + i); i > 0; i--) + { + temp = b; + b *= di; + b = b / x - a; + a = temp; + di -= two; + } + } + else + { + for (i = n - 1, di = (double) (i + i); i > 0; i--) + { + temp = b; + b *= di; + b = b / x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if (b > 1e100) + { + a /= b; + t /= b; + b = one; + } + } + } + /* j0() and j1() suffer enormous loss of precision at and + * near zero; however, we know that their zero points never + * coincide, so just choose the one further away from zero. + */ + z = __ieee754_j0 (x); + w = __ieee754_j1 (x); + if (fabs (z) >= fabs (w)) + b = (t * z / b); + else + b = (t * w / a); + } + } + if (sgn == 1) + ret = -b; + else + ret = b; + ret = math_narrow_eval (ret); + } + if (ret == 0) + { + ret = math_narrow_eval (__copysign (DBL_MIN, ret) * DBL_MIN); + __set_errno (ERANGE); + } + else + math_check_force_underflow (ret); + return ret; +} +strong_alias (__ieee754_jn, __jn_finite) + +double +__ieee754_yn (int n, double x) +{ + int32_t i, hx, ix, lx; + int32_t sign; + double a, b, temp, ret; + + EXTRACT_WORDS (hx, lx, x); + ix = 0x7fffffff & hx; + /* if Y(n,NaN) is NaN */ + if (__glibc_unlikely ((ix | ((u_int32_t) (lx | -lx)) >> 31) > 0x7ff00000)) + return x + x; + if (__glibc_unlikely ((ix | lx) == 0)) + return -HUGE_VAL + x; + /* -inf and overflow exception. */; + if (__glibc_unlikely (hx < 0)) + return zero / (zero * x); + sign = 1; + if (n < 0) + { + n = -n; + sign = 1 - ((n & 1) << 1); + } + if (n == 0) + return (__ieee754_y0 (x)); + { + SET_RESTORE_ROUND (FE_TONEAREST); + if (n == 1) + { + ret = sign * __ieee754_y1 (x); + goto out; + } + if (__glibc_unlikely (ix == 0x7ff00000)) + return zero; + if (ix >= 0x52D00000) /* x > 2**302 */ + { /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + double c; + double s; + __sincos (x, &s, &c); + switch (n & 3) + { + case 0: temp = s - c; break; + case 1: temp = -s - c; break; + case 2: temp = -s + c; break; + case 3: temp = s + c; break; + } + b = invsqrtpi * temp / __ieee754_sqrt (x); + } + else + { + u_int32_t high; + a = __ieee754_y0 (x); + b = __ieee754_y1 (x); + /* quit if b is -inf */ + GET_HIGH_WORD (high, b); + for (i = 1; i < n && high != 0xfff00000; i++) + { + temp = b; + b = ((double) (i + i) / x) * b - a; + GET_HIGH_WORD (high, b); + a = temp; + } + /* If B is +-Inf, set up errno accordingly. */ + if (!isfinite (b)) + __set_errno (ERANGE); + } + if (sign > 0) + ret = b; + else + ret = -b; + } + out: + if (isinf (ret)) + ret = __copysign (DBL_MAX, ret) * DBL_MAX; + return ret; +} +strong_alias (__ieee754_yn, __yn_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_lgamma_r.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_lgamma_r.c new file mode 100644 index 0000000000..b5860d8a24 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_lgamma_r.c @@ -0,0 +1,310 @@ +/* @(#)er_lgamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_lgamma_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: + * 1. Argument Reduction for 0 < x <= 8 + * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may + * reduce x to a number in [1.5,2.5] by + * lgamma(1+s) = log(s) + lgamma(s) + * for example, + * lgamma(7.3) = log(6.3) + lgamma(6.3) + * = log(6.3*5.3) + lgamma(5.3) + * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) + * 2. Polynomial approximation of lgamma around its + * minimun ymin=1.461632144968362245 to maintain monotonicity. + * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use + * Let z = x-ymin; + * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) + * where + * poly(z) is a 14 degree polynomial. + * 2. Rational approximation in the primary interval [2,3] + * We use the following approximation: + * s = x-2.0; + * lgamma(x) = 0.5*s + s*P(s)/Q(s) + * with accuracy + * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 + * Our algorithms are based on the following observation + * + * zeta(2)-1 2 zeta(3)-1 3 + * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... + * 2 3 + * + * where Euler = 0.5771... is the Euler constant, which is very + * close to 0.5. + * + * 3. For x>=8, we have + * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... + * (better formula: + * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) + * Let z = 1/x, then we approximation + * f(z) = lgamma(x) - (x-0.5)(log(x)-1) + * by + * 3 5 11 + * w = w0 + w1*z + w2*z + w3*z + ... + w6*z + * where + * |w - f(z)| < 2**-58.74 + * + * 4. For negative x, since (G is gamma function) + * -x*G(-x)*G(x) = pi/sin(pi*x), + * we have + * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) + * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 + * Hence, for x<0, signgam = sign(sin(pi*x)) and + * lgamma(x) = log(|Gamma(x)|) + * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); + * Note: one should avoid compute pi*(-x) directly in the + * computation of sin(pi*(-x)). + * + * 5. Special Cases + * lgamma(2+s) ~ s*(1-Euler) for tiny s + * lgamma(1)=lgamma(2)=0 + * lgamma(x) ~ -log(x) for tiny x + * lgamma(0) = lgamma(inf) = inf + * lgamma(-integer) = +-inf + * + */ + +#include <math.h> +#include <math_private.h> +#include <libc-diag.h> + +static const double +two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */ +a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */ +a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */ +a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */ +a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */ +a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */ +a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */ +a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */ +a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */ +a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */ +a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */ +a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */ +tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */ +tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */ +/* tt = -(tail of tf) */ +tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */ +t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */ +t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */ +t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */ +t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */ +t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */ +t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */ +t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */ +t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */ +t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */ +t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */ +t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */ +t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */ +t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */ +t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */ +t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */ +u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */ +u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */ +u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */ +u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */ +u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */ +v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */ +v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */ +v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */ +v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */ +v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */ +s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */ +s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */ +s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */ +s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */ +s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */ +s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */ +r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */ +r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */ +r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */ +r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */ +r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */ +r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */ +w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */ +w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */ +w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */ +w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */ +w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */ +w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */ +w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */ + +static const double zero= 0.00000000000000000000e+00; + +static double +sin_pi(double x) +{ + double y,z; + int n,ix; + + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3fd00000) return __sin(pi*x); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = __floor(y); + if(z!=y) { /* inexact anyway */ + y *= 0.5; + y = 2.0*(y - __floor(y)); /* y = |x| mod 2.0 */ + n = (int) (y*4.0); + } else { + if(ix>=0x43400000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x43300000) z = y+two52; /* exact */ + GET_LOW_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __sin(pi*y); break; + case 1: + case 2: y = __cos(pi*(0.5-y)); break; + case 3: + case 4: y = __sin(pi*(one-y)); break; + case 5: + case 6: y = -__cos(pi*(y-1.5)); break; + default: y = __sin(pi*(y-2.0)); break; + } + return -y; +} + + +double +__ieee754_lgamma_r(double x, int *signgamp) +{ + double t,y,z,nadj,p,p1,p2,p3,q,r,w; + int i,hx,lx,ix; + + EXTRACT_WORDS(hx,lx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + *signgamp = 1; + ix = hx&0x7fffffff; + if(__builtin_expect(ix>=0x7ff00000, 0)) return x*x; + if(__builtin_expect((ix|lx)==0, 0)) + { + if (hx < 0) + *signgamp = -1; + return one/fabs(x); + } + if(__builtin_expect(ix<0x3b900000, 0)) { + /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -__ieee754_log(-x); + } else return -__ieee754_log(x); + } + if(hx<0) { + if(__builtin_expect(ix>=0x43300000, 0)) + /* |x|>=2**52, must be -integer */ + return __fabs (x)/zero; + if (x < -2.0 && x > -28.0) + return __lgamma_neg (x, signgamp); + t = sin_pi(x); + if(t==zero) return one/fabsf(t); /* -integer */ + nadj = __ieee754_log(pi/fabs(t*x)); + if(t<zero) *signgamp = -1; + x = -x; + } + + /* purge off 1 and 2 */ + if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0; + /* for x < 2.0 */ + else if(ix<0x40000000) { + if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */ + r = -__ieee754_log(x); + if(ix>=0x3FE76944) {y = one-x; i= 0;} + else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-0.5*y + p1/p2); + } + } + else if(ix<0x40200000) { /* x < 8.0 */ + i = (int)x; + t = zero; + y = x-(double)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+6.0); /* FALLTHRU */ + case 6: z *= (y+5.0); /* FALLTHRU */ + case 5: z *= (y+4.0); /* FALLTHRU */ + case 4: z *= (y+3.0); /* FALLTHRU */ + case 3: z *= (y+2.0); /* FALLTHRU */ + r += __ieee754_log(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x43900000) { + t = __ieee754_log(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = math_narrow_eval (x*(__ieee754_log(x)-one)); + /* NADJ is set for negative arguments but not otherwise, + resulting in warnings that it may be used uninitialized + although in the cases where it is used it has always been + set. */ + DIAG_PUSH_NEEDS_COMMENT; + DIAG_IGNORE_NEEDS_COMMENT (4.9, "-Wmaybe-uninitialized"); + if(hx<0) r = nadj - r; + DIAG_POP_NEEDS_COMMENT; + return r; +} +strong_alias (__ieee754_lgamma_r, __lgamma_r_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_log.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log.c new file mode 100644 index 0000000000..e7cddc29c8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log.c @@ -0,0 +1,262 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*********************************************************************/ +/* */ +/* MODULE_NAME:ulog.c */ +/* */ +/* FUNCTION:ulog */ +/* */ +/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h ulog.h */ +/* mpexp.c mplog.c mpa.c */ +/* ulog.tbl */ +/* */ +/* An ultimate log routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of log(x). */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/*********************************************************************/ + + +#include "endian.h" +#include <dla.h> +#include "mpa.h" +#include "MathLib.h" +#include <math.h> +#include <math_private.h> +#include <stap-probe.h> + +#ifndef SECTION +# define SECTION +#endif + +void __mplog (mp_no *, mp_no *, int); + +/*********************************************************************/ +/* An ultimate log routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of log(x). */ +/*********************************************************************/ +double +SECTION +__ieee754_log (double x) +{ +#define M 4 + static const int pr[M] = { 8, 10, 18, 32 }; + int i, j, n, ux, dx, p; + double dbl_n, u, p0, q, r0, w, nln2a, luai, lubi, lvaj, lvbj, + sij, ssij, ttij, A, B, B0, y, y1, y2, polI, polII, sa, sb, + t1, t2, t7, t8, t, ra, rb, ww, + a0, aa0, s1, s2, ss2, s3, ss3, a1, aa1, a, aa, b, bb, c; +#ifndef DLA_FMS + double t3, t4, t5, t6; +#endif + number num; + mp_no mpx, mpy, mpy1, mpy2, mperr; + +#include "ulog.tbl" +#include "ulog.h" + + /* Treating special values of x ( x<=0, x=INF, x=NaN etc.). */ + + num.d = x; + ux = num.i[HIGH_HALF]; + dx = num.i[LOW_HALF]; + n = 0; + if (__glibc_unlikely (ux < 0x00100000)) + { + if (__glibc_unlikely (((ux & 0x7fffffff) | dx) == 0)) + return MHALF / 0.0; /* return -INF */ + if (__glibc_unlikely (ux < 0)) + return (x - x) / 0.0; /* return NaN */ + n -= 54; + x *= two54.d; /* scale x */ + num.d = x; + } + if (__glibc_unlikely (ux >= 0x7ff00000)) + return x + x; /* INF or NaN */ + + /* Regular values of x */ + + w = x - 1; + if (__glibc_likely (fabs (w) > U03)) + goto case_03; + + /* log (1) is +0 in all rounding modes. */ + if (w == 0.0) + return 0.0; + + /*--- Stage I, the case abs(x-1) < 0.03 */ + + t8 = MHALF * w; + EMULV (t8, w, a, aa, t1, t2, t3, t4, t5); + EADD (w, a, b, bb); + /* Evaluate polynomial II */ + polII = b7.d + w * b8.d; + polII = b6.d + w * polII; + polII = b5.d + w * polII; + polII = b4.d + w * polII; + polII = b3.d + w * polII; + polII = b2.d + w * polII; + polII = b1.d + w * polII; + polII = b0.d + w * polII; + polII *= w * w * w; + c = (aa + bb) + polII; + + /* End stage I, case abs(x-1) < 0.03 */ + if ((y = b + (c + b * E2)) == b + (c - b * E2)) + return y; + + /*--- Stage II, the case abs(x-1) < 0.03 */ + + a = d19.d + w * d20.d; + a = d18.d + w * a; + a = d17.d + w * a; + a = d16.d + w * a; + a = d15.d + w * a; + a = d14.d + w * a; + a = d13.d + w * a; + a = d12.d + w * a; + a = d11.d + w * a; + + EMULV (w, a, s2, ss2, t1, t2, t3, t4, t5); + ADD2 (d10.d, dd10.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d9.d, dd9.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d8.d, dd8.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d7.d, dd7.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d6.d, dd6.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d5.d, dd5.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d4.d, dd4.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d3.d, dd3.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d2.d, dd2.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (w, 0, s2, ss2, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (w, 0, s3, ss3, b, bb, t1, t2); + + /* End stage II, case abs(x-1) < 0.03 */ + if ((y = b + (bb + b * E4)) == b + (bb - b * E4)) + return y; + goto stage_n; + + /*--- Stage I, the case abs(x-1) > 0.03 */ +case_03: + + /* Find n,u such that x = u*2**n, 1/sqrt(2) < u < sqrt(2) */ + n += (num.i[HIGH_HALF] >> 20) - 1023; + num.i[HIGH_HALF] = (num.i[HIGH_HALF] & 0x000fffff) | 0x3ff00000; + if (num.d > SQRT_2) + { + num.d *= HALF; + n++; + } + u = num.d; + dbl_n = (double) n; + + /* Find i such that ui=1+(i-75)/2**8 is closest to u (i= 0,1,2,...,181) */ + num.d += h1.d; + i = (num.i[HIGH_HALF] & 0x000fffff) >> 12; + + /* Find j such that vj=1+(j-180)/2**16 is closest to v=u/ui (j= 0,...,361) */ + num.d = u * Iu[i].d + h2.d; + j = (num.i[HIGH_HALF] & 0x000fffff) >> 4; + + /* Compute w=(u-ui*vj)/(ui*vj) */ + p0 = (1 + (i - 75) * DEL_U) * (1 + (j - 180) * DEL_V); + q = u - p0; + r0 = Iu[i].d * Iv[j].d; + w = q * r0; + + /* Evaluate polynomial I */ + polI = w + (a2.d + a3.d * w) * w * w; + + /* Add up everything */ + nln2a = dbl_n * LN2A; + luai = Lu[i][0].d; + lubi = Lu[i][1].d; + lvaj = Lv[j][0].d; + lvbj = Lv[j][1].d; + EADD (luai, lvaj, sij, ssij); + EADD (nln2a, sij, A, ttij); + B0 = (((lubi + lvbj) + ssij) + ttij) + dbl_n * LN2B; + B = polI + B0; + + /* End stage I, case abs(x-1) >= 0.03 */ + if ((y = A + (B + E1)) == A + (B - E1)) + return y; + + + /*--- Stage II, the case abs(x-1) > 0.03 */ + + /* Improve the accuracy of r0 */ + EMULV (p0, r0, sa, sb, t1, t2, t3, t4, t5); + t = r0 * ((1 - sa) - sb); + EADD (r0, t, ra, rb); + + /* Compute w */ + MUL2 (q, 0, ra, rb, w, ww, t1, t2, t3, t4, t5, t6, t7, t8); + + EADD (A, B0, a0, aa0); + + /* Evaluate polynomial III */ + s1 = (c3.d + (c4.d + c5.d * w) * w) * w; + EADD (c2.d, s1, s2, ss2); + MUL2 (s2, ss2, w, ww, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (s3, ss3, w, ww, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (s2, ss2, w, ww, s3, ss3, t1, t2); + ADD2 (s3, ss3, a0, aa0, a1, aa1, t1, t2); + + /* End stage II, case abs(x-1) >= 0.03 */ + if ((y = a1 + (aa1 + E3)) == a1 + (aa1 - E3)) + return y; + + + /* Final stages. Use multi-precision arithmetic. */ +stage_n: + + for (i = 0; i < M; i++) + { + p = pr[i]; + __dbl_mp (x, &mpx, p); + __dbl_mp (y, &mpy, p); + __mplog (&mpx, &mpy, p); + __dbl_mp (e[i].d, &mperr, p); + __add (&mpy, &mperr, &mpy1, p); + __sub (&mpy, &mperr, &mpy2, p); + __mp_dbl (&mpy1, &y1, p); + __mp_dbl (&mpy2, &y2, p); + if (y1 == y2) + { + LIBC_PROBE (slowlog, 3, &p, &x, &y1); + return y1; + } + } + LIBC_PROBE (slowlog_inexact, 3, &p, &x, &y1); + return y1; +} + +#ifndef __ieee754_log +strong_alias (__ieee754_log, __log_finite) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_log10.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log10.c new file mode 100644 index 0000000000..bf40bca874 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log10.c @@ -0,0 +1,88 @@ +/* @(#)e_log10.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_log10(x) + * Return the base 10 logarithm of x + * + * Method : + * Let log10_2hi = leading 40 bits of log10(2) and + * log10_2lo = log10(2) - log10_2hi, + * ivln10 = 1/log(10) rounded. + * Then + * n = ilogb(x), + * if(n<0) n = n+1; + * x = scalbn(x,-n); + * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) + * + * Note 1: + * To guarantee log10(10**n)=n, where 10**n is normal, the rounding + * mode must set to Round-to-Nearest. + * Note 2: + * [1/log(10)] rounded to 53 bits has error .198 ulps; + * log10 is monotonic at all binary break points. + * + * Special cases: + * log10(x) is NaN with signal if x < 0; + * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; + * log10(NaN) is that NaN with no signal; + * log10(10**N) = N for N=0,1,...,22. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include <math.h> +#include <math_private.h> +#include <fix-int-fp-convert-zero.h> + +static const double two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */ +static const double ivln10 = 4.34294481903251816668e-01; /* 0x3FDBCB7B, 0x1526E50E */ +static const double log10_2hi = 3.01029995663611771306e-01; /* 0x3FD34413, 0x509F6000 */ +static const double log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ + +double +__ieee754_log10 (double x) +{ + double y, z; + int32_t i, k, hx; + u_int32_t lx; + + EXTRACT_WORDS (hx, lx, x); + + k = 0; + if (hx < 0x00100000) + { /* x < 2**-1022 */ + if (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 0)) + return -two54 / __fabs (x); /* log(+-0)=-inf */ + if (__glibc_unlikely (hx < 0)) + return (x - x) / (x - x); /* log(-#) = NaN */ + k -= 54; + x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD (hx, x); + } + if (__glibc_unlikely (hx >= 0x7ff00000)) + return x + x; + k += (hx >> 20) - 1023; + i = ((u_int32_t) k & 0x80000000) >> 31; + hx = (hx & 0x000fffff) | ((0x3ff - i) << 20); + y = (double) (k + i); + if (FIX_INT_FP_CONVERT_ZERO && y == 0.0) + y = 0.0; + SET_HIGH_WORD (x, hx); + z = y * log10_2lo + ivln10 * __ieee754_log (x); + return z + y * log10_2hi; +} + +strong_alias (__ieee754_log10, __log10_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_log2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log2.c new file mode 100644 index 0000000000..5af68d8ecc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log2.c @@ -0,0 +1,133 @@ +/* Adapted for log2 by Ulrich Drepper <drepper@cygnus.com>. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_log2(x) + * Return the logarithm to base 2 of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k + log(1+f). + * = k+(f-(hfsq-(s*(hfsq+R)))) + * + * Special cases: + * log2(x) is NaN with signal if x < 0 (including -INF) ; + * log2(+INF) is +INF; log(0) is -INF with signal; + * log2(NaN) is that NaN with no signal. + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <math.h> +#include <math_private.h> +#include <fix-int-fp-convert-zero.h> + +static const double ln2 = 0.69314718055994530942; +static const double two54 = 1.80143985094819840000e+16; /* 43500000 00000000 */ +static const double Lg1 = 6.666666666666735130e-01; /* 3FE55555 55555593 */ +static const double Lg2 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */ +static const double Lg3 = 2.857142874366239149e-01; /* 3FD24924 94229359 */ +static const double Lg4 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */ +static const double Lg5 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */ +static const double Lg6 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */ +static const double Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; + +double +__ieee754_log2 (double x) +{ + double hfsq, f, s, z, R, w, t1, t2, dk; + int32_t k, hx, i, j; + u_int32_t lx; + + EXTRACT_WORDS (hx, lx, x); + + k = 0; + if (hx < 0x00100000) + { /* x < 2**-1022 */ + if (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 0)) + return -two54 / __fabs (x); /* log(+-0)=-inf */ + if (__glibc_unlikely (hx < 0)) + return (x - x) / (x - x); /* log(-#) = NaN */ + k -= 54; + x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD (hx, x); + } + if (__glibc_unlikely (hx >= 0x7ff00000)) + return x + x; + k += (hx >> 20) - 1023; + hx &= 0x000fffff; + i = (hx + 0x95f64) & 0x100000; + SET_HIGH_WORD (x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */ + k += (i >> 20); + dk = (double) k; + f = x - 1.0; + if ((0x000fffff & (2 + hx)) < 3) + { /* |f| < 2**-20 */ + if (f == zero) + { + if (FIX_INT_FP_CONVERT_ZERO && dk == 0.0) + dk = 0.0; + return dk; + } + R = f * f * (0.5 - 0.33333333333333333 * f); + return dk - (R - f) / ln2; + } + s = f / (2.0 + f); + z = s * s; + i = hx - 0x6147a; + w = z * z; + j = 0x6b851 - hx; + t1 = w * (Lg2 + w * (Lg4 + w * Lg6)); + t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7))); + i |= j; + R = t2 + t1; + if (i > 0) + { + hfsq = 0.5 * f * f; + return dk - ((hfsq - (s * (hfsq + R))) - f) / ln2; + } + else + { + return dk - ((s * (f - R)) - f) / ln2; + } +} + +strong_alias (__ieee754_log2, __log2_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_pow.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_pow.c new file mode 100644 index 0000000000..9f6439ee42 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_pow.c @@ -0,0 +1,481 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/***************************************************************************/ +/* MODULE_NAME: upow.c */ +/* */ +/* FUNCTIONS: upow */ +/* power1 */ +/* my_log2 */ +/* log1 */ +/* checkint */ +/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h */ +/* halfulp.c mpexp.c mplog.c slowexp.c slowpow.c mpa.c */ +/* uexp.c upow.c */ +/* root.tbl uexp.tbl upow.tbl */ +/* An ultimate power routine. Given two IEEE double machine numbers y,x */ +/* it computes the correctly rounded (to nearest) value of x^y. */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/***************************************************************************/ +#include <math.h> +#include "endian.h" +#include "upow.h" +#include <dla.h> +#include "mydefs.h" +#include "MathLib.h" +#include "upow.tbl" +#include <math_private.h> +#include <fenv.h> + +#ifndef SECTION +# define SECTION +#endif + +static const double huge = 1.0e300, tiny = 1.0e-300; + +double __exp1 (double x, double xx, double error); +static double log1 (double x, double *delta, double *error); +static double my_log2 (double x, double *delta, double *error); +double __slowpow (double x, double y, double z); +static double power1 (double x, double y); +static int checkint (double x); + +/* An ultimate power routine. Given two IEEE double machine numbers y, x it + computes the correctly rounded (to nearest) value of X^y. */ +double +SECTION +__ieee754_pow (double x, double y) +{ + double z, a, aa, error, t, a1, a2, y1, y2; + mynumber u, v; + int k; + int4 qx, qy; + v.x = y; + u.x = x; + if (v.i[LOW_HALF] == 0) + { /* of y */ + qx = u.i[HIGH_HALF] & 0x7fffffff; + /* Is x a NaN? */ + if ((((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000)) + && (y != 0 || issignaling (x))) + return x + x; + if (y == 1.0) + return x; + if (y == 2.0) + return x * x; + if (y == -1.0) + return 1.0 / x; + if (y == 0) + return 1.0; + } + /* else */ + if (((u.i[HIGH_HALF] > 0 && u.i[HIGH_HALF] < 0x7ff00000) || /* x>0 and not x->0 */ + (u.i[HIGH_HALF] == 0 && u.i[LOW_HALF] != 0)) && + /* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */ + (v.i[HIGH_HALF] & 0x7fffffff) < 0x4ff00000) + { /* if y<-1 or y>1 */ + double retval; + + { + SET_RESTORE_ROUND (FE_TONEAREST); + + /* Avoid internal underflow for tiny y. The exact value of y does + not matter if |y| <= 2**-64. */ + if (fabs (y) < 0x1p-64) + y = y < 0 ? -0x1p-64 : 0x1p-64; + z = log1 (x, &aa, &error); /* x^y =e^(y log (X)) */ + t = y * CN; + y1 = t - (t - y); + y2 = y - y1; + t = z * CN; + a1 = t - (t - z); + a2 = (z - a1) + aa; + a = y1 * a1; + aa = y2 * a1 + y * a2; + a1 = a + aa; + a2 = (a - a1) + aa; + error = error * fabs (y); + t = __exp1 (a1, a2, 1.9e16 * error); /* return -10 or 0 if wasn't computed exactly */ + retval = (t > 0) ? t : power1 (x, y); + } + + if (isinf (retval)) + retval = huge * huge; + else if (retval == 0) + retval = tiny * tiny; + else + math_check_force_underflow_nonneg (retval); + return retval; + } + + if (x == 0) + { + if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0) + || (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */ + return y + y; + if (fabs (y) > 1.0e20) + return (y > 0) ? 0 : 1.0 / 0.0; + k = checkint (y); + if (k == -1) + return y < 0 ? 1.0 / x : x; + else + return y < 0 ? 1.0 / 0.0 : 0.0; /* return 0 */ + } + + qx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */ + qy = v.i[HIGH_HALF] & 0x7fffffff; /* no sign */ + + if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) /* NaN */ + return x + y; + if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */ + return x == 1.0 && !issignaling (y) ? 1.0 : y + y; + + /* if x<0 */ + if (u.i[HIGH_HALF] < 0) + { + k = checkint (y); + if (k == 0) + { + if (qy == 0x7ff00000) + { + if (x == -1.0) + return 1.0; + else if (x > -1.0) + return v.i[HIGH_HALF] < 0 ? INF.x : 0.0; + else + return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x; + } + else if (qx == 0x7ff00000) + return y < 0 ? 0.0 : INF.x; + return (x - x) / (x - x); /* y not integer and x<0 */ + } + else if (qx == 0x7ff00000) + { + if (k < 0) + return y < 0 ? nZERO.x : nINF.x; + else + return y < 0 ? 0.0 : INF.x; + } + /* if y even or odd */ + if (k == 1) + return __ieee754_pow (-x, y); + else + { + double retval; + { + SET_RESTORE_ROUND (FE_TONEAREST); + retval = -__ieee754_pow (-x, y); + } + if (isinf (retval)) + retval = -huge * huge; + else if (retval == 0) + retval = -tiny * tiny; + return retval; + } + } + /* x>0 */ + + if (qx == 0x7ff00000) /* x= 2^-0x3ff */ + return y > 0 ? x : 0; + + if (qy > 0x45f00000 && qy < 0x7ff00000) + { + if (x == 1.0) + return 1.0; + if (y > 0) + return (x > 1.0) ? huge * huge : tiny * tiny; + if (y < 0) + return (x < 1.0) ? huge * huge : tiny * tiny; + } + + if (x == 1.0) + return 1.0; + if (y > 0) + return (x > 1.0) ? INF.x : 0; + if (y < 0) + return (x < 1.0) ? INF.x : 0; + return 0; /* unreachable, to make the compiler happy */ +} + +#ifndef __ieee754_pow +strong_alias (__ieee754_pow, __pow_finite) +#endif + +/* Compute x^y using more accurate but more slow log routine. */ +static double +SECTION +power1 (double x, double y) +{ + double z, a, aa, error, t, a1, a2, y1, y2; + z = my_log2 (x, &aa, &error); + t = y * CN; + y1 = t - (t - y); + y2 = y - y1; + t = z * CN; + a1 = t - (t - z); + a2 = z - a1; + a = y * z; + aa = ((y1 * a1 - a) + y1 * a2 + y2 * a1) + y2 * a2 + aa * y; + a1 = a + aa; + a2 = (a - a1) + aa; + error = error * fabs (y); + t = __exp1 (a1, a2, 1.9e16 * error); + return (t >= 0) ? t : __slowpow (x, y, z); +} + +/* Compute log(x) (x is left argument). The result is the returned double + the + parameter DELTA. The result is bounded by ERROR. */ +static double +SECTION +log1 (double x, double *delta, double *error) +{ + unsigned int i, j; + int m; + double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0; + mynumber u, v; +#ifdef BIG_ENDI + mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */ +#else +# ifdef LITTLE_ENDI + mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */ +# endif +#endif + + u.x = x; + m = u.i[HIGH_HALF]; + *error = 0; + *delta = 0; + if (m < 0x00100000) /* 1<x<2^-1007 */ + { + x = x * t52.x; + add = -52.0; + u.x = x; + m = u.i[HIGH_HALF]; + } + + if ((m & 0x000fffff) < 0x0006a09e) + { + u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000; + two52.i[LOW_HALF] = (m >> 20); + } + else + { + u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000; + two52.i[LOW_HALF] = (m >> 20) + 1; + } + + v.x = u.x + bigu.x; + uu = v.x - bigu.x; + i = (v.i[LOW_HALF] & 0x000003ff) << 2; + if (two52.i[LOW_HALF] == 1023) /* nx = 0 */ + { + if (i > 1192 && i < 1208) /* |x-1| < 1.5*2**-10 */ + { + t = x - 1.0; + t1 = (t + 5.0e6) - 5.0e6; + t2 = t - t1; + e1 = t - 0.5 * t1 * t1; + e2 = (t * t * t * (r3 + t * (r4 + t * (r5 + t * (r6 + t + * (r7 + t * r8))))) + - 0.5 * t2 * (t + t1)); + res = e1 + e2; + *error = 1.0e-21 * fabs (t); + *delta = (e1 - res) + e2; + return res; + } /* |x-1| < 1.5*2**-10 */ + else + { + v.x = u.x * (ui.x[i] + ui.x[i + 1]) + bigv.x; + vv = v.x - bigv.x; + j = v.i[LOW_HALF] & 0x0007ffff; + j = j + j + j; + eps = u.x - uu * vv; + e1 = eps * ui.x[i]; + e2 = eps * (ui.x[i + 1] + vj.x[j] * (ui.x[i] + ui.x[i + 1])); + e = e1 + e2; + e2 = ((e1 - e) + e2); + t = ui.x[i + 2] + vj.x[j + 1]; + t1 = t + e; + t2 = ((((t - t1) + e) + (ui.x[i + 3] + vj.x[j + 2])) + e2 + e * e + * (p2 + e * (p3 + e * p4))); + res = t1 + t2; + *error = 1.0e-24; + *delta = (t1 - res) + t2; + return res; + } + } /* nx = 0 */ + else /* nx != 0 */ + { + eps = u.x - uu; + nx = (two52.x - two52e.x) + add; + e1 = eps * ui.x[i]; + e2 = eps * ui.x[i + 1]; + e = e1 + e2; + e2 = (e1 - e) + e2; + t = nx * ln2a.x + ui.x[i + 2]; + t1 = t + e; + t2 = ((((t - t1) + e) + nx * ln2b.x + ui.x[i + 3] + e2) + e * e + * (q2 + e * (q3 + e * (q4 + e * (q5 + e * q6))))); + res = t1 + t2; + *error = 1.0e-21; + *delta = (t1 - res) + t2; + return res; + } /* nx != 0 */ +} + +/* Slower but more accurate routine of log. The returned result is double + + DELTA. The result is bounded by ERROR. */ +static double +SECTION +my_log2 (double x, double *delta, double *error) +{ + unsigned int i, j; + int m; + double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0; + double ou1, ou2, lu1, lu2, ov, lv1, lv2, a, a1, a2; + double y, yy, z, zz, j1, j2, j7, j8; +#ifndef DLA_FMS + double j3, j4, j5, j6; +#endif + mynumber u, v; +#ifdef BIG_ENDI + mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */ +#else +# ifdef LITTLE_ENDI + mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */ +# endif +#endif + + u.x = x; + m = u.i[HIGH_HALF]; + *error = 0; + *delta = 0; + add = 0; + if (m < 0x00100000) + { /* x < 2^-1022 */ + x = x * t52.x; + add = -52.0; + u.x = x; + m = u.i[HIGH_HALF]; + } + + if ((m & 0x000fffff) < 0x0006a09e) + { + u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000; + two52.i[LOW_HALF] = (m >> 20); + } + else + { + u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000; + two52.i[LOW_HALF] = (m >> 20) + 1; + } + + v.x = u.x + bigu.x; + uu = v.x - bigu.x; + i = (v.i[LOW_HALF] & 0x000003ff) << 2; + /*------------------------------------- |x-1| < 2**-11------------------------------- */ + if ((two52.i[LOW_HALF] == 1023) && (i == 1200)) + { + t = x - 1.0; + EMULV (t, s3, y, yy, j1, j2, j3, j4, j5); + ADD2 (-0.5, 0, y, yy, z, zz, j1, j2); + MUL2 (t, 0, z, zz, y, yy, j1, j2, j3, j4, j5, j6, j7, j8); + MUL2 (t, 0, y, yy, z, zz, j1, j2, j3, j4, j5, j6, j7, j8); + + e1 = t + z; + e2 = ((((t - e1) + z) + zz) + t * t * t + * (ss3 + t * (s4 + t * (s5 + t * (s6 + t * (s7 + t * s8)))))); + res = e1 + e2; + *error = 1.0e-25 * fabs (t); + *delta = (e1 - res) + e2; + return res; + } + /*----------------------------- |x-1| > 2**-11 -------------------------- */ + else + { /*Computing log(x) according to log table */ + nx = (two52.x - two52e.x) + add; + ou1 = ui.x[i]; + ou2 = ui.x[i + 1]; + lu1 = ui.x[i + 2]; + lu2 = ui.x[i + 3]; + v.x = u.x * (ou1 + ou2) + bigv.x; + vv = v.x - bigv.x; + j = v.i[LOW_HALF] & 0x0007ffff; + j = j + j + j; + eps = u.x - uu * vv; + ov = vj.x[j]; + lv1 = vj.x[j + 1]; + lv2 = vj.x[j + 2]; + a = (ou1 + ou2) * (1.0 + ov); + a1 = (a + 1.0e10) - 1.0e10; + a2 = a * (1.0 - a1 * uu * vv); + e1 = eps * a1; + e2 = eps * a2; + e = e1 + e2; + e2 = (e1 - e) + e2; + t = nx * ln2a.x + lu1 + lv1; + t1 = t + e; + t2 = ((((t - t1) + e) + (lu2 + lv2 + nx * ln2b.x + e2)) + e * e + * (p2 + e * (p3 + e * p4))); + res = t1 + t2; + *error = 1.0e-27; + *delta = (t1 - res) + t2; + return res; + } +} + +/* This function receives a double x and checks if it is an integer. If not, + it returns 0, else it returns 1 if even or -1 if odd. */ +static int +SECTION +checkint (double x) +{ + union + { + int4 i[2]; + double x; + } u; + int k, m, n; + u.x = x; + m = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */ + if (m >= 0x7ff00000) + return 0; /* x is +/-inf or NaN */ + if (m >= 0x43400000) + return 1; /* |x| >= 2**53 */ + if (m < 0x40000000) + return 0; /* |x| < 2, can not be 0 or 1 */ + n = u.i[LOW_HALF]; + k = (m >> 20) - 1023; /* 1 <= k <= 52 */ + if (k == 52) + return (n & 1) ? -1 : 1; /* odd or even */ + if (k > 20) + { + if (n << (k - 20) != 0) + return 0; /* if not integer */ + return (n << (k - 21) != 0) ? -1 : 1; + } + if (n) + return 0; /*if not integer */ + if (k == 20) + return (m & 1) ? -1 : 1; + if (m << (k + 12) != 0) + return 0; + return (m << (k + 11) != 0) ? -1 : 1; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_rem_pio2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_rem_pio2.c new file mode 100644 index 0000000000..2f55ca294b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_rem_pio2.c @@ -0,0 +1,193 @@ +#ifdef NOT_NEEDED_ANYMORE + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include <math.h> +#include <math_private.h> + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +static const int32_t two_over_pi[] = { +0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, +0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, +0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, +0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, +0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, +0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, +0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, +0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, +0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, +0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, +0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, +}; + +static const int32_t npio2_hw[] = { +0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, +0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, +0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, +0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, +0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, +0x404858EB, 0x404921FB, +}; + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 33 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 33 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +static const double + zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ + two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ + invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ + pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ + pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ + pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ + pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ + pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ + +int32_t +__ieee754_rem_pio2 (double x, double *y) +{ + double z, w, t, r, fn; + double tx[3]; + int32_t e0, i, j, nx, n, ix, hx; + u_int32_t low; + + GET_HIGH_WORD (hx, x); /* high word of x */ + ix = hx & 0x7fffffff; + if (ix <= 0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ + { + y[0] = x; y[1] = 0; return 0; + } + if (ix < 0x4002d97c) /* |x| < 3pi/4, special case with n=+-1 */ + { + if (hx > 0) + { + z = x - pio2_1; + if (ix != 0x3ff921fb) /* 33+53 bit pi is good enough */ + { + y[0] = z - pio2_1t; + y[1] = (z - y[0]) - pio2_1t; + } + else /* near pi/2, use 33+33+53 bit pi */ + { + z -= pio2_2; + y[0] = z - pio2_2t; + y[1] = (z - y[0]) - pio2_2t; + } + return 1; + } + else /* negative x */ + { + z = x + pio2_1; + if (ix != 0x3ff921fb) /* 33+53 bit pi is good enough */ + { + y[0] = z + pio2_1t; + y[1] = (z - y[0]) + pio2_1t; + } + else /* near pi/2, use 33+33+53 bit pi */ + { + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z - y[0]) + pio2_2t; + } + return -1; + } + } + if (ix <= 0x413921fb) /* |x| ~<= 2^19*(pi/2), medium size */ + { + t = fabs (x); + n = (int32_t) (t * invpio2 + half); + fn = (double) n; + r = t - fn * pio2_1; + w = fn * pio2_1t; /* 1st round good to 85 bit */ + if (n < 32 && ix != npio2_hw[n - 1]) + { + y[0] = r - w; /* quick check no cancellation */ + } + else + { + u_int32_t high; + j = ix >> 20; + y[0] = r - w; + GET_HIGH_WORD (high, y[0]); + i = j - ((high >> 20) & 0x7ff); + if (i > 16) /* 2nd iteration needed, good to 118 */ + { + t = r; + w = fn * pio2_2; + r = t - w; + w = fn * pio2_2t - ((t - r) - w); + y[0] = r - w; + GET_HIGH_WORD (high, y[0]); + i = j - ((high >> 20) & 0x7ff); + if (i > 49) /* 3rd iteration need, 151 bits acc */ + { + t = r; /* will cover all possible cases */ + w = fn * pio2_3; + r = t - w; + w = fn * pio2_3t - ((t - r) - w); + y[0] = r - w; + } + } + } + y[1] = (r - y[0]) - w; + if (hx < 0) + { + y[0] = -y[0]; y[1] = -y[1]; return -n; + } + else + return n; + } + /* + * all other (large) arguments + */ + if (ix >= 0x7ff00000) /* x is inf or NaN */ + { + y[0] = y[1] = x - x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-23) */ + GET_LOW_WORD (low, x); + SET_LOW_WORD (z, low); + e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */ + SET_HIGH_WORD (z, ix - ((int32_t) (e0 << 20))); + for (i = 0; i < 2; i++) + { + tx[i] = (double) ((int32_t) (z)); + z = (z - tx[i]) * two24; + } + tx[2] = z; + nx = 3; + while (tx[nx - 1] == zero) + nx--; /* skip zero term */ + n = __kernel_rem_pio2 (tx, y, e0, nx, 2, two_over_pi); + if (hx < 0) + { + y[0] = -y[0]; y[1] = -y[1]; return -n; + } + return n; +} +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_remainder.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_remainder.c new file mode 100644 index 0000000000..1a2eeed2e1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_remainder.c @@ -0,0 +1,152 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/**************************************************************************/ +/* MODULE_NAME urem.c */ +/* */ +/* FUNCTION: uremainder */ +/* */ +/* An ultimate remainder routine. Given two IEEE double machine numbers x */ +/* ,y it computes the correctly rounded (to nearest) value of remainder */ +/* of dividing x by y. */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/* ************************************************************************/ + +#include "endian.h" +#include "mydefs.h" +#include "urem.h" +#include "MathLib.h" +#include <math.h> +#include <math_private.h> + +/**************************************************************************/ +/* An ultimate remainder routine. Given two IEEE double machine numbers x */ +/* ,y it computes the correctly rounded (to nearest) value of remainder */ +/**************************************************************************/ +double +__ieee754_remainder (double x, double y) +{ + double z, d, xx; + int4 kx, ky, n, nn, n1, m1, l; + mynumber u, t, w = { { 0, 0 } }, v = { { 0, 0 } }, ww = { { 0, 0 } }, r; + u.x = x; + t.x = y; + kx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign for x*/ + t.i[HIGH_HALF] &= 0x7fffffff; /*no sign for y */ + ky = t.i[HIGH_HALF]; + /*------ |x| < 2^1023 and 2^-970 < |y| < 2^1024 ------------------*/ + if (kx < 0x7fe00000 && ky < 0x7ff00000 && ky >= 0x03500000) + { + SET_RESTORE_ROUND_NOEX (FE_TONEAREST); + if (kx + 0x00100000 < ky) + return x; + if ((kx - 0x01500000) < ky) + { + z = x / t.x; + v.i[HIGH_HALF] = t.i[HIGH_HALF]; + d = (z + big.x) - big.x; + xx = (x - d * v.x) - d * (t.x - v.x); + if (d - z != 0.5 && d - z != -0.5) + return (xx != 0) ? xx : ((x > 0) ? ZERO.x : nZERO.x); + else + { + if (fabs (xx) > 0.5 * t.x) + return (z > d) ? xx - t.x : xx + t.x; + else + return xx; + } + } /* (kx<(ky+0x01500000)) */ + else + { + r.x = 1.0 / t.x; + n = t.i[HIGH_HALF]; + nn = (n & 0x7ff00000) + 0x01400000; + w.i[HIGH_HALF] = n; + ww.x = t.x - w.x; + l = (kx - nn) & 0xfff00000; + n1 = ww.i[HIGH_HALF]; + m1 = r.i[HIGH_HALF]; + while (l > 0) + { + r.i[HIGH_HALF] = m1 - l; + z = u.x * r.x; + w.i[HIGH_HALF] = n + l; + ww.i[HIGH_HALF] = (n1) ? n1 + l : n1; + d = (z + big.x) - big.x; + u.x = (u.x - d * w.x) - d * ww.x; + l = (u.i[HIGH_HALF] & 0x7ff00000) - nn; + } + r.i[HIGH_HALF] = m1; + w.i[HIGH_HALF] = n; + ww.i[HIGH_HALF] = n1; + z = u.x * r.x; + d = (z + big.x) - big.x; + u.x = (u.x - d * w.x) - d * ww.x; + if (fabs (u.x) < 0.5 * t.x) + return (u.x != 0) ? u.x : ((x > 0) ? ZERO.x : nZERO.x); + else + if (fabs (u.x) > 0.5 * t.x) + return (d > z) ? u.x + t.x : u.x - t.x; + else + { + z = u.x / t.x; d = (z + big.x) - big.x; + return ((u.x - d * w.x) - d * ww.x); + } + } + } /* (kx<0x7fe00000&&ky<0x7ff00000&&ky>=0x03500000) */ + else + { + if (kx < 0x7fe00000 && ky < 0x7ff00000 && (ky > 0 || t.i[LOW_HALF] != 0)) + { + y = fabs (y) * t128.x; + z = __ieee754_remainder (x, y) * t128.x; + z = __ieee754_remainder (z, y) * tm128.x; + return z; + } + else + { + if ((kx & 0x7ff00000) == 0x7fe00000 && ky < 0x7ff00000 && + (ky > 0 || t.i[LOW_HALF] != 0)) + { + y = fabs (y); + z = 2.0 * __ieee754_remainder (0.5 * x, y); + d = fabs (z); + if (d <= fabs (d - y)) + return z; + else if (d == y) + return 0.0 * x; + else + return (z > 0) ? z - y : z + y; + } + else /* if x is too big */ + { + if (ky == 0 && t.i[LOW_HALF] == 0) /* y = 0 */ + return (x * y) / (x * y); + else if (kx >= 0x7ff00000 /* x not finite */ + || (ky > 0x7ff00000 /* y is NaN */ + || (ky == 0x7ff00000 && t.i[LOW_HALF] != 0))) + return (x * y) / (x * y); + else + return x; + } + } + } +} +strong_alias (__ieee754_remainder, __remainder_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_sinh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_sinh.c new file mode 100644 index 0000000000..8479bdd9b8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_sinh.c @@ -0,0 +1,90 @@ +/* @(#)e_sinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $"; +#endif + +/* __ieee754_sinh(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinh(-x) = -sinh(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) + * 2 + * + * 22 <= x <= lnovft : sinh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : sinh(x) := x*shuge (overflow) + * + * Special cases: + * sinh(x) is |x| if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite x. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const double one = 1.0, shuge = 1.0e307; + +double +__ieee754_sinh (double x) +{ + double t, w, h; + int32_t ix, jx; + u_int32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD (jx, x); + ix = jx & 0x7fffffff; + + /* x is INF or NaN */ + if (__glibc_unlikely (ix >= 0x7ff00000)) + return x + x; + + h = 0.5; + if (jx < 0) + h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x40360000) /* |x|<22 */ + { + if (__glibc_unlikely (ix < 0x3e300000)) { /* |x|<2**-28 */ + math_check_force_underflow (x); + if (shuge + x > one) + return x; + /* sinh(tiny) = tiny with inexact */ + } + t = __expm1 (fabs (x)); + if (ix < 0x3ff00000) + return h * (2.0 * t - t * t / (t + one)); + return h * (t + t / (t + one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x40862e42) + return h * __ieee754_exp (fabs (x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD (lx, x); + if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (u_int32_t) 0x8fb9f87d))) + { + w = __ieee754_exp (0.5 * fabs (x)); + t = h * w; + return t * w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return math_narrow_eval (x * shuge); +} +strong_alias (__ieee754_sinh, __sinh_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_sqrt.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_sqrt.c new file mode 100644 index 0000000000..017d30416c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_sqrt.c @@ -0,0 +1,139 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*********************************************************************/ +/* MODULE_NAME: uroot.c */ +/* */ +/* FUNCTION: usqrt */ +/* */ +/* FILES NEEDED: dla.h endian.h mydefs.h */ +/* uroot.tbl */ +/* */ +/* An ultimate sqrt routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of square */ +/* root of x. */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/*********************************************************************/ + +#include "endian.h" +#include "mydefs.h" +#include <dla.h> +#include "MathLib.h" +#include "root.tbl" +#include <math_private.h> + +/*********************************************************************/ +/* An ultimate sqrt routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of square */ +/* root of x. */ +/*********************************************************************/ +double +__ieee754_sqrt (double x) +{ + static const double + rt0 = 9.99999999859990725855365213134618E-01, + rt1 = 4.99999999495955425917856814202739E-01, + rt2 = 3.75017500867345182581453026130850E-01, + rt3 = 3.12523626554518656309172508769531E-01; + static const double big = 134217728.0; + double y, t, del, res, res1, hy, z, zz, p, hx, tx, ty, s; + mynumber a, c = { { 0, 0 } }; + int4 k; + + a.x = x; + k = a.i[HIGH_HALF]; + a.i[HIGH_HALF] = (k & 0x001fffff) | 0x3fe00000; + t = inroot[(k & 0x001fffff) >> 14]; + s = a.x; + /*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/ + if (k > 0x000fffff && k < 0x7ff00000) + { + int rm = __fegetround (); + fenv_t env; + libc_feholdexcept_setround (&env, FE_TONEAREST); + double ret; + y = 1.0 - t * (t * s); + t = t * (rt0 + y * (rt1 + y * (rt2 + y * rt3))); + c.i[HIGH_HALF] = 0x20000000 + ((k & 0x7fe00000) >> 1); + y = t * s; + hy = (y + big) - big; + del = 0.5 * t * ((s - hy * hy) - (y - hy) * (y + hy)); + res = y + del; + if (res == (res + 1.002 * ((y - res) + del))) + ret = res * c.x; + else + { + res1 = res + 1.5 * ((y - res) + del); + EMULV (res, res1, z, zz, p, hx, tx, hy, ty); /* (z+zz)=res*res1 */ + res = ((((z - s) + zz) < 0) ? max (res, res1) : + min (res, res1)); + ret = res * c.x; + } + math_force_eval (ret); + libc_fesetenv (&env); + double dret = x / ret; + if (dret != ret) + { + double force_inexact = 1.0 / 3.0; + math_force_eval (force_inexact); + /* The square root is inexact, ret is the round-to-nearest + value which may need adjusting for other rounding + modes. */ + switch (rm) + { +#ifdef FE_UPWARD + case FE_UPWARD: + if (dret > ret) + ret = (res + 0x1p-1022) * c.x; + break; +#endif + +#ifdef FE_DOWNWARD + case FE_DOWNWARD: +#endif +#ifdef FE_TOWARDZERO + case FE_TOWARDZERO: +#endif +#if defined FE_DOWNWARD || defined FE_TOWARDZERO + if (dret < ret) + ret = (res - 0x1p-1022) * c.x; + break; +#endif + + default: + break; + } + } + /* Otherwise (x / ret == ret), either the square root was exact or + the division was inexact. */ + return ret; + } + else + { + if ((k & 0x7ff00000) == 0x7ff00000) + return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */ + if (x == 0) + return x; /* sqrt(+0)=+0, sqrt(-0)=-0 */ + if (k < 0) + return (x - x) / (x - x); /* sqrt(-ve)=sNaN */ + return 0x1p-256 * __ieee754_sqrt (x * 0x1p512); + } +} +strong_alias (__ieee754_sqrt, __sqrt_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/gamma_product.c b/REORG.TODO/sysdeps/ieee754/dbl-64/gamma_product.c new file mode 100644 index 0000000000..d946b3c845 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/gamma_product.c @@ -0,0 +1,45 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_split.h> + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +double +__gamma_product (double x, double x_eps, int n, double *eps) +{ + SET_RESTORE_ROUND (FE_TONEAREST); + double ret = x; + *eps = x_eps / x; + for (int i = 1; i < n; i++) + { + *eps += x_eps / (x + i); + double lo; + mul_split (&ret, &lo, ret, x + i); + *eps += lo / ret; + } + return ret; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/gamma_productf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/gamma_productf.c new file mode 100644 index 0000000000..49c15b14b4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/gamma_productf.c @@ -0,0 +1,43 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +float +__gamma_productf (float x, float x_eps, int n, float *eps) +{ + double x_full = (double) x + (double) x_eps; + double ret = x_full; + for (int i = 1; i < n; i++) + ret *= x_full + i; + + float fret = math_narrow_eval ((float) ret); + *eps = (ret - fret) / fret; + + return fret; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/halfulp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/halfulp.c new file mode 100644 index 0000000000..d5f8a010e2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/halfulp.c @@ -0,0 +1,152 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/************************************************************************/ +/* */ +/* MODULE_NAME:halfulp.c */ +/* */ +/* FUNCTIONS:halfulp */ +/* FILES NEEDED: mydefs.h dla.h endian.h */ +/* uroot.c */ +/* */ +/*Routine halfulp(double x, double y) computes x^y where result does */ +/*not need rounding. If the result is closer to 0 than can be */ +/*represented it returns 0. */ +/* In the following cases the function does not compute anything */ +/*and returns a negative number: */ +/*1. if the result needs rounding, */ +/*2. if y is outside the interval [0, 2^20-1], */ +/*3. if x can be represented by x=2**n for some integer n. */ +/************************************************************************/ + +#include "endian.h" +#include "mydefs.h" +#include <dla.h> +#include <math_private.h> + +#ifndef SECTION +# define SECTION +#endif + +static const int4 tab54[32] = { + 262143, 11585, 1782, 511, 210, 107, 63, 42, + 30, 22, 17, 14, 12, 10, 9, 7, + 7, 6, 5, 5, 5, 4, 4, 4, + 3, 3, 3, 3, 3, 3, 3, 3 +}; + + +double +SECTION +__halfulp (double x, double y) +{ + mynumber v; + double z, u, uu; +#ifndef DLA_FMS + double j1, j2, j3, j4, j5; +#endif + int4 k, l, m, n; + if (y <= 0) /*if power is negative or zero */ + { + v.x = y; + if (v.i[LOW_HALF] != 0) + return -10.0; + v.x = x; + if (v.i[LOW_HALF] != 0) + return -10.0; + if ((v.i[HIGH_HALF] & 0x000fffff) != 0) + return -10; /* if x =2 ^ n */ + k = ((v.i[HIGH_HALF] & 0x7fffffff) >> 20) - 1023; /* find this n */ + z = (double) k; + return (z * y == -1075.0) ? 0 : -10.0; + } + /* if y > 0 */ + v.x = y; + if (v.i[LOW_HALF] != 0) + return -10.0; + + v.x = x; + /* case where x = 2**n for some integer n */ + if (((v.i[HIGH_HALF] & 0x000fffff) | v.i[LOW_HALF]) == 0) + { + k = (v.i[HIGH_HALF] >> 20) - 1023; + return (((double) k) * y == -1075.0) ? 0 : -10.0; + } + + v.x = y; + k = v.i[HIGH_HALF]; + m = k << 12; + l = 0; + while (m) + { + m = m << 1; l++; + } + n = (k & 0x000fffff) | 0x00100000; + n = n >> (20 - l); /* n is the odd integer of y */ + k = ((k >> 20) - 1023) - l; /* y = n*2**k */ + if (k > 5) + return -10.0; + if (k > 0) + for (; k > 0; k--) + n *= 2; + if (n > 34) + return -10.0; + k = -k; + if (k > 5) + return -10.0; + + /* now treat x */ + while (k > 0) + { + z = __ieee754_sqrt (x); + EMULV (z, z, u, uu, j1, j2, j3, j4, j5); + if (((u - x) + uu) != 0) + break; + x = z; + k--; + } + if (k) + return -10.0; + + /* it is impossible that n == 2, so the mantissa of x must be short */ + + v.x = x; + if (v.i[LOW_HALF]) + return -10.0; + k = v.i[HIGH_HALF]; + m = k << 12; + l = 0; + while (m) + { + m = m << 1; l++; + } + m = (k & 0x000fffff) | 0x00100000; + m = m >> (20 - l); /* m is the odd integer of x */ + + /* now check whether the length of m**n is at most 54 bits */ + + if (m > tab54[n - 3]) + return -10.0; + + /* yes, it is - now compute x**n by simple multiplications */ + + u = x; + for (k = 1; k < n; k++) + u = u * x; + return u; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/k_cos.c b/REORG.TODO/sysdeps/ieee754/dbl-64/k_cos.c new file mode 100644 index 0000000000..cc5c205a5f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/k_cos.c @@ -0,0 +1 @@ +/* Not needed anymore. */ diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/k_rem_pio2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/k_rem_pio2.c new file mode 100644 index 0000000000..2b5add6976 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/k_rem_pio2.c @@ -0,0 +1,362 @@ +/* @(#)k_rem_pio2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $"; +#endif + +/* + * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) + * double x[],y[]; int e0,nx,prec; int ipio2[]; + * + * __kernel_rem_pio2 return the last three digits of N with + * y = x - N*pi/2 + * so that |y| < pi/2. + * + * The method is to compute the integer (mod 8) and fraction parts of + * (2/pi)*x without doing the full multiplication. In general we + * skip the part of the product that are known to be a huge integer ( + * more accurately, = 0 mod 8 ). Thus the number of operations are + * independent of the exponent of the input. + * + * (2/pi) is represented by an array of 24-bit integers in ipio2[]. + * + * Input parameters: + * x[] The input value (must be positive) is broken into nx + * pieces of 24-bit integers in double precision format. + * x[i] will be the i-th 24 bit of x. The scaled exponent + * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 + * match x's up to 24 bits. + * + * Example of breaking a double positive z into x[0]+x[1]+x[2]: + * e0 = ilogb(z)-23 + * z = scalbn(z,-e0) + * for i = 0,1,2 + * x[i] = floor(z) + * z = (z-x[i])*2**24 + * + * + * y[] ouput result in an array of double precision numbers. + * The dimension of y[] is: + * 24-bit precision 1 + * 53-bit precision 2 + * 64-bit precision 2 + * 113-bit precision 3 + * The actual value is the sum of them. Thus for 113-bit + * precision, one may have to do something like: + * + * long double t,w,r_head, r_tail; + * t = (long double)y[2] + (long double)y[1]; + * w = (long double)y[0]; + * r_head = t+w; + * r_tail = w - (r_head - t); + * + * e0 The exponent of x[0] + * + * nx dimension of x[] + * + * prec an integer indicating the precision: + * 0 24 bits (single) + * 1 53 bits (double) + * 2 64 bits (extended) + * 3 113 bits (quad) + * + * ipio2[] + * integer array, contains the (24*i)-th to (24*i+23)-th + * bit of 2/pi after binary point. The corresponding + * floating value is + * + * ipio2[i] * 2^(-24(i+1)). + * + * External function: + * double scalbn(), floor(); + * + * + * Here is the description of some local variables: + * + * jk jk+1 is the initial number of terms of ipio2[] needed + * in the computation. The recommended value is 2,3,4, + * 6 for single, double, extended,and quad. + * + * jz local integer variable indicating the number of + * terms of ipio2[] used. + * + * jx nx - 1 + * + * jv index for pointing to the suitable ipio2[] for the + * computation. In general, we want + * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 + * is an integer. Thus + * e0-3-24*jv >= 0 or (e0-3)/24 >= jv + * Hence jv = max(0,(e0-3)/24). + * + * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. + * + * q[] double array with integral value, representing the + * 24-bits chunk of the product of x and 2/pi. + * + * q0 the corresponding exponent of q[0]. Note that the + * exponent for q[i] would be q0-24*i. + * + * PIo2[] double precision array, obtained by cutting pi/2 + * into 24 bits chunks. + * + * f[] ipio2[] in floating point + * + * iq[] integer array by breaking up q[] in 24-bits chunk. + * + * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] + * + * ih integer. If >0 it indicates q[] is >= 0.5, hence + * it also indicates the *sign* of the result. + * + */ + + +/* + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <math.h> +#include <math_private.h> +#include <libc-diag.h> + +static const int init_jk[] = {2,3,4,6}; /* initial value for jk */ + +static const double PIo2[] = { + 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ + 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ + 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ + 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ + 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ + 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ + 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ + 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ +}; + +static const double + zero = 0.0, + one = 1.0, + two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ + twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ + +int +__kernel_rem_pio2 (double *x, double *y, int e0, int nx, int prec, + const int32_t *ipio2) +{ + int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih; + double z, fw, f[20], fq[20], q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx - 1; + jv = (e0 - 3) / 24; if (jv < 0) + jv = 0; + q0 = e0 - 24 * (jv + 1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv - jx; m = jx + jk; + for (i = 0; i <= m; i++, j++) + f[i] = (j < 0) ? zero : (double) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i = 0; i <= jk; i++) + { + for (j = 0, fw = 0.0; j <= jx; j++) + fw += x[j] * f[jx + i - j]; + q[i] = fw; + } + + jz = jk; +recompute: + /* distill q[] into iq[] reversingly */ + for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--) + { + fw = (double) ((int32_t) (twon24 * z)); + iq[i] = (int32_t) (z - two24 * fw); + z = q[j - 1] + fw; + } + + /* compute n */ + z = __scalbn (z, q0); /* actual value of z */ + z -= 8.0 * __floor (z * 0.125); /* trim off integer >= 8 */ + n = (int32_t) z; + z -= (double) n; + ih = 0; + if (q0 > 0) /* need iq[jz-1] to determine n */ + { + i = (iq[jz - 1] >> (24 - q0)); n += i; + iq[jz - 1] -= i << (24 - q0); + ih = iq[jz - 1] >> (23 - q0); + } + else if (q0 == 0) + ih = iq[jz - 1] >> 23; + else if (z >= 0.5) + ih = 2; + + if (ih > 0) /* q > 0.5 */ + { + n += 1; carry = 0; + for (i = 0; i < jz; i++) /* compute 1-q */ + { + j = iq[i]; + if (carry == 0) + { + if (j != 0) + { + carry = 1; iq[i] = 0x1000000 - j; + } + } + else + iq[i] = 0xffffff - j; + } + if (q0 > 0) /* rare case: chance is 1 in 12 */ + { + switch (q0) + { + case 1: + iq[jz - 1] &= 0x7fffff; break; + case 2: + iq[jz - 1] &= 0x3fffff; break; + } + } + if (ih == 2) + { + z = one - z; + if (carry != 0) + z -= __scalbn (one, q0); + } + } + + /* check if recomputation is needed */ + if (z == zero) + { + j = 0; + for (i = jz - 1; i >= jk; i--) + j |= iq[i]; + if (j == 0) /* need recomputation */ + { + /* On s390x gcc 6.1 -O3 produces the warning "array subscript is below + array bounds [-Werror=array-bounds]". Only __ieee754_rem_pio2l + calls __kernel_rem_pio2 for normal numbers and |x| > pi/4 in case + of ldbl-96 and |x| > 3pi/4 in case of ldbl-128[ibm]. + Thus x can't be zero and ipio2 is not zero, too. Thus not all iq[] + values can't be zero. */ + DIAG_PUSH_NEEDS_COMMENT; + DIAG_IGNORE_NEEDS_COMMENT (6.1, "-Warray-bounds"); + for (k = 1; iq[jk - k] == 0; k++) + ; /* k = no. of terms needed */ + DIAG_POP_NEEDS_COMMENT; + + for (i = jz + 1; i <= jz + k; i++) /* add q[jz+1] to q[jz+k] */ + { + f[jx + i] = (double) ipio2[jv + i]; + for (j = 0, fw = 0.0; j <= jx; j++) + fw += x[j] * f[jx + i - j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } + + /* chop off zero terms */ + if (z == 0.0) + { + jz -= 1; q0 -= 24; + while (iq[jz] == 0) + { + jz--; q0 -= 24; + } + } + else /* break z into 24-bit if necessary */ + { + z = __scalbn (z, -q0); + if (z >= two24) + { + fw = (double) ((int32_t) (twon24 * z)); + iq[jz] = (int32_t) (z - two24 * fw); + jz += 1; q0 += 24; + iq[jz] = (int32_t) fw; + } + else + iq[jz] = (int32_t) z; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = __scalbn (one, q0); + for (i = jz; i >= 0; i--) + { + q[i] = fw * (double) iq[i]; fw *= twon24; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for (i = jz; i >= 0; i--) + { + for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++) + fw += PIo2[k] * q[i + k]; + fq[jz - i] = fw; + } + + /* compress fq[] into y[] */ + switch (prec) + { + case 0: + fw = 0.0; + for (i = jz; i >= 0; i--) + fw += fq[i]; + y[0] = (ih == 0) ? fw : -fw; + break; + case 1: + case 2:; + double fv = 0.0; + for (i = jz; i >= 0; i--) + fv = math_narrow_eval (fv + fq[i]); + y[0] = (ih == 0) ? fv : -fv; + fv = math_narrow_eval (fq[0] - fv); + for (i = 1; i <= jz; i++) + fv = math_narrow_eval (fv + fq[i]); + y[1] = (ih == 0) ? fv : -fv; + break; + case 3: /* painful */ + for (i = jz; i > 0; i--) + { + double fv = math_narrow_eval (fq[i - 1] + fq[i]); + fq[i] += fq[i - 1] - fv; + fq[i - 1] = fv; + } + for (i = jz; i > 1; i--) + { + double fv = math_narrow_eval (fq[i - 1] + fq[i]); + fq[i] += fq[i - 1] - fv; + fq[i - 1] = fv; + } + for (fw = 0.0, i = jz; i >= 2; i--) + fw += fq[i]; + if (ih == 0) + { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } + else + { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n & 7; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/k_sin.c b/REORG.TODO/sysdeps/ieee754/dbl-64/k_sin.c new file mode 100644 index 0000000000..cc5c205a5f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/k_sin.c @@ -0,0 +1 @@ +/* Not needed anymore. */ diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/k_tan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/k_tan.c new file mode 100644 index 0000000000..cc5c205a5f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/k_tan.c @@ -0,0 +1 @@ +/* Not needed anymore. */ diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/lgamma_neg.c b/REORG.TODO/sysdeps/ieee754/dbl-64/lgamma_neg.c new file mode 100644 index 0000000000..ccde9a1fe5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/lgamma_neg.c @@ -0,0 +1,383 @@ +/* lgamma expanding around zeros. + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const double lgamma_zeros[][2] = + { + { -0x2.74ff92c01f0d8p+0, -0x2.abec9f315f1ap-56 }, + { -0x2.bf6821437b202p+0, 0x6.866a5b4b9be14p-56 }, + { -0x3.24c1b793cb35ep+0, -0xf.b8be699ad3d98p-56 }, + { -0x3.f48e2a8f85fcap+0, -0x1.70d4561291237p-56 }, + { -0x4.0a139e1665604p+0, 0xf.3c60f4f21e7fp-56 }, + { -0x4.fdd5de9bbabf4p+0, 0xa.ef2f55bf89678p-56 }, + { -0x5.021a95fc2db64p+0, -0x3.2a4c56e595394p-56 }, + { -0x5.ffa4bd647d034p+0, -0x1.7dd4ed62cbd32p-52 }, + { -0x6.005ac9625f234p+0, 0x4.9f83d2692e9c8p-56 }, + { -0x6.fff2fddae1bcp+0, 0xc.29d949a3dc03p-60 }, + { -0x7.000cff7b7f87cp+0, 0x1.20bb7d2324678p-52 }, + { -0x7.fffe5fe05673cp+0, -0x3.ca9e82b522b0cp-56 }, + { -0x8.0001a01459fc8p+0, -0x1.f60cb3cec1cedp-52 }, + { -0x8.ffffd1c425e8p+0, -0xf.fc864e9574928p-56 }, + { -0x9.00002e3bb47d8p+0, -0x6.d6d843fedc35p-56 }, + { -0x9.fffffb606bep+0, 0x2.32f9d51885afap-52 }, + { -0xa.0000049f93bb8p+0, -0x1.927b45d95e154p-52 }, + { -0xa.ffffff9466eap+0, 0xe.4c92532d5243p-56 }, + { -0xb.0000006b9915p+0, -0x3.15d965a6ffea4p-52 }, + { -0xb.fffffff708938p+0, -0x7.387de41acc3d4p-56 }, + { -0xc.00000008f76c8p+0, 0x8.cea983f0fdafp-56 }, + { -0xc.ffffffff4f6ep+0, 0x3.09e80685a0038p-52 }, + { -0xd.00000000b092p+0, -0x3.09c06683dd1bap-52 }, + { -0xd.fffffffff3638p+0, 0x3.a5461e7b5c1f6p-52 }, + { -0xe.000000000c9c8p+0, -0x3.a545e94e75ec6p-52 }, + { -0xe.ffffffffff29p+0, 0x3.f9f399fb10cfcp-52 }, + { -0xf.0000000000d7p+0, -0x3.f9f399bd0e42p-52 }, + { -0xf.fffffffffff28p+0, -0xc.060c6621f513p-56 }, + { -0x1.000000000000dp+4, -0x7.3f9f399da1424p-52 }, + { -0x1.0ffffffffffffp+4, -0x3.569c47e7a93e2p-52 }, + { -0x1.1000000000001p+4, 0x3.569c47e7a9778p-52 }, + { -0x1.2p+4, 0xb.413c31dcbecdp-56 }, + { -0x1.2p+4, -0xb.413c31dcbeca8p-56 }, + { -0x1.3p+4, 0x9.7a4da340a0ab8p-60 }, + { -0x1.3p+4, -0x9.7a4da340a0ab8p-60 }, + { -0x1.4p+4, 0x7.950ae90080894p-64 }, + { -0x1.4p+4, -0x7.950ae90080894p-64 }, + { -0x1.5p+4, 0x5.c6e3bdb73d5c8p-68 }, + { -0x1.5p+4, -0x5.c6e3bdb73d5c8p-68 }, + { -0x1.6p+4, 0x4.338e5b6dfe14cp-72 }, + { -0x1.6p+4, -0x4.338e5b6dfe14cp-72 }, + { -0x1.7p+4, 0x2.ec368262c7034p-76 }, + { -0x1.7p+4, -0x2.ec368262c7034p-76 }, + { -0x1.8p+4, 0x1.f2cf01972f578p-80 }, + { -0x1.8p+4, -0x1.f2cf01972f578p-80 }, + { -0x1.9p+4, 0x1.3f3ccdd165fa9p-84 }, + { -0x1.9p+4, -0x1.3f3ccdd165fa9p-84 }, + { -0x1.ap+4, 0xc.4742fe35272dp-92 }, + { -0x1.ap+4, -0xc.4742fe35272dp-92 }, + { -0x1.bp+4, 0x7.46ac70b733a8cp-96 }, + { -0x1.bp+4, -0x7.46ac70b733a8cp-96 }, + { -0x1.cp+4, 0x4.2862898d42174p-100 }, + }; + +static const double e_hi = 0x2.b7e151628aed2p+0, e_lo = 0xa.6abf7158809dp-56; + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) in Stirling's + approximation to lgamma function. */ + +static const double lgamma_coeff[] = + { + 0x1.5555555555555p-4, + -0xb.60b60b60b60b8p-12, + 0x3.4034034034034p-12, + -0x2.7027027027028p-12, + 0x3.72a3c5631fe46p-12, + -0x7.daac36664f1f4p-12, + 0x1.a41a41a41a41ap-8, + -0x7.90a1b2c3d4e6p-8, + 0x2.dfd2c703c0dp-4, + -0x1.6476701181f3ap+0, + 0xd.672219167003p+0, + -0x9.cd9292e6660d8p+4, + }; + +#define NCOEFF (sizeof (lgamma_coeff) / sizeof (lgamma_coeff[0])) + +/* Polynomial approximations to (|gamma(x)|-1)(x-n)/(x-x0), where n is + the integer end-point of the half-integer interval containing x and + x0 is the zero of lgamma in that half-integer interval. Each + polynomial is expressed in terms of x-xm, where xm is the midpoint + of the interval for which the polynomial applies. */ + +static const double poly_coeff[] = + { + /* Interval [-2.125, -2] (polynomial degree 10). */ + -0x1.0b71c5c54d42fp+0, + -0xc.73a1dc05f3758p-4, + -0x1.ec84140851911p-4, + -0xe.37c9da23847e8p-4, + -0x1.03cd87cdc0ac6p-4, + -0xe.ae9aedce12eep-4, + 0x9.b11a1780cfd48p-8, + -0xe.f25fc460bdebp-4, + 0x2.6e984c61ca912p-4, + -0xf.83fea1c6d35p-4, + 0x4.760c8c8909758p-4, + /* Interval [-2.25, -2.125] (polynomial degree 11). */ + -0xf.2930890d7d678p-4, + -0xc.a5cfde054eaa8p-4, + 0x3.9c9e0fdebd99cp-4, + -0x1.02a5ad35619d9p+0, + 0x9.6e9b1167c164p-4, + -0x1.4d8332eba090ap+0, + 0x1.1c0c94b1b2b6p+0, + -0x1.c9a70d138c74ep+0, + 0x1.d7d9cf1d4c196p+0, + -0x2.91fbf4cd6abacp+0, + 0x2.f6751f74b8ff8p+0, + -0x3.e1bb7b09e3e76p+0, + /* Interval [-2.375, -2.25] (polynomial degree 12). */ + -0xd.7d28d505d618p-4, + -0xe.69649a3040958p-4, + 0xb.0d74a2827cd6p-4, + -0x1.924b09228a86ep+0, + 0x1.d49b12bcf6175p+0, + -0x3.0898bb530d314p+0, + 0x4.207a6be8fda4cp+0, + -0x6.39eef56d4e9p+0, + 0x8.e2e42acbccec8p+0, + -0xd.0d91c1e596a68p+0, + 0x1.2e20d7099c585p+4, + -0x1.c4eb6691b4ca9p+4, + 0x2.96a1a11fd85fep+4, + /* Interval [-2.5, -2.375] (polynomial degree 13). */ + -0xb.74ea1bcfff948p-4, + -0x1.2a82bd590c376p+0, + 0x1.88020f828b81p+0, + -0x3.32279f040d7aep+0, + 0x5.57ac8252ce868p+0, + -0x9.c2aedd093125p+0, + 0x1.12c132716e94cp+4, + -0x1.ea94dfa5c0a6dp+4, + 0x3.66b61abfe858cp+4, + -0x6.0cfceb62a26e4p+4, + 0xa.beeba09403bd8p+4, + -0x1.3188d9b1b288cp+8, + 0x2.37f774dd14c44p+8, + -0x3.fdf0a64cd7136p+8, + /* Interval [-2.625, -2.5] (polynomial degree 13). */ + -0x3.d10108c27ebbp-4, + 0x1.cd557caff7d2fp+0, + 0x3.819b4856d36cep+0, + 0x6.8505cbacfc42p+0, + 0xb.c1b2e6567a4dp+0, + 0x1.50a53a3ce6c73p+4, + 0x2.57adffbb1ec0cp+4, + 0x4.2b15549cf400cp+4, + 0x7.698cfd82b3e18p+4, + 0xd.2decde217755p+4, + 0x1.7699a624d07b9p+8, + 0x2.98ecf617abbfcp+8, + 0x4.d5244d44d60b4p+8, + 0x8.e962bf7395988p+8, + /* Interval [-2.75, -2.625] (polynomial degree 12). */ + -0x6.b5d252a56e8a8p-4, + 0x1.28d60383da3a6p+0, + 0x1.db6513ada89bep+0, + 0x2.e217118fa8c02p+0, + 0x4.450112c651348p+0, + 0x6.4af990f589b8cp+0, + 0x9.2db5963d7a238p+0, + 0xd.62c03647da19p+0, + 0x1.379f81f6416afp+4, + 0x1.c5618b4fdb96p+4, + 0x2.9342d0af2ac4ep+4, + 0x3.d9cdf56d2b186p+4, + 0x5.ab9f91d5a27a4p+4, + /* Interval [-2.875, -2.75] (polynomial degree 11). */ + -0x8.a41b1e4f36ff8p-4, + 0xc.da87d3b69dbe8p-4, + 0x1.1474ad5c36709p+0, + 0x1.761ecb90c8c5cp+0, + 0x1.d279bff588826p+0, + 0x2.4e5d003fb36a8p+0, + 0x2.d575575566842p+0, + 0x3.85152b0d17756p+0, + 0x4.5213d921ca13p+0, + 0x5.55da7dfcf69c4p+0, + 0x6.acef729b9404p+0, + 0x8.483cc21dd0668p+0, + /* Interval [-3, -2.875] (polynomial degree 11). */ + -0xa.046d667e468f8p-4, + 0x9.70b88dcc006cp-4, + 0xa.a8a39421c94dp-4, + 0xd.2f4d1363f98ep-4, + 0xd.ca9aa19975b7p-4, + 0xf.cf09c2f54404p-4, + 0x1.04b1365a9adfcp+0, + 0x1.22b54ef213798p+0, + 0x1.2c52c25206bf5p+0, + 0x1.4aa3d798aace4p+0, + 0x1.5c3f278b504e3p+0, + 0x1.7e08292cc347bp+0, + }; + +static const size_t poly_deg[] = + { + 10, + 11, + 12, + 13, + 13, + 12, + 11, + 11, + }; + +static const size_t poly_end[] = + { + 10, + 22, + 35, + 49, + 63, + 76, + 88, + 100, + }; + +/* Compute sin (pi * X) for -0.25 <= X <= 0.5. */ + +static double +lg_sinpi (double x) +{ + if (x <= 0.25) + return __sin (M_PI * x); + else + return __cos (M_PI * (0.5 - x)); +} + +/* Compute cos (pi * X) for -0.25 <= X <= 0.5. */ + +static double +lg_cospi (double x) +{ + if (x <= 0.25) + return __cos (M_PI * x); + else + return __sin (M_PI * (0.5 - x)); +} + +/* Compute cot (pi * X) for -0.25 <= X <= 0.5. */ + +static double +lg_cotpi (double x) +{ + return lg_cospi (x) / lg_sinpi (x); +} + +/* Compute lgamma of a negative argument -28 < X < -2, setting + *SIGNGAMP accordingly. */ + +double +__lgamma_neg (double x, int *signgamp) +{ + /* Determine the half-integer region X lies in, handle exact + integers and determine the sign of the result. */ + int i = __floor (-2 * x); + if ((i & 1) == 0 && i == -2 * x) + return 1.0 / 0.0; + double xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2); + i -= 4; + *signgamp = ((i & 2) == 0 ? -1 : 1); + + SET_RESTORE_ROUND (FE_TONEAREST); + + /* Expand around the zero X0 = X0_HI + X0_LO. */ + double x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1]; + double xdiff = x - x0_hi - x0_lo; + + /* For arguments in the range -3 to -2, use polynomial + approximations to an adjusted version of the gamma function. */ + if (i < 2) + { + int j = __floor (-8 * x) - 16; + double xm = (-33 - 2 * j) * 0.0625; + double x_adj = x - xm; + size_t deg = poly_deg[j]; + size_t end = poly_end[j]; + double g = poly_coeff[end]; + for (size_t j = 1; j <= deg; j++) + g = g * x_adj + poly_coeff[end - j]; + return __log1p (g * xdiff / (x - xn)); + } + + /* The result we want is log (sinpi (X0) / sinpi (X)) + + log (gamma (1 - X0) / gamma (1 - X)). */ + double x_idiff = fabs (xn - x), x0_idiff = fabs (xn - x0_hi - x0_lo); + double log_sinpi_ratio; + if (x0_idiff < x_idiff * 0.5) + /* Use log not log1p to avoid inaccuracy from log1p of arguments + close to -1. */ + log_sinpi_ratio = __ieee754_log (lg_sinpi (x0_idiff) + / lg_sinpi (x_idiff)); + else + { + /* Use log1p not log to avoid inaccuracy from log of arguments + close to 1. X0DIFF2 has positive sign if X0 is further from + XN than X is from XN, negative sign otherwise. */ + double x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * 0.5; + double sx0d2 = lg_sinpi (x0diff2); + double cx0d2 = lg_cospi (x0diff2); + log_sinpi_ratio = __log1p (2 * sx0d2 + * (-sx0d2 + cx0d2 * lg_cotpi (x_idiff))); + } + + double log_gamma_ratio; + double y0 = math_narrow_eval (1 - x0_hi); + double y0_eps = -x0_hi + (1 - y0) - x0_lo; + double y = math_narrow_eval (1 - x); + double y_eps = -x + (1 - y); + /* We now wish to compute LOG_GAMMA_RATIO + = log (gamma (Y0 + Y0_EPS) / gamma (Y + Y_EPS)). XDIFF + accurately approximates the difference Y0 + Y0_EPS - Y - + Y_EPS. Use Stirling's approximation. First, we may need to + adjust into the range where Stirling's approximation is + sufficiently accurate. */ + double log_gamma_adj = 0; + if (i < 6) + { + int n_up = (7 - i) / 2; + double ny0, ny0_eps, ny, ny_eps; + ny0 = math_narrow_eval (y0 + n_up); + ny0_eps = y0 - (ny0 - n_up) + y0_eps; + y0 = ny0; + y0_eps = ny0_eps; + ny = math_narrow_eval (y + n_up); + ny_eps = y - (ny - n_up) + y_eps; + y = ny; + y_eps = ny_eps; + double prodm1 = __lgamma_product (xdiff, y - n_up, y_eps, n_up); + log_gamma_adj = -__log1p (prodm1); + } + double log_gamma_high + = (xdiff * __log1p ((y0 - e_hi - e_lo + y0_eps) / e_hi) + + (y - 0.5 + y_eps) * __log1p (xdiff / y) + log_gamma_adj); + /* Compute the sum of (B_2k / 2k(2k-1))(Y0^-(2k-1) - Y^-(2k-1)). */ + double y0r = 1 / y0, yr = 1 / y; + double y0r2 = y0r * y0r, yr2 = yr * yr; + double rdiff = -xdiff / (y * y0); + double bterm[NCOEFF]; + double dlast = rdiff, elast = rdiff * yr * (yr + y0r); + bterm[0] = dlast * lgamma_coeff[0]; + for (size_t j = 1; j < NCOEFF; j++) + { + double dnext = dlast * y0r2 + elast; + double enext = elast * yr2; + bterm[j] = dnext * lgamma_coeff[j]; + dlast = dnext; + elast = enext; + } + double log_gamma_low = 0; + for (size_t j = 0; j < NCOEFF; j++) + log_gamma_low += bterm[NCOEFF - 1 - j]; + log_gamma_ratio = log_gamma_high + log_gamma_low; + + return log_sinpi_ratio + log_gamma_ratio; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/lgamma_product.c b/REORG.TODO/sysdeps/ieee754/dbl-64/lgamma_product.c new file mode 100644 index 0000000000..a894f488b0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/lgamma_product.c @@ -0,0 +1,52 @@ +/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), .... + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_split.h> + +/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS + + 1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that + all the values X + 1, ..., X + N - 1 are exactly representable, and + X_EPS / X is small enough that factors quadratic in it can be + neglected. */ + +double +__lgamma_product (double t, double x, double x_eps, int n) +{ + double ret = 0, ret_eps = 0; + for (int i = 0; i < n; i++) + { + double xi = x + i; + double quot = t / xi; + double mhi, mlo; + mul_split (&mhi, &mlo, quot, xi); + double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi); + /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */ + double rhi, rlo; + mul_split (&rhi, &rlo, ret, quot); + double rpq = ret + quot; + double rpq_eps = (ret - rpq) + quot; + double nret = rpq + rhi; + double nret_eps = (rpq - nret) + rhi; + ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot + + quot_lo + quot_lo * (ret + ret_eps)); + ret = nret; + } + return ret + ret_eps; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpa-arch.h b/REORG.TODO/sysdeps/ieee754/dbl-64/mpa-arch.h new file mode 100644 index 0000000000..4428ac1301 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpa-arch.h @@ -0,0 +1,47 @@ +/* Overridable constants and operations. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + + This program is free software; you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation; either version 2.1 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program; if not, see <http://www.gnu.org/licenses/>. */ + +#include <stdint.h> + +typedef long mantissa_t; +typedef int64_t mantissa_store_t; + +#define TWOPOW(i) (1L << i) + +#define RADIX_EXP 24 +#define RADIX TWOPOW (RADIX_EXP) /* 2^24 */ + +/* Divide D by RADIX and put the remainder in R. D must be a non-negative + integral value. */ +#define DIV_RADIX(d, r) \ + ({ \ + r = d & (RADIX - 1); \ + d >>= RADIX_EXP; \ + }) + +/* Put the integer component of a double X in R and retain the fraction in + X. This is used in extracting mantissa digits for MP_NO by using the + integer portion of the current value of the number as the current mantissa + digit and then scaling by RADIX to get the next mantissa digit in the same + manner. */ +#define INTEGER_OF(x, i) \ + ({ \ + i = (mantissa_t) x; \ + x -= i; \ + }) + +/* Align IN down to F. The code assumes that F is a power of two. */ +#define ALIGN_DOWN_TO(in, f) ((in) & - (f)) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpa.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mpa.c new file mode 100644 index 0000000000..3820335172 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpa.c @@ -0,0 +1,906 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/************************************************************************/ +/* MODULE_NAME: mpa.c */ +/* */ +/* FUNCTIONS: */ +/* mcr */ +/* acr */ +/* cpy */ +/* norm */ +/* denorm */ +/* mp_dbl */ +/* dbl_mp */ +/* add_magnitudes */ +/* sub_magnitudes */ +/* add */ +/* sub */ +/* mul */ +/* inv */ +/* dvd */ +/* */ +/* Arithmetic functions for multiple precision numbers. */ +/* Relative errors are bounded */ +/************************************************************************/ + + +#include "endian.h" +#include "mpa.h" +#include <sys/param.h> +#include <alloca.h> + +#ifndef SECTION +# define SECTION +#endif + +#ifndef NO__CONST +const mp_no __mpone = { 1, { 1.0, 1.0 } }; +const mp_no __mptwo = { 1, { 1.0, 2.0 } }; +#endif + +#ifndef NO___ACR +/* Compare mantissa of two multiple precision numbers regardless of the sign + and exponent of the numbers. */ +static int +mcr (const mp_no *x, const mp_no *y, int p) +{ + long i; + long p2 = p; + for (i = 1; i <= p2; i++) + { + if (X[i] == Y[i]) + continue; + else if (X[i] > Y[i]) + return 1; + else + return -1; + } + return 0; +} + +/* Compare the absolute values of two multiple precision numbers. */ +int +__acr (const mp_no *x, const mp_no *y, int p) +{ + long i; + + if (X[0] == 0) + { + if (Y[0] == 0) + i = 0; + else + i = -1; + } + else if (Y[0] == 0) + i = 1; + else + { + if (EX > EY) + i = 1; + else if (EX < EY) + i = -1; + else + i = mcr (x, y, p); + } + + return i; +} +#endif + +#ifndef NO___CPY +/* Copy multiple precision number X into Y. They could be the same + number. */ +void +__cpy (const mp_no *x, mp_no *y, int p) +{ + long i; + + EY = EX; + for (i = 0; i <= p; i++) + Y[i] = X[i]; +} +#endif + +#ifndef NO___MP_DBL +/* Convert a multiple precision number *X into a double precision + number *Y, normalized case (|x| >= 2**(-1022))). X has precision + P, which is positive. */ +static void +norm (const mp_no *x, double *y, int p) +{ +# define R RADIXI + long i; + double c; + mantissa_t a, u, v, z[5]; + if (p < 5) + { + if (p == 1) + c = X[1]; + else if (p == 2) + c = X[1] + R * X[2]; + else if (p == 3) + c = X[1] + R * (X[2] + R * X[3]); + else /* p == 4. */ + c = (X[1] + R * X[2]) + R * R * (X[3] + R * X[4]); + } + else + { + for (a = 1, z[1] = X[1]; z[1] < TWO23; ) + { + a *= 2; + z[1] *= 2; + } + + for (i = 2; i < 5; i++) + { + mantissa_store_t d, r; + d = X[i] * (mantissa_store_t) a; + DIV_RADIX (d, r); + z[i] = r; + z[i - 1] += d; + } + + u = ALIGN_DOWN_TO (z[3], TWO19); + v = z[3] - u; + + if (v == TWO18) + { + if (z[4] == 0) + { + for (i = 5; i <= p; i++) + { + if (X[i] == 0) + continue; + else + { + z[3] += 1; + break; + } + } + } + else + z[3] += 1; + } + + c = (z[1] + R * (z[2] + R * z[3])) / a; + } + + c *= X[0]; + + for (i = 1; i < EX; i++) + c *= RADIX; + for (i = 1; i > EX; i--) + c *= RADIXI; + + *y = c; +# undef R +} + +/* Convert a multiple precision number *X into a double precision + number *Y, Denormal case (|x| < 2**(-1022))). */ +static void +denorm (const mp_no *x, double *y, int p) +{ + long i, k; + long p2 = p; + double c; + mantissa_t u, z[5]; + +# define R RADIXI + if (EX < -44 || (EX == -44 && X[1] < TWO5)) + { + *y = 0; + return; + } + + if (p2 == 1) + { + if (EX == -42) + { + z[1] = X[1] + TWO10; + z[2] = 0; + z[3] = 0; + k = 3; + } + else if (EX == -43) + { + z[1] = TWO10; + z[2] = X[1]; + z[3] = 0; + k = 2; + } + else + { + z[1] = TWO10; + z[2] = 0; + z[3] = X[1]; + k = 1; + } + } + else if (p2 == 2) + { + if (EX == -42) + { + z[1] = X[1] + TWO10; + z[2] = X[2]; + z[3] = 0; + k = 3; + } + else if (EX == -43) + { + z[1] = TWO10; + z[2] = X[1]; + z[3] = X[2]; + k = 2; + } + else + { + z[1] = TWO10; + z[2] = 0; + z[3] = X[1]; + k = 1; + } + } + else + { + if (EX == -42) + { + z[1] = X[1] + TWO10; + z[2] = X[2]; + k = 3; + } + else if (EX == -43) + { + z[1] = TWO10; + z[2] = X[1]; + k = 2; + } + else + { + z[1] = TWO10; + z[2] = 0; + k = 1; + } + z[3] = X[k]; + } + + u = ALIGN_DOWN_TO (z[3], TWO5); + + if (u == z[3]) + { + for (i = k + 1; i <= p2; i++) + { + if (X[i] == 0) + continue; + else + { + z[3] += 1; + break; + } + } + } + + c = X[0] * ((z[1] + R * (z[2] + R * z[3])) - TWO10); + + *y = c * TWOM1032; +# undef R +} + +/* Convert multiple precision number *X into double precision number *Y. The + result is correctly rounded to the nearest/even. */ +void +__mp_dbl (const mp_no *x, double *y, int p) +{ + if (X[0] == 0) + { + *y = 0; + return; + } + + if (__glibc_likely (EX > -42 || (EX == -42 && X[1] >= TWO10))) + norm (x, y, p); + else + denorm (x, y, p); +} +#endif + +/* Get the multiple precision equivalent of X into *Y. If the precision is too + small, the result is truncated. */ +void +SECTION +__dbl_mp (double x, mp_no *y, int p) +{ + long i, n; + long p2 = p; + + /* Sign. */ + if (x == 0) + { + Y[0] = 0; + return; + } + else if (x > 0) + Y[0] = 1; + else + { + Y[0] = -1; + x = -x; + } + + /* Exponent. */ + for (EY = 1; x >= RADIX; EY += 1) + x *= RADIXI; + for (; x < 1; EY -= 1) + x *= RADIX; + + /* Digits. */ + n = MIN (p2, 4); + for (i = 1; i <= n; i++) + { + INTEGER_OF (x, Y[i]); + x *= RADIX; + } + for (; i <= p2; i++) + Y[i] = 0; +} + +/* Add magnitudes of *X and *Y assuming that abs (*X) >= abs (*Y) > 0. The + sign of the sum *Z is not changed. X and Y may overlap but not X and Z or + Y and Z. No guard digit is used. The result equals the exact sum, + truncated. */ +static void +SECTION +add_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p) +{ + long i, j, k; + long p2 = p; + mantissa_t zk; + + EZ = EX; + + i = p2; + j = p2 + EY - EX; + k = p2 + 1; + + if (__glibc_unlikely (j < 1)) + { + __cpy (x, z, p); + return; + } + + zk = 0; + + for (; j > 0; i--, j--) + { + zk += X[i] + Y[j]; + if (zk >= RADIX) + { + Z[k--] = zk - RADIX; + zk = 1; + } + else + { + Z[k--] = zk; + zk = 0; + } + } + + for (; i > 0; i--) + { + zk += X[i]; + if (zk >= RADIX) + { + Z[k--] = zk - RADIX; + zk = 1; + } + else + { + Z[k--] = zk; + zk = 0; + } + } + + if (zk == 0) + { + for (i = 1; i <= p2; i++) + Z[i] = Z[i + 1]; + } + else + { + Z[1] = zk; + EZ += 1; + } +} + +/* Subtract the magnitudes of *X and *Y assuming that abs (*x) > abs (*y) > 0. + The sign of the difference *Z is not changed. X and Y may overlap but not X + and Z or Y and Z. One guard digit is used. The error is less than one + ULP. */ +static void +SECTION +sub_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p) +{ + long i, j, k; + long p2 = p; + mantissa_t zk; + + EZ = EX; + i = p2; + j = p2 + EY - EX; + k = p2; + + /* Y is too small compared to X, copy X over to the result. */ + if (__glibc_unlikely (j < 1)) + { + __cpy (x, z, p); + return; + } + + /* The relevant least significant digit in Y is non-zero, so we factor it in + to enhance accuracy. */ + if (j < p2 && Y[j + 1] > 0) + { + Z[k + 1] = RADIX - Y[j + 1]; + zk = -1; + } + else + zk = Z[k + 1] = 0; + + /* Subtract and borrow. */ + for (; j > 0; i--, j--) + { + zk += (X[i] - Y[j]); + if (zk < 0) + { + Z[k--] = zk + RADIX; + zk = -1; + } + else + { + Z[k--] = zk; + zk = 0; + } + } + + /* We're done with digits from Y, so it's just digits in X. */ + for (; i > 0; i--) + { + zk += X[i]; + if (zk < 0) + { + Z[k--] = zk + RADIX; + zk = -1; + } + else + { + Z[k--] = zk; + zk = 0; + } + } + + /* Normalize. */ + for (i = 1; Z[i] == 0; i++) + ; + EZ = EZ - i + 1; + for (k = 1; i <= p2 + 1; ) + Z[k++] = Z[i++]; + for (; k <= p2; ) + Z[k++] = 0; +} + +/* Add *X and *Y and store the result in *Z. X and Y may overlap, but not X + and Z or Y and Z. One guard digit is used. The error is less than one + ULP. */ +void +SECTION +__add (const mp_no *x, const mp_no *y, mp_no *z, int p) +{ + int n; + + if (X[0] == 0) + { + __cpy (y, z, p); + return; + } + else if (Y[0] == 0) + { + __cpy (x, z, p); + return; + } + + if (X[0] == Y[0]) + { + if (__acr (x, y, p) > 0) + { + add_magnitudes (x, y, z, p); + Z[0] = X[0]; + } + else + { + add_magnitudes (y, x, z, p); + Z[0] = Y[0]; + } + } + else + { + if ((n = __acr (x, y, p)) == 1) + { + sub_magnitudes (x, y, z, p); + Z[0] = X[0]; + } + else if (n == -1) + { + sub_magnitudes (y, x, z, p); + Z[0] = Y[0]; + } + else + Z[0] = 0; + } +} + +/* Subtract *Y from *X and return the result in *Z. X and Y may overlap but + not X and Z or Y and Z. One guard digit is used. The error is less than + one ULP. */ +void +SECTION +__sub (const mp_no *x, const mp_no *y, mp_no *z, int p) +{ + int n; + + if (X[0] == 0) + { + __cpy (y, z, p); + Z[0] = -Z[0]; + return; + } + else if (Y[0] == 0) + { + __cpy (x, z, p); + return; + } + + if (X[0] != Y[0]) + { + if (__acr (x, y, p) > 0) + { + add_magnitudes (x, y, z, p); + Z[0] = X[0]; + } + else + { + add_magnitudes (y, x, z, p); + Z[0] = -Y[0]; + } + } + else + { + if ((n = __acr (x, y, p)) == 1) + { + sub_magnitudes (x, y, z, p); + Z[0] = X[0]; + } + else if (n == -1) + { + sub_magnitudes (y, x, z, p); + Z[0] = -Y[0]; + } + else + Z[0] = 0; + } +} + +#ifndef NO__MUL +/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X + and Z or Y and Z. For P in [1, 2, 3], the exact result is truncated to P + digits. In case P > 3 the error is bounded by 1.001 ULP. */ +void +SECTION +__mul (const mp_no *x, const mp_no *y, mp_no *z, int p) +{ + long i, j, k, ip, ip2; + long p2 = p; + mantissa_store_t zk; + const mp_no *a; + mantissa_store_t *diag; + + /* Is z=0? */ + if (__glibc_unlikely (X[0] * Y[0] == 0)) + { + Z[0] = 0; + return; + } + + /* We need not iterate through all X's and Y's since it's pointless to + multiply zeroes. Here, both are zero... */ + for (ip2 = p2; ip2 > 0; ip2--) + if (X[ip2] != 0 || Y[ip2] != 0) + break; + + a = X[ip2] != 0 ? y : x; + + /* ... and here, at least one of them is still zero. */ + for (ip = ip2; ip > 0; ip--) + if (a->d[ip] != 0) + break; + + /* The product looks like this for p = 3 (as an example): + + + a1 a2 a3 + x b1 b2 b3 + ----------------------------- + a1*b3 a2*b3 a3*b3 + a1*b2 a2*b2 a3*b2 + a1*b1 a2*b1 a3*b1 + + So our K needs to ideally be P*2, but we're limiting ourselves to P + 3 + for P >= 3. We compute the above digits in two parts; the last P-1 + digits and then the first P digits. The last P-1 digits are a sum of + products of the input digits from P to P-k where K is 0 for the least + significant digit and increases as we go towards the left. The product + term is of the form X[k]*X[P-k] as can be seen in the above example. + + The first P digits are also a sum of products with the same product term, + except that the sum is from 1 to k. This is also evident from the above + example. + + Another thing that becomes evident is that only the most significant + ip+ip2 digits of the result are non-zero, where ip and ip2 are the + 'internal precision' of the input numbers, i.e. digits after ip and ip2 + are all 0. */ + + k = (__glibc_unlikely (p2 < 3)) ? p2 + p2 : p2 + 3; + + while (k > ip + ip2 + 1) + Z[k--] = 0; + + zk = 0; + + /* Precompute sums of diagonal elements so that we can directly use them + later. See the next comment to know we why need them. */ + diag = alloca (k * sizeof (mantissa_store_t)); + mantissa_store_t d = 0; + for (i = 1; i <= ip; i++) + { + d += X[i] * (mantissa_store_t) Y[i]; + diag[i] = d; + } + while (i < k) + diag[i++] = d; + + while (k > p2) + { + long lim = k / 2; + + if (k % 2 == 0) + /* We want to add this only once, but since we subtract it in the sum + of products above, we add twice. */ + zk += 2 * X[lim] * (mantissa_store_t) Y[lim]; + + for (i = k - p2, j = p2; i < j; i++, j--) + zk += (X[i] + X[j]) * (mantissa_store_t) (Y[i] + Y[j]); + + zk -= diag[k - 1]; + + DIV_RADIX (zk, Z[k]); + k--; + } + + /* The real deal. Mantissa digit Z[k] is the sum of all X[i] * Y[j] where i + goes from 1 -> k - 1 and j goes the same range in reverse. To reduce the + number of multiplications, we halve the range and if k is an even number, + add the diagonal element X[k/2]Y[k/2]. Through the half range, we compute + X[i] * Y[j] as (X[i] + X[j]) * (Y[i] + Y[j]) - X[i] * Y[i] - X[j] * Y[j]. + + This reduction tells us that we're summing two things, the first term + through the half range and the negative of the sum of the product of all + terms of X and Y in the full range. i.e. + + SUM(X[i] * Y[i]) for k terms. This is precalculated above for each k in + a single loop so that it completes in O(n) time and can hence be directly + used in the loop below. */ + while (k > 1) + { + long lim = k / 2; + + if (k % 2 == 0) + /* We want to add this only once, but since we subtract it in the sum + of products above, we add twice. */ + zk += 2 * X[lim] * (mantissa_store_t) Y[lim]; + + for (i = 1, j = k - 1; i < j; i++, j--) + zk += (X[i] + X[j]) * (mantissa_store_t) (Y[i] + Y[j]); + + zk -= diag[k - 1]; + + DIV_RADIX (zk, Z[k]); + k--; + } + Z[k] = zk; + + /* Get the exponent sum into an intermediate variable. This is a subtle + optimization, where given enough registers, all operations on the exponent + happen in registers and the result is written out only once into EZ. */ + int e = EX + EY; + + /* Is there a carry beyond the most significant digit? */ + if (__glibc_unlikely (Z[1] == 0)) + { + for (i = 1; i <= p2; i++) + Z[i] = Z[i + 1]; + e--; + } + + EZ = e; + Z[0] = X[0] * Y[0]; +} +#endif + +#ifndef NO__SQR +/* Square *X and store result in *Y. X and Y may not overlap. For P in + [1, 2, 3], the exact result is truncated to P digits. In case P > 3 the + error is bounded by 1.001 ULP. This is a faster special case of + multiplication. */ +void +SECTION +__sqr (const mp_no *x, mp_no *y, int p) +{ + long i, j, k, ip; + mantissa_store_t yk; + + /* Is z=0? */ + if (__glibc_unlikely (X[0] == 0)) + { + Y[0] = 0; + return; + } + + /* We need not iterate through all X's since it's pointless to + multiply zeroes. */ + for (ip = p; ip > 0; ip--) + if (X[ip] != 0) + break; + + k = (__glibc_unlikely (p < 3)) ? p + p : p + 3; + + while (k > 2 * ip + 1) + Y[k--] = 0; + + yk = 0; + + while (k > p) + { + mantissa_store_t yk2 = 0; + long lim = k / 2; + + if (k % 2 == 0) + yk += X[lim] * (mantissa_store_t) X[lim]; + + /* In __mul, this loop (and the one within the next while loop) run + between a range to calculate the mantissa as follows: + + Z[k] = X[k] * Y[n] + X[k+1] * Y[n-1] ... + X[n-1] * Y[k+1] + + X[n] * Y[k] + + For X == Y, we can get away with summing halfway and doubling the + result. For cases where the range size is even, the mid-point needs + to be added separately (above). */ + for (i = k - p, j = p; i < j; i++, j--) + yk2 += X[i] * (mantissa_store_t) X[j]; + + yk += 2 * yk2; + + DIV_RADIX (yk, Y[k]); + k--; + } + + while (k > 1) + { + mantissa_store_t yk2 = 0; + long lim = k / 2; + + if (k % 2 == 0) + yk += X[lim] * (mantissa_store_t) X[lim]; + + /* Likewise for this loop. */ + for (i = 1, j = k - 1; i < j; i++, j--) + yk2 += X[i] * (mantissa_store_t) X[j]; + + yk += 2 * yk2; + + DIV_RADIX (yk, Y[k]); + k--; + } + Y[k] = yk; + + /* Squares are always positive. */ + Y[0] = 1; + + /* Get the exponent sum into an intermediate variable. This is a subtle + optimization, where given enough registers, all operations on the exponent + happen in registers and the result is written out only once into EZ. */ + int e = EX * 2; + + /* Is there a carry beyond the most significant digit? */ + if (__glibc_unlikely (Y[1] == 0)) + { + for (i = 1; i <= p; i++) + Y[i] = Y[i + 1]; + e--; + } + + EY = e; +} +#endif + +/* Invert *X and store in *Y. Relative error bound: + - For P = 2: 1.001 * R ^ (1 - P) + - For P = 3: 1.063 * R ^ (1 - P) + - For P > 3: 2.001 * R ^ (1 - P) + + *X = 0 is not permissible. */ +static void +SECTION +__inv (const mp_no *x, mp_no *y, int p) +{ + long i; + double t; + mp_no z, w; + static const int np1[] = + { 0, 0, 0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, + 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 + }; + + __cpy (x, &z, p); + z.e = 0; + __mp_dbl (&z, &t, p); + t = 1 / t; + __dbl_mp (t, y, p); + EY -= EX; + + for (i = 0; i < np1[p]; i++) + { + __cpy (y, &w, p); + __mul (x, &w, y, p); + __sub (&__mptwo, y, &z, p); + __mul (&w, &z, y, p); + } +} + +/* Divide *X by *Y and store result in *Z. X and Y may overlap but not X and Z + or Y and Z. Relative error bound: + - For P = 2: 2.001 * R ^ (1 - P) + - For P = 3: 2.063 * R ^ (1 - P) + - For P > 3: 3.001 * R ^ (1 - P) + + *X = 0 is not permissible. */ +void +SECTION +__dvd (const mp_no *x, const mp_no *y, mp_no *z, int p) +{ + mp_no w; + + if (X[0] == 0) + Z[0] = 0; + else + { + __inv (y, &w, p); + __mul (x, &w, z, p); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpa.h b/REORG.TODO/sysdeps/ieee754/dbl-64/mpa.h new file mode 100644 index 0000000000..a665e6b8f7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpa.h @@ -0,0 +1,154 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: mpa.h */ +/* */ +/* FUNCTIONS: */ +/* mcr */ +/* acr */ +/* cpy */ +/* mp_dbl */ +/* dbl_mp */ +/* add */ +/* sub */ +/* mul */ +/* dvd */ +/* */ +/* Arithmetic functions for multiple precision numbers. */ +/* Common types and definition */ +/************************************************************************/ + +#include <mpa-arch.h> + +/* The mp_no structure holds the details of a multi-precision floating point + number. + + - The radix of the number (R) is 2 ^ 24. + + - E: The exponent of the number. + + - D[0]: The sign (-1, 1) or 0 if the value is 0. In the latter case, the + values of the remaining members of the structure are ignored. + + - D[1] - D[p]: The mantissa of the number where: + + 0 <= D[i] < R and + P is the precision of the number and 1 <= p <= 32 + + D[p+1] ... D[39] have no significance. + + - The value of the number is: + + D[1] * R ^ (E - 1) + D[2] * R ^ (E - 2) ... D[p] * R ^ (E - p) + + */ +typedef struct +{ + int e; + mantissa_t d[40]; +} mp_no; + +typedef union +{ + int i[2]; + double d; +} number; + +extern const mp_no __mpone; +extern const mp_no __mptwo; + +#define X x->d +#define Y y->d +#define Z z->d +#define EX x->e +#define EY y->e +#define EZ z->e + +#ifndef RADIXI +# define RADIXI 0x1.0p-24 /* 2^-24 */ +#endif + +#ifndef TWO52 +# define TWO52 0x1.0p52 /* 2^52 */ +#endif + +#define TWO5 TWOPOW (5) /* 2^5 */ +#define TWO8 TWOPOW (8) /* 2^52 */ +#define TWO10 TWOPOW (10) /* 2^10 */ +#define TWO18 TWOPOW (18) /* 2^18 */ +#define TWO19 TWOPOW (19) /* 2^19 */ +#define TWO23 TWOPOW (23) /* 2^23 */ + +#define HALFRAD TWO23 + +#define TWO57 0x1.0p57 /* 2^57 */ +#define TWO71 0x1.0p71 /* 2^71 */ +#define TWOM1032 0x1.0p-1032 /* 2^-1032 */ +#define TWOM1022 0x1.0p-1022 /* 2^-1022 */ + +#define HALF 0x1.0p-1 /* 1/2 */ +#define MHALF -0x1.0p-1 /* -1/2 */ + +int __acr (const mp_no *, const mp_no *, int); +void __cpy (const mp_no *, mp_no *, int); +void __mp_dbl (const mp_no *, double *, int); +void __dbl_mp (double, mp_no *, int); +void __add (const mp_no *, const mp_no *, mp_no *, int); +void __sub (const mp_no *, const mp_no *, mp_no *, int); +void __mul (const mp_no *, const mp_no *, mp_no *, int); +void __sqr (const mp_no *, mp_no *, int); +void __dvd (const mp_no *, const mp_no *, mp_no *, int); + +extern void __mpatan (mp_no *, mp_no *, int); +extern void __mpatan2 (mp_no *, mp_no *, mp_no *, int); +extern void __mpsqrt (mp_no *, mp_no *, int); +extern void __mpexp (mp_no *, mp_no *, int); +extern void __c32 (mp_no *, mp_no *, mp_no *, int); +extern int __mpranred (double, mp_no *, int); + +/* Given a power POW, build a multiprecision number 2^POW. */ +static inline void +__pow_mp (int pow, mp_no *y, int p) +{ + int i, rem; + + /* The exponent is E such that E is a factor of 2^24. The remainder (of the + form 2^x) goes entirely into the first digit of the mantissa as it is + always less than 2^24. */ + EY = pow / 24; + rem = pow - EY * 24; + EY++; + + /* If the remainder is negative, it means that POW was negative since + |EY * 24| <= |pow|. Adjust so that REM is positive and still less than + 24 because of which, the mantissa digit is less than 2^24. */ + if (rem < 0) + { + EY--; + rem += 24; + } + /* The sign of any 2^x is always positive. */ + Y[0] = 1; + Y[1] = 1 << rem; + + /* Everything else is 0. */ + for (i = 2; i <= p; i++) + Y[i] = 0; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan.c new file mode 100644 index 0000000000..b84fbc5e41 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan.c @@ -0,0 +1,116 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/******************************************************************/ +/* */ +/* MODULE_NAME:mpatan.c */ +/* */ +/* FUNCTIONS:mpatan */ +/* */ +/* FILES NEEDED: mpa.h endian.h mpatan.h */ +/* mpa.c */ +/* */ +/* Multi-Precision Atan function subroutine, for precision p >= 4.*/ +/* The relative error of the result is bounded by 34.32*r**(1-p), */ +/* where r=2**24. */ +/******************************************************************/ + +#include "endian.h" +#include "mpa.h" +#include <math.h> + +#ifndef SECTION +# define SECTION +#endif + +#include "mpatan.h" + +void +SECTION +__mpatan (mp_no *x, mp_no *y, int p) +{ + int i, m, n; + double dx; + mp_no mptwoim1 = + { + 0, + { + 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 + } + }; + + mp_no mps, mpsm, mpt, mpt1, mpt2, mpt3; + + /* Choose m and initiate mptwoim1. */ + if (EX > 0) + m = 7; + else if (EX < 0) + m = 0; + else + { + __mp_dbl (x, &dx, p); + dx = fabs (dx); + for (m = 6; m > 0; m--) + { + if (dx > __atan_xm[m].d) + break; + } + } + mptwoim1.e = 1; + mptwoim1.d[0] = 1; + + /* Reduce x m times. */ + __sqr (x, &mpsm, p); + if (m == 0) + __cpy (x, &mps, p); + else + { + for (i = 0; i < m; i++) + { + __add (&__mpone, &mpsm, &mpt1, p); + __mpsqrt (&mpt1, &mpt2, p); + __add (&mpt2, &mpt2, &mpt1, p); + __add (&__mptwo, &mpsm, &mpt2, p); + __add (&mpt1, &mpt2, &mpt3, p); + __dvd (&mpsm, &mpt3, &mpt1, p); + __cpy (&mpt1, &mpsm, p); + } + __mpsqrt (&mpsm, &mps, p); + mps.d[0] = X[0]; + } + + /* Evaluate a truncated power series for Atan(s). */ + n = __atan_np[p]; + mptwoim1.d[1] = __atan_twonm1[p].d; + __dvd (&mpsm, &mptwoim1, &mpt, p); + for (i = n - 1; i > 1; i--) + { + mptwoim1.d[1] -= 2; + __dvd (&mpsm, &mptwoim1, &mpt1, p); + __mul (&mpsm, &mpt, &mpt2, p); + __sub (&mpt1, &mpt2, &mpt, p); + } + __mul (&mps, &mpt, &mpt1, p); + __sub (&mps, &mpt1, &mpt, p); + + /* Compute Atan(x). */ + mptwoim1.d[1] = 1 << m; + __mul (&mptwoim1, &mpt, y, p); +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan.h b/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan.h new file mode 100644 index 0000000000..65c856be17 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan.h @@ -0,0 +1,145 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:mpatan.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef MPATAN_H +#define MPATAN_H + +extern const number __atan_xm[8] attribute_hidden; +extern const number __atan_twonm1[33] attribute_hidden; +extern const number __atan_twom[8] attribute_hidden; +extern const int __atan_np[33] attribute_hidden; + + +#ifndef AVOID_MPATAN_H +#ifdef BIG_ENDI + const number + __atan_xm[8] = { /* x[m] */ +/**/ {{0x00000000, 0x00000000} }, /* 0.0 */ +/**/ {{0x3f8930be, 0x00000000} }, /* 0.0123 */ +/**/ {{0x3f991687, 0x00000000} }, /* 0.0245 */ +/**/ {{0x3fa923a2, 0x00000000} }, /* 0.0491 */ +/**/ {{0x3fb930be, 0x00000000} }, /* 0.0984 */ +/**/ {{0x3fc95810, 0x00000000} }, /* 0.198 */ +/**/ {{0x3fda7ef9, 0x00000000} }, /* 0.414 */ +/**/ {{0x3ff00000, 0x00000000} }, /* 1.0 */ + }; + const number + __atan_twonm1[33] = { /* 2n-1 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x40260000, 0x00000000} }, /* 11 */ +/**/ {{0x402e0000, 0x00000000} }, /* 15 */ +/**/ {{0x40330000, 0x00000000} }, /* 19 */ +/**/ {{0x40350000, 0x00000000} }, /* 21 */ +/**/ {{0x40390000, 0x00000000} }, /* 25 */ +/**/ {{0x403d0000, 0x00000000} }, /* 29 */ +/**/ {{0x40408000, 0x00000000} }, /* 33 */ +/**/ {{0x40428000, 0x00000000} }, /* 37 */ +/**/ {{0x40448000, 0x00000000} }, /* 41 */ +/**/ {{0x40468000, 0x00000000} }, /* 45 */ +/**/ {{0x40488000, 0x00000000} }, /* 49 */ +/**/ {{0x404a8000, 0x00000000} }, /* 53 */ +/**/ {{0x404b8000, 0x00000000} }, /* 55 */ +/**/ {{0x404d8000, 0x00000000} }, /* 59 */ +/**/ {{0x404f8000, 0x00000000} }, /* 63 */ +/**/ {{0x4050c000, 0x00000000} }, /* 67 */ +/**/ {{0x4051c000, 0x00000000} }, /* 71 */ +/**/ {{0x4052c000, 0x00000000} }, /* 75 */ +/**/ {{0x4053c000, 0x00000000} }, /* 79 */ +/**/ {{0x4054c000, 0x00000000} }, /* 83 */ +/**/ {{0x40554000, 0x00000000} }, /* 85 */ +/**/ {{0x40564000, 0x00000000} }, /* 89 */ +/**/ {{0x40574000, 0x00000000} }, /* 93 */ +/**/ {{0x40584000, 0x00000000} }, /* 97 */ +/**/ {{0x40594000, 0x00000000} }, /* 101 */ +/**/ {{0x405a4000, 0x00000000} }, /* 105 */ +/**/ {{0x405b4000, 0x00000000} }, /* 109 */ +/**/ {{0x405c4000, 0x00000000} }, /* 113 */ +/**/ {{0x405d4000, 0x00000000} }, /* 117 */ + }; + +#else +#ifdef LITTLE_ENDI + + const number + __atan_xm[8] = { /* x[m] */ +/**/ {{0x00000000, 0x00000000} }, /* 0.0 */ +/**/ {{0x00000000, 0x3f8930be} }, /* 0.0123 */ +/**/ {{0x00000000, 0x3f991687} }, /* 0.0245 */ +/**/ {{0x00000000, 0x3fa923a2} }, /* 0.0491 */ +/**/ {{0x00000000, 0x3fb930be} }, /* 0.0984 */ +/**/ {{0x00000000, 0x3fc95810} }, /* 0.198 */ +/**/ {{0x00000000, 0x3fda7ef9} }, /* 0.414 */ +/**/ {{0x00000000, 0x3ff00000} }, /* 1.0 */ + }; + const number +__atan_twonm1[33] = { /* 2n-1 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x40260000} }, /* 11 */ +/**/ {{0x00000000, 0x402e0000} }, /* 15 */ +/**/ {{0x00000000, 0x40330000} }, /* 19 */ +/**/ {{0x00000000, 0x40350000} }, /* 21 */ +/**/ {{0x00000000, 0x40390000} }, /* 25 */ +/**/ {{0x00000000, 0x403d0000} }, /* 29 */ +/**/ {{0x00000000, 0x40408000} }, /* 33 */ +/**/ {{0x00000000, 0x40428000} }, /* 37 */ +/**/ {{0x00000000, 0x40448000} }, /* 41 */ +/**/ {{0x00000000, 0x40468000} }, /* 45 */ +/**/ {{0x00000000, 0x40488000} }, /* 49 */ +/**/ {{0x00000000, 0x404a8000} }, /* 53 */ +/**/ {{0x00000000, 0x404b8000} }, /* 55 */ +/**/ {{0x00000000, 0x404d8000} }, /* 59 */ +/**/ {{0x00000000, 0x404f8000} }, /* 63 */ +/**/ {{0x00000000, 0x4050c000} }, /* 67 */ +/**/ {{0x00000000, 0x4051c000} }, /* 71 */ +/**/ {{0x00000000, 0x4052c000} }, /* 75 */ +/**/ {{0x00000000, 0x4053c000} }, /* 79 */ +/**/ {{0x00000000, 0x4054c000} }, /* 83 */ +/**/ {{0x00000000, 0x40554000} }, /* 85 */ +/**/ {{0x00000000, 0x40564000} }, /* 89 */ +/**/ {{0x00000000, 0x40574000} }, /* 93 */ +/**/ {{0x00000000, 0x40584000} }, /* 97 */ +/**/ {{0x00000000, 0x40594000} }, /* 101 */ +/**/ {{0x00000000, 0x405a4000} }, /* 105 */ +/**/ {{0x00000000, 0x405b4000} }, /* 109 */ +/**/ {{0x00000000, 0x405c4000} }, /* 113 */ +/**/ {{0x00000000, 0x405d4000} }, /* 117 */ + }; + +#endif +#endif + + const int + __atan_np[33] = { 0, 0, 0, 0, 6, 8,10,11,13,15,17,19,21,23,25,27,28, + 30,32,34,36,38,40,42,43,45,47,49,51,53,55,57,59}; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan2.c new file mode 100644 index 0000000000..94e4a66148 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan2.c @@ -0,0 +1,67 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/******************************************************************/ +/* MODULE_NAME: mpatan2.c */ +/* */ +/* FUNCTIONS:mpatan2 */ +/* */ +/* FILES NEEDED: mpa.h */ +/* mpa.c mpatan.c mpsqrt.c */ +/* */ +/* Multi-Precision Atan2(y,x) function subroutine, */ +/* for precision p >= 4. */ +/* y=0 is not permitted if x<=0. No error messages are given. */ +/* The relative error of the result is bounded by 44.84*r**(1-p) */ +/* if x <= 0, y != 0 and by 37.33*r**(1-p) if x>0. here r=2**24. */ +/* */ +/******************************************************************/ + +#include "mpa.h" + +#ifndef SECTION +# define SECTION +#endif + +/* Multi-Precision Atan2 (y, x) function subroutine, for p >= 4. + y = 0 is not permitted if x <= 0. No error messages are given. */ +void +SECTION +__mpatan2 (mp_no *y, mp_no *x, mp_no *z, int p) +{ + mp_no mpt1, mpt2, mpt3; + + if (X[0] <= 0) + { + __dvd (x, y, &mpt1, p); + __mul (&mpt1, &mpt1, &mpt2, p); + if (mpt1.d[0] != 0) + mpt1.d[0] = 1; + __add (&mpt2, &__mpone, &mpt3, p); + __mpsqrt (&mpt3, &mpt2, p); + __add (&mpt1, &mpt2, &mpt3, p); + mpt3.d[0] = Y[0]; + __mpatan (&mpt3, &mpt1, p); + __add (&mpt1, &mpt1, z, p); + } + else + { + __dvd (y, x, &mpt1, p); + __mpatan (&mpt1, z, p); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpexp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mpexp.c new file mode 100644 index 0000000000..e08f424133 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpexp.c @@ -0,0 +1,163 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*************************************************************************/ +/* MODULE_NAME:mpexp.c */ +/* */ +/* FUNCTIONS: mpexp */ +/* */ +/* FILES NEEDED: mpa.h endian.h mpexp.h */ +/* mpa.c */ +/* */ +/* Multi-Precision exponential function subroutine */ +/* ( for p >= 4, 2**(-55) <= abs(x) <= 1024 ). */ +/*************************************************************************/ + +#include "endian.h" +#include "mpa.h" +#include <assert.h> + +#ifndef SECTION +# define SECTION +#endif + +/* Multi-Precision exponential function subroutine (for p >= 4, + 2**(-55) <= abs(x) <= 1024). */ +void +SECTION +__mpexp (mp_no *x, mp_no *y, int p) +{ + int i, j, k, m, m1, m2, n; + mantissa_t b; + static const int np[33] = + { + 0, 0, 0, 0, 3, 3, 4, 4, 5, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, + 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8 + }; + + static const int m1p[33] = + { + 0, 0, 0, 0, + 17, 23, 23, 28, + 27, 38, 42, 39, + 43, 47, 43, 47, + 50, 54, 57, 60, + 64, 67, 71, 74, + 68, 71, 74, 77, + 70, 73, 76, 78, + 81 + }; + static const int m1np[7][18] = + { + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 36, 48, 60, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 24, 32, 40, 48, 56, 64, 72, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 17, 23, 29, 35, 41, 47, 53, 59, 65, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 23, 28, 33, 38, 42, 47, 52, 57, 62, 66, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 27, 0, 0, 39, 43, 47, 51, 55, 59, 63}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43, 47, 50, 54} + }; + mp_no mps, mpk, mpt1, mpt2; + + /* Choose m,n and compute a=2**(-m). */ + n = np[p]; + m1 = m1p[p]; + b = X[1]; + m2 = 24 * EX; + for (; b < HALFRAD; m2--) + b *= 2; + if (b == HALFRAD) + { + for (i = 2; i <= p; i++) + { + if (X[i] != 0) + break; + } + if (i == p + 1) + m2--; + } + + m = m1 + m2; + if (__glibc_unlikely (m <= 0)) + { + /* The m1np array which is used to determine if we can reduce the + polynomial expansion iterations, has only 18 elements. Besides, + numbers smaller than those required by p >= 18 should not come here + at all since the fast phase of exp returns 1.0 for anything less + than 2^-55. */ + assert (p < 18); + m = 0; + for (i = n - 1; i > 0; i--, n--) + if (m1np[i][p] + m2 > 0) + break; + } + + /* Compute s=x*2**(-m). Put result in mps. This is the range-reduced input + that we will use to compute e^s. For the final result, simply raise it + to 2^m. */ + __pow_mp (-m, &mpt1, p); + __mul (x, &mpt1, &mps, p); + + /* Compute the Taylor series for e^s: + + 1 + x/1! + x^2/2! + x^3/3! ... + + for N iterations. We compute this as: + + e^x = 1 + (x * n!/1! + x^2 * n!/2! + x^3 * n!/3!) / n! + = 1 + (x * (n!/1! + x * (n!/2! + x * (n!/3! + x ...)))) / n! + + k! is computed on the fly as KF and at the end of the polynomial loop, KF + is n!, which can be used directly. */ + __cpy (&mps, &mpt2, p); + + double kf = 1.0; + + /* Evaluate the rest. The result will be in mpt2. */ + for (k = n - 1; k > 0; k--) + { + /* n! / k! = n * (n - 1) ... * (n - k + 1) */ + kf *= k + 1; + + __dbl_mp (kf, &mpk, p); + __add (&mpt2, &mpk, &mpt1, p); + __mul (&mps, &mpt1, &mpt2, p); + } + __dbl_mp (kf, &mpk, p); + __dvd (&mpt2, &mpk, &mpt1, p); + __add (&__mpone, &mpt1, &mpt2, p); + + /* Raise polynomial value to the power of 2**m. Put result in y. */ + for (k = 0, j = 0; k < m;) + { + __sqr (&mpt2, &mpt1, p); + k++; + if (k == m) + { + j = 1; + break; + } + __sqr (&mpt1, &mpt2, p); + k++; + } + if (j) + __cpy (&mpt1, y, p); + else + __cpy (&mpt2, y, p); + return; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mplog.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mplog.c new file mode 100644 index 0000000000..5b03117d07 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mplog.c @@ -0,0 +1,65 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/************************************************************************/ +/* */ +/* MODULE_NAME:mplog.c */ +/* */ +/* FUNCTIONS: mplog */ +/* */ +/* FILES NEEDED: endian.h mpa.h mplog.h */ +/* mpexp.c */ +/* */ +/* Multi-Precision logarithm function subroutine (for precision p >= 4, */ +/* 2**(-1024) < x < 2**1024) and x is outside of the interval */ +/* [1-2**(-54),1+2**(-54)]. Upon entry, x should be set to the */ +/* multi-precision value of the input and y should be set into a multi- */ +/* precision value of an approximation of log(x) with relative error */ +/* bound of at most 2**(-52). The routine improves the accuracy of y. */ +/* */ +/************************************************************************/ +#include "endian.h" +#include "mpa.h" + +void +__mplog (mp_no *x, mp_no *y, int p) +{ + int i, m; + static const int mp[33] = + { + 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, + 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 + }; + mp_no mpt1, mpt2; + + /* Choose m. */ + m = mp[p]; + + /* Perform m newton iterations to solve for y: exp(y) - x = 0. The + iterations formula is: y(n + 1) = y(n) + (x * exp(-y(n)) - 1). */ + __cpy (y, &mpt1, p); + for (i = 0; i < m; i++) + { + mpt1.d[0] = -mpt1.d[0]; + __mpexp (&mpt1, &mpt2, p); + __mul (x, &mpt2, &mpt1, p); + __sub (&mpt1, &__mpone, &mpt2, p); + __add (y, &mpt2, &mpt1, p); + __cpy (&mpt1, y, p); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpn2dbl.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mpn2dbl.c new file mode 100644 index 0000000000..1fec0ce920 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpn2dbl.c @@ -0,0 +1,47 @@ +/* Copyright (C) 1995-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include <ieee754.h> +#include <float.h> + +/* Convert a multi-precision integer of the needed number of bits (53 for + double) and an integral power of two to a `double' in IEEE754 double- + precision format. */ + +double +__mpn_construct_double (mp_srcptr frac_ptr, int expt, int negative) +{ + union ieee754_double u; + + u.ieee.negative = negative; + u.ieee.exponent = expt + IEEE754_DOUBLE_BIAS; +#if BITS_PER_MP_LIMB == 32 + u.ieee.mantissa1 = frac_ptr[0]; + u.ieee.mantissa0 = frac_ptr[1] & (((mp_limb_t) 1 + << (DBL_MANT_DIG - 32)) - 1); +#elif BITS_PER_MP_LIMB == 64 + u.ieee.mantissa1 = frac_ptr[0] & (((mp_limb_t) 1 << 32) - 1); + u.ieee.mantissa0 = (frac_ptr[0] >> 32) & (((mp_limb_t) 1 + << (DBL_MANT_DIG - 32)) - 1); +#else + # error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif + + return u.d; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpsqrt.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mpsqrt.c new file mode 100644 index 0000000000..be6d01eeef --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpsqrt.c @@ -0,0 +1,111 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/****************************************************************************/ +/* MODULE_NAME:mpsqrt.c */ +/* */ +/* FUNCTION:mpsqrt */ +/* fastiroot */ +/* */ +/* FILES NEEDED:endian.h mpa.h mpsqrt.h */ +/* mpa.c */ +/* Multi-Precision square root function subroutine for precision p >= 4. */ +/* The relative error is bounded by 3.501*r**(1-p), where r=2**24. */ +/* */ +/****************************************************************************/ +#include "endian.h" +#include "mpa.h" + +#ifndef SECTION +# define SECTION +#endif + +#include "mpsqrt.h" + +/****************************************************************************/ +/* Multi-Precision square root function subroutine for precision p >= 4. */ +/* The relative error is bounded by 3.501*r**(1-p), where r=2**24. */ +/* Routine receives two pointers to Multi Precision numbers: */ +/* x (left argument) and y (next argument). Routine also receives precision */ +/* p as integer. Routine computes sqrt(*x) and stores result in *y */ +/****************************************************************************/ + +static double fastiroot (double); + +void +SECTION +__mpsqrt (mp_no *x, mp_no *y, int p) +{ + int i, m, ey; + double dx, dy; + static const mp_no mphalf = {0, {1.0, HALFRAD}}; + static const mp_no mp3halfs = {1, {1.0, 1.0, HALFRAD}}; + mp_no mpxn, mpz, mpu, mpt1, mpt2; + + ey = EX / 2; + __cpy (x, &mpxn, p); + mpxn.e -= (ey + ey); + __mp_dbl (&mpxn, &dx, p); + dy = fastiroot (dx); + __dbl_mp (dy, &mpu, p); + __mul (&mpxn, &mphalf, &mpz, p); + + m = __mpsqrt_mp[p]; + for (i = 0; i < m; i++) + { + __sqr (&mpu, &mpt1, p); + __mul (&mpt1, &mpz, &mpt2, p); + __sub (&mp3halfs, &mpt2, &mpt1, p); + __mul (&mpu, &mpt1, &mpt2, p); + __cpy (&mpt2, &mpu, p); + } + __mul (&mpxn, &mpu, y, p); + EY += ey; +} + +/***********************************************************/ +/* Compute a double precision approximation for 1/sqrt(x) */ +/* with the relative error bounded by 2**-51. */ +/***********************************************************/ +static double +SECTION +fastiroot (double x) +{ + union + { + int i[2]; + double d; + } p, q; + double y, z, t; + int n; + static const double c0 = 0.99674, c1 = -0.53380; + static const double c2 = 0.45472, c3 = -0.21553; + + p.d = x; + p.i[HIGH_HALF] = (p.i[HIGH_HALF] & 0x3FFFFFFF) | 0x3FE00000; + q.d = x; + y = p.d; + z = y - 1.0; + n = (q.i[HIGH_HALF] - p.i[HIGH_HALF]) >> 1; + z = ((c3 * z + c2) * z + c1) * z + c0; /* 2**-7 */ + z = z * (1.5 - 0.5 * y * z * z); /* 2**-14 */ + p.d = z * (1.5 - 0.5 * y * z * z); /* 2**-28 */ + p.i[HIGH_HALF] -= n; + t = x * p.d; + return p.d * (1.5 - 0.5 * p.d * t); +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpsqrt.h b/REORG.TODO/sysdeps/ieee754/dbl-64/mpsqrt.h new file mode 100644 index 0000000000..66c3dc684f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpsqrt.h @@ -0,0 +1,38 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:mpatan.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef MPSQRT_H +#define MPSQRT_H + +extern const int __mpsqrt_mp[33] attribute_hidden; + + +#ifndef AVOID_MPSQRT_H + const int __mpsqrt_mp[33] = {0,0,0,0,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4, + 4,4,4,4,4,4,4,4,4}; +#endif + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mptan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mptan.c new file mode 100644 index 0000000000..6976028f8f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mptan.c @@ -0,0 +1,63 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/**********************************************************************/ +/* MODULE_NAME:mptan.c */ +/* */ +/* FUNCTION: mptan */ +/* */ +/* FILES NEEDED: endian.h mpa.h */ +/* mpa.c sincos32.c branred.c */ +/* */ +/* Multi-Precision tan() function subroutine, for p=32. It is based */ +/* on the routines mpranred() and c32(). mpranred() performs range */ +/* reduction of a double number x into a multiple precision number */ +/* y, such that y=x-n*pi/2, abs(y)<pi/4, n=0,+-1,+-2,.... c32() */ +/* computes both sin(y), cos(y). tan(x) is either sin(y)/cos(y) */ +/* or -cos(y)/sin(y). The precision of the result is of about 559 */ +/* significant bits. */ +/* */ +/**********************************************************************/ +#include "endian.h" +#include "mpa.h" + +#ifndef SECTION +# define SECTION +#endif + +void +SECTION +__mptan (double x, mp_no *mpy, int p) +{ + int n; + mp_no mpw, mpc, mps; + + /* Negative or positive result. */ + n = __mpranred (x, &mpw, p) & 0x00000001; + /* Computing sin(x) and cos(x). */ + __c32 (&mpw, &mpc, &mps, p); + /* Second or fourth quarter of unit circle. */ + if (n) + { + __dvd (&mpc, &mps, mpy, p); + mpy->d[0] *= -1; + } + /* tan is negative in this area. */ + else + __dvd (&mps, &mpc, mpy, p); +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mydefs.h b/REORG.TODO/sysdeps/ieee754/dbl-64/mydefs.h new file mode 100644 index 0000000000..027398e861 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mydefs.h @@ -0,0 +1,35 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:mydefs.h */ +/* */ +/* common data and definition */ +/******************************************************************/ + +#ifndef MY_H +#define MY_H + +typedef int int4; +typedef union { int4 i[2]; double x; } mynumber; + +#define max(x, y) (((y) > (x)) ? (y) : (x)) +#define min(x, y) (((y) < (x)) ? (y) : (x)) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/powtwo.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/powtwo.tbl new file mode 100644 index 0000000000..7d5ae52174 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/powtwo.tbl @@ -0,0 +1,31 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE upow() FUNCTION */ +/****************************************************************/ + + + +static const double powtwo[] = { 1.0, 2.0, 4.0, + 8.0, 16.0, 32.0, 64.0, 128.0, + 256.0, 512.0, 1024.0, 2048.0, 4096.0, + 8192.0, 16384.0, 32768.0, 65536.0, 131072.0, + 262144.0, 524288.0, 1048576.0, 2097152.0, 4194304.0, + 8388608.0, 16777216.0, 33554432.0, 67108864.0, 134217728.0 }; diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/root.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/root.tbl new file mode 100644 index 0000000000..6d2760aa1f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/root.tbl @@ -0,0 +1,57 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE usqrt() FUNCTION */ +/****************************************************************/ + + +static const double inroot[128] = { + 1.40872145012100, 1.39792649065766, 1.38737595123859, 1.37706074531819, + 1.36697225234682, 1.35710228748795, 1.34744307370643, 1.33798721601135, + 1.32872767765984, 1.31965775814772, 1.31077107283046, 1.30206153403386, + 1.29352333352711, 1.28515092624400, 1.27693901514820, 1.26888253714903, + 1.26097664998256, 1.25321671998073, 1.24559831065844, 1.23811717205462, + 1.23076923076923, 1.22355058064300, 1.21645747403153, 1.20948631362953, + 1.20263364480453, 1.19589614840310, 1.18927063399547, 1.18275403352732, + 1.17634339535009, 1.17003587860341, 1.16382874792529, 1.15771936846787, + 1.15170520119791, 1.14578379846309, 1.13995279980655, 1.13420992801334, + 1.12855298537376, 1.12297985014975, 1.11748847323133, 1.11207687497107, + 1.10674314218572, 1.10148542531442, 1.09630193572405, 1.09119094315276, + 1.08615077328341, 1.08117980543918, 1.07627647039410, 1.07143924829188, + 1.06666666666667, 1.06195729855996, 1.05730976072814, 1.05272271193563, + 1.04819485132867, 1.04372491688551, 1.03931168393861, 1.03495396376504, + 1.03065060224133, 1.02640047855933, 1.02220250399990, 1.01805562076124, + 1.01395880083916, 1.00991104495649, 1.00591138153909, 1.00195886573624, + 0.99611649018350, 0.98848330114434, 0.98102294317595, 0.97372899112030, + 0.96659534932828, 0.95961623024651, 0.95278613468066, 0.94609983358253, + 0.93955235122353, 0.93313894963169, 0.92685511418159, 0.92069654023750, + 0.91465912076005, 0.90873893479530, 0.90293223677296, 0.89723544654727, + 0.89164514012056, 0.88615804099474, 0.88077101210109, 0.87548104826333, + 0.87028526915267, 0.86518091269740, 0.86016532891275, 0.85523597411976, + 0.85039040552437, 0.84562627613070, 0.84094132996422, 0.83633339758291, + 0.83180039185606, 0.82734030399203, 0.82295119979782, 0.81863121615464, + 0.81437855769486, 0.81019149366693, 0.80606835497581, 0.80200753138734, + 0.79800746888611, 0.79406666717674, 0.79018367731967, 0.78635709949278, + 0.78258558087123, 0.77886781361798, 0.77520253297841, 0.77158851547266, + 0.76802457717971, 0.76450957210799, 0.76104239064719, 0.75762195809661, + 0.75424723326565, 0.75091720714229, 0.74763090162560, 0.74438736831878, + 0.74118568737933, 0.73802496642311, 0.73490433947940, 0.73182296599416, + 0.72878002987884, 0.72577473860242, 0.72280632232420, 0.71987403306536, + 0.71697714391715, 0.71411494828392, 0.71128675915902, 0.70849190843208 }; diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_asinh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_asinh.c new file mode 100644 index 0000000000..9193301b5e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_asinh.c @@ -0,0 +1,72 @@ +/* @(#)s_asinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const double + one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ + ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ + huge = 1.00000000000000000000e+300; + +double +__asinh (double x) +{ + double w; + int32_t hx, ix; + GET_HIGH_WORD (hx, x); + ix = hx & 0x7fffffff; + if (__glibc_unlikely (ix < 0x3e300000)) /* |x|<2**-28 */ + { + math_check_force_underflow (x); + if (huge + x > one) + return x; /* return x inexact except 0 */ + } + if (__glibc_unlikely (ix > 0x41b00000)) /* |x| > 2**28 */ + { + if (ix >= 0x7ff00000) + return x + x; /* x is inf or NaN */ + w = __ieee754_log (fabs (x)) + ln2; + } + else + { + double xa = fabs (x); + if (ix > 0x40000000) /* 2**28 > |x| > 2.0 */ + { + w = __ieee754_log (2.0 * xa + one / (__ieee754_sqrt (xa * xa + one) + + xa)); + } + else /* 2.0 > |x| > 2**-28 */ + { + double t = xa * xa; + w = __log1p (xa + t / (one + __ieee754_sqrt (one + t))); + } + } + return __copysign (w, x); +} +weak_alias (__asinh, asinh) +#ifdef NO_LONG_DOUBLE +strong_alias (__asinh, __asinhl) +weak_alias (__asinh, asinhl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_atan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_atan.c new file mode 100644 index 0000000000..3641a35ce1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_atan.c @@ -0,0 +1,328 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/************************************************************************/ +/* MODULE_NAME: atnat.c */ +/* */ +/* FUNCTIONS: uatan */ +/* atanMp */ +/* signArctan */ +/* */ +/* */ +/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat.h */ +/* mpatan.c mpatan2.c mpsqrt.c */ +/* uatan.tbl */ +/* */ +/* An ultimate atan() routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of atan(x). */ +/* */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/************************************************************************/ + +#include <dla.h> +#include "mpa.h" +#include "MathLib.h" +#include "uatan.tbl" +#include "atnat.h" +#include <fenv.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <stap-probe.h> + +void __mpatan (mp_no *, mp_no *, int); /* see definition in mpatan.c */ +static double atanMp (double, const int[]); + + /* Fix the sign of y and return */ +static double +__signArctan (double x, double y) +{ + return __copysign (y, x); +} + + +/* An ultimate atan() routine. Given an IEEE double machine number x, */ +/* routine computes the correctly rounded (to nearest) value of atan(x). */ +double +atan (double x) +{ + double cor, s1, ss1, s2, ss2, t1, t2, t3, t7, t8, t9, t10, u, u2, u3, + v, vv, w, ww, y, yy, z, zz; +#ifndef DLA_FMS + double t4, t5, t6; +#endif + int i, ux, dx; + static const int pr[M] = { 6, 8, 10, 32 }; + number num; + + num.d = x; + ux = num.i[HIGH_HALF]; + dx = num.i[LOW_HALF]; + + /* x=NaN */ + if (((ux & 0x7ff00000) == 0x7ff00000) + && (((ux & 0x000fffff) | dx) != 0x00000000)) + return x + x; + + /* Regular values of x, including denormals +-0 and +-INF */ + SET_RESTORE_ROUND (FE_TONEAREST); + u = (x < 0) ? -x : x; + if (u < C) + { + if (u < B) + { + if (u < A) + { + math_check_force_underflow_nonneg (u); + return x; + } + else + { /* A <= u < B */ + v = x * x; + yy = d11.d + v * d13.d; + yy = d9.d + v * yy; + yy = d7.d + v * yy; + yy = d5.d + v * yy; + yy = d3.d + v * yy; + yy *= x * v; + + if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x)) + return y; + + EMULV (x, x, v, vv, t1, t2, t3, t4, t5); /* v+vv=x^2 */ + + s1 = f17.d + v * f19.d; + s1 = f15.d + v * s1; + s1 = f13.d + v * s1; + s1 = f11.d + v * s1; + s1 *= v; + + ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, + t8); + ADD2 (x, 0, s2, ss2, s1, ss1, t1, t2); + if ((y = s1 + (ss1 - U5 * s1)) == s1 + (ss1 + U5 * s1)) + return y; + + return atanMp (x, pr); + } + } + else + { /* B <= u < C */ + i = (TWO52 + TWO8 * u) - TWO52; + i -= 16; + z = u - cij[i][0].d; + yy = cij[i][5].d + z * cij[i][6].d; + yy = cij[i][4].d + z * yy; + yy = cij[i][3].d + z * yy; + yy = cij[i][2].d + z * yy; + yy *= z; + + t1 = cij[i][1].d; + if (i < 112) + { + if (i < 48) + u2 = U21; /* u < 1/4 */ + else + u2 = U22; + } /* 1/4 <= u < 1/2 */ + else + { + if (i < 176) + u2 = U23; /* 1/2 <= u < 3/4 */ + else + u2 = U24; + } /* 3/4 <= u <= 1 */ + if ((y = t1 + (yy - u2 * t1)) == t1 + (yy + u2 * t1)) + return __signArctan (x, y); + + z = u - hij[i][0].d; + + s1 = hij[i][14].d + z * hij[i][15].d; + s1 = hij[i][13].d + z * s1; + s1 = hij[i][12].d + z * s1; + s1 = hij[i][11].d + z * s1; + s1 *= z; + + ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); + MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + if ((y = s2 + (ss2 - U6 * s2)) == s2 + (ss2 + U6 * s2)) + return __signArctan (x, y); + + return atanMp (x, pr); + } + } + else + { + if (u < D) + { /* C <= u < D */ + w = 1 / u; + EMULV (w, u, t1, t2, t3, t4, t5, t6, t7); + ww = w * ((1 - t1) - t2); + i = (TWO52 + TWO8 * w) - TWO52; + i -= 16; + z = (w - cij[i][0].d) + ww; + + yy = cij[i][5].d + z * cij[i][6].d; + yy = cij[i][4].d + z * yy; + yy = cij[i][3].d + z * yy; + yy = cij[i][2].d + z * yy; + yy = HPI1 - z * yy; + + t1 = HPI - cij[i][1].d; + if (i < 112) + u3 = U31; /* w < 1/2 */ + else + u3 = U32; /* w >= 1/2 */ + if ((y = t1 + (yy - u3)) == t1 + (yy + u3)) + return __signArctan (x, y); + + DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + t1 = w - hij[i][0].d; + EADD (t1, ww, z, zz); + + s1 = hij[i][14].d + z * hij[i][15].d; + s1 = hij[i][13].d + z * s1; + s1 = hij[i][12].d + z * s1; + s1 = hij[i][11].d + z * s1; + s1 *= z; + + ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); + MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + SUB2 (HPI, HPI1, s2, ss2, s1, ss1, t1, t2); + if ((y = s1 + (ss1 - U7)) == s1 + (ss1 + U7)) + return __signArctan (x, y); + + return atanMp (x, pr); + } + else + { + if (u < E) + { /* D <= u < E */ + w = 1 / u; + v = w * w; + EMULV (w, u, t1, t2, t3, t4, t5, t6, t7); + + yy = d11.d + v * d13.d; + yy = d9.d + v * yy; + yy = d7.d + v * yy; + yy = d5.d + v * yy; + yy = d3.d + v * yy; + yy *= w * v; + + ww = w * ((1 - t1) - t2); + ESUB (HPI, w, t3, cor); + yy = ((HPI1 + cor) - ww) - yy; + if ((y = t3 + (yy - U4)) == t3 + (yy + U4)) + return __signArctan (x, y); + + DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, + t9, t10); + MUL2 (w, ww, w, ww, v, vv, t1, t2, t3, t4, t5, t6, t7, t8); + + s1 = f17.d + v * f19.d; + s1 = f15.d + v * s1; + s1 = f13.d + v * s1; + s1 = f11.d + v * s1; + s1 *= v; + + ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (w, ww, s2, ss2, s1, ss1, t1, t2); + SUB2 (HPI, HPI1, s1, ss1, s2, ss2, t1, t2); + + if ((y = s2 + (ss2 - U8)) == s2 + (ss2 + U8)) + return __signArctan (x, y); + + return atanMp (x, pr); + } + else + { + /* u >= E */ + if (x > 0) + return HPI; + else + return MHPI; + } + } + } +} + + /* Final stages. Compute atan(x) by multiple precision arithmetic */ +static double +atanMp (double x, const int pr[]) +{ + mp_no mpx, mpy, mpy2, mperr, mpt1, mpy1; + double y1, y2; + int i, p; + + for (i = 0; i < M; i++) + { + p = pr[i]; + __dbl_mp (x, &mpx, p); + __mpatan (&mpx, &mpy, p); + __dbl_mp (u9[i].d, &mpt1, p); + __mul (&mpy, &mpt1, &mperr, p); + __add (&mpy, &mperr, &mpy1, p); + __sub (&mpy, &mperr, &mpy2, p); + __mp_dbl (&mpy1, &y1, p); + __mp_dbl (&mpy2, &y2, p); + if (y1 == y2) + { + LIBC_PROBE (slowatan, 3, &p, &x, &y1); + return y1; + } + } + LIBC_PROBE (slowatan_inexact, 3, &p, &x, &y1); + return y1; /*if impossible to do exact computing */ +} + +#ifdef NO_LONG_DOUBLE +weak_alias (atan, atanl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_cbrt.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_cbrt.c new file mode 100644 index 0000000000..689abc89ec --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_cbrt.c @@ -0,0 +1,76 @@ +/* Compute cubic root of double value. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Dirk Alboth <dirka@uni-paderborn.de> and + Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + + +#define CBRT2 1.2599210498948731648 /* 2^(1/3) */ +#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */ + +static const double factor[5] = +{ + 1.0 / SQR_CBRT2, + 1.0 / CBRT2, + 1.0, + CBRT2, + SQR_CBRT2 +}; + + +double +__cbrt (double x) +{ + double xm, ym, u, t2; + int xe; + + /* Reduce X. XM now is an range 1.0 to 0.5. */ + xm = __frexp (fabs (x), &xe); + + /* If X is not finite or is null return it (with raising exceptions + if necessary. + Note: *Our* version of `frexp' sets XE to zero if the argument is + Inf or NaN. This is not portable but faster. */ + if (xe == 0 && fpclassify (x) <= FP_ZERO) + return x + x; + + u = (0.354895765043919860 + + ((1.50819193781584896 + + ((-2.11499494167371287 + + ((2.44693122563534430 + + ((-1.83469277483613086 + + (0.784932344976639262 - 0.145263899385486377 * xm) + * xm) + * xm)) + * xm)) + * xm)) + * xm)); + + t2 = u * u * u; + + ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3]; + + return __ldexp (x > 0.0 ? ym : -ym, xe / 3); +} +weak_alias (__cbrt, cbrt) +#ifdef NO_LONG_DOUBLE +strong_alias (__cbrt, __cbrtl) +weak_alias (__cbrt, cbrtl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_ceil.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_ceil.c new file mode 100644 index 0000000000..c291c26f57 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_ceil.c @@ -0,0 +1,89 @@ +/* @(#)s_ceil.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * ceil(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + */ + +#include <math.h> +#include <math_private.h> + +double +__ceil (double x) +{ + int32_t i0, i1, j0; + u_int32_t i, j; + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 20) + { + if (j0 < 0) + { + /* return 0*sign(x) if |x|<1 */ + if (i0 < 0) + { + i0 = 0x80000000; i1 = 0; + } + else if ((i0 | i1) != 0) + { + i0 = 0x3ff00000; i1 = 0; + } + } + else + { + i = (0x000fffff) >> j0; + if (((i0 & i) | i1) == 0) + return x; /* x is integral */ + if (i0 > 0) + i0 += (0x00100000) >> j0; + i0 &= (~i); i1 = 0; + } + } + else if (j0 > 51) + { + if (j0 == 0x400) + return x + x; /* inf or NaN */ + else + return x; /* x is integral */ + } + else + { + i = ((u_int32_t) (0xffffffff)) >> (j0 - 20); + if ((i1 & i) == 0) + return x; /* x is integral */ + if (i0 > 0) + { + if (j0 == 20) + i0 += 1; + else + { + j = i1 + (1 << (52 - j0)); + if (j < i1) + i0 += 1; /* got a carry */ + i1 = j; + } + } + i1 &= (~i); + } + INSERT_WORDS (x, i0, i1); + return x; +} +#ifndef __ceil +weak_alias (__ceil, ceil) +# ifdef NO_LONG_DOUBLE +strong_alias (__ceil, __ceill) +weak_alias (__ceil, ceill) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_copysign.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_copysign.c new file mode 100644 index 0000000000..9caf24e8f2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_copysign.c @@ -0,0 +1,39 @@ +/* @(#)s_copysign.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_copysign.c,v 1.8 1995/05/10 20:46:57 jtc Exp $"; +#endif + +/* + * copysign(double x, double y) + * copysign(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include <math.h> +#include <math_private.h> + +double +__copysign (double x, double y) +{ + u_int32_t hx, hy; + GET_HIGH_WORD (hx, x); + GET_HIGH_WORD (hy, y); + SET_HIGH_WORD (x, (hx & 0x7fffffff) | (hy & 0x80000000)); + return x; +} +weak_alias (__copysign, copysign) +#ifdef NO_LONG_DOUBLE +strong_alias (__copysign, __copysignl) +weak_alias (__copysign, copysignl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_cos.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_cos.c new file mode 100644 index 0000000000..4be1276ccb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_cos.c @@ -0,0 +1 @@ +/* In s_sin.c. */ diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_erf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_erf.c new file mode 100644 index 0000000000..b4975a8af8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_erf.c @@ -0,0 +1,428 @@ +/* @(#)s_erf.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; +#endif + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. For |x| in [0, 0.84375] + * erf(x) = x + x*R(x^2) + * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] + * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] + * where R = P/Q where P is an odd poly of degree 8 and + * Q is an odd poly of degree 10. + * -57.90 + * | R - (erf(x)-x)/x | <= 2 + * + * + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. The interval is chosen because the fix + * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is + * near 0.6174), and by some experiment, 0.84375 is chosen to + * guarantee the error is less than one ulp for erf. + * + * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(x) = sign(x) * (c + P1(s)/Q1(s)) + * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 + * 1+(c+P1(s)/Q1(s)) if x < 0 + * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06 + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * That is, we use rational approximation to approximate + * erf(1+s) - (c = (single)0.84506291151) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * where + * P1(s) = degree 6 poly in s + * Q1(s) = degree 6 poly in s + * + * 3. For x in [1.25,1/0.35(~2.857143)], + * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) + * erf(x) = 1 - erfc(x) + * where + * R1(z) = degree 7 poly in z, (z=1/x^2) + * S1(z) = degree 8 poly in z + * + * 4. For x in [1/0.35,28] + * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 + * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0 + * = 2.0 - tiny (if x <= -6) + * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else + * erf(x) = sign(x)*(1.0 - tiny) + * where + * R2(z) = degree 6 poly in z, (z=1/x^2) + * S2(z) = degree 7 poly in z + * + * Note1: + * To compute exp(-x*x-0.5625+R/S), let s be a single + * precision number and s := x; then + * -x*x = -s*s + (s-x)*(s+x) + * exp(-x*x-0.5626+R/S) = + * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); + * Note2: + * Here 4 and 5 make use of the asymptotic series + * exp(-x*x) + * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) + * x*sqrt(pi) + * We use rational approximation to approximate + * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625 + * Here is the error bound for R1/S1 and R2/S2 + * |R1/S1 - f(x)| < 2**(-62.57) + * |R2/S2 - f(x)| < 2**(-61.52) + * + * 5. For inf > x >= 28 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <fix-int-fp-convert-zero.h> + +static const double + tiny = 1e-300, + half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ + one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ + two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ +/* c = (float)0.84506291151 */ + erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ + efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ + pp[] = { 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ + -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ + -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ + -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ + -2.37630166566501626084e-05 }, /* 0xBEF8EAD6, 0x120016AC */ + qq[] = { 0.0, 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ + 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ + 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ + 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ + -3.96022827877536812320e-06 }, /* 0xBED09C43, 0x42A26120 */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ + pa[] = { -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ + 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ + -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ + 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ + -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ + 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ + -2.16637559486879084300e-03 }, /* 0xBF61BF38, 0x0A96073F */ + qa[] = { 0.0, 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ + 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ + 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ + 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ + 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ + 1.19844998467991074170e-02 }, /* 0x3F888B54, 0x5735151D */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ + ra[] = { -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ + -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ + -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ + -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ + -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ + -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ + -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ + -9.81432934416914548592e+00 }, /* 0xC023A0EF, 0xC69AC25C */ + sa[] = { 0.0, 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ + 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ + 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ + 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ + 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ + 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ + 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ + -6.04244152148580987438e-02 }, /* 0xBFAEEFF2, 0xEE749A62 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ + rb[] = { -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ + -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ + -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ + -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ + -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ + -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ + -4.83519191608651397019e+02 }, /* 0xC07E384E, 0x9BDC383F */ + sb[] = { 0.0, 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ + 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ + 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ + 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ + 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ + 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ + -2.24409524465858183362e+01 }; /* 0xC03670E2, 0x42712D62 */ + +double +__erf (double x) +{ + int32_t hx, ix, i; + double R, S, P, Q, s, y, z, r; + GET_HIGH_WORD (hx, x); + ix = hx & 0x7fffffff; + if (ix >= 0x7ff00000) /* erf(nan)=nan */ + { + i = ((u_int32_t) hx >> 31) << 1; + return (double) (1 - i) + one / x; /* erf(+-inf)=+-1 */ + } + + if (ix < 0x3feb0000) /* |x|<0.84375 */ + { + double r1, r2, s1, s2, s3, z2, z4; + if (ix < 0x3e300000) /* |x|<2**-28 */ + { + if (ix < 0x00800000) + { + /* Avoid spurious underflow. */ + double ret = 0.0625 * (16.0 * x + (16.0 * efx) * x); + math_check_force_underflow (ret); + return ret; + } + return x + efx * x; + } + z = x * x; + r1 = pp[0] + z * pp[1]; z2 = z * z; + r2 = pp[2] + z * pp[3]; z4 = z2 * z2; + s1 = one + z * qq[1]; + s2 = qq[2] + z * qq[3]; + s3 = qq[4] + z * qq[5]; + r = r1 + z2 * r2 + z4 * pp[4]; + s = s1 + z2 * s2 + z4 * s3; + y = r / s; + return x + x * y; + } + if (ix < 0x3ff40000) /* 0.84375 <= |x| < 1.25 */ + { + double s2, s4, s6, P1, P2, P3, P4, Q1, Q2, Q3, Q4; + s = fabs (x) - one; + P1 = pa[0] + s * pa[1]; s2 = s * s; + Q1 = one + s * qa[1]; s4 = s2 * s2; + P2 = pa[2] + s * pa[3]; s6 = s4 * s2; + Q2 = qa[2] + s * qa[3]; + P3 = pa[4] + s * pa[5]; + Q3 = qa[4] + s * qa[5]; + P4 = pa[6]; + Q4 = qa[6]; + P = P1 + s2 * P2 + s4 * P3 + s6 * P4; + Q = Q1 + s2 * Q2 + s4 * Q3 + s6 * Q4; + if (hx >= 0) + return erx + P / Q; + else + return -erx - P / Q; + } + if (ix >= 0x40180000) /* inf>|x|>=6 */ + { + if (hx >= 0) + return one - tiny; + else + return tiny - one; + } + x = fabs (x); + s = one / (x * x); + if (ix < 0x4006DB6E) /* |x| < 1/0.35 */ + { + double R1, R2, R3, R4, S1, S2, S3, S4, s2, s4, s6, s8; + R1 = ra[0] + s * ra[1]; s2 = s * s; + S1 = one + s * sa[1]; s4 = s2 * s2; + R2 = ra[2] + s * ra[3]; s6 = s4 * s2; + S2 = sa[2] + s * sa[3]; s8 = s4 * s4; + R3 = ra[4] + s * ra[5]; + S3 = sa[4] + s * sa[5]; + R4 = ra[6] + s * ra[7]; + S4 = sa[6] + s * sa[7]; + R = R1 + s2 * R2 + s4 * R3 + s6 * R4; + S = S1 + s2 * S2 + s4 * S3 + s6 * S4 + s8 * sa[8]; + } + else /* |x| >= 1/0.35 */ + { + double R1, R2, R3, S1, S2, S3, S4, s2, s4, s6; + R1 = rb[0] + s * rb[1]; s2 = s * s; + S1 = one + s * sb[1]; s4 = s2 * s2; + R2 = rb[2] + s * rb[3]; s6 = s4 * s2; + S2 = sb[2] + s * sb[3]; + R3 = rb[4] + s * rb[5]; + S3 = sb[4] + s * sb[5]; + S4 = sb[6] + s * sb[7]; + R = R1 + s2 * R2 + s4 * R3 + s6 * rb[6]; + S = S1 + s2 * S2 + s4 * S3 + s6 * S4; + } + z = x; + SET_LOW_WORD (z, 0); + r = __ieee754_exp (-z * z - 0.5625) * + __ieee754_exp ((z - x) * (z + x) + R / S); + if (hx >= 0) + return one - r / x; + else + return r / x - one; +} +weak_alias (__erf, erf) +#ifdef NO_LONG_DOUBLE +strong_alias (__erf, __erfl) +weak_alias (__erf, erfl) +#endif + +double +__erfc (double x) +{ + int32_t hx, ix; + double R, S, P, Q, s, y, z, r; + GET_HIGH_WORD (hx, x); + ix = hx & 0x7fffffff; + if (ix >= 0x7ff00000) /* erfc(nan)=nan */ + { /* erfc(+-inf)=0,2 */ + double ret = (double) (((u_int32_t) hx >> 31) << 1) + one / x; + if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0) + return 0.0; + return ret; + } + + if (ix < 0x3feb0000) /* |x|<0.84375 */ + { + double r1, r2, s1, s2, s3, z2, z4; + if (ix < 0x3c700000) /* |x|<2**-56 */ + return one - x; + z = x * x; + r1 = pp[0] + z * pp[1]; z2 = z * z; + r2 = pp[2] + z * pp[3]; z4 = z2 * z2; + s1 = one + z * qq[1]; + s2 = qq[2] + z * qq[3]; + s3 = qq[4] + z * qq[5]; + r = r1 + z2 * r2 + z4 * pp[4]; + s = s1 + z2 * s2 + z4 * s3; + y = r / s; + if (hx < 0x3fd00000) /* x<1/4 */ + { + return one - (x + x * y); + } + else + { + r = x * y; + r += (x - half); + return half - r; + } + } + if (ix < 0x3ff40000) /* 0.84375 <= |x| < 1.25 */ + { + double s2, s4, s6, P1, P2, P3, P4, Q1, Q2, Q3, Q4; + s = fabs (x) - one; + P1 = pa[0] + s * pa[1]; s2 = s * s; + Q1 = one + s * qa[1]; s4 = s2 * s2; + P2 = pa[2] + s * pa[3]; s6 = s4 * s2; + Q2 = qa[2] + s * qa[3]; + P3 = pa[4] + s * pa[5]; + Q3 = qa[4] + s * qa[5]; + P4 = pa[6]; + Q4 = qa[6]; + P = P1 + s2 * P2 + s4 * P3 + s6 * P4; + Q = Q1 + s2 * Q2 + s4 * Q3 + s6 * Q4; + if (hx >= 0) + { + z = one - erx; return z - P / Q; + } + else + { + z = erx + P / Q; return one + z; + } + } + if (ix < 0x403c0000) /* |x|<28 */ + { + x = fabs (x); + s = one / (x * x); + if (ix < 0x4006DB6D) /* |x| < 1/.35 ~ 2.857143*/ + { + double R1, R2, R3, R4, S1, S2, S3, S4, s2, s4, s6, s8; + R1 = ra[0] + s * ra[1]; s2 = s * s; + S1 = one + s * sa[1]; s4 = s2 * s2; + R2 = ra[2] + s * ra[3]; s6 = s4 * s2; + S2 = sa[2] + s * sa[3]; s8 = s4 * s4; + R3 = ra[4] + s * ra[5]; + S3 = sa[4] + s * sa[5]; + R4 = ra[6] + s * ra[7]; + S4 = sa[6] + s * sa[7]; + R = R1 + s2 * R2 + s4 * R3 + s6 * R4; + S = S1 + s2 * S2 + s4 * S3 + s6 * S4 + s8 * sa[8]; + } + else /* |x| >= 1/.35 ~ 2.857143 */ + { + double R1, R2, R3, S1, S2, S3, S4, s2, s4, s6; + if (hx < 0 && ix >= 0x40180000) + return two - tiny; /* x < -6 */ + R1 = rb[0] + s * rb[1]; s2 = s * s; + S1 = one + s * sb[1]; s4 = s2 * s2; + R2 = rb[2] + s * rb[3]; s6 = s4 * s2; + S2 = sb[2] + s * sb[3]; + R3 = rb[4] + s * rb[5]; + S3 = sb[4] + s * sb[5]; + S4 = sb[6] + s * sb[7]; + R = R1 + s2 * R2 + s4 * R3 + s6 * rb[6]; + S = S1 + s2 * S2 + s4 * S3 + s6 * S4; + } + z = x; + SET_LOW_WORD (z, 0); + r = __ieee754_exp (-z * z - 0.5625) * + __ieee754_exp ((z - x) * (z + x) + R / S); + if (hx > 0) + { + double ret = math_narrow_eval (r / x); + if (ret == 0) + __set_errno (ERANGE); + return ret; + } + else + return two - r / x; + } + else + { + if (hx > 0) + { + __set_errno (ERANGE); + return tiny * tiny; + } + else + return two - tiny; + } +} +weak_alias (__erfc, erfc) +#ifdef NO_LONG_DOUBLE +strong_alias (__erfc, __erfcl) +weak_alias (__erfc, erfcl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_expm1.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_expm1.c new file mode 100644 index 0000000000..54d771007a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_expm1.c @@ -0,0 +1,262 @@ +/* @(#)s_expm1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. + */ + +/* expm1(x) + * Returns exp(x)-1, the exponential of x minus 1. + * + * Method + * 1. Argument reduction: + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 + * + * Here a correction term c will be computed to compensate + * the error in r when rounded to a floating-point number. + * + * 2. Approximating expm1(r) by a special rational function on + * the interval [0,0.34658]: + * Since + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ... + * we define R1(r*r) by + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r) + * That is, + * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r) + * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r)) + * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... + * We use a special Reme algorithm on [0,0.347] to generate + * a polynomial of degree 5 in r*r to approximate R1. The + * maximum error of this polynomial approximation is bounded + * by 2**-61. In other words, + * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 + * where Q1 = -1.6666666666666567384E-2, + * Q2 = 3.9682539681370365873E-4, + * Q3 = -9.9206344733435987357E-6, + * Q4 = 2.5051361420808517002E-7, + * Q5 = -6.2843505682382617102E-9; + * (where z=r*r, and the values of Q1 to Q5 are listed below) + * with error bounded by + * | 5 | -61 + * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 + * | | + * + * expm1(r) = exp(r)-1 is then computed by the following + * specific way which minimize the accumulation rounding error: + * 2 3 + * r r [ 3 - (R1 + R1*r/2) ] + * expm1(r) = r + --- + --- * [--------------------] + * 2 2 [ 6 - r*(3 - R1*r/2) ] + * + * To compensate the error in the argument reduction, we use + * expm1(r+c) = expm1(r) + c + expm1(r)*c + * ~ expm1(r) + c + r*c + * Thus c+r*c will be added in as the correction terms for + * expm1(r+c). Now rearrange the term to avoid optimization + * screw up: + * ( 2 2 ) + * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) + * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) + * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) + * ( ) + * + * = r - E + * 3. Scale back to obtain expm1(x): + * From step 1, we have + * expm1(x) = either 2^k*[expm1(r)+1] - 1 + * = or 2^k*[expm1(r) + (1-2^-k)] + * 4. Implementation notes: + * (A). To save one multiplication, we scale the coefficient Qi + * to Qi*2^i, and replace z by (x^2)/2. + * (B). To achieve maximum accuracy, we compute expm1(x) by + * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf) + * (ii) if k=0, return r-E + * (iii) if k=-1, return 0.5*(r-E)-0.5 + * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) + * else return 1.0+2.0*(r-E); + * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1) + * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else + * (vii) return 2^k(1-((E+2^-k)-r)) + * + * Special cases: + * expm1(INF) is INF, expm1(NaN) is NaN; + * expm1(-INF) is -1, and + * for finite argument, only expm1(0)=0 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then expm1(x) overflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#define one Q[0] +static const double + huge = 1.0e+300, + tiny = 1.0e-300, + o_threshold = 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ + ln2_hi = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ + ln2_lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ + invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ +/* scaled coefficients related to expm1 */ + Q[] = { 1.0, -3.33333333333331316428e-02, /* BFA11111 111110F4 */ + 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ + -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ + 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ + -2.01099218183624371326e-07 }; /* BE8AFDB7 6E09C32D */ + +double +__expm1 (double x) +{ + double y, hi, lo, c, t, e, hxs, hfx, r1, h2, h4, R1, R2, R3; + int32_t k, xsb; + u_int32_t hx; + + GET_HIGH_WORD (hx, x); + xsb = hx & 0x80000000; /* sign bit of x */ + if (xsb == 0) + y = x; + else + y = -x; /* y = |x| */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if (hx >= 0x4043687A) /* if |x|>=56*ln2 */ + { + if (hx >= 0x40862E42) /* if |x|>=709.78... */ + { + if (hx >= 0x7ff00000) + { + u_int32_t low; + GET_LOW_WORD (low, x); + if (((hx & 0xfffff) | low) != 0) + return x + x; /* NaN */ + else + return (xsb == 0) ? x : -1.0; /* exp(+-inf)={inf,-1} */ + } + if (x > o_threshold) + { + __set_errno (ERANGE); + return huge * huge; /* overflow */ + } + } + if (xsb != 0) /* x < -56*ln2, return -1.0 with inexact */ + { + math_force_eval (x + tiny); /* raise inexact */ + return tiny - one; /* return -1 */ + } + } + + /* argument reduction */ + if (hx > 0x3fd62e42) /* if |x| > 0.5 ln2 */ + { + if (hx < 0x3FF0A2B2) /* and |x| < 1.5 ln2 */ + { + if (xsb == 0) + { + hi = x - ln2_hi; lo = ln2_lo; k = 1; + } + else + { + hi = x + ln2_hi; lo = -ln2_lo; k = -1; + } + } + else + { + k = invln2 * x + ((xsb == 0) ? 0.5 : -0.5); + t = k; + hi = x - t * ln2_hi; /* t*ln2_hi is exact here */ + lo = t * ln2_lo; + } + x = hi - lo; + c = (hi - x) - lo; + } + else if (hx < 0x3c900000) /* when |x|<2**-54, return x */ + { + math_check_force_underflow (x); + t = huge + x; /* return x with inexact flags when x!=0 */ + return x - (t - (huge + x)); + } + else + k = 0; + + /* x is now in primary range */ + hfx = 0.5 * x; + hxs = x * hfx; + R1 = one + hxs * Q[1]; h2 = hxs * hxs; + R2 = Q[2] + hxs * Q[3]; h4 = h2 * h2; + R3 = Q[4] + hxs * Q[5]; + r1 = R1 + h2 * R2 + h4 * R3; + t = 3.0 - r1 * hfx; + e = hxs * ((r1 - t) / (6.0 - x * t)); + if (k == 0) + return x - (x * e - hxs); /* c is 0 */ + else + { + e = (x * (e - c) - c); + e -= hxs; + if (k == -1) + return 0.5 * (x - e) - 0.5; + if (k == 1) + { + if (x < -0.25) + return -2.0 * (e - (x + 0.5)); + else + return one + 2.0 * (x - e); + } + if (k <= -2 || k > 56) /* suffice to return exp(x)-1 */ + { + u_int32_t high; + y = one - (e - x); + GET_HIGH_WORD (high, y); + SET_HIGH_WORD (y, high + (k << 20)); /* add k to y's exponent */ + return y - one; + } + t = one; + if (k < 20) + { + u_int32_t high; + SET_HIGH_WORD (t, 0x3ff00000 - (0x200000 >> k)); /* t=1-2^-k */ + y = t - (e - x); + GET_HIGH_WORD (high, y); + SET_HIGH_WORD (y, high + (k << 20)); /* add k to y's exponent */ + } + else + { + u_int32_t high; + SET_HIGH_WORD (t, ((0x3ff - k) << 20)); /* 2^-k */ + y = x - (e + t); + y += one; + GET_HIGH_WORD (high, y); + SET_HIGH_WORD (y, high + (k << 20)); /* add k to y's exponent */ + } + } + return y; +} +weak_alias (__expm1, expm1) +#ifdef NO_LONG_DOUBLE +strong_alias (__expm1, __expm1l) +weak_alias (__expm1, expm1l) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fabs.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fabs.c new file mode 100644 index 0000000000..73c09a269e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fabs.c @@ -0,0 +1,32 @@ +/* @(#)s_fabs.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_fabs.c,v 1.7 1995/05/10 20:47:13 jtc Exp $"; +#endif + +/* + * fabs(x) returns the absolute value of x. + */ + +#include <math.h> + +double +__fabs (double x) +{ + return __builtin_fabs (x); +} +weak_alias (__fabs, fabs) +#ifdef NO_LONG_DOUBLE +strong_alias (__fabs, __fabsl) +weak_alias (__fabs, fabsl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_finite.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_finite.c new file mode 100644 index 0000000000..69141db75d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_finite.c @@ -0,0 +1,50 @@ +/* @(#)s_finite.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_finite.c,v 1.8 1995/05/10 20:47:17 jtc Exp $"; +#endif + +/* + * finite(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <shlib-compat.h> + +#undef __finite + +#ifndef FINITE +# define FINITE __finite +#endif + +int FINITE(double x) +{ + int32_t hx; + GET_HIGH_WORD (hx, x); + return (int) ((u_int32_t) ((hx & 0x7ff00000) - 0x7ff00000) >> 31); +} +hidden_def (__finite) +weak_alias (__finite, finite) +#ifdef NO_LONG_DOUBLE +# ifdef LDBL_CLASSIFY_COMPAT +# if SHLIB_COMPAT (libc, GLIBC_2_0, GLIBC_2_23) +compat_symbol (libc, __finite, __finitel, GLIBC_2_0); +# endif +# if SHLIB_COMPAT (libm, GLIBC_2_1, GLIBC_2_23) +compat_symbol (libm, __finite, __finitel, GLIBC_2_1); +# endif +# endif +weak_alias (__finite, finitel) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_floor.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_floor.c new file mode 100644 index 0000000000..8f86aa31ee --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_floor.c @@ -0,0 +1,89 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * floor(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + */ + +#include <math.h> +#include <math_private.h> + +double +__floor (double x) +{ + int32_t i0, i1, j0; + u_int32_t i, j; + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 20) + { + if (j0 < 0) + { + /* return 0*sign(x) if |x|<1 */ + if (i0 >= 0) + { + i0 = i1 = 0; + } + else if (((i0 & 0x7fffffff) | i1) != 0) + { + i0 = 0xbff00000; i1 = 0; + } + } + else + { + i = (0x000fffff) >> j0; + if (((i0 & i) | i1) == 0) + return x; /* x is integral */ + if (i0 < 0) + i0 += (0x00100000) >> j0; + i0 &= (~i); i1 = 0; + } + } + else if (j0 > 51) + { + if (j0 == 0x400) + return x + x; /* inf or NaN */ + else + return x; /* x is integral */ + } + else + { + i = ((u_int32_t) (0xffffffff)) >> (j0 - 20); + if ((i1 & i) == 0) + return x; /* x is integral */ + if (i0 < 0) + { + if (j0 == 20) + i0 += 1; + else + { + j = i1 + (1 << (52 - j0)); + if (j < i1) + i0 += 1; /* got a carry */ + i1 = j; + } + } + i1 &= (~i); + } + INSERT_WORDS (x, i0, i1); + return x; +} +#ifndef __floor +weak_alias (__floor, floor) +# ifdef NO_LONG_DOUBLE +strong_alias (__floor, __floorl) +weak_alias (__floor, floorl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fma.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fma.c new file mode 100644 index 0000000000..68c8515fb1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fma.c @@ -0,0 +1,301 @@ +/* Compute x * y + z as ternary operation. + Copyright (C) 2010-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <fenv.h> +#include <ieee754.h> +#include <math_private.h> +#include <tininess.h> + +/* This implementation uses rounding to odd to avoid problems with + double rounding. See a paper by Boldo and Melquiond: + http://www.lri.fr/~melquion/doc/08-tc.pdf */ + +double +__fma (double x, double y, double z) +{ + union ieee754_double u, v, w; + int adjust = 0; + u.d = x; + v.d = y; + w.d = z; + if (__builtin_expect (u.ieee.exponent + v.ieee.exponent + >= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0) + || __builtin_expect (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0) + || __builtin_expect (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent + v.ieee.exponent + <= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG, 0)) + { + /* If z is Inf, but x and y are finite, the result should be + z rather than NaN. */ + if (w.ieee.exponent == 0x7ff + && u.ieee.exponent != 0x7ff + && v.ieee.exponent != 0x7ff) + return (z + x) + y; + /* If z is zero and x are y are nonzero, compute the result + as x * y to avoid the wrong sign of a zero result if x * y + underflows to 0. */ + if (z == 0 && x != 0 && y != 0) + return x * y; + /* If x or y or z is Inf/NaN, or if x * y is zero, compute as + x * y + z. */ + if (u.ieee.exponent == 0x7ff + || v.ieee.exponent == 0x7ff + || w.ieee.exponent == 0x7ff + || x == 0 + || y == 0) + return x * y + z; + /* If fma will certainly overflow, compute as x * y. */ + if (u.ieee.exponent + v.ieee.exponent > 0x7ff + IEEE754_DOUBLE_BIAS) + return x * y; + /* If x * y is less than 1/4 of DBL_TRUE_MIN, neither the + result nor whether there is underflow depends on its exact + value, only on its sign. */ + if (u.ieee.exponent + v.ieee.exponent + < IEEE754_DOUBLE_BIAS - DBL_MANT_DIG - 2) + { + int neg = u.ieee.negative ^ v.ieee.negative; + double tiny = neg ? -0x1p-1074 : 0x1p-1074; + if (w.ieee.exponent >= 3) + return tiny + z; + /* Scaling up, adding TINY and scaling down produces the + correct result, because in round-to-nearest mode adding + TINY has no effect and in other modes double rounding is + harmless. But it may not produce required underflow + exceptions. */ + v.d = z * 0x1p54 + tiny; + if (TININESS_AFTER_ROUNDING + ? v.ieee.exponent < 55 + : (w.ieee.exponent == 0 + || (w.ieee.exponent == 1 + && w.ieee.negative != neg + && w.ieee.mantissa1 == 0 + && w.ieee.mantissa0 == 0))) + { + double force_underflow = x * y; + math_force_eval (force_underflow); + } + return v.d * 0x1p-54; + } + if (u.ieee.exponent + v.ieee.exponent + >= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG) + { + /* Compute 1p-53 times smaller result and multiply + at the end. */ + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent -= DBL_MANT_DIG; + else + v.ieee.exponent -= DBL_MANT_DIG; + /* If x + y exponent is very large and z exponent is very small, + it doesn't matter if we don't adjust it. */ + if (w.ieee.exponent > DBL_MANT_DIG) + w.ieee.exponent -= DBL_MANT_DIG; + adjust = 1; + } + else if (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG) + { + /* Similarly. + If z exponent is very large and x and y exponents are + very small, adjust them up to avoid spurious underflows, + rather than down. */ + if (u.ieee.exponent + v.ieee.exponent + <= IEEE754_DOUBLE_BIAS + 2 * DBL_MANT_DIG) + { + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent += 2 * DBL_MANT_DIG + 2; + else + v.ieee.exponent += 2 * DBL_MANT_DIG + 2; + } + else if (u.ieee.exponent > v.ieee.exponent) + { + if (u.ieee.exponent > DBL_MANT_DIG) + u.ieee.exponent -= DBL_MANT_DIG; + } + else if (v.ieee.exponent > DBL_MANT_DIG) + v.ieee.exponent -= DBL_MANT_DIG; + w.ieee.exponent -= DBL_MANT_DIG; + adjust = 1; + } + else if (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG) + { + u.ieee.exponent -= DBL_MANT_DIG; + if (v.ieee.exponent) + v.ieee.exponent += DBL_MANT_DIG; + else + v.d *= 0x1p53; + } + else if (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG) + { + v.ieee.exponent -= DBL_MANT_DIG; + if (u.ieee.exponent) + u.ieee.exponent += DBL_MANT_DIG; + else + u.d *= 0x1p53; + } + else /* if (u.ieee.exponent + v.ieee.exponent + <= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG) */ + { + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent += 2 * DBL_MANT_DIG + 2; + else + v.ieee.exponent += 2 * DBL_MANT_DIG + 2; + if (w.ieee.exponent <= 4 * DBL_MANT_DIG + 6) + { + if (w.ieee.exponent) + w.ieee.exponent += 2 * DBL_MANT_DIG + 2; + else + w.d *= 0x1p108; + adjust = -1; + } + /* Otherwise x * y should just affect inexact + and nothing else. */ + } + x = u.d; + y = v.d; + z = w.d; + } + + /* Ensure correct sign of exact 0 + 0. */ + if (__glibc_unlikely ((x == 0 || y == 0) && z == 0)) + { + x = math_opt_barrier (x); + return x * y + z; + } + + fenv_t env; + libc_feholdexcept_setround (&env, FE_TONEAREST); + + /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ +#define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1) + double x1 = x * C; + double y1 = y * C; + double m1 = x * y; + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + double x2 = x - x1; + double y2 = y - y1; + double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2; + + /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */ + double a1 = z + m1; + double t1 = a1 - z; + double t2 = a1 - t1; + t1 = m1 - t1; + t2 = z - t2; + double a2 = t1 + t2; + /* Ensure the arithmetic is not scheduled after feclearexcept call. */ + math_force_eval (m2); + math_force_eval (a2); + feclearexcept (FE_INEXACT); + + /* If the result is an exact zero, ensure it has the correct sign. */ + if (a1 == 0 && m2 == 0) + { + libc_feupdateenv (&env); + /* Ensure that round-to-nearest value of z + m1 is not reused. */ + z = math_opt_barrier (z); + return z + m1; + } + + libc_fesetround (FE_TOWARDZERO); + + /* Perform m2 + a2 addition with round to odd. */ + u.d = a2 + m2; + + if (__glibc_unlikely (adjust < 0)) + { + if ((u.ieee.mantissa1 & 1) == 0) + u.ieee.mantissa1 |= libc_fetestexcept (FE_INEXACT) != 0; + v.d = a1 + u.d; + /* Ensure the addition is not scheduled after fetestexcept call. */ + math_force_eval (v.d); + } + + /* Reset rounding mode and test for inexact simultaneously. */ + int j = libc_feupdateenv_test (&env, FE_INEXACT) != 0; + + if (__glibc_likely (adjust == 0)) + { + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff) + u.ieee.mantissa1 |= j; + /* Result is a1 + u.d. */ + return a1 + u.d; + } + else if (__glibc_likely (adjust > 0)) + { + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff) + u.ieee.mantissa1 |= j; + /* Result is a1 + u.d, scaled up. */ + return (a1 + u.d) * 0x1p53; + } + else + { + /* If a1 + u.d is exact, the only rounding happens during + scaling down. */ + if (j == 0) + return v.d * 0x1p-108; + /* If result rounded to zero is not subnormal, no double + rounding will occur. */ + if (v.ieee.exponent > 108) + return (a1 + u.d) * 0x1p-108; + /* If v.d * 0x1p-108 with round to zero is a subnormal above + or equal to DBL_MIN / 2, then v.d * 0x1p-108 shifts mantissa + down just by 1 bit, which means v.ieee.mantissa1 |= j would + change the round bit, not sticky or guard bit. + v.d * 0x1p-108 never normalizes by shifting up, + so round bit plus sticky bit should be already enough + for proper rounding. */ + if (v.ieee.exponent == 108) + { + /* If the exponent would be in the normal range when + rounding to normal precision with unbounded exponent + range, the exact result is known and spurious underflows + must be avoided on systems detecting tininess after + rounding. */ + if (TININESS_AFTER_ROUNDING) + { + w.d = a1 + u.d; + if (w.ieee.exponent == 109) + return w.d * 0x1p-108; + } + /* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding, + v.ieee.mantissa1 & 1 is the round bit and j is our sticky + bit. */ + w.d = 0.0; + w.ieee.mantissa1 = ((v.ieee.mantissa1 & 3) << 1) | j; + w.ieee.negative = v.ieee.negative; + v.ieee.mantissa1 &= ~3U; + v.d *= 0x1p-108; + w.d *= 0x1p-2; + return v.d + w.d; + } + v.ieee.mantissa1 |= j; + return v.d * 0x1p-108; + } +} +#ifndef __fma +weak_alias (__fma, fma) +#endif + +#ifdef NO_LONG_DOUBLE +strong_alias (__fma, __fmal) +weak_alias (__fmal, fmal) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fmaf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fmaf.c new file mode 100644 index 0000000000..e6c0fed64d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fmaf.c @@ -0,0 +1,64 @@ +/* Compute x * y + z as ternary operation. + Copyright (C) 2010-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <fenv.h> +#include <ieee754.h> +#include <math_private.h> + +/* This implementation relies on double being more than twice as + precise as float and uses rounding to odd in order to avoid problems + with double rounding. + See a paper by Boldo and Melquiond: + http://www.lri.fr/~melquion/doc/08-tc.pdf */ + +float +__fmaf (float x, float y, float z) +{ + fenv_t env; + + /* Multiplication is always exact. */ + double temp = (double) x * (double) y; + + /* Ensure correct sign of an exact zero result by performing the + addition in the original rounding mode in that case. */ + if (temp == -z) + return (float) temp + z; + + union ieee754_double u; + + libc_feholdexcept_setround (&env, FE_TOWARDZERO); + + /* Perform addition with round to odd. */ + u.d = temp + (double) z; + /* Ensure the addition is not scheduled after fetestexcept call. */ + math_force_eval (u.d); + + /* Reset rounding mode and test for inexact simultaneously. */ + int j = libc_feupdateenv_test (&env, FE_INEXACT) != 0; + + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff) + u.ieee.mantissa1 |= j; + + /* And finally truncation with round to nearest. */ + return (float) u.d; +} +#ifndef __fmaf +weak_alias (__fmaf, fmaf) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fpclassify.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fpclassify.c new file mode 100644 index 0000000000..3fa9117ff0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fpclassify.c @@ -0,0 +1,43 @@ +/* Return classification value corresponding to argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +int +__fpclassify (double x) +{ + u_int32_t hx, lx; + int retval = FP_NORMAL; + + EXTRACT_WORDS (hx, lx, x); + lx |= hx & 0xfffff; + hx &= 0x7ff00000; + if ((hx | lx) == 0) + retval = FP_ZERO; + else if (hx == 0) + retval = FP_SUBNORMAL; + else if (hx == 0x7ff00000) + retval = lx != 0 ? FP_NAN : FP_INFINITE; + + return retval; +} +libm_hidden_def (__fpclassify) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_frexp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_frexp.c new file mode 100644 index 0000000000..874214ec7c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_frexp.c @@ -0,0 +1,58 @@ +/* @(#)s_frexp.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_frexp.c,v 1.9 1995/05/10 20:47:24 jtc Exp $"; +#endif + +/* + * for non-zero x + * x = frexp(arg,&exp); + * return a double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg + * with *exp=0. + */ + +#include <math.h> +#include <math_private.h> + +static const double + two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */ + +double +__frexp (double x, int *eptr) +{ + int32_t hx, ix, lx; + EXTRACT_WORDS (hx, lx, x); + ix = 0x7fffffff & hx; + *eptr = 0; + if (ix >= 0x7ff00000 || ((ix | lx) == 0)) + return x + x; /* 0,inf,nan */ + if (ix < 0x00100000) /* subnormal */ + { + x *= two54; + GET_HIGH_WORD (hx, x); + ix = hx & 0x7fffffff; + *eptr = -54; + } + *eptr += (ix >> 20) - 1022; + hx = (hx & 0x800fffff) | 0x3fe00000; + SET_HIGH_WORD (x, hx); + return x; +} +weak_alias (__frexp, frexp) +#ifdef NO_LONG_DOUBLE +strong_alias (__frexp, __frexpl) +weak_alias (__frexp, frexpl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfp.c new file mode 100644 index 0000000000..92fbe0c162 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfp.c @@ -0,0 +1,7 @@ +#define UNSIGNED 0 +#define INEXACT 0 +#define FUNC fromfp +#include <s_fromfp_main.c> +#ifdef NO_LONG_DOUBLE +weak_alias (fromfp, fromfpl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfp_main.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfp_main.c new file mode 100644 index 0000000000..ca0aa82092 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfp_main.c @@ -0,0 +1,82 @@ +/* Round to integer type. dbl-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <fenv.h> +#include <math.h> +#include <math_private.h> +#include <stdbool.h> +#include <stdint.h> + +#define BIAS 0x3ff +#define MANT_DIG 53 + +#if UNSIGNED +# define RET_TYPE uintmax_t +#else +# define RET_TYPE intmax_t +#endif + +#include <fromfp.h> + +RET_TYPE +FUNC (double x, int round, unsigned int width) +{ + if (width > INTMAX_WIDTH) + width = INTMAX_WIDTH; + uint64_t ix; + EXTRACT_WORDS64 (ix, x); + bool negative = (ix & 0x8000000000000000ULL) != 0; + if (width == 0) + return fromfp_domain_error (negative, width); + ix &= 0x7fffffffffffffffULL; + if (ix == 0) + return 0; + int exponent = ix >> (MANT_DIG - 1); + exponent -= BIAS; + int max_exponent = fromfp_max_exponent (negative, width); + if (exponent > max_exponent) + return fromfp_domain_error (negative, width); + + ix &= ((1ULL << (MANT_DIG - 1)) - 1); + ix |= 1ULL << (MANT_DIG - 1); + uintmax_t uret; + bool half_bit, more_bits; + if (exponent >= MANT_DIG - 1) + { + uret = ix; + uret <<= exponent - (MANT_DIG - 1); + half_bit = false; + more_bits = false; + } + else if (exponent >= -1) + { + uint64_t h = 1ULL << (MANT_DIG - 2 - exponent); + half_bit = (ix & h) != 0; + more_bits = (ix & (h - 1)) != 0; + uret = ix >> (MANT_DIG - 1 - exponent); + } + else + { + uret = 0; + half_bit = false; + more_bits = true; + } + return fromfp_round_and_return (negative, uret, half_bit, more_bits, round, + exponent, max_exponent, width); +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfpx.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfpx.c new file mode 100644 index 0000000000..bbfb969813 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfpx.c @@ -0,0 +1,7 @@ +#define UNSIGNED 0 +#define INEXACT 1 +#define FUNC fromfpx +#include <s_fromfp_main.c> +#ifdef NO_LONG_DOUBLE +weak_alias (fromfpx, fromfpxl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_getpayload.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_getpayload.c new file mode 100644 index 0000000000..63288e0f45 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_getpayload.c @@ -0,0 +1,37 @@ +/* Get NaN payload. dbl-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fix-int-fp-convert-zero.h> +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +double +getpayload (const double *x) +{ + uint32_t hx, lx; + EXTRACT_WORDS (hx, lx, *x); + hx &= 0x7ffff; + uint64_t ix = ((uint64_t) hx << 32) | lx; + if (FIX_INT_FP_CONVERT_ZERO && ix == 0) + return 0.0f; + return (double) ix; +} +#ifdef NO_LONG_DOUBLE +weak_alias (getpayload, getpayloadl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_isinf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_isinf.c new file mode 100644 index 0000000000..c0ad54538a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_isinf.c @@ -0,0 +1,36 @@ +/* + * Written by J.T. Conklin <jtc@netbsd.org>. + * Changed to return -1 for -Inf by Ulrich Drepper <drepper@cygnus.com>. + * Public domain. + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_isinf.c,v 1.3 1995/05/11 23:20:14 jtc Exp $"; +#endif + +/* + * isinf(x) returns 1 is x is inf, -1 if x is -inf, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <shlib-compat.h> + +int +__isinf (double x) +{ + int32_t hx, lx; + EXTRACT_WORDS (hx, lx, x); + lx |= (hx & 0x7fffffff) ^ 0x7ff00000; + lx |= -lx; + return ~(lx >> 31) & (hx >> 30); +} +hidden_def (__isinf) +weak_alias (__isinf, isinf) +#ifdef NO_LONG_DOUBLE +# if defined LDBL_CLASSIFY_COMPAT && SHLIB_COMPAT (libc, GLIBC_2_0, GLIBC_2_23) +compat_symbol (libc, __isinf, __isinfl, GLIBC_2_0); +# endif +weak_alias (__isinf, isinfl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_isnan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_isnan.c new file mode 100644 index 0000000000..2174d988d8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_isnan.c @@ -0,0 +1,44 @@ +/* @(#)s_isnan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_isnan.c,v 1.8 1995/05/10 20:47:36 jtc Exp $"; +#endif + +/* + * isnan(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <shlib-compat.h> + +#undef __isnan +int +__isnan (double x) +{ + int32_t hx, lx; + EXTRACT_WORDS (hx, lx, x); + hx &= 0x7fffffff; + hx |= (u_int32_t) (lx | (-lx)) >> 31; + hx = 0x7ff00000 - hx; + return (int) (((u_int32_t) hx) >> 31); +} +hidden_def (__isnan) +weak_alias (__isnan, isnan) +#ifdef NO_LONG_DOUBLE +# if defined LDBL_CLASSIFY_COMPAT && SHLIB_COMPAT (libc, GLIBC_2_0, GLIBC_2_23) +compat_symbol (libc, __isnan, __isnanl, GLIBC_2_0); +# endif +weak_alias (__isnan, isnanl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_issignaling.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_issignaling.c new file mode 100644 index 0000000000..09e12f9a6a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_issignaling.c @@ -0,0 +1,47 @@ +/* Test for signaling NaN. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> + +int +__issignaling (double x) +{ +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + u_int32_t hxi; + GET_HIGH_WORD (hxi, x); + /* We only have to care about the high-order bit of x's significand, because + having it set (sNaN) already makes the significand different from that + used to designate infinity. */ + return (hxi & 0x7ff80000) == 0x7ff80000; +#else + u_int32_t hxi, lxi; + EXTRACT_WORDS (hxi, lxi, x); + /* To keep the following comparison simple, toggle the quiet/signaling bit, + so that it is set for sNaNs. This is inverse to IEEE 754-2008 (as well as + common practice for IEEE 754-1985). */ + hxi ^= 0x00080000; + /* If lxi != 0, then set any suitable bit of the significand in hxi. */ + hxi |= (lxi | -lxi) >> 31; + /* We have to compare for greater (instead of greater or equal), because x's + significand being all-zero designates infinity not NaN. */ + return (hxi & 0x7fffffff) > 0x7ff80000; +#endif +} +libm_hidden_def (__issignaling) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_llrint.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_llrint.c new file mode 100644 index 0000000000..08781c3acd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_llrint.c @@ -0,0 +1,103 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + +static const double two52[2] = +{ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + + +long long int +__llrint (double x) +{ + int32_t j0; + u_int32_t i1, i0; + long long int result; + double w; + double t; + int sx; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + sx = i0 >> 31; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 < 20) + { + w = math_narrow_eval (two52[sx] + x); + t = w - two52[sx]; + EXTRACT_WORDS (i0, i1, t); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + i0 &= 0xfffff; + i0 |= 0x100000; + + result = (j0 < 0 ? 0 : i0 >> (20 - j0)); + } + else if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 >= 52) + result = (((long long int) i0 << 32) | i1) << (j0 - 52); + else + { + w = math_narrow_eval (two52[sx] + x); + t = w - two52[sx]; + EXTRACT_WORDS (i0, i1, t); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 == 20) + result = (long long int) i0; + else + result = ((long long int) i0 << (j0 - 20)) | (i1 >> (52 - j0)); + } + } + else + { +#ifdef FE_INVALID + /* The number is too large. Unless it rounds to LLONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ + if (FIX_DBL_LLONG_CONVERT_OVERFLOW && x != (double) LLONG_MIN) + { + feraiseexcept (FE_INVALID); + return sx == 0 ? LLONG_MAX : LLONG_MIN; + } +#endif + return (long long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__llrint, llrint) +#ifdef NO_LONG_DOUBLE +strong_alias (__llrint, __llrintl) +weak_alias (__llrint, llrintl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_llround.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_llround.c new file mode 100644 index 0000000000..8790e9df57 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_llround.c @@ -0,0 +1,91 @@ +/* Round double value to long long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + + +long long int +__llround (double x) +{ + int32_t j0; + u_int32_t i1, i0; + long long int result; + int sign; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + sign = (i0 & 0x80000000) != 0 ? -1 : 1; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 < 20) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + i0 += 0x80000 >> j0; + + result = i0 >> (20 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 >= 52) + result = (((long long int) i0 << 32) | i1) << (j0 - 52); + else + { + u_int32_t j = i1 + (0x80000000 >> (j0 - 20)); + if (j < i1) + ++i0; + + if (j0 == 20) + result = (long long int) i0; + else + result = ((long long int) i0 << (j0 - 20)) | (j >> (52 - j0)); + } + } + else + { +#ifdef FE_INVALID + /* The number is too large. Unless it rounds to LLONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ + if (FIX_DBL_LLONG_CONVERT_OVERFLOW && x != (double) LLONG_MIN) + { + feraiseexcept (FE_INVALID); + return sign == 1 ? LLONG_MAX : LLONG_MIN; + } +#endif + return (long long int) x; + } + + return sign * result; +} + +weak_alias (__llround, llround) +#ifdef NO_LONG_DOUBLE +strong_alias (__llround, __llroundl) +weak_alias (__llround, llroundl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_log1p.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_log1p.c new file mode 100644 index 0000000000..340f6377f7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_log1p.c @@ -0,0 +1,195 @@ +/* @(#)s_log1p.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. + */ + +/* double log1p(double x) + * + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * Note. If k=0, then f=x is exact. However, if k!=0, then f + * may not be representable exactly. In that case, a correction + * term is need. Let u=1+x rounded. Let c = (1+x)-u, then + * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), + * and add back the correction term c/u. + * (Note: when x > 2**53, one can simply return log(x)) + * + * 2. Approximation of log1p(f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s + * (the values of Lp1 to Lp7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lp1*s +...+Lp7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log1p(f) = f - (hfsq - s*(hfsq+R)). + * + * 3. Finally, log1p(x) = k*ln2 + log1p(f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log1p(x) is NaN with signal if x < -1 (including -INF) ; + * log1p(+INF) is +INF; log1p(-1) is -INF with signal; + * log1p(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + * + * Note: Assuming log() return accurate answer, the following + * algorithm can be used to compute log1p(x) to within a few ULP: + * + * u = 1+x; + * if(u==1.0) return x ; else + * return log(u)*(x/(u-1.0)); + * + * See HP-15C Advanced Functions Handbook, p.193. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const double + ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ + ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ + two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ + Lp[] = { 0.0, 6.666666666666735130e-01, /* 3FE55555 55555593 */ + 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ + 2.857142874366239149e-01, /* 3FD24924 94229359 */ + 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ + 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ + 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ + 1.479819860511658591e-01 }; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; + +double +__log1p (double x) +{ + double hfsq, f, c, s, z, R, u, z2, z4, z6, R1, R2, R3, R4; + int32_t k, hx, hu, ax; + + GET_HIGH_WORD (hx, x); + ax = hx & 0x7fffffff; + + k = 1; + if (hx < 0x3FDA827A) /* x < 0.41422 */ + { + if (__glibc_unlikely (ax >= 0x3ff00000)) /* x <= -1.0 */ + { + if (x == -1.0) + return -two54 / zero; /* log1p(-1)=-inf */ + else + return (x - x) / (x - x); /* log1p(x<-1)=NaN */ + } + if (__glibc_unlikely (ax < 0x3e200000)) /* |x| < 2**-29 */ + { + math_force_eval (two54 + x); /* raise inexact */ + if (ax < 0x3c900000) /* |x| < 2**-54 */ + { + math_check_force_underflow (x); + return x; + } + else + return x - x * x * 0.5; + } + if (hx > 0 || hx <= ((int32_t) 0xbfd2bec3)) + { + k = 0; f = x; hu = 1; + } /* -0.2929<x<0.41422 */ + } + else if (__glibc_unlikely (hx >= 0x7ff00000)) + return x + x; + if (k != 0) + { + if (hx < 0x43400000) + { + u = 1.0 + x; + GET_HIGH_WORD (hu, u); + k = (hu >> 20) - 1023; + c = (k > 0) ? 1.0 - (u - x) : x - (u - 1.0); /* correction term */ + c /= u; + } + else + { + u = x; + GET_HIGH_WORD (hu, u); + k = (hu >> 20) - 1023; + c = 0; + } + hu &= 0x000fffff; + if (hu < 0x6a09e) + { + SET_HIGH_WORD (u, hu | 0x3ff00000); /* normalize u */ + } + else + { + k += 1; + SET_HIGH_WORD (u, hu | 0x3fe00000); /* normalize u/2 */ + hu = (0x00100000 - hu) >> 2; + } + f = u - 1.0; + } + hfsq = 0.5 * f * f; + if (hu == 0) /* |f| < 2**-20 */ + { + if (f == zero) + { + if (k == 0) + return zero; + else + { + c += k * ln2_lo; return k * ln2_hi + c; + } + } + R = hfsq * (1.0 - 0.66666666666666666 * f); + if (k == 0) + return f - R; + else + return k * ln2_hi - ((R - (k * ln2_lo + c)) - f); + } + s = f / (2.0 + f); + z = s * s; + R1 = z * Lp[1]; z2 = z * z; + R2 = Lp[2] + z * Lp[3]; z4 = z2 * z2; + R3 = Lp[4] + z * Lp[5]; z6 = z4 * z2; + R4 = Lp[6] + z * Lp[7]; + R = R1 + z2 * R2 + z4 * R3 + z6 * R4; + if (k == 0) + return f - (hfsq - s * (hfsq + R)); + else + return k * ln2_hi - ((hfsq - (s * (hfsq + R) + (k * ln2_lo + c))) - f); +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_logb.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_logb.c new file mode 100644 index 0000000000..3a26b18f78 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_logb.c @@ -0,0 +1,52 @@ +/* @(#)s_logb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * double logb(x) + * IEEE 754 logb. Included to pass IEEE test suite. Not recommend. + * Use ilogb instead. + */ + +#include <math.h> +#include <math_private.h> +#include <fix-int-fp-convert-zero.h> + +double +__logb (double x) +{ + int32_t lx, ix, rix; + + EXTRACT_WORDS (ix, lx, x); + ix &= 0x7fffffff; /* high |x| */ + if ((ix | lx) == 0) + return -1.0 / fabs (x); + if (ix >= 0x7ff00000) + return x * x; + if (__glibc_unlikely ((rix = ix >> 20) == 0)) + { + /* POSIX specifies that denormal number is treated as + though it were normalized. */ + int ma; + if (ix == 0) + ma = __builtin_clz (lx) + 32; + else + ma = __builtin_clz (ix); + rix -= ma - 12; + } + if (FIX_INT_FP_CONVERT_ZERO && rix == 1023) + return 0.0; + return (double) (rix - 1023); +} +weak_alias (__logb, logb) +#ifdef NO_LONG_DOUBLE +strong_alias (__logb, __logbl) weak_alias (__logb, logbl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_lrint.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_lrint.c new file mode 100644 index 0000000000..ac610bfbd0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_lrint.c @@ -0,0 +1,127 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + +static const double two52[2] = +{ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + + +long int +__lrint (double x) +{ + int32_t j0; + u_int32_t i0, i1; + double w; + double t; + long int result; + int sx; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + sx = i0 >> 31; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 < 20) + { + w = math_narrow_eval (two52[sx] + x); + t = w - two52[sx]; + EXTRACT_WORDS (i0, i1, t); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + i0 &= 0xfffff; + i0 |= 0x100000; + + result = (j0 < 0 ? 0 : i0 >> (20 - j0)); + } + else if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 >= 52) + result = ((long int) i0 << (j0 - 20)) | ((long int) i1 << (j0 - 52)); + else + { +#if defined FE_INVALID || defined FE_INEXACT + /* X < LONG_MAX + 1 implied by J0 < 31. */ + if (sizeof (long int) == 4 + && x > (double) LONG_MAX) + { + /* In the event of overflow we must raise the "invalid" + exception, but not "inexact". */ + t = __nearbyint (x); + feraiseexcept (t == LONG_MAX ? FE_INEXACT : FE_INVALID); + } + else +#endif + { + w = math_narrow_eval (two52[sx] + x); + t = w - two52[sx]; + } + EXTRACT_WORDS (i0, i1, t); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 == 20) + result = (long int) i0; + else + result = ((long int) i0 << (j0 - 20)) | (i1 >> (52 - j0)); + } + } + else + { + /* The number is too large. Unless it rounds to LONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ +#if defined FE_INVALID || defined FE_INEXACT + if (sizeof (long int) == 4 + && x < (double) LONG_MIN + && x > (double) LONG_MIN - 1.0) + { + /* If truncation produces LONG_MIN, the cast will not raise + the exception, but may raise "inexact". */ + t = __nearbyint (x); + feraiseexcept (t == LONG_MIN ? FE_INEXACT : FE_INVALID); + return LONG_MIN; + } + else if (FIX_DBL_LONG_CONVERT_OVERFLOW && x != (double) LONG_MIN) + { + feraiseexcept (FE_INVALID); + return sx == 0 ? LONG_MAX : LONG_MIN; + } +#endif + return (long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__lrint, lrint) +#ifdef NO_LONG_DOUBLE +strong_alias (__lrint, __lrintl) +weak_alias (__lrint, lrintl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_lround.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_lround.c new file mode 100644 index 0000000000..df4775e344 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_lround.c @@ -0,0 +1,113 @@ +/* Round double value to long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + + +long int +__lround (double x) +{ + int32_t j0; + u_int32_t i1, i0; + long int result; + int sign; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + sign = (i0 & 0x80000000) != 0 ? -1 : 1; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 < 20) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + i0 += 0x80000 >> j0; + + result = i0 >> (20 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 >= 52) + result = ((long int) i0 << (j0 - 20)) | ((long int) i1 << (j0 - 52)); + else + { + u_int32_t j = i1 + (0x80000000 >> (j0 - 20)); + if (j < i1) + ++i0; + + if (j0 == 20) + result = (long int) i0; + else + { + result = ((long int) i0 << (j0 - 20)) | (j >> (52 - j0)); +#ifdef FE_INVALID + if (sizeof (long int) == 4 + && sign == 1 + && result == LONG_MIN) + /* Rounding brought the value out of range. */ + feraiseexcept (FE_INVALID); +#endif + } + } + } + else + { + /* The number is too large. Unless it rounds to LONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ +#ifdef FE_INVALID + if (FIX_DBL_LONG_CONVERT_OVERFLOW + && !(sign == -1 + && (sizeof (long int) == 4 + ? x > (double) LONG_MIN - 0.5 + : x >= (double) LONG_MIN))) + { + feraiseexcept (FE_INVALID); + return sign == 1 ? LONG_MAX : LONG_MIN; + } + else if (!FIX_DBL_LONG_CONVERT_OVERFLOW + && sizeof (long int) == 4 + && x <= (double) LONG_MIN - 0.5) + { + /* If truncation produces LONG_MIN, the cast will not raise + the exception, but may raise "inexact". */ + feraiseexcept (FE_INVALID); + return LONG_MIN; + } +#endif + return (long int) x; + } + + return sign * result; +} + +weak_alias (__lround, lround) +#ifdef NO_LONG_DOUBLE +strong_alias (__lround, __lroundl) +weak_alias (__lround, lroundl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_modf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_modf.c new file mode 100644 index 0000000000..0a1e13008f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_modf.c @@ -0,0 +1,86 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * modf(double x, double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include <math.h> +#include <math_private.h> + +static const double one = 1.0; + +double +__modf (double x, double *iptr) +{ + int32_t i0, i1, j0; + u_int32_t i; + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; /* exponent of x */ + if (j0 < 20) /* integer part in high x */ + { + if (j0 < 0) /* |x|<1 */ + { + INSERT_WORDS (*iptr, i0 & 0x80000000, 0); /* *iptr = +-0 */ + return x; + } + else + { + i = (0x000fffff) >> j0; + if (((i0 & i) | i1) == 0) /* x is integral */ + { + *iptr = x; + INSERT_WORDS (x, i0 & 0x80000000, 0); /* return +-0 */ + return x; + } + else + { + INSERT_WORDS (*iptr, i0 & (~i), 0); + return x - *iptr; + } + } + } + else if (__glibc_unlikely (j0 > 51)) /* no fraction part */ + { + *iptr = x * one; + /* We must handle NaNs separately. */ + if (j0 == 0x400 && ((i0 & 0xfffff) | i1)) + return x * one; + INSERT_WORDS (x, i0 & 0x80000000, 0); /* return +-0 */ + return x; + } + else /* fraction part in low x */ + { + i = ((u_int32_t) (0xffffffff)) >> (j0 - 20); + if ((i1 & i) == 0) /* x is integral */ + { + *iptr = x; + INSERT_WORDS (x, i0 & 0x80000000, 0); /* return +-0 */ + return x; + } + else + { + INSERT_WORDS (*iptr, i0, i1 & (~i)); + return x - *iptr; + } + } +} +weak_alias (__modf, modf) +#ifdef NO_LONG_DOUBLE +strong_alias (__modf, __modfl) +weak_alias (__modf, modfl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_nearbyint.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_nearbyint.c new file mode 100644 index 0000000000..dec0c5d6ee --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_nearbyint.c @@ -0,0 +1,78 @@ +/* Adapted for use as nearbyint by Ulrich Drepper <drepper@cygnus.com>. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_rint.c,v 1.8 1995/05/10 20:48:04 jtc Exp $"; +#endif + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include <fenv.h> +#include <math.h> +#include <math_private.h> + +static const double + TWO52[2] = { + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +double +__nearbyint (double x) +{ + fenv_t env; + int32_t i0, j0, sx; + double w, t; + GET_HIGH_WORD (i0, x); + sx = (i0 >> 31) & 1; + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 52) + { + if (j0 < 0) + { + libc_feholdexcept (&env); + w = TWO52[sx] + x; + t = w - TWO52[sx]; + math_force_eval (t); + libc_fesetenv (&env); + GET_HIGH_WORD (i0, t); + SET_HIGH_WORD (t, (i0 & 0x7fffffff) | (sx << 31)); + return t; + } + } + else + { + if (j0 == 0x400) + return x + x; /* inf or NaN */ + else + return x; /* x is integral */ + } + libc_feholdexcept (&env); + w = TWO52[sx] + x; + t = w - TWO52[sx]; + math_force_eval (t); + libc_fesetenv (&env); + return t; +} +weak_alias (__nearbyint, nearbyint) +#ifdef NO_LONG_DOUBLE +strong_alias (__nearbyint, __nearbyintl) +weak_alias (__nearbyint, nearbyintl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_nexttoward.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_nexttoward.c new file mode 100644 index 0000000000..c68ba98cb3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_nexttoward.c @@ -0,0 +1 @@ +/* This function is the same as nextafter so we use an alias there. */ diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_nextup.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_nextup.c new file mode 100644 index 0000000000..983bd662b7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_nextup.c @@ -0,0 +1,58 @@ +/* Return the least floating-point number greater than X. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* Return the least floating-point number greater than X. */ +double +__nextup (double x) +{ + int32_t hx, ix; + u_int32_t lx; + + EXTRACT_WORDS (hx, lx, x); + ix = hx & 0x7fffffff; + + if (((ix >= 0x7ff00000) && ((ix - 0x7ff00000) | lx) != 0)) /* x is nan. */ + return x + x; + if ((ix | lx) == 0) + return DBL_TRUE_MIN; + if (hx >= 0) + { /* x > 0. */ + if (isinf (x)) + return x; + lx += 1; + if (lx == 0) + hx += 1; + } + else + { /* x < 0. */ + if (lx == 0) + hx -= 1; + lx -= 1; + } + INSERT_WORDS (x, hx, lx); + return x; +} + +weak_alias (__nextup, nextup) +#ifdef NO_LONG_DOUBLE +strong_alias (__nextup, __nextupl) +weak_alias (__nextup, nextupl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_remquo.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_remquo.c new file mode 100644 index 0000000000..2693c0e62c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_remquo.c @@ -0,0 +1,115 @@ +/* Compute remainder and a congruent to the quotient. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +static const double zero = 0.0; + + +double +__remquo (double x, double y, int *quo) +{ + int32_t hx, hy; + u_int32_t sx, lx, ly; + int cquo, qs; + + EXTRACT_WORDS (hx, lx, x); + EXTRACT_WORDS (hy, ly, y); + sx = hx & 0x80000000; + qs = sx ^ (hy & 0x80000000); + hy &= 0x7fffffff; + hx &= 0x7fffffff; + + /* Purge off exception values. */ + if ((hy | ly) == 0) + return (x * y) / (x * y); /* y = 0 */ + if ((hx >= 0x7ff00000) /* x not finite */ + || ((hy >= 0x7ff00000) /* p is NaN */ + && (((hy - 0x7ff00000) | ly) != 0))) + return (x * y) / (x * y); + + if (hy <= 0x7fbfffff) + x = __ieee754_fmod (x, 8 * y); /* now x < 8y */ + + if (((hx - hy) | (lx - ly)) == 0) + { + *quo = qs ? -1 : 1; + return zero * x; + } + + x = fabs (x); + y = fabs (y); + cquo = 0; + + if (hy <= 0x7fcfffff && x >= 4 * y) + { + x -= 4 * y; + cquo += 4; + } + if (hy <= 0x7fdfffff && x >= 2 * y) + { + x -= 2 * y; + cquo += 2; + } + + if (hy < 0x00200000) + { + if (x + x > y) + { + x -= y; + ++cquo; + if (x + x >= y) + { + x -= y; + ++cquo; + } + } + } + else + { + double y_half = 0.5 * y; + if (x > y_half) + { + x -= y; + ++cquo; + if (x >= y_half) + { + x -= y; + ++cquo; + } + } + } + + *quo = qs ? -cquo : cquo; + + /* Ensure correct sign of zero result in round-downward mode. */ + if (x == 0.0) + x = 0.0; + if (sx) + x = -x; + return x; +} +weak_alias (__remquo, remquo) +#ifdef NO_LONG_DOUBLE +strong_alias (__remquo, __remquol) +weak_alias (__remquo, remquol) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_rint.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_rint.c new file mode 100644 index 0000000000..a9c0d27842 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_rint.c @@ -0,0 +1,67 @@ +/* @(#)s_rint.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include <math.h> +#include <math_private.h> + +static const double + TWO52[2] = { + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +double +__rint (double x) +{ + int32_t i0, j0, sx; + double w, t; + GET_HIGH_WORD (i0, x); + sx = (i0 >> 31) & 1; + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 52) + { + if (j0 < 0) + { + w = TWO52[sx] + x; + t = w - TWO52[sx]; + GET_HIGH_WORD (i0, t); + SET_HIGH_WORD (t, (i0 & 0x7fffffff) | (sx << 31)); + return t; + } + } + else + { + if (j0 == 0x400) + return x + x; /* inf or NaN */ + else + return x; /* x is integral */ + } + w = TWO52[sx] + x; + return w - TWO52[sx]; +} +#ifndef __rint +weak_alias (__rint, rint) +# ifdef NO_LONG_DOUBLE +strong_alias (__rint, __rintl) +weak_alias (__rint, rintl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_round.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_round.c new file mode 100644 index 0000000000..390e3f7180 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_round.c @@ -0,0 +1,83 @@ +/* Round double to integer away from zero. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +double +__round (double x) +{ + int32_t i0, j0; + u_int32_t i1; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 20) + { + if (j0 < 0) + { + i0 &= 0x80000000; + if (j0 == -1) + i0 |= 0x3ff00000; + i1 = 0; + } + else + { + u_int32_t i = 0x000fffff >> j0; + if (((i0 & i) | i1) == 0) + /* X is integral. */ + return x; + + i0 += 0x00080000 >> j0; + i0 &= ~i; + i1 = 0; + } + } + else if (j0 > 51) + { + if (j0 == 0x400) + /* Inf or NaN. */ + return x + x; + else + return x; + } + else + { + u_int32_t i = 0xffffffff >> (j0 - 20); + if ((i1 & i) == 0) + /* X is integral. */ + return x; + + u_int32_t j = i1 + (1 << (51 - j0)); + if (j < i1) + i0 += 1; + i1 = j; + i1 &= ~i; + } + + INSERT_WORDS (x, i0, i1); + return x; +} +weak_alias (__round, round) +#ifdef NO_LONG_DOUBLE +strong_alias (__round, __roundl) +weak_alias (__round, roundl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_roundeven.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_roundeven.c new file mode 100644 index 0000000000..78d81a070c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_roundeven.c @@ -0,0 +1,106 @@ +/* Round to nearest integer value, rounding halfway cases to even. + dbl-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +#define BIAS 0x3ff +#define MANT_DIG 53 +#define MAX_EXP (2 * BIAS + 1) + +double +roundeven (double x) +{ + uint32_t hx, lx, uhx; + EXTRACT_WORDS (hx, lx, x); + uhx = hx & 0x7fffffff; + int exponent = uhx >> (MANT_DIG - 1 - 32); + if (exponent >= BIAS + MANT_DIG - 1) + { + /* Integer, infinity or NaN. */ + if (exponent == MAX_EXP) + /* Infinity or NaN; quiet signaling NaNs. */ + return x + x; + else + return x; + } + else if (exponent >= BIAS + MANT_DIG - 32) + { + /* Not necessarily an integer; integer bit is in low word. + Locate the bits with exponents 0 and -1. */ + int int_pos = (BIAS + MANT_DIG - 1) - exponent; + int half_pos = int_pos - 1; + uint32_t half_bit = 1U << half_pos; + uint32_t int_bit = 1U << int_pos; + if ((lx & (int_bit | (half_bit - 1))) != 0) + { + /* Carry into the exponent works correctly. No need to test + whether HALF_BIT is set. */ + lx += half_bit; + hx += lx < half_bit; + } + lx &= ~(int_bit - 1); + } + else if (exponent == BIAS + MANT_DIG - 33) + { + /* Not necessarily an integer; integer bit is bottom of high + word, half bit is top of low word. */ + if (((hx & 1) | (lx & 0x7fffffff)) != 0) + { + lx += 0x80000000; + hx += lx < 0x80000000; + } + lx = 0; + } + else if (exponent >= BIAS) + { + /* At least 1; not necessarily an integer, integer bit and half + bit are in the high word. Locate the bits with exponents 0 + and -1 (when the unbiased exponent is 0, the bit with + exponent 0 is implicit, but as the bias is odd it is OK to + take it from the low bit of the exponent). */ + int int_pos = (BIAS + MANT_DIG - 33) - exponent; + int half_pos = int_pos - 1; + uint32_t half_bit = 1U << half_pos; + uint32_t int_bit = 1U << int_pos; + if (((hx & (int_bit | (half_bit - 1))) | lx) != 0) + hx += half_bit; + hx &= ~(int_bit - 1); + lx = 0; + } + else if (exponent == BIAS - 1 && (uhx > 0x3fe00000 || lx != 0)) + { + /* Interval (0.5, 1). */ + hx = (hx & 0x80000000) | 0x3ff00000; + lx = 0; + } + else + { + /* Rounds to 0. */ + hx &= 0x80000000; + lx = 0; + } + INSERT_WORDS (x, hx, lx); + return x; +} +hidden_def (roundeven) +#ifdef NO_LONG_DOUBLE +weak_alias (roundeven, roundevenl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_scalbln.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_scalbln.c new file mode 100644 index 0000000000..32cd12e3b0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_scalbln.c @@ -0,0 +1,63 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> + +static const double + two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ + twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ + huge = 1.0e+300, + tiny = 1.0e-300; + +double +__scalbln (double x, long int n) +{ + int32_t k, hx, lx; + EXTRACT_WORDS (hx, lx, x); + k = (hx & 0x7ff00000) >> 20; /* extract exponent */ + if (__glibc_unlikely (k == 0)) /* 0 or subnormal x */ + { + if ((lx | (hx & 0x7fffffff)) == 0) + return x; /* +-0 */ + x *= two54; + GET_HIGH_WORD (hx, x); + k = ((hx & 0x7ff00000) >> 20) - 54; + } + if (__glibc_unlikely (k == 0x7ff)) + return x + x; /* NaN or Inf */ + if (__glibc_unlikely (n < -50000)) + return tiny * __copysign (tiny, x); /*underflow*/ + if (__glibc_unlikely (n > 50000 || k + n > 0x7fe)) + return huge * __copysign (huge, x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k + n; + if (__glibc_likely (k > 0)) /* normal result */ + { + SET_HIGH_WORD (x, (hx & 0x800fffff) | (k << 20)); return x; + } + if (k <= -54) + return tiny * __copysign (tiny, x); /*underflow*/ + k += 54; /* subnormal result */ + SET_HIGH_WORD (x, (hx & 0x800fffff) | (k << 20)); + return x * twom54; +} +#ifdef NO_LONG_DOUBLE +strong_alias (__scalbln, __scalblnl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_scalbn.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_scalbn.c new file mode 100644 index 0000000000..58c7e1b33a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_scalbn.c @@ -0,0 +1,63 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> + +static const double + two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ + twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ + huge = 1.0e+300, + tiny = 1.0e-300; + +double +__scalbn (double x, int n) +{ + int32_t k, hx, lx; + EXTRACT_WORDS (hx, lx, x); + k = (hx & 0x7ff00000) >> 20; /* extract exponent */ + if (__glibc_unlikely (k == 0)) /* 0 or subnormal x */ + { + if ((lx | (hx & 0x7fffffff)) == 0) + return x; /* +-0 */ + x *= two54; + GET_HIGH_WORD (hx, x); + k = ((hx & 0x7ff00000) >> 20) - 54; + } + if (__glibc_unlikely (k == 0x7ff)) + return x + x; /* NaN or Inf */ + if (__glibc_unlikely (n < -50000)) + return tiny * __copysign (tiny, x); /*underflow*/ + if (__glibc_unlikely (n > 50000 || k + n > 0x7fe)) + return huge * __copysign (huge, x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k + n; + if (__glibc_likely (k > 0)) /* normal result */ + { + SET_HIGH_WORD (x, (hx & 0x800fffff) | (k << 20)); return x; + } + if (k <= -54) + return tiny * __copysign (tiny, x); /*underflow*/ + k += 54; /* subnormal result */ + SET_HIGH_WORD (x, (hx & 0x800fffff) | (k << 20)); + return x * twom54; +} +#ifdef NO_LONG_DOUBLE +strong_alias (__scalbn, __scalbnl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayload.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayload.c new file mode 100644 index 0000000000..5ab70dee73 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayload.c @@ -0,0 +1,6 @@ +#define SIG 0 +#define FUNC setpayload +#include <s_setpayload_main.c> +#ifdef NO_LONG_DOUBLE +weak_alias (setpayload, setpayloadl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayload_main.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayload_main.c new file mode 100644 index 0000000000..c6128c7fe4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayload_main.c @@ -0,0 +1,69 @@ +/* Set NaN payload. dbl-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +#define SET_HIGH_BIT (HIGH_ORDER_BIT_IS_SET_FOR_SNAN ? SIG : !SIG) +#define BIAS 0x3ff +#define PAYLOAD_DIG 51 +#define EXPLICIT_MANT_DIG 52 + +int +FUNC (double *x, double payload) +{ + uint32_t hx, lx; + EXTRACT_WORDS (hx, lx, payload); + int exponent = hx >> (EXPLICIT_MANT_DIG - 32); + /* Test if argument is (a) negative or too large; (b) too small, + except for 0 when allowed; (c) not an integer. */ + if (exponent >= BIAS + PAYLOAD_DIG + || (exponent < BIAS && !(SET_HIGH_BIT && hx == 0 && lx == 0))) + { + INSERT_WORDS (*x, 0, 0); + return 1; + } + int shift = BIAS + EXPLICIT_MANT_DIG - exponent; + if (shift < 32 + ? (lx & ((1U << shift) - 1)) != 0 + : (lx != 0 || (hx & ((1U << (shift - 32)) - 1)) != 0)) + { + INSERT_WORDS (*x, 0, 0); + return 1; + } + if (exponent != 0) + { + hx &= (1U << (EXPLICIT_MANT_DIG - 32)) - 1; + hx |= 1U << (EXPLICIT_MANT_DIG - 32); + if (shift >= 32) + { + lx = hx >> (shift - 32); + hx = 0; + } + else if (shift != 0) + { + lx = (lx >> shift) | (hx << (32 - shift)); + hx >>= shift; + } + } + hx |= 0x7ff00000 | (SET_HIGH_BIT ? 0x80000 : 0); + INSERT_WORDS (*x, hx, lx); + return 0; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayloadsig.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayloadsig.c new file mode 100644 index 0000000000..c3d1ba1e6e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayloadsig.c @@ -0,0 +1,6 @@ +#define SIG 1 +#define FUNC setpayloadsig +#include <s_setpayload_main.c> +#ifdef NO_LONG_DOUBLE +weak_alias (setpayloadsig, setpayloadsigl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_signbit.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_signbit.c new file mode 100644 index 0000000000..1beab1025c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_signbit.c @@ -0,0 +1,26 @@ +/* Return nonzero value if number is negative. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +int +__signbit (double x) +{ + return __builtin_signbit (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_sin.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_sin.c new file mode 100644 index 0000000000..c258d39e49 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_sin.c @@ -0,0 +1,927 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/****************************************************************************/ +/* */ +/* MODULE_NAME:usncs.c */ +/* */ +/* FUNCTIONS: usin */ +/* ucos */ +/* slow */ +/* slow1 */ +/* slow2 */ +/* sloww */ +/* sloww1 */ +/* sloww2 */ +/* bsloww */ +/* bsloww1 */ +/* bsloww2 */ +/* cslow2 */ +/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */ +/* branred.c sincos32.c dosincos.c mpa.c */ +/* sincos.tbl */ +/* */ +/* An ultimate sin and routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of sin(x) or cos(x) */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/****************************************************************************/ + + +#include <errno.h> +#include <float.h> +#include "endian.h" +#include "mydefs.h" +#include "usncs.h" +#include "MathLib.h" +#include <math.h> +#include <math_private.h> +#include <fenv.h> + +/* Helper macros to compute sin of the input values. */ +#define POLYNOMIAL2(xx) ((((s5 * (xx) + s4) * (xx) + s3) * (xx) + s2) * (xx)) + +#define POLYNOMIAL(xx) (POLYNOMIAL2 (xx) + s1) + +/* The computed polynomial is a variation of the Taylor series expansion for + sin(a): + + a - a^3/3! + a^5/5! - a^7/7! + a^9/9! + (1 - a^2) * da / 2 + + The constants s1, s2, s3, etc. are pre-computed values of 1/3!, 1/5! and so + on. The result is returned to LHS and correction in COR. */ +#define TAYLOR_SIN(xx, a, da, cor) \ +({ \ + double t = ((POLYNOMIAL (xx) * (a) - 0.5 * (da)) * (xx) + (da)); \ + double res = (a) + t; \ + (cor) = ((a) - res) + t; \ + res; \ +}) + +/* This is again a variation of the Taylor series expansion with the term + x^3/3! expanded into the following for better accuracy: + + bb * x ^ 3 + 3 * aa * x * x1 * x2 + aa * x1 ^ 3 + aa * x2 ^ 3 + + The correction term is dx and bb + aa = -1/3! + */ +#define TAYLOR_SLOW(x0, dx, cor) \ +({ \ + static const double th2_36 = 206158430208.0; /* 1.5*2**37 */ \ + double xx = (x0) * (x0); \ + double x1 = ((x0) + th2_36) - th2_36; \ + double y = aa * x1 * x1 * x1; \ + double r = (x0) + y; \ + double x2 = ((x0) - x1) + (dx); \ + double t = (((POLYNOMIAL2 (xx) + bb) * xx + 3.0 * aa * x1 * x2) \ + * (x0) + aa * x2 * x2 * x2 + (dx)); \ + t = (((x0) - r) + y) + t; \ + double res = r + t; \ + (cor) = (r - res) + t; \ + res; \ +}) + +#define SINCOS_TABLE_LOOKUP(u, sn, ssn, cs, ccs) \ +({ \ + int4 k = u.i[LOW_HALF] << 2; \ + sn = __sincostab.x[k]; \ + ssn = __sincostab.x[k + 1]; \ + cs = __sincostab.x[k + 2]; \ + ccs = __sincostab.x[k + 3]; \ +}) + +#ifndef SECTION +# define SECTION +#endif + +extern const union +{ + int4 i[880]; + double x[440]; +} __sincostab attribute_hidden; + +static const double + sn3 = -1.66666666666664880952546298448555E-01, + sn5 = 8.33333214285722277379541354343671E-03, + cs2 = 4.99999999999999999999950396842453E-01, + cs4 = -4.16666666666664434524222570944589E-02, + cs6 = 1.38888874007937613028114285595617E-03; + +static const double t22 = 0x1.8p22; + +void __dubsin (double x, double dx, double w[]); +void __docos (double x, double dx, double w[]); +double __mpsin (double x, double dx, bool reduce_range); +double __mpcos (double x, double dx, bool reduce_range); +static double slow (double x); +static double slow1 (double x); +static double slow2 (double x); +static double sloww (double x, double dx, double orig, bool shift_quadrant); +static double sloww1 (double x, double dx, double orig, bool shift_quadrant); +static double sloww2 (double x, double dx, double orig, int n); +static double bsloww (double x, double dx, double orig, int n); +static double bsloww1 (double x, double dx, double orig, int n); +static double bsloww2 (double x, double dx, double orig, int n); +int __branred (double x, double *a, double *aa); +static double cslow2 (double x); + +/* Given a number partitioned into X and DX, this function computes the cosine + of the number by combining the sin and cos of X (as computed by a variation + of the Taylor series) with the values looked up from the sin/cos table to + get the result in RES and a correction value in COR. */ +static inline double +__always_inline +do_cos (double x, double dx, double *corp) +{ + mynumber u; + + if (x < 0) + dx = -dx; + + u.x = big + fabs (x); + x = fabs (x) - (u.x - big) + dx; + + double xx, s, sn, ssn, c, cs, ccs, res, cor; + xx = x * x; + s = x + x * xx * (sn3 + xx * sn5); + c = xx * (cs2 + xx * (cs4 + xx * cs6)); + SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); + cor = (ccs - s * ssn - cs * c) - sn * s; + res = cs + cor; + cor = (cs - res) + cor; + *corp = cor; + return res; +} + +/* A more precise variant of DO_COS. EPS is the adjustment to the correction + COR. */ +static inline double +__always_inline +do_cos_slow (double x, double dx, double eps, double *corp) +{ + mynumber u; + + if (x <= 0) + dx = -dx; + + u.x = big + fabs (x); + x = fabs (x) - (u.x - big); + + double xx, y, x1, x2, e1, e2, res, cor; + double s, sn, ssn, c, cs, ccs; + xx = x * x; + s = x * xx * (sn3 + xx * sn5); + c = x * dx + xx * (cs2 + xx * (cs4 + xx * cs6)); + SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); + x1 = (x + t22) - t22; + x2 = (x - x1) + dx; + e1 = (sn + t22) - t22; + e2 = (sn - e1) + ssn; + cor = (ccs - cs * c - e1 * x2 - e2 * x) - sn * s; + y = cs - e1 * x1; + cor = cor + ((cs - y) - e1 * x1); + res = y + cor; + cor = (y - res) + cor; + cor = 1.0005 * cor + __copysign (eps, cor); + *corp = cor; + return res; +} + +/* Given a number partitioned into X and DX, this function computes the sine of + the number by combining the sin and cos of X (as computed by a variation of + the Taylor series) with the values looked up from the sin/cos table to get + the result in RES and a correction value in COR. */ +static inline double +__always_inline +do_sin (double x, double dx, double *corp) +{ + mynumber u; + + if (x <= 0) + dx = -dx; + u.x = big + fabs (x); + x = fabs (x) - (u.x - big); + + double xx, s, sn, ssn, c, cs, ccs, cor, res; + xx = x * x; + s = x + (dx + x * xx * (sn3 + xx * sn5)); + c = x * dx + xx * (cs2 + xx * (cs4 + xx * cs6)); + SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); + cor = (ssn + s * ccs - sn * c) + cs * s; + res = sn + cor; + cor = (sn - res) + cor; + *corp = cor; + return res; +} + +/* A more precise variant of DO_SIN. EPS is the adjustment to the correction + COR. */ +static inline double +__always_inline +do_sin_slow (double x, double dx, double eps, double *corp) +{ + mynumber u; + + if (x <= 0) + dx = -dx; + u.x = big + fabs (x); + x = fabs (x) - (u.x - big); + + double xx, y, x1, x2, c1, c2, res, cor; + double s, sn, ssn, c, cs, ccs; + xx = x * x; + s = x * xx * (sn3 + xx * sn5); + c = xx * (cs2 + xx * (cs4 + xx * cs6)); + SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); + x1 = (x + t22) - t22; + x2 = (x - x1) + dx; + c1 = (cs + t22) - t22; + c2 = (cs - c1) + ccs; + cor = (ssn + s * ccs + cs * s + c2 * x + c1 * x2 - sn * x * dx) - sn * c; + y = sn + c1 * x1; + cor = cor + ((sn - y) + c1 * x1); + res = y + cor; + cor = (y - res) + cor; + cor = 1.0005 * cor + __copysign (eps, cor); + *corp = cor; + return res; +} + +/* Reduce range of X and compute sin of a + da. When SHIFT_QUADRANT is true, + the routine returns the cosine of a + da by rotating the quadrant once and + computing the sine of the result. */ +static inline double +__always_inline +reduce_and_compute (double x, bool shift_quadrant) +{ + double retval = 0, a, da; + unsigned int n = __branred (x, &a, &da); + int4 k = (n + shift_quadrant) % 4; + switch (k) + { + case 2: + a = -a; + da = -da; + /* Fall through. */ + case 0: + if (a * a < 0.01588) + retval = bsloww (a, da, x, n); + else + retval = bsloww1 (a, da, x, n); + break; + + case 1: + case 3: + retval = bsloww2 (a, da, x, n); + break; + } + return retval; +} + +static inline int4 +__always_inline +reduce_sincos_1 (double x, double *a, double *da) +{ + mynumber v; + + double t = (x * hpinv + toint); + double xn = t - toint; + v.x = t; + double y = (x - xn * mp1) - xn * mp2; + int4 n = v.i[LOW_HALF] & 3; + double db = xn * mp3; + double b = y - db; + db = (y - b) - db; + + *a = b; + *da = db; + + return n; +} + +/* Compute sin (A + DA). cos can be computed by passing SHIFT_QUADRANT as + true, which results in shifting the quadrant N clockwise. */ +static double +__always_inline +do_sincos_1 (double a, double da, double x, int4 n, bool shift_quadrant) +{ + double xx, retval, res, cor; + double eps = fabs (x) * 1.2e-30; + + int k1 = (n + shift_quadrant) & 3; + switch (k1) + { /* quarter of unit circle */ + case 2: + a = -a; + da = -da; + /* Fall through. */ + case 0: + xx = a * a; + if (xx < 0.01588) + { + /* Taylor series. */ + res = TAYLOR_SIN (xx, a, da, cor); + cor = 1.02 * cor + __copysign (eps, cor); + retval = (res == res + cor) ? res : sloww (a, da, x, shift_quadrant); + } + else + { + res = do_sin (a, da, &cor); + cor = 1.035 * cor + __copysign (eps, cor); + retval = ((res == res + cor) ? __copysign (res, a) + : sloww1 (a, da, x, shift_quadrant)); + } + break; + + case 1: + case 3: + res = do_cos (a, da, &cor); + cor = 1.025 * cor + __copysign (eps, cor); + retval = ((res == res + cor) ? ((n & 2) ? -res : res) + : sloww2 (a, da, x, n)); + break; + } + + return retval; +} + +static inline int4 +__always_inline +reduce_sincos_2 (double x, double *a, double *da) +{ + mynumber v; + + double t = (x * hpinv + toint); + double xn = t - toint; + v.x = t; + double xn1 = (xn + 8.0e22) - 8.0e22; + double xn2 = xn - xn1; + double y = ((((x - xn1 * mp1) - xn1 * mp2) - xn2 * mp1) - xn2 * mp2); + int4 n = v.i[LOW_HALF] & 3; + double db = xn1 * pp3; + t = y - db; + db = (y - t) - db; + db = (db - xn2 * pp3) - xn * pp4; + double b = t + db; + db = (t - b) + db; + + *a = b; + *da = db; + + return n; +} + +/* Compute sin (A + DA). cos can be computed by passing SHIFT_QUADRANT as + true, which results in shifting the quadrant N clockwise. */ +static double +__always_inline +do_sincos_2 (double a, double da, double x, int4 n, bool shift_quadrant) +{ + double res, retval, cor, xx; + + double eps = 1.0e-24; + + int4 k = (n + shift_quadrant) & 3; + + switch (k) + { + case 2: + a = -a; + da = -da; + /* Fall through. */ + case 0: + xx = a * a; + if (xx < 0.01588) + { + /* Taylor series. */ + res = TAYLOR_SIN (xx, a, da, cor); + cor = 1.02 * cor + __copysign (eps, cor); + retval = (res == res + cor) ? res : bsloww (a, da, x, n); + } + else + { + res = do_sin (a, da, &cor); + cor = 1.035 * cor + __copysign (eps, cor); + retval = ((res == res + cor) ? __copysign (res, a) + : bsloww1 (a, da, x, n)); + } + break; + + case 1: + case 3: + res = do_cos (a, da, &cor); + cor = 1.025 * cor + __copysign (eps, cor); + retval = ((res == res + cor) ? ((n & 2) ? -res : res) + : bsloww2 (a, da, x, n)); + break; + } + + return retval; +} + +/*******************************************************************/ +/* An ultimate sin routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of sin(x) */ +/*******************************************************************/ +#ifdef IN_SINCOS +static double +#else +double +SECTION +#endif +__sin (double x) +{ + double xx, res, t, cor; + mynumber u; + int4 k, m; + double retval = 0; + +#ifndef IN_SINCOS + SET_RESTORE_ROUND_53BIT (FE_TONEAREST); +#endif + + u.x = x; + m = u.i[HIGH_HALF]; + k = 0x7fffffff & m; /* no sign */ + if (k < 0x3e500000) /* if x->0 =>sin(x)=x */ + { + math_check_force_underflow (x); + retval = x; + } + /*---------------------------- 2^-26 < |x|< 0.25 ----------------------*/ + else if (k < 0x3fd00000) + { + xx = x * x; + /* Taylor series. */ + t = POLYNOMIAL (xx) * (xx * x); + res = x + t; + cor = (x - res) + t; + retval = (res == res + 1.07 * cor) ? res : slow (x); + } /* else if (k < 0x3fd00000) */ +/*---------------------------- 0.25<|x|< 0.855469---------------------- */ + else if (k < 0x3feb6000) + { + res = do_sin (x, 0, &cor); + retval = (res == res + 1.096 * cor) ? res : slow1 (x); + retval = __copysign (retval, x); + } /* else if (k < 0x3feb6000) */ + +/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/ + else if (k < 0x400368fd) + { + + t = hp0 - fabs (x); + res = do_cos (t, hp1, &cor); + retval = (res == res + 1.020 * cor) ? res : slow2 (x); + retval = __copysign (retval, x); + } /* else if (k < 0x400368fd) */ + +#ifndef IN_SINCOS +/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/ + else if (k < 0x419921FB) + { + double a, da; + int4 n = reduce_sincos_1 (x, &a, &da); + retval = do_sincos_1 (a, da, x, n, false); + } /* else if (k < 0x419921FB ) */ + +/*---------------------105414350 <|x|< 281474976710656 --------------------*/ + else if (k < 0x42F00000) + { + double a, da; + + int4 n = reduce_sincos_2 (x, &a, &da); + retval = do_sincos_2 (a, da, x, n, false); + } /* else if (k < 0x42F00000 ) */ + +/* -----------------281474976710656 <|x| <2^1024----------------------------*/ + else if (k < 0x7ff00000) + retval = reduce_and_compute (x, false); + +/*--------------------- |x| > 2^1024 ----------------------------------*/ + else + { + if (k == 0x7ff00000 && u.i[LOW_HALF] == 0) + __set_errno (EDOM); + retval = x / x; + } +#endif + + return retval; +} + + +/*******************************************************************/ +/* An ultimate cos routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of cos(x) */ +/*******************************************************************/ + +#ifdef IN_SINCOS +static double +#else +double +SECTION +#endif +__cos (double x) +{ + double y, xx, res, cor, a, da; + mynumber u; + int4 k, m; + + double retval = 0; + +#ifndef IN_SINCOS + SET_RESTORE_ROUND_53BIT (FE_TONEAREST); +#endif + + u.x = x; + m = u.i[HIGH_HALF]; + k = 0x7fffffff & m; + + /* |x|<2^-27 => cos(x)=1 */ + if (k < 0x3e400000) + retval = 1.0; + + else if (k < 0x3feb6000) + { /* 2^-27 < |x| < 0.855469 */ + res = do_cos (x, 0, &cor); + retval = (res == res + 1.020 * cor) ? res : cslow2 (x); + } /* else if (k < 0x3feb6000) */ + + else if (k < 0x400368fd) + { /* 0.855469 <|x|<2.426265 */ ; + y = hp0 - fabs (x); + a = y + hp1; + da = (y - a) + hp1; + xx = a * a; + if (xx < 0.01588) + { + res = TAYLOR_SIN (xx, a, da, cor); + cor = 1.02 * cor + __copysign (1.0e-31, cor); + retval = (res == res + cor) ? res : sloww (a, da, x, true); + } + else + { + res = do_sin (a, da, &cor); + cor = 1.035 * cor + __copysign (1.0e-31, cor); + retval = ((res == res + cor) ? __copysign (res, a) + : sloww1 (a, da, x, true)); + } + + } /* else if (k < 0x400368fd) */ + + +#ifndef IN_SINCOS + else if (k < 0x419921FB) + { /* 2.426265<|x|< 105414350 */ + double a, da; + int4 n = reduce_sincos_1 (x, &a, &da); + retval = do_sincos_1 (a, da, x, n, true); + } /* else if (k < 0x419921FB ) */ + + else if (k < 0x42F00000) + { + double a, da; + + int4 n = reduce_sincos_2 (x, &a, &da); + retval = do_sincos_2 (a, da, x, n, true); + } /* else if (k < 0x42F00000 ) */ + + /* 281474976710656 <|x| <2^1024 */ + else if (k < 0x7ff00000) + retval = reduce_and_compute (x, true); + + else + { + if (k == 0x7ff00000 && u.i[LOW_HALF] == 0) + __set_errno (EDOM); + retval = x / x; /* |x| > 2^1024 */ + } +#endif + + return retval; +} + +/************************************************************************/ +/* Routine compute sin(x) for 2^-26 < |x|< 0.25 by Taylor with more */ +/* precision and if still doesn't accurate enough by mpsin or dubsin */ +/************************************************************************/ + +static inline double +__always_inline +slow (double x) +{ + double res, cor, w[2]; + res = TAYLOR_SLOW (x, 0, cor); + if (res == res + 1.0007 * cor) + return res; + + __dubsin (fabs (x), 0, w); + if (w[0] == w[0] + 1.000000001 * w[1]) + return __copysign (w[0], x); + + return __copysign (__mpsin (fabs (x), 0, false), x); +} + +/*******************************************************************************/ +/* Routine compute sin(x) for 0.25<|x|< 0.855469 by __sincostab.tbl and Taylor */ +/* and if result still doesn't accurate enough by mpsin or dubsin */ +/*******************************************************************************/ + +static inline double +__always_inline +slow1 (double x) +{ + double w[2], cor, res; + + res = do_sin_slow (x, 0, 0, &cor); + if (res == res + cor) + return res; + + __dubsin (fabs (x), 0, w); + if (w[0] == w[0] + 1.000000005 * w[1]) + return w[0]; + + return __mpsin (fabs (x), 0, false); +} + +/**************************************************************************/ +/* Routine compute sin(x) for 0.855469 <|x|<2.426265 by __sincostab.tbl */ +/* and if result still doesn't accurate enough by mpsin or dubsin */ +/**************************************************************************/ +static inline double +__always_inline +slow2 (double x) +{ + double w[2], y, y1, y2, cor, res; + + double t = hp0 - fabs (x); + res = do_cos_slow (t, hp1, 0, &cor); + if (res == res + cor) + return res; + + y = fabs (x) - hp0; + y1 = y - hp1; + y2 = (y - y1) - hp1; + __docos (y1, y2, w); + if (w[0] == w[0] + 1.000000005 * w[1]) + return w[0]; + + return __mpsin (fabs (x), 0, false); +} + +/* Compute sin(x + dx) where X is small enough to use Taylor series around zero + and (x + dx) in the first or third quarter of the unit circle. ORIG is the + original value of X for computing error of the result. If the result is not + accurate enough, the routine calls mpsin or dubsin. SHIFT_QUADRANT rotates + the unit circle by 1 to compute the cosine instead of sine. */ +static inline double +__always_inline +sloww (double x, double dx, double orig, bool shift_quadrant) +{ + double y, t, res, cor, w[2], a, da, xn; + mynumber v; + int4 n; + res = TAYLOR_SLOW (x, dx, cor); + + double eps = fabs (orig) * 3.1e-30; + + cor = 1.0005 * cor + __copysign (eps, cor); + + if (res == res + cor) + return res; + + a = fabs (x); + da = (x > 0) ? dx : -dx; + __dubsin (a, da, w); + eps = fabs (orig) * 1.1e-30; + cor = 1.000000001 * w[1] + __copysign (eps, w[1]); + + if (w[0] == w[0] + cor) + return __copysign (w[0], x); + + t = (orig * hpinv + toint); + xn = t - toint; + v.x = t; + y = (orig - xn * mp1) - xn * mp2; + n = (v.i[LOW_HALF] + shift_quadrant) & 3; + da = xn * pp3; + t = y - da; + da = (y - t) - da; + y = xn * pp4; + a = t - y; + da = ((t - a) - y) + da; + + if (n & 2) + { + a = -a; + da = -da; + } + x = fabs (a); + dx = (a > 0) ? da : -da; + __dubsin (x, dx, w); + eps = fabs (orig) * 1.1e-40; + cor = 1.000000001 * w[1] + __copysign (eps, w[1]); + + if (w[0] == w[0] + cor) + return __copysign (w[0], a); + + return shift_quadrant ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); +} + +/* Compute sin(x + dx) where X is in the first or third quarter of the unit + circle. ORIG is the original value of X for computing error of the result. + If the result is not accurate enough, the routine calls mpsin or dubsin. + SHIFT_QUADRANT rotates the unit circle by 1 to compute the cosine instead of + sine. */ +static inline double +__always_inline +sloww1 (double x, double dx, double orig, bool shift_quadrant) +{ + double w[2], cor, res; + + res = do_sin_slow (x, dx, 3.1e-30 * fabs (orig), &cor); + + if (res == res + cor) + return __copysign (res, x); + + dx = (x > 0 ? dx : -dx); + __dubsin (fabs (x), dx, w); + + double eps = 1.1e-30 * fabs (orig); + cor = 1.000000005 * w[1] + __copysign (eps, w[1]); + + if (w[0] == w[0] + cor) + return __copysign (w[0], x); + + return shift_quadrant ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); +} + +/***************************************************************************/ +/* Routine compute sin(x+dx) (Double-Length number) where x in second or */ +/* fourth quarter of unit circle.Routine receive also the original value */ +/* and quarter(n= 1or 3)of x for computing error of result.And if result not*/ +/* accurate enough routine calls mpsin1 or dubsin */ +/***************************************************************************/ + +static inline double +__always_inline +sloww2 (double x, double dx, double orig, int n) +{ + double w[2], cor, res; + + res = do_cos_slow (x, dx, 3.1e-30 * fabs (orig), &cor); + + if (res == res + cor) + return (n & 2) ? -res : res; + + dx = x > 0 ? dx : -dx; + __docos (fabs (x), dx, w); + + double eps = 1.1e-30 * fabs (orig); + cor = 1.000000005 * w[1] + __copysign (eps, w[1]); + + if (w[0] == w[0] + cor) + return (n & 2) ? -w[0] : w[0]; + + return (n & 1) ? __mpsin (orig, 0, true) : __mpcos (orig, 0, true); +} + +/***************************************************************************/ +/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */ +/* is small enough to use Taylor series around zero and (x+dx) */ +/* in first or third quarter of unit circle.Routine receive also */ +/* (right argument) the original value of x for computing error of */ +/* result.And if result not accurate enough routine calls other routines */ +/***************************************************************************/ + +static inline double +__always_inline +bsloww (double x, double dx, double orig, int n) +{ + double res, cor, w[2], a, da; + + res = TAYLOR_SLOW (x, dx, cor); + cor = 1.0005 * cor + __copysign (1.1e-24, cor); + if (res == res + cor) + return res; + + a = fabs (x); + da = (x > 0) ? dx : -dx; + __dubsin (a, da, w); + cor = 1.000000001 * w[1] + __copysign (1.1e-24, w[1]); + + if (w[0] == w[0] + cor) + return __copysign (w[0], x); + + return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); +} + +/***************************************************************************/ +/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */ +/* in first or third quarter of unit circle.Routine receive also */ +/* (right argument) the original value of x for computing error of result.*/ +/* And if result not accurate enough routine calls other routines */ +/***************************************************************************/ + +static inline double +__always_inline +bsloww1 (double x, double dx, double orig, int n) +{ + double w[2], cor, res; + + res = do_sin_slow (x, dx, 1.1e-24, &cor); + if (res == res + cor) + return (x > 0) ? res : -res; + + dx = (x > 0) ? dx : -dx; + __dubsin (fabs (x), dx, w); + + cor = 1.000000005 * w[1] + __copysign (1.1e-24, w[1]); + + if (w[0] == w[0] + cor) + return __copysign (w[0], x); + + return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); +} + +/***************************************************************************/ +/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */ +/* in second or fourth quarter of unit circle.Routine receive also the */ +/* original value and quarter(n= 1or 3)of x for computing error of result. */ +/* And if result not accurate enough routine calls other routines */ +/***************************************************************************/ + +static inline double +__always_inline +bsloww2 (double x, double dx, double orig, int n) +{ + double w[2], cor, res; + + res = do_cos_slow (x, dx, 1.1e-24, &cor); + if (res == res + cor) + return (n & 2) ? -res : res; + + dx = (x > 0) ? dx : -dx; + __docos (fabs (x), dx, w); + + cor = 1.000000005 * w[1] + __copysign (1.1e-24, w[1]); + + if (w[0] == w[0] + cor) + return (n & 2) ? -w[0] : w[0]; + + return (n & 1) ? __mpsin (orig, 0, true) : __mpcos (orig, 0, true); +} + +/************************************************************************/ +/* Routine compute cos(x) for 2^-27 < |x|< 0.25 by Taylor with more */ +/* precision and if still doesn't accurate enough by mpcos or docos */ +/************************************************************************/ + +static inline double +__always_inline +cslow2 (double x) +{ + double w[2], cor, res; + + res = do_cos_slow (x, 0, 0, &cor); + if (res == res + cor) + return res; + + __docos (fabs (x), 0, w); + if (w[0] == w[0] + 1.000000005 * w[1]) + return w[0]; + + return __mpcos (x, 0, false); +} + +#ifndef __cos +weak_alias (__cos, cos) +# ifdef NO_LONG_DOUBLE +strong_alias (__cos, __cosl) +weak_alias (__cos, cosl) +# endif +#endif +#ifndef __sin +weak_alias (__sin, sin) +# ifdef NO_LONG_DOUBLE +strong_alias (__sin, __sinl) +weak_alias (__sin, sinl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_sincos.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_sincos.c new file mode 100644 index 0000000000..05cff50ce8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_sincos.c @@ -0,0 +1,113 @@ +/* Compute sine and cosine of argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <math.h> + +#include <math_private.h> + +#define __sin __sin_local +#define __cos __cos_local +#define IN_SINCOS 1 +#include "s_sin.c" + +/* Consolidated version of reduce_and_compute in s_sin.c that does range + reduction only once and computes sin and cos together. */ +static inline void +__always_inline +reduce_and_compute_sincos (double x, double *sinx, double *cosx) +{ + double a, da; + unsigned int n = __branred (x, &a, &da); + + n = n & 3; + + if (n == 1 || n == 2) + { + a = -a; + da = -da; + } + + if (n & 1) + { + double *temp = cosx; + cosx = sinx; + sinx = temp; + } + + if (a * a < 0.01588) + *sinx = bsloww (a, da, x, n); + else + *sinx = bsloww1 (a, da, x, n); + *cosx = bsloww2 (a, da, x, n); +} + +void +__sincos (double x, double *sinx, double *cosx) +{ + mynumber u; + int k; + + SET_RESTORE_ROUND_53BIT (FE_TONEAREST); + + u.x = x; + k = 0x7fffffff & u.i[HIGH_HALF]; + + if (k < 0x400368fd) + { + *sinx = __sin_local (x); + *cosx = __cos_local (x); + return; + } + if (k < 0x419921FB) + { + double a, da; + int4 n = reduce_sincos_1 (x, &a, &da); + + *sinx = do_sincos_1 (a, da, x, n, false); + *cosx = do_sincos_1 (a, da, x, n, true); + + return; + } + if (k < 0x42F00000) + { + double a, da; + int4 n = reduce_sincos_2 (x, &a, &da); + + *sinx = do_sincos_2 (a, da, x, n, false); + *cosx = do_sincos_2 (a, da, x, n, true); + + return; + } + if (k < 0x7ff00000) + { + reduce_and_compute_sincos (x, sinx, cosx); + return; + } + + if (isinf (x)) + __set_errno (EDOM); + + *sinx = *cosx = x / x; +} +weak_alias (__sincos, sincos) +#ifdef NO_LONG_DOUBLE +strong_alias (__sincos, __sincosl) +weak_alias (__sincos, sincosl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_tan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_tan.c new file mode 100644 index 0000000000..b2a8681a6d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_tan.c @@ -0,0 +1,848 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*********************************************************************/ +/* MODULE_NAME: utan.c */ +/* */ +/* FUNCTIONS: utan */ +/* tanMp */ +/* */ +/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h utan.h */ +/* branred.c sincos32.c mptan.c */ +/* utan.tbl */ +/* */ +/* An ultimate tan routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of tan(x). */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/*********************************************************************/ + +#include <errno.h> +#include <float.h> +#include "endian.h" +#include <dla.h> +#include "mpa.h" +#include "MathLib.h" +#include <math.h> +#include <math_private.h> +#include <fenv.h> +#include <stap-probe.h> + +#ifndef SECTION +# define SECTION +#endif + +static double tanMp (double); +void __mptan (double, mp_no *, int); + +double +SECTION +tan (double x) +{ +#include "utan.h" +#include "utan.tbl" + + int ux, i, n; + double a, da, a2, b, db, c, dc, c1, cc1, c2, cc2, c3, cc3, fi, ffi, gi, pz, + s, sy, t, t1, t2, t3, t4, t7, t8, t9, t10, w, x2, xn, xx2, y, ya, + yya, z0, z, zz, z2, zz2; +#ifndef DLA_FMS + double t5, t6; +#endif + int p; + number num, v; + mp_no mpa, mpt1, mpt2; + + double retval; + + int __branred (double, double *, double *); + int __mpranred (double, mp_no *, int); + + SET_RESTORE_ROUND_53BIT (FE_TONEAREST); + + /* x=+-INF, x=NaN */ + num.d = x; + ux = num.i[HIGH_HALF]; + if ((ux & 0x7ff00000) == 0x7ff00000) + { + if ((ux & 0x7fffffff) == 0x7ff00000) + __set_errno (EDOM); + retval = x - x; + goto ret; + } + + w = (x < 0.0) ? -x : x; + + /* (I) The case abs(x) <= 1.259e-8 */ + if (w <= g1.d) + { + math_check_force_underflow_nonneg (w); + retval = x; + goto ret; + } + + /* (II) The case 1.259e-8 < abs(x) <= 0.0608 */ + if (w <= g2.d) + { + /* First stage */ + x2 = x * x; + + t2 = d9.d + x2 * d11.d; + t2 = d7.d + x2 * t2; + t2 = d5.d + x2 * t2; + t2 = d3.d + x2 * t2; + t2 *= x * x2; + + if ((y = x + (t2 - u1.d * t2)) == x + (t2 + u1.d * t2)) + { + retval = y; + goto ret; + } + + /* Second stage */ + c1 = a25.d + x2 * a27.d; + c1 = a23.d + x2 * c1; + c1 = a21.d + x2 * c1; + c1 = a19.d + x2 * c1; + c1 = a17.d + x2 * c1; + c1 = a15.d + x2 * c1; + c1 *= x2; + + EMULV (x, x, x2, xx2, t1, t2, t3, t4, t5); + ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (x, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (x, 0.0, c2, cc2, c1, cc1, t1, t2); + if ((y = c1 + (cc1 - u2.d * c1)) == c1 + (cc1 + u2.d * c1)) + { + retval = y; + goto ret; + } + retval = tanMp (x); + goto ret; + } + + /* (III) The case 0.0608 < abs(x) <= 0.787 */ + if (w <= g3.d) + { + /* First stage */ + i = ((int) (mfftnhf.d + TWO8 * w)); + z = w - xfg[i][0].d; + z2 = z * z; + s = (x < 0.0) ? -1 : 1; + pz = z + z * z2 * (e0.d + z2 * e1.d); + fi = xfg[i][1].d; + gi = xfg[i][2].d; + t2 = pz * (gi + fi) / (gi - pz); + if ((y = fi + (t2 - fi * u3.d)) == fi + (t2 + fi * u3.d)) + { + retval = (s * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = fi * ua3.d + t3 * ub3.d; + if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) + { + retval = (s * y); + goto ret; + } + + /* Second stage */ + ffi = xfg[i][3].d; + c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); + EMULV (z, z, z2, zz2, t1, t2, t3, t4, t5); + ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (z, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (z, 0.0, c2, cc2, c1, cc1, t1, t2); + + ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); + MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); + SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); + DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + + if ((y = c3 + (cc3 - u4.d * c3)) == c3 + (cc3 + u4.d * c3)) + { + retval = (s * y); + goto ret; + } + retval = tanMp (x); + goto ret; + } + + /* (---) The case 0.787 < abs(x) <= 25 */ + if (w <= g4.d) + { + /* Range reduction by algorithm i */ + t = (x * hpinv.d + toint.d); + xn = t - toint.d; + v.d = t; + t1 = (x - xn * mp1.d) - xn * mp2.d; + n = v.i[LOW_HALF] & 0x00000001; + da = xn * mp3.d; + a = t1 - da; + da = (t1 - a) - da; + if (a < 0.0) + { + ya = -a; + yya = -da; + sy = -1; + } + else + { + ya = a; + yya = da; + sy = 1; + } + + /* (IV),(V) The case 0.787 < abs(x) <= 25, abs(y) <= 1e-7 */ + if (ya <= gy1.d) + { + retval = tanMp (x); + goto ret; + } + + /* (VI) The case 0.787 < abs(x) <= 25, 1e-7 < abs(y) <= 0.0608 */ + if (ya <= gy2.d) + { + a2 = a * a; + t2 = d9.d + a2 * d11.d; + t2 = d7.d + a2 * t2; + t2 = d5.d + a2 * t2; + t2 = d3.d + a2 * t2; + t2 = da + a * a2 * t2; + + if (n) + { + /* First stage -cot */ + EADD (a, t2, b, db); + DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8, + t9, t10); + if ((y = c + (dc - u6.d * c)) == c + (dc + u6.d * c)) + { + retval = (-y); + goto ret; + } + } + else + { + /* First stage tan */ + if ((y = a + (t2 - u5.d * a)) == a + (t2 + u5.d * a)) + { + retval = y; + goto ret; + } + } + /* Second stage */ + /* Range reduction by algorithm ii */ + t = (x * hpinv.d + toint.d); + xn = t - toint.d; + v.d = t; + t1 = (x - xn * mp1.d) - xn * mp2.d; + n = v.i[LOW_HALF] & 0x00000001; + da = xn * pp3.d; + t = t1 - da; + da = (t1 - t) - da; + t1 = xn * pp4.d; + a = t - t1; + da = ((t - a) - t1) + da; + + /* Second stage */ + EADD (a, da, t1, t2); + a = t1; + da = t2; + MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8); + + c1 = a25.d + x2 * a27.d; + c1 = a23.d + x2 * c1; + c1 = a21.d + x2 * c1; + c1 = a19.d + x2 * c1; + c1 = a17.d + x2 * c1; + c1 = a15.d + x2 * c1; + c1 *= x2; + + ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); + + if (n) + { + /* Second stage -cot */ + DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, + t8, t9, t10); + if ((y = c2 + (cc2 - u8.d * c2)) == c2 + (cc2 + u8.d * c2)) + { + retval = (-y); + goto ret; + } + } + else + { + /* Second stage tan */ + if ((y = c1 + (cc1 - u7.d * c1)) == c1 + (cc1 + u7.d * c1)) + { + retval = y; + goto ret; + } + } + retval = tanMp (x); + goto ret; + } + + /* (VII) The case 0.787 < abs(x) <= 25, 0.0608 < abs(y) <= 0.787 */ + + /* First stage */ + i = ((int) (mfftnhf.d + TWO8 * ya)); + z = (z0 = (ya - xfg[i][0].d)) + yya; + z2 = z * z; + pz = z + z * z2 * (e0.d + z2 * e1.d); + fi = xfg[i][1].d; + gi = xfg[i][2].d; + + if (n) + { + /* -cot */ + t2 = pz * (fi + gi) / (fi + pz); + if ((y = gi - (t2 - gi * u10.d)) == gi - (t2 + gi * u10.d)) + { + retval = (-sy * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = gi * ua10.d + t3 * ub10.d; + if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) + { + retval = (-sy * y); + goto ret; + } + } + else + { + /* tan */ + t2 = pz * (gi + fi) / (gi - pz); + if ((y = fi + (t2 - fi * u9.d)) == fi + (t2 + fi * u9.d)) + { + retval = (sy * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = fi * ua9.d + t3 * ub9.d; + if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) + { + retval = (sy * y); + goto ret; + } + } + + /* Second stage */ + ffi = xfg[i][3].d; + EADD (z0, yya, z, zz) + MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8); + c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); + ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); + + ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); + MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); + SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); + + if (n) + { + /* -cot */ + DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c3 + (cc3 - u12.d * c3)) == c3 + (cc3 + u12.d * c3)) + { + retval = (-sy * y); + goto ret; + } + } + else + { + /* tan */ + DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c3 + (cc3 - u11.d * c3)) == c3 + (cc3 + u11.d * c3)) + { + retval = (sy * y); + goto ret; + } + } + + retval = tanMp (x); + goto ret; + } + + /* (---) The case 25 < abs(x) <= 1e8 */ + if (w <= g5.d) + { + /* Range reduction by algorithm ii */ + t = (x * hpinv.d + toint.d); + xn = t - toint.d; + v.d = t; + t1 = (x - xn * mp1.d) - xn * mp2.d; + n = v.i[LOW_HALF] & 0x00000001; + da = xn * pp3.d; + t = t1 - da; + da = (t1 - t) - da; + t1 = xn * pp4.d; + a = t - t1; + da = ((t - a) - t1) + da; + EADD (a, da, t1, t2); + a = t1; + da = t2; + if (a < 0.0) + { + ya = -a; + yya = -da; + sy = -1; + } + else + { + ya = a; + yya = da; + sy = 1; + } + + /* (+++) The case 25 < abs(x) <= 1e8, abs(y) <= 1e-7 */ + if (ya <= gy1.d) + { + retval = tanMp (x); + goto ret; + } + + /* (VIII) The case 25 < abs(x) <= 1e8, 1e-7 < abs(y) <= 0.0608 */ + if (ya <= gy2.d) + { + a2 = a * a; + t2 = d9.d + a2 * d11.d; + t2 = d7.d + a2 * t2; + t2 = d5.d + a2 * t2; + t2 = d3.d + a2 * t2; + t2 = da + a * a2 * t2; + + if (n) + { + /* First stage -cot */ + EADD (a, t2, b, db); + DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8, + t9, t10); + if ((y = c + (dc - u14.d * c)) == c + (dc + u14.d * c)) + { + retval = (-y); + goto ret; + } + } + else + { + /* First stage tan */ + if ((y = a + (t2 - u13.d * a)) == a + (t2 + u13.d * a)) + { + retval = y; + goto ret; + } + } + + /* Second stage */ + MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8); + c1 = a25.d + x2 * a27.d; + c1 = a23.d + x2 * c1; + c1 = a21.d + x2 * c1; + c1 = a19.d + x2 * c1; + c1 = a17.d + x2 * c1; + c1 = a15.d + x2 * c1; + c1 *= x2; + + ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); + + if (n) + { + /* Second stage -cot */ + DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, + t8, t9, t10); + if ((y = c2 + (cc2 - u16.d * c2)) == c2 + (cc2 + u16.d * c2)) + { + retval = (-y); + goto ret; + } + } + else + { + /* Second stage tan */ + if ((y = c1 + (cc1 - u15.d * c1)) == c1 + (cc1 + u15.d * c1)) + { + retval = (y); + goto ret; + } + } + retval = tanMp (x); + goto ret; + } + + /* (IX) The case 25 < abs(x) <= 1e8, 0.0608 < abs(y) <= 0.787 */ + /* First stage */ + i = ((int) (mfftnhf.d + TWO8 * ya)); + z = (z0 = (ya - xfg[i][0].d)) + yya; + z2 = z * z; + pz = z + z * z2 * (e0.d + z2 * e1.d); + fi = xfg[i][1].d; + gi = xfg[i][2].d; + + if (n) + { + /* -cot */ + t2 = pz * (fi + gi) / (fi + pz); + if ((y = gi - (t2 - gi * u18.d)) == gi - (t2 + gi * u18.d)) + { + retval = (-sy * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = gi * ua18.d + t3 * ub18.d; + if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) + { + retval = (-sy * y); + goto ret; + } + } + else + { + /* tan */ + t2 = pz * (gi + fi) / (gi - pz); + if ((y = fi + (t2 - fi * u17.d)) == fi + (t2 + fi * u17.d)) + { + retval = (sy * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = fi * ua17.d + t3 * ub17.d; + if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) + { + retval = (sy * y); + goto ret; + } + } + + /* Second stage */ + ffi = xfg[i][3].d; + EADD (z0, yya, z, zz); + MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8); + c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); + ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); + + ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); + MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); + SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); + + if (n) + { + /* -cot */ + DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c3 + (cc3 - u20.d * c3)) == c3 + (cc3 + u20.d * c3)) + { + retval = (-sy * y); + goto ret; + } + } + else + { + /* tan */ + DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c3 + (cc3 - u19.d * c3)) == c3 + (cc3 + u19.d * c3)) + { + retval = (sy * y); + goto ret; + } + } + retval = tanMp (x); + goto ret; + } + + /* (---) The case 1e8 < abs(x) < 2**1024 */ + /* Range reduction by algorithm iii */ + n = (__branred (x, &a, &da)) & 0x00000001; + EADD (a, da, t1, t2); + a = t1; + da = t2; + if (a < 0.0) + { + ya = -a; + yya = -da; + sy = -1; + } + else + { + ya = a; + yya = da; + sy = 1; + } + + /* (+++) The case 1e8 < abs(x) < 2**1024, abs(y) <= 1e-7 */ + if (ya <= gy1.d) + { + retval = tanMp (x); + goto ret; + } + + /* (X) The case 1e8 < abs(x) < 2**1024, 1e-7 < abs(y) <= 0.0608 */ + if (ya <= gy2.d) + { + a2 = a * a; + t2 = d9.d + a2 * d11.d; + t2 = d7.d + a2 * t2; + t2 = d5.d + a2 * t2; + t2 = d3.d + a2 * t2; + t2 = da + a * a2 * t2; + if (n) + { + /* First stage -cot */ + EADD (a, t2, b, db); + DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c + (dc - u22.d * c)) == c + (dc + u22.d * c)) + { + retval = (-y); + goto ret; + } + } + else + { + /* First stage tan */ + if ((y = a + (t2 - u21.d * a)) == a + (t2 + u21.d * a)) + { + retval = y; + goto ret; + } + } + + /* Second stage */ + /* Reduction by algorithm iv */ + p = 10; + n = (__mpranred (x, &mpa, p)) & 0x00000001; + __mp_dbl (&mpa, &a, p); + __dbl_mp (a, &mpt1, p); + __sub (&mpa, &mpt1, &mpt2, p); + __mp_dbl (&mpt2, &da, p); + + MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8); + + c1 = a25.d + x2 * a27.d; + c1 = a23.d + x2 * c1; + c1 = a21.d + x2 * c1; + c1 = a19.d + x2 * c1; + c1 = a17.d + x2 * c1; + c1 = a15.d + x2 * c1; + c1 *= x2; + + ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); + + if (n) + { + /* Second stage -cot */ + DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8, + t9, t10); + if ((y = c2 + (cc2 - u24.d * c2)) == c2 + (cc2 + u24.d * c2)) + { + retval = (-y); + goto ret; + } + } + else + { + /* Second stage tan */ + if ((y = c1 + (cc1 - u23.d * c1)) == c1 + (cc1 + u23.d * c1)) + { + retval = y; + goto ret; + } + } + retval = tanMp (x); + goto ret; + } + + /* (XI) The case 1e8 < abs(x) < 2**1024, 0.0608 < abs(y) <= 0.787 */ + /* First stage */ + i = ((int) (mfftnhf.d + TWO8 * ya)); + z = (z0 = (ya - xfg[i][0].d)) + yya; + z2 = z * z; + pz = z + z * z2 * (e0.d + z2 * e1.d); + fi = xfg[i][1].d; + gi = xfg[i][2].d; + + if (n) + { + /* -cot */ + t2 = pz * (fi + gi) / (fi + pz); + if ((y = gi - (t2 - gi * u26.d)) == gi - (t2 + gi * u26.d)) + { + retval = (-sy * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = gi * ua26.d + t3 * ub26.d; + if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) + { + retval = (-sy * y); + goto ret; + } + } + else + { + /* tan */ + t2 = pz * (gi + fi) / (gi - pz); + if ((y = fi + (t2 - fi * u25.d)) == fi + (t2 + fi * u25.d)) + { + retval = (sy * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = fi * ua25.d + t3 * ub25.d; + if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) + { + retval = (sy * y); + goto ret; + } + } + + /* Second stage */ + ffi = xfg[i][3].d; + EADD (z0, yya, z, zz); + MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8); + c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); + ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); + + ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); + MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); + SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); + + if (n) + { + /* -cot */ + DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c3 + (cc3 - u28.d * c3)) == c3 + (cc3 + u28.d * c3)) + { + retval = (-sy * y); + goto ret; + } + } + else + { + /* tan */ + DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c3 + (cc3 - u27.d * c3)) == c3 + (cc3 + u27.d * c3)) + { + retval = (sy * y); + goto ret; + } + } + retval = tanMp (x); + goto ret; + +ret: + return retval; +} + +/* multiple precision stage */ +/* Convert x to multi precision number,compute tan(x) by mptan() routine */ +/* and converts result back to double */ +static double +SECTION +tanMp (double x) +{ + int p; + double y; + mp_no mpy; + p = 32; + __mptan (x, &mpy, p); + __mp_dbl (&mpy, &y, p); + LIBC_PROBE (slowtan, 2, &x, &y); + return y; +} + +#ifdef NO_LONG_DOUBLE +weak_alias (tan, tanl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_tanh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_tanh.c new file mode 100644 index 0000000000..344a2f0330 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_tanh.c @@ -0,0 +1,98 @@ +/* @(#)s_tanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $"; +#endif + +/* Tanh(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanh(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanh(-x) = -tanh(x). + * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) + * -t + * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) + * t + 2 + * 2 + * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) + * t + 2 + * 22.0 < x <= INF : tanh(x) := 1. + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const double one = 1.0, two = 2.0, tiny = 1.0e-300; + +double +__tanh (double x) +{ + double t, z; + int32_t jx, ix, lx; + + /* High word of |x|. */ + EXTRACT_WORDS (jx, lx, x); + ix = jx & 0x7fffffff; + + /* x is INF or NaN */ + if (ix >= 0x7ff00000) + { + if (jx >= 0) + return one / x + one; /* tanh(+-inf)=+-1 */ + else + return one / x - one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x40360000) /* |x|<22 */ + { + if ((ix | lx) == 0) + return x; /* x == +-0 */ + if (ix < 0x3c800000) /* |x|<2**-55 */ + { + math_check_force_underflow (x); + return x * (one + x); /* tanh(small) = small */ + } + if (ix >= 0x3ff00000) /* |x|>=1 */ + { + t = __expm1 (two * fabs (x)); + z = one - two / (t + two); + } + else + { + t = __expm1 (-two * fabs (x)); + z = -t / (t + two); + } + /* |x| > 22, return +-1 */ + } + else + { + z = one - tiny; /* raised inexact flag */ + } + return (jx >= 0) ? z : -z; +} +weak_alias (__tanh, tanh) +#ifdef NO_LONG_DOUBLE +strong_alias (__tanh, __tanhl) +weak_alias (__tanh, tanhl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_totalorder.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_totalorder.c new file mode 100644 index 0000000000..f229119c27 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_totalorder.c @@ -0,0 +1,54 @@ +/* Total order operation. dbl-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalorder (double x, double y) +{ + int32_t hx, hy; + uint32_t lx, ly; + EXTRACT_WORDS (hx, lx, x); + EXTRACT_WORDS (hy, ly, y); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + uint32_t uhx = hx & 0x7fffffff, uhy = hy & 0x7fffffff; + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the arguments interpreted as + sign-magnitude integers. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if ((uhx > 0x7ff00000 || (uhx == 0x7ff00000 && lx != 0)) + && (uhy > 0x7ff00000 || (uhy == 0x7ff00000 && ly != 0))) + { + hx ^= 0x00080000; + hy ^= 0x00080000; + } +#endif + uint32_t hx_sign = hx >> 31; + uint32_t hy_sign = hy >> 31; + hx ^= hx_sign >> 1; + lx ^= hx_sign; + hy ^= hy_sign >> 1; + ly ^= hy_sign; + return hx < hy || (hx == hy && lx <= ly); +} +#ifdef NO_LONG_DOUBLE +weak_alias (totalorder, totalorderl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_totalordermag.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_totalordermag.c new file mode 100644 index 0000000000..b1bdd833db --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_totalordermag.c @@ -0,0 +1,49 @@ +/* Total order operation on absolute values. dbl-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalordermag (double x, double y) +{ + uint32_t hx, hy; + uint32_t lx, ly; + EXTRACT_WORDS (hx, lx, x); + EXTRACT_WORDS (hy, ly, y); + hx &= 0x7fffffff; + hy &= 0x7fffffff; +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the absolute values of the + arguments. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if ((hx > 0x7ff00000 || (hx == 0x7ff00000 && lx != 0)) + && (hy > 0x7ff00000 || (hy == 0x7ff00000 && ly != 0))) + { + hx ^= 0x00080000; + hy ^= 0x00080000; + } +#endif + return hx < hy || (hx == hy && lx <= ly); +} +#ifdef NO_LONG_DOUBLE +weak_alias (totalordermag, totalordermagl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_trunc.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_trunc.c new file mode 100644 index 0000000000..730c1b377c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_trunc.c @@ -0,0 +1,62 @@ +/* Truncate argument to nearest integral value not larger than the argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +double +__trunc (double x) +{ + int32_t i0, j0; + u_int32_t i1; + int sx; + + EXTRACT_WORDS (i0, i1, x); + sx = i0 & 0x80000000; + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 20) + { + if (j0 < 0) + /* The magnitude of the number is < 1 so the result is +-0. */ + INSERT_WORDS (x, sx, 0); + else + INSERT_WORDS (x, sx | (i0 & ~(0x000fffff >> j0)), 0); + } + else if (j0 > 51) + { + if (j0 == 0x400) + /* x is inf or NaN. */ + return x + x; + } + else + { + INSERT_WORDS (x, i0, i1 & ~(0xffffffffu >> (j0 - 20))); + } + + return x; +} +#ifndef __trunc +weak_alias (__trunc, trunc) +# ifdef NO_LONG_DOUBLE +strong_alias (__trunc, __truncl) +weak_alias (__trunc, truncl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_ufromfp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_ufromfp.c new file mode 100644 index 0000000000..c3d9047930 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_ufromfp.c @@ -0,0 +1,7 @@ +#define UNSIGNED 1 +#define INEXACT 0 +#define FUNC ufromfp +#include <s_fromfp_main.c> +#ifdef NO_LONG_DOUBLE +weak_alias (ufromfp, ufromfpl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_ufromfpx.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_ufromfpx.c new file mode 100644 index 0000000000..dee607f8c0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_ufromfpx.c @@ -0,0 +1,7 @@ +#define UNSIGNED 1 +#define INEXACT 1 +#define FUNC ufromfpx +#include <s_fromfp_main.c> +#ifdef NO_LONG_DOUBLE +weak_alias (ufromfpx, ufromfpxl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/sincos32.c b/REORG.TODO/sysdeps/ieee754/dbl-64/sincos32.c new file mode 100644 index 0000000000..9cd8e2f97f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/sincos32.c @@ -0,0 +1,369 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/****************************************************************/ +/* MODULE_NAME: sincos32.c */ +/* */ +/* FUNCTIONS: ss32 */ +/* cc32 */ +/* c32 */ +/* sin32 */ +/* cos32 */ +/* mpsin */ +/* mpcos */ +/* mpranred */ +/* mpsin1 */ +/* mpcos1 */ +/* */ +/* FILES NEEDED: endian.h mpa.h sincos32.h */ +/* mpa.c */ +/* */ +/* Multi Precision sin() and cos() function with p=32 for sin()*/ +/* cos() arcsin() and arccos() routines */ +/* In addition mpranred() routine performs range reduction of */ +/* a double number x into multi precision number y, */ +/* such that y=x-n*pi/2, abs(y)<pi/4, n=0,+-1,+-2,.... */ +/****************************************************************/ +#include "endian.h" +#include "mpa.h" +#include "sincos32.h" +#include <math.h> +#include <math_private.h> +#include <stap-probe.h> + +#ifndef SECTION +# define SECTION +#endif + +/* Compute Multi-Precision sin() function for given p. Receive Multi Precision + number x and result stored at y. */ +static void +SECTION +ss32 (mp_no *x, mp_no *y, int p) +{ + int i; + double a; + mp_no mpt1, x2, gor, sum, mpk = {1, {1.0}}; + for (i = 1; i <= p; i++) + mpk.d[i] = 0; + + __sqr (x, &x2, p); + __cpy (&oofac27, &gor, p); + __cpy (&gor, &sum, p); + for (a = 27.0; a > 1.0; a -= 2.0) + { + mpk.d[1] = a * (a - 1.0); + __mul (&gor, &mpk, &mpt1, p); + __cpy (&mpt1, &gor, p); + __mul (&x2, &sum, &mpt1, p); + __sub (&gor, &mpt1, &sum, p); + } + __mul (x, &sum, y, p); +} + +/* Compute Multi-Precision cos() function for given p. Receive Multi Precision + number x and result stored at y. */ +static void +SECTION +cc32 (mp_no *x, mp_no *y, int p) +{ + int i; + double a; + mp_no mpt1, x2, gor, sum, mpk = {1, {1.0}}; + for (i = 1; i <= p; i++) + mpk.d[i] = 0; + + __sqr (x, &x2, p); + mpk.d[1] = 27.0; + __mul (&oofac27, &mpk, &gor, p); + __cpy (&gor, &sum, p); + for (a = 26.0; a > 2.0; a -= 2.0) + { + mpk.d[1] = a * (a - 1.0); + __mul (&gor, &mpk, &mpt1, p); + __cpy (&mpt1, &gor, p); + __mul (&x2, &sum, &mpt1, p); + __sub (&gor, &mpt1, &sum, p); + } + __mul (&x2, &sum, y, p); +} + +/* Compute both sin(x), cos(x) as Multi precision numbers. */ +void +SECTION +__c32 (mp_no *x, mp_no *y, mp_no *z, int p) +{ + mp_no u, t, t1, t2, c, s; + int i; + __cpy (x, &u, p); + u.e = u.e - 1; + cc32 (&u, &c, p); + ss32 (&u, &s, p); + for (i = 0; i < 24; i++) + { + __mul (&c, &s, &t, p); + __sub (&s, &t, &t1, p); + __add (&t1, &t1, &s, p); + __sub (&__mptwo, &c, &t1, p); + __mul (&t1, &c, &t2, p); + __add (&t2, &t2, &c, p); + } + __sub (&__mpone, &c, y, p); + __cpy (&s, z, p); +} + +/* Receive double x and two double results of sin(x) and return result which is + more accurate, computing sin(x) with multi precision routine c32. */ +double +SECTION +__sin32 (double x, double res, double res1) +{ + int p; + mp_no a, b, c; + p = 32; + __dbl_mp (res, &a, p); + __dbl_mp (0.5 * (res1 - res), &b, p); + __add (&a, &b, &c, p); + if (x > 0.8) + { + __sub (&hp, &c, &a, p); + __c32 (&a, &b, &c, p); + } + else + __c32 (&c, &a, &b, p); /* b=sin(0.5*(res+res1)) */ + __dbl_mp (x, &c, p); /* c = x */ + __sub (&b, &c, &a, p); + /* if a > 0 return min (res, res1), otherwise return max (res, res1). */ + if ((a.d[0] > 0 && res >= res1) || (a.d[0] <= 0 && res <= res1)) + res = res1; + LIBC_PROBE (slowasin, 2, &res, &x); + return res; +} + +/* Receive double x and two double results of cos(x) and return result which is + more accurate, computing cos(x) with multi precision routine c32. */ +double +SECTION +__cos32 (double x, double res, double res1) +{ + int p; + mp_no a, b, c; + p = 32; + __dbl_mp (res, &a, p); + __dbl_mp (0.5 * (res1 - res), &b, p); + __add (&a, &b, &c, p); + if (x > 2.4) + { + __sub (&pi, &c, &a, p); + __c32 (&a, &b, &c, p); + b.d[0] = -b.d[0]; + } + else if (x > 0.8) + { + __sub (&hp, &c, &a, p); + __c32 (&a, &c, &b, p); + } + else + __c32 (&c, &b, &a, p); /* b=cos(0.5*(res+res1)) */ + __dbl_mp (x, &c, p); /* c = x */ + __sub (&b, &c, &a, p); + /* if a > 0 return max (res, res1), otherwise return min (res, res1). */ + if ((a.d[0] > 0 && res <= res1) || (a.d[0] <= 0 && res >= res1)) + res = res1; + LIBC_PROBE (slowacos, 2, &res, &x); + return res; +} + +/* Compute sin() of double-length number (X + DX) as Multi Precision number and + return result as double. If REDUCE_RANGE is true, X is assumed to be the + original input and DX is ignored. */ +double +SECTION +__mpsin (double x, double dx, bool reduce_range) +{ + double y; + mp_no a, b, c, s; + int n; + int p = 32; + + if (reduce_range) + { + n = __mpranred (x, &a, p); /* n is 0, 1, 2 or 3. */ + __c32 (&a, &c, &s, p); + } + else + { + n = -1; + __dbl_mp (x, &b, p); + __dbl_mp (dx, &c, p); + __add (&b, &c, &a, p); + if (x > 0.8) + { + __sub (&hp, &a, &b, p); + __c32 (&b, &s, &c, p); + } + else + __c32 (&a, &c, &s, p); /* b = sin(x+dx) */ + } + + /* Convert result based on which quarter of unit circle y is in. */ + switch (n) + { + case 1: + __mp_dbl (&c, &y, p); + break; + + case 3: + __mp_dbl (&c, &y, p); + y = -y; + break; + + case 2: + __mp_dbl (&s, &y, p); + y = -y; + break; + + /* Quadrant not set, so the result must be sin (X + DX), which is also in + S. */ + case 0: + default: + __mp_dbl (&s, &y, p); + } + LIBC_PROBE (slowsin, 3, &x, &dx, &y); + return y; +} + +/* Compute cos() of double-length number (X + DX) as Multi Precision number and + return result as double. If REDUCE_RANGE is true, X is assumed to be the + original input and DX is ignored. */ +double +SECTION +__mpcos (double x, double dx, bool reduce_range) +{ + double y; + mp_no a, b, c, s; + int n; + int p = 32; + + if (reduce_range) + { + n = __mpranred (x, &a, p); /* n is 0, 1, 2 or 3. */ + __c32 (&a, &c, &s, p); + } + else + { + n = -1; + __dbl_mp (x, &b, p); + __dbl_mp (dx, &c, p); + __add (&b, &c, &a, p); + if (x > 0.8) + { + __sub (&hp, &a, &b, p); + __c32 (&b, &s, &c, p); + } + else + __c32 (&a, &c, &s, p); /* a = cos(x+dx) */ + } + + /* Convert result based on which quarter of unit circle y is in. */ + switch (n) + { + case 1: + __mp_dbl (&s, &y, p); + y = -y; + break; + + case 3: + __mp_dbl (&s, &y, p); + break; + + case 2: + __mp_dbl (&c, &y, p); + y = -y; + break; + + /* Quadrant not set, so the result must be cos (X + DX), which is also + stored in C. */ + case 0: + default: + __mp_dbl (&c, &y, p); + } + LIBC_PROBE (slowcos, 3, &x, &dx, &y); + return y; +} + +/* Perform range reduction of a double number x into multi precision number y, + such that y = x - n * pi / 2, abs (y) < pi / 4, n = 0, +-1, +-2, ... + Return int which indicates in which quarter of circle x is. */ +int +SECTION +__mpranred (double x, mp_no *y, int p) +{ + number v; + double t, xn; + int i, k, n; + mp_no a, b, c; + + if (fabs (x) < 2.8e14) + { + t = (x * hpinv.d + toint.d); + xn = t - toint.d; + v.d = t; + n = v.i[LOW_HALF] & 3; + __dbl_mp (xn, &a, p); + __mul (&a, &hp, &b, p); + __dbl_mp (x, &c, p); + __sub (&c, &b, y, p); + return n; + } + else + { + /* If x is very big more precision required. */ + __dbl_mp (x, &a, p); + a.d[0] = 1.0; + k = a.e - 5; + if (k < 0) + k = 0; + b.e = -k; + b.d[0] = 1.0; + for (i = 0; i < p; i++) + b.d[i + 1] = toverp[i + k]; + __mul (&a, &b, &c, p); + t = c.d[c.e]; + for (i = 1; i <= p - c.e; i++) + c.d[i] = c.d[i + c.e]; + for (i = p + 1 - c.e; i <= p; i++) + c.d[i] = 0; + c.e = 0; + if (c.d[1] >= HALFRAD) + { + t += 1.0; + __sub (&c, &__mpone, &b, p); + __mul (&b, &hp, y, p); + } + else + __mul (&c, &hp, y, p); + n = (int) t; + if (x < 0) + { + y->d[0] = -y->d[0]; + n = -n; + } + return (n & 3); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/sincos32.h b/REORG.TODO/sysdeps/ieee754/dbl-64/sincos32.h new file mode 100644 index 0000000000..8265a23e77 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/sincos32.h @@ -0,0 +1,81 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:sincos32.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef SINCOS32_H +#define SINCCOS32_H + +#ifdef BIG_ENDI +static const number +/**/ hpinv = {{0x3FE45F30, 0x6DC9C883}}, /* 0.63661977236758138 */ +/**/ toint = {{0x43380000, 0x00000000}}; /* 6755399441055744 */ + +#else +#ifdef LITTLE_ENDI +static const number +/**/ hpinv = {{0x6DC9C883, 0x3FE45F30}}, /* 0.63661977236758138 */ +/**/ toint = {{0x00000000, 0x43380000}}; /* 6755399441055744 */ + +#endif +#endif + +static const mp_no + oofac27 = {-3,{1.0,7.0,4631664.0,12006312.0,13118056.0,6538613.0,646354.0, + 8508025.0,9131256.0,7548776.0,2529842.0,8864927.0,660489.0,15595125.0,12777885.0, + 11618489.0,13348664.0,5486686.0,514518.0,11275535.0,4727621.0,3575562.0, + 13579710.0,5829745.0,7531862.0,9507898.0,6915060.0,4079264.0,1907586.0, + 6078398.0,13789314.0,5504104.0,14136.0}}, + pi = {1,{1.0,3.0, + 2375530.0,8947107.0,578323.0,1673774.0,225395.0,4498441.0,3678761.0, + 10432976.0,536314.0,10021966.0,7113029.0,2630118.0,3723283.0,7847508.0, + 6737716.0,15273068.0,12626985.0,12044668.0,5299519.0,8705461.0,11880201.0, + 1544726.0,14014857.0,7994139.0,13709579.0,10918111.0,11906095.0,16610011.0, + 13638367.0,12040417.0,11529578.0,2522774.0}}, + hp = {1,{1.0, 1.0, + 9576373.0,4473553.0,8677769.0,9225495.0,112697.0,10637828.0, + 10227988.0,13605096.0,268157.0,5010983.0,3556514.0,9703667.0, + 1861641.0,12312362.0,3368858.0,7636534.0,6313492.0,14410942.0, + 2649759.0,12741338.0,14328708.0,9160971.0,7007428.0,12385677.0, + 15243397.0,13847663.0,14341655.0,16693613.0,15207791.0,14408816.0, + 14153397.0,1261387.0,6110792.0,2291862.0,4181138.0,5295267.0}}; + +static const double toverp[75] = { + 10680707.0, 7228996.0, 1387004.0, 2578385.0, 16069853.0, + 12639074.0, 9804092.0, 4427841.0, 16666979.0, 11263675.0, + 12935607.0, 2387514.0, 4345298.0, 14681673.0, 3074569.0, + 13734428.0, 16653803.0, 1880361.0, 10960616.0, 8533493.0, + 3062596.0, 8710556.0, 7349940.0, 6258241.0, 3772886.0, + 3769171.0, 3798172.0, 8675211.0, 12450088.0, 3874808.0, + 9961438.0, 366607.0, 15675153.0, 9132554.0, 7151469.0, + 3571407.0, 2607881.0, 12013382.0, 4155038.0, 6285869.0, + 7677882.0, 13102053.0, 15825725.0, 473591.0, 9065106.0, + 15363067.0, 6271263.0, 9264392.0, 5636912.0, 4652155.0, + 7056368.0, 13614112.0, 10155062.0, 1944035.0, 9527646.0, + 15080200.0, 6658437.0, 6231200.0, 6832269.0, 16767104.0, + 5075751.0, 3212806.0, 1398474.0, 7579849.0, 6349435.0, + 12618859.0, 4703257.0, 12806093.0, 14477321.0, 2786137.0, + 12875403.0, 9837734.0, 14528324.0, 13719321.0, 343717.0 }; + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/sincostab.c b/REORG.TODO/sysdeps/ieee754/dbl-64/sincostab.c new file mode 100644 index 0000000000..b3e06bfebd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/sincostab.c @@ -0,0 +1,914 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +#include <mydefs.h> +#include <endian.h> + +/****************************************************************/ +/* TABLES FOR THE usin() and ucos() FUNCTION */ +/****************************************************************/ + + +#ifdef BIG_ENDI +const union {int4 i[880]; double x[440];}__sincostab = { .i = { +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0x3FF00000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0x3F7FFFEA, 0xAAAEEEEF, +/**/ 0xBC1E45E2, 0xEC67B77C, +/**/ 0x3FEFFFC0, 0x00155552, +/**/ 0x3C8F4A01, 0xA0196DAE, +/**/ 0x3F8FFFAA, 0xAAEEEED5, +/**/ 0xBC02AB63, 0x9A9F0777, +/**/ 0x3FEFFF00, 0x0155549F, +/**/ 0x3C828A28, 0xA03A5EF3, +/**/ 0x3F97FF70, 0x01033255, +/**/ 0x3BFEFE2B, 0x51527336, +/**/ 0x3FEFFDC0, 0x06BFF7E6, +/**/ 0x3C8AE6DA, 0xE86977BD, +/**/ 0x3F9FFEAA, 0xAEEEE86F, +/**/ 0xBC3CD406, 0xFB224AE2, +/**/ 0x3FEFFC00, 0x155527D3, +/**/ 0xBC83B544, 0x92D89B5B, +/**/ 0x3FA3FEB2, 0xB12D45D5, +/**/ 0x3C34EC54, 0x203D1C11, +/**/ 0x3FEFF9C0, 0x3414A7BA, +/**/ 0x3C6991F4, 0xBE6C59BF, +/**/ 0x3FA7FDC0, 0x1032FBA9, +/**/ 0xBC4599BD, 0xF46E997A, +/**/ 0x3FEFF700, 0x6BFDF99F, +/**/ 0xBC78B3B5, 0x60648D5F, +/**/ 0x3FABFC6D, 0x78586DAC, +/**/ 0x3C18E4FD, 0x03DBF236, +/**/ 0x3FEFF3C0, 0xC8103A31, +/**/ 0x3C74856D, 0xBDDC0E66, +/**/ 0x3FAFFAAA, 0xEEED4EDB, +/**/ 0xBC42D16D, 0x32684B69, +/**/ 0x3FEFF001, 0x5549F4D3, +/**/ 0x3C832838, 0x7B99426F, +/**/ 0x3FB1FC34, 0x3D808BEF, +/**/ 0xBC5F3D32, 0xE6F3BE4F, +/**/ 0x3FEFEBC2, 0x22A8EF9F, +/**/ 0x3C579349, 0x34F54C77, +/**/ 0x3FB3FACB, 0x12D1755B, +/**/ 0xBC592191, 0x5299468C, +/**/ 0x3FEFE703, 0x4129EF6F, +/**/ 0xBC6CBF43, 0x37C96F97, +/**/ 0x3FB5F911, 0xFD10B737, +/**/ 0xBC50184F, 0x02BE9102, +/**/ 0x3FEFE1C4, 0xC3C873EB, +/**/ 0xBC35A9C9, 0x057C4A02, +/**/ 0x3FB7F701, 0x032550E4, +/**/ 0x3C3AFC2D, 0x1800501A, +/**/ 0x3FEFDC06, 0xBF7E6B9B, +/**/ 0x3C831902, 0xB535F8DB, +/**/ 0x3FB9F490, 0x2D55D1F9, +/**/ 0x3C52696D, 0x7EAC1DC1, +/**/ 0x3FEFD5C9, 0x4B43E000, +/**/ 0xBC62E768, 0xCB4F92F9, +/**/ 0x3FBBF1B7, 0x8568391D, +/**/ 0x3C5E9184, 0x1DEA4CC8, +/**/ 0x3FEFCF0C, 0x800E99B1, +/**/ 0x3C6EA3D7, 0x86D186AC, +/**/ 0x3FBDEE6F, 0x16C1CCE6, +/**/ 0xBC450F8E, 0x2FB71673, +/**/ 0x3FEFC7D0, 0x78D1BC88, +/**/ 0x3C8075D2, 0x447DB685, +/**/ 0x3FBFEAAE, 0xEE86EE36, +/**/ 0xBC4AFCB2, 0xBCC6F03B, +/**/ 0x3FEFC015, 0x527D5BD3, +/**/ 0x3C8B68F3, 0x5094EFB8, +/**/ 0x3FC0F337, 0x8DDD71D1, +/**/ 0x3C6D8468, 0x724F0F9E, +/**/ 0x3FEFB7DB, 0x2BFE0695, +/**/ 0x3C821DAD, 0xF4F65AB1, +/**/ 0x3FC1F0D3, 0xD7AFCEAF, +/**/ 0xBC66EF95, 0x099769A5, +/**/ 0x3FEFAF22, 0x263C4BD3, +/**/ 0xBC552ACE, 0x133A2769, +/**/ 0x3FC2EE28, 0x5E4AB88F, +/**/ 0xBC6E4D0F, 0x05DEE058, +/**/ 0x3FEFA5EA, 0x641C36F2, +/**/ 0x3C404DA6, 0xED17CC7C, +/**/ 0x3FC3EB31, 0x2C5D66CB, +/**/ 0x3C647D66, 0x6B66CB91, +/**/ 0x3FEF9C34, 0x0A7CC428, +/**/ 0x3C8C5B6B, 0x063B7462, +/**/ 0x3FC4E7EA, 0x4DC5F27B, +/**/ 0x3C5949DB, 0x2AC072FC, +/**/ 0x3FEF91FF, 0x40374D01, +/**/ 0xBC67D03F, 0x4D3A9E4C, +/**/ 0x3FC5E44F, 0xCFA126F3, +/**/ 0xBC66F443, 0x063F89B6, +/**/ 0x3FEF874C, 0x2E1EECF6, +/**/ 0xBC8C6514, 0xE1332B16, +/**/ 0x3FC6E05D, 0xC05A4D4C, +/**/ 0xBBD32C5C, 0x8B81C940, +/**/ 0x3FEF7C1A, 0xFEFFDE24, +/**/ 0xBC78F55B, 0xC47540B1, +/**/ 0x3FC7DC10, 0x2FBAF2B5, +/**/ 0x3C45AB50, 0xE23C97C3, +/**/ 0x3FEF706B, 0xDF9ECE1C, +/**/ 0xBC8698C8, 0x0C36DCB4, +/**/ 0x3FC8D763, 0x2EFAA944, +/**/ 0xBC620FA2, 0x62CBB953, +/**/ 0x3FEF643E, 0xFEB82ACD, +/**/ 0x3C76B00A, 0xC1FE28AC, +/**/ 0x3FC9D252, 0xD0CEC312, +/**/ 0x3C59C43D, 0x80B1137D, +/**/ 0x3FEF5794, 0x8CFF6797, +/**/ 0x3C6E3A0D, 0x3E03B1D5, +/**/ 0x3FCACCDB, 0x297A0765, +/**/ 0xBC59883B, 0x57D6CDEB, +/**/ 0x3FEF4A6C, 0xBD1E3A79, +/**/ 0x3C813DF0, 0xEDAEBB57, +/**/ 0x3FCBC6F8, 0x4EDC6199, +/**/ 0x3C69C1A5, 0x6A7B0CAB, +/**/ 0x3FEF3CC7, 0xC3B3D16E, +/**/ 0xBC621A3A, 0xD28A3494, +/**/ 0x3FCCC0A6, 0x588289A3, +/**/ 0xBC6868D0, 0x9BC87C6B, +/**/ 0x3FEF2EA5, 0xD753FFED, +/**/ 0x3C8CC421, 0x5F56D583, +/**/ 0x3FCDB9E1, 0x5FB5A5D0, +/**/ 0xBC632E20, 0xD6CC6FC2, +/**/ 0x3FEF2007, 0x3086649F, +/**/ 0x3C7B9404, 0x16C1984B, +/**/ 0x3FCEB2A5, 0x7F8AE5A3, +/**/ 0xBC60BE06, 0xAF572CEB, +/**/ 0x3FEF10EC, 0x09C5873B, +/**/ 0x3C8D9072, 0x762C1283, +/**/ 0x3FCFAAEE, 0xD4F31577, +/**/ 0xBC615D88, 0x508E32B8, +/**/ 0x3FEF0154, 0x9F7DEEA1, +/**/ 0x3C8D3C1E, 0x99E5CAFD, +/**/ 0x3FD0515C, 0xBF65155C, +/**/ 0xBC79B8C2, 0x9DFD8EC8, +/**/ 0x3FEEF141, 0x300D2F26, +/**/ 0xBC82AA1B, 0x08DED372, +/**/ 0x3FD0CD00, 0xCEF36436, +/**/ 0xBC79FB0A, 0x0C93E2B5, +/**/ 0x3FEEE0B1, 0xFBC0F11C, +/**/ 0xBC4BFD23, 0x80BBC3B1, +/**/ 0x3FD14861, 0xAA94DDEB, +/**/ 0xBC6BE881, 0xB5B615A4, +/**/ 0x3FEECFA7, 0x44D5EFA1, +/**/ 0xBC556D0A, 0x4AF541D0, +/**/ 0x3FD1C37D, 0x64C6B876, +/**/ 0x3C746076, 0xFE0DCFF5, +/**/ 0x3FEEBE21, 0x4F76EFA8, +/**/ 0xBC802F9F, 0x12BA543E, +/**/ 0x3FD23E52, 0x111AAF36, +/**/ 0xBC74F080, 0x334EFF18, +/**/ 0x3FEEAC20, 0x61BBAF4F, +/**/ 0x3C62C1D5, 0x3E94658D, +/**/ 0x3FD2B8DD, 0xC43EB49F, +/**/ 0x3C615538, 0x99F2D807, +/**/ 0x3FEE99A4, 0xC3A7CD83, +/**/ 0xBC82264B, 0x1BC53CE8, +/**/ 0x3FD3331E, 0x94049F87, +/**/ 0x3C7E0CB6, 0xB40C302C, +/**/ 0x3FEE86AE, 0xBF29A9ED, +/**/ 0x3C89397A, 0xFDBB58A7, +/**/ 0x3FD3AD12, 0x9769D3D8, +/**/ 0x3C003D55, 0x04878398, +/**/ 0x3FEE733E, 0xA0193D40, +/**/ 0xBC86428B, 0x3546CE13, +/**/ 0x3FD426B7, 0xE69EE697, +/**/ 0xBC7F09C7, 0x5705C59F, +/**/ 0x3FEE5F54, 0xB436E9D0, +/**/ 0x3C87EB0F, 0xD02FC8BC, +/**/ 0x3FD4A00C, 0x9B0F3D20, +/**/ 0x3C7823BA, 0x6BB08EAD, +/**/ 0x3FEE4AF1, 0x4B2A449C, +/**/ 0xBC868CA0, 0x2E8A6833, +/**/ 0x3FD5190E, 0xCF68A77A, +/**/ 0x3C7B3571, 0x55EEF0F3, +/**/ 0x3FEE3614, 0xB680D6A5, +/**/ 0xBC727793, 0xAA015237, +/**/ 0x3FD591BC, 0x9FA2F597, +/**/ 0x3C67C74B, 0xAC3FE0CB, +/**/ 0x3FEE20BF, 0x49ACD6C1, +/**/ 0xBC5660AE, 0xC7EF636C, +/**/ 0x3FD60A14, 0x29078775, +/**/ 0x3C5B1FD8, 0x0BA89133, +/**/ 0x3FEE0AF1, 0x5A03DBCE, +/**/ 0x3C5FE8E7, 0x02771AE6, +/**/ 0x3FD68213, 0x8A38D7F7, +/**/ 0xBC7D8892, 0x02444AAD, +/**/ 0x3FEDF4AB, 0x3EBD875E, +/**/ 0xBC8E2D8A, 0x7E6736C4, +/**/ 0x3FD6F9B8, 0xE33A0255, +/**/ 0x3C742BC1, 0x4EE9DA0D, +/**/ 0x3FEDDDED, 0x50F228D6, +/**/ 0xBC6E80C8, 0xD42BA2BF, +/**/ 0x3FD77102, 0x55764214, +/**/ 0xBC66EAD7, 0x314BB6CE, +/**/ 0x3FEDC6B7, 0xEB995912, +/**/ 0x3C54B364, 0x776DCD35, +/**/ 0x3FD7E7EE, 0x03C86D4E, +/**/ 0xBC7B63BC, 0xDABF5AF2, +/**/ 0x3FEDAF0B, 0x6B888E83, +/**/ 0x3C8A249E, 0x2B5E5CEA, +/**/ 0x3FD85E7A, 0x12826949, +/**/ 0x3C78A40E, 0x9B5FACE0, +/**/ 0x3FED96E8, 0x2F71A9DC, +/**/ 0x3C8FF61B, 0xD5D2039D, +/**/ 0x3FD8D4A4, 0xA774992F, +/**/ 0x3C744A02, 0xEA766326, +/**/ 0x3FED7E4E, 0x97E17B4A, +/**/ 0xBC63B770, 0x352BED94, +/**/ 0x3FD94A6B, 0xE9F546C5, +/**/ 0xBC769CE1, 0x3E683F58, +/**/ 0x3FED653F, 0x073E4040, +/**/ 0xBC876236, 0x434BEC37, +/**/ 0x3FD9BFCE, 0x02E80510, +/**/ 0x3C709E39, 0xA320B0A4, +/**/ 0x3FED4BB9, 0xE1C619E0, +/**/ 0x3C8F34BB, 0x77858F61, +/**/ 0x3FDA34C9, 0x1CC50CCA, +/**/ 0xBC5A310E, 0x3B50CECD, +/**/ 0x3FED31BF, 0x8D8D7C06, +/**/ 0x3C7E60DD, 0x3089CBDD, +/**/ 0x3FDAA95B, 0x63A09277, +/**/ 0xBC66293E, 0xB13C0381, +/**/ 0x3FED1750, 0x727D94F0, +/**/ 0x3C80D52B, 0x1EC1A48E, +/**/ 0x3FDB1D83, 0x05321617, +/**/ 0xBC7AE242, 0xCB99F519, +/**/ 0x3FECFC6C, 0xFA52AD9F, +/**/ 0x3C88B5B5, 0x508F2A0D, +/**/ 0x3FDB913E, 0x30DBAC43, +/**/ 0xBC7E38AD, 0x2F6C3FF1, +/**/ 0x3FECE115, 0x909A82E5, +/**/ 0x3C81F139, 0xBB31109A, +/**/ 0x3FDC048B, 0x17B140A3, +/**/ 0x3C619FE6, 0x757E9FA7, +/**/ 0x3FECC54A, 0xA2B2972E, +/**/ 0x3C64EE16, 0x2BA83A98, +/**/ 0x3FDC7767, 0xEC7FD19E, +/**/ 0xBC5EB14D, 0x1A3D5826, +/**/ 0x3FECA90C, 0x9FC67D0B, +/**/ 0xBC646A81, 0x485E3462, +/**/ 0x3FDCE9D2, 0xE3D4A51F, +/**/ 0xBC62FC8A, 0x12DAE298, +/**/ 0x3FEC8C5B, 0xF8CE1A84, +/**/ 0x3C7AB3D1, 0xA1590123, +/**/ 0x3FDD5BCA, 0x34047661, +/**/ 0x3C728A44, 0xA75FC29C, +/**/ 0x3FEC6F39, 0x208BE53B, +/**/ 0xBC8741DB, 0xFBAADB42, +/**/ 0x3FDDCD4C, 0x15329C9A, +/**/ 0x3C70D4C6, 0xE171FD9A, +/**/ 0x3FEC51A4, 0x8B8B175E, +/**/ 0xBC61BBB4, 0x3B9AA880, +/**/ 0x3FDE3E56, 0xC1582A69, +/**/ 0xBC50A482, 0x1099F88F, +/**/ 0x3FEC339E, 0xB01DDD81, +/**/ 0xBC8CAAF5, 0xEE82C5C0, +/**/ 0x3FDEAEE8, 0x744B05F0, +/**/ 0xBC5789B4, 0x3C9B027D, +/**/ 0x3FEC1528, 0x065B7D50, +/**/ 0xBC889211, 0x1312E828, +/**/ 0x3FDF1EFF, 0x6BC4F97B, +/**/ 0x3C717212, 0xF8A7525C, +/**/ 0x3FEBF641, 0x081E7536, +/**/ 0x3C8B7BD7, 0x1628A9A1, +/**/ 0x3FDF8E99, 0xE76ABC97, +/**/ 0x3C59D950, 0xAF2D00A3, +/**/ 0x3FEBD6EA, 0x310294F5, +/**/ 0x3C731BBC, 0xC88C109D, +/**/ 0x3FDFFDB6, 0x28D2F57A, +/**/ 0x3C6F4A99, 0x2E905B6A, +/**/ 0x3FEBB723, 0xFE630F32, +/**/ 0x3C772BD2, 0x452D0A39, +/**/ 0x3FE03629, 0x39C69955, +/**/ 0xBC82D8CD, 0x78397B01, +/**/ 0x3FEB96EE, 0xEF58840E, +/**/ 0x3C545A3C, 0xC78FADE0, +/**/ 0x3FE06D36, 0x86946E5B, +/**/ 0x3C83F5AE, 0x4538FF1B, +/**/ 0x3FEB764B, 0x84B704C2, +/**/ 0xBC8F5848, 0xC21B389B, +/**/ 0x3FE0A402, 0x1E9E1001, +/**/ 0xBC86F643, 0xA13914F6, +/**/ 0x3FEB553A, 0x410C104E, +/**/ 0x3C58FF79, 0x47027A16, +/**/ 0x3FE0DA8B, 0x26B5672E, +/**/ 0xBC8A58DE, 0xF0BEE909, +/**/ 0x3FEB33BB, 0xA89C8948, +/**/ 0x3C8EA6A5, 0x1D1F6CA9, +/**/ 0x3FE110D0, 0xC4B69C3B, +/**/ 0x3C8D9189, 0x98809981, +/**/ 0x3FEB11D0, 0x4162A4C6, +/**/ 0x3C71DD56, 0x1EFBC0C2, +/**/ 0x3FE146D2, 0x1F8B7F82, +/**/ 0x3C7BF953, 0x5E2739A8, +/**/ 0x3FEAEF78, 0x930BD275, +/**/ 0xBC7F8362, 0x79746F94, +/**/ 0x3FE17C8E, 0x5F2EEDB0, +/**/ 0x3C635E57, 0x102E2488, +/**/ 0x3FEACCB5, 0x26F69DE5, +/**/ 0x3C88FB6A, 0x8DD6B6CC, +/**/ 0x3FE1B204, 0xACB02FDD, +/**/ 0xBC5F190C, 0x70CBB5FF, +/**/ 0x3FEAA986, 0x88308913, +/**/ 0xBC0B83D6, 0x07CD5070, +/**/ 0x3FE1E734, 0x3236574C, +/**/ 0x3C722A3F, 0xA4F41D5A, +/**/ 0x3FEA85ED, 0x4373E02D, +/**/ 0x3C69BE06, 0x385EC792, +/**/ 0x3FE21C1C, 0x1B0394CF, +/**/ 0x3C5E5B32, 0x4B23AA31, +/**/ 0x3FEA61E9, 0xE72586AF, +/**/ 0x3C858330, 0xE2FD453F, +/**/ 0x3FE250BB, 0x93788BBB, +/**/ 0x3C7EA3D0, 0x2457BCCE, +/**/ 0x3FEA3D7D, 0x0352BDCF, +/**/ 0xBC868DBA, 0xECA19669, +/**/ 0x3FE28511, 0xC917A067, +/**/ 0xBC801DF1, 0xD9A16B70, +/**/ 0x3FEA18A7, 0x29AEE445, +/**/ 0x3C395E25, 0x736C0358, +/**/ 0x3FE2B91D, 0xEA88421E, +/**/ 0xBC8FA371, 0xDB216AB0, +/**/ 0x3FE9F368, 0xED912F85, +/**/ 0xBC81D200, 0xC5791606, +/**/ 0x3FE2ECDF, 0x279A3082, +/**/ 0x3C8D3557, 0xE0E7E37E, +/**/ 0x3FE9CDC2, 0xE3F25E5C, +/**/ 0x3C83F991, 0x12993F62, +/**/ 0x3FE32054, 0xB148BC4F, +/**/ 0x3C8F6B42, 0x095A135B, +/**/ 0x3FE9A7B5, 0xA36A6514, +/**/ 0x3C8722CF, 0xCC9FA7A9, +/**/ 0x3FE3537D, 0xB9BE0367, +/**/ 0x3C6B327E, 0x7AF040F0, +/**/ 0x3FE98141, 0xC42E1310, +/**/ 0x3C8D1FF8, 0x0488F08D, +/**/ 0x3FE38659, 0x7456282B, +/**/ 0xBC710FAD, 0xA93B07A8, +/**/ 0x3FE95A67, 0xE00CB1FD, +/**/ 0xBC80BEFD, 0xA21F862D, +/**/ 0x3FE3B8E7, 0x15A2840A, +/**/ 0xBC797653, 0xA7D2F07B, +/**/ 0x3FE93328, 0x926D9E92, +/**/ 0xBC8BB770, 0x03600CDA, +/**/ 0x3FE3EB25, 0xD36CD53A, +/**/ 0xBC5BE570, 0xE1570FC0, +/**/ 0x3FE90B84, 0x784DDAF7, +/**/ 0xBC70FEB1, 0x0AB93B87, +/**/ 0x3FE41D14, 0xE4BA6790, +/**/ 0x3C84608F, 0xD287ECF5, +/**/ 0x3FE8E37C, 0x303D9AD1, +/**/ 0xBC6463A4, 0xB53D4BF8, +/**/ 0x3FE44EB3, 0x81CF386B, +/**/ 0xBC83ED6C, 0x1E6A5505, +/**/ 0x3FE8BB10, 0x5A5DC900, +/**/ 0x3C8863E0, 0x3E9474C1, +/**/ 0x3FE48000, 0xE431159F, +/**/ 0xBC8B194A, 0x7463ED10, +/**/ 0x3FE89241, 0x985D871F, +/**/ 0x3C8C48D9, 0xC413ED84, +/**/ 0x3FE4B0FC, 0x46AAB761, +/**/ 0x3C20DA05, 0x738CC59A, +/**/ 0x3FE86910, 0x8D77A6C6, +/**/ 0x3C7338FF, 0xE2BFE9DD, +/**/ 0x3FE4E1A4, 0xE54ED51B, +/**/ 0xBC8A492F, 0x89B7C76A, +/**/ 0x3FE83F7D, 0xDE701CA0, +/**/ 0xBC4152CF, 0x609BC6E8, +/**/ 0x3FE511F9, 0xFD7B351C, +/**/ 0xBC85C0E8, 0x61C48831, +/**/ 0x3FE8158A, 0x31916D5D, +/**/ 0xBC6DE8B9, 0x0B8228DE, +/**/ 0x3FE541FA, 0xCDDBB724, +/**/ 0x3C7232C2, 0x8520D391, +/**/ 0x3FE7EB36, 0x2EAA1488, +/**/ 0x3C5A1D65, 0xA4A5959F, +/**/ 0x3FE571A6, 0x966D59B3, +/**/ 0x3C5C843B, 0x4D0FB198, +/**/ 0x3FE7C082, 0x7F09E54F, +/**/ 0xBC6C73D6, 0xD72AEE68, +/**/ 0x3FE5A0FC, 0x98813A12, +/**/ 0xBC8D82E2, 0xB7D4227B, +/**/ 0x3FE7956F, 0xCD7F6543, +/**/ 0xBC8AB276, 0xE9D45AE4, +/**/ 0x3FE5CFFC, 0x16BF8F0D, +/**/ 0x3C896CB3, 0x70EB578A, +/**/ 0x3FE769FE, 0xC655211F, +/**/ 0xBC6827D5, 0xCF8C68C5, +/**/ 0x3FE5FEA4, 0x552A9E57, +/**/ 0x3C80B6CE, 0xF7EE20B7, +/**/ 0x3FE73E30, 0x174EFBA1, +/**/ 0xBC65D3AE, 0x3D94AD5F, +/**/ 0x3FE62CF4, 0x9921AC79, +/**/ 0xBC8EDD98, 0x55B6241A, +/**/ 0x3FE71204, 0x6FA77678, +/**/ 0x3C8425B0, 0xA5029C81, +/**/ 0x3FE65AEC, 0x2963E755, +/**/ 0x3C8126F9, 0x6B71053C, +/**/ 0x3FE6E57C, 0x800CF55E, +/**/ 0x3C860286, 0xDEDBD0A6, +/**/ 0x3FE6888A, 0x4E134B2F, +/**/ 0xBC86B7D3, 0x7644D5E6, +/**/ 0x3FE6B898, 0xFA9EFB5D, +/**/ 0x3C715AC7, 0x86CCF4B2, +/**/ 0x3FE6B5CE, 0x50B7821A, +/**/ 0xBC65D515, 0x8F702E0F, +/**/ 0x3FE68B5A, 0x92EB6253, +/**/ 0xBC89A91A, 0xD985F89C, +/**/ 0x3FE6E2B7, 0x7C40BDE1, +/**/ 0xBC70E729, 0x857FAD53, +/**/ 0x3FE65DC1, 0xFDEB8CBA, +/**/ 0xBC597C1B, 0x47337C77, +/**/ 0x3FE70F45, 0x1D0A8C40, +/**/ 0x3C697EDE, 0x3885770D, +/**/ 0x3FE62FCF, 0xF20191C7, +/**/ 0x3C6D9143, 0x895756EF, +/**/ 0x3FE73B76, 0x80DEA578, +/**/ 0xBC722483, 0x06DC12A2, +/**/ 0x3FE60185, 0x26F563DF, +/**/ 0x3C846CA5, 0xE0E432D0, +/**/ 0x3FE7674A, 0xF6F7B524, +/**/ 0x3C7E9D3F, 0x94AC84A8, +/**/ 0x3FE5D2E2, 0x55F1F17A, +/**/ 0x3C803141, 0x04C8892B, +/**/ 0x3FE792C1, 0xD0041D52, +/**/ 0xBC8ABF05, 0xEEB354EB, +/**/ 0x3FE5A3E8, 0x39824077, +/**/ 0x3C8428AA, 0x2759BE62, +/**/ 0x3FE7BDDA, 0x5E28B3C2, +/**/ 0x3C4AD119, 0x7CCD0393, +/**/ 0x3FE57497, 0x8D8E83F2, +/**/ 0x3C8F4714, 0xAF282D23, +/**/ 0x3FE7E893, 0xF5037959, +/**/ 0x3C80EEFB, 0xAA650C4C, +/**/ 0x3FE544F1, 0x0F592CA5, +/**/ 0xBC8E7AE8, 0xE6C7A62F, +/**/ 0x3FE812ED, 0xE9AE4BA4, +/**/ 0xBC87830A, 0xDF402DDA, +/**/ 0x3FE514F5, 0x7D7BF3DA, +/**/ 0x3C747A10, 0x8073C259 } }; +#else +#ifdef LITTLE_ENDI +const union {int4 i[880]; double x[440];} __sincostab = { .i = { +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x3FF00000, +/**/ 0x00000000, 0x00000000, +/**/ 0xAAAEEEEF, 0x3F7FFFEA, +/**/ 0xEC67B77C, 0xBC1E45E2, +/**/ 0x00155552, 0x3FEFFFC0, +/**/ 0xA0196DAE, 0x3C8F4A01, +/**/ 0xAAEEEED5, 0x3F8FFFAA, +/**/ 0x9A9F0777, 0xBC02AB63, +/**/ 0x0155549F, 0x3FEFFF00, +/**/ 0xA03A5EF3, 0x3C828A28, +/**/ 0x01033255, 0x3F97FF70, +/**/ 0x51527336, 0x3BFEFE2B, +/**/ 0x06BFF7E6, 0x3FEFFDC0, +/**/ 0xE86977BD, 0x3C8AE6DA, +/**/ 0xAEEEE86F, 0x3F9FFEAA, +/**/ 0xFB224AE2, 0xBC3CD406, +/**/ 0x155527D3, 0x3FEFFC00, +/**/ 0x92D89B5B, 0xBC83B544, +/**/ 0xB12D45D5, 0x3FA3FEB2, +/**/ 0x203D1C11, 0x3C34EC54, +/**/ 0x3414A7BA, 0x3FEFF9C0, +/**/ 0xBE6C59BF, 0x3C6991F4, +/**/ 0x1032FBA9, 0x3FA7FDC0, +/**/ 0xF46E997A, 0xBC4599BD, +/**/ 0x6BFDF99F, 0x3FEFF700, +/**/ 0x60648D5F, 0xBC78B3B5, +/**/ 0x78586DAC, 0x3FABFC6D, +/**/ 0x03DBF236, 0x3C18E4FD, +/**/ 0xC8103A31, 0x3FEFF3C0, +/**/ 0xBDDC0E66, 0x3C74856D, +/**/ 0xEEED4EDB, 0x3FAFFAAA, +/**/ 0x32684B69, 0xBC42D16D, +/**/ 0x5549F4D3, 0x3FEFF001, +/**/ 0x7B99426F, 0x3C832838, +/**/ 0x3D808BEF, 0x3FB1FC34, +/**/ 0xE6F3BE4F, 0xBC5F3D32, +/**/ 0x22A8EF9F, 0x3FEFEBC2, +/**/ 0x34F54C77, 0x3C579349, +/**/ 0x12D1755B, 0x3FB3FACB, +/**/ 0x5299468C, 0xBC592191, +/**/ 0x4129EF6F, 0x3FEFE703, +/**/ 0x37C96F97, 0xBC6CBF43, +/**/ 0xFD10B737, 0x3FB5F911, +/**/ 0x02BE9102, 0xBC50184F, +/**/ 0xC3C873EB, 0x3FEFE1C4, +/**/ 0x057C4A02, 0xBC35A9C9, +/**/ 0x032550E4, 0x3FB7F701, +/**/ 0x1800501A, 0x3C3AFC2D, +/**/ 0xBF7E6B9B, 0x3FEFDC06, +/**/ 0xB535F8DB, 0x3C831902, +/**/ 0x2D55D1F9, 0x3FB9F490, +/**/ 0x7EAC1DC1, 0x3C52696D, +/**/ 0x4B43E000, 0x3FEFD5C9, +/**/ 0xCB4F92F9, 0xBC62E768, +/**/ 0x8568391D, 0x3FBBF1B7, +/**/ 0x1DEA4CC8, 0x3C5E9184, +/**/ 0x800E99B1, 0x3FEFCF0C, +/**/ 0x86D186AC, 0x3C6EA3D7, +/**/ 0x16C1CCE6, 0x3FBDEE6F, +/**/ 0x2FB71673, 0xBC450F8E, +/**/ 0x78D1BC88, 0x3FEFC7D0, +/**/ 0x447DB685, 0x3C8075D2, +/**/ 0xEE86EE36, 0x3FBFEAAE, +/**/ 0xBCC6F03B, 0xBC4AFCB2, +/**/ 0x527D5BD3, 0x3FEFC015, +/**/ 0x5094EFB8, 0x3C8B68F3, +/**/ 0x8DDD71D1, 0x3FC0F337, +/**/ 0x724F0F9E, 0x3C6D8468, +/**/ 0x2BFE0695, 0x3FEFB7DB, +/**/ 0xF4F65AB1, 0x3C821DAD, +/**/ 0xD7AFCEAF, 0x3FC1F0D3, +/**/ 0x099769A5, 0xBC66EF95, +/**/ 0x263C4BD3, 0x3FEFAF22, +/**/ 0x133A2769, 0xBC552ACE, +/**/ 0x5E4AB88F, 0x3FC2EE28, +/**/ 0x05DEE058, 0xBC6E4D0F, +/**/ 0x641C36F2, 0x3FEFA5EA, +/**/ 0xED17CC7C, 0x3C404DA6, +/**/ 0x2C5D66CB, 0x3FC3EB31, +/**/ 0x6B66CB91, 0x3C647D66, +/**/ 0x0A7CC428, 0x3FEF9C34, +/**/ 0x063B7462, 0x3C8C5B6B, +/**/ 0x4DC5F27B, 0x3FC4E7EA, +/**/ 0x2AC072FC, 0x3C5949DB, +/**/ 0x40374D01, 0x3FEF91FF, +/**/ 0x4D3A9E4C, 0xBC67D03F, +/**/ 0xCFA126F3, 0x3FC5E44F, +/**/ 0x063F89B6, 0xBC66F443, +/**/ 0x2E1EECF6, 0x3FEF874C, +/**/ 0xE1332B16, 0xBC8C6514, +/**/ 0xC05A4D4C, 0x3FC6E05D, +/**/ 0x8B81C940, 0xBBD32C5C, +/**/ 0xFEFFDE24, 0x3FEF7C1A, +/**/ 0xC47540B1, 0xBC78F55B, +/**/ 0x2FBAF2B5, 0x3FC7DC10, +/**/ 0xE23C97C3, 0x3C45AB50, +/**/ 0xDF9ECE1C, 0x3FEF706B, +/**/ 0x0C36DCB4, 0xBC8698C8, +/**/ 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0x8D8E83F2, 0x3FE57497, +/**/ 0xAF282D23, 0x3C8F4714, +/**/ 0xF5037959, 0x3FE7E893, +/**/ 0xAA650C4C, 0x3C80EEFB, +/**/ 0x0F592CA5, 0x3FE544F1, +/**/ 0xE6C7A62F, 0xBC8E7AE8, +/**/ 0xE9AE4BA4, 0x3FE812ED, +/**/ 0xDF402DDA, 0xBC87830A, +/**/ 0x7D7BF3DA, 0x3FE514F5, +/**/ 0x8073C259, 0x3C747A10 } }; +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/slowexp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/slowexp.c new file mode 100644 index 0000000000..e8fa2e263b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/slowexp.c @@ -0,0 +1,86 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/**************************************************************************/ +/* MODULE_NAME:slowexp.c */ +/* */ +/* FUNCTION:slowexp */ +/* */ +/* FILES NEEDED:mpa.h */ +/* mpa.c mpexp.c */ +/* */ +/*Converting from double precision to Multi-precision and calculating */ +/* e^x */ +/**************************************************************************/ +#include <math_private.h> + +#include <stap-probe.h> + +#ifndef USE_LONG_DOUBLE_FOR_MP +# include "mpa.h" +void __mpexp (mp_no *x, mp_no *y, int p); +#endif + +#ifndef SECTION +# define SECTION +#endif + +/*Converting from double precision to Multi-precision and calculating e^x */ +double +SECTION +__slowexp (double x) +{ +#ifndef USE_LONG_DOUBLE_FOR_MP + double w, z, res, eps = 3.0e-26; + int p; + mp_no mpx, mpy, mpz, mpw, mpeps, mpcor; + + /* Use the multiple precision __MPEXP function to compute the exponential + First at 144 bits and if it is not accurate enough, at 768 bits. */ + p = 6; + __dbl_mp (x, &mpx, p); + __mpexp (&mpx, &mpy, p); + __dbl_mp (eps, &mpeps, p); + __mul (&mpeps, &mpy, &mpcor, p); + __add (&mpy, &mpcor, &mpw, p); + __sub (&mpy, &mpcor, &mpz, p); + __mp_dbl (&mpw, &w, p); + __mp_dbl (&mpz, &z, p); + if (w == z) + { + /* Track how often we get to the slow exp code plus + its input/output values. */ + LIBC_PROBE (slowexp_p6, 2, &x, &w); + return w; + } + else + { + p = 32; + __dbl_mp (x, &mpx, p); + __mpexp (&mpx, &mpy, p); + __mp_dbl (&mpy, &res, p); + + /* Track how often we get to the uber-slow exp code plus + its input/output values. */ + LIBC_PROBE (slowexp_p32, 2, &x, &res); + return res; + } +#else + return (double) __ieee754_expl((long double)x); +#endif +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/slowpow.c b/REORG.TODO/sysdeps/ieee754/dbl-64/slowpow.c new file mode 100644 index 0000000000..1176b2689c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/slowpow.c @@ -0,0 +1,125 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*************************************************************************/ +/* MODULE_NAME:slowpow.c */ +/* */ +/* FUNCTION:slowpow */ +/* */ +/*FILES NEEDED:mpa.h */ +/* mpa.c mpexp.c mplog.c halfulp.c */ +/* */ +/* Given two IEEE double machine numbers y,x , routine computes the */ +/* correctly rounded (to nearest) value of x^y. Result calculated by */ +/* multiplication (in halfulp.c) or if result isn't accurate enough */ +/* then routine converts x and y into multi-precision doubles and */ +/* calls to mpexp routine */ +/*************************************************************************/ + +#include "mpa.h" +#include <math_private.h> + +#include <stap-probe.h> + +#ifndef SECTION +# define SECTION +#endif + +void __mpexp (mp_no *x, mp_no *y, int p); +void __mplog (mp_no *x, mp_no *y, int p); +double ulog (double); +double __halfulp (double x, double y); + +double +SECTION +__slowpow (double x, double y, double z) +{ + double res, res1; + mp_no mpx, mpy, mpz, mpw, mpp, mpr, mpr1; + static const mp_no eps = {-3, {1.0, 4.0}}; + int p; + + /* __HALFULP returns -10 or X^Y. */ + res = __halfulp (x, y); + + /* Return if the result was computed by __HALFULP. */ + if (res >= 0) + return res; + + /* Compute pow as long double. This is currently only used by powerpc, where + one may get 106 bits of accuracy. */ +#ifdef USE_LONG_DOUBLE_FOR_MP + long double ldw, ldz, ldpp; + static const long double ldeps = 0x4.0p-96; + + ldz = __ieee754_logl ((long double) x); + ldw = (long double) y *ldz; + ldpp = __ieee754_expl (ldw); + res = (double) (ldpp + ldeps); + res1 = (double) (ldpp - ldeps); + + /* Return the result if it is accurate enough. */ + if (res == res1) + return res; +#endif + + /* Or else, calculate using multiple precision. P = 10 implies accuracy of + 240 bits accuracy, since MP_NO has a radix of 2^24. */ + p = 10; + __dbl_mp (x, &mpx, p); + __dbl_mp (y, &mpy, p); + __dbl_mp (z, &mpz, p); + + /* z = x ^ y + log (z) = y * log (x) + z = exp (y * log (x)) */ + __mplog (&mpx, &mpz, p); + __mul (&mpy, &mpz, &mpw, p); + __mpexp (&mpw, &mpp, p); + + /* Add and subtract EPS to ensure that the result remains unchanged, i.e. we + have last bit accuracy. */ + __add (&mpp, &eps, &mpr, p); + __mp_dbl (&mpr, &res, p); + __sub (&mpp, &eps, &mpr1, p); + __mp_dbl (&mpr1, &res1, p); + if (res == res1) + { + /* Track how often we get to the slow pow code plus + its input/output values. */ + LIBC_PROBE (slowpow_p10, 4, &x, &y, &z, &res); + return res; + } + + /* If we don't, then we repeat using a higher precision. 768 bits of + precision ought to be enough for anybody. */ + p = 32; + __dbl_mp (x, &mpx, p); + __dbl_mp (y, &mpy, p); + __dbl_mp (z, &mpz, p); + __mplog (&mpx, &mpz, p); + __mul (&mpy, &mpz, &mpw, p); + __mpexp (&mpw, &mpp, p); + __mp_dbl (&mpp, &res, p); + + /* Track how often we get to the uber-slow pow code plus + its input/output values. */ + LIBC_PROBE (slowpow_p32, 4, &x, &y, &z, &res); + + return res; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/t_exp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/t_exp.c new file mode 100644 index 0000000000..58866e7794 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/t_exp.c @@ -0,0 +1,435 @@ +/* Accurate tables for exp(). + Copyright (C) 1998-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* This table has the property that, for all integers -177 <= i <= 177, + exp(i/512.0 + __exp_deltatable[abs(i)]) == __exp_atable[i+177] + r + for some -2^-64 < r < 2^-64 (abs(r) < 2^-65 if i <= 0); and that + __exp_deltatable[abs(i)] == t * 2^-60 + for integer t so that abs(t) <= 8847927 * 2^8. */ + +#define W52 (2.22044605e-16) +#define W55 (2.77555756e-17) +#define W58 (3.46944695e-18) +#define W59 (1.73472348e-18) +#define W60 (8.67361738e-19) +const float __exp_deltatable[178] = { + 0*W60, 16558714*W60, -10672149*W59, 1441652*W60, + -15787963*W55, 462888*W60, 7291806*W60, 1698880*W60, + -14375103*W58, -2021016*W60, 728829*W60, -3759654*W60, + 3202123*W60, -10916019*W58, -251570*W60, -1043086*W60, + 8207536*W60, -409964*W60, -5993931*W60, -475500*W60, + 2237522*W60, 324170*W60, -244117*W60, 32077*W60, + 123907*W60, -1019734*W60, -143*W60, 813077*W60, + 743345*W60, 462461*W60, 629794*W60, 2125066*W60, + -2339121*W60, -337951*W60, 9922067*W60, -648704*W60, + 149407*W60, -2687209*W60, -631608*W60, 2128280*W60, + -4882082*W60, 2001360*W60, 175074*W60, 2923216*W60, + -538947*W60, -1212193*W60, -1920926*W60, -1080577*W60, + 3690196*W60, 2643367*W60, 2911937*W60, 671455*W60, + -1128674*W60, 593282*W60, -5219347*W60, -1941490*W60, + 11007953*W60, 239609*W60, -2969658*W60, -1183650*W60, + 942998*W60, 699063*W60, 450569*W60, -329250*W60, + -7257875*W60, -312436*W60, 51626*W60, 555877*W60, + -641761*W60, 1565666*W60, 884327*W60, -10960035*W60, + -2004679*W60, -995793*W60, -2229051*W60, -146179*W60, + -510327*W60, 1453482*W60, -3778852*W60, -2238056*W60, + -4895983*W60, 3398883*W60, -252738*W60, 1230155*W60, + 346918*W60, 1109352*W60, 268941*W60, -2930483*W60, + -1036263*W60, -1159280*W60, 1328176*W60, 2937642*W60, + -9371420*W60, -6902650*W60, -1419134*W60, 1442904*W60, + -1319056*W60, -16369*W60, 696555*W60, -279987*W60, + -7919763*W60, 252741*W60, 459711*W60, -1709645*W60, + 354913*W60, 6025867*W60, -421460*W60, -853103*W60, + -338649*W60, 962151*W60, 955965*W60, 784419*W60, + -3633653*W60, 2277133*W60, -8847927*W52, 1223028*W60, + 5907079*W60, 623167*W60, 5142888*W60, 2599099*W60, + 1214280*W60, 4870359*W60, 593349*W60, -57705*W60, + 7761209*W60, -5564097*W60, 2051261*W60, 6216869*W60, + 4692163*W60, 601691*W60, -5264906*W60, 1077872*W60, + -3205949*W60, 1833082*W60, 2081746*W60, -987363*W60, + -1049535*W60, 2015244*W60, 874230*W60, 2168259*W60, + -1740124*W60, -10068269*W60, -18242*W60, -3013583*W60, + 580601*W60, -2547161*W60, -535689*W60, 2220815*W60, + 1285067*W60, 2806933*W60, -983086*W60, -1729097*W60, + -1162985*W60, -2561904*W60, 801988*W60, 244351*W60, + 1441893*W60, -7517981*W60, 271781*W60, -15021588*W60, + -2341588*W60, -919198*W60, 1642232*W60, 4771771*W60, + -1220099*W60, -3062372*W60, 628624*W60, 1278114*W60, + 13083513*W60, -10521925*W60, 3180310*W60, -1659307*W60, + 3543773*W60, 2501203*W60, 4151*W60, -340748*W60, + -2285625*W60, 2495202*W60 +}; + +const double __exp_atable[355] /* __attribute__((mode(DF))) */ = { + 0.707722561055888932371, /* 0x0.b52d4e46605c27ffd */ + 0.709106182438804188967, /* 0x0.b587fb96f75097ffb */ + 0.710492508843861281234, /* 0x0.b5e2d649899167ffd */ + 0.711881545564593931623, /* 0x0.b63dde74d36bdfffe */ + 0.713273297897442870573, /* 0x0.b699142f945f87ffc */ + 0.714667771153751463236, /* 0x0.b6f477909c4ea0001 */ + 0.716064970655995725059, /* 0x0.b75008aec758f8004 */ + 0.717464901723956938193, /* 0x0.b7abc7a0eea7e0002 */ + 0.718867569715736398602, /* 0x0.b807b47e1586c7ff8 */ + 0.720272979947266023271, /* 0x0.b863cf5d10e380003 */ + 0.721681137825144314297, /* 0x0.b8c01855195c37ffb */ + 0.723092048691992950199, /* 0x0.b91c8f7d213740004 */ + 0.724505717938892290800, /* 0x0.b97934ec5002d0007 */ + 0.725922150953176470431, /* 0x0.b9d608b9c92ea7ffc */ + 0.727341353138962865022, /* 0x0.ba330afcc29e98003 */ + 0.728763329918453162104, /* 0x0.ba903bcc8618b7ffc */ + 0.730188086709957051568, /* 0x0.baed9b40591ba0000 */ + 0.731615628948127705309, /* 0x0.bb4b296f931e30002 */ + 0.733045962086486091436, /* 0x0.bba8e671a05617ff9 */ + 0.734479091556371366251, /* 0x0.bc06d25dd49568001 */ + 0.735915022857225542529, /* 0x0.bc64ed4bce8f6fff9 */ + 0.737353761441304711410, /* 0x0.bcc33752f915d7ff9 */ + 0.738795312814142124419, /* 0x0.bd21b08af98e78005 */ + 0.740239682467211168593, /* 0x0.bd80590b65e9a8000 */ + 0.741686875913991849885, /* 0x0.bddf30ebec4a10000 */ + 0.743136898669507939299, /* 0x0.be3e38443c84e0007 */ + 0.744589756269486091620, /* 0x0.be9d6f2c1d32a0002 */ + 0.746045454254026796384, /* 0x0.befcd5bb59baf8004 */ + 0.747503998175051087583, /* 0x0.bf5c6c09ca84c0003 */ + 0.748965393601880857739, /* 0x0.bfbc322f5b18b7ff8 */ + 0.750429646104262104698, /* 0x0.c01c2843f776fffff */ + 0.751896761271877989160, /* 0x0.c07c4e5fa18b88002 */ + 0.753366744698445112140, /* 0x0.c0dca49a5fb18fffd */ + 0.754839601988627206827, /* 0x0.c13d2b0c444db0005 */ + 0.756315338768691947122, /* 0x0.c19de1cd798578006 */ + 0.757793960659406629066, /* 0x0.c1fec8f623723fffd */ + 0.759275473314173443536, /* 0x0.c25fe09e8a0f47ff8 */ + 0.760759882363831851927, /* 0x0.c2c128dedc88f8000 */ + 0.762247193485956486805, /* 0x0.c322a1cf7d6e7fffa */ + 0.763737412354726363781, /* 0x0.c3844b88cb9347ffc */ + 0.765230544649828092739, /* 0x0.c3e626232bd8f7ffc */ + 0.766726596071518051729, /* 0x0.c44831b719bf18002 */ + 0.768225572321911687194, /* 0x0.c4aa6e5d12d078001 */ + 0.769727479119219348810, /* 0x0.c50cdc2da64a37ffb */ + 0.771232322196981678892, /* 0x0.c56f7b41744490001 */ + 0.772740107296721268087, /* 0x0.c5d24bb1259e70004 */ + 0.774250840160724651565, /* 0x0.c6354d95640dd0007 */ + 0.775764526565368872643, /* 0x0.c6988106fec447fff */ + 0.777281172269557396602, /* 0x0.c6fbe61eb1bd0ffff */ + 0.778800783068235302750, /* 0x0.c75f7cf560942fffc */ + 0.780323364758801041312, /* 0x0.c7c345a3f1983fffe */ + 0.781848923151573727006, /* 0x0.c8274043594cb0002 */ + 0.783377464064598849602, /* 0x0.c88b6cec94b3b7ff9 */ + 0.784908993312207869935, /* 0x0.c8efcbb89cba27ffe */ + 0.786443516765346961618, /* 0x0.c9545cc0a88c70003 */ + 0.787981040257604625744, /* 0x0.c9b9201dc643bfffa */ + 0.789521569657452682047, /* 0x0.ca1e15e92a5410007 */ + 0.791065110849462849192, /* 0x0.ca833e3c1ae510005 */ + 0.792611669712891875319, /* 0x0.cae8992fd84667ffd */ + 0.794161252150049179450, /* 0x0.cb4e26ddbc207fff8 */ + 0.795713864077794763584, /* 0x0.cbb3e75f301b60003 */ + 0.797269511407239561694, /* 0x0.cc19dacd978cd8002 */ + 0.798828200086368567220, /* 0x0.cc8001427e55d7ffb */ + 0.800389937624300440456, /* 0x0.cce65ade24d360006 */ + 0.801954725261124767840, /* 0x0.cd4ce7a5de839fffb */ + 0.803522573691593189330, /* 0x0.cdb3a7c79a678fffd */ + 0.805093487311204114563, /* 0x0.ce1a9b563965ffffc */ + 0.806667472122675088819, /* 0x0.ce81c26b838db8000 */ + 0.808244534127439906441, /* 0x0.cee91d213f8428002 */ + 0.809824679342317166307, /* 0x0.cf50ab9144d92fff9 */ + 0.811407913793616542005, /* 0x0.cfb86dd5758c2ffff */ + 0.812994243520784198882, /* 0x0.d0206407c20e20005 */ + 0.814583674571603966162, /* 0x0.d0888e4223facfff9 */ + 0.816176213022088536960, /* 0x0.d0f0ec9eb3f7c8002 */ + 0.817771864936188586101, /* 0x0.d1597f377d6768002 */ + 0.819370636400374108252, /* 0x0.d1c24626a46eafff8 */ + 0.820972533518165570298, /* 0x0.d22b41865ff1e7ff9 */ + 0.822577562404315121269, /* 0x0.d2947170f32ec7ff9 */ + 0.824185729164559344159, /* 0x0.d2fdd60097795fff8 */ + 0.825797039949601741075, /* 0x0.d3676f4fb796d0001 */ + 0.827411500902565544264, /* 0x0.d3d13d78b5f68fffb */ + 0.829029118181348834154, /* 0x0.d43b40960546d8001 */ + 0.830649897953322891022, /* 0x0.d4a578c222a058000 */ + 0.832273846408250750368, /* 0x0.d50fe617a3ba78005 */ + 0.833900969738858188772, /* 0x0.d57a88b1218e90002 */ + 0.835531274148056613016, /* 0x0.d5e560a94048f8006 */ + 0.837164765846411529371, /* 0x0.d6506e1aac8078003 */ + 0.838801451086016225394, /* 0x0.d6bbb1204074e0001 */ + 0.840441336100884561780, /* 0x0.d72729d4c28518004 */ + 0.842084427144139224814, /* 0x0.d792d8530e12b0001 */ + 0.843730730487052604790, /* 0x0.d7febcb61273e7fff */ + 0.845380252404570153833, /* 0x0.d86ad718c308dfff9 */ + 0.847032999194574087728, /* 0x0.d8d727962c69d7fff */ + 0.848688977161248581090, /* 0x0.d943ae49621ce7ffb */ + 0.850348192619261200615, /* 0x0.d9b06b4d832ef8005 */ + 0.852010651900976245816, /* 0x0.da1d5ebdc22220005 */ + 0.853676361342631029337, /* 0x0.da8a88b555baa0006 */ + 0.855345327311054837175, /* 0x0.daf7e94f965f98004 */ + 0.857017556155879489641, /* 0x0.db6580a7c98f7fff8 */ + 0.858693054267390953857, /* 0x0.dbd34ed9617befff8 */ + 0.860371828028939855647, /* 0x0.dc4153ffc8b65fff9 */ + 0.862053883854957292436, /* 0x0.dcaf90368bfca8004 */ + 0.863739228154875360306, /* 0x0.dd1e0399328d87ffe */ + 0.865427867361348468455, /* 0x0.dd8cae435d303fff9 */ + 0.867119807911702289458, /* 0x0.ddfb9050b1cee8006 */ + 0.868815056264353846599, /* 0x0.de6aa9dced8448001 */ + 0.870513618890481399881, /* 0x0.ded9fb03db7320006 */ + 0.872215502247877139094, /* 0x0.df4983e1380657ff8 */ + 0.873920712852848668986, /* 0x0.dfb94490ffff77ffd */ + 0.875629257204025623884, /* 0x0.e0293d2f1cb01fff9 */ + 0.877341141814212965880, /* 0x0.e0996dd786fff0007 */ + 0.879056373217612985183, /* 0x0.e109d6a64f5d57ffc */ + 0.880774957955916648615, /* 0x0.e17a77b78e72a7ffe */ + 0.882496902590150900078, /* 0x0.e1eb5127722cc7ff8 */ + 0.884222213673356738383, /* 0x0.e25c63121fb0c8006 */ + 0.885950897802399772740, /* 0x0.e2cdad93ec5340003 */ + 0.887682961567391237685, /* 0x0.e33f30c925fb97ffb */ + 0.889418411575228162725, /* 0x0.e3b0ecce2d05ffff9 */ + 0.891157254447957902797, /* 0x0.e422e1bf727718006 */ + 0.892899496816652704641, /* 0x0.e4950fb9713fc7ffe */ + 0.894645145323828439008, /* 0x0.e50776d8b0e60fff8 */ + 0.896394206626591749641, /* 0x0.e57a1739c8fadfffc */ + 0.898146687421414902124, /* 0x0.e5ecf0f97c5798007 */ + 0.899902594367530173098, /* 0x0.e660043464e378005 */ + 0.901661934163603406867, /* 0x0.e6d3510747e150006 */ + 0.903424713533971135418, /* 0x0.e746d78f06cd97ffd */ + 0.905190939194458810123, /* 0x0.e7ba97e879c91fffc */ + 0.906960617885092856864, /* 0x0.e82e92309390b0007 */ + 0.908733756358986566306, /* 0x0.e8a2c6845544afffa */ + 0.910510361377119825629, /* 0x0.e9173500c8abc7ff8 */ + 0.912290439722343249336, /* 0x0.e98bddc30f98b0002 */ + 0.914073998177417412765, /* 0x0.ea00c0e84bc4c7fff */ + 0.915861043547953501680, /* 0x0.ea75de8db8094fffe */ + 0.917651582652244779397, /* 0x0.eaeb36d09d3137ffe */ + 0.919445622318405764159, /* 0x0.eb60c9ce4ed3dffff */ + 0.921243169397334638073, /* 0x0.ebd697a43995b0007 */ + 0.923044230737526172328, /* 0x0.ec4ca06fc7768fffa */ + 0.924848813220121135342, /* 0x0.ecc2e44e865b6fffb */ + 0.926656923710931002014, /* 0x0.ed39635df34e70006 */ + 0.928468569126343790092, /* 0x0.edb01dbbc2f5b7ffa */ + 0.930283756368834757725, /* 0x0.ee2713859aab57ffa */ + 0.932102492359406786818, /* 0x0.ee9e44d9342870004 */ + 0.933924784042873379360, /* 0x0.ef15b1d4635438005 */ + 0.935750638358567643520, /* 0x0.ef8d5a94f60f50007 */ + 0.937580062297704630580, /* 0x0.f0053f38f345cffff */ + 0.939413062815381727516, /* 0x0.f07d5fde3a2d98001 */ + 0.941249646905368053689, /* 0x0.f0f5bca2d481a8004 */ + 0.943089821583810716806, /* 0x0.f16e55a4e497d7ffe */ + 0.944933593864477061592, /* 0x0.f1e72b028a2827ffb */ + 0.946780970781518460559, /* 0x0.f2603cd9fb5430001 */ + 0.948631959382661205081, /* 0x0.f2d98b497d2a87ff9 */ + 0.950486566729423554277, /* 0x0.f353166f63e3dffff */ + 0.952344799896018723290, /* 0x0.f3ccde6a11ae37ffe */ + 0.954206665969085765512, /* 0x0.f446e357f66120000 */ + 0.956072172053890279009, /* 0x0.f4c12557964f0fff9 */ + 0.957941325265908139014, /* 0x0.f53ba48781046fffb */ + 0.959814132734539637840, /* 0x0.f5b66106555d07ffa */ + 0.961690601603558903308, /* 0x0.f6315af2c2027fffc */ + 0.963570739036113010927, /* 0x0.f6ac926b8aeb80004 */ + 0.965454552202857141381, /* 0x0.f728078f7c5008002 */ + 0.967342048278315158608, /* 0x0.f7a3ba7d66a908001 */ + 0.969233234469444204768, /* 0x0.f81fab543e1897ffb */ + 0.971128118008140250896, /* 0x0.f89bda33122c78007 */ + 0.973026706099345495256, /* 0x0.f9184738d4cf97ff8 */ + 0.974929006031422851235, /* 0x0.f994f284d3a5c0008 */ + 0.976835024947348973265, /* 0x0.fa11dc35bc7820002 */ + 0.978744770239899142285, /* 0x0.fa8f046b4fb7f8007 */ + 0.980658249138918636210, /* 0x0.fb0c6b449ab1cfff9 */ + 0.982575468959622777535, /* 0x0.fb8a10e1088fb7ffa */ + 0.984496437054508843888, /* 0x0.fc07f5602d79afffc */ + 0.986421160608523028820, /* 0x0.fc8618e0e55e47ffb */ + 0.988349647107594098099, /* 0x0.fd047b83571b1fffa */ + 0.990281903873210800357, /* 0x0.fd831d66f4c018002 */ + 0.992217938695037382475, /* 0x0.fe01fead3320bfff8 */ + 0.994157757657894713987, /* 0x0.fe811f703491e8006 */ + 0.996101369488558541238, /* 0x0.ff007fd5744490005 */ + 0.998048781093141101932, /* 0x0.ff801ffa9b9280007 */ + 1.000000000000000000000, /* 0x1.00000000000000000 */ + 1.001955033605393285965, /* 0x1.0080200565d29ffff */ + 1.003913889319761887310, /* 0x1.0100802aa0e80fff0 */ + 1.005876574715736104818, /* 0x1.01812090377240007 */ + 1.007843096764807100351, /* 0x1.020201541aad7fff6 */ + 1.009813464316352327214, /* 0x1.0283229c4c9820007 */ + 1.011787683565730677817, /* 0x1.030484836910a000e */ + 1.013765762469146736174, /* 0x1.0386272b9c077fffe */ + 1.015747708536026694351, /* 0x1.04080ab526304fff0 */ + 1.017733529475172815584, /* 0x1.048a2f412375ffff0 */ + 1.019723232714418781378, /* 0x1.050c94ef7ad5e000a */ + 1.021716825883923762690, /* 0x1.058f3be0f1c2d0004 */ + 1.023714316605201180057, /* 0x1.06122436442e2000e */ + 1.025715712440059545995, /* 0x1.06954e0fec63afff2 */ + 1.027721021151397406936, /* 0x1.0718b98f41c92fff6 */ + 1.029730250269221158939, /* 0x1.079c66d49bb2ffff1 */ + 1.031743407506447551857, /* 0x1.082056011a9230009 */ + 1.033760500517691527387, /* 0x1.08a487359ebd50002 */ + 1.035781537016238873464, /* 0x1.0928fa93490d4fff3 */ + 1.037806524719013578963, /* 0x1.09adb03b3e5b3000d */ + 1.039835471338248051878, /* 0x1.0a32a84e9e5760004 */ + 1.041868384612101516848, /* 0x1.0ab7e2eea5340ffff */ + 1.043905272300907460835, /* 0x1.0b3d603ca784f0009 */ + 1.045946142174331239262, /* 0x1.0bc3205a042060000 */ + 1.047991002016745332165, /* 0x1.0c4923682a086fffe */ + 1.050039859627715177527, /* 0x1.0ccf698898f3a000d */ + 1.052092722826109660856, /* 0x1.0d55f2dce5d1dfffb */ + 1.054149599440827866881, /* 0x1.0ddcbf86b09a5fff6 */ + 1.056210497317612961855, /* 0x1.0e63cfa7abc97fffd */ + 1.058275424318780855142, /* 0x1.0eeb23619c146fffb */ + 1.060344388322010722446, /* 0x1.0f72bad65714bffff */ + 1.062417397220589476718, /* 0x1.0ffa9627c38d30004 */ + 1.064494458915699715017, /* 0x1.1082b577d0eef0003 */ + 1.066575581342167566880, /* 0x1.110b18e893a90000a */ + 1.068660772440545025953, /* 0x1.1193c09c267610006 */ + 1.070750040138235936705, /* 0x1.121cacb4959befff6 */ + 1.072843392435016474095, /* 0x1.12a5dd543cf36ffff */ + 1.074940837302467588937, /* 0x1.132f529d59552000b */ + 1.077042382749654914030, /* 0x1.13b90cb250d08fff5 */ + 1.079148036789447484528, /* 0x1.14430bb58da3dfff9 */ + 1.081257807444460983297, /* 0x1.14cd4fc984c4a000e */ + 1.083371702785017154417, /* 0x1.1557d910df9c7000e */ + 1.085489730853784307038, /* 0x1.15e2a7ae292d30002 */ + 1.087611899742884524772, /* 0x1.166dbbc422d8c0004 */ + 1.089738217537583819804, /* 0x1.16f9157586772ffff */ + 1.091868692357631731528, /* 0x1.1784b4e533cacfff0 */ + 1.094003332327482702577, /* 0x1.18109a360fc23fff2 */ + 1.096142145591650907149, /* 0x1.189cc58b155a70008 */ + 1.098285140311341168136, /* 0x1.1929370751ea50002 */ + 1.100432324652149906842, /* 0x1.19b5eecdd79cefff0 */ + 1.102583706811727015711, /* 0x1.1a42ed01dbdba000e */ + 1.104739294993289488947, /* 0x1.1ad031c69a2eafff0 */ + 1.106899097422573863281, /* 0x1.1b5dbd3f66e120003 */ + 1.109063122341542140286, /* 0x1.1beb8f8fa8150000b */ + 1.111231377994659874592, /* 0x1.1c79a8dac6ad0fff4 */ + 1.113403872669181282605, /* 0x1.1d0809445a97ffffc */ + 1.115580614653132185460, /* 0x1.1d96b0effc9db000e */ + 1.117761612217810673898, /* 0x1.1e25a001332190000 */ + 1.119946873713312474002, /* 0x1.1eb4d69bdb2a9fff1 */ + 1.122136407473298902480, /* 0x1.1f4454e3bfae00006 */ + 1.124330221845670330058, /* 0x1.1fd41afcbb48bfff8 */ + 1.126528325196519908506, /* 0x1.2064290abc98c0001 */ + 1.128730725913251964394, /* 0x1.20f47f31c9aa7000f */ + 1.130937432396844410880, /* 0x1.21851d95f776dfff0 */ + 1.133148453059692917203, /* 0x1.2216045b6784efffa */ + 1.135363796355857157764, /* 0x1.22a733a6692ae0004 */ + 1.137583470716100553249, /* 0x1.2338ab9b3221a0004 */ + 1.139807484614418608939, /* 0x1.23ca6c5e27aadfff7 */ + 1.142035846532929888057, /* 0x1.245c7613b7f6c0004 */ + 1.144268564977221958089, /* 0x1.24eec8e06b035000c */ + 1.146505648458203463465, /* 0x1.258164e8cea85fff8 */ + 1.148747105501412235671, /* 0x1.26144a5180d380009 */ + 1.150992944689175123667, /* 0x1.26a7793f5de2efffa */ + 1.153243174560058870217, /* 0x1.273af1d712179000d */ + 1.155497803703682491111, /* 0x1.27ceb43d81d42fff1 */ + 1.157756840726344771440, /* 0x1.2862c097a3d29000c */ + 1.160020294239811677834, /* 0x1.28f7170a74cf4fff1 */ + 1.162288172883275239058, /* 0x1.298bb7bb0faed0004 */ + 1.164560485298402170388, /* 0x1.2a20a2ce920dffff4 */ + 1.166837240167474476460, /* 0x1.2ab5d86a4631ffff6 */ + 1.169118446164539637555, /* 0x1.2b4b58b36d5220009 */ + 1.171404112007080167155, /* 0x1.2be123cf786790002 */ + 1.173694246390975415341, /* 0x1.2c7739e3c0aac000d */ + 1.175988858069749065617, /* 0x1.2d0d9b15deb58fff6 */ + 1.178287955789017793514, /* 0x1.2da4478b627040002 */ + 1.180591548323240091978, /* 0x1.2e3b3f69fb794fffc */ + 1.182899644456603782686, /* 0x1.2ed282d76421d0004 */ + 1.185212252993012693694, /* 0x1.2f6a11f96c685fff3 */ + 1.187529382762033236513, /* 0x1.3001ecf60082ffffa */ + 1.189851042595508889847, /* 0x1.309a13f30f28a0004 */ + 1.192177241354644978669, /* 0x1.31328716a758cfff7 */ + 1.194507987909589896687, /* 0x1.31cb4686e1e85fffb */ + 1.196843291137896336843, /* 0x1.32645269dfd04000a */ + 1.199183159977805113226, /* 0x1.32fdaae604c39000f */ + 1.201527603343041317132, /* 0x1.339750219980dfff3 */ + 1.203876630171082595692, /* 0x1.3431424300e480007 */ + 1.206230249419600664189, /* 0x1.34cb8170b3fee000e */ + 1.208588470077065268869, /* 0x1.35660dd14dbd4fffc */ + 1.210951301134513435915, /* 0x1.3600e78b6bdfc0005 */ + 1.213318751604272271958, /* 0x1.369c0ec5c38ebfff2 */ + 1.215690830512196507537, /* 0x1.373783a718d29000f */ + 1.218067546930756250870, /* 0x1.37d3465662f480007 */ + 1.220448909901335365929, /* 0x1.386f56fa770fe0008 */ + 1.222834928513994334780, /* 0x1.390bb5ba5fc540004 */ + 1.225225611877684750397, /* 0x1.39a862bd3c7a8fff3 */ + 1.227620969111500981433, /* 0x1.3a455e2a37bcafffd */ + 1.230021009336254911271, /* 0x1.3ae2a8287dfbefff6 */ + 1.232425741726685064472, /* 0x1.3b8040df76f39fffa */ + 1.234835175450728295084, /* 0x1.3c1e287682e48fff1 */ + 1.237249319699482263931, /* 0x1.3cbc5f151b86bfff8 */ + 1.239668183679933477545, /* 0x1.3d5ae4e2cc0a8000f */ + 1.242091776620540377629, /* 0x1.3df9ba07373bf0006 */ + 1.244520107762172811399, /* 0x1.3e98deaa0d8cafffe */ + 1.246953186383919165383, /* 0x1.3f3852f32973efff0 */ + 1.249391019292643401078, /* 0x1.3fd816ffc72b90001 */ + 1.251833623164381181797, /* 0x1.40782b17863250005 */ + 1.254280999953110153911, /* 0x1.41188f42caf400000 */ + 1.256733161434815393410, /* 0x1.41b943b42945bfffd */ + 1.259190116985283935980, /* 0x1.425a4893e5f10000a */ + 1.261651875958665236542, /* 0x1.42fb9e0a2df4c0009 */ + 1.264118447754797758244, /* 0x1.439d443f608c4fff9 */ + 1.266589841787181258708, /* 0x1.443f3b5bebf850008 */ + 1.269066067469190262045, /* 0x1.44e183883e561fff7 */ + 1.271547134259576328224, /* 0x1.45841cecf7a7a0001 */ + 1.274033051628237434048, /* 0x1.462707b2c43020009 */ + 1.276523829025464573684, /* 0x1.46ca44023aa410007 */ + 1.279019475999373156531, /* 0x1.476dd2045d46ffff0 */ + 1.281520002043128991825, /* 0x1.4811b1e1f1f19000b */ + 1.284025416692967214122, /* 0x1.48b5e3c3edd74fff4 */ + 1.286535729509738823464, /* 0x1.495a67d3613c8fff7 */ + 1.289050950070396384145, /* 0x1.49ff3e396e19d000b */ + 1.291571087985403654081, /* 0x1.4aa4671f5b401fff1 */ + 1.294096152842774794011, /* 0x1.4b49e2ae56d19000d */ + 1.296626154297237043484, /* 0x1.4befb10fd84a3fff4 */ + 1.299161101984141142272, /* 0x1.4c95d26d41d84fff8 */ + 1.301701005575179204100, /* 0x1.4d3c46f01d9f0fff3 */ + 1.304245874766450485904, /* 0x1.4de30ec21097d0003 */ + 1.306795719266019562007, /* 0x1.4e8a2a0ccce3d0002 */ + 1.309350548792467483458, /* 0x1.4f3198fa10346fff5 */ + 1.311910373099227200545, /* 0x1.4fd95bb3be8cffffd */ + 1.314475201942565174546, /* 0x1.50817263bf0e5fffb */ + 1.317045045107389400535, /* 0x1.5129dd3418575000e */ + 1.319619912422941299109, /* 0x1.51d29c4f01c54ffff */ + 1.322199813675649204855, /* 0x1.527bafde83a310009 */ + 1.324784758729532718739, /* 0x1.5325180cfb8b3fffd */ + 1.327374757430096474625, /* 0x1.53ced504b2bd0fff4 */ + 1.329969819671041886272, /* 0x1.5478e6f02775e0001 */ + 1.332569955346704748651, /* 0x1.55234df9d8a59fff8 */ + 1.335175174370685002822, /* 0x1.55ce0a4c5a6a9fff6 */ + 1.337785486688218616860, /* 0x1.56791c1263abefff7 */ + 1.340400902247843806217, /* 0x1.57248376aef21fffa */ + 1.343021431036279800211, /* 0x1.57d040a420c0bfff3 */ + 1.345647083048053138662, /* 0x1.587c53c5a630f0002 */ + 1.348277868295411074918, /* 0x1.5928bd063fd7bfff9 */ + 1.350913796821875845231, /* 0x1.59d57c9110ad60006 */ + 1.353554878672557082439, /* 0x1.5a8292913d68cfffc */ + 1.356201123929036356254, /* 0x1.5b2fff3212db00007 */ + 1.358852542671913132777, /* 0x1.5bddc29edcc06fff3 */ + 1.361509145047255398051, /* 0x1.5c8bdd032ed16000f */ + 1.364170941142184734180, /* 0x1.5d3a4e8a5bf61fff4 */ + 1.366837941171020309735, /* 0x1.5de9176042f1effff */ + 1.369510155261156381121, /* 0x1.5e9837b062f4e0005 */ + 1.372187593620959988833, /* 0x1.5f47afa69436cfff1 */ + 1.374870266463378287715, /* 0x1.5ff77f6eb3f8cfffd */ + 1.377558184010425845733, /* 0x1.60a7a734a9742fff9 */ + 1.380251356531521533853, /* 0x1.6158272490016000c */ + 1.382949794301995272203, /* 0x1.6208ff6a8978a000f */ + 1.385653507605306700170, /* 0x1.62ba3032c0a280004 */ + 1.388362506772382154503, /* 0x1.636bb9a994784000f */ + 1.391076802081129493127, /* 0x1.641d9bfb29a7bfff6 */ + 1.393796403973427855412, /* 0x1.64cfd7545928b0002 */ + 1.396521322756352656542, /* 0x1.65826be167badfff8 */ + 1.399251568859207761660, /* 0x1.663559cf20826000c */ + 1.401987152677323100733, /* 0x1.66e8a14a29486fffc */ + 1.404728084651919228815, /* 0x1.679c427f5a4b6000b */ + 1.407474375243217723560, /* 0x1.68503d9ba0add000f */ + 1.410226034922914983815, /* 0x1.690492cbf6303fff9 */ + 1.412983074197955213304, /* 0x1.69b9423d7b548fff6 */ +}; diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/t_exp2.h b/REORG.TODO/sysdeps/ieee754/dbl-64/t_exp2.h new file mode 100644 index 0000000000..1fd73338cf --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/t_exp2.h @@ -0,0 +1,585 @@ +/* These values are accurate to 52+12 bits when represented as + a double. */ +static const double exp2_accuratetable[512] = { +0.707106781187802013759 /* 0x0.b504f333fb3f80007 */, +0.708064712808760599040 /* 0x0.b543baa0f71b38000 */, +0.709023942160304065938 /* 0x0.b58297d3a8d518002 */, +0.709984470998547667624 /* 0x0.b5c18ad39b4ba0001 */, +0.710946301084324217006 /* 0x0.b60093a85e8d30001 */, +0.711909434180505784637 /* 0x0.b63fb25984e628005 */, +0.712873872052760648733 /* 0x0.b67ee6eea3b5f8003 */, +0.713839616467838999908 /* 0x0.b6be316f518c98001 */, +0.714806669195984345523 /* 0x0.b6fd91e328d148007 */, +0.715775032009894562898 /* 0x0.b73d0851c69e20002 */, +0.716744706683768884058 /* 0x0.b77c94c2c9b3d0003 */, +0.717715694995770148178 /* 0x0.b7bc373dd52eb0003 */, +0.718687998724665488852 /* 0x0.b7fbefca8cd530004 */, +0.719661619652575468291 /* 0x0.b83bbe70981da8001 */, +0.720636559564428180758 /* 0x0.b87ba337a194b0006 */, +0.721612820246623098989 /* 0x0.b8bb9e27556508004 */, +0.722590403488338473025 /* 0x0.b8fbaf4762c798006 */, +0.723569311081411870036 /* 0x0.b93bd69f7be1d0000 */, +0.724549544820974333906 /* 0x0.b97c1437567828007 */, +0.725531106502312561633 /* 0x0.b9bc6816a87ae8002 */, +0.726513997924421062181 /* 0x0.b9fcd2452bee00000 */, +0.727498220889519875430 /* 0x0.ba3d52ca9e6148002 */, +0.728483777200401694265 /* 0x0.ba7de9aebe05c8003 */, +0.729470668664712662563 /* 0x0.babe96f94e62a8002 */, +0.730458897090379144517 /* 0x0.baff5ab2134df0004 */, +0.731448464287988597833 /* 0x0.bb4034e0d38ab0000 */, +0.732439372072965166897 /* 0x0.bb81258d5b2d60001 */, +0.733431622260458326859 /* 0x0.bbc22cbf75fd28001 */, +0.734425216668725511232 /* 0x0.bc034a7ef32c00001 */, +0.735420157118880535324 /* 0x0.bc447ed3a50fe0005 */, +0.736416445434497690674 /* 0x0.bc85c9c560b350001 */, +0.737414083433310718618 /* 0x0.bcc72b5bf4b4e0000 */, +0.738413072966152328496 /* 0x0.bd08a39f5417a8007 */, +0.739413415848264365956 /* 0x0.bd4a32974abcd0002 */, +0.740415113911250699637 /* 0x0.bd8bd84bb68300002 */, +0.741418168994518067562 /* 0x0.bdcd94c47ddd30003 */, +0.742422582936659858376 /* 0x0.be0f6809865968006 */, +0.743428357577745613238 /* 0x0.be515222b72530003 */, +0.744435494762383687126 /* 0x0.be935317fc6ba0002 */, +0.745443996335090397492 /* 0x0.bed56af1423de8001 */, +0.746453864145572798553 /* 0x0.bf1799b67a6248007 */, +0.747465100043933849969 /* 0x0.bf59df6f970e70002 */, +0.748477705883256683178 /* 0x0.bf9c3c248dbee8001 */, +0.749491683518965001732 /* 0x0.bfdeafdd568308000 */, +0.750507034813367890373 /* 0x0.c0213aa1f0fc38004 */, +0.751523761622240105153 /* 0x0.c063dc7a559ca0003 */, +0.752541865811731880422 /* 0x0.c0a6956e883ed8000 */, +0.753561349247157341600 /* 0x0.c0e965868bd220006 */, +0.754582213796583967110 /* 0x0.c12c4cca664cb8002 */, +0.755604461332336940791 /* 0x0.c16f4b42225350006 */, +0.756628093726406381068 /* 0x0.c1b260f5ca2c48002 */, +0.757653112855631305506 /* 0x0.c1f58ded6d72d8001 */, +0.758679520599333412360 /* 0x0.c238d2311e7d08001 */, +0.759707318837184453227 /* 0x0.c27c2dc8f00368005 */, +0.760736509456435783249 /* 0x0.c2bfa0bcfd1400000 */, +0.761767094336480043995 /* 0x0.c3032b155818d0000 */, +0.762799075372231349951 /* 0x0.c346ccda248cc0001 */, +0.763832454453522768941 /* 0x0.c38a8613805488005 */, +0.764867233473625618441 /* 0x0.c3ce56c98d1ca8005 */, +0.765903414329434539816 /* 0x0.c4123f04708d80002 */, +0.766940998920452976510 /* 0x0.c4563ecc532dc0001 */, +0.767979989148100838946 /* 0x0.c49a56295f9f88006 */, +0.769020386915772125040 /* 0x0.c4de8523c2b0a0001 */, +0.770062194131770905170 /* 0x0.c522cbc3ae94e0003 */, +0.771105412703856241146 /* 0x0.c5672a1154e6b8004 */, +0.772150044545352520777 /* 0x0.c5aba014ed5f18003 */, +0.773196091570364285606 /* 0x0.c5f02dd6b09288003 */, +0.774243555696622731700 /* 0x0.c634d35edb1260003 */, +0.775292438842697939641 /* 0x0.c67990b5aa5c18004 */, +0.776342742931542928455 /* 0x0.c6be65e360bed8000 */, +0.777394469888802008854 /* 0x0.c70352f0437f50004 */, +0.778447621641124243320 /* 0x0.c74857e498fd00006 */, +0.779502200118583399303 /* 0x0.c78d74c8ab5b60000 */, +0.780558207255445668515 /* 0x0.c7d2a9a4c959f8000 */, +0.781615644985491186966 /* 0x0.c817f681412f80002 */, +0.782674515247667956808 /* 0x0.c85d5b6666c150006 */, +0.783734819983036512536 /* 0x0.c8a2d85c904760003 */, +0.784796561133562109454 /* 0x0.c8e86d6c14f850002 */, +0.785859740645942328471 /* 0x0.c92e1a9d513ec8002 */, +0.786924360469767103536 /* 0x0.c973dff8a4b390007 */, +0.787990422552312885808 /* 0x0.c9b9bd866c6440007 */, +0.789057928854407064640 /* 0x0.c9ffb34f1444b0001 */, +0.790126881326406182996 /* 0x0.ca45c15afcc570001 */, +0.791197281930050233534 /* 0x0.ca8be7b292db38000 */, +0.792269132620954885659 /* 0x0.cad2265e3cbee8000 */, +0.793342435380726906957 /* 0x0.cb187d667d3d38006 */, +0.794417192158282659010 /* 0x0.cb5eecd3b33158006 */, +0.795493404931386649540 /* 0x0.cba574ae5d2e80001 */, +0.796571075671306805268 /* 0x0.cbec14fef2a348004 */, +0.797650206352955137846 /* 0x0.cc32cdcdef0000000 */, +0.798730798954342069432 /* 0x0.cc799f23d11d18000 */, +0.799812855456121796232 /* 0x0.ccc089091abb28004 */, +0.800896377841454287795 /* 0x0.cd078b86505c18003 */, +0.801981368096190028208 /* 0x0.cd4ea6a3f97720007 */, +0.803067828208752554378 /* 0x0.cd95da6aa057b8007 */, +0.804155760170129796375 /* 0x0.cddd26e2d21b28001 */, +0.805245165974338261710 /* 0x0.ce248c151f3330001 */, +0.806336047619038653883 /* 0x0.ce6c0a0a1c1350001 */, +0.807428407102107836855 /* 0x0.ceb3a0ca5d6be0006 */, +0.808522246427078927792 /* 0x0.cefb505e7e2550007 */, +0.809617567597010201484 /* 0x0.cf4318cf18a268002 */, +0.810714372621179513182 /* 0x0.cf8afa24ce1c98004 */, +0.811812663508675536069 /* 0x0.cfd2f4683f9810005 */, +0.812912442272482604912 /* 0x0.d01b07a2126188003 */, +0.814013710929394895825 /* 0x0.d06333daeff618001 */, +0.815116471495287542325 /* 0x0.d0ab791b80d028006 */, +0.816220725993571205593 /* 0x0.d0f3d76c75b330000 */, +0.817326476447408967199 /* 0x0.d13c4ed67f1cf8000 */, +0.818433724883006474832 /* 0x0.d184df6250e3b0001 */, +0.819542473330909460055 /* 0x0.d1cd8918a3a328004 */, +0.820652723822034690935 /* 0x0.d2164c02305fa0002 */, +0.821764478391968422618 /* 0x0.d25f2827b53fb0005 */, +0.822877739077315761840 /* 0x0.d2a81d91f188b8000 */, +0.823992507918612782109 /* 0x0.d2f12c49a8d290005 */, +0.825108786960634610365 /* 0x0.d33a5457a35e40003 */, +0.826226578247117093869 /* 0x0.d38395c4a84848007 */, +0.827345883828319528258 /* 0x0.d3ccf09985d958004 */, +0.828466705754248966560 /* 0x0.d41664df0a1320005 */, +0.829589046080638992111 /* 0x0.d45ff29e094330000 */, +0.830712906863802391671 /* 0x0.d4a999df585a20005 */, +0.831838290163696481037 /* 0x0.d4f35aabd04a60006 */, +0.832965198041969556729 /* 0x0.d53d350c4be258002 */, +0.834093632565442222342 /* 0x0.d5872909aba050007 */, +0.835223595802037643865 /* 0x0.d5d136acd138e8006 */, +0.836355089820669306292 /* 0x0.d61b5dfe9f7780004 */, +0.837488116698010487424 /* 0x0.d6659f0801afa8005 */, +0.838622678508982644113 /* 0x0.d6aff9d1e147d8004 */, +0.839758777333464490056 /* 0x0.d6fa6e652d19e0000 */, +0.840896415254110962690 /* 0x0.d744fccad70d00003 */, +0.842035594355151628676 /* 0x0.d78fa50bd2c3b0000 */, +0.843176316724478125433 /* 0x0.d7da673117e730007 */, +0.844318584453106590905 /* 0x0.d8254343a19038003 */, +0.845462399634695271912 /* 0x0.d870394c6dbf30003 */, +0.846607764365415071965 /* 0x0.d8bb49547d37c0004 */, +0.847754680744707056494 /* 0x0.d9067364d45608003 */, +0.848903150873708822763 /* 0x0.d951b7867953b0006 */, +0.850053176859071113491 /* 0x0.d99d15c2787a30006 */, +0.851204760807439786431 /* 0x0.d9e88e21de11a0003 */, +0.852357904828824897169 /* 0x0.da3420adba1508003 */, +0.853512611037803181642 /* 0x0.da7fcd6f2184d8005 */, +0.854668881550406100980 /* 0x0.dacb946f2afaf8000 */, +0.855826718478671755185 /* 0x0.db1775b6e8ad48000 */, +0.856986123964844970247 /* 0x0.db63714f8e0818006 */, +0.858147100114499461478 /* 0x0.dbaf87422625b8000 */, +0.859309649060962410524 /* 0x0.dbfbb797daa460002 */, +0.860473772936213743282 /* 0x0.dc480259d3a710001 */, +0.861639473872910177676 /* 0x0.dc9467913a0f48006 */, +0.862806754008130227807 /* 0x0.dce0e7473b9b28003 */, +0.863975615481124226159 /* 0x0.dd2d8185086c20006 */, +0.865146060433749419813 /* 0x0.dd7a3653d38168005 */, +0.866318091005120138881 /* 0x0.ddc705bcccd628000 */, +0.867491709362415264210 /* 0x0.de13efc9434100004 */, +0.868666917636779056818 /* 0x0.de60f4825df9b8005 */, +0.869843717989716047624 /* 0x0.deae13f16599c0003 */, +0.871022112578215268471 /* 0x0.defb4e1f9dc388002 */, +0.872202103559697183859 /* 0x0.df48a3164a92f0001 */, +0.873383693097737778847 /* 0x0.df9612deb6e878007 */, +0.874566883362160263365 /* 0x0.dfe39d82348310001 */, +0.875751676517234511901 /* 0x0.e031430a0f0688000 */, +0.876938074732511840819 /* 0x0.e07f037f97e548001 */, +0.878126080186539592654 /* 0x0.e0ccdeec2a75e0006 */, +0.879315695055312818168 /* 0x0.e11ad5591f4078001 */, +0.880506921518618312932 /* 0x0.e168e6cfd2f880004 */, +0.881699761760385225541 /* 0x0.e1b71359a6df60003 */, +0.882894217964411143207 /* 0x0.e2055afffc1178000 */, +0.884090292325693805080 /* 0x0.e253bdcc3ffbb8001 */, +0.885287987031581180559 /* 0x0.e2a23bc7d7a1d8002 */, +0.886487304278189114386 /* 0x0.e2f0d4fc31ab80004 */, +0.887688246263368285778 /* 0x0.e33f8972bea8a8005 */, +0.888890815189881999840 /* 0x0.e38e5934f49010007 */, +0.890095013257492739835 /* 0x0.e3dd444c460bd0007 */, +0.891300842677948068626 /* 0x0.e42c4ac232f380000 */, +0.892508305659222567226 /* 0x0.e47b6ca036f8b8005 */, +0.893717404414979710310 /* 0x0.e4caa9efd40e58002 */, +0.894928141160697743242 /* 0x0.e51a02ba8e2610007 */, +0.896140518115016826430 /* 0x0.e5697709ecab90000 */, +0.897354537501434679237 /* 0x0.e5b906e77c61d0006 */, +0.898570201543732793877 /* 0x0.e608b25cca5ba8005 */, +0.899787512470129891014 /* 0x0.e6587973688ce8002 */, 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0x0.ec58f3f16a3910002 */, +0.924483034755387955725 /* 0x0.ecaaeb8ffb3168005 */, +0.925735450311948926408 /* 0x0.ecfcff9bd67078000 */, +0.926989562542820610982 /* 0x0.ed4f301edad1a0007 */, +0.928245373740515189457 /* 0x0.eda17d22e0f9b0001 */, +0.929502886213858126045 /* 0x0.edf3e6b1d37d40001 */, +0.930762102264245716494 /* 0x0.ee466cd594c5c8005 */, +0.932023024199046146183 /* 0x0.ee990f980dcdb0005 */, +0.933285654329454095216 /* 0x0.eeebcf032bc470007 */, +0.934549994971191289044 /* 0x0.ef3eab20e0d3c0001 */, +0.935816048439005676599 /* 0x0.ef91a3fb1e1340004 */, +0.937083817055075818404 /* 0x0.efe4b99bdcc618006 */, +0.938353303143720007819 /* 0x0.f037ec0d1889b8000 */, +0.939624509028518128972 /* 0x0.f08b3b58cc2bb8006 */, +0.940897437041863904384 /* 0x0.f0dea788fc2a90000 */, +0.942172089516254085427 /* 0x0.f13230a7ad21b8003 */, +0.943448468787511540534 /* 0x0.f185d6bee754e0006 */, +0.944726577195256100890 /* 0x0.f1d999d8b73478005 */, +0.946006417082291717338 /* 0x0.f22d79ff2cb130000 */, 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0x1.60d84fd155d15000e */, +1.380167867259843417228 /* 0x1.6152ae6cdf0030003 */, +1.382037608124419003675 /* 0x1.61cd3778bc879000d */, +1.383909881963391264069 /* 0x1.6247eb03a4dc40009 */, +1.385784692209972801544 /* 0x1.62c2c91c56d9b0002 */, +1.387662042298923203992 /* 0x1.633dd1d1930ec0001 */, +1.389541935670444372533 /* 0x1.63b90532200630004 */, +1.391424375772021271329 /* 0x1.6434634ccc4cc0007 */, +1.393309366052102982208 /* 0x1.64afec30677e90008 */, +1.395196909966106124701 /* 0x1.652b9febc8e0f000d */, +1.397087010973788290271 /* 0x1.65a77e8dcc7f10004 */, +1.398979672539331309267 /* 0x1.66238825534170000 */, +1.400874898129892187656 /* 0x1.669fbcc1415600008 */, +1.402772691220124823310 /* 0x1.671c1c708328e000a */, +1.404673055288671035301 /* 0x1.6798a7420988b000d */, +1.406575993818903302975 /* 0x1.68155d44ca77a000f */, +1.408481510297352468121 /* 0x1.68923e87bf70e000a */, +1.410389608216942924956 /* 0x1.690f4b19e8f74000c */, +1.412300291075172076232 /* 0x1.698c830a4c94c0008 */ +}; +#define S (1.0/4503599627370496.0) /* 2^-52 */ +static const float exp2_deltatable[512] = { + 11527*S, -963*S, 884*S, -781*S, -2363*S, -3441*S, 123*S, 526*S, + -6*S, 1254*S, -1138*S, 1519*S, 1576*S, -65*S, 1040*S, 793*S, + -1662*S, -5063*S, -387*S, 968*S, -941*S, 984*S, -2856*S, -545*S, + 495*S, -5246*S, -2109*S, 1281*S, 2075*S, 909*S, -1642*S,-78233*S, +-31653*S, -265*S, 130*S, 430*S, 2482*S, -742*S, 1616*S, -2213*S, + -519*S, 20*S, -3134*S,-13981*S, 1343*S, -1740*S, 247*S, 1679*S, + -1097*S, 3131*S, 871*S, -1480*S, 1936*S, -1827*S, 17325*S, 528*S, + -322*S, 1404*S, -152*S, -1845*S, -212*S, 2639*S, -476*S, 2960*S, + -962*S, -1012*S, -1231*S, 3030*S, 1659*S, -486*S, 2154*S, 1728*S, + -2793*S, 699*S, -1560*S, -2125*S, 2156*S, 142*S, -1888*S, 4426*S, +-13443*S, 1970*S, -50*S, 1771*S,-43399*S, 4979*S, -2448*S, -370*S, + 1414*S, 1075*S, 232*S, 206*S, 873*S, 2141*S, 2970*S, 1279*S, + -2331*S, 336*S, -2595*S, 753*S, -3384*S, -616*S, 89*S, -818*S, + 5755*S, -241*S, -528*S, -661*S, -3777*S, -354*S, 250*S, 3881*S, + 2632*S, -2131*S, 2565*S, -316*S, 1746*S, -2541*S, -1324*S, -50*S, + 2564*S, -782*S, 1176*S, 6452*S, -1002*S, 1288*S, 336*S, -185*S, + 3063*S, 3784*S, 2169*S, 686*S, 328*S, -400*S, 312*S, -4517*S, + -1457*S, 1046*S, -1530*S, -685*S, 1328*S,-49815*S, -895*S, 1063*S, + -2091*S, -672*S, -1710*S, -665*S, 1545*S, 1819*S,-45265*S, 3548*S, + -554*S, -568*S, 4752*S, -1907*S,-13738*S, 675*S, 9611*S, -1115*S, + -815*S, 408*S, -1281*S, -937*S,-16376*S, -4772*S, -1440*S, 992*S, + 788*S, 10364*S, -1602*S, -661*S, -1783*S, -265*S, -20*S, -3781*S, + -861*S, -345*S, -994*S, 1364*S, -5339*S, 1620*S, 9390*S, -1066*S, + -305*S, -170*S, 175*S, 2461*S, -490*S, -769*S, -1450*S, 3315*S, + 2418*S, -45*S, -852*S, -1295*S, -488*S, -96*S, 1142*S, -2639*S, + 7905*S, -9306*S, -3859*S, 760*S, 1057*S, -1570*S, 3977*S, 209*S, + -514*S, 7151*S, 1646*S, 627*S, 599*S, -774*S, -1468*S, 633*S, + -473*S, 851*S, 2406*S, 143*S, 74*S, 4260*S, 1177*S, -913*S, + 2670*S, -3298*S, -1662*S, -120*S, -3264*S, -2148*S, 410*S, 2078*S, + -2098*S, -926*S, 3580*S, -1289*S, 2450*S, -1158*S, 907*S, -590*S, + 986*S, 1801*S, 1145*S, -1677*S, 3455*S, 956*S, 710*S, 144*S, + 153*S, -255*S, -1898*S, 28102*S, 2748*S, 1194*S, -3009*S, 7076*S, + 0*S, -2720*S, 711*S, 1225*S, -3034*S, -473*S, 378*S, -1046*S, + 962*S, -2006*S, 4647*S, 3206*S, 1769*S, -2665*S, 1254*S, 2025*S, + -2430*S, 6193*S, 1224*S, -856*S, -1592*S, -325*S, -1521*S, 1827*S, + -264*S, 2403*S, -1065*S, 967*S, -681*S, -2106*S, -474*S, 1333*S, + -893*S, 2296*S, 592*S, -1220*S, -326*S, 990*S, 139*S, 206*S, + -779*S, -1683*S, 1238*S, 6098*S, 136*S, 1197*S, 790*S, -107*S, + -1004*S, -2449*S, 939*S, 5568*S, 156*S, 1812*S, 2792*S, -1094*S, + -2677*S, -251*S, 2297*S, 943*S, -1329*S, 2883*S, -853*S, -2626*S, +-105929*S, -6552*S, 1095*S, -1508*S, 1003*S, 5039*S, -2600*S, -749*S, + 1790*S, 890*S, 2016*S, -1073*S, 624*S, -2084*S, -1536*S, -1330*S, + 358*S, 2444*S, -179*S,-25759*S, -243*S, -552*S, -124*S, 3766*S, + 1192*S, -1614*S, 6*S, -1227*S, 345*S, -981*S, -295*S, -1006*S, + -995*S, -1195*S, 706*S, 2512*S, -1758*S, -734*S, -6286*S, -922*S, + 1530*S, 1542*S, 1223*S, 61*S, -83*S, 522*S,116937*S, -914*S, + -418*S, -7339*S, 249*S, -520*S, -762*S, 426*S, -505*S, 2664*S, + -1093*S, -1035*S, 2130*S, 4878*S, 1982*S, 1551*S, 2304*S, 193*S, + 1532*S, -7268*S, 24357*S, 531*S, 2676*S, -1170*S, 1465*S, -1917*S, + 2143*S, 1466*S, -7*S, -7300*S, 3297*S, -1197*S, -289*S, -1548*S, + 26226*S, 4401*S, 4123*S, -1588*S, 4243*S, 4069*S, -1276*S, -2010*S, + 1407*S, 1478*S, 488*S, -2366*S, -2909*S, -2534*S, -1285*S, 7095*S, + -645*S, -2089*S, -944*S, -40*S, -1363*S, -833*S, 917*S, 1609*S, + 1286*S, 1677*S, 1613*S, -2295*S, -1248*S, 40*S, 26*S, 2038*S, + 698*S, 2675*S, -1755*S, -3522*S, -1614*S, -6111*S, 270*S, 1822*S, + -234*S, -2844*S, -1201*S, -830*S, 1193*S, 2354*S, 47*S, 1522*S, + -78*S, -640*S, 2425*S, -1596*S, 1563*S, 1169*S, -1006*S, -83*S, + 2362*S, -3521*S, -314*S, 1814*S, -1751*S, 305*S, 1715*S, -3741*S, + 7847*S, 1291*S, 1206*S, 36*S, 1397*S, -1419*S, -1194*S, -2014*S, + 1742*S, -578*S, -207*S, 875*S, 1539*S, 2826*S, -1165*S, -909*S, + 1849*S, 927*S, 2018*S, -981*S, 1637*S, -463*S, 905*S, 6618*S, + 400*S, 630*S, 2614*S, 900*S, 2323*S, -1094*S, -1858*S, -212*S, + -2069*S, 747*S, 1845*S, -1450*S, 444*S, -213*S, -438*S, 1158*S, + 4738*S, 2497*S, -370*S, -2016*S, -518*S, -1160*S, -1510*S, 123*S +}; +/* Maximum magnitude in above table: 116937 */ +#undef S diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/uasncs.h b/REORG.TODO/sysdeps/ieee754/dbl-64/uasncs.h new file mode 100644 index 0000000000..d754932558 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/uasncs.h @@ -0,0 +1,69 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:uasncs.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef UANSNCS_H +#define UANSNCS_H + +#ifdef BIG_ENDI + static const mynumber +/**/ a1 = {{0x3FC55580, 0x00000000 }}, /* 0.1666717529296875 */ +/**/ a2 = {{0xBED55555, 0x55552330 }}, /* -5.0862630208224597e-06 */ +/**/ hp0 = {{0x3FF921FB, 0x54442D18 }}, /* 1.5707963267948966 */ +/**/ hp1 = {{0x3C91A626, 0x33145C07 }}; /* 6.123233995736766e-17 */ + +#else +#ifdef LITTLE_ENDI + static const mynumber +/**/ a1 = {{0x00000000, 0x3FC55580 }}, /* 0.1666717529296875 */ +/**/ a2 = {{0x55552330, 0xBED55555 }}, /* -5.0862630208224597e-06 */ +/**/ hp0 = {{0x54442D18, 0x3FF921FB }}, /* 1.5707963267948966 */ +/**/ hp1 = {{0x33145C07, 0x3C91A626 }}; /* 6.123233995736766e-17 */ + +#endif +#endif + +static const double + f1 = 1.66666666666664110590506577996662E-01, + f2 = 7.50000000026122686814431784722623E-02, + f3 = 4.46428561421059750978517350006940E-02, + f4 = 3.03821268582119319911193410625235E-02, + f5 = 2.23551211026525610742786300334557E-02, + f6 = 1.81382903404565056280372531963613E-02; +static const double + c2 = 0.74999999999985410757087492918602258E-01, + c3 = 0.44642857150311968932423372477866076E-01, + c4 = 0.30381942574778615766200591683810471E-01, + c5 = 0.22372413472984868331447708777000650E-01, + c6 = 0.17333630246451830686009693735025490E-01, + c7 = 0.14710362893628210269950864741085777E-01; + +static const double big = 103079215104.0, t24 = 16777216.0, t27 = 134217728.0; +static const double + rt0 = 9.99999999859990725855365213134618E-01, + rt1 = 4.99999999495955425917856814202739E-01, + rt2 = 3.75017500867345182581453026130850E-01, + rt3 = 3.12523626554518656309172508769531E-01; +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/uatan.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/uatan.tbl new file mode 100644 index 0000000000..06608a3edb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/uatan.tbl @@ -0,0 +1,11134 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE uatan() FUNCTION */ +/****************************************************************/ + +#include "endian.h" + +#ifdef BIG_ENDI + + static const number + cij[241][7] = { /* x0,cij for (1/16,1) */ +/**/ {{{0X3FB04006, 0X65E0244E} }, +/**/ {{0X3FB03A73, 0X7B53DD20} }, +/**/ {{0X3FEFDF1F, 0XCF5CFB72} }, +/**/ {{0XBFB01EB3, 0XCE2AE4C2} }, +/**/ {{0XBFD4D29E, 0XDD58A40D} }, +/**/ {{0X3FAFDA4A, 0XD907A18A} }, +/**/ {{0X3FC814DF, 0X4DF65B18} } }, +/**/ {{{0X3FB0FFFD, 0XB9B88CD8} }, +/**/ {{0X3FB0F99C, 0X63645300} }, +/**/ {{0X3FEFDC08, 0XA3DED30F} }, +/**/ {{0XBFB0D9DC, 0X669C1AED} }, +/**/ {{0XBFD4C669, 0XF7138DE2} }, +/**/ {{0X3FB0A12F, 0X29D085A7} }, +/**/ {{0X3FC7F0EE, 0XCFD48D20} } }, +/**/ {{{0X3FB1FFF1, 0X5A73D4F1} }, +/**/ {{0X3FB1F85F, 0X2BEE2040} }, +/**/ {{0X3FEFD7B3, 0X42B56D31} }, +/**/ {{0XBFB1D2B7, 0XB69DEA40} }, +/**/ {{0XBFD4B552, 0X3922ECC9} }, +/**/ {{0X3FB18F93, 0X522B1A04} }, +/**/ {{0X3FC7BEAD, 0X5660F061} } }, +/**/ {{{0X3FB2FFFD, 0XB2524AA2} }, +/**/ {{0X3FB2F716, 0XE71790A0} }, +/**/ {{0X3FEFD31F, 0X53B496A4} }, +/**/ {{0XBFB2CAD8, 0X4AAB7374} }, +/**/ {{0XBFD4A34B, 0X58DD2FB2} }, +/**/ {{0X3FB27C0A, 0XD0CECC18} }, +/**/ {{0X3FC789D2, 0X5D2743D7} } }, +/**/ {{{0X3FB3FFFE, 0X0573F3AC} }, +/**/ {{0X3FB3F59D, 0X1702F6A0} }, +/**/ {{0X3FEFCE4D, 0XB071ACC2} }, +/**/ {{0XBFB3C20F, 0X64DB3686} }, +/**/ {{0XBFD49059, 0XEB3BFE93} }, +/**/ {{0X3FB36659, 0XCAF74FED} }, +/**/ {{0X3FC75269, 0X1C011FB0} } }, +/**/ {{{0X3FB4FFEF, 0X894384D6} }, +/**/ {{0X3FB4F3ED, 0X0CE204C0} }, +/**/ {{0X3FEFC93E, 0XA8EA5A01} }, +/**/ {{0XBFB4B84F, 0X7B5457C9} }, +/**/ {{0XBFD47C80, 0X7401F2F9} }, +/**/ {{0X3FB44E64, 0XB4F67209} }, +/**/ {{0X3FC7187D, 0X4C540B77} } }, +/**/ {{{0X3FB5FFF8, 0XDF406528} }, +/**/ {{0X3FB5F22B, 0X3C73D820} }, +/**/ {{0X3FEFC3F1, 0XB1F60F13} }, +/**/ {{0XBFB5ADB2, 0XCB7FA73B} }, +/**/ {{0XBFD467BE, 0X2B1EB555} }, +/**/ {{0X3FB53435, 0X99EDC463} }, +/**/ {{0X3FC6DC1B, 0X238F5059} } }, +/**/ {{{0X3FB7000F, 0X8C4F0D56} }, +/**/ {{0X3FB6F04B, 0X495A2FA0} }, +/**/ {{0X3FEFBE67, 0X340DCE97} }, +/**/ {{0XBFB6A224, 0X4D98E1AD} }, +/**/ {{0XBFD45216, 0X14064DF1} }, +/**/ {{0X3FB617AA, 0X2BA78A66} }, +/**/ {{0X3FC69D4F, 0X50A3D7AC} } }, +/**/ {{{0X3FB8000F, 0XBB4057CF} }, +/**/ {{0X3FB7EE27, 0XBE2CD3A0} }, +/**/ {{0X3FEFB8A0, 0X39EC9246} }, +/**/ {{0XBFB79577, 0X31D9C773} }, +/**/ {{0XBFD43B8D, 0XB6DC7D72} }, +/**/ {{0X3FB6F88A, 0XD69547DF} }, +/**/ {{0X3FC65C26, 0XF633CE8C} } }, +/**/ {{{0X3FB8FFF2, 0X39CF2B7F} }, +/**/ {{0X3FB8EBB7, 0X9F979E80} }, +/**/ {{0X3FEFB29D, 0X435506E1} }, +/**/ {{0XBFB8879A, 0X69B9CDB5} }, +/**/ {{0XBFD42428, 0X85FEAFA9} }, +/**/ {{0X3FB7D6BA, 0XB6191A0E} }, +/**/ {{0X3FC618AF, 0XA7CB8BB5} } }, +/**/ {{{0X3FB9FFF9, 0X6E2F0772} }, +/**/ {{0X3FB9E93A, 0XD32A9480} }, +/**/ {{0X3FEFAC5D, 0X04A3EC40} }, +/**/ {{0XBFB978C2, 0X53F6EA97} }, +/**/ {{0XBFD40BE3, 0X089C36F6} }, +/**/ {{0X3FB8B25C, 0X885AEB77} }, +/**/ {{0X3FC5D2F7, 0X63CADCE1} } }, +/**/ {{{0X3FBB0002, 0X6316B097} }, +/**/ {{0X3FBAE68C, 0XCE24CC00} }, +/**/ {{0X3FEFA5E0, 0X938C5C66} }, +/**/ {{0XBFBA68C3, 0X76F14E4B} }, +/**/ {{0XBFD3F2C3, 0X1696CD7C} }, +/**/ {{0X3FB98B3B, 0X722A2CB4} }, +/**/ {{0X3FC58B0C, 0X9067AD62} } }, +/**/ {{{0X3FBC0008, 0X604F58B1} }, +/**/ {{0X3FBBE3A7, 0X05650780} }, +/**/ {{0X3FEF9F28, 0X5A7A2773} }, +/**/ {{0XBFBB578F, 0X3D5AC0A4} }, +/**/ {{0XBFD3D8CB, 0XF767119F} }, +/**/ {{0X3FBA613D, 0XC7E31B88} }, +/**/ {{0X3FC540FD, 0XF5594565} } }, +/**/ {{{0X3FBD0002, 0X6CCA4EBA} }, +/**/ {{0X3FBCE07E, 0XC1298A80} }, +/**/ {{0X3FEF9834, 0XE8D36C4A} }, +/**/ {{0XBFBC4513, 0X5BCAC5FE} }, +/**/ {{0XBFD3BE01, 0X8B5236F1} }, +/**/ {{0X3FBB3447, 0X2E991970} }, +/**/ {{0X3FC4F4DA, 0XB8ADB373} } }, +/**/ {{{0X3FBDFFF4, 0XB2B47FCA} }, +/**/ {{0X3FBDDD16, 0X4A051D80} }, +/**/ {{0X3FEF9106, 0X78DCC895} }, +/**/ {{0XBFBD3149, 0XF0966844} }, +/**/ {{0XBFD3A266, 0X744F9A5F} }, +/**/ {{0X3FBC0446, 0XEDB7F27A} }, +/**/ {{0X3FC4A6B2, 0X583F9ECA} } }, +/**/ {{{0X3FBF000A, 0XA9A05BE0} }, +/**/ {{0X3FBED996, 0XA3BDA540} }, +/**/ {{0X3FEF899C, 0X1B8BA97F} }, +/**/ {{0XBFBE1C51, 0X2287A677} }, +/**/ {{0XBFD385F8, 0XEDC130BB} }, +/**/ {{0X3FBCD14B, 0XF306FF50} }, +/**/ {{0X3FC45694, 0XA667A72B} } }, +/**/ {{{0X3FBFFFFA, 0XBA8F63DE} }, +/**/ {{0X3FBFD5B5, 0X69FE4780} }, +/**/ {{0X3FEF81F8, 0X4863DC7D} }, +/**/ {{0XBFBF05DB, 0XD1518706} }, +/**/ {{0XBFD368C4, 0X4687A69C} }, +/**/ {{0X3FBD9B08, 0X1B3868DA} }, +/**/ {{0X3FC40491, 0XC345ADFC} } }, +/**/ {{{0X3FC07FFA, 0X6ECCADA8} }, +/**/ {{0X3FC068D0, 0X0A396400} }, +/**/ {{0X3FEF7A19, 0XF1FCFC6B} }, +/**/ {{0XBFBFEE0C, 0X861DF0DF} }, +/**/ {{0XBFD34AC6, 0X5A586C0C} }, +/**/ {{0X3FBE618F, 0X189D637A} }, +/**/ {{0X3FC3B0BA, 0X195779D4} } }, +/**/ 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{{{0X3FEEC000, 0X5A13BA60} }, +/**/ {{0X3FE87ED1, 0X19B163E0} }, +/**/ {{0X3FE0A31F, 0X2EBB7AD7} }, +/**/ {{0XBFD09FBE, 0X33A3FCE1} }, +/**/ {{0X3FB53AA8, 0X89D9AF5D} }, +/**/ {{0X3F760799, 0XF7F7040B} }, +/**/ {{0XBF9EE456, 0XD3F0B3FB} } }, +/**/ {{{0X3FEEDFFF, 0X58F8DD18} }, +/**/ {{0X3FE88F6B, 0X6681CA80} }, +/**/ {{0X3FE09287, 0XEC4360B3} }, +/**/ {{0XBFD08FD0, 0XB7CE07E5} }, +/**/ {{0X3FB53FDD, 0X7BDEDD3F} }, +/**/ {{0X3F73A366, 0X70C52E66} }, +/**/ {{0XBF9E5630, 0X5DCA7315} } }, +/**/ {{{0X3FEEFFFF, 0XBE033400} }, +/**/ {{0X3FE89FF5, 0XDD4D7960} }, +/**/ {{0X3FE081FF, 0XDFFE15BD} }, +/**/ {{0XBFD07FDE, 0XDAE56C0F} }, +/**/ {{0X3FB5447A, 0XF84D6F5D} }, +/**/ {{0X3F714A24, 0X7982941E} }, +/**/ {{0XBF9DC982, 0X81E68835} } }, +/**/ {{{0X3FEF2001, 0XE6B5125D} }, +/**/ {{0X3FE8B070, 0XBBE88160} }, +/**/ {{0X3FE07186, 0XDF7122E2} }, +/**/ {{0XBFD06FE8, 0XDE905325} }, +/**/ {{0X3FB54883, 0XB5DEEC7A} }, +/**/ {{0X3F6DF762, 0XB4A186D5} }, +/**/ {{0XBF9D3E4E, 0XDE20F495} } }, +/**/ {{{0X3FEF3FFD, 0XF770E0DB} }, +/**/ {{0X3FE8C0D8, 0X09E96380} }, +/**/ {{0X3FE06120, 0XF5A576A9} }, +/**/ {{0XBFD05FF3, 0X1D2912FF} }, +/**/ {{0X3FB54BF9, 0X8CD1001F} }, +/**/ {{0X3F6970FC, 0X6E90DC16} }, +/**/ {{0XBF9CB496, 0XD8EB587E} } }, +/**/ {{{0X3FEF5FFE, 0X4E16DA33} }, +/**/ {{0X3FE8D131, 0X29BCCDC0} }, +/**/ {{0X3FE050C8, 0XD33BA4E9} }, +/**/ {{0XBFD04FF8, 0XD74C83D2} }, +/**/ {{0X3FB54EE0, 0X592BB252} }, +/**/ {{0X3F64FF61, 0X7193EEB5} }, +/**/ {{0XBF9C2C5B, 0XA459AC86} } }, +/**/ {{{0X3FEF8000, 0X4576FF2E} }, +/**/ {{0X3FE8E17A, 0XCCE443A0} }, +/**/ {{0X3FE0407F, 0XD8A97B6C} }, +/**/ {{0XBFD03FFB, 0XC91B3E55} }, +/**/ {{0X3FB5513A, 0X5F3357F7} }, +/**/ {{0X3F60A2BA, 0X14C92B53} }, +/**/ {{0XBF9BA59E, 0X3E70DF71} } }, +/**/ {{{0X3FEF9FFF, 0X39B6A330} }, +/**/ {{0X3FE8F1B2, 0XA7F515A0} }, +/**/ {{0X3FE03048, 0X63064158} }, +/**/ {{0XBFD02FFE, 0XACBAADA8} }, +/**/ {{0X3FB55309, 0XF27448C0} }, +/**/ {{0X3F58B6D6, 0X4850006B} }, +/**/ {{0XBF9B205F, 0X742323DF} } }, +/**/ {{{0X3FEFC001, 0XAA76C0B9} }, +/**/ {{0X3FE901DC, 0X15D66D80} }, +/**/ {{0X3FE0201F, 0X28D9B4AA} }, +/**/ {{0XBFD01FFE, 0XA98D4C38} }, +/**/ {{0X3FB55452, 0X089780F8} }, +/**/ {{0X3F5050B5, 0X7F35C5BB} }, +/**/ {{0XBF9A9C9F, 0XE19247AF} } }, +/**/ {{{0X3FEFDFFE, 0X39A592CA} }, +/**/ {{0X3FE911F2, 0X6D88A780} }, +/**/ {{0X3FE01008, 0XE40C6538} }, +/**/ {{0XBFD01000, 0XD31688DE} }, +/**/ {{0X3FB55514, 0XE32F1816} }, +/**/ {{0X3F402A15, 0X4E1628D2} }, +/**/ {{0XBF9A1A5F, 0XF4FAF5A0} } }, +/**/ {{{0X3FEFF801, 0X8E92D1B0} }, +/**/ {{0X3FE91DFB, 0X9BB4BF00} }, +/**/ {{0X3FE003FF, 0XB884C5A9} }, +/**/ {{0XBFD003FF, 0X3876A954} }, +/**/ {{0X3FB55551, 0X5539DDFB} }, +/**/ {{0X3F2007E7, 0X7B95E6C2} }, +/**/ {{0XBF99B9A7, 0X18A3BA58} } }, + }; + + static const number + hij[241][16] = { /* x0,hij for (1/16,1) */ +/**/ {{{0x3fb04000, 0x00000000} }, +/**/ {{0x3fb03a6d, 0x1c06693d} }, +/**/ {{0xbc428a02, 0xd4e7f128} }, +/**/ {{0x3fefdf1f, 0xe92592ae} }, +/**/ {{0x3c88bfc0, 0xb5490162} }, +/**/ {{0xbfb01ead, 0x8f7e4151} }, +/**/ {{0xbc5395e8, 0x0b64d205} }, +/**/ {{0xbfd4d29f, 0x433dd49b} }, +/**/ {{0xbc75b19d, 0x4aa42633} }, +/**/ {{0x3fafda41, 0xce35961d} }, +/**/ {{0x3c4e6a5f, 0x425d7696} }, +/**/ {{0x3fc814dd, 0x6c1bb5e2} }, +/**/ {{0xbfaf4cb7, 0x2b33739f} }, +/**/ {{0xbfc048b2, 0xc267d8ec} }, +/**/ {{0x3fae9649, 0xe8ababc6} }, +/**/ {{0x3fb78293, 0xfe802692} } }, +/**/ {{{0x3fb10000, 0x00000000} }, +/**/ {{0x3fb0f99e, 0xa71d52a7} }, +/**/ {{0xbc22069f, 0xeec3624f} }, +/**/ {{0x3fefdc08, 0x9a49d2a9} }, +/**/ {{0x3c7780f7, 0x68b2ce25} }, +/**/ {{0xbfb0d9de, 0x9da73e1d} }, +/**/ {{0x3c4ebf46, 0xa1a487bf} }, +/**/ {{0xbfd4c669, 0xd13ea108} }, +/**/ {{0x3c7354bc, 0xebb4528c} }, +/**/ {{0x3fb0a137, 0x789374c1} }, +/**/ {{0xbc56c223, 0xc3f2c5c2} }, +/**/ {{0x3fc7f0e7, 0x79c60cda} }, +/**/ {{0xbfb05062, 0xcdcc7b81} }, +/**/ {{0xbfc019e4, 0xc5266783} }, +/**/ {{0x3fafd0b2, 0xf2540289} }, +/**/ {{0x3fb71107, 0xf6d3cd8a} } }, +/**/ {{{0x3fb20000, 0x00000000} }, +/**/ {{0x3fb1f86d, 0xbf082d59} }, +/**/ {{0xbc4095dc, 0x7732ef81} }, +/**/ {{0x3fefd7b3, 0x01722b81} }, +/**/ {{0xbc5e618c, 0x8a212e02} }, +/**/ {{0xbfb1d2c5, 0xee4e9cfa} }, +/**/ {{0x3c426273, 0x29abece0} }, +/**/ {{0xbfd4b551, 0x37eb7f46} }, +/**/ {{0x3c73b360, 0x01d8bf12} }, +/**/ {{0x3fb18fa7, 0x6adb6a7c} }, +/**/ {{0xbc5c00d8, 0x398999ad} }, +/**/ {{0x3fc7bea5, 0xf4a7cff3} }, +/**/ {{0xbfb13008, 0x61f84829} }, +/**/ {{0xbfbfb14f, 0xa8e135a1} }, +/**/ {{0x3fb0b532, 0x4324f177} }, +/**/ {{0x3fb6734a, 0x3498dd9d} } }, +/**/ {{{0x3fb30000, 0x00000000} }, +/**/ {{0x3fb2f719, 0x318a4a9a} }, +/**/ {{0x3c03fd17, 0x79b9801f} }, +/**/ {{0x3fefd31f, 0x48e238fe} }, +/**/ {{0xbc876a7a, 0xd8c45327} }, +/**/ {{0xbfb2cada, 0x852096e2} }, +/**/ {{0x3c460860, 0x11efd787} }, +/**/ {{0xbfd4a34b, 0x2e476a39} }, +/**/ {{0x3c7254f2, 0xeb11ee51} }, +/**/ {{0x3fb27c13, 0xc54ae225} }, +/**/ {{0x3c513096, 0x4ae66f0c} }, +/**/ {{0x3fc789ca, 0xef0d59d0} }, +/**/ {{0xbfb20c06, 0x6d9aaa8c} }, +/**/ {{0xbfbf2885, 0x846ba912} }, +/**/ {{0x3fb17c5f, 0xc697ef5e} }, +/**/ {{0x3fb5ce93, 0xcad31e6e} } }, +/**/ {{{0x3fb40000, 0x00000000} }, +/**/ {{0x3fb3f59f, 0x0e7c559d} }, +/**/ {{0x3c5ac4ce, 0x285df847} }, +/**/ {{0x3fefce4d, 0xa6ab93e9} }, +/**/ {{0xbc6be46b, 0x18a97736} }, +/**/ {{0xbfb3c211, 0x4d22b635} }, +/**/ {{0x3c42033c, 0x6950679f} }, +/**/ {{0xbfd49059, 0xc4d74033} }, +/**/ {{0x3c57dd7c, 0xd7e376aa} }, +/**/ {{0x3fb36662, 0xc0896a7c} }, +/**/ {{0xbc36cf6a, 0xd79232cf} }, +/**/ {{0x3fc75261, 0xa13a97a2} }, +/**/ {{0xbfb2e431, 0x5fdd1509} }, +/**/ {{0xbfbe9999, 0x6e52db32} }, +/**/ {{0x3fb23da4, 0xb0a71e9f} }, +/**/ {{0x3fb52335, 0xe3bc8178} } }, +/**/ {{{0x3fb50000, 0x00000000} }, +/**/ {{0x3fb4f3fd, 0x677292fb} }, +/**/ {{0x3c4008d3, 0x6264979e} }, +/**/ {{0x3fefc93e, 0x53a1ee0d} }, +/**/ {{0xbc64421a, 0x20fd2bdf} }, +/**/ {{0xbfb4b85f, 0x4aba88e3} }, +/**/ {{0x3c54f184, 0x3c9d1e89} }, +/**/ {{0xbfd47c7f, 0x25ae4668} }, +/**/ {{0xbc7d7581, 0x816630d1} }, +/**/ {{0x3fb44e7b, 0x07f85056} }, +/**/ {{0x3c56d63c, 0x910bdf4f} }, +/**/ {{0x3fc71875, 0xc439029c} }, +/**/ {{0xbfb3b85e, 0xf2bcfa10} }, +/**/ {{0xbfbe04bb, 0x9707b205} }, +/**/ {{0x3fb2f8c6, 0x95e3e0cc} }, +/**/ {{0x3fb47184, 0x8093431b} } }, +/**/ {{{0x3fb60000, 0x00000000} }, +/**/ {{0x3fb5f232, 0x4fd2d7b2} }, +/**/ {{0x3c58a8da, 0x4401318e} }, +/**/ {{0x3fefc3f1, 0x8b549418} }, +/**/ {{0x3c34d896, 0x836f8130} }, +/**/ {{0xbfb5adb9, 0x9cdd92e7} }, +/**/ {{0x3c4d4161, 0xeb397cc3} }, +/**/ {{0xbfd467bd, 0x93f8f1dc} }, +/**/ {{0xbc609d7b, 0xffc760ad} }, +/**/ {{0x3fb53443, 0xbea6b2fe} }, +/**/ {{0x3c5eb03c, 0x4b24f5db} }, +/**/ {{0x3fc6dc13, 0x8de3d005} }, +/**/ {{0xbfb48866, 0x37d2d99d} }, +/**/ {{0xbfbd6a1d, 0xf6663fcb} }, +/**/ {{0x3fb3ad8e, 0x0adff464} }, +/**/ {{0x3fb3b9d6, 0x4159c223} } }, +/**/ {{{0x3fb70000, 0x00000000} }, +/**/ {{0x3fb6f03b, 0xdcea4b0d} }, +/**/ {{0xbc33f00e, 0x512fa17d} }, +/**/ {{0x3fefbe67, 0x8c07a436} }, +/**/ {{0xbc84baaa, 0x46250d6f} }, +/**/ {{0xbfb6a215, 0x7e3ba4c7} }, +/**/ {{0xbc3504e7, 0x54503f8d} }, +/**/ {{0xbfd45217, 0x6b82d03a} }, +/**/ {{0x3c7d1f0d, 0xbebdd1db} }, +/**/ {{0x3fb617a4, 0x841d5604} }, +/**/ {{0xbc47168b, 0x6681c436} }, +/**/ {{0x3fc69d47, 0xaccec6ce} }, +/**/ {{0xbfb5541f, 0xa4715800} }, +/**/ {{0xbfbcc9f4, 0x335a1c1b} }, +/**/ {{0x3fb45bc6, 0xbac0061f} }, +/**/ {{0x3fb2fc84, 0x2b3853b6} } }, +/**/ {{{0x3fb80000, 0x00000000} }, +/**/ {{0x3fb7ee18, 0x2602f10f} }, +/**/ {{0xbc5cfb65, 0x4c0c3d98} }, +/**/ {{0x3fefb8a0, 0x96acfacc} }, +/**/ {{0xbc82962e, 0x18495af3} }, +/**/ {{0xbfb79568, 0x46635c89} }, +/**/ {{0x3c5ac468, 0xa6bfd498} }, +/**/ {{0xbfd43b8f, 0x2037b997} }, +/**/ {{0xbc72ad53, 0xe2f12373} }, +/**/ {{0x3fb6f885, 0x7900c4ee} }, +/**/ {{0x3c53145d, 0x0aef1f9d} }, +/**/ {{0x3fc65c1f, 0x4409ba0e} }, +/**/ {{0xbfb61b65, 0x1d176e0c} }, +/**/ {{0xbfbc2473, 0x8ad65152} }, +/**/ {{0x3fb5033f, 0x7bc246c1} }, +/**/ {{0x3fb239e9, 0x6db30b46} } }, +/**/ {{{0x3fb90000, 0x00000000} }, +/**/ {{0x3fb8ebc5, 0x4478fb28} }, +/**/ {{0x3c473288, 0x0cad24cc} }, +/**/ {{0x3fefb29c, 0xeedcd6d7} }, +/**/ {{0x3c8efa9e, 0x23ea50f0} }, +/**/ {{0xbfb887a7, 0x6ae09982} }, +/**/ {{0x3c5b2275, 0x53801511} }, +/**/ {{0xbfd42427, 0x3da0757c} }, +/**/ {{0xbc7199e5, 0x311c7ac8} }, +/**/ {{0x3fb7d6cf, 0x4388717b} }, +/**/ {{0xbc5c4eb2, 0x3dd070b4} }, +/**/ {{0x3fc618a7, 0xe6c2b5f3} }, +/**/ {{0xbfb6de12, 0x00313569} }, +/**/ {{0xbfbb79d2, 0xb6316619} }, +/**/ {{0x3fb5a3ca, 0x61af5c21} }, +/**/ {{0x3fb17263, 0x26e60289} } }, +/**/ {{{0x3fba0000, 0x00000000} }, +/**/ {{0x3fb9e941, 0x53cfdcf1} }, +/**/ {{0x3c5a332e, 0x1d69c47e} }, +/**/ {{0x3fefac5c, 0xdace3776} }, +/**/ {{0xbc8c9a78, 0x1ad91ab5} }, +/**/ {{0xbfb978c8, 0x8054ad75} }, +/**/ {{0xbc5e35b8, 0x8ed66c17} }, +/**/ {{0xbfd40be2, 0x665afed1} }, +/**/ {{0x3c62eeef, 0x08ef10fb} }, +/**/ {{0x3fb8b26b, 0x13c989d2} }, +/**/ {{0x3c329f11, 0xbfeab3ba} }, +/**/ {{0x3fc5d2ef, 0x93c8f97c} }, +/**/ {{0xbfb79c03, 0x30234881} }, +/**/ {{0xbfbaca49, 0xd0f650c8} }, +/**/ {{0x3fb63d3c, 0xce2dcccc} }, +/**/ {{0x3fb0a650, 0x26fb0af2} } }, +/**/ {{{0x3fbb0000, 0x00000000} }, +/**/ {{0x3fbae68a, 0x71c722b8} }, +/**/ {{0x3c4c014e, 0x6910b9db} }, +/**/ {{0x3fefa5e0, 0xa34ef42b} }, +/**/ {{0xbc836583, 0xeb56d5b9} }, +/**/ {{0xbfba68c1, 0x3b881779} }, +/**/ {{0xbc473a0d, 0x13a09314} }, +/**/ {{0xbfd3f2c3, 0x538e939c} }, +/**/ {{0xbc68ed49, 0xee53e648} }, +/**/ {{0x3fb98b42, 0xa7d45973} }, +/**/ {{0xbc523943, 0x461ca7c4} }, +/**/ {{0x3fc58b04, 0xb0f2e2bb} }, +/**/ {{0xbfb85517, 0x1c9d23dc} }, +/**/ {{0xbfba1612, 0x3e3b5a66} }, +/**/ {{0x3fb6cf6f, 0x7ef1d0b9} }, +/**/ {{0x3fafac21, 0x6617b315} } }, +/**/ {{{0x3fbc0000, 0x00000000} }, +/**/ {{0x3fbbe39e, 0xbe6f07c3} }, +/**/ {{0x3c5f7b8f, 0x29a05987} }, +/**/ {{0x3fef9f28, 0x93bb9192} }, +/**/ {{0x3c78260b, 0x7cd1bdab} }, +/**/ {{0xbfbb5787, 0x72759741} }, +/**/ {{0x3c52f93f, 0xa6767247} }, +/**/ {{0xbfd3d8cc, 0xd45bbe91} }, +/**/ {{0x3c664839, 0x2edc0762} }, +/**/ {{0x3fba6140, 0x4fa31d26} }, +/**/ {{0x3c400647, 0x97891510} }, +/**/ {{0x3fc540f6, 0x0668fd66} }, +/**/ {{0xbfb9092d, 0xcb2f6e8f} }, +/**/ {{0xbfb95d66, 0x8d902073} }, +/**/ {{0x3fb75a3e, 0x99c53d16} }, +/**/ {{0x3fae040c, 0x8f475e61} } }, +/**/ {{{0x3fbd0000, 0x00000000} }, +/**/ {{0x3fbce07c, 0x5c3cca32} }, +/**/ {{0x3c4138e6, 0x425918a7} }, +/**/ {{0x3fef9834, 0xf9f6d421} }, +/**/ {{0x3c6f3089, 0x8c22a239} }, +/**/ {{0xbfbc4511, 0x1d4e69a5} }, +/**/ {{0x3c254c0f, 0xd2083ce8} }, +/**/ {{0xbfd3be01, 0xcd488978} }, +/**/ {{0x3c5612db, 0x6362ec0f} }, +/**/ {{0x3fbb344e, 0xf0d94873} }, +/**/ {{0xbc182beb, 0xfdf7db72} }, +/**/ {{0x3fc4f4d2, 0xb9d86c04} }, +/**/ {{0xbfb9b828, 0xdf238807} }, +/**/ {{0xbfb8a082, 0x5f93ffd6} }, +/**/ {{0x3fb7dd89, 0xb6650b0c} }, +/**/ {{0x3fac5526, 0xb62676ef} } }, +/**/ {{{0x3fbe0000, 0x00000000} }, +/**/ {{0x3fbddd21, 0x701eba6e} }, +/**/ {{0x3c594eff, 0xcd76fe58} }, +/**/ {{0x3fef9106, 0x266112ba} }, +/**/ {{0x3c74c302, 0x6b7e18b1} }, +/**/ {{0xbfbd3154, 0x5777816c} }, +/**/ {{0x3c5dc7e4, 0x1f9dbddd} }, +/**/ {{0xbfd3a265, 0x37a90881} }, +/**/ {{0xbc75bd61, 0xeb7ba840} }, +/**/ {{0x3fbc045a, 0x0a52514b} }, +/**/ {{0xbc35ca88, 0xcff49a99} }, +/**/ {{0x3fc4a6aa, 0x498eeb56} }, +/**/ {{0xbfba61eb, 0xa09232cf} }, +/**/ {{0xbfb7dfa2, 0x4a464027} }, +/**/ {{0x3fb85933, 0xe633c053} }, +/**/ {{0x3faaa036, 0x3f920107} } }, +/**/ {{{0x3fbf0000, 0x00000000} }, +/**/ {{0x3fbed98c, 0x2190043b} }, +/**/ {{0xbc23a598, 0x592c7b13} }, +/**/ {{0x3fef899c, 0x6bcf4ad8} }, +/**/ {{0x3c55fd73, 0x912c09b0} }, +/**/ {{0xbfbe1c47, 0x607f91a0} }, +/**/ {{0x3c576677, 0x5b5db022} }, +/**/ {{0xbfd385fa, 0x21046f5f} }, +/**/ {{0x3c7f01c3, 0x4487f4b8} }, +/**/ {{0x3fbcd14d, 0xb77f2d51} }, +/**/ {{0x3c57a86d, 0x30a2ccfe} }, +/**/ {{0x3fc4568c, 0x8782b530} }, +/**/ {{0xbfbb065b, 0x02b7ad2d} }, +/**/ {{0xbfb71b03, 0xbd215555} }, +/**/ {{0x3fb8cd23, 0xb9c1c1de} }, +/**/ {{0x3fa8e602, 0x8dbfa69b} } }, +/**/ {{{0x3fc00000, 0x00000000} }, +/**/ {{0x3fbfd5ba, 0x9aac2f6e} }, +/**/ {{0xbc4cd376, 0x86760c17} }, +/**/ {{0x3fef81f8, 0x1f81f820} }, +/**/ {{0xbc8f81f8, 0x1f81f820} }, +/**/ {{0xbfbf05e0, 0x9d0dc11b} }, +/**/ {{0xbc35a199, 0x1d821725} }, +/**/ {{0xbfd368c3, 0xaa76e1d7} }, +/**/ {{0xbc672d4c, 0xc796f8cd} }, +/**/ {{0x3fbd9b16, 0xb391c2e3} }, +/**/ {{0x3c58051b, 0x8086c51d} }, +/**/ {{0x3fc40489, 0x94488c86} }, +/**/ {{0xbfbba55d, 0xa98401c8} }, +/**/ {{0xbfb652e4, 0xe5127e64} }, +/**/ {{0x3fb93943, 0x442e53ae} }, +/**/ {{0x3fa72753, 0x86286f75} } }, +/**/ {{{0x3fc08000, 0x00000000} }, +/**/ {{0x3fc068d5, 0x84212b3e} }, +/**/ {{0xbc69e2d2, 0x83019bfd} }, +/**/ {{0x3fef7a19, 0x991bb133} }, +/**/ {{0x3c7a956a, 0x66627723} }, +/**/ {{0xbfbfee16, 0x97c8e137} }, +/**/ {{0x3c4d9399, 0x66dbe7af} }, +/**/ {{0xbfd34ac5, 0x0810323a} }, +/**/ {{0x3c6a1a57, 0x6bc6c512} }, +/**/ {{0x3fbe61a2, 0x5c75a6f9} }, +/**/ {{0xbc492b99, 0xd75c8f85} }, +/**/ {{0x3fc3b0b1, 0xd9fa3f20} }, +/**/ {{0xbfbc3edb, 0xee66d309} }, +/**/ {{0xbfb58784, 0x905eeb33} }, +/**/ {{0x3fb99d80, 0x1c65bb14} }, +/**/ {{0x3fa564f1, 0x18a09884} } }, +/**/ {{{0x3fc10000, 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{{0x3fc0ad06, 0xf5c213ab} }, +/**/ {{0x3c625bf2, 0xabea9e66} }, +/**/ {{0x3fc25054, 0x5f93bbb2} }, +/**/ {{0xbfbe6c0c, 0xc80a32c8} }, +/**/ {{0xbfb23e6c, 0x678d0d1e} }, +/**/ {{0x3fbadea2, 0xebf8ae4b} }, +/**/ {{0x3f9c8bd7, 0x527f133b} } }, +/**/ {{{0x3fc30000, 0x00000000} }, +/**/ {{0x3fc2dcbd, 0xb2fba1ff} }, +/**/ {{0x3c58f287, 0x05561534} }, +/**/ {{0x3fef4f64, 0x2ee76e94} }, +/**/ {{0x3c80ec89, 0xc6da5865} }, +/**/ {{0xbfc23089, 0xb322f867} }, +/**/ {{0x3c4c2b54, 0x5fcd0d6f} }, +/**/ {{0xbfd2a986, 0x45802261} }, +/**/ {{0xbc79a132, 0x5ae78b8a} }, +/**/ {{0x3fc107b3, 0x35a9d974} }, +/**/ {{0x3c5ef22d, 0xb725e335} }, +/**/ {{0x3fc1f453, 0x9bd98832} }, +/**/ {{0xbfbee8cf, 0x2057aad4} }, +/**/ {{0xbfb16681, 0x1e1bc3a1} }, +/**/ {{0x3fbb1ad8, 0x759c8f58} }, +/**/ {{0x3f98f941, 0x0b15b4aa} } }, +/**/ {{{0x3fc38000, 0x00000000} }, +/**/ {{0x3fc359e8, 0xedeb99a4} }, +/**/ {{0xbc6a5fd7, 0x4e4604c6} }, +/**/ {{0x3fef462f, 0xfce28238} }, +/**/ {{0x3c83dc01, 0xd90595d1} }, +/**/ {{0xbfc2a01b, 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{{{0x3fd80000, 0x00000000} }, +/**/ {{0x3fd6f619, 0x41e4def1} }, +/**/ {{0xbc7c63aa, 0xe6f6e918} }, +/**/ {{0x3fec0e07, 0x0381c0e0} }, +/**/ {{0x3c8c0e07, 0x0381c0e0} }, +/**/ {{0xbfd2726d, 0xd135c174} }, +/**/ {{0xbc2d352d, 0xe0951cf8} }, +/**/ {{0xbfc09f37, 0xb38cc8cf} }, +/**/ {{0xbc69db81, 0xae75327f} }, +/**/ {{0x3fc85eac, 0xd7da413c} }, +/**/ {{0x3c5b1a89, 0x6ebae2bc} }, +/**/ {{0xbfa04d69, 0x80fcc815} }, +/**/ {{0xbfb8054c, 0x1df326f9} }, +/**/ {{0x3fb2a47e, 0x082bda60} }, +/**/ {{0x3f944639, 0x7091d5a4} }, +/**/ {{0xbfaf5961, 0xe072e48c} } }, +/**/ {{{0x3fd84000, 0x00000000} }, +/**/ {{0x3fd72e22, 0xd53aa2aa} }, +/**/ {{0xbc7d9c93, 0x4e79f27c} }, +/**/ {{0x3febfb88, 0x36a04729} }, +/**/ {{0xbc872745, 0x9ac2ea21} }, +/**/ {{0xbfd28b13, 0x9d7702cf} }, +/**/ {{0x3c7819b9, 0x4be8bff6} }, +/**/ {{0xbfc03de6, 0xb0a35176} }, +/**/ {{0x3c5dbfb0, 0xc83347af} }, +/**/ {{0x3fc84999, 0x332a4f86} }, +/**/ {{0x3c5d304e, 0x0a22d12d} }, +/**/ {{0xbfa16a97, 0xed6b2d30} }, +/**/ {{0xbfb78243, 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{{0xbc8ce80d, 0xf30411fb} }, +/**/ {{0x3fe16f10, 0x6bbc577a} }, +/**/ {{0xbc7d0db6, 0xbd8abf47} }, +/**/ {{0xbfd15d1b, 0x58355b5f} }, +/**/ {{0xbc5b5457, 0xbcc70038} }, +/**/ {{0x3fb4c9e4, 0xe8fdd51d} }, +/**/ {{0x3c462959, 0x28ac9383} }, +/**/ {{0x3f8b20c3, 0x2029f143} }, +/**/ {{0xbc2f8a44, 0x2b420400} }, +/**/ {{0xbfa2fea7, 0x7b921c49} }, +/**/ {{0x3f9a9aa0, 0xf468e79e} }, +/**/ {{0xbf7fb66c, 0xcccbcb4f} }, +/**/ {{0xbf6fb0d0, 0x9bd39a5f} }, +/**/ {{0x3f7b7748, 0x8813998f} } }, +/**/ {{{0x3fed6000, 0x00000000} }, +/**/ {{0x3fe7c3d3, 0x11a6092b} }, +/**/ {{0x3c8bb3cb, 0x2d303288} }, +/**/ {{0x3fe15dbb, 0x1dc61b17} }, +/**/ {{0xbc8f0487, 0xbb77dc56} }, +/**/ {{0xbfd14d7e, 0xee0771ca} }, +/**/ {{0x3c72d38b, 0xdc2fcbd0} }, +/**/ {{0x3fb4d716, 0xd6080f0e} }, +/**/ {{0xbc5cb5bc, 0xa9fbc2c3} }, +/**/ {{0x3f89a7f9, 0xfc42e02f} }, +/**/ {{0xbc201eec, 0x857be8a4} }, +/**/ {{0xbfa2af2b, 0x44ceebb3} }, +/**/ {{0x3f9a62b5, 0x08511639} }, +/**/ {{0xbf8018ad, 0xc8de23de} }, +/**/ {{0xbf6dc8a2, 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+/**/ {{0xbfa21230, 0x34b94b56} }, +/**/ {{0x3f99f078, 0xa827f95a} }, +/**/ {{0xbf808869, 0x19caa997} }, +/**/ {{0xbf6a1d29, 0xf8c46d26} }, +/**/ {{0x3f796b9a, 0xae59da17} } }, +/**/ {{{0x3fedc000, 0x00000000} }, +/**/ {{0x3fe7f79e, 0xacb97898} }, +/**/ {{0x3c8fd5ca, 0x80ead221} }, +/**/ {{0x3fe12a19, 0x20604825} }, +/**/ {{0xbc5cc7d6, 0xa18970f8} }, +/**/ {{0xbfd11e72, 0x1dfe6ba4} }, +/**/ {{0x3c706717, 0x9d653d1c} }, +/**/ {{0x3fb4fa57, 0xd5fcbb3b} }, +/**/ {{0x3c1922c8, 0x5f50bc06} }, +/**/ {{0x3f856283, 0xe93a179f} }, +/**/ {{0xbc01c2ec, 0x5ea7135a} }, +/**/ {{0xbfa1c4b5, 0xf0c06b4f} }, +/**/ {{0x3f99b641, 0xe48a3b04} }, +/**/ {{0xbf80badd, 0xe1280a21} }, +/**/ {{0xbf68599e, 0x1be3c5dd} }, +/**/ {{0x3f78c0b3, 0x3a72c8e6} } }, +/**/ {{{0x3fede000, 0x00000000} }, +/**/ {{0x3fe808c0, 0x3940694b} }, +/**/ {{0xbc800f32, 0x7715f6a5} }, +/**/ {{0x3fe11902, 0x8d73d98e} }, +/**/ {{0x3c71d158, 0x30f8e290} }, +/**/ {{0xbfd10eb2, 0x6fc305eb} }, +/**/ {{0xbc7fd2e3, 0x3858c4b7} }, +/**/ 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+/**/ {{{0x3fee6000, 0x00000000} }, +/**/ {{0x3fe84c9c, 0x7653f7eb} }, +/**/ {{0xbc383611, 0xfe0a3e8f} }, +/**/ {{0x3fe0d546, 0x2a7f71b5} }, +/**/ {{0x3c757061, 0x596848c6} }, +/**/ {{0xbfd0cf6d, 0xb4cf51a6} }, +/**/ {{0x3c4c99ab, 0x5b18bb8c} }, +/**/ {{0x3fb5275f, 0x24486227} }, +/**/ {{0x3c5b4a59, 0xbb1f4f56} }, +/**/ {{0x3f7d77be, 0x36238bb2} }, +/**/ {{0x3c1ddbd1, 0xcaec6ba2} }, +/**/ {{0xbfa04bc1, 0xe1406cd0} }, +/**/ {{0x3f988a1e, 0x7f96d6ca} }, +/**/ {{0xbf8184c5, 0xcdffc380} }, +/**/ {{0xbf603841, 0x12561f8b} }, +/**/ {{0x3f7588b9, 0x4d81a668} } }, +/**/ {{{0x3fee8000, 0x00000000} }, +/**/ {{0x3fe85d69, 0x576cc2c5} }, +/**/ {{0x3c66b66e, 0x7fc8b8c3} }, +/**/ {{0x3fe0c47e, 0xac74fadc} }, +/**/ {{0xbc8035f8, 0x77bb1887} }, +/**/ {{0xbfd0bf8d, 0x7e8202a9} }, +/**/ {{0x3c798048, 0x1f4d2357} }, +/**/ {{0x3fb52e6c, 0x13725c73} }, +/**/ {{0xbc34c3af, 0xf5b19ded} }, +/**/ {{0x3f7af1a3, 0x7d9c2711} }, +/**/ {{0x3bea7ec7, 0x1af1098d} }, +/**/ {{0xbfa0027f, 0xb643d11f} }, +/**/ 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0x0844ff86} }, +/**/ {{0x3f76077c, 0xacf1a65c} }, +/**/ {{0xbc19a3b2, 0xb13331a9} }, +/**/ {{0xbf9ee450, 0x472733eb} }, +/**/ {{0x3f97d05c, 0x21e541d7} }, +/**/ {{0xbf81d8da, 0x9d9d4dfc} }, +/**/ {{0xbf57be45, 0xd3ce1b4a} }, +/**/ {{0x3f73b4ba, 0x7cb60047} } }, +/**/ {{{0x3feee000, 0x00000000} }, +/**/ {{0x3fe88f6b, 0xbd023119} }, +/**/ {{0xbc532d1d, 0x25aba660} }, +/**/ {{0x3fe09287, 0x95d126c6} }, +/**/ {{0x3c85aad3, 0xeccc37a6} }, +/**/ {{0xbfd08fd0, 0x649e7367} }, +/**/ {{0x3c71e96c, 0xed21a127} }, +/**/ {{0x3fb53fdd, 0x957ec910} }, +/**/ {{0xbc339c23, 0xaf97a601} }, +/**/ {{0x3f73a336, 0x5a18e5a2} }, +/**/ {{0xbc1f7225, 0x477571de} }, +/**/ {{0xbf9e5629, 0xd4044135} }, +/**/ {{0x3f9791bd, 0x32786dc4} }, +/**/ {{0xbf81ef39, 0xbdf030c4} }, +/**/ {{0xbf550386, 0xe21b8bcb} }, +/**/ {{0x3f731d62, 0x97aa7fb2} } }, +/**/ {{{0x3fef0000, 0x00000000} }, +/**/ {{0x3fe89ff5, 0xff57f1f8} }, +/**/ {{0xbc855b9a, 0x5e177a1b} }, +/**/ {{0x3fe081ff, 0xbdf80108} }, +/**/ {{0x3c6ffbdf, 0x80108200} }, +/**/ {{0xbfd07fde, 0xba010928} }, +/**/ {{0x3c38d37f, 0x7bae0295} }, +/**/ {{0x3fb5447b, 0x0136e69f} }, +/**/ {{0x3c50316a, 0x0dda278d} }, +/**/ {{0x3f7149fc, 0x55103947} }, +/**/ {{0x3c176e96, 0x849e505f} }, +/**/ {{0xbf9dc97b, 0xfbe9a2ee} }, +/**/ {{0x3f9752d4, 0xb08adda9} }, +/**/ {{0xbf8202e8, 0xb540d106} }, +/**/ {{0xbf525de5, 0x859de3e9} }, +/**/ {{0x3f72886c, 0x4afd9f21} } }, +/**/ {{{0x3fef2000, 0x00000000} }, +/**/ {{0x3fe8b06f, 0xc1cf3dff} }, +/**/ {{0xbc80fb31, 0x2656db6d} }, +/**/ {{0x3fe07187, 0xd971cd38} }, +/**/ {{0x3c89baa4, 0x202c20ac} }, +/**/ {{0xbfd06fe9, 0xd15893ab} }, +/**/ {{0xbc7a864b, 0xdc0cb586} }, +/**/ {{0x3fb54883, 0x7ce57fed} }, +/**/ {{0xbc49498e, 0x294f4b18} }, +/**/ {{0x3f6df762, 0x426ebecc} }, +/**/ {{0xbc022f08, 0xf28644c0} }, +/**/ {{0xbf9d3e48, 0x5c564b44} }, +/**/ {{0x3f9713ab, 0xdfea7acf} }, +/**/ {{0xbf8213fc, 0x761db35c} }, +/**/ {{0xbf4f9a17, 0x10d60f49} }, +/**/ {{0x3f71f5de, 0x58700e9b} } }, +/**/ {{{0x3fef4000, 0x00000000} }, +/**/ {{0x3fe8c0d9, 0x145cf49d} }, +/**/ {{0x3c8bea40, 0x76dc4333} }, +/**/ {{0x3fe0611f, 0xeb45139a} }, +/**/ {{0x3c7e4998, 0x65aadb1f} }, +/**/ {{0xbfd05ff2, 0x1953a316} }, +/**/ {{0x3c759922, 0xa1b67b0f} }, +/**/ {{0x3fb54bf9, 0xc08c1d66} }, +/**/ {{0x3c5b9353, 0xd220330c} }, +/**/ {{0x3f69706e, 0x478cb604} }, +/**/ {{0xbbfdb6d3, 0xa22fd45a} }, +/**/ {{0xbf9cb490, 0x5c0d1d38} }, +/**/ {{0x3f96d44b, 0xbbaba2f2} }, +/**/ {{0xbf822289, 0x9c6b7de1} }, +/**/ {{0xbf4aa143, 0xa49803b6} }, +/**/ {{0x3f7165be, 0x9270e49e} } }, +/**/ {{{0x3fef6000, 0x00000000} }, +/**/ {{0x3fe8d132, 0x06f8c4cb} }, +/**/ {{0xbc7b018c, 0xbaa89a8b} }, +/**/ {{0x3fe050c7, 0xf60ab1f4} }, +/**/ {{0x3c63f8e2, 0xc6cf5796} }, +/**/ {{0xbfd04ff7, 0xfe998dc0} }, +/**/ {{0x3c77873c, 0x7dc56419} }, +/**/ {{0x3fb54ee0, 0x7cc24121} }, +/**/ {{0x3c313117, 0x8e5c84c5} }, +/**/ {{0x3f64fee1, 0x50066301} }, +/**/ {{0x3c043698, 0x017261a1} }, +/**/ {{0xbf9c2c55, 0x2cc5b4f1} }, +/**/ {{0x3f9694bc, 0xf759f369} }, +/**/ {{0xbf822ea4, 0x6c93426a} }, +/**/ {{0xbf45d0a1, 0x135d6c51} }, +/**/ {{0x3f70d811, 0xe62dc18f} } }, +/**/ {{{0x3fef8000, 0x00000000} }, +/**/ {{0x3fe8e17a, 0xa99cc05e} }, +/**/ {{0xbc7ec182, 0xab042f61} }, +/**/ {{0x3fe0407f, 0xfbefe001} }, +/**/ {{0x3c401ffe, 0xfbf80041} }, +/**/ {{0xbfd03ffb, 0xebd00209} }, +/**/ {{0xbc53ff3c, 0xb9004112} }, +/**/ {{0x3fb5513a, 0x5aaf6d91} }, +/**/ {{0x3c54a20d, 0xc0516ddb} }, +/**/ {{0x3f60a27f, 0xc6ac4038} }, +/**/ {{0x3bf06bee, 0x2a340912} }, +/**/ {{0xbf9ba597, 0xccd6032a} }, +/**/ {{0x3f965508, 0x002bb974} }, +/**/ {{0xbf823860, 0xd2d1068b} }, +/**/ {{0xbf41277e, 0x666265bc} }, +/**/ {{0x3f704cdc, 0x656b66ea} } }, +/**/ {{{0x3fefa000, 0x00000000} }, +/**/ {{0x3fe8f1b3, 0x0c44f167} }, +/**/ {{0x3c6dd1ca, 0xb93933fd} }, +/**/ {{0x3fe03047, 0xfeb82e4e} }, +/**/ {{0x3c69ee56, 0x5272e5ac} }, +/**/ {{0xbfd02ffe, 0x49a09c45} }, +/**/ {{0xbc700a59, 0xb26267bb} }, +/**/ {{0x3fb55309, 0xfc062d2f} }, +/**/ {{0x3c5dba48, 0xb11938e0} }, +/**/ {{0x3f58b61b, 0xe4f365be} }, +/**/ {{0x3bf8b585, 0xa79ad31a} }, +/**/ {{0xbf9b2059, 0x08d4ad17} }, +/**/ {{0x3f961534, 0xfe379940} }, +/**/ {{0xbf823fd2, 0x62a1270e} }, +/**/ {{0xbf394a53, 0x3f3a0aec} }, +/**/ {{0x3f6f8842, 0xa04bcae2} } }, +/**/ {{{0x3fefc000, 0x00000000} }, +/**/ {{0x3fe901db, 0x3eeef187} }, +/**/ {{0x3c868665, 0xe5603c8f} }, +/**/ {{0x3fe0201f, 0xffbf7f80} }, +/**/ {{0x3c20201f, 0xffbf7f80} }, +/**/ {{0xbfd01fff, 0x7ebe8004} }, +/**/ {{0xbc4213ff, 0xcf979001} }, +/**/ {{0x3fb55451, 0xfb0012db} }, +/**/ {{0xbc395606, 0xf73aa59f} }, +/**/ {{0x3f50509f, 0xfc757100} }, +/**/ {{0x3bebc7da, 0xfee554d0} }, +/**/ {{0xbf9a9c99, 0x7d3424d0} }, +/**/ {{0x3f95d54b, 0xd5ac0217} }, +/**/ {{0xbf82450c, 0x564b3c49} }, +/**/ {{0xbf3091df, 0xe6d3e986} }, +/**/ {{0x3f6e7bc6, 0x3bef5a22} } }, +/**/ {{{0x3fefe000, 0x00000000} }, +/**/ {{0x3fe911f3, 0x5199833b} }, +/**/ {{0x3c63ae8a, 0x0edbf522} }, +/**/ {{0x3fe01007, 0xfffbfbfe} }, +/**/ {{0x3ba01007, 0xfffbfbfe} }, +/**/ {{0xbfd00fff, 0xefebf400} }, +/**/ {{0xbc401209, 0xfff9f97d} }, +/**/ {{0x3fb55514, 0xea5aaaf6} }, +/**/ {{0xbc529baa, 0xb5b7b240} }, +/**/ {{0x3f402827, 0xffc7abc4} }, +/**/ {{0x3b5ba3d6, 0xbfee6ab3} }, +/**/ {{0xbf9a1a59, 0x97d67093} }, +/**/ {{0x3f959554, 0x28080aaf} }, +/**/ {{0xbf824821, 0x8e892ce2} }, +/**/ {{0xbf204877, 0xfe70a2a6} }, +/**/ {{0x3f6d7447, 0x0e8ddd67} } }, +/**/ {{{0x3feff800, 0x00000000} }, +/**/ {{0x3fe91dfa, 0xd439826e} }, +/**/ {{0xbc786a19, 0x6df48d55} }, +/**/ {{0x3fe00400, 0x7ffffbff} }, +/**/ {{0xbbeffffe, 0xffbff800} }, +/**/ {{0xbfd003ff, 0xffbfebfd} }, +/**/ {{0xbb600480, 0x9ffff9fe} }, +/**/ {{0x3fb55551, 0x53aa5aab} }, +/**/ {{0xbc542a4a, 0x9baaab5b} }, +/**/ {{0x3f200a02, 0x7fffc7eb} }, +/**/ {{0xbb7dfffe, 0x4770e940} }, +/**/ {{0xbf99b9a5, 0x9997d8d0} }, +/**/ {{0x3f956555, 0x50a80a03} }, +/**/ {{0xbf824914, 0x86456493} }, +/**/ {{0xbf001207, 0x7ffe7329} }, +/**/ {{0x3f6cb1ef, 0x1c63fe2a} } }, + }; + +#else +#ifdef LITTLE_ENDI + + static const number + cij[241][7] = { /* x0,cij for (1/16,1) */ +/**/ {{{0X65E0244E, 0X3FB04006} }, +/**/ {{0X7B53DD20, 0X3FB03A73} }, +/**/ {{0XCF5CFB72, 0X3FEFDF1F} }, +/**/ {{0XCE2AE4C2, 0XBFB01EB3} }, +/**/ {{0XDD58A40D, 0XBFD4D29E} }, +/**/ {{0XD907A18A, 0X3FAFDA4A} }, +/**/ {{0X4DF65B18, 0X3FC814DF} } }, +/**/ {{{0XB9B88CD8, 0X3FB0FFFD} }, +/**/ {{0X63645300, 0X3FB0F99C} }, +/**/ {{0XA3DED30F, 0X3FEFDC08} }, +/**/ {{0X669C1AED, 0XBFB0D9DC} }, +/**/ {{0XF7138DE2, 0XBFD4C669} }, +/**/ {{0X29D085A7, 0X3FB0A12F} }, +/**/ {{0XCFD48D20, 0X3FC7F0EE} } }, +/**/ {{{0X5A73D4F1, 0X3FB1FFF1} }, +/**/ {{0X2BEE2040, 0X3FB1F85F} }, +/**/ {{0X42B56D31, 0X3FEFD7B3} }, +/**/ {{0XB69DEA40, 0XBFB1D2B7} }, +/**/ {{0X3922ECC9, 0XBFD4B552} }, +/**/ {{0X522B1A04, 0X3FB18F93} }, +/**/ {{0X5660F061, 0X3FC7BEAD} } }, +/**/ {{{0XB2524AA2, 0X3FB2FFFD} }, +/**/ {{0XE71790A0, 0X3FB2F716} }, +/**/ {{0X53B496A4, 0X3FEFD31F} }, +/**/ {{0X4AAB7374, 0XBFB2CAD8} }, +/**/ {{0X58DD2FB2, 0XBFD4A34B} }, +/**/ {{0XD0CECC18, 0X3FB27C0A} }, +/**/ {{0X5D2743D7, 0X3FC789D2} } }, +/**/ {{{0X0573F3AC, 0X3FB3FFFE} }, +/**/ {{0X1702F6A0, 0X3FB3F59D} }, +/**/ {{0XB071ACC2, 0X3FEFCE4D} }, +/**/ {{0X64DB3686, 0XBFB3C20F} }, +/**/ {{0XEB3BFE93, 0XBFD49059} }, +/**/ {{0XCAF74FED, 0X3FB36659} }, +/**/ {{0X1C011FB0, 0X3FC75269} } }, +/**/ {{{0X894384D6, 0X3FB4FFEF} }, +/**/ {{0X0CE204C0, 0X3FB4F3ED} }, +/**/ {{0XA8EA5A01, 0X3FEFC93E} }, +/**/ {{0X7B5457C9, 0XBFB4B84F} }, +/**/ {{0X7401F2F9, 0XBFD47C80} }, +/**/ {{0XB4F67209, 0X3FB44E64} }, +/**/ {{0X4C540B77, 0X3FC7187D} } }, +/**/ {{{0XDF406528, 0X3FB5FFF8} }, +/**/ {{0X3C73D820, 0X3FB5F22B} }, +/**/ {{0XB1F60F13, 0X3FEFC3F1} }, +/**/ {{0XCB7FA73B, 0XBFB5ADB2} }, +/**/ {{0X2B1EB555, 0XBFD467BE} }, +/**/ {{0X99EDC463, 0X3FB53435} }, +/**/ {{0X238F5059, 0X3FC6DC1B} } }, +/**/ {{{0X8C4F0D56, 0X3FB7000F} }, +/**/ {{0X495A2FA0, 0X3FB6F04B} }, +/**/ {{0X340DCE97, 0X3FEFBE67} }, +/**/ {{0X4D98E1AD, 0XBFB6A224} }, +/**/ {{0X14064DF1, 0XBFD45216} }, +/**/ {{0X2BA78A66, 0X3FB617AA} }, +/**/ {{0X50A3D7AC, 0X3FC69D4F} } }, +/**/ {{{0XBB4057CF, 0X3FB8000F} }, +/**/ {{0XBE2CD3A0, 0X3FB7EE27} }, +/**/ {{0X39EC9246, 0X3FEFB8A0} }, +/**/ {{0X31D9C773, 0XBFB79577} }, +/**/ {{0XB6DC7D72, 0XBFD43B8D} }, +/**/ {{0XD69547DF, 0X3FB6F88A} }, +/**/ {{0XF633CE8C, 0X3FC65C26} } }, +/**/ {{{0X39CF2B7F, 0X3FB8FFF2} }, +/**/ {{0X9F979E80, 0X3FB8EBB7} }, +/**/ {{0X435506E1, 0X3FEFB29D} }, +/**/ {{0X69B9CDB5, 0XBFB8879A} }, +/**/ {{0X85FEAFA9, 0XBFD42428} }, +/**/ {{0XB6191A0E, 0X3FB7D6BA} }, +/**/ {{0XA7CB8BB5, 0X3FC618AF} } }, +/**/ {{{0X6E2F0772, 0X3FB9FFF9} }, +/**/ {{0XD32A9480, 0X3FB9E93A} }, +/**/ {{0X04A3EC40, 0X3FEFAC5D} }, +/**/ {{0X53F6EA97, 0XBFB978C2} }, +/**/ {{0X089C36F6, 0XBFD40BE3} }, +/**/ {{0X885AEB77, 0X3FB8B25C} }, +/**/ {{0X63CADCE1, 0X3FC5D2F7} } }, +/**/ {{{0X6316B097, 0X3FBB0002} }, +/**/ {{0XCE24CC00, 0X3FBAE68C} }, +/**/ {{0X938C5C66, 0X3FEFA5E0} }, +/**/ {{0X76F14E4B, 0XBFBA68C3} }, +/**/ {{0X1696CD7C, 0XBFD3F2C3} }, +/**/ {{0X722A2CB4, 0X3FB98B3B} }, +/**/ {{0X9067AD62, 0X3FC58B0C} } }, +/**/ {{{0X604F58B1, 0X3FBC0008} }, +/**/ {{0X05650780, 0X3FBBE3A7} }, +/**/ {{0X5A7A2773, 0X3FEF9F28} }, +/**/ {{0X3D5AC0A4, 0XBFBB578F} }, +/**/ {{0XF767119F, 0XBFD3D8CB} }, +/**/ {{0XC7E31B88, 0X3FBA613D} }, +/**/ {{0XF5594565, 0X3FC540FD} } }, +/**/ {{{0X6CCA4EBA, 0X3FBD0002} }, +/**/ {{0XC1298A80, 0X3FBCE07E} }, +/**/ {{0XE8D36C4A, 0X3FEF9834} }, +/**/ {{0X5BCAC5FE, 0XBFBC4513} }, +/**/ {{0X8B5236F1, 0XBFD3BE01} }, +/**/ {{0X2E991970, 0X3FBB3447} }, +/**/ {{0XB8ADB373, 0X3FC4F4DA} } }, +/**/ {{{0XB2B47FCA, 0X3FBDFFF4} }, +/**/ {{0X4A051D80, 0X3FBDDD16} }, +/**/ {{0X78DCC895, 0X3FEF9106} }, +/**/ {{0XF0966844, 0XBFBD3149} }, +/**/ {{0X744F9A5F, 0XBFD3A266} }, +/**/ {{0XEDB7F27A, 0X3FBC0446} }, +/**/ {{0X583F9ECA, 0X3FC4A6B2} } }, +/**/ {{{0XA9A05BE0, 0X3FBF000A} }, +/**/ {{0XA3BDA540, 0X3FBED996} }, +/**/ {{0X1B8BA97F, 0X3FEF899C} }, +/**/ {{0X2287A677, 0XBFBE1C51} }, +/**/ {{0XEDC130BB, 0XBFD385F8} }, +/**/ {{0XF306FF50, 0X3FBCD14B} }, +/**/ {{0XA667A72B, 0X3FC45694} } }, +/**/ {{{0XBA8F63DE, 0X3FBFFFFA} }, +/**/ {{0X69FE4780, 0X3FBFD5B5} }, +/**/ {{0X4863DC7D, 0X3FEF81F8} }, +/**/ {{0XD1518706, 0XBFBF05DB} }, +/**/ {{0X4687A69C, 0XBFD368C4} }, +/**/ {{0X1B3868DA, 0X3FBD9B08} }, +/**/ {{0XC345ADFC, 0X3FC40491} } }, +/**/ {{{0X6ECCADA8, 0X3FC07FFA} }, +/**/ {{0X0A396400, 0X3FC068D0} }, +/**/ {{0XF1FCFC6B, 0X3FEF7A19} }, +/**/ {{0X861DF0DF, 0XBFBFEE0C} }, +/**/ {{0X5A586C0C, 0XBFD34AC6} }, +/**/ {{0X189D637A, 0X3FBE618F} }, +/**/ {{0X195779D4, 0X3FC3B0BA} } }, +/**/ {{{0X33432713, 0X3FC10003} }, +/**/ {{0XF203D1A0, 0X3FC0E6B0} }, +/**/ {{0XFE0EB463, 0X3FEF7200} }, +/**/ {{0XE15CB19A, 0XBFC06A72} }, +/**/ {{0XB8DB761E, 0XBFD32C00} }, +/**/ {{0XA11F5E3E, 0X3FBF24D8} }, +/**/ {{0X569E85DD, 0X3FC35B1E} } }, +/**/ {{{0XDA1C4811, 0X3FC17FFC} }, +/**/ {{0X29EBDA00, 0X3FC16462} }, +/**/ {{0X7D558737, 0X3FEF69AF} }, +/**/ {{0X0B33969B, 0XBFC0DD17} }, +/**/ {{0X33AC50D1, 0XBFD30C7D} }, +/**/ {{0X9BE43F0F, 0X3FBFE4AA} }, +/**/ {{0X692539CB, 0X3FC303CF} } }, +/**/ {{{0X3CCA418D, 0X3FC1FFFF} }, +/**/ {{0X3B978EA0, 0X3FC1E1FA} }, +/**/ {{0X45D421A9, 0X3FEF6124} }, +/**/ {{0XACAC8AA8, 0XBFC14F03} }, +/**/ {{0X62E675A3, 0XBFD2EC39} }, +/**/ {{0X2FA6B426, 0X3FC0508C} }, +/**/ {{0X780A6467, 0X3FC2AADE} } }, +/**/ {{{0XD9C78922, 0X3FC27FF7} }, +/**/ {{0X1B91E640, 0X3FC25F66} }, +/**/ {{0XF52E192C, 0X3FEF5860} }, +/**/ {{0XE5DE2394, 0XBFC1C023} }, +/**/ {{0X6BEE0ABD, 0XBFD2CB3D} }, +/**/ {{0X5E075C1A, 0X3FC0ACFB} }, +/**/ {{0XDFFE453A, 0X3FC2505C} } }, +/**/ {{{0XA1FC1AAA, 0X3FC2FFF7} }, +/**/ {{0X83257C40, 0X3FC2DCB5} }, +/**/ {{0XC719B6FB, 0X3FEF4F64} }, +/**/ {{0X61514083, 0XBFC23082} }, +/**/ {{0X7F7B72D5, 0XBFD2A988} }, +/**/ {{0X7C887402, 0X3FC107A7} }, +/**/ {{0X2C3CD6D1, 0X3FC1F45C} } }, +/**/ {{{0X9D78E15E, 0X3FC38005} }, +/**/ {{0X6AC98EE0, 0X3FC359EE} }, +/**/ {{0X944CEC16, 0X3FEF462F} }, +/**/ {{0XD85B87A9, 0XBFC2A020} }, +/**/ {{0X2E4AB369, 0XBFD2871C} }, +/**/ {{0XC31A65D9, 0X3FC1608D} }, +/**/ {{0X130BBE50, 0X3FC196EE} } }, +/**/ {{{0X9F431B1A, 0X3FC40004} }, +/**/ {{0X6BD65360, 0X3FC3D6F3} }, +/**/ {{0XDD99B68A, 0X3FEF3CC3} }, +/**/ {{0XB3DD00ED, 0XBFC30EE1} }, +/**/ {{0XF8482664, 0XBFD26403} }, +/**/ {{0XFE136626, 0X3FC1B792} }, +/**/ {{0X6EAC7440, 0X3FC13824} } }, +/**/ {{{0XE01D95A1, 0X3FC48004} }, +/**/ {{0X86F00CC0, 0X3FC453D3} }, +/**/ {{0XE3970539, 0X3FEF3320} }, +/**/ {{0X0A5279AA, 0XBFC37CCF} }, +/**/ {{0X3B151D5D, 0XBFD2403F} }, +/**/ {{0XE331C9E6, 0X3FC20CBB} }, +/**/ {{0X39E3F097, 0X3FC0D811} } }, +/**/ {{{0XAA9382DD, 0X3FC4FFF7} }, +/**/ {{0X8C590A80, 0X3FC4D07F} }, +/**/ {{0X34DF28E0, 0X3FEF2948} }, +/**/ {{0X5B43915C, 0XBFC3E9D8} }, +/**/ {{0XEB8845A2, 0XBFD21BD5} }, +/**/ {{0XAC6AC8AD, 0X3FC25FF8} }, +/**/ {{0X88ED96CA, 0X3FC076C6} } }, +/**/ {{{0X352408BE, 0X3FC58006} }, +/**/ {{0XC39A73E0, 0X3FC54D1E} }, +/**/ {{0X09AE009C, 0X3FEF1F37} }, +/**/ {{0XB9BE8550, 0XBFC4561C} }, +/**/ {{0X0053F52E, 0XBFD1F6C0} }, +/**/ {{0XEF783BE9, 0X3FC2B15D} }, +/**/ {{0X8615239B, 0X3FC01456} } }, +/**/ 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{{{0X57F250B8, 0X3FEA8001} }, +/**/ {{0XDD6453A0, 0X3FE6220D} }, +/**/ {{0XCFFFCC1E, 0X3FE2FB6F} }, +/**/ {{0X6F8D8291, 0XBFD2A648} }, +/**/ {{0X03654CC3, 0X3FB2D56F} }, +/**/ {{0X4BB6E7A6, 0X3FA07EE3} }, +/**/ {{0X87992F03, 0XBFAA5F2A} } }, +/**/ {{{0XDD839D49, 0X3FEAA000} }, +/**/ {{0XB412C9A0, 0X3FE634FF} }, +/**/ {{0XE2D59E01, 0X3FE2E8D0} }, +/**/ {{0X5467CFDD, 0XBFD2981C} }, +/**/ {{0XFF1FADB5, 0X3FB2F5E8} }, +/**/ {{0XA3BA803C, 0X3F9FF7D6} }, +/**/ {{0X46AF8DB7, 0XBFAA04E3} } }, +/**/ {{{0X770DF220, 0X3FEAC000} }, +/**/ {{0XFEF70020, 0X3FE647DE} }, +/**/ {{0X220AFF7F, 0X3FE2D640} }, +/**/ {{0X36F9E74F, 0XBFD289D8} }, +/**/ {{0XE509140A, 0X3FB3155E} }, +/**/ {{0X61AB0B7F, 0X3F9EF56B} }, +/**/ {{0X98CE391F, 0XBFA9AAE2} } }, +/**/ {{{0X125BBE48, 0X3FEAE001} }, +/**/ {{0X57A24D20, 0X3FE65AAC} }, +/**/ {{0X1BFB3559, 0X3FE2C3BD} }, +/**/ {{0X6DDE55DD, 0XBFD27B7C} }, +/**/ {{0X15C4C270, 0X3FB333D5} }, +/**/ {{0X9BAC4ECF, 0X3F9DF67A} }, +/**/ {{0X363A972B, 0XBFA9512F} } }, +/**/ {{{0X7C321839, 0X3FEAFFFE} }, +/**/ {{0X569B83C0, 0X3FE66D65} }, +/**/ {{0X53FBF8D9, 0X3FE2B14A} }, +/**/ {{0X9CFA03CE, 0XBFD26D0B} }, +/**/ {{0X2CAA2E0C, 0X3FB3514B} }, +/**/ {{0X4597BE9A, 0X3F9CFB22} }, +/**/ {{0X99110022, 0XBFA8F7CF} } }, +/**/ {{{0X75486924, 0X3FEB1FFE} }, +/**/ {{0X68CEFB40, 0X3FE6800D} }, +/**/ {{0X8E6AA814, 0X3FE29EE4} }, +/**/ {{0XE8AFA7EB, 0XBFD25E83} }, +/**/ {{0XFB0E8AC8, 0X3FB36DC9} }, +/**/ {{0XAD5D66CA, 0X3F9C0331} }, +/**/ {{0XFEDB1E8B, 0XBFA89EC9} } }, +/**/ {{{0X5FB8DEB8, 0X3FEB4001} }, +/**/ {{0XD137C500, 0X3FE692A4} }, +/**/ {{0XABFF668E, 0X3FE28C8B} }, +/**/ {{0XD8E71E0A, 0XBFD24FE5} }, +/**/ {{0X1297317A, 0X3FB38955} }, +/**/ {{0X1D844655, 0X3F9B0EA3} }, +/**/ {{0X6914067D, 0XBFA84624} } }, +/**/ {{{0X386C27B9, 0X3FEB6000} }, +/**/ {{0X8CDF6FC0, 0X3FE6A527} }, +/**/ {{0XC5758DB8, 0X3FE27A43} }, +/**/ {{0X59CADCE0, 0XBFD24135} }, +/**/ {{0XEE34AE91, 0X3FB3A3E9} }, +/**/ {{0X1C5FFF05, 0X3F9A1DA8} }, +/**/ {{0X9EC8AAC6, 0XBFA7EDE4} } }, +/**/ {{{0XD1EFDDB3, 0X3FEB8000} }, +/**/ {{0X0ACCB660, 0X3FE6B799} }, +/**/ {{0X9983AAB2, 0X3FE26809} }, +/**/ {{0X76047E08, 0XBFD23270} }, +/**/ {{0XF132139B, 0X3FB3BD90} }, +/**/ {{0X58DEB3E1, 0X3F993010} }, +/**/ {{0X2D194CE9, 0XBFA79610} } }, +/**/ {{{0X42CC4047, 0X3FEB9FFE} }, +/**/ {{0X86445E60, 0X3FE6C9F6} }, +/**/ {{0X069F871F, 0X3FE255E0} }, +/**/ {{0X25461639, 0XBFD2239A} }, +/**/ {{0XA926C127, 0X3FB3D649} }, +/**/ {{0XC5A21F70, 0X3F9845FB} }, +/**/ {{0X68E20BE6, 0XBFA73EAC} } }, +/**/ {{{0X951AEAAD, 0X3FEBC001} }, +/**/ {{0X3C4E45A0, 0X3FE6DC45} }, +/**/ {{0XFF6573B0, 0X3FE243C1} }, +/**/ {{0XE38FA7E7, 0XBFD214AE} }, +/**/ {{0X5EA1330F, 0X3FB3EE1E} }, +/**/ {{0X2BCCE6DF, 0X3F975F24} }, +/**/ {{0X6F3902C5, 0XBFA6E7BE} } }, +/**/ {{{0X6616FE11, 0X3FEBDFFE} }, +/**/ {{0X27106FE0, 0X3FE6EE7E} }, +/**/ {{0X97B587F0, 0X3FE231B6} }, +/**/ {{0X240FEF32, 0XBFD205B5} }, +/**/ {{0X44EB818C, 0X3FB40509} }, +/**/ {{0X108160F9, 0X3F967BDE} }, +/**/ {{0X271D18AD, 0XBFA6914B} } }, +/**/ {{{0X54511C72, 0X3FEBFFFF} }, +/**/ {{0X643BBB40, 0X3FE700A7} }, +/**/ {{0XE1823C8B, 0X3FE21FB7} }, +/**/ {{0X9A854F7A, 0XBFD1F6A8} }, +/**/ {{0X71F04837, 0X3FB41B15} }, +/**/ {{0XBBD10F7C, 0X3F959BD8} }, +/**/ {{0X41F03711, 0XBFA63B57} } }, +/**/ {{{0XC537593E, 0X3FEC2000} }, +/**/ {{0XF36D6400, 0X3FE712BE} }, +/**/ {{0XF754B2D5, 0X3FE20DC7} }, +/**/ {{0X9D24DBED, 0XBFD1E78B} }, +/**/ {{0X94F485E0, 0X3FB43043} }, +/**/ {{0X122A6884, 0X3F94BF29} }, +/**/ {{0X3D2AA4E9, 0XBFA5E5E7} } }, +/**/ {{{0XDDD35719, 0X3FEC4000} }, +/**/ {{0XD7FA3000, 0X3FE724C3} }, +/**/ {{0XF2A8B1BF, 0X3FE1FBE7} }, +/**/ {{0XB25DDDF6, 0XBFD1D85F} }, +/**/ {{0XD2E3B20F, 0X3FB44495} }, +/**/ {{0X7FCC1B30, 0X3F93E5D6} }, +/**/ {{0X62D0D00F, 0XBFA590FF} } }, +/**/ {{{0X402375B6, 0X3FEC6000} }, +/**/ {{0X7DFF3720, 0X3FE736B6} }, +/**/ {{0X86C92387, 0X3FE1EA17} }, +/**/ {{0X31DDFC58, 0XBFD1C925} }, +/**/ {{0XF8B6CBC2, 0X3FB4580F} }, +/**/ {{0X00CE998E, 0X3F930FD7} }, +/**/ {{0XCB299E5F, 0XBFA53CA3} } }, +/**/ {{{0X19904FE4, 0X3FEC7FFF} }, +/**/ {{0X0F395860, 0X3FE74897} }, +/**/ {{0XA825BA33, 0X3FE1D856} }, +/**/ {{0XA75E0FC5, 0XBFD1B9DC} }, +/**/ {{0X79F8FD7D, 0X3FB46AB5} }, +/**/ {{0XA5A90AFE, 0X3F923D23} }, +/**/ {{0X5D2F574B, 0XBFA4E8D8} } }, +/**/ {{{0XF9E2409D, 0X3FEC9FFE} }, +/**/ {{0X79E7F1C0, 0X3FE75A66} }, +/**/ {{0X8740D2E9, 0X3FE1C6A4} }, +/**/ {{0XF198392C, 0XBFD1AA85} }, +/**/ {{0X808C583A, 0X3FB47C8A} }, +/**/ {{0X857F2526, 0X3F916DAC} }, +/**/ {{0XD0477576, 0XBFA495A0} } }, +/**/ {{{0XE038EF72, 0X3FECC001} }, +/**/ {{0XE6815140, 0X3FE76C25} }, +/**/ {{0X19BDADF8, 0X3FE1B500} }, +/**/ {{0XB4A469AE, 0XBFD19B20} }, +/**/ {{0X42387EA2, 0X3FB48D93} }, +/**/ {{0X7305BAF5, 0X3F90A15F} }, +/**/ {{0XACAE4E17, 0XBFA44300} } }, +/**/ {{{0XEB72037F, 0X3FECDFFE} }, +/**/ {{0X7A7A4AA0, 0X3FE77DD0} }, +/**/ {{0X4F1F6702, 0X3FE1A36E} }, +/**/ {{0XD0992CF8, 0XBFD18BB1} }, +/**/ {{0X5AA4990D, 0X3FB49DCE} }, +/**/ {{0X63759665, 0X3F8FB0DD} }, +/**/ {{0X4D2F0C0F, 0XBFA3F0FB} } }, +/**/ {{{0XEA4839ED, 0X3FECFFFF} }, +/**/ {{0XB17088C0, 0X3FE78F6B} }, +/**/ {{0XCF32122F, 0X3FE191E9} }, +/**/ {{0X220400AC, 0XBFD17C35} }, +/**/ {{0X0A159641, 0X3FB4AD44} }, +/**/ {{0X80894CA9, 0X3F8E252C} }, +/**/ {{0XDF89C265, 0XBFA39F93} } }, +/**/ {{{0XEC3EC8B2, 0X3FED1FFD} }, +/**/ {{0XC8C6C880, 0X3FE7A0F3} }, +/**/ {{0X729F01D6, 0X3FE18076} }, +/**/ {{0X98515540, 0XBFD16CAE} }, +/**/ {{0X1B0933FF, 0X3FB4BBF4} }, +/**/ {{0XE09A60CD, 0X3F8C9FF5} }, +/**/ {{0X662A5704, 0XBFA34ECD} } }, +/**/ {{{0X7084EDD4, 0X3FED3FFF} }, +/**/ {{0X5F02F220, 0X3FE7B26C} }, +/**/ {{0XB9973206, 0X3FE16F10} }, +/**/ {{0X9E1E0A54, 0XBFD15D1B} }, +/**/ {{0XAC2C9A30, 0X3FB4C9E4} }, +/**/ {{0XEFCE76CC, 0X3F8B20DD} }, +/**/ {{0XB888BC37, 0XBFA2FEAA} } }, +/**/ {{{0X8D728E7C, 0X3FED5FFE} }, +/**/ {{0X488D7E80, 0X3FE7C3D2} }, +/**/ {{0XE622A5A7, 0X3FE15DBB} }, +/**/ {{0XA305CEB2, 0XBFD14D7F} }, +/**/ {{0X417BF1C7, 0X3FB4D716} }, +/**/ {{0XE19FE239, 0X3F89A81E} }, +/**/ {{0X84DDAD07, 0XBFA2AF2E} } }, +/**/ {{{0X70AA3B03, 0X3FED7FFF} }, +/**/ {{0XDB239580, 0X3FE7D527} }, +/**/ {{0XBE4FEA01, 0X3FE14C75} }, +/**/ {{0X2AD706AA, 0XBFD13DD9} }, +/**/ {{0XB49D32AA, 0X3FB4E38D} }, +/**/ {{0X37DF2B6D, 0X3F88357A} }, +/**/ {{0X507CD77B, 0XBFA2605B} } }, +/**/ {{{0X1434FBA3, 0X3FED9FFF} }, +/**/ {{0X82C8A720, 0X3FE7E66B} }, +/**/ {{0XED9B7FED, 0X3FE13B3F} }, +/**/ {{0X3AC9D646, 0XBFD12E2A} }, +/**/ {{0XE7B01CF5, 0X3FB4EF4C} }, +/**/ {{0XD25FD52D, 0X3F86C905} }, +/**/ {{0X798666EF, 0XBFA21233} } }, +/**/ {{{0XA8C8DE8C, 0X3FEDBFFE} }, +/**/ {{0XF4A0A520, 0X3FE7F79D} }, +/**/ {{0XD7FC2119, 0X3FE12A19} }, +/**/ {{0XC6BE19DF, 0XBFD11E72} }, +/**/ {{0X634E1B91, 0X3FB4FA57} }, +/**/ {{0X47F96DF5, 0X3F8562A6} }, +/**/ {{0X373AF599, 0XBFA1C4B9} } }, +/**/ {{{0X26573DF5, 0X3FEDE000} }, +/**/ {{0X4DBCB960, 0X3FE808C0} }, +/**/ {{0X7903E4B9, 0X3FE11902} }, +/**/ {{0X5CDFED06, 0XBFD10EB2} }, +/**/ {{0XCCA681FA, 0X3FB504B0} }, +/**/ {{0X6F3CDE09, 0X3F840238} }, +/**/ {{0X9BA8FA6A, 0XBFA177EE} } }, +/**/ {{{0X35009B66, 0X3FEDFFFE} }, +/**/ {{0XC2CB5340, 0X3FE819CF} }, +/**/ {{0XB1C942B5, 0X3FE107FC} }, +/**/ {{0X230D7D92, 0XBFD0FEEC} }, +/**/ {{0X75C5B4F1, 0X3FB50E5A} }, +/**/ {{0XE3C139D8, 0X3F82A7E8} }, +/**/ {{0X93FA642B, 0XBFA12BD5} } }, +/**/ {{{0X492D4C68, 0X3FEE2000} }, +/**/ {{0X5CCB8680, 0X3FE82AD0} }, +/**/ {{0X928E55DF, 0X3FE0F704} }, +/**/ {{0XEE0B0721, 0XBFD0EF1C} }, +/**/ {{0X937BFB74, 0X3FB51759} }, +/**/ {{0X2BC9FDDB, 0X3F815359} }, +/**/ {{0XEA1D1824, 0XBFA0E06F} } }, +/**/ {{{0X9412BB65, 0X3FEE4000} }, +/**/ {{0X14001A60, 0X3FE83BBF} }, +/**/ {{0X37F485DA, 0X3FE0E61D} }, +/**/ {{0X1B2BD37D, 0XBFD0DF48} }, +/**/ {{0X64024D14, 0X3FB51FAF} }, +/**/ {{0X9B849698, 0X3F8004B9} }, +/**/ {{0X450A2434, 0XBFA095BF} } }, +/**/ {{{0X4758EF2F, 0X3FEE5FFF} }, +/**/ {{0X1531C180, 0X3FE84C9C} }, +/**/ {{0X8B7FECE7, 0X3FE0D546} }, +/**/ {{0X105BFE1E, 0XBFD0CF6E} }, +/**/ {{0XF9C5E03A, 0X3FB5275E} }, +/**/ {{0X17AA1137, 0X3F7D77F2} }, +/**/ {{0X2A6891E1, 0XBFA04BC5} } }, +/**/ {{{0X380F819F, 0X3FEE8000} }, +/**/ {{0X74CCC060, 0X3FE85D69} }, +/**/ {{0X8F1DA5B5, 0X3FE0C47E} }, +/**/ {{0X62AD700F, 0XBFD0BF8D} }, +/**/ {{0X1F3FBC2B, 0X3FB52E6C} }, +/**/ {{0XEE24AD7D, 0X3F7AF1C3} }, +/**/ {{0XFECE26C9, 0XBFA00282} } }, +/**/ {{{0XA6D8CB7B, 0X3FEEA000} }, +/**/ {{0XD00E3A60, 0X3FE86E25} }, +/**/ {{0XBA314D62, 0X3FE0B3C6} }, +/**/ {{0XE7CB2D84, 0XBFD0AFA7} }, +/**/ {{0X08E9071F, 0X3FB534D9} }, +/**/ {{0X4CE5E5C9, 0X3F787704} }, +/**/ {{0X0EB7C9D5, 0XBF9F73F4} } }, +/**/ {{{0X5A13BA60, 0X3FEEC000} }, +/**/ {{0X19B163E0, 0X3FE87ED1} }, +/**/ {{0X2EBB7AD7, 0X3FE0A31F} }, +/**/ {{0X33A3FCE1, 0XBFD09FBE} }, +/**/ {{0X89D9AF5D, 0X3FB53AA8} }, +/**/ {{0XF7F7040B, 0X3F760799} }, +/**/ {{0XD3F0B3FB, 0XBF9EE456} } }, +/**/ {{{0X58F8DD18, 0X3FEEDFFF} }, +/**/ {{0X6681CA80, 0X3FE88F6B} }, +/**/ {{0XEC4360B3, 0X3FE09287} }, +/**/ {{0XB7CE07E5, 0XBFD08FD0} }, +/**/ {{0X7BDEDD3F, 0X3FB53FDD} }, +/**/ {{0X70C52E66, 0X3F73A366} }, +/**/ {{0X5DCA7315, 0XBF9E5630} } }, +/**/ {{{0XBE033400, 0X3FEEFFFF} }, +/**/ {{0XDD4D7960, 0X3FE89FF5} }, +/**/ {{0XDFFE15BD, 0X3FE081FF} }, +/**/ {{0XDAE56C0F, 0XBFD07FDE} }, +/**/ {{0XF84D6F5D, 0X3FB5447A} }, +/**/ {{0X7982941E, 0X3F714A24} }, +/**/ {{0X81E68835, 0XBF9DC982} } }, +/**/ {{{0XE6B5125D, 0X3FEF2001} }, +/**/ {{0XBBE88160, 0X3FE8B070} }, +/**/ {{0XDF7122E2, 0X3FE07186} }, +/**/ {{0XDE905325, 0XBFD06FE8} }, +/**/ {{0XB5DEEC7A, 0X3FB54883} }, +/**/ {{0XB4A186D5, 0X3F6DF762} }, +/**/ {{0XDE20F495, 0XBF9D3E4E} } }, +/**/ {{{0XF770E0DB, 0X3FEF3FFD} }, +/**/ {{0X09E96380, 0X3FE8C0D8} }, +/**/ {{0XF5A576A9, 0X3FE06120} }, +/**/ {{0X1D2912FF, 0XBFD05FF3} }, +/**/ {{0X8CD1001F, 0X3FB54BF9} }, +/**/ {{0X6E90DC16, 0X3F6970FC} }, +/**/ {{0XD8EB587E, 0XBF9CB496} } }, +/**/ {{{0X4E16DA33, 0X3FEF5FFE} }, +/**/ {{0X29BCCDC0, 0X3FE8D131} }, +/**/ {{0XD33BA4E9, 0X3FE050C8} }, +/**/ {{0XD74C83D2, 0XBFD04FF8} }, +/**/ {{0X592BB252, 0X3FB54EE0} }, +/**/ {{0X7193EEB5, 0X3F64FF61} }, +/**/ {{0XA459AC86, 0XBF9C2C5B} } }, +/**/ {{{0X4576FF2E, 0X3FEF8000} }, +/**/ {{0XCCE443A0, 0X3FE8E17A} }, +/**/ {{0XD8A97B6C, 0X3FE0407F} }, +/**/ {{0XC91B3E55, 0XBFD03FFB} }, +/**/ {{0X5F3357F7, 0X3FB5513A} }, +/**/ {{0X14C92B53, 0X3F60A2BA} }, +/**/ {{0X3E70DF71, 0XBF9BA59E} } }, +/**/ {{{0X39B6A330, 0X3FEF9FFF} }, +/**/ {{0XA7F515A0, 0X3FE8F1B2} }, +/**/ {{0X63064158, 0X3FE03048} }, +/**/ {{0XACBAADA8, 0XBFD02FFE} }, +/**/ {{0XF27448C0, 0X3FB55309} }, +/**/ {{0X4850006B, 0X3F58B6D6} }, +/**/ {{0X742323DF, 0XBF9B205F} } }, +/**/ {{{0XAA76C0B9, 0X3FEFC001} }, +/**/ {{0X15D66D80, 0X3FE901DC} }, +/**/ {{0X28D9B4AA, 0X3FE0201F} }, +/**/ {{0XA98D4C38, 0XBFD01FFE} }, +/**/ {{0X089780F8, 0X3FB55452} }, +/**/ {{0X7F35C5BB, 0X3F5050B5} }, +/**/ {{0XE19247AF, 0XBF9A9C9F} } }, +/**/ {{{0X39A592CA, 0X3FEFDFFE} }, +/**/ {{0X6D88A780, 0X3FE911F2} }, +/**/ {{0XE40C6538, 0X3FE01008} }, +/**/ {{0XD31688DE, 0XBFD01000} }, +/**/ {{0XE32F1816, 0X3FB55514} }, +/**/ {{0X4E1628D2, 0X3F402A15} }, +/**/ {{0XF4FAF5A0, 0XBF9A1A5F} } }, +/**/ {{{0X8E92D1B0, 0X3FEFF801} }, +/**/ {{0X9BB4BF00, 0X3FE91DFB} }, +/**/ {{0XB884C5A9, 0X3FE003FF} }, +/**/ {{0X3876A954, 0XBFD003FF} }, +/**/ {{0X5539DDFB, 0X3FB55551} }, +/**/ {{0X7B95E6C2, 0X3F2007E7} }, +/**/ {{0X18A3BA58, 0XBF99B9A7} } }, + }; + + static const number + hij[241][16] = { /* x0,hij for (1/16,1) */ +/**/ {{{0x00000000, 0x3fb04000} }, +/**/ {{0x1c06693d, 0x3fb03a6d} }, +/**/ {{0xd4e7f128, 0xbc428a02} }, +/**/ {{0xe92592ae, 0x3fefdf1f} }, +/**/ {{0xb5490162, 0x3c88bfc0} }, +/**/ {{0x8f7e4151, 0xbfb01ead} }, +/**/ {{0x0b64d205, 0xbc5395e8} }, +/**/ {{0x433dd49b, 0xbfd4d29f} }, +/**/ {{0x4aa42633, 0xbc75b19d} }, +/**/ {{0xce35961d, 0x3fafda41} }, +/**/ {{0x425d7696, 0x3c4e6a5f} }, +/**/ {{0x6c1bb5e2, 0x3fc814dd} }, +/**/ {{0x2b33739f, 0xbfaf4cb7} }, +/**/ {{0xc267d8ec, 0xbfc048b2} }, +/**/ {{0xe8ababc6, 0x3fae9649} }, +/**/ {{0xfe802692, 0x3fb78293} } }, +/**/ {{{0x00000000, 0x3fb10000} }, +/**/ {{0xa71d52a7, 0x3fb0f99e} }, +/**/ {{0xeec3624f, 0xbc22069f} }, +/**/ {{0x9a49d2a9, 0x3fefdc08} }, +/**/ {{0x68b2ce25, 0x3c7780f7} }, +/**/ {{0x9da73e1d, 0xbfb0d9de} }, +/**/ {{0xa1a487bf, 0x3c4ebf46} }, +/**/ {{0xd13ea108, 0xbfd4c669} }, +/**/ {{0xebb4528c, 0x3c7354bc} }, +/**/ {{0x789374c1, 0x3fb0a137} }, +/**/ {{0xc3f2c5c2, 0xbc56c223} }, +/**/ {{0x79c60cda, 0x3fc7f0e7} }, +/**/ {{0xcdcc7b81, 0xbfb05062} }, +/**/ {{0xc5266783, 0xbfc019e4} }, +/**/ {{0xf2540289, 0x3fafd0b2} }, +/**/ {{0xf6d3cd8a, 0x3fb71107} } }, +/**/ {{{0x00000000, 0x3fb20000} }, +/**/ {{0xbf082d59, 0x3fb1f86d} }, +/**/ {{0x7732ef81, 0xbc4095dc} }, +/**/ {{0x01722b81, 0x3fefd7b3} }, +/**/ {{0x8a212e02, 0xbc5e618c} }, +/**/ {{0xee4e9cfa, 0xbfb1d2c5} }, +/**/ {{0x29abece0, 0x3c426273} }, +/**/ {{0x37eb7f46, 0xbfd4b551} }, +/**/ {{0x01d8bf12, 0x3c73b360} }, +/**/ {{0x6adb6a7c, 0x3fb18fa7} }, +/**/ {{0x398999ad, 0xbc5c00d8} }, +/**/ {{0xf4a7cff3, 0x3fc7bea5} }, +/**/ {{0x61f84829, 0xbfb13008} }, +/**/ {{0xa8e135a1, 0xbfbfb14f} }, +/**/ {{0x4324f177, 0x3fb0b532} }, +/**/ {{0x3498dd9d, 0x3fb6734a} } }, +/**/ {{{0x00000000, 0x3fb30000} }, +/**/ {{0x318a4a9a, 0x3fb2f719} }, +/**/ {{0x79b9801f, 0x3c03fd17} }, +/**/ {{0x48e238fe, 0x3fefd31f} }, +/**/ {{0xd8c45327, 0xbc876a7a} }, +/**/ {{0x852096e2, 0xbfb2cada} }, +/**/ {{0x11efd787, 0x3c460860} }, +/**/ {{0x2e476a39, 0xbfd4a34b} }, +/**/ {{0xeb11ee51, 0x3c7254f2} }, +/**/ {{0xc54ae225, 0x3fb27c13} }, +/**/ {{0x4ae66f0c, 0x3c513096} }, +/**/ {{0xef0d59d0, 0x3fc789ca} }, +/**/ {{0x6d9aaa8c, 0xbfb20c06} }, +/**/ {{0x846ba912, 0xbfbf2885} }, +/**/ {{0xc697ef5e, 0x3fb17c5f} }, +/**/ {{0xcad31e6e, 0x3fb5ce93} } }, +/**/ {{{0x00000000, 0x3fb40000} }, +/**/ {{0x0e7c559d, 0x3fb3f59f} }, +/**/ {{0x285df847, 0x3c5ac4ce} }, +/**/ {{0xa6ab93e9, 0x3fefce4d} }, +/**/ {{0x18a97736, 0xbc6be46b} }, +/**/ {{0x4d22b635, 0xbfb3c211} }, +/**/ {{0x6950679f, 0x3c42033c} }, +/**/ {{0xc4d74033, 0xbfd49059} }, +/**/ {{0xd7e376aa, 0x3c57dd7c} }, +/**/ {{0xc0896a7c, 0x3fb36662} }, +/**/ {{0xd79232cf, 0xbc36cf6a} }, +/**/ {{0xa13a97a2, 0x3fc75261} }, +/**/ {{0x5fdd1509, 0xbfb2e431} }, +/**/ {{0x6e52db32, 0xbfbe9999} }, +/**/ {{0xb0a71e9f, 0x3fb23da4} }, +/**/ {{0xe3bc8178, 0x3fb52335} } }, +/**/ {{{0x00000000, 0x3fb50000} }, +/**/ {{0x677292fb, 0x3fb4f3fd} }, +/**/ {{0x6264979e, 0x3c4008d3} }, +/**/ {{0x53a1ee0d, 0x3fefc93e} }, +/**/ {{0x20fd2bdf, 0xbc64421a} }, +/**/ {{0x4aba88e3, 0xbfb4b85f} }, +/**/ {{0x3c9d1e89, 0x3c54f184} }, +/**/ {{0x25ae4668, 0xbfd47c7f} }, +/**/ {{0x816630d1, 0xbc7d7581} }, +/**/ {{0x07f85056, 0x3fb44e7b} }, +/**/ {{0x910bdf4f, 0x3c56d63c} }, +/**/ {{0xc439029c, 0x3fc71875} }, +/**/ {{0xf2bcfa10, 0xbfb3b85e} }, +/**/ {{0x9707b205, 0xbfbe04bb} }, +/**/ {{0x95e3e0cc, 0x3fb2f8c6} }, +/**/ {{0x8093431b, 0x3fb47184} } }, +/**/ {{{0x00000000, 0x3fb60000} }, +/**/ {{0x4fd2d7b2, 0x3fb5f232} }, +/**/ {{0x4401318e, 0x3c58a8da} }, +/**/ {{0x8b549418, 0x3fefc3f1} }, +/**/ {{0x836f8130, 0x3c34d896} }, +/**/ {{0x9cdd92e7, 0xbfb5adb9} }, +/**/ {{0xeb397cc3, 0x3c4d4161} }, +/**/ {{0x93f8f1dc, 0xbfd467bd} }, +/**/ {{0xffc760ad, 0xbc609d7b} }, +/**/ {{0xbea6b2fe, 0x3fb53443} }, +/**/ {{0x4b24f5db, 0x3c5eb03c} }, +/**/ {{0x8de3d005, 0x3fc6dc13} }, +/**/ {{0x37d2d99d, 0xbfb48866} }, +/**/ {{0xf6663fcb, 0xbfbd6a1d} }, +/**/ {{0x0adff464, 0x3fb3ad8e} }, +/**/ {{0x4159c223, 0x3fb3b9d6} } }, +/**/ {{{0x00000000, 0x3fb70000} }, +/**/ {{0xdcea4b0d, 0x3fb6f03b} }, +/**/ {{0x512fa17d, 0xbc33f00e} }, +/**/ {{0x8c07a436, 0x3fefbe67} }, +/**/ {{0x46250d6f, 0xbc84baaa} }, +/**/ {{0x7e3ba4c7, 0xbfb6a215} }, +/**/ {{0x54503f8d, 0xbc3504e7} }, +/**/ {{0x6b82d03a, 0xbfd45217} }, +/**/ {{0xbebdd1db, 0x3c7d1f0d} }, +/**/ {{0x841d5604, 0x3fb617a4} }, +/**/ {{0x6681c436, 0xbc47168b} }, +/**/ {{0xaccec6ce, 0x3fc69d47} }, +/**/ {{0xa4715800, 0xbfb5541f} }, +/**/ {{0x335a1c1b, 0xbfbcc9f4} }, +/**/ {{0xbac0061f, 0x3fb45bc6} }, +/**/ {{0x2b3853b6, 0x3fb2fc84} } }, +/**/ {{{0x00000000, 0x3fb80000} }, +/**/ {{0x2602f10f, 0x3fb7ee18} }, +/**/ {{0x4c0c3d98, 0xbc5cfb65} }, +/**/ {{0x96acfacc, 0x3fefb8a0} }, +/**/ {{0x18495af3, 0xbc82962e} }, +/**/ {{0x46635c89, 0xbfb79568} }, +/**/ {{0xa6bfd498, 0x3c5ac468} }, +/**/ {{0x2037b997, 0xbfd43b8f} }, +/**/ {{0xe2f12373, 0xbc72ad53} }, +/**/ {{0x7900c4ee, 0x3fb6f885} }, +/**/ {{0x0aef1f9d, 0x3c53145d} }, +/**/ {{0x4409ba0e, 0x3fc65c1f} }, +/**/ {{0x1d176e0c, 0xbfb61b65} }, +/**/ {{0x8ad65152, 0xbfbc2473} }, +/**/ {{0x7bc246c1, 0x3fb5033f} }, +/**/ {{0x6db30b46, 0x3fb239e9} } }, +/**/ {{{0x00000000, 0x3fb90000} }, +/**/ {{0x4478fb28, 0x3fb8ebc5} }, +/**/ {{0x0cad24cc, 0x3c473288} }, +/**/ {{0xeedcd6d7, 0x3fefb29c} }, +/**/ {{0x23ea50f0, 0x3c8efa9e} }, +/**/ {{0x6ae09982, 0xbfb887a7} }, +/**/ {{0x53801511, 0x3c5b2275} }, +/**/ {{0x3da0757c, 0xbfd42427} }, +/**/ {{0x311c7ac8, 0xbc7199e5} }, +/**/ {{0x4388717b, 0x3fb7d6cf} }, +/**/ {{0x3dd070b4, 0xbc5c4eb2} }, +/**/ {{0xe6c2b5f3, 0x3fc618a7} }, +/**/ {{0x00313569, 0xbfb6de12} }, +/**/ {{0xb6316619, 0xbfbb79d2} }, +/**/ {{0x61af5c21, 0x3fb5a3ca} }, +/**/ {{0x26e60289, 0x3fb17263} } }, +/**/ {{{0x00000000, 0x3fba0000} }, +/**/ {{0x53cfdcf1, 0x3fb9e941} }, +/**/ {{0x1d69c47e, 0x3c5a332e} }, +/**/ {{0xdace3776, 0x3fefac5c} }, +/**/ {{0x1ad91ab5, 0xbc8c9a78} }, +/**/ {{0x8054ad75, 0xbfb978c8} }, +/**/ {{0x8ed66c17, 0xbc5e35b8} }, +/**/ {{0x665afed1, 0xbfd40be2} }, +/**/ {{0x08ef10fb, 0x3c62eeef} }, +/**/ {{0x13c989d2, 0x3fb8b26b} }, +/**/ {{0xbfeab3ba, 0x3c329f11} }, +/**/ {{0x93c8f97c, 0x3fc5d2ef} }, +/**/ {{0x30234881, 0xbfb79c03} }, +/**/ {{0xd0f650c8, 0xbfbaca49} }, +/**/ {{0xce2dcccc, 0x3fb63d3c} }, +/**/ {{0x26fb0af2, 0x3fb0a650} } }, +/**/ {{{0x00000000, 0x3fbb0000} }, +/**/ {{0x71c722b8, 0x3fbae68a} }, +/**/ {{0x6910b9db, 0x3c4c014e} }, +/**/ {{0xa34ef42b, 0x3fefa5e0} }, +/**/ {{0xeb56d5b9, 0xbc836583} }, +/**/ {{0x3b881779, 0xbfba68c1} }, +/**/ {{0x13a09314, 0xbc473a0d} }, +/**/ {{0x538e939c, 0xbfd3f2c3} }, +/**/ {{0xee53e648, 0xbc68ed49} }, +/**/ {{0xa7d45973, 0x3fb98b42} }, +/**/ {{0x461ca7c4, 0xbc523943} }, +/**/ {{0xb0f2e2bb, 0x3fc58b04} }, +/**/ {{0x1c9d23dc, 0xbfb85517} }, +/**/ {{0x3e3b5a66, 0xbfba1612} }, +/**/ {{0x7ef1d0b9, 0x3fb6cf6f} }, +/**/ {{0x6617b315, 0x3fafac21} } }, +/**/ {{{0x00000000, 0x3fbc0000} }, +/**/ {{0xbe6f07c3, 0x3fbbe39e} }, +/**/ {{0x29a05987, 0x3c5f7b8f} }, +/**/ {{0x93bb9192, 0x3fef9f28} }, +/**/ {{0x7cd1bdab, 0x3c78260b} }, +/**/ {{0x72759741, 0xbfbb5787} }, +/**/ {{0xa6767247, 0x3c52f93f} }, +/**/ {{0xd45bbe91, 0xbfd3d8cc} }, +/**/ {{0x2edc0762, 0x3c664839} }, +/**/ {{0x4fa31d26, 0x3fba6140} }, +/**/ {{0x97891510, 0x3c400647} }, +/**/ {{0x0668fd66, 0x3fc540f6} }, +/**/ {{0xcb2f6e8f, 0xbfb9092d} }, +/**/ {{0x8d902073, 0xbfb95d66} }, +/**/ {{0x99c53d16, 0x3fb75a3e} }, +/**/ {{0x8f475e61, 0x3fae040c} } }, +/**/ {{{0x00000000, 0x3fbd0000} }, +/**/ {{0x5c3cca32, 0x3fbce07c} }, +/**/ {{0x425918a7, 0x3c4138e6} }, +/**/ {{0xf9f6d421, 0x3fef9834} }, +/**/ {{0x8c22a239, 0x3c6f3089} }, +/**/ {{0x1d4e69a5, 0xbfbc4511} }, +/**/ {{0xd2083ce8, 0x3c254c0f} }, +/**/ {{0xcd488978, 0xbfd3be01} }, +/**/ {{0x6362ec0f, 0x3c5612db} }, +/**/ {{0xf0d94873, 0x3fbb344e} }, +/**/ {{0xfdf7db72, 0xbc182beb} }, +/**/ {{0xb9d86c04, 0x3fc4f4d2} }, +/**/ {{0xdf238807, 0xbfb9b828} }, +/**/ {{0x5f93ffd6, 0xbfb8a082} }, +/**/ {{0xb6650b0c, 0x3fb7dd89} }, +/**/ {{0xb62676ef, 0x3fac5526} } }, +/**/ {{{0x00000000, 0x3fbe0000} }, +/**/ {{0x701eba6e, 0x3fbddd21} }, +/**/ {{0xcd76fe58, 0x3c594eff} }, +/**/ {{0x266112ba, 0x3fef9106} }, +/**/ {{0x6b7e18b1, 0x3c74c302} }, +/**/ {{0x5777816c, 0xbfbd3154} }, +/**/ {{0x1f9dbddd, 0x3c5dc7e4} }, +/**/ {{0x37a90881, 0xbfd3a265} }, +/**/ {{0xeb7ba840, 0xbc75bd61} }, +/**/ {{0x0a52514b, 0x3fbc045a} }, +/**/ {{0xcff49a99, 0xbc35ca88} }, +/**/ {{0x498eeb56, 0x3fc4a6aa} }, +/**/ {{0xa09232cf, 0xbfba61eb} }, +/**/ {{0x4a464027, 0xbfb7dfa2} }, +/**/ {{0xe633c053, 0x3fb85933} }, +/**/ {{0x3f920107, 0x3faaa036} } }, +/**/ {{{0x00000000, 0x3fbf0000} }, +/**/ {{0x2190043b, 0x3fbed98c} }, +/**/ {{0x592c7b13, 0xbc23a598} }, +/**/ {{0x6bcf4ad8, 0x3fef899c} }, +/**/ {{0x912c09b0, 0x3c55fd73} }, +/**/ {{0x607f91a0, 0xbfbe1c47} }, +/**/ {{0x5b5db022, 0x3c576677} }, +/**/ {{0x21046f5f, 0xbfd385fa} }, +/**/ {{0x4487f4b8, 0x3c7f01c3} }, +/**/ {{0xb77f2d51, 0x3fbcd14d} }, +/**/ {{0x30a2ccfe, 0x3c57a86d} }, +/**/ {{0x8782b530, 0x3fc4568c} }, +/**/ {{0x02b7ad2d, 0xbfbb065b} }, +/**/ {{0xbd215555, 0xbfb71b03} }, +/**/ {{0xb9c1c1de, 0x3fb8cd23} }, +/**/ {{0x8dbfa69b, 0x3fa8e602} } }, +/**/ {{{0x00000000, 0x3fc00000} }, +/**/ {{0x9aac2f6e, 0x3fbfd5ba} }, +/**/ {{0x86760c17, 0xbc4cd376} }, +/**/ {{0x1f81f820, 0x3fef81f8} }, +/**/ {{0x1f81f820, 0xbc8f81f8} }, +/**/ {{0x9d0dc11b, 0xbfbf05e0} }, +/**/ {{0x1d821725, 0xbc35a199} }, +/**/ {{0xaa76e1d7, 0xbfd368c3} }, +/**/ {{0xc796f8cd, 0xbc672d4c} }, +/**/ {{0xb391c2e3, 0x3fbd9b16} }, +/**/ {{0x8086c51d, 0x3c58051b} }, +/**/ {{0x94488c86, 0x3fc40489} }, +/**/ {{0xa98401c8, 0xbfbba55d} }, +/**/ {{0xe5127e64, 0xbfb652e4} }, +/**/ {{0x442e53ae, 0x3fb93943} }, +/**/ {{0x86286f75, 0x3fa72753} } }, +/**/ {{{0x00000000, 0x3fc08000} }, +/**/ {{0x84212b3e, 0x3fc068d5} }, +/**/ {{0x83019bfd, 0xbc69e2d2} }, +/**/ {{0x991bb133, 0x3fef7a19} }, +/**/ {{0x66627723, 0x3c7a956a} }, +/**/ {{0x97c8e137, 0xbfbfee16} }, +/**/ {{0x66dbe7af, 0x3c4d9399} }, +/**/ {{0x0810323a, 0xbfd34ac5} }, +/**/ {{0x6bc6c512, 0x3c6a1a57} }, +/**/ {{0x5c75a6f9, 0x3fbe61a2} }, +/**/ {{0xd75c8f85, 0xbc492b99} }, +/**/ {{0xd9fa3f20, 0x3fc3b0b1} }, +/**/ {{0xee66d309, 0xbfbc3edb} }, +/**/ {{0x905eeb33, 0xbfb58784} }, +/**/ {{0x1c65bb14, 0x3fb99d80} }, +/**/ {{0x18a09884, 0x3fa564f1} } }, +/**/ {{{0x00000000, 0x3fc10000} }, +/**/ {{0xccf40882, 0x3fc0e6ad} }, +/**/ {{0x1bb98d0d, 0xbc6d71a3} }, +/**/ {{0x32978bad, 0x3fef7201} }, +/**/ {{0x599381e9, 0x3c816476} }, +/**/ {{0x011b81fd, 0xbfc06a70} }, +/**/ {{0x9ba697ca, 0xbc422f5d} }, +/**/ {{0x802fc0a5, 0xbfd32c01} }, +/**/ {{0x08a20868, 0x3c7d8e47} }, +/**/ {{0xb59597fe, 0x3fbf24de} }, +/**/ {{0x410d31eb, 0xbc43288f} }, +/**/ {{0x070feb24, 0x3fc35b16} }, +/**/ {{0xe4565b78, 0xbfbcd2bf} }, +/**/ {{0x128768c6, 0xbfb4b922} }, +/**/ {{0x5c42a097, 0x3fb9f9cb} }, +/**/ {{0xc7f97f2e, 0x3fa39fa2} } }, +/**/ {{{0x00000000, 0x3fc18000} }, +/**/ {{0x41060850, 0x3fc16465} }, +/**/ {{0x8ae7ea92, 0x3c66bcee} }, +/**/ {{0x483f492b, 0x3fef69af} }, +/**/ {{0x57db963e, 0xbc6e3280} }, +/**/ {{0xdacaa844, 0xbfc0dd19} }, +/**/ {{0xad7fc21e, 0xbc6133c7} }, +/**/ {{0x6addaea8, 0xbfd30c7c} }, +/**/ {{0x89161c76, 0xbc71443d} }, +/**/ {{0x6a6d3cd2, 0x3fbfe4ba} }, +/**/ {{0x423ee67a, 0x3c50d4b8} }, +/**/ {{0x092e569a, 0x3fc303c7} }, +/**/ {{0x5b11d3b6, 0xbfbd60f5} }, +/**/ {{0x283b5c55, 0xbfb3e7fd} }, +/**/ {{0x9d9a6ab7, 0x3fba4e19} }, +/**/ {{0x3487cc29, 0x3fa1d82f} } }, +/**/ {{{0x00000000, 0x3fc20000} }, +/**/ {{0xfb043727, 0x3fc1e1fa} }, +/**/ {{0x14dacf8c, 0xbc4b4859} }, +/**/ {{0x38a14f5e, 0x3fef6124} }, +/**/ {{0x001f6124, 0x3c798e9e} }, +/**/ {{0x59d3fb7c, 0xbfc14f04} }, +/**/ {{0x4cc99cb2, 0x3c531efa} }, +/**/ {{0x31219b34, 0xbfd2ec39} }, +/**/ {{0x6e004611, 0xbc618697} }, +/**/ {{0x68736312, 0x3fc05092} }, +/**/ {{0x8a06e4b5, 0x3c67aad4} }, +/**/ {{0x07eca5ec, 0x3fc2aad6} }, +/**/ {{0xe19fe31c, 0xbfbde969} }, +/**/ {{0xdb6b9127, 0xbfb31455} }, +/**/ {{0xf53dd9ee, 0x3fba9a62} }, +/**/ {{0xa8e4ede0, 0x3fa00f5b} } }, +/**/ {{{0x00000000, 0x3fc28000} }, +/**/ {{0x171a535c, 0x3fc25f6e} }, +/**/ {{0xbde1a310, 0x3c67c6d7} }, +/**/ {{0x64866d22, 0x3fef5860} }, +/**/ {{0xd1f6326c, 0x3c88c6ff} }, +/**/ {{0x13c11396, 0xbfc1c02b} }, +/**/ {{0xffeb1a0f, 0xbc51b469} }, +/**/ {{0x4c571b0f, 0xbfd2cb3b} }, +/**/ {{0x2fb0b163, 0x3c6e4f76} }, +/**/ {{0xf5c213ab, 0x3fc0ad06} }, +/**/ {{0xabea9e66, 0x3c625bf2} }, +/**/ {{0x5f93bbb2, 0x3fc25054} }, +/**/ {{0xc80a32c8, 0xbfbe6c0c} }, +/**/ {{0x678d0d1e, 0xbfb23e6c} }, +/**/ {{0xebf8ae4b, 0x3fbadea2} }, +/**/ {{0x527f133b, 0x3f9c8bd7} } }, +/**/ {{{0x00000000, 0x3fc30000} }, +/**/ {{0xb2fba1ff, 0x3fc2dcbd} }, +/**/ {{0x05561534, 0x3c58f287} }, +/**/ {{0x2ee76e94, 0x3fef4f64} }, +/**/ {{0xc6da5865, 0x3c80ec89} }, +/**/ {{0xb322f867, 0xbfc23089} }, +/**/ {{0x5fcd0d6f, 0x3c4c2b54} }, +/**/ 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{{0x280318fd, 0xbfb11c35} } }, +/**/ {{{0x00000000, 0x3fd44000} }, +/**/ {{0xeb76157c, 0x3fd39cb4} }, +/**/ {{0x5a214713, 0xbc72f4da} }, +/**/ {{0x22c31625, 0x3fed1682} }, +/**/ {{0xd5e51b41, 0x3c8ac111} }, +/**/ {{0x07e9a89a, 0xbfd0bb6b} }, +/**/ {{0x7faa1dda, 0x3c76fb53} }, +/**/ {{0xb75f0772, 0xbfc66be7} }, +/**/ {{0xee6d618b, 0xbc69a77d} }, +/**/ {{0x6e943d69, 0x3fc8e1eb} }, +/**/ {{0xc5ec9ebe, 0xbc6982c4} }, +/**/ {{0x9c2d3c0c, 0x3f78e73c} }, +/**/ {{0x7059f387, 0xbfbee752} }, +/**/ {{0x16982f58, 0x3fac73f0} }, +/**/ {{0xc146b407, 0x3fabd0e4} }, +/**/ {{0x82f43254, 0xbfb12b5c} } }, +/**/ {{{0x00000000, 0x3fd48000} }, +/**/ {{0x29271134, 0x3fd3d6d1} }, +/**/ {{0x41cc958a, 0x3c7137ca} }, +/**/ {{0xffb0304c, 0x3fed05b5} }, +/**/ {{0x33e896e5, 0xbc8fc921} }, +/**/ {{0x3a49e254, 0xbfd0dcc2} }, +/**/ {{0x925cb599, 0x3c704578} }, +/**/ {{0x75708502, 0xbfc60859} }, +/**/ {{0x9feebe6c, 0xbc5f88bc} }, +/**/ {{0xc3fb5c1c, 0x3fc8e4e8} }, +/**/ {{0xd6b77a05, 0x3c6de114} }, +/**/ {{0xdbc6c857, 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{{0x5e282403, 0x3fc8b25b} }, +/**/ {{0x707e09fa, 0xbbef7d58} }, +/**/ {{0xb65add31, 0xbf94c1e0} }, +/**/ {{0xafa52f1b, 0xbfba815f} }, +/**/ {{0x63712acc, 0x3fb1a16f} }, +/**/ {{0x95a8d3ad, 0x3f9fa5b5} }, +/**/ {{0x72814750, 0xbfb09d01} } }, +/**/ {{{0x00000000, 0x3fd70000} }, +/**/ {{0x0309cfe2, 0x3fd61484} }, +/**/ {{0x15711f00, 0xbc7a7257} }, +/**/ {{0x27afd9eb, 0x3fec5703} }, +/**/ {{0xb32c1d72, 0x3c63c2ab} }, +/**/ {{0x06000419, 0xbfd20a1c} }, +/**/ {{0xf51a3a28, 0xbc7b5fe7} }, +/**/ {{0x486ad2c8, 0xbfc22771} }, +/**/ {{0xf84a7eae, 0xbc499ab5} }, +/**/ {{0x9d027817, 0x3fc8a49c} }, +/**/ {{0x2e376ecc, 0xbc53fcab} }, +/**/ {{0xeaabcb23, 0xbf973831} }, +/**/ {{0x8c46fbce, 0xbfba051d} }, +/**/ {{0x9132e9cc, 0x3fb1de66} }, +/**/ {{0xd48d5d65, 0x3f9d5269} }, +/**/ {{0x712354a4, 0xbfb074bb} } }, +/**/ {{{0x00000000, 0x3fd74000} }, +/**/ {{0xf635c1c6, 0x3fd64d1f} }, +/**/ {{0xe7c0fdbe, 0xbc7fa403} }, +/**/ {{0x86b5cbf8, 0x3fec44eb} }, +/**/ {{0xbc5b562d, 0xbc6a4101} }, +/**/ {{0x50fb21ad, 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{{0x0ef9b688, 0x3c50e395} }, +/**/ {{0xc8a9b4c0, 0xbf922b65} }, +/**/ {{0xd319146f, 0x3c2835ee} }, +/**/ {{0x00b681bd, 0x3fc16fb8} }, +/**/ {{0x279133b0, 0x3c1df633} }, +/**/ {{0x0a3b410c, 0xbfb54af9} }, +/**/ {{0xebe14682, 0xbf889682} }, +/**/ {{0xdf89e086, 0x3fabe94c} }, +/**/ {{0x0e55a6f8, 0xbfa0ec0e} }, +/**/ {{0x08af68f3, 0xbf809a3e} } }, +/**/ {{{0x00000000, 0x3fe18000} }, +/**/ {{0x73c1a40c, 0x3fe0039c} }, +/**/ {{0x49c9d593, 0xbc8b32c9} }, +/**/ {{0xe931fcd3, 0x3fe8a209} }, +/**/ {{0x8e68c94c, 0x3c6cb8f0} }, +/**/ {{0xb35ad2d8, 0xbfd4bd59} }, +/**/ {{0xcaa606b4, 0xbc61ac1a} }, +/**/ {{0x6dc339ef, 0xbf9000c3} }, +/**/ {{0xaeaeaa73, 0x3c2c62e2} }, +/**/ {{0x7812ee2d, 0x3fc13a66} }, +/**/ {{0x948ffe5b, 0x3c6a8cc2} }, +/**/ {{0xb5955c9c, 0xbfb55c46} }, +/**/ {{0x0fd2b503, 0xbf85906b} }, +/**/ {{0x577de2da, 0x3fab615d} }, +/**/ {{0xa34d31ec, 0xbfa10f0a} }, +/**/ {{0xefe48ad0, 0xbf7d02cb} } }, +/**/ {{{0x00000000, 0x3fe1a000} }, +/**/ {{0x1e82422d, 0x3fe01c34} }, +/**/ {{0xfcca90ee, 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{{{0x00000000, 0x3fe2c000} }, +/**/ {{0x8b67e295, 0x3fe0f5e2} }, +/**/ {{0x7ec990d0, 0x3be311b1} }, +/**/ {{0xa145af59, 0x3fe7d24f} }, +/**/ {{0xabdb623b, 0xbc83c6d1} }, +/**/ {{0x6b9bdb30, 0xbfd4c7fc} }, +/**/ {{0xd3bbb84b, 0x3c7c2fae} }, +/**/ {{0xc729b366, 0x3f70e125} }, +/**/ {{0x7a19993c, 0x3c1291fb} }, +/**/ {{0x66cf0dd8, 0x3fbe3fef} }, +/**/ {{0xcd5e7640, 0xbc5428b7} }, +/**/ {{0xa3273c21, 0xbfb59517} }, +/**/ {{0x36891acb, 0x3f65adcf} }, +/**/ {{0xe121c017, 0x3fa5f05a} }, +/**/ {{0x384bad65, 0xbfa180c2} }, +/**/ {{0xd31e02a7, 0x3f5bd6f1} } }, +/**/ {{{0x00000000, 0x3fe2e000} }, +/**/ {{0x77307a0d, 0x3fe10daa} }, +/**/ {{0xd44c7b05, 0x3c869c33} }, +/**/ {{0x19337139, 0x3fe7bd88} }, +/**/ {{0x00e777ef, 0xbc7fd248} }, +/**/ {{0xb3e16264, 0xbfd4c704} }, +/**/ {{0xd46ed4e3, 0xbc7ed720} }, +/**/ {{0x62c1daf7, 0x3f7863a5} }, +/**/ {{0x30cc82d1, 0x3c155e73} }, +/**/ {{0x97a241da, 0x3fbdd411} }, +/**/ {{0x9ac44edd, 0x3c27a15a} }, +/**/ {{0x9a6c71a6, 0xbfb59022} }, +/**/ {{0xb5534ebe, 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{{0xf45873a6, 0x3c3cd061} }, +/**/ {{0x88dfb80c, 0x3fac2f8b} }, +/**/ {{0x53add20b, 0xbc14fcbc} }, +/**/ {{0x08c71945, 0xbfb0ba99} }, +/**/ {{0x3d79f13f, 0x3f9d7b0c} }, +/**/ {{0x357dfc67, 0x3f795393} }, +/**/ {{0x3aa97829, 0xbf937822} }, +/**/ {{0xa8b90db0, 0x3f8aec90} } }, +/**/ {{{0x00000000, 0x3fe82000} }, +/**/ {{0xb1c71762, 0x3fe4ac00} }, +/**/ {{0x2382b900, 0x3c8b20e7} }, +/**/ {{0xe8e45252, 0x3fe4673d} }, +/**/ {{0x67458f9c, 0x3c57d208} }, +/**/ {{0x6c24e1b3, 0xbfd39d8c} }, +/**/ {{0x973c6d15, 0xbc7830c5} }, +/**/ {{0x12b78147, 0x3faf318c} }, +/**/ {{0xd318184c, 0xbc4fa440} }, +/**/ {{0x158b44e7, 0x3fab891f} }, +/**/ {{0x45d7f1f3, 0x3c4d5f9f} }, +/**/ {{0x47a3e8ba, 0xbfb08e40} }, +/**/ {{0xc4c1a21a, 0x3f9da541} }, +/**/ {{0x3c0d1d71, 0x3f76ec1e} }, +/**/ {{0x152e0bfc, 0xbf92ff48} }, +/**/ {{0x9955298f, 0x3f8ac8f0} } }, +/**/ {{{0x00000000, 0x3fe84000} }, +/**/ {{0x22de94e5, 0x3fe4c05e} }, +/**/ {{0xf09f2edf, 0xbc8c0ac1} }, +/**/ {{0x3c9a6560, 0x3fe453a6} }, +/**/ {{0x828bba02, 0x3c77a95f} }, +/**/ {{0x5a0e5b1c, 0xbfd391c5} }, +/**/ {{0xcd3f76d2, 0x3c7d553d} }, +/**/ {{0x9adede86, 0x3faf9e66} }, +/**/ {{0xd6d2bac0, 0xbc225e54} }, +/**/ {{0x4bdf89d7, 0x3faae46f} }, +/**/ {{0x2b25b8d9, 0x3c39c98c} }, +/**/ {{0x5765a5c1, 0xbfb061ab} }, +/**/ {{0x7127d649, 0x3f9dcb4f} }, +/**/ {{0x13002646, 0x3f7493ba} }, +/**/ {{0xa397d1a6, 0xbf928718} }, +/**/ {{0x494648b5, 0x3f8aa0bc} } }, +/**/ {{{0x00000000, 0x3fe86000} }, +/**/ {{0x023414e8, 0x3fe4d4a8} }, +/**/ {{0x1daa88b0, 0x3c6e3a89} }, +/**/ {{0x6ba2786e, 0x3fe4401a} }, +/**/ {{0xe3b5f317, 0xbc4b8213} }, +/**/ {{0xf11905c0, 0xbfd385d5} }, +/**/ {{0xa2f42dd1, 0xbc72a1e9} }, +/**/ {{0xf07a526f, 0x3fb00458} }, +/**/ {{0xac5fd817, 0xbc14f965} }, +/**/ {{0x66ca7da2, 0x3faa417e} }, +/**/ {{0xa050b433, 0x3c4b1e1a} }, +/**/ {{0x60182e4f, 0xbfb034e0} }, +/**/ {{0x8cafa41b, 0x3f9ded4f} }, +/**/ {{0x1fa4f037, 0x3f724a50} }, +/**/ {{0xfd90e915, 0xbf920fa7} }, +/**/ {{0xf59e7acf, 0x3f8a742d} } }, +/**/ {{{0x00000000, 0x3fe88000} }, +/**/ {{0x5bb6ec04, 0x3fe4e8de} }, +/**/ {{0xbeb3796c, 0x3c84a33d} }, +/**/ {{0x9dd8fdc1, 0x3fe42c9a} }, +/**/ {{0xaf80050b, 0x3c5192da} }, +/**/ {{0x25adf97f, 0xbfd379bf} }, +/**/ {{0x20cd3651, 0xbc774019} }, +/**/ {{0x724dbb01, 0x3fb0383a} }, +/**/ {{0xeb93e538, 0x3c5c4e67} }, +/**/ {{0x646e65df, 0x3fa9a04e} }, +/**/ {{0x894a6b77, 0x3c21a7cb} }, +/**/ {{0x62771c79, 0xbfb007e5} }, +/**/ {{0x37a45544, 0x3f9e0b5c} }, +/**/ {{0x54993092, 0x3f700fc7} }, +/**/ {{0x37534c25, 0xbf919909} }, +/**/ {{0xae51732a, 0x3f8a437e} } }, +/**/ {{{0x00000000, 0x3fe8a000} }, +/**/ {{0x3b7dd17e, 0x3fe4fd01} }, +/**/ {{0x3e7c24b5, 0x3c7d513f} }, +/**/ {{0xfa274ef1, 0x3fe41926} }, +/**/ {{0x4d72ecb3, 0x3c8ad830} }, +/**/ {{0xe995018a, 0xbfd36d81} }, +/**/ {{0x6fd6094d, 0x3c7e7ec5} }, +/**/ {{0x567bb975, 0x3fb06adb} }, +/**/ {{0xf0d7364f, 0x3c5212c1} }, +/**/ {{0x07a9b624, 0x3fa900e1} }, +/**/ {{0xc16bcc85, 0xbc4e5b5b} }, +/**/ {{0x705f052b, 0xbfafb580} }, +/**/ {{0x646ce12e, 0x3f9e258f} }, +/**/ {{0xa3c63841, 0x3f6bc808} }, +/**/ {{0x67043d41, 0xbf91234e} }, +/**/ {{0x4f11b221, 0x3f8a0ee6} } }, +/**/ {{{0x00000000, 0x3fe8c000} }, +/**/ {{0xadc5ed81, 0x3fe51110} }, +/**/ {{0x6832a63e, 0x3c723dcd} }, +/**/ {{0xa6864f90, 0x3fe405bf} }, +/**/ {{0x662cd5df, 0xbc7419c5} }, +/**/ {{0x2bf1f7e4, 0xbfd3611f} }, +/**/ {{0x65483b78, 0xbc6e94dd} }, +/**/ {{0x23e21be9, 0x3fb09c3f} }, +/**/ {{0xcaca858d, 0x3c22db63} }, +/**/ {{0xd99c3f1d, 0x3fa86337} }, +/**/ {{0xdc0a6dfc, 0x3c034382} }, +/**/ {{0x284f8093, 0xbfaf5aed} }, +/**/ {{0xd396fb43, 0x3f9e3c02} }, +/**/ {{0x08b96150, 0x3f678dd3} }, +/**/ {{0xaa2dcc3a, 0xbf90ae88} }, +/**/ {{0x79128ee7, 0x3f89d69b} } }, +/**/ {{{0x00000000, 0x3fe8e000} }, +/**/ {{0xbef1e9fb, 0x3fe5250c} }, +/**/ {{0xa3228870, 0xbc5539b7} }, +/**/ {{0xc8011245, 0x3fe3f264} }, +/**/ {{0x44cc720b, 0xbc6641f1} }, +/**/ {{0xd942778a, 0xbfd35497} }, +/**/ {{0x9bd7dbd6, 0x3c750a5a} }, +/**/ {{0x6438739e, 0x3fb0cc69} }, +/**/ {{0x435f798d, 0x3bf5d933} }, +/**/ {{0x2b29722f, 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+/**/ {{0x5f3d8fd8, 0x3c6ef16e} }, +/**/ {{0x703d3bf6, 0x3fb1291f} }, +/**/ {{0xb04e0672, 0xbc566e82} }, +/**/ {{0x806b26f2, 0x3fa694e1} }, +/**/ {{0xafcee740, 0x3c302819} }, +/**/ {{0x16dcee96, 0xbfae49eb} }, +/**/ {{0xfbfdb35f, 0x3f9e69dc} }, +/**/ {{0x70c48510, 0x3f571910} }, +/**/ {{0xe90198c8, 0xbf8ead25} }, +/**/ {{0xa1c723cb, 0x3f89199b} } }, +/**/ {{{0x00000000, 0x3fe94000} }, +/**/ {{0x29c70c34, 0x3fe5608d} }, +/**/ {{0xf0de8088, 0x3c89939c} }, +/**/ {{0x4fcf28c3, 0x3fe3b8a0} }, +/**/ {{0xcb80013c, 0xbc469c2b} }, +/**/ {{0x77ec4ef9, 0xbfd32e2f} }, +/**/ {{0xc61f7341, 0x3c7f9d06} }, +/**/ {{0x59c3bcdf, 0x3fb155b2} }, +/**/ {{0x3583c01b, 0xbc2d692e} }, +/**/ {{0x1a1fe15d, 0x3fa5fe54} }, +/**/ {{0x5d9bad81, 0x3c430dc5} }, +/**/ {{0x01d944a8, 0xbfadeea0} }, +/**/ {{0x9683b244, 0x3f9e724e} }, +/**/ {{0x491379ef, 0x3f4f13d4} }, +/**/ {{0x0b7cf74b, 0xbf8dcc74} }, +/**/ {{0xff5f0625, 0x3f88d48f} } }, +/**/ {{{0x00000000, 0x3fe96000} }, +/**/ {{0x352b33ba, 0x3fe5743c} }, +/**/ {{0x34c87ea6, 0xbc8ea00d} }, +/**/ {{0xa5f05e48, 0x3fe3a578} }, +/**/ {{0x00e4639b, 0xbc8ba1ec} }, +/**/ {{0xd8b7a43f, 0xbfd3211e} }, +/**/ {{0x676e23a8, 0xbc6d4b54} }, +/**/ {{0xf11b2c2d, 0x3fb18119} }, +/**/ {{0x3a3bf5fa, 0x3c34855b} }, +/**/ {{0x625c76bf, 0x3fa5698f} }, +/**/ {{0xbedb0264, 0xbc2f758a} }, +/**/ {{0x81b60103, 0xbfad9340} }, +/**/ {{0xce91900f, 0x3f9e777d} }, +/**/ {{0x34fddb2f, 0x3f406543} }, +/**/ {{0xe6077f81, 0xbf8cee3b} }, +/**/ {{0xfe42afde, 0x3f888ccf} } }, +/**/ {{{0x00000000, 0x3fe98000} }, +/**/ {{0x1f732fbb, 0x3fe587d8} }, +/**/ {{0xd8c5a950, 0xbc75e5c9} }, +/**/ {{0x1cd28c98, 0x3fe3925e} }, +/**/ {{0x1ffec6da, 0x3c8c8443} }, +/**/ {{0x1af2c622, 0xbfd313ee} }, +/**/ {{0xbc3f7ac8, 0x3c0a0e9b} }, +/**/ {{0xc7f683c3, 0x3fb1ab59} }, +/**/ {{0x12c04500, 0x3c5eaf17} }, +/**/ {{0xa7039179, 0x3fa4d693} }, +/**/ {{0xa4ce58a2, 0xbc4c8d74} }, +/**/ {{0x391400b3, 0xbfad37d6} }, +/**/ {{0xf2148a36, 0x3f9e7982} }, +/**/ {{0xb6df63ca, 0x3f112956} }, +/**/ {{0xfbd0f7ee, 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+/**/ {{0x6f398221, 0xbfac8106} }, +/**/ {{0xc97073c7, 0x3f9e746e} }, +/**/ {{0xecfc2d6a, 0xbf4914de} }, +/**/ {{0xcfa74bd5, 0xbf8a6350} }, +/**/ {{0x6f38ad9e, 0x3f87a724} } }, +/**/ {{{0x00000000, 0x3fe9e000} }, +/**/ {{0x9c244261, 0x3fe5c239} }, +/**/ {{0xe9e56b35, 0xbc831bd4} }, +/**/ {{0x7e9af2dc, 0x3fe3595e} }, +/**/ {{0x9dc90e6a, 0x3c81ef2d} }, +/**/ {{0xb99eb689, 0xbfd2eba3} }, +/**/ {{0x6a2f2701, 0xbc7b12ef} }, +/**/ {{0x7ec46b9b, 0x3fb2234e} }, +/**/ {{0x8d415d66, 0x3c59f30c} }, +/**/ {{0xaabf0d26, 0x3fa32856} }, +/**/ {{0x3f33d7ea, 0xbc122571} }, +/**/ {{0xcc3da9ce, 0xbfac25b2} }, +/**/ {{0xa8630cad, 0x3f9e6d84} }, +/**/ {{0xbeba707a, 0xbf5308c5} }, +/**/ {{0xa1585fd1, 0xbf898fda} }, +/**/ {{0x0dc54356, 0x3f87565b} } }, +/**/ {{{0x00000000, 0x3fea0000} }, +/**/ {{0x87169b18, 0x3fe5d589} }, +/**/ {{0x4bc5e7ca, 0x3c60028e} }, +/**/ {{0xace01346, 0x3fe34679} }, +/**/ {{0x04d19e6b, 0x3c8e6b38} }, +/**/ {{0x03913da2, 0xbfd2ddfb} }, +/**/ {{0x9a19adbd, 0xbc763ec8} }, +/**/ {{0x07b46905, 0x3fb24913} }, +/**/ {{0xd6f0307f, 0xbc4e7be8} }, +/**/ {{0x4b96b773, 0x3fa29c7e} }, +/**/ {{0x9182d783, 0xbc24c2cd} }, +/**/ {{0x1f071f44, 0xbfabca78} }, +/**/ {{0xc4b7b7c4, 0x3f9e63ce} }, +/**/ {{0x125f35b0, 0xbf59529a} }, +/**/ {{0xed369b2b, 0xbf88bf43} }, +/**/ {{0xc97185cd, 0x3f8703ba} } }, +/**/ {{{0x00000000, 0x3fea2000} }, +/**/ {{0x941043d0, 0x3fe5e8c6} }, +/**/ {{0xbe451e70, 0xbc70bf75} }, +/**/ {{0x91e21aec, 0x3fe333a2} }, +/**/ {{0x7acfc84f, 0x3c7ae035} }, +/**/ {{0x628d5861, 0xbfd2d036} }, +/**/ {{0xe463d006, 0x3c67c5fb} }, +/**/ {{0xa7d77fb2, 0x3fb26dc1} }, +/**/ {{0xc47ba861, 0xbc5432bd} }, +/**/ {{0xc229bece, 0x3fa2126d} }, +/**/ {{0x1da8ed9e, 0xbc4be1bf} }, +/**/ {{0xa890e568, 0xbfab6f5e} }, +/**/ {{0xeec5339a, 0x3f9e5763} }, +/**/ {{0x5274aa52, 0xbf5f68a6} }, +/**/ {{0x8a9df558, 0xbf87f19c} }, +/**/ {{0xff809dc5, 0x3f86af6b} } }, +/**/ {{{0x00000000, 0x3fea4000} }, +/**/ {{0xd0d5cc4a, 0x3fe5fbf0} }, +/**/ {{0x000b7158, 0xbc5b4cfd} }, +/**/ {{0x49243ad8, 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{{{0x00000000, 0x3fed6000} }, +/**/ {{0x11a6092b, 0x3fe7c3d3} }, +/**/ {{0x2d303288, 0x3c8bb3cb} }, +/**/ {{0x1dc61b17, 0x3fe15dbb} }, +/**/ {{0xbb77dc56, 0xbc8f0487} }, +/**/ {{0xee0771ca, 0xbfd14d7e} }, +/**/ {{0xdc2fcbd0, 0x3c72d38b} }, +/**/ {{0xd6080f0e, 0x3fb4d716} }, +/**/ {{0xa9fbc2c3, 0xbc5cb5bc} }, +/**/ {{0xfc42e02f, 0x3f89a7f9} }, +/**/ {{0x857be8a4, 0xbc201eec} }, +/**/ {{0x44ceebb3, 0xbfa2af2b} }, +/**/ {{0x08511639, 0x3f9a62b5} }, +/**/ {{0xc8de23de, 0xbf8018ad} }, +/**/ {{0xc964501a, 0xbf6dc8a2} }, +/**/ {{0xeb913697, 0x3f7ac6f9} } }, +/**/ {{{0x00000000, 0x3fed8000} }, +/**/ {{0x289fa093, 0x3fe7d528} }, +/**/ {{0x1e2f3aa9, 0x3c856082} }, +/**/ {{0x711551bb, 0x3fe14c75} }, +/**/ {{0x71970f2c, 0xbc80c88e} }, +/**/ {{0xe4aa5095, 0xbfd13dd8} }, +/**/ {{0xb4b7ae12, 0x3c66dd31} }, +/**/ {{0xead4c211, 0x3fb4e38d} }, +/**/ {{0xe392a31e, 0x3c513fb0} }, +/**/ {{0xf6b74576, 0x3f88355f} }, +/**/ {{0xf3561ab7, 0x3ba8cb44} }, +/**/ {{0x0de0faaa, 0xbfa26058} }, +/**/ {{0x989371f0, 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+/**/ {{0xd971cd38, 0x3fe07187} }, +/**/ {{0x202c20ac, 0x3c89baa4} }, +/**/ {{0xd15893ab, 0xbfd06fe9} }, +/**/ {{0xdc0cb586, 0xbc7a864b} }, +/**/ {{0x7ce57fed, 0x3fb54883} }, +/**/ {{0x294f4b18, 0xbc49498e} }, +/**/ {{0x426ebecc, 0x3f6df762} }, +/**/ {{0xf28644c0, 0xbc022f08} }, +/**/ {{0x5c564b44, 0xbf9d3e48} }, +/**/ {{0xdfea7acf, 0x3f9713ab} }, +/**/ {{0x761db35c, 0xbf8213fc} }, +/**/ {{0x10d60f49, 0xbf4f9a17} }, +/**/ {{0x58700e9b, 0x3f71f5de} } }, +/**/ {{{0x00000000, 0x3fef4000} }, +/**/ {{0x145cf49d, 0x3fe8c0d9} }, +/**/ {{0x76dc4333, 0x3c8bea40} }, +/**/ {{0xeb45139a, 0x3fe0611f} }, +/**/ {{0x65aadb1f, 0x3c7e4998} }, +/**/ {{0x1953a316, 0xbfd05ff2} }, +/**/ {{0xa1b67b0f, 0x3c759922} }, +/**/ {{0xc08c1d66, 0x3fb54bf9} }, +/**/ {{0xd220330c, 0x3c5b9353} }, +/**/ {{0x478cb604, 0x3f69706e} }, +/**/ {{0xa22fd45a, 0xbbfdb6d3} }, +/**/ {{0x5c0d1d38, 0xbf9cb490} }, +/**/ {{0xbbaba2f2, 0x3f96d44b} }, +/**/ {{0x9c6b7de1, 0xbf822289} }, +/**/ {{0xa49803b6, 0xbf4aa143} }, +/**/ {{0x9270e49e, 0x3f7165be} } }, +/**/ {{{0x00000000, 0x3fef6000} }, +/**/ {{0x06f8c4cb, 0x3fe8d132} }, +/**/ {{0xbaa89a8b, 0xbc7b018c} }, +/**/ {{0xf60ab1f4, 0x3fe050c7} }, +/**/ {{0xc6cf5796, 0x3c63f8e2} }, +/**/ {{0xfe998dc0, 0xbfd04ff7} }, +/**/ {{0x7dc56419, 0x3c77873c} }, +/**/ {{0x7cc24121, 0x3fb54ee0} }, +/**/ {{0x8e5c84c5, 0x3c313117} }, +/**/ {{0x50066301, 0x3f64fee1} }, +/**/ {{0x017261a1, 0x3c043698} }, +/**/ {{0x2cc5b4f1, 0xbf9c2c55} }, +/**/ {{0xf759f369, 0x3f9694bc} }, +/**/ {{0x6c93426a, 0xbf822ea4} }, +/**/ {{0x135d6c51, 0xbf45d0a1} }, +/**/ {{0xe62dc18f, 0x3f70d811} } }, +/**/ {{{0x00000000, 0x3fef8000} }, +/**/ {{0xa99cc05e, 0x3fe8e17a} }, +/**/ {{0xab042f61, 0xbc7ec182} }, +/**/ {{0xfbefe001, 0x3fe0407f} }, +/**/ {{0xfbf80041, 0x3c401ffe} }, +/**/ {{0xebd00209, 0xbfd03ffb} }, +/**/ {{0xb9004112, 0xbc53ff3c} }, +/**/ {{0x5aaf6d91, 0x3fb5513a} }, +/**/ {{0xc0516ddb, 0x3c54a20d} }, +/**/ {{0xc6ac4038, 0x3f60a27f} }, +/**/ {{0x2a340912, 0x3bf06bee} }, +/**/ {{0xccd6032a, 0xbf9ba597} }, +/**/ {{0x002bb974, 0x3f965508} }, +/**/ {{0xd2d1068b, 0xbf823860} }, +/**/ {{0x666265bc, 0xbf41277e} }, +/**/ {{0x656b66ea, 0x3f704cdc} } }, +/**/ {{{0x00000000, 0x3fefa000} }, +/**/ {{0x0c44f167, 0x3fe8f1b3} }, +/**/ {{0xb93933fd, 0x3c6dd1ca} }, +/**/ {{0xfeb82e4e, 0x3fe03047} }, +/**/ {{0x5272e5ac, 0x3c69ee56} }, +/**/ {{0x49a09c45, 0xbfd02ffe} }, +/**/ {{0xb26267bb, 0xbc700a59} }, +/**/ {{0xfc062d2f, 0x3fb55309} }, +/**/ {{0xb11938e0, 0x3c5dba48} }, +/**/ {{0xe4f365be, 0x3f58b61b} }, +/**/ {{0xa79ad31a, 0x3bf8b585} }, +/**/ {{0x08d4ad17, 0xbf9b2059} }, +/**/ {{0xfe379940, 0x3f961534} }, +/**/ {{0x62a1270e, 0xbf823fd2} }, +/**/ {{0x3f3a0aec, 0xbf394a53} }, +/**/ {{0xa04bcae2, 0x3f6f8842} } }, +/**/ {{{0x00000000, 0x3fefc000} }, +/**/ {{0x3eeef187, 0x3fe901db} }, +/**/ {{0xe5603c8f, 0x3c868665} }, +/**/ {{0xffbf7f80, 0x3fe0201f} }, +/**/ {{0xffbf7f80, 0x3c20201f} }, +/**/ {{0x7ebe8004, 0xbfd01fff} }, +/**/ {{0xcf979001, 0xbc4213ff} }, +/**/ {{0xfb0012db, 0x3fb55451} }, +/**/ {{0xf73aa59f, 0xbc395606} }, +/**/ {{0xfc757100, 0x3f50509f} }, +/**/ {{0xfee554d0, 0x3bebc7da} }, +/**/ {{0x7d3424d0, 0xbf9a9c99} }, +/**/ {{0xd5ac0217, 0x3f95d54b} }, +/**/ {{0x564b3c49, 0xbf82450c} }, +/**/ {{0xe6d3e986, 0xbf3091df} }, +/**/ {{0x3bef5a22, 0x3f6e7bc6} } }, +/**/ {{{0x00000000, 0x3fefe000} }, +/**/ {{0x5199833b, 0x3fe911f3} }, +/**/ {{0x0edbf522, 0x3c63ae8a} }, +/**/ {{0xfffbfbfe, 0x3fe01007} }, +/**/ {{0xfffbfbfe, 0x3ba01007} }, +/**/ {{0xefebf400, 0xbfd00fff} }, +/**/ {{0xfff9f97d, 0xbc401209} }, +/**/ {{0xea5aaaf6, 0x3fb55514} }, +/**/ {{0xb5b7b240, 0xbc529baa} }, +/**/ {{0xffc7abc4, 0x3f402827} }, +/**/ {{0xbfee6ab3, 0x3b5ba3d6} }, +/**/ {{0x97d67093, 0xbf9a1a59} }, +/**/ {{0x28080aaf, 0x3f959554} }, +/**/ {{0x8e892ce2, 0xbf824821} }, +/**/ {{0xfe70a2a6, 0xbf204877} }, +/**/ {{0x0e8ddd67, 0x3f6d7447} } }, +/**/ {{{0x00000000, 0x3feff800} }, +/**/ {{0xd439826e, 0x3fe91dfa} }, +/**/ {{0x6df48d55, 0xbc786a19} }, +/**/ {{0x7ffffbff, 0x3fe00400} }, +/**/ {{0xffbff800, 0xbbeffffe} }, +/**/ {{0xffbfebfd, 0xbfd003ff} }, +/**/ {{0x9ffff9fe, 0xbb600480} }, +/**/ {{0x53aa5aab, 0x3fb55551} }, +/**/ {{0x9baaab5b, 0xbc542a4a} }, +/**/ {{0x7fffc7eb, 0x3f200a02} }, +/**/ {{0x4770e940, 0xbb7dfffe} }, +/**/ {{0x9997d8d0, 0xbf99b9a5} }, +/**/ {{0x50a80a03, 0x3f956555} }, +/**/ {{0x86456493, 0xbf824914} }, +/**/ {{0x7ffe7329, 0xbf001207} }, +/**/ {{0x1c63fe2a, 0x3f6cb1ef} } }, + }; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/uexp.h b/REORG.TODO/sysdeps/ieee754/dbl-64/uexp.h new file mode 100644 index 0000000000..83f9b618f6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/uexp.h @@ -0,0 +1,69 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:uexp.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef UEXP_H +#define UEXP_H + +#include "mydefs.h" + +const static double zero = 0.0, hhuge = 1.0e300, tiny = 1.0e-300, +err_0 = 1.000014, err_1 = 0.000016; +const static int4 bigint = 0x40862002, + badint = 0x40876000,smallint = 0x3C8fffff; +const static int4 hugeint = 0x7FFFFFFF, infint = 0x7ff00000; + +#ifdef BIG_ENDI +const static mynumber inf = {{0x7FF00000, 0}}; /* inf */ +const static mynumber t256 = {{0x4ff00000, 0}}; /* 2^256 */ + +const static mynumber ln_two1 = {{0x3FE62E42, 0xFEFA3800}};/*0.69314718055989033 */ +const static mynumber ln_two2 = {{0x3D2EF357, 0x93C76730}};/*5.4979230187083712e-14*/ +const static mynumber log2e = {{0x3FF71547, 0x652B82FE}};/* 1.4426950408889634 */ + +const static mynumber p2 = {{0x3FE00000, 0x000004DC}};/* 0.50000000000013811 */ +const static mynumber p3 = {{0x3FC55555, 0x55555A0F}};/* 0.16666666666670024 */ + +const static mynumber three33 = {{0x42180000, 0}}; /* 25769803776 */ +const static mynumber three51 = {{0x43380000, 0}}; /* 6755399441055744 */ + +#else +#ifdef LITTLE_ENDI + const static mynumber inf = {{0, 0x7FF00000}}; /* inf */ + const static mynumber t256 = {{0, 0x4ff00000}}; /* 2^256 */ + + const static mynumber ln_two1 = {{0xFEFA3800, 0x3FE62E42}};/*0.69314718055989033 */ + const static mynumber ln_two2 = {{0x93C76730, 0x3D2EF357}};/*5.4979230187083712e-14*/ + const static mynumber log2e = {{0x652B82FE, 0x3FF71547}};/* 1.4426950408889634 */ + + const static mynumber p2 = {{0x000004DC, 0x3FE00000}};/* 0.50000000000013811 */ + const static mynumber p3 = {{0x55555A0F, 0x3FC55555}};/* 0.16666666666670024 */ + + const static mynumber three33 = {{0, 0x42180000}}; /* 25769803776 */ + const static mynumber three51 = {{0, 0x43380000}}; /* 6755399441055744 */ + +#endif +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/uexp.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/uexp.tbl new file mode 100644 index 0000000000..3e5fdc5783 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/uexp.tbl @@ -0,0 +1,1786 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE ulog() FUNCTION */ +/****************************************************************/ + +#ifdef BIG_ENDI + +static const union { + int i[1424]; + double x[712]; +} coar = { .i = { + 0x3FE69A59, 0xC8000000, 0x3DF22D4D, 0x6079C9F7, + 0x3FE6A5A9, 0xC8000000, 0x3E19882D, 0x25AF6823, + 0x3FE6B0FF, 0x74000000, 0xBE221476, 0x31DABF59, + 0x3FE6BC5A, 0xC8000000, 0x3E2312AC, 0x99A2DC0A, + 0x3FE6C7BB, 0xD0000000, 0xBE265926, 0xCE9F9355, + 0x3FE6D322, 0x84000000, 0x3E2F2C26, 0x2D298DED, + 0x3FE6DE8E, 0xF4000000, 0xBE2EC28E, 0x1E748D2F, + 0x3FE6EA01, 0x14000000, 0x3E2D8C6D, 0xC68CB7E5, + 0x3FE6F578, 0xF4000000, 0x3DEE1A9E, 0x419FE2F0, + 0x3FE700F6, 0x90000000, 0xBDFF1AFD, 0xDEAEAE34, + 0x3FE70C79, 0xEC000000, 0xBE0730FE, 0x558B7122, + 0x3FE71803, 0x0C000000, 0xBE25CB85, 0x2D280C3B, + 0x3FE72391, 0xF0000000, 0xBE06F2CE, 0x337B7B54, + 0x3FE72F26, 0x9C000000, 0x3E289BCA, 0x45C02B72, + 0x3FE73AC1, 0x18000000, 0xBE18DEA6, 0x5039F1CA, + 0x3FE74661, 0x60000000, 0xBE09D090, 0x86CE0538, + 0x3FE75207, 0x78000000, 0x3E290E79, 0xCFCE5DDB, + 0x3FE75DB3, 0x68000000, 0x3DD61DF0, 0xB249A17C, + 0x3FE76965, 0x2C000000, 0x3E2F22F7, 0xE13445F7, + 0x3FE7751C, 0xD0000000, 0xBE2CD454, 0x874E75CE, + 0x3FE780DA, 0x4C000000, 0xBE0159CE, 0xDF43E3BC, + 0x3FE78C9D, 0xA8000000, 0x3E279291, 0x699A1332, + 0x3FE79866, 0xEC000000, 0xBE2A0BCD, 0x2DD98C6C, + 0x3FE7A436, 0x10000000, 0x3E25F375, 0x15AC979E, + 0x3FE7B00B, 0x20000000, 0x3E26CCF5, 0x2FEAFCF6, + 0x3FE7BBE6, 0x1C000000, 0x3E27D4F4, 0x53ADAD67, + 0x3FE7C7C7, 0x08000000, 0x3E10EEC7, 0x7FBD9566, + 0x3FE7D3AD, 0xE4000000, 0x3E2837F0, 0x9A831D86, + 0x3FE7DF9A, 0xB8000000, 0xBE129BE0, 0x5CB4C35B, + 0x3FE7EB8D, 0x80000000, 0x3E23990A, 0x0234F04D, + 0x3FE7F786, 0x44000000, 0x3E2EB807, 0x64D5C842, + 0x3FE80385, 0x08000000, 0x3E0FC86F, 0x02B4E9E8, + 0x3FE80F89, 0xCC000000, 0xBDD7B5B3, 0x7B4274BF, + 0x3FE81B94, 0x94000000, 0xBE16888B, 0xB899B00F, + 0x3FE827A5, 0x60000000, 0x3E288971, 0x5E94D155, + 0x3FE833BC, 0x38000000, 0x3E2AEEB2, 0x099F3E5E, + 0x3FE83FD9, 0x20000000, 0xBE23B922, 0x3FF60B7C, + 0x3FE84BFC, 0x14000000, 0xBDF7D3B1, 0x2DBD8012, + 0x3FE85825, 0x1C000000, 0xBDF24BA3, 0xA8872BEB, + 0x3FE86454, 0x38000000, 0x3E2EFE04, 0x01AA18A7, + 0x3FE87089, 0x70000000, 0x3E21986C, 0x944496A2, + 0x3FE87CC4, 0xC4000000, 0x3E096A8B, 0xB71FFAFF, + 0x3FE88906, 0x38000000, 0xBE21CE0A, 0xBC4C7AC5, + 0x3FE8954D, 0xCC000000, 0xBE076F45, 0xBAC02491, + 0x3FE8A19B, 0x84000000, 0x3E2B4FA2, 0xD922B925, + 0x3FE8ADEF, 0x68000000, 0x3DF759DB, 0x641863AF, + 0x3FE8BA49, 0x78000000, 0xBE2DB97C, 0xC6AB5E04, + 0x3FE8C6A9, 0xB4000000, 0xBE25364C, 0xE2156713, + 0x3FE8D310, 0x20000000, 0x3E1BEB7C, 0x862BEFF7, + 0x3FE8DF7C, 0xC4000000, 0xBDF4DD0C, 0x1CEA33A5, + 0x3FE8EBEF, 0xA0000000, 0xBE2537DF, 0x51797D47, + 0x3FE8F868, 0xB4000000, 0x3E0FB1C4, 0xF0107B28, + 0x3FE904E8, 0x08000000, 0x3E0AD6A1, 0xE01B68BD, + 0x3FE9116D, 0x9C000000, 0x3E292117, 0x1F78D9D9, + 0x3FE91DF9, 0x78000000, 0xBE1D75DA, 0x4F50E5CF, + 0x3FE92A8B, 0x98000000, 0x3DE5102B, 0x74959E58, + 0x3FE93724, 0x04000000, 0xBE01CA50, 0xD2216C35, + 0x3FE943C2, 0xBC000000, 0x3E225BFD, 0xB0B05884, + 0x3FE95067, 0xC8000000, 0xBE0F2183, 0x60B7C5C1, + 0x3FE95D13, 0x24000000, 0x3E2FB47A, 0xB5860441, + 0x3FE969C4, 0xDC000000, 0xBE01FFD2, 0xE2D4059E, + 0x3FE9767C, 0xEC000000, 0xBDE9ED72, 0x12BB6A8D, + 0x3FE9833B, 0x58000000, 0x3E2B3815, 0x43BFFB24, + 0x3FE99000, 0x28000000, 0x3E03FA22, 0xEE9EAD1E, + 0x3FE99CCB, 0x5C000000, 0xBE213841, 0x377138F7, + 0x3FE9A99C, 0xF4000000, 0x3E178105, 0xDB636C94, + 0x3FE9B674, 0xF8000000, 0x3E1E5E7A, 0xF5720122, + 0x3FE9C353, 0x6C000000, 0xBE238BFF, 0xA2AC5AAE, + 0x3FE9D038, 0x4C000000, 0x3E270893, 0xF93BDBD8, + 0x3FE9DD23, 0xA4000000, 0x3DF40420, 0x354B86CF, + 0x3FE9EA15, 0x74000000, 0xBE2D76D3, 0x88CB06B7, + 0x3FE9F70D, 0xBC000000, 0xBE251639, 0x9ED0EC60, + 0x3FEA040C, 0x80000000, 0x3E1F06E9, 0xE2DDE506, + 0x3FEA1111, 0xC8000000, 0x3E014549, 0x8E6DB477, + 0x3FEA1E1D, 0x94000000, 0xBDF4BC17, 0xF8716509, + 0x3FEA2B2F, 0xE8000000, 0xBE2107DB, 0xDA723A49, + 0x3FEA3848, 0xC4000000, 0x3E1A932A, 0x986AA369, + 0x3FEA4568, 0x30000000, 0x3E198092, 0x41592CDB, + 0x3FEA528E, 0x30000000, 0xBE2E260F, 0x676BCAB8, + 0x3FEA5FBA, 0xC0000000, 0x3DE2E821, 0x2D5D5610, + 0x3FEA6CED, 0xE8000000, 0x3E2F7046, 0x7DA20167, + 0x3FEA7A27, 0xB0000000, 0xBE1D2832, 0xF9FAAD30, + 0x3FEA8768, 0x14000000, 0xBE23F788, 0x43FA6C45, + 0x3FEA94AF, 0x18000000, 0x3E011E27, 0xAA082732, + 0x3FEAA1FC, 0xC4000000, 0xBE20BACB, 0xC682F0BF, + 0x3FEAAF51, 0x18000000, 0xBE2DC7DD, 0x7BD08C78, + 0x3FEABCAC, 0x14000000, 0x3E2271A2, 0xA3B10F9A, + 0x3FEACA0D, 0xC4000000, 0xBE15449C, 0x7966F94C, + 0x3FEAD776, 0x24000000, 0x3DD06137, 0x6FD8F3EE, + 0x3FEAE4E5, 0x3C000000, 0xBE267CD1, 0x8C5A144A, + 0x3FEAF25B, 0x0C000000, 0xBE29E584, 0xB59DA94B, + 0x3FEAFFD7, 0x98000000, 0xBE23DFCF, 0x7B52192F, + 0x3FEB0D5A, 0xE4000000, 0xBE1CF2FE, 0x78A76B45, + 0x3FEB1AE4, 0xF4000000, 0xBE23A561, 0x7EC80FF6, + 0x3FEB2875, 0xC8000000, 0x3E22C4C9, 0x932EED68, + 0x3FEB360D, 0x68000000, 0x3E2B085C, 0xB5833C97, + 0x3FEB43AB, 0xD8000000, 0xBE01F093, 0x93B9319A, + 0x3FEB5151, 0x18000000, 0xBE254F01, 0xFABCE670, + 0x3FEB5EFD, 0x28000000, 0x3E2F24C2, 0x627ABFB0, + 0x3FEB6CB0, 0x14000000, 0x3E1F1EEC, 0xE6AC0B48, + 0x3FEB7A69, 0xDC000000, 0xBE1A8671, 0x127F9ABC, + 0x3FEB882A, 0x80000000, 0xBDCB0C28, 0xC87C73B3, + 0x3FEB95F2, 0x08000000, 0xBE22E8DD, 0x7F2B5A97, + 0x3FEBA3C0, 0x74000000, 0xBE1B3645, 0x2D22A9D5, + 0x3FEBB195, 0xC8000000, 0x3E0ADACA, 0x428F8B88, + 0x3FEBBF72, 0x0C000000, 0xBE2E9E07, 0xCDF9F681, + 0x3FEBCD55, 0x3C000000, 0xBE08A127, 0x7FA54ACF, + 0x3FEBDB3F, 0x60000000, 0x3E0E92CE, 0x8225B385, + 0x3FEBE930, 0x7C000000, 0x3DF38C2A, 0x7BB09485, + 0x3FEBF728, 0x94000000, 0xBE2DFD64, 0xF681FA5F, + 0x3FEC0527, 0xA4000000, 0x3E2E384D, 0xDCE88BD2, + 0x3FEC132D, 0xBC000000, 0xBE20F111, 0xFE46A893, + 0x3FEC213A, 0xD4000000, 0x3E193DA1, 0xB189BFDA, + 0x3FEC2F4E, 0xF8000000, 0xBE20E3A1, 0x0E39FB00, + 0x3FEC3D6A, 0x24000000, 0x3E1DB044, 0x30F0FAC5, + 0x3FEC4B8C, 0x64000000, 0xBE2BC12C, 0x97446B17, + 0x3FEC59B5, 0xB4000000, 0xBE282696, 0x963F4150, + 0x3FEC67E6, 0x18000000, 0x3E224D26, 0x3049824B, + 0x3FEC761D, 0x98000000, 0x3E2C5BA5, 0x87F84C7D, + 0x3FEC845C, 0x38000000, 0xBDE1D14D, 0xC4852339, + 0x3FEC92A1, 0xF8000000, 0xBE1A451E, 0x5588D9E1, + 0x3FECA0EE, 0xDC000000, 0xBE1D3B96, 0x68BFF457, + 0x3FECAF42, 0xE8000000, 0xBE18B670, 0x4DADF774, + 0x3FECBD9E, 0x20000000, 0xBE1A1548, 0x7FB1FC01, + 0x3FECCC00, 0x88000000, 0xBE273F2E, 0x78FC5AF0, + 0x3FECDA6A, 0x20000000, 0x3E1D218F, 0xA6F4A841, + 0x3FECE8DA, 0xF0000000, 0x3E2E0BA9, 0x4D002CA0, + 0x3FECF752, 0xFC000000, 0x3E20F4BB, 0x065EF979, + 0x3FED05D2, 0x48000000, 0xBE2ED3D5, 0x11793B33, + 0x3FED1458, 0xD0000000, 0x3E115E3C, 0x913341B3, + 0x3FED22E6, 0xA0000000, 0x3DE97C02, 0xB3546109, + 0x3FED317B, 0xB8000000, 0x3E087540, 0x1BF898EF, + 0x3FED4018, 0x1C000000, 0x3E209430, 0x346F9641, + 0x3FED4EBB, 0xD0000000, 0x3E2B6DF4, 0x88F4B20B, + 0x3FED5D66, 0xDC000000, 0xBE2EC68F, 0x0CB26035, + 0x3FED6C19, 0x38000000, 0x3E2CA2C8, 0x1F44D9C3, + 0x3FED7AD2, 0xF4000000, 0x3E10E6F4, 0x41704EE0, + 0x3FED8994, 0x0C000000, 0x3E2F9273, 0x25F8F0E2, + 0x3FED985C, 0x88000000, 0x3E2D041A, 0x318798DE, + 0x3FEDA72C, 0x6C000000, 0xBE005680, 0x9349CF58, + 0x3FEDB603, 0xB8000000, 0xBE10F665, 0xCF0C934D, + 0x3FEDC4E2, 0x70000000, 0x3E166124, 0x19461C64, + 0x3FEDD3C8, 0x9C000000, 0xBE1B2ED6, 0x405624C8, + 0x3FEDE2B6, 0x3C000000, 0xBE273A7F, 0x62171501, + 0x3FEDF1AB, 0x54000000, 0xBE26022B, 0xE36E1450, + 0x3FEE00A7, 0xE8000000, 0xBE1C341E, 0x2E07AE15, + 0x3FEE0FAB, 0xFC000000, 0xBDFC7EAE, 0x18D0E701, + 0x3FEE1EB7, 0x94000000, 0x3E06B34F, 0xECD1FF8B, + 0x3FEE2DCA, 0xB4000000, 0x3E1394A3, 0x6813A649, + 0x3FEE3CE5, 0x60000000, 0x3E045496, 0xC1754D14, + 0x3FEE4C07, 0x9C000000, 0xBE180FFF, 0xF5C6087C, + 0x3FEE5B31, 0x68000000, 0x3E22FBCD, 0xADD9A300, + 0x3FEE6A62, 0xCC000000, 0x3E2EC7C7, 0xAF0289E5, + 0x3FEE799B, 0xCC000000, 0x3E242182, 0x3FB3EDD4, + 0x3FEE88DC, 0x6C000000, 0xBE201304, 0x04E39885, + 0x3FEE9824, 0xAC000000, 0xBE20D352, 0xE6831D31, + 0x3FEEA774, 0x90000000, 0x3E1E032D, 0x618DFCEB, + 0x3FEEB6CC, 0x20000000, 0x3E1956A3, 0xF9BB457E, + 0x3FEEC62B, 0x60000000, 0xBE2A77E0, 0x50845DB2, + 0x3FEED592, 0x4C000000, 0x3E2714F7, 0x47C43858, + 0x3FEEE500, 0xF0000000, 0x3E2EED96, 0x71813A66, + 0x3FEEF477, 0x50000000, 0xBE04CDBE, 0x4FB4AA34, + 0x3FEF03F5, 0x6C000000, 0xBE2774A2, 0x86EB4FF5, + 0x3FEF137B, 0x48000000, 0xBE29DD95, 0xAD43B2D2, + 0x3FEF2308, 0xE8000000, 0xBE1CADB0, 0xAC16E506, + 0x3FEF329E, 0x50000000, 0x3E12AC33, 0x58745C7B, + 0x3FEF423B, 0x88000000, 0xBE248118, 0x6EC2D854, + 0x3FEF51E0, 0x8C000000, 0x3E26986B, 0x304ACE08, + 0x3FEF618D, 0x68000000, 0x3E126D81, 0x3B09354E, + 0x3FEF7142, 0x1C000000, 0x3DF06AAE, 0x773C23B3, + 0x3FEF80FE, 0xAC000000, 0xBDA105B6, 0xD82EF423, + 0x3FEF90C3, 0x1C000000, 0x3DECDEED, 0x465499B8, + 0x3FEFA08F, 0x70000000, 0x3E0AEFD4, 0xE2EF03AE, + 0x3FEFB063, 0xAC000000, 0x3E1BD4C0, 0x0567B2E7, + 0x3FEFC03F, 0xD4000000, 0x3E26AA22, 0x4F97FCBF, + 0x3FEFD023, 0xF0000000, 0xBE2F9420, 0x5E4E88D1, + 0x3FEFE00F, 0xFC000000, 0xBE254004, 0x438E52E2, + 0x3FEFF004, 0x00000000, 0xBE1552AA, 0xEEE93EFC, + 0x3FF00000, 0x00000000, 0x00000000, 0x00000000, + 0x3FF00802, 0x00000000, 0x3E155800, 0x4449F507, + 0x3FF01008, 0x04000000, 0xBE354AA8, 0x882D75D6, + 0x3FF01812, 0x08000000, 0x3E303610, 0x3740DE56, + 0x3FF02020, 0x14000000, 0x3E360044, 0x5B0C3264, + 0x3FF02832, 0x28000000, 0x3E3C4C26, 0x0197EDC3, + 0x3FF03048, 0x48000000, 0x3E0B103B, 0x5046CA09, + 0x3FF03862, 0x74000000, 0xBE34659C, 0xF9A62624, + 0x3FF04080, 0xAC000000, 0xBE254438, 0xDD0A8F37, + 0x3FF048A2, 0xF4000000, 0x3DF256C2, 0x97AFB6E2, + 0x3FF050C9, 0x50000000, 0xBE3085DF, 0x923D25E1, + 0x3FF058F3, 0xC0000000, 0xBE3F0A93, 0x5EA3B091, + 0x3FF06122, 0x44000000, 0xBE237DE4, 0x5D63534C, + 0x3FF06954, 0xE0000000, 0x3E301719, 0xFF0C58B7, + 0x3FF0718B, 0x98000000, 0x3E2E8410, 0x9DF7B665, + 0x3FF079C6, 0x6C000000, 0x3E349CB9, 0x3B127222, + 0x3FF08205, 0x60000000, 0x3DF127EC, 0x98E0BD08, + 0x3FF08A48, 0x74000000, 0xBE24C1B6, 0x706CC41F, + 0x3FF0928F, 0xA8000000, 0x3E334EF9, 0x093044EF, + 0x3FF09ADB, 0x04000000, 0xBE1304B1, 0x56BC6C83, + 0x3FF0A32A, 0x84000000, 0x3E2D383E, 0xB028B984, + 0x3FF0AB7E, 0x30000000, 0xBE315B1E, 0x64E7A202, + 0x3FF0B3D6, 0x04000000, 0xBE0AC1E6, 0xC678291E, + 0x3FF0BC32, 0x04000000, 0x3E3A0418, 0x2F12FFE2, + 0x3FF0C492, 0x38000000, 0xBE37D617, 0x43D6D302, + 0x3FF0CCF6, 0x98000000, 0x3E2133F2, 0x152CC8FA, + 0x3FF0D55F, 0x2C000000, 0x3E3CE5D1, 0xE966E6B7, + 0x3FF0DDCB, 0xF8000000, 0x3E1ABF24, 0x7BCACA64, + 0x3FF0E63C, 0xFC000000, 0xBE3854F6, 0x2E8CDBED, + 0x3FF0EEB2, 0x38000000, 0xBE3E6463, 0x0C32156B, + 0x3FF0F72B, 0xAC000000, 0x3E365671, 0xB69772CC, + 0x3FF0FFA9, 0x64000000, 0xBE383E9A, 0x02B1201A, + 0x3FF1082B, 0x58000000, 0xBE205962, 0x50549CC0, + 0x3FF110B1, 0x90000000, 0xBE376BFE, 0xFFDACA72, + 0x3FF1193C, 0x08000000, 0x3E3C1C59, 0x5C43E2F3, + 0x3FF121CA, 0xCC000000, 0xBE26D374, 0xF7067C8B, + 0x3FF12A5D, 0xD4000000, 0x3E343CCC, 0x4DDAFE1D, + 0x3FF132F5, 0x28000000, 0x3E3D5C16, 0x58EBCB7F, + 0x3FF13B90, 0xCC000000, 0xBE2B5D12, 0xB66E8B53, + 0x3FF14430, 0xBC000000, 0xBE24E919, 0xB326B482, + 0x3FF14CD4, 0xFC000000, 0x3E23139A, 0xC8AABD43, + 0x3FF1557D, 0x90000000, 0x3E30DD8B, 0x16743B55, + 0x3FF15E2A, 0x7C000000, 0xBE31D701, 0x35904C50, + 0x3FF166DB, 0xBC000000, 0x3E107F42, 0x30E0CA83, + 0x3FF16F91, 0x58000000, 0xBE24F1F2, 0xDA1B7123, + 0x3FF1784B, 0x50000000, 0xBE3ACAF2, 0x0DC79E23, + 0x3FF18109, 0xA4000000, 0xBE23DC79, 0x609374EE, + 0x3FF189CC, 0x58000000, 0x3E262CF7, 0x3A40C3B7, + 0x3FF19293, 0x70000000, 0x3E1D3833, 0x5A24F463, + 0x3FF19B5E, 0xEC000000, 0x3E2BA9AD, 0x8A2E4440, + 0x3FF1A42E, 0xD0000000, 0x3DFD8CBC, 0x61C41828, + 0x3FF1AD03, 0x1C000000, 0x3E1A65E6, 0x5A4DDF0D, + 0x3FF1B5DB, 0xD4000000, 0xBDE2FDBB, 0x9F828DB5, + 0x3FF1BEB8, 0xF8000000, 0x3E2F4EE8, 0xB79B700F, + 0x3FF1C79A, 0x8C000000, 0x3E3ACC35, 0x0DE1D7E8, + 0x3FF1D080, 0x94000000, 0x3E11729E, 0xFF9E20A0, + 0x3FF1D96B, 0x10000000, 0xBE300F18, 0x6C2EA70B, + 0x3FF1E25A, 0x00000000, 0x3DF32E02, 0xCE425A35, + 0x3FF1EB4D, 0x68000000, 0x3E3BDE56, 0x9A322D12, + 0x3FF1F445, 0x50000000, 0xBE3C3F0D, 0xBA737AEF, + 0x3FF1FD41, 0xB0000000, 0xBE0A2DD0, 0xC896DB7A, + 0x3FF20642, 0x90000000, 0x3E2577B0, 0xF8B782F6, + 0x3FF20F47, 0xF4000000, 0xBE2C6DA3, 0x73607FC8, + 0x3FF21851, 0xD8000000, 0x3E35F7D1, 0xC8917348, + 0x3FF22160, 0x44000000, 0x3E3B6F5C, 0xCF9CED69, + 0x3FF22A73, 0x3C000000, 0xBE39967E, 0x85775C2E, + 0x3FF2338A, 0xB8000000, 0x3E3B3213, 0x497226D4, + 0x3FF23CA6, 0xC4000000, 0x3E3E2710, 0x30733227, + 0x3FF245C7, 0x60000000, 0x3E33B8A9, 0xAF215A72, + 0x3FF24EEC, 0x90000000, 0xBE3F96B2, 0x1365623F, + 0x3FF25816, 0x50000000, 0xBE37324F, 0x27DEE202, + 0x3FF26144, 0xA4000000, 0x3E318CD5, 0x4E484D87, + 0x3FF26A77, 0x94000000, 0xBDE3FD37, 0xA94519E8, + 0x3FF273AF, 0x1C000000, 0x3E37132F, 0xEE788C29, + 0x3FF27CEB, 0x44000000, 0xBE03DDB7, 0xE842E5C0, + 0x3FF2862C, 0x08000000, 0x3E37A3FB, 0xE17C9693, + 0x3FF28F71, 0x70000000, 0x3E24EABF, 0xAEB3D9A0, + 0x3FF298BB, 0x7C000000, 0xBE13C7B6, 0x853B0733, + 0x3FF2A20A, 0x2C000000, 0x3E2D2C80, 0xC7B588B5, + 0x3FF2AB5D, 0x88000000, 0xBE35B750, 0x708F3912, + 0x3FF2B4B5, 0x8C000000, 0xBE291A70, 0xD5FD9130, + 0x3FF2BE12, 0x3C000000, 0x3E2EE937, 0x0CCF9F73, + 0x3FF2C773, 0xA0000000, 0xBE3C3F0C, 0xD42CF76C, + 0x3FF2D0D9, 0xB0000000, 0x3E35DD54, 0x60763D61, + 0x3FF2DA44, 0x78000000, 0x3E26C418, 0xE7D6AA3B, + 0x3FF2E3B3, 0xF8000000, 0xBE3605C6, 0x6FB9B7A8, + 0x3FF2ED28, 0x2C000000, 0x3E3763D4, 0x24DCDDF5, + 0x3FF2F6A1, 0x20000000, 0xBE1A411E, 0xA8EC1AA8, + 0x3FF3001E, 0xD0000000, 0xBE23FCA1, 0x1FE8546F, + 0x3FF309A1, 0x40000000, 0xBE29DF0D, 0x3AAEE75E, + 0x3FF31328, 0x70000000, 0x3E36A5D6, 0x3C2C4206, + 0x3FF31CB4, 0x68000000, 0x3E1B7A3E, 0xB4C979B0, + 0x3FF32645, 0x28000000, 0xBE36157D, 0x706CD593, + 0x3FF32FDA, 0xB0000000, 0xBE39F357, 0x8DA4C646, + 0x3FF33975, 0x04000000, 0xBE3E64DE, 0xD575FE6F, + 0x3FF34314, 0x24000000, 0x3E07F9E3, 0x44D008E0, + 0x3FF34CB8, 0x18000000, 0xBE2E94F9, 0x5A563E77, + 0x3FF35660, 0xDC000000, 0x3E314DC2, 0x2475EF19, + 0x3FF3600E, 0x78000000, 0x3E26D623, 0xA33AC606, + 0x3FF369C0, 0xEC000000, 0x3E170F86, 0xC05B3160, + 0x3FF37378, 0x3C000000, 0xBE38DDFE, 0xDB0AE31A, + 0x3FF37D34, 0x64000000, 0x3E3662A9, 0x5706B570, + 0x3FF386F5, 0x70000000, 0xBE1625E4, 0x6770731E, + 0x3FF390BB, 0x5C000000, 0xBE1678F1, 0x62971091, + 0x3FF39A86, 0x2C000000, 0xBE061F7C, 0xD045CB0C, + 0x3FF3A455, 0xE4000000, 0xBE35CF51, 0x568B1CA2, + 0x3FF3AE2A, 0x84000000, 0xBE378185, 0x7FB61F58, + 0x3FF3B804, 0x0C000000, 0x3E3F77F4, 0x4FA133AF, + 0x3FF3C1E2, 0x88000000, 0xBE22F96A, 0xB00B73FE, + 0x3FF3CBC5, 0xF0000000, 0x3E351A64, 0x1EB4CE2F, + 0x3FF3D5AE, 0x50000000, 0xBE3D3516, 0xD3755639, + 0x3FF3DF9B, 0xA0000000, 0x3E1CD938, 0x43E8C10E, + 0x3FF3E98D, 0xEC000000, 0xBE35EE23, 0x455C8842, + 0x3FF3F385, 0x30000000, 0xBE29B282, 0x96C9F4ED, + 0x3FF3FD81, 0x70000000, 0x3E24A40E, 0x3168CC0B, + 0x3FF40782, 0xB0000000, 0x3E3784BC, 0x86C72839, + 0x3FF41188, 0xF4000000, 0x3E061F19, 0x0785D847, + 0x3FF41B94, 0x3C000000, 0xBE27AEF2, 0xE654A9C9, + 0x3FF425A4, 0x88000000, 0x3E33DFC3, 0xF9E4C1BA, + 0x3FF42FB9, 0xE0000000, 0x3E2455A8, 0x593D0C75, + 0x3FF439D4, 0x44000000, 0xBDE41D4E, 0x238B65D1, + 0x3FF443F3, 0xB4000000, 0x3E3BE616, 0x454CBECB, + 0x3FF44E18, 0x38000000, 0x3E207B3C, 0x931C5332, + 0x3FF45841, 0xD0000000, 0xBE330846, 0x7615DCC9, + 0x3FF46270, 0x7C000000, 0xBE2A8A7B, 0xE497F84E, + 0x3FF46CA4, 0x40000000, 0x3E020B50, 0xF737AF78, + 0x3FF476DD, 0x20000000, 0x3E116B19, 0xE34AFBD3, + 0x3FF4811B, 0x20000000, 0xBE3E15A7, 0x841EDB52, + 0x3FF48B5E, 0x3C000000, 0x3E0F40C3, 0x33B3DE1E, + 0x3FF495A6, 0x7C000000, 0x3E33607F, 0x92EFEE02, + 0x3FF49FF3, 0xE4000000, 0xBE1A2DB5, 0x14F7E168, + 0x3FF4AA46, 0x70000000, 0x3E3F59EC, 0x3EBA1C94, + 0x3FF4B49E, 0x2C000000, 0xBE31A539, 0x8B9AE885, + 0x3FF4BEFB, 0x10000000, 0x3E2FAC0B, 0xF13C8C95, + 0x3FF4C95D, 0x28000000, 0xBE32C0BB, 0xF8B74775, + 0x3FF4D3C4, 0x70000000, 0xBE2FC24E, 0x4F9474BB, + 0x3FF4DE30, 0xEC000000, 0x3E008F30, 0x09DA911F, + 0x3FF4E8A2, 0xA0000000, 0x3E2994C1, 0xBAF8D98B, + 0x3FF4F319, 0x90000000, 0xBE17C38C, 0x18648D0A, + 0x3FF4FD95, 0xBC000000, 0xBE288852, 0xF22F8698, + 0x3FF50817, 0x28000000, 0xBE3C3EC3, 0x30A2C153, + 0x3FF5129D, 0xD4000000, 0xBE27B606, 0x968492AA, + 0x3FF51D29, 0xC4000000, 0x3E2E0396, 0x61101629, + 0x3FF527BA, 0xFC000000, 0x3E3E876F, 0xDAEEAB38, + 0x3FF53251, 0x80000000, 0x3E29F59E, 0xED945B30, + 0x3FF53CED, 0x50000000, 0x3E12D7DA, 0x0B4AE3F1, + 0x3FF5478E, 0x70000000, 0xBE2FAFB8, 0x5FB946D0, + 0x3FF55234, 0xE0000000, 0xBE18A8B3, 0x87D80C66, + 0x3FF55CE0, 0xA4000000, 0x3E28B18F, 0x764CF85C, + 0x3FF56791, 0xC0000000, 0x3E326017, 0x2BDBC6F4, + 0x3FF57248, 0x38000000, 0xBE229F98, 0x53D523FE, + 0x3FF57D04, 0x0C000000, 0xBE3BDD08, 0x4D9B8720, + 0x3FF587C5, 0x3C000000, 0x3E169EBC, 0x09D8749E, + 0x3FF5928B, 0xD0000000, 0x3E190C8C, 0x339C2080, + 0x3FF59D57, 0xC8000000, 0x3E310FA4, 0xDE75E9CA, + 0x3FF5A829, 0x28000000, 0x3E313D18, 0x1097F186, + 0x3FF5B2FF, 0xF4000000, 0xBE2BDE04, 0xD51C23F6, + 0x3FF5BDDC, 0x28000000, 0x3E3EE67E, 0x8938C386, + 0x3FF5C8BD, 0xD0000000, 0x3E0973B8, 0x47DF6575, + 0x3FF5D3A4, 0xE8000000, 0x3E24DF02, 0x1DB97781, + 0x3FF5DE91, 0x78000000, 0xBE3FBA00, 0xAC4AECDC, + 0x3FF5E983, 0x7C000000, 0xBE2F37AF, 0x939F646A, + 0x3FF5F47A, 0xFC000000, 0xBE396DEF, 0x58A6EEE9, + 0x3FF5FF77, 0xF8000000, 0xBE315248, 0xE3613C7B, + 0x3FF60A7A, 0x74000000, 0xBE26A9E2, 0xF1553706, + 0x3FF61582, 0x74000000, 0xBE3B6BF6, 0xAE4D7CB6, + 0x3FF6208F, 0xF8000000, 0xBE35775B, 0x9EB5EBA5, + 0x3FF62BA3, 0x04000000, 0xBE2A821B, 0xC1E43506, + 0x3FF636BB, 0x9C000000, 0xBE367CDA, 0x7B2D8CF4, + 0x3FF641D9, 0xC0000000, 0xBE13218B, 0x3E907A1D, + 0x3FF64CFD, 0x74000000, 0x3E3454EE, 0x7BF5DFE4, + 0x3FF65826, 0xC0000000, 0xBE3E960F, 0x6366C5FD, + 0x3FF66355, 0x9C000000, 0x3E2E378F, 0x8B43C17E, + 0x3FF66E8A, 0x14000000, 0x3E244BE0, 0xA4306535, + 0x3FF679C4, 0x28000000, 0xBDE4B6C1, 0x8DF63D6E, + 0x3FF68503, 0xD8000000, 0x3E3BA122, 0xE6A239CF, + 0x3FF69049, 0x2C000000, 0x3E27F286, 0x59FB5F30, + 0x3FF69B94, 0x24000000, 0xBE044041, 0x971D3970 } }; + +static const union { + int4 i[2048]; + double x[1024]; +} fine = { .i = { + 0x3FF00000, 0x00000000, 0x00000000, 0x00000000, + 0x3FF00004, 0x00000000, 0x3DA00001, 0x55556AAB, + 0x3FF00008, 0x00000000, 0x3DC00002, 0xAAAB0000, + 0x3FF0000C, 0x00000000, 0x3DD20004, 0x8000D800, + 0x3FF00010, 0x00000000, 0x3DE00005, 0x5556AAAB, + 0x3FF00014, 0x00000000, 0x3DE9000A, 0x6AADEC01, + 0x3FF00018, 0x00000000, 0x3DF20009, 0x00036001, + 0x3FF0001C, 0x00000000, 0x3DF8800E, 0x4AB0EB58, + 0x3FF00020, 0x00000000, 0x3E00000A, 0xAAB00002, + 0x3FF00024, 0x00000000, 0x3E04400F, 0x30088B04, + 0x3FF00028, 0x00000000, 0x3E090014, 0xD5625AB1, + 0x3FF0002C, 0x00000000, 0x3E0E401B, 0xBABDBB0A, + 0x3FF00030, 0x00000000, 0x3E120012, 0x000D8008, + 0x3FF00034, 0x00000000, 0x3E152016, 0xE2BD42E1, + 0x3FF00038, 0x00000000, 0x3E18801C, 0x956E5812, + 0x3FF0003C, 0x00000000, 0x3E1C2023, 0x2820F599, + 0x3FF00040, 0x00000000, 0x3E200015, 0x556AAABC, + 0x3FF00044, 0x00000000, 0x3E221019, 0x96C5DAD7, + 0x3FF00048, 0x00000000, 0x3E24401E, 0x60222C1F, + 0x3FF0004C, 0x00000000, 0x3E269023, 0xB97FC193, + 0x3FF00050, 0x00000000, 0x3E290029, 0xAADEC034, + 0x3FF00054, 0x00000000, 0x3E2B9030, 0x3C3F4F02, + 0x3FF00058, 0x00000000, 0x3E2E4037, 0x75A196FF, + 0x3FF0005C, 0x00000000, 0x3E30881F, 0xAF82E194, + 0x3FF00060, 0x00000000, 0x3E320024, 0x00360041, + 0x3FF00064, 0x00000000, 0x3E338828, 0xB0EA3F05, + 0x3FF00068, 0x00000000, 0x3E35202D, 0xC59FB661, + 0x3FF0006C, 0x00000000, 0x3E36C833, 0x42567FD5, + 0x3FF00070, 0x00000000, 0x3E388039, 0x2B0EB5E1, + 0x3FF00074, 0x00000000, 0x3E3A483F, 0x83C87407, + 0x3FF00078, 0x00000000, 0x3E3C2046, 0x5083D6C6, + 0x3FF0007C, 0x00000000, 0x3E3E084D, 0x9540FB9E, + 0x3FF00080, 0x04000000, 0xBE3FFFAA, 0xA9FFFEEF, + 0x3FF00084, 0x04000000, 0xBE3DF7A2, 0x693EF962, + 0x3FF00088, 0x04000000, 0xBE3BDF99, 0xA47BD339, + 0x3FF0008C, 0x04000000, 0xBE39B790, 0x57B66AF5, + 0x3FF00090, 0x04000000, 0xBE377F86, 0x7EEE9E14, + 0x3FF00094, 0x04000000, 0xBE35377C, 0x16244916, + 0x3FF00098, 0x04000000, 0xBE32DF71, 0x1957477B, + 0x3FF0009C, 0x04000000, 0xBE307765, 0x848773C2, + 0x3FF000A0, 0x04000000, 0xBE2BFEB2, 0xA7694ED3, + 0x3FF000A4, 0x04000000, 0xBE26EE99, 0x05BD75E2, + 0x3FF000A8, 0x04000000, 0xBE21BE7E, 0x1C0B0BB1, + 0x3FF000AC, 0x04000000, 0xBE18DCC3, 0xC4A37A79, + 0x3FF000B0, 0x04000000, 0xBE0BF911, 0x4244D60F, + 0x3FF000B4, 0x04000000, 0xBDE6E255, 0xEC91D848, + 0x3FF000B8, 0x04000000, 0x3E0107EB, 0xEC1B8F0C, + 0x3FF000BC, 0x04000000, 0x3E142439, 0x89BE52AA, + 0x3FF000C0, 0x04000000, 0x3E200240, 0x06C01033, + 0x3FF000C4, 0x04000000, 0x3E261264, 0xC8A9F760, + 0x3FF000C8, 0x04000000, 0x3E2C428B, 0x129D3FDE, + 0x3FF000CC, 0x04000000, 0x3E314959, 0x764D2658, + 0x3FF000D0, 0x04000000, 0x3E34816E, 0x2F50C16C, + 0x3FF000D4, 0x04000000, 0x3E37C983, 0xB859A4AB, + 0x3FF000D8, 0x04000000, 0x3E3B219A, 0x15680499, + 0x3FF000DC, 0x04000000, 0x3E3E89B1, 0x4A7C16B5, + 0x3FF000E0, 0x08000000, 0xBE3DFE36, 0xA469EE7E, + 0x3FF000E4, 0x08000000, 0xBE3A761D, 0xB349D37F, + 0x3FF000E8, 0x08000000, 0xBE36DE03, 0xDE235FCD, + 0x3FF000EC, 0x08000000, 0xBE3335E9, 0x20F659E6, + 0x3FF000F0, 0x08000000, 0xBE2EFB9A, 0xEF850E8F, + 0x3FF000F4, 0x08000000, 0xBE276B61, 0xBD0F58E2, + 0x3FF000F8, 0x08000000, 0xBE1F764D, 0x45163381, + 0x3FF000FC, 0x08000000, 0xBE0FABA6, 0x5FDF589A, + 0x3FF00100, 0x08000000, 0x3D8555AA, 0xABBBBE94, + 0x3FF00104, 0x08000000, 0x3E102B2C, 0xDABB690B, + 0x3FF00108, 0x08000000, 0x3E2045D9, 0x7820FBA0, + 0x3FF0010C, 0x08000000, 0x3E28961E, 0x92F54742, + 0x3FF00110, 0x08000000, 0x3E308332, 0xE2ED8E39, + 0x3FF00114, 0x08000000, 0x3E34CB57, 0x8C698119, + 0x3FF00118, 0x08000000, 0x3E39237D, 0x49EEC0C4, + 0x3FF0011C, 0x08000000, 0x3E3D8BA4, 0x1F7D92BC, + 0x3FF00120, 0x0C000000, 0xBE3DFC33, 0xEEE9C27D, + 0x3FF00124, 0x0C000000, 0xBE39740A, 0xDD46F763, + 0x3FF00128, 0x0C000000, 0xBE34DBE0, 0xA799C375, + 0x3FF0012C, 0x0C000000, 0xBE3033B5, 0x49E1DD2F, + 0x3FF00130, 0x0C000000, 0xBE26F711, 0x803DF41F, + 0x3FF00134, 0x0C000000, 0xBE1ACD6C, 0x19433A4C, + 0x3FF00138, 0x0C000000, 0xBDFDB2C1, 0x8770E36F, + 0x3FF0013C, 0x0C000000, 0x3E086820, 0x6B74A43E, + 0x3FF00140, 0x0C000000, 0x3E200A6A, 0xDEC0D058, + 0x3FF00144, 0x0C000000, 0x3E2A1AD0, 0x22BD7872, + 0x3FF00148, 0x0C000000, 0x3E32259B, 0xF769E132, + 0x3FF0014C, 0x0C000000, 0x3E374DD1, 0x2582289A, + 0x3FF00150, 0x0C000000, 0x3E3C8607, 0x9FA7E4F4, + 0x3FF00154, 0x10000000, 0xBE3E31C0, 0x9624963C, + 0x3FF00158, 0x10000000, 0xBE38D987, 0x77E2F472, + 0x3FF0015C, 0x10000000, 0xBE33714D, 0x0192E02C, + 0x3FF00160, 0x10000000, 0xBE2BF222, 0x5E6805CB, + 0x3FF00164, 0x10000000, 0xBE20E1A7, 0xF98C0A34, + 0x3FF00168, 0x10000000, 0xBE06C4AB, 0x32447238, + 0x3FF0016C, 0x10000000, 0x3E067D54, 0xC225D8C1, + 0x3FF00170, 0x10000000, 0x3E210FD8, 0x05C4630F, + 0x3FF00174, 0x10000000, 0x3E2CA05D, 0xBB206115, + 0x3FF00178, 0x10000000, 0x3E342873, 0x2C4F14A6, + 0x3FF0017C, 0x10000000, 0x3E3A10B8, 0xF31F3B5E, + 0x3FF00180, 0x14000000, 0xBE3FF6FF, 0xC9FEFCC9, + 0x3FF00184, 0x14000000, 0xBE39EEB7, 0x070B344A, + 0x3FF00188, 0x14000000, 0xBE33D66C, 0xC0050AA2, + 0x3FF0018C, 0x14000000, 0xBE2B5C41, 0xE1D83C97, + 0x3FF00190, 0x14000000, 0xBE1DD74E, 0x57003305, + 0x3FF00194, 0x14000000, 0xBDF2D84A, 0xA80727F1, + 0x3FF00198, 0x14000000, 0x3E14AB2F, 0x534C5401, + 0x3FF0019C, 0x14000000, 0x3E27263B, 0xD875DE83, + 0x3FF001A0, 0x14000000, 0x3E320B71, 0x9FB782CA, + 0x3FF001A4, 0x14000000, 0x3E3893C6, 0xF349371F, + 0x3FF001A8, 0x14000000, 0x3E3F2C1D, 0xEAF074C6, + 0x3FF001AC, 0x18000000, 0xBE3A2B89, 0x75525ABC, + 0x3FF001B0, 0x18000000, 0xBE33732F, 0x297ECCE2, + 0x3FF001B4, 0x18000000, 0xBE2955A6, 0x5B28EC49, + 0x3FF001B8, 0x18000000, 0xBE1749D5, 0xF64BA7FD, + 0x3FF001BC, 0x18000000, 0x3DF15E9E, 0xA8645141, + 0x3FF001C0, 0x18000000, 0x3E201C96, 0x1D6F0B37, + 0x3FF001C4, 0x18000000, 0x3E2E2D5B, 0xE6028E39, + 0x3FF001C8, 0x18000000, 0x3E362F12, 0x9B63FA1E, + 0x3FF001CC, 0x18000000, 0x3E3D5779, 0x0BE01026, + 0x3FF001D0, 0x1C000000, 0xBE3B701E, 0xB78A0445, + 0x3FF001D4, 0x1C000000, 0xBE3427B4, 0xAAD9CF9D, + 0x3FF001D8, 0x1C000000, 0xBE299E91, 0x941DBAB5, + 0x3FF001DC, 0x1C000000, 0xBE159B6C, 0x44A2DFDD, + 0x3FF001E0, 0x1C000000, 0x3E008CA4, 0x1EC8B89C, + 0x3FF001E4, 0x1C000000, 0x3E23340B, 0xF1EE0E9A, + 0x3FF001E8, 0x1C000000, 0x3E313279, 0x5231913C, + 0x3FF001EC, 0x1C000000, 0x3E38DAEE, 0x93892E68, + 0x3FF001F0, 0x20000000, 0xBE3F6C9A, 0x3F01A6A8, + 0x3FF001F4, 0x20000000, 0xBE37A421, 0x216E726C, + 0x3FF001F8, 0x20000000, 0xBE2F974C, 0x1F7970B9, + 0x3FF001FC, 0x20000000, 0xBE1F8CA4, 0x17AFEBC8, + 0x3FF00200, 0x20000000, 0x3DB55600, 0x04445B06, + 0x3FF00204, 0x20000000, 0x3E203BAE, 0x0C290A26, + 0x3FF00208, 0x20000000, 0x3E30365A, 0x104547BD, + 0x3FF0020C, 0x20000000, 0x3E385EDF, 0x22970DE3, + 0x3FF00210, 0x24000000, 0xBE3F6899, 0xBEF5A5F4, + 0x3FF00214, 0x24000000, 0xBE372010, 0x90605040, + 0x3FF00218, 0x24000000, 0xBE2D8F0A, 0x9B50D8EE, + 0x3FF0021C, 0x24000000, 0xBE197BDF, 0xCB35D444, + 0x3FF00220, 0x24000000, 0x3E00CCBC, 0x2188E3D5, + 0x3FF00224, 0x24000000, 0x3E254452, 0x36A79F6A, + 0x3FF00228, 0x24000000, 0x3E333ABC, 0xD69B2D28, + 0x3FF0022C, 0x24000000, 0x3E3BE352, 0xBA07BE5B, + 0x3FF00230, 0x28000000, 0xBE3B6415, 0x3665F227, + 0x3FF00234, 0x28000000, 0xBE329B7A, 0xF6AD58D5, + 0x3FF00238, 0x28000000, 0xBE2385BD, 0x059BD24A, + 0x3FF0023C, 0x28000000, 0xBDEB47FA, 0xD8E2B1B4, + 0x3FF00240, 0x28000000, 0x3E203CC2, 0x22CF60F6, + 0x3FF00244, 0x28000000, 0x3E312704, 0x39BEF87F, + 0x3FF00248, 0x28000000, 0x3E3A3FA9, 0xA63F5309, + 0x3FF0024C, 0x2C000000, 0xBE3C97AE, 0xA516AE5E, + 0x3FF00250, 0x2C000000, 0xBE335F04, 0xA442792A, + 0x3FF00254, 0x2C000000, 0xBE242CB0, 0xA686F3A2, + 0x3FF00258, 0x2C000000, 0xBDE7B535, 0xC3237903, + 0x3FF0025C, 0x2C000000, 0x3E21560E, 0x9E7A6CF7, + 0x3FF00260, 0x2C000000, 0x3E3223BA, 0xA8C01385, + 0x3FF00264, 0x2C000000, 0x3E3BAC70, 0x627012DF, + 0x3FF00268, 0x30000000, 0xBE3ABAD7, 0x7FB232EA, + 0x3FF0026C, 0x30000000, 0xBE31121C, 0xF9A6244B, + 0x3FF00270, 0x30000000, 0xBE1D6580, 0x1DAC9AE4, + 0x3FF00274, 0x30000000, 0x3E037AFA, 0xD7FB0AC3, + 0x3FF00278, 0x30000000, 0x3E289042, 0x633420EB, + 0x3FF0027C, 0x30000000, 0x3E3630E5, 0x8065842A, + 0x3FF00280, 0x34000000, 0xBE3FD653, 0xB49DA4FF, + 0x3FF00284, 0x34000000, 0xBE35CD8A, 0x696ECB76, + 0x3FF00288, 0x34000000, 0xBE27697D, 0x341A9D63, + 0x3FF0028C, 0x34000000, 0xBDF8BF04, 0x2788D238, + 0x3FF00290, 0x34000000, 0x3E2159C1, 0x42A03782, + 0x3FF00294, 0x34000000, 0x3E32F5B4, 0x154D4F89, + 0x3FF00298, 0x34000000, 0x3E3D4E8A, 0x1D7FB2C1, + 0x3FF0029C, 0x38000000, 0xBE38489D, 0x42181508, + 0x3FF002A0, 0x38000000, 0xBE2B9F84, 0x0AF2C28C, + 0x3FF002A4, 0x38000000, 0xBE0A3721, 0x451C5357, + 0x3FF002A8, 0x38000000, 0x3E1D47F1, 0x61A8605E, + 0x3FF002AC, 0x38000000, 0x3E31FADF, 0x81B02FCF, + 0x3FF002B0, 0x38000000, 0x3E3CB3C5, 0x572F674A, + 0x3FF002B4, 0x3C000000, 0xBE388352, 0x231795EA, + 0x3FF002B8, 0x3C000000, 0xBE2B54CD, 0xD248367A, + 0x3FF002BC, 0x3C000000, 0xBE060BC7, 0xB7ABD90D, + 0x3FF002C0, 0x3C000000, 0x3E206EEF, 0x6EE9F1EF, + 0x3FF002C4, 0x3C000000, 0x3E33406B, 0x261BF09E, + 0x3FF002C8, 0x3C000000, 0x3E3E5961, 0x59001C60, + 0x3FF002CC, 0x40000000, 0xBE367DA5, 0xABDDD232, + 0x3FF002D0, 0x40000000, 0xBE268953, 0xC8FA5113, + 0x3FF002D4, 0x40000000, 0x3D9152CC, 0x8B33A701, + 0x3FF002D8, 0x40000000, 0x3E26BAAC, 0x3E058570, + 0x3FF002DC, 0x40000000, 0x3E36C65A, 0x63236E71, + 0x3FF002E0, 0x44000000, 0xBE3DC09E, 0x7C7A795C, + 0x3FF002E4, 0x44000000, 0xBE323794, 0x7BD63D1D, + 0x3FF002E8, 0x44000000, 0xBE1A7A1E, 0x5BBC9105, + 0x3FF002EC, 0x44000000, 0x3E142A20, 0xD8EE2B1B, + 0x3FF002F0, 0x44000000, 0x3E30C39A, 0xEFAA8A8D, + 0x3FF002F4, 0x44000000, 0x3E3C8CB0, 0x995E96A2, + 0x3FF002F8, 0x48000000, 0xBE379A36, 0xC8A79469, + 0x3FF002FC, 0x48000000, 0xBE276236, 0x64CE7203, + 0x3FF00300, 0x48000000, 0x3DD200D8, 0x0819DA68, + 0x3FF00304, 0x48000000, 0x3E28A249, 0xE5E018D4, + 0x3FF00308, 0x48000000, 0x3E386A49, 0x8A087692, + 0x3FF0030C, 0x4C000000, 0xBE3B6C8E, 0xD695988B, + 0x3FF00310, 0x4C000000, 0xBE2E66C8, 0x55D2BCBA, + 0x3FF00314, 0x4C000000, 0xBE0751B3, 0x7790BA7A, + 0x3FF00318, 0x4C000000, 0x3E22DDF4, 0xC2A20261, + 0x3FF0031C, 0x4C000000, 0x3E35D82E, 0x49E0B0B5, + 0x3FF00320, 0x50000000, 0xBE3DAE9A, 0xB142422E, + 0x3FF00324, 0x50000000, 0xBE312560, 0x8C170FE6, + 0x3FF00328, 0x50000000, 0xBE12308D, 0x0A73BF77, + 0x3FF0032C, 0x50000000, 0x3E203A3A, 0x5E59CEFA, + 0x3FF00330, 0x50000000, 0x3E34D660, 0xCD4740BF, + 0x3FF00334, 0x54000000, 0xBE3E6058, 0x644D1883, + 0x3FF00338, 0x54000000, 0xBE31870E, 0x618F57B6, + 0x3FF0033C, 0x54000000, 0xBE127704, 0x99FABD0F, + 0x3FF00340, 0x54000000, 0x3E20B71E, 0xA1CB5ECF, + 0x3FF00344, 0x54000000, 0x3E3564E3, 0x089E93E1, + 0x3FF00348, 0x58000000, 0xBE3D81C5, 0xFB533142, + 0x3FF0034C, 0x58000000, 0xBE30586B, 0xB6EECE6C, + 0x3FF00350, 0x58000000, 0xBE08F871, 0x319B883E, + 0x3FF00354, 0x58000000, 0x3E2454A5, 0x75BF7503, + 0x3FF00358, 0x58000000, 0x3E3783B6, 0xF04B88C5, + 0x3FF0035C, 0x5C000000, 0xBE3B12E1, 0x81EF30A7, + 0x3FF00360, 0x5C000000, 0xBE2B32ED, 0x2F9F3657, + 0x3FF00364, 0x5C000000, 0xBDB0084D, 0x54DF31BC, + 0x3FF00368, 0x5C000000, 0x3E2B12D2, 0xC303B7B9, + 0x3FF0036C, 0x5C000000, 0x3E3B32DE, 0x78B56F97, + 0x3FF00370, 0x60000000, 0xBE3713A9, 0x03B9496C, + 0x3FF00374, 0x60000000, 0xBE22945A, 0x1F92E726, + 0x3FF00378, 0x60000000, 0x3E123D49, 0x621736DF, + 0x3FF0037C, 0x60000000, 0x3E3278D5, 0x3935580D, + 0x3FF00380, 0x64000000, 0xBE3F8DA4, 0x69B9F5FB, + 0x3FF00384, 0x64000000, 0xBE31841A, 0x8C473CC8, + 0x3FF00388, 0x64000000, 0xBE0B5469, 0x538CDE07, + 0x3FF0038C, 0x64000000, 0x3E257E07, 0x7F8F9D65, + 0x3FF00390, 0x64000000, 0x3E38F898, 0x3665E52B, + 0x3FF00394, 0x68000000, 0xBE38BDCF, 0xC29674BD, + 0x3FF00398, 0x68000000, 0xBE24C868, 0x4E58B4D9, + 0x3FF0039C, 0x68000000, 0x3E1015AC, 0x329466D7, + 0x3FF003A0, 0x68000000, 0x3E327F0D, 0xDCDECE44, + 0x3FF003A4, 0x6C000000, 0xBE3EF74B, 0xB27E5528, + 0x3FF003A8, 0x6C000000, 0xBE305DA1, 0x9D7167F2, + 0x3FF003AC, 0x6C000000, 0xBDFB3F3D, 0xFF980820, + 0x3FF003B0, 0x6C000000, 0x3E2A0B7B, 0x13D49789, + 0x3FF003B4, 0x6C000000, 0x3E3BCF72, 0xA43AE87C, + 0x3FF003B8, 0x70000000, 0xBE3556D4, 0x8D06BDC0, + 0x3FF003BC, 0x70000000, 0xBE19B460, 0x1766E54D, + 0x3FF003C0, 0x70000000, 0x3E211950, 0x7B85C8BA, + 0x3FF003C4, 0x70000000, 0x3E37966C, 0x41D00AED, + 0x3FF003C8, 0x74000000, 0xBE394FCB, 0xF5B15507, + 0x3FF003CC, 0x74000000, 0xBE244C00, 0xC98093C4, + 0x3FF003D0, 0x74000000, 0x3E144F3B, 0xE2907BDF, + 0x3FF003D4, 0x74000000, 0x3E345DA2, 0x267CD924, + 0x3FF003D8, 0x78000000, 0xBE3C4886, 0xD73526C0, + 0x3FF003DC, 0x78000000, 0xBE29BD57, 0xF8E1D62E, + 0x3FF003E0, 0x78000000, 0x3E04D995, 0xD65415E1, + 0x3FF003E4, 0x78000000, 0x3E322515, 0x527E1A58, + 0x3FF003E8, 0x7C000000, 0xBE3E4104, 0x31552BA5, + 0x3FF003EC, 0x7C000000, 0xBE2D2E33, 0x995CAB3B, + 0x3FF003F0, 0x7C000000, 0x3DF22D48, 0x473970DC, + 0x3FF003F4, 0x7C000000, 0x3E30ECC6, 0xC61195FC, + 0x3FF003F8, 0x80000000, 0xBE3F3943, 0x03D35C34, + 0x3FF003FC, 0x80000000, 0xBE2E9E91, 0xAA7483C7, + 0x3FF00400, 0x80000000, 0x3DE556AA, 0xBBBC71CE, + 0x3FF00404, 0x80000000, 0x3E30B4B7, 0x817613C1, + 0x3FF00408, 0x84000000, 0xBE3F3142, 0x4E70B0AC, + 0x3FF0040C, 0x84000000, 0xBE2E0E70, 0x2BAAD02F, + 0x3FF00410, 0x84000000, 0x3DF32D62, 0xF48F01F2, + 0x3FF00414, 0x84000000, 0x3E317CE8, 0x84EB5B98, + 0x3FF00418, 0x88000000, 0xBE3E2901, 0x10ED210B, + 0x3FF0041C, 0x88000000, 0xBE2B7DCD, 0x1C7F0051, + 0x3FF00420, 0x88000000, 0x3E05D9C0, 0x87AA2706, + 0x3FF00424, 0x88000000, 0x3E33455A, 0xD0B235B3, + 0x3FF00428, 0x8C000000, 0xBE3C207E, 0x4B07A510, + 0x3FF0042C, 0x8C000000, 0xBE26ECA6, 0x7C6E838B, + 0x3FF00430, 0x8C000000, 0x3E150F6F, 0xEC91A8D5, + 0x3FF00434, 0x8C000000, 0x3E360E0F, 0x650C6A83, + 0x3FF00438, 0x90000000, 0xBE3917B8, 0xFC7E3439, + 0x3FF0043C, 0x90000000, 0xBE205AFA, 0x4AF4C8B6, + 0x3FF00440, 0x90000000, 0x3E219985, 0xDC31D181, + 0x3FF00444, 0x90000000, 0x3E39D707, 0x423CC2BE, + 0x3FF00448, 0x94000000, 0xBE350EB0, 0x250DC5BF, + 0x3FF0044C, 0x94000000, 0xBE0F231A, 0x1E2CF893, + 0x3FF00450, 0x94000000, 0x3E2AABDB, 0xD42C92D4, + 0x3FF00454, 0x94000000, 0x3E3EA043, 0x6887075B, + 0x3FF00458, 0x98000000, 0xBE300562, 0xC472509B, + 0x3FF0045C, 0x98000000, 0x3DF64FB6, 0x72B572E0, + 0x3FF00460, 0x98000000, 0x3E32DF5D, 0xEF61155C, + 0x3FF00464, 0x9C000000, 0xBE3B963B, 0x27CFFE6A, + 0x3FF00468, 0x9C000000, 0xBE23F79F, 0xB4CD96FE, + 0x3FF0046C, 0x9C000000, 0x3E1EBA7F, 0x6E771F13, + 0x3FF00470, 0x9C000000, 0x3E396913, 0xFE3ED608, + 0x3FF00474, 0xA0000000, 0xBE34CC73, 0x6E82850F, + 0x3FF00478, 0xA0000000, 0xBE078FB3, 0x352966B7, + 0x3FF0047C, 0xA0000000, 0x3E2DF116, 0x33AFF8AE, + 0x3FF00480, 0xA4000000, 0xBE3F0CEE, 0xE909EADD, + 0x3FF00484, 0xA4000000, 0xBE2A04C8, 0xD6938597, + 0x3FF00488, 0xA4000000, 0x3E1460AA, 0x5C6654D8, + 0x3FF0048C, 0xA4000000, 0x3E3742BE, 0x22213ECF, + 0x3FF00490, 0xA8000000, 0xBE3682A9, 0xC631A356, + 0x3FF00494, 0xA8000000, 0xBE10E034, 0x7777B644, + 0x3FF00498, 0xA8000000, 0x3E2C4528, 0x3E3B0991, + 0x3FF0049C, 0xAC000000, 0xBE3F72C6, 0x0B3E269F, + 0x3FF004A0, 0xAC000000, 0xBE29F037, 0x31DF923B, + 0x3FF004A4, 0xAC000000, 0x3E164A4D, 0xE82713DE, + 0x3FF004A8, 0xAC000000, 0x3E382D47, 0x31AFAC4B, + 0x3FF004AC, 0xB0000000, 0xBE352800, 0x6DFCE978, + 0x3FF004B0, 0xB0000000, 0xBE036A1B, 0x07D68D27, + 0x3FF004B4, 0xB0000000, 0x3E305D7E, 0x5CB71F6F, + 0x3FF004B8, 0xB4000000, 0xBE3CC7BB, 0x30E5E990, + 0x3FF004BC, 0xB4000000, 0xBE23B9E0, 0x0BA17DEA, + 0x3FF004C0, 0xB4000000, 0x3E223BBF, 0xC3EF9BD8, + 0x3FF004C4, 0xB4000000, 0x3E3C28B4, 0x8A74ECC0, + 0x3FF004C8, 0xB8000000, 0xBE30BC72, 0x085831CA, + 0x3FF004CC, 0xB8000000, 0x3E037361, 0x6C8D1FC8, + 0x3FF004D0, 0xB8000000, 0x3E35A94F, 0x3033A0B8, + 0x3FF004D4, 0xBC000000, 0xBE370BC8, 0xFC7107DE, + 0x3FF004D8, 0xBC000000, 0xBE0D86E2, 0xA2D908DA, + 0x3FF004DC, 0xBC000000, 0x3E2F742A, 0x58ED155E, + 0x3FF004E0, 0xC0000000, 0xBE3CCAF4, 0x75FACDD0, + 0x3FF004E4, 0xC0000000, 0xBE227FF2, 0x6F5BE5D3, + 0x3FF004E8, 0xC0000000, 0x3E24B60D, 0xD6BCA827, + 0x3FF004EC, 0xC0000000, 0x3E3E060B, 0xF72B40D6, + 0x3FF004F0, 0xC4000000, 0xBE2C7DD4, 0x208BE3E3, + 0x3FF004F4, 0xC4000000, 0x3E163093, 0x642FDDB8, + 0x3FF004F8, 0xC4000000, 0x3E396738, 0xB72239A5, + 0x3FF004FC, 0xC8000000, 0xBE32ADAE, 0x7201ED9B, + 0x3FF00500, 0xC8000000, 0x3DF4D6F6, 0x1A0C05F3, + 0x3FF00504, 0xC8000000, 0x3E355892, 0x360B8346, + 0x3FF00508, 0xCC000000, 0xBE368C45, 0xF0C06435, + 0x3FF0050C, 0xCC000000, 0xBE0308C8, 0x760DA2F6, + 0x3FF00510, 0xCC000000, 0x3E31DA18, 0xE008D57B, + 0x3FF00514, 0xD0000000, 0xBE39DAB0, 0x205F82F4, + 0x3FF00518, 0xD0000000, 0xBE15FDD0, 0x2FE5E3E3, + 0x3FF0051C, 0xD0000000, 0x3E2DD79A, 0x42787241, + 0x3FF00520, 0xD4000000, 0xBE3C98EC, 0x94BD25F4, + 0x3FF00524, 0xD4000000, 0xBE201B42, 0x53C89D03, + 0x3FF00528, 0xD4000000, 0x3E291B5E, 0xCB901057, + 0x3FF0052C, 0xD8000000, 0xBE3EC6FA, 0xE1B6D837, + 0x3FF00530, 0xD8000000, 0xBE24173F, 0xF8BF49E7, + 0x3FF00534, 0xD8000000, 0x3E257F80, 0x339DDB57, + 0x3FF00538, 0xD8000000, 0x3E3F9B25, 0x64D62C5C, + 0x3FF0053C, 0xDC000000, 0xBE26F2E0, 0x2E913659, + 0x3FF00540, 0xDC000000, 0x3E2303FF, 0x52E7CB93, + 0x3FF00544, 0xDC000000, 0x3E3E8D74, 0xAB0CFEF5, + 0x3FF00548, 0xE0000000, 0xBE28AE22, 0x1CF7FDE6, + 0x3FF0054C, 0xE0000000, 0x3E21A8DD, 0x01B47B93, + 0x3FF00550, 0xE0000000, 0x3E3E0FF3, 0x5D1107E2, + 0x3FF00554, 0xE4000000, 0xBE294904, 0xEBAC99E1, + 0x3FF00558, 0xE4000000, 0x3E216E1A, 0x184B2814, + 0x3FF0055C, 0xE4000000, 0x3E3E22A1, 0xE706008B, + 0x3FF00560, 0xE8000000, 0xBE28C387, 0xC267616A, + 0x3FF00564, 0xE8000000, 0x3E2253B7, 0x6EF3B008, + 0x3FF00568, 0xE8000000, 0x3E3EC580, 0xB50FF371, + 0x3FF0056C, 0xEC000000, 0xBE271DA9, 0xC8E0096B, + 0x3FF00570, 0xEC000000, 0x3E2459B5, 0xDDF69498, + 0x3FF00574, 0xEC000000, 0x3E3FF890, 0x33533C31, + 0x3FF00578, 0xF0000000, 0xBE24576A, 0x26CDA497, + 0x3FF0057C, 0xF0000000, 0x3E278016, 0x3D9CF923, + 0x3FF00580, 0xF4000000, 0xBE3E442F, 0x320B787B, + 0x3FF00584, 0xF4000000, 0xBE2070C8, 0x03E6A36B, + 0x3FF00588, 0xF4000000, 0x3E2BC6D9, 0x6630A33F, + 0x3FF0058C, 0xF8000000, 0xBE3BF0BD, 0x0EE72CBF, + 0x3FF00590, 0xF8000000, 0xBE16D385, 0x0FC1A853, + 0x3FF00594, 0xF8000000, 0x3E309700, 0x17FDFD5D, + 0x3FF00598, 0xFC000000, 0xBE390D18, 0xF71A91AC, + 0x3FF0059C, 0xFC000000, 0xBE050963, 0x69C58B86, + 0x3FF005A0, 0xFC000000, 0x3E33DAC5, 0xB9A504CD, + 0x3FF005A5, 0x00000000, 0xBE359942, 0x7E800734, + 0x3FF005A9, 0x00000000, 0x3DF02BAE, 0xE59934CD, + 0x3FF005AD, 0x00000000, 0x3E37AEBE, 0x04333E0E, + 0x3FF005B1, 0x04000000, 0xBE319539, 0x38F19C2F, + 0x3FF005B5, 0x04000000, 0x3E14DB54, 0xEBB1C157, + 0x3FF005B9, 0x04000000, 0x3E3C12E9, 0x63CED05D, + 0x3FF005BD, 0x08000000, 0xBE2A01F9, 0x74921CAF, + 0x3FF005C1, 0x08000000, 0x3E23F645, 0xC94C85F2, + 0x3FF005C5, 0x0C000000, 0xBE3EF8B7, 0xBB61CBEE, + 0x3FF005C9, 0x0C000000, 0xBE1F7232, 0x597F2931, + 0x3FF005CD, 0x0C000000, 0x3E2E9F48, 0xAF5B7345, + 0x3FF005D1, 0x10000000, 0xBE397424, 0xED37CD5F, + 0x3FF005D5, 0x10000000, 0xBE013F43, 0x08775C6B, + 0x3FF005D9, 0x10000000, 0x3E35345A, 0x0029D3DB, + 0x3FF005DD, 0x14000000, 0xBE335F5D, 0xC58C1962, + 0x3FF005E1, 0x14000000, 0x3E1073C1, 0x47430E04, + 0x3FF005E5, 0x14000000, 0x3E3BA944, 0x4A41E248, + 0x3FF005E9, 0x18000000, 0xBE2974C3, 0xB06E888E, + 0x3FF005ED, 0x18000000, 0x3E25E3FB, 0xDCCD9333, + 0x3FF005F1, 0x1C000000, 0xBE3D519C, 0x5DE27951, + 0x3FF005F5, 0x1C000000, 0xBE1614C2, 0xE4464502, + 0x3FF005F9, 0x1C000000, 0x3E325740, 0xE0DAFE93, + 0x3FF005FD, 0x20000000, 0xBE35BC47, 0x8C1B4C10, + 0x3FF00601, 0x20000000, 0x3E0201B0, 0x20686CE9, + 0x3FF00605, 0x20000000, 0x3E3A4CB9, 0x95558B63, + 0x3FF00609, 0x24000000, 0xBE2B2D79, 0xA880A3EB, + 0x3FF0060D, 0x24000000, 0x3E252BA5, 0x9699EEB7, + 0x3FF00611, 0x28000000, 0xBE3D2D97, 0x880115E1, + 0x3FF00615, 0x28000000, 0xBE1383EF, 0x28A3D788, + 0x3FF00619, 0x28000000, 0x3E337BA6, 0x08D6DC23, + 0x3FF0061D, 0x2C000000, 0xBE3417B2, 0x0B001A08, + 0x3FF00621, 0x2C000000, 0x3E1193EF, 0xF94EB99A, + 0x3FF00625, 0x2C000000, 0x3E3CF1B0, 0x28D3BD3B, + 0x3FF00629, 0x30000000, 0xBE24E32B, 0x0EFCC982, + 0x3FF0062D, 0x30000000, 0x3E2C7655, 0xE2BDA47F, + 0x3FF00631, 0x34000000, 0xBE39080E, 0x689312F8, + 0x3FF00635, 0x34000000, 0xBDCDA0C8, 0xA9444DB4, + 0x3FF00639, 0x34000000, 0x3E38A191, 0x7B21FE23, + 0x3FF0063D, 0x38000000, 0xBE2CE32A, 0x7E67E1E1, + 0x3FF00641, 0x38000000, 0x3E251694, 0x875A71F0, + 0x3FF00645, 0x3C000000, 0xBE3C67CF, 0xF838F455, + 0x3FF00649, 0x3C000000, 0xBE0A571F, 0x77274052, + 0x3FF0064D, 0x3C000000, 0x3E35E20E, 0x63AAEFA8, + 0x3FF00651, 0x40000000, 0xBE30E0F8, 0xFC87DA70, + 0x3FF00655, 0x40000000, 0x3E20D80B, 0xE9089AFD, + 0x3FF00659, 0x44000000, 0xBE3E36F4, 0xC52F03BD, + 0x3FF0065D, 0x44000000, 0xBE1327A4, 0x9680E14E, + 0x3FF00661, 0x44000000, 0x3E34B328, 0xD732468D, + 0x3FF00665, 0x48000000, 0xBE31BFBE, 0xCAB5EF4A, + 0x3FF00669, 0x48000000, 0x3E1F757F, 0xE2A2FBE1, + 0x3FF0066D, 0x4C000000, 0xBE3E757A, 0xDAB014DA, + 0x3FF00671, 0x4C000000, 0xBE12E13D, 0x02FB3FBB, + 0x3FF00675, 0x4C000000, 0x3E3514E2, 0xCA7E298D, + 0x3FF00679, 0x50000000, 0xBE310DE4, 0xB4F78B94, + 0x3FF0067D, 0x50000000, 0x3E21BEB4, 0x89C35D05, + 0x3FF00681, 0x54000000, 0xBE3D2360, 0x43F4895C, + 0x3FF00685, 0x54000000, 0xBE08B0A2, 0x5BC49ADF, + 0x3FF00689, 0x54000000, 0x3E37073E, 0x32573159, + 0x3FF0068D, 0x58000000, 0xBE2D96D1, 0x8D0732D2, + 0x3FF00691, 0x58000000, 0x3E26E3ED, 0x9BF15E67, + 0x3FF00695, 0x5C000000, 0xBE3A40A3, 0x0C3250FB, + 0x3FF00699, 0x5C000000, 0x3DBCC9AE, 0xFD0AE214, + 0x3FF0069D, 0x5C000000, 0x3E3A8A3D, 0x038868A1, + 0x3FF006A1, 0x60000000, 0xBE25F092, 0x151D21CE, + 0x3FF006A5, 0x60000000, 0x3E2F2A6F, 0x11738C43, + 0x3FF006A9, 0x64000000, 0xBE35CD41, 0x3E9CE96D, + 0x3FF006AD, 0x64000000, 0x3E138132, 0x8DBC2918, + 0x3FF006B1, 0x64000000, 0x3E3F9DE1, 0x32DF4C13, + 0x3FF006B5, 0x68000000, 0xBE16520E, 0x3129E0B2, + 0x3FF006B9, 0x68000000, 0x3E35491E, 0x69F36A61, + 0x3FF006BD, 0x6C000000, 0xBE2F9271, 0xCCCABCD4, + 0x3FF006C1, 0x6C000000, 0x3E2668ED, 0x0D59B899, + 0x3FF006C5, 0x70000000, 0xBE39BDD3, 0x4AD435A0, + 0x3FF006C9, 0x70000000, 0x3DF5FE9A, 0x9191CABB, + 0x3FF006CD, 0x70000000, 0x3E3C8DAD, 0x6676850B, + 0x3FF006D1, 0x74000000, 0xBE206910, 0x1D74934A, + 0x3FF006D5, 0x74000000, 0x3E331949, 0x4D886478, + 0x3FF006D9, 0x78000000, 0xBE3188DE, 0x80BFBBC2, + 0x3FF006DD, 0x78000000, 0x3E23CA01, 0x14DE1719, + 0x3FF006E1, 0x7C000000, 0xBE3A9D19, 0x8CE98EC0, + 0x3FF006E5, 0x7C000000, 0x3DEE1A67, 0xA705A6E7, + 0x3FF006E9, 0x7C000000, 0x3E3C8EC6, 0xECD5F851, + 0x3FF006ED, 0x80000000, 0xBE1F0CF9, 0xE839CE4D, + 0x3FF006F1, 0x80000000, 0x3E33FAC3, 0x0C8CA46A, + 0x3FF006F5, 0x84000000, 0xBE303734, 0x7B5703D8, + 0x3FF006F9, 0x84000000, 0x3E274DB5, 0xE490A112, + 0x3FF006FD, 0x88000000, 0xBE386B0E, 0xA693A093, + 0x3FF00701, 0x88000000, 0x3E0C9875, 0xF0B73DAA, + 0x3FF00705, 0x88000000, 0x3E3FA133, 0x2449A944, + 0x3FF00709, 0x8C000000, 0xBE110285, 0xBFE66C14, + 0x3FF0070D, 0x8C000000, 0x3E37ED91, 0x054EDCBD, + 0x3FF00711, 0x90000000, 0xBE27A86A, 0xEFB65924, + 0x3FF00715, 0x90000000, 0x3E307A0B, 0x1C8A0CF1, + 0x3FF00719, 0x94000000, 0xBE3327AD, 0x397FB1D6, + 0x3FF0071D, 0x94000000, 0x3E228D43, 0x1412B9FB, + 0x3FF00721, 0x98000000, 0xBE3A3B08, 0x94D8FFB0, + 0x3FF00725, 0x98000000, 0x3E029AA3, 0x6ED80040, + 0x3FF00729, 0x98000000, 0x3E3EF1B8, 0x9627250A, + 0x3FF0072D, 0x9C000000, 0xBE117F70, 0x5FCB1B09, + 0x3FF00731, 0x9C000000, 0x3E385E96, 0x678F0789, + 0x3FF00735, 0xA0000000, 0xBE25A5DF, 0xCEA3485B, + 0x3FF00739, 0xA0000000, 0x3E320B90, 0xFF6D0303, + 0x3FF0073D, 0xA4000000, 0xBE3105E6, 0xE03334FF, + 0x3FF00741, 0xA4000000, 0x3E27F150, 0xFB9F056D, + 0x3FF00745, 0xA8000000, 0xBE36F8C0, 0xE28905F4, + 0x3FF00749, 0xA8000000, 0x3E189774, 0x0B1407AA, + 0x3FF0074D, 0xAC000000, 0xBE3CAB7D, 0xCE4493C4, + 0x3FF00751, 0xAC000000, 0x3DE265D5, 0xCB817D78, + 0x3FF00755, 0xAC000000, 0x3E3DE1E2, 0x7CA8B4E3, + 0x3FF00759, 0xB0000000, 0xBE12FD89, 0x7D730FC6, + 0x3FF0075D, 0xB0000000, 0x3E38AF60, 0x1E4D7759, + 0x3FF00761, 0xB4000000, 0xBE23A3AC, 0x0CAD84A2, + 0x3FF00765, 0xB4000000, 0x3E33BCFB, 0x36B866FD, + 0x3FF00769, 0xB8000000, 0xBE2D4858, 0x4D0667A1, + 0x3FF0076D, 0xB8000000, 0x3E2E1567, 0xCBF08E6A, + 0x3FF00771, 0xBC000000, 0xBE333664, 0x9FD34D05, + 0x3FF00775, 0xBC000000, 0x3E253114, 0x9837D6E0, + 0x3FF00779, 0xC0000000, 0xBE37887F, 0x5238327D, + 0x3FF0077D, 0xC0000000, 0x3E1999FA, 0x24C8DC90, + 0x3FF00781, 0xC4000000, 0xBE3B9A7C, 0x1DA2F8BE, + 0x3FF00785, 0xC4000000, 0x3E03A485, 0xEA50EE6A, + 0x3FF00789, 0xC8000000, 0xBE3F6C5A, 0xE204A449, + 0x3FF0078D, 0xC8000000, 0xBDF3D3EF, 0x78D5D0F3, + 0x3FF00791, 0xC8000000, 0x3E3D01E4, 0x80B1D66C, + 0x3FF00795, 0xCC000000, 0xBE12BBC1, 0xD5149796, + 0x3FF00799, 0xCC000000, 0x3E39B042, 0x2A8F92F0, + 0x3FF0079D, 0xD0000000, 0xBE1F820E, 0x6F386487, + 0x3FF007A1, 0xD0000000, 0x3E369EBE, 0x3BA3BCDA, + 0x3FF007A5, 0xD4000000, 0xBE25A3F0, 0x96320652, + 0x3FF007A9, 0xD4000000, 0x3E33CD58, 0xD3FD8FCA, + 0x3FF007AD, 0xD8000000, 0xBE2B069C, 0xC62D40B1, + 0x3FF007B1, 0xD8000000, 0x3E313C12, 0x13AC5766, + 0x3FF007B5, 0xDC000000, 0xBE2FE90B, 0x876F3A0B, + 0x3FF007B9, 0xDC000000, 0x3E2DD5D4, 0x357EDEB8, + 0x3FF007BD, 0xE0000000, 0xBE32259E, 0x4CEC957E, + 0x3FF007C1, 0xE0000000, 0x3E29B3C2, 0x128C86C6, + 0x3FF007C5, 0xE4000000, 0xBE341697, 0xDEA61608, + 0x3FF007C9, 0xE4000000, 0x3E2611ED, 0xFEA09E70, + 0x3FF007CD, 0xE8000000, 0xBE35C772, 0x58D49AE3, + 0x3FF007D1, 0xE8000000, 0x3E22F058, 0x39DA3D42, + 0x3FF007D5, 0xEC000000, 0xBE37382D, 0x9B689043, + 0x3FF007D9, 0xEC000000, 0x3E204F01, 0x04589AD6, + 0x3FF007DD, 0xF0000000, 0xBE3868C9, 0x86525259, + 0x3FF007E1, 0xF0000000, 0x3E1C5BD1, 0x3C761DAC, + 0x3FF007E5, 0xF4000000, 0xBE395945, 0xF9822D4C, + 0x3FF007E9, 0xF4000000, 0x3E191A1E, 0x8F4221F9, + 0x3FF007ED, 0xF8000000, 0xBE3A09A2, 0xD4E85D3A, + 0x3FF007F1, 0xF8000000, 0x3E16D8EA, 0x81547225, + 0x3FF007F5, 0xFC000000, 0xBE3A79DF, 0xF8750E3B, + 0x3FF007F9, 0xFC000000, 0x3E159835, 0x92EC7DE3, + 0x3FF007FE, 0x00000000, 0xBE3AA9FD, 0x44185C5D } }; + +#else +#ifdef LITTLE_ENDI + +static const union { + int i[1424]; + double x[712]; +} coar = { .i = { + 0xC8000000, 0x3FE69A59, 0x6079C9F7, 0x3DF22D4D, + 0xC8000000, 0x3FE6A5A9, 0x25AF6823, 0x3E19882D, + 0x74000000, 0x3FE6B0FF, 0x31DABF59, 0xBE221476, + 0xC8000000, 0x3FE6BC5A, 0x99A2DC0A, 0x3E2312AC, + 0xD0000000, 0x3FE6C7BB, 0xCE9F9355, 0xBE265926, + 0x84000000, 0x3FE6D322, 0x2D298DED, 0x3E2F2C26, + 0xF4000000, 0x3FE6DE8E, 0x1E748D2F, 0xBE2EC28E, + 0x14000000, 0x3FE6EA01, 0xC68CB7E5, 0x3E2D8C6D, + 0xF4000000, 0x3FE6F578, 0x419FE2F0, 0x3DEE1A9E, + 0x90000000, 0x3FE700F6, 0xDEAEAE34, 0xBDFF1AFD, + 0xEC000000, 0x3FE70C79, 0x558B7122, 0xBE0730FE, + 0x0C000000, 0x3FE71803, 0x2D280C3B, 0xBE25CB85, + 0xF0000000, 0x3FE72391, 0x337B7B54, 0xBE06F2CE, + 0x9C000000, 0x3FE72F26, 0x45C02B72, 0x3E289BCA, + 0x18000000, 0x3FE73AC1, 0x5039F1CA, 0xBE18DEA6, + 0x60000000, 0x3FE74661, 0x86CE0538, 0xBE09D090, + 0x78000000, 0x3FE75207, 0xCFCE5DDB, 0x3E290E79, + 0x68000000, 0x3FE75DB3, 0xB249A17C, 0x3DD61DF0, + 0x2C000000, 0x3FE76965, 0xE13445F7, 0x3E2F22F7, + 0xD0000000, 0x3FE7751C, 0x874E75CE, 0xBE2CD454, + 0x4C000000, 0x3FE780DA, 0xDF43E3BC, 0xBE0159CE, + 0xA8000000, 0x3FE78C9D, 0x699A1332, 0x3E279291, + 0xEC000000, 0x3FE79866, 0x2DD98C6C, 0xBE2A0BCD, + 0x10000000, 0x3FE7A436, 0x15AC979E, 0x3E25F375, + 0x20000000, 0x3FE7B00B, 0x2FEAFCF6, 0x3E26CCF5, + 0x1C000000, 0x3FE7BBE6, 0x53ADAD67, 0x3E27D4F4, + 0x08000000, 0x3FE7C7C7, 0x7FBD9566, 0x3E10EEC7, + 0xE4000000, 0x3FE7D3AD, 0x9A831D86, 0x3E2837F0, + 0xB8000000, 0x3FE7DF9A, 0x5CB4C35B, 0xBE129BE0, + 0x80000000, 0x3FE7EB8D, 0x0234F04D, 0x3E23990A, + 0x44000000, 0x3FE7F786, 0x64D5C842, 0x3E2EB807, + 0x08000000, 0x3FE80385, 0x02B4E9E8, 0x3E0FC86F, + 0xCC000000, 0x3FE80F89, 0x7B4274BF, 0xBDD7B5B3, + 0x94000000, 0x3FE81B94, 0xB899B00F, 0xBE16888B, + 0x60000000, 0x3FE827A5, 0x5E94D155, 0x3E288971, + 0x38000000, 0x3FE833BC, 0x099F3E5E, 0x3E2AEEB2, + 0x20000000, 0x3FE83FD9, 0x3FF60B7C, 0xBE23B922, + 0x14000000, 0x3FE84BFC, 0x2DBD8012, 0xBDF7D3B1, + 0x1C000000, 0x3FE85825, 0xA8872BEB, 0xBDF24BA3, + 0x38000000, 0x3FE86454, 0x01AA18A7, 0x3E2EFE04, + 0x70000000, 0x3FE87089, 0x944496A2, 0x3E21986C, + 0xC4000000, 0x3FE87CC4, 0xB71FFAFF, 0x3E096A8B, + 0x38000000, 0x3FE88906, 0xBC4C7AC5, 0xBE21CE0A, + 0xCC000000, 0x3FE8954D, 0xBAC02491, 0xBE076F45, + 0x84000000, 0x3FE8A19B, 0xD922B925, 0x3E2B4FA2, + 0x68000000, 0x3FE8ADEF, 0x641863AF, 0x3DF759DB, + 0x78000000, 0x3FE8BA49, 0xC6AB5E04, 0xBE2DB97C, + 0xB4000000, 0x3FE8C6A9, 0xE2156713, 0xBE25364C, + 0x20000000, 0x3FE8D310, 0x862BEFF7, 0x3E1BEB7C, + 0xC4000000, 0x3FE8DF7C, 0x1CEA33A5, 0xBDF4DD0C, + 0xA0000000, 0x3FE8EBEF, 0x51797D47, 0xBE2537DF, + 0xB4000000, 0x3FE8F868, 0xF0107B28, 0x3E0FB1C4, + 0x08000000, 0x3FE904E8, 0xE01B68BD, 0x3E0AD6A1, + 0x9C000000, 0x3FE9116D, 0x1F78D9D9, 0x3E292117, + 0x78000000, 0x3FE91DF9, 0x4F50E5CF, 0xBE1D75DA, + 0x98000000, 0x3FE92A8B, 0x74959E58, 0x3DE5102B, + 0x04000000, 0x3FE93724, 0xD2216C35, 0xBE01CA50, + 0xBC000000, 0x3FE943C2, 0xB0B05884, 0x3E225BFD, + 0xC8000000, 0x3FE95067, 0x60B7C5C1, 0xBE0F2183, + 0x24000000, 0x3FE95D13, 0xB5860441, 0x3E2FB47A, + 0xDC000000, 0x3FE969C4, 0xE2D4059E, 0xBE01FFD2, + 0xEC000000, 0x3FE9767C, 0x12BB6A8D, 0xBDE9ED72, + 0x58000000, 0x3FE9833B, 0x43BFFB24, 0x3E2B3815, + 0x28000000, 0x3FE99000, 0xEE9EAD1E, 0x3E03FA22, + 0x5C000000, 0x3FE99CCB, 0x377138F7, 0xBE213841, + 0xF4000000, 0x3FE9A99C, 0xDB636C94, 0x3E178105, + 0xF8000000, 0x3FE9B674, 0xF5720122, 0x3E1E5E7A, + 0x6C000000, 0x3FE9C353, 0xA2AC5AAE, 0xBE238BFF, + 0x4C000000, 0x3FE9D038, 0xF93BDBD8, 0x3E270893, + 0xA4000000, 0x3FE9DD23, 0x354B86CF, 0x3DF40420, + 0x74000000, 0x3FE9EA15, 0x88CB06B7, 0xBE2D76D3, + 0xBC000000, 0x3FE9F70D, 0x9ED0EC60, 0xBE251639, + 0x80000000, 0x3FEA040C, 0xE2DDE506, 0x3E1F06E9, + 0xC8000000, 0x3FEA1111, 0x8E6DB477, 0x3E014549, + 0x94000000, 0x3FEA1E1D, 0xF8716509, 0xBDF4BC17, + 0xE8000000, 0x3FEA2B2F, 0xDA723A49, 0xBE2107DB, + 0xC4000000, 0x3FEA3848, 0x986AA369, 0x3E1A932A, + 0x30000000, 0x3FEA4568, 0x41592CDB, 0x3E198092, + 0x30000000, 0x3FEA528E, 0x676BCAB8, 0xBE2E260F, + 0xC0000000, 0x3FEA5FBA, 0x2D5D5610, 0x3DE2E821, + 0xE8000000, 0x3FEA6CED, 0x7DA20167, 0x3E2F7046, + 0xB0000000, 0x3FEA7A27, 0xF9FAAD30, 0xBE1D2832, + 0x14000000, 0x3FEA8768, 0x43FA6C45, 0xBE23F788, + 0x18000000, 0x3FEA94AF, 0xAA082732, 0x3E011E27, + 0xC4000000, 0x3FEAA1FC, 0xC682F0BF, 0xBE20BACB, + 0x18000000, 0x3FEAAF51, 0x7BD08C78, 0xBE2DC7DD, + 0x14000000, 0x3FEABCAC, 0xA3B10F9A, 0x3E2271A2, + 0xC4000000, 0x3FEACA0D, 0x7966F94C, 0xBE15449C, + 0x24000000, 0x3FEAD776, 0x6FD8F3EE, 0x3DD06137, + 0x3C000000, 0x3FEAE4E5, 0x8C5A144A, 0xBE267CD1, + 0x0C000000, 0x3FEAF25B, 0xB59DA94B, 0xBE29E584, + 0x98000000, 0x3FEAFFD7, 0x7B52192F, 0xBE23DFCF, + 0xE4000000, 0x3FEB0D5A, 0x78A76B45, 0xBE1CF2FE, + 0xF4000000, 0x3FEB1AE4, 0x7EC80FF6, 0xBE23A561, + 0xC8000000, 0x3FEB2875, 0x932EED68, 0x3E22C4C9, + 0x68000000, 0x3FEB360D, 0xB5833C97, 0x3E2B085C, + 0xD8000000, 0x3FEB43AB, 0x93B9319A, 0xBE01F093, + 0x18000000, 0x3FEB5151, 0xFABCE670, 0xBE254F01, + 0x28000000, 0x3FEB5EFD, 0x627ABFB0, 0x3E2F24C2, + 0x14000000, 0x3FEB6CB0, 0xE6AC0B48, 0x3E1F1EEC, + 0xDC000000, 0x3FEB7A69, 0x127F9ABC, 0xBE1A8671, + 0x80000000, 0x3FEB882A, 0xC87C73B3, 0xBDCB0C28, + 0x08000000, 0x3FEB95F2, 0x7F2B5A97, 0xBE22E8DD, + 0x74000000, 0x3FEBA3C0, 0x2D22A9D5, 0xBE1B3645, + 0xC8000000, 0x3FEBB195, 0x428F8B88, 0x3E0ADACA, + 0x0C000000, 0x3FEBBF72, 0xCDF9F681, 0xBE2E9E07, + 0x3C000000, 0x3FEBCD55, 0x7FA54ACF, 0xBE08A127, + 0x60000000, 0x3FEBDB3F, 0x8225B385, 0x3E0E92CE, + 0x7C000000, 0x3FEBE930, 0x7BB09485, 0x3DF38C2A, + 0x94000000, 0x3FEBF728, 0xF681FA5F, 0xBE2DFD64, + 0xA4000000, 0x3FEC0527, 0xDCE88BD2, 0x3E2E384D, + 0xBC000000, 0x3FEC132D, 0xFE46A893, 0xBE20F111, + 0xD4000000, 0x3FEC213A, 0xB189BFDA, 0x3E193DA1, + 0xF8000000, 0x3FEC2F4E, 0x0E39FB00, 0xBE20E3A1, + 0x24000000, 0x3FEC3D6A, 0x30F0FAC5, 0x3E1DB044, + 0x64000000, 0x3FEC4B8C, 0x97446B17, 0xBE2BC12C, + 0xB4000000, 0x3FEC59B5, 0x963F4150, 0xBE282696, + 0x18000000, 0x3FEC67E6, 0x3049824B, 0x3E224D26, + 0x98000000, 0x3FEC761D, 0x87F84C7D, 0x3E2C5BA5, + 0x38000000, 0x3FEC845C, 0xC4852339, 0xBDE1D14D, + 0xF8000000, 0x3FEC92A1, 0x5588D9E1, 0xBE1A451E, + 0xDC000000, 0x3FECA0EE, 0x68BFF457, 0xBE1D3B96, + 0xE8000000, 0x3FECAF42, 0x4DADF774, 0xBE18B670, + 0x20000000, 0x3FECBD9E, 0x7FB1FC01, 0xBE1A1548, + 0x88000000, 0x3FECCC00, 0x78FC5AF0, 0xBE273F2E, + 0x20000000, 0x3FECDA6A, 0xA6F4A841, 0x3E1D218F, + 0xF0000000, 0x3FECE8DA, 0x4D002CA0, 0x3E2E0BA9, + 0xFC000000, 0x3FECF752, 0x065EF979, 0x3E20F4BB, + 0x48000000, 0x3FED05D2, 0x11793B33, 0xBE2ED3D5, + 0xD0000000, 0x3FED1458, 0x913341B3, 0x3E115E3C, + 0xA0000000, 0x3FED22E6, 0xB3546109, 0x3DE97C02, + 0xB8000000, 0x3FED317B, 0x1BF898EF, 0x3E087540, + 0x1C000000, 0x3FED4018, 0x346F9641, 0x3E209430, + 0xD0000000, 0x3FED4EBB, 0x88F4B20B, 0x3E2B6DF4, + 0xDC000000, 0x3FED5D66, 0x0CB26035, 0xBE2EC68F, + 0x38000000, 0x3FED6C19, 0x1F44D9C3, 0x3E2CA2C8, + 0xF4000000, 0x3FED7AD2, 0x41704EE0, 0x3E10E6F4, + 0x0C000000, 0x3FED8994, 0x25F8F0E2, 0x3E2F9273, + 0x88000000, 0x3FED985C, 0x318798DE, 0x3E2D041A, + 0x6C000000, 0x3FEDA72C, 0x9349CF58, 0xBE005680, + 0xB8000000, 0x3FEDB603, 0xCF0C934D, 0xBE10F665, + 0x70000000, 0x3FEDC4E2, 0x19461C64, 0x3E166124, + 0x9C000000, 0x3FEDD3C8, 0x405624C8, 0xBE1B2ED6, + 0x3C000000, 0x3FEDE2B6, 0x62171501, 0xBE273A7F, + 0x54000000, 0x3FEDF1AB, 0xE36E1450, 0xBE26022B, + 0xE8000000, 0x3FEE00A7, 0x2E07AE15, 0xBE1C341E, + 0xFC000000, 0x3FEE0FAB, 0x18D0E701, 0xBDFC7EAE, + 0x94000000, 0x3FEE1EB7, 0xECD1FF8B, 0x3E06B34F, + 0xB4000000, 0x3FEE2DCA, 0x6813A649, 0x3E1394A3, + 0x60000000, 0x3FEE3CE5, 0xC1754D14, 0x3E045496, + 0x9C000000, 0x3FEE4C07, 0xF5C6087C, 0xBE180FFF, + 0x68000000, 0x3FEE5B31, 0xADD9A300, 0x3E22FBCD, + 0xCC000000, 0x3FEE6A62, 0xAF0289E5, 0x3E2EC7C7, + 0xCC000000, 0x3FEE799B, 0x3FB3EDD4, 0x3E242182, + 0x6C000000, 0x3FEE88DC, 0x04E39885, 0xBE201304, + 0xAC000000, 0x3FEE9824, 0xE6831D31, 0xBE20D352, + 0x90000000, 0x3FEEA774, 0x618DFCEB, 0x3E1E032D, + 0x20000000, 0x3FEEB6CC, 0xF9BB457E, 0x3E1956A3, + 0x60000000, 0x3FEEC62B, 0x50845DB2, 0xBE2A77E0, + 0x4C000000, 0x3FEED592, 0x47C43858, 0x3E2714F7, + 0xF0000000, 0x3FEEE500, 0x71813A66, 0x3E2EED96, + 0x50000000, 0x3FEEF477, 0x4FB4AA34, 0xBE04CDBE, + 0x6C000000, 0x3FEF03F5, 0x86EB4FF5, 0xBE2774A2, + 0x48000000, 0x3FEF137B, 0xAD43B2D2, 0xBE29DD95, + 0xE8000000, 0x3FEF2308, 0xAC16E506, 0xBE1CADB0, + 0x50000000, 0x3FEF329E, 0x58745C7B, 0x3E12AC33, + 0x88000000, 0x3FEF423B, 0x6EC2D854, 0xBE248118, + 0x8C000000, 0x3FEF51E0, 0x304ACE08, 0x3E26986B, + 0x68000000, 0x3FEF618D, 0x3B09354E, 0x3E126D81, + 0x1C000000, 0x3FEF7142, 0x773C23B3, 0x3DF06AAE, + 0xAC000000, 0x3FEF80FE, 0xD82EF423, 0xBDA105B6, + 0x1C000000, 0x3FEF90C3, 0x465499B8, 0x3DECDEED, + 0x70000000, 0x3FEFA08F, 0xE2EF03AE, 0x3E0AEFD4, + 0xAC000000, 0x3FEFB063, 0x0567B2E7, 0x3E1BD4C0, + 0xD4000000, 0x3FEFC03F, 0x4F97FCBF, 0x3E26AA22, + 0xF0000000, 0x3FEFD023, 0x5E4E88D1, 0xBE2F9420, + 0xFC000000, 0x3FEFE00F, 0x438E52E2, 0xBE254004, + 0x00000000, 0x3FEFF004, 0xEEE93EFC, 0xBE1552AA, + 0x00000000, 0x3FF00000, 0x00000000, 0x00000000, + 0x00000000, 0x3FF00802, 0x4449F507, 0x3E155800, + 0x04000000, 0x3FF01008, 0x882D75D6, 0xBE354AA8, + 0x08000000, 0x3FF01812, 0x3740DE56, 0x3E303610, + 0x14000000, 0x3FF02020, 0x5B0C3264, 0x3E360044, + 0x28000000, 0x3FF02832, 0x0197EDC3, 0x3E3C4C26, + 0x48000000, 0x3FF03048, 0x5046CA09, 0x3E0B103B, + 0x74000000, 0x3FF03862, 0xF9A62624, 0xBE34659C, + 0xAC000000, 0x3FF04080, 0xDD0A8F37, 0xBE254438, + 0xF4000000, 0x3FF048A2, 0x97AFB6E2, 0x3DF256C2, + 0x50000000, 0x3FF050C9, 0x923D25E1, 0xBE3085DF, + 0xC0000000, 0x3FF058F3, 0x5EA3B091, 0xBE3F0A93, + 0x44000000, 0x3FF06122, 0x5D63534C, 0xBE237DE4, + 0xE0000000, 0x3FF06954, 0xFF0C58B7, 0x3E301719, + 0x98000000, 0x3FF0718B, 0x9DF7B665, 0x3E2E8410, + 0x6C000000, 0x3FF079C6, 0x3B127222, 0x3E349CB9, + 0x60000000, 0x3FF08205, 0x98E0BD08, 0x3DF127EC, + 0x74000000, 0x3FF08A48, 0x706CC41F, 0xBE24C1B6, + 0xA8000000, 0x3FF0928F, 0x093044EF, 0x3E334EF9, + 0x04000000, 0x3FF09ADB, 0x56BC6C83, 0xBE1304B1, + 0x84000000, 0x3FF0A32A, 0xB028B984, 0x3E2D383E, + 0x30000000, 0x3FF0AB7E, 0x64E7A202, 0xBE315B1E, + 0x04000000, 0x3FF0B3D6, 0xC678291E, 0xBE0AC1E6, + 0x04000000, 0x3FF0BC32, 0x2F12FFE2, 0x3E3A0418, + 0x38000000, 0x3FF0C492, 0x43D6D302, 0xBE37D617, + 0x98000000, 0x3FF0CCF6, 0x152CC8FA, 0x3E2133F2, + 0x2C000000, 0x3FF0D55F, 0xE966E6B7, 0x3E3CE5D1, + 0xF8000000, 0x3FF0DDCB, 0x7BCACA64, 0x3E1ABF24, + 0xFC000000, 0x3FF0E63C, 0x2E8CDBED, 0xBE3854F6, + 0x38000000, 0x3FF0EEB2, 0x0C32156B, 0xBE3E6463, + 0xAC000000, 0x3FF0F72B, 0xB69772CC, 0x3E365671, + 0x64000000, 0x3FF0FFA9, 0x02B1201A, 0xBE383E9A, + 0x58000000, 0x3FF1082B, 0x50549CC0, 0xBE205962, + 0x90000000, 0x3FF110B1, 0xFFDACA72, 0xBE376BFE, + 0x08000000, 0x3FF1193C, 0x5C43E2F3, 0x3E3C1C59, + 0xCC000000, 0x3FF121CA, 0xF7067C8B, 0xBE26D374, + 0xD4000000, 0x3FF12A5D, 0x4DDAFE1D, 0x3E343CCC, + 0x28000000, 0x3FF132F5, 0x58EBCB7F, 0x3E3D5C16, + 0xCC000000, 0x3FF13B90, 0xB66E8B53, 0xBE2B5D12, + 0xBC000000, 0x3FF14430, 0xB326B482, 0xBE24E919, + 0xFC000000, 0x3FF14CD4, 0xC8AABD43, 0x3E23139A, + 0x90000000, 0x3FF1557D, 0x16743B55, 0x3E30DD8B, + 0x7C000000, 0x3FF15E2A, 0x35904C50, 0xBE31D701, + 0xBC000000, 0x3FF166DB, 0x30E0CA83, 0x3E107F42, + 0x58000000, 0x3FF16F91, 0xDA1B7123, 0xBE24F1F2, + 0x50000000, 0x3FF1784B, 0x0DC79E23, 0xBE3ACAF2, + 0xA4000000, 0x3FF18109, 0x609374EE, 0xBE23DC79, + 0x58000000, 0x3FF189CC, 0x3A40C3B7, 0x3E262CF7, + 0x70000000, 0x3FF19293, 0x5A24F463, 0x3E1D3833, + 0xEC000000, 0x3FF19B5E, 0x8A2E4440, 0x3E2BA9AD, + 0xD0000000, 0x3FF1A42E, 0x61C41828, 0x3DFD8CBC, + 0x1C000000, 0x3FF1AD03, 0x5A4DDF0D, 0x3E1A65E6, + 0xD4000000, 0x3FF1B5DB, 0x9F828DB5, 0xBDE2FDBB, + 0xF8000000, 0x3FF1BEB8, 0xB79B700F, 0x3E2F4EE8, + 0x8C000000, 0x3FF1C79A, 0x0DE1D7E8, 0x3E3ACC35, + 0x94000000, 0x3FF1D080, 0xFF9E20A0, 0x3E11729E, + 0x10000000, 0x3FF1D96B, 0x6C2EA70B, 0xBE300F18, + 0x00000000, 0x3FF1E25A, 0xCE425A35, 0x3DF32E02, + 0x68000000, 0x3FF1EB4D, 0x9A322D12, 0x3E3BDE56, + 0x50000000, 0x3FF1F445, 0xBA737AEF, 0xBE3C3F0D, + 0xB0000000, 0x3FF1FD41, 0xC896DB7A, 0xBE0A2DD0, + 0x90000000, 0x3FF20642, 0xF8B782F6, 0x3E2577B0, + 0xF4000000, 0x3FF20F47, 0x73607FC8, 0xBE2C6DA3, + 0xD8000000, 0x3FF21851, 0xC8917348, 0x3E35F7D1, + 0x44000000, 0x3FF22160, 0xCF9CED69, 0x3E3B6F5C, + 0x3C000000, 0x3FF22A73, 0x85775C2E, 0xBE39967E, + 0xB8000000, 0x3FF2338A, 0x497226D4, 0x3E3B3213, + 0xC4000000, 0x3FF23CA6, 0x30733227, 0x3E3E2710, + 0x60000000, 0x3FF245C7, 0xAF215A72, 0x3E33B8A9, + 0x90000000, 0x3FF24EEC, 0x1365623F, 0xBE3F96B2, + 0x50000000, 0x3FF25816, 0x27DEE202, 0xBE37324F, + 0xA4000000, 0x3FF26144, 0x4E484D87, 0x3E318CD5, + 0x94000000, 0x3FF26A77, 0xA94519E8, 0xBDE3FD37, + 0x1C000000, 0x3FF273AF, 0xEE788C29, 0x3E37132F, + 0x44000000, 0x3FF27CEB, 0xE842E5C0, 0xBE03DDB7, + 0x08000000, 0x3FF2862C, 0xE17C9693, 0x3E37A3FB, + 0x70000000, 0x3FF28F71, 0xAEB3D9A0, 0x3E24EABF, + 0x7C000000, 0x3FF298BB, 0x853B0733, 0xBE13C7B6, + 0x2C000000, 0x3FF2A20A, 0xC7B588B5, 0x3E2D2C80, + 0x88000000, 0x3FF2AB5D, 0x708F3912, 0xBE35B750, + 0x8C000000, 0x3FF2B4B5, 0xD5FD9130, 0xBE291A70, + 0x3C000000, 0x3FF2BE12, 0x0CCF9F73, 0x3E2EE937, + 0xA0000000, 0x3FF2C773, 0xD42CF76C, 0xBE3C3F0C, + 0xB0000000, 0x3FF2D0D9, 0x60763D61, 0x3E35DD54, + 0x78000000, 0x3FF2DA44, 0xE7D6AA3B, 0x3E26C418, + 0xF8000000, 0x3FF2E3B3, 0x6FB9B7A8, 0xBE3605C6, + 0x2C000000, 0x3FF2ED28, 0x24DCDDF5, 0x3E3763D4, + 0x20000000, 0x3FF2F6A1, 0xA8EC1AA8, 0xBE1A411E, + 0xD0000000, 0x3FF3001E, 0x1FE8546F, 0xBE23FCA1, + 0x40000000, 0x3FF309A1, 0x3AAEE75E, 0xBE29DF0D, + 0x70000000, 0x3FF31328, 0x3C2C4206, 0x3E36A5D6, + 0x68000000, 0x3FF31CB4, 0xB4C979B0, 0x3E1B7A3E, + 0x28000000, 0x3FF32645, 0x706CD593, 0xBE36157D, + 0xB0000000, 0x3FF32FDA, 0x8DA4C646, 0xBE39F357, + 0x04000000, 0x3FF33975, 0xD575FE6F, 0xBE3E64DE, + 0x24000000, 0x3FF34314, 0x44D008E0, 0x3E07F9E3, + 0x18000000, 0x3FF34CB8, 0x5A563E77, 0xBE2E94F9, + 0xDC000000, 0x3FF35660, 0x2475EF19, 0x3E314DC2, + 0x78000000, 0x3FF3600E, 0xA33AC606, 0x3E26D623, + 0xEC000000, 0x3FF369C0, 0xC05B3160, 0x3E170F86, + 0x3C000000, 0x3FF37378, 0xDB0AE31A, 0xBE38DDFE, + 0x64000000, 0x3FF37D34, 0x5706B570, 0x3E3662A9, + 0x70000000, 0x3FF386F5, 0x6770731E, 0xBE1625E4, + 0x5C000000, 0x3FF390BB, 0x62971091, 0xBE1678F1, + 0x2C000000, 0x3FF39A86, 0xD045CB0C, 0xBE061F7C, + 0xE4000000, 0x3FF3A455, 0x568B1CA2, 0xBE35CF51, + 0x84000000, 0x3FF3AE2A, 0x7FB61F58, 0xBE378185, + 0x0C000000, 0x3FF3B804, 0x4FA133AF, 0x3E3F77F4, + 0x88000000, 0x3FF3C1E2, 0xB00B73FE, 0xBE22F96A, + 0xF0000000, 0x3FF3CBC5, 0x1EB4CE2F, 0x3E351A64, + 0x50000000, 0x3FF3D5AE, 0xD3755639, 0xBE3D3516, + 0xA0000000, 0x3FF3DF9B, 0x43E8C10E, 0x3E1CD938, + 0xEC000000, 0x3FF3E98D, 0x455C8842, 0xBE35EE23, + 0x30000000, 0x3FF3F385, 0x96C9F4ED, 0xBE29B282, + 0x70000000, 0x3FF3FD81, 0x3168CC0B, 0x3E24A40E, + 0xB0000000, 0x3FF40782, 0x86C72839, 0x3E3784BC, + 0xF4000000, 0x3FF41188, 0x0785D847, 0x3E061F19, + 0x3C000000, 0x3FF41B94, 0xE654A9C9, 0xBE27AEF2, + 0x88000000, 0x3FF425A4, 0xF9E4C1BA, 0x3E33DFC3, + 0xE0000000, 0x3FF42FB9, 0x593D0C75, 0x3E2455A8, + 0x44000000, 0x3FF439D4, 0x238B65D1, 0xBDE41D4E, + 0xB4000000, 0x3FF443F3, 0x454CBECB, 0x3E3BE616, + 0x38000000, 0x3FF44E18, 0x931C5332, 0x3E207B3C, + 0xD0000000, 0x3FF45841, 0x7615DCC9, 0xBE330846, + 0x7C000000, 0x3FF46270, 0xE497F84E, 0xBE2A8A7B, + 0x40000000, 0x3FF46CA4, 0xF737AF78, 0x3E020B50, + 0x20000000, 0x3FF476DD, 0xE34AFBD3, 0x3E116B19, + 0x20000000, 0x3FF4811B, 0x841EDB52, 0xBE3E15A7, + 0x3C000000, 0x3FF48B5E, 0x33B3DE1E, 0x3E0F40C3, + 0x7C000000, 0x3FF495A6, 0x92EFEE02, 0x3E33607F, + 0xE4000000, 0x3FF49FF3, 0x14F7E168, 0xBE1A2DB5, + 0x70000000, 0x3FF4AA46, 0x3EBA1C94, 0x3E3F59EC, + 0x2C000000, 0x3FF4B49E, 0x8B9AE885, 0xBE31A539, + 0x10000000, 0x3FF4BEFB, 0xF13C8C95, 0x3E2FAC0B, + 0x28000000, 0x3FF4C95D, 0xF8B74775, 0xBE32C0BB, + 0x70000000, 0x3FF4D3C4, 0x4F9474BB, 0xBE2FC24E, + 0xEC000000, 0x3FF4DE30, 0x09DA911F, 0x3E008F30, + 0xA0000000, 0x3FF4E8A2, 0xBAF8D98B, 0x3E2994C1, + 0x90000000, 0x3FF4F319, 0x18648D0A, 0xBE17C38C, + 0xBC000000, 0x3FF4FD95, 0xF22F8698, 0xBE288852, + 0x28000000, 0x3FF50817, 0x30A2C153, 0xBE3C3EC3, + 0xD4000000, 0x3FF5129D, 0x968492AA, 0xBE27B606, + 0xC4000000, 0x3FF51D29, 0x61101629, 0x3E2E0396, + 0xFC000000, 0x3FF527BA, 0xDAEEAB38, 0x3E3E876F, + 0x80000000, 0x3FF53251, 0xED945B30, 0x3E29F59E, + 0x50000000, 0x3FF53CED, 0x0B4AE3F1, 0x3E12D7DA, + 0x70000000, 0x3FF5478E, 0x5FB946D0, 0xBE2FAFB8, + 0xE0000000, 0x3FF55234, 0x87D80C66, 0xBE18A8B3, + 0xA4000000, 0x3FF55CE0, 0x764CF85C, 0x3E28B18F, + 0xC0000000, 0x3FF56791, 0x2BDBC6F4, 0x3E326017, + 0x38000000, 0x3FF57248, 0x53D523FE, 0xBE229F98, + 0x0C000000, 0x3FF57D04, 0x4D9B8720, 0xBE3BDD08, + 0x3C000000, 0x3FF587C5, 0x09D8749E, 0x3E169EBC, + 0xD0000000, 0x3FF5928B, 0x339C2080, 0x3E190C8C, + 0xC8000000, 0x3FF59D57, 0xDE75E9CA, 0x3E310FA4, + 0x28000000, 0x3FF5A829, 0x1097F186, 0x3E313D18, + 0xF4000000, 0x3FF5B2FF, 0xD51C23F6, 0xBE2BDE04, + 0x28000000, 0x3FF5BDDC, 0x8938C386, 0x3E3EE67E, + 0xD0000000, 0x3FF5C8BD, 0x47DF6575, 0x3E0973B8, + 0xE8000000, 0x3FF5D3A4, 0x1DB97781, 0x3E24DF02, + 0x78000000, 0x3FF5DE91, 0xAC4AECDC, 0xBE3FBA00, + 0x7C000000, 0x3FF5E983, 0x939F646A, 0xBE2F37AF, + 0xFC000000, 0x3FF5F47A, 0x58A6EEE9, 0xBE396DEF, + 0xF8000000, 0x3FF5FF77, 0xE3613C7B, 0xBE315248, + 0x74000000, 0x3FF60A7A, 0xF1553706, 0xBE26A9E2, + 0x74000000, 0x3FF61582, 0xAE4D7CB6, 0xBE3B6BF6, + 0xF8000000, 0x3FF6208F, 0x9EB5EBA5, 0xBE35775B, + 0x04000000, 0x3FF62BA3, 0xC1E43506, 0xBE2A821B, + 0x9C000000, 0x3FF636BB, 0x7B2D8CF4, 0xBE367CDA, + 0xC0000000, 0x3FF641D9, 0x3E907A1D, 0xBE13218B, + 0x74000000, 0x3FF64CFD, 0x7BF5DFE4, 0x3E3454EE, + 0xC0000000, 0x3FF65826, 0x6366C5FD, 0xBE3E960F, + 0x9C000000, 0x3FF66355, 0x8B43C17E, 0x3E2E378F, + 0x14000000, 0x3FF66E8A, 0xA4306535, 0x3E244BE0, + 0x28000000, 0x3FF679C4, 0x8DF63D6E, 0xBDE4B6C1, + 0xD8000000, 0x3FF68503, 0xE6A239CF, 0x3E3BA122, + 0x2C000000, 0x3FF69049, 0x59FB5F30, 0x3E27F286, + 0x24000000, 0x3FF69B94, 0x971D3970, 0xBE044041 } }; + +static const union { + int4 i[2048]; + double x[1024]; +} fine = { .i = { + 0x00000000, 0x3FF00000, 0x00000000, 0x00000000, + 0x00000000, 0x3FF00004, 0x55556AAB, 0x3DA00001, + 0x00000000, 0x3FF00008, 0xAAAB0000, 0x3DC00002, + 0x00000000, 0x3FF0000C, 0x8000D800, 0x3DD20004, + 0x00000000, 0x3FF00010, 0x5556AAAB, 0x3DE00005, + 0x00000000, 0x3FF00014, 0x6AADEC01, 0x3DE9000A, + 0x00000000, 0x3FF00018, 0x00036001, 0x3DF20009, + 0x00000000, 0x3FF0001C, 0x4AB0EB58, 0x3DF8800E, + 0x00000000, 0x3FF00020, 0xAAB00002, 0x3E00000A, + 0x00000000, 0x3FF00024, 0x30088B04, 0x3E04400F, + 0x00000000, 0x3FF00028, 0xD5625AB1, 0x3E090014, + 0x00000000, 0x3FF0002C, 0xBABDBB0A, 0x3E0E401B, + 0x00000000, 0x3FF00030, 0x000D8008, 0x3E120012, + 0x00000000, 0x3FF00034, 0xE2BD42E1, 0x3E152016, + 0x00000000, 0x3FF00038, 0x956E5812, 0x3E18801C, + 0x00000000, 0x3FF0003C, 0x2820F599, 0x3E1C2023, + 0x00000000, 0x3FF00040, 0x556AAABC, 0x3E200015, + 0x00000000, 0x3FF00044, 0x96C5DAD7, 0x3E221019, + 0x00000000, 0x3FF00048, 0x60222C1F, 0x3E24401E, + 0x00000000, 0x3FF0004C, 0xB97FC193, 0x3E269023, + 0x00000000, 0x3FF00050, 0xAADEC034, 0x3E290029, + 0x00000000, 0x3FF00054, 0x3C3F4F02, 0x3E2B9030, + 0x00000000, 0x3FF00058, 0x75A196FF, 0x3E2E4037, + 0x00000000, 0x3FF0005C, 0xAF82E194, 0x3E30881F, + 0x00000000, 0x3FF00060, 0x00360041, 0x3E320024, + 0x00000000, 0x3FF00064, 0xB0EA3F05, 0x3E338828, + 0x00000000, 0x3FF00068, 0xC59FB661, 0x3E35202D, + 0x00000000, 0x3FF0006C, 0x42567FD5, 0x3E36C833, + 0x00000000, 0x3FF00070, 0x2B0EB5E1, 0x3E388039, + 0x00000000, 0x3FF00074, 0x83C87407, 0x3E3A483F, + 0x00000000, 0x3FF00078, 0x5083D6C6, 0x3E3C2046, + 0x00000000, 0x3FF0007C, 0x9540FB9E, 0x3E3E084D, + 0x04000000, 0x3FF00080, 0xA9FFFEEF, 0xBE3FFFAA, + 0x04000000, 0x3FF00084, 0x693EF962, 0xBE3DF7A2, + 0x04000000, 0x3FF00088, 0xA47BD339, 0xBE3BDF99, + 0x04000000, 0x3FF0008C, 0x57B66AF5, 0xBE39B790, + 0x04000000, 0x3FF00090, 0x7EEE9E14, 0xBE377F86, + 0x04000000, 0x3FF00094, 0x16244916, 0xBE35377C, + 0x04000000, 0x3FF00098, 0x1957477B, 0xBE32DF71, + 0x04000000, 0x3FF0009C, 0x848773C2, 0xBE307765, + 0x04000000, 0x3FF000A0, 0xA7694ED3, 0xBE2BFEB2, + 0x04000000, 0x3FF000A4, 0x05BD75E2, 0xBE26EE99, + 0x04000000, 0x3FF000A8, 0x1C0B0BB1, 0xBE21BE7E, + 0x04000000, 0x3FF000AC, 0xC4A37A79, 0xBE18DCC3, + 0x04000000, 0x3FF000B0, 0x4244D60F, 0xBE0BF911, + 0x04000000, 0x3FF000B4, 0xEC91D848, 0xBDE6E255, + 0x04000000, 0x3FF000B8, 0xEC1B8F0C, 0x3E0107EB, + 0x04000000, 0x3FF000BC, 0x89BE52AA, 0x3E142439, + 0x04000000, 0x3FF000C0, 0x06C01033, 0x3E200240, + 0x04000000, 0x3FF000C4, 0xC8A9F760, 0x3E261264, + 0x04000000, 0x3FF000C8, 0x129D3FDE, 0x3E2C428B, + 0x04000000, 0x3FF000CC, 0x764D2658, 0x3E314959, + 0x04000000, 0x3FF000D0, 0x2F50C16C, 0x3E34816E, + 0x04000000, 0x3FF000D4, 0xB859A4AB, 0x3E37C983, + 0x04000000, 0x3FF000D8, 0x15680499, 0x3E3B219A, + 0x04000000, 0x3FF000DC, 0x4A7C16B5, 0x3E3E89B1, + 0x08000000, 0x3FF000E0, 0xA469EE7E, 0xBE3DFE36, + 0x08000000, 0x3FF000E4, 0xB349D37F, 0xBE3A761D, + 0x08000000, 0x3FF000E8, 0xDE235FCD, 0xBE36DE03, + 0x08000000, 0x3FF000EC, 0x20F659E6, 0xBE3335E9, + 0x08000000, 0x3FF000F0, 0xEF850E8F, 0xBE2EFB9A, + 0x08000000, 0x3FF000F4, 0xBD0F58E2, 0xBE276B61, + 0x08000000, 0x3FF000F8, 0x45163381, 0xBE1F764D, + 0x08000000, 0x3FF000FC, 0x5FDF589A, 0xBE0FABA6, + 0x08000000, 0x3FF00100, 0xABBBBE94, 0x3D8555AA, + 0x08000000, 0x3FF00104, 0xDABB690B, 0x3E102B2C, + 0x08000000, 0x3FF00108, 0x7820FBA0, 0x3E2045D9, + 0x08000000, 0x3FF0010C, 0x92F54742, 0x3E28961E, + 0x08000000, 0x3FF00110, 0xE2ED8E39, 0x3E308332, + 0x08000000, 0x3FF00114, 0x8C698119, 0x3E34CB57, + 0x08000000, 0x3FF00118, 0x49EEC0C4, 0x3E39237D, + 0x08000000, 0x3FF0011C, 0x1F7D92BC, 0x3E3D8BA4, + 0x0C000000, 0x3FF00120, 0xEEE9C27D, 0xBE3DFC33, + 0x0C000000, 0x3FF00124, 0xDD46F763, 0xBE39740A, + 0x0C000000, 0x3FF00128, 0xA799C375, 0xBE34DBE0, + 0x0C000000, 0x3FF0012C, 0x49E1DD2F, 0xBE3033B5, + 0x0C000000, 0x3FF00130, 0x803DF41F, 0xBE26F711, + 0x0C000000, 0x3FF00134, 0x19433A4C, 0xBE1ACD6C, + 0x0C000000, 0x3FF00138, 0x8770E36F, 0xBDFDB2C1, + 0x0C000000, 0x3FF0013C, 0x6B74A43E, 0x3E086820, + 0x0C000000, 0x3FF00140, 0xDEC0D058, 0x3E200A6A, + 0x0C000000, 0x3FF00144, 0x22BD7872, 0x3E2A1AD0, + 0x0C000000, 0x3FF00148, 0xF769E132, 0x3E32259B, + 0x0C000000, 0x3FF0014C, 0x2582289A, 0x3E374DD1, + 0x0C000000, 0x3FF00150, 0x9FA7E4F4, 0x3E3C8607, + 0x10000000, 0x3FF00154, 0x9624963C, 0xBE3E31C0, + 0x10000000, 0x3FF00158, 0x77E2F472, 0xBE38D987, + 0x10000000, 0x3FF0015C, 0x0192E02C, 0xBE33714D, + 0x10000000, 0x3FF00160, 0x5E6805CB, 0xBE2BF222, + 0x10000000, 0x3FF00164, 0xF98C0A34, 0xBE20E1A7, + 0x10000000, 0x3FF00168, 0x32447238, 0xBE06C4AB, + 0x10000000, 0x3FF0016C, 0xC225D8C1, 0x3E067D54, + 0x10000000, 0x3FF00170, 0x05C4630F, 0x3E210FD8, + 0x10000000, 0x3FF00174, 0xBB206115, 0x3E2CA05D, + 0x10000000, 0x3FF00178, 0x2C4F14A6, 0x3E342873, + 0x10000000, 0x3FF0017C, 0xF31F3B5E, 0x3E3A10B8, + 0x14000000, 0x3FF00180, 0xC9FEFCC9, 0xBE3FF6FF, + 0x14000000, 0x3FF00184, 0x070B344A, 0xBE39EEB7, + 0x14000000, 0x3FF00188, 0xC0050AA2, 0xBE33D66C, + 0x14000000, 0x3FF0018C, 0xE1D83C97, 0xBE2B5C41, + 0x14000000, 0x3FF00190, 0x57003305, 0xBE1DD74E, + 0x14000000, 0x3FF00194, 0xA80727F1, 0xBDF2D84A, + 0x14000000, 0x3FF00198, 0x534C5401, 0x3E14AB2F, + 0x14000000, 0x3FF0019C, 0xD875DE83, 0x3E27263B, + 0x14000000, 0x3FF001A0, 0x9FB782CA, 0x3E320B71, + 0x14000000, 0x3FF001A4, 0xF349371F, 0x3E3893C6, + 0x14000000, 0x3FF001A8, 0xEAF074C6, 0x3E3F2C1D, + 0x18000000, 0x3FF001AC, 0x75525ABC, 0xBE3A2B89, + 0x18000000, 0x3FF001B0, 0x297ECCE2, 0xBE33732F, + 0x18000000, 0x3FF001B4, 0x5B28EC49, 0xBE2955A6, + 0x18000000, 0x3FF001B8, 0xF64BA7FD, 0xBE1749D5, + 0x18000000, 0x3FF001BC, 0xA8645141, 0x3DF15E9E, + 0x18000000, 0x3FF001C0, 0x1D6F0B37, 0x3E201C96, + 0x18000000, 0x3FF001C4, 0xE6028E39, 0x3E2E2D5B, + 0x18000000, 0x3FF001C8, 0x9B63FA1E, 0x3E362F12, + 0x18000000, 0x3FF001CC, 0x0BE01026, 0x3E3D5779, + 0x1C000000, 0x3FF001D0, 0xB78A0445, 0xBE3B701E, + 0x1C000000, 0x3FF001D4, 0xAAD9CF9D, 0xBE3427B4, + 0x1C000000, 0x3FF001D8, 0x941DBAB5, 0xBE299E91, + 0x1C000000, 0x3FF001DC, 0x44A2DFDD, 0xBE159B6C, + 0x1C000000, 0x3FF001E0, 0x1EC8B89C, 0x3E008CA4, + 0x1C000000, 0x3FF001E4, 0xF1EE0E9A, 0x3E23340B, + 0x1C000000, 0x3FF001E8, 0x5231913C, 0x3E313279, + 0x1C000000, 0x3FF001EC, 0x93892E68, 0x3E38DAEE, + 0x20000000, 0x3FF001F0, 0x3F01A6A8, 0xBE3F6C9A, + 0x20000000, 0x3FF001F4, 0x216E726C, 0xBE37A421, + 0x20000000, 0x3FF001F8, 0x1F7970B9, 0xBE2F974C, + 0x20000000, 0x3FF001FC, 0x17AFEBC8, 0xBE1F8CA4, + 0x20000000, 0x3FF00200, 0x04445B06, 0x3DB55600, + 0x20000000, 0x3FF00204, 0x0C290A26, 0x3E203BAE, + 0x20000000, 0x3FF00208, 0x104547BD, 0x3E30365A, + 0x20000000, 0x3FF0020C, 0x22970DE3, 0x3E385EDF, + 0x24000000, 0x3FF00210, 0xBEF5A5F4, 0xBE3F6899, + 0x24000000, 0x3FF00214, 0x90605040, 0xBE372010, + 0x24000000, 0x3FF00218, 0x9B50D8EE, 0xBE2D8F0A, + 0x24000000, 0x3FF0021C, 0xCB35D444, 0xBE197BDF, + 0x24000000, 0x3FF00220, 0x2188E3D5, 0x3E00CCBC, + 0x24000000, 0x3FF00224, 0x36A79F6A, 0x3E254452, + 0x24000000, 0x3FF00228, 0xD69B2D28, 0x3E333ABC, + 0x24000000, 0x3FF0022C, 0xBA07BE5B, 0x3E3BE352, + 0x28000000, 0x3FF00230, 0x3665F227, 0xBE3B6415, + 0x28000000, 0x3FF00234, 0xF6AD58D5, 0xBE329B7A, + 0x28000000, 0x3FF00238, 0x059BD24A, 0xBE2385BD, + 0x28000000, 0x3FF0023C, 0xD8E2B1B4, 0xBDEB47FA, + 0x28000000, 0x3FF00240, 0x22CF60F6, 0x3E203CC2, + 0x28000000, 0x3FF00244, 0x39BEF87F, 0x3E312704, + 0x28000000, 0x3FF00248, 0xA63F5309, 0x3E3A3FA9, + 0x2C000000, 0x3FF0024C, 0xA516AE5E, 0xBE3C97AE, + 0x2C000000, 0x3FF00250, 0xA442792A, 0xBE335F04, + 0x2C000000, 0x3FF00254, 0xA686F3A2, 0xBE242CB0, + 0x2C000000, 0x3FF00258, 0xC3237903, 0xBDE7B535, + 0x2C000000, 0x3FF0025C, 0x9E7A6CF7, 0x3E21560E, + 0x2C000000, 0x3FF00260, 0xA8C01385, 0x3E3223BA, + 0x2C000000, 0x3FF00264, 0x627012DF, 0x3E3BAC70, + 0x30000000, 0x3FF00268, 0x7FB232EA, 0xBE3ABAD7, + 0x30000000, 0x3FF0026C, 0xF9A6244B, 0xBE31121C, + 0x30000000, 0x3FF00270, 0x1DAC9AE4, 0xBE1D6580, + 0x30000000, 0x3FF00274, 0xD7FB0AC3, 0x3E037AFA, + 0x30000000, 0x3FF00278, 0x633420EB, 0x3E289042, + 0x30000000, 0x3FF0027C, 0x8065842A, 0x3E3630E5, + 0x34000000, 0x3FF00280, 0xB49DA4FF, 0xBE3FD653, + 0x34000000, 0x3FF00284, 0x696ECB76, 0xBE35CD8A, + 0x34000000, 0x3FF00288, 0x341A9D63, 0xBE27697D, + 0x34000000, 0x3FF0028C, 0x2788D238, 0xBDF8BF04, + 0x34000000, 0x3FF00290, 0x42A03782, 0x3E2159C1, + 0x34000000, 0x3FF00294, 0x154D4F89, 0x3E32F5B4, + 0x34000000, 0x3FF00298, 0x1D7FB2C1, 0x3E3D4E8A, + 0x38000000, 0x3FF0029C, 0x42181508, 0xBE38489D, + 0x38000000, 0x3FF002A0, 0x0AF2C28C, 0xBE2B9F84, + 0x38000000, 0x3FF002A4, 0x451C5357, 0xBE0A3721, + 0x38000000, 0x3FF002A8, 0x61A8605E, 0x3E1D47F1, + 0x38000000, 0x3FF002AC, 0x81B02FCF, 0x3E31FADF, + 0x38000000, 0x3FF002B0, 0x572F674A, 0x3E3CB3C5, + 0x3C000000, 0x3FF002B4, 0x231795EA, 0xBE388352, + 0x3C000000, 0x3FF002B8, 0xD248367A, 0xBE2B54CD, + 0x3C000000, 0x3FF002BC, 0xB7ABD90D, 0xBE060BC7, + 0x3C000000, 0x3FF002C0, 0x6EE9F1EF, 0x3E206EEF, + 0x3C000000, 0x3FF002C4, 0x261BF09E, 0x3E33406B, + 0x3C000000, 0x3FF002C8, 0x59001C60, 0x3E3E5961, + 0x40000000, 0x3FF002CC, 0xABDDD232, 0xBE367DA5, + 0x40000000, 0x3FF002D0, 0xC8FA5113, 0xBE268953, + 0x40000000, 0x3FF002D4, 0x8B33A701, 0x3D9152CC, + 0x40000000, 0x3FF002D8, 0x3E058570, 0x3E26BAAC, + 0x40000000, 0x3FF002DC, 0x63236E71, 0x3E36C65A, + 0x44000000, 0x3FF002E0, 0x7C7A795C, 0xBE3DC09E, + 0x44000000, 0x3FF002E4, 0x7BD63D1D, 0xBE323794, + 0x44000000, 0x3FF002E8, 0x5BBC9105, 0xBE1A7A1E, + 0x44000000, 0x3FF002EC, 0xD8EE2B1B, 0x3E142A20, + 0x44000000, 0x3FF002F0, 0xEFAA8A8D, 0x3E30C39A, + 0x44000000, 0x3FF002F4, 0x995E96A2, 0x3E3C8CB0, + 0x48000000, 0x3FF002F8, 0xC8A79469, 0xBE379A36, + 0x48000000, 0x3FF002FC, 0x64CE7203, 0xBE276236, + 0x48000000, 0x3FF00300, 0x0819DA68, 0x3DD200D8, + 0x48000000, 0x3FF00304, 0xE5E018D4, 0x3E28A249, + 0x48000000, 0x3FF00308, 0x8A087692, 0x3E386A49, + 0x4C000000, 0x3FF0030C, 0xD695988B, 0xBE3B6C8E, + 0x4C000000, 0x3FF00310, 0x55D2BCBA, 0xBE2E66C8, + 0x4C000000, 0x3FF00314, 0x7790BA7A, 0xBE0751B3, + 0x4C000000, 0x3FF00318, 0xC2A20261, 0x3E22DDF4, + 0x4C000000, 0x3FF0031C, 0x49E0B0B5, 0x3E35D82E, + 0x50000000, 0x3FF00320, 0xB142422E, 0xBE3DAE9A, + 0x50000000, 0x3FF00324, 0x8C170FE6, 0xBE312560, + 0x50000000, 0x3FF00328, 0x0A73BF77, 0xBE12308D, + 0x50000000, 0x3FF0032C, 0x5E59CEFA, 0x3E203A3A, + 0x50000000, 0x3FF00330, 0xCD4740BF, 0x3E34D660, + 0x54000000, 0x3FF00334, 0x644D1883, 0xBE3E6058, + 0x54000000, 0x3FF00338, 0x618F57B6, 0xBE31870E, + 0x54000000, 0x3FF0033C, 0x99FABD0F, 0xBE127704, + 0x54000000, 0x3FF00340, 0xA1CB5ECF, 0x3E20B71E, + 0x54000000, 0x3FF00344, 0x089E93E1, 0x3E3564E3, + 0x58000000, 0x3FF00348, 0xFB533142, 0xBE3D81C5, + 0x58000000, 0x3FF0034C, 0xB6EECE6C, 0xBE30586B, + 0x58000000, 0x3FF00350, 0x319B883E, 0xBE08F871, + 0x58000000, 0x3FF00354, 0x75BF7503, 0x3E2454A5, + 0x58000000, 0x3FF00358, 0xF04B88C5, 0x3E3783B6, + 0x5C000000, 0x3FF0035C, 0x81EF30A7, 0xBE3B12E1, + 0x5C000000, 0x3FF00360, 0x2F9F3657, 0xBE2B32ED, + 0x5C000000, 0x3FF00364, 0x54DF31BC, 0xBDB0084D, + 0x5C000000, 0x3FF00368, 0xC303B7B9, 0x3E2B12D2, + 0x5C000000, 0x3FF0036C, 0x78B56F97, 0x3E3B32DE, + 0x60000000, 0x3FF00370, 0x03B9496C, 0xBE3713A9, + 0x60000000, 0x3FF00374, 0x1F92E726, 0xBE22945A, + 0x60000000, 0x3FF00378, 0x621736DF, 0x3E123D49, + 0x60000000, 0x3FF0037C, 0x3935580D, 0x3E3278D5, + 0x64000000, 0x3FF00380, 0x69B9F5FB, 0xBE3F8DA4, + 0x64000000, 0x3FF00384, 0x8C473CC8, 0xBE31841A, + 0x64000000, 0x3FF00388, 0x538CDE07, 0xBE0B5469, + 0x64000000, 0x3FF0038C, 0x7F8F9D65, 0x3E257E07, + 0x64000000, 0x3FF00390, 0x3665E52B, 0x3E38F898, + 0x68000000, 0x3FF00394, 0xC29674BD, 0xBE38BDCF, + 0x68000000, 0x3FF00398, 0x4E58B4D9, 0xBE24C868, + 0x68000000, 0x3FF0039C, 0x329466D7, 0x3E1015AC, + 0x68000000, 0x3FF003A0, 0xDCDECE44, 0x3E327F0D, + 0x6C000000, 0x3FF003A4, 0xB27E5528, 0xBE3EF74B, + 0x6C000000, 0x3FF003A8, 0x9D7167F2, 0xBE305DA1, + 0x6C000000, 0x3FF003AC, 0xFF980820, 0xBDFB3F3D, + 0x6C000000, 0x3FF003B0, 0x13D49789, 0x3E2A0B7B, + 0x6C000000, 0x3FF003B4, 0xA43AE87C, 0x3E3BCF72, + 0x70000000, 0x3FF003B8, 0x8D06BDC0, 0xBE3556D4, + 0x70000000, 0x3FF003BC, 0x1766E54D, 0xBE19B460, + 0x70000000, 0x3FF003C0, 0x7B85C8BA, 0x3E211950, + 0x70000000, 0x3FF003C4, 0x41D00AED, 0x3E37966C, + 0x74000000, 0x3FF003C8, 0xF5B15507, 0xBE394FCB, + 0x74000000, 0x3FF003CC, 0xC98093C4, 0xBE244C00, + 0x74000000, 0x3FF003D0, 0xE2907BDF, 0x3E144F3B, + 0x74000000, 0x3FF003D4, 0x267CD924, 0x3E345DA2, + 0x78000000, 0x3FF003D8, 0xD73526C0, 0xBE3C4886, + 0x78000000, 0x3FF003DC, 0xF8E1D62E, 0xBE29BD57, + 0x78000000, 0x3FF003E0, 0xD65415E1, 0x3E04D995, + 0x78000000, 0x3FF003E4, 0x527E1A58, 0x3E322515, + 0x7C000000, 0x3FF003E8, 0x31552BA5, 0xBE3E4104, + 0x7C000000, 0x3FF003EC, 0x995CAB3B, 0xBE2D2E33, + 0x7C000000, 0x3FF003F0, 0x473970DC, 0x3DF22D48, + 0x7C000000, 0x3FF003F4, 0xC61195FC, 0x3E30ECC6, + 0x80000000, 0x3FF003F8, 0x03D35C34, 0xBE3F3943, + 0x80000000, 0x3FF003FC, 0xAA7483C7, 0xBE2E9E91, + 0x80000000, 0x3FF00400, 0xBBBC71CE, 0x3DE556AA, + 0x80000000, 0x3FF00404, 0x817613C1, 0x3E30B4B7, + 0x84000000, 0x3FF00408, 0x4E70B0AC, 0xBE3F3142, + 0x84000000, 0x3FF0040C, 0x2BAAD02F, 0xBE2E0E70, + 0x84000000, 0x3FF00410, 0xF48F01F2, 0x3DF32D62, + 0x84000000, 0x3FF00414, 0x84EB5B98, 0x3E317CE8, + 0x88000000, 0x3FF00418, 0x10ED210B, 0xBE3E2901, + 0x88000000, 0x3FF0041C, 0x1C7F0051, 0xBE2B7DCD, + 0x88000000, 0x3FF00420, 0x87AA2706, 0x3E05D9C0, + 0x88000000, 0x3FF00424, 0xD0B235B3, 0x3E33455A, + 0x8C000000, 0x3FF00428, 0x4B07A510, 0xBE3C207E, + 0x8C000000, 0x3FF0042C, 0x7C6E838B, 0xBE26ECA6, + 0x8C000000, 0x3FF00430, 0xEC91A8D5, 0x3E150F6F, + 0x8C000000, 0x3FF00434, 0x650C6A83, 0x3E360E0F, + 0x90000000, 0x3FF00438, 0xFC7E3439, 0xBE3917B8, + 0x90000000, 0x3FF0043C, 0x4AF4C8B6, 0xBE205AFA, + 0x90000000, 0x3FF00440, 0xDC31D181, 0x3E219985, + 0x90000000, 0x3FF00444, 0x423CC2BE, 0x3E39D707, + 0x94000000, 0x3FF00448, 0x250DC5BF, 0xBE350EB0, + 0x94000000, 0x3FF0044C, 0x1E2CF893, 0xBE0F231A, + 0x94000000, 0x3FF00450, 0xD42C92D4, 0x3E2AABDB, + 0x94000000, 0x3FF00454, 0x6887075B, 0x3E3EA043, + 0x98000000, 0x3FF00458, 0xC472509B, 0xBE300562, + 0x98000000, 0x3FF0045C, 0x72B572E0, 0x3DF64FB6, + 0x98000000, 0x3FF00460, 0xEF61155C, 0x3E32DF5D, + 0x9C000000, 0x3FF00464, 0x27CFFE6A, 0xBE3B963B, + 0x9C000000, 0x3FF00468, 0xB4CD96FE, 0xBE23F79F, + 0x9C000000, 0x3FF0046C, 0x6E771F13, 0x3E1EBA7F, + 0x9C000000, 0x3FF00470, 0xFE3ED608, 0x3E396913, + 0xA0000000, 0x3FF00474, 0x6E82850F, 0xBE34CC73, + 0xA0000000, 0x3FF00478, 0x352966B7, 0xBE078FB3, + 0xA0000000, 0x3FF0047C, 0x33AFF8AE, 0x3E2DF116, + 0xA4000000, 0x3FF00480, 0xE909EADD, 0xBE3F0CEE, + 0xA4000000, 0x3FF00484, 0xD6938597, 0xBE2A04C8, + 0xA4000000, 0x3FF00488, 0x5C6654D8, 0x3E1460AA, + 0xA4000000, 0x3FF0048C, 0x22213ECF, 0x3E3742BE, + 0xA8000000, 0x3FF00490, 0xC631A356, 0xBE3682A9, + 0xA8000000, 0x3FF00494, 0x7777B644, 0xBE10E034, + 0xA8000000, 0x3FF00498, 0x3E3B0991, 0x3E2C4528, + 0xAC000000, 0x3FF0049C, 0x0B3E269F, 0xBE3F72C6, + 0xAC000000, 0x3FF004A0, 0x31DF923B, 0xBE29F037, + 0xAC000000, 0x3FF004A4, 0xE82713DE, 0x3E164A4D, + 0xAC000000, 0x3FF004A8, 0x31AFAC4B, 0x3E382D47, + 0xB0000000, 0x3FF004AC, 0x6DFCE978, 0xBE352800, + 0xB0000000, 0x3FF004B0, 0x07D68D27, 0xBE036A1B, + 0xB0000000, 0x3FF004B4, 0x5CB71F6F, 0x3E305D7E, + 0xB4000000, 0x3FF004B8, 0x30E5E990, 0xBE3CC7BB, + 0xB4000000, 0x3FF004BC, 0x0BA17DEA, 0xBE23B9E0, + 0xB4000000, 0x3FF004C0, 0xC3EF9BD8, 0x3E223BBF, + 0xB4000000, 0x3FF004C4, 0x8A74ECC0, 0x3E3C28B4, + 0xB8000000, 0x3FF004C8, 0x085831CA, 0xBE30BC72, + 0xB8000000, 0x3FF004CC, 0x6C8D1FC8, 0x3E037361, + 0xB8000000, 0x3FF004D0, 0x3033A0B8, 0x3E35A94F, + 0xBC000000, 0x3FF004D4, 0xFC7107DE, 0xBE370BC8, + 0xBC000000, 0x3FF004D8, 0xA2D908DA, 0xBE0D86E2, + 0xBC000000, 0x3FF004DC, 0x58ED155E, 0x3E2F742A, + 0xC0000000, 0x3FF004E0, 0x75FACDD0, 0xBE3CCAF4, + 0xC0000000, 0x3FF004E4, 0x6F5BE5D3, 0xBE227FF2, + 0xC0000000, 0x3FF004E8, 0xD6BCA827, 0x3E24B60D, + 0xC0000000, 0x3FF004EC, 0xF72B40D6, 0x3E3E060B, + 0xC4000000, 0x3FF004F0, 0x208BE3E3, 0xBE2C7DD4, + 0xC4000000, 0x3FF004F4, 0x642FDDB8, 0x3E163093, + 0xC4000000, 0x3FF004F8, 0xB72239A5, 0x3E396738, + 0xC8000000, 0x3FF004FC, 0x7201ED9B, 0xBE32ADAE, + 0xC8000000, 0x3FF00500, 0x1A0C05F3, 0x3DF4D6F6, + 0xC8000000, 0x3FF00504, 0x360B8346, 0x3E355892, + 0xCC000000, 0x3FF00508, 0xF0C06435, 0xBE368C45, + 0xCC000000, 0x3FF0050C, 0x760DA2F6, 0xBE0308C8, + 0xCC000000, 0x3FF00510, 0xE008D57B, 0x3E31DA18, + 0xD0000000, 0x3FF00514, 0x205F82F4, 0xBE39DAB0, + 0xD0000000, 0x3FF00518, 0x2FE5E3E3, 0xBE15FDD0, + 0xD0000000, 0x3FF0051C, 0x42787241, 0x3E2DD79A, + 0xD4000000, 0x3FF00520, 0x94BD25F4, 0xBE3C98EC, + 0xD4000000, 0x3FF00524, 0x53C89D03, 0xBE201B42, + 0xD4000000, 0x3FF00528, 0xCB901057, 0x3E291B5E, + 0xD8000000, 0x3FF0052C, 0xE1B6D837, 0xBE3EC6FA, + 0xD8000000, 0x3FF00530, 0xF8BF49E7, 0xBE24173F, + 0xD8000000, 0x3FF00534, 0x339DDB57, 0x3E257F80, + 0xD8000000, 0x3FF00538, 0x64D62C5C, 0x3E3F9B25, + 0xDC000000, 0x3FF0053C, 0x2E913659, 0xBE26F2E0, + 0xDC000000, 0x3FF00540, 0x52E7CB93, 0x3E2303FF, + 0xDC000000, 0x3FF00544, 0xAB0CFEF5, 0x3E3E8D74, + 0xE0000000, 0x3FF00548, 0x1CF7FDE6, 0xBE28AE22, + 0xE0000000, 0x3FF0054C, 0x01B47B93, 0x3E21A8DD, + 0xE0000000, 0x3FF00550, 0x5D1107E2, 0x3E3E0FF3, + 0xE4000000, 0x3FF00554, 0xEBAC99E1, 0xBE294904, + 0xE4000000, 0x3FF00558, 0x184B2814, 0x3E216E1A, + 0xE4000000, 0x3FF0055C, 0xE706008B, 0x3E3E22A1, + 0xE8000000, 0x3FF00560, 0xC267616A, 0xBE28C387, + 0xE8000000, 0x3FF00564, 0x6EF3B008, 0x3E2253B7, + 0xE8000000, 0x3FF00568, 0xB50FF371, 0x3E3EC580, + 0xEC000000, 0x3FF0056C, 0xC8E0096B, 0xBE271DA9, + 0xEC000000, 0x3FF00570, 0xDDF69498, 0x3E2459B5, + 0xEC000000, 0x3FF00574, 0x33533C31, 0x3E3FF890, + 0xF0000000, 0x3FF00578, 0x26CDA497, 0xBE24576A, + 0xF0000000, 0x3FF0057C, 0x3D9CF923, 0x3E278016, + 0xF4000000, 0x3FF00580, 0x320B787B, 0xBE3E442F, + 0xF4000000, 0x3FF00584, 0x03E6A36B, 0xBE2070C8, + 0xF4000000, 0x3FF00588, 0x6630A33F, 0x3E2BC6D9, + 0xF8000000, 0x3FF0058C, 0x0EE72CBF, 0xBE3BF0BD, + 0xF8000000, 0x3FF00590, 0x0FC1A853, 0xBE16D385, + 0xF8000000, 0x3FF00594, 0x17FDFD5D, 0x3E309700, + 0xFC000000, 0x3FF00598, 0xF71A91AC, 0xBE390D18, + 0xFC000000, 0x3FF0059C, 0x69C58B86, 0xBE050963, + 0xFC000000, 0x3FF005A0, 0xB9A504CD, 0x3E33DAC5, + 0x00000000, 0x3FF005A5, 0x7E800734, 0xBE359942, + 0x00000000, 0x3FF005A9, 0xE59934CD, 0x3DF02BAE, + 0x00000000, 0x3FF005AD, 0x04333E0E, 0x3E37AEBE, + 0x04000000, 0x3FF005B1, 0x38F19C2F, 0xBE319539, + 0x04000000, 0x3FF005B5, 0xEBB1C157, 0x3E14DB54, + 0x04000000, 0x3FF005B9, 0x63CED05D, 0x3E3C12E9, + 0x08000000, 0x3FF005BD, 0x74921CAF, 0xBE2A01F9, + 0x08000000, 0x3FF005C1, 0xC94C85F2, 0x3E23F645, + 0x0C000000, 0x3FF005C5, 0xBB61CBEE, 0xBE3EF8B7, + 0x0C000000, 0x3FF005C9, 0x597F2931, 0xBE1F7232, + 0x0C000000, 0x3FF005CD, 0xAF5B7345, 0x3E2E9F48, + 0x10000000, 0x3FF005D1, 0xED37CD5F, 0xBE397424, + 0x10000000, 0x3FF005D5, 0x08775C6B, 0xBE013F43, + 0x10000000, 0x3FF005D9, 0x0029D3DB, 0x3E35345A, + 0x14000000, 0x3FF005DD, 0xC58C1962, 0xBE335F5D, + 0x14000000, 0x3FF005E1, 0x47430E04, 0x3E1073C1, + 0x14000000, 0x3FF005E5, 0x4A41E248, 0x3E3BA944, + 0x18000000, 0x3FF005E9, 0xB06E888E, 0xBE2974C3, + 0x18000000, 0x3FF005ED, 0xDCCD9333, 0x3E25E3FB, + 0x1C000000, 0x3FF005F1, 0x5DE27951, 0xBE3D519C, + 0x1C000000, 0x3FF005F5, 0xE4464502, 0xBE1614C2, + 0x1C000000, 0x3FF005F9, 0xE0DAFE93, 0x3E325740, + 0x20000000, 0x3FF005FD, 0x8C1B4C10, 0xBE35BC47, + 0x20000000, 0x3FF00601, 0x20686CE9, 0x3E0201B0, + 0x20000000, 0x3FF00605, 0x95558B63, 0x3E3A4CB9, + 0x24000000, 0x3FF00609, 0xA880A3EB, 0xBE2B2D79, + 0x24000000, 0x3FF0060D, 0x9699EEB7, 0x3E252BA5, + 0x28000000, 0x3FF00611, 0x880115E1, 0xBE3D2D97, + 0x28000000, 0x3FF00615, 0x28A3D788, 0xBE1383EF, + 0x28000000, 0x3FF00619, 0x08D6DC23, 0x3E337BA6, + 0x2C000000, 0x3FF0061D, 0x0B001A08, 0xBE3417B2, + 0x2C000000, 0x3FF00621, 0xF94EB99A, 0x3E1193EF, + 0x2C000000, 0x3FF00625, 0x28D3BD3B, 0x3E3CF1B0, + 0x30000000, 0x3FF00629, 0x0EFCC982, 0xBE24E32B, + 0x30000000, 0x3FF0062D, 0xE2BDA47F, 0x3E2C7655, + 0x34000000, 0x3FF00631, 0x689312F8, 0xBE39080E, + 0x34000000, 0x3FF00635, 0xA9444DB4, 0xBDCDA0C8, + 0x34000000, 0x3FF00639, 0x7B21FE23, 0x3E38A191, + 0x38000000, 0x3FF0063D, 0x7E67E1E1, 0xBE2CE32A, + 0x38000000, 0x3FF00641, 0x875A71F0, 0x3E251694, + 0x3C000000, 0x3FF00645, 0xF838F455, 0xBE3C67CF, + 0x3C000000, 0x3FF00649, 0x77274052, 0xBE0A571F, + 0x3C000000, 0x3FF0064D, 0x63AAEFA8, 0x3E35E20E, + 0x40000000, 0x3FF00651, 0xFC87DA70, 0xBE30E0F8, + 0x40000000, 0x3FF00655, 0xE9089AFD, 0x3E20D80B, + 0x44000000, 0x3FF00659, 0xC52F03BD, 0xBE3E36F4, + 0x44000000, 0x3FF0065D, 0x9680E14E, 0xBE1327A4, + 0x44000000, 0x3FF00661, 0xD732468D, 0x3E34B328, + 0x48000000, 0x3FF00665, 0xCAB5EF4A, 0xBE31BFBE, + 0x48000000, 0x3FF00669, 0xE2A2FBE1, 0x3E1F757F, + 0x4C000000, 0x3FF0066D, 0xDAB014DA, 0xBE3E757A, + 0x4C000000, 0x3FF00671, 0x02FB3FBB, 0xBE12E13D, + 0x4C000000, 0x3FF00675, 0xCA7E298D, 0x3E3514E2, + 0x50000000, 0x3FF00679, 0xB4F78B94, 0xBE310DE4, + 0x50000000, 0x3FF0067D, 0x89C35D05, 0x3E21BEB4, + 0x54000000, 0x3FF00681, 0x43F4895C, 0xBE3D2360, + 0x54000000, 0x3FF00685, 0x5BC49ADF, 0xBE08B0A2, + 0x54000000, 0x3FF00689, 0x32573159, 0x3E37073E, + 0x58000000, 0x3FF0068D, 0x8D0732D2, 0xBE2D96D1, + 0x58000000, 0x3FF00691, 0x9BF15E67, 0x3E26E3ED, + 0x5C000000, 0x3FF00695, 0x0C3250FB, 0xBE3A40A3, + 0x5C000000, 0x3FF00699, 0xFD0AE214, 0x3DBCC9AE, + 0x5C000000, 0x3FF0069D, 0x038868A1, 0x3E3A8A3D, + 0x60000000, 0x3FF006A1, 0x151D21CE, 0xBE25F092, + 0x60000000, 0x3FF006A5, 0x11738C43, 0x3E2F2A6F, + 0x64000000, 0x3FF006A9, 0x3E9CE96D, 0xBE35CD41, + 0x64000000, 0x3FF006AD, 0x8DBC2918, 0x3E138132, + 0x64000000, 0x3FF006B1, 0x32DF4C13, 0x3E3F9DE1, + 0x68000000, 0x3FF006B5, 0x3129E0B2, 0xBE16520E, + 0x68000000, 0x3FF006B9, 0x69F36A61, 0x3E35491E, + 0x6C000000, 0x3FF006BD, 0xCCCABCD4, 0xBE2F9271, + 0x6C000000, 0x3FF006C1, 0x0D59B899, 0x3E2668ED, + 0x70000000, 0x3FF006C5, 0x4AD435A0, 0xBE39BDD3, + 0x70000000, 0x3FF006C9, 0x9191CABB, 0x3DF5FE9A, + 0x70000000, 0x3FF006CD, 0x6676850B, 0x3E3C8DAD, + 0x74000000, 0x3FF006D1, 0x1D74934A, 0xBE206910, + 0x74000000, 0x3FF006D5, 0x4D886478, 0x3E331949, + 0x78000000, 0x3FF006D9, 0x80BFBBC2, 0xBE3188DE, + 0x78000000, 0x3FF006DD, 0x14DE1719, 0x3E23CA01, + 0x7C000000, 0x3FF006E1, 0x8CE98EC0, 0xBE3A9D19, + 0x7C000000, 0x3FF006E5, 0xA705A6E7, 0x3DEE1A67, + 0x7C000000, 0x3FF006E9, 0xECD5F851, 0x3E3C8EC6, + 0x80000000, 0x3FF006ED, 0xE839CE4D, 0xBE1F0CF9, + 0x80000000, 0x3FF006F1, 0x0C8CA46A, 0x3E33FAC3, + 0x84000000, 0x3FF006F5, 0x7B5703D8, 0xBE303734, + 0x84000000, 0x3FF006F9, 0xE490A112, 0x3E274DB5, + 0x88000000, 0x3FF006FD, 0xA693A093, 0xBE386B0E, + 0x88000000, 0x3FF00701, 0xF0B73DAA, 0x3E0C9875, + 0x88000000, 0x3FF00705, 0x2449A944, 0x3E3FA133, + 0x8C000000, 0x3FF00709, 0xBFE66C14, 0xBE110285, + 0x8C000000, 0x3FF0070D, 0x054EDCBD, 0x3E37ED91, + 0x90000000, 0x3FF00711, 0xEFB65924, 0xBE27A86A, + 0x90000000, 0x3FF00715, 0x1C8A0CF1, 0x3E307A0B, + 0x94000000, 0x3FF00719, 0x397FB1D6, 0xBE3327AD, + 0x94000000, 0x3FF0071D, 0x1412B9FB, 0x3E228D43, + 0x98000000, 0x3FF00721, 0x94D8FFB0, 0xBE3A3B08, + 0x98000000, 0x3FF00725, 0x6ED80040, 0x3E029AA3, + 0x98000000, 0x3FF00729, 0x9627250A, 0x3E3EF1B8, + 0x9C000000, 0x3FF0072D, 0x5FCB1B09, 0xBE117F70, + 0x9C000000, 0x3FF00731, 0x678F0789, 0x3E385E96, + 0xA0000000, 0x3FF00735, 0xCEA3485B, 0xBE25A5DF, + 0xA0000000, 0x3FF00739, 0xFF6D0303, 0x3E320B90, + 0xA4000000, 0x3FF0073D, 0xE03334FF, 0xBE3105E6, + 0xA4000000, 0x3FF00741, 0xFB9F056D, 0x3E27F150, + 0xA8000000, 0x3FF00745, 0xE28905F4, 0xBE36F8C0, + 0xA8000000, 0x3FF00749, 0x0B1407AA, 0x3E189774, + 0xAC000000, 0x3FF0074D, 0xCE4493C4, 0xBE3CAB7D, + 0xAC000000, 0x3FF00751, 0xCB817D78, 0x3DE265D5, + 0xAC000000, 0x3FF00755, 0x7CA8B4E3, 0x3E3DE1E2, + 0xB0000000, 0x3FF00759, 0x7D730FC6, 0xBE12FD89, + 0xB0000000, 0x3FF0075D, 0x1E4D7759, 0x3E38AF60, + 0xB4000000, 0x3FF00761, 0x0CAD84A2, 0xBE23A3AC, + 0xB4000000, 0x3FF00765, 0x36B866FD, 0x3E33BCFB, + 0xB8000000, 0x3FF00769, 0x4D0667A1, 0xBE2D4858, + 0xB8000000, 0x3FF0076D, 0xCBF08E6A, 0x3E2E1567, + 0xBC000000, 0x3FF00771, 0x9FD34D05, 0xBE333664, + 0xBC000000, 0x3FF00775, 0x9837D6E0, 0x3E253114, + 0xC0000000, 0x3FF00779, 0x5238327D, 0xBE37887F, + 0xC0000000, 0x3FF0077D, 0x24C8DC90, 0x3E1999FA, + 0xC4000000, 0x3FF00781, 0x1DA2F8BE, 0xBE3B9A7C, + 0xC4000000, 0x3FF00785, 0xEA50EE6A, 0x3E03A485, + 0xC8000000, 0x3FF00789, 0xE204A449, 0xBE3F6C5A, + 0xC8000000, 0x3FF0078D, 0x78D5D0F3, 0xBDF3D3EF, + 0xC8000000, 0x3FF00791, 0x80B1D66C, 0x3E3D01E4, + 0xCC000000, 0x3FF00795, 0xD5149796, 0xBE12BBC1, + 0xCC000000, 0x3FF00799, 0x2A8F92F0, 0x3E39B042, + 0xD0000000, 0x3FF0079D, 0x6F386487, 0xBE1F820E, + 0xD0000000, 0x3FF007A1, 0x3BA3BCDA, 0x3E369EBE, + 0xD4000000, 0x3FF007A5, 0x96320652, 0xBE25A3F0, + 0xD4000000, 0x3FF007A9, 0xD3FD8FCA, 0x3E33CD58, + 0xD8000000, 0x3FF007AD, 0xC62D40B1, 0xBE2B069C, + 0xD8000000, 0x3FF007B1, 0x13AC5766, 0x3E313C12, + 0xDC000000, 0x3FF007B5, 0x876F3A0B, 0xBE2FE90B, + 0xDC000000, 0x3FF007B9, 0x357EDEB8, 0x3E2DD5D4, + 0xE0000000, 0x3FF007BD, 0x4CEC957E, 0xBE32259E, + 0xE0000000, 0x3FF007C1, 0x128C86C6, 0x3E29B3C2, + 0xE4000000, 0x3FF007C5, 0xDEA61608, 0xBE341697, + 0xE4000000, 0x3FF007C9, 0xFEA09E70, 0x3E2611ED, + 0xE8000000, 0x3FF007CD, 0x58D49AE3, 0xBE35C772, + 0xE8000000, 0x3FF007D1, 0x39DA3D42, 0x3E22F058, + 0xEC000000, 0x3FF007D5, 0x9B689043, 0xBE37382D, + 0xEC000000, 0x3FF007D9, 0x04589AD6, 0x3E204F01, + 0xF0000000, 0x3FF007DD, 0x86525259, 0xBE3868C9, + 0xF0000000, 0x3FF007E1, 0x3C761DAC, 0x3E1C5BD1, + 0xF4000000, 0x3FF007E5, 0xF9822D4C, 0xBE395945, + 0xF4000000, 0x3FF007E9, 0x8F4221F9, 0x3E191A1E, + 0xF8000000, 0x3FF007ED, 0xD4E85D3A, 0xBE3A09A2, + 0xF8000000, 0x3FF007F1, 0x81547225, 0x3E16D8EA, + 0xFC000000, 0x3FF007F5, 0xF8750E3B, 0xBE3A79DF, + 0xFC000000, 0x3FF007F9, 0x92EC7DE3, 0x3E159835, + 0x00000000, 0x3FF007FE, 0x44185C5D, 0xBE3AA9FD } }; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/ulog.h b/REORG.TODO/sysdeps/ieee754/dbl-64/ulog.h new file mode 100644 index 0000000000..e5fbad044e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/ulog.h @@ -0,0 +1,187 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:ulog.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef ULOG_H +#define ULOG_H + +#ifdef BIG_ENDI + static const number + /* polynomial I */ +/**/ a2 = {{0xbfe00000, 0x0001aa8f} }, /* -0.500... */ +/**/ a3 = {{0x3fd55555, 0x55588d2e} }, /* 0.333... */ + /* polynomial II */ +/**/ b0 = {{0x3fd55555, 0x55555555} }, /* 0.333... */ +/**/ b1 = {{0xbfcfffff, 0xffffffbb} }, /* -0.249... */ +/**/ b2 = {{0x3fc99999, 0x9999992f} }, /* 0.199... */ +/**/ b3 = {{0xbfc55555, 0x556503fd} }, /* -0.166... */ +/**/ b4 = {{0x3fc24924, 0x925b3d62} }, /* 0.142... */ +/**/ b5 = {{0xbfbffffe, 0x160472fc} }, /* -0.124... */ +/**/ b6 = {{0x3fbc71c5, 0x25db58ac} }, /* 0.111... */ +/**/ b7 = {{0xbfb9a4ac, 0x11a2a61c} }, /* -0.100... */ +/**/ b8 = {{0x3fb75077, 0x0df2b591} }, /* 0.091... */ + /* polynomial III */ +#if 0 +/**/ c1 = {{0x3ff00000, 0x00000000} }, /* 1 */ +#endif +/**/ c2 = {{0xbfe00000, 0x00000000} }, /* -1/2 */ +/**/ c3 = {{0x3fd55555, 0x55555555} }, /* 1/3 */ +/**/ c4 = {{0xbfd00000, 0x00000000} }, /* -1/4 */ +/**/ c5 = {{0x3fc99999, 0x9999999a} }, /* 1/5 */ + /* polynomial IV */ +/**/ d2 = {{0xbfe00000, 0x00000000} }, /* -1/2 */ +/**/ dd2 = {{0x00000000, 0x00000000} }, /* -1/2-d2 */ +/**/ d3 = {{0x3fd55555, 0x55555555} }, /* 1/3 */ +/**/ dd3 = {{0x3c755555, 0x55555555} }, /* 1/3-d3 */ +/**/ d4 = {{0xbfd00000, 0x00000000} }, /* -1/4 */ +/**/ dd4 = {{0x00000000, 0x00000000} }, /* -1/4-d4 */ +/**/ d5 = {{0x3fc99999, 0x9999999a} }, /* 1/5 */ +/**/ dd5 = {{0xbc699999, 0x9999999a} }, /* 1/5-d5 */ +/**/ d6 = {{0xbfc55555, 0x55555555} }, /* -1/6 */ +/**/ dd6 = {{0xbc655555, 0x55555555} }, /* -1/6-d6 */ +/**/ d7 = {{0x3fc24924, 0x92492492} }, /* 1/7 */ +/**/ dd7 = {{0x3c624924, 0x92492492} }, /* 1/7-d7 */ +/**/ d8 = {{0xbfc00000, 0x00000000} }, /* -1/8 */ +/**/ dd8 = {{0x00000000, 0x00000000} }, /* -1/8-d8 */ +/**/ d9 = {{0x3fbc71c7, 0x1c71c71c} }, /* 1/9 */ +/**/ dd9 = {{0x3c5c71c7, 0x1c71c71c} }, /* 1/9-d9 */ +/**/ d10 = {{0xbfb99999, 0x9999999a} }, /* -1/10 */ +/**/ dd10 = {{0x3c599999, 0x9999999a} }, /* -1/10-d10 */ +/**/ d11 = {{0x3fb745d1, 0x745d1746} }, /* 1/11 */ +/**/ d12 = {{0xbfb55555, 0x55555555} }, /* -1/12 */ +/**/ d13 = {{0x3fb3b13b, 0x13b13b14} }, /* 1/13 */ +/**/ d14 = {{0xbfb24924, 0x92492492} }, /* -1/14 */ +/**/ d15 = {{0x3fb11111, 0x11111111} }, /* 1/15 */ +/**/ d16 = {{0xbfb00000, 0x00000000} }, /* -1/16 */ +/**/ d17 = {{0x3fae1e1e, 0x1e1e1e1e} }, /* 1/17 */ +/**/ d18 = {{0xbfac71c7, 0x1c71c71c} }, /* -1/18 */ +/**/ d19 = {{0x3faaf286, 0xbca1af28} }, /* 1/19 */ +/**/ d20 = {{0xbfa99999, 0x9999999a} }, /* -1/20 */ + /* constants */ +/**/ sqrt_2 = {{0x3ff6a09e, 0x667f3bcc} }, /* sqrt(2) */ +/**/ h1 = {{0x3fd2e000, 0x00000000} }, /* 151/2**9 */ +/**/ h2 = {{0x3f669000, 0x00000000} }, /* 361/2**17 */ +/**/ delu = {{0x3f700000, 0x00000000} }, /* 1/2**8 */ +/**/ delv = {{0x3ef00000, 0x00000000} }, /* 1/2**16 */ +/**/ ln2a = {{0x3fe62e42, 0xfefa3800} }, /* ln(2) 43 bits */ +/**/ ln2b = {{0x3d2ef357, 0x93c76730} }, /* ln(2)-ln2a */ +/**/ e1 = {{0x3bbcc868, 0x00000000} }, /* 6.095e-21 */ +/**/ e2 = {{0x3c1138ce, 0x00000000} }, /* 2.334e-19 */ +/**/ e3 = {{0x3aa1565d, 0x00000000} }, /* 2.801e-26 */ +/**/ e4 = {{0x39809d88, 0x00000000} }, /* 1.024e-31 */ +/**/ e[M] ={{{0x37da223a, 0x00000000} }, /* 1.2e-39 */ +/**/ {{0x35c851c4, 0x00000000} }, /* 1.3e-49 */ +/**/ {{0x2ab85e51, 0x00000000} }, /* 6.8e-103 */ +/**/ {{0x17383827, 0x00000000} }},/* 8.1e-197 */ +/**/ two54 = {{0x43500000, 0x00000000} }, /* 2**54 */ +/**/ u03 = {{0x3f9eb851, 0xeb851eb8} }; /* 0.03 */ + +#else +#ifdef LITTLE_ENDI + static const number + /* polynomial I */ +/**/ a2 = {{0x0001aa8f, 0xbfe00000} }, /* -0.500... */ +/**/ a3 = {{0x55588d2e, 0x3fd55555} }, /* 0.333... */ + /* polynomial II */ +/**/ b0 = {{0x55555555, 0x3fd55555} }, /* 0.333... */ +/**/ b1 = {{0xffffffbb, 0xbfcfffff} }, /* -0.249... */ +/**/ b2 = {{0x9999992f, 0x3fc99999} }, /* 0.199... */ +/**/ b3 = {{0x556503fd, 0xbfc55555} }, /* -0.166... */ +/**/ b4 = {{0x925b3d62, 0x3fc24924} }, /* 0.142... */ +/**/ b5 = {{0x160472fc, 0xbfbffffe} }, /* -0.124... */ +/**/ b6 = {{0x25db58ac, 0x3fbc71c5} }, /* 0.111... */ +/**/ b7 = {{0x11a2a61c, 0xbfb9a4ac} }, /* -0.100... */ +/**/ b8 = {{0x0df2b591, 0x3fb75077} }, /* 0.091... */ + /* polynomial III */ +#if 0 +/**/ c1 = {{0x00000000, 0x3ff00000} }, /* 1 */ +#endif +/**/ c2 = {{0x00000000, 0xbfe00000} }, /* -1/2 */ +/**/ c3 = {{0x55555555, 0x3fd55555} }, /* 1/3 */ +/**/ c4 = {{0x00000000, 0xbfd00000} }, /* -1/4 */ +/**/ c5 = {{0x9999999a, 0x3fc99999} }, /* 1/5 */ + /* polynomial IV */ +/**/ d2 = {{0x00000000, 0xbfe00000} }, /* -1/2 */ +/**/ dd2 = {{0x00000000, 0x00000000} }, /* -1/2-d2 */ +/**/ d3 = {{0x55555555, 0x3fd55555} }, /* 1/3 */ +/**/ dd3 = {{0x55555555, 0x3c755555} }, /* 1/3-d3 */ +/**/ d4 = {{0x00000000, 0xbfd00000} }, /* -1/4 */ +/**/ dd4 = {{0x00000000, 0x00000000} }, /* -1/4-d4 */ +/**/ d5 = {{0x9999999a, 0x3fc99999} }, /* 1/5 */ +/**/ dd5 = {{0x9999999a, 0xbc699999} }, /* 1/5-d5 */ +/**/ d6 = {{0x55555555, 0xbfc55555} }, /* -1/6 */ +/**/ dd6 = {{0x55555555, 0xbc655555} }, /* -1/6-d6 */ +/**/ d7 = {{0x92492492, 0x3fc24924} }, /* 1/7 */ +/**/ dd7 = {{0x92492492, 0x3c624924} }, /* 1/7-d7 */ +/**/ d8 = {{0x00000000, 0xbfc00000} }, /* -1/8 */ +/**/ dd8 = {{0x00000000, 0x00000000} }, /* -1/8-d8 */ +/**/ d9 = {{0x1c71c71c, 0x3fbc71c7} }, /* 1/9 */ +/**/ dd9 = {{0x1c71c71c, 0x3c5c71c7} }, /* 1/9-d9 */ +/**/ d10 = {{0x9999999a, 0xbfb99999} }, /* -1/10 */ +/**/ dd10 = {{0x9999999a, 0x3c599999} }, /* -1/10-d10 */ +/**/ d11 = {{0x745d1746, 0x3fb745d1} }, /* 1/11 */ +/**/ d12 = {{0x55555555, 0xbfb55555} }, /* -1/12 */ +/**/ d13 = {{0x13b13b14, 0x3fb3b13b} }, /* 1/13 */ +/**/ d14 = {{0x92492492, 0xbfb24924} }, /* -1/14 */ +/**/ d15 = {{0x11111111, 0x3fb11111} }, /* 1/15 */ +/**/ d16 = {{0x00000000, 0xbfb00000} }, /* -1/16 */ +/**/ d17 = {{0x1e1e1e1e, 0x3fae1e1e} }, /* 1/17 */ +/**/ d18 = {{0x1c71c71c, 0xbfac71c7} }, /* -1/18 */ +/**/ d19 = {{0xbca1af28, 0x3faaf286} }, /* 1/19 */ +/**/ d20 = {{0x9999999a, 0xbfa99999} }, /* -1/20 */ + /* constants */ +/**/ sqrt_2 = {{0x667f3bcc, 0x3ff6a09e} }, /* sqrt(2) */ +/**/ h1 = {{0x00000000, 0x3fd2e000} }, /* 151/2**9 */ +/**/ h2 = {{0x00000000, 0x3f669000} }, /* 361/2**17 */ +/**/ delu = {{0x00000000, 0x3f700000} }, /* 1/2**8 */ +/**/ delv = {{0x00000000, 0x3ef00000} }, /* 1/2**16 */ +/**/ ln2a = {{0xfefa3800, 0x3fe62e42} }, /* ln(2) 43 bits */ +/**/ ln2b = {{0x93c76730, 0x3d2ef357} }, /* ln(2)-ln2a */ +/**/ e1 = {{0x00000000, 0x3bbcc868} }, /* 6.095e-21 */ +/**/ e2 = {{0x00000000, 0x3c1138ce} }, /* 2.334e-19 */ +/**/ e3 = {{0x00000000, 0x3aa1565d} }, /* 2.801e-26 */ +/**/ e4 = {{0x00000000, 0x39809d88} }, /* 1.024e-31 */ +/**/ e[M] ={{{0x00000000, 0x37da223a} }, /* 1.2e-39 */ +/**/ {{0x00000000, 0x35c851c4} }, /* 1.3e-49 */ +/**/ {{0x00000000, 0x2ab85e51} }, /* 6.8e-103 */ +/**/ {{0x00000000, 0x17383827} }},/* 8.1e-197 */ +/**/ two54 = {{0x00000000, 0x43500000} }, /* 2**54 */ +/**/ u03 = {{0xeb851eb8, 0x3f9eb851} }; /* 0.03 */ + +#endif +#endif + +#define SQRT_2 sqrt_2.d +#define DEL_U delu.d +#define DEL_V delv.d +#define LN2A ln2a.d +#define LN2B ln2b.d +#define E1 e1.d +#define E2 e2.d +#define E3 e3.d +#define E4 e4.d +#define U03 u03.d + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/ulog.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/ulog.tbl new file mode 100644 index 0000000000..8714ea3a6a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/ulog.tbl @@ -0,0 +1,3326 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE ulog() FUNCTION */ +/****************************************************************/ + +#ifdef BIG_ENDI + static const number + Iu[182] = { /* 1/ui */ +/**/ {{0x3ff6a13c, 0xd1537290} }, +/**/ {{0x3ff68168, 0x16816817} }, +/**/ {{0x3ff661ec, 0x6a5122f9} }, +/**/ {{0x3ff642c8, 0x590b2164} }, +/**/ {{0x3ff623fa, 0x77016240} }, +/**/ {{0x3ff60581, 0x60581606} }, +/**/ {{0x3ff5e75b, 0xb8d015e7} }, +/**/ {{0x3ff5c988, 0x2b931057} }, +/**/ {{0x3ff5ac05, 0x6b015ac0} }, +/**/ {{0x3ff58ed2, 0x308158ed} }, +/**/ {{0x3ff571ed, 0x3c506b3a} }, +/**/ {{0x3ff55555, 0x55555555} }, +/**/ {{0x3ff53909, 0x48f40feb} }, +/**/ {{0x3ff51d07, 0xeae2f815} }, +/**/ {{0x3ff50150, 0x15015015} }, +/**/ {{0x3ff4e5e0, 0xa72f0539} }, +/**/ {{0x3ff4cab8, 0x8725af6e} }, +/**/ {{0x3ff4afd6, 0xa052bf5b} }, +/**/ {{0x3ff49539, 0xe3b2d067} }, +/**/ {{0x3ff47ae1, 0x47ae147b} }, +/**/ {{0x3ff460cb, 0xc7f5cf9a} }, +/**/ {{0x3ff446f8, 0x6562d9fb} }, +/**/ {{0x3ff42d66, 0x25d51f87} }, +/**/ {{0x3ff41414, 0x14141414} }, +/**/ {{0x3ff3fb01, 0x3fb013fb} }, +/**/ {{0x3ff3e22c, 0xbce4a902} }, +/**/ {{0x3ff3c995, 0xa47babe7} }, +/**/ {{0x3ff3b13b, 0x13b13b14} }, +/**/ {{0x3ff3991c, 0x2c187f63} }, +/**/ {{0x3ff38138, 0x13813814} }, +/**/ {{0x3ff3698d, 0xf3de0748} }, +/**/ {{0x3ff3521c, 0xfb2b78c1} }, +/**/ {{0x3ff33ae4, 0x5b57bcb2} }, +/**/ {{0x3ff323e3, 0x4a2b10bf} }, +/**/ {{0x3ff30d19, 0x0130d190} }, +/**/ {{0x3ff2f684, 0xbda12f68} }, +/**/ {{0x3ff2e025, 0xc04b8097} }, +/**/ {{0x3ff2c9fb, 0x4d812ca0} }, +/**/ {{0x3ff2b404, 0xad012b40} }, +/**/ {{0x3ff29e41, 0x29e4129e} }, +/**/ {{0x3ff288b0, 0x1288b013} }, +/**/ {{0x3ff27350, 0xb8812735} }, +/**/ {{0x3ff25e22, 0x708092f1} }, +/**/ {{0x3ff24924, 0x92492492} }, +/**/ {{0x3ff23456, 0x789abcdf} }, +/**/ {{0x3ff21fb7, 0x8121fb78} }, +/**/ {{0x3ff20b47, 0x0c67c0d9} }, +/**/ {{0x3ff1f704, 0x7dc11f70} }, +/**/ {{0x3ff1e2ef, 0x3b3fb874} }, +/**/ {{0x3ff1cf06, 0xada2811d} }, +/**/ {{0x3ff1bb4a, 0x4046ed29} }, +/**/ {{0x3ff1a7b9, 0x611a7b96} }, +/**/ {{0x3ff19453, 0x808ca29c} }, +/**/ {{0x3ff18118, 0x11811812} }, +/**/ {{0x3ff16e06, 0x89427379} }, +/**/ {{0x3ff15b1e, 0x5f75270d} }, +/**/ {{0x3ff1485f, 0x0e0acd3b} }, +/**/ {{0x3ff135c8, 0x1135c811} }, +/**/ {{0x3ff12358, 0xe75d3033} }, +/**/ {{0x3ff11111, 0x11111111} }, +/**/ {{0x3ff0fef0, 0x10fef011} }, +/**/ {{0x3ff0ecf5, 0x6be69c90} }, +/**/ {{0x3ff0db20, 0xa88f4696} }, +/**/ {{0x3ff0c971, 0x4fbcda3b} }, +/**/ {{0x3ff0b7e6, 0xec259dc8} }, +/**/ {{0x3ff0a681, 0x0a6810a7} }, +/**/ {{0x3ff0953f, 0x39010954} }, +/**/ {{0x3ff08421, 0x08421084} }, +/**/ {{0x3ff07326, 0x0a47f7c6} }, +/**/ {{0x3ff0624d, 0xd2f1a9fc} }, +/**/ {{0x3ff05197, 0xf7d73404} }, +/**/ {{0x3ff04104, 0x10410410} }, +/**/ {{0x3ff03091, 0xb51f5e1a} }, +/**/ {{0x3ff02040, 0x81020408} }, +/**/ {{0x3ff01010, 0x10101010} }, +/**/ {{0x3ff00000, 0x00000000} }, +/**/ {{0x3fefe01f, 0xe01fe020} }, +/**/ {{0x3fefc07f, 0x01fc07f0} }, +/**/ {{0x3fefa11c, 0xaa01fa12} }, +/**/ {{0x3fef81f8, 0x1f81f820} }, +/**/ {{0x3fef6310, 0xaca0dbb5} }, +/**/ {{0x3fef4465, 0x9e4a4271} }, +/**/ {{0x3fef25f6, 0x44230ab5} }, +/**/ {{0x3fef07c1, 0xf07c1f08} }, +/**/ {{0x3feee9c7, 0xf8458e02} }, +/**/ {{0x3feecc07, 0xb301ecc0} }, +/**/ {{0x3feeae80, 0x7aba01eb} }, +/**/ {{0x3fee9131, 0xabf0b767} }, +/**/ {{0x3fee741a, 0xa59750e4} }, +/**/ {{0x3fee573a, 0xc901e574} }, +/**/ {{0x3fee3a91, 0x79dc1a73} }, +/**/ {{0x3fee1e1e, 0x1e1e1e1e} }, +/**/ {{0x3fee01e0, 0x1e01e01e} }, +/**/ {{0x3fede5d6, 0xe3f8868a} }, +/**/ {{0x3fedca01, 0xdca01dca} }, +/**/ {{0x3fedae60, 0x76b981db} }, +/**/ {{0x3fed92f2, 0x231e7f8a} }, +/**/ {{0x3fed77b6, 0x54b82c34} }, +/**/ {{0x3fed5cac, 0x807572b2} }, +/**/ {{0x3fed41d4, 0x1d41d41d} }, +/**/ {{0x3fed272c, 0xa3fc5b1a} }, +/**/ {{0x3fed0cb5, 0x8f6ec074} }, +/**/ {{0x3fecf26e, 0x5c44bfc6} }, +/**/ {{0x3fecd856, 0x89039b0b} }, +/**/ {{0x3fecbe6d, 0x9601cbe7} }, +/**/ {{0x3feca4b3, 0x055ee191} }, +/**/ {{0x3fec8b26, 0x5afb8a42} }, +/**/ {{0x3fec71c7, 0x1c71c71c} }, +/**/ {{0x3fec5894, 0xd10d4986} }, +/**/ {{0x3fec3f8f, 0x01c3f8f0} }, +/**/ {{0x3fec26b5, 0x392ea01c} }, +/**/ {{0x3fec0e07, 0x0381c0e0} }, +/**/ {{0x3febf583, 0xee868d8b} }, +/**/ {{0x3febdd2b, 0x899406f7} }, +/**/ {{0x3febc4fd, 0x65883e7b} }, +/**/ {{0x3febacf9, 0x14c1bad0} }, +/**/ {{0x3feb951e, 0x2b18ff23} }, +/**/ {{0x3feb7d6c, 0x3dda338b} }, +/**/ {{0x3feb65e2, 0xe3beee05} }, +/**/ {{0x3feb4e81, 0xb4e81b4f} }, +/**/ {{0x3feb3748, 0x4ad806ce} }, +/**/ {{0x3feb2036, 0x406c80d9} }, +/**/ {{0x3feb094b, 0x31d922a4} }, +/**/ {{0x3feaf286, 0xbca1af28} }, +/**/ {{0x3feadbe8, 0x7f94905e} }, +/**/ {{0x3feac570, 0x1ac5701b} }, +/**/ {{0x3feaaf1d, 0x2f87ebfd} }, +/**/ {{0x3fea98ef, 0x606a63be} }, +/**/ {{0x3fea82e6, 0x5130e159} }, +/**/ {{0x3fea6d01, 0xa6d01a6d} }, +/**/ {{0x3fea5741, 0x07688a4a} }, +/**/ {{0x3fea41a4, 0x1a41a41a} }, +/**/ {{0x3fea2c2a, 0x87c51ca0} }, +/**/ {{0x3fea16d3, 0xf97a4b02} }, +/**/ {{0x3fea01a0, 0x1a01a01a} }, +/**/ {{0x3fe9ec8e, 0x951033d9} }, +/**/ {{0x3fe9d79f, 0x176b682d} }, +/**/ {{0x3fe9c2d1, 0x4ee4a102} }, +/**/ {{0x3fe9ae24, 0xea5510da} }, +/**/ {{0x3fe99999, 0x9999999a} }, +/**/ {{0x3fe9852f, 0x0d8ec0ff} }, +/**/ {{0x3fe970e4, 0xf80cb872} }, +/**/ {{0x3fe95cbb, 0x0be377ae} }, +/**/ {{0x3fe948b0, 0xfcd6e9e0} }, +/**/ {{0x3fe934c6, 0x7f9b2ce6} }, +/**/ {{0x3fe920fb, 0x49d0e229} }, +/**/ {{0x3fe90d4f, 0x120190d5} }, +/**/ {{0x3fe8f9c1, 0x8f9c18fa} }, +/**/ {{0x3fe8e652, 0x7af1373f} }, +/**/ {{0x3fe8d301, 0x8d3018d3} }, +/**/ {{0x3fe8bfce, 0x8062ff3a} }, +/**/ {{0x3fe8acb9, 0x0f6bf3aa} }, +/**/ {{0x3fe899c0, 0xf601899c} }, +/**/ {{0x3fe886e5, 0xf0abb04a} }, +/**/ {{0x3fe87427, 0xbcc092b9} }, +/**/ {{0x3fe86186, 0x18618618} }, +/**/ {{0x3fe84f00, 0xc2780614} }, +/**/ {{0x3fe83c97, 0x7ab2bedd} }, +/**/ {{0x3fe82a4a, 0x0182a4a0} }, +/**/ {{0x3fe81818, 0x18181818} }, +/**/ {{0x3fe80601, 0x80601806} }, +/**/ {{0x3fe7f405, 0xfd017f40} }, +/**/ {{0x3fe7e225, 0x515a4f1d} }, +/**/ {{0x3fe7d05f, 0x417d05f4} }, +/**/ {{0x3fe7beb3, 0x922e017c} }, +/**/ {{0x3fe7ad22, 0x08e0ecc3} }, +/**/ {{0x3fe79baa, 0x6bb6398b} }, +/**/ {{0x3fe78a4c, 0x8178a4c8} }, +/**/ {{0x3fe77908, 0x119ac60d} }, +/**/ {{0x3fe767dc, 0xe434a9b1} }, +/**/ {{0x3fe756ca, 0xc201756d} }, +/**/ {{0x3fe745d1, 0x745d1746} }, +/**/ {{0x3fe734f0, 0xc541fe8d} }, +/**/ {{0x3fe72428, 0x7f46debc} }, +/**/ {{0x3fe71378, 0x6d9c7c09} }, +/**/ {{0x3fe702e0, 0x5c0b8170} }, +/**/ {{0x3fe6f260, 0x16f26017} }, +/**/ {{0x3fe6e1f7, 0x6b4337c7} }, +/**/ {{0x3fe6d1a6, 0x2681c861} }, +/**/ {{0x3fe6c16c, 0x16c16c17} }, +/**/ {{0x3fe6b149, 0x0aa31a3d} }, +/**/ {{0x3fe6a13c, 0xd1537290} }, + }; + + static const number + Iv[362] = { /* 1/vj */ +/**/ {{0x3ff00b47, 0xee93bfe3} }, +/**/ {{0x3ff00b37, 0xd80c106f} }, +/**/ {{0x3ff00b27, 0xc1a4a47a} }, +/**/ {{0x3ff00b17, 0xab5d7ba2} }, +/**/ {{0x3ff00b07, 0x95369587} }, +/**/ {{0x3ff00af7, 0x7f2ff1c6} }, +/**/ {{0x3ff00ae7, 0x69499000} }, +/**/ {{0x3ff00ad7, 0x53836fd3} }, +/**/ {{0x3ff00ac7, 0x3ddd90dd} }, +/**/ {{0x3ff00ab7, 0x2857f2bf} }, +/**/ {{0x3ff00aa7, 0x12f29517} }, +/**/ {{0x3ff00a96, 0xfdad7784} }, +/**/ {{0x3ff00a86, 0xe88899a5} }, +/**/ {{0x3ff00a76, 0xd383fb19} }, +/**/ {{0x3ff00a66, 0xbe9f9b7f} }, +/**/ {{0x3ff00a56, 0xa9db7a76} }, +/**/ {{0x3ff00a46, 0x9537979d} }, +/**/ {{0x3ff00a36, 0x80b3f293} }, +/**/ {{0x3ff00a26, 0x6c508af8} }, +/**/ {{0x3ff00a16, 0x580d606a} }, +/**/ {{0x3ff00a06, 0x43ea7288} }, +/**/ {{0x3ff009f6, 0x2fe7c0f1} }, +/**/ {{0x3ff009e6, 0x1c054b44} }, +/**/ {{0x3ff009d6, 0x08431122} }, +/**/ {{0x3ff009c5, 0xf4a11227} }, +/**/ {{0x3ff009b5, 0xe11f4df4} }, +/**/ {{0x3ff009a5, 0xcdbdc428} }, +/**/ {{0x3ff00995, 0xba7c7462} }, +/**/ {{0x3ff00985, 0xa75b5e40} }, +/**/ {{0x3ff00975, 0x945a8162} }, +/**/ {{0x3ff00965, 0x8179dd68} }, +/**/ {{0x3ff00955, 0x6eb971ef} }, +/**/ {{0x3ff00945, 0x5c193e98} }, +/**/ {{0x3ff00935, 0x49994301} }, +/**/ {{0x3ff00925, 0x37397eca} }, +/**/ {{0x3ff00915, 0x24f9f192} }, +/**/ {{0x3ff00905, 0x12da9af7} }, +/**/ {{0x3ff008f5, 0x00db7a99} }, +/**/ {{0x3ff008e4, 0xeefc9018} }, +/**/ {{0x3ff008d4, 0xdd3ddb12} }, +/**/ {{0x3ff008c4, 0xcb9f5b26} }, +/**/ {{0x3ff008b4, 0xba210ff4} }, +/**/ {{0x3ff008a4, 0xa8c2f91a} }, +/**/ {{0x3ff00894, 0x97851639} }, +/**/ {{0x3ff00884, 0x866766ef} }, +/**/ {{0x3ff00874, 0x7569eadb} }, +/**/ {{0x3ff00864, 0x648ca19d} }, +/**/ {{0x3ff00854, 0x53cf8ad3} }, +/**/ {{0x3ff00844, 0x4332a61e} }, +/**/ {{0x3ff00834, 0x32b5f31b} }, +/**/ {{0x3ff00824, 0x2259716c} }, +/**/ {{0x3ff00814, 0x121d20ad} }, +/**/ {{0x3ff00804, 0x02010080} }, +/**/ {{0x3ff007f3, 0xf2051083} }, +/**/ {{0x3ff007e3, 0xe2295056} }, +/**/ {{0x3ff007d3, 0xd26dbf97} }, +/**/ {{0x3ff007c3, 0xc2d25de5} }, +/**/ {{0x3ff007b3, 0xb3572ae2} }, +/**/ {{0x3ff007a3, 0xa3fc262a} }, +/**/ {{0x3ff00793, 0x94c14f5f} }, +/**/ {{0x3ff00783, 0x85a6a61e} }, +/**/ {{0x3ff00773, 0x76ac2a08} }, +/**/ {{0x3ff00763, 0x67d1dabb} }, +/**/ {{0x3ff00753, 0x5917b7d7} }, +/**/ {{0x3ff00743, 0x4a7dc0fb} }, +/**/ {{0x3ff00733, 0x3c03f5c7} }, +/**/ {{0x3ff00723, 0x2daa55da} }, +/**/ {{0x3ff00713, 0x1f70e0d3} }, +/**/ {{0x3ff00703, 0x11579652} }, +/**/ {{0x3ff006f3, 0x035e75f5} }, +/**/ {{0x3ff006e2, 0xf5857f5d} }, +/**/ {{0x3ff006d2, 0xe7ccb228} }, +/**/ {{0x3ff006c2, 0xda340df6} }, +/**/ {{0x3ff006b2, 0xccbb9266} }, +/**/ {{0x3ff006a2, 0xbf633f18} }, +/**/ {{0x3ff00692, 0xb22b13ab} }, +/**/ {{0x3ff00682, 0xa5130fbe} }, +/**/ {{0x3ff00672, 0x981b32f1} }, +/**/ {{0x3ff00662, 0x8b437ce4} }, +/**/ {{0x3ff00652, 0x7e8bed35} }, +/**/ {{0x3ff00642, 0x71f48383} }, +/**/ {{0x3ff00632, 0x657d3f70} }, +/**/ {{0x3ff00622, 0x59262098} }, +/**/ {{0x3ff00612, 0x4cef269e} }, +/**/ {{0x3ff00602, 0x40d8511e} }, +/**/ {{0x3ff005f2, 0x34e19fba} }, +/**/ {{0x3ff005e2, 0x290b1211} }, +/**/ {{0x3ff005d2, 0x1d54a7c1} }, +/**/ {{0x3ff005c2, 0x11be606b} }, +/**/ {{0x3ff005b2, 0x06483bad} }, +/**/ {{0x3ff005a1, 0xfaf23928} }, +/**/ {{0x3ff00591, 0xefbc587b} }, +/**/ {{0x3ff00581, 0xe4a69945} }, +/**/ {{0x3ff00571, 0xd9b0fb25} }, +/**/ {{0x3ff00561, 0xcedb7dbc} }, +/**/ {{0x3ff00551, 0xc42620a9} }, +/**/ {{0x3ff00541, 0xb990e38b} }, +/**/ {{0x3ff00531, 0xaf1bc601} }, +/**/ {{0x3ff00521, 0xa4c6c7ac} }, +/**/ {{0x3ff00511, 0x9a91e82a} }, +/**/ {{0x3ff00501, 0x907d271c} }, +/**/ {{0x3ff004f1, 0x86888421} }, +/**/ {{0x3ff004e1, 0x7cb3fed8} }, +/**/ {{0x3ff004d1, 0x72ff96e0} }, +/**/ {{0x3ff004c1, 0x696b4bdb} }, +/**/ {{0x3ff004b1, 0x5ff71d66} }, +/**/ {{0x3ff004a1, 0x56a30b21} }, +/**/ {{0x3ff00491, 0x4d6f14ad} }, +/**/ {{0x3ff00481, 0x445b39a8} }, +/**/ {{0x3ff00471, 0x3b6779b3} }, +/**/ {{0x3ff00461, 0x3293d46c} }, +/**/ {{0x3ff00451, 0x29e04974} }, +/**/ {{0x3ff00441, 0x214cd869} }, +/**/ {{0x3ff00431, 0x18d980ed} }, +/**/ {{0x3ff00421, 0x1086429d} }, +/**/ {{0x3ff00411, 0x08531d1a} }, +/**/ {{0x3ff00401, 0x00401004} }, +/**/ {{0x3ff003f0, 0xf84d1afa} }, +/**/ {{0x3ff003e0, 0xf07a3d9b} }, +/**/ {{0x3ff003d0, 0xe8c77787} }, +/**/ {{0x3ff003c0, 0xe134c85f} }, +/**/ {{0x3ff003b0, 0xd9c22fc1} }, +/**/ {{0x3ff003a0, 0xd26fad4d} }, +/**/ {{0x3ff00390, 0xcb3d40a3} }, +/**/ {{0x3ff00380, 0xc42ae963} }, +/**/ {{0x3ff00370, 0xbd38a72c} }, +/**/ {{0x3ff00360, 0xb666799e} }, +/**/ {{0x3ff00350, 0xafb46058} }, +/**/ {{0x3ff00340, 0xa9225afa} }, +/**/ {{0x3ff00330, 0xa2b06925} }, +/**/ {{0x3ff00320, 0x9c5e8a77} }, +/**/ {{0x3ff00310, 0x962cbe90} }, +/**/ {{0x3ff00300, 0x901b0511} }, +/**/ {{0x3ff002f0, 0x8a295d98} }, +/**/ {{0x3ff002e0, 0x8457c7c6} }, +/**/ {{0x3ff002d0, 0x7ea6433a} }, +/**/ {{0x3ff002c0, 0x7914cf94} }, +/**/ {{0x3ff002b0, 0x73a36c73} }, +/**/ {{0x3ff002a0, 0x6e521978} }, +/**/ {{0x3ff00290, 0x6920d642} }, +/**/ {{0x3ff00280, 0x640fa271} }, +/**/ {{0x3ff00270, 0x5f1e7da5} }, +/**/ {{0x3ff00260, 0x5a4d677d} }, +/**/ {{0x3ff00250, 0x559c5f9a} }, +/**/ {{0x3ff00240, 0x510b659a} }, +/**/ {{0x3ff00230, 0x4c9a791f} }, +/**/ {{0x3ff00220, 0x484999c6} }, +/**/ {{0x3ff00210, 0x4418c732} }, +/**/ {{0x3ff00200, 0x40080100} }, +/**/ {{0x3ff001f0, 0x3c1746d2} }, +/**/ {{0x3ff001e0, 0x38469846} }, +/**/ {{0x3ff001d0, 0x3495f4fd} }, +/**/ {{0x3ff001c0, 0x31055c96} }, +/**/ {{0x3ff001b0, 0x2d94ceb2} }, +/**/ {{0x3ff001a0, 0x2a444af0} }, +/**/ {{0x3ff00190, 0x2713d0ef} }, +/**/ {{0x3ff00180, 0x24036051} }, +/**/ {{0x3ff00170, 0x2112f8b4} }, +/**/ {{0x3ff00160, 0x1e4299b9} }, +/**/ {{0x3ff00150, 0x1b9242ff} }, +/**/ {{0x3ff00140, 0x1901f427} }, +/**/ {{0x3ff00130, 0x1691acd0} }, +/**/ {{0x3ff00120, 0x14416c9a} }, +/**/ {{0x3ff00110, 0x12113324} }, +/**/ {{0x3ff00100, 0x10010010} }, +/**/ {{0x3ff000f0, 0x0e10d2fc} }, +/**/ {{0x3ff000e0, 0x0c40ab89} }, +/**/ {{0x3ff000d0, 0x0a908957} }, +/**/ {{0x3ff000c0, 0x09006c05} }, +/**/ {{0x3ff000b0, 0x07905334} }, +/**/ {{0x3ff000a0, 0x06403e82} }, +/**/ {{0x3ff00090, 0x05102d92} }, +/**/ {{0x3ff00080, 0x04002001} }, +/**/ {{0x3ff00070, 0x03101571} }, +/**/ {{0x3ff00060, 0x02400d80} }, +/**/ {{0x3ff00050, 0x019007d0} }, +/**/ {{0x3ff00040, 0x01000400} }, +/**/ {{0x3ff00030, 0x009001b0} }, +/**/ {{0x3ff00020, 0x00400080} }, +/**/ {{0x3ff00010, 0x00100010} }, +/**/ {{0x3ff00000, 0x00000000} }, +/**/ {{0x3fefffe0, 0x001fffe0} }, +/**/ {{0x3fefffc0, 0x007fff00} }, +/**/ {{0x3fefffa0, 0x011ffca0} }, +/**/ {{0x3fefff80, 0x01fff800} }, +/**/ {{0x3fefff60, 0x031ff060} }, +/**/ {{0x3fefff40, 0x047fe501} }, +/**/ {{0x3fefff20, 0x061fd521} }, +/**/ {{0x3fefff00, 0x07ffc002} }, +/**/ {{0x3feffee0, 0x0a1fa4e3} }, +/**/ {{0x3feffec0, 0x0c7f8305} }, +/**/ {{0x3feffea0, 0x0f1f59a7} }, +/**/ {{0x3feffe80, 0x11ff280a} }, +/**/ {{0x3feffe60, 0x151eed6e} }, +/**/ {{0x3feffe40, 0x187ea913} }, +/**/ {{0x3feffe20, 0x1c1e5a39} }, +/**/ {{0x3feffe00, 0x1ffe0020} }, +/**/ {{0x3feffde0, 0x241d9a09} }, +/**/ {{0x3feffdc0, 0x287d2733} }, +/**/ {{0x3feffda0, 0x2d1ca6e0} }, +/**/ {{0x3feffd80, 0x31fc184e} }, +/**/ {{0x3feffd60, 0x371b7abf} }, +/**/ {{0x3feffd40, 0x3c7acd72} }, +/**/ {{0x3feffd20, 0x421a0fa9} }, +/**/ {{0x3feffd00, 0x47f940a2} }, +/**/ {{0x3feffce0, 0x4e185f9f} }, +/**/ {{0x3feffcc0, 0x54776bdf} }, +/**/ {{0x3feffca0, 0x5b1664a3} }, +/**/ {{0x3feffc80, 0x61f5492c} }, +/**/ {{0x3feffc60, 0x691418b9} }, +/**/ {{0x3feffc40, 0x7072d28b} }, +/**/ {{0x3feffc20, 0x781175e3} }, +/**/ {{0x3feffc00, 0x7ff00200} }, +/**/ {{0x3feffbe0, 0x880e7623} }, +/**/ {{0x3feffbc0, 0x906cd18c} }, +/**/ {{0x3feffba0, 0x990b137c} }, +/**/ {{0x3feffb80, 0xa1e93b34} }, +/**/ {{0x3feffb60, 0xab0747f3} }, +/**/ {{0x3feffb40, 0xb46538fa} }, +/**/ {{0x3feffb20, 0xbe030d89} }, +/**/ {{0x3feffb00, 0xc7e0c4e1} }, +/**/ {{0x3feffae0, 0xd1fe5e43} }, +/**/ {{0x3feffac0, 0xdc5bd8ee} }, +/**/ {{0x3feffaa0, 0xe6f93424} }, +/**/ {{0x3feffa80, 0xf1d66f25} }, +/**/ {{0x3feffa60, 0xfcf38931} }, +/**/ {{0x3feffa41, 0x08508189} }, +/**/ {{0x3feffa21, 0x13ed576d} }, +/**/ {{0x3feffa01, 0x1fca0a1e} }, +/**/ {{0x3feff9e1, 0x2be698dd} }, +/**/ {{0x3feff9c1, 0x384302e9} }, +/**/ {{0x3feff9a1, 0x44df4785} }, +/**/ {{0x3feff981, 0x51bb65ef} }, +/**/ {{0x3feff961, 0x5ed75d6a} }, +/**/ {{0x3feff941, 0x6c332d34} }, +/**/ {{0x3feff921, 0x79ced490} }, +/**/ {{0x3feff901, 0x87aa52be} }, +/**/ {{0x3feff8e1, 0x95c5a6fe} }, +/**/ {{0x3feff8c1, 0xa420d091} }, +/**/ {{0x3feff8a1, 0xb2bbceb7} }, +/**/ {{0x3feff881, 0xc196a0b2} }, +/**/ {{0x3feff861, 0xd0b145c2} }, +/**/ {{0x3feff841, 0xe00bbd28} }, +/**/ {{0x3feff821, 0xefa60624} }, +/**/ {{0x3feff801, 0xff801ff8} }, +/**/ {{0x3feff7e2, 0x0f9a09e3} }, +/**/ {{0x3feff7c2, 0x1ff3c328} }, +/**/ {{0x3feff7a2, 0x308d4b05} }, +/**/ {{0x3feff782, 0x4166a0bd} }, +/**/ {{0x3feff762, 0x527fc390} }, +/**/ {{0x3feff742, 0x63d8b2bf} }, +/**/ {{0x3feff722, 0x75716d8b} }, +/**/ {{0x3feff702, 0x8749f334} }, +/**/ {{0x3feff6e2, 0x996242fb} }, +/**/ {{0x3feff6c2, 0xabba5c21} }, +/**/ {{0x3feff6a2, 0xbe523de8} }, +/**/ {{0x3feff682, 0xd129e78f} }, +/**/ {{0x3feff662, 0xe4415858} }, +/**/ {{0x3feff642, 0xf7988f84} }, +/**/ {{0x3feff623, 0x0b2f8c54} }, +/**/ {{0x3feff603, 0x1f064e08} }, +/**/ {{0x3feff5e3, 0x331cd3e1} }, +/**/ {{0x3feff5c3, 0x47731d21} }, +/**/ {{0x3feff5a3, 0x5c092908} }, +/**/ {{0x3feff583, 0x70def6d7} }, +/**/ {{0x3feff563, 0x85f485d0} }, +/**/ {{0x3feff543, 0x9b49d532} }, +/**/ {{0x3feff523, 0xb0dee440} }, +/**/ {{0x3feff503, 0xc6b3b23b} }, +/**/ {{0x3feff4e3, 0xdcc83e62} }, +/**/ {{0x3feff4c3, 0xf31c87f8} }, +/**/ {{0x3feff4a4, 0x09b08e3d} }, +/**/ {{0x3feff484, 0x20845073} }, +/**/ {{0x3feff464, 0x3797cdda} }, +/**/ {{0x3feff444, 0x4eeb05b4} }, +/**/ {{0x3feff424, 0x667df741} }, +/**/ {{0x3feff404, 0x7e50a1c3} }, +/**/ {{0x3feff3e4, 0x9663047b} }, +/**/ {{0x3feff3c4, 0xaeb51eaa} }, +/**/ {{0x3feff3a4, 0xc746ef91} }, +/**/ {{0x3feff384, 0xe0187672} }, +/**/ {{0x3feff364, 0xf929b28d} }, +/**/ {{0x3feff345, 0x127aa323} }, +/**/ {{0x3feff325, 0x2c0b4776} }, +/**/ {{0x3feff305, 0x45db9ec7} }, +/**/ {{0x3feff2e5, 0x5feba858} }, +/**/ {{0x3feff2c5, 0x7a3b6369} }, +/**/ {{0x3feff2a5, 0x94cacf3b} }, +/**/ {{0x3feff285, 0xaf99eb11} }, +/**/ {{0x3feff265, 0xcaa8b62a} }, +/**/ {{0x3feff245, 0xe5f72fc9} }, +/**/ {{0x3feff226, 0x0185572f} }, +/**/ {{0x3feff206, 0x1d532b9d} }, +/**/ {{0x3feff1e6, 0x3960ac54} }, +/**/ {{0x3feff1c6, 0x55add896} }, +/**/ {{0x3feff1a6, 0x723aafa3} }, +/**/ {{0x3feff186, 0x8f0730be} }, +/**/ {{0x3feff166, 0xac135b27} }, +/**/ {{0x3feff146, 0xc95f2e21} }, +/**/ {{0x3feff126, 0xe6eaa8eb} }, +/**/ {{0x3feff107, 0x04b5cac9} }, +/**/ {{0x3feff0e7, 0x22c092fb} }, +/**/ {{0x3feff0c7, 0x410b00c2} }, +/**/ {{0x3feff0a7, 0x5f951360} }, +/**/ {{0x3feff087, 0x7e5eca16} }, +/**/ {{0x3feff067, 0x9d682426} }, +/**/ {{0x3feff047, 0xbcb120d2} }, +/**/ {{0x3feff027, 0xdc39bf5a} }, +/**/ {{0x3feff007, 0xfc01ff00} }, +/**/ {{0x3fefefe8, 0x1c09df07} }, +/**/ {{0x3fefefc8, 0x3c515eae} }, +/**/ {{0x3fefefa8, 0x5cd87d38} }, +/**/ {{0x3fefef88, 0x7d9f39e6} }, +/**/ {{0x3fefef68, 0x9ea593fa} }, +/**/ {{0x3fefef48, 0xbfeb8ab5} }, +/**/ {{0x3fefef28, 0xe1711d5a} }, +/**/ {{0x3fefef09, 0x03364b28} }, +/**/ {{0x3fefeee9, 0x253b1363} }, +/**/ {{0x3fefeec9, 0x477f754b} }, +/**/ {{0x3fefeea9, 0x6a037022} }, +/**/ {{0x3fefee89, 0x8cc7032a} }, +/**/ {{0x3fefee69, 0xafca2da5} }, +/**/ {{0x3fefee49, 0xd30ceed4} }, +/**/ {{0x3fefee29, 0xf68f45f8} }, +/**/ {{0x3fefee0a, 0x1a513254} }, +/**/ {{0x3fefedea, 0x3e52b329} }, +/**/ {{0x3fefedca, 0x6293c7b8} }, +/**/ {{0x3fefedaa, 0x87146f44} }, +/**/ {{0x3fefed8a, 0xabd4a90e} }, +/**/ {{0x3fefed6a, 0xd0d47458} }, +/**/ {{0x3fefed4a, 0xf613d064} }, +/**/ {{0x3fefed2b, 0x1b92bc73} }, +/**/ {{0x3fefed0b, 0x415137c7} }, +/**/ {{0x3fefeceb, 0x674f41a2} }, +/**/ {{0x3fefeccb, 0x8d8cd945} }, +/**/ {{0x3fefecab, 0xb409fdf3} }, +/**/ {{0x3fefec8b, 0xdac6aeed} }, +/**/ {{0x3fefec6c, 0x01c2eb76} }, +/**/ {{0x3fefec4c, 0x28feb2ce} }, +/**/ {{0x3fefec2c, 0x507a0437} }, +/**/ {{0x3fefec0c, 0x7834def5} }, +/**/ {{0x3fefebec, 0xa02f4247} }, +/**/ {{0x3fefebcc, 0xc8692d71} }, +/**/ {{0x3fefebac, 0xf0e29fb4} }, +/**/ {{0x3fefeb8d, 0x199b9852} }, +/**/ {{0x3fefeb6d, 0x4294168d} }, +/**/ {{0x3fefeb4d, 0x6bcc19a7} }, +/**/ {{0x3fefeb2d, 0x9543a0e2} }, +/**/ {{0x3fefeb0d, 0xbefaab7f} }, +/**/ {{0x3fefeaed, 0xe8f138c2} }, +/**/ {{0x3fefeace, 0x132747ea} }, +/**/ {{0x3fefeaae, 0x3d9cd83c} }, +/**/ {{0x3fefea8e, 0x6851e8f7} }, +/**/ {{0x3fefea6e, 0x93467960} }, +/**/ {{0x3fefea4e, 0xbe7a88b7} }, +/**/ {{0x3fefea2e, 0xe9ee163f} }, +/**/ {{0x3fefea0f, 0x15a12139} }, +/**/ {{0x3fefe9ef, 0x4193a8e8} }, +/**/ {{0x3fefe9cf, 0x6dc5ac8e} }, +/**/ {{0x3fefe9af, 0x9a372b6d} }, +/**/ {{0x3fefe98f, 0xc6e824c6} }, +/**/ {{0x3fefe96f, 0xf3d897dd} }, + }; + + static const number + Lu[182][2] = { /* log(ui) */ +/**/ {{{0xbfd63003, 0x0b3aac49} }, +/**/ {{0xbc6dc18c, 0xe51fff99} },}, +/**/ {{{0xbfd5d5bd, 0xdf595f30} }, +/**/ {{0x3c765411, 0x48cbb8a2} },}, +/**/ {{{0xbfd57bf7, 0x53c8d1fb} }, +/**/ {{0x3c60908d, 0x15f88b63} },}, +/**/ {{{0xbfd522ae, 0x0738a3d8} }, +/**/ {{0x3c68f7e9, 0xb38a6979} },}, +/**/ {{{0xbfd4c9e0, 0x9e172c3c} }, +/**/ {{0x3c512361, 0x5b147a5d} },}, +/**/ {{{0xbfd4718d, 0xc271c41b} }, +/**/ {{0xbc38fb4c, 0x14c56eef} },}, +/**/ {{{0xbfd419b4, 0x23d5e8c7} }, +/**/ {{0xbc60dbb2, 0x43827392} },}, +/**/ {{{0xbfd3c252, 0x77333184} }, +/**/ {{0x3c72ad27, 0xe50a8ec6} },}, +/**/ {{{0xbfd36b67, 0x76be1117} }, +/**/ {{0x3c5324f0, 0xe883858e} },}, +/**/ {{{0xbfd314f1, 0xe1d35ce4} }, +/**/ {{0x3c73d699, 0x09e5c3dc} },}, +/**/ {{{0xbfd2bef0, 0x7cdc9354} }, +/**/ {{0x3c782dad, 0x7fd86088} },}, +/**/ {{{0xbfd26962, 0x1134db92} }, +/**/ {{0xbc7e0efa, 0xdd9db02b} },}, +/**/ {{{0xbfd21445, 0x6d0eb8d4} }, +/**/ {{0xbc6f7ae9, 0x1aeba60a} },}, +/**/ {{{0xbfd1bf99, 0x635a6b95} }, +/**/ {{0x3c612aeb, 0x84249223} },}, +/**/ {{{0xbfd16b5c, 0xcbacfb73} }, +/**/ {{0xbc766fbd, 0x28b40935} },}, +/**/ {{{0xbfd1178e, 0x8227e47c} }, +/**/ {{0x3c60e63a, 0x5f01c691} },}, +/**/ {{{0xbfd0c42d, 0x676162e3} }, +/**/ {{0xbc5162c7, 0x9d5d11ee} },}, +/**/ {{{0xbfd07138, 0x604d5862} }, +/**/ {{0xbc7cdb16, 0xed4e9138} },}, +/**/ {{{0xbfd01eae, 0x5626c691} }, +/**/ {{0x3c418290, 0xbd2932e2} },}, +/**/ {{{0xbfcf991c, 0x6cb3b379} }, +/**/ {{0xbc6f6650, 0x66f980a2} },}, +/**/ {{{0xbfcef5ad, 0xe4dcffe6} }, +/**/ {{0x3c508ab2, 0xddc708a0} },}, +/**/ {{{0xbfce530e, 0xffe71012} }, +/**/ {{0xbc422760, 0x41f43042} },}, +/**/ {{{0xbfcdb13d, 0xb0d48940} }, +/**/ {{0xbc5aa11d, 0x49f96cb9} },}, +/**/ {{{0xbfcd1037, 0xf2655e7b} }, +/**/ {{0xbc660629, 0x242471a2} },}, +/**/ {{{0xbfcc6ffb, 0xc6f00f71} }, +/**/ {{0x3c68e58b, 0x2c57a4a5} },}, +/**/ {{{0xbfcbd087, 0x383bd8ad} }, +/**/ {{0xbc3dd355, 0xf6a516d7} },}, +/**/ {{{0xbfcb31d8, 0x575bce3d} }, +/**/ {{0x3c66353a, 0xb386a94d} },}, +/**/ {{{0xbfca93ed, 0x3c8ad9e3} }, +/**/ {{0xbc6bcafa, 0x9de97203} },}, +/**/ {{{0xbfc9f6c4, 0x07089664} }, +/**/ {{0xbc435a19, 0x605e67ef} },}, +/**/ {{{0xbfc95a5a, 0xdcf7017f} }, +/**/ {{0xbc5142c5, 0x07fb7a3d} },}, +/**/ {{{0xbfc8beaf, 0xeb38fe8c} }, +/**/ {{0xbc555aa8, 0xb6997a40} },}, +/**/ {{{0xbfc823c1, 0x6551a3c2} }, +/**/ {{0x3c61232c, 0xe70be781} },}, +/**/ {{{0xbfc7898d, 0x85444c73} }, +/**/ {{0xbc5ef8f6, 0xebcfb201} },}, +/**/ {{{0xbfc6f012, 0x8b756abc} }, +/**/ {{0x3c68de59, 0xc21e166c} },}, +/**/ {{{0xbfc6574e, 0xbe8c133a} }, +/**/ {{0x3c3d34f0, 0xf4621bed} },}, +/**/ {{{0xbfc5bf40, 0x6b543db2} }, +/**/ {{0x3c21f5b4, 0x4c0df7e7} },}, +/**/ {{{0xbfc527e5, 0xe4a1b58d} }, +/**/ {{0x3c271a96, 0x82395bfd} },}, +/**/ {{{0xbfc4913d, 0x8333b561} }, +/**/ {{0x3c50d560, 0x4930f135} },}, +/**/ {{{0xbfc3fb45, 0xa59928cc} }, +/**/ {{0x3c6d87e6, 0xa354d056} },}, +/**/ {{{0xbfc365fc, 0xb0159016} }, +/**/ {{0xbc57d411, 0xa5b944ad} },}, +/**/ {{{0xbfc2d161, 0x0c86813a} }, +/**/ {{0x3c5499a3, 0xf25af95f} },}, +/**/ {{{0xbfc23d71, 0x2a49c202} }, +/**/ {{0x3c66e381, 0x61051d69} },}, +/**/ {{{0xbfc1aa2b, 0x7e23f72a} }, +/**/ {{0x3c4c6ef1, 0xd9b2ef7e} },}, +/**/ {{{0xbfc1178e, 0x8227e47c} }, +/**/ {{0x3c50e63a, 0x5f01c691} },}, +/**/ {{{0xbfc08598, 0xb59e3a07} }, +/**/ {{0x3c6dd700, 0x9902bf32} },}, +/**/ {{{0xbfbfe891, 0x39dbd566} }, +/**/ {{0x3c5ac9f4, 0x215f9393} },}, +/**/ {{{0xbfbec739, 0x830a1120} }, +/**/ {{0x3c4a2bf9, 0x91780d3f} },}, +/**/ {{{0xbfbda727, 0x638446a2} }, +/**/ {{0xbc5401fa, 0x71733019} },}, +/**/ {{{0xbfbc8858, 0x01bc4b23} }, +/**/ {{0xbc5a38cb, 0x559a6706} },}, +/**/ {{{0xbfbb6ac8, 0x8dad5b1c} }, +/**/ {{0x3c40057e, 0xed1ca59f} },}, +/**/ {{{0xbfba4e76, 0x40b1bc38} }, +/**/ {{0x3c55b5ca, 0x203e4259} },}, +/**/ {{{0xbfb9335e, 0x5d594989} }, +/**/ {{0x3c5478a8, 0x5704ccb7} },}, +/**/ {{{0xbfb8197e, 0x2f40e3f0} }, +/**/ {{0xbc3b9f2d, 0xffbeed43} },}, +/**/ {{{0xbfb700d3, 0x0aeac0e1} }, +/**/ {{0x3c272566, 0x212cdd05} },}, +/**/ {{{0xbfb5e95a, 0x4d9791cb} }, +/**/ {{0xbc5f3874, 0x5c5c450a} },}, +/**/ {{{0xbfb4d311, 0x5d207eac} }, +/**/ {{0xbc5769f4, 0x2c7842cc} },}, +/**/ {{{0xbfb3bdf5, 0xa7d1ee64} }, +/**/ {{0xbc47a976, 0xd3b5b45f} },}, +/**/ {{{0xbfb2aa04, 0xa44717a5} }, +/**/ {{0x3c5d15d3, 0x8d2fa3f7} },}, +/**/ {{{0xbfb1973b, 0xd1465567} }, +/**/ {{0x3c475583, 0x67a6acf6} },}, +/**/ {{{0xbfb08598, 0xb59e3a07} }, +/**/ {{0x3c5dd700, 0x9902bf32} },}, +/**/ {{{0xbfaeea31, 0xc006b87c} }, +/**/ {{0x3c43e4fc, 0x93b7b66c} },}, +/**/ {{{0xbfaccb73, 0xcdddb2cc} }, +/**/ {{0x3c4e48fb, 0x0500efd4} },}, +/**/ {{{0xbfaaaef2, 0xd0fb10fc} }, +/**/ {{0xbc2a353b, 0xb42e0add} },}, +/**/ {{{0xbfa894aa, 0x149fb343} }, +/**/ {{0xbc3a8be9, 0x7660a23d} },}, +/**/ {{{0xbfa67c94, 0xf2d4bb58} }, +/**/ {{0xbc40413e, 0x6505e603} },}, +/**/ {{{0xbfa466ae, 0xd42de3ea} }, +/**/ {{0x3c4cdd6f, 0x7f4a137e} },}, +/**/ {{{0xbfa252f3, 0x2f8d183f} }, +/**/ {{0x3c4947f7, 0x92615916} },}, +/**/ {{{0xbfa0415d, 0x89e74444} }, +/**/ {{0xbc4c05cf, 0x1d753622} },}, +/**/ {{{0xbf9c63d2, 0xec14aaf2} }, +/**/ {{0x3c3ce030, 0xa686bd86} },}, +/**/ {{{0xbf984925, 0x28c8cabf} }, +/**/ {{0x3c3d192d, 0x0619fa67} },}, +/**/ {{{0xbf9432a9, 0x25980cc1} }, +/**/ {{0x3c38cdaf, 0x39004192} },}, +/**/ {{{0xbf902056, 0x58935847} }, +/**/ {{0xbc327c8e, 0x8416e71f} },}, +/**/ {{{0xbf882448, 0xa388a2aa} }, +/**/ {{0xbc104b16, 0x137f09a0} },}, +/**/ {{{0xbf801015, 0x7588de71} }, +/**/ {{0xbc146662, 0xd417ced0} },}, +/**/ {{{0xbf700805, 0x59588b35} }, +/**/ {{0xbc1f9663, 0x8cf63677} },}, +/**/ {{{0x00000000, 0x00000000} }, +/**/ {{0x00000000, 0x00000000} },}, +/**/ {{{0x3f6ff00a, 0xa2b10bc0} }, +/**/ {{0x3c02821a, 0xd5a6d353} },}, +/**/ {{{0x3f7fe02a, 0x6b106789} }, +/**/ {{0xbbce44b7, 0xe3711ebf} },}, +/**/ {{{0x3f87dc47, 0x5f810a77} }, +/**/ {{0xbc116d76, 0x87d3df21} },}, +/**/ {{{0x3f8fc0a8, 0xb0fc03e4} }, +/**/ {{0xbc183092, 0xc59642a1} },}, +/**/ {{{0x3f93cea4, 0x4346a575} }, +/**/ {{0xbc10cb5a, 0x902b3a1c} },}, +/**/ {{{0x3f97b91b, 0x07d5b11b} }, +/**/ {{0xbc35b602, 0xace3a510} },}, +/**/ {{{0x3f9b9fc0, 0x27af9198} }, +/**/ {{0xbbf0ae69, 0x229dc868} },}, +/**/ {{{0x3f9f829b, 0x0e783300} }, +/**/ {{0x3c333e3f, 0x04f1ef23} },}, +/**/ {{{0x3fa1b0d9, 0x8923d980} }, +/**/ {{0xbc3e9ae8, 0x89bac481} },}, +/**/ {{{0x3fa39e87, 0xb9febd60} }, +/**/ {{0xbc45bfa9, 0x37f551bb} },}, +/**/ {{{0x3fa58a5b, 0xafc8e4d5} }, +/**/ {{0xbc4ce55c, 0x2b4e2b72} },}, +/**/ {{{0x3fa77458, 0xf632dcfc} }, +/**/ {{0x3c418d3c, 0xa87b9296} },}, +/**/ {{{0x3fa95c83, 0x0ec8e3eb} }, +/**/ {{0x3c4f5a0e, 0x80520bf2} },}, +/**/ {{{0x3fab42dd, 0x711971bf} }, +/**/ {{0xbc3eb975, 0x9c130499} },}, +/**/ {{{0x3fad276b, 0x8adb0b52} }, +/**/ {{0x3c21e3c5, 0x3257fd47} },}, +/**/ {{{0x3faf0a30, 0xc01162a6} }, +/**/ {{0x3c485f32, 0x5c5bbacd} },}, +/**/ {{{0x3fb07598, 0x3598e471} }, +/**/ {{0x3c480da5, 0x333c45b8} },}, +/**/ {{{0x3fb16536, 0xeea37ae1} }, +/**/ {{0xbc379da3, 0xe8c22cda} },}, +/**/ {{{0x3fb253f6, 0x2f0a1417} }, +/**/ {{0xbc1c1259, 0x63fc4cfd} },}, +/**/ {{{0x3fb341d7, 0x961bd1d1} }, +/**/ {{0xbc5b599f, 0x227becbb} },}, +/**/ {{{0x3fb42edc, 0xbea646f0} }, +/**/ {{0x3c4ddd4f, 0x935996c9} },}, +/**/ {{{0x3fb51b07, 0x3f06183f} }, +/**/ {{0x3c5a49e3, 0x9a1a8be4} },}, +/**/ {{{0x3fb60658, 0xa93750c4} }, +/**/ {{0xbc538845, 0x8ec21b6a} },}, +/**/ {{{0x3fb6f0d2, 0x8ae56b4c} }, +/**/ {{0xbc5906d9, 0x9184b992} },}, +/**/ {{{0x3fb7da76, 0x6d7b12cd} }, +/**/ {{0xbc5eeedf, 0xcdd94131} },}, +/**/ {{{0x3fb8c345, 0xd6319b21} }, +/**/ {{0xbc24a697, 0xab3424a9} },}, +/**/ {{{0x3fb9ab42, 0x462033ad} }, +/**/ {{0xbc42099e, 0x1c184e8e} },}, +/**/ {{{0x3fba926d, 0x3a4ad563} }, +/**/ {{0x3c5942f4, 0x8aa70ea9} },}, +/**/ {{{0x3fbb78c8, 0x2bb0eda1} }, +/**/ {{0x3c20878c, 0xf0327e21} },}, +/**/ {{{0x3fbc5e54, 0x8f5bc743} }, +/**/ {{0x3c35d617, 0xef8161b1} },}, +/**/ {{{0x3fbd4313, 0xd66cb35d} }, +/**/ {{0x3c5790dd, 0x951d90fa} },}, +/**/ {{{0x3fbe2707, 0x6e2af2e6} }, +/**/ {{0xbc361578, 0x001e0162} },}, +/**/ {{{0x3fbf0a30, 0xc01162a6} }, +/**/ {{0x3c585f32, 0x5c5bbacd} },}, +/**/ {{{0x3fbfec91, 0x31dbeabb} }, +/**/ {{0xbc55746b, 0x9981b36c} },}, +/**/ {{{0x3fc06715, 0x12ca596e} }, +/**/ {{0x3c550c64, 0x7eb86499} },}, +/**/ {{{0x3fc0d77e, 0x7cd08e59} }, +/**/ {{0x3c69a5dc, 0x5e9030ac} },}, +/**/ {{{0x3fc14785, 0x846742ac} }, +/**/ {{0x3c6a2881, 0x3e3a7f07} },}, +/**/ {{{0x3fc1b72a, 0xd52f67a0} }, +/**/ {{0x3c548302, 0x3472cd74} },}, +/**/ {{{0x3fc2266f, 0x190a5acb} }, +/**/ {{0x3c6f547b, 0xf1809e88} },}, +/**/ {{{0x3fc29552, 0xf81ff523} }, +/**/ {{0x3c630177, 0x1c407dbf} },}, +/**/ {{{0x3fc303d7, 0x18e47fd3} }, +/**/ {{0xbc06b9c7, 0xd96091fa} },}, +/**/ {{{0x3fc371fc, 0x201e8f74} }, +/**/ {{0x3c5de6cb, 0x62af18a0} },}, +/**/ {{{0x3fc3dfc2, 0xb0ecc62a} }, +/**/ {{0xbc5ab3a8, 0xe7d81017} },}, +/**/ {{{0x3fc44d2b, 0x6ccb7d1e} }, +/**/ {{0x3c69f4f6, 0x543e1f88} },}, +/**/ {{{0x3fc4ba36, 0xf39a55e5} }, +/**/ {{0x3c668981, 0xbcc36756} },}, +/**/ {{{0x3fc526e5, 0xe3a1b438} }, +/**/ {{0xbc6746ff, 0x8a470d3a} },}, +/**/ {{{0x3fc59338, 0xd9982086} }, +/**/ {{0xbc565d22, 0xaa8ad7cf} },}, +/**/ {{{0x3fc5ff30, 0x70a793d4} }, +/**/ {{0xbc5bc60e, 0xfafc6f6e} },}, +/**/ {{{0x3fc66acd, 0x4272ad51} }, +/**/ {{0xbc50900e, 0x4e1ea8b2} },}, +/**/ {{{0x3fc6d60f, 0xe719d21d} }, +/**/ {{0xbc6caae2, 0x68ecd179} },}, +/**/ {{{0x3fc740f8, 0xf54037a5} }, +/**/ {{0xbc5b2640, 0x62a84cdb} },}, +/**/ {{{0x3fc7ab89, 0x0210d909} }, +/**/ {{0x3c4be36b, 0x2d6a0608} },}, +/**/ {{{0x3fc815c0, 0xa14357eb} }, +/**/ {{0xbc54be48, 0x073a0564} },}, +/**/ {{{0x3fc87fa0, 0x6520c911} }, +/**/ {{0xbc6bf7fd, 0xbfa08d9a} },}, +/**/ {{{0x3fc8e928, 0xde886d41} }, +/**/ {{0xbc6569d8, 0x51a56770} },}, +/**/ {{{0x3fc9525a, 0x9cf456b4} }, +/**/ {{0x3c6d904c, 0x1d4e2e26} },}, +/**/ {{{0x3fc9bb36, 0x2e7dfb83} }, +/**/ {{0x3c6575e3, 0x1f003e0c} },}, +/**/ {{{0x3fca23bc, 0x1fe2b563} }, +/**/ {{0x3c493711, 0xb07a998c} },}, +/**/ {{{0x3fca8bec, 0xfc882f19} }, +/**/ {{0xbc5e8c37, 0x918c39eb} },}, +/**/ {{{0x3fcaf3c9, 0x4e80bff3} }, +/**/ {{0xbc5398cf, 0xf3641985} },}, +/**/ {{{0x3fcb5b51, 0x9e8fb5a4} }, +/**/ {{0x3c6ba27f, 0xdc19e1a0} },}, +/**/ {{{0x3fcbc286, 0x742d8cd6} }, +/**/ {{0x3c54fce7, 0x44870f55} },}, +/**/ {{{0x3fcc2968, 0x558c18c1} }, +/**/ {{0xbc673dee, 0x38a3fb6b} },}, +/**/ {{{0x3fcc8ff7, 0xc79a9a22} }, +/**/ {{0xbc64f689, 0xf8434012} },}, +/**/ {{{0x3fccf635, 0x4e09c5dc} }, +/**/ {{0x3c6239a0, 0x7d55b695} },}, +/**/ {{{0x3fcd5c21, 0x6b4fbb91} }, +/**/ {{0x3c66e443, 0x597e4d40} },}, +/**/ {{{0x3fcdc1bc, 0xa0abec7d} }, +/**/ {{0x3c6834c5, 0x1998b6fc} },}, +/**/ {{{0x3fce2707, 0x6e2af2e6} }, +/**/ {{0xbc461578, 0x001e0162} },}, +/**/ {{{0x3fce8c02, 0x52aa5a60} }, +/**/ {{0xbc46e03a, 0x39bfc89b} },}, +/**/ {{{0x3fcef0ad, 0xcbdc5936} }, +/**/ {{0x3c648637, 0x950dc20d} },}, +/**/ {{{0x3fcf550a, 0x564b7b37} }, +/**/ {{0x3c2c5f6d, 0xfd018c37} },}, +/**/ {{{0x3fcfb918, 0x6d5e3e2b} }, +/**/ {{0xbc6caaae, 0x64f21acb} },}, +/**/ {{{0x3fd00e6c, 0x45ad501d} }, +/**/ {{0xbc6cb956, 0x8ff6fead} },}, +/**/ {{{0x3fd04025, 0x94b4d041} }, +/**/ {{0xbc628ec2, 0x17a5022d} },}, +/**/ {{{0x3fd071b8, 0x5fcd590d} }, +/**/ {{0x3c5d1707, 0xf97bde80} },}, +/**/ {{{0x3fd0a324, 0xe27390e3} }, +/**/ {{0x3c77dcfd, 0xe8061c03} },}, +/**/ {{{0x3fd0d46b, 0x579ab74b} }, +/**/ {{0x3c603ec8, 0x1c3cbd92} },}, +/**/ {{{0x3fd1058b, 0xf9ae4ad5} }, +/**/ {{0x3c589fa0, 0xab4cb31d} },}, +/**/ {{{0x3fd13687, 0x0293a8b0} }, +/**/ {{0x3c77b662, 0x98edd24a} },}, +/**/ {{{0x3fd1675c, 0xababa60e} }, +/**/ {{0x3c2ce63e, 0xab883717} },}, +/**/ {{{0x3fd1980d, 0x2dd4236f} }, +/**/ {{0x3c79d3d1, 0xb0e4d147} },}, +/**/ {{{0x3fd1c898, 0xc16999fb} }, +/**/ {{0xbc30e5c6, 0x2aff1c44} },}, +/**/ {{{0x3fd1f8ff, 0x9e48a2f3} }, +/**/ {{0xbc7c9fdf, 0x9a0c4b07} },}, +/**/ {{{0x3fd22941, 0xfbcf7966} }, +/**/ {{0xbc776f5e, 0xb09628af} },}, +/**/ {{{0x3fd25960, 0x10df763a} }, +/**/ {{0xbc50f76c, 0x57075e9e} },}, +/**/ {{{0x3fd2895a, 0x13de86a3} }, +/**/ {{0x3c77ad24, 0xc13f040e} },}, +/**/ {{{0x3fd2b930, 0x3ab89d25} }, +/**/ {{0xbc7896b5, 0xfd852ad4} },}, +/**/ {{{0x3fd2e8e2, 0xbae11d31} }, +/**/ {{0xbc78f4cd, 0xb95ebdf9} },}, +/**/ {{{0x3fd31871, 0xc9544185} }, +/**/ {{0xbc351acc, 0x4c09b379} },}, +/**/ {{{0x3fd347dd, 0x9a987d55} }, +/**/ {{0xbc64dd4c, 0x580919f8} },}, +/**/ {{{0x3fd37726, 0x62bfd85b} }, +/**/ {{0xbc4b5629, 0xd8117de7} },}, +/**/ {{{0x3fd3a64c, 0x556945ea} }, +/**/ {{0xbc6c6865, 0x1945f97c} },}, +/**/ {{{0x3fd3d54f, 0xa5c1f710} }, +/**/ {{0xbc7e3265, 0xc6a1c98d} },}, +/**/ {{{0x3fd40430, 0x8686a7e4} }, +/**/ {{0xbc70bcfb, 0x6082ce6d} },}, +/**/ {{{0x3fd432ef, 0x2a04e814} }, +/**/ {{0xbc729931, 0x715ac903} },}, +/**/ {{{0x3fd4618b, 0xc21c5ec2} }, +/**/ {{0x3c7f42de, 0xcdeccf1d} },}, +/**/ {{{0x3fd49006, 0x804009d1} }, +/**/ {{0xbc69ffc3, 0x41f177dc} },}, +/**/ {{{0x3fd4be5f, 0x957778a1} }, +/**/ {{0xbc6259b3, 0x5b04813d} },}, +/**/ {{{0x3fd4ec97, 0x3260026a} }, +/**/ {{0xbc742a87, 0xd977dc5e} },}, +/**/ {{{0x3fd51aad, 0x872df82d} }, +/**/ {{0x3c43927a, 0xc19f55e3} },}, +/**/ {{{0x3fd548a2, 0xc3add263} }, +/**/ {{0xbc6819cf, 0x7e308ddb} },}, +/**/ {{{0x3fd57677, 0x17455a6c} }, +/**/ {{0x3c7526ad, 0xb283660c} },}, +/**/ {{{0x3fd5a42a, 0xb0f4cfe2} }, +/**/ {{0xbc78ebcb, 0x7dee9a3d} },}, +/**/ {{{0x3fd5d1bd, 0xbf5809ca} }, +/**/ {{0x3c742363, 0x83dc7fe1} },}, +/**/ {{{0x3fd5ff30, 0x70a793d4} }, +/**/ {{0xbc6bc60e, 0xfafc6f6e} },}, +/**/ {{{0x3fd62c82, 0xf2b9c795} }, +/**/ {{0x3c67b7af, 0x915300e5} },}, + }; + + static const number + Lv[362][2] = { /* log(vj) */ + +/**/ {{{0xbf6687ec, 0xb72daabf} }, +/**/ {{0x3c052c69, 0x0f13318f} },}, +/**/ {{{0xbf6667d6, 0x3767104f} }, +/**/ {{0x3bd3efa3, 0xd27a7bac} },}, +/**/ {{{0xbf6647bf, 0xd7cd64fb} }, +/**/ {{0x3c09b725, 0x55a89c36} },}, +/**/ {{{0xbf6627a9, 0x9860683b} }, +/**/ {{0x3bcbae22, 0xfebc844a} },}, +/**/ {{{0xbf660793, 0x791fd98a} }, +/**/ {{0xbbfe34af, 0x78fa1cb5} },}, +/**/ {{{0xbf65e77d, 0x7a0b7863} }, +/**/ {{0xbc02f1b1, 0xea78fdd0} },}, +/**/ {{{0xbf65c767, 0x9b230442} }, +/**/ {{0x3bf70d8c, 0x2202b2ca} },}, +/**/ {{{0xbf65a751, 0xdc663ca2} }, +/**/ {{0xbbfdc63d, 0xc3444e64} },}, +/**/ {{{0xbf65873c, 0x3dd4e102} }, +/**/ {{0x3c021b11, 0x370d69c3} },}, +/**/ {{{0xbf656726, 0xbf6eb0de} }, +/**/ {{0xbbfb6da8, 0x154dd8d8} },}, +/**/ {{{0xbf654711, 0x61336bb6} }, +/**/ {{0xbc0b12d2, 0xdf9a4709} },}, +/**/ {{{0xbf6526fc, 0x2322d10a} }, +/**/ {{0x3bf997f2, 0x68d1274f} },}, +/**/ {{{0xbf6506e7, 0x053ca059} }, +/**/ {{0x3c0c2a1f, 0xe70c852a} },}, +/**/ {{{0xbf64e6d2, 0x07809924} }, +/**/ {{0x3c04cc9e, 0xa808538f} },}, +/**/ {{{0xbf64c6bd, 0x29ee7aed} }, +/**/ {{0x3befe68c, 0x7797a4bd} },}, +/**/ {{{0xbf64a6a8, 0x6c860537} }, +/**/ {{0x3c06794d, 0x9efaae3d} },}, +/**/ {{{0xbf648693, 0xcf46f784} }, +/**/ {{0xbbfed318, 0xb2ddd9d1} },}, +/**/ {{{0xbf64667f, 0x5231115a} }, +/**/ {{0x3c061f62, 0x4643624b} },}, +/**/ {{{0xbf64466a, 0xf544123c} }, +/**/ {{0x3c0666a0, 0x9387f11e} },}, +/**/ {{{0xbf642656, 0xb87fb9b0} }, +/**/ {{0x3c0043b2, 0x116ec598} },}, +/**/ {{{0xbf640642, 0x9be3c73c} }, +/**/ {{0xbbfbd84d, 0xd2de6e3e} },}, +/**/ {{{0xbf63e62e, 0x9f6ffa68} }, +/**/ {{0xbbe9149b, 0x433d8c65} },}, +/**/ {{{0xbf63c61a, 0xc32412bb} }, +/**/ {{0xbbf6b88d, 0x08e5a7bb} },}, +/**/ {{{0xbf63a607, 0x06ffcfbe} }, +/**/ {{0xbb9f3c7a, 0xccfac9e2} },}, +/**/ {{{0xbf6385f3, 0x6b02f0fa} }, +/**/ {{0x3bee405c, 0xbec6f6e4} },}, +/**/ {{{0xbf6365df, 0xef2d35f9} }, +/**/ {{0x3bf02993, 0xaf0c0b4c} },}, +/**/ {{{0xbf6345cc, 0x937e5e46} }, +/**/ {{0x3bf9be97, 0xaa64716f} },}, +/**/ {{{0xbf6325b9, 0x57f6296c} }, +/**/ {{0xbbfdeb4d, 0xa2e863ae} },}, +/**/ {{{0xbf6305a6, 0x3c9456f9} }, +/**/ {{0x3c0f3c7f, 0x636d2b2c} },}, +/**/ {{{0xbf62e593, 0x4158a678} }, +/**/ {{0x3c01a8df, 0xb166ca7f} },}, +/**/ {{{0xbf62c580, 0x6642d778} }, +/**/ {{0x3c020ff1, 0x53a2d534} },}, +/**/ {{{0xbf62a56d, 0xab52a987} }, +/**/ {{0xbbe8fef1, 0x0412f1e7} },}, +/**/ {{{0xbf62855b, 0x1087dc35} }, +/**/ {{0xbbfcd17e, 0x4b7ac6c6} },}, +/**/ {{{0xbf626548, 0x95e22f12} }, +/**/ {{0xbbfbfc21, 0x9a8127bf} },}, +/**/ {{{0xbf624536, 0x3b6161af} }, +/**/ {{0x3bd7eda1, 0x66d42390} },}, +/**/ {{{0xbf622524, 0x0105339d} }, +/**/ {{0xbbdf374e, 0x77fedcad} },}, +/**/ {{{0xbf620511, 0xe6cd646f} }, +/**/ {{0x3be1d1fb, 0x52d05dea} },}, +/**/ {{{0xbf61e4ff, 0xecb9b3b8} }, +/**/ {{0x3c02c2fc, 0xffd8e706} },}, +/**/ {{{0xbf61c4ee, 0x12c9e10b} }, +/**/ {{0xbc02b4f8, 0xf1d5cc2c} },}, +/**/ {{{0xbf61a4dc, 0x58fdabfe} }, +/**/ {{0xbc0618c3, 0x1315b191} },}, +/**/ {{{0xbf6184ca, 0xbf54d426} }, +/**/ {{0xbc01f8d5, 0xcb3cdab0} },}, +/**/ {{{0xbf6164b9, 0x45cf1919} }, +/**/ {{0xbc014ff7, 0xc025605a} },}, +/**/ {{{0xbf6144a7, 0xec6c3a6e} }, +/**/ {{0xbbff04ff, 0x87cb08cd} },}, +/**/ {{{0xbf612496, 0xb32bf7bd} }, +/**/ {{0x3bee89b4, 0xe6af1b84} },}, +/**/ {{{0xbf610485, 0x9a0e109e} }, +/**/ {{0x3c07e99e, 0x35a60879} },}, +/**/ {{{0xbf60e474, 0xa11244aa} }, +/**/ {{0x3c04b698, 0x20f2325a} },}, +/**/ {{{0xbf60c463, 0xc838537b} }, +/**/ {{0x3bc0657e, 0x3617200d} },}, +/**/ {{{0xbf60a453, 0x0f7ffcac} }, +/**/ {{0xbc008feb, 0xa5080961} },}, +/**/ {{{0xbf608442, 0x76e8ffd9} }, +/**/ {{0x3bd13002, 0xbb5e1df7} },}, +/**/ {{{0xbf606431, 0xfe731c9d} }, +/**/ {{0xbc0509f3, 0x6e2858c0} },}, +/**/ {{{0xbf604421, 0xa61e1296} }, +/**/ {{0xbc04b556, 0x5f5d9695} },}, +/**/ {{{0xbf602411, 0x6de9a162} }, +/**/ {{0x3c042b89, 0xe79a4e00} },}, +/**/ {{{0xbf600401, 0x55d5889e} }, +/**/ {{0x3be8f98e, 0x1113f403} },}, +/**/ {{{0xbf5fc7e2, 0xbbc30fd4} }, +/**/ {{0xbbfc709b, 0x93382bc9} },}, 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{{0x3bf838ca, 0xe3a09391} },}, +/**/ {{{0xbf5c0621, 0xc9eb99ee} }, +/**/ {{0xbbdc2a9e, 0x61b7de71} },}, +/**/ {{{0xbf5bc605, 0xddc2388e} }, +/**/ {{0xbbea9808, 0x4accb195} },}, +/**/ {{{0xbf5b85ea, 0x31d07b5c} }, +/**/ {{0xbbd811a2, 0x032e030b} },}, +/**/ {{{0xbf5b45ce, 0xc615e1b1} }, +/**/ {{0xbbfd5427, 0x821e0b81} },}, +/**/ {{{0xbf5b05b3, 0x9a91eaea} }, +/**/ {{0x3bfffeba, 0x2619306b} },}, +/**/ {{{0xbf5ac598, 0xaf441661} }, +/**/ {{0x3bd22824, 0x9eac7d15} },}, +/**/ {{{0xbf5a857e, 0x042be376} }, +/**/ {{0x3bc20736, 0x24893f0e} },}, +/**/ {{{0xbf5a4563, 0x9948d188} }, +/**/ {{0xbbf58ab4, 0x04d734cd} },}, +/**/ {{{0xbf5a0549, 0x6e9a5ff9} }, +/**/ {{0xbbf22673, 0x5723a6c3} },}, +/**/ {{{0xbf59c52f, 0x84200e2c} }, +/**/ {{0x3bfc81da, 0xa538e8e1} },}, +/**/ {{{0xbf598515, 0xd9d95b83} }, +/**/ {{0xbbfa1a37, 0x2a8e3feb} },}, +/**/ {{{0xbf5944fc, 0x6fc5c767} }, +/**/ {{0x3bf8e1ce, 0x385159f9} },}, +/**/ {{{0xbf5904e3, 0x45e4d13c} }, +/**/ {{0xbbfc4737, 0x1567c7a7} },}, +/**/ {{{0xbf58c4ca, 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{{0x3bfb055a, 0x54100f9e} },}, +/**/ {{{0xbf51c276, 0x949a2c12} }, +/**/ {{0xbbff6978, 0xa2e9f1b4} },}, +/**/ {{{0xbf518264, 0xefbe402a} }, +/**/ {{0x3bf01fb9, 0xbc188323} },}, +/**/ {{{0xbf514253, 0x8b0562a1} }, +/**/ {{0xbbf7c87c, 0x957bf23a} },}, +/**/ {{{0xbf510242, 0x666f1311} }, +/**/ {{0x3bdc2cb9, 0xc8be6880} },}, +/**/ {{{0xbf50c231, 0x81fad111} }, +/**/ {{0xbbf59fc1, 0x07ba000d} },}, +/**/ {{{0xbf508220, 0xdda81c3d} }, +/**/ {{0xbbf06a0a, 0xbf5c8a0b} },}, +/**/ {{{0xbf504210, 0x79767431} }, +/**/ {{0x3bf3a6cf, 0xa9a705bc} },}, +/**/ {{{0xbf500200, 0x55655889} }, +/**/ {{0xbbe9abe6, 0xbf0fa436} },}, +/**/ {{{0xbf4f83e0, 0xe2e891cc} }, +/**/ {{0x3be4aa59, 0x1b81bf62} },}, +/**/ {{{0xbf4f03c1, 0x9b4589ce} }, +/**/ {{0xbbe60518, 0x8a47f50a} },}, +/**/ {{{0xbf4e83a2, 0xd3e0985f} }, +/**/ {{0x3bed32d8, 0x5ef17e96} },}, +/**/ {{{0xbf4e0384, 0x8cb8bcc3} }, +/**/ {{0xbbeb7b30, 0xf09afa4d} },}, +/**/ {{{0xbf4d8366, 0xc5ccf647} }, +/**/ {{0xbbd527fc, 0xf586cec2} },}, +/**/ {{{0xbf4d0349, 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+/**/ {{{0xbf080024, 0x004800a2} }, +/**/ {{0xbb484d09, 0x8d690542} },}, +/**/ {{{0xbf000010, 0x00155575} }, +/**/ {{0xbba56222, 0x37779c0a} },}, +/**/ {{{0xbef00008, 0x00055559} }, +/**/ {{0xbb955622, 0x22cccd5f} },}, +/**/ {{{0x00000000, 0x00000000} }, +/**/ {{0x00000000, 0x00000000} },}, +/**/ {{{0x3eeffff0, 0x000aaaa3} }, +/**/ {{0xbb8553bb, 0xbd110fec} },}, +/**/ {{{0x3effffe0, 0x002aaa6b} }, +/**/ {{0xbb953bbb, 0xe6661d42} },}, +/**/ {{{0x3f07ffdc, 0x0047ff5e} }, +/**/ {{0x3b484c90, 0x0d69020e} },}, +/**/ {{{0x3f0fffc0, 0x00aaa8ab} }, +/**/ {{0xbba3bbc1, 0x10fec82c} },}, +/**/ {{{0x3f13ffce, 0x00a6a83a} }, +/**/ {{0xbbb2e45f, 0x81546808} },}, +/**/ {{{0x3f17ffb8, 0x011ffaf0} }, +/**/ {{0x3b984c53, 0x4f3d9b6a} },}, +/**/ {{{0x3f1bff9e, 0x01c94bf5} }, +/**/ {{0xbbbd8990, 0xdaa368ee} },}, +/**/ {{{0x3f1fff80, 0x02aa9aab} }, +/**/ {{0x3b910e66, 0x78af0afc} },}, +/**/ {{{0x3f21ffaf, 0x01e5f330} }, +/**/ {{0xbbb1df8d, 0x26467402} },}, +/**/ {{{0x3f23ff9c, 0x029a9723} }, +/**/ {{0x3bc1b965, 0x303b23b1} },}, +/**/ {{{0x3f25ff87, 0x037738be} }, +/**/ {{0xbbb787a3, 0x53d3dc06} },}, +/**/ {{{0x3f27ff70, 0x047fd782} }, +/**/ {{0xbbced098, 0xa5c0aff0} },}, +/**/ {{{0x3f29ff57, 0x05b872e4} }, +/**/ {{0x3bcbadd4, 0x81c30d42} },}, +/**/ {{{0x3f2bff3c, 0x07250a51} }, +/**/ {{0xbbc89dd6, 0xd6bad8c1} },}, +/**/ {{{0x3f2dff1f, 0x08c99d24} }, +/**/ {{0x3bb12609, 0xaede8ad0} },}, +/**/ {{{0x3f2fff00, 0x0aaa2ab1} }, +/**/ {{0x3ba0bbc0, 0x4dc4e3dc} },}, +/**/ {{{0x3f30ff6f, 0x8665591f} }, +/**/ {{0xbbd013d3, 0x80357b54} },}, +/**/ {{{0x3f31ff5e, 0x07979982} }, +/**/ {{0xbbce0e70, 0x4817ebcd} },}, +/**/ {{{0x3f32ff4b, 0x88edd619} }, +/**/ {{0xbbd72b9e, 0xc582abc3} },}, +/**/ {{{0x3f33ff38, 0x0a6a0e74} }, +/**/ {{0x3bdb81fc, 0xb95bc1fe} },}, +/**/ {{{0x3f34ff23, 0x8c0e4220} }, +/**/ {{0x3bcaed12, 0x9b549aae} },}, +/**/ {{{0x3f35ff0e, 0x0ddc70a1} }, +/**/ {{0x3bacf6f3, 0xd97a3c05} },}, +/**/ {{{0x3f36fef7, 0x8fd69976} }, +/**/ {{0x3bab2dcf, 0x6f810a3c} },}, +/**/ {{{0x3f37fee0, 0x11febc18} }, +/**/ {{0x3bd2b9bc, 0xf5d3f323} },}, +/**/ {{{0x3f38fec7, 0x9456d7fb} }, +/**/ {{0xbbbfb258, 0x6eaa1d6a} },}, +/**/ {{{0x3f39feae, 0x16e0ec8b} }, +/**/ {{0xbbb6137a, 0xceeb34b1} },}, +/**/ {{{0x3f3afe93, 0x999ef930} }, +/**/ {{0xbbde70e0, 0xdc639b08} },}, +/**/ {{{0x3f3bfe78, 0x1c92fd4a} }, +/**/ {{0xbbc4ed10, 0x713cc126} },}, +/**/ {{{0x3f3cfe5b, 0x9fbef835} }, +/**/ {{0xbb873d63, 0xcc0e81bd} },}, +/**/ {{{0x3f3dfe3e, 0x2324e946} }, +/**/ {{0x3bc09164, 0x62dd5deb} },}, +/**/ {{{0x3f3efe1f, 0xa6c6cfcc} }, +/**/ {{0x3bdac2da, 0x3512d15c} },}, +/**/ {{{0x3f3ffe00, 0x2aa6ab11} }, +/**/ {{0x3b999e2b, 0x62cc632d} },}, +/**/ {{{0x3f407eef, 0xd7633d2c} }, +/**/ {{0xbbebc98b, 0x63ff6024} },}, +/**/ {{{0x3f40fedf, 0x19941e6e} }, +/**/ {{0xbbb194c2, 0xe0aa6338} },}, +/**/ {{{0x3f417ecd, 0xdbe6f8eb} }, +/**/ {{0x3be4241b, 0x57b0f571} },}, +/**/ {{{0x3f41febc, 0x1e5ccc3c} }, +/**/ {{0x3bdc657d, 0x895d3592} },}, +/**/ {{{0x3f427ea9, 0xe0f697f6} }, +/**/ {{0x3be35a5d, 0x1c0ec17c} },}, +/**/ {{{0x3f42fe97, 0x23b55bac} }, +/**/ {{0x3bd6cfb7, 0x3e538464} },}, +/**/ {{{0x3f437e83, 0xe69a16ed} }, +/**/ {{0x3bee96f7, 0x7cef2478} },}, +/**/ {{{0x3f43fe70, 0x29a5c947} }, +/**/ {{0xbbd4d578, 0xbf46e36a} },}, +/**/ {{{0x3f447e5b, 0xecd97242} }, +/**/ {{0xbbc9eb66, 0x3ff7dd44} },}, +/**/ {{{0x3f44fe47, 0x30361165} }, +/**/ {{0x3be400d7, 0x7e93f2fd} },}, +/**/ {{{0x3f457e31, 0xf3bca635} }, +/**/ {{0xbbe0e2a2, 0xd375017f} },}, +/**/ {{{0x3f45fe1c, 0x376e3031} }, +/**/ {{0xbbd524eb, 0x8a5ae7f6} },}, +/**/ {{{0x3f467e05, 0xfb4baed7} }, +/**/ {{0x3be204fb, 0x4e85c4e9} },}, +/**/ {{{0x3f46fdef, 0x3f5621a3} }, +/**/ {{0xbbdf09d7, 0x34886d52} },}, +/**/ {{{0x3f477dd8, 0x038e880b} }, +/**/ {{0xbbb8900e, 0x14e596a3} },}, +/**/ {{{0x3f47fdc0, 0x47f5e185} }, +/**/ {{0xbbebfa5c, 0x57d202d3} },}, +/**/ {{{0x3f487da8, 0x0c8d2d81} }, +/**/ {{0x3be2f6ae, 0xd68c0614} },}, +/**/ {{{0x3f48fd8f, 0x51556b70} }, +/**/ {{0xbbd0f4f2, 0xe08fd201} },}, +/**/ {{{0x3f497d76, 0x164f9abc} }, +/**/ {{0x3b5296b7, 0xa871af60} },}, +/**/ {{{0x3f49fd5c, 0x5b7cbace} }, +/**/ {{0x3beb6ed4, 0x9f17d42d} },}, +/**/ {{{0x3f4a7d42, 0x20ddcb0d} }, +/**/ {{0xbbcb1149, 0x67c30397} },}, +/**/ {{{0x3f4afd27, 0x6673cada} }, +/**/ {{0x3bd32225, 0x45da594f} },}, +/**/ {{{0x3f4b7d0c, 0x2c3fb996} }, +/**/ {{0xbbb68893, 0x208d4630} },}, +/**/ {{{0x3f4bfcf0, 0x7242969d} }, +/**/ {{0x3bc5db4d, 0x2b3efe1c} },}, +/**/ {{{0x3f4c7cd4, 0x387d6149} }, +/**/ {{0x3be46eff, 0xed57d98a} },}, +/**/ {{{0x3f4cfcb7, 0x7ef118f1} }, +/**/ {{0x3becc554, 0x06f300fb} },}, +/**/ {{{0x3f4d7c9a, 0x459ebce9} }, +/**/ {{0x3be1d251, 0x13638eb6} },}, +/**/ {{{0x3f4dfc7c, 0x8c874c82} }, +/**/ {{0xbbe863e9, 0xd57a176f} },}, +/**/ {{{0x3f4e7c5e, 0x53abc708} }, +/**/ {{0x3be2d95c, 0x9528e50d} },}, +/**/ {{{0x3f4efc3f, 0x9b0d2bc8} }, +/**/ {{0x3bd1e8e8, 0xa5f5b8b7} },}, +/**/ {{{0x3f4f7c20, 0x62ac7a09} }, +/**/ {{0x3b5c8123, 0x17802a46} },}, +/**/ {{{0x3f4ffc00, 0xaa8ab110} }, +/**/ {{0xbbe0fecb, 0xeb9b6cdb} },}, +/**/ {{{0x3f503df0, 0x3954680f} }, +/**/ {{0x3bdac89b, 0x1c693678} },}, +/**/ {{{0x3f507ddf, 0xdd83eb3a} }, +/**/ {{0xbbf638f6, 0x0a75ad5f} },}, +/**/ {{{0x3f50bdcf, 0x41d461a5} }, +/**/ {{0x3bfd4bc9, 0x45f05b10} },}, +/**/ {{{0x3f50fdbe, 0x66464aef} }, +/**/ {{0xbbbd0554, 0x6abbf59c} },}, +/**/ {{{0x3f513dad, 0x4ada26b1} }, +/**/ {{0x3be38c65, 0x6036fe6f} },}, +/**/ {{{0x3f517d9b, 0xef907485} }, +/**/ {{0x3bfdc8a1, 0xf158bbc3} },}, +/**/ {{{0x3f51bd8a, 0x5469b404} }, +/**/ {{0xbbdea231, 0x55632e3f} },}, +/**/ {{{0x3f51fd78, 0x796664c3} }, +/**/ {{0xbbe00849, 0x2edb73c2} },}, +/**/ {{{0x3f523d66, 0x5e870657} }, +/**/ {{0x3bfba943, 0x0789343e} },}, +/**/ {{{0x3f527d54, 0x03cc1855} }, +/**/ {{0x3bc5f644, 0xeafafc52} },}, +/**/ {{{0x3f52bd41, 0x69361a4e} }, +/**/ {{0xbbf2f743, 0xa4a6e79f} },}, +/**/ {{{0x3f52fd2e, 0x8ec58bd2} }, +/**/ {{0xbbd4f786, 0x5ceb1abf} },}, +/**/ {{{0x3f533d1b, 0x747aec71} }, +/**/ {{0xbbf369e3, 0x49dc497d} },}, +/**/ {{{0x3f537d08, 0x1a56bbb8} }, +/**/ {{0xbbfc5e6f, 0x3726b14a} },}, +/**/ {{{0x3f53bcf4, 0x80597933} }, +/**/ {{0xbbfe8b82, 0x808f75a7} },}, +/**/ {{{0x3f53fce0, 0xa683a46c} }, +/**/ {{0x3be02719, 0x9cd06ae6} },}, +/**/ {{{0x3f543ccc, 0x8cd5bced} }, +/**/ {{0x3bf9f98d, 0x758f80f8} },}, +/**/ {{{0x3f547cb8, 0x3350423e} }, +/**/ {{0xbbd79c3d, 0x48401f45} },}, +/**/ {{{0x3f54bca3, 0x99f3b3e4} }, +/**/ {{0xbbf422b8, 0x2fba8948} },}, +/**/ {{{0x3f54fc8e, 0xc0c09163} }, +/**/ {{0x3bf32cc1, 0xf4044be8} },}, +/**/ {{{0x3f553c79, 0xa7b75a40} }, +/**/ {{0xbbe72cac, 0xf2249008} },}, +/**/ {{{0x3f557c64, 0x4ed88dfb} }, +/**/ {{0xbbe7183c, 0x459a204f} },}, +/**/ {{{0x3f55bc4e, 0xb624ac14} }, +/**/ {{0x3bf8aa64, 0xba26d3d7} },}, +/**/ {{{0x3f55fc38, 0xdd9c340b} }, +/**/ {{0x3bdbb2ff, 0x45fa193c} },}, +/**/ {{{0x3f563c22, 0xc53fa55c} }, +/**/ {{0x3bd67249, 0x0484397b} },}, +/**/ {{{0x3f567c0c, 0x6d0f7f83} }, +/**/ {{0xbbd183d7, 0xf1e73188} },}, +/**/ {{{0x3f56bbf5, 0xd50c41fa} }, +/**/ {{0xbbef433d, 0x4ab68187} },}, +/**/ {{{0x3f56fbde, 0xfd366c39} }, +/**/ {{0x3be796b8, 0x66e09e58} },}, +/**/ {{{0x3f573bc7, 0xe58e7db8} }, +/**/ {{0x3bf65ec5, 0x81e6e7e6} },}, +/**/ {{{0x3f577bb0, 0x8e14f5ed} }, +/**/ {{0xbbdb944d, 0xa9463a9c} },}, +/**/ {{{0x3f57bb98, 0xf6ca544b} }, +/**/ {{0xbbc396ec, 0xc5eda344} },}, +/**/ {{{0x3f57fb81, 0x1faf1845} }, +/**/ {{0x3beb9e6d, 0xbb624f97} },}, +/**/ {{{0x3f583b69, 0x08c3c14d} }, +/**/ {{0xbbe6ee13, 0xe6295bf2} },}, +/**/ {{{0x3f587b50, 0xb208ced1} }, +/**/ {{0x3bfcf1a5, 0x6ca19875} },}, +/**/ {{{0x3f58bb38, 0x1b7ec041} }, +/**/ {{0x3bf2d181, 0x07b4fc7e} },}, +/**/ {{{0x3f58fb1f, 0x45261509} }, +/**/ {{0x3bc419c5, 0x21bad336} },}, +/**/ {{{0x3f593b06, 0x2eff4c94} }, +/**/ {{0xbbdc2a4c, 0x700b305b} },}, +/**/ {{{0x3f597aec, 0xd90ae64c} }, +/**/ {{0xbbfc53d3, 0xa23f359c} },}, +/**/ {{{0x3f59bad3, 0x43496198} }, +/**/ {{0x3bf0c270, 0xaed6b50f} },}, +/**/ {{{0x3f59fab9, 0x6dbb3de1} }, +/**/ {{0xbbf11464, 0x7a8be031} },}, +/**/ {{{0x3f5a3a9f, 0x5860fa8a} }, +/**/ {{0x3beae9e7, 0x470dbe32} },}, +/**/ {{{0x3f5a7a85, 0x033b16f8} }, +/**/ {{0x3bfc4721, 0xda1f8579} },}, +/**/ {{{0x3f5aba6a, 0x6e4a128e} }, +/**/ {{0xbbf41852, 0x029258ce} },}, +/**/ {{{0x3f5afa4f, 0x998e6cab} }, +/**/ {{0xbbf28584, 0x2eb18782} },}, +/**/ {{{0x3f5b3a34, 0x8508a4af} }, +/**/ {{0xbbea7970, 0x23241a2c} },}, +/**/ {{{0x3f5b7a19, 0x30b939f8} }, +/**/ {{0xbbf1d8db, 0x600551b6} },}, +/**/ {{{0x3f5bb9fd, 0x9ca0abe2} }, +/**/ {{0xbbeaa412, 0x8c26cc71} },}, +/**/ {{{0x3f5bf9e1, 0xc8bf79c8} }, +/**/ {{0xbbe7f81b, 0x30427cfc} },}, +/**/ {{{0x3f5c39c5, 0xb5162303} }, +/**/ {{0x3bd9ec5f, 0xd1f134e1} },}, +/**/ {{{0x3f5c79a9, 0x61a526eb} }, +/**/ {{0x3bff0cb0, 0x8980e47d} },}, +/**/ {{{0x3f5cb98c, 0xce6d04d7} }, +/**/ {{0x3bf35aca, 0xe84ca4e2} },}, +/**/ {{{0x3f5cf96f, 0xfb6e3c1b} }, +/**/ {{0x3bf9b1b8, 0x1b0bd69f} },}, +/**/ {{{0x3f5d3952, 0xe8a94c0b} }, +/**/ {{0x3be21310, 0x3ce51832} },}, +/**/ {{{0x3f5d7935, 0x961eb3f8} }, +/**/ {{0x3bf90786, 0x840c58ce} },}, +/**/ {{{0x3f5db918, 0x03cef334} }, +/**/ {{0xbbfe0048, 0xf2dfb3f4} },}, +/**/ {{{0x3f5df8fa, 0x31ba890b} }, +/**/ {{0x3bfcf652, 0x3e295bec} },}, +/**/ {{{0x3f5e38dc, 0x1fe1f4ce} }, +/**/ {{0xbbfc5ebe, 0x151c9300} },}, +/**/ {{{0x3f5e78bd, 0xce45b5c6} }, +/**/ {{0xbbef2cc4, 0x8a25b9c7} },}, +/**/ {{{0x3f5eb89f, 0x3ce64b3e} }, +/**/ {{0x3bfe6d27, 0xa6fea7bd} },}, +/**/ {{{0x3f5ef880, 0x6bc43481} }, +/**/ {{0xbbf68037, 0x914a6dab} },}, +/**/ {{{0x3f5f3861, 0x5adff0d4} }, +/**/ {{0xbbf1d2f3, 0xf909e0e6} },}, +/**/ {{{0x3f5f7842, 0x0a39ff7e} }, +/**/ {{0xbbf64661, 0xff1e1f71} },}, +/**/ {{{0x3f5fb822, 0x79d2dfc3} }, +/**/ {{0xbbd76ce8, 0x5a6f9e9a} },}, +/**/ {{{0x3f5ff802, 0xa9ab10e6} }, +/**/ {{0x3bfe29e3, 0xa153e3b2} },}, +/**/ {{{0x3f601bf1, 0x4ce18915} }, +/**/ {{0xbbe57c28, 0xa3a73044} },}, +/**/ {{{0x3f603be1, 0x250db166} }, +/**/ {{0x3c0fd271, 0xc1ad9590} },}, +/**/ {{{0x3f605bd0, 0xdd5a4107} }, +/**/ {{0x3bfe4b5d, 0xc424c676} },}, +/**/ {{{0x3f607bc0, 0x75c77796} }, +/**/ {{0xbc068804, 0xc0eff1ba} },}, +/**/ {{{0x3f609baf, 0xee5594b0} }, +/**/ {{0xbc0ff798, 0x51dbded5} },}, +/**/ {{{0x3f60bb9f, 0x4704d7f2} }, +/**/ {{0xbbf70ef4, 0x2d5aba70} },}, +/**/ {{{0x3f60db8e, 0x7fd580f9} }, +/**/ {{0xbbeccb65, 0x7ae804b5} },}, +/**/ {{{0x3f60fb7d, 0x98c7cf60} }, +/**/ {{0x3bfede2f, 0x1775134d} },}, +/**/ {{{0x3f611b6c, 0x91dc02c3} }, +/**/ {{0xbc04d41e, 0x91ca4a67} },}, +/**/ {{{0x3f613b5b, 0x6b125aba} }, +/**/ {{0x3bfe6d0c, 0x4a12201d} },}, +/**/ {{{0x3f615b4a, 0x246b16e0} }, +/**/ {{0x3bfe507d, 0x4d4238d3} },}, +/**/ {{{0x3f617b38, 0xbde676cd} }, +/**/ {{0x3bfe0272, 0x0640462a} },}, +/**/ {{{0x3f619b27, 0x3784ba19} }, +/**/ {{0x3bd94ab3, 0x02285659} },}, +/**/ {{{0x3f61bb15, 0x9146205b} }, +/**/ {{0xbbff1e2e, 0x1cc35b7b} },}, +/**/ {{{0x3f61db03, 0xcb2ae929} }, +/**/ {{0xbc03ee8e, 0x12f6bf8d} },}, +/**/ {{{0x3f61faf1, 0xe5335418} }, +/**/ {{0x3c0bae5f, 0x7b7d619b} },}, +/**/ {{{0x3f621adf, 0xdf5fa0bf} }, +/**/ {{0xbbf5546a, 0xb3b731b0} },}, +/**/ {{{0x3f623acd, 0xb9b00eb0} }, +/**/ {{0xbbafb2b0, 0x105fd253} },}, +/**/ {{{0x3f625abb, 0x7424dd7f} }, +/**/ {{0x3c011647, 0xca53444b} },}, +/**/ {{{0x3f627aa9, 0x0ebe4cbf} }, +/**/ {{0x3c01678f, 0x592f3be8} },}, +/**/ {{{0x3f629a96, 0x897c9c02} }, +/**/ {{0xbbef2b12, 0x4347451d} },}, +/**/ {{{0x3f62ba83, 0xe4600ad8} }, +/**/ {{0x3bfb5bb7, 0xb2a477bc} },}, +/**/ {{{0x3f62da71, 0x1f68d8d3} }, +/**/ {{0xbc0590e1, 0x7a5822e4} },}, +/**/ {{{0x3f62fa5e, 0x3a974581} }, +/**/ {{0xbbf0f2e5, 0x53123101} },}, +/**/ {{{0x3f631a4b, 0x35eb9072} }, +/**/ {{0xbc018db4, 0x0e3f5fde} },}, +/**/ {{{0x3f633a38, 0x1165f933} }, +/**/ {{0x3c0921d5, 0x8d0afb38} },}, +/**/ {{{0x3f635a24, 0xcd06bf53} }, +/**/ {{0x3c01f6ba, 0xb5791b80} },}, +/**/ {{{0x3f637a11, 0x68ce225e} }, +/**/ {{0x3bde2af8, 0xa1894236} },}, +/**/ {{{0x3f6399fd, 0xe4bc61e0} }, +/**/ {{0xbc062a48, 0xd0f06ff3} },}, +/**/ {{{0x3f63b9ea, 0x40d1bd63} }, +/**/ {{0x3bffc80c, 0x4b4f9c11} },}, +/**/ {{{0x3f63d9d6, 0x7d0e7473} }, +/**/ {{0x3c02219b, 0x6a92c891} },}, +/**/ {{{0x3f63f9c2, 0x9972c699} }, +/**/ {{0x3c0d3590, 0x790ade9e} },}, +/**/ {{{0x3f6419ae, 0x95fef35f} }, +/**/ {{0xbc01c279, 0x792a458c} },}, +/**/ {{{0x3f64399a, 0x72b33a4b} }, +/**/ {{0x3c02ce64, 0x327bffae} },}, +/**/ {{{0x3f645986, 0x2f8fdae7} }, +/**/ {{0xbc070aec, 0xd231155c} },}, +/**/ {{{0x3f647971, 0xcc9514b7} }, +/**/ {{0x3c0f373d, 0xe4bbf776} },}, +/**/ {{{0x3f64995d, 0x49c32744} }, +/**/ {{0xbbf6d7e5, 0xbf22b2a7} },}, +/**/ {{{0x3f64b948, 0xa71a5211} }, +/**/ {{0xbbedec69, 0x64fe2936} },}, +/**/ {{{0x3f64d933, 0xe49ad4a3} }, +/**/ {{0x3bf5fc4b, 0xabee4257} },}, +/**/ {{{0x3f64f91f, 0x0244ee7e} }, +/**/ {{0x3c0c6fe3, 0x3cd1474f} },}, +/**/ {{{0x3f65190a, 0x0018df26} }, +/**/ {{0xbc023957, 0xd11e7fa5} },}, +/**/ {{{0x3f6538f4, 0xde16e61b} }, +/**/ {{0x3c006c31, 0x55380346} },}, +/**/ {{{0x3f6558df, 0x9c3f42e1} }, +/**/ {{0xbc09b7d4, 0xc4a5134c} },}, +/**/ {{{0x3f6578ca, 0x3a9234f7} }, +/**/ {{0xbc0e3f10, 0x2772c19c} },}, +/**/ {{{0x3f6598b4, 0xb90ffbdd} }, +/**/ {{0x3be6f110, 0x5592b468} },}, +/**/ {{{0x3f65b89f, 0x17b8d714} }, +/**/ {{0xbc0a5fea, 0xb251ace2} },}, +/**/ {{{0x3f65d889, 0x568d0619} }, +/**/ {{0xbc0aacc9, 0x315da285} },}, +/**/ {{{0x3f65f873, 0x758cc86a} }, +/**/ {{0xbbeb0782, 0xba64d81a} },}, +/**/ {{{0x3f66185d, 0x74b85d85} }, +/**/ {{0xbc09b459, 0x8e1eb3fa} },}, +/**/ {{{0x3f663847, 0x541004e5} }, +/**/ {{0x3bce9c22, 0x1d86e863} },}, +/**/ {{{0x3f665831, 0x1393fe07} }, +/**/ {{0xbbfbeb77, 0xcf37ee90} },}, +/**/ {{{0x3f66781a, 0xb3448865} }, +/**/ {{0xbc02dc68, 0xc252e3c9} },}, +/**/ {{{0x3f669804, 0x3321e379} }, +/**/ {{0xbbe73a0b, 0xb40b3741} },}, + }; + +#else +#ifdef LITTLE_ENDI + static const number + Iu[182] = { /* 1/ui */ +/**/ {{0xd1537290, 0x3ff6a13c} }, +/**/ {{0x16816817, 0x3ff68168} }, +/**/ {{0x6a5122f9, 0x3ff661ec} }, +/**/ {{0x590b2164, 0x3ff642c8} }, +/**/ {{0x77016240, 0x3ff623fa} }, +/**/ {{0x60581606, 0x3ff60581} }, +/**/ {{0xb8d015e7, 0x3ff5e75b} }, +/**/ {{0x2b931057, 0x3ff5c988} }, +/**/ {{0x6b015ac0, 0x3ff5ac05} }, +/**/ {{0x308158ed, 0x3ff58ed2} }, +/**/ {{0x3c506b3a, 0x3ff571ed} }, +/**/ {{0x55555555, 0x3ff55555} }, +/**/ {{0x48f40feb, 0x3ff53909} }, +/**/ {{0xeae2f815, 0x3ff51d07} }, +/**/ {{0x15015015, 0x3ff50150} }, +/**/ {{0xa72f0539, 0x3ff4e5e0} }, +/**/ {{0x8725af6e, 0x3ff4cab8} }, +/**/ {{0xa052bf5b, 0x3ff4afd6} }, +/**/ {{0xe3b2d067, 0x3ff49539} }, +/**/ {{0x47ae147b, 0x3ff47ae1} }, +/**/ {{0xc7f5cf9a, 0x3ff460cb} }, +/**/ {{0x6562d9fb, 0x3ff446f8} }, +/**/ {{0x25d51f87, 0x3ff42d66} }, +/**/ {{0x14141414, 0x3ff41414} }, +/**/ {{0x3fb013fb, 0x3ff3fb01} }, +/**/ {{0xbce4a902, 0x3ff3e22c} }, +/**/ {{0xa47babe7, 0x3ff3c995} }, +/**/ {{0x13b13b14, 0x3ff3b13b} }, +/**/ {{0x2c187f63, 0x3ff3991c} }, +/**/ {{0x13813814, 0x3ff38138} }, +/**/ {{0xf3de0748, 0x3ff3698d} }, +/**/ {{0xfb2b78c1, 0x3ff3521c} }, +/**/ {{0x5b57bcb2, 0x3ff33ae4} }, +/**/ {{0x4a2b10bf, 0x3ff323e3} }, +/**/ {{0x0130d190, 0x3ff30d19} }, +/**/ {{0xbda12f68, 0x3ff2f684} }, +/**/ {{0xc04b8097, 0x3ff2e025} }, +/**/ {{0x4d812ca0, 0x3ff2c9fb} }, +/**/ {{0xad012b40, 0x3ff2b404} }, +/**/ {{0x29e4129e, 0x3ff29e41} }, +/**/ {{0x1288b013, 0x3ff288b0} }, +/**/ {{0xb8812735, 0x3ff27350} }, +/**/ {{0x708092f1, 0x3ff25e22} }, +/**/ {{0x92492492, 0x3ff24924} }, +/**/ {{0x789abcdf, 0x3ff23456} }, +/**/ {{0x8121fb78, 0x3ff21fb7} }, +/**/ {{0x0c67c0d9, 0x3ff20b47} }, +/**/ {{0x7dc11f70, 0x3ff1f704} }, +/**/ {{0x3b3fb874, 0x3ff1e2ef} }, +/**/ {{0xada2811d, 0x3ff1cf06} }, +/**/ {{0x4046ed29, 0x3ff1bb4a} }, +/**/ {{0x611a7b96, 0x3ff1a7b9} }, +/**/ {{0x808ca29c, 0x3ff19453} }, +/**/ {{0x11811812, 0x3ff18118} }, +/**/ {{0x89427379, 0x3ff16e06} }, +/**/ {{0x5f75270d, 0x3ff15b1e} }, +/**/ {{0x0e0acd3b, 0x3ff1485f} }, +/**/ {{0x1135c811, 0x3ff135c8} }, +/**/ {{0xe75d3033, 0x3ff12358} }, +/**/ {{0x11111111, 0x3ff11111} }, +/**/ {{0x10fef011, 0x3ff0fef0} }, +/**/ {{0x6be69c90, 0x3ff0ecf5} }, +/**/ {{0xa88f4696, 0x3ff0db20} }, +/**/ {{0x4fbcda3b, 0x3ff0c971} }, +/**/ {{0xec259dc8, 0x3ff0b7e6} }, +/**/ {{0x0a6810a7, 0x3ff0a681} }, +/**/ {{0x39010954, 0x3ff0953f} }, +/**/ {{0x08421084, 0x3ff08421} }, +/**/ {{0x0a47f7c6, 0x3ff07326} }, +/**/ {{0xd2f1a9fc, 0x3ff0624d} }, +/**/ {{0xf7d73404, 0x3ff05197} }, +/**/ {{0x10410410, 0x3ff04104} }, +/**/ {{0xb51f5e1a, 0x3ff03091} }, +/**/ {{0x81020408, 0x3ff02040} }, +/**/ {{0x10101010, 0x3ff01010} }, +/**/ {{0x00000000, 0x3ff00000} }, +/**/ {{0xe01fe020, 0x3fefe01f} }, +/**/ {{0x01fc07f0, 0x3fefc07f} }, +/**/ {{0xaa01fa12, 0x3fefa11c} }, +/**/ {{0x1f81f820, 0x3fef81f8} }, +/**/ {{0xaca0dbb5, 0x3fef6310} }, +/**/ {{0x9e4a4271, 0x3fef4465} }, +/**/ {{0x44230ab5, 0x3fef25f6} }, +/**/ {{0xf07c1f08, 0x3fef07c1} }, +/**/ {{0xf8458e02, 0x3feee9c7} }, +/**/ {{0xb301ecc0, 0x3feecc07} }, +/**/ {{0x7aba01eb, 0x3feeae80} }, +/**/ {{0xabf0b767, 0x3fee9131} }, +/**/ {{0xa59750e4, 0x3fee741a} }, +/**/ {{0xc901e574, 0x3fee573a} }, +/**/ {{0x79dc1a73, 0x3fee3a91} }, +/**/ {{0x1e1e1e1e, 0x3fee1e1e} }, +/**/ {{0x1e01e01e, 0x3fee01e0} }, +/**/ {{0xe3f8868a, 0x3fede5d6} }, +/**/ {{0xdca01dca, 0x3fedca01} }, +/**/ {{0x76b981db, 0x3fedae60} }, +/**/ {{0x231e7f8a, 0x3fed92f2} }, +/**/ {{0x54b82c34, 0x3fed77b6} }, +/**/ {{0x807572b2, 0x3fed5cac} }, +/**/ {{0x1d41d41d, 0x3fed41d4} }, +/**/ {{0xa3fc5b1a, 0x3fed272c} }, +/**/ {{0x8f6ec074, 0x3fed0cb5} }, +/**/ {{0x5c44bfc6, 0x3fecf26e} }, +/**/ {{0x89039b0b, 0x3fecd856} }, +/**/ {{0x9601cbe7, 0x3fecbe6d} }, +/**/ {{0x055ee191, 0x3feca4b3} }, +/**/ {{0x5afb8a42, 0x3fec8b26} }, +/**/ {{0x1c71c71c, 0x3fec71c7} }, +/**/ {{0xd10d4986, 0x3fec5894} }, +/**/ {{0x01c3f8f0, 0x3fec3f8f} }, +/**/ {{0x392ea01c, 0x3fec26b5} }, +/**/ {{0x0381c0e0, 0x3fec0e07} }, +/**/ {{0xee868d8b, 0x3febf583} }, +/**/ {{0x899406f7, 0x3febdd2b} }, +/**/ {{0x65883e7b, 0x3febc4fd} }, +/**/ {{0x14c1bad0, 0x3febacf9} }, +/**/ {{0x2b18ff23, 0x3feb951e} }, +/**/ {{0x3dda338b, 0x3feb7d6c} }, +/**/ {{0xe3beee05, 0x3feb65e2} }, +/**/ {{0xb4e81b4f, 0x3feb4e81} }, +/**/ {{0x4ad806ce, 0x3feb3748} }, +/**/ {{0x406c80d9, 0x3feb2036} }, +/**/ {{0x31d922a4, 0x3feb094b} }, +/**/ {{0xbca1af28, 0x3feaf286} }, +/**/ {{0x7f94905e, 0x3feadbe8} }, +/**/ {{0x1ac5701b, 0x3feac570} }, +/**/ {{0x2f87ebfd, 0x3feaaf1d} }, +/**/ {{0x606a63be, 0x3fea98ef} }, +/**/ {{0x5130e159, 0x3fea82e6} }, +/**/ {{0xa6d01a6d, 0x3fea6d01} }, +/**/ {{0x07688a4a, 0x3fea5741} }, +/**/ {{0x1a41a41a, 0x3fea41a4} }, +/**/ {{0x87c51ca0, 0x3fea2c2a} }, +/**/ {{0xf97a4b02, 0x3fea16d3} }, +/**/ {{0x1a01a01a, 0x3fea01a0} }, +/**/ {{0x951033d9, 0x3fe9ec8e} }, +/**/ {{0x176b682d, 0x3fe9d79f} }, +/**/ {{0x4ee4a102, 0x3fe9c2d1} }, +/**/ {{0xea5510da, 0x3fe9ae24} }, +/**/ {{0x9999999a, 0x3fe99999} }, +/**/ {{0x0d8ec0ff, 0x3fe9852f} }, +/**/ {{0xf80cb872, 0x3fe970e4} }, +/**/ {{0x0be377ae, 0x3fe95cbb} }, +/**/ {{0xfcd6e9e0, 0x3fe948b0} }, +/**/ {{0x7f9b2ce6, 0x3fe934c6} }, +/**/ {{0x49d0e229, 0x3fe920fb} }, +/**/ {{0x120190d5, 0x3fe90d4f} }, +/**/ {{0x8f9c18fa, 0x3fe8f9c1} }, +/**/ {{0x7af1373f, 0x3fe8e652} }, +/**/ {{0x8d3018d3, 0x3fe8d301} }, +/**/ {{0x8062ff3a, 0x3fe8bfce} }, +/**/ {{0x0f6bf3aa, 0x3fe8acb9} }, +/**/ {{0xf601899c, 0x3fe899c0} }, +/**/ {{0xf0abb04a, 0x3fe886e5} }, +/**/ {{0xbcc092b9, 0x3fe87427} }, +/**/ {{0x18618618, 0x3fe86186} }, +/**/ {{0xc2780614, 0x3fe84f00} }, +/**/ {{0x7ab2bedd, 0x3fe83c97} }, +/**/ {{0x0182a4a0, 0x3fe82a4a} }, +/**/ {{0x18181818, 0x3fe81818} }, +/**/ {{0x80601806, 0x3fe80601} }, +/**/ {{0xfd017f40, 0x3fe7f405} }, +/**/ {{0x515a4f1d, 0x3fe7e225} }, +/**/ {{0x417d05f4, 0x3fe7d05f} }, +/**/ {{0x922e017c, 0x3fe7beb3} }, +/**/ {{0x08e0ecc3, 0x3fe7ad22} }, +/**/ {{0x6bb6398b, 0x3fe79baa} }, +/**/ {{0x8178a4c8, 0x3fe78a4c} }, +/**/ {{0x119ac60d, 0x3fe77908} }, +/**/ {{0xe434a9b1, 0x3fe767dc} }, +/**/ {{0xc201756d, 0x3fe756ca} }, +/**/ {{0x745d1746, 0x3fe745d1} }, +/**/ {{0xc541fe8d, 0x3fe734f0} }, +/**/ {{0x7f46debc, 0x3fe72428} }, +/**/ {{0x6d9c7c09, 0x3fe71378} }, +/**/ {{0x5c0b8170, 0x3fe702e0} }, +/**/ {{0x16f26017, 0x3fe6f260} }, +/**/ {{0x6b4337c7, 0x3fe6e1f7} }, +/**/ {{0x2681c861, 0x3fe6d1a6} }, +/**/ {{0x16c16c17, 0x3fe6c16c} }, +/**/ {{0x0aa31a3d, 0x3fe6b149} }, +/**/ {{0xd1537290, 0x3fe6a13c} }, + }; + + static const number + Iv[362] = { /* 1/vj */ +/**/ {{0xee93bfe3, 0x3ff00b47} }, +/**/ {{0xd80c106f, 0x3ff00b37} }, +/**/ {{0xc1a4a47a, 0x3ff00b27} }, +/**/ {{0xab5d7ba2, 0x3ff00b17} }, +/**/ {{0x95369587, 0x3ff00b07} }, +/**/ {{0x7f2ff1c6, 0x3ff00af7} }, +/**/ {{0x69499000, 0x3ff00ae7} }, +/**/ {{0x53836fd3, 0x3ff00ad7} }, +/**/ {{0x3ddd90dd, 0x3ff00ac7} }, +/**/ {{0x2857f2bf, 0x3ff00ab7} }, +/**/ {{0x12f29517, 0x3ff00aa7} }, +/**/ {{0xfdad7784, 0x3ff00a96} }, +/**/ {{0xe88899a5, 0x3ff00a86} }, +/**/ {{0xd383fb19, 0x3ff00a76} }, +/**/ {{0xbe9f9b7f, 0x3ff00a66} }, +/**/ {{0xa9db7a76, 0x3ff00a56} }, +/**/ {{0x9537979d, 0x3ff00a46} }, +/**/ {{0x80b3f293, 0x3ff00a36} }, +/**/ {{0x6c508af8, 0x3ff00a26} }, +/**/ {{0x580d606a, 0x3ff00a16} }, +/**/ {{0x43ea7288, 0x3ff00a06} }, +/**/ {{0x2fe7c0f1, 0x3ff009f6} }, +/**/ {{0x1c054b44, 0x3ff009e6} }, +/**/ {{0x08431122, 0x3ff009d6} }, +/**/ {{0xf4a11227, 0x3ff009c5} }, +/**/ {{0xe11f4df4, 0x3ff009b5} }, +/**/ {{0xcdbdc428, 0x3ff009a5} }, +/**/ {{0xba7c7462, 0x3ff00995} }, +/**/ {{0xa75b5e40, 0x3ff00985} }, +/**/ {{0x945a8162, 0x3ff00975} }, +/**/ {{0x8179dd68, 0x3ff00965} }, +/**/ {{0x6eb971ef, 0x3ff00955} }, +/**/ {{0x5c193e98, 0x3ff00945} }, +/**/ {{0x49994301, 0x3ff00935} }, +/**/ {{0x37397eca, 0x3ff00925} }, +/**/ {{0x24f9f192, 0x3ff00915} }, +/**/ {{0x12da9af7, 0x3ff00905} }, +/**/ {{0x00db7a99, 0x3ff008f5} }, +/**/ {{0xeefc9018, 0x3ff008e4} }, +/**/ {{0xdd3ddb12, 0x3ff008d4} }, +/**/ {{0xcb9f5b26, 0x3ff008c4} }, +/**/ {{0xba210ff4, 0x3ff008b4} }, +/**/ {{0xa8c2f91a, 0x3ff008a4} }, +/**/ {{0x97851639, 0x3ff00894} }, +/**/ {{0x866766ef, 0x3ff00884} }, +/**/ {{0x7569eadb, 0x3ff00874} }, +/**/ {{0x648ca19d, 0x3ff00864} }, +/**/ {{0x53cf8ad3, 0x3ff00854} }, +/**/ {{0x4332a61e, 0x3ff00844} }, +/**/ {{0x32b5f31b, 0x3ff00834} }, +/**/ {{0x2259716c, 0x3ff00824} }, +/**/ {{0x121d20ad, 0x3ff00814} }, +/**/ {{0x02010080, 0x3ff00804} }, +/**/ {{0xf2051083, 0x3ff007f3} }, +/**/ {{0xe2295056, 0x3ff007e3} }, +/**/ {{0xd26dbf97, 0x3ff007d3} }, +/**/ {{0xc2d25de5, 0x3ff007c3} }, +/**/ {{0xb3572ae2, 0x3ff007b3} }, +/**/ {{0xa3fc262a, 0x3ff007a3} }, +/**/ {{0x94c14f5f, 0x3ff00793} }, +/**/ {{0x85a6a61e, 0x3ff00783} }, +/**/ {{0x76ac2a08, 0x3ff00773} }, +/**/ {{0x67d1dabb, 0x3ff00763} }, +/**/ {{0x5917b7d7, 0x3ff00753} }, +/**/ {{0x4a7dc0fb, 0x3ff00743} }, +/**/ {{0x3c03f5c7, 0x3ff00733} }, +/**/ {{0x2daa55da, 0x3ff00723} }, +/**/ {{0x1f70e0d3, 0x3ff00713} }, +/**/ {{0x11579652, 0x3ff00703} }, +/**/ {{0x035e75f5, 0x3ff006f3} }, +/**/ {{0xf5857f5d, 0x3ff006e2} }, +/**/ {{0xe7ccb228, 0x3ff006d2} }, +/**/ {{0xda340df6, 0x3ff006c2} }, +/**/ {{0xccbb9266, 0x3ff006b2} }, +/**/ {{0xbf633f18, 0x3ff006a2} }, +/**/ {{0xb22b13ab, 0x3ff00692} }, +/**/ {{0xa5130fbe, 0x3ff00682} }, +/**/ {{0x981b32f1, 0x3ff00672} }, +/**/ {{0x8b437ce4, 0x3ff00662} }, +/**/ {{0x7e8bed35, 0x3ff00652} }, +/**/ {{0x71f48383, 0x3ff00642} }, +/**/ {{0x657d3f70, 0x3ff00632} }, +/**/ {{0x59262098, 0x3ff00622} }, +/**/ {{0x4cef269e, 0x3ff00612} }, +/**/ {{0x40d8511e, 0x3ff00602} }, +/**/ {{0x34e19fba, 0x3ff005f2} }, +/**/ {{0x290b1211, 0x3ff005e2} }, +/**/ {{0x1d54a7c1, 0x3ff005d2} }, +/**/ {{0x11be606b, 0x3ff005c2} }, +/**/ {{0x06483bad, 0x3ff005b2} }, +/**/ {{0xfaf23928, 0x3ff005a1} }, +/**/ {{0xefbc587b, 0x3ff00591} }, +/**/ {{0xe4a69945, 0x3ff00581} }, +/**/ {{0xd9b0fb25, 0x3ff00571} }, +/**/ {{0xcedb7dbc, 0x3ff00561} }, +/**/ {{0xc42620a9, 0x3ff00551} }, +/**/ {{0xb990e38b, 0x3ff00541} }, +/**/ {{0xaf1bc601, 0x3ff00531} }, +/**/ {{0xa4c6c7ac, 0x3ff00521} }, +/**/ {{0x9a91e82a, 0x3ff00511} }, +/**/ {{0x907d271c, 0x3ff00501} }, +/**/ {{0x86888421, 0x3ff004f1} }, +/**/ {{0x7cb3fed8, 0x3ff004e1} }, +/**/ {{0x72ff96e0, 0x3ff004d1} }, +/**/ {{0x696b4bdb, 0x3ff004c1} }, +/**/ {{0x5ff71d66, 0x3ff004b1} }, +/**/ {{0x56a30b21, 0x3ff004a1} }, +/**/ {{0x4d6f14ad, 0x3ff00491} }, +/**/ {{0x445b39a8, 0x3ff00481} }, +/**/ {{0x3b6779b3, 0x3ff00471} }, +/**/ {{0x3293d46c, 0x3ff00461} }, +/**/ {{0x29e04974, 0x3ff00451} }, +/**/ {{0x214cd869, 0x3ff00441} }, +/**/ {{0x18d980ed, 0x3ff00431} }, +/**/ {{0x1086429d, 0x3ff00421} }, +/**/ {{0x08531d1a, 0x3ff00411} }, +/**/ {{0x00401004, 0x3ff00401} }, +/**/ {{0xf84d1afa, 0x3ff003f0} }, +/**/ {{0xf07a3d9b, 0x3ff003e0} }, +/**/ {{0xe8c77787, 0x3ff003d0} }, +/**/ {{0xe134c85f, 0x3ff003c0} }, +/**/ {{0xd9c22fc1, 0x3ff003b0} }, +/**/ {{0xd26fad4d, 0x3ff003a0} }, +/**/ {{0xcb3d40a3, 0x3ff00390} }, +/**/ {{0xc42ae963, 0x3ff00380} }, +/**/ {{0xbd38a72c, 0x3ff00370} }, +/**/ {{0xb666799e, 0x3ff00360} }, +/**/ {{0xafb46058, 0x3ff00350} }, +/**/ {{0xa9225afa, 0x3ff00340} }, +/**/ {{0xa2b06925, 0x3ff00330} }, +/**/ {{0x9c5e8a77, 0x3ff00320} }, +/**/ {{0x962cbe90, 0x3ff00310} }, +/**/ {{0x901b0511, 0x3ff00300} }, +/**/ {{0x8a295d98, 0x3ff002f0} }, +/**/ {{0x8457c7c6, 0x3ff002e0} }, +/**/ {{0x7ea6433a, 0x3ff002d0} }, +/**/ {{0x7914cf94, 0x3ff002c0} }, +/**/ {{0x73a36c73, 0x3ff002b0} }, +/**/ {{0x6e521978, 0x3ff002a0} }, +/**/ {{0x6920d642, 0x3ff00290} }, +/**/ {{0x640fa271, 0x3ff00280} }, +/**/ {{0x5f1e7da5, 0x3ff00270} }, +/**/ {{0x5a4d677d, 0x3ff00260} }, +/**/ {{0x559c5f9a, 0x3ff00250} }, +/**/ {{0x510b659a, 0x3ff00240} }, +/**/ {{0x4c9a791f, 0x3ff00230} }, +/**/ {{0x484999c6, 0x3ff00220} }, +/**/ {{0x4418c732, 0x3ff00210} }, +/**/ {{0x40080100, 0x3ff00200} }, +/**/ {{0x3c1746d2, 0x3ff001f0} }, +/**/ {{0x38469846, 0x3ff001e0} }, +/**/ {{0x3495f4fd, 0x3ff001d0} }, +/**/ {{0x31055c96, 0x3ff001c0} }, +/**/ {{0x2d94ceb2, 0x3ff001b0} }, +/**/ {{0x2a444af0, 0x3ff001a0} }, +/**/ {{0x2713d0ef, 0x3ff00190} }, +/**/ {{0x24036051, 0x3ff00180} }, +/**/ {{0x2112f8b4, 0x3ff00170} }, +/**/ {{0x1e4299b9, 0x3ff00160} }, +/**/ {{0x1b9242ff, 0x3ff00150} }, +/**/ {{0x1901f427, 0x3ff00140} }, +/**/ {{0x1691acd0, 0x3ff00130} }, +/**/ {{0x14416c9a, 0x3ff00120} }, +/**/ {{0x12113324, 0x3ff00110} }, +/**/ {{0x10010010, 0x3ff00100} }, +/**/ {{0x0e10d2fc, 0x3ff000f0} }, +/**/ {{0x0c40ab89, 0x3ff000e0} }, +/**/ {{0x0a908957, 0x3ff000d0} }, +/**/ {{0x09006c05, 0x3ff000c0} }, +/**/ {{0x07905334, 0x3ff000b0} }, +/**/ {{0x06403e82, 0x3ff000a0} }, +/**/ {{0x05102d92, 0x3ff00090} }, +/**/ {{0x04002001, 0x3ff00080} }, +/**/ {{0x03101571, 0x3ff00070} }, +/**/ {{0x02400d80, 0x3ff00060} }, +/**/ {{0x019007d0, 0x3ff00050} }, +/**/ {{0x01000400, 0x3ff00040} }, +/**/ {{0x009001b0, 0x3ff00030} }, +/**/ {{0x00400080, 0x3ff00020} }, +/**/ {{0x00100010, 0x3ff00010} }, +/**/ {{0x00000000, 0x3ff00000} }, +/**/ {{0x001fffe0, 0x3fefffe0} }, +/**/ {{0x007fff00, 0x3fefffc0} }, +/**/ {{0x011ffca0, 0x3fefffa0} }, +/**/ {{0x01fff800, 0x3fefff80} }, +/**/ {{0x031ff060, 0x3fefff60} }, +/**/ {{0x047fe501, 0x3fefff40} }, +/**/ {{0x061fd521, 0x3fefff20} }, +/**/ {{0x07ffc002, 0x3fefff00} }, +/**/ {{0x0a1fa4e3, 0x3feffee0} }, +/**/ {{0x0c7f8305, 0x3feffec0} }, +/**/ {{0x0f1f59a7, 0x3feffea0} }, +/**/ {{0x11ff280a, 0x3feffe80} }, +/**/ {{0x151eed6e, 0x3feffe60} }, +/**/ {{0x187ea913, 0x3feffe40} }, +/**/ {{0x1c1e5a39, 0x3feffe20} }, +/**/ {{0x1ffe0020, 0x3feffe00} }, +/**/ {{0x241d9a09, 0x3feffde0} }, +/**/ {{0x287d2733, 0x3feffdc0} }, +/**/ {{0x2d1ca6e0, 0x3feffda0} }, +/**/ {{0x31fc184e, 0x3feffd80} }, +/**/ {{0x371b7abf, 0x3feffd60} }, +/**/ {{0x3c7acd72, 0x3feffd40} }, +/**/ {{0x421a0fa9, 0x3feffd20} }, +/**/ {{0x47f940a2, 0x3feffd00} }, +/**/ {{0x4e185f9f, 0x3feffce0} }, +/**/ {{0x54776bdf, 0x3feffcc0} }, +/**/ {{0x5b1664a3, 0x3feffca0} }, +/**/ {{0x61f5492c, 0x3feffc80} }, +/**/ {{0x691418b9, 0x3feffc60} }, +/**/ {{0x7072d28b, 0x3feffc40} }, +/**/ {{0x781175e3, 0x3feffc20} }, +/**/ {{0x7ff00200, 0x3feffc00} }, +/**/ {{0x880e7623, 0x3feffbe0} }, +/**/ {{0x906cd18c, 0x3feffbc0} }, +/**/ {{0x990b137c, 0x3feffba0} }, +/**/ {{0xa1e93b34, 0x3feffb80} }, +/**/ {{0xab0747f3, 0x3feffb60} }, +/**/ {{0xb46538fa, 0x3feffb40} }, +/**/ {{0xbe030d89, 0x3feffb20} }, +/**/ {{0xc7e0c4e1, 0x3feffb00} }, +/**/ {{0xd1fe5e43, 0x3feffae0} }, +/**/ {{0xdc5bd8ee, 0x3feffac0} }, +/**/ {{0xe6f93424, 0x3feffaa0} }, +/**/ {{0xf1d66f25, 0x3feffa80} }, +/**/ {{0xfcf38931, 0x3feffa60} }, +/**/ {{0x08508189, 0x3feffa41} }, +/**/ {{0x13ed576d, 0x3feffa21} }, +/**/ {{0x1fca0a1e, 0x3feffa01} }, +/**/ {{0x2be698dd, 0x3feff9e1} }, +/**/ {{0x384302e9, 0x3feff9c1} }, +/**/ {{0x44df4785, 0x3feff9a1} }, +/**/ {{0x51bb65ef, 0x3feff981} }, +/**/ {{0x5ed75d6a, 0x3feff961} }, +/**/ {{0x6c332d34, 0x3feff941} }, +/**/ {{0x79ced490, 0x3feff921} }, +/**/ {{0x87aa52be, 0x3feff901} }, +/**/ {{0x95c5a6fe, 0x3feff8e1} }, +/**/ {{0xa420d091, 0x3feff8c1} }, +/**/ {{0xb2bbceb7, 0x3feff8a1} }, +/**/ {{0xc196a0b2, 0x3feff881} }, +/**/ {{0xd0b145c2, 0x3feff861} }, +/**/ {{0xe00bbd28, 0x3feff841} }, +/**/ {{0xefa60624, 0x3feff821} }, +/**/ {{0xff801ff8, 0x3feff801} }, +/**/ {{0x0f9a09e3, 0x3feff7e2} }, +/**/ {{0x1ff3c328, 0x3feff7c2} }, +/**/ {{0x308d4b05, 0x3feff7a2} }, +/**/ {{0x4166a0bd, 0x3feff782} }, +/**/ {{0x527fc390, 0x3feff762} }, +/**/ {{0x63d8b2bf, 0x3feff742} }, +/**/ {{0x75716d8b, 0x3feff722} }, +/**/ {{0x8749f334, 0x3feff702} }, +/**/ {{0x996242fb, 0x3feff6e2} }, +/**/ {{0xabba5c21, 0x3feff6c2} }, +/**/ {{0xbe523de8, 0x3feff6a2} }, +/**/ {{0xd129e78f, 0x3feff682} }, +/**/ {{0xe4415858, 0x3feff662} }, +/**/ {{0xf7988f84, 0x3feff642} }, +/**/ {{0x0b2f8c54, 0x3feff623} }, +/**/ {{0x1f064e08, 0x3feff603} }, +/**/ {{0x331cd3e1, 0x3feff5e3} }, +/**/ {{0x47731d21, 0x3feff5c3} }, +/**/ {{0x5c092908, 0x3feff5a3} }, +/**/ {{0x70def6d7, 0x3feff583} }, +/**/ {{0x85f485d0, 0x3feff563} }, +/**/ {{0x9b49d532, 0x3feff543} }, +/**/ {{0xb0dee440, 0x3feff523} }, +/**/ {{0xc6b3b23b, 0x3feff503} }, +/**/ {{0xdcc83e62, 0x3feff4e3} }, +/**/ {{0xf31c87f8, 0x3feff4c3} }, +/**/ {{0x09b08e3d, 0x3feff4a4} }, +/**/ {{0x20845073, 0x3feff484} }, +/**/ {{0x3797cdda, 0x3feff464} }, +/**/ {{0x4eeb05b4, 0x3feff444} }, +/**/ {{0x667df741, 0x3feff424} }, +/**/ {{0x7e50a1c3, 0x3feff404} }, +/**/ {{0x9663047b, 0x3feff3e4} }, +/**/ {{0xaeb51eaa, 0x3feff3c4} }, +/**/ {{0xc746ef91, 0x3feff3a4} }, +/**/ {{0xe0187672, 0x3feff384} }, +/**/ {{0xf929b28d, 0x3feff364} }, +/**/ {{0x127aa323, 0x3feff345} }, +/**/ {{0x2c0b4776, 0x3feff325} }, +/**/ {{0x45db9ec7, 0x3feff305} }, +/**/ {{0x5feba858, 0x3feff2e5} }, +/**/ {{0x7a3b6369, 0x3feff2c5} }, +/**/ {{0x94cacf3b, 0x3feff2a5} }, +/**/ {{0xaf99eb11, 0x3feff285} }, +/**/ {{0xcaa8b62a, 0x3feff265} }, +/**/ {{0xe5f72fc9, 0x3feff245} }, +/**/ {{0x0185572f, 0x3feff226} }, +/**/ {{0x1d532b9d, 0x3feff206} }, +/**/ {{0x3960ac54, 0x3feff1e6} }, +/**/ {{0x55add896, 0x3feff1c6} }, +/**/ {{0x723aafa3, 0x3feff1a6} }, +/**/ {{0x8f0730be, 0x3feff186} }, +/**/ {{0xac135b27, 0x3feff166} }, +/**/ {{0xc95f2e21, 0x3feff146} }, +/**/ {{0xe6eaa8eb, 0x3feff126} }, +/**/ {{0x04b5cac9, 0x3feff107} }, +/**/ {{0x22c092fb, 0x3feff0e7} }, +/**/ {{0x410b00c2, 0x3feff0c7} }, +/**/ {{0x5f951360, 0x3feff0a7} }, +/**/ {{0x7e5eca16, 0x3feff087} }, +/**/ {{0x9d682426, 0x3feff067} }, +/**/ {{0xbcb120d2, 0x3feff047} }, +/**/ {{0xdc39bf5a, 0x3feff027} }, +/**/ {{0xfc01ff00, 0x3feff007} }, +/**/ {{0x1c09df07, 0x3fefefe8} }, +/**/ {{0x3c515eae, 0x3fefefc8} }, +/**/ {{0x5cd87d38, 0x3fefefa8} }, +/**/ {{0x7d9f39e6, 0x3fefef88} }, +/**/ {{0x9ea593fa, 0x3fefef68} }, +/**/ {{0xbfeb8ab5, 0x3fefef48} }, +/**/ {{0xe1711d5a, 0x3fefef28} }, +/**/ {{0x03364b28, 0x3fefef09} }, +/**/ {{0x253b1363, 0x3fefeee9} }, +/**/ {{0x477f754b, 0x3fefeec9} }, +/**/ {{0x6a037022, 0x3fefeea9} }, +/**/ {{0x8cc7032a, 0x3fefee89} }, +/**/ {{0xafca2da5, 0x3fefee69} }, +/**/ {{0xd30ceed4, 0x3fefee49} }, +/**/ {{0xf68f45f8, 0x3fefee29} }, +/**/ {{0x1a513254, 0x3fefee0a} }, +/**/ {{0x3e52b329, 0x3fefedea} }, +/**/ {{0x6293c7b8, 0x3fefedca} }, +/**/ {{0x87146f44, 0x3fefedaa} }, +/**/ {{0xabd4a90e, 0x3fefed8a} }, +/**/ {{0xd0d47458, 0x3fefed6a} }, +/**/ {{0xf613d064, 0x3fefed4a} }, +/**/ {{0x1b92bc73, 0x3fefed2b} }, +/**/ {{0x415137c7, 0x3fefed0b} }, +/**/ {{0x674f41a2, 0x3fefeceb} }, +/**/ {{0x8d8cd945, 0x3fefeccb} }, +/**/ {{0xb409fdf3, 0x3fefecab} }, +/**/ {{0xdac6aeed, 0x3fefec8b} }, +/**/ {{0x01c2eb76, 0x3fefec6c} }, +/**/ {{0x28feb2ce, 0x3fefec4c} }, +/**/ {{0x507a0437, 0x3fefec2c} }, +/**/ {{0x7834def5, 0x3fefec0c} }, +/**/ {{0xa02f4247, 0x3fefebec} }, +/**/ {{0xc8692d71, 0x3fefebcc} }, +/**/ {{0xf0e29fb4, 0x3fefebac} }, +/**/ {{0x199b9852, 0x3fefeb8d} }, +/**/ {{0x4294168d, 0x3fefeb6d} }, +/**/ {{0x6bcc19a7, 0x3fefeb4d} }, +/**/ {{0x9543a0e2, 0x3fefeb2d} }, +/**/ {{0xbefaab7f, 0x3fefeb0d} }, +/**/ {{0xe8f138c2, 0x3fefeaed} }, +/**/ {{0x132747ea, 0x3fefeace} }, +/**/ {{0x3d9cd83c, 0x3fefeaae} }, +/**/ {{0x6851e8f7, 0x3fefea8e} }, +/**/ {{0x93467960, 0x3fefea6e} }, +/**/ {{0xbe7a88b7, 0x3fefea4e} }, +/**/ {{0xe9ee163f, 0x3fefea2e} }, +/**/ {{0x15a12139, 0x3fefea0f} }, +/**/ {{0x4193a8e8, 0x3fefe9ef} }, +/**/ {{0x6dc5ac8e, 0x3fefe9cf} }, +/**/ {{0x9a372b6d, 0x3fefe9af} }, +/**/ {{0xc6e824c6, 0x3fefe98f} }, +/**/ {{0xf3d897dd, 0x3fefe96f} }, + }; + + static const number + Lu[182][2] = { /* log(ui) */ +/**/ {{{0x0b3aac49, 0xbfd63003} }, +/**/ {{0xe51fff99, 0xbc6dc18c} },}, +/**/ {{{0xdf595f30, 0xbfd5d5bd} }, +/**/ {{0x48cbb8a2, 0x3c765411} },}, +/**/ {{{0x53c8d1fb, 0xbfd57bf7} }, +/**/ {{0x15f88b63, 0x3c60908d} },}, +/**/ {{{0x0738a3d8, 0xbfd522ae} }, +/**/ {{0xb38a6979, 0x3c68f7e9} },}, +/**/ {{{0x9e172c3c, 0xbfd4c9e0} }, +/**/ {{0x5b147a5d, 0x3c512361} },}, +/**/ {{{0xc271c41b, 0xbfd4718d} }, +/**/ {{0x14c56eef, 0xbc38fb4c} },}, +/**/ {{{0x23d5e8c7, 0xbfd419b4} }, +/**/ {{0x43827392, 0xbc60dbb2} },}, +/**/ {{{0x77333184, 0xbfd3c252} }, +/**/ {{0xe50a8ec6, 0x3c72ad27} },}, +/**/ {{{0x76be1117, 0xbfd36b67} }, +/**/ {{0xe883858e, 0x3c5324f0} },}, +/**/ {{{0xe1d35ce4, 0xbfd314f1} }, +/**/ {{0x09e5c3dc, 0x3c73d699} },}, +/**/ {{{0x7cdc9354, 0xbfd2bef0} }, +/**/ {{0x7fd86088, 0x3c782dad} },}, +/**/ {{{0x1134db92, 0xbfd26962} }, +/**/ {{0xdd9db02b, 0xbc7e0efa} },}, +/**/ {{{0x6d0eb8d4, 0xbfd21445} }, +/**/ {{0x1aeba60a, 0xbc6f7ae9} },}, +/**/ {{{0x635a6b95, 0xbfd1bf99} }, +/**/ {{0x84249223, 0x3c612aeb} },}, +/**/ {{{0xcbacfb73, 0xbfd16b5c} }, +/**/ {{0x28b40935, 0xbc766fbd} },}, +/**/ {{{0x8227e47c, 0xbfd1178e} }, +/**/ {{0x5f01c691, 0x3c60e63a} },}, +/**/ {{{0x676162e3, 0xbfd0c42d} }, +/**/ {{0x9d5d11ee, 0xbc5162c7} },}, +/**/ {{{0x604d5862, 0xbfd07138} }, +/**/ {{0xed4e9138, 0xbc7cdb16} },}, +/**/ {{{0x5626c691, 0xbfd01eae} }, +/**/ {{0xbd2932e2, 0x3c418290} },}, +/**/ {{{0x6cb3b379, 0xbfcf991c} }, +/**/ {{0x66f980a2, 0xbc6f6650} },}, +/**/ {{{0xe4dcffe6, 0xbfcef5ad} }, +/**/ {{0xddc708a0, 0x3c508ab2} },}, +/**/ {{{0xffe71012, 0xbfce530e} }, +/**/ {{0x41f43042, 0xbc422760} },}, +/**/ {{{0xb0d48940, 0xbfcdb13d} }, +/**/ {{0x49f96cb9, 0xbc5aa11d} },}, +/**/ {{{0xf2655e7b, 0xbfcd1037} }, +/**/ {{0x242471a2, 0xbc660629} },}, +/**/ {{{0xc6f00f71, 0xbfcc6ffb} }, +/**/ {{0x2c57a4a5, 0x3c68e58b} },}, +/**/ {{{0x383bd8ad, 0xbfcbd087} }, +/**/ {{0xf6a516d7, 0xbc3dd355} },}, +/**/ {{{0x575bce3d, 0xbfcb31d8} }, +/**/ {{0xb386a94d, 0x3c66353a} },}, +/**/ {{{0x3c8ad9e3, 0xbfca93ed} }, +/**/ {{0x9de97203, 0xbc6bcafa} },}, +/**/ {{{0x07089664, 0xbfc9f6c4} }, +/**/ {{0x605e67ef, 0xbc435a19} },}, +/**/ {{{0xdcf7017f, 0xbfc95a5a} }, +/**/ {{0x07fb7a3d, 0xbc5142c5} },}, +/**/ {{{0xeb38fe8c, 0xbfc8beaf} }, +/**/ {{0xb6997a40, 0xbc555aa8} },}, +/**/ {{{0x6551a3c2, 0xbfc823c1} }, +/**/ {{0xe70be781, 0x3c61232c} },}, +/**/ {{{0x85444c73, 0xbfc7898d} }, +/**/ {{0xebcfb201, 0xbc5ef8f6} },}, +/**/ {{{0x8b756abc, 0xbfc6f012} }, +/**/ {{0xc21e166c, 0x3c68de59} },}, +/**/ {{{0xbe8c133a, 0xbfc6574e} }, +/**/ {{0xf4621bed, 0x3c3d34f0} },}, +/**/ {{{0x6b543db2, 0xbfc5bf40} }, +/**/ {{0x4c0df7e7, 0x3c21f5b4} },}, +/**/ {{{0xe4a1b58d, 0xbfc527e5} }, +/**/ {{0x82395bfd, 0x3c271a96} },}, +/**/ {{{0x8333b561, 0xbfc4913d} }, +/**/ {{0x4930f135, 0x3c50d560} },}, +/**/ {{{0xa59928cc, 0xbfc3fb45} }, +/**/ {{0xa354d056, 0x3c6d87e6} },}, +/**/ {{{0xb0159016, 0xbfc365fc} }, +/**/ {{0xa5b944ad, 0xbc57d411} },}, +/**/ {{{0x0c86813a, 0xbfc2d161} }, +/**/ {{0xf25af95f, 0x3c5499a3} },}, +/**/ {{{0x2a49c202, 0xbfc23d71} }, +/**/ {{0x61051d69, 0x3c66e381} },}, +/**/ {{{0x7e23f72a, 0xbfc1aa2b} }, +/**/ {{0xd9b2ef7e, 0x3c4c6ef1} },}, +/**/ {{{0x8227e47c, 0xbfc1178e} }, +/**/ {{0x5f01c691, 0x3c50e63a} },}, +/**/ {{{0xb59e3a07, 0xbfc08598} }, +/**/ {{0x9902bf32, 0x3c6dd700} },}, +/**/ {{{0x39dbd566, 0xbfbfe891} }, +/**/ {{0x215f9393, 0x3c5ac9f4} },}, +/**/ {{{0x830a1120, 0xbfbec739} }, +/**/ {{0x91780d3f, 0x3c4a2bf9} },}, +/**/ {{{0x638446a2, 0xbfbda727} }, +/**/ {{0x71733019, 0xbc5401fa} },}, +/**/ {{{0x01bc4b23, 0xbfbc8858} }, +/**/ {{0x559a6706, 0xbc5a38cb} },}, +/**/ {{{0x8dad5b1c, 0xbfbb6ac8} }, +/**/ {{0xed1ca59f, 0x3c40057e} },}, +/**/ {{{0x40b1bc38, 0xbfba4e76} }, +/**/ {{0x203e4259, 0x3c55b5ca} },}, +/**/ {{{0x5d594989, 0xbfb9335e} }, +/**/ {{0x5704ccb7, 0x3c5478a8} },}, +/**/ {{{0x2f40e3f0, 0xbfb8197e} }, +/**/ {{0xffbeed43, 0xbc3b9f2d} },}, +/**/ {{{0x0aeac0e1, 0xbfb700d3} }, +/**/ {{0x212cdd05, 0x3c272566} },}, +/**/ {{{0x4d9791cb, 0xbfb5e95a} }, +/**/ {{0x5c5c450a, 0xbc5f3874} },}, +/**/ {{{0x5d207eac, 0xbfb4d311} }, +/**/ {{0x2c7842cc, 0xbc5769f4} },}, +/**/ {{{0xa7d1ee64, 0xbfb3bdf5} }, +/**/ {{0xd3b5b45f, 0xbc47a976} },}, +/**/ {{{0xa44717a5, 0xbfb2aa04} }, +/**/ {{0x8d2fa3f7, 0x3c5d15d3} },}, +/**/ {{{0xd1465567, 0xbfb1973b} }, +/**/ {{0x67a6acf6, 0x3c475583} },}, +/**/ {{{0xb59e3a07, 0xbfb08598} }, +/**/ {{0x9902bf32, 0x3c5dd700} },}, +/**/ {{{0xc006b87c, 0xbfaeea31} }, +/**/ {{0x93b7b66c, 0x3c43e4fc} },}, +/**/ {{{0xcdddb2cc, 0xbfaccb73} }, +/**/ {{0x0500efd4, 0x3c4e48fb} },}, +/**/ {{{0xd0fb10fc, 0xbfaaaef2} }, +/**/ {{0xb42e0add, 0xbc2a353b} },}, +/**/ {{{0x149fb343, 0xbfa894aa} }, +/**/ {{0x7660a23d, 0xbc3a8be9} },}, +/**/ {{{0xf2d4bb58, 0xbfa67c94} }, +/**/ {{0x6505e603, 0xbc40413e} },}, +/**/ {{{0xd42de3ea, 0xbfa466ae} }, +/**/ {{0x7f4a137e, 0x3c4cdd6f} },}, +/**/ {{{0x2f8d183f, 0xbfa252f3} }, +/**/ {{0x92615916, 0x3c4947f7} },}, +/**/ {{{0x89e74444, 0xbfa0415d} }, +/**/ {{0x1d753622, 0xbc4c05cf} },}, +/**/ {{{0xec14aaf2, 0xbf9c63d2} }, +/**/ {{0xa686bd86, 0x3c3ce030} },}, +/**/ {{{0x28c8cabf, 0xbf984925} }, +/**/ {{0x0619fa67, 0x3c3d192d} },}, +/**/ {{{0x25980cc1, 0xbf9432a9} }, +/**/ {{0x39004192, 0x3c38cdaf} },}, +/**/ {{{0x58935847, 0xbf902056} }, +/**/ {{0x8416e71f, 0xbc327c8e} },}, +/**/ {{{0xa388a2aa, 0xbf882448} }, +/**/ {{0x137f09a0, 0xbc104b16} },}, +/**/ {{{0x7588de71, 0xbf801015} }, +/**/ {{0xd417ced0, 0xbc146662} },}, +/**/ {{{0x59588b35, 0xbf700805} }, +/**/ {{0x8cf63677, 0xbc1f9663} },}, +/**/ {{{0x00000000, 0x00000000} }, +/**/ {{0x00000000, 0x00000000} },}, +/**/ {{{0xa2b10bc0, 0x3f6ff00a} }, +/**/ {{0xd5a6d353, 0x3c02821a} },}, +/**/ {{{0x6b106789, 0x3f7fe02a} }, +/**/ {{0xe3711ebf, 0xbbce44b7} },}, +/**/ {{{0x5f810a77, 0x3f87dc47} }, +/**/ {{0x87d3df21, 0xbc116d76} },}, +/**/ {{{0xb0fc03e4, 0x3f8fc0a8} }, +/**/ {{0xc59642a1, 0xbc183092} },}, +/**/ {{{0x4346a575, 0x3f93cea4} }, +/**/ {{0x902b3a1c, 0xbc10cb5a} },}, +/**/ {{{0x07d5b11b, 0x3f97b91b} }, +/**/ {{0xace3a510, 0xbc35b602} },}, +/**/ {{{0x27af9198, 0x3f9b9fc0} }, +/**/ {{0x229dc868, 0xbbf0ae69} },}, +/**/ {{{0x0e783300, 0x3f9f829b} }, +/**/ {{0x04f1ef23, 0x3c333e3f} },}, +/**/ {{{0x8923d980, 0x3fa1b0d9} }, +/**/ {{0x89bac481, 0xbc3e9ae8} },}, +/**/ {{{0xb9febd60, 0x3fa39e87} }, +/**/ {{0x37f551bb, 0xbc45bfa9} },}, +/**/ {{{0xafc8e4d5, 0x3fa58a5b} }, +/**/ {{0x2b4e2b72, 0xbc4ce55c} },}, +/**/ {{{0xf632dcfc, 0x3fa77458} }, +/**/ {{0xa87b9296, 0x3c418d3c} },}, +/**/ {{{0x0ec8e3eb, 0x3fa95c83} }, +/**/ {{0x80520bf2, 0x3c4f5a0e} },}, +/**/ {{{0x711971bf, 0x3fab42dd} }, +/**/ {{0x9c130499, 0xbc3eb975} },}, +/**/ {{{0x8adb0b52, 0x3fad276b} }, +/**/ {{0x3257fd47, 0x3c21e3c5} },}, +/**/ {{{0xc01162a6, 0x3faf0a30} }, +/**/ {{0x5c5bbacd, 0x3c485f32} },}, +/**/ {{{0x3598e471, 0x3fb07598} }, +/**/ {{0x333c45b8, 0x3c480da5} },}, +/**/ {{{0xeea37ae1, 0x3fb16536} }, +/**/ {{0xe8c22cda, 0xbc379da3} },}, +/**/ {{{0x2f0a1417, 0x3fb253f6} }, +/**/ {{0x63fc4cfd, 0xbc1c1259} },}, +/**/ {{{0x961bd1d1, 0x3fb341d7} }, +/**/ {{0x227becbb, 0xbc5b599f} },}, +/**/ {{{0xbea646f0, 0x3fb42edc} }, +/**/ {{0x935996c9, 0x3c4ddd4f} },}, +/**/ {{{0x3f06183f, 0x3fb51b07} }, +/**/ {{0x9a1a8be4, 0x3c5a49e3} },}, +/**/ {{{0xa93750c4, 0x3fb60658} }, +/**/ {{0x8ec21b6a, 0xbc538845} },}, +/**/ {{{0x8ae56b4c, 0x3fb6f0d2} }, +/**/ {{0x9184b992, 0xbc5906d9} },}, +/**/ {{{0x6d7b12cd, 0x3fb7da76} }, +/**/ {{0xcdd94131, 0xbc5eeedf} },}, +/**/ {{{0xd6319b21, 0x3fb8c345} }, +/**/ {{0xab3424a9, 0xbc24a697} },}, +/**/ {{{0x462033ad, 0x3fb9ab42} }, +/**/ {{0x1c184e8e, 0xbc42099e} },}, +/**/ {{{0x3a4ad563, 0x3fba926d} }, +/**/ {{0x8aa70ea9, 0x3c5942f4} },}, +/**/ {{{0x2bb0eda1, 0x3fbb78c8} }, +/**/ {{0xf0327e21, 0x3c20878c} },}, +/**/ {{{0x8f5bc743, 0x3fbc5e54} }, +/**/ {{0xef8161b1, 0x3c35d617} },}, +/**/ {{{0xd66cb35d, 0x3fbd4313} }, +/**/ {{0x951d90fa, 0x3c5790dd} },}, +/**/ {{{0x6e2af2e6, 0x3fbe2707} }, +/**/ {{0x001e0162, 0xbc361578} },}, +/**/ {{{0xc01162a6, 0x3fbf0a30} }, +/**/ {{0x5c5bbacd, 0x3c585f32} },}, +/**/ {{{0x31dbeabb, 0x3fbfec91} }, +/**/ {{0x9981b36c, 0xbc55746b} },}, +/**/ {{{0x12ca596e, 0x3fc06715} }, +/**/ {{0x7eb86499, 0x3c550c64} },}, +/**/ {{{0x7cd08e59, 0x3fc0d77e} }, +/**/ {{0x5e9030ac, 0x3c69a5dc} },}, +/**/ {{{0x846742ac, 0x3fc14785} }, +/**/ {{0x3e3a7f07, 0x3c6a2881} },}, +/**/ {{{0xd52f67a0, 0x3fc1b72a} }, +/**/ {{0x3472cd74, 0x3c548302} },}, +/**/ {{{0x190a5acb, 0x3fc2266f} }, +/**/ {{0xf1809e88, 0x3c6f547b} },}, +/**/ {{{0xf81ff523, 0x3fc29552} }, +/**/ {{0x1c407dbf, 0x3c630177} },}, +/**/ {{{0x18e47fd3, 0x3fc303d7} }, +/**/ {{0xd96091fa, 0xbc06b9c7} },}, +/**/ {{{0x201e8f74, 0x3fc371fc} }, +/**/ {{0x62af18a0, 0x3c5de6cb} },}, +/**/ {{{0xb0ecc62a, 0x3fc3dfc2} }, +/**/ {{0xe7d81017, 0xbc5ab3a8} },}, +/**/ {{{0x6ccb7d1e, 0x3fc44d2b} }, +/**/ {{0x543e1f88, 0x3c69f4f6} },}, +/**/ {{{0xf39a55e5, 0x3fc4ba36} }, +/**/ {{0xbcc36756, 0x3c668981} },}, +/**/ {{{0xe3a1b438, 0x3fc526e5} }, +/**/ {{0x8a470d3a, 0xbc6746ff} },}, +/**/ {{{0xd9982086, 0x3fc59338} }, +/**/ {{0xaa8ad7cf, 0xbc565d22} },}, +/**/ {{{0x70a793d4, 0x3fc5ff30} }, +/**/ {{0xfafc6f6e, 0xbc5bc60e} },}, +/**/ {{{0x4272ad51, 0x3fc66acd} }, +/**/ {{0x4e1ea8b2, 0xbc50900e} },}, +/**/ {{{0xe719d21d, 0x3fc6d60f} }, +/**/ {{0x68ecd179, 0xbc6caae2} },}, +/**/ {{{0xf54037a5, 0x3fc740f8} }, +/**/ {{0x62a84cdb, 0xbc5b2640} },}, +/**/ {{{0x0210d909, 0x3fc7ab89} }, +/**/ {{0x2d6a0608, 0x3c4be36b} },}, +/**/ {{{0xa14357eb, 0x3fc815c0} }, +/**/ {{0x073a0564, 0xbc54be48} },}, +/**/ {{{0x6520c911, 0x3fc87fa0} }, +/**/ {{0xbfa08d9a, 0xbc6bf7fd} },}, +/**/ {{{0xde886d41, 0x3fc8e928} }, +/**/ {{0x51a56770, 0xbc6569d8} },}, +/**/ {{{0x9cf456b4, 0x3fc9525a} }, +/**/ {{0x1d4e2e26, 0x3c6d904c} },}, +/**/ {{{0x2e7dfb83, 0x3fc9bb36} }, +/**/ {{0x1f003e0c, 0x3c6575e3} },}, +/**/ {{{0x1fe2b563, 0x3fca23bc} }, +/**/ {{0xb07a998c, 0x3c493711} },}, +/**/ {{{0xfc882f19, 0x3fca8bec} }, +/**/ {{0x918c39eb, 0xbc5e8c37} },}, +/**/ {{{0x4e80bff3, 0x3fcaf3c9} }, +/**/ {{0xf3641985, 0xbc5398cf} },}, +/**/ {{{0x9e8fb5a4, 0x3fcb5b51} }, +/**/ {{0xdc19e1a0, 0x3c6ba27f} },}, +/**/ {{{0x742d8cd6, 0x3fcbc286} }, +/**/ {{0x44870f55, 0x3c54fce7} },}, +/**/ {{{0x558c18c1, 0x3fcc2968} }, +/**/ {{0x38a3fb6b, 0xbc673dee} },}, +/**/ {{{0xc79a9a22, 0x3fcc8ff7} }, +/**/ {{0xf8434012, 0xbc64f689} },}, +/**/ {{{0x4e09c5dc, 0x3fccf635} }, +/**/ {{0x7d55b695, 0x3c6239a0} },}, +/**/ {{{0x6b4fbb91, 0x3fcd5c21} }, +/**/ {{0x597e4d40, 0x3c66e443} },}, +/**/ {{{0xa0abec7d, 0x3fcdc1bc} }, +/**/ {{0x1998b6fc, 0x3c6834c5} },}, +/**/ {{{0x6e2af2e6, 0x3fce2707} }, +/**/ {{0x001e0162, 0xbc461578} },}, +/**/ {{{0x52aa5a60, 0x3fce8c02} }, +/**/ {{0x39bfc89b, 0xbc46e03a} },}, +/**/ {{{0xcbdc5936, 0x3fcef0ad} }, +/**/ {{0x950dc20d, 0x3c648637} },}, +/**/ {{{0x564b7b37, 0x3fcf550a} }, +/**/ {{0xfd018c37, 0x3c2c5f6d} },}, +/**/ {{{0x6d5e3e2b, 0x3fcfb918} }, +/**/ {{0x64f21acb, 0xbc6caaae} },}, +/**/ {{{0x45ad501d, 0x3fd00e6c} }, +/**/ {{0x8ff6fead, 0xbc6cb956} },}, +/**/ {{{0x94b4d041, 0x3fd04025} }, +/**/ {{0x17a5022d, 0xbc628ec2} },}, +/**/ {{{0x5fcd590d, 0x3fd071b8} }, +/**/ {{0xf97bde80, 0x3c5d1707} },}, +/**/ {{{0xe27390e3, 0x3fd0a324} }, +/**/ {{0xe8061c03, 0x3c77dcfd} },}, +/**/ {{{0x579ab74b, 0x3fd0d46b} }, +/**/ {{0x1c3cbd92, 0x3c603ec8} },}, +/**/ {{{0xf9ae4ad5, 0x3fd1058b} }, +/**/ {{0xab4cb31d, 0x3c589fa0} },}, +/**/ {{{0x0293a8b0, 0x3fd13687} }, +/**/ {{0x98edd24a, 0x3c77b662} },}, +/**/ {{{0xababa60e, 0x3fd1675c} }, +/**/ {{0xab883717, 0x3c2ce63e} },}, +/**/ {{{0x2dd4236f, 0x3fd1980d} }, +/**/ {{0xb0e4d147, 0x3c79d3d1} },}, +/**/ {{{0xc16999fb, 0x3fd1c898} }, +/**/ {{0x2aff1c44, 0xbc30e5c6} },}, +/**/ {{{0x9e48a2f3, 0x3fd1f8ff} }, +/**/ {{0x9a0c4b07, 0xbc7c9fdf} },}, +/**/ {{{0xfbcf7966, 0x3fd22941} }, +/**/ {{0xb09628af, 0xbc776f5e} },}, +/**/ {{{0x10df763a, 0x3fd25960} }, +/**/ {{0x57075e9e, 0xbc50f76c} },}, +/**/ {{{0x13de86a3, 0x3fd2895a} }, +/**/ {{0xc13f040e, 0x3c77ad24} },}, +/**/ {{{0x3ab89d25, 0x3fd2b930} }, +/**/ {{0xfd852ad4, 0xbc7896b5} },}, +/**/ {{{0xbae11d31, 0x3fd2e8e2} }, +/**/ {{0xb95ebdf9, 0xbc78f4cd} },}, +/**/ {{{0xc9544185, 0x3fd31871} }, +/**/ {{0x4c09b379, 0xbc351acc} },}, +/**/ {{{0x9a987d55, 0x3fd347dd} }, +/**/ {{0x580919f8, 0xbc64dd4c} },}, +/**/ {{{0x62bfd85b, 0x3fd37726} }, +/**/ {{0xd8117de7, 0xbc4b5629} },}, +/**/ {{{0x556945ea, 0x3fd3a64c} }, +/**/ {{0x1945f97c, 0xbc6c6865} },}, +/**/ {{{0xa5c1f710, 0x3fd3d54f} }, +/**/ {{0xc6a1c98d, 0xbc7e3265} },}, +/**/ {{{0x8686a7e4, 0x3fd40430} }, +/**/ {{0x6082ce6d, 0xbc70bcfb} },}, +/**/ {{{0x2a04e814, 0x3fd432ef} }, +/**/ {{0x715ac903, 0xbc729931} },}, +/**/ {{{0xc21c5ec2, 0x3fd4618b} }, +/**/ {{0xcdeccf1d, 0x3c7f42de} },}, +/**/ {{{0x804009d1, 0x3fd49006} }, +/**/ {{0x41f177dc, 0xbc69ffc3} },}, +/**/ {{{0x957778a1, 0x3fd4be5f} }, +/**/ {{0x5b04813d, 0xbc6259b3} },}, +/**/ {{{0x3260026a, 0x3fd4ec97} }, +/**/ {{0xd977dc5e, 0xbc742a87} },}, +/**/ {{{0x872df82d, 0x3fd51aad} }, +/**/ {{0xc19f55e3, 0x3c43927a} },}, +/**/ {{{0xc3add263, 0x3fd548a2} }, +/**/ {{0x7e308ddb, 0xbc6819cf} },}, +/**/ {{{0x17455a6c, 0x3fd57677} }, +/**/ {{0xb283660c, 0x3c7526ad} },}, +/**/ {{{0xb0f4cfe2, 0x3fd5a42a} }, +/**/ {{0x7dee9a3d, 0xbc78ebcb} },}, +/**/ {{{0xbf5809ca, 0x3fd5d1bd} }, +/**/ {{0x83dc7fe1, 0x3c742363} },}, +/**/ {{{0x70a793d4, 0x3fd5ff30} }, +/**/ {{0xfafc6f6e, 0xbc6bc60e} },}, +/**/ {{{0xf2b9c795, 0x3fd62c82} }, +/**/ {{0x915300e5, 0x3c67b7af} },}, + }; + + static const number + Lv[362][2] = { /* log(vj) */ + +/**/ {{{0xb72daabf, 0xbf6687ec} }, +/**/ {{0x0f13318f, 0x3c052c69} },}, +/**/ {{{0x3767104f, 0xbf6667d6} }, +/**/ {{0xd27a7bac, 0x3bd3efa3} },}, +/**/ {{{0xd7cd64fb, 0xbf6647bf} }, +/**/ {{0x55a89c36, 0x3c09b725} },}, +/**/ {{{0x9860683b, 0xbf6627a9} }, +/**/ {{0xfebc844a, 0x3bcbae22} },}, +/**/ {{{0x791fd98a, 0xbf660793} }, +/**/ {{0x78fa1cb5, 0xbbfe34af} },}, +/**/ {{{0x7a0b7863, 0xbf65e77d} }, +/**/ {{0xea78fdd0, 0xbc02f1b1} },}, +/**/ {{{0x9b230442, 0xbf65c767} }, +/**/ {{0x2202b2ca, 0x3bf70d8c} },}, +/**/ {{{0xdc663ca2, 0xbf65a751} }, +/**/ {{0xc3444e64, 0xbbfdc63d} },}, +/**/ {{{0x3dd4e102, 0xbf65873c} }, +/**/ {{0x370d69c3, 0x3c021b11} },}, +/**/ {{{0xbf6eb0de, 0xbf656726} }, +/**/ {{0x154dd8d8, 0xbbfb6da8} },}, +/**/ {{{0x61336bb6, 0xbf654711} }, +/**/ {{0xdf9a4709, 0xbc0b12d2} },}, +/**/ {{{0x2322d10a, 0xbf6526fc} }, +/**/ {{0x68d1274f, 0x3bf997f2} },}, +/**/ {{{0x053ca059, 0xbf6506e7} }, +/**/ {{0xe70c852a, 0x3c0c2a1f} },}, +/**/ {{{0x07809924, 0xbf64e6d2} }, +/**/ {{0xa808538f, 0x3c04cc9e} },}, +/**/ {{{0x29ee7aed, 0xbf64c6bd} }, +/**/ {{0x7797a4bd, 0x3befe68c} },}, +/**/ {{{0x6c860537, 0xbf64a6a8} }, +/**/ {{0x9efaae3d, 0x3c06794d} },}, +/**/ {{{0xcf46f784, 0xbf648693} }, +/**/ {{0xb2ddd9d1, 0xbbfed318} },}, +/**/ {{{0x5231115a, 0xbf64667f} }, +/**/ {{0x4643624b, 0x3c061f62} },}, +/**/ {{{0xf544123c, 0xbf64466a} }, +/**/ {{0x9387f11e, 0x3c0666a0} },}, +/**/ {{{0xb87fb9b0, 0xbf642656} }, +/**/ {{0x116ec598, 0x3c0043b2} },}, +/**/ {{{0x9be3c73c, 0xbf640642} }, +/**/ {{0xd2de6e3e, 0xbbfbd84d} },}, +/**/ {{{0x9f6ffa68, 0xbf63e62e} }, +/**/ {{0x433d8c65, 0xbbe9149b} },}, +/**/ {{{0xc32412bb, 0xbf63c61a} }, +/**/ {{0x08e5a7bb, 0xbbf6b88d} },}, +/**/ {{{0x06ffcfbe, 0xbf63a607} }, +/**/ {{0xccfac9e2, 0xbb9f3c7a} },}, +/**/ {{{0x6b02f0fa, 0xbf6385f3} }, +/**/ {{0xbec6f6e4, 0x3bee405c} },}, +/**/ {{{0xef2d35f9, 0xbf6365df} }, +/**/ {{0xaf0c0b4c, 0x3bf02993} },}, +/**/ {{{0x937e5e46, 0xbf6345cc} }, +/**/ {{0xaa64716f, 0x3bf9be97} },}, +/**/ {{{0x57f6296c, 0xbf6325b9} }, +/**/ {{0xa2e863ae, 0xbbfdeb4d} },}, +/**/ {{{0x3c9456f9, 0xbf6305a6} }, +/**/ {{0x636d2b2c, 0x3c0f3c7f} },}, +/**/ {{{0x4158a678, 0xbf62e593} }, +/**/ {{0xb166ca7f, 0x3c01a8df} },}, +/**/ {{{0x6642d778, 0xbf62c580} }, +/**/ {{0x53a2d534, 0x3c020ff1} },}, +/**/ {{{0xab52a987, 0xbf62a56d} }, +/**/ {{0x0412f1e7, 0xbbe8fef1} },}, +/**/ {{{0x1087dc35, 0xbf62855b} }, +/**/ {{0x4b7ac6c6, 0xbbfcd17e} },}, +/**/ {{{0x95e22f12, 0xbf626548} }, +/**/ {{0x9a8127bf, 0xbbfbfc21} },}, +/**/ {{{0x3b6161af, 0xbf624536} }, +/**/ {{0x66d42390, 0x3bd7eda1} },}, +/**/ {{{0x0105339d, 0xbf622524} }, +/**/ {{0x77fedcad, 0xbbdf374e} },}, +/**/ {{{0xe6cd646f, 0xbf620511} }, +/**/ {{0x52d05dea, 0x3be1d1fb} },}, +/**/ {{{0xecb9b3b8, 0xbf61e4ff} }, +/**/ {{0xffd8e706, 0x3c02c2fc} },}, +/**/ {{{0x12c9e10b, 0xbf61c4ee} }, +/**/ {{0xf1d5cc2c, 0xbc02b4f8} },}, +/**/ {{{0x58fdabfe, 0xbf61a4dc} }, +/**/ {{0x1315b191, 0xbc0618c3} },}, +/**/ {{{0xbf54d426, 0xbf6184ca} }, +/**/ {{0xcb3cdab0, 0xbc01f8d5} },}, +/**/ {{{0x45cf1919, 0xbf6164b9} }, +/**/ {{0xc025605a, 0xbc014ff7} },}, +/**/ {{{0xec6c3a6e, 0xbf6144a7} }, +/**/ {{0x87cb08cd, 0xbbff04ff} },}, +/**/ {{{0xb32bf7bd, 0xbf612496} }, +/**/ {{0xe6af1b84, 0x3bee89b4} },}, +/**/ {{{0x9a0e109e, 0xbf610485} }, +/**/ {{0x35a60879, 0x3c07e99e} },}, +/**/ {{{0xa11244aa, 0xbf60e474} }, +/**/ {{0x20f2325a, 0x3c04b698} },}, +/**/ {{{0xc838537b, 0xbf60c463} }, +/**/ {{0x3617200d, 0x3bc0657e} },}, +/**/ {{{0x0f7ffcac, 0xbf60a453} }, +/**/ {{0xa5080961, 0xbc008feb} },}, +/**/ {{{0x76e8ffd9, 0xbf608442} }, +/**/ {{0xbb5e1df7, 0x3bd13002} },}, +/**/ {{{0xfe731c9d, 0xbf606431} }, +/**/ {{0x6e2858c0, 0xbc0509f3} },}, +/**/ {{{0xa61e1296, 0xbf604421} }, +/**/ {{0x5f5d9695, 0xbc04b556} },}, +/**/ {{{0x6de9a162, 0xbf602411} }, +/**/ {{0xe79a4e00, 0x3c042b89} },}, +/**/ {{{0x55d5889e, 0xbf600401} }, +/**/ {{0x1113f403, 0x3be8f98e} },}, +/**/ {{{0xbbc30fd4, 0xbf5fc7e2} }, +/**/ {{0x93382bc9, 0xbbfc709b} },}, +/**/ {{{0x0c1abdcd, 0xbf5f87c3} }, +/**/ {{0x76a55d1c, 0xbbf2a90d} },}, +/**/ {{{0x9cb19a68, 0xbf5f47a3} }, +/**/ {{0x76e7826b, 0x3be1b815} },}, +/**/ {{{0x6d8724e7, 0xbf5f0784} }, +/**/ {{0x2b63756d, 0xbbe72d46} },}, +/**/ {{{0x7e9adc90, 0xbf5ec765} }, +/**/ {{0x73bb17c5, 0x3beb1a66} },}, +/**/ {{{0xcfec40a8, 0xbf5e8746} }, +/**/ {{0xb5e5a553, 0x3bf11af5} },}, +/**/ {{{0x617ad077, 0xbf5e4728} }, +/**/ {{0xf57dd14f, 0x3bfb2cad} },}, +/**/ {{{0x33460b45, 0xbf5e070a} }, +/**/ {{0x4902c8d5, 0xbbf8db75} },}, +/**/ {{{0x454d705f, 0xbf5dc6ec} }, +/**/ {{0xe8a41057, 0x3bef5cc6} },}, +/**/ {{{0x97907f0f, 0xbf5d86ce} }, +/**/ {{0xdf8672ef, 0x3bed8277} },}, +/**/ {{{0x2a0eb6a3, 0xbf5d46b1} }, +/**/ {{0x3717e5ee, 0xbbc2f9c2} },}, +/**/ {{{0xfcc7966b, 0xbf5d0693} }, +/**/ {{0xab4852c6, 0x3bf4deed} },}, +/**/ {{{0x0fba9db6, 0xbf5cc677} }, +/**/ {{0x9db2a368, 0xbbf3a2b4} },}, +/**/ {{{0x62e74bd8, 0xbf5c865a} }, +/**/ {{0x58fa0c24, 0xbbd2c51d} },}, +/**/ {{{0xf64d2024, 0xbf5c463d} }, +/**/ {{0xe3a09391, 0x3bf838ca} },}, +/**/ {{{0xc9eb99ee, 0xbf5c0621} }, +/**/ {{0x61b7de71, 0xbbdc2a9e} },}, +/**/ {{{0xddc2388e, 0xbf5bc605} }, +/**/ {{0x4accb195, 0xbbea9808} },}, +/**/ {{{0x31d07b5c, 0xbf5b85ea} }, +/**/ {{0x032e030b, 0xbbd811a2} },}, +/**/ {{{0xc615e1b1, 0xbf5b45ce} }, +/**/ {{0x821e0b81, 0xbbfd5427} },}, +/**/ {{{0x9a91eaea, 0xbf5b05b3} }, +/**/ {{0x2619306b, 0x3bfffeba} },}, +/**/ {{{0xaf441661, 0xbf5ac598} }, +/**/ {{0x9eac7d15, 0x3bd22824} },}, +/**/ {{{0x042be376, 0xbf5a857e} }, +/**/ {{0x24893f0e, 0x3bc20736} },}, +/**/ {{{0x9948d188, 0xbf5a4563} }, +/**/ {{0x04d734cd, 0xbbf58ab4} },}, +/**/ {{{0x6e9a5ff9, 0xbf5a0549} }, +/**/ {{0x5723a6c3, 0xbbf22673} },}, +/**/ {{{0x84200e2c, 0xbf59c52f} }, +/**/ {{0xa538e8e1, 0x3bfc81da} },}, +/**/ {{{0xd9d95b83, 0xbf598515} }, +/**/ {{0x2a8e3feb, 0xbbfa1a37} },}, +/**/ {{{0x6fc5c767, 0xbf5944fc} }, +/**/ {{0x385159f9, 0x3bf8e1ce} },}, +/**/ {{{0x45e4d13c, 0xbf5904e3} }, +/**/ {{0x1567c7a7, 0xbbfc4737} },}, +/**/ {{{0x5c35f86e, 0xbf58c4ca} }, +/**/ {{0x23c9ae0c, 0x3bf41581} },}, +/**/ {{{0xb2b8bc65, 0xbf5884b1} }, +/**/ {{0x2b66cfb6, 0x3bf70c2c} },}, +/**/ {{{0x496c9c8d, 0xbf584499} }, +/**/ {{0xe5a11e3e, 0xbbdb9042} },}, +/**/ {{{0x20511854, 0xbf580481} }, +/**/ {{0x61bcb040, 0xbbf9cf9d} },}, +/**/ {{{0x3765af29, 0xbf57c469} }, +/**/ {{0xe26a419b, 0xbbf65ceb} },}, +/**/ {{{0x8ea9e07c, 0xbf578451} }, +/**/ {{0xb70a4088, 0xbbf1c2f5} },}, +/**/ {{{0x261d2bbf, 0xbf57443a} }, +/**/ {{0x29704ba7, 0xbbbc7b8f} },}, +/**/ {{{0xfdbf1065, 0xbf570422} }, +/**/ {{0x433ccb3b, 0x3bca0a54} },}, +/**/ {{{0x158f0de3, 0xbf56c40c} }, +/**/ {{0x207cde2d, 0x3bd9e257} },}, +/**/ {{{0x6d8ca3af, 0xbf5683f5} }, +/**/ {{0xf7b51b49, 0xbbef17a4} },}, +/**/ {{{0x05b75142, 0xbf5643df} }, +/**/ {{0x9d345bf8, 0x3be28239} },}, +/**/ {{{0xde0e9614, 0xbf5603c8} }, +/**/ {{0x0918d1bf, 0xbbde6c21} },}, +/**/ {{{0xf691f1a1, 0xbf55c3b2} }, +/**/ {{0x377de4c8, 0x3bd37d78} },}, +/**/ {{{0x4f40e365, 0xbf55839d} }, +/**/ {{0xbbf7c9d1, 0x3bf52b7d} },}, +/**/ {{{0xe81aeadd, 0xbf554387} }, +/**/ {{0x679c3d9a, 0xbbf0be6a} },}, +/**/ {{{0xc11f878a, 0xbf550372} }, +/**/ {{0xb6cdd88e, 0xbbdd9e20} },}, +/**/ {{{0xda4e38ec, 0xbf54c35d} }, +/**/ {{0x09302da0, 0xbbe3b1e7} },}, +/**/ {{{0x33a67e86, 0xbf548349} }, +/**/ {{0x085b922d, 0x3be8cba8} },}, +/**/ {{{0xcd27d7db, 0xbf544334} }, +/**/ {{0xf024ab43, 0xbba5f2c9} },}, +/**/ {{{0xa6d1c471, 0xbf540320} }, +/**/ {{0xf686cf3d, 0xbbeb31f3} },}, +/**/ {{{0xc0a3c3cf, 0xbf53c30c} }, +/**/ {{0xd4ad32f6, 0xbbf74ffe} },}, +/**/ {{{0x1a9d557e, 0xbf5382f9} }, +/**/ {{0x4acb368f, 0x3bd2e555} },}, +/**/ {{{0xb4bdf907, 0xbf5342e5} }, +/**/ {{0x07812806, 0x3be13442} },}, +/**/ {{{0x8f052df6, 0xbf5302d2} }, +/**/ {{0x70b1e756, 0x3bf5f429} },}, +/**/ {{{0xa97273d7, 0xbf52c2bf} }, +/**/ {{0x43a03fff, 0xbbf20aa3} },}, +/**/ {{{0x04054a3a, 0xbf5282ad} }, +/**/ {{0x8bebd7ad, 0xbbed4d57} },}, +/**/ {{{0x9ebd30ae, 0xbf52429a} }, +/**/ {{0x5a71c5a4, 0xbbff9529} },}, +/**/ {{{0x7999a6c6, 0xbf520288} }, +/**/ {{0x54100f9e, 0x3bfb055a} },}, +/**/ {{{0x949a2c12, 0xbf51c276} }, +/**/ {{0xa2e9f1b4, 0xbbff6978} },}, +/**/ {{{0xefbe402a, 0xbf518264} }, +/**/ {{0xbc188323, 0x3bf01fb9} },}, +/**/ {{{0x8b0562a1, 0xbf514253} }, +/**/ {{0x957bf23a, 0xbbf7c87c} },}, +/**/ {{{0x666f1311, 0xbf510242} }, +/**/ {{0xc8be6880, 0x3bdc2cb9} },}, +/**/ {{{0x81fad111, 0xbf50c231} }, +/**/ {{0x07ba000d, 0xbbf59fc1} },}, +/**/ {{{0xdda81c3d, 0xbf508220} }, +/**/ {{0xbf5c8a0b, 0xbbf06a0a} },}, +/**/ {{{0x79767431, 0xbf504210} }, +/**/ {{0xa9a705bc, 0x3bf3a6cf} },}, +/**/ {{{0x55655889, 0xbf500200} }, +/**/ {{0xbf0fa436, 0xbbe9abe6} },}, +/**/ {{{0xe2e891cc, 0xbf4f83e0} }, +/**/ {{0x1b81bf62, 0x3be4aa59} },}, +/**/ {{{0x9b4589ce, 0xbf4f03c1} }, +/**/ {{0x8a47f50a, 0xbbe60518} },}, +/**/ {{{0xd3e0985f, 0xbf4e83a2} }, +/**/ {{0x5ef17e96, 0x3bed32d8} },}, +/**/ {{{0x8cb8bcc3, 0xbf4e0384} }, +/**/ {{0xf09afa4d, 0xbbeb7b30} },}, +/**/ {{{0xc5ccf647, 0xbf4d8366} }, +/**/ {{0xf586cec2, 0xbbd527fc} },}, +/**/ {{{0x7f1c4437, 0xbf4d0349} }, +/**/ {{0x4a686886, 0x3bc2bcf0} },}, +/**/ {{{0xb8a5a5e3, 0xbf4c832c} }, +/**/ {{0x721c2ebe, 0x3bc98f93} },}, +/**/ {{{0x72681a9e, 0xbf4c0310} }, +/**/ {{0xb5308d22, 0xbbe20f00} },}, +/**/ {{{0xac62a1bf, 0xbf4b82f4} }, +/**/ {{0x9737b561, 0xbbe1edd0} },}, +/**/ {{{0x66943a9f, 0xbf4b02d9} }, +/**/ {{0x23f894a1, 0xbbcc950b} },}, +/**/ {{{0xa0fbe49a, 0xbf4a82be} }, +/**/ {{0x866bc982, 0xbb81da04} },}, +/**/ {{{0x5b989f0f, 0xbf4a02a4} }, +/**/ {{0x9d76196e, 0xbbd9114d} },}, +/**/ {{{0x96696961, 0xbf49828a} }, +/**/ {{0xd3292fd6, 0x3bc10d20} },}, +/**/ {{{0x516d42f4, 0xbf490271} }, +/**/ {{0x2e9a5dd5, 0xbbee53a3} },}, +/**/ {{{0x8ca32b32, 0xbf488258} }, +/**/ {{0xd18f8004, 0xbbc55af5} },}, +/**/ {{{0x480a2185, 0xbf480240} }, +/**/ {{0xa9b0178a, 0xbbb32d23} },}, +/**/ {{{0x83a1255c, 0xbf478228} }, +/**/ {{0x8152093a, 0x3be84cc3} },}, +/**/ {{{0x3f673627, 0xbf470211} }, +/**/ {{0xf4881c71, 0xbbd0055a} },}, +/**/ {{{0x7b5b535c, 0xbf4681fa} }, +/**/ {{0xb98336ea, 0x3bd2b73f} },}, +/**/ {{{0x377c7c71, 0xbf4601e4} }, +/**/ {{0x2ed05089, 0xbbcdcbed} },}, +/**/ {{{0x73c9b0e1, 0xbf4581ce} }, +/**/ {{0x61414697, 0xbbdda0c2} },}, +/**/ {{{0x3041f02a, 0xbf4501b9} }, +/**/ {{0x22f8b33c, 0x3bee5d53} },}, +/**/ {{{0x6ce439ca, 0xbf4481a4} }, +/**/ {{0x9c25c999, 0xbbe5512f} },}, +/**/ {{{0x29af8d47, 0xbf440190} }, +/**/ {{0xa4df0dfd, 0x3b7f48c2} },}, +/**/ {{{0x66a2ea26, 0xbf43817c} }, +/**/ {{0x517febd8, 0x3bd157c0} },}, +/**/ {{{0x23bd4ff0, 0xbf430169} }, +/**/ {{0x0176d244, 0xbbe2e229} },}, +/**/ {{{0x60fdbe33, 0xbf428156} }, +/**/ {{0x175812b3, 0x3be64664} },}, +/**/ {{{0x1e63347c, 0xbf420144} }, +/**/ {{0xd9355524, 0xbbe39ab4} },}, +/**/ {{{0x5becb260, 0xbf418132} }, +/**/ {{0xb6e1edc9, 0x3be74b27} },}, +/**/ {{{0x19993772, 0xbf410121} }, +/**/ {{0x393ab56a, 0xbbaa390b} },}, +/**/ {{{0x5767c34c, 0xbf408110} }, +/**/ {{0xf8c7783b, 0x3bd128e6} },}, +/**/ {{{0x15575589, 0xbf400100} }, +/**/ {{0xf23ef222, 0x3bec8863} },}, +/**/ {{{0xa6cddb8d, 0xbf3f01e0} }, +/**/ {{0xcdd29c3f, 0x3b8a9419} },}, +/**/ {{{0x232b174e, 0xbf3e01c2} }, +/**/ {{0xd5f5b191, 0xbbc7cf55} },}, +/**/ {{{0x9fc45d9e, 0xbf3d01a4} }, +/**/ {{0xb5038e7e, 0x3bddc58f} },}, +/**/ {{{0x1c97adca, 0xbf3c0188} }, +/**/ {{0xbb933e41, 0x3bc0238d} },}, +/**/ {{{0x99a30728, 0xbf3b016c} }, +/**/ {{0xc3c43664, 0xbbabde04} },}, +/**/ {{{0x16e46913, 0xbf3a0152} }, +/**/ {{0x5adc3673, 0x3bafe081} },}, +/**/ {{{0x9459d2eb, 0xbf390138} }, +/**/ {{0xc2a33d26, 0xbbd949da} },}, +/**/ {{{0x12014418, 0xbf380120} }, +/**/ {{0xf76e0326, 0xbbd3acbc} },}, +/**/ {{{0x8fd8bc07, 0xbf370108} }, +/**/ {{0x4cd6ce34, 0x3bdbde09} },}, +/**/ {{{0x0dde3a29, 0xbf3600f2} }, +/**/ {{0x05442a35, 0xbbb0bc28} },}, +/**/ {{{0x8c0fbdf9, 0xbf3500dc} }, +/**/ {{0x0908cbf7, 0x3bd21c68} },}, +/**/ {{{0x0a6b46f4, 0xbf3400c8} }, +/**/ {{0x0f107564, 0xbbdbd35e} },}, +/**/ {{{0x88eed4a1, 0xbf3300b4} }, +/**/ {{0x49a3dcb8, 0xbbc22067} },}, +/**/ {{{0x0798668a, 0xbf3200a2} }, +/**/ {{0xe7c5d0e5, 0x3bcdb7f0} },}, +/**/ {{{0x8665fc3f, 0xbf310090} }, +/**/ {{0xc7f9d69c, 0xbbd00add} },}, +/**/ {{{0x05559559, 0xbf300080} }, +/**/ {{0xa0e20e2f, 0x3bddd332} },}, +/**/ {{{0x08ca62e5, 0xbf2e00e1} }, +/**/ {{0x3a04bb77, 0xbbb15ff9} },}, +/**/ {{{0x0725a061, 0xbf2c00c4} }, +/**/ {{0xcc052f3e, 0x3bc88ab0} },}, +/**/ {{{0x05b8e275, 0xbf2a00a9} }, +/**/ {{0xf5f3cbcf, 0xbbcbba1a} },}, +/**/ {{{0x04802882, 0xbf280090} }, +/**/ {{0xa5bd7bd0, 0x3bcec900} },}, +/**/ {{{0x037771ef, 0xbf260079} }, +/**/ {{0x9b7b54fa, 0x3bb77ea0} },}, +/**/ {{{0x029abe33, 0xbf240064} }, +/**/ {{0x3ae68d18, 0xbbc1bbf0} },}, +/**/ {{{0x01e60cd1, 0xbf220051} }, +/**/ {{0x2b45cfcd, 0x3bb1dcd9} },}, +/**/ {{{0x01555d56, 0xbf200040} }, +/**/ {{0x863f53f6, 0x3bcddd88} },}, +/**/ {{{0x01c95eb7, 0xbf1c0062} }, +/**/ {{0xaa4dfd9a, 0x3bbd88f7} },}, +/**/ {{{0x01200510, 0xbf180048} }, +/**/ {{0x4f3db50b, 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{{{0x0ddc70a1, 0x3f35ff0e} }, +/**/ {{0xd97a3c05, 0x3bacf6f3} },}, +/**/ {{{0x8fd69976, 0x3f36fef7} }, +/**/ {{0x6f810a3c, 0x3bab2dcf} },}, +/**/ {{{0x11febc18, 0x3f37fee0} }, +/**/ {{0xf5d3f323, 0x3bd2b9bc} },}, +/**/ {{{0x9456d7fb, 0x3f38fec7} }, +/**/ {{0x6eaa1d6a, 0xbbbfb258} },}, +/**/ {{{0x16e0ec8b, 0x3f39feae} }, +/**/ {{0xceeb34b1, 0xbbb6137a} },}, +/**/ {{{0x999ef930, 0x3f3afe93} }, +/**/ {{0xdc639b08, 0xbbde70e0} },}, +/**/ {{{0x1c92fd4a, 0x3f3bfe78} }, +/**/ {{0x713cc126, 0xbbc4ed10} },}, +/**/ {{{0x9fbef835, 0x3f3cfe5b} }, +/**/ {{0xcc0e81bd, 0xbb873d63} },}, +/**/ {{{0x2324e946, 0x3f3dfe3e} }, +/**/ {{0x62dd5deb, 0x3bc09164} },}, +/**/ {{{0xa6c6cfcc, 0x3f3efe1f} }, +/**/ {{0x3512d15c, 0x3bdac2da} },}, +/**/ {{{0x2aa6ab11, 0x3f3ffe00} }, +/**/ {{0x62cc632d, 0x3b999e2b} },}, +/**/ {{{0xd7633d2c, 0x3f407eef} }, +/**/ {{0x63ff6024, 0xbbebc98b} },}, +/**/ {{{0x19941e6e, 0x3f40fedf} }, +/**/ {{0xe0aa6338, 0xbbb194c2} },}, +/**/ {{{0xdbe6f8eb, 0x3f417ecd} }, +/**/ {{0x57b0f571, 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{{{0x62ac7a09, 0x3f4f7c20} }, +/**/ {{0x17802a46, 0x3b5c8123} },}, +/**/ {{{0xaa8ab110, 0x3f4ffc00} }, +/**/ {{0xeb9b6cdb, 0xbbe0fecb} },}, +/**/ {{{0x3954680f, 0x3f503df0} }, +/**/ {{0x1c693678, 0x3bdac89b} },}, +/**/ {{{0xdd83eb3a, 0x3f507ddf} }, +/**/ {{0x0a75ad5f, 0xbbf638f6} },}, +/**/ {{{0x41d461a5, 0x3f50bdcf} }, +/**/ {{0x45f05b10, 0x3bfd4bc9} },}, +/**/ {{{0x66464aef, 0x3f50fdbe} }, +/**/ {{0x6abbf59c, 0xbbbd0554} },}, +/**/ {{{0x4ada26b1, 0x3f513dad} }, +/**/ {{0x6036fe6f, 0x3be38c65} },}, +/**/ {{{0xef907485, 0x3f517d9b} }, +/**/ {{0xf158bbc3, 0x3bfdc8a1} },}, +/**/ {{{0x5469b404, 0x3f51bd8a} }, +/**/ {{0x55632e3f, 0xbbdea231} },}, +/**/ {{{0x796664c3, 0x3f51fd78} }, +/**/ {{0x2edb73c2, 0xbbe00849} },}, +/**/ {{{0x5e870657, 0x3f523d66} }, +/**/ {{0x0789343e, 0x3bfba943} },}, +/**/ {{{0x03cc1855, 0x3f527d54} }, +/**/ {{0xeafafc52, 0x3bc5f644} },}, +/**/ {{{0x69361a4e, 0x3f52bd41} }, +/**/ {{0xa4a6e79f, 0xbbf2f743} },}, +/**/ {{{0x8ec58bd2, 0x3f52fd2e} }, +/**/ {{0x5ceb1abf, 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{{{0x6dbb3de1, 0x3f59fab9} }, +/**/ {{0x7a8be031, 0xbbf11464} },}, +/**/ {{{0x5860fa8a, 0x3f5a3a9f} }, +/**/ {{0x470dbe32, 0x3beae9e7} },}, +/**/ {{{0x033b16f8, 0x3f5a7a85} }, +/**/ {{0xda1f8579, 0x3bfc4721} },}, +/**/ {{{0x6e4a128e, 0x3f5aba6a} }, +/**/ {{0x029258ce, 0xbbf41852} },}, +/**/ {{{0x998e6cab, 0x3f5afa4f} }, +/**/ {{0x2eb18782, 0xbbf28584} },}, +/**/ {{{0x8508a4af, 0x3f5b3a34} }, +/**/ {{0x23241a2c, 0xbbea7970} },}, +/**/ {{{0x30b939f8, 0x3f5b7a19} }, +/**/ {{0x600551b6, 0xbbf1d8db} },}, +/**/ {{{0x9ca0abe2, 0x3f5bb9fd} }, +/**/ {{0x8c26cc71, 0xbbeaa412} },}, +/**/ {{{0xc8bf79c8, 0x3f5bf9e1} }, +/**/ {{0x30427cfc, 0xbbe7f81b} },}, +/**/ {{{0xb5162303, 0x3f5c39c5} }, +/**/ {{0xd1f134e1, 0x3bd9ec5f} },}, +/**/ {{{0x61a526eb, 0x3f5c79a9} }, +/**/ {{0x8980e47d, 0x3bff0cb0} },}, +/**/ {{{0xce6d04d7, 0x3f5cb98c} }, +/**/ {{0xe84ca4e2, 0x3bf35aca} },}, +/**/ {{{0xfb6e3c1b, 0x3f5cf96f} }, +/**/ {{0x1b0bd69f, 0x3bf9b1b8} },}, +/**/ {{{0xe8a94c0b, 0x3f5d3952} }, +/**/ {{0x3ce51832, 0x3be21310} },}, +/**/ {{{0x961eb3f8, 0x3f5d7935} }, +/**/ {{0x840c58ce, 0x3bf90786} },}, +/**/ {{{0x03cef334, 0x3f5db918} }, +/**/ {{0xf2dfb3f4, 0xbbfe0048} },}, +/**/ {{{0x31ba890b, 0x3f5df8fa} }, +/**/ {{0x3e295bec, 0x3bfcf652} },}, +/**/ {{{0x1fe1f4ce, 0x3f5e38dc} }, +/**/ {{0x151c9300, 0xbbfc5ebe} },}, +/**/ {{{0xce45b5c6, 0x3f5e78bd} }, +/**/ {{0x8a25b9c7, 0xbbef2cc4} },}, +/**/ {{{0x3ce64b3e, 0x3f5eb89f} }, +/**/ {{0xa6fea7bd, 0x3bfe6d27} },}, +/**/ {{{0x6bc43481, 0x3f5ef880} }, +/**/ {{0x914a6dab, 0xbbf68037} },}, +/**/ {{{0x5adff0d4, 0x3f5f3861} }, +/**/ {{0xf909e0e6, 0xbbf1d2f3} },}, +/**/ {{{0x0a39ff7e, 0x3f5f7842} }, +/**/ {{0xff1e1f71, 0xbbf64661} },}, +/**/ {{{0x79d2dfc3, 0x3f5fb822} }, +/**/ {{0x5a6f9e9a, 0xbbd76ce8} },}, +/**/ {{{0xa9ab10e6, 0x3f5ff802} }, +/**/ {{0xa153e3b2, 0x3bfe29e3} },}, +/**/ {{{0x4ce18915, 0x3f601bf1} }, +/**/ {{0xa3a73044, 0xbbe57c28} },}, +/**/ {{{0x250db166, 0x3f603be1} }, +/**/ {{0xc1ad9590, 0x3c0fd271} },}, +/**/ {{{0xdd5a4107, 0x3f605bd0} }, +/**/ {{0xc424c676, 0x3bfe4b5d} },}, +/**/ {{{0x75c77796, 0x3f607bc0} }, +/**/ {{0xc0eff1ba, 0xbc068804} },}, +/**/ {{{0xee5594b0, 0x3f609baf} }, +/**/ {{0x51dbded5, 0xbc0ff798} },}, +/**/ {{{0x4704d7f2, 0x3f60bb9f} }, +/**/ {{0x2d5aba70, 0xbbf70ef4} },}, +/**/ {{{0x7fd580f9, 0x3f60db8e} }, +/**/ {{0x7ae804b5, 0xbbeccb65} },}, +/**/ {{{0x98c7cf60, 0x3f60fb7d} }, +/**/ {{0x1775134d, 0x3bfede2f} },}, +/**/ {{{0x91dc02c3, 0x3f611b6c} }, +/**/ {{0x91ca4a67, 0xbc04d41e} },}, +/**/ {{{0x6b125aba, 0x3f613b5b} }, +/**/ {{0x4a12201d, 0x3bfe6d0c} },}, +/**/ {{{0x246b16e0, 0x3f615b4a} }, +/**/ {{0x4d4238d3, 0x3bfe507d} },}, +/**/ {{{0xbde676cd, 0x3f617b38} }, +/**/ {{0x0640462a, 0x3bfe0272} },}, +/**/ {{{0x3784ba19, 0x3f619b27} }, +/**/ {{0x02285659, 0x3bd94ab3} },}, +/**/ {{{0x9146205b, 0x3f61bb15} }, +/**/ {{0x1cc35b7b, 0xbbff1e2e} },}, +/**/ {{{0xcb2ae929, 0x3f61db03} }, +/**/ {{0x12f6bf8d, 0xbc03ee8e} },}, +/**/ {{{0xe5335418, 0x3f61faf1} }, +/**/ {{0x7b7d619b, 0x3c0bae5f} },}, +/**/ {{{0xdf5fa0bf, 0x3f621adf} }, +/**/ {{0xb3b731b0, 0xbbf5546a} },}, +/**/ {{{0xb9b00eb0, 0x3f623acd} }, +/**/ {{0x105fd253, 0xbbafb2b0} },}, +/**/ {{{0x7424dd7f, 0x3f625abb} }, +/**/ {{0xca53444b, 0x3c011647} },}, +/**/ {{{0x0ebe4cbf, 0x3f627aa9} }, +/**/ {{0x592f3be8, 0x3c01678f} },}, +/**/ {{{0x897c9c02, 0x3f629a96} }, +/**/ {{0x4347451d, 0xbbef2b12} },}, +/**/ {{{0xe4600ad8, 0x3f62ba83} }, +/**/ {{0xb2a477bc, 0x3bfb5bb7} },}, +/**/ {{{0x1f68d8d3, 0x3f62da71} }, +/**/ {{0x7a5822e4, 0xbc0590e1} },}, +/**/ {{{0x3a974581, 0x3f62fa5e} }, +/**/ {{0x53123101, 0xbbf0f2e5} },}, +/**/ {{{0x35eb9072, 0x3f631a4b} }, +/**/ {{0x0e3f5fde, 0xbc018db4} },}, +/**/ {{{0x1165f933, 0x3f633a38} }, +/**/ {{0x8d0afb38, 0x3c0921d5} },}, +/**/ {{{0xcd06bf53, 0x3f635a24} }, +/**/ {{0xb5791b80, 0x3c01f6ba} },}, +/**/ {{{0x68ce225e, 0x3f637a11} }, +/**/ {{0xa1894236, 0x3bde2af8} },}, +/**/ {{{0xe4bc61e0, 0x3f6399fd} }, +/**/ {{0xd0f06ff3, 0xbc062a48} },}, +/**/ {{{0x40d1bd63, 0x3f63b9ea} }, +/**/ {{0x4b4f9c11, 0x3bffc80c} },}, +/**/ {{{0x7d0e7473, 0x3f63d9d6} }, +/**/ {{0x6a92c891, 0x3c02219b} },}, +/**/ {{{0x9972c699, 0x3f63f9c2} }, +/**/ {{0x790ade9e, 0x3c0d3590} },}, +/**/ {{{0x95fef35f, 0x3f6419ae} }, +/**/ {{0x792a458c, 0xbc01c279} },}, +/**/ {{{0x72b33a4b, 0x3f64399a} }, +/**/ {{0x327bffae, 0x3c02ce64} },}, +/**/ {{{0x2f8fdae7, 0x3f645986} }, +/**/ {{0xd231155c, 0xbc070aec} },}, +/**/ {{{0xcc9514b7, 0x3f647971} }, +/**/ {{0xe4bbf776, 0x3c0f373d} },}, +/**/ {{{0x49c32744, 0x3f64995d} }, +/**/ {{0xbf22b2a7, 0xbbf6d7e5} },}, +/**/ {{{0xa71a5211, 0x3f64b948} }, +/**/ {{0x64fe2936, 0xbbedec69} },}, +/**/ {{{0xe49ad4a3, 0x3f64d933} }, +/**/ {{0xabee4257, 0x3bf5fc4b} },}, +/**/ {{{0x0244ee7e, 0x3f64f91f} }, +/**/ {{0x3cd1474f, 0x3c0c6fe3} },}, +/**/ {{{0x0018df26, 0x3f65190a} }, +/**/ {{0xd11e7fa5, 0xbc023957} },}, +/**/ {{{0xde16e61b, 0x3f6538f4} }, +/**/ {{0x55380346, 0x3c006c31} },}, +/**/ {{{0x9c3f42e1, 0x3f6558df} }, +/**/ {{0xc4a5134c, 0xbc09b7d4} },}, +/**/ {{{0x3a9234f7, 0x3f6578ca} }, +/**/ {{0x2772c19c, 0xbc0e3f10} },}, +/**/ {{{0xb90ffbdd, 0x3f6598b4} }, +/**/ {{0x5592b468, 0x3be6f110} },}, +/**/ {{{0x17b8d714, 0x3f65b89f} }, +/**/ {{0xb251ace2, 0xbc0a5fea} },}, +/**/ {{{0x568d0619, 0x3f65d889} }, +/**/ {{0x315da285, 0xbc0aacc9} },}, +/**/ {{{0x758cc86a, 0x3f65f873} }, +/**/ {{0xba64d81a, 0xbbeb0782} },}, +/**/ {{{0x74b85d85, 0x3f66185d} }, +/**/ {{0x8e1eb3fa, 0xbc09b459} },}, +/**/ {{{0x541004e5, 0x3f663847} }, +/**/ {{0x1d86e863, 0x3bce9c22} },}, +/**/ {{{0x1393fe07, 0x3f665831} }, +/**/ {{0xcf37ee90, 0xbbfbeb77} },}, +/**/ {{{0xb3448865, 0x3f66781a} }, +/**/ {{0xc252e3c9, 0xbc02dc68} },}, +/**/ {{{0x3321e379, 0x3f669804} }, +/**/ {{0xb40b3741, 0xbbe73a0b} },}, + }; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/upow.h b/REORG.TODO/sysdeps/ieee754/dbl-64/upow.h new file mode 100644 index 0000000000..9dcbd3eb2b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/upow.h @@ -0,0 +1,76 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:upow.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef UPOW_H +#define UPOW_H + +#include "mydefs.h" + +#ifdef BIG_ENDI + const static mynumber +/**/ nZERO = {{0x80000000, 0}}, /* -0.0 */ +/**/ INF = {{0x7ff00000, 0x00000000}}, /* INF */ +/**/ nINF = {{0xfff00000, 0x00000000}}, /* -INF */ +/**/ ln2a = {{0x3fe62e42, 0xfefa3800}}, /* ln(2) 43 bits */ +/**/ ln2b = {{0x3d2ef357, 0x93c76730}}, /* ln(2)-ln2a */ +/**/ bigu = {{0x4297ffff, 0xfffffd2c}}, /* 1.5*2**42 -724*2**-10 */ +/**/ bigv = {{0x4207ffff, 0xfff8016a}}, /* 1.5*2**33-1+362*2**-19 */ +/**/ t52 = {{0x43300000, 0x00000000}}, /* 2**52 */ +/**/ two52e = {{0x43300000, 0x000003ff}}; /* 2**52' */ + +#else +#ifdef LITTLE_ENDI + const static mynumber +/**/ nZERO = {{0, 0x80000000}}, /* -0.0 */ +/**/ INF = {{0x00000000, 0x7ff00000}}, /* INF */ +/**/ nINF = {{0x00000000, 0xfff00000}}, /* -INF */ +/**/ ln2a = {{0xfefa3800, 0x3fe62e42}}, /* ln(2) 43 bits */ +/**/ ln2b = {{0x93c76730, 0x3d2ef357}}, /* ln(2)-ln2a */ +/**/ bigu = {{0xfffffd2c, 0x4297ffff}}, /* 1.5*2**42 -724*2**-10 */ +/**/ bigv = {{0xfff8016a, 0x4207ffff}}, /* 1.5*2**33-1+362*2**-19 */ +/**/ t52 = {{0x00000000, 0x43300000}}, /* 2**52 */ +/**/ two52e = {{0x000003ff, 0x43300000}}; /* 2**52' */ + +#endif +#endif + +const static double p2=-0.5, p3 = 3.3333333333333333333e-1, p4 = -0.25, + q2 = -0.5, q3 = 3.3333333333331404e-01, q4 = -2.4999999999996436e-01, + q5 = 2.0000010500004459e-01, q6 = -1.6666678916688004e-01, + r3 = 3.33333333333333333372884096563030E-01, + r4 = -2.50000000000000000213574153875908E-01, + r5 = 1.99999999999683593814072199830603E-01, + r6 = -1.66666666666065494878165510225378E-01, + r7 = 1.42857517857114380606360005067609E-01, + r8 = -1.25000449999974370683775964001702E-01, + s3 = 0.333251953125000000e0, + ss3 = 8.138020833333333333e-05, + s4 = -2.500000000000000000e-01, + s5 = 1.999999999999960937e-01, + s6 = -1.666666666666592447e-01, + s7 = 1.428571845238194705e-01, + s8 = -1.250000500000149097e-01; +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/upow.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/upow.tbl new file mode 100644 index 0000000000..f92c69c521 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/upow.tbl @@ -0,0 +1,10188 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE upow() FUNCTION */ +/****************************************************************/ + + + +#ifdef BIG_ENDI +static const union {int4 i[5800]; double x[2900];} ui = { .i = { +/**/ 0x3FF6A000, 0x00000000, +/**/ 0x3F33CD15, 0x3729043E, +/**/ 0xBFD63003, 0x0B3AB000, +/**/ 0x3D2DB623, 0xE731AE00, +/**/ 0x3FF69800, 0x00000000, +/**/ 0x3F33F349, 0xCC7267D0, +/**/ 0xBFD61965, 0xCDB03000, +/**/ 0x3D2F08AD, 0x603C488E, +/**/ 0x3FF69000, 0x00000000, +/**/ 0x3F3473A8, 0x8D0BFD2E, +/**/ 0xBFD602D0, 0x8AF09000, +/**/ 0xBD1EBE91, 0x76DF3F65, +/**/ 0x3FF68800, 0x00000000, +/**/ 0x3F354DD2, 0x390B9ED0, +/**/ 0xBFD5EC43, 0x3D5C3000, +/**/ 0xBD36B71A, 0x1229D17F, +/**/ 0x3FF68000, 0x00000000, +/**/ 0x3F368168, 0x16816817, +/**/ 0xBFD5D5BD, 0xDF596000, +/**/ 0x3D0A0B2A, 0x08A465DC, +/**/ 0x3FF67800, 0x00000000, +/**/ 0x3F380E0B, 0xF08C7765, +/**/ 0xBFD5BF40, 0x6B544000, +/**/ 0x3D227023, 0xEB68981C, +/**/ 0x3FF67000, 0x00000000, +/**/ 0x3F39F360, 0x16719F36, +/**/ 0xBFD5A8CA, 0xDBBEE000, +/**/ 0x3CF7C79B, 0x0AF7ECF8, +/**/ 0x3FF66800, 0x00000000, +/**/ 0x3F3C3107, 0x5AB40167, +/**/ 0xBFD5925D, 0x2B113000, +/**/ 0x3D369BF5, 0xA7A56F34, +/**/ 0x3FF66000, 0x00000000, +/**/ 0x3F3EC6A5, 0x122F9016, +/**/ 0xBFD57BF7, 0x53C8D000, +/**/ 0xBD1FADED, 0xEE5D40EF, +/**/ 0x3FF65C00, 0x00000000, +/**/ 0xBF3E4C22, 0xECCA9097, +/**/ 0xBFD56599, 0x50695000, +/**/ 0xBD14C5FD, 0x2BADC774, +/**/ 0x3FF65400, 0x00000000, +/**/ 0xBF3B07AC, 0x4B55CC62, +/**/ 0xBFD54F43, 0x1B7BE000, +/**/ 0xBD1A8954, 0xC0910952, +/**/ 0x3FF64C00, 0x00000000, +/**/ 0xBF376C52, 0x32DA090E, +/**/ 0xBFD538F4, 0xAF8F7000, +/**/ 0xBD27EC02, 0xE45547CE, +/**/ 0x3FF64400, 0x00000000, +/**/ 0xBF337A6F, 0x4DE9BD38, +/**/ 0xBFD522AE, 0x0738A000, +/**/ 0xBD2EBE70, 0x8164C759, +/**/ 0x3FF63C00, 0x00000000, +/**/ 0xBF2E64BB, 0x923C708B, +/**/ 0xBFD50C6F, 0x1D11C000, +/**/ 0x3D3A0E6B, 0x7E827C2C, +/**/ 0x3FF63400, 0x00000000, +/**/ 0xBF2528EE, 0xA7E43FD4, +/**/ 0xBFD4F637, 0xEBBAA000, +/**/ 0x3D3FC158, 0xCB3124B9, +/**/ 0x3FF62C00, 0x00000000, +/**/ 0xBF168454, 0x86689DF7, +/**/ 0xBFD4E008, 0x6DD8C000, +/**/ 0x3D34D692, 0xA1E44788, +/**/ 0x3FF62400, 0x00000000, +/**/ 0xBED623FA, 0x77016240, +/**/ 0xBFD4C9E0, 0x9E173000, +/**/ 0x3D2E2089, 0x1B0AD8A4, +/**/ 0x3FF61C00, 0x00000000, +/**/ 0x3F151300, 0x58715130, +/**/ 0xBFD4B3C0, 0x77268000, +/**/ 0x3D165B46, 0x81052B9F, +/**/ 0x3FF61400, 0x00000000, +/**/ 0x3F266D06, 0x35D2754E, +/**/ 0xBFD49DA7, 0xF3BCC000, +/**/ 0xBD307B33, 0x4DAF4B9A, +/**/ 0x3FF60C00, 0x00000000, +/**/ 0x3F317C61, 0xDA197F23, +/**/ 0xBFD48797, 0x0E958000, +/**/ 0xBD3DC1B8, 0x465CF25F, +/**/ 0x3FF60400, 0x00000000, +/**/ 0x3F381605, 0x81605816, +/**/ 0xBFD4718D, 0xC271C000, +/**/ 0xBD306C18, 0xFB4C14C5, +/**/ 0x3FF5FC00, 0x00000000, +/**/ 0x3F3F0317, 0xB5C6F559, +/**/ 0xBFD45B8C, 0x0A17E000, +/**/ 0x3D0D9120, 0xE7D0A853, +/**/ 0x3FF5F800, 0x00000000, +/**/ 0xBF39BCBD, 0x6D2041E3, +/**/ 0xBFD44591, 0xE053A000, +/**/ 0x3D06E958, 0x92923D88, +/**/ 0x3FF5F000, 0x00000000, +/**/ 0xBF3229CF, 0x5604CC40, +/**/ 0xBFD42F9F, 0x3FF62000, +/**/ 0xBD390644, 0x0F7D3354, +/**/ 0x3FF5E800, 0x00000000, +/**/ 0xBF2488E5, 0xFD431489, +/**/ 0xBFD419B4, 0x23D5F000, +/**/ 0x3D3CE379, 0x226DE3EC, +/**/ 0x3FF5E000, 0x00000000, +/**/ 0xBF0067E7, 0x6424E9C9, +/**/ 0xBFD403D0, 0x86CEA000, +/**/ 0xBD3E6EF5, 0x74487308, +/**/ 0x3FF5D800, 0x00000000, +/**/ 0x3F19F0FB, 0x38A94D24, +/**/ 0xBFD3EDF4, 0x63C17000, +/**/ 0x3D3F067C, 0x297F2C3F, +/**/ 0x3FF5D000, 0x00000000, +/**/ 0x3F2EADD9, 0x23CAD2AA, +/**/ 0xBFD3D81F, 0xB5947000, +/**/ 0x3D222C7C, 0x2A9D37A4, +/**/ 0x3FF5C800, 0x00000000, +/**/ 0x3F3882B9, 0x31057262, +/**/ 0xBFD3C252, 0x77333000, +/**/ 0xBD183B54, 0xB606BD5C, +/**/ 0x3FF5C400, 0x00000000, +/**/ 0xBF3E00AE, 0x10FFA8F8, +/**/ 0xBFD3AC8C, 0xA38E6000, +/**/ 0x3D2D0BEF, 0xBC02BE4A, +/**/ 0x3FF5BC00, 0x00000000, +/**/ 0xBF34339B, 0x8056EAF3, +/**/ 0xBFD396CE, 0x359BC000, +/**/ 0x3D05839C, 0x5663663D, +/**/ 0x3FF5B400, 0x00000000, +/**/ 0xBF242CC1, 0xF31D7FD5, +/**/ 0xBFD38117, 0x28565000, +/**/ 0x3D2A71E4, 0x93A0702B, +/**/ 0x3FF5AC00, 0x00000000, +/**/ 0x3ED5AC05, 0x6B015AC0, +/**/ 0xBFD36B67, 0x76BE1000, +/**/ 0xBD116ECD, 0xB0F177C8, +/**/ 0x3FF5A400, 0x00000000, +/**/ 0x3F26268D, 0x5BA55E5A, +/**/ 0xBFD355BF, 0x1BD83000, +/**/ 0x3D2BA99B, 0x8964F0E8, +/**/ 0x3FF59C00, 0x00000000, +/**/ 0x3F361F12, 0x3CCAA376, +/**/ 0xBFD3401E, 0x12AED000, +/**/ 0x3D317C73, 0x556E291D, +/**/ 0x3FF59800, 0x00000000, +/**/ 0xBF3E863D, 0x62D32417, +/**/ 0xBFD32A84, 0x56512000, +/**/ 0xBD04F928, 0x139AF5D6, +/**/ 0x3FF59000, 0x00000000, +/**/ 0xBF32DCF7, 0xEA712DCF, +/**/ 0xBFD314F1, 0xE1D36000, +/**/ 0x3D28E27A, 0xD3213CB8, +/**/ 0x3FF58800, 0x00000000, +/**/ 0xBF1B95B2, 0xA0CC87E8, +/**/ 0xBFD2FF66, 0xB04EB000, +/**/ 0x3D38AED2, 0x541E6E2E, +/**/ 0x3FF58000, 0x00000000, +/**/ 0x3F158056, 0x01580560, +/**/ 0xBFD2E9E2, 0xBCE12000, +/**/ 0xBD24300C, 0x128D1DC2, +/**/ 0x3FF57800, 0x00000000, +/**/ 0x3F31F340, 0x15791F34, +/**/ 0xBFD2D466, 0x02ADD000, +/**/ 0x3D288D0D, 0xDCD54196, +/**/ 0x3FF57000, 0x00000000, +/**/ 0x3F3ED3C5, 0x06B39A23, +/**/ 0xBFD2BEF0, 0x7CDC9000, +/**/ 0xBD2A9CFA, 0x4A5004F4, +/**/ 0x3FF56C00, 0x00000000, +/**/ 0xBF33FEA9, 0x53FEA954, +/**/ 0xBFD2A982, 0x269A4000, +/**/ 0x3D22058E, 0x557285CF, +/**/ 0x3FF56400, 0x00000000, +/**/ 0xBF1A1160, 0xEB478503, +/**/ 0xBFD2941A, 0xFB187000, +/**/ 0x3D3210C2, 0xB730E28B, +/**/ 0x3FF55C00, 0x00000000, +/**/ 0x3F1D09AD, 0xE4A18B2E, +/**/ 0xBFD27EBA, 0xF58D9000, +/**/ 0x3D2B1988, 0x00B4BDA7, +/**/ 0x3FF55400, 0x00000000, +/**/ 0x3F355555, 0x55555555, +/**/ 0xBFD26962, 0x1134E000, +/**/ 0x3D31B61F, 0x10522625, +/**/ 0x3FF55000, 0x00000000, +/**/ 0xBF3C4BE6, 0xB319A21F, +/**/ 0xBFD25410, 0x494E5000, +/**/ 0xBD3B1D7A, 0xC0EF77F2, +/**/ 0x3FF54800, 0x00000000, +/**/ 0xBF2B4328, 0x8FA03FD5, +/**/ 0xBFD23EC5, 0x991EC000, +/**/ 0x3D36DBE4, 0x48A2E522, +/**/ 0x3FF54000, 0x00000000, +/**/ 0x3EF54015, 0x40154015, +/**/ 0xBFD22981, 0xFBEF8000, +/**/ 0x3D3A1421, 0x609580DA, +/**/ 0x3FF53800, 0x00000000, +/**/ 0x3F30948F, 0x40FEAC6F, +/**/ 0xBFD21445, 0x6D0EC000, +/**/ 0x3D3CAF04, 0x28B728A3, +/**/ 0x3FF53400, 0x00000000, +/**/ 0xBF3FE034, 0xFD04F7B8, +/**/ 0xBFD1FF0F, 0xE7CF4000, +/**/ 0xBD3E9D5B, 0x513FF0C1, +/**/ 0x3FF52C00, 0x00000000, +/**/ 0xBF300A95, 0x7FAB5403, +/**/ 0xBFD1E9E1, 0x6788A000, +/**/ 0x3D382EAE, 0xD3C8B65E, +/**/ 0x3FF52400, 0x00000000, +/**/ 0x3EB52401, 0x52401524, +/**/ 0xBFD1D4B9, 0xE796C000, +/**/ 0xBD222A66, 0x7C42E56D, +/**/ 0x3FF51C00, 0x00000000, +/**/ 0x3F307EAE, 0x2F8151D0, +/**/ 0xBFD1BF99, 0x635A7000, +/**/ 0x3D31AC89, 0x575C2125, +/**/ 0x3FF51800, 0x00000000, +/**/ 0xBF3ECE3F, 0xEAE9ECE4, +/**/ 0xBFD1AA7F, 0xD638D000, +/**/ 0xBD29F60A, 0x9616F7A0, +/**/ 0x3FF51000, 0x00000000, +/**/ 0xBF2BA3DD, 0xC7675243, +/**/ 0xBFD1956D, 0x3B9BC000, +/**/ 0xBD27D2F7, 0x3AD1AA14, +/**/ 0x3FF50800, 0x00000000, +/**/ 0x3F0B9AC8, 0x764E368D, +/**/ 0xBFD18061, 0x8EF19000, +/**/ 0x3D3482FF, 0xC86D38E5, +/**/ 0x3FF50000, 0x00000000, +/**/ 0x3F350150, 0x15015015, +/**/ 0xBFD16B5C, 0xCBAD0000, +/**/ 0x3D323299, 0x042D74BF, +/**/ 0x3FF4FC00, 0x00000000, +/**/ 0xBF392851, 0x4A683C50, +/**/ 0xBFD1565E, 0xED456000, +/**/ 0x3CEE75AD, 0xFB6ABA25, +/**/ 0x3FF4F400, 0x00000000, +/**/ 0xBF1C2748, 0xACD95EF0, +/**/ 0xBFD14167, 0xEF367000, +/**/ 0xBD3E0C07, 0x824DAAF5, +/**/ 0x3FF4EC00, 0x00000000, +/**/ 0x3F26B90D, 0x67A47465, +/**/ 0xBFD12C77, 0xCD007000, +/**/ 0xBD13B294, 0x8A11F797, +/**/ 0x3FF4E400, 0x00000000, +/**/ 0x3F3E0A72, 0xF0539783, +/**/ 0xBFD1178E, 0x8227E000, +/**/ 0xBD31EF78, 0xCE2D07F2, +/**/ 0x3FF4E000, 0x00000000, +/**/ 0xBF2E00A6, 0xF87FD642, +/**/ 0xBFD102AC, 0x0A35D000, +/**/ 0x3D2F1FBD, 0xDFDFD686, +/**/ 0x3FF4D800, 0x00000000, +/**/ 0x3F10EFB7, 0x0B12E3FD, +/**/ 0xBFD0EDD0, 0x60B78000, +/**/ 0xBD0019B5, 0x2D8435F5, +/**/ 0x3FF4D000, 0x00000000, +/**/ 0x3F37BEF1, 0x5CB4DBE5, +/**/ 0xBFD0D8FB, 0x813EB000, +/**/ 0xBD1EE8C8, 0x8753FA35, +/**/ 0x3FF4CC00, 0x00000000, +/**/ 0xBF34778D, 0xA50918B1, +/**/ 0xBFD0C42D, 0x67616000, +/**/ 0xBD27188B, 0x163CEAE9, +/**/ 0x3FF4C400, 0x00000000, +/**/ 0xBED9F4F7, 0xE37288EC, +/**/ 0xBFD0AF66, 0x0EB9E000, +/**/ 0xBD23C7C3, 0xF528D80A, +/**/ 0x3FF4BC00, 0x00000000, +/**/ 0x3F33EDDA, 0x68FE0E42, +/**/ 0xBFD09AA5, 0x72E6C000, +/**/ 0xBD3B50A1, 0xE1734342, +/**/ 0x3FF4B800, 0x00000000, +/**/ 0xBF3776C6, 0xB72E47D9, +/**/ 0xBFD085EB, 0x8F8AE000, +/**/ 0xBD3E5D51, 0x3F45FE7B, +/**/ 0x3FF4B000, 0x00000000, +/**/ 0xBF04AFD6, 0xA052BF5B, +/**/ 0xBFD07138, 0x604D6000, +/**/ 0x3D3E7632, 0x4E912B17, +/**/ 0x3FF4A800, 0x00000000, +/**/ 0x3F328FFA, 0xD5B5C015, +/**/ 0xBFD05C8B, 0xE0D96000, +/**/ 0xBD2AD0F1, 0xC77CCB58, +/**/ 0x3FF4A400, 0x00000000, +/**/ 0xBF380528, 0x9FEB5D80, +/**/ 0xBFD047E6, 0x0CDE8000, +/**/ 0xBD2DBDF1, 0x0D397F3C, +/**/ 0x3FF49C00, 0x00000000, +/**/ 0xBF02AD3E, 0x25FF5B21, +/**/ 0xBFD03346, 0xE0106000, +/**/ 0xBCF89FF8, 0xA966395C, +/**/ 0x3FF49400, 0x00000000, +/**/ 0x3F339E3B, 0x2D066EA2, +/**/ 0xBFD01EAE, 0x5626C000, +/**/ 0xBD3A43DC, 0xFADE85AE, +/**/ 0x3FF49000, 0x00000000, +/**/ 0xBF3629C1, 0xAFB2E932, +/**/ 0xBFD00A1C, 0x6ADDA000, +/**/ 0xBD31CD8D, 0x688B9E18, +/**/ 0x3FF48800, 0x00000000, +/**/ 0x3ED48805, 0x22014880, +/**/ 0xBFCFEB22, 0x33EA0000, +/**/ 0xBD2F3418, 0xDE00938B, +/**/ 0x3FF48000, 0x00000000, +/**/ 0x3F37119F, 0x3D324D89, +/**/ 0xBFCFC218, 0xBE620000, +/**/ 0xBD34BBA4, 0x6F1CF6A0, +/**/ 0x3FF47C00, 0x00000000, +/**/ 0xBF31EB85, 0x1EB851EC, +/**/ 0xBFCF991C, 0x6CB3C000, +/**/ 0x3D390D04, 0xCD7CC834, +/**/ 0x3FF47400, 0x00000000, +/**/ 0x3F1569C9, 0xAAFC7C01, +/**/ 0xBFCF702D, 0x36778000, +/**/ 0x3D108195, 0x16673E23, +/**/ 0x3FF46C00, 0x00000000, +/**/ 0x3F3CE345, 0x96066250, +/**/ 0xBFCF474B, 0x134E0000, +/**/ 0x3D3BAE49, 0xF1DF7B5E, +/**/ 0x3FF46800, 0x00000000, +/**/ 0xBF26A297, 0x1D02DE87, +/**/ 0xBFCF1E75, 0xFADFA000, +/**/ 0x3D20862B, 0x25D83F6D, +/**/ 0x3FF46000, 0x00000000, +/**/ 0x3F2978FE, 0xB9F34381, +/**/ 0xBFCEF5AD, 0xE4DD0000, +/**/ 0x3CCA2115, 0x65BB8E11, +/**/ 0x3FF45C00, 0x00000000, +/**/ 0xBF3AF398, 0xF6C71366, +/**/ 0xBFCECCF2, 0xC8FEA000, +/**/ 0x3D3BEC63, 0xA3E75640, +/**/ 0x3FF45400, 0x00000000, +/**/ 0xBF030E9C, 0x449AFF5D, +/**/ 0xBFCEA444, 0x9F04A000, +/**/ 0xBD35E916, 0x63732A36, +/**/ 0x3FF44C00, 0x00000000, +/**/ 0x3F367190, 0xF8B42EF3, +/**/ 0xBFCE7BA3, 0x5EB78000, +/**/ 0x3D0D5EEE, 0x23793649, +/**/ 0x3FF44800, 0x00000000, +/**/ 0xBF3079A9, 0xD260511C, +/**/ 0xBFCE530E, 0xFFE72000, +/**/ 0x3D3FDBDB, 0xB13F7C18, +/**/ 0x3FF44000, 0x00000000, +/**/ 0x3F21B87C, 0x0B644FBE, +/**/ 0xBFCE2A87, 0x7A6B2000, +/**/ 0xBD382381, 0x7787081A, +/**/ 0x3FF43C00, 0x00000000, +/**/ 0xBF3D8CF5, 0x411B2E25, +/**/ 0xBFCE020C, 0xC6236000, +/**/ 0x3D252B00, 0xADB91424, +/**/ 0x3FF43400, 0x00000000, +/**/ 0xBF0DAC08, 0xD6A60978, +/**/ 0xBFCDD99E, 0xDAF6E000, +/**/ 0x3D302EC6, 0x69C756EB, +/**/ 0x3FF42C00, 0x00000000, +/**/ 0x3F36625D, 0x51F86EFA, +/**/ 0xBFCDB13D, 0xB0D48000, +/**/ 0xBD32806A, 0x847527E6, +/**/ 0x3FF42800, 0x00000000, +/**/ 0xBF2E8B2D, 0xA8766564, +/**/ 0xBFCD88E9, 0x3FB30000, +/**/ 0x3D375F28, 0x0234BF51, +/**/ 0x3FF42000, 0x00000000, +/**/ 0x3F26A4CB, 0xCB2A247B, +/**/ 0xBFCD60A1, 0x7F904000, +/**/ 0x3D35D6E0, 0x6FC20D39, +/**/ 0x3FF41C00, 0x00000000, +/**/ 0xBF39D5E8, 0xC17DF552, +/**/ 0xBFCD3866, 0x68720000, +/**/ 0x3D373650, 0xB38932BC, +/**/ 0x3FF41400, 0x00000000, +/**/ 0x3EF41414, 0x14141414, +/**/ 0xBFCD1037, 0xF2656000, +/**/ 0x3D084A7E, 0x75B6F6E4, +/**/ 0x3FF40C00, 0x00000000, +/**/ 0x3F3C97A8, 0x43AE87FD, +/**/ 0xBFCCE816, 0x157F2000, +/**/ 0x3D29E0AB, 0xA2099515, +/**/ 0x3FF40800, 0x00000000, +/**/ 0xBF1F4BBC, 0x66A67E6F, +/**/ 0xBFCCC000, 0xC9DB4000, +/**/ 0x3D1D6D58, 0x5D57AFF9, +/**/ 0x3FF40000, 0x00000000, +/**/ 0x3F340140, 0x14014014, +/**/ 0xBFCC97F8, 0x079D4000, +/**/ 0xBD23B161, 0xA8C6E6C5, +/**/ 0x3FF3FC00, 0x00000000, +/**/ 0xBF2FD809, 0xFD809FD8, +/**/ 0xBFCC6FFB, 0xC6F00000, +/**/ 0xBD3EE138, 0xD3A69D43, +/**/ 0x3FF3F400, 0x00000000, +/**/ 0x3F28CA0E, 0x57EE89D2, +/**/ 0xBFCC480C, 0x0005C000, +/**/ 0xBD39A294, 0xD5E44E76, +/**/ 0x3FF3F000, 0x00000000, +/**/ 0xBF370BD5, 0xA50F9260, +/**/ 0xBFCC2028, 0xAB180000, +/**/ 0x3D292E0E, 0xE55C7AC6, +/**/ 0x3FF3E800, 0x00000000, +/**/ 0x3F1704AA, 0x75945FCE, +/**/ 0xBFCBF851, 0xC0676000, +/**/ 0x3D35420E, 0x4C0854AD, +/**/ 0x3FF3E400, 0x00000000, +/**/ 0xBF3D3431, 0xB56FD83C, +/**/ 0xBFCBD087, 0x383BE000, +/**/ 0x3D2D4BC4, 0x595412B6, +/**/ 0x3FF3DC00, 0x00000000, +/**/ 0x3EB3DC01, 0x3DC013DC, +/**/ 0xBFCBA8C9, 0x0AE4A000, +/**/ 0xBD3A32E7, 0xF44432DA, +/**/ 0x3FF3D400, 0x00000000, +/**/ 0x3F3D991A, 0xA75C5BBD, +/**/ 0xBFCB8117, 0x30B82000, +/**/ 0xBD1E9068, 0x3B9CD768, +/**/ 0x3FF3D000, 0x00000000, +/**/ 0xBF1292BA, 0x59C52F5D, +/**/ 0xBFCB5971, 0xA213A000, +/**/ 0xBD39B50E, 0x83AA91DF, +/**/ 0x3FF3C800, 0x00000000, +/**/ 0x3F395A47, 0xBABE7440, +/**/ 0xBFCB31D8, 0x575BC000, +/**/ 0xBD3C794E, 0x562A63CB, +/**/ 0x3FF3C400, 0x00000000, +/**/ 0xBF20D475, 0x58A0943A, +/**/ 0xBFCB0A4B, 0x48FC2000, +/**/ 0x3D22E72D, 0x5C3998ED, +/**/ 0x3FF3BC00, 0x00000000, +/**/ 0x3F360D92, 0x3295482C, +/**/ 0xBFCAE2CA, 0x6F672000, +/**/ 0xBD37A8D5, 0xAE54F550, +/**/ 0x3FF3B800, 0x00000000, +/**/ 0xBF267D12, 0xCAB48651, +/**/ 0xBFCABB55, 0xC316A000, +/**/ 0x3D38A65A, 0xCAF14CD8, +/**/ 0x3FF3B000, 0x00000000, +/**/ 0x3F33B13B, 0x13B13B14, +/**/ 0xBFCA93ED, 0x3C8AE000, +/**/ 0x3D287243, 0x50562169, +/**/ 0x3FF3AC00, 0x00000000, +/**/ 0xBF2A46AF, 0x2C8FD3BF, +/**/ 0xBFCA6C90, 0xD44B8000, +/**/ 0x3D3F63B7, 0xF037B0C6, +/**/ 0x3FF3A400, 0x00000000, +/**/ 0x3F324387, 0xAC822610, +/**/ 0xBFCA4540, 0x82E6A000, +/**/ 0xBD360A77, 0xC81F7171, +/**/ 0x3FF3A000, 0x00000000, +/**/ 0xBF2C34BB, 0xA1923DEE, +/**/ 0xBFCA1DFC, 0x40F1C000, +/**/ 0x3D301E0F, 0x004F3781, +/**/ 0x3FF39800, 0x00000000, +/**/ 0x3F31C2C1, 0x87F63372, +/**/ 0xBFC9F6C4, 0x0708A000, +/**/ 0x3D3337D9, 0x4BCD3F43, +/**/ 0x3FF39400, 0x00000000, +/**/ 0xBF2C4AA0, 0xE11BD52E, +/**/ 0xBFC9CF97, 0xCDCE0000, +/**/ 0xBD3D862F, 0x10C414E3, +/**/ 0x3FF38C00, 0x00000000, +/**/ 0x3F322D36, 0x6088DBF4, +/**/ 0xBFC9A877, 0x8DEBA000, +/**/ 0xBD3470FA, 0x3EFEC390, +/**/ 0x3FF38800, 0x00000000, +/**/ 0xBF2A8BBF, 0x503F774E, +/**/ 0xBFC98163, 0x4011A000, +/**/ 0xBD34EADD, 0x9E9045E2, +/**/ 0x3FF38000, 0x00000000, +/**/ 0x3F338138, 0x13813814, +/**/ 0xBFC95A5A, 0xDCF70000, +/**/ 0xBD07F228, 0x58A0FF6F, +/**/ 0x3FF37C00, 0x00000000, +/**/ 0xBF26FB6F, 0x1B177053, +/**/ 0xBFC9335E, 0x5D594000, +/**/ 0xBD33115C, 0x3ABD47DA, +/**/ 0x3FF37400, 0x00000000, +/**/ 0x3F35BD1C, 0x945EDC20, +/**/ 0xBFC90C6D, 0xB9FCC000, +/**/ 0x3D1935F5, 0x7718D7CA, +/**/ 0x3FF37000, 0x00000000, +/**/ 0xBF219D00, 0x4DBDCC60, +/**/ 0xBFC8E588, 0xEBAC2000, +/**/ 0xBD3B7D5C, 0xAB2D1140, +/**/ 0x3FF36800, 0x00000000, +/**/ 0x3F38DF3D, 0xE0747954, +/**/ 0xBFC8BEAF, 0xEB390000, +/**/ 0x3D073D54, 0xAAE92CD1, +/**/ 0x3FF36400, 0x00000000, +/**/ 0xBF14E775, 0xD9D3C49F, +/**/ 0xBFC897E2, 0xB17B2000, +/**/ 0x3D296B37, 0x380CBE9E, +/**/ 0x3FF35C00, 0x00000000, +/**/ 0x3F3CE5F9, 0xF2AF821E, +/**/ 0xBFC87121, 0x3750E000, +/**/ 0xBD3328EB, 0x42F9AF75, +/**/ 0x3FF35800, 0x00000000, +/**/ 0xBEE82DF0, 0xE34971F2, +/**/ 0xBFC84A6B, 0x759F6000, +/**/ 0x3D3DA280, 0x2ADF8609, +/**/ 0x3FF35400, 0x00000000, +/**/ 0xBF3E304D, 0x4873ECAE, +/**/ 0xBFC823C1, 0x6551A000, +/**/ 0xBD1E0DDB, 0x9A631E83, +/**/ 0x3FF34C00, 0x00000000, +/**/ 0x3F1264B6, 0x1FF659DB, +/**/ 0xBFC7FD22, 0xFF59A000, +/**/ 0x3D158BEB, 0xF457B7D2, +/**/ 0x3FF34800, 0x00000000, +/**/ 0xBF386531, 0xFECB9865, +/**/ 0xBFC7D690, 0x3CAF6000, +/**/ 0x3D24C06B, 0x17C301D7, +/**/ 0x3FF34000, 0x00000000, +/**/ 0x3F25A8C2, 0xEEDA65AE, +/**/ 0xBFC7B009, 0x16516000, +/**/ 0x3D3AE75F, 0xCB067E57, +/**/ 0x3FF33C00, 0x00000000, +/**/ 0xBF31BA4A, 0x8434E1F4, +/**/ 0xBFC7898D, 0x85444000, +/**/ 0xBD38E67B, 0xE3DBAF3F, +/**/ 0x3FF33400, 0x00000000, +/**/ 0x3F31EE97, 0xDBFC660A, +/**/ 0xBFC7631D, 0x82936000, +/**/ 0x3D25E77D, 0xC7C5F3E1, +/**/ 0x3FF33000, 0x00000000, +/**/ 0xBF246252, 0xBC40BFDA, +/**/ 0xBFC73CB9, 0x074FE000, +/**/ 0x3D3D66A9, 0x0D0005A6, +/**/ 0x3FF32800, 0x00000000, +/**/ 0x3F39E640, 0x13299E64, +/**/ 0xBFC71660, 0x0C914000, +/**/ 0xBCE51B15, 0x7CEC3838, +/**/ 0x3FF32400, 0x00000000, +/**/ 0xBEFCB5D4, 0xEF40991F, +/**/ 0xBFC6F012, 0x8B756000, +/**/ 0xBD357739, 0x0D31EF0F, +/**/ 0x3FF32000, 0x00000000, +/**/ 0xBF3D4632, 0xC823D892, +/**/ 0xBFC6C9D0, 0x7D204000, +/**/ 0x3CDC73FA, 0xFD9B2DCA, +/**/ 0x3FF31800, 0x00000000, +/**/ 0x3F1DD63A, 0x7AED804C, +/**/ 0xBFC6A399, 0xDABBE000, +/**/ 0x3D38F934, 0xE66A15A6, +/**/ 0x3FF31400, 0x00000000, +/**/ 0xBF339849, 0xE8C11E1A, +/**/ 0xBFC67D6E, 0x9D786000, +/**/ 0x3D311E88, 0x30A706D3, +/**/ 0x3FF30C00, 0x00000000, +/**/ 0x3F319013, 0x0D190131, +/**/ 0xBFC6574E, 0xBE8C2000, +/**/ 0x3D398C1D, 0x34F0F462, +/**/ 0x3FF30800, 0x00000000, +/**/ 0xBF222315, 0xB47A7FDA, +/**/ 0xBFC6313A, 0x37336000, +/**/ 0x3D144DF5, 0x4F21EA6D, +/**/ 0x3FF30000, 0x00000000, +/**/ 0x3F3C82AC, 0x40260390, +/**/ 0xBFC60B31, 0x00B0A000, +/**/ 0x3D371456, 0xC988F814, +/**/ 0x3FF2FC00, 0x00000000, +/**/ 0x3F026443, 0xA2430A62, +/**/ 0xBFC5E533, 0x144C2000, +/**/ 0x3D31CE0B, 0xF3B290EA, +/**/ 0x3FF2F800, 0x00000000, +/**/ 0xBF37B425, 0xED097B42, +/**/ 0xBFC5BF40, 0x6B544000, +/**/ 0x3D127023, 0xEB68981C, +/**/ 0x3FF2F000, 0x00000000, +/**/ 0x3F2D00E3, 0x4AE0553C, +/**/ 0xBFC59958, 0xFF1D6000, +/**/ 0x3D3A1D05, 0x9769CA05, +/**/ 0x3FF2EC00, 0x00000000, +/**/ 0xBF262BC0, 0x25D69D44, +/**/ 0xBFC5737C, 0xC9018000, +/**/ 0xBD39BAA7, 0xA6B887F6, +/**/ 0x3FF2E400, 0x00000000, +/**/ 0x3F3B88B5, 0xE3103D6B, +/**/ 0xBFC54DAB, 0xC2610000, +/**/ 0xBD2746FE, 0xE5C8D0D8, +/**/ 0x3FF2E000, 0x00000000, +/**/ 0x3F02E025, 0xC04B8097, +/**/ 0xBFC527E5, 0xE4A1C000, +/**/ 0x3D34E60B, 0x8D4B411D, +/**/ 0x3FF2DC00, 0x00000000, +/**/ 0xBF369C22, 0x2C305021, +/**/ 0xBFC5022B, 0x292F6000, +/**/ 0xBD348A05, 0xFF36A25B, +/**/ 0x3FF2D400, 0x00000000, +/**/ 0x3F30A012, 0xD50A012D, +/**/ 0xBFC4DC7B, 0x897BC000, +/**/ 0xBD0C79B6, 0x0AE1FF0F, +/**/ 0x3FF2D000, 0x00000000, +/**/ 0xBF1FBE29, 0xBC66484E, +/**/ 0xBFC4B6D6, 0xFEFE2000, +/**/ 0xBD1522EC, 0xF56E7952, +/**/ 0x3FF2C800, 0x00000000, +/**/ 0x3F3FB4D8, 0x12C9FB4E, +/**/ 0xBFC4913D, 0x8333C000, +/**/ 0x3D353E43, 0x558124C4, +/**/ 0x3FF2C400, 0x00000000, +/**/ 0x3F1E3432, 0x7004B11E, +/**/ 0xBFC46BAF, 0x0F9F6000, +/**/ 0x3D1249CD, 0x0790841A, +/**/ 0x3FF2C000, 0x00000000, +/**/ 0xBF30671A, 0x5C8EF02F, +/**/ 0xBFC4462B, 0x9DC9C000, +/**/ 0x3D384858, 0xA711B062, +/**/ 0x3FF2B800, 0x00000000, +/**/ 0x3F37D835, 0xD548D9AC, +/**/ 0xBFC420B3, 0x27410000, +/**/ 0x3D116282, 0xC85A0884, +/**/ 0x3FF2B400, 0x00000000, +/**/ 0x3ED2B404, 0xAD012B40, +/**/ 0xBFC3FB45, 0xA5992000, +/**/ 0xBD319713, 0xC0CAE559, +/**/ 0x3FF2B000, 0x00000000, +/**/ 0xBF370F78, 0x8E7302A1, +/**/ 0xBFC3D5E3, 0x126BC000, +/**/ 0xBD13FB2F, 0x85096C4B, +/**/ 0x3FF2A800, 0x00000000, +/**/ 0x3F31C92F, 0x3C1053F9, +/**/ 0xBFC3B08B, 0x67580000, +/**/ 0x3D3AADE8, 0xF29320FB, +/**/ 0x3FF2A400, 0x00000000, +/**/ 0xBF14AD94, 0x3DBE2E04, +/**/ 0xBFC38B3E, 0x9E028000, +/**/ 0x3D370EF0, 0x545C17F9, +/**/ 0x3FF2A000, 0x00000000, +/**/ 0xBF3BED61, 0xBED61BED, +/**/ 0xBFC365FC, 0xB015A000, +/**/ 0x3D3FD3A0, 0xAFB9691B, +/**/ 0x3FF29800, 0x00000000, +/**/ 0x3F2B061A, 0x26F004A6, +/**/ 0xBFC340C5, 0x97412000, +/**/ 0x3D37A3DC, 0xF7D9D386, +/**/ 0x3FF29400, 0x00000000, +/**/ 0xBF21B488, 0xFF6B646D, +/**/ 0xBFC31B99, 0x4D3A4000, +/**/ 0xBD3F098E, 0xE3A50810, +/**/ 0x3FF29000, 0x00000000, +/**/ 0xBF3F0582, 0x2CA5D5AC, +/**/ 0xBFC2F677, 0xCBBC0000, +/**/ 0xBD352B30, 0x2160F40D, +/**/ 0x3FF28800, 0x00000000, +/**/ 0x3F260251, 0x16025116, +/**/ 0xBFC2D161, 0x0C868000, +/**/ 0xBD039D6C, 0xCB81B4A1, +/**/ 0x3FF28400, 0x00000000, +/**/ 0xBF258CDF, 0x502065D2, +/**/ 0xBFC2AC55, 0x095F6000, +/**/ 0x3D1D3466, 0xD0C6C8A8, +/**/ 0x3FF27C00, 0x00000000, +/**/ 0x3F3FA38A, 0x1CE4D6F8, +/**/ 0xBFC28753, 0xBC11A000, +/**/ 0xBD37494E, 0x359302E6, +/**/ 0x3FF27800, 0x00000000, +/**/ 0x3F247DD5, 0xDCCA0781, +/**/ 0xBFC2625D, 0x1E6DE000, +/**/ 0x3CF52962, 0xF09E3D82, +/**/ 0x3FF27400, 0x00000000, +/**/ 0xBF25E8EF, 0xDB195E8F, +/**/ 0xBFC23D71, 0x2A49C000, +/**/ 0xBD100D23, 0x8FD3DF5C, +/**/ 0x3FF27000, 0x00000000, +/**/ 0xBF3FF6C8, 0xFFB647FE, +/**/ 0xBFC2188F, 0xD9808000, +/**/ 0x3D3B3A1E, 0x7F50C701, +/**/ 0x3FF26800, 0x00000000, +/**/ 0x3F266F9A, 0xC024D167, +/**/ 0xBFC1F3B9, 0x25F26000, +/**/ 0x3D15F74E, 0x9B083633, +/**/ 0x3FF26400, 0x00000000, +/**/ 0xBF22D1BD, 0xEABD0E14, +/**/ 0xBFC1CEED, 0x09854000, +/**/ 0x3D315C1C, 0x39192AF9, +/**/ 0x3FF26000, 0x00000000, +/**/ 0xBF3DD8F7, 0xF6D0EEC8, +/**/ 0xBFC1AA2B, 0x7E240000, +/**/ 0x3D31AC38, 0xDDE3B366, +/**/ 0x3FF25800, 0x00000000, +/**/ 0x3F2BCEB1, 0x2A241EF6, +/**/ 0xBFC18574, 0x7DBEC000, +/**/ 0xBD3E6744, 0x45BD9B49, +/**/ 0x3FF25400, 0x00000000, +/**/ 0xBF18A05B, 0xA21378D7, +/**/ 0xBFC160C8, 0x024B2000, +/**/ 0xBD2EC2D2, 0xA9009E3D, +/**/ 0x3FF25000, 0x00000000, +/**/ 0xBF3A076F, 0xD6CFA90C, +/**/ 0xBFC13C26, 0x05C3A000, +/**/ 0x3D2CF5FD, 0xD94F6509, +/**/ 0x3FF24800, 0x00000000, +/**/ 0x3F324924, 0x92492492, +/**/ 0xBFC1178E, 0x8227E000, +/**/ 0xBD21EF78, 0xCE2D07F2, +/**/ 0x3FF24400, 0x00000000, +/**/ 0xBEF3682B, 0x6151E899, +/**/ 0xBFC0F301, 0x717D0000, +/**/ 0x3D3E09B4, 0x41AE86C5, +/**/ 0x3FF24000, 0x00000000, +/**/ 0xBF34868E, 0x89FA4C67, +/**/ 0xBFC0CE7E, 0xCDCCC000, +/**/ 0xBD14652D, 0xABFF5447, +/**/ 0x3FF23800, 0x00000000, +/**/ 0x3F3858D8, 0x6B11F09F, +/**/ 0xBFC0AA06, 0x91268000, +/**/ 0x3D345519, 0xD7032129, +/**/ 0x3FF23400, 0x00000000, +/**/ 0x3F159E26, 0xAF37C049, +/**/ 0xBFC08598, 0xB59E4000, +/**/ 0x3D27E5DD, 0x7009902C, +/**/ 0x3FF23000, 0x00000000, +/**/ 0xBF2AB546, 0x2E076329, +/**/ 0xBFC06135, 0x354D4000, +/**/ 0xBD363046, 0x28340EE9, +/**/ 0x3FF22C00, 0x00000000, +/**/ 0xBF3FEDD5, 0xFEDD5FEE, +/**/ 0xBFC03CDC, 0x0A51E000, +/**/ 0xBD381A9C, 0xF169FC5C, +/**/ 0x3FF22400, 0x00000000, +/**/ 0x3F2B5B92, 0x009126D7, +/**/ 0xBFC0188D, 0x2ECF6000, +/**/ 0xBD03F965, 0x1CFF9DFE, +/**/ 0x3FF22000, 0x00000000, +/**/ 0xBF121FB7, 0x8121FB78, +/**/ 0xBFBFE891, 0x39DBC000, +/**/ 0xBD356594, 0xD82F7A82, +/**/ 0x3FF21C00, 0x00000000, +/**/ 0xBF368F22, 0x3A459635, +/**/ 0xBFBFA01C, 0x9DB58000, +/**/ 0x3D08F351, 0xFA48A730, +/**/ 0x3FF21400, 0x00000000, +/**/ 0x3F379804, 0x855E6012, +/**/ 0xBFBF57BC, 0x7D900000, +/**/ 0xBD176A6C, 0x9EA8B04E, +/**/ 0x3FF21000, 0x00000000, +/**/ 0x3F17B57C, 0x78CD7A37, +/**/ 0xBFBF0F70, 0xCDD98000, +/**/ 0xBD32E31F, 0x6C272C1E, +/**/ 0x3FF20C00, 0x00000000, +/**/ 0xBF271E73, 0x07E4EF15, +/**/ 0xBFBEC739, 0x830A0000, +/**/ 0xBD311FCB, 0xA80CDD10, +/**/ 0x3FF20800, 0x00000000, +/**/ 0xBF3CDDEC, 0x49392BA7, +/**/ 0xBFBE7F16, 0x91A34000, +/**/ 0x3D32C1C5, 0x9BC77BFA, +/**/ 0x3FF20000, 0x00000000, +/**/ 0x3F320120, 0x12012012, +/**/ 0xBFBE3707, 0xEE304000, +/**/ 0xBD20F684, 0xE6766ABD, +/**/ 0x3FF1FC00, 0x00000000, +/**/ 0x3EF0DC4F, 0xCE8AD1A2, +/**/ 0xBFBDEF0D, 0x8D468000, +/**/ 0x3D324750, 0x412E9A74, +/**/ 0x3FF1F800, 0x00000000, +/**/ 0xBF2F7047, 0xDC11F704, +/**/ 0xBFBDA727, 0x63844000, +/**/ 0xBD1A8940, 0x1FA71733, +/**/ 0x3FF1F000, 0x00000000, +/**/ 0x3F3FAF3F, 0x16B6419D, +/**/ 0xBFBD5F55, 0x65920000, +/**/ 0xBD30E239, 0xCC185469, +/**/ 0x3FF1EC00, 0x00000000, +/**/ 0x3F2E878F, 0xF70985E2, +/**/ 0xBFBD1797, 0x88218000, +/**/ 0xBD336433, 0xB5EFBEED, +/**/ 0x3FF1E800, 0x00000000, +/**/ 0xBEEF55E4, 0x94D7FDC3, +/**/ 0xBFBCCFED, 0xBFEE0000, +/**/ 0xBD33A823, 0x2FE71256, +/**/ 0x3FF1E400, 0x00000000, +/**/ 0xBF310C4C, 0x0478BBCF, +/**/ 0xBFBC8858, 0x01BC4000, +/**/ 0xBD2646D1, 0xC65AACD3, +/**/ 0x3FF1DC00, 0x00000000, +/**/ 0x3F3F0ECB, 0xCB840C49, +/**/ 0xBFBC40D6, 0x425A4000, +/**/ 0xBD3CB112, 0x1D1930DD, +/**/ 0x3FF1D800, 0x00000000, +/**/ 0x3F2EACE5, 0xC9579074, +/**/ 0xBFBBF968, 0x769FC000, +/**/ 0xBD24218C, 0x8D824283, +/**/ 0x3FF1D400, 0x00000000, +/**/ 0xBECABDFA, 0xFC60F0AE, +/**/ 0xBFBBB20E, 0x936D8000, +/**/ 0x3D368BA8, 0x35459B8E, +/**/ 0x3FF1D000, 0x00000000, +/**/ 0xBF2F2A4B, 0xAFDC61F3, +/**/ 0xBFBB6AC8, 0x8DAD4000, +/**/ 0xBD3B1BDF, 0xF50225C7, +/**/ 0x3FF1CC00, 0x00000000, +/**/ 0xBF3EC8AF, 0xAB802394, +/**/ 0xBFBB2396, 0x5A530000, +/**/ 0x3CEFF64E, 0xEA137079, +/**/ 0x3FF1C400, 0x00000000, +/**/ 0x3F322FC1, 0xCE058D9B, +/**/ 0xBFBADC77, 0xEE5B0000, +/**/ 0x3D3573B2, 0x09C31904, +/**/ 0x3FF1C000, 0x00000000, +/**/ 0x3F0AA04F, 0xE0EFA2CF, +/**/ 0xBFBA956D, 0x3ECAC000, +/**/ 0xBD3E6379, 0x4C02C4AF, +/**/ 0x3FF1BC00, 0x00000000, +/**/ 0xBF26B7F7, 0x225ADFDD, +/**/ 0xBFBA4E76, 0x40B1C000, +/**/ 0x3D0E42B6, 0xB94407C8, +/**/ 0x3FF1B800, 0x00000000, +/**/ 0xBF39E073, 0x217CD13A, +/**/ 0xBFBA0792, 0xE9278000, +/**/ 0x3D0A9CE6, 0xC9AD51BF, +/**/ 0x3FF1B000, 0x00000000, +/**/ 0x3F37C67F, 0x2BAE2B21, +/**/ 0xBFB9C0C3, 0x2D4D4000, +/**/ 0x3D3AB7C0, 0x9E838668, +/**/ 0x3FF1AC00, 0x00000000, +/**/ 0x3F23316E, 0xBD720DCF, +/**/ 0xBFB97A07, 0x024CC000, +/**/ 0x3CF8BCC1, 0x732093CE, +/**/ 0x3FF1A800, 0x00000000, +/**/ 0xBF11A7B9, 0x611A7B96, +/**/ 0xBFB9335E, 0x5D594000, +/**/ 0xBD23115C, 0x3ABD47DA, +/**/ 0x3FF1A400, 0x00000000, +/**/ 0xBF324195, 0xA1C1B8E7, +/**/ 0xBFB8ECC9, 0x33AEC000, +/**/ 0x3D222F39, 0xBE67F7AA, +/**/ 0x3FF1A000, 0x00000000, +/**/ 0xBF3FEE61, 0xFEE61FEE, +/**/ 0xBFB8A647, 0x7A91C000, +/**/ 0xBD3C28C0, 0xAF9BD6DF, +/**/ 0x3FF19800, 0x00000000, +/**/ 0x3F328F89, 0x362B721D, +/**/ 0xBFB85FD9, 0x27508000, +/**/ 0x3D35B818, 0x19970C1C, +/**/ 0x3FF19400, 0x00000000, +/**/ 0x3F14E023, 0x28A70119, +/**/ 0xBFB8197E, 0x2F410000, +/**/ 0x3D3C0FE4, 0x60D20041, +/**/ 0x3FF19000, 0x00000000, +/**/ 0xBF1FD419, 0x3E48FC6F, +/**/ 0xBFB7D336, 0x87C28000, +/**/ 0xBD33C88C, 0x3E706706, +/**/ 0x3FF18C00, 0x00000000, +/**/ 0xBF34F7C6, 0xFD42546B, +/**/ 0xBFB78D02, 0x263D8000, +/**/ 0xBD069B57, 0x94B69FB7, +/**/ 0x3FF18400, 0x00000000, +/**/ 0x3F3E2FA4, 0x01185E30, +/**/ 0xBFB746E1, 0x00228000, +/**/ 0x3D3126D1, 0x6E1E21D2, +/**/ 0x3FF18000, 0x00000000, +/**/ 0x3F318118, 0x11811812, +/**/ 0xBFB700D3, 0x0AEAC000, +/**/ 0xBCEC1E8D, 0xA99DED32, +/**/ 0x3FF17C00, 0x00000000, +/**/ 0x3F13F1CA, 0xFF2E2C43, +/**/ 0xBFB6BAD8, 0x3C188000, +/**/ 0xBD0DAF3C, 0xC08926AE, +/**/ 0x3FF17800, 0x00000000, +/**/ 0xBF1D79B9, 0x0A5EF9FF, +/**/ 0xBFB674F0, 0x89364000, +/**/ 0xBD3A7999, 0x4C9D3302, +/**/ 0x3FF17400, 0x00000000, +/**/ 0xBF338FAD, 0x1ECEA765, +/**/ 0xBFB62F1B, 0xE7D78000, +/**/ 0x3D217995, 0x7ED63C4E, +/**/ 0x3FF17000, 0x00000000, +/**/ 0xBF3F976B, 0xD8C8714B, +/**/ 0xBFB5E95A, 0x4D978000, +/**/ 0xBD31CB7C, 0xE1D17171, +/**/ 0x3FF16800, 0x00000000, +/**/ 0x3F348A33, 0xB08FA497, +/**/ 0xBFB5A3AB, 0xB01AC000, +/**/ 0xBD3E2574, 0x9E6AFA18, +/**/ 0x3FF16400, 0x00000000, +/**/ 0x3F21AA1F, 0x864022C9, +/**/ 0xBFB55E10, 0x050E0000, +/**/ 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0xBD2A47F8, 0x8FCCE5BA, +/**/ 0x3FE87800, 0x00000000, +/**/ 0x3F1A9336, 0xDEECB0A8, +/**/ 0x3FD12A4B, 0xC3912000, +/**/ 0xBD35A750, 0x61473259, +/**/ 0x3FE87800, 0x00000000, +/**/ 0xBF3EC219, 0xFB6A388D, +/**/ 0x3FD13687, 0x0293B000, +/**/ 0xBD3D3E84, 0x99D67123, +/**/ 0x3FE87000, 0x00000000, +/**/ 0xBF106AE7, 0xC1625090, +/**/ 0x3FD142BF, 0xEB9A0000, +/**/ 0x3D31CE61, 0x85B58A9E, +/**/ 0x3FE86800, 0x00000000, +/**/ 0x3F369AE5, 0xACD4200C, +/**/ 0x3FD14EF6, 0x7F887000, +/**/ 0xBD3E97A6, 0x5DFC9794, +/**/ 0x3FE86800, 0x00000000, +/**/ 0xBF2D4286, 0x9389D11C, +/**/ 0x3FD15B2A, 0xBF429000, +/**/ 0xBD2D8E3B, 0x49B629B2, +/**/ 0x3FE86000, 0x00000000, +/**/ 0x3F286186, 0x18618618, +/**/ 0x3FD1675C, 0xABABA000, +/**/ 0x3D38380E, 0x731F55C4, +/**/ 0x3FE86000, 0x00000000, +/**/ 0xBF38EF0F, 0x6AC71708, +/**/ 0x3FD1738C, 0x45A67000, +/**/ 0xBD39C6E9, 0x0032C176, +/**/ 0x3FE85800, 0x00000000, +/**/ 0x3EFFF3D3, 0xE00C2C20, +/**/ 0x3FD17FB9, 0x8E151000, +/**/ 0xBD3A8A8B, 0xA74A2684, +/**/ 0x3FE85000, 0x00000000, +/**/ 0x3F3CFBA0, 0xF9592266, +/**/ 0x3FD18BE4, 0x85D93000, +/**/ 0x3D3C167F, 0x6F3604AB, +/**/ 0x3FE85000, 0x00000000, +/**/ 0xBF1FE7B0, 0xFF3D87FA, +/**/ 0x3FD1980D, 0x2DD42000, +/**/ 0x3D2B7B3A, 0x7A361C9A, +/**/ 0x3FE84800, 0x00000000, +/**/ 0x3F331E8D, 0x918DC223, +/**/ 0x3FD1A433, 0x86E68000, +/**/ 0xBD07A850, 0x634E0AAC, +/**/ 0x3FE84800, 0x00000000, +/**/ 0xBF31BAF9, 0x8D76B549, +/**/ 0x3FD1B057, 0x91F08000, +/**/ 0xBD32DD46, 0x6DC55E2D, +/**/ 0x3FE84000, 0x00000000, +/**/ 0x3F22F2EC, 0xDC90C512, +/**/ 0x3FD1BC79, 0x4FD1D000, +/**/ 0xBD3CCF0C, 0x747BA7BE, +/**/ 0x3FE84000, 0x00000000, +/**/ 0xBF3B442A, 0x6A0916B9, +/**/ 0x3FD1C898, 0xC169A000, +/**/ 0xBD381410, 0xE5C62AFF, +/**/ 0x3FE83800, 0x00000000, +/**/ 0x3EA83801, 0x83801838, +/**/ 0x3FD1D4B5, 0xE796A000, +/**/ 0x3D222A5B, 0xD197BAC2, +/**/ 0x3FE83000, 0x00000000, +/**/ 0x3F3B6A41, 0xCBD11C5C, +/**/ 0x3FD1E0D0, 0xC3371000, +/**/ 0x3D3AF8F2, 0xA9B0D4A0, +/**/ 0x3FE83000, 0x00000000, +/**/ 0xBF225381, 0xCB7A3CD6, +/**/ 0x3FD1ECE9, 0x5528B000, +/**/ 0xBD184E7B, 0x09B4A3B8, +/**/ 0x3FE82800, 0x00000000, +/**/ 0x3F32500C, 0x152500C1, +/**/ 0x3FD1F8FF, 0x9E48A000, +/**/ 0x3D27946C, 0x040CBE77, +/**/ 0x3FE82800, 0x00000000, +/**/ 0xBF32285F, 0x14902134, +/**/ 0x3FD20513, 0x9F73B000, +/**/ 0x3CF6E15E, 0x1609E0A4, +/**/ 0x3FE82000, 0x00000000, +/**/ 0x3F22D9EB, 0xA4018213, +/**/ 0x3FD21125, 0x59861000, +/**/ 0x3D382E78, 0xBA2950C4, +/**/ 0x3FE82000, 0x00000000, +/**/ 0xBF3AEFFC, 0xFC6BBFF4, +/**/ 0x3FD21D34, 0xCD5B9000, +/**/ 0x3D3B552F, 0xB28BADAA, +/**/ 0x3FE81800, 0x00000000, +/**/ 0x3EE81818, 0x18181818, +/**/ 0x3FD22941, 0xFBCF8000, +/**/ 0xBD3A6976, 0xF5EB0963, +/**/ 0x3FE81000, 0x00000000, +/**/ 0x3F3C7F27, 0x4FF0F3C6, +/**/ 0x3FD2354C, 0xE5BC9000, +/**/ 0xBD3D78ED, 0x0602A663, +/**/ 0x3FE81000, 0x00000000, +/**/ 0xBF1ED344, 0x0A86941D, +/**/ 0x3FD24155, 0x8BFD1000, +/**/ 0x3D300FFF, 0x3228FCAD, +/**/ 0x3FE80800, 0x00000000, +/**/ 0x3F3424D0, 0x1B0BD52D, +/**/ 0x3FD24D5B, 0xEF6AF000, +/**/ 0xBCBDD780, 0xFC9FABDD, +/**/ 0x3FE80800, 0x00000000, +/**/ 0xBF2FE7F9, 0xFE7F9FE8, +/**/ 0x3FD25960, 0x10DF7000, +/**/ 0x3D38E7BC, 0x224EA3E3, +/**/ 0x3FE80000, 0x00000000, +/**/ 0x3F280180, 0x18018018, +/**/ 0x3FD26561, 0xF1338000, +/**/ 0x3D38B488, 0x66FAA45F, +/**/ 0x3FE80000, 0x00000000, +/**/ 0xBF37FD00, 0x5FF40180, +/**/ 0x3FD27161, 0x913F8000, +/**/ 0x3D34F4F1, 0xF61564B4, +/**/ 0x3FE7F800, 0x00000000, +/**/ 0x3F104AE8, 0x9750B6C7, +/**/ 0x3FD27D5E, 0xF1DB6000, +/**/ 0xBD092374, 0x78CAC9F4, +/**/ 0x3FE7F800, 0x00000000, +/**/ 0xBF3FD017, 0xF405FD01, +/**/ 0x3FD2895A, 0x13DE8000, +/**/ 0x3D3A8D7A, 0xD24C13F0, +/**/ 0x3FE7F000, 0x00000000, +/**/ 0xBF0D2BF1, 0xC9C5485E, +/**/ 0x3FD29552, 0xF81FF000, +/**/ 0x3D348D30, 0x1771C408, +/**/ 0x3FE7E800, 0x00000000, +/**/ 0x3F38927F, 0xD029DB60, +/**/ 0x3FD2A149, 0x9F763000, +/**/ 0xBD30DBBF, 0x51F3AADC, +/**/ 0x3FE7E800, 0x00000000, +/**/ 0xBF26504A, 0xB0A45169, +/**/ 0x3FD2AD3E, 0x0AB73000, +/**/ 0x3D2B972E, 0x488C359F, +/**/ 0x3FE7E000, 0x00000000, +/**/ 0x3F312A8A, 0xD278E8DD, +/**/ 0x3FD2B930, 0x3AB8A000, +/**/ 0xBD26DB12, 0xD6BFB0A5, +/**/ 0x3FE7E000, 0x00000000, +/**/ 0xBF327577, 0x24BB32E7, +/**/ 0x3FD2C520, 0x304F8000, +/**/ 0x3D230852, 0x8C342F39, +/**/ 0x3FE7D800, 0x00000000, +/**/ 0x3F23EF9A, 0xA4B45AEC, +/**/ 0x3FD2D10D, 0xEC508000, +/**/ 0x3D360C61, 0xF7088353, +/**/ 0x3FE7D800, 0x00000000, +/**/ 0xBF398DAF, 0x32748CC1, +/**/ 0x3FD2DCF9, 0x6F8FD000, +/**/ 0x3D20B4A2, 0x8E33C9CE, +/**/ 0x3FE7D000, 0x00000000, +/**/ 0x3F07D05F, 0x417D05F4, +/**/ 0x3FD2E8E2, 0xBAE12000, +/**/ 0xBD267B1E, 0x99B72BD8, +/**/ 0x3FE7C800, 0x00000000, +/**/ 0x3F3F8EF7, 0x431D3027, +/**/ 0x3FD2F4C9, 0xCF17A000, +/**/ 0x3D371F04, 0x9374B87B, +/**/ 0x3FE7C800, 0x00000000, +/**/ 0xBF0E77A3, 0xDAD83E6C, +/**/ 0x3FD300AE, 0xAD063000, +/**/ 0x3D342F56, 0x8B75FCAC, +/**/ 0x3FE7C000, 0x00000000, +/**/ 0x3F38E041, 0x588D1676, +/**/ 0x3FD30C91, 0x557F2000, +/**/ 0xBD142958, 0xA1451755, +/**/ 0x3FE7C000, 0x00000000, +/**/ 0xBF24C6DD, 0x1FE8414C, +/**/ 0x3FD31871, 0xC9544000, +/**/ 0x3D184FAB, 0x94CECFD9, +/**/ 0x3FE7B800, 0x00000000, +/**/ 0x3F3265F4, 0x81C2D3B2, +/**/ 0x3FD32450, 0x09570000, +/**/ 0x3D3D271B, 0x9BDAE59D, +/**/ 0x3FE7B800, 0x00000000, +/**/ 0xBF30C39C, 0xB6466407, +/**/ 0x3FD3302C, 0x16586000, +/**/ 0x3D36217D, 0xC2A3E08B, +/**/ 0x3FE7B000, 0x00000000, +/**/ 0x3F283FAD, 0x12B21224, +/**/ 0x3FD33C05, 0xF128E000, +/**/ 0xBD22B906, 0x380E1A7D, +/**/ 0x3FE7B000, 0x00000000, +/**/ 0xBF36EFB8, 0xF899E55D, +/**/ 0x3FD347DD, 0x9A988000, +/**/ 0xBD25594D, 0xD4C58092, +/**/ 0x3FE7A800, 0x00000000, +/**/ 0x3F1836B6, 0x3FF42B9F, +/**/ 0x3FD353B3, 0x1376E000, +/**/ 0xBD1331AF, 0xE6C26D9B, +/**/ 0x3FE7A800, 0x00000000, +/**/ 0xBF3CE7FD, 0x0B739FF4, +/**/ 0x3FD35F86, 0x5C933000, +/**/ 0xBD3B07DE, 0x4EA1A54A, +/**/ 0x3FE7A000, 0x00000000, +/**/ 0x3EC7A005, 0xE8017A00, +/**/ 0x3FD36B57, 0x76BC1000, +/**/ 0x3D116978, 0x5A9C223F, +/**/ 0x3FE79800, 0x00000000, +/**/ 0x3F3D535D, 0xB1CC5B7B, +/**/ 0x3FD37726, 0x62BFE000, +/**/ 0xBD3E9436, 0xAC53B023, +/**/ 0x3FE79800, 0x00000000, +/**/ 0xBF15EEAC, 0xE0DA37A9, +/**/ 0x3FD382F3, 0x216C5000, +/**/ 0xBD1061D2, 0x1D1A7F6D, +/**/ 0x3FE79000, 0x00000000, +/**/ 0x3F37C21E, 0x344E16D6, +/**/ 0x3FD38EBD, 0xB38ED000, +/**/ 0x3D290582, 0xE67D4CA0, +/**/ 0x3FE79000, 0x00000000, +/**/ 0xBF25E69A, 0x39C9E465, +/**/ 0x3FD39A86, 0x19F45000, +/**/ 0x3D18EE51, 0x937354F5, +/**/ 0x3FE78800, 0x00000000, +/**/ 0x3F32640B, 0xC52640BC, +/**/ 0x3FD3A64C, 0x55694000, +/**/ 0x3D37A71C, 0xBCD735D0, +/**/ 0x3FE78800, 0x00000000, +/**/ 0xBF3037DE, 0x2F6A09ED, +/**/ 0x3FD3B210, 0x66B9C000, +/**/ 0xBD33C1ED, 0x9811560E, +/**/ 0x3FE78000, 0x00000000, +/**/ 0x3F2A71DC, 0x01781A72, +/**/ 0x3FD3BDD2, 0x4EB15000, +/**/ 0xBD3257B4, 0x970E6ED9, +/**/ 0x3FE78000, 0x00000000, +/**/ 0xBF354996, 0xA9EEBFF4, +/**/ 0x3FD3C992, 0x0E1B2000, +/**/ 0x3D141C28, 0xAA680B76, +/**/ 0x3FE77800, 0x00000000, +/**/ 0x3F208119, 0xAC60D341, +/**/ 0x3FD3D54F, 0xA5C1F000, +/**/ 0x3D3C3E1C, 0xD9A395E3, +/**/ 0x3FE77800, 0x00000000, +/**/ 0xBF3A28AE, 0x742E2DD0, +/**/ 0x3FD3E10B, 0x16701000, +/**/ 0x3D3F3BCF, 0x145429C7, +/**/ 0x3FE77000, 0x00000000, +/**/ 0x3F0BD584, 0x36340177, +/**/ 0x3FD3ECC4, 0x60EF6000, +/**/ 0xBD060286, 0x27C1300F, +/**/ 0x3FE77000, 0x00000000, +/**/ 0xBF3ED55D, 0x240C7174, +/**/ 0x3FD3F87B, 0x86094000, +/**/ 0xBD35DFD7, 0x54589889, +/**/ 0x3FE76800, 0x00000000, +/**/ 0xBEF18DE5, 0xAB277F45, +/**/ 0x3FD40430, 0x8686A000, +/**/ 0x3D3F8EF4, 0x3049F7D3, +/**/ 0x3FE76000, 0x00000000, +/**/ 0x3F3CB026, 0x01D3C7B8, +/**/ 0x3FD40FE3, 0x63303000, +/**/ 0x3D3E5C5F, 0xE79F05C6, +/**/ 0x3FE76000, 0x00000000, +/**/ 0xBF15E95B, 0xA9D08664, +/**/ 0x3FD41B94, 0x1CCE1000, +/**/ 0xBD304690, 0x13E43FC9, +/**/ 0x3FE75800, 0x00000000, +/**/ 0x3F3867A4, 0x097CFD43, +/**/ 0x3FD42742, 0xB427E000, +/**/ 0xBD398727, 0x02B82675, +/**/ 0x3FE75800, 0x00000000, +/**/ 0xBF2353DF, 0xE8A9353E, +/**/ 0x3FD432EF, 0x2A04F000, +/**/ 0xBD3FB129, 0x931715AD, +/**/ 0x3FE75000, 0x00000000, +/**/ 0x3F3450E6, 0x4F13DC4A, +/**/ 0x3FD43E99, 0x7F2C1000, +/**/ 0x3D1C3F72, 0x40C41A04, +/**/ 0x3FE75000, 0x00000000, +/**/ 0xBF2B4FBF, 0xE8B1B4FC, +/**/ 0x3FD44A41, 0xB463C000, +/**/ 0x3D31EE28, 0xF37CF612, +/**/ 0x3FE74800, 0x00000000, +/**/ 0x3F306BB6, 0x7E458100, +/**/ 0x3FD455E7, 0xCA720000, +/**/ 0x3D1AD8C6, 0x36629AED, +/**/ 0x3FE74800, 0x00000000, +/**/ 0xBF31745D, 0x1745D174, +/**/ 0x3FD4618B, 0xC21C6000, +/**/ 0xBD13D82F, 0x484C84CC, +/**/ 0x3FE74000, 0x00000000, +/**/ 0x3F296FBD, 0x236DEC04, +/**/ 0x3FD46D2D, 0x9C280000, +/**/ 0x3D359B27, 0x5F67F75A, +/**/ 0x3FE74000, 0x00000000, +/**/ 0xBF350F9D, 0x3B304B87, +/**/ 0x3FD478CD, 0x5959B000, +/**/ 0x3D2EC89B, 0xF0C8D098, +/**/ 0x3FE73800, 0x00000000, +/**/ 0x3F226A51, 0xA4EBDC70, +/**/ 0x3FD4846A, 0xFA75C000, +/**/ 0xBD263EA2, 0xE3798DCE, +/**/ 0x3FE73800, 0x00000000, +/**/ 0xBF3879D5, 0xF00B9A78, +/**/ 0x3FD49006, 0x80401000, +/**/ 0xBD38BCCF, 0xFE1A0F8C, +/**/ 0x3FE73000, 0x00000000, +/**/ 0x3F178D7F, 0x5DAAD90C, +/**/ 0x3FD49B9F, 0xEB7C1000, +/**/ 0x3D3DAC1C, 0x58AB60D7, +/**/ 0x3FE73000, 0x00000000, +/**/ 0xBF3BB33C, 0x783709C7, +/**/ 0x3FD4A737, 0x3CED0000, +/**/ 0xBD39A234, 0xEBF35449, +/**/ 0x3FE72800, 0x00000000, +/**/ 0x3F061274, 0x265AD23A, +/**/ 0x3FD4B2CC, 0x75556000, +/**/ 0xBD380FCB, 0xC78BFA4B, +/**/ 0x3FE72800, 0x00000000, +/**/ 0xBF3EBC05, 0xC90A1FD2, +/**/ 0x3FD4BE5F, 0x95778000, +/**/ 0xBD3D7C92, 0xCD9AD824, +/**/ 0x3FE72000, 0x00000000, +/**/ 0xBEC71FFA, 0x38017200, +/**/ 0x3FD4C9F0, 0x9E153000, +/**/ 0xBD2E1DDE, 0x70E02DE0, +/**/ 0x3FE71800, 0x00000000, +/**/ 0x3F3E6B99, 0x74A050E1, +/**/ 0x3FD4D57F, 0x8FEFE000, +/**/ 0x3D23F926, 0x7FD06868, +/**/ 0x3FE71800, 0x00000000, +/**/ 0xBF077400, 0xB8BD1180, +/**/ 0x3FD4E10C, 0x6BC8A000, +/**/ 0x3CF8283F, 0x1636F061, +/**/ 0x3FE71000, 0x00000000, +/**/ 0x3F3BC36C, 0xE3E0453A, +/**/ 0x3FD4EC97, 0x32600000, +/**/ 0x3D234D7A, 0xAF04D104, +/**/ 0x3FE71000, 0x00000000, +/**/ 0xBF15FA98, 0x6935DDC5, +/**/ 0x3FD4F81F, 0xE4764000, +/**/ 0xBD27FCF6, 0x434FF08D, +/**/ 0x3FE70800, 0x00000000, +/**/ 0x3F394B40, 0x7337CF08, +/**/ 0x3FD503A6, 0x82CB2000, +/**/ 0xBD2A68C8, 0xF16F9B5D, +/**/ 0x3FE70800, 0x00000000, +/**/ 0xBF1F7B97, 0xA835403A, +/**/ 0x3FD50F2B, 0x0E1E0000, +/**/ 0x3D3A0940, 0x8C47B8D8, +/**/ 0x3FE70000, 0x00000000, +/**/ 0x3F3702E0, 0x5C0B8170, +/**/ 0x3FD51AAD, 0x872E0000, +/**/ 0xBD3F4BD8, 0xDB0A7CC1, +/**/ 0x3FE70000, 0x00000000, +/**/ 0xBF241EE6, 0x4F67A855, +/**/ 0x3FD5262D, 0xEEB99000, +/**/ 0xBD3E1B9F, 0x70894A01, +/**/ 0x3FE6F800, 0x00000000, +/**/ 0x3F34EA19, 0x221C0170, +/**/ 0x3FD531AC, 0x457EE000, +/**/ 0x3D3DF83B, 0x7D931501, +/**/ 0x3FE6F800, 0x00000000, +/**/ 0xBF282102, 0x5508CA5C, +/**/ 0x3FD53D28, 0x8C3BE000, +/**/ 0xBD111397, 0xEB6DFAC5, +/**/ 0x3FE6F000, 0x00000000, +/**/ 0x3F3300B7, 0x9300B793, +/**/ 0x3FD548A2, 0xC3ADD000, +/**/ 0x3D23167E, 0x63081CF7, +/**/ 0x3FE6F000, 0x00000000, +/**/ 0xBF2BC486, 0x005BB90F, +/**/ 0x3FD5541A, 0xEC91C000, +/**/ 0xBCF816AA, 0xDC72EEBA, +/**/ 0x3FE6E800, 0x00000000, +/**/ 0x3F314688, 0xC5A3A00B, +/**/ 0x3FD55F91, 0x07A44000, +/**/ 0xBD11E647, 0x78DF4A62, +/**/ 0x3FE6E800, 0x00000000, +/**/ 0xBF2F09D6, 0xDA9C5AE1, +/**/ 0x3FD56B05, 0x15A18000, +/**/ 0x3D29247B, 0xBC4A23FC, +/**/ 0x3FE6E000, 0x00000000, +/**/ 0x3F2F76B4, 0x337C6CB1, +/**/ 0x3FD57677, 0x17456000, +/**/ 0xBD364EAD, 0x9524D7CA, +/**/ 0x3FE6E000, 0x00000000, +/**/ 0xBF30F8AC, 0xEDF4EC87, +/**/ 0x3FD581E7, 0x0D4B3000, +/**/ 0xBD1F31E1, 0xB12D8F1D, +/**/ 0x3FE6D800, 0x00000000, +/**/ 0x3F2CBDF2, 0x6EAEF381, +/**/ 0x3FD58D54, 0xF86E0000, +/**/ 0x3D2791F3, 0x0A795215, +/**/ 0x3FE6D800, 0x00000000, +/**/ 0xBF323DB9, 0xB624BFF5, +/**/ 0x3FD598C0, 0xD9688000, +/**/ 0xBD385F49, 0x70D96DA4, +/**/ 0x3FE6D000, 0x00000000, +/**/ 0x3F2A6268, 0x1C860FB0, +/**/ 0x3FD5A42A, 0xB0F4D000, +/**/ 0xBCDE63AF, 0x2DF7BA69, +/**/ 0x3FE6D000, 0x00000000, +/**/ 0xBF335443, 0xB253BAE1, +/**/ 0x3FD5AF92, 0x7FCCE000, +/**/ 0xBD1C032F, 0xF5FFC77A, +/**/ 0x3FE6C800, 0x00000000, +/**/ 0x3F2863B1, 0xAB4294D4, +/**/ 0x3FD5BAF8, 0x46AA2000, +/**/ 0xBD339AE8, 0xF873FA41, +/**/ 0x3FE6C800, 0x00000000, +/**/ 0xBF343C7C, 0x87EAA6DF, +/**/ 0x3FD5C65C, 0x0645A000, +/**/ 0xBD39FE06, 0x0180EE65, +/**/ 0x3FE6C000, 0x00000000, +/**/ 0x3F26C16C, 0x16C16C17, +/**/ 0x3FD5D1BD, 0xBF581000, +/**/ 0xBD38D6BD, 0xC9C7C238, +/**/ 0x3FE6C000, 0x00000000, +/**/ 0xBF34F695, 0x95C33E00, +/**/ 0x3FD5DD1D, 0x7299C000, +/**/ 0xBD38AF61, 0x8815CE17, +/**/ 0x3FE6B800, 0x00000000, +/**/ 0x3F257B34, 0xE7802D73, +/**/ 0x3FD5E87B, 0x20C29000, +/**/ 0x3D3527D1, 0x8F7738FA, +/**/ 0x3FE6B800, 0x00000000, +/**/ 0xBF3582BF, 0xF4A5582C, +/**/ 0x3FD5F3D6, 0xCA8A2000, +/**/ 0x3D37AF84, 0x8E19CC75, +/**/ 0x3FE6B000, 0x00000000, +/**/ 0x3F2490AA, 0x31A3CFC7, +/**/ 0x3FD5FF30, 0x70A79000, +/**/ 0x3D2E9E43, 0x9F105039, +/**/ 0x3FE6B000, 0x00000000, +/**/ 0xBF35E12C, 0x77C30E5A, +/**/ 0x3FD60A88, 0x13D1A000, +/**/ 0x3D36E9B9, 0xC879AF55, +/**/ 0x3FE6A800, 0x00000000, +/**/ 0x3F24016A, 0x94016A94, +/**/ 0x3FD615DD, 0xB4BEC000, +/**/ 0x3D13C7CA, 0x90BC04B2, +/**/ 0x3FE6A800, 0x00000000, +/**/ 0xBF36120B, 0xAD33D63F, +/**/ 0x3FD62131, 0x5424F000, +/**/ 0xBD3382FC, 0x4AA68669, +/**/ 0x3FE6A000, 0x00000000, +/**/ 0x3F23CD15, 0x3729043E, +/**/ 0x3FD62C82, 0xF2B9C000, +/**/ 0x3D3E54BD, 0xBD7C8A98 } }; + +static const union {int4 i[4350]; double x[2175]; } vj = { .i = { +/**/ 0x3F46A400, 0x7D161C28, +/**/ 0xBF46A200, 0x20600000, +/**/ 0x3D27DC4E, 0xAA7623D9, +/**/ 0x3F4693FA, 0xD596E639, +/**/ 0xBF4691FD, 0x4CE00000, +/**/ 0x3D26B0CF, 0x29C3F0AD, +/**/ 0x3F4683F5, 0x3219CE89, +/**/ 0xBF4681FA, 0x7B600000, +/**/ 0x3D22B290, 0x95B9FDCC, +/**/ 0x3F4673EF, 0x929ED397, +/**/ 0xBF4671F7, 0xABE00000, +/**/ 0x3D17C727, 0xFA2F2D87, +/**/ 0x3F4663E9, 0xF725F3E2, +/**/ 0xBF4661F4, 0xDE600000, +/**/ 0x3CF22ED3, 0x6EDBFF1C, +/**/ 0x3F4653E4, 0x5FAF2DE9, +/**/ 0xBF4651F2, 0x12E00000, +/**/ 0xBD144936, 0x157812BB, +/**/ 0x3F4643DE, 0xCC3A802B, +/**/ 0xBF4641EF, 0x49600000, +/**/ 0xBD2959CB, 0x60314E05, +/**/ 0x3F4633D9, 0x3CC7E927, +/**/ 0xBF4631EC, 0x81E00000, +/**/ 0xBD35ABDA, 0xC3638E99, +/**/ 0x3F4623D3, 0xB157675C, +/**/ 0xBF4621E9, 0xBC800000, +/**/ 0x3D3FF1D3, 0xC63F9A21, +/**/ 0x3F4613CE, 0x29E8F948, +/**/ 0xBF4611E6, 0xF9000000, +/**/ 0x3D342D26, 0x71EEE611, +/**/ 0x3F4603C8, 0xA67C9D6B, +/**/ 0xBF4601E4, 0x37800000, +/**/ 0x3D1C1C77, 0x11A09689, +/**/ 0x3F45F3C3, 0x27125244, +/**/ 0xBF45F1E1, 0x78000000, +/**/ 0xBD1DFD16, 0xF7DC643C, +/**/ 0x3F45E3BD, 0xABAA1651, +/**/ 0xBF45E1DE, 0xBA800000, +/**/ 0xBD376503, 0x91318A02, +/**/ 0x3F45D3B8, 0x3443E812, +/**/ 0xBF45D1DB, 0xFF200000, +/**/ 0x3D3756E4, 0xCE55DCDD, +/**/ 0x3F45C3B2, 0xC0DFC606, +/**/ 0xBF45C1D9, 0x45A00000, +/**/ 0x3D12D5CF, 0x8F6F8FA0, +/**/ 0x3F45B3AD, 0x517DAEAB, +/**/ 0xBF45B1D6, 0x8E200000, +/**/ 0xBD2E90AB, 0x9B85DC2C, +/**/ 0x3F45A3A7, 0xE61DA081, +/**/ 0xBF45A1D3, 0xD8C00000, +/**/ 0x3D3B5E88, 0x3BF5AC54, +/**/ 0x3F4593A2, 0x7EBF9A07, +/**/ 0xBF4591D1, 0x25400000, +/**/ 0x3D12AC3A, 0x0C86DDB1, +/**/ 0x3F45839D, 0x1B6399BB, +/**/ 0xBF4581CE, 0x73C00000, +/**/ 0xBD3361C2, 0x76830985, +/**/ 0x3F457397, 0xBC099E1C, +/**/ 0xBF4571CB, 0xC4600000, +/**/ 0x3D333915, 0xD062EBFF, +/**/ 0x3F456392, 0x60B1A5AA, +/**/ 0xBF4561C9, 0x16E00000, +/**/ 0xBD1E0DA0, 0x9CC4988F, +/**/ 0x3F45538D, 0x095BAEE4, +/**/ 0xBF4551C6, 0x6B800000, +/**/ 0x3D3C69C4, 0x235BC18A, +/**/ 0x3F454387, 0xB607B848, +/**/ 0xBF4541C3, 0xC2000000, +/**/ 0xBCEFCC99, 0xF7737723, +/**/ 0x3F453382, 0x66B5C056, +/**/ 0xBF4531C1, 0x1A800000, +/**/ 0xBD3FBAE2, 0x809CBCBB, +/**/ 0x3F45237D, 0x1B65C58C, +/**/ 0xBF4521BE, 0x75200000, +/**/ 0x3CCAA5C8, 0x194FEE63, +/**/ 0x3F451377, 0xD417C66A, +/**/ 0xBF4511BB, 0xD1C00000, +/**/ 0x3D3ED325, 0xE1CC7BBC, +/**/ 0x3F450372, 0x90CBC16E, +/**/ 0xBF4501B9, 0x30400000, +/**/ 0xBD0F0298, 0x68AB3742, +/**/ 0x3F44F36D, 0x5181B517, +/**/ 0xBF44F1B6, 0x90E00000, +/**/ 0x3D381BE1, 0x41E67AD9, +/**/ 0x3F44E368, 0x16399FE6, +/**/ 0xBF44E1B3, 0xF3600000, +/**/ 0xBD2A6E79, 0x668D3662, +/**/ 0x3F44D362, 0xDEF38058, +/**/ 0xBF44D1B1, 0x58000000, +/**/ 0x3D284EA7, 0x21F8B7C2, +/**/ 0x3F44C35D, 0xABAF54EC, +/**/ 0xBF44C1AE, 0xBE800000, +/**/ 0xBD3BC76D, 0x7417D9C5, +/**/ 0x3F44B358, 0x7C6D1C22, +/**/ 0xBF44B1AC, 0x27200000, +/**/ 0xBD1409FD, 0x16AAD1FC, +/**/ 0x3F44A353, 0x512CD479, +/**/ 0xBF44A1A9, 0x91C00000, +/**/ 0x3D30771E, 0x98BC14FD, +/**/ 0x3F44934E, 0x29EE7C70, +/**/ 0xBF4491A6, 0xFE400000, +/**/ 0xBD3B5993, 0x5CCB7232, +/**/ 0x3F448349, 0x06B21285, +/**/ 0xBF4481A4, 0x6CE00000, +/**/ 0xBD20E729, 0x5512F9C2, +/**/ 0x3F447343, 0xE7779538, +/**/ 0xBF4471A1, 0xDD800000, +/**/ 0x3D225436, 0x55B30899, +/**/ 0x3F44633E, 0xCC3F0308, +/**/ 0xBF44619F, 0x50200000, +/**/ 0x3D39807C, 0x9E54E31F, +/**/ 0x3F445339, 0xB5085A73, +/**/ 0xBF44519C, 0xC4A00000, +/**/ 0xBD376F6F, 0xD5804C0E, +/**/ 0x3F444334, 0xA1D399FA, +/**/ 0xBF44419A, 0x3B400000, +/**/ 0xBD234953, 0x6CDE6425, +/**/ 0x3F44332F, 0x92A0C01A, +/**/ 0xBF443197, 0xB3E00000, +/**/ 0x3D070E7B, 0xAAF6596F, +/**/ 0x3F44232A, 0x876FCB54, +/**/ 0xBF442195, 0x2E800000, +/**/ 0x3D2C49F8, 0x4EC011F1, +/**/ 0x3F441325, 0x8040BA25, +/**/ 0xBF441192, 0xAB200000, +/**/ 0x3D3825DC, 0xD8AAA7EB, +/**/ 0x3F440320, 0x7D138B0E, +/**/ 0xBF440190, 0x29A00000, +/**/ 0xBD3F1A8D, 0xFE0B73D6, +/**/ 0x3F43F31B, 0x7DE83C8C, +/**/ 0xBF43F18D, 0xAA400000, +/**/ 0xBD379B43, 0xE46CA26B, +/**/ 0x3F43E316, 0x82BECD20, +/**/ 0xBF43E18B, 0x2CE00000, +/**/ 0xBD315B44, 0x6283780D, +/**/ 0x3F43D311, 0x8B973B49, +/**/ 0xBF43D188, 0xB1800000, +/**/ 0xBD28B31E, 0x017589BE, +/**/ 0x3F43C30C, 0x98718584, +/**/ 0xBF43C186, 0x38200000, +/**/ 0xBD212A46, 0x8FBB296E, +/**/ 0x3F43B307, 0xA94DAA52, +/**/ 0xBF43B183, 0xC0C00000, +/**/ 0xBD183403, 0x045CBBD2, +/**/ 0x3F43A302, 0xBE2BA832, +/**/ 0xBF43A181, 0x4B600000, +/**/ 0xBD13009B, 0xD7CC5936, +/**/ 0x3F4392FD, 0xD70B7DA2, +/**/ 0xBF43917E, 0xD8000000, +/**/ 0xBD12B655, 0xC1742279, +/**/ 0x3F4382F8, 0xF3ED2921, +/**/ 0xBF43817C, 0x66A00000, +/**/ 0xBD17512E, 0xEA83FAE8, +/**/ 0x3F4372F4, 0x14D0A930, +/**/ 0xBF437179, 0xF7400000, +/**/ 0xBD206692, 0xBED65875, +/**/ 0x3F4362EF, 0x39B5FC4C, +/**/ 0xBF436177, 0x89E00000, +/**/ 0xBD27931B, 0xD38FFE9E, +/**/ 0x3F4352EA, 0x629D20F5, +/**/ 0xBF435175, 0x1E800000, +/**/ 0xBD309618, 0xE524208F, +/**/ 0x3F4342E5, 0x8F8615AA, +/**/ 0xBF434172, 0xB5200000, +/**/ 0xBD3697E9, 0xDD4C72C5, +/**/ 0x3F4332E0, 0xC070D8EB, +/**/ 0xBF433170, 0x4DC00000, +/**/ 0xBD3DCE00, 0x5E6E12C3, +/**/ 0x3F4322DB, 0xF55D6935, +/**/ 0xBF43216D, 0xE8800000, +/**/ 0x3D39C8A4, 0x0AE9A8CE, +/**/ 0x3F4312D7, 0x2E4BC509, +/**/ 0xBF43116B, 0x85200000, +/**/ 0x3D302D03, 0xD1CD2FA1, +/**/ 0x3F4302D2, 0x6B3BEAE5, +/**/ 0xBF430169, 0x23C00000, +/**/ 0x3D15807D, 0xA3BADFD1, +/**/ 0x3F42F2CD, 0xAC2DD949, +/**/ 0xBF42F166, 0xC4600000, +/**/ 0xBD1A7422, 0xF57F0504, +/**/ 0x3F42E2C8, 0xF1218EB3, +/**/ 0xBF42E164, 0x67000000, +/**/ 0xBD33C974, 0x2F2C781C, +/**/ 0x3F42D2C4, 0x3A1709A3, +/**/ 0xBF42D162, 0x0BC00000, +/**/ 0x3D3DDBDD, 0x851A1E61, +/**/ 0x3F42C2BF, 0x870E4898, +/**/ 0xBF42C15F, 0xB2600000, +/**/ 0x3D2CA7D9, 0xA14AA8FD, +/**/ 0x3F42B2BA, 0xD8074A10, +/**/ 0xBF42B15D, 0x5B000000, +/**/ 0xBD03022E, 0xDDCDDFF5, +/**/ 0x3F42A2B6, 0x2D020C8C, +/**/ 0xBF42A15B, 0x05A00000, +/**/ 0xBD343FBA, 0x0F9231A8, +/**/ 0x3F4292B1, 0x85FE8E8A, +/**/ 0xBF429158, 0xB2600000, +/**/ 0x3D38B690, 0xA52C9CCF, +/**/ 0x3F4282AC, 0xE2FCCE8A, +/**/ 0xBF428156, 0x61000000, +/**/ 0x3D120E6A, 0xC8CC82EB, +/**/ 0x3F4272A8, 0x43FCCB0A, +/**/ 0xBF427154, 0x11A00000, +/**/ 0xBD30D79B, 0x792E6C51, +/**/ 0x3F4262A3, 0xA8FE8289, +/**/ 0xBF426151, 0xC4600000, +/**/ 0x3D38A5EE, 0x91F7F7AA, +/**/ 0x3F42529F, 0x1201F387, +/**/ 0xBF42514F, 0x79000000, +/**/ 0x3CEFA728, 0x46C2E8BA, +/**/ 0x3F42429A, 0x7F071C84, +/**/ 0xBF42414D, 0x2FA00000, +/**/ 0xBD37D0BA, 0xFA447A17, +/**/ 0x3F423295, 0xF00DFBFD, +/**/ 0xBF42314A, 0xE8600000, +/**/ 0x3D2C7A24, 0x94AF3FED, +/**/ 0x3F422291, 0x65169072, +/**/ 0xBF422148, 0xA3000000, +/**/ 0xBD29B0BD, 0x050CEA04, +/**/ 0x3F42128C, 0xDE20D863, +/**/ 0xBF421146, 0x5FC00000, +/**/ 0x3D36EFF3, 0x0C3035EB, +/**/ 0x3F420288, 0x5B2CD24E, +/**/ 0xBF420144, 0x1E600000, +/**/ 0xBD19A3E2, 0x73569B27, +/**/ 0x3F41F283, 0xDC3A7CB2, +/**/ 0xBF41F141, 0xDF200000, +/**/ 0x3D3B1DDE, 0xEEB67715, +/**/ 0x3F41E27F, 0x6149D610, +/**/ 0xBF41E13F, 0xA1C00000, +/**/ 0xBD11EA17, 0x94F49154, +/**/ 0x3F41D27A, 0xEA5ADCE5, +/**/ 0xBF41D13D, 0x66800000, +/**/ 0x3D3ACED9, 0x52DD9D37, +/**/ 0x3F41C276, 0x776D8FB1, +/**/ 0xBF41C13B, 0x2D200000, +/**/ 0xBD1C140B, 0xF72D8EEB, +/**/ 0x3F41B272, 0x0881ECF4, +/**/ 0xBF41B138, 0xF5E00000, +/**/ 0x3D360AE5, 0x939583E1, +/**/ 0x3F41A26D, 0x9D97F32C, +/**/ 0xBF41A136, 0xC0800000, +/**/ 0xBD2C00D9, 0x1D246C7C, +/**/ 0x3F419269, 0x36AFA0D9, +/**/ 0xBF419134, 0x8D400000, +/**/ 0x3D29B40E, 0x0B955CFB, +/**/ 0x3F418264, 0xD3C8F479, +/**/ 0xBF418132, 0x5BE00000, +/**/ 0xBD3964BF, 0x45A6C249, +/**/ 0x3F417260, 0x74E3EC8D, +/**/ 0xBF417130, 0x2CA00000, +/**/ 0xBCE777E0, 0xF3363612, +/**/ 0x3F41625C, 0x1A008792, +/**/ 0xBF41612D, 0xFF600000, +/**/ 0x3D36D608, 0x28DE8296, +/**/ 0x3F415257, 0xC31EC409, +/**/ 0xBF41512B, 0xD4000000, +/**/ 0xBD32AE69, 0x4BB1B788, +/**/ 0x3F414253, 0x703EA071, +/**/ 0xBF414129, 0xAAC00000, +/**/ 0x3D05BF68, 0x170ECD8C, +/**/ 0x3F41324F, 0x21601B48, +/**/ 0xBF413127, 0x83800000, +/**/ 0x3D370A0B, 0x7C653BFC, +/**/ 0x3F41224A, 0xD683330E, +/**/ 0xBF412125, 0x5E200000, +/**/ 0xBD35B70D, 0x77BBBEBF, +/**/ 0x3F411246, 0x8FA7E642, +/**/ 0xBF411123, 0x3AE00000, +/**/ 0xBD0C52EB, 0x93ABC1CD, +/**/ 0x3F410242, 0x4CCE3363, +/**/ 0xBF410121, 0x19A00000, +/**/ 0x3D2B2237, 0xE5C6F4C7, +/**/ 0x3F40F23E, 0x0DF618F1, +/**/ 0xBF40F11E, 0xFA600000, +/**/ 0x3D3D9C5F, 0x1E9A50AD, +/**/ 0x3F40E239, 0xD31F956A, +/**/ 0xBF40E11C, 0xDD000000, +/**/ 0xBD336793, 0x8965F0DA, +/**/ 0x3F40D235, 0x9C4AA74E, +/**/ 0xBF40D11A, 0xC1C00000, +/**/ 0xBD15E6EE, 0x7E49E231, +/**/ 0x3F40C231, 0x69774D1D, +/**/ 0xBF40C118, 0xA8800000, +/**/ 0x3D1D9B9D, 0x04FD621C, +/**/ 0x3F40B22D, 0x3AA58554, +/**/ 0xBF40B116, 0x91400000, +/**/ 0x3D333B55, 0x7DD9EED3, +/**/ 0x3F40A229, 0x0FD54E74, +/**/ 0xBF40A114, 0x7C000000, +/**/ 0x3D3E048F, 0x7AA78478, +/**/ 0x3F409224, 0xE906A6FC, +/**/ 0xBF409112, 0x68A00000, +/**/ 0xBD383C6A, 0x644DDE88, +/**/ 0x3F408220, 0xC6398D6B, +/**/ 0xBF408110, 0x57600000, +/**/ 0xBD2F0D2F, 0x76B8C83A, +/**/ 0x3F40721C, 0xA76E0040, +/**/ 0xBF40710E, 0x48200000, +/**/ 0xBD1F63E0, 0x9CE99FD3, +/**/ 0x3F406218, 0x8CA3FDFB, +/**/ 0xBF40610C, 0x3AE00000, +/**/ 0xBCF328B4, 0x4FE774F2, +/**/ 0x3F405214, 0x75DB851A, +/**/ 0xBF40510A, 0x2FA00000, +/**/ 0x3D11B6BD, 0x3782BCD4, +/**/ 0x3F404210, 0x6314941D, +/**/ 0xBF404108, 0x26600000, +/**/ 0x3D22116F, 0xE7183792, +/**/ 0x3F40320C, 0x544F2983, +/**/ 0xBF403106, 0x1F200000, +/**/ 0x3D293F1E, 0x1B995B3D, +/**/ 0x3F402208, 0x498B43CB, +/**/ 0xBF402104, 0x19E00000, +/**/ 0x3D2E6669, 0xFC162630, +/**/ 0x3F401204, 0x42C8E175, +/**/ 0xBF401102, 0x16A00000, +/**/ 0x3D30C4AA, 0x254FC9F8, +/**/ 0x3F400200, 0x40080100, +/**/ 0xBF400100, 0x15600000, +/**/ 0x3D3154EE, 0xE4431F92, +/**/ 0x3F3FE3F8, 0x829141D6, +/**/ 0xBF3FE1FC, 0x2C400000, +/**/ 0x3D30E503, 0x9B2D30FB, +/**/ 0x3F3FC3F0, 0x8D157F6B, +/**/ 0xBF3FC1F8, 0x31C00000, +/**/ 0x3D2EEBD1, 0x53EBD670, +/**/ 0x3F3FA3E8, 0x9F9CB7BC, +/**/ 0xBF3FA1F4, 0x3B400000, +/**/ 0x3D2A113C, 0xE04A16E0, +/**/ 0x3F3F83E0, 0xBA26E7CA, +/**/ 0xBF3F81F0, 0x48C00000, +/**/ 0x3D233C4A, 0x99C43E34, +/**/ 0x3F3F63D8, 0xDCB40C91, +/**/ 0xBF3F61EC, 0x5A400000, +/**/ 0x3D14DDF6, 0x7BD210C1, +/**/ 0x3F3F43D1, 0x07442311, +/**/ 0xBF3F41E8, 0x6FC00000, +/**/ 0xBCC52C1D, 0x9E4B51C8, +/**/ 0x3F3F23C9, 0x39D72849, +/**/ 0xBF3F21E4, 0x89400000, +/**/ 0xBD1A196F, 0x8EA8C754, +/**/ 0x3F3F03C1, 0x746D1936, +/**/ 0xBF3F01E0, 0xA6C00000, +/**/ 0xBD2BB719, 0xF95AF98D, +/**/ 0x3F3EE3B9, 0xB705F2D8, +/**/ 0xBF3EE1DC, 0xC8400000, +/**/ 0xBD3628EB, 0x28FFD598, +/**/ 0x3F3EC3B2, 0x01A1B22C, +/**/ 0xBF3EC1D8, 0xEDC00000, +/**/ 0xBD3F6D76, 0x0BBAC8F8, +/**/ 0x3F3EA3AA, 0x54405432, +/**/ 0xBF3EA1D5, 0x17800000, +/**/ 0x3D3657D2, 0xB7A7EE0D, +/**/ 0x3F3E83A2, 0xAEE1D5E8, +/**/ 0xBF3E81D1, 0x45000000, +/**/ 0x3D264FDE, 0xFA9CCC78, +/**/ 0x3F3E639B, 0x1186344C, +/**/ 0xBF3E61CD, 0x76800000, +/**/ 0xBCEF83EB, 0xE02EF455, +/**/ 0x3F3E4393, 0x7C2D6C5E, +/**/ 0xBF3E41C9, 0xAC000000, +/**/ 0xBD2C26B3, 0x03C3E129, +/**/ 0x3F3E238B, 0xEED77B1B, +/**/ 0xBF3E21C5, 0xE5800000, +/**/ 0xBD3C1CBE, 0x904D773D, +/**/ 0x3F3E0384, 0x69845D83, +/**/ 0xBF3E01C2, 0x23400000, +/**/ 0x3D34E8B1, 0xD0615454, +/**/ 0x3F3DE37C, 0xEC341093, +/**/ 0xBF3DE1BE, 0x64C00000, +/**/ 0x3D13F7DF, 0xE9BE933E, +/**/ 0x3F3DC375, 0x76E6914B, +/**/ 0xBF3DC1BA, 0xAA400000, +/**/ 0xBD27B7D7, 0x707B004A, +/**/ 0x3F3DA36E, 0x099BDCA9, +/**/ 0xBF3DA1B6, 0xF3C00000, +/**/ 0xBD3DA3F8, 0xEE2141C3, +/**/ 0x3F3D8366, 0xA453EFAC, +/**/ 0xBF3D81B3, 0x41800000, +/**/ 0x3D2F4DA1, 0x63D21825, +/**/ 0x3F3D635F, 0x470EC752, +/**/ 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0xBF2C80CB, 0x17800000, +/**/ 0xBD12D119, 0x8D8D1C8F, +/**/ 0x3F2C418F, 0x1E05880E, +/**/ 0xBF2C40C7, 0x8B800000, +/**/ 0x3D347649, 0x544D2574, +/**/ 0x3F2C0188, 0x15712C30, +/**/ 0xBF2C00C4, 0x07000000, +/**/ 0xBD32D030, 0x4EEA9E68, +/**/ 0x3F2BC181, 0x1CDF709C, +/**/ 0xBF2BC0C0, 0x8B000000, +/**/ 0x3D15E533, 0x74A84109, +/**/ 0x3F2B817A, 0x34504F50, +/**/ 0xBF2B80BD, 0x17000000, +/**/ 0x3D3D53C1, 0x025FBF68, +/**/ 0x3F2B4173, 0x5BC3C24B, +/**/ 0xBF2B40B9, 0xAA800000, +/**/ 0xBD267FA7, 0x6BAA2FA8, +/**/ 0x3F2B016C, 0x9339C38C, +/**/ 0xBF2B00B6, 0x46800000, +/**/ 0x3D277F1D, 0xBB3FDE1E, +/**/ 0x3F2AC165, 0xDAB24D11, +/**/ 0xBF2AC0B2, 0xEA000000, +/**/ 0xBD3DAD17, 0x1A8CDBE2, +/**/ 0x3F2A815F, 0x322D58D9, +/**/ 0xBF2A80AF, 0x96000000, +/**/ 0xBD1E1315, 0xD81CF36E, +/**/ 0x3F2A4158, 0x99AAE0E3, +/**/ 0xBF2A40AC, 0x4A000000, +/**/ 0x3D2C7307, 0xE649E7B4, +/**/ 0x3F2A0152, 0x112ADF2D, +/**/ 0xBF2A00A9, 0x05800000, +/**/ 0xBD3C713A, 0xB77435EC, +/**/ 0x3F29C14B, 0x98AD4DB7, +/**/ 0xBF29C0A5, 0xC9800000, +/**/ 0xBD1E1005, 0x3A7AE827, +/**/ 0x3F298145, 0x3032267F, +/**/ 0xBF2980A2, 0x95800000, +/**/ 0x3D2A0460, 0xA8F2A842, +/**/ 0x3F29413E, 0xD7B96385, +/**/ 0xBF29409F, 0x69000000, +/**/ 0xBD3EDDA5, 0xA7B8321E, +/**/ 0x3F290138, 0x8F42FEC5, +/**/ 0xBF29009C, 0x45000000, +/**/ 0xBD264506, 0x3A3F0D33, +/**/ 0x3F28C132, 0x56CEF241, +/**/ 0xBF28C099, 0x29000000, +/**/ 0x3D206930, 0x33EE13CD, +/**/ 0x3F28812C, 0x2E5D37F6, +/**/ 0xBF288096, 0x15000000, +/**/ 0x3D3B28AC, 0x22DF1FDA, +/**/ 0x3F284126, 0x15EDC9E3, +/**/ 0xBF284093, 0x08800000, +/**/ 0xBD324546, 0xDD73B6DB, +/**/ 0x3F280120, 0x0D80A208, +/**/ 0xBF280090, 0x04800000, +/**/ 0xBCB440C2, 0x6DFEB485, +/**/ 0x3F27C11A, 0x1515BA62, +/**/ 0xBF27C08D, 0x08800000, +/**/ 0x3D31BCBE, 0x9823B19D, +/**/ 0x3F278114, 0x2CAD0CF1, +/**/ 0xBF27808A, 0x14000000, +/**/ 0xBD3CD148, 0xA9EB4E97, +/**/ 0x3F27410E, 0x544693B4, +/**/ 0xBF274087, 0x28000000, +/**/ 0xBD277AAC, 0xCA4F73AA, +/**/ 0x3F270108, 0x8BE248AA, +/**/ 0xBF270084, 0x44000000, +/**/ 0x3D13E656, 0x26068EF7, +/**/ 0x3F26C102, 0xD38025D2, +/**/ 0xBF26C081, 0x68000000, +/**/ 0x3D35547B, 0x44C3EC8A, +/**/ 0x3F2680FD, 0x2B20252A, +/**/ 0xBF26807E, 0x93800000, +/**/ 0xBD3AABA5, 0x110DCE4B, +/**/ 0x3F2640F7, 0x92C240B1, +/**/ 0xBF26407B, 0xC7800000, +/**/ 0xBD260B96, 0xAC011956, +/**/ 0x3F2600F2, 0x0A667267, +/**/ 0xBF260079, 0x03800000, +/**/ 0x3D111C22, 0x5DFA826E, +/**/ 0x3F25C0EC, 0x920CB44A, +/**/ 0xBF25C076, 0x47800000, +/**/ 0x3D333BD6, 0xD8A2980A, +/**/ 0x3F2580E7, 0x29B5005A, +/**/ 0xBF258073, 0x93000000, +/**/ 0xBD3E2660, 0x71C1D861, +/**/ 0x3F2540E1, 0xD15F5095, +/**/ 0xBF254070, 0xE7000000, +/**/ 0xBD2FBD3A, 0x4E77E5EE, +/**/ 0x3F2500DC, 0x890B9EFA, +/**/ 0xBF25006E, 0x43000000, +/**/ 0xBCFEBDF2, 0x7B90A2D9, +/**/ 0x3F24C0D7, 0x50B9E589, +/**/ 0xBF24C06B, 0xA7000000, +/**/ 0x3D2765B3, 0x58F2FF2C, +/**/ 0x3F2480D2, 0x286A1E40, +/**/ 0xBF248069, 0x13000000, +/**/ 0x3D38FE8D, 0x74AE382C, +/**/ 0x3F2440CD, 0x101C431E, +/**/ 0xBF244066, 0x86800000, +/**/ 0xBD3A07C3, 0xB0286224, +/**/ 0x3F2400C8, 0x07D04E23, +/**/ 0xBF240064, 0x02800000, +/**/ 0xBD2ABE33, 0x46EFC0EC, +/**/ 0x3F23C0C3, 0x0F86394D, +/**/ 0xBF23C061, 0x86800000, +/**/ 0xBCF06744, 0x70DE3151, +/**/ 0x3F2380BE, 0x273DFE9C, +/**/ 0xBF23805F, 0x12800000, +/**/ 0x3D260659, 0x05CFCD61, +/**/ 0x3F2340B9, 0x4EF7980F, +/**/ 0xBF23405C, 0xA6800000, +/**/ 0x3D36BEC8, 0xD7DBBEBC, +/**/ 0x3F2300B4, 0x86B2FFA4, +/**/ 0xBF23005A, 0x42000000, +/**/ 0xBD3DD29F, 0x2B2027B4, +/**/ 0x3F22C0AF, 0xCE702F5C, +/**/ 0xBF22C057, 0xE6000000, +/**/ 0xBD32B00B, 0x6959A7D0, +/**/ 0x3F2280AB, 0x262F2134, +/**/ 0xBF228055, 0x92000000, +/**/ 0xBD1F61EF, 0x19FAAC2D, +/**/ 0x3F2240A6, 0x8DEFCF2C, +/**/ 0xBF224053, 0x46000000, +/**/ 0x3D05A87E, 0xCB16B8A8, +/**/ 0x3F2200A2, 0x05B23344, +/**/ 0xBF220051, 0x02000000, +/**/ 0x3D29F32F, 0x23B9B257, +/**/ 0x3F21C09D, 0x8D76477A, +/**/ 0xBF21C04E, 0xC6000000, +/**/ 0x3D36F61B, 0x7E214821, +/**/ 0x3F218099, 0x253C05CD, +/**/ 0xBF21804C, 0x91800000, +/**/ 0xBD3F5464, 0x46FDFCA2, +/**/ 0x3F214094, 0xCD03683D, +/**/ 0xBF21404A, 0x65800000, +/**/ 0xBD35E4E7, 0xA30F2308, +/**/ 0x3F210090, 0x84CC68C9, +/**/ 0xBF210048, 0x41800000, +/**/ 0xBD2974DC, 0xF800CC34, +/**/ 0x3F20C08C, 0x4C970171, +/**/ 0xBF20C046, 0x25800000, +/**/ 0xBD0E9FC5, 0xC1006E9D, +/**/ 0x3F208088, 0x24632C32, +/**/ 0xBF208044, 0x11800000, +/**/ 0x3D133DE7, 0x078E4438, +/**/ 0x3F204084, 0x0C30E30D, +/**/ 0xBF204042, 0x05800000, +/**/ 0x3D2A61D2, 0x15F82A7B, +/**/ 0x3F200080, 0x04002001, +/**/ 0xBF200040, 0x01800000, +/**/ 0x3D355155, 0x3BBB110C, +/**/ 0x3F1F80F8, 0x17A1BA1A, +/**/ 0xBF1F807C, 0x0B000000, +/**/ 0x3D3D31BE, 0x6C520A9B, +/**/ 0x3F1F00F0, 0x47462860, +/**/ 0xBF1F0078, 0x22000000, +/**/ 0xBD3B2CDB, 0x4B6D83F6, +/**/ 0x3F1E80E8, 0x96ED7ED3, +/**/ 0xBF1E8074, 0x4A000000, +/**/ 0xBD33C977, 0xD4122C5A, +/**/ 0x3F1E00E1, 0x0697B172, +/**/ 0xBF1E0070, 0x82000000, +/**/ 0xBD29462E, 0x2D1517C4, +/**/ 0x3F1D80D9, 0x9644B43B, +/**/ 0xBF1D806C, 0xCA000000, +/**/ 0xBD16E2E3, 0xF0952D45, +/**/ 0x3F1D00D2, 0x45F47B2C, +/**/ 0xBF1D0069, 0x22000000, +/**/ 0x3CEED452, 0x2DDC2A8D, +/**/ 0x3F1C80CB, 0x15A6FA46, +/**/ 0xBF1C8065, 0x8A000000, +/**/ 0x3D1DAFEE, 0xA08CEBE8, +/**/ 0x3F1C00C4, 0x055C2585, +/**/ 0xBF1C0062, 0x02000000, +/**/ 0x3D2B50A4, 0xBB11EF55, +/**/ 0x3F1B80BD, 0x1513F0E9, +/**/ 0xBF1B805E, 0x8A000000, +/**/ 0x3D33ACA6, 0xC6D142BF, +/**/ 0x3F1B00B6, 0x44CE5071, +/**/ 0xBF1B005B, 0x22000000, +/**/ 0x3D3979F8, 0xF8CD3D11, +/**/ 0x3F1A80AF, 0x948B381A, +/**/ 0xBF1A8057, 0xCA000000, +/**/ 0x3D3F1149, 0x07EDFD29, +/**/ 0x3F1A00A9, 0x044A9BE5, +/**/ 0xBF1A0054, 0x81000000, +/**/ 0xBD3B8C68, 0xF7BB7092, +/**/ 0x3F1980A2, 0x940C6FCF, +/**/ 0xBF198051, 0x49000000, +/**/ 0xBD365E1C, 0xF27E09A9, +/**/ 0x3F19009C, 0x43D0A7D8, +/**/ 0xBF19004E, 0x21000000, +/**/ 0xBD3162D2, 0xD508D564, +/**/ 0x3F188096, 0x139737FE, +/**/ 0xBF18804B, 0x09000000, +/**/ 0xBD293315, 0x18D5C93E, +/**/ 0x3F180090, 0x03601440, +/**/ 0xBF180048, 0x01000000, +/**/ 0xBD200288, 0x0C26A328, +/**/ 0x3F17808A, 0x132B309E, +/**/ 0xBF178045, 0x09000000, +/**/ 0xBD0CC7F9, 0x7E89FD6F, +/**/ 0x3F170084, 0x42F88115, +/**/ 0xBF170042, 0x21000000, +/**/ 0x3CE40881, 0x058494DC, +/**/ 0x3F16807E, 0x92C7F9A5, +/**/ 0xBF16803F, 0x49000000, +/**/ 0x3D12AE16, 0xCD5698B9, +/**/ 0x3F160079, 0x02998E4D, +/**/ 0xBF16003C, 0x81000000, +/**/ 0x3D21138B, 0xC5780E17, +/**/ 0x3F158073, 0x926D330B, +/**/ 0xBF158039, 0xC9000000, +/**/ 0x3D287809, 0x4E2001E2, +/**/ 0x3F15006E, 0x4242DBDF, +/**/ 0xBF150037, 0x21000000, +/**/ 0x3D2F8684, 0x21448AA2, +/**/ 0x3F148069, 0x121A7CC8, +/**/ 0xBF148034, 0x89000000, +/**/ 0x3D33207E, 0x2F637D8E, +/**/ 0x3F140064, 0x01F409C4, +/**/ 0xBF140032, 0x01000000, +/**/ 0x3D3654B9, 0x12E44B29, +/**/ 0x3F13805F, 0x11CF76D3, +/**/ 0xBF13802F, 0x89000000, +/**/ 0x3D3960F2, 0xCA5547F3, +/**/ 0x3F13005A, 0x41ACB7F4, +/**/ 0xBF13002D, 0x21000000, +/**/ 0x3D3C462B, 0x6487063D, +/**/ 0x3F128055, 0x918BC126, +/**/ 0xBF12802A, 0xC9000000, +/**/ 0x3D3F0562, 0xEFEA1107, +/**/ 0x3F120051, 0x016C8668, +/**/ 0xBF120028, 0x80000000, +/**/ 0xBD3E6066, 0x857113CE, +/**/ 0x3F11804C, 0x914EFBBA, +/**/ 0xBF118026, 0x48000000, +/**/ 0xBD3BEA30, 0xEDD9EB54, +/**/ 0x3F110048, 0x41331519, +/**/ 0xBF110024, 0x20000000, +/**/ 0xBD3996FC, 0x3BFFFF5A, +/**/ 0x3F108044, 0x1118C686, +/**/ 0xBF108022, 0x08000000, +/**/ 0xBD3765C8, 0x62F2E042, +/**/ 0x3F100040, 0x01000400, +/**/ 0xBF100020, 0x00000000, +/**/ 0xBD355595, 0x562224CD, +/**/ 0x3F0F0078, 0x21D1830C, +/**/ 0xBF0F003C, 0x10000000, +/**/ 0xBD336563, 0x095D69EB, +/**/ 0x3F0E0070, 0x81A5E62E, +/**/ 0xBF0E0038, 0x40000000, +/**/ 0xBD319431, 0x70D45290, +/**/ 0x3F0D0069, 0x217D1965, +/**/ 0xBF0D0034, 0x90000000, +/**/ 0xBD2FC201, 0x022D0EF6, +/**/ 0x3F0C0062, 0x015704B1, +/**/ 0xBF0C0031, 0x00000000, +/**/ 0xBD2C95A0, 0x5E276E21, +/**/ 0x3F0B005B, 0x2133900E, +/**/ 0xBF0B002D, 0x90000000, +/**/ 0xBD29A140, 0xE0372A42, +/**/ 0x3F0A0054, 0x8112A37D, +/**/ 0xBF0A002A, 0x40000000, +/**/ 0xBD26E2E2, 0x73BBB580, +/**/ 0x3F09004E, 0x20F426FB, +/**/ 0xBF090027, 0x10000000, +/**/ 0xBD245885, 0x04D48C20, +/**/ 0x3F080048, 0x00D80288, +/**/ 0xBF080024, 0x00000000, +/**/ 0xBD220028, 0x80613426, +/**/ 0x3F070042, 0x20BE1E23, +/**/ 0xBF070021, 0x10000000, +/**/ 0xBD1FAF99, 0xA80279F3, +/**/ 0x3F06003C, 0x80A661CA, +/**/ 0xBF06001E, 0x40000000, +/**/ 0xBD1BBAE3, 0xDC287DFE, +/**/ 0x3F050037, 0x2090B57C, +/**/ 0xBF05001B, 0x90000000, +/**/ 0xBD181E2F, 0x7B73B67C, +/**/ 0x3F040032, 0x007D0139, +/**/ 0xBF040019, 0x00000000, +/**/ 0xBD14D57C, 0x65A375F8, +/**/ 0x3F03002D, 0x206B2CFF, +/**/ 0xBF030016, 0x90000000, +/**/ 0xBD11DCCA, 0x7BF71EC1, +/**/ 0x3F020028, 0x805B20CD, +/**/ 0xBF020014, 0x40000000, +/**/ 0xBD0E6033, 0x425C4447, +/**/ 0x3F010024, 0x204CC4A3, +/**/ 0xBF010012, 0x10000000, +/**/ 0xBD0996D3, 0x730FFF5C, +/**/ 0x3F000020, 0x00400080, +/**/ 0xBF000010, 0x00000000, +/**/ 0xBD055575, 0x558888DE, +/**/ 0x3EFE0038, 0x406978C6, +/**/ 0xBEFE001C, 0x20000000, +/**/ 0xBD019418, 0xB845146A, +/**/ 0x3EFC0031, 0x0055C096, +/**/ 0xBEFC0018, 0x80000000, +/**/ 0xBCFC957A, 0xD989DB3C, +/**/ 0x3EFA002A, 0x4044A870, +/**/ 0xBEFA0015, 0x20000000, +/**/ 0xBCF6E2C6, 0x8F0EED2F, +/**/ 0x3EF80024, 0x00360051, +/**/ 0xBEF80012, 0x00000000, +/**/ 0xBCF20014, 0x40184CEB, +/**/ 0x3EF6001E, 0x40299839, +/**/ 0xBEF6000F, 0x20000000, +/**/ 0xBCEBBAC7, 0x434A1F5C, +/**/ 0x3EF40019, 0x001F4027, +/**/ 0xBEF4000C, 0x80000000, +/**/ 0xBCE4D568, 0xDD68DD6A, +/**/ 0x3EF20014, 0x4016C81A, +/**/ 0xBEF2000A, 0x20000000, +/**/ 0xBCDE6019, 0xA11710FC, +/**/ 0x3EF00010, 0x00100010, +/**/ 0xBEF00008, 0x00000000, +/**/ 0xBCD55565, 0x5562222D, +/**/ 0x3EEC0018, 0x80157013, +/**/ 0xBEEC000C, 0x40000000, +/**/ 0xBCCC9568, 0x176276C5, +/**/ 0x3EE80012, 0x000D800A, +/**/ 0xBEE80009, 0x00000000, +/**/ 0xBCC2000A, 0x20061337, +/**/ 0x3EE4000C, 0x8007D005, +/**/ 0xBEE40006, 0x40000000, +/**/ 0xBCB4D55F, 0x195A3758, +/**/ 0x3EE00008, 0x00040002, +/**/ 0xBEE00004, 0x00000000, +/**/ 0xBCA5555D, 0x5558888A, +/**/ 0x3ED80009, 0x00036001, +/**/ 0xBED80004, 0x80000000, +/**/ 0xBC920005, 0x100184CD, +/**/ 0x3ED00004, 0x00010000, +/**/ 0xBED00002, 0x00000000, +/**/ 0xBC755559, 0x55562222, +/**/ 0x3EC00002, 0x00004000, +/**/ 0xBEC00001, 0x00000000, +/**/ 0xBC455557, 0x55558889, +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0xBEBFFFFC, 0x00008000, +/**/ 0x3EBFFFFE, 0x00000000, +/**/ 0x3C455553, 0x55558889, +/**/ 0xBECFFFF8, 0x00020000, +/**/ 0x3ECFFFFC, 0x00000000, +/**/ 0x3C755551, 0x55562222, +/**/ 0xBED7FFF7, 0x00035FFF, +/**/ 0x3ED7FFFB, 0x80000000, +/**/ 0x3C91FFFA, 0xF00184CC, +/**/ 0xBEDFFFF0, 0x0007FFFC, +/**/ 0x3EDFFFF8, 0x00000000, +/**/ 0x3CA5554D, 0x55588887, +/**/ 0xBEE3FFF3, 0x8007CFFB, +/**/ 0x3EE3FFF9, 0xC0000000, +/**/ 0x3CB4D54B, 0x915A3753, +/**/ 0xBEE7FFEE, 0x000D7FF6, +/**/ 0x3EE7FFF7, 0x00000000, +/**/ 0x3CC1FFF5, 0xE006132F, +/**/ 0xBEEBFFE7, 0x80156FED, +/**/ 0x3EEBFFF3, 0xC0000000, +/**/ 0x3CCC9542, 0x936276B2, +/**/ 0xBEEFFFE0, 0x001FFFE0, +/**/ 0x3EEFFFF0, 0x00000000, +/**/ 0x3CD55545, 0x55622217, +/**/ 0xBEF1FFEB, 0xC016C7E6, +/**/ 0x3EF1FFF5, 0xE0000000, +/**/ 0x3CDE5FE6, 0x5F1710D1, +/**/ 0xBEF3FFE7, 0x001F3FD9, +/**/ 0x3EF3FFF3, 0x80000000, +/**/ 0x3CE4D541, 0xCD68DD41, +/**/ 0xBEF5FFE1, 0xC02997C7, +/**/ 0x3EF5FFF0, 0xE0000000, +/**/ 0x3CEBBA8E, 0x124A1F13, +/**/ 0xBEF7FFDC, 0x0035FFAF, +/**/ 0x3EF7FFEE, 0x00000000, +/**/ 0x3CF1FFEB, 0xC0184CAE, +/**/ 0xBEF9FFD5, 0xC044A790, +/**/ 0x3EF9FFEA, 0xE0000000, +/**/ 0x3CF6E28E, 0xC68EECCD, +/**/ 0xBEFBFFCF, 0x0055BF6A, +/**/ 0x3EFBFFE7, 0x80000000, +/**/ 0x3CFC952F, 0xD189DAA2, +/**/ 0xBEFDFFC7, 0xC069773A, +/**/ 0x3EFDFFE3, 0xE0000000, +/**/ 0x3D0193E7, 0x480513F6, +/**/ 0xBEFFFFC0, 0x007FFF00, +/**/ 0x3EFFFFE0, 0x00000000, +/**/ 0x3D055535, 0x55888833, +/**/ 0xBF00FFDB, 0xE04CC35D, +/**/ 0x3F00FFED, 0xF0000000, +/**/ 0x3D099681, 0xE2CFFE66, +/**/ 0xBF01FFD7, 0x805B1F33, +/**/ 0x3F01FFEB, 0xC0000000, +/**/ 0x3D0E5FCC, 0xBE5C42ED, +/**/ 0xBF02FFD2, 0xE06B2B01, +/**/ 0x3F02FFE9, 0x70000000, +/**/ 0x3D11DC8A, 0xD9D71DD1, +/**/ 0xBF03FFCE, 0x007CFEC8, +/**/ 0x3F03FFE7, 0x00000000, +/**/ 0x3D14D52E, 0x45A374B3, +/**/ 0xBF04FFC8, 0xE090B284, +/**/ 0x3F04FFE4, 0x70000000, +/**/ 0x3D181DD0, 0x8553B4C7, +/**/ 0xBF05FFC3, 0x80A65E36, +/**/ 0x3F05FFE1, 0xC0000000, +/**/ 0x3D1BBA71, 0x7A287BBE, +/**/ 0xBF06FFBD, 0xE0BE19DD, +/**/ 0x3F06FFDE, 0xF0000000, +/**/ 0x3D1FAF11, 0x03E27702, +/**/ 0xBF07FFB8, 0x00D7FD78, +/**/ 0x3F07FFDC, 0x00000000, +/**/ 0x3D21FFD7, 0x80613240, +/**/ 0xBF08FFB1, 0xE0F42105, +/**/ 0x3F08FFD8, 0xF0000000, +/**/ 0x3D245825, 0xA6C489B3, +/**/ 0xBF09FFAB, 0x81129C84, +/**/ 0x3F09FFD5, 0xC0000000, +/**/ 0x3D26E272, 0xE2BBB26F, +/**/ 0xBF0AFFA4, 0xE13387F2, +/**/ 0x3F0AFFD2, 0x70000000, +/**/ 0x3D29A0BF, 0x21272669, +/**/ 0xBF0BFF9E, 0x0156FB50, +/**/ 0x3F0BFFCF, 0x00000000, +/**/ 0x3D2C950A, 0x4E276957, +/**/ 0xBF0CFF96, 0xE17D0E9B, +/**/ 0x3F0CFFCB, 0x70000000, +/**/ 0x3D2FC154, 0x551D090E, +/**/ 0xBF0DFF8F, 0x81A5D9D2, +/**/ 0x3F0DFFC7, 0xC0000000, +/**/ 0x3D3193CE, 0x90544EF1, +/**/ 0xBF0EFF87, 0xE1D174F4, +/**/ 0x3F0EFFC3, 0xF0000000, +/**/ 0x3D3364F2, 0x4D556583, +/**/ 0xBF0FFF80, 0x01FFF800, +/**/ 0x3F0FFFC0, 0x00000000, +/**/ 0x3D355515, 0x56221F78, +/**/ 0xBF107FBB, 0xF118BD7A, +/**/ 0x3F107FDD, 0xF8000000, +/**/ 0x3D376537, 0x9EEAD9D8, +/**/ 0xBF10FFB7, 0xC1330AE7, +/**/ 0x3F10FFDB, 0xE0000000, +/**/ 0x3D399659, 0x1B7FF7AE, +/**/ 0xBF117FB3, 0x714EF047, +/**/ 0x3F117FD9, 0xB8000000, +/**/ 0x3D3BE979, 0xBF51E233, +/**/ 0xBF11FFAF, 0x016C7998, +/**/ 0x3F11FFD7, 0x80000000, +/**/ 0x3D3E5F99, 0x7D7108FF, +/**/ 0xBF127FAA, 0x718BB2DA, +/**/ 0x3F127FD5, 0x39000000, +/**/ 0xBD3F0647, 0xB7721DC6, +/**/ 0xBF12FFA5, 0xC1ACA80C, +/**/ 0x3F12FFD2, 0xE1000000, +/**/ 0xBD3C4729, 0xED071532, +/**/ 0xBF137FA0, 0xF1CF652D, +/**/ 0x3F137FD0, 0x79000000, +/**/ 0xBD39620D, 0x315D596D, +/**/ 0xBF13FF9C, 0x01F3F63C, +/**/ 0x3F13FFCE, 0x01000000, +/**/ 0xBD3655F1, 0x92E45F81, +/**/ 0xBF147F96, 0xF21A6739, +/**/ 0x3F147FCB, 0x79000000, +/**/ 0xBD3321D7, 0x206B9526, +/**/ 0xBF14FF91, 0xC242C421, +/**/ 0x3F14FFC8, 0xE1000000, +/**/ 0xBD2F897B, 0xD244C12A, +/**/ 0xBF157F8C, 0x726D18F6, +/**/ 0x3F157FC6, 0x39000000, +/**/ 0xBD287B4B, 0xF93040AE, +/**/ 0xBF15FF87, 0x029971B4, +/**/ 0x3F15FFC3, 0x81000000, +/**/ 0xBD21171E, 0xD578562C, +/**/ 0xBF167F81, 0x72C7DA5C, +/**/ 0x3F167FC0, 0xB9000000, +/**/ 0xBD12B5E9, 0x0F773DB4, +/**/ 0xBF16FF7B, 0xC2F85EEC, +/**/ 0x3F16FFBD, 0xE1000000, +/**/ 0xBCE44CD3, 0x158A76C2, +/**/ 0xBF177F75, 0xF32B0B63, +/**/ 0x3F177FBA, 0xF9000000, +/**/ 0x3D0CB55C, 0x2E48511B, +/**/ 0xBF17FF70, 0x035FEBC0, +/**/ 0x3F17FFB8, 0x01000000, +/**/ 0x3D1FFAF0, 0x184C534F, +/**/ 0xBF187F69, 0xF3970C03, +/**/ 0x3F187FB4, 0xF9000000, +/**/ 0x3D292D95, 0xACC53FBE, +/**/ 0xBF18FF63, 0xC3D07829, +/**/ 0x3F18FFB1, 0xE1000000, +/**/ 0x3D315FD7, 0xE48887C8, +/**/ 0xBF197F5D, 0x740C3C32, +/**/ 0x3F197FAE, 0xB9000000, +/**/ 0x3D365AE3, 0x1DF5B242, +/**/ 0xBF19FF57, 0x044A641C, +/**/ 0x3F19FFAB, 0x81000000, +/**/ 0x3D3B88EC, 0x6FBB0E5F, +/**/ 0xBF1A7F50, 0x748AFBE7, +/**/ 0x3F1A7FA8, 0x3A000000, +/**/ 0xBD3F150C, 0x39766B40, +/**/ 0xBF1AFF49, 0xC4CE0F91, +/**/ 0x3F1AFFA4, 0xE2000000, +/**/ 0xBD397E06, 0xF14DB839, +/**/ 0xBF1B7F42, 0xF513AB19, +/**/ 0x3F1B7FA1, 0x7A000000, +/**/ 0xBD33B103, 0xCBD9CC3D, +/**/ 0xBF1BFF3C, 0x055BDA7D, +/**/ 0x3F1BFF9E, 0x02000000, +/**/ 0xBD2B5A05, 0xBB1321B5, +/**/ 0xBF1C7F34, 0xF5A6A9BD, +/**/ 0x3F1C7F9A, 0x7A000000, +/**/ 0xBD1DC410, 0xECAF9551, +/**/ 0xBF1CFF2D, 0xC5F424D6, +/**/ 0x3F1CFF96, 0xE2000000, +/**/ 0xBCEF80FF, 0x3DF3CD68, +/**/ 0xBF1D7F26, 0x764457C8, +/**/ 0x3F1D7F93, 0x3A000000, +/**/ 0x3D16CBC7, 0x4271E737, +/**/ 0xBF1DFF1F, 0x06974E91, +/**/ 0x3F1DFF8F, 0x82000000, +/**/ 0x3D2939D2, 0x1D134848, +/**/ 0xBF1E7F17, 0x76ED1530, +/**/ 0x3F1E7F8B, 0xBA000000, +/**/ 0x3D33C2DD, 0xA9892C73, +/**/ 0xBF1EFF0F, 0xC745B7A4, +/**/ 0x3F1EFF87, 0xE2000000, +/**/ 0x3D3B25CF, 0x8AEC69D5, +/**/ 0xBF1F7F07, 0xF7A141EA, +/**/ 0x3F1F7F83, 0xFB000000, +/**/ 0xBD3D3941, 0x645B412A, +/**/ 0xBF1FFF00, 0x07FFC002, +/**/ 0x3F1FFF80, 0x03000000, +/**/ 0xBD355955, 0x3BBC6662, +/**/ 0xBF203F7B, 0xFC309EF5, +/**/ 0x3F203FBD, 0xFD800000, +/**/ 0xBD2A72D8, 0x260B17B3, +/**/ 0xBF207F77, 0xE462E3D0, +/**/ 0x3F207FBB, 0xF1800000, +/**/ 0xBD136218, 0x0994AE68, +/**/ 0xBF20BF73, 0xBC96B492, +/**/ 0x3F20BFB9, 0xDD800000, +/**/ 0x3D0E52E6, 0xECB2641F, +/**/ 0xBF20FF6F, 0x84CC1739, +/**/ 0x3F20FFB7, 0xC1800000, +/**/ 0x3D296078, 0xE7FCF60B, +/**/ 0xBF213F6B, 0x3D0311C6, +/**/ 0x3F213FB5, 0x9D800000, +/**/ 0x3D35DA18, 0xA7850AFF, +/**/ 0xBF217F66, 0xE53BAA36, +/**/ 0x3F217FB3, 0x71800000, +/**/ 0x3D3F48F1, 0x5E7BB444, +/**/ 0xBF21BF62, 0x7D75E68A, +/**/ 0x3F21BFB1, 0x3E000000, +/**/ 0xBD370239, 0x812BC469, +/**/ 0xBF21FF5E, 0x05B1CCC0, +/**/ 0x3F21FFAF, 0x02000000, +/**/ 0xBD2A0CD0, 0x23BF1A4D, +/**/ 0xBF223F59, 0x7DEF62D8, +/**/ 0x3F223FAC, 0xBE000000, +/**/ 0xBD0614D3, 0x736E3623, +/**/ 0xBF227F54, 0xE62EAED0, +/**/ 0x3F227FAA, 0x72000000, +/**/ 0x3D1F28BD, 0x37EDEDB0, +/**/ 0xBF22BF50, 0x3E6FB6A9, +/**/ 0x3F22BFA8, 0x1E000000, +/**/ 0x3D32A0F5, 0x07CE33C8, +/**/ 0xBF22FF4B, 0x86B28060, +/**/ 0x3F22FFA5, 0xC2000000, +/**/ 0x3D3DC2B6, 0xA31C6A8D, +/**/ 0xBF233F46, 0xBEF711F6, +/**/ 0x3F233FA3, 0x5E800000, +/**/ 0xBD36CF8B, 0xFC67C9FB, +/**/ 0xBF237F41, 0xE73D7169, +/**/ 0x3F237FA0, 0xF2800000, +/**/ 0xBD2629A5, 0xE6D88A89, +/**/ 0xBF23BF3C, 0xFF85A4B8, +/**/ 0x3F23BF9E, 0x7E800000, +/**/ 0x3CEE7C34, 0x202574EC, +/**/ 0xBF23FF38, 0x07CFB1E3, +/**/ 0x3F23FF9C, 0x02800000, +/**/ 0x3D2A9723, 0x46E594C1, +/**/ 0xBF243F33, 0x001B9EE8, +/**/ 0x3F243F99, 0x7E800000, +/**/ 0x3D39F33C, 0xF61AE74C, +/**/ 0xBF247F2D, 0xE86971C7, +/**/ 0x3F247F96, 0xF3000000, +/**/ 0xBD39141C, 0x85341E31, +/**/ 0xBF24BF28, 0xC0B9307F, +/**/ 0x3F24BF94, 0x5F000000, +/**/ 0xBD2792F5, 0xDA0FAF09, +/**/ 0xBF24FF23, 0x890AE10E, +/**/ 0x3F24FF91, 0xC3000000, +/**/ 0x3CFD4219, 0xFB239430, +/**/ 0xBF253F1E, 0x415E8974, +/**/ 0x3F253F8F, 0x1F000000, +/**/ 0x3D2F8B72, 0x0359434A, +/**/ 0xBF257F18, 0xE9B42FAF, +/**/ 0x3F257F8C, 0x73000000, +/**/ 0x3D3E0C4B, 0x1939FEDF, +/**/ 0xBF25BF13, 0x820BD9BF, +/**/ 0x3F25BF89, 0xBF800000, +/**/ 0xBD335728, 0x39B301E2, +/**/ 0xBF25FF0E, 0x0A658DA3, +/**/ 0x3F25FF87, 0x03800000, +/**/ 0xBD118E84, 0x5E1E8D4F, +/**/ 0xBF263F08, 0x82C15159, +/**/ 0x3F263F84, 0x3F800000, +/**/ 0x3D25CFC0, 0xBDDDD045, +/**/ 0xBF267F02, 0xEB1F2AE1, +/**/ 0x3F267F81, 0x73800000, +/**/ 0x3D3A8C5C, 0x08837E99, +/**/ 0xBF26BEFD, 0x437F203A, +/**/ 0x3F26BF7E, 0xA0000000, +/**/ 0xBD35752E, 0x3C56F12D, +/**/ 0xBF26FEF7, 0x8BE13762, +/**/ 0x3F26FF7B, 0xC4000000, +/**/ 0xBD146EFA, 0x46359E28, +/**/ 0xBF273EF1, 0xC4457659, +/**/ 0x3F273F78, 0xE0000000, +/**/ 0x3D273355, 0xCD265865, +/**/ 0xBF277EEB, 0xECABE31C, +/**/ 0x3F277F75, 0xF4000000, +/**/ 0x3D3CAC0E, 0x095DEBF8, +/**/ 0xBF27BEE6, 0x051483AC, +/**/ 0x3F27BF73, 0x00800000, +/**/ 0xBD31E395, 0x4C39F4DB, +/**/ 0xBF27FEE0, 0x0D7F5E08, +/**/ 0x3F27FF70, 0x04800000, +/**/ 0xBCB43F3D, 0xA1314B81, +/**/ 0xBF283EDA, 0x05EC782D, +/**/ 0x3F283F6D, 0x00800000, +/**/ 0x3D321B10, 0x115B8D70, +/**/ 0xBF287ED3, 0xEE5BD81B, +/**/ 0x3F287F69, 0xF5000000, +/**/ 0xBD3B54A7, 0x83704FE1, +/**/ 0xBF28BECD, 0xC6CD83D1, +/**/ 0x3F28BF66, 0xE1000000, +/**/ 0xBD20C4CC, 0x41229C91, +/**/ 0xBF28FEC7, 0x8F41814D, +/**/ 0x3F28FF63, 0xC5000000, +/**/ 0x3D25E5A8, 0x2A183F17, +/**/ 0xBF293EC1, 0x47B7D68F, +/**/ 0x3F293F60, 0xA1000000, +/**/ 0x3D3EAC06, 0xF81B997D, +/**/ 0xBF297EBA, 0xF0308995, +/**/ 0x3F297F5D, 0x75800000, +/**/ 0xBD2A6B9B, 0x3A1E5BAD, +/**/ 0xBF29BEB4, 0x88ABA05E, +/**/ 0x3F29BF5A, 0x41800000, +/**/ 0x3D1D3958, 0xBDFE3C77, +/**/ 0xBF29FEAE, 0x112920E9, +/**/ 0x3F29FF57, 0x05800000, +/**/ 0x3D3C3972, 0x375BA904, +/**/ 0xBF2A3EA7, 0x89A91135, +/**/ 0x3F2A3F53, 0xC2000000, +/**/ 0xBD2CE6F3, 0x588DE85B, +/**/ 0xBF2A7EA0, 0xF22B7740, +/**/ 0x3F2A7F50, 0x76000000, +/**/ 0x3D1D2249, 0x75AEDBFD, +/**/ 0xBF2ABE9A, 0x4AB05909, +/**/ 0x3F2ABF4D, 0x22000000, +/**/ 0x3D3D6E96, 0x2CE7BDAC, +/**/ 0xBF2AFE93, 0x9337BC90, +/**/ 0x3F2AFF49, 0xC6800000, +/**/ 0xBD2800DC, 0xCB7D724C, +/**/ 0xBF2B3E8C, 0xCBC1A7D1, +/**/ 0x3F2B3F46, 0x62800000, +/**/ 0x3D25F908, 0xFA591B29, +/**/ 0xBF2B7E85, 0xF44E20CE, +/**/ 0x3F2B7F42, 0xF7000000, +/**/ 0xBD3D9991, 0x53021ED8, +/**/ 0xBF2BBE7F, 0x0CDD2D83, +/**/ 0x3F2BBF3F, 0x83000000, +/**/ 0xBD1706BF, 0xFD596AD6, +/**/ 0xBF2BFE78, 0x156ED3F0, +/**/ 0x3F2BFF3C, 0x07000000, +/**/ 0x3D328528, 0x4EC45253, +/**/ 0xBF2C3E71, 0x0E031A14, +/**/ 0x3F2C3F38, 0x83800000, +/**/ 0xBD34C408, 0x927D8A9E, +/**/ 0xBF2C7E69, 0xF69A05ED, +/**/ 0x3F2C7F34, 0xF7800000, +/**/ 0x3D118EF4, 0xCAE2C25F, +/**/ 0xBF2CBE62, 0xCF339D7A, +/**/ 0x3F2CBF31, 0x63800000, +/**/ 0x3D3DFD79, 0x73DBBB41, +/**/ 0xBF2CFE5B, 0x97CFE6B9, +/**/ 0x3F2CFF2D, 0xC8000000, +/**/ 0xBD1FD74F, 0xE7FE77E6, +/**/ 0xBF2D3E54, 0x506EE7AA, +/**/ 0x3F2D3F2A, 0x24000000, +/**/ 0x3D328AD4, 0xBDDB871F, +/**/ 0xBF2D7E4C, 0xF910A64A, +/**/ 0x3F2D7F26, 0x78800000, +/**/ 0xBD327F8C, 0x903DDD81, +/**/ 0xBF2DBE45, 0x91B52899, +/**/ 0x3F2DBF22, 0xC4800000, +/**/ 0x3D21D80F, 0xDF52840A, +/**/ 0xBF2DFE3E, 0x1A5C7495, +/**/ 0x3F2DFF1F, 0x09000000, +/**/ 0xBD3B316D, 0xEED9F651, +/**/ 0xBF2E3E36, 0x9306903D, +/**/ 0x3F2E3F1B, 0x45000000, +/**/ 0x3CF2911A, 0x76DB3C6B, +/**/ 0xBF2E7E2E, 0xFBB3818F, +/**/ 0x3F2E7F17, 0x79000000, +/**/ 0x3D3DFC86, 0x85559113, +/**/ 0xBF2EBE27, 0x54634E89, +/**/ 0x3F2EBF13, 0xA5800000, +/**/ 0xBD12D83E, 0x0AB3DBE7, +/**/ 0xBF2EFE1F, 0x9D15FD2B, +/**/ 0x3F2EFF0F, 0xC9800000, +/**/ 0x3D39124F, 0x617B99F1, +/**/ 0xBF2F3E17, 0xD5CB9373, +/**/ 0x3F2F3F0B, 0xE6000000, +/**/ 0xBD2152B9, 0xF8F64DA1, +/**/ 0xBF2F7E0F, 0xFE841760, +/**/ 0x3F2F7F07, 0xFA000000, +/**/ 0x3D3617EB, 0x34C4735B, +/**/ 0xBF2FBE08, 0x173F8EEF, +/**/ 0x3F2FBF04, 0x06800000, +/**/ 0xBD2551B0, 0x739FA712, +/**/ 0xBF2FFE00, 0x1FFE0020, +/**/ 0x3F2FFF00, 0x0A800000, +/**/ 0x3D351558, 0x885DE027, +/**/ 0xBF301EFC, 0x0C5FB879, +/**/ 0x3F301F7E, 0x03800000, +/**/ 0xBD255905, 0x68F8FC50, +/**/ 0xBF303EF8, 0x00C1F3B0, +/**/ 0x3F303F7B, 0xFD800000, +/**/ 0x3D361295, 0xDF771CF4, +/**/ 0xBF305EF3, 0xED25B4B7, +/**/ 0x3F305F79, 0xF3C00000, +/**/ 0xBD2158BB, 0xD8A255DB, +/**/ 0xBF307EEF, 0xD18AFE8B, +/**/ 0x3F307F77, 0xE5C00000, +/**/ 0x3D3917A1, 0xB740E625, +/**/ 0xBF309EEB, 0xADF1D42C, +/**/ 0x3F309F75, 0xD4000000, +/**/ 0xBD1281AD, 0x9C716D59, +/**/ 0xBF30BEE7, 0x825A3899, +/**/ 0x3F30BF73, 0xBE000000, +/**/ 0x3D3E2C7A, 0x86ED7DDC, +/**/ 0xBF30DEE3, 0x4EC42ED1, +/**/ 0x3F30DF71, 0xA4400000, +/**/ 0x3CF7F534, 0xF54F7E28, +/**/ 0xBF30FEDF, 0x132FB9D5, +/**/ 0x3F30FF6F, 0x86800000, +/**/ 0xBD3AA6E1, 0x404F4E01, +/**/ 0xBF311EDA, 0xCF9CDCA2, +/**/ 0x3F311F6D, 0x64800000, +/**/ 0x3D2375B9, 0x4A6EC981, +/**/ 0xBF313ED6, 0x840B9A38, +/**/ 0x3F313F6B, 0x3EC00000, +/**/ 0xBD315A73, 0x33401DD0, +/**/ 0xBF315ED2, 0x307BF596, +/**/ 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0x3F3DBE45, 0x9A400000, +/**/ 0x3D1787DF, 0x67DCC15E, +/**/ 0xBF3DDC83, 0xE41BC143, +/**/ 0x3F3DDE41, 0xE0C00000, +/**/ 0xBD262398, 0x352F961F, +/**/ 0xBF3DFC7C, 0x696BA563, +/**/ 0x3F3DFE3E, 0x23400000, +/**/ 0xBD3B16B9, 0xDEDD373A, +/**/ 0xBF3E1C74, 0xE6BE58DA, +/**/ 0x3F3E1E3A, 0x61800000, +/**/ 0x3D35D42E, 0x336BE94B, +/**/ 0xBF3E3C6D, 0x5C13DEA7, +/**/ 0x3F3E3E36, 0x9C000000, +/**/ 0x3D1EBFAF, 0x08A303A2, +/**/ 0xBF3E5C65, 0xC96C39C9, +/**/ 0x3F3E5E32, 0xD2800000, +/**/ 0xBD160A06, 0x34856362, +/**/ 0xBF3E7C5E, 0x2EC76D3D, +/**/ 0x3F3E7E2F, 0x05000000, +/**/ 0xBD31C21A, 0x154CDF1A, +/**/ 0xBF3E9C56, 0x8C257C04, +/**/ 0x3F3E9E2B, 0x33800000, +/**/ 0xBD3D0DDE, 0x31941F7F, +/**/ 0xBF3EBC4E, 0xE186691B, +/**/ 0x3F3EBE27, 0x5DC00000, +/**/ 0x3D389B31, 0xC26EC60D, +/**/ 0xBF3EDC47, 0x2EEA3781, +/**/ 0x3F3EDE23, 0x84400000, +/**/ 0x3D2E742A, 0xD583BEF8, +/**/ 0xBF3EFC3F, 0x7450EA34, +/**/ 0x3F3EFE1F, 0xA6C00000, +/**/ 0x3D1B3F31, 0xAC2DA351, +/**/ 0xBF3F1C37, 0xB1BA8433, +/**/ 0x3F3F1E1B, 0xC5400000, +/**/ 0xBCE45533, 0x2DC67430, +/**/ 0xBF3F3C2F, 0xE727087C, +/**/ 0x3F3F3E17, 0xDFC00000, +/**/ 0xBD1C7133, 0xFF1174AE, +/**/ 0xBF3F5C28, 0x14967A0F, +/**/ 0x3F3F5E13, 0xF6400000, +/**/ 0xBD29383C, 0x4AE098DC, +/**/ 0xBF3F7C20, 0x3A08DBE9, +/**/ 0x3F3F7E10, 0x08C00000, +/**/ 0xBD31211D, 0x684B0B3B, +/**/ 0xBF3F9C18, 0x577E3109, +/**/ 0x3F3F9E0C, 0x17400000, +/**/ 0xBD34AA4B, 0x268D7464, +/**/ 0xBF3FBC10, 0x6CF67C6E, +/**/ 0x3F3FBE08, 0x21C00000, +/**/ 0xBD3736A7, 0xBED03388, +/**/ 0xBF3FDC08, 0x7A71C116, +/**/ 0x3F3FDE04, 0x28400000, +/**/ 0xBD38C533, 0x900BC4E5, +/**/ 0xBF3FFC00, 0x7FF00200, +/**/ 0x3F3FFE00, 0x2AC00000, +/**/ 0xBD3954EE, 0xF9987527, +/**/ 0xBF400DFC, 0x3EB8A115, +/**/ 0x3F400EFE, 0x14A00000, +/**/ 0xBD38E4DA, 0x5B2E613B, +/**/ 0xBF401DF8, 0x397AC249, +/**/ 0x3F401EFC, 0x11E00000, +/**/ 0xBD3773F6, 0x14E5761B, +/**/ 0xBF402DF4, 0x303E661C, +/**/ 0x3F402EFA, 0x0D200000, +/**/ 0xBD350142, 0x873570A0, +/**/ 0xBF403DF0, 0x23038E0C, +/**/ 0x3F403EF8, 0x06600000, +/**/ 0xBD318BC0, 0x12F5DD53, +/**/ 0xBF404DEC, 0x11CA3B9A, +/**/ 0x3F404EF5, 0xFDA00000, +/**/ 0xBD2A24DE, 0x32BC307C, +/**/ 0xBF405DE7, 0xFC927044, +/**/ 0x3F405EF3, 0xF2E00000, +/**/ 0xBD1E513F, 0xF01532DA, +/**/ 0xBF406DE3, 0xE35C2D8A, +/**/ 0x3F406EF1, 0xE6200000, +/**/ 0xBCF10631, 0xCE27534E, +/**/ 0xBF407DDF, 0xC62774EA, +/**/ 0x3F407EEF, 0xD7600000, +/**/ 0x3D19E95C, 0x86CE9380, +/**/ 0xBF408DDB, 0xA4F447E4, +/**/ 0x3F408EED, 0xC6A00000, +/**/ 0x3D2E19BC, 0xBA0CD2C3, +/**/ 0xBF409DD7, 0x7FC2A7F8, +/**/ 0x3F409EEB, 0xB3E00000, +/**/ 0x3D38A832, 0x31FF7199, +/**/ 0xBF40ADD3, 0x569296A4, +/**/ 0x3F40AEE9, 0x9F400000, +/**/ 0xBD3CB2AD, 0xC2D77791, +/**/ 0xBF40BDCF, 0x29641567, +/**/ 0x3F40BEE7, 0x88800000, +/**/ 0xBD3102C1, 0xE5545563, +/**/ 0xBF40CDCA, 0xF83725C2, +/**/ 0x3F40CEE5, 0x6FC00000, +/**/ 0xBD111C2A, 0x66B3E48D, +/**/ 0xBF40DDC6, 0xC30BC932, +/**/ 0x3F40DEE3, 0x55000000, +/**/ 0x3D2302EF, 0x7711FC2A, +/**/ 0xBF40EDC2, 0x89E20138, +/**/ 0x3F40EEE1, 0x38400000, +/**/ 0x3D3857C4, 0xB558238E, +/**/ 0xBF40FDBE, 0x4CB9CF52, +/**/ 0x3F40FEDF, 0x19A00000, +/**/ 0xBD37C324, 0x1194C2E1, +/**/ 0xBF410DBA, 0x0B933501, +/**/ 0x3F410EDC, 0xF8E00000, +/**/ 0xBD1B390B, 0xFBCAF285, +/**/ 0xBF411DB5, 0xC66E33C2, +/**/ 0x3F411EDA, 0xD6200000, +/**/ 0x3D266ECF, 0x0E52C3A4, +/**/ 0xBF412DB1, 0x7D4ACD15, +/**/ 0x3F412ED8, 0xB1600000, +/**/ 0x3D3E4EDB, 0x1A4AF71D, +/**/ 0xBF413DAD, 0x30290279, +/**/ 0x3F413ED6, 0x8AC00000, +/**/ 0xBD2B0DD1, 0x58C4D599, +/**/ 0xBF414DA8, 0xDF08D56E, +/**/ 0x3F414ED4, 0x62000000, +/**/ 0x3D1EDC6F, 0x2FB4061D, +/**/ 0xBF415DA4, 0x89EA4773, +/**/ 0x3F415ED2, 0x37400000, +/**/ 0x3D3E09E8, 0x1BA53538, +/**/ 0xBF416DA0, 0x30CD5A06, +/**/ 0x3F416ED0, 0x0AA00000, +/**/ 0xBD251B08, 0x4A5B4574, +/**/ 0xBF417D9B, 0xD3B20EA8, +/**/ 0x3F417ECD, 0xDBE00000, +/**/ 0x3D2BE3AD, 0x4241B57B, +/**/ 0xBF418D97, 0x729866D7, +/**/ 0x3F418ECB, 0xAB400000, +/**/ 0xBD387707, 0xFA22BD16, +/**/ 0xBF419D93, 0x0D806412, +/**/ 0x3F419EC9, 0x78800000, +/**/ 0x3D01C6FC, 0xFFA2FC2F, +/**/ 0xBF41AD8E, 0xA46A07D9, +/**/ 0x3F41AEC7, 0x43C00000, +/**/ 0x3D3E028D, 0x05F32EE8, +/**/ 0xBF41BD8A, 0x375553AB, +/**/ 0x3F41BEC5, 0x0D200000, +/**/ 0xBD146400, 0xC7E46F2B, +/**/ 0xBF41CD85, 0xC6424907, +/**/ 0x3F41CEC2, 0xD4600000, +/**/ 0x3D38E737, 0x8DFCE791, +/**/ 0xBF41DD81, 0x5130E96B, +/**/ 0x3F41DEC0, 0x99C00000, +/**/ 0xBD1FEF30, 0x92F4A6CE, +/**/ 0xBF41ED7C, 0xD8213659, +/**/ 0x3F41EEBE, 0x5D000000, +/**/ 0x3D383EF4, 0x4AE68315, +/**/ 0xBF41FD78, 0x5B13314D, +/**/ 0x3F41FEBC, 0x1E600000, +/**/ 0xBD199E1E, 0x39A8276A, +/**/ 0xBF420D73, 0xDA06DBC8, +/**/ 0x3F420EB9, 0xDDA00000, +/**/ 0x3D3C11BF, 0xE39F6D77, +/**/ 0xBF421D6F, 0x54FC3749, +/**/ 0x3F421EB7, 0x9B000000, +/**/ 0xBCD50D72, 0xC3A8C440, +/**/ 0xBF422D6A, 0xCBF3454F, +/**/ 0x3F422EB5, 0x56600000, +/**/ 0xBD3B9869, 0x06E59170, +/**/ 0xBF423D66, 0x3EEC0759, +/**/ 0x3F423EB3, 0x0FA00000, +/**/ 0x3D248C4B, 0x86930551, +/**/ 0xBF424D61, 0xADE67EE6, +/**/ 0x3F424EB0, 0xC7000000, +/**/ 0xBD2D6F13, 0xB3649FF7, +/**/ 0xBF425D5D, 0x18E2AD76, +/**/ 0x3F425EAE, 0x7C400000, +/**/ 0x3D396F87, 0xB496441D, +/**/ 0xBF426D58, 0x7FE09487, +/**/ 0x3F426EAC, 0x2FA00000, +/**/ 0x3D05E2D0, 0x01961A2F, +/**/ 0xBF427D53, 0xE2E03598, +/**/ 0x3F427EA9, 0xE1000000, +/**/ 0xBD32D013, 0x652D1720, +/**/ 0xBF428D4F, 0x41E1922A, +/**/ 0x3F428EA7, 0x90400000, +/**/ 0x3D38CB3F, 0x15C6A78A, +/**/ 0xBF429D4A, 0x9CE4ABBA, +/**/ 0x3F429EA5, 0x3DA00000, +/**/ 0x3D163D44, 0x07F8A52A, +/**/ 0xBF42AD45, 0xF3E983C8, +/**/ 0x3F42AEA2, 0xE9000000, +/**/ 0xBD2905BC, 0x1FEC6070, +/**/ 0xBF42BD41, 0x46F01BD4, +/**/ 0x3F42BEA0, 0x92600000, +/**/ 0xBD3D6A4E, 0x8FE5CB8E, +/**/ 0xBF42CD3C, 0x95F8755C, +/**/ 0x3F42CE9E, 0x39A00000, +/**/ 0x3D32D9FF, 0x120028B6, +/**/ 0xBF42DD37, 0xE10291DF, +/**/ 0x3F42DE9B, 0xDF000000, +/**/ 0x3D112C29, 0x94B2D8A6, +/**/ 0xBF42ED33, 0x280E72DD, +/**/ 0x3F42EE99, 0x82600000, +/**/ 0xBD222C5A, 0x0E9DC27F, +/**/ 0xBF42FD2E, 0x6B1C19D4, +/**/ 0x3F42FE97, 0x23C00000, +/**/ 0xBD3548A7, 0xA4C12307, +/**/ 0xBF430D29, 0xAA2B8844, +/**/ 0x3F430E94, 0xC3000000, +/**/ 0x3D3FB49A, 0x1B27A40C, +/**/ 0xBF431D24, 0xE53CBFAC, +/**/ 0x3F431E92, 0x60600000, +/**/ 0x3D35E297, 0xC65D601D, +/**/ 0xBF432D20, 0x1C4FC18B, +/**/ 0x3F432E8F, 0xFBC00000, +/**/ 0x3D2A84A1, 0xD4E46CD5, +/**/ 0xBF433D1B, 0x4F648F60, +/**/ 0x3F433E8D, 0x95200000, +/**/ 0x3D175314, 0x526215F8, +/**/ 0xBF434D16, 0x7E7B2AAB, +/**/ 0x3F434E8B, 0x2C800000, +/**/ 0xBCD9430B, 0x9746A94C, +/**/ 0xBF435D11, 0xA99394E9, +/**/ 0x3F435E88, 0xC1E00000, +/**/ 0xBD15A88D, 0x47EF6144, +/**/ 0xBF436D0C, 0xD0ADCF9B, +/**/ 0x3F436E86, 0x55400000, +/**/ 0xBD227301, 0x94614FFB, +/**/ 0xBF437D07, 0xF3C9DC3F, +/**/ 0x3F437E83, 0xE6A00000, +/**/ 0xBD27A44A, 0x16908831, +/**/ 0xBF438D03, 0x12E7BC55, +/**/ 0x3F438E81, 0x76000000, +/**/ 0xBD2A6621, 0x13DE59AC, +/**/ 0xBF439CFE, 0x2E07715C, +/**/ 0x3F439E7F, 0x03600000, +/**/ 0xBD2AB687, 0x76635000, +/**/ 0xBF43ACF9, 0x4528FCD2, +/**/ 0x3F43AE7C, 0x8EC00000, +/**/ 0xBD28937E, 0x28F7818F, +/**/ 0xBF43BCF4, 0x584C6037, +/**/ 0x3F43BE7A, 0x18200000, +/**/ 0xBD23FB06, 0x17328F27, +/**/ 0xBF43CCEF, 0x67719D0A, +/**/ 0x3F43CE77, 0x9F800000, +/**/ 0xBD19D640, 0x5AD74747, +/**/ 0xBF43DCEA, 0x7298B4CA, +/**/ 0x3F43DE75, 0x24E00000, +/**/ 0xBCFB0E6A, 0xC5CB9C74, +/**/ 0xBF43ECE5, 0x79C1A8F6, +/**/ 0x3F43EE72, 0xA8400000, +/**/ 0x3D1145E2, 0xF21B8682, +/**/ 0xBF43FCE0, 0x7CEC7B0D, +/**/ 0x3F43FE70, 0x29A00000, +/**/ 0x3D27251B, 0x59543A06, +/**/ 0xBF440CDB, 0x7C192C8E, +/**/ 0x3F440E6D, 0xA9000000, +/**/ 0x3D341357, 0xAC6250B6, +/**/ 0xBF441CD6, 0x7747BEF8, +/**/ 0x3F441E6B, 0x26600000, +/**/ 0x3D3DD4D6, 0x43A510F7, +/**/ 0xBF442CD1, 0x6E7833CB, +/**/ 0x3F442E68, 0xA1E00000, +/**/ 0xBD3727F7, 0x05F7D1E1, +/**/ 0xBF443CCC, 0x61AA8C85, +/**/ 0x3F443E66, 0x1B400000, +/**/ 0xBD25C421, 0x527C9668, +/**/ 0xBF444CC7, 0x50DECAA5, +/**/ 0x3F444E63, 0x92A00000, +/**/ 0x3D053C47, 0x053F70AC, +/**/ 0xBF445CC2, 0x3C14EFAB, +/**/ 0x3F445E61, 0x08000000, +/**/ 0x3D3175D5, 0x1E315FBB, +/**/ 0xBF446CBD, 0x234CFD15, +/**/ 0x3F446E5E, 0x7B800000, +/**/ 0xBD3E762C, 0x6A8B33AC, +/**/ 0xBF447CB8, 0x0686F463, +/**/ 0x3F447E5B, 0xECE00000, +/**/ 0xBD2A36F8, 0x67AD9900, +/**/ 0xBF448CB2, 0xE5C2D713, +/**/ 0x3F448E59, 0x5C400000, +/**/ 0x3D161B95, 0x1E974853, +/**/ 0xBF449CAD, 0xC100A6A5, +/**/ 0x3F449E56, 0xC9A00000, +/**/ 0x3D3971F7, 0x8CE22250, +/**/ 0xBF44ACA8, 0x98406498, +/**/ 0x3F44AE54, 0x35200000, +/**/ 0xBD315945, 0xDF8A23F8, +/**/ 0xBF44BCA3, 0x6B82126A, +/**/ 0x3F44BE51, 0x9E800000, +/**/ 0x3D1498B2, 0x1A63D360, +/**/ 0xBF44CC9E, 0x3AC5B19B, +/**/ 0x3F44CE4F, 0x05E00000, +/**/ 0x3D3CF14E, 0x4323A054, +/**/ 0xBF44DC99, 0x060B43AA, +/**/ 0x3F44DE4C, 0x6B600000, +/**/ 0xBD23EDC2, 0x4CE35F94, +/**/ 0xBF44EC93, 0xCD52CA15, +/**/ 0x3F44EE49, 0xCEC00000, +/**/ 0x3D306E9D, 0xCCF1B48E, +/**/ 0xBF44FC8E, 0x909C465C, +/**/ 0x3F44FE47, 0x30400000, +/**/ 0xBD33DD35, 0x5FF9440B, +/**/ 0xBF450C89, 0x4FE7B9FF, +/**/ 0x3F450E44, 0x8FA00000, +/**/ 0x3D224D49, 0xAA4D276D, +/**/ 0xBF451C84, 0x0B35267A, +/**/ 0x3F451E41, 0xED200000, +/**/ 0xBD3884D4, 0x11B557F9, +/**/ 0xBF452C7E, 0xC2848D4F, +/**/ 0x3F452E3F, 0x48800000, +/**/ 0x3D1C857D, 0xB43290C4, +/**/ 0xBF453C79, 0x75D5EFFC, +/**/ 0x3F453E3C, 0xA2000000, +/**/ 0xBD37E5C1, 0x2D598D3C, +/**/ 0xBF454C74, 0x25294FFF, +/**/ 0x3F454E39, 0xF9600000, +/**/ 0x3D24CD93, 0x3FE47B89, +/**/ 0xBF455C6E, 0xD07EAED8, +/**/ 0x3F455E37, 0x4EE00000, +/**/ 0xBD31F800, 0xAA959122, +/**/ 0xBF456C69, 0x77D60E06, +/**/ 0x3F456E34, 0xA2400000, +/**/ 0x3D32FEDF, 0x7329AF92, +/**/ 0xBF457C64, 0x1B2F6F08, +/**/ 0x3F457E31, 0xF3C00000, +/**/ 0xBD1ACE5A, 0x1C545A6F, +/**/ 0xBF458C5E, 0xBA8AD35D, +/**/ 0x3F458E2F, 0x43400000, +/**/ 0xBD3F0E63, 0x19F6B9EF, +/**/ 0xBF459C59, 0x55E83C84, +/**/ 0x3F459E2C, 0x90A00000, +/**/ 0x3D23DEF2, 0x73005F6F, +/**/ 0xBF45AC53, 0xED47ABFB, +/**/ 0x3F45AE29, 0xDC200000, +/**/ 0xBD277204, 0x1C295DE7, +/**/ 0xBF45BC4E, 0x80A92343, +/**/ 0x3F45BE27, 0x25800000, +/**/ 0x3D3FF92A, 0x8D869589, +/**/ 0xBF45CC49, 0x100CA3D9, +/**/ 0x3F45CE24, 0x6D000000, +/**/ 0x3D2A0DFD, 0x145C5335, +/**/ 0xBF45DC43, 0x9B722F3C, +/**/ 0x3F45DE21, 0xB2800000, +/**/ 0xBD123A1A, 0x6A8614B3, +/**/ 0xBF45EC3E, 0x22D9C6ED, +/**/ 0x3F45EE1E, 0xF6000000, +/**/ 0xBD34C665, 0x63CBC7E7, +/**/ 0xBF45FC38, 0xA6436C69, +/**/ 0x3F45FE1C, 0x37600000, +/**/ 0x3D3C6061, 0xAB6C51D7, +/**/ 0xBF460C33, 0x25AF2130, +/**/ 0x3F460E19, 0x76E00000, +/**/ 0x3D2DCD9C, 0x1EC7F453, +/**/ 0xBF461C2D, 0xA11CE6C1, +/**/ 0x3F461E16, 0xB4600000, +/**/ 0x3D066EFA, 0x20C52899, +/**/ 0xBF462C28, 0x188CBE9A, +/**/ 0x3F462E13, 0xEFE00000, +/**/ 0xBD1FA5AC, 0xEB5FDD5C, +/**/ 0xBF463C22, 0x8BFEAA3B, +/**/ 0x3F463E11, 0x29600000, +/**/ 0xBD313E11, 0xF22FE2BC, +/**/ 0xBF464C1C, 0xFB72AB23, +/**/ 0x3F464E0E, 0x60E00000, +/**/ 0xBD392F15, 0x6710E251, +/**/ 0xBF465C17, 0x66E8C2D0, +/**/ 0x3F465E0B, 0x96600000, +/**/ 0xBD3FBB76, 0x1EFC78A7, +/**/ 0xBF466C11, 0xCE60F2C1, +/**/ 0x3F466E08, 0xC9C00000, +/**/ 0x3D3B1DCB, 0x602C1A84, +/**/ 0xBF467C0C, 0x31DB3C76, +/**/ 0x3F467E05, 0xFB400000, +/**/ 0x3D375DAE, 0x9027DA74, +/**/ 0xBF468C06, 0x9157A16E, +/**/ 0x3F468E03, 0x2AC00000, +/**/ 0x3D350532, 0xEA560DA0, +/**/ 0xBF469C00, 0xECD62326, +/**/ 0x3F469E00, 0x58400000, +/**/ 0x3D341557, 0xE7B63DE2 } }; + +#else +#ifdef LITTLE_ENDI +static const union {int4 i[5800]; double x[2900];} ui = { .i = { +/**/ 0x00000000, 0x3FF6A000, +/**/ 0x3729043E, 0x3F33CD15, +/**/ 0x0B3AB000, 0xBFD63003, +/**/ 0xE731AE00, 0x3D2DB623, +/**/ 0x00000000, 0x3FF69800, +/**/ 0xCC7267D0, 0x3F33F349, +/**/ 0xCDB03000, 0xBFD61965, +/**/ 0x603C488E, 0x3D2F08AD, +/**/ 0x00000000, 0x3FF69000, +/**/ 0x8D0BFD2E, 0x3F3473A8, +/**/ 0x8AF09000, 0xBFD602D0, +/**/ 0x76DF3F65, 0xBD1EBE91, +/**/ 0x00000000, 0x3FF68800, +/**/ 0x390B9ED0, 0x3F354DD2, +/**/ 0x3D5C3000, 0xBFD5EC43, +/**/ 0x1229D17F, 0xBD36B71A, +/**/ 0x00000000, 0x3FF68000, +/**/ 0x16816817, 0x3F368168, +/**/ 0xDF596000, 0xBFD5D5BD, +/**/ 0x08A465DC, 0x3D0A0B2A, +/**/ 0x00000000, 0x3FF67800, +/**/ 0xF08C7765, 0x3F380E0B, +/**/ 0x6B544000, 0xBFD5BF40, +/**/ 0xEB68981C, 0x3D227023, +/**/ 0x00000000, 0x3FF67000, +/**/ 0x16719F36, 0x3F39F360, +/**/ 0xDBBEE000, 0xBFD5A8CA, +/**/ 0x0AF7ECF8, 0x3CF7C79B, +/**/ 0x00000000, 0x3FF66800, +/**/ 0x5AB40167, 0x3F3C3107, +/**/ 0x2B113000, 0xBFD5925D, +/**/ 0xA7A56F34, 0x3D369BF5, +/**/ 0x00000000, 0x3FF66000, +/**/ 0x122F9016, 0x3F3EC6A5, +/**/ 0x53C8D000, 0xBFD57BF7, +/**/ 0xEE5D40EF, 0xBD1FADED, +/**/ 0x00000000, 0x3FF65C00, +/**/ 0xECCA9097, 0xBF3E4C22, +/**/ 0x50695000, 0xBFD56599, +/**/ 0x2BADC774, 0xBD14C5FD, +/**/ 0x00000000, 0x3FF65400, +/**/ 0x4B55CC62, 0xBF3B07AC, +/**/ 0x1B7BE000, 0xBFD54F43, +/**/ 0xC0910952, 0xBD1A8954, +/**/ 0x00000000, 0x3FF64C00, +/**/ 0x32DA090E, 0xBF376C52, +/**/ 0xAF8F7000, 0xBFD538F4, +/**/ 0xE45547CE, 0xBD27EC02, +/**/ 0x00000000, 0x3FF64400, +/**/ 0x4DE9BD38, 0xBF337A6F, +/**/ 0x0738A000, 0xBFD522AE, +/**/ 0x8164C759, 0xBD2EBE70, +/**/ 0x00000000, 0x3FF63C00, +/**/ 0x923C708B, 0xBF2E64BB, +/**/ 0x1D11C000, 0xBFD50C6F, +/**/ 0x7E827C2C, 0x3D3A0E6B, +/**/ 0x00000000, 0x3FF63400, +/**/ 0xA7E43FD4, 0xBF2528EE, +/**/ 0xEBBAA000, 0xBFD4F637, +/**/ 0xCB3124B9, 0x3D3FC158, +/**/ 0x00000000, 0x3FF62C00, +/**/ 0x86689DF7, 0xBF168454, +/**/ 0x6DD8C000, 0xBFD4E008, +/**/ 0xA1E44788, 0x3D34D692, +/**/ 0x00000000, 0x3FF62400, +/**/ 0x77016240, 0xBED623FA, +/**/ 0x9E173000, 0xBFD4C9E0, +/**/ 0x1B0AD8A4, 0x3D2E2089, +/**/ 0x00000000, 0x3FF61C00, +/**/ 0x58715130, 0x3F151300, +/**/ 0x77268000, 0xBFD4B3C0, +/**/ 0x81052B9F, 0x3D165B46, +/**/ 0x00000000, 0x3FF61400, +/**/ 0x35D2754E, 0x3F266D06, +/**/ 0xF3BCC000, 0xBFD49DA7, +/**/ 0x4DAF4B9A, 0xBD307B33, +/**/ 0x00000000, 0x3FF60C00, +/**/ 0xDA197F23, 0x3F317C61, +/**/ 0x0E958000, 0xBFD48797, +/**/ 0x465CF25F, 0xBD3DC1B8, +/**/ 0x00000000, 0x3FF60400, +/**/ 0x81605816, 0x3F381605, +/**/ 0xC271C000, 0xBFD4718D, +/**/ 0xFB4C14C5, 0xBD306C18, +/**/ 0x00000000, 0x3FF5FC00, +/**/ 0xB5C6F559, 0x3F3F0317, +/**/ 0x0A17E000, 0xBFD45B8C, +/**/ 0xE7D0A853, 0x3D0D9120, +/**/ 0x00000000, 0x3FF5F800, +/**/ 0x6D2041E3, 0xBF39BCBD, +/**/ 0xE053A000, 0xBFD44591, +/**/ 0x92923D88, 0x3D06E958, +/**/ 0x00000000, 0x3FF5F000, +/**/ 0x5604CC40, 0xBF3229CF, +/**/ 0x3FF62000, 0xBFD42F9F, +/**/ 0x0F7D3354, 0xBD390644, +/**/ 0x00000000, 0x3FF5E800, +/**/ 0xFD431489, 0xBF2488E5, +/**/ 0x23D5F000, 0xBFD419B4, +/**/ 0x226DE3EC, 0x3D3CE379, +/**/ 0x00000000, 0x3FF5E000, +/**/ 0x6424E9C9, 0xBF0067E7, +/**/ 0x86CEA000, 0xBFD403D0, +/**/ 0x74487308, 0xBD3E6EF5, +/**/ 0x00000000, 0x3FF5D800, +/**/ 0x38A94D24, 0x3F19F0FB, +/**/ 0x63C17000, 0xBFD3EDF4, +/**/ 0x297F2C3F, 0x3D3F067C, +/**/ 0x00000000, 0x3FF5D000, +/**/ 0x23CAD2AA, 0x3F2EADD9, +/**/ 0xB5947000, 0xBFD3D81F, +/**/ 0x2A9D37A4, 0x3D222C7C, +/**/ 0x00000000, 0x3FF5C800, +/**/ 0x31057262, 0x3F3882B9, +/**/ 0x77333000, 0xBFD3C252, +/**/ 0xB606BD5C, 0xBD183B54, +/**/ 0x00000000, 0x3FF5C400, +/**/ 0x10FFA8F8, 0xBF3E00AE, +/**/ 0xA38E6000, 0xBFD3AC8C, +/**/ 0xBC02BE4A, 0x3D2D0BEF, +/**/ 0x00000000, 0x3FF5BC00, +/**/ 0x8056EAF3, 0xBF34339B, +/**/ 0x359BC000, 0xBFD396CE, +/**/ 0x5663663D, 0x3D05839C, +/**/ 0x00000000, 0x3FF5B400, +/**/ 0xF31D7FD5, 0xBF242CC1, +/**/ 0x28565000, 0xBFD38117, +/**/ 0x93A0702B, 0x3D2A71E4, +/**/ 0x00000000, 0x3FF5AC00, +/**/ 0x6B015AC0, 0x3ED5AC05, +/**/ 0x76BE1000, 0xBFD36B67, +/**/ 0xB0F177C8, 0xBD116ECD, +/**/ 0x00000000, 0x3FF5A400, +/**/ 0x5BA55E5A, 0x3F26268D, +/**/ 0x1BD83000, 0xBFD355BF, +/**/ 0x8964F0E8, 0x3D2BA99B, +/**/ 0x00000000, 0x3FF59C00, +/**/ 0x3CCAA376, 0x3F361F12, +/**/ 0x12AED000, 0xBFD3401E, +/**/ 0x556E291D, 0x3D317C73, +/**/ 0x00000000, 0x3FF59800, +/**/ 0x62D32417, 0xBF3E863D, +/**/ 0x56512000, 0xBFD32A84, +/**/ 0x139AF5D6, 0xBD04F928, +/**/ 0x00000000, 0x3FF59000, +/**/ 0xEA712DCF, 0xBF32DCF7, +/**/ 0xE1D36000, 0xBFD314F1, +/**/ 0xD3213CB8, 0x3D28E27A, +/**/ 0x00000000, 0x3FF58800, +/**/ 0xA0CC87E8, 0xBF1B95B2, +/**/ 0xB04EB000, 0xBFD2FF66, +/**/ 0x541E6E2E, 0x3D38AED2, +/**/ 0x00000000, 0x3FF58000, +/**/ 0x01580560, 0x3F158056, +/**/ 0xBCE12000, 0xBFD2E9E2, +/**/ 0x128D1DC2, 0xBD24300C, +/**/ 0x00000000, 0x3FF57800, +/**/ 0x15791F34, 0x3F31F340, +/**/ 0x02ADD000, 0xBFD2D466, +/**/ 0xDCD54196, 0x3D288D0D, +/**/ 0x00000000, 0x3FF57000, +/**/ 0x06B39A23, 0x3F3ED3C5, +/**/ 0x7CDC9000, 0xBFD2BEF0, +/**/ 0x4A5004F4, 0xBD2A9CFA, +/**/ 0x00000000, 0x3FF56C00, +/**/ 0x53FEA954, 0xBF33FEA9, +/**/ 0x269A4000, 0xBFD2A982, +/**/ 0x557285CF, 0x3D22058E, +/**/ 0x00000000, 0x3FF56400, +/**/ 0xEB478503, 0xBF1A1160, +/**/ 0xFB187000, 0xBFD2941A, +/**/ 0xB730E28B, 0x3D3210C2, +/**/ 0x00000000, 0x3FF55C00, +/**/ 0xE4A18B2E, 0x3F1D09AD, +/**/ 0xF58D9000, 0xBFD27EBA, +/**/ 0x00B4BDA7, 0x3D2B1988, +/**/ 0x00000000, 0x3FF55400, +/**/ 0x55555555, 0x3F355555, +/**/ 0x1134E000, 0xBFD26962, +/**/ 0x10522625, 0x3D31B61F, +/**/ 0x00000000, 0x3FF55000, +/**/ 0xB319A21F, 0xBF3C4BE6, +/**/ 0x494E5000, 0xBFD25410, +/**/ 0xC0EF77F2, 0xBD3B1D7A, +/**/ 0x00000000, 0x3FF54800, +/**/ 0x8FA03FD5, 0xBF2B4328, +/**/ 0x991EC000, 0xBFD23EC5, +/**/ 0x48A2E522, 0x3D36DBE4, +/**/ 0x00000000, 0x3FF54000, +/**/ 0x40154015, 0x3EF54015, +/**/ 0xFBEF8000, 0xBFD22981, +/**/ 0x609580DA, 0x3D3A1421, +/**/ 0x00000000, 0x3FF53800, +/**/ 0x40FEAC6F, 0x3F30948F, +/**/ 0x6D0EC000, 0xBFD21445, +/**/ 0x28B728A3, 0x3D3CAF04, +/**/ 0x00000000, 0x3FF53400, +/**/ 0xFD04F7B8, 0xBF3FE034, +/**/ 0xE7CF4000, 0xBFD1FF0F, +/**/ 0x513FF0C1, 0xBD3E9D5B, +/**/ 0x00000000, 0x3FF52C00, +/**/ 0x7FAB5403, 0xBF300A95, +/**/ 0x6788A000, 0xBFD1E9E1, +/**/ 0xD3C8B65E, 0x3D382EAE, +/**/ 0x00000000, 0x3FF52400, +/**/ 0x52401524, 0x3EB52401, +/**/ 0xE796C000, 0xBFD1D4B9, +/**/ 0x7C42E56D, 0xBD222A66, +/**/ 0x00000000, 0x3FF51C00, +/**/ 0x2F8151D0, 0x3F307EAE, +/**/ 0x635A7000, 0xBFD1BF99, +/**/ 0x575C2125, 0x3D31AC89, +/**/ 0x00000000, 0x3FF51800, +/**/ 0xEAE9ECE4, 0xBF3ECE3F, +/**/ 0xD638D000, 0xBFD1AA7F, +/**/ 0x9616F7A0, 0xBD29F60A, +/**/ 0x00000000, 0x3FF51000, +/**/ 0xC7675243, 0xBF2BA3DD, +/**/ 0x3B9BC000, 0xBFD1956D, +/**/ 0x3AD1AA14, 0xBD27D2F7, +/**/ 0x00000000, 0x3FF50800, +/**/ 0x764E368D, 0x3F0B9AC8, +/**/ 0x8EF19000, 0xBFD18061, +/**/ 0xC86D38E5, 0x3D3482FF, +/**/ 0x00000000, 0x3FF50000, +/**/ 0x15015015, 0x3F350150, +/**/ 0xCBAD0000, 0xBFD16B5C, +/**/ 0x042D74BF, 0x3D323299, +/**/ 0x00000000, 0x3FF4FC00, +/**/ 0x4A683C50, 0xBF392851, +/**/ 0xED456000, 0xBFD1565E, +/**/ 0xFB6ABA25, 0x3CEE75AD, +/**/ 0x00000000, 0x3FF4F400, +/**/ 0xACD95EF0, 0xBF1C2748, +/**/ 0xEF367000, 0xBFD14167, +/**/ 0x824DAAF5, 0xBD3E0C07, +/**/ 0x00000000, 0x3FF4EC00, +/**/ 0x67A47465, 0x3F26B90D, +/**/ 0xCD007000, 0xBFD12C77, +/**/ 0x8A11F797, 0xBD13B294, +/**/ 0x00000000, 0x3FF4E400, +/**/ 0xF0539783, 0x3F3E0A72, +/**/ 0x8227E000, 0xBFD1178E, +/**/ 0xCE2D07F2, 0xBD31EF78, +/**/ 0x00000000, 0x3FF4E000, +/**/ 0xF87FD642, 0xBF2E00A6, +/**/ 0x0A35D000, 0xBFD102AC, +/**/ 0xDFDFD686, 0x3D2F1FBD, +/**/ 0x00000000, 0x3FF4D800, +/**/ 0x0B12E3FD, 0x3F10EFB7, +/**/ 0x60B78000, 0xBFD0EDD0, +/**/ 0x2D8435F5, 0xBD0019B5, +/**/ 0x00000000, 0x3FF4D000, +/**/ 0x5CB4DBE5, 0x3F37BEF1, +/**/ 0x813EB000, 0xBFD0D8FB, +/**/ 0x8753FA35, 0xBD1EE8C8, +/**/ 0x00000000, 0x3FF4CC00, +/**/ 0xA50918B1, 0xBF34778D, +/**/ 0x67616000, 0xBFD0C42D, +/**/ 0x163CEAE9, 0xBD27188B, +/**/ 0x00000000, 0x3FF4C400, +/**/ 0xE37288EC, 0xBED9F4F7, +/**/ 0x0EB9E000, 0xBFD0AF66, +/**/ 0xF528D80A, 0xBD23C7C3, +/**/ 0x00000000, 0x3FF4BC00, +/**/ 0x68FE0E42, 0x3F33EDDA, +/**/ 0x72E6C000, 0xBFD09AA5, +/**/ 0xE1734342, 0xBD3B50A1, +/**/ 0x00000000, 0x3FF4B800, +/**/ 0xB72E47D9, 0xBF3776C6, +/**/ 0x8F8AE000, 0xBFD085EB, +/**/ 0x3F45FE7B, 0xBD3E5D51, +/**/ 0x00000000, 0x3FF4B000, +/**/ 0xA052BF5B, 0xBF04AFD6, +/**/ 0x604D6000, 0xBFD07138, +/**/ 0x4E912B17, 0x3D3E7632, +/**/ 0x00000000, 0x3FF4A800, +/**/ 0xD5B5C015, 0x3F328FFA, +/**/ 0xE0D96000, 0xBFD05C8B, +/**/ 0xC77CCB58, 0xBD2AD0F1, +/**/ 0x00000000, 0x3FF4A400, +/**/ 0x9FEB5D80, 0xBF380528, +/**/ 0x0CDE8000, 0xBFD047E6, +/**/ 0x0D397F3C, 0xBD2DBDF1, +/**/ 0x00000000, 0x3FF49C00, +/**/ 0x25FF5B21, 0xBF02AD3E, +/**/ 0xE0106000, 0xBFD03346, +/**/ 0xA966395C, 0xBCF89FF8, +/**/ 0x00000000, 0x3FF49400, +/**/ 0x2D066EA2, 0x3F339E3B, +/**/ 0x5626C000, 0xBFD01EAE, +/**/ 0xFADE85AE, 0xBD3A43DC, +/**/ 0x00000000, 0x3FF49000, +/**/ 0xAFB2E932, 0xBF3629C1, +/**/ 0x6ADDA000, 0xBFD00A1C, +/**/ 0x688B9E18, 0xBD31CD8D, +/**/ 0x00000000, 0x3FF48800, +/**/ 0x22014880, 0x3ED48805, +/**/ 0x33EA0000, 0xBFCFEB22, +/**/ 0xDE00938B, 0xBD2F3418, +/**/ 0x00000000, 0x3FF48000, +/**/ 0x3D324D89, 0x3F37119F, +/**/ 0xBE620000, 0xBFCFC218, +/**/ 0x6F1CF6A0, 0xBD34BBA4, +/**/ 0x00000000, 0x3FF47C00, +/**/ 0x1EB851EC, 0xBF31EB85, +/**/ 0x6CB3C000, 0xBFCF991C, +/**/ 0xCD7CC834, 0x3D390D04, +/**/ 0x00000000, 0x3FF47400, +/**/ 0xAAFC7C01, 0x3F1569C9, +/**/ 0x36778000, 0xBFCF702D, +/**/ 0x16673E23, 0x3D108195, +/**/ 0x00000000, 0x3FF46C00, +/**/ 0x96066250, 0x3F3CE345, +/**/ 0x134E0000, 0xBFCF474B, +/**/ 0xF1DF7B5E, 0x3D3BAE49, +/**/ 0x00000000, 0x3FF46800, +/**/ 0x1D02DE87, 0xBF26A297, +/**/ 0xFADFA000, 0xBFCF1E75, +/**/ 0x25D83F6D, 0x3D20862B, +/**/ 0x00000000, 0x3FF46000, +/**/ 0xB9F34381, 0x3F2978FE, +/**/ 0xE4DD0000, 0xBFCEF5AD, +/**/ 0x65BB8E11, 0x3CCA2115, +/**/ 0x00000000, 0x3FF45C00, +/**/ 0xF6C71366, 0xBF3AF398, +/**/ 0xC8FEA000, 0xBFCECCF2, +/**/ 0xA3E75640, 0x3D3BEC63, +/**/ 0x00000000, 0x3FF45400, +/**/ 0x449AFF5D, 0xBF030E9C, +/**/ 0x9F04A000, 0xBFCEA444, +/**/ 0x63732A36, 0xBD35E916, +/**/ 0x00000000, 0x3FF44C00, +/**/ 0xF8B42EF3, 0x3F367190, +/**/ 0x5EB78000, 0xBFCE7BA3, +/**/ 0x23793649, 0x3D0D5EEE, +/**/ 0x00000000, 0x3FF44800, +/**/ 0xD260511C, 0xBF3079A9, +/**/ 0xFFE72000, 0xBFCE530E, +/**/ 0xB13F7C18, 0x3D3FDBDB, +/**/ 0x00000000, 0x3FF44000, +/**/ 0x0B644FBE, 0x3F21B87C, +/**/ 0x7A6B2000, 0xBFCE2A87, +/**/ 0x7787081A, 0xBD382381, +/**/ 0x00000000, 0x3FF43C00, +/**/ 0x411B2E25, 0xBF3D8CF5, +/**/ 0xC6236000, 0xBFCE020C, +/**/ 0xADB91424, 0x3D252B00, +/**/ 0x00000000, 0x3FF43400, +/**/ 0xD6A60978, 0xBF0DAC08, +/**/ 0xDAF6E000, 0xBFCDD99E, +/**/ 0x69C756EB, 0x3D302EC6, +/**/ 0x00000000, 0x3FF42C00, +/**/ 0x51F86EFA, 0x3F36625D, +/**/ 0xB0D48000, 0xBFCDB13D, +/**/ 0x847527E6, 0xBD32806A, +/**/ 0x00000000, 0x3FF42800, +/**/ 0xA8766564, 0xBF2E8B2D, +/**/ 0x3FB30000, 0xBFCD88E9, +/**/ 0x0234BF51, 0x3D375F28, +/**/ 0x00000000, 0x3FF42000, +/**/ 0xCB2A247B, 0x3F26A4CB, +/**/ 0x7F904000, 0xBFCD60A1, +/**/ 0x6FC20D39, 0x3D35D6E0, +/**/ 0x00000000, 0x3FF41C00, +/**/ 0xC17DF552, 0xBF39D5E8, +/**/ 0x68720000, 0xBFCD3866, +/**/ 0xB38932BC, 0x3D373650, +/**/ 0x00000000, 0x3FF41400, +/**/ 0x14141414, 0x3EF41414, +/**/ 0xF2656000, 0xBFCD1037, +/**/ 0x75B6F6E4, 0x3D084A7E, +/**/ 0x00000000, 0x3FF40C00, +/**/ 0x43AE87FD, 0x3F3C97A8, +/**/ 0x157F2000, 0xBFCCE816, +/**/ 0xA2099515, 0x3D29E0AB, +/**/ 0x00000000, 0x3FF40800, +/**/ 0x66A67E6F, 0xBF1F4BBC, +/**/ 0xC9DB4000, 0xBFCCC000, +/**/ 0x5D57AFF9, 0x3D1D6D58, +/**/ 0x00000000, 0x3FF40000, +/**/ 0x14014014, 0x3F340140, +/**/ 0x079D4000, 0xBFCC97F8, +/**/ 0xA8C6E6C5, 0xBD23B161, +/**/ 0x00000000, 0x3FF3FC00, +/**/ 0xFD809FD8, 0xBF2FD809, +/**/ 0xC6F00000, 0xBFCC6FFB, +/**/ 0xD3A69D43, 0xBD3EE138, +/**/ 0x00000000, 0x3FF3F400, +/**/ 0x57EE89D2, 0x3F28CA0E, +/**/ 0x0005C000, 0xBFCC480C, +/**/ 0xD5E44E76, 0xBD39A294, +/**/ 0x00000000, 0x3FF3F000, +/**/ 0xA50F9260, 0xBF370BD5, +/**/ 0xAB180000, 0xBFCC2028, +/**/ 0xE55C7AC6, 0x3D292E0E, +/**/ 0x00000000, 0x3FF3E800, +/**/ 0x75945FCE, 0x3F1704AA, +/**/ 0xC0676000, 0xBFCBF851, +/**/ 0x4C0854AD, 0x3D35420E, +/**/ 0x00000000, 0x3FF3E400, +/**/ 0xB56FD83C, 0xBF3D3431, +/**/ 0x383BE000, 0xBFCBD087, +/**/ 0x595412B6, 0x3D2D4BC4, +/**/ 0x00000000, 0x3FF3DC00, +/**/ 0x3DC013DC, 0x3EB3DC01, +/**/ 0x0AE4A000, 0xBFCBA8C9, +/**/ 0xF44432DA, 0xBD3A32E7, +/**/ 0x00000000, 0x3FF3D400, +/**/ 0xA75C5BBD, 0x3F3D991A, +/**/ 0x30B82000, 0xBFCB8117, +/**/ 0x3B9CD768, 0xBD1E9068, +/**/ 0x00000000, 0x3FF3D000, +/**/ 0x59C52F5D, 0xBF1292BA, +/**/ 0xA213A000, 0xBFCB5971, +/**/ 0x83AA91DF, 0xBD39B50E, +/**/ 0x00000000, 0x3FF3C800, +/**/ 0xBABE7440, 0x3F395A47, +/**/ 0x575BC000, 0xBFCB31D8, +/**/ 0x562A63CB, 0xBD3C794E, +/**/ 0x00000000, 0x3FF3C400, +/**/ 0x58A0943A, 0xBF20D475, +/**/ 0x48FC2000, 0xBFCB0A4B, +/**/ 0x5C3998ED, 0x3D22E72D, +/**/ 0x00000000, 0x3FF3BC00, +/**/ 0x3295482C, 0x3F360D92, +/**/ 0x6F672000, 0xBFCAE2CA, +/**/ 0xAE54F550, 0xBD37A8D5, +/**/ 0x00000000, 0x3FF3B800, +/**/ 0xCAB48651, 0xBF267D12, +/**/ 0xC316A000, 0xBFCABB55, +/**/ 0xCAF14CD8, 0x3D38A65A, +/**/ 0x00000000, 0x3FF3B000, +/**/ 0x13B13B14, 0x3F33B13B, +/**/ 0x3C8AE000, 0xBFCA93ED, +/**/ 0x50562169, 0x3D287243, +/**/ 0x00000000, 0x3FF3AC00, +/**/ 0x2C8FD3BF, 0xBF2A46AF, +/**/ 0xD44B8000, 0xBFCA6C90, +/**/ 0xF037B0C6, 0x3D3F63B7, +/**/ 0x00000000, 0x3FF3A400, +/**/ 0xAC822610, 0x3F324387, +/**/ 0x82E6A000, 0xBFCA4540, +/**/ 0xC81F7171, 0xBD360A77, +/**/ 0x00000000, 0x3FF3A000, +/**/ 0xA1923DEE, 0xBF2C34BB, +/**/ 0x40F1C000, 0xBFCA1DFC, +/**/ 0x004F3781, 0x3D301E0F, +/**/ 0x00000000, 0x3FF39800, +/**/ 0x87F63372, 0x3F31C2C1, +/**/ 0x0708A000, 0xBFC9F6C4, +/**/ 0x4BCD3F43, 0x3D3337D9, +/**/ 0x00000000, 0x3FF39400, +/**/ 0xE11BD52E, 0xBF2C4AA0, +/**/ 0xCDCE0000, 0xBFC9CF97, +/**/ 0x10C414E3, 0xBD3D862F, +/**/ 0x00000000, 0x3FF38C00, +/**/ 0x6088DBF4, 0x3F322D36, +/**/ 0x8DEBA000, 0xBFC9A877, +/**/ 0x3EFEC390, 0xBD3470FA, +/**/ 0x00000000, 0x3FF38800, +/**/ 0x503F774E, 0xBF2A8BBF, +/**/ 0x4011A000, 0xBFC98163, +/**/ 0x9E9045E2, 0xBD34EADD, +/**/ 0x00000000, 0x3FF38000, +/**/ 0x13813814, 0x3F338138, +/**/ 0xDCF70000, 0xBFC95A5A, +/**/ 0x58A0FF6F, 0xBD07F228, +/**/ 0x00000000, 0x3FF37C00, +/**/ 0x1B177053, 0xBF26FB6F, +/**/ 0x5D594000, 0xBFC9335E, +/**/ 0x3ABD47DA, 0xBD33115C, +/**/ 0x00000000, 0x3FF37400, +/**/ 0x945EDC20, 0x3F35BD1C, +/**/ 0xB9FCC000, 0xBFC90C6D, +/**/ 0x7718D7CA, 0x3D1935F5, +/**/ 0x00000000, 0x3FF37000, +/**/ 0x4DBDCC60, 0xBF219D00, +/**/ 0xEBAC2000, 0xBFC8E588, +/**/ 0xAB2D1140, 0xBD3B7D5C, +/**/ 0x00000000, 0x3FF36800, +/**/ 0xE0747954, 0x3F38DF3D, +/**/ 0xEB390000, 0xBFC8BEAF, +/**/ 0xAAE92CD1, 0x3D073D54, +/**/ 0x00000000, 0x3FF36400, +/**/ 0xD9D3C49F, 0xBF14E775, +/**/ 0xB17B2000, 0xBFC897E2, +/**/ 0x380CBE9E, 0x3D296B37, +/**/ 0x00000000, 0x3FF35C00, +/**/ 0xF2AF821E, 0x3F3CE5F9, +/**/ 0x3750E000, 0xBFC87121, +/**/ 0x42F9AF75, 0xBD3328EB, +/**/ 0x00000000, 0x3FF35800, +/**/ 0xE34971F2, 0xBEE82DF0, +/**/ 0x759F6000, 0xBFC84A6B, +/**/ 0x2ADF8609, 0x3D3DA280, +/**/ 0x00000000, 0x3FF35400, +/**/ 0x4873ECAE, 0xBF3E304D, +/**/ 0x6551A000, 0xBFC823C1, +/**/ 0x9A631E83, 0xBD1E0DDB, +/**/ 0x00000000, 0x3FF34C00, +/**/ 0x1FF659DB, 0x3F1264B6, +/**/ 0xFF59A000, 0xBFC7FD22, +/**/ 0xF457B7D2, 0x3D158BEB, +/**/ 0x00000000, 0x3FF34800, +/**/ 0xFECB9865, 0xBF386531, +/**/ 0x3CAF6000, 0xBFC7D690, +/**/ 0x17C301D7, 0x3D24C06B, +/**/ 0x00000000, 0x3FF34000, +/**/ 0xEEDA65AE, 0x3F25A8C2, +/**/ 0x16516000, 0xBFC7B009, +/**/ 0xCB067E57, 0x3D3AE75F, +/**/ 0x00000000, 0x3FF33C00, +/**/ 0x8434E1F4, 0xBF31BA4A, +/**/ 0x85444000, 0xBFC7898D, +/**/ 0xE3DBAF3F, 0xBD38E67B, +/**/ 0x00000000, 0x3FF33400, +/**/ 0xDBFC660A, 0x3F31EE97, +/**/ 0x82936000, 0xBFC7631D, +/**/ 0xC7C5F3E1, 0x3D25E77D, +/**/ 0x00000000, 0x3FF33000, +/**/ 0xBC40BFDA, 0xBF246252, +/**/ 0x074FE000, 0xBFC73CB9, +/**/ 0x0D0005A6, 0x3D3D66A9, +/**/ 0x00000000, 0x3FF32800, +/**/ 0x13299E64, 0x3F39E640, +/**/ 0x0C914000, 0xBFC71660, +/**/ 0x7CEC3838, 0xBCE51B15, +/**/ 0x00000000, 0x3FF32400, +/**/ 0xEF40991F, 0xBEFCB5D4, +/**/ 0x8B756000, 0xBFC6F012, +/**/ 0x0D31EF0F, 0xBD357739, +/**/ 0x00000000, 0x3FF32000, +/**/ 0xC823D892, 0xBF3D4632, +/**/ 0x7D204000, 0xBFC6C9D0, +/**/ 0xFD9B2DCA, 0x3CDC73FA, +/**/ 0x00000000, 0x3FF31800, +/**/ 0x7AED804C, 0x3F1DD63A, +/**/ 0xDABBE000, 0xBFC6A399, +/**/ 0xE66A15A6, 0x3D38F934, +/**/ 0x00000000, 0x3FF31400, +/**/ 0xE8C11E1A, 0xBF339849, +/**/ 0x9D786000, 0xBFC67D6E, +/**/ 0x30A706D3, 0x3D311E88, +/**/ 0x00000000, 0x3FF30C00, +/**/ 0x0D190131, 0x3F319013, +/**/ 0xBE8C2000, 0xBFC6574E, +/**/ 0x34F0F462, 0x3D398C1D, +/**/ 0x00000000, 0x3FF30800, +/**/ 0xB47A7FDA, 0xBF222315, +/**/ 0x37336000, 0xBFC6313A, +/**/ 0x4F21EA6D, 0x3D144DF5, +/**/ 0x00000000, 0x3FF30000, +/**/ 0x40260390, 0x3F3C82AC, +/**/ 0x00B0A000, 0xBFC60B31, +/**/ 0xC988F814, 0x3D371456, +/**/ 0x00000000, 0x3FF2FC00, +/**/ 0xA2430A62, 0x3F026443, +/**/ 0x144C2000, 0xBFC5E533, +/**/ 0xF3B290EA, 0x3D31CE0B, +/**/ 0x00000000, 0x3FF2F800, +/**/ 0xED097B42, 0xBF37B425, +/**/ 0x6B544000, 0xBFC5BF40, +/**/ 0xEB68981C, 0x3D127023, +/**/ 0x00000000, 0x3FF2F000, +/**/ 0x4AE0553C, 0x3F2D00E3, +/**/ 0xFF1D6000, 0xBFC59958, +/**/ 0x9769CA05, 0x3D3A1D05, +/**/ 0x00000000, 0x3FF2EC00, +/**/ 0x25D69D44, 0xBF262BC0, +/**/ 0xC9018000, 0xBFC5737C, +/**/ 0xA6B887F6, 0xBD39BAA7, +/**/ 0x00000000, 0x3FF2E400, +/**/ 0xE3103D6B, 0x3F3B88B5, +/**/ 0xC2610000, 0xBFC54DAB, +/**/ 0xE5C8D0D8, 0xBD2746FE, +/**/ 0x00000000, 0x3FF2E000, +/**/ 0xC04B8097, 0x3F02E025, +/**/ 0xE4A1C000, 0xBFC527E5, +/**/ 0x8D4B411D, 0x3D34E60B, +/**/ 0x00000000, 0x3FF2DC00, +/**/ 0x2C305021, 0xBF369C22, +/**/ 0x292F6000, 0xBFC5022B, +/**/ 0xFF36A25B, 0xBD348A05, +/**/ 0x00000000, 0x3FF2D400, +/**/ 0xD50A012D, 0x3F30A012, +/**/ 0x897BC000, 0xBFC4DC7B, +/**/ 0x0AE1FF0F, 0xBD0C79B6, +/**/ 0x00000000, 0x3FF2D000, +/**/ 0xBC66484E, 0xBF1FBE29, +/**/ 0xFEFE2000, 0xBFC4B6D6, +/**/ 0xF56E7952, 0xBD1522EC, +/**/ 0x00000000, 0x3FF2C800, +/**/ 0x12C9FB4E, 0x3F3FB4D8, +/**/ 0x8333C000, 0xBFC4913D, +/**/ 0x558124C4, 0x3D353E43, +/**/ 0x00000000, 0x3FF2C400, +/**/ 0x7004B11E, 0x3F1E3432, +/**/ 0x0F9F6000, 0xBFC46BAF, +/**/ 0x0790841A, 0x3D1249CD, +/**/ 0x00000000, 0x3FF2C000, +/**/ 0x5C8EF02F, 0xBF30671A, +/**/ 0x9DC9C000, 0xBFC4462B, +/**/ 0xA711B062, 0x3D384858, +/**/ 0x00000000, 0x3FF2B800, +/**/ 0xD548D9AC, 0x3F37D835, +/**/ 0x27410000, 0xBFC420B3, +/**/ 0xC85A0884, 0x3D116282, +/**/ 0x00000000, 0x3FF2B400, +/**/ 0xAD012B40, 0x3ED2B404, +/**/ 0xA5992000, 0xBFC3FB45, +/**/ 0xC0CAE559, 0xBD319713, +/**/ 0x00000000, 0x3FF2B000, +/**/ 0x8E7302A1, 0xBF370F78, +/**/ 0x126BC000, 0xBFC3D5E3, +/**/ 0x85096C4B, 0xBD13FB2F, +/**/ 0x00000000, 0x3FF2A800, +/**/ 0x3C1053F9, 0x3F31C92F, +/**/ 0x67580000, 0xBFC3B08B, +/**/ 0xF29320FB, 0x3D3AADE8, +/**/ 0x00000000, 0x3FF2A400, +/**/ 0x3DBE2E04, 0xBF14AD94, +/**/ 0x9E028000, 0xBFC38B3E, +/**/ 0x545C17F9, 0x3D370EF0, +/**/ 0x00000000, 0x3FF2A000, +/**/ 0xBED61BED, 0xBF3BED61, +/**/ 0xB015A000, 0xBFC365FC, +/**/ 0xAFB9691B, 0x3D3FD3A0, +/**/ 0x00000000, 0x3FF29800, +/**/ 0x26F004A6, 0x3F2B061A, +/**/ 0x97412000, 0xBFC340C5, +/**/ 0xF7D9D386, 0x3D37A3DC, +/**/ 0x00000000, 0x3FF29400, +/**/ 0xFF6B646D, 0xBF21B488, +/**/ 0x4D3A4000, 0xBFC31B99, +/**/ 0xE3A50810, 0xBD3F098E, +/**/ 0x00000000, 0x3FF29000, +/**/ 0x2CA5D5AC, 0xBF3F0582, +/**/ 0xCBBC0000, 0xBFC2F677, +/**/ 0x2160F40D, 0xBD352B30, +/**/ 0x00000000, 0x3FF28800, +/**/ 0x16025116, 0x3F260251, +/**/ 0x0C868000, 0xBFC2D161, +/**/ 0xCB81B4A1, 0xBD039D6C, +/**/ 0x00000000, 0x3FF28400, +/**/ 0x502065D2, 0xBF258CDF, +/**/ 0x095F6000, 0xBFC2AC55, +/**/ 0xD0C6C8A8, 0x3D1D3466, +/**/ 0x00000000, 0x3FF27C00, +/**/ 0x1CE4D6F8, 0x3F3FA38A, +/**/ 0xBC11A000, 0xBFC28753, +/**/ 0x359302E6, 0xBD37494E, +/**/ 0x00000000, 0x3FF27800, +/**/ 0xDCCA0781, 0x3F247DD5, +/**/ 0x1E6DE000, 0xBFC2625D, +/**/ 0xF09E3D82, 0x3CF52962, +/**/ 0x00000000, 0x3FF27400, +/**/ 0xDB195E8F, 0xBF25E8EF, +/**/ 0x2A49C000, 0xBFC23D71, +/**/ 0x8FD3DF5C, 0xBD100D23, +/**/ 0x00000000, 0x3FF27000, +/**/ 0xFFB647FE, 0xBF3FF6C8, +/**/ 0xD9808000, 0xBFC2188F, +/**/ 0x7F50C701, 0x3D3B3A1E, +/**/ 0x00000000, 0x3FF26800, +/**/ 0xC024D167, 0x3F266F9A, +/**/ 0x25F26000, 0xBFC1F3B9, +/**/ 0x9B083633, 0x3D15F74E, +/**/ 0x00000000, 0x3FF26400, +/**/ 0xEABD0E14, 0xBF22D1BD, +/**/ 0x09854000, 0xBFC1CEED, +/**/ 0x39192AF9, 0x3D315C1C, +/**/ 0x00000000, 0x3FF26000, +/**/ 0xF6D0EEC8, 0xBF3DD8F7, +/**/ 0x7E240000, 0xBFC1AA2B, +/**/ 0xDDE3B366, 0x3D31AC38, +/**/ 0x00000000, 0x3FF25800, +/**/ 0x2A241EF6, 0x3F2BCEB1, +/**/ 0x7DBEC000, 0xBFC18574, +/**/ 0x45BD9B49, 0xBD3E6744, +/**/ 0x00000000, 0x3FF25400, +/**/ 0xA21378D7, 0xBF18A05B, +/**/ 0x024B2000, 0xBFC160C8, +/**/ 0xA9009E3D, 0xBD2EC2D2, +/**/ 0x00000000, 0x3FF25000, +/**/ 0xD6CFA90C, 0xBF3A076F, +/**/ 0x05C3A000, 0xBFC13C26, +/**/ 0xD94F6509, 0x3D2CF5FD, +/**/ 0x00000000, 0x3FF24800, +/**/ 0x92492492, 0x3F324924, +/**/ 0x8227E000, 0xBFC1178E, +/**/ 0xCE2D07F2, 0xBD21EF78, +/**/ 0x00000000, 0x3FF24400, +/**/ 0x6151E899, 0xBEF3682B, +/**/ 0x717D0000, 0xBFC0F301, +/**/ 0x41AE86C5, 0x3D3E09B4, +/**/ 0x00000000, 0x3FF24000, +/**/ 0x89FA4C67, 0xBF34868E, +/**/ 0xCDCCC000, 0xBFC0CE7E, +/**/ 0xABFF5447, 0xBD14652D, +/**/ 0x00000000, 0x3FF23800, +/**/ 0x6B11F09F, 0x3F3858D8, +/**/ 0x91268000, 0xBFC0AA06, +/**/ 0xD7032129, 0x3D345519, +/**/ 0x00000000, 0x3FF23400, +/**/ 0xAF37C049, 0x3F159E26, +/**/ 0xB59E4000, 0xBFC08598, +/**/ 0x7009902C, 0x3D27E5DD, +/**/ 0x00000000, 0x3FF23000, +/**/ 0x2E076329, 0xBF2AB546, +/**/ 0x354D4000, 0xBFC06135, +/**/ 0x28340EE9, 0xBD363046, +/**/ 0x00000000, 0x3FF22C00, +/**/ 0xFEDD5FEE, 0xBF3FEDD5, +/**/ 0x0A51E000, 0xBFC03CDC, +/**/ 0xF169FC5C, 0xBD381A9C, +/**/ 0x00000000, 0x3FF22400, +/**/ 0x009126D7, 0x3F2B5B92, +/**/ 0x2ECF6000, 0xBFC0188D, +/**/ 0x1CFF9DFE, 0xBD03F965, +/**/ 0x00000000, 0x3FF22000, +/**/ 0x8121FB78, 0xBF121FB7, +/**/ 0x39DBC000, 0xBFBFE891, +/**/ 0xD82F7A82, 0xBD356594, +/**/ 0x00000000, 0x3FF21C00, +/**/ 0x3A459635, 0xBF368F22, +/**/ 0x9DB58000, 0xBFBFA01C, +/**/ 0xFA48A730, 0x3D08F351, +/**/ 0x00000000, 0x3FF21400, +/**/ 0x855E6012, 0x3F379804, +/**/ 0x7D900000, 0xBFBF57BC, +/**/ 0x9EA8B04E, 0xBD176A6C, +/**/ 0x00000000, 0x3FF21000, +/**/ 0x78CD7A37, 0x3F17B57C, +/**/ 0xCDD98000, 0xBFBF0F70, +/**/ 0x6C272C1E, 0xBD32E31F, +/**/ 0x00000000, 0x3FF20C00, +/**/ 0x07E4EF15, 0xBF271E73, +/**/ 0x830A0000, 0xBFBEC739, +/**/ 0xA80CDD10, 0xBD311FCB, +/**/ 0x00000000, 0x3FF20800, +/**/ 0x49392BA7, 0xBF3CDDEC, +/**/ 0x91A34000, 0xBFBE7F16, +/**/ 0x9BC77BFA, 0x3D32C1C5, +/**/ 0x00000000, 0x3FF20000, +/**/ 0x12012012, 0x3F320120, +/**/ 0xEE304000, 0xBFBE3707, +/**/ 0xE6766ABD, 0xBD20F684, +/**/ 0x00000000, 0x3FF1FC00, +/**/ 0xCE8AD1A2, 0x3EF0DC4F, +/**/ 0x8D468000, 0xBFBDEF0D, +/**/ 0x412E9A74, 0x3D324750, +/**/ 0x00000000, 0x3FF1F800, +/**/ 0xDC11F704, 0xBF2F7047, +/**/ 0x63844000, 0xBFBDA727, +/**/ 0x1FA71733, 0xBD1A8940, +/**/ 0x00000000, 0x3FF1F000, +/**/ 0x16B6419D, 0x3F3FAF3F, +/**/ 0x65920000, 0xBFBD5F55, +/**/ 0xCC185469, 0xBD30E239, +/**/ 0x00000000, 0x3FF1EC00, +/**/ 0xF70985E2, 0x3F2E878F, +/**/ 0x88218000, 0xBFBD1797, +/**/ 0xB5EFBEED, 0xBD336433, +/**/ 0x00000000, 0x3FF1E800, +/**/ 0x94D7FDC3, 0xBEEF55E4, +/**/ 0xBFEE0000, 0xBFBCCFED, +/**/ 0x2FE71256, 0xBD33A823, +/**/ 0x00000000, 0x3FF1E400, +/**/ 0x0478BBCF, 0xBF310C4C, +/**/ 0x01BC4000, 0xBFBC8858, +/**/ 0xC65AACD3, 0xBD2646D1, +/**/ 0x00000000, 0x3FF1DC00, +/**/ 0xCB840C49, 0x3F3F0ECB, +/**/ 0x425A4000, 0xBFBC40D6, +/**/ 0x1D1930DD, 0xBD3CB112, +/**/ 0x00000000, 0x3FF1D800, +/**/ 0xC9579074, 0x3F2EACE5, +/**/ 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0xEB7C1000, 0x3FD49B9F, +/**/ 0x58AB60D7, 0x3D3DAC1C, +/**/ 0x00000000, 0x3FE73000, +/**/ 0x783709C7, 0xBF3BB33C, +/**/ 0x3CED0000, 0x3FD4A737, +/**/ 0xEBF35449, 0xBD39A234, +/**/ 0x00000000, 0x3FE72800, +/**/ 0x265AD23A, 0x3F061274, +/**/ 0x75556000, 0x3FD4B2CC, +/**/ 0xC78BFA4B, 0xBD380FCB, +/**/ 0x00000000, 0x3FE72800, +/**/ 0xC90A1FD2, 0xBF3EBC05, +/**/ 0x95778000, 0x3FD4BE5F, +/**/ 0xCD9AD824, 0xBD3D7C92, +/**/ 0x00000000, 0x3FE72000, +/**/ 0x38017200, 0xBEC71FFA, +/**/ 0x9E153000, 0x3FD4C9F0, +/**/ 0x70E02DE0, 0xBD2E1DDE, +/**/ 0x00000000, 0x3FE71800, +/**/ 0x74A050E1, 0x3F3E6B99, +/**/ 0x8FEFE000, 0x3FD4D57F, +/**/ 0x7FD06868, 0x3D23F926, +/**/ 0x00000000, 0x3FE71800, +/**/ 0xB8BD1180, 0xBF077400, +/**/ 0x6BC8A000, 0x3FD4E10C, +/**/ 0x1636F061, 0x3CF8283F, +/**/ 0x00000000, 0x3FE71000, +/**/ 0xE3E0453A, 0x3F3BC36C, +/**/ 0x32600000, 0x3FD4EC97, +/**/ 0xAF04D104, 0x3D234D7A, +/**/ 0x00000000, 0x3FE71000, +/**/ 0x6935DDC5, 0xBF15FA98, +/**/ 0xE4764000, 0x3FD4F81F, +/**/ 0x434FF08D, 0xBD27FCF6, +/**/ 0x00000000, 0x3FE70800, +/**/ 0x7337CF08, 0x3F394B40, +/**/ 0x82CB2000, 0x3FD503A6, +/**/ 0xF16F9B5D, 0xBD2A68C8, +/**/ 0x00000000, 0x3FE70800, +/**/ 0xA835403A, 0xBF1F7B97, +/**/ 0x0E1E0000, 0x3FD50F2B, +/**/ 0x8C47B8D8, 0x3D3A0940, +/**/ 0x00000000, 0x3FE70000, +/**/ 0x5C0B8170, 0x3F3702E0, +/**/ 0x872E0000, 0x3FD51AAD, +/**/ 0xDB0A7CC1, 0xBD3F4BD8, +/**/ 0x00000000, 0x3FE70000, +/**/ 0x4F67A855, 0xBF241EE6, +/**/ 0xEEB99000, 0x3FD5262D, +/**/ 0x70894A01, 0xBD3E1B9F, +/**/ 0x00000000, 0x3FE6F800, +/**/ 0x221C0170, 0x3F34EA19, +/**/ 0x457EE000, 0x3FD531AC, +/**/ 0x7D931501, 0x3D3DF83B, +/**/ 0x00000000, 0x3FE6F800, +/**/ 0x5508CA5C, 0xBF282102, +/**/ 0x8C3BE000, 0x3FD53D28, +/**/ 0xEB6DFAC5, 0xBD111397, +/**/ 0x00000000, 0x3FE6F000, +/**/ 0x9300B793, 0x3F3300B7, +/**/ 0xC3ADD000, 0x3FD548A2, +/**/ 0x63081CF7, 0x3D23167E, +/**/ 0x00000000, 0x3FE6F000, +/**/ 0x005BB90F, 0xBF2BC486, +/**/ 0xEC91C000, 0x3FD5541A, +/**/ 0xDC72EEBA, 0xBCF816AA, +/**/ 0x00000000, 0x3FE6E800, +/**/ 0xC5A3A00B, 0x3F314688, +/**/ 0x07A44000, 0x3FD55F91, +/**/ 0x78DF4A62, 0xBD11E647, +/**/ 0x00000000, 0x3FE6E800, +/**/ 0xDA9C5AE1, 0xBF2F09D6, +/**/ 0x15A18000, 0x3FD56B05, +/**/ 0xBC4A23FC, 0x3D29247B, +/**/ 0x00000000, 0x3FE6E000, +/**/ 0x337C6CB1, 0x3F2F76B4, +/**/ 0x17456000, 0x3FD57677, +/**/ 0x9524D7CA, 0xBD364EAD, +/**/ 0x00000000, 0x3FE6E000, +/**/ 0xEDF4EC87, 0xBF30F8AC, +/**/ 0x0D4B3000, 0x3FD581E7, +/**/ 0xB12D8F1D, 0xBD1F31E1, +/**/ 0x00000000, 0x3FE6D800, +/**/ 0x6EAEF381, 0x3F2CBDF2, +/**/ 0xF86E0000, 0x3FD58D54, +/**/ 0x0A795215, 0x3D2791F3, +/**/ 0x00000000, 0x3FE6D800, +/**/ 0xB624BFF5, 0xBF323DB9, +/**/ 0xD9688000, 0x3FD598C0, +/**/ 0x70D96DA4, 0xBD385F49, +/**/ 0x00000000, 0x3FE6D000, +/**/ 0x1C860FB0, 0x3F2A6268, +/**/ 0xB0F4D000, 0x3FD5A42A, +/**/ 0x2DF7BA69, 0xBCDE63AF, +/**/ 0x00000000, 0x3FE6D000, +/**/ 0xB253BAE1, 0xBF335443, +/**/ 0x7FCCE000, 0x3FD5AF92, +/**/ 0xF5FFC77A, 0xBD1C032F, +/**/ 0x00000000, 0x3FE6C800, +/**/ 0xAB4294D4, 0x3F2863B1, +/**/ 0x46AA2000, 0x3FD5BAF8, +/**/ 0xF873FA41, 0xBD339AE8, +/**/ 0x00000000, 0x3FE6C800, +/**/ 0x87EAA6DF, 0xBF343C7C, +/**/ 0x0645A000, 0x3FD5C65C, +/**/ 0x0180EE65, 0xBD39FE06, +/**/ 0x00000000, 0x3FE6C000, +/**/ 0x16C16C17, 0x3F26C16C, +/**/ 0xBF581000, 0x3FD5D1BD, +/**/ 0xC9C7C238, 0xBD38D6BD, +/**/ 0x00000000, 0x3FE6C000, +/**/ 0x95C33E00, 0xBF34F695, +/**/ 0x7299C000, 0x3FD5DD1D, +/**/ 0x8815CE17, 0xBD38AF61, +/**/ 0x00000000, 0x3FE6B800, +/**/ 0xE7802D73, 0x3F257B34, +/**/ 0x20C29000, 0x3FD5E87B, +/**/ 0x8F7738FA, 0x3D3527D1, +/**/ 0x00000000, 0x3FE6B800, +/**/ 0xF4A5582C, 0xBF3582BF, +/**/ 0xCA8A2000, 0x3FD5F3D6, +/**/ 0x8E19CC75, 0x3D37AF84, +/**/ 0x00000000, 0x3FE6B000, +/**/ 0x31A3CFC7, 0x3F2490AA, +/**/ 0x70A79000, 0x3FD5FF30, +/**/ 0x9F105039, 0x3D2E9E43, +/**/ 0x00000000, 0x3FE6B000, +/**/ 0x77C30E5A, 0xBF35E12C, +/**/ 0x13D1A000, 0x3FD60A88, +/**/ 0xC879AF55, 0x3D36E9B9, +/**/ 0x00000000, 0x3FE6A800, +/**/ 0x94016A94, 0x3F24016A, +/**/ 0xB4BEC000, 0x3FD615DD, +/**/ 0x90BC04B2, 0x3D13C7CA, +/**/ 0x00000000, 0x3FE6A800, +/**/ 0xAD33D63F, 0xBF36120B, +/**/ 0x5424F000, 0x3FD62131, +/**/ 0x4AA68669, 0xBD3382FC, +/**/ 0x00000000, 0x3FE6A000, +/**/ 0x3729043E, 0x3F23CD15, +/**/ 0xF2B9C000, 0x3FD62C82, +/**/ 0xBD7C8A98, 0x3D3E54BD } }; + +static const union {int4 i[4350]; double x[2175]; } vj = { .i = { +/**/ 0x7D161C28, 0x3F46A400, +/**/ 0x20600000, 0xBF46A200, +/**/ 0xAA7623D9, 0x3D27DC4E, +/**/ 0xD596E639, 0x3F4693FA, +/**/ 0x4CE00000, 0xBF4691FD, +/**/ 0x29C3F0AD, 0x3D26B0CF, +/**/ 0x3219CE89, 0x3F4683F5, +/**/ 0x7B600000, 0xBF4681FA, +/**/ 0x95B9FDCC, 0x3D22B290, +/**/ 0x929ED397, 0x3F4673EF, +/**/ 0xABE00000, 0xBF4671F7, +/**/ 0xFA2F2D87, 0x3D17C727, +/**/ 0xF725F3E2, 0x3F4663E9, +/**/ 0xDE600000, 0xBF4661F4, +/**/ 0x6EDBFF1C, 0x3CF22ED3, +/**/ 0x5FAF2DE9, 0x3F4653E4, +/**/ 0x12E00000, 0xBF4651F2, +/**/ 0x157812BB, 0xBD144936, +/**/ 0xCC3A802B, 0x3F4643DE, +/**/ 0x49600000, 0xBF4641EF, +/**/ 0x60314E05, 0xBD2959CB, +/**/ 0x3CC7E927, 0x3F4633D9, +/**/ 0x81E00000, 0xBF4631EC, +/**/ 0xC3638E99, 0xBD35ABDA, +/**/ 0xB157675C, 0x3F4623D3, +/**/ 0xBC800000, 0xBF4621E9, +/**/ 0xC63F9A21, 0x3D3FF1D3, +/**/ 0x29E8F948, 0x3F4613CE, +/**/ 0xF9000000, 0xBF4611E6, +/**/ 0x71EEE611, 0x3D342D26, +/**/ 0xA67C9D6B, 0x3F4603C8, +/**/ 0x37800000, 0xBF4601E4, +/**/ 0x11A09689, 0x3D1C1C77, +/**/ 0x27125244, 0x3F45F3C3, +/**/ 0x78000000, 0xBF45F1E1, +/**/ 0xF7DC643C, 0xBD1DFD16, +/**/ 0xABAA1651, 0x3F45E3BD, +/**/ 0xBA800000, 0xBF45E1DE, +/**/ 0x91318A02, 0xBD376503, +/**/ 0x3443E812, 0x3F45D3B8, +/**/ 0xFF200000, 0xBF45D1DB, +/**/ 0xCE55DCDD, 0x3D3756E4, +/**/ 0xC0DFC606, 0x3F45C3B2, +/**/ 0x45A00000, 0xBF45C1D9, +/**/ 0x8F6F8FA0, 0x3D12D5CF, +/**/ 0x517DAEAB, 0x3F45B3AD, +/**/ 0x8E200000, 0xBF45B1D6, +/**/ 0x9B85DC2C, 0xBD2E90AB, +/**/ 0xE61DA081, 0x3F45A3A7, +/**/ 0xD8C00000, 0xBF45A1D3, +/**/ 0x3BF5AC54, 0x3D3B5E88, +/**/ 0x7EBF9A07, 0x3F4593A2, +/**/ 0x25400000, 0xBF4591D1, +/**/ 0x0C86DDB1, 0x3D12AC3A, +/**/ 0x1B6399BB, 0x3F45839D, +/**/ 0x73C00000, 0xBF4581CE, +/**/ 0x76830985, 0xBD3361C2, +/**/ 0xBC099E1C, 0x3F457397, +/**/ 0xC4600000, 0xBF4571CB, +/**/ 0xD062EBFF, 0x3D333915, +/**/ 0x60B1A5AA, 0x3F456392, +/**/ 0x16E00000, 0xBF4561C9, +/**/ 0x9CC4988F, 0xBD1E0DA0, +/**/ 0x095BAEE4, 0x3F45538D, +/**/ 0x6B800000, 0xBF4551C6, +/**/ 0x235BC18A, 0x3D3C69C4, +/**/ 0xB607B848, 0x3F454387, +/**/ 0xC2000000, 0xBF4541C3, +/**/ 0xF7737723, 0xBCEFCC99, +/**/ 0x66B5C056, 0x3F453382, +/**/ 0x1A800000, 0xBF4531C1, +/**/ 0x809CBCBB, 0xBD3FBAE2, +/**/ 0x1B65C58C, 0x3F45237D, +/**/ 0x75200000, 0xBF4521BE, +/**/ 0x194FEE63, 0x3CCAA5C8, +/**/ 0xD417C66A, 0x3F451377, +/**/ 0xD1C00000, 0xBF4511BB, +/**/ 0xE1CC7BBC, 0x3D3ED325, +/**/ 0x90CBC16E, 0x3F450372, +/**/ 0x30400000, 0xBF4501B9, +/**/ 0x68AB3742, 0xBD0F0298, +/**/ 0x5181B517, 0x3F44F36D, +/**/ 0x90E00000, 0xBF44F1B6, +/**/ 0x41E67AD9, 0x3D381BE1, +/**/ 0x16399FE6, 0x3F44E368, +/**/ 0xF3600000, 0xBF44E1B3, +/**/ 0x668D3662, 0xBD2A6E79, +/**/ 0xDEF38058, 0x3F44D362, +/**/ 0x58000000, 0xBF44D1B1, +/**/ 0x21F8B7C2, 0x3D284EA7, +/**/ 0xABAF54EC, 0x3F44C35D, +/**/ 0xBE800000, 0xBF44C1AE, +/**/ 0x7417D9C5, 0xBD3BC76D, +/**/ 0x7C6D1C22, 0x3F44B358, +/**/ 0x27200000, 0xBF44B1AC, +/**/ 0x16AAD1FC, 0xBD1409FD, +/**/ 0x512CD479, 0x3F44A353, +/**/ 0x91C00000, 0xBF44A1A9, +/**/ 0x98BC14FD, 0x3D30771E, +/**/ 0x29EE7C70, 0x3F44934E, +/**/ 0xFE400000, 0xBF4491A6, +/**/ 0x5CCB7232, 0xBD3B5993, +/**/ 0x06B21285, 0x3F448349, +/**/ 0x6CE00000, 0xBF4481A4, +/**/ 0x5512F9C2, 0xBD20E729, +/**/ 0xE7779538, 0x3F447343, +/**/ 0xDD800000, 0xBF4471A1, +/**/ 0x55B30899, 0x3D225436, +/**/ 0xCC3F0308, 0x3F44633E, +/**/ 0x50200000, 0xBF44619F, +/**/ 0x9E54E31F, 0x3D39807C, +/**/ 0xB5085A73, 0x3F445339, +/**/ 0xC4A00000, 0xBF44519C, +/**/ 0xD5804C0E, 0xBD376F6F, +/**/ 0xA1D399FA, 0x3F444334, +/**/ 0x3B400000, 0xBF44419A, +/**/ 0x6CDE6425, 0xBD234953, +/**/ 0x92A0C01A, 0x3F44332F, +/**/ 0xB3E00000, 0xBF443197, +/**/ 0xAAF6596F, 0x3D070E7B, +/**/ 0x876FCB54, 0x3F44232A, +/**/ 0x2E800000, 0xBF442195, +/**/ 0x4EC011F1, 0x3D2C49F8, +/**/ 0x8040BA25, 0x3F441325, +/**/ 0xAB200000, 0xBF441192, +/**/ 0xD8AAA7EB, 0x3D3825DC, +/**/ 0x7D138B0E, 0x3F440320, +/**/ 0x29A00000, 0xBF440190, +/**/ 0xFE0B73D6, 0xBD3F1A8D, +/**/ 0x7DE83C8C, 0x3F43F31B, +/**/ 0xAA400000, 0xBF43F18D, +/**/ 0xE46CA26B, 0xBD379B43, +/**/ 0x82BECD20, 0x3F43E316, +/**/ 0x2CE00000, 0xBF43E18B, +/**/ 0x6283780D, 0xBD315B44, +/**/ 0x8B973B49, 0x3F43D311, +/**/ 0xB1800000, 0xBF43D188, +/**/ 0x017589BE, 0xBD28B31E, +/**/ 0x98718584, 0x3F43C30C, +/**/ 0x38200000, 0xBF43C186, +/**/ 0x8FBB296E, 0xBD212A46, +/**/ 0xA94DAA52, 0x3F43B307, +/**/ 0xC0C00000, 0xBF43B183, +/**/ 0x045CBBD2, 0xBD183403, +/**/ 0xBE2BA832, 0x3F43A302, +/**/ 0x4B600000, 0xBF43A181, +/**/ 0xD7CC5936, 0xBD13009B, +/**/ 0xD70B7DA2, 0x3F4392FD, +/**/ 0xD8000000, 0xBF43917E, +/**/ 0xC1742279, 0xBD12B655, +/**/ 0xF3ED2921, 0x3F4382F8, +/**/ 0x66A00000, 0xBF43817C, +/**/ 0xEA83FAE8, 0xBD17512E, +/**/ 0x14D0A930, 0x3F4372F4, +/**/ 0xF7400000, 0xBF437179, +/**/ 0xBED65875, 0xBD206692, +/**/ 0x39B5FC4C, 0x3F4362EF, +/**/ 0x89E00000, 0xBF436177, +/**/ 0xD38FFE9E, 0xBD27931B, +/**/ 0x629D20F5, 0x3F4352EA, +/**/ 0x1E800000, 0xBF435175, +/**/ 0xE524208F, 0xBD309618, +/**/ 0x8F8615AA, 0x3F4342E5, +/**/ 0xB5200000, 0xBF434172, +/**/ 0xDD4C72C5, 0xBD3697E9, +/**/ 0xC070D8EB, 0x3F4332E0, +/**/ 0x4DC00000, 0xBF433170, +/**/ 0x5E6E12C3, 0xBD3DCE00, +/**/ 0xF55D6935, 0x3F4322DB, +/**/ 0xE8800000, 0xBF43216D, +/**/ 0x0AE9A8CE, 0x3D39C8A4, +/**/ 0x2E4BC509, 0x3F4312D7, +/**/ 0x85200000, 0xBF43116B, +/**/ 0xD1CD2FA1, 0x3D302D03, +/**/ 0x6B3BEAE5, 0x3F4302D2, +/**/ 0x23C00000, 0xBF430169, +/**/ 0xA3BADFD1, 0x3D15807D, +/**/ 0xAC2DD949, 0x3F42F2CD, +/**/ 0xC4600000, 0xBF42F166, +/**/ 0xF57F0504, 0xBD1A7422, +/**/ 0xF1218EB3, 0x3F42E2C8, +/**/ 0x67000000, 0xBF42E164, +/**/ 0x2F2C781C, 0xBD33C974, +/**/ 0x3A1709A3, 0x3F42D2C4, +/**/ 0x0BC00000, 0xBF42D162, +/**/ 0x851A1E61, 0x3D3DDBDD, +/**/ 0x870E4898, 0x3F42C2BF, +/**/ 0xB2600000, 0xBF42C15F, +/**/ 0xA14AA8FD, 0x3D2CA7D9, +/**/ 0xD8074A10, 0x3F42B2BA, +/**/ 0x5B000000, 0xBF42B15D, +/**/ 0xDDCDDFF5, 0xBD03022E, +/**/ 0x2D020C8C, 0x3F42A2B6, +/**/ 0x05A00000, 0xBF42A15B, +/**/ 0x0F9231A8, 0xBD343FBA, +/**/ 0x85FE8E8A, 0x3F4292B1, +/**/ 0xB2600000, 0xBF429158, +/**/ 0xA52C9CCF, 0x3D38B690, +/**/ 0xE2FCCE8A, 0x3F4282AC, +/**/ 0x61000000, 0xBF428156, +/**/ 0xC8CC82EB, 0x3D120E6A, +/**/ 0x43FCCB0A, 0x3F4272A8, +/**/ 0x11A00000, 0xBF427154, +/**/ 0x792E6C51, 0xBD30D79B, +/**/ 0xA8FE8289, 0x3F4262A3, +/**/ 0xC4600000, 0xBF426151, +/**/ 0x91F7F7AA, 0x3D38A5EE, +/**/ 0x1201F387, 0x3F42529F, +/**/ 0x79000000, 0xBF42514F, +/**/ 0x46C2E8BA, 0x3CEFA728, +/**/ 0x7F071C84, 0x3F42429A, +/**/ 0x2FA00000, 0xBF42414D, +/**/ 0xFA447A17, 0xBD37D0BA, +/**/ 0xF00DFBFD, 0x3F423295, +/**/ 0xE8600000, 0xBF42314A, +/**/ 0x94AF3FED, 0x3D2C7A24, +/**/ 0x65169072, 0x3F422291, +/**/ 0xA3000000, 0xBF422148, +/**/ 0x050CEA04, 0xBD29B0BD, +/**/ 0xDE20D863, 0x3F42128C, +/**/ 0x5FC00000, 0xBF421146, +/**/ 0x0C3035EB, 0x3D36EFF3, +/**/ 0x5B2CD24E, 0x3F420288, +/**/ 0x1E600000, 0xBF420144, +/**/ 0x73569B27, 0xBD19A3E2, +/**/ 0xDC3A7CB2, 0x3F41F283, +/**/ 0xDF200000, 0xBF41F141, +/**/ 0xEEB67715, 0x3D3B1DDE, +/**/ 0x6149D610, 0x3F41E27F, +/**/ 0xA1C00000, 0xBF41E13F, +/**/ 0x94F49154, 0xBD11EA17, +/**/ 0xEA5ADCE5, 0x3F41D27A, +/**/ 0x66800000, 0xBF41D13D, +/**/ 0x52DD9D37, 0x3D3ACED9, +/**/ 0x776D8FB1, 0x3F41C276, +/**/ 0x2D200000, 0xBF41C13B, +/**/ 0xF72D8EEB, 0xBD1C140B, +/**/ 0x0881ECF4, 0x3F41B272, +/**/ 0xF5E00000, 0xBF41B138, +/**/ 0x939583E1, 0x3D360AE5, +/**/ 0x9D97F32C, 0x3F41A26D, +/**/ 0xC0800000, 0xBF41A136, +/**/ 0x1D246C7C, 0xBD2C00D9, +/**/ 0x36AFA0D9, 0x3F419269, +/**/ 0x8D400000, 0xBF419134, +/**/ 0x0B955CFB, 0x3D29B40E, +/**/ 0xD3C8F479, 0x3F418264, +/**/ 0x5BE00000, 0xBF418132, +/**/ 0x45A6C249, 0xBD3964BF, +/**/ 0x74E3EC8D, 0x3F417260, +/**/ 0x2CA00000, 0xBF417130, +/**/ 0xF3363612, 0xBCE777E0, +/**/ 0x1A008792, 0x3F41625C, +/**/ 0xFF600000, 0xBF41612D, +/**/ 0x28DE8296, 0x3D36D608, +/**/ 0xC31EC409, 0x3F415257, +/**/ 0xD4000000, 0xBF41512B, +/**/ 0x4BB1B788, 0xBD32AE69, +/**/ 0x703EA071, 0x3F414253, +/**/ 0xAAC00000, 0xBF414129, +/**/ 0x170ECD8C, 0x3D05BF68, +/**/ 0x21601B48, 0x3F41324F, +/**/ 0x83800000, 0xBF413127, +/**/ 0x7C653BFC, 0x3D370A0B, +/**/ 0xD683330E, 0x3F41224A, +/**/ 0x5E200000, 0xBF412125, +/**/ 0x77BBBEBF, 0xBD35B70D, +/**/ 0x8FA7E642, 0x3F411246, +/**/ 0x3AE00000, 0xBF411123, +/**/ 0x93ABC1CD, 0xBD0C52EB, +/**/ 0x4CCE3363, 0x3F410242, +/**/ 0x19A00000, 0xBF410121, +/**/ 0xE5C6F4C7, 0x3D2B2237, +/**/ 0x0DF618F1, 0x3F40F23E, +/**/ 0xFA600000, 0xBF40F11E, +/**/ 0x1E9A50AD, 0x3D3D9C5F, +/**/ 0xD31F956A, 0x3F40E239, +/**/ 0xDD000000, 0xBF40E11C, +/**/ 0x8965F0DA, 0xBD336793, +/**/ 0x9C4AA74E, 0x3F40D235, +/**/ 0xC1C00000, 0xBF40D11A, +/**/ 0x7E49E231, 0xBD15E6EE, +/**/ 0x69774D1D, 0x3F40C231, +/**/ 0xA8800000, 0xBF40C118, +/**/ 0x04FD621C, 0x3D1D9B9D, +/**/ 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0x132B309E, 0x3F17808A, +/**/ 0x09000000, 0xBF178045, +/**/ 0x7E89FD6F, 0xBD0CC7F9, +/**/ 0x42F88115, 0x3F170084, +/**/ 0x21000000, 0xBF170042, +/**/ 0x058494DC, 0x3CE40881, +/**/ 0x92C7F9A5, 0x3F16807E, +/**/ 0x49000000, 0xBF16803F, +/**/ 0xCD5698B9, 0x3D12AE16, +/**/ 0x02998E4D, 0x3F160079, +/**/ 0x81000000, 0xBF16003C, +/**/ 0xC5780E17, 0x3D21138B, +/**/ 0x926D330B, 0x3F158073, +/**/ 0xC9000000, 0xBF158039, +/**/ 0x4E2001E2, 0x3D287809, +/**/ 0x4242DBDF, 0x3F15006E, +/**/ 0x21000000, 0xBF150037, +/**/ 0x21448AA2, 0x3D2F8684, +/**/ 0x121A7CC8, 0x3F148069, +/**/ 0x89000000, 0xBF148034, +/**/ 0x2F637D8E, 0x3D33207E, +/**/ 0x01F409C4, 0x3F140064, +/**/ 0x01000000, 0xBF140032, +/**/ 0x12E44B29, 0x3D3654B9, +/**/ 0x11CF76D3, 0x3F13805F, +/**/ 0x89000000, 0xBF13802F, +/**/ 0xCA5547F3, 0x3D3960F2, +/**/ 0x41ACB7F4, 0x3F13005A, +/**/ 0x21000000, 0xBF13002D, +/**/ 0x6487063D, 0x3D3C462B, +/**/ 0x918BC126, 0x3F128055, +/**/ 0xC9000000, 0xBF12802A, +/**/ 0xEFEA1107, 0x3D3F0562, +/**/ 0x016C8668, 0x3F120051, +/**/ 0x80000000, 0xBF120028, +/**/ 0x857113CE, 0xBD3E6066, +/**/ 0x914EFBBA, 0x3F11804C, +/**/ 0x48000000, 0xBF118026, +/**/ 0xEDD9EB54, 0xBD3BEA30, +/**/ 0x41331519, 0x3F110048, +/**/ 0x20000000, 0xBF110024, +/**/ 0x3BFFFF5A, 0xBD3996FC, +/**/ 0x1118C686, 0x3F108044, +/**/ 0x08000000, 0xBF108022, +/**/ 0x62F2E042, 0xBD3765C8, +/**/ 0x01000400, 0x3F100040, +/**/ 0x00000000, 0xBF100020, +/**/ 0x562224CD, 0xBD355595, +/**/ 0x21D1830C, 0x3F0F0078, +/**/ 0x10000000, 0xBF0F003C, +/**/ 0x095D69EB, 0xBD336563, +/**/ 0x81A5E62E, 0x3F0E0070, +/**/ 0x40000000, 0xBF0E0038, +/**/ 0x70D45290, 0xBD319431, +/**/ 0x217D1965, 0x3F0D0069, +/**/ 0x90000000, 0xBF0D0034, +/**/ 0x022D0EF6, 0xBD2FC201, +/**/ 0x015704B1, 0x3F0C0062, +/**/ 0x00000000, 0xBF0C0031, +/**/ 0x5E276E21, 0xBD2C95A0, +/**/ 0x2133900E, 0x3F0B005B, +/**/ 0x90000000, 0xBF0B002D, +/**/ 0xE0372A42, 0xBD29A140, +/**/ 0x8112A37D, 0x3F0A0054, +/**/ 0x40000000, 0xBF0A002A, +/**/ 0x73BBB580, 0xBD26E2E2, +/**/ 0x20F426FB, 0x3F09004E, +/**/ 0x10000000, 0xBF090027, +/**/ 0x04D48C20, 0xBD245885, +/**/ 0x00D80288, 0x3F080048, +/**/ 0x00000000, 0xBF080024, +/**/ 0x80613426, 0xBD220028, +/**/ 0x20BE1E23, 0x3F070042, +/**/ 0x10000000, 0xBF070021, +/**/ 0xA80279F3, 0xBD1FAF99, +/**/ 0x80A661CA, 0x3F06003C, +/**/ 0x40000000, 0xBF06001E, +/**/ 0xDC287DFE, 0xBD1BBAE3, +/**/ 0x2090B57C, 0x3F050037, +/**/ 0x90000000, 0xBF05001B, +/**/ 0x7B73B67C, 0xBD181E2F, +/**/ 0x007D0139, 0x3F040032, +/**/ 0x00000000, 0xBF040019, +/**/ 0x65A375F8, 0xBD14D57C, +/**/ 0x206B2CFF, 0x3F03002D, +/**/ 0x90000000, 0xBF030016, +/**/ 0x7BF71EC1, 0xBD11DCCA, +/**/ 0x805B20CD, 0x3F020028, +/**/ 0x40000000, 0xBF020014, +/**/ 0x425C4447, 0xBD0E6033, +/**/ 0x204CC4A3, 0x3F010024, +/**/ 0x10000000, 0xBF010012, +/**/ 0x730FFF5C, 0xBD0996D3, +/**/ 0x00400080, 0x3F000020, +/**/ 0x00000000, 0xBF000010, +/**/ 0x558888DE, 0xBD055575, +/**/ 0x406978C6, 0x3EFE0038, +/**/ 0x20000000, 0xBEFE001C, +/**/ 0xB845146A, 0xBD019418, +/**/ 0x0055C096, 0x3EFC0031, +/**/ 0x80000000, 0xBEFC0018, +/**/ 0xD989DB3C, 0xBCFC957A, +/**/ 0x4044A870, 0x3EFA002A, +/**/ 0x20000000, 0xBEFA0015, +/**/ 0x8F0EED2F, 0xBCF6E2C6, +/**/ 0x00360051, 0x3EF80024, +/**/ 0x00000000, 0xBEF80012, +/**/ 0x40184CEB, 0xBCF20014, +/**/ 0x40299839, 0x3EF6001E, +/**/ 0x20000000, 0xBEF6000F, +/**/ 0x434A1F5C, 0xBCEBBAC7, +/**/ 0x001F4027, 0x3EF40019, +/**/ 0x80000000, 0xBEF4000C, +/**/ 0xDD68DD6A, 0xBCE4D568, +/**/ 0x4016C81A, 0x3EF20014, +/**/ 0x20000000, 0xBEF2000A, +/**/ 0xA11710FC, 0xBCDE6019, +/**/ 0x00100010, 0x3EF00010, +/**/ 0x00000000, 0xBEF00008, +/**/ 0x5562222D, 0xBCD55565, +/**/ 0x80157013, 0x3EEC0018, +/**/ 0x40000000, 0xBEEC000C, +/**/ 0x176276C5, 0xBCCC9568, +/**/ 0x000D800A, 0x3EE80012, +/**/ 0x00000000, 0xBEE80009, +/**/ 0x20061337, 0xBCC2000A, +/**/ 0x8007D005, 0x3EE4000C, +/**/ 0x40000000, 0xBEE40006, +/**/ 0x195A3758, 0xBCB4D55F, +/**/ 0x00040002, 0x3EE00008, +/**/ 0x00000000, 0xBEE00004, +/**/ 0x5558888A, 0xBCA5555D, +/**/ 0x00036001, 0x3ED80009, +/**/ 0x80000000, 0xBED80004, +/**/ 0x100184CD, 0xBC920005, +/**/ 0x00010000, 0x3ED00004, +/**/ 0x00000000, 0xBED00002, +/**/ 0x55562222, 0xBC755559, +/**/ 0x00004000, 0x3EC00002, +/**/ 0x00000000, 0xBEC00001, +/**/ 0x55558889, 0xBC455557, +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0x00008000, 0xBEBFFFFC, +/**/ 0x00000000, 0x3EBFFFFE, +/**/ 0x55558889, 0x3C455553, +/**/ 0x00020000, 0xBECFFFF8, +/**/ 0x00000000, 0x3ECFFFFC, +/**/ 0x55562222, 0x3C755551, +/**/ 0x00035FFF, 0xBED7FFF7, +/**/ 0x80000000, 0x3ED7FFFB, +/**/ 0xF00184CC, 0x3C91FFFA, +/**/ 0x0007FFFC, 0xBEDFFFF0, +/**/ 0x00000000, 0x3EDFFFF8, +/**/ 0x55588887, 0x3CA5554D, +/**/ 0x8007CFFB, 0xBEE3FFF3, +/**/ 0xC0000000, 0x3EE3FFF9, +/**/ 0x915A3753, 0x3CB4D54B, +/**/ 0x000D7FF6, 0xBEE7FFEE, +/**/ 0x00000000, 0x3EE7FFF7, +/**/ 0xE006132F, 0x3CC1FFF5, +/**/ 0x80156FED, 0xBEEBFFE7, +/**/ 0xC0000000, 0x3EEBFFF3, +/**/ 0x936276B2, 0x3CCC9542, +/**/ 0x001FFFE0, 0xBEEFFFE0, +/**/ 0x00000000, 0x3EEFFFF0, +/**/ 0x55622217, 0x3CD55545, +/**/ 0xC016C7E6, 0xBEF1FFEB, +/**/ 0xE0000000, 0x3EF1FFF5, +/**/ 0x5F1710D1, 0x3CDE5FE6, +/**/ 0x001F3FD9, 0xBEF3FFE7, +/**/ 0x80000000, 0x3EF3FFF3, +/**/ 0xCD68DD41, 0x3CE4D541, +/**/ 0xC02997C7, 0xBEF5FFE1, +/**/ 0xE0000000, 0x3EF5FFF0, +/**/ 0x124A1F13, 0x3CEBBA8E, +/**/ 0x0035FFAF, 0xBEF7FFDC, +/**/ 0x00000000, 0x3EF7FFEE, +/**/ 0xC0184CAE, 0x3CF1FFEB, +/**/ 0xC044A790, 0xBEF9FFD5, +/**/ 0xE0000000, 0x3EF9FFEA, +/**/ 0xC68EECCD, 0x3CF6E28E, +/**/ 0x0055BF6A, 0xBEFBFFCF, +/**/ 0x80000000, 0x3EFBFFE7, +/**/ 0xD189DAA2, 0x3CFC952F, +/**/ 0xC069773A, 0xBEFDFFC7, +/**/ 0xE0000000, 0x3EFDFFE3, +/**/ 0x480513F6, 0x3D0193E7, +/**/ 0x007FFF00, 0xBEFFFFC0, +/**/ 0x00000000, 0x3EFFFFE0, +/**/ 0x55888833, 0x3D055535, +/**/ 0xE04CC35D, 0xBF00FFDB, +/**/ 0xF0000000, 0x3F00FFED, +/**/ 0xE2CFFE66, 0x3D099681, +/**/ 0x805B1F33, 0xBF01FFD7, +/**/ 0xC0000000, 0x3F01FFEB, +/**/ 0xBE5C42ED, 0x3D0E5FCC, +/**/ 0xE06B2B01, 0xBF02FFD2, +/**/ 0x70000000, 0x3F02FFE9, +/**/ 0xD9D71DD1, 0x3D11DC8A, +/**/ 0x007CFEC8, 0xBF03FFCE, +/**/ 0x00000000, 0x3F03FFE7, +/**/ 0x45A374B3, 0x3D14D52E, +/**/ 0xE090B284, 0xBF04FFC8, +/**/ 0x70000000, 0x3F04FFE4, +/**/ 0x8553B4C7, 0x3D181DD0, +/**/ 0x80A65E36, 0xBF05FFC3, +/**/ 0xC0000000, 0x3F05FFE1, +/**/ 0x7A287BBE, 0x3D1BBA71, +/**/ 0xE0BE19DD, 0xBF06FFBD, +/**/ 0xF0000000, 0x3F06FFDE, +/**/ 0x03E27702, 0x3D1FAF11, +/**/ 0x00D7FD78, 0xBF07FFB8, +/**/ 0x00000000, 0x3F07FFDC, +/**/ 0x80613240, 0x3D21FFD7, +/**/ 0xE0F42105, 0xBF08FFB1, +/**/ 0xF0000000, 0x3F08FFD8, +/**/ 0xA6C489B3, 0x3D245825, +/**/ 0x81129C84, 0xBF09FFAB, +/**/ 0xC0000000, 0x3F09FFD5, +/**/ 0xE2BBB26F, 0x3D26E272, +/**/ 0xE13387F2, 0xBF0AFFA4, +/**/ 0x70000000, 0x3F0AFFD2, +/**/ 0x21272669, 0x3D29A0BF, +/**/ 0x0156FB50, 0xBF0BFF9E, +/**/ 0x00000000, 0x3F0BFFCF, +/**/ 0x4E276957, 0x3D2C950A, +/**/ 0xE17D0E9B, 0xBF0CFF96, +/**/ 0x70000000, 0x3F0CFFCB, +/**/ 0x551D090E, 0x3D2FC154, +/**/ 0x81A5D9D2, 0xBF0DFF8F, +/**/ 0xC0000000, 0x3F0DFFC7, +/**/ 0x90544EF1, 0x3D3193CE, +/**/ 0xE1D174F4, 0xBF0EFF87, +/**/ 0xF0000000, 0x3F0EFFC3, +/**/ 0x4D556583, 0x3D3364F2, +/**/ 0x01FFF800, 0xBF0FFF80, +/**/ 0x00000000, 0x3F0FFFC0, +/**/ 0x56221F78, 0x3D355515, +/**/ 0xF118BD7A, 0xBF107FBB, +/**/ 0xF8000000, 0x3F107FDD, +/**/ 0x9EEAD9D8, 0x3D376537, +/**/ 0xC1330AE7, 0xBF10FFB7, +/**/ 0xE0000000, 0x3F10FFDB, +/**/ 0x1B7FF7AE, 0x3D399659, +/**/ 0x714EF047, 0xBF117FB3, +/**/ 0xB8000000, 0x3F117FD9, +/**/ 0xBF51E233, 0x3D3BE979, +/**/ 0x016C7998, 0xBF11FFAF, +/**/ 0x80000000, 0x3F11FFD7, +/**/ 0x7D7108FF, 0x3D3E5F99, +/**/ 0x718BB2DA, 0xBF127FAA, +/**/ 0x39000000, 0x3F127FD5, +/**/ 0xB7721DC6, 0xBD3F0647, +/**/ 0xC1ACA80C, 0xBF12FFA5, +/**/ 0xE1000000, 0x3F12FFD2, +/**/ 0xED071532, 0xBD3C4729, +/**/ 0xF1CF652D, 0xBF137FA0, +/**/ 0x79000000, 0x3F137FD0, +/**/ 0x315D596D, 0xBD39620D, +/**/ 0x01F3F63C, 0xBF13FF9C, +/**/ 0x01000000, 0x3F13FFCE, +/**/ 0x92E45F81, 0xBD3655F1, +/**/ 0xF21A6739, 0xBF147F96, +/**/ 0x79000000, 0x3F147FCB, +/**/ 0x206B9526, 0xBD3321D7, +/**/ 0xC242C421, 0xBF14FF91, +/**/ 0xE1000000, 0x3F14FFC8, +/**/ 0xD244C12A, 0xBD2F897B, +/**/ 0x726D18F6, 0xBF157F8C, +/**/ 0x39000000, 0x3F157FC6, +/**/ 0xF93040AE, 0xBD287B4B, +/**/ 0x029971B4, 0xBF15FF87, +/**/ 0x81000000, 0x3F15FFC3, +/**/ 0xD578562C, 0xBD21171E, +/**/ 0x72C7DA5C, 0xBF167F81, +/**/ 0xB9000000, 0x3F167FC0, +/**/ 0x0F773DB4, 0xBD12B5E9, +/**/ 0xC2F85EEC, 0xBF16FF7B, +/**/ 0xE1000000, 0x3F16FFBD, +/**/ 0x158A76C2, 0xBCE44CD3, +/**/ 0xF32B0B63, 0xBF177F75, +/**/ 0xF9000000, 0x3F177FBA, +/**/ 0x2E48511B, 0x3D0CB55C, +/**/ 0x035FEBC0, 0xBF17FF70, +/**/ 0x01000000, 0x3F17FFB8, +/**/ 0x184C534F, 0x3D1FFAF0, +/**/ 0xF3970C03, 0xBF187F69, +/**/ 0xF9000000, 0x3F187FB4, +/**/ 0xACC53FBE, 0x3D292D95, +/**/ 0xC3D07829, 0xBF18FF63, +/**/ 0xE1000000, 0x3F18FFB1, +/**/ 0xE48887C8, 0x3D315FD7, +/**/ 0x740C3C32, 0xBF197F5D, +/**/ 0xB9000000, 0x3F197FAE, +/**/ 0x1DF5B242, 0x3D365AE3, +/**/ 0x044A641C, 0xBF19FF57, +/**/ 0x81000000, 0x3F19FFAB, +/**/ 0x6FBB0E5F, 0x3D3B88EC, +/**/ 0x748AFBE7, 0xBF1A7F50, +/**/ 0x3A000000, 0x3F1A7FA8, +/**/ 0x39766B40, 0xBD3F150C, +/**/ 0xC4CE0F91, 0xBF1AFF49, +/**/ 0xE2000000, 0x3F1AFFA4, +/**/ 0xF14DB839, 0xBD397E06, +/**/ 0xF513AB19, 0xBF1B7F42, +/**/ 0x7A000000, 0x3F1B7FA1, +/**/ 0xCBD9CC3D, 0xBD33B103, +/**/ 0x055BDA7D, 0xBF1BFF3C, +/**/ 0x02000000, 0x3F1BFF9E, +/**/ 0xBB1321B5, 0xBD2B5A05, +/**/ 0xF5A6A9BD, 0xBF1C7F34, +/**/ 0x7A000000, 0x3F1C7F9A, +/**/ 0xECAF9551, 0xBD1DC410, +/**/ 0xC5F424D6, 0xBF1CFF2D, +/**/ 0xE2000000, 0x3F1CFF96, +/**/ 0x3DF3CD68, 0xBCEF80FF, +/**/ 0x764457C8, 0xBF1D7F26, +/**/ 0x3A000000, 0x3F1D7F93, +/**/ 0x4271E737, 0x3D16CBC7, +/**/ 0x06974E91, 0xBF1DFF1F, +/**/ 0x82000000, 0x3F1DFF8F, +/**/ 0x1D134848, 0x3D2939D2, +/**/ 0x76ED1530, 0xBF1E7F17, +/**/ 0xBA000000, 0x3F1E7F8B, +/**/ 0xA9892C73, 0x3D33C2DD, +/**/ 0xC745B7A4, 0xBF1EFF0F, +/**/ 0xE2000000, 0x3F1EFF87, +/**/ 0x8AEC69D5, 0x3D3B25CF, +/**/ 0xF7A141EA, 0xBF1F7F07, +/**/ 0xFB000000, 0x3F1F7F83, +/**/ 0x645B412A, 0xBD3D3941, +/**/ 0x07FFC002, 0xBF1FFF00, +/**/ 0x03000000, 0x3F1FFF80, +/**/ 0x3BBC6662, 0xBD355955, +/**/ 0xFC309EF5, 0xBF203F7B, +/**/ 0xFD800000, 0x3F203FBD, +/**/ 0x260B17B3, 0xBD2A72D8, +/**/ 0xE462E3D0, 0xBF207F77, +/**/ 0xF1800000, 0x3F207FBB, +/**/ 0x0994AE68, 0xBD136218, +/**/ 0xBC96B492, 0xBF20BF73, +/**/ 0xDD800000, 0x3F20BFB9, +/**/ 0xECB2641F, 0x3D0E52E6, +/**/ 0x84CC1739, 0xBF20FF6F, +/**/ 0xC1800000, 0x3F20FFB7, +/**/ 0xE7FCF60B, 0x3D296078, +/**/ 0x3D0311C6, 0xBF213F6B, +/**/ 0x9D800000, 0x3F213FB5, +/**/ 0xA7850AFF, 0x3D35DA18, +/**/ 0xE53BAA36, 0xBF217F66, +/**/ 0x71800000, 0x3F217FB3, +/**/ 0x5E7BB444, 0x3D3F48F1, +/**/ 0x7D75E68A, 0xBF21BF62, +/**/ 0x3E000000, 0x3F21BFB1, +/**/ 0x812BC469, 0xBD370239, +/**/ 0x05B1CCC0, 0xBF21FF5E, +/**/ 0x02000000, 0x3F21FFAF, +/**/ 0x23BF1A4D, 0xBD2A0CD0, +/**/ 0x7DEF62D8, 0xBF223F59, +/**/ 0xBE000000, 0x3F223FAC, +/**/ 0x736E3623, 0xBD0614D3, +/**/ 0xE62EAED0, 0xBF227F54, +/**/ 0x72000000, 0x3F227FAA, +/**/ 0x37EDEDB0, 0x3D1F28BD, +/**/ 0x3E6FB6A9, 0xBF22BF50, +/**/ 0x1E000000, 0x3F22BFA8, +/**/ 0x07CE33C8, 0x3D32A0F5, +/**/ 0x86B28060, 0xBF22FF4B, +/**/ 0xC2000000, 0x3F22FFA5, +/**/ 0xA31C6A8D, 0x3D3DC2B6, +/**/ 0xBEF711F6, 0xBF233F46, +/**/ 0x5E800000, 0x3F233FA3, +/**/ 0xFC67C9FB, 0xBD36CF8B, +/**/ 0xE73D7169, 0xBF237F41, +/**/ 0xF2800000, 0x3F237FA0, +/**/ 0xE6D88A89, 0xBD2629A5, +/**/ 0xFF85A4B8, 0xBF23BF3C, +/**/ 0x7E800000, 0x3F23BF9E, +/**/ 0x202574EC, 0x3CEE7C34, +/**/ 0x07CFB1E3, 0xBF23FF38, +/**/ 0x02800000, 0x3F23FF9C, +/**/ 0x46E594C1, 0x3D2A9723, +/**/ 0x001B9EE8, 0xBF243F33, +/**/ 0x7E800000, 0x3F243F99, +/**/ 0xF61AE74C, 0x3D39F33C, +/**/ 0xE86971C7, 0xBF247F2D, +/**/ 0xF3000000, 0x3F247F96, +/**/ 0x85341E31, 0xBD39141C, +/**/ 0xC0B9307F, 0xBF24BF28, +/**/ 0x5F000000, 0x3F24BF94, +/**/ 0xDA0FAF09, 0xBD2792F5, +/**/ 0x890AE10E, 0xBF24FF23, +/**/ 0xC3000000, 0x3F24FF91, +/**/ 0xFB239430, 0x3CFD4219, +/**/ 0x415E8974, 0xBF253F1E, +/**/ 0x1F000000, 0x3F253F8F, +/**/ 0x0359434A, 0x3D2F8B72, +/**/ 0xE9B42FAF, 0xBF257F18, +/**/ 0x73000000, 0x3F257F8C, +/**/ 0x1939FEDF, 0x3D3E0C4B, +/**/ 0x820BD9BF, 0xBF25BF13, +/**/ 0xBF800000, 0x3F25BF89, +/**/ 0x39B301E2, 0xBD335728, +/**/ 0x0A658DA3, 0xBF25FF0E, +/**/ 0x03800000, 0x3F25FF87, +/**/ 0x5E1E8D4F, 0xBD118E84, +/**/ 0x82C15159, 0xBF263F08, +/**/ 0x3F800000, 0x3F263F84, +/**/ 0xBDDDD045, 0x3D25CFC0, +/**/ 0xEB1F2AE1, 0xBF267F02, +/**/ 0x73800000, 0x3F267F81, +/**/ 0x08837E99, 0x3D3A8C5C, +/**/ 0x437F203A, 0xBF26BEFD, +/**/ 0xA0000000, 0x3F26BF7E, +/**/ 0x3C56F12D, 0xBD35752E, +/**/ 0x8BE13762, 0xBF26FEF7, +/**/ 0xC4000000, 0x3F26FF7B, +/**/ 0x46359E28, 0xBD146EFA, +/**/ 0xC4457659, 0xBF273EF1, +/**/ 0xE0000000, 0x3F273F78, +/**/ 0xCD265865, 0x3D273355, +/**/ 0xECABE31C, 0xBF277EEB, +/**/ 0xF4000000, 0x3F277F75, +/**/ 0x095DEBF8, 0x3D3CAC0E, +/**/ 0x051483AC, 0xBF27BEE6, +/**/ 0x00800000, 0x3F27BF73, +/**/ 0x4C39F4DB, 0xBD31E395, +/**/ 0x0D7F5E08, 0xBF27FEE0, +/**/ 0x04800000, 0x3F27FF70, +/**/ 0xA1314B81, 0xBCB43F3D, +/**/ 0x05EC782D, 0xBF283EDA, +/**/ 0x00800000, 0x3F283F6D, +/**/ 0x115B8D70, 0x3D321B10, +/**/ 0xEE5BD81B, 0xBF287ED3, +/**/ 0xF5000000, 0x3F287F69, +/**/ 0x83704FE1, 0xBD3B54A7, +/**/ 0xC6CD83D1, 0xBF28BECD, +/**/ 0xE1000000, 0x3F28BF66, +/**/ 0x41229C91, 0xBD20C4CC, +/**/ 0x8F41814D, 0xBF28FEC7, +/**/ 0xC5000000, 0x3F28FF63, +/**/ 0x2A183F17, 0x3D25E5A8, +/**/ 0x47B7D68F, 0xBF293EC1, +/**/ 0xA1000000, 0x3F293F60, +/**/ 0xF81B997D, 0x3D3EAC06, +/**/ 0xF0308995, 0xBF297EBA, +/**/ 0x75800000, 0x3F297F5D, +/**/ 0x3A1E5BAD, 0xBD2A6B9B, +/**/ 0x88ABA05E, 0xBF29BEB4, +/**/ 0x41800000, 0x3F29BF5A, +/**/ 0xBDFE3C77, 0x3D1D3958, +/**/ 0x112920E9, 0xBF29FEAE, +/**/ 0x05800000, 0x3F29FF57, +/**/ 0x375BA904, 0x3D3C3972, +/**/ 0x89A91135, 0xBF2A3EA7, +/**/ 0xC2000000, 0x3F2A3F53, +/**/ 0x588DE85B, 0xBD2CE6F3, +/**/ 0xF22B7740, 0xBF2A7EA0, +/**/ 0x76000000, 0x3F2A7F50, +/**/ 0x75AEDBFD, 0x3D1D2249, +/**/ 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0x234CFD15, 0xBF446CBD, +/**/ 0x7B800000, 0x3F446E5E, +/**/ 0x6A8B33AC, 0xBD3E762C, +/**/ 0x0686F463, 0xBF447CB8, +/**/ 0xECE00000, 0x3F447E5B, +/**/ 0x67AD9900, 0xBD2A36F8, +/**/ 0xE5C2D713, 0xBF448CB2, +/**/ 0x5C400000, 0x3F448E59, +/**/ 0x1E974853, 0x3D161B95, +/**/ 0xC100A6A5, 0xBF449CAD, +/**/ 0xC9A00000, 0x3F449E56, +/**/ 0x8CE22250, 0x3D3971F7, +/**/ 0x98406498, 0xBF44ACA8, +/**/ 0x35200000, 0x3F44AE54, +/**/ 0xDF8A23F8, 0xBD315945, +/**/ 0x6B82126A, 0xBF44BCA3, +/**/ 0x9E800000, 0x3F44BE51, +/**/ 0x1A63D360, 0x3D1498B2, +/**/ 0x3AC5B19B, 0xBF44CC9E, +/**/ 0x05E00000, 0x3F44CE4F, +/**/ 0x4323A054, 0x3D3CF14E, +/**/ 0x060B43AA, 0xBF44DC99, +/**/ 0x6B600000, 0x3F44DE4C, +/**/ 0x4CE35F94, 0xBD23EDC2, +/**/ 0xCD52CA15, 0xBF44EC93, +/**/ 0xCEC00000, 0x3F44EE49, +/**/ 0xCCF1B48E, 0x3D306E9D, +/**/ 0x909C465C, 0xBF44FC8E, +/**/ 0x30400000, 0x3F44FE47, +/**/ 0x5FF9440B, 0xBD33DD35, +/**/ 0x4FE7B9FF, 0xBF450C89, +/**/ 0x8FA00000, 0x3F450E44, +/**/ 0xAA4D276D, 0x3D224D49, +/**/ 0x0B35267A, 0xBF451C84, +/**/ 0xED200000, 0x3F451E41, +/**/ 0x11B557F9, 0xBD3884D4, +/**/ 0xC2848D4F, 0xBF452C7E, +/**/ 0x48800000, 0x3F452E3F, +/**/ 0xB43290C4, 0x3D1C857D, +/**/ 0x75D5EFFC, 0xBF453C79, +/**/ 0xA2000000, 0x3F453E3C, +/**/ 0x2D598D3C, 0xBD37E5C1, +/**/ 0x25294FFF, 0xBF454C74, +/**/ 0xF9600000, 0x3F454E39, +/**/ 0x3FE47B89, 0x3D24CD93, +/**/ 0xD07EAED8, 0xBF455C6E, +/**/ 0x4EE00000, 0x3F455E37, +/**/ 0xAA959122, 0xBD31F800, +/**/ 0x77D60E06, 0xBF456C69, +/**/ 0xA2400000, 0x3F456E34, +/**/ 0x7329AF92, 0x3D32FEDF, +/**/ 0x1B2F6F08, 0xBF457C64, +/**/ 0xF3C00000, 0x3F457E31, +/**/ 0x1C545A6F, 0xBD1ACE5A, +/**/ 0xBA8AD35D, 0xBF458C5E, +/**/ 0x43400000, 0x3F458E2F, +/**/ 0x19F6B9EF, 0xBD3F0E63, +/**/ 0x55E83C84, 0xBF459C59, +/**/ 0x90A00000, 0x3F459E2C, +/**/ 0x73005F6F, 0x3D23DEF2, +/**/ 0xED47ABFB, 0xBF45AC53, +/**/ 0xDC200000, 0x3F45AE29, +/**/ 0x1C295DE7, 0xBD277204, +/**/ 0x80A92343, 0xBF45BC4E, +/**/ 0x25800000, 0x3F45BE27, +/**/ 0x8D869589, 0x3D3FF92A, +/**/ 0x100CA3D9, 0xBF45CC49, +/**/ 0x6D000000, 0x3F45CE24, +/**/ 0x145C5335, 0x3D2A0DFD, +/**/ 0x9B722F3C, 0xBF45DC43, +/**/ 0xB2800000, 0x3F45DE21, +/**/ 0x6A8614B3, 0xBD123A1A, +/**/ 0x22D9C6ED, 0xBF45EC3E, +/**/ 0xF6000000, 0x3F45EE1E, +/**/ 0x63CBC7E7, 0xBD34C665, +/**/ 0xA6436C69, 0xBF45FC38, +/**/ 0x37600000, 0x3F45FE1C, +/**/ 0xAB6C51D7, 0x3D3C6061, +/**/ 0x25AF2130, 0xBF460C33, +/**/ 0x76E00000, 0x3F460E19, +/**/ 0x1EC7F453, 0x3D2DCD9C, +/**/ 0xA11CE6C1, 0xBF461C2D, +/**/ 0xB4600000, 0x3F461E16, +/**/ 0x20C52899, 0x3D066EFA, +/**/ 0x188CBE9A, 0xBF462C28, +/**/ 0xEFE00000, 0x3F462E13, +/**/ 0xEB5FDD5C, 0xBD1FA5AC, +/**/ 0x8BFEAA3B, 0xBF463C22, +/**/ 0x29600000, 0x3F463E11, +/**/ 0xF22FE2BC, 0xBD313E11, +/**/ 0xFB72AB23, 0xBF464C1C, +/**/ 0x60E00000, 0x3F464E0E, +/**/ 0x6710E251, 0xBD392F15, +/**/ 0x66E8C2D0, 0xBF465C17, +/**/ 0x96600000, 0x3F465E0B, +/**/ 0x1EFC78A7, 0xBD3FBB76, +/**/ 0xCE60F2C1, 0xBF466C11, +/**/ 0xC9C00000, 0x3F466E08, +/**/ 0x602C1A84, 0x3D3B1DCB, +/**/ 0x31DB3C76, 0xBF467C0C, +/**/ 0xFB400000, 0x3F467E05, +/**/ 0x9027DA74, 0x3D375DAE, +/**/ 0x9157A16E, 0xBF468C06, +/**/ 0x2AC00000, 0x3F468E03, +/**/ 0xEA560DA0, 0x3D350532, +/**/ 0xECD62326, 0xBF469C00, +/**/ 0x58400000, 0x3F469E00, +/**/ 0xE7B63DE2, 0x3D341557 } }; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/urem.h b/REORG.TODO/sysdeps/ieee754/dbl-64/urem.h new file mode 100644 index 0000000000..d9e5696fdd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/urem.h @@ -0,0 +1,46 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: urem.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + +#ifndef UREM_H +#define UREM_H + +#ifdef BIG_ENDI +static const mynumber big = {{0x43380000, 0}}, /* 6755399441055744 */ + t128 = {{0x47f00000, 0}}, /* 2^ 128 */ + tm128 = {{0x37f00000, 0}}, /* 2^-128 */ + ZERO = {{0, 0}}, /* 0.0 */ + nZERO = {{0x80000000, 0}}; /* -0.0 */ +#else +#ifdef LITTLE_ENDI +static const mynumber big = {{0, 0x43380000}}, /* 6755399441055744 */ + t128 = {{0, 0x47f00000}}, /* 2^ 128 */ + tm128 = {{0, 0x37f00000}}, /* 2^-128 */ + ZERO = {{0, 0}}, /* 0.0 */ + nZERO = {{0, 0x80000000}}; /* -0.0 */ +#endif +#endif + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/usncs.h b/REORG.TODO/sysdeps/ieee754/dbl-64/usncs.h new file mode 100644 index 0000000000..09f76ae8ea --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/usncs.h @@ -0,0 +1,48 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: dosincos.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + +#ifndef USNCS_H +#define USNCS_H + +static const double s1 = -0x1.5555555555555p-3; /* -0.16666666666666666 */ +static const double s2 = 0x1.1111111110ECEp-7; /* 0.0083333333333323288 */ +static const double s3 = -0x1.A01A019DB08B8p-13; /* -0.00019841269834414642 */ +static const double s4 = 0x1.71DE27B9A7ED9p-19; /* 2.755729806860771e-06 */ +static const double s5 = -0x1.ADDFFC2FCDF59p-26; /* -2.5022014848318398e-08 */ +static const double aa = -0x1.5558000000000p-3; /* -0.1666717529296875 */ +static const double bb = 0x1.5555555556E24p-18; /* 5.0862630208387126e-06 */ +static const double big = 0x1.8000000000000p45; /* 52776558133248 */ +static const double hp0 = 0x1.921FB54442D18p0; /* 1.5707963267948966 */ +static const double hp1 = 0x1.1A62633145C07p-54; /* 6.123233995736766e-17 */ +static const double mp1 = 0x1.921FB58000000p0; /* 1.5707963407039642 */ +static const double mp2 = -0x1.DDE973C000000p-27; /* -1.3909067564377153e-08 */ +static const double mp3 = -0x1.CB3B399D747F2p-55; /* -4.9789962505147994e-17 */ +static const double pp3 = -0x1.CB3B398000000p-55; /* -4.9789962314799099e-17 */ +static const double pp4 = -0x1.d747f23e32ed7p-83; /* -1.9034889620193266e-25 */ +static const double hpinv = 0x1.45F306DC9C883p-1; /* 0.63661977236758138 */ +static const double toint = 0x1.8000000000000p52; /* 6755399441055744 */ + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/utan.h b/REORG.TODO/sysdeps/ieee754/dbl-64/utan.h new file mode 100644 index 0000000000..b34e52f1fb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/utan.h @@ -0,0 +1,265 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:utan.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef UTAN_H +#define UTAN_H + +#ifdef BIG_ENDI + static const number + /* polynomial I */ +/**/ d3 = {{0x3FD55555, 0x55555555} }, /* 0.333... */ +/**/ d5 = {{0x3FC11111, 0x111107C6} }, /* 0.133... */ +/**/ d7 = {{0x3FABA1BA, 0x1CDB8745} }, /* . */ +/**/ d9 = {{0x3F9664ED, 0x49CFC666} }, /* . */ +/**/ d11 = {{0x3F82385A, 0x3CF2E4EA} }, /* . */ + /* polynomial II */ +/**/ a3 = {{0x3fd55555, 0x55555555} }, /* 1/3 */ +/**/ aa3 = {{0x3c755555, 0x55555555} }, /* 1/3-a3 */ +/**/ a5 = {{0x3fc11111, 0x11111111} }, /* 2/15 */ +/**/ aa5 = {{0x3c411111, 0x11111111} }, /* 2/15-a5 */ +/**/ a7 = {{0x3faba1ba, 0x1ba1ba1c} }, /* 17/315 */ +/**/ aa7 = {{0xbc479179, 0x17917918} }, /* ()-a7 */ +/**/ a9 = {{0x3f9664f4, 0x882c10fa} }, /* 62/2835 */ +/**/ aa9 = {{0xbc09a528, 0x8b6c44fd} }, /* ()-a9 */ +/**/ a11 = {{0x3f8226e3, 0x55e6c23d} }, /* . */ +/**/ aa11 = {{0xbc2c292b, 0x8f1a2c13} }, /* . */ +/**/ a13 = {{0x3f6d6d3d, 0x0e157de0} }, /* . */ +/**/ aa13 = {{0xbc0280cf, 0xc968d971} }, /* . */ +/**/ a15 = {{0x3f57da36, 0x452b75e3} }, /* . */ +#if 0 +/**/ aa15 = {{0xbbf25789, 0xb285d2ed} }, /* . */ +#endif +/**/ a17 = {{0x3f435582, 0x48036744} }, /* . */ +#if 0 +/**/ aa17 = {{0x3be488d9, 0x563f1f23} }, /* . */ +#endif +/**/ a19 = {{0x3f2f57d7, 0x734d1664} }, /* . */ +#if 0 +/**/ aa19 = {{0x3bb0d55a, 0x913ccb50} }, /* . */ +#endif +/**/ a21 = {{0x3f1967e1, 0x8afcafad} }, /* . */ +#if 0 +/**/ aa21 = {{0xbbbd7614, 0xa42d44e6} }, /* . */ +#endif +/**/ a23 = {{0x3f0497d8, 0xeea25259} }, /* . */ +#if 0 +/**/ aa23 = {{0x3b99f2d0, 0x2e4d2863} }, /* . */ +#endif +/**/ a25 = {{0x3ef0b132, 0xd39a6050} }, /* . */ +#if 0 +/**/ aa25 = {{0x3b93b274, 0xc2c19614} }, /* . */ +#endif +/**/ a27 = {{0x3edb0f72, 0xd3ee24e9} }, /* . */ +#if 0 +/**/ aa27 = {{0x3b61688d, 0xdd595609} }, /* . */ +#endif + /* polynomial III */ +/**/ e0 = {{0x3FD55555, 0x55554DBD} }, /* . */ +/**/ e1 = {{0x3FC11112, 0xE0A6B45F} }, /* . */ + + /* constants */ +/**/ mfftnhf = {{0xc02f0000, 0x00000000} }, /*-15.5 */ + +/**/ g1 = {{0x3e4b096c, 0x00000000} }, /* 1.259e-8 */ +/**/ g2 = {{0x3faf212d, 0x00000000} }, /* 0.0608 */ +/**/ g3 = {{0x3fe92f1a, 0x00000000} }, /* 0.787 */ +/**/ g4 = {{0x40390000, 0x00000000} }, /* 25.0 */ +/**/ g5 = {{0x4197d784, 0x00000000} }, /* 1e8 */ +/**/ gy1 = {{0x3e7ad7f2, 0x9abcaf48} }, /* 1e-7 */ +/**/ gy2 = {{0x3faf212d, 0x00000000} }, /* 0.0608 */ + +/**/ u1 = {{0x3cc8c33a, 0x00000000} }, /* 6.873e-16 */ +/**/ u2 = {{0x3983dc4d, 0x00000000} }, /* 1.224e-31 */ +/**/ u3 = {{0x3c78e14b, 0x00000000} }, /* 2.158e-17 */ +/**/ ua3 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */ +/**/ ub3 = {{0x3cc81898, 0x00000000} }, /* 6.688e-16 */ +/**/ u4 = {{0x399856c2, 0x00000000} }, /* 3e-31 */ +/**/ u5 = {{0x3c39d80a, 0x00000000} }, /* 1.401e-18 */ +/**/ u6 = {{0x3c374c5a, 0x00000000} }, /* 1.263e-18 */ +/**/ u7 = {{0x39903beb, 0x00000000} }, /* 2.001e-31 */ +/**/ u8 = {{0x399c56ae, 0x00000000} }, /* 3.493e-31 */ +/**/ u9 = {{0x3c7d0ac7, 0x00000000} }, /* 2.519e-17 */ +/**/ ua9 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */ +/**/ ub9 = {{0x3ccc2375, 0x00000000} }, /* 7.810e-16 */ +/**/ u10 = {{0x3c7e40af, 0x00000000} }, /* 2.624e-17 */ +/**/ ua10 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */ +/**/ ub10 = {{0x3ccc6405, 0x00000000} }, /* 7.880e-16 */ +/**/ u11 = {{0x39e509b6, 0x00000000} }, /* 8.298e-30 */ +/**/ u12 = {{0x39e509b6, 0x00000000} }, /* 8.298e-30 */ +/**/ u13 = {{0x3c39d80a, 0x00000000} }, /* 1.401e-18 */ +/**/ u14 = {{0x3c374c5a, 0x00000000} }, /* 1.263e-18 */ +/**/ u15 = {{0x3ab5767a, 0x00000000} }, /* 6.935e-26 */ +/**/ u16 = {{0x3ab57744, 0x00000000} }, /* 6.936e-26 */ +/**/ u17 = {{0x3c7d0ac7, 0x00000000} }, /* 2.519e-17 */ +/**/ ua17 = {{0x3bfdb11f, 0x00000000} }, /* 1.006e-19 */ +/**/ ub17 = {{0x3ccc2375, 0x00000000} }, /* 7.810e-16 */ +/**/ u18 = {{0x3c7e40af, 0x00000000} }, /* 2.624e-17 */ +/**/ ua18 = {{0x3bfdb11f, 0x00000000} }, /* 1.006e-19 */ +/**/ ub18 = {{0x3ccc6405, 0x00000000} }, /* 7.880e-16 */ +/**/ u19 = {{0x39a13b61, 0x00000000} }, /* 4.248e-31 */ +/**/ u20 = {{0x39a13b61, 0x00000000} }, /* 4.248e-31 */ +/**/ u21 = {{0x3c3bb9b8, 0x00000000} }, /* 1.503e-18 */ +/**/ u22 = {{0x3c392e08, 0x00000000} }, /* 1.365e-18 */ +/**/ u23 = {{0x3a0ce706, 0x00000000} }, /* 4.560e-29 */ +/**/ u24 = {{0x3a0cff5d, 0x00000000} }, /* 4.575e-29 */ +/**/ u25 = {{0x3c7d0ac7, 0x00000000} }, /* 2.519e-17 */ +/**/ ua25 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */ +/**/ ub25 = {{0x3ccc2375, 0x00000000} }, /* 7.810e-16 */ +/**/ u26 = {{0x3c7e40af, 0x00000000} }, /* 2.624e-17 */ +/**/ ua26 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */ +/**/ ub26 = {{0x3ccc6405, 0x00000000} }, /* 7.880e-16 */ +/**/ u27 = {{0x3ad421cb, 0x00000000} }, /* 2.602e-25 */ +/**/ u28 = {{0x3ad421cb, 0x00000000} }, /* 2.602e-25 */ + +/**/ mp1 = {{0x3FF921FB, 0x58000000} }, +/**/ mp2 = {{0xBE4DDE97, 0x3C000000} }, +/**/ mp3 = {{0xBC8CB3B3, 0x99D747F2} }, +/**/ pp3 = {{0xBC8CB3B3, 0x98000000} }, +/**/ pp4 = {{0xbacd747f, 0x23e32ed7} }, +/**/ hpinv = {{0x3FE45F30, 0x6DC9C883} }, +/**/ toint = {{0x43380000, 0x00000000} }; + +#else +#ifdef LITTLE_ENDI + + static const number + /* polynomial I */ +/**/ d3 = {{0x55555555, 0x3FD55555} }, /* 0.333... */ +/**/ d5 = {{0x111107C6, 0x3FC11111} }, /* 0.133... */ +/**/ d7 = {{0x1CDB8745, 0x3FABA1BA} }, /* . */ +/**/ d9 = {{0x49CFC666, 0x3F9664ED} }, /* . */ +/**/ d11 = {{0x3CF2E4EA, 0x3F82385A} }, /* . */ + /* polynomial II */ +/**/ a3 = {{0x55555555, 0x3fd55555} }, /* 1/3 */ +/**/ aa3 = {{0x55555555, 0x3c755555} }, /* 1/3-a3 */ +/**/ a5 = {{0x11111111, 0x3fc11111} }, /* 2/15 */ +/**/ aa5 = {{0x11111111, 0x3c411111} }, /* 2/15-a5 */ +/**/ a7 = {{0x1ba1ba1c, 0x3faba1ba} }, /* 17/315 */ +/**/ aa7 = {{0x17917918, 0xbc479179} }, /* ()-a7 */ +/**/ a9 = {{0x882c10fa, 0x3f9664f4} }, /* 62/2835 */ +/**/ aa9 = {{0x8b6c44fd, 0xbc09a528} }, /* ()-a9 */ +/**/ a11 = {{0x55e6c23d, 0x3f8226e3} }, /* . */ +/**/ aa11 = {{0x8f1a2c13, 0xbc2c292b} }, /* . */ +/**/ a13 = {{0x0e157de0, 0x3f6d6d3d} }, /* . */ +/**/ aa13 = {{0xc968d971, 0xbc0280cf} }, /* . */ +/**/ a15 = {{0x452b75e3, 0x3f57da36} }, /* . */ +#if 0 +/**/ aa15 = {{0xb285d2ed, 0xbbf25789} }, /* . */ +#endif +/**/ a17 = {{0x48036744, 0x3f435582} }, /* . */ +#if 0 +/**/ aa17 = {{0x563f1f23, 0x3be488d9} }, /* . */ +#endif +/**/ a19 = {{0x734d1664, 0x3f2f57d7} }, /* . */ +#if 0 +/**/ aa19 = {{0x913ccb50, 0x3bb0d55a} }, /* . */ +#endif +/**/ a21 = {{0x8afcafad, 0x3f1967e1} }, /* . */ +#if 0 +/**/ aa21 = {{0xa42d44e6, 0xbbbd7614} }, /* . */ +#endif +/**/ a23 = {{0xeea25259, 0x3f0497d8} }, /* . */ +#if 0 +/**/ aa23 = {{0x2e4d2863, 0x3b99f2d0} }, /* . */ +#endif +/**/ a25 = {{0xd39a6050, 0x3ef0b132} }, /* . */ +#if 0 +/**/ aa25 = {{0xc2c19614, 0x3b93b274} }, /* . */ +#endif +/**/ a27 = {{0xd3ee24e9, 0x3edb0f72} }, /* . */ +#if 0 +/**/ aa27 = {{0xdd595609, 0x3b61688d} }, /* . */ +#endif + /* polynomial III */ +/**/ e0 = {{0x55554DBD, 0x3FD55555} }, /* . */ +/**/ e1 = {{0xE0A6B45F, 0x3FC11112} }, /* . */ + + /* constants */ +/**/ mfftnhf = {{0x00000000, 0xc02f0000} }, /*-15.5 */ + +/**/ g1 = {{0x00000000, 0x3e4b096c} }, /* 1.259e-8 */ +/**/ g2 = {{0x00000000, 0x3faf212d} }, /* 0.0608 */ +/**/ g3 = {{0x00000000, 0x3fe92f1a} }, /* 0.787 */ +/**/ g4 = {{0x00000000, 0x40390000} }, /* 25.0 */ +/**/ g5 = {{0x00000000, 0x4197d784} }, /* 1e8 */ +/**/ gy1 = {{0x9abcaf48, 0x3e7ad7f2} }, /* 1e-7 */ +/**/ gy2 = {{0x00000000, 0x3faf212d} }, /* 0.0608 */ + +/**/ u1 = {{0x00000000, 0x3cc8c33a} }, /* 6.873e-16 */ +/**/ u2 = {{0x00000000, 0x3983dc4d} }, /* 1.224e-31 */ +/**/ u3 = {{0x00000000, 0x3c78e14b} }, /* 2.158e-17 */ +/**/ ua3 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */ +/**/ ub3 = {{0x00000000, 0x3cc81898} }, /* 6.688e-16 */ +/**/ u4 = {{0x00000000, 0x399856c2} }, /* 3e-31 */ +/**/ u5 = {{0x00000000, 0x3c39d80a} }, /* 1.401e-18 */ +/**/ u6 = {{0x00000000, 0x3c374c5a} }, /* 1.263e-18 */ +/**/ u7 = {{0x00000000, 0x39903beb} }, /* 2.001e-31 */ +/**/ u8 = {{0x00000000, 0x399c56ae} }, /* 3.493e-31 */ +/**/ u9 = {{0x00000000, 0x3c7d0ac7} }, /* 2.519e-17 */ +/**/ ua9 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */ +/**/ ub9 = {{0x00000000, 0x3ccc2375} }, /* 7.810e-16 */ +/**/ u10 = {{0x00000000, 0x3c7e40af} }, /* 2.624e-17 */ +/**/ ua10 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */ +/**/ ub10 = {{0x00000000, 0x3ccc6405} }, /* 7.880e-16 */ +/**/ u11 = {{0x00000000, 0x39e509b6} }, /* 8.298e-30 */ +/**/ u12 = {{0x00000000, 0x39e509b6} }, /* 8.298e-30 */ +/**/ u13 = {{0x00000000, 0x3c39d80a} }, /* 1.401e-18 */ +/**/ u14 = {{0x00000000, 0x3c374c5a} }, /* 1.263e-18 */ +/**/ u15 = {{0x00000000, 0x3ab5767a} }, /* 6.935e-26 */ +/**/ u16 = {{0x00000000, 0x3ab57744} }, /* 6.936e-26 */ +/**/ u17 = {{0x00000000, 0x3c7d0ac7} }, /* 2.519e-17 */ +/**/ ua17 = {{0x00000000, 0x3bfdb11f} }, /* 1.006e-19 */ +/**/ ub17 = {{0x00000000, 0x3ccc2375} }, /* 7.810e-16 */ +/**/ u18 = {{0x00000000, 0x3c7e40af} }, /* 2.624e-17 */ +/**/ ua18 = {{0x00000000, 0x3bfdb11f} }, /* 1.006e-19 */ +/**/ ub18 = {{0x00000000, 0x3ccc6405} }, /* 7.880e-16 */ +/**/ u19 = {{0x00000000, 0x39a13b61} }, /* 4.248e-31 */ +/**/ u20 = {{0x00000000, 0x39a13b61} }, /* 4.248e-31 */ +/**/ u21 = {{0x00000000, 0x3c3bb9b8} }, /* 1.503e-18 */ +/**/ u22 = {{0x00000000, 0x3c392e08} }, /* 1.365e-18 */ +/**/ u23 = {{0x00000000, 0x3a0ce706} }, /* 4.560e-29 */ +/**/ u24 = {{0x00000000, 0x3a0cff5d} }, /* 4.575e-29 */ +/**/ u25 = {{0x00000000, 0x3c7d0ac7} }, /* 2.519e-17 */ +/**/ ua25 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */ +/**/ ub25 = {{0x00000000, 0x3ccc2375} }, /* 7.810e-16 */ +/**/ u26 = {{0x00000000, 0x3c7e40af} }, /* 2.624e-17 */ +/**/ ua26 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */ +/**/ ub26 = {{0x00000000, 0x3ccc6405} }, /* 7.880e-16 */ +/**/ u27 = {{0x00000000, 0x3ad421cb} }, /* 2.602e-25 */ +/**/ u28 = {{0x00000000, 0x3ad421cb} }, /* 2.602e-25 */ + +/**/ mp1 = {{0x58000000, 0x3FF921FB} }, +/**/ mp2 = {{0x3C000000, 0xBE4DDE97} }, +/**/ mp3 = {{0x99D747F2, 0xBC8CB3B3} }, +/**/ pp3 = {{0x98000000, 0xBC8CB3B3} }, +/**/ pp4 = {{0x23e32ed7, 0xbacd747f} }, +/**/ hpinv = {{0x6DC9C883, 0x3FE45F30} }, +/**/ toint = {{0x00000000, 0x43380000} }; + +#endif +#endif + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/utan.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/utan.tbl new file mode 100644 index 0000000000..8b536e9235 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/utan.tbl @@ -0,0 +1,1525 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE utan() FUNCTION */ +/****************************************************************/ + + +#ifdef BIG_ENDI +static const number + xfg[186][4] = { /* xi,Fi,Gi,FFi, i=16..201 */ +/**/ {{{0x3fb00000, 0x1e519d60} }, +/**/ {{0x3fb00557, 0x96c4e240} }, +/**/ {{0x402ff554, 0x628127b7} }, +/**/ {{0xbb9a1dee, 0x9e355b06} },}, +/**/ {{{0x3fb10000, 0x1b1a7010} }, +/**/ {{0x3fb10668, 0xaab892b7} }, +/**/ {{0x402e12c7, 0xbe3fdf74} }, +/**/ {{0x3ba89234, 0x037da741} },}, +/**/ {{{0x3fb20000, 0x2505e350} }, +/**/ {{0x3fb2079b, 0xff547824} }, +/**/ {{0x402c65c5, 0xde853633} }, +/**/ {{0x3bb7486e, 0xe9614250} },}, +/**/ {{{0x3fb2ffff, 0xfcdc4252} }, +/**/ {{0x3fb308f3, 0x5eb16c68} }, +/**/ {{0x402ae5da, 0xe56be74f} }, +/**/ {{0xbb82c726, 0x91a23034} },}, +/**/ {{{0x3fb3ffff, 0xe3ff849f} }, +/**/ {{0x3fb40a71, 0x154999cc} }, +/**/ {{0x40298c43, 0x046b7352} }, +/**/ {{0x3b9aceaf, 0x3843738f} },}, +/**/ {{{0x3fb4ffff, 0xedc9590f} }, +/**/ {{0x3fb50c17, 0x429bdd80} }, +/**/ {{0x40285384, 0x91b5d674} }, +/**/ {{0xbbc1d02d, 0xb4403d22} },}, +/**/ {{{0x3fb60000, 0x00ee83f7} }, +/**/ {{0x3fb60de7, 0xda80cc21} }, +/**/ {{0x40273724, 0xef21a2a7} }, +/**/ {{0xbb95e53c, 0x72523ffd} },}, +/**/ {{{0x3fb6ffff, 0xeb05ea41} }, +/**/ {{0x3fb70fe4, 0xb8c51bea} }, +/**/ {{0x40263370, 0xfae562ff} }, +/**/ {{0xbb99ad0e, 0x8ffe0626} },}, +/**/ {{{0x3fb7ffff, 0xdc0515f7} }, +/**/ {{0x3fb81210, 0x1db54498} }, +/**/ {{0x40254553, 0x0e7eab5c} }, +/**/ {{0xbb914c87, 0xd62ed686} },}, +/**/ {{{0x3fb8ffff, 0xe384d7ab} }, +/**/ {{0x3fb9146c, 0x2a8d3727} }, +/**/ {{0x40246a33, 0xfd57f3fd} }, +/**/ {{0xbbbbda8d, 0x5381e06d} },}, +/**/ {{{0x3fb9ffff, 0xe4832347} }, +/**/ {{0x3fba16fa, 0xd50e1050} }, +/**/ {{0x40239fe2, 0xc5537a96} }, +/**/ {{0x3bc7f695, 0xc111eabb} },}, +/**/ {{{0x3fbb0000, 0x274540e3} }, +/**/ {{0x3fbb19be, 0x7ae68517} }, +/**/ {{0x4022e481, 0x3637e946} }, +/**/ {{0x3bc307f8, 0x8dbd9d93} },}, +/**/ {{{0x3fbbffff, 0xfebf2e9b} }, +/**/ {{0x3fbc1cb8, 0x8369cd19} }, +/**/ {{0x40223676, 0x17aef223} }, +/**/ {{0x3bc50038, 0x424a9cf3} },}, +/**/ {{{0x3fbd0000, 0x23529045} }, +/**/ {{0x3fbd1feb, 0xc11d7ef7} }, +/**/ {{0x4021945f, 0xb8e43d4e} }, +/**/ {{0x3b812007, 0x52a6f224} },}, +/**/ {{{0x3fbdffff, 0xd872a829} }, +/**/ {{0x3fbe2359, 0x8ee4d6b7} }, +/**/ {{0x4020fd0c, 0x76195d5f} }, +/**/ {{0xbbb4d9ab, 0x85fdca85} },}, +/**/ {{{0x3fbeffff, 0xff323b84} }, +/**/ {{0x3fbf2704, 0xec9073e5} }, +/**/ {{0x40206f71, 0x3020200f} }, +/**/ {{0x3bb77aa2, 0x12836992} },}, +/**/ {{{0x3fc00000, 0x0ce79195} }, +/**/ {{0x3fc01577, 0xbc30cc61} }, +/**/ {{0x401fd549, 0xd6564a88} }, +/**/ {{0xbbc8926f, 0x965c0ad0} },}, +/**/ {{{0x3fc07fff, 0xee40e918} }, +/**/ {{0x3fc0978d, 0x8279ac01} }, +/**/ {{0x401edbb5, 0x9294bc03} }, +/**/ {{0xbb80a533, 0x4aae45d6} },}, +/**/ {{{0x3fc10000, 0x0cc091fd} }, +/**/ {{0x3fc119c5, 0x44dfb2f7} }, +/**/ {{0x401df0bb, 0x067d8e18} }, +/**/ {{0xbbcc2c18, 0x4ff642a4} },}, +/**/ {{{0x3fc18000, 0x0d9936a1} }, +/**/ {{0x3fc19c1f, 0xb9085a4b} }, +/**/ {{0x401d131a, 0x71ce3629} }, +/**/ {{0xbbc36553, 0x0669355b} },}, +/**/ {{{0x3fc1ffff, 0xed5f3188} }, +/**/ {{0x3fc21e9d, 0xee74bf2d} }, +/**/ {{0x401c41b6, 0xff0cd655} }, +/**/ {{0x3b8867f5, 0x478ecfc5} },}, +/**/ {{{0x3fc28000, 0x05f06a51} }, +/**/ {{0x3fc2a141, 0x550b313f} }, +/**/ {{0x401b7b92, 0x1702e6d2} }, +/**/ {{0xbbadab51, 0x380131fe} },}, +/**/ {{{0x3fc2ffff, 0xfe3d339e} }, +/**/ {{0x3fc3240a, 0xa75f76df} }, +/**/ {{0x401abfc8, 0xfcb6409d} }, +/**/ {{0x3bc60bcf, 0x0d291d83} },}, +/**/ {{{0x3fc37fff, 0xed888d6f} }, +/**/ {{0x3fc3a6fb, 0x13cc5db7} }, +/**/ {{0x401a0d8f, 0x8ed5320d} }, +/**/ {{0x3bb8a48e, 0x4eef03ab} },}, +/**/ {{{0x3fc40000, 0x02ca050d} }, +/**/ {{0x3fc42a13, 0xe25776bb} }, +/**/ {{0x4019642d, 0xfa84c2bc} }, +/**/ {{0xbbd0bd5d, 0xcc56516f} },}, +/**/ {{{0x3fc47fff, 0xf2531f5c} }, +/**/ {{0x3fc4ad55, 0xdeb73404} }, +/**/ {{0x4018c2fe, 0xf86e9035} }, +/**/ {{0x3b9cffe7, 0x5aa287c8} },}, +/**/ {{{0x3fc50000, 0x13774992} }, +/**/ {{0x3fc530c2, 0x7d0ee307} }, +/**/ {{0x4018296c, 0x370caf35} }, +/**/ {{0xbbcf75d1, 0xf91d6532} },}, +/**/ {{{0x3fc57fff, 0xedddcb2d} }, +/**/ {{0x3fc5b45a, 0x5db4347d} }, +/**/ {{0x401796ee, 0x52190c0e} }, +/**/ {{0x3b88a25f, 0x17d5d076} },}, +/**/ {{{0x3fc5ffff, 0xf41949a0} }, +/**/ {{0x3fc6381f, 0x13bf986a} }, +/**/ {{0x40170b09, 0x2d2255fd} }, +/**/ {{0xbb9bfb23, 0xb1bcd5e7} },}, +/**/ {{{0x3fc67fff, 0xf834d3a1} }, +/**/ {{0x3fc6bc11, 0x8ec85952} }, +/**/ {{0x4016854c, 0x62cf2268} }, +/**/ {{0x3b9ee53b, 0x82e39e04} },}, +/**/ {{{0x3fc6ffff, 0xfd9106ea} }, +/**/ {{0x3fc74032, 0xf298f6f7} }, +/**/ {{0x40160551, 0x1f4f84a9} }, +/**/ {{0xbbb59c4a, 0x112634b8} },}, +/**/ {{{0x3fc78000, 0x0f649a4f} }, +/**/ {{0x3fc7c484, 0x6ca53abc} }, +/**/ {{0x40158ab9, 0x4809d175} }, +/**/ {{0x3bc91c75, 0x73d3cd2e} },}, +/**/ {{{0x3fc7ffff, 0xef06bbd8} }, +/**/ {{0x3fc84906, 0xdf7d76ad} }, +/**/ {{0x4015152e, 0xdd2b30a6} }, +/**/ {{0xbbbfa2da, 0x084c3eef} },}, +/**/ {{{0x3fc88000, 0x021c6334} }, +/**/ {{0x3fc8cdbb, 0xd965f986} }, +/**/ {{0x4014a462, 0x51b74296} }, +/**/ {{0xbb9ec02e, 0x74dcfe0b} },}, +/**/ {{{0x3fc8ffff, 0xf38d0756} }, +/**/ {{0x3fc952a4, 0x28e173c7} }, +/**/ {{0x4014380b, 0x17b59ebd} }, +/**/ {{0xbbcd0f1c, 0xb77589f0} },}, +/**/ {{{0x3fc98000, 0x104efca1} }, +/**/ {{0x3fc9d7c1, 0x4644d23c} }, +/**/ {{0x4013cfe5, 0xcb1eabd5} }, +/**/ {{0xbbd5d6f7, 0xea188d9e} },}, +/**/ {{{0x3fca0000, 0x09417b30} }, +/**/ {{0x3fca5d14, 0x096d76aa} }, +/**/ {{0x40136bb4, 0xb3723db0} }, +/**/ {{0x3bbe3e0d, 0xfbf3979c} },}, +/**/ {{{0x3fca7fff, 0xeb1c23ec} }, +/**/ {{0x3fcae29d, 0xab60288d} }, +/**/ {{0x40130b3e, 0x783071d7} }, +/**/ {{0xbbc7dd82, 0x3d5384bf} },}, +/**/ {{{0x3fcaffff, 0xfb171c13} }, +/**/ {{0x3fcb685f, 0xa221a96b} }, +/**/ {{0x4012ae4d, 0xd8c0747d} }, +/**/ {{0x3bd4644b, 0xd5554972} },}, +/**/ {{{0x3fcb8000, 0x0aba44be} }, +/**/ {{0x3fcbee5a, 0xecdf241f} }, +/**/ {{0x401254b1, 0xc6fad63b} }, +/**/ {{0x3ba41916, 0xd092b85a} },}, +/**/ {{{0x3fcc0000, 0x113d2a3e} }, +/**/ {{0x3fcc7490, 0xb3e92543} }, +/**/ {{0x4011fe3c, 0x9a62c035} }, +/**/ {{0xbba3cc39, 0x41a03739} },}, +/**/ {{{0x3fcc7fff, 0xf49e00ce} }, +/**/ {{0x3fccfb02, 0x0f59eab0} }, +/**/ {{0x4011aac3, 0xe956a631} }, +/**/ {{0xbbb7a383, 0xbfa8cb5b} },}, +/**/ {{{0x3fcd0000, 0x05f611ab} }, +/**/ {{0x3fcd81b0, 0x89e6844e} }, +/**/ {{0x40115a1f, 0xf391268d} }, +/**/ {{0x3bd39b5c, 0xb2dc91f3} },}, +/**/ {{{0x3fcd8000, 0x14764ceb} }, +/**/ {{0x3fce089d, 0x27debf0d} }, +/**/ {{0x40110c2b, 0xfbc84740} }, +/**/ {{0x3bc14d4d, 0x84712510} },}, +/**/ {{{0x3fce0000, 0x14bcea76} }, +/**/ {{0x3fce8fc9, 0x16dbc820} }, +/**/ {{0x4010c0c5, 0xa00ca48e} }, +/**/ {{0xbbd33788, 0x640f1b9e} },}, +/**/ {{{0x3fce7fff, 0xfd7995bd} }, +/**/ {{0x3fcf1735, 0x88b50424} }, +/**/ {{0x401077cc, 0xbe02169a} }, +/**/ {{0xbbb61fee, 0x221fdf77} },}, +/**/ {{{0x3fcf0000, 0x0cc35436} }, +/**/ {{0x3fcf9ee3, 0xfd21a40b} }, +/**/ {{0x40103123, 0x1ee7ffe8} }, +/**/ {{0x3bd427e3, 0xc79ff5c1} },}, +/**/ {{{0x3fcf8000, 0x01d1da33} }, +/**/ {{0x3fd0136a, 0xb7dbe15c} }, +/**/ {{0x400fd959, 0x77d559e5} }, +/**/ {{0x3bb0c6a1, 0xd67948d7} },}, +/**/ {{{0x3fd00000, 0x060c13b2} }, +/**/ {{0x3fd05785, 0xaaad4f18} }, +/**/ {{0x400f549e, 0x2675d182} }, +/**/ {{0xbbc15208, 0x18f0dd10} },}, +/**/ {{{0x3fd04000, 0x03885492} }, +/**/ {{0x3fd09bc3, 0x660542d7} }, +/**/ {{0x400ed3e2, 0xdf3f5fec} }, +/**/ {{0xbbd95657, 0xb883ae62} },}, +/**/ {{{0x3fd08000, 0x052f5a13} }, +/**/ {{0x3fd0e024, 0x9a195045} }, +/**/ {{0x400e56f8, 0xfa68f2c8} }, +/**/ {{0x3bded7ba, 0x5a543e8e} },}, +/**/ {{{0x3fd0c000, 0x02ba1af5} }, +/**/ {{0x3fd124a9, 0xe2e7f24b} }, +/**/ {{0x400dddb4, 0xbffe633f} }, +/**/ {{0xbbdcba86, 0x0c60278f} },}, +/**/ {{{0x3fd0ffff, 0xf76642c1} }, +/**/ {{0x3fd16953, 0xe162ffe6} }, +/**/ {{0x400d67ed, 0x0311d5d5} }, +/**/ {{0x3b7b1f4a, 0xe40c5f9e} },}, +/**/ {{{0x3fd14000, 0x033602f0} }, +/**/ {{0x3fd1ae23, 0x5f49508e} }, +/**/ {{0x400cf57a, 0xb8708266} }, +/**/ {{0xbbd6a6c2, 0x8620f301} },}, +/**/ {{{0x3fd17fff, 0xfefd1a13} }, +/**/ {{0x3fd1f318, 0xdb2a9ba1} }, +/**/ {{0x400c8639, 0x8d11009e} }, +/**/ {{0x3bd3a9c6, 0x69b21d3b} },}, +/**/ {{{0x3fd1bfff, 0xf718365d} }, +/**/ {{0x3fd23835, 0x0c41e3ac} }, +/**/ {{0x400c1a06, 0xe02be47c} }, +/**/ {{0x3bdb961a, 0x129e8cd1} },}, +/**/ {{{0x3fd1ffff, 0xff001e00} }, +/**/ {{0x3fd27d78, 0xb2f6395e} }, +/**/ {{0x400bb0c1, 0xf2fe9a85} }, +/**/ {{0x3be074a9, 0xe68fd7d8} },}, +/**/ {{{0x3fd23fff, 0xfe425a6a} }, +/**/ {{0x3fd2c2e4, 0x618faabe} }, +/**/ {{0x400b4a4c, 0x190b18df} }, +/**/ {{0xbbdf0d1f, 0xf615aad1} },}, +/**/ {{{0x3fd28000, 0x059ec1db} }, +/**/ {{0x3fd30878, 0xd8583884} }, +/**/ {{0x400ae688, 0x0cd82bc2} }, +/**/ {{0xbbd563c3, 0x141c1f8d} },}, +/**/ {{{0x3fd2c000, 0x000dd081} }, +/**/ {{0x3fd34e36, 0xaffdb6d8} }, +/**/ {{0x400a855a, 0x5270fc15} }, +/**/ {{0xbbc6d88d, 0x9f2cdafd} },}, +/**/ {{{0x3fd2ffff, 0xfc1dcd2b} }, +/**/ {{0x3fd3941e, 0xa95875bc} }, +/**/ {{0x400a26a8, 0xaa9502b6} }, +/**/ {{0xbbe13cad, 0x8389b15c} },}, +/**/ {{{0x3fd33fff, 0xf6c0d4a0} }, +/**/ {{0x3fd3da31, 0x739845f5} }, +/**/ {{0x4009ca5a, 0x4d2573a0} }, +/**/ {{0xbbc71636, 0xacaee379} },}, +/**/ {{{0x3fd38000, 0x06b16793} }, +/**/ {{0x3fd4206f, 0xdbc088f0} }, +/**/ {{0x40097057, 0x9344e33a} }, +/**/ {{0xbbc2c052, 0x1d7a4f81} },}, +/**/ {{{0x3fd3c000, 0x07358fa3} }, +/**/ {{0x3fd466da, 0x6f23311d} }, +/**/ {{0x4009188a, 0x5aa612ea} }, +/**/ {{0x3b8653a5, 0x685e8edc} },}, +/**/ {{{0x3fd3ffff, 0xfc3b18cf} }, +/**/ {{0x3fd4ad71, 0xe9282e6b} }, +/**/ {{0x4008c2dd, 0x641e643d} }, +/**/ {{0x3b95f0ef, 0x3f567c64} },}, +/**/ {{{0x3fd44000, 0x000dd2a8} }, +/**/ {{0x3fd4f437, 0x1fa3f2d1} }, +/**/ {{0x40086f3c, 0x6072f821} }, +/**/ {{0x3bb68efa, 0x95ff68b5} },}, +/**/ {{{0x3fd47fff, 0xfbb43713} }, +/**/ {{0x3fd53b2a, 0xb3ac333c} }, +/**/ {{0x40081d94, 0x3da56692} }, +/**/ {{0xbbbf4d7f, 0x2985fd3f} },}, +/**/ {{{0x3fd4bfff, 0xfb113bf4} }, +/**/ {{0x3fd5824d, 0x6e8ed9c2} }, +/**/ {{0x4007cdd2, 0xa8add00f} }, +/**/ {{0x3bcf478a, 0x1c9b3657} },}, +/**/ {{{0x3fd4ffff, 0xf7f087c9} }, +/**/ {{0x3fd5c9a0, 0x07446496} }, +/**/ {{0x40077fe6, 0x444588eb} }, +/**/ {{0xbbc177dc, 0xa4eabb0c} },}, +/**/ {{{0x3fd54000, 0x088b3814} }, +/**/ {{0x3fd61123, 0x564125f9} }, +/**/ {{0x400733be, 0x6281a765} }, +/**/ {{0xbbc2c52c, 0xf57051c4} },}, +/**/ {{{0x3fd57fff, 0xf7d55966} }, +/**/ {{0x3fd658d7, 0xe194a5d5} }, +/**/ {{0x4006e94b, 0x73b47d1f} }, +/**/ {{0x3bda2fcf, 0xf9996dc6} },}, +/**/ {{{0x3fd5c000, 0x08bf2490} }, +/**/ {{0x3fd6a0be, 0xb775b28d} }, +/**/ {{0x4006a07e, 0x15b6ec28} }, +/**/ {{0xbbe0ca90, 0xaa5285b8} },}, +/**/ {{{0x3fd60000, 0x09fa853f} }, +/**/ {{0x3fd6e8d8, 0x65a66cfd} }, +/**/ {{0x40065948, 0x1c701269} }, +/**/ {{0x3bd9ea95, 0x8591e13a} },}, +/**/ {{{0x3fd64000, 0x07595fca} }, +/**/ {{0x3fd73125, 0xc0556a7c} }, +/**/ {{0x4006139b, 0xbaae9d02} }, +/**/ {{0x3bd88aff, 0x40152b83} },}, +/**/ {{{0x3fd68000, 0x031687da} }, +/**/ {{0x3fd779a7, 0x92e2cfd0} }, +/**/ {{0x4005cf6b, 0xcae0882b} }, +/**/ {{0xbbd8a4a2, 0x9f439451} },}, +/**/ {{{0x3fd6bfff, 0xf5c8cfe2} }, +/**/ {{0x3fd7c25e, 0x9fb452ed} }, +/**/ {{0x40058cab, 0xc561f1cd} }, +/**/ {{0xbbe371a6, 0xf6a37d74} },}, +/**/ {{{0x3fd6ffff, 0xf81df231} }, +/**/ {{0x3fd80b4b, 0xcfb4dab5} }, +/**/ {{0x40054b4f, 0x8d3ca5d3} }, +/**/ {{0x3bcb4686, 0x679dc99f} },}, +/**/ {{{0x3fd73fff, 0xfa71385e} }, +/**/ {{0x3fd8546f, 0xe007a9b6} }, +/**/ {{0x40050b4b, 0xb3b22176} }, +/**/ {{0xbbcd1540, 0xa5c73477} },}, +/**/ {{{0x3fd78000, 0x024a9c2b} }, +/**/ {{0x3fd89dcb, 0xa7fcf5cf} }, +/**/ {{0x4004cc95, 0x3159cbe1} }, +/**/ {{0xbbdc25ea, 0xd58a6ad0} },}, +/**/ {{{0x3fd7c000, 0x02eb62b8} }, +/**/ {{0x3fd8e75f, 0xec0ba5cf} }, +/**/ {{0x40048f21, 0x8731eeea} }, +/**/ {{0xbbc1cb73, 0xcc1adafb} },}, +/**/ {{{0x3fd80000, 0x054a52d1} }, +/**/ {{0x3fd9312d, 0x8bb822e9} }, +/**/ {{0x400452e6, 0x9170a729} }, +/**/ {{0xbbd8bb17, 0xeac002ee} },}, +/**/ {{{0x3fd83fff, 0xf93a00a3} }, +/**/ {{0x3fd97b35, 0x4bb9ad2a} }, +/**/ {{0x400417da, 0xae924e7f} }, +/**/ {{0x3bd4b800, 0x9a378cc7} },}, +/**/ {{{0x3fd87fff, 0xfbdc91c1} }, +/**/ {{0x3fd9c578, 0x2771b601} }, +/**/ {{0x4003ddf4, 0x78855799} }, +/**/ {{0x3bd9077d, 0xa00445d9} },}, +/**/ {{{0x3fd8bfff, 0xf6d215e6} }, +/**/ {{0x3fda0ff6, 0xe0ea4a0b} }, +/**/ {{0x4003a52b, 0x189a0989} }, +/**/ {{0xbbda6831, 0x89c0613d} },}, +/**/ {{{0x3fd90000, 0x02f734ef} }, +/**/ {{0x3fda5ab2, 0x736bf579} }, +/**/ {{0x40036d75, 0xe9244ca6} }, +/**/ {{0x3be3a6d8, 0x4b722377} },}, +/**/ {{{0x3fd94000, 0x04eef8b4} }, +/**/ {{0x3fdaa5ab, 0x9fb6e3d0} }, +/**/ {{0x400336cc, 0xc9089cb7} }, +/**/ {{0x3b9f6963, 0x22cc00bb} },}, +/**/ {{{0x3fd98000, 0x041ec76a} }, +/**/ {{0x3fdaf0e3, 0x5176c7e4} }, +/**/ {{0x40030127, 0xcb0b9506} }, +/**/ {{0x3bb1ffdb, 0x5385a849} },}, +/**/ {{{0x3fd9c000, 0x08044e47} }, +/**/ {{0x3fdb3c5a, 0x77071224} }, +/**/ {{0x4002cc7f, 0x50d75ec7} }, +/**/ {{0xbbb0fade, 0x78effc8a} },}, +/**/ {{{0x3fda0000, 0x01f8235b} }, +/**/ {{0x3fdb8811, 0xe725782e} }, +/**/ {{0x400298cc, 0x18fbfb37} }, +/**/ {{0xbbe55ed3, 0x3b50e71b} },}, +/**/ {{{0x3fda3fff, 0xfb8c6f08} }, +/**/ {{0x3fdbd40a, 0x97b086f3} }, +/**/ {{0x40026607, 0x154de04b} }, +/**/ {{0xbbdec65e, 0x455faae3} },}, +/**/ {{{0x3fda7fff, 0xfb3d63e1} }, +/**/ {{0x3fdc2045, 0x7d9a3b8a} }, +/**/ {{0x40023429, 0x7e60bfbb} }, +/**/ {{0x3be3001c, 0x154ebd33} },}, +/**/ {{{0x3fdabfff, 0xf5f45c48} }, +/**/ {{0x3fdc6cc3, 0x7b8d45e6} }, +/**/ {{0x4002032c, 0xdb1ace69} }, +/**/ {{0xbbe5ebf8, 0x3ed33616} },}, +/**/ {{{0x3fdb0000, 0x0508b34c} }, +/**/ {{0x3fdcb985, 0xa27e8d37} }, +/**/ {{0x4001d30a, 0xd4459a2b} }, +/**/ {{0xbbd01432, 0xae61e2d1} },}, +/**/ {{{0x3fdb4000, 0x0a84710c} }, +/**/ {{0x3fdd068c, 0xc3e50155} }, +/**/ {{0x4001a3bd, 0x775034dd} }, +/**/ {{0xbbe80b1e, 0x58e0e228} },}, +/**/ {{{0x3fdb7fff, 0xf692e9d8} }, +/**/ {{0x3fdd53d9, 0xc49d6627} }, +/**/ {{0x4001753e, 0xfe18066a} }, +/**/ {{0xbbb004c8, 0xf760d33e} },}, +/**/ {{{0x3fdbc000, 0x0280f14d} }, +/**/ {{0x3fdda16d, 0xe4e81013} }, +/**/ {{0x40014789, 0xa38ea052} }, +/**/ {{0x3be848bc, 0x27c9c4ea} },}, +/**/ {{{0x3fdc0000, 0x001121d1} }, +/**/ {{0x3fddef49, 0xeac018f0} }, +/**/ {{0x40011a98, 0x20b8be0c} }, +/**/ {{0xbbe1527e, 0xd0d6010e} },}, +/**/ {{{0x3fdc3fff, 0xfef662aa} }, +/**/ {{0x3fde3d6e, 0xea0c7070} }, +/**/ {{0x4000ee65, 0x32f46ccd} }, +/**/ {{0x3be8d241, 0x189a000d} },}, +/**/ {{{0x3fdc8000, 0x09845818} }, +/**/ {{0x3fde8bdd, 0xf36a8b1b} }, +/**/ {{0x4000c2eb, 0xcac73476} }, +/**/ {{0x3bd221f7, 0x12bed284} },}, +/**/ {{{0x3fdcbfff, 0xfb0493bf} }, +/**/ {{0x3fdeda97, 0xe0c60d10} }, +/**/ {{0x40009827, 0x251c7836} }, +/**/ {{0xbbe0bd54, 0x6eec41b7} },}, +/**/ {{{0x3fdcffff, 0xfd52961f} }, +/**/ {{0x3fdf299d, 0xefb3e44b} }, +/**/ {{0x40006e12, 0x74e459f5} }, +/**/ {{0xbbd93f77, 0xe969c82f} },}, +/**/ {{{0x3fdd3fff, 0xfe2319a4} }, +/**/ {{0x3fdf78f1, 0x17139490} }, +/**/ {{0x400044a9, 0x3e737e94} }, +/**/ {{0xbb91e7cc, 0x49594b7a} },}, +/**/ {{{0x3fdd7fff, 0xfa4de596} }, +/**/ {{0x3fdfc892, 0x638f49e8} }, +/**/ {{0x40001be7, 0x231057a5} }, +/**/ {{0x3bd482b0, 0xf5af9f5f} },}, +/**/ {{{0x3fddbfff, 0xfe729a69} }, +/**/ {{0x3fe00c41, 0x7c6ab019} }, +/**/ {{0x3fffe78f, 0xbf612660} }, +/**/ {{0x3bea5cda, 0x00da681e} },}, +/**/ {{{0x3fde0000, 0x09d66802} }, +/**/ {{0x3fe03461, 0xf6b883cf} }, +/**/ {{0x3fff988e, 0xbc05a87c} }, +/**/ {{0xbbe06c33, 0xf2372669} },}, +/**/ {{{0x3fde3fff, 0xfb211657} }, +/**/ {{0x3fe05cab, 0x191db8e8} }, +/**/ {{0x3fff4ac3, 0x7bcfe6be} }, +/**/ {{0xbbd5d51f, 0x5ed8d35b} },}, +/**/ {{{0x3fde8000, 0x0a3f068a} }, +/**/ {{0x3fe0851d, 0x95fb54f0} }, +/**/ {{0x3ffefe26, 0x144ca408} }, +/**/ {{0xbbc7c894, 0xa2c169c5} },}, +/**/ {{{0x3fdec000, 0x01adb060} }, +/**/ {{0x3fe0adb9, 0xdc7b54f9} }, +/**/ {{0x3ffeb2af, 0x5ebe52a7} }, +/**/ {{0x3bd4e740, 0x312c5ffd} },}, +/**/ {{{0x3fdeffff, 0xff5c0d01} }, +/**/ {{0x3fe0d680, 0x92550a8d} }, +/**/ {{0x3ffe6858, 0x0d71fdf0} }, +/**/ {{0x3bddd8a6, 0x96b35499} },}, +/**/ {{{0x3fdf3fff, 0xf93d5fcc} }, +/**/ {{0x3fe0ff72, 0x45cb4374} }, +/**/ {{0x3ffe1f19, 0x3cce5040} }, +/**/ {{0xbbc9f0ec, 0x7c1efab4} },}, +/**/ {{{0x3fdf7fff, 0xfa0dd18f} }, +/**/ {{0x3fe1288f, 0x944dd508} }, +/**/ {{0x3ffdd6ec, 0x298b874d} }, +/**/ {{0x3bea6ebd, 0x9642a0a6} },}, +/**/ {{{0x3fdfbfff, 0xfd3a9f1a} }, +/**/ {{0x3fe151d9, 0x13750f3e} }, +/**/ {{0x3ffd8fca, 0x5806a27e} }, +/**/ {{0x3bda2a03, 0xfc65ac7a} },}, +/**/ {{{0x3fdfffff, 0xfc481400} }, +/**/ {{0x3fe17b4f, 0x598944ca} }, +/**/ {{0x3ffd49ad, 0x82532170} }, +/**/ {{0x3bc4412e, 0x3d236dc3} },}, +/**/ {{{0x3fe01fff, 0xff53786c} }, +/**/ {{0x3fe1a4f3, 0x07d83d47} }, +/**/ {{0x3ffd048f, 0x851bffeb} }, +/**/ {{0x3bd1589d, 0x29f81b14} },}, +/**/ {{{0x3fe03fff, 0xfee301b7} }, +/**/ {{0x3fe1cec4, 0xb8a6a382} }, +/**/ {{0x3ffcc06a, 0x7c519db6} }, +/**/ {{0x3bd370e6, 0x5b24d6b2} },}, +/**/ {{{0x3fe06000, 0x006e36bf} }, +/**/ {{0x3fe1f8c5, 0x114eb8be} }, +/**/ {{0x3ffc7d38, 0xa34d6786} }, +/**/ {{0xbbea92de, 0x4b98c1d4} },}, +/**/ {{{0x3fe07fff, 0xfd60aa43} }, +/**/ {{0x3fe222f4, 0xabeccecb} }, +/**/ {{0x3ffc3af4, 0x77342ac4} }, +/**/ {{0xbbdd47f6, 0x03a5c2c2} },}, +/**/ {{{0x3fe0a000, 0x037762e8} }, +/**/ {{0x3fe24d54, 0x3f99efe8} }, +/**/ {{0x3ffbf998, 0x75f54fab} }, +/**/ {{0x3bedf7f4, 0x15771a46} },}, +/**/ {{{0x3fe0bfff, 0xff1c6921} }, +/**/ {{0x3fe277e4, 0x598e35d0} }, +/**/ {{0x3ffbb91f, 0x8addd186} }, +/**/ {{0x3be0f16c, 0x5e0e5a73} },}, +/**/ {{{0x3fe0dfff, 0xff07154b} }, +/**/ {{0x3fe2a2a5, 0xb6bc3986} }, +/**/ {{0x3ffb7984, 0x8301646d} }, +/**/ {{0xbbf02dd0, 0xbbaa5310} },}, +/**/ {{{0x3fe10000, 0x02fcdda4} }, +/**/ {{0x3fe2cd99, 0x02a59f1e} }, +/**/ {{0x3ffb3ac2, 0x705219bf} }, +/**/ {{0xbbe59357, 0x112fa616} },}, +/**/ {{{0x3fe12000, 0x01ce1140} }, +/**/ {{0x3fe2f8be, 0xdf0a67c2} }, +/**/ {{0x3ffafcd4, 0x9ab8ae2a} }, +/**/ {{0x3be2c542, 0x9303f346} },}, +/**/ {{{0x3fe14000, 0x04d0f355} }, +/**/ {{0x3fe32418, 0x08fcc7bf} }, +/**/ {{0x3ffabfb6, 0x497b9a36} }, +/**/ {{0x3bebc044, 0xb5a59234} },}, +/**/ {{{0x3fe16000, 0x00fb0c8a} }, +/**/ {{0x3fe34fa5, 0x2471618b} }, +/**/ {{0x3ffa8363, 0x0d26d117} }, +/**/ {{0xbbdbfbb2, 0x3f7bb7c9} },}, +/**/ {{{0x3fe18000, 0x026f10b3} }, +/**/ {{0x3fe37b66, 0xf7579056} }, +/**/ {{0x3ffa47d6, 0x6b4cf4b1} }, +/**/ {{0x3bf0f6b4, 0xaf0b5de9} },}, +/**/ {{{0x3fe19fff, 0xfd0978f8} }, +/**/ {{0x3fe3a75e, 0x290cc78c} }, +/**/ {{0x3ffa0d0c, 0x36c21315} }, +/**/ {{0x3beb2129, 0xa296b262} },}, +/**/ {{{0x3fe1bfff, 0xfd94840b} }, +/**/ {{0x3fe3d38b, 0x85b4e4a4} }, +/**/ {{0x3ff9d300, 0x32f2ecef} }, +/**/ {{0xbbdbab1a, 0xb9bb7d74} },}, +/**/ {{{0x3fe1dfff, 0xfbda1ea1} }, +/**/ {{0x3fe3ffef, 0xbf3cee2f} }, +/**/ {{0x3ff999ae, 0x6770fed8} }, +/**/ {{0x3bda0bdc, 0xb4ace9a4} },}, +/**/ {{{0x3fe1ffff, 0xfc989533} }, +/**/ {{0x3fe42c8b, 0x9c27900c} }, +/**/ {{0x3ff96112, 0xe0d9f1ac} }, +/**/ {{0xbbee19eb, 0x2fa2d81a} },}, +/**/ {{{0x3fe22000, 0x012b8d26} }, +/**/ {{0x3fe4595f, 0xe11975ca} }, +/**/ {{0x3ff92929, 0xcdaa4e80} }, +/**/ {{0x3bf23382, 0xacc82d4b} },}, +/**/ {{{0x3fe24000, 0x04f4d6af} }, +/**/ {{0x3fe4866d, 0x4d224131} }, +/**/ {{0x3ff8f1ef, 0x815c34e8} }, +/**/ {{0xbbd0c6ff, 0x3b740a99} },}, +/**/ {{{0x3fe25fff, 0xfcc07bda} }, +/**/ {{0x3fe4b3b4, 0x98b7d010} }, +/**/ {{0x3ff8bb60, 0x73e7ffa1} }, +/**/ {{0x3bebc31b, 0x1ad7a9c2} },}, +/**/ {{{0x3fe28000, 0x042d9639} }, +/**/ {{0x3fe4e136, 0xb64540d1} }, +/**/ {{0x3ff88578, 0xf4374938} }, +/**/ {{0x3be36de9, 0x1b85e901} },}, +/**/ {{{0x3fe2a000, 0x03be29a0} }, +/**/ {{0x3fe50ef4, 0x52bffd96} }, +/**/ {{0x3ff85035, 0xc0042c06} }, +/**/ {{0x3be15d01, 0x76f5efbd} },}, +/**/ {{{0x3fe2bfff, 0xfaa91f12} }, +/**/ {{0x3fe53cee, 0x3e2f4e0d} }, +/**/ {{0x3ff81b93, 0x8542df07} }, +/**/ {{0x3be555cd, 0x17662a2b} },}, +/**/ {{{0x3fe2dfff, 0xfe884891} }, +/**/ {{0x3fe56b25, 0x6c1a2470} }, +/**/ {{0x3ff7e78e, 0xe422ea70} }, +/**/ {{0x3bf03504, 0xbd030c11} },}, +/**/ {{{0x3fe2ffff, 0xfe87152b} }, +/**/ {{0x3fe5999a, 0x9beaaaa1} }, +/**/ {{0x3ff7b424, 0xd18fe9b3} }, +/**/ {{0xbb649a5f, 0x773e0e64} },}, +/**/ {{{0x3fe31fff, 0xffc1a721} }, +/**/ {{0x3fe5c84e, 0xafe0e564} }, +/**/ {{0x3ff78152, 0x338db8d4} }, +/**/ {{0x3beaf428, 0x5da8e935} },}, +/**/ {{{0x3fe33fff, 0xff70a372} }, +/**/ {{0x3fe5f742, 0x82191d64} }, +/**/ {{0x3ff74f14, 0x1122bcae} }, +/**/ {{0x3bdb1c4b, 0xdee4bfaf} },}, +/**/ {{{0x3fe36000, 0x0436e836} }, +/**/ {{0x3fe62676, 0xfde6ccff} }, +/**/ {{0x3ff71d67, 0x7644252c} }, +/**/ {{0xbbec3d10, 0xe08c3afb} },}, +/**/ {{{0x3fe37fff, 0xfcbe9641} }, +/**/ {{0x3fe655ec, 0xee9ffdaf} }, +/**/ {{0x3ff6ec49, 0xa6fc0515} }, +/**/ {{0x3bdda453, 0x2ed29567} },}, +/**/ {{{0x3fe39fff, 0xffb6d6ca} }, +/**/ {{0x3fe685a5, 0x5e67a1e1} }, +/**/ {{0x3ff6bbb7, 0xbc2ae969} }, +/**/ {{0x3becbf7b, 0x2ef43882} },}, +/**/ {{{0x3fe3c000, 0x04934fec} }, +/**/ {{0x3fe6b5a1, 0x2cc07d75} }, +/**/ {{0x3ff68baf, 0x10b02ef8} }, +/**/ {{0xbbe7c8fb, 0xfeb7cabd} },}, +/**/ {{{0x3fe3e000, 0x03f5cf7f} }, +/**/ {{0x3fe6e5e1, 0x3e59def6} }, +/**/ {{0x3ff65c2d, 0x0e61500f} }, +/**/ {{0xbbe30ba4, 0x035f7845} },}, +/**/ {{{0x3fe40000, 0x05280ad9} }, +/**/ {{0x3fe71666, 0x91ab4c3e} }, +/**/ {{0x3ff62d2f, 0x19f01c90} }, +/**/ {{0xbbf1e9f5, 0xffe95f6a} },}, +/**/ {{{0x3fe42000, 0x049efb65} }, +/**/ {{0x3fe74732, 0x18af3b9d} }, +/**/ {{0x3ff5feb2, 0xb86465e4} }, +/**/ {{0x3bc4cad7, 0x280d591e} },}, +/**/ {{{0x3fe44000, 0x0035ccb6} }, +/**/ {{0x3fe77844, 0xcb4ff1e5} }, +/**/ {{0x3ff5d0b5, 0x7c455428} }, +/**/ {{0x3bed8c18, 0x7ba5617c} },}, +/**/ {{{0x3fe46000, 0x03346717} }, +/**/ {{0x3fe7a99f, 0xba258778} }, +/**/ {{0x3ff5a334, 0xf4392254} }, +/**/ {{0xbbefd14a, 0xfc84a570} },}, +/**/ {{{0x3fe48000, 0x03002575} }, +/**/ {{0x3fe7db43, 0xd836768f} }, +/**/ {{0x3ff5762e, 0xdcf97e0c} }, +/**/ {{0xbbdd7eba, 0x5f5df49e} },}, +/**/ {{{0x3fe4a000, 0x055bf381} }, +/**/ {{0x3fe80d32, 0x35edeefa} }, +/**/ {{0x3ff549a0, 0xea46e31f} }, +/**/ {{0xbbdba522, 0x76823eac} },}, +/**/ {{{0x3fe4c000, 0x04ce10e3} }, +/**/ {{0x3fe83f6b, 0xd67dc1a8} }, +/**/ {{0x3ff51d88, 0xed82bcc4} }, +/**/ {{0xbbeae92d, 0x077d29ea} },}, +/**/ {{{0x3fe4e000, 0x016c60e1} }, +/**/ {{0x3fe871f1, 0xca0aaf31} }, +/**/ {{0x3ff4f1e4, 0xbdacbf16} }, +/**/ {{0x3be82958, 0x46ee425e} },}, +/**/ {{{0x3fe4ffff, 0xff966f0a} }, +/**/ {{0x3fe8a4c5, 0x2bff2dae} }, +/**/ {{0x3ff4c6b2, 0x3917657e} }, +/**/ {{0xbbf127c2, 0x5c86c705} },}, +/**/ {{{0x3fe52000, 0x0076e6eb} }, +/**/ {{0x3fe8d7e7, 0x175651e8} }, +/**/ {{0x3ff49bef, 0x4f459b05} }, +/**/ {{0xbbb1e9d1, 0x4181bbfc} },}, +/**/ {{{0x3fe54000, 0x03d12d3b} }, +/**/ {{0x3fe90b58, 0xa976ed56} }, +/**/ {{0x3ff47199, 0xfdf24af4} }, +/**/ {{0x3be38c17, 0xc30decaf} },}, +/**/ {{{0x3fe55fff, 0xfce7fa8d} }, +/**/ {{0x3fe93f1a, 0xf03a3a09} }, +/**/ {{0x3ff447b0, 0x5f13234b} }, +/**/ {{0x3bf1b8b2, 0x70df7e20} },}, +/**/ {{{0x3fe58000, 0x0331b46a} }, +/**/ {{0x3fe9732f, 0x38e83134} }, +/**/ {{0x3ff41e30, 0x68d8b41b} }, +/**/ {{0xbbee24d8, 0xb90bc28b} },}, +/**/ {{{0x3fe59fff, 0xfc14848e} }, +/**/ {{0x3fe9a796, 0x8471b489} }, +/**/ {{0x3ff3f518, 0x5de3aa73} }, +/**/ {{0xbbecacd9, 0xe0761536} },}, +/**/ {{{0x3fe5bfff, 0xfb7cd395} }, +/**/ {{0x3fe9dc52, 0x24a8b955} }, +/**/ {{0x3ff3cc66, 0x4f8fff15} }, +/**/ {{0xbbf67c97, 0x82045611} },}, +/**/ {{{0x3fe5e000, 0x000dcc40} }, +/**/ {{0x3fea1163, 0x4df5b93e} }, +/**/ {{0x3ff3a418, 0x75853228} }, +/**/ {{0xbbf585da, 0xd481f350} },}, +/**/ {{{0x3fe60000, 0x02efd2fc} }, +/**/ {{0x3fea46cb, 0x30d16323} }, +/**/ {{0x3ff37c2d, 0x187962ae} }, +/**/ {{0x3bf004c3, 0xa5f77bb0} },}, +/**/ {{{0x3fe61fff, 0xfeb8088a} }, +/**/ {{0x3fea7c8b, 0x053920c0} }, +/**/ {{0x3ff354a2, 0x891769a9} }, +/**/ {{0x3bbc6b30, 0x3fee3029} },}, +/**/ {{{0x3fe64000, 0x00f3ca06} }, +/**/ {{0x3feab2a4, 0x28a1911a} }, +/**/ {{0x3ff32d77, 0x0a6f0a4a} }, +/**/ {{0x3bf2a6f8, 0xfac5081a} },}, +/**/ {{{0x3fe65fff, 0xfe9ec2f4} }, +/**/ {{0x3feae917, 0xd4ce7239} }, +/**/ {{0x3ff306a9, 0x0751a948} }, +/**/ {{0xbbe950b5, 0x51ab9dbd} },}, +/**/ {{{0x3fe68000, 0x03d43966} }, +/**/ {{0x3feb1fe7, 0x708b998a} }, +/**/ {{0x3ff2e036, 0xd7a153c7} }, +/**/ {{0x3bdd36e2, 0xa1e4a14e} },}, +/**/ {{{0x3fe69fff, 0xfab67783} }, +/**/ {{0x3feb5714, 0x2e575464} }, +/**/ {{0x3ff2ba1f, 0x05006cb6} }, +/**/ {{0x3bea9a4a, 0x473c2e31} },}, +/**/ {{{0x3fe6bfff, 0xfcb65f89} }, +/**/ {{0x3feb8e9f, 0x981efd2f} }, +/**/ {{0x3ff2945f, 0xe948d9f7} }, +/**/ {{0xbbca5294, 0xe802df72} },}, +/**/ {{{0x3fe6dfff, 0xfc5609a9} }, +/**/ {{0x3febc68a, 0xfaed6ff1} }, +/**/ {{0x3ff26ef8, 0x1533411e} }, +/**/ {{0xbbf89153, 0xf51bc566} },}, +/**/ {{{0x3fe6ffff, 0xfc4eef86} }, +/**/ {{0x3febfed7, 0xc62205fe} }, +/**/ {{0x3ff249e6, 0x0e70978c} }, +/**/ {{0x3bc39021, 0xa2b9ff56} },}, +/**/ {{{0x3fe72000, 0x004d98b3} }, +/**/ {{0x3fec3787, 0x716968ad} }, +/**/ {{0x3ff22528, 0x61be7751} }, +/**/ {{0x3befc9c5, 0x74ee2211} },}, +/**/ {{{0x3fe73fff, 0xfc155075} }, +/**/ {{0x3fec709b, 0x5ec6fd4e} }, +/**/ {{0x3ff200bd, 0xb5d53311} }, +/**/ {{0x3be28a4d, 0xa269ae63} },}, +/**/ {{{0x3fe76000, 0x0498c203} }, +/**/ {{0x3fecaa15, 0x323d08c1} }, +/**/ {{0x3ff1dca4, 0x93433f65} }, +/**/ {{0x3bf8cae4, 0x14a28fb7} },}, +/**/ {{{0x3fe77fff, 0xff1e5636} }, +/**/ {{0x3fece3f6, 0x4147c12c} }, +/**/ {{0x3ff1b8db, 0xbfe294a8} }, +/**/ {{0xbbe7e19c, 0x4b56a744} },}, +/**/ {{{0x3fe7a000, 0x0226d45a} }, +/**/ {{0x3fed1e40, 0x4120eb7f} }, +/**/ {{0x3ff19561, 0xd15f8278} }, +/**/ {{0x3be64b28, 0x032c5d4c} },}, +/**/ {{{0x3fe7c000, 0x0250a5aa} }, +/**/ {{0x3fed58f4, 0xb112a1e1} }, +/**/ {{0x3ff17235, 0x8a59d565} }, +/**/ {{0xbbe716de, 0xb8dc7867} },}, +/**/ {{{0x3fe7e000, 0x0482f82e} }, +/**/ {{0x3fed9415, 0x3576bdf0} }, +/**/ {{0x3ff14f55, 0xa22a1c5b} }, +/**/ {{0x3bf207e1, 0xe1305604} },}, +/**/ {{{0x3fe80000, 0x0205003e} }, +/**/ {{0x3fedcfa3, 0x64d69ff7} }, +/**/ {{0x3ff12cc0, 0xe37eb26f} }, +/**/ {{0xbbd52ec6, 0xe32395f8} },}, +/**/ {{{0x3fe81fff, 0xfbf99411} }, +/**/ {{0x3fee0ba0, 0xebf98f51} }, +/**/ {{0x3ff10a76, 0x16ddd5d6} }, +/**/ {{0xbbece0d6, 0x59866045} },}, +/**/ {{{0x3fe84000, 0x0248e3a3} }, +/**/ {{0x3fee480f, 0x9bb7f565} }, +/**/ {{0x3ff0e873, 0xfb84e05c} }, +/**/ {{0x3bf4e5e8, 0x1595df92} },}, +/**/ {{{0x3fe86000, 0x0145c157} }, +/**/ {{0x3fee84f1, 0x0a10b3ab} }, +/**/ {{0x3ff0c6b9, 0x7cbd7b1e} }, +/**/ {{0xbbe19de6, 0xd5f121d0} },}, +/**/ {{{0x3fe88000, 0x022631b9} }, +/**/ {{0x3feec247, 0x0be1f047} }, +/**/ {{0x3ff0a545, 0x6d0b3ee6} }, +/**/ {{0xbbc272b1, 0xa3ba2c6f} },}, +/**/ {{{0x3fe8a000, 0x045f7828} }, +/**/ {{0x3fef0013, 0x6c45ba1c} }, +/**/ {{0x3ff08416, 0xaf2a0f09} }, +/**/ {{0x3be82b56, 0x5b63c799} },}, +/**/ {{{0x3fe8bfff, 0xffc686cf} }, +/**/ {{0x3fef3e57, 0xf03c824b} }, +/**/ {{0x3ff0632c, 0x33502220} }, +/**/ {{0xbbd039ad, 0x2dbeeb25} },}, +/**/ {{{0x3fe8dfff, 0xfd8644c6} }, +/**/ {{0x3fef7d16, 0x8774261d} }, +/**/ {{0x3ff04284, 0xdd5b3019} }, +/**/ {{0x3bd79f33, 0xe1eba933} },}, +/**/ {{{0x3fe8ffff, 0xfe4e7937} }, +/**/ {{0x3fefbc51, 0x1a99a641} }, +/**/ {{0x3ff0221f, 0x9f69840b} }, +/**/ {{0xbbea9e84, 0x7beee018} },}, +/**/ {{{0x3fe92000, 0x0435251f} }, +/**/ {{0x3feffc09, 0x9eb22390} }, +/**/ {{0x3ff001fb, 0x6f7c51e8} }, +/**/ {{0xbb5a12e7, 0x31032e0a} },}, + }; + +#else +#ifdef LITTLE_ENDI +static const number + xfg[186][4] = { /* xi,Fi,Gi,FFi, i=16..201 */ +/**/ {{{0x1e519d60, 0x3fb00000} }, +/**/ {{0x96c4e240, 0x3fb00557} }, +/**/ {{0x628127b7, 0x402ff554} }, +/**/ {{0x9e355b06, 0xbb9a1dee} },}, +/**/ {{{0x1b1a7010, 0x3fb10000} }, +/**/ {{0xaab892b7, 0x3fb10668} }, +/**/ {{0xbe3fdf74, 0x402e12c7} }, +/**/ {{0x037da741, 0x3ba89234} },}, +/**/ {{{0x2505e350, 0x3fb20000} }, +/**/ {{0xff547824, 0x3fb2079b} }, +/**/ {{0xde853633, 0x402c65c5} }, +/**/ {{0xe9614250, 0x3bb7486e} },}, +/**/ {{{0xfcdc4252, 0x3fb2ffff} }, +/**/ {{0x5eb16c68, 0x3fb308f3} }, +/**/ {{0xe56be74f, 0x402ae5da} }, +/**/ {{0x91a23034, 0xbb82c726} },}, +/**/ {{{0xe3ff849f, 0x3fb3ffff} }, +/**/ {{0x154999cc, 0x3fb40a71} }, +/**/ {{0x046b7352, 0x40298c43} }, +/**/ {{0x3843738f, 0x3b9aceaf} },}, +/**/ {{{0xedc9590f, 0x3fb4ffff} }, +/**/ {{0x429bdd80, 0x3fb50c17} }, +/**/ {{0x91b5d674, 0x40285384} }, +/**/ {{0xb4403d22, 0xbbc1d02d} },}, +/**/ {{{0x00ee83f7, 0x3fb60000} }, +/**/ {{0xda80cc21, 0x3fb60de7} }, +/**/ {{0xef21a2a7, 0x40273724} }, +/**/ {{0x72523ffd, 0xbb95e53c} },}, +/**/ {{{0xeb05ea41, 0x3fb6ffff} }, +/**/ {{0xb8c51bea, 0x3fb70fe4} }, +/**/ {{0xfae562ff, 0x40263370} }, +/**/ {{0x8ffe0626, 0xbb99ad0e} },}, +/**/ {{{0xdc0515f7, 0x3fb7ffff} }, +/**/ {{0x1db54498, 0x3fb81210} }, +/**/ {{0x0e7eab5c, 0x40254553} }, +/**/ {{0xd62ed686, 0xbb914c87} },}, +/**/ {{{0xe384d7ab, 0x3fb8ffff} }, +/**/ {{0x2a8d3727, 0x3fb9146c} }, +/**/ {{0xfd57f3fd, 0x40246a33} }, +/**/ {{0x5381e06d, 0xbbbbda8d} },}, +/**/ {{{0xe4832347, 0x3fb9ffff} }, +/**/ {{0xd50e1050, 0x3fba16fa} }, +/**/ {{0xc5537a96, 0x40239fe2} }, +/**/ {{0xc111eabb, 0x3bc7f695} },}, +/**/ {{{0x274540e3, 0x3fbb0000} }, +/**/ {{0x7ae68517, 0x3fbb19be} }, +/**/ {{0x3637e946, 0x4022e481} }, +/**/ {{0x8dbd9d93, 0x3bc307f8} },}, +/**/ {{{0xfebf2e9b, 0x3fbbffff} }, +/**/ {{0x8369cd19, 0x3fbc1cb8} }, +/**/ {{0x17aef223, 0x40223676} }, +/**/ {{0x424a9cf3, 0x3bc50038} },}, +/**/ {{{0x23529045, 0x3fbd0000} }, +/**/ {{0xc11d7ef7, 0x3fbd1feb} }, +/**/ {{0xb8e43d4e, 0x4021945f} }, +/**/ {{0x52a6f224, 0x3b812007} },}, +/**/ {{{0xd872a829, 0x3fbdffff} }, +/**/ {{0x8ee4d6b7, 0x3fbe2359} }, +/**/ {{0x76195d5f, 0x4020fd0c} }, +/**/ {{0x85fdca85, 0xbbb4d9ab} },}, +/**/ {{{0xff323b84, 0x3fbeffff} }, +/**/ {{0xec9073e5, 0x3fbf2704} }, +/**/ {{0x3020200f, 0x40206f71} }, +/**/ {{0x12836992, 0x3bb77aa2} },}, +/**/ {{{0x0ce79195, 0x3fc00000} }, +/**/ {{0xbc30cc61, 0x3fc01577} }, +/**/ {{0xd6564a88, 0x401fd549} }, +/**/ {{0x965c0ad0, 0xbbc8926f} },}, +/**/ {{{0xee40e918, 0x3fc07fff} }, +/**/ {{0x8279ac01, 0x3fc0978d} }, +/**/ {{0x9294bc03, 0x401edbb5} }, +/**/ {{0x4aae45d6, 0xbb80a533} },}, +/**/ {{{0x0cc091fd, 0x3fc10000} }, +/**/ {{0x44dfb2f7, 0x3fc119c5} }, +/**/ {{0x067d8e18, 0x401df0bb} }, +/**/ {{0x4ff642a4, 0xbbcc2c18} },}, +/**/ {{{0x0d9936a1, 0x3fc18000} }, +/**/ {{0xb9085a4b, 0x3fc19c1f} }, +/**/ {{0x71ce3629, 0x401d131a} }, +/**/ {{0x0669355b, 0xbbc36553} },}, +/**/ {{{0xed5f3188, 0x3fc1ffff} }, +/**/ {{0xee74bf2d, 0x3fc21e9d} }, +/**/ {{0xff0cd655, 0x401c41b6} }, +/**/ {{0x478ecfc5, 0x3b8867f5} },}, +/**/ {{{0x05f06a51, 0x3fc28000} }, +/**/ {{0x550b313f, 0x3fc2a141} }, +/**/ {{0x1702e6d2, 0x401b7b92} }, +/**/ {{0x380131fe, 0xbbadab51} },}, +/**/ {{{0xfe3d339e, 0x3fc2ffff} }, +/**/ {{0xa75f76df, 0x3fc3240a} }, +/**/ {{0xfcb6409d, 0x401abfc8} }, +/**/ {{0x0d291d83, 0x3bc60bcf} },}, +/**/ {{{0xed888d6f, 0x3fc37fff} }, +/**/ {{0x13cc5db7, 0x3fc3a6fb} }, +/**/ {{0x8ed5320d, 0x401a0d8f} }, +/**/ {{0x4eef03ab, 0x3bb8a48e} },}, +/**/ {{{0x02ca050d, 0x3fc40000} }, +/**/ {{0xe25776bb, 0x3fc42a13} }, +/**/ {{0xfa84c2bc, 0x4019642d} }, +/**/ {{0xcc56516f, 0xbbd0bd5d} },}, +/**/ {{{0xf2531f5c, 0x3fc47fff} }, +/**/ {{0xdeb73404, 0x3fc4ad55} }, +/**/ {{0xf86e9035, 0x4018c2fe} }, +/**/ {{0x5aa287c8, 0x3b9cffe7} },}, +/**/ {{{0x13774992, 0x3fc50000} }, +/**/ {{0x7d0ee307, 0x3fc530c2} }, +/**/ {{0x370caf35, 0x4018296c} }, +/**/ {{0xf91d6532, 0xbbcf75d1} },}, +/**/ {{{0xedddcb2d, 0x3fc57fff} }, +/**/ {{0x5db4347d, 0x3fc5b45a} }, +/**/ {{0x52190c0e, 0x401796ee} }, +/**/ {{0x17d5d076, 0x3b88a25f} },}, +/**/ {{{0xf41949a0, 0x3fc5ffff} }, +/**/ {{0x13bf986a, 0x3fc6381f} }, +/**/ {{0x2d2255fd, 0x40170b09} }, +/**/ {{0xb1bcd5e7, 0xbb9bfb23} },}, +/**/ {{{0xf834d3a1, 0x3fc67fff} }, +/**/ {{0x8ec85952, 0x3fc6bc11} }, +/**/ {{0x62cf2268, 0x4016854c} }, +/**/ {{0x82e39e04, 0x3b9ee53b} },}, +/**/ {{{0xfd9106ea, 0x3fc6ffff} }, +/**/ {{0xf298f6f7, 0x3fc74032} }, +/**/ {{0x1f4f84a9, 0x40160551} }, +/**/ {{0x112634b8, 0xbbb59c4a} },}, +/**/ {{{0x0f649a4f, 0x3fc78000} }, +/**/ {{0x6ca53abc, 0x3fc7c484} }, +/**/ {{0x4809d175, 0x40158ab9} }, +/**/ {{0x73d3cd2e, 0x3bc91c75} },}, +/**/ {{{0xef06bbd8, 0x3fc7ffff} }, +/**/ {{0xdf7d76ad, 0x3fc84906} }, +/**/ {{0xdd2b30a6, 0x4015152e} }, +/**/ {{0x084c3eef, 0xbbbfa2da} },}, +/**/ {{{0x021c6334, 0x3fc88000} }, +/**/ {{0xd965f986, 0x3fc8cdbb} }, +/**/ {{0x51b74296, 0x4014a462} }, +/**/ {{0x74dcfe0b, 0xbb9ec02e} },}, +/**/ {{{0xf38d0756, 0x3fc8ffff} }, +/**/ {{0x28e173c7, 0x3fc952a4} }, +/**/ {{0x17b59ebd, 0x4014380b} }, +/**/ {{0xb77589f0, 0xbbcd0f1c} },}, +/**/ {{{0x104efca1, 0x3fc98000} }, +/**/ {{0x4644d23c, 0x3fc9d7c1} }, +/**/ {{0xcb1eabd5, 0x4013cfe5} }, +/**/ {{0xea188d9e, 0xbbd5d6f7} },}, +/**/ {{{0x09417b30, 0x3fca0000} }, +/**/ {{0x096d76aa, 0x3fca5d14} }, +/**/ {{0xb3723db0, 0x40136bb4} }, +/**/ {{0xfbf3979c, 0x3bbe3e0d} },}, +/**/ {{{0xeb1c23ec, 0x3fca7fff} }, +/**/ {{0xab60288d, 0x3fcae29d} }, +/**/ {{0x783071d7, 0x40130b3e} }, +/**/ {{0x3d5384bf, 0xbbc7dd82} },}, +/**/ {{{0xfb171c13, 0x3fcaffff} }, +/**/ {{0xa221a96b, 0x3fcb685f} }, +/**/ {{0xd8c0747d, 0x4012ae4d} }, +/**/ {{0xd5554972, 0x3bd4644b} },}, +/**/ {{{0x0aba44be, 0x3fcb8000} }, +/**/ {{0xecdf241f, 0x3fcbee5a} }, +/**/ {{0xc6fad63b, 0x401254b1} }, +/**/ {{0xd092b85a, 0x3ba41916} },}, +/**/ {{{0x113d2a3e, 0x3fcc0000} }, +/**/ {{0xb3e92543, 0x3fcc7490} }, +/**/ {{0x9a62c035, 0x4011fe3c} }, +/**/ {{0x41a03739, 0xbba3cc39} },}, +/**/ {{{0xf49e00ce, 0x3fcc7fff} }, +/**/ {{0x0f59eab0, 0x3fccfb02} }, +/**/ {{0xe956a631, 0x4011aac3} }, +/**/ {{0xbfa8cb5b, 0xbbb7a383} },}, +/**/ {{{0x05f611ab, 0x3fcd0000} }, +/**/ {{0x89e6844e, 0x3fcd81b0} }, +/**/ {{0xf391268d, 0x40115a1f} }, +/**/ {{0xb2dc91f3, 0x3bd39b5c} },}, +/**/ {{{0x14764ceb, 0x3fcd8000} }, +/**/ {{0x27debf0d, 0x3fce089d} }, +/**/ {{0xfbc84740, 0x40110c2b} }, +/**/ {{0x84712510, 0x3bc14d4d} },}, +/**/ {{{0x14bcea76, 0x3fce0000} }, +/**/ {{0x16dbc820, 0x3fce8fc9} }, +/**/ {{0xa00ca48e, 0x4010c0c5} }, +/**/ {{0x640f1b9e, 0xbbd33788} },}, +/**/ {{{0xfd7995bd, 0x3fce7fff} }, +/**/ {{0x88b50424, 0x3fcf1735} }, +/**/ {{0xbe02169a, 0x401077cc} }, +/**/ {{0x221fdf77, 0xbbb61fee} },}, +/**/ {{{0x0cc35436, 0x3fcf0000} }, +/**/ {{0xfd21a40b, 0x3fcf9ee3} }, +/**/ {{0x1ee7ffe8, 0x40103123} }, +/**/ {{0xc79ff5c1, 0x3bd427e3} },}, +/**/ {{{0x01d1da33, 0x3fcf8000} }, +/**/ {{0xb7dbe15c, 0x3fd0136a} }, +/**/ {{0x77d559e5, 0x400fd959} }, +/**/ {{0xd67948d7, 0x3bb0c6a1} },}, +/**/ {{{0x060c13b2, 0x3fd00000} }, +/**/ {{0xaaad4f18, 0x3fd05785} }, +/**/ {{0x2675d182, 0x400f549e} }, +/**/ {{0x18f0dd10, 0xbbc15208} },}, +/**/ {{{0x03885492, 0x3fd04000} }, +/**/ {{0x660542d7, 0x3fd09bc3} }, +/**/ {{0xdf3f5fec, 0x400ed3e2} }, +/**/ {{0xb883ae62, 0xbbd95657} },}, +/**/ {{{0x052f5a13, 0x3fd08000} }, +/**/ {{0x9a195045, 0x3fd0e024} }, +/**/ {{0xfa68f2c8, 0x400e56f8} }, +/**/ {{0x5a543e8e, 0x3bded7ba} },}, +/**/ {{{0x02ba1af5, 0x3fd0c000} }, +/**/ {{0xe2e7f24b, 0x3fd124a9} }, +/**/ {{0xbffe633f, 0x400dddb4} }, +/**/ {{0x0c60278f, 0xbbdcba86} },}, +/**/ {{{0xf76642c1, 0x3fd0ffff} }, +/**/ {{0xe162ffe6, 0x3fd16953} }, +/**/ {{0x0311d5d5, 0x400d67ed} }, +/**/ {{0xe40c5f9e, 0x3b7b1f4a} },}, +/**/ {{{0x033602f0, 0x3fd14000} }, +/**/ {{0x5f49508e, 0x3fd1ae23} }, +/**/ {{0xb8708266, 0x400cf57a} }, +/**/ {{0x8620f301, 0xbbd6a6c2} },}, +/**/ {{{0xfefd1a13, 0x3fd17fff} }, +/**/ {{0xdb2a9ba1, 0x3fd1f318} }, +/**/ {{0x8d11009e, 0x400c8639} }, +/**/ {{0x69b21d3b, 0x3bd3a9c6} },}, +/**/ {{{0xf718365d, 0x3fd1bfff} }, +/**/ {{0x0c41e3ac, 0x3fd23835} }, +/**/ {{0xe02be47c, 0x400c1a06} }, +/**/ {{0x129e8cd1, 0x3bdb961a} },}, +/**/ {{{0xff001e00, 0x3fd1ffff} }, +/**/ {{0xb2f6395e, 0x3fd27d78} }, +/**/ {{0xf2fe9a85, 0x400bb0c1} }, +/**/ {{0xe68fd7d8, 0x3be074a9} },}, +/**/ {{{0xfe425a6a, 0x3fd23fff} }, +/**/ {{0x618faabe, 0x3fd2c2e4} }, +/**/ {{0x190b18df, 0x400b4a4c} }, +/**/ {{0xf615aad1, 0xbbdf0d1f} },}, +/**/ {{{0x059ec1db, 0x3fd28000} }, +/**/ {{0xd8583884, 0x3fd30878} }, +/**/ {{0x0cd82bc2, 0x400ae688} }, +/**/ {{0x141c1f8d, 0xbbd563c3} },}, +/**/ {{{0x000dd081, 0x3fd2c000} }, +/**/ {{0xaffdb6d8, 0x3fd34e36} }, +/**/ {{0x5270fc15, 0x400a855a} }, +/**/ {{0x9f2cdafd, 0xbbc6d88d} },}, +/**/ {{{0xfc1dcd2b, 0x3fd2ffff} }, +/**/ {{0xa95875bc, 0x3fd3941e} }, +/**/ {{0xaa9502b6, 0x400a26a8} }, +/**/ {{0x8389b15c, 0xbbe13cad} },}, +/**/ {{{0xf6c0d4a0, 0x3fd33fff} }, +/**/ {{0x739845f5, 0x3fd3da31} }, +/**/ {{0x4d2573a0, 0x4009ca5a} }, +/**/ {{0xacaee379, 0xbbc71636} },}, +/**/ {{{0x06b16793, 0x3fd38000} }, +/**/ {{0xdbc088f0, 0x3fd4206f} }, +/**/ {{0x9344e33a, 0x40097057} }, +/**/ {{0x1d7a4f81, 0xbbc2c052} },}, +/**/ {{{0x07358fa3, 0x3fd3c000} }, +/**/ {{0x6f23311d, 0x3fd466da} }, +/**/ {{0x5aa612ea, 0x4009188a} }, +/**/ {{0x685e8edc, 0x3b8653a5} },}, +/**/ {{{0xfc3b18cf, 0x3fd3ffff} }, +/**/ {{0xe9282e6b, 0x3fd4ad71} }, +/**/ {{0x641e643d, 0x4008c2dd} }, +/**/ {{0x3f567c64, 0x3b95f0ef} },}, +/**/ {{{0x000dd2a8, 0x3fd44000} }, +/**/ {{0x1fa3f2d1, 0x3fd4f437} }, +/**/ {{0x6072f821, 0x40086f3c} }, +/**/ {{0x95ff68b5, 0x3bb68efa} },}, +/**/ {{{0xfbb43713, 0x3fd47fff} }, +/**/ {{0xb3ac333c, 0x3fd53b2a} }, +/**/ {{0x3da56692, 0x40081d94} }, +/**/ {{0x2985fd3f, 0xbbbf4d7f} },}, +/**/ {{{0xfb113bf4, 0x3fd4bfff} }, +/**/ {{0x6e8ed9c2, 0x3fd5824d} }, +/**/ {{0xa8add00f, 0x4007cdd2} }, +/**/ {{0x1c9b3657, 0x3bcf478a} },}, +/**/ {{{0xf7f087c9, 0x3fd4ffff} }, +/**/ {{0x07446496, 0x3fd5c9a0} }, +/**/ {{0x444588eb, 0x40077fe6} }, +/**/ {{0xa4eabb0c, 0xbbc177dc} },}, +/**/ {{{0x088b3814, 0x3fd54000} }, +/**/ {{0x564125f9, 0x3fd61123} }, +/**/ {{0x6281a765, 0x400733be} }, +/**/ {{0xf57051c4, 0xbbc2c52c} },}, +/**/ {{{0xf7d55966, 0x3fd57fff} }, +/**/ {{0xe194a5d5, 0x3fd658d7} }, +/**/ {{0x73b47d1f, 0x4006e94b} }, +/**/ {{0xf9996dc6, 0x3bda2fcf} },}, +/**/ {{{0x08bf2490, 0x3fd5c000} }, +/**/ {{0xb775b28d, 0x3fd6a0be} }, +/**/ {{0x15b6ec28, 0x4006a07e} }, +/**/ {{0xaa5285b8, 0xbbe0ca90} },}, +/**/ {{{0x09fa853f, 0x3fd60000} }, +/**/ {{0x65a66cfd, 0x3fd6e8d8} }, +/**/ {{0x1c701269, 0x40065948} }, +/**/ {{0x8591e13a, 0x3bd9ea95} },}, +/**/ {{{0x07595fca, 0x3fd64000} }, +/**/ {{0xc0556a7c, 0x3fd73125} }, +/**/ {{0xbaae9d02, 0x4006139b} }, +/**/ {{0x40152b83, 0x3bd88aff} },}, +/**/ {{{0x031687da, 0x3fd68000} }, +/**/ {{0x92e2cfd0, 0x3fd779a7} }, +/**/ {{0xcae0882b, 0x4005cf6b} }, +/**/ {{0x9f439451, 0xbbd8a4a2} },}, +/**/ {{{0xf5c8cfe2, 0x3fd6bfff} }, +/**/ {{0x9fb452ed, 0x3fd7c25e} }, +/**/ {{0xc561f1cd, 0x40058cab} }, +/**/ {{0xf6a37d74, 0xbbe371a6} },}, +/**/ {{{0xf81df231, 0x3fd6ffff} }, +/**/ {{0xcfb4dab5, 0x3fd80b4b} }, +/**/ {{0x8d3ca5d3, 0x40054b4f} }, +/**/ {{0x679dc99f, 0x3bcb4686} },}, +/**/ {{{0xfa71385e, 0x3fd73fff} }, +/**/ {{0xe007a9b6, 0x3fd8546f} }, +/**/ {{0xb3b22176, 0x40050b4b} }, +/**/ {{0xa5c73477, 0xbbcd1540} },}, +/**/ {{{0x024a9c2b, 0x3fd78000} }, +/**/ {{0xa7fcf5cf, 0x3fd89dcb} }, +/**/ {{0x3159cbe1, 0x4004cc95} }, +/**/ {{0xd58a6ad0, 0xbbdc25ea} },}, +/**/ {{{0x02eb62b8, 0x3fd7c000} }, +/**/ {{0xec0ba5cf, 0x3fd8e75f} }, +/**/ {{0x8731eeea, 0x40048f21} }, +/**/ {{0xcc1adafb, 0xbbc1cb73} },}, +/**/ {{{0x054a52d1, 0x3fd80000} }, +/**/ {{0x8bb822e9, 0x3fd9312d} }, +/**/ {{0x9170a729, 0x400452e6} }, +/**/ {{0xeac002ee, 0xbbd8bb17} },}, +/**/ {{{0xf93a00a3, 0x3fd83fff} }, +/**/ {{0x4bb9ad2a, 0x3fd97b35} }, +/**/ {{0xae924e7f, 0x400417da} }, +/**/ {{0x9a378cc7, 0x3bd4b800} },}, +/**/ {{{0xfbdc91c1, 0x3fd87fff} }, +/**/ {{0x2771b601, 0x3fd9c578} }, +/**/ {{0x78855799, 0x4003ddf4} }, +/**/ {{0xa00445d9, 0x3bd9077d} },}, +/**/ {{{0xf6d215e6, 0x3fd8bfff} }, +/**/ {{0xe0ea4a0b, 0x3fda0ff6} }, +/**/ {{0x189a0989, 0x4003a52b} }, +/**/ {{0x89c0613d, 0xbbda6831} },}, +/**/ {{{0x02f734ef, 0x3fd90000} }, +/**/ {{0x736bf579, 0x3fda5ab2} }, +/**/ {{0xe9244ca6, 0x40036d75} }, +/**/ {{0x4b722377, 0x3be3a6d8} },}, +/**/ {{{0x04eef8b4, 0x3fd94000} }, +/**/ {{0x9fb6e3d0, 0x3fdaa5ab} }, +/**/ {{0xc9089cb7, 0x400336cc} }, +/**/ {{0x22cc00bb, 0x3b9f6963} },}, +/**/ {{{0x041ec76a, 0x3fd98000} }, +/**/ {{0x5176c7e4, 0x3fdaf0e3} }, +/**/ {{0xcb0b9506, 0x40030127} }, +/**/ {{0x5385a849, 0x3bb1ffdb} },}, +/**/ {{{0x08044e47, 0x3fd9c000} }, +/**/ {{0x77071224, 0x3fdb3c5a} }, +/**/ {{0x50d75ec7, 0x4002cc7f} }, +/**/ {{0x78effc8a, 0xbbb0fade} },}, +/**/ {{{0x01f8235b, 0x3fda0000} }, +/**/ {{0xe725782e, 0x3fdb8811} }, +/**/ {{0x18fbfb37, 0x400298cc} }, +/**/ {{0x3b50e71b, 0xbbe55ed3} },}, +/**/ {{{0xfb8c6f08, 0x3fda3fff} }, +/**/ {{0x97b086f3, 0x3fdbd40a} }, +/**/ {{0x154de04b, 0x40026607} }, +/**/ {{0x455faae3, 0xbbdec65e} },}, +/**/ {{{0xfb3d63e1, 0x3fda7fff} }, +/**/ {{0x7d9a3b8a, 0x3fdc2045} }, +/**/ {{0x7e60bfbb, 0x40023429} }, +/**/ {{0x154ebd33, 0x3be3001c} },}, +/**/ {{{0xf5f45c48, 0x3fdabfff} }, +/**/ {{0x7b8d45e6, 0x3fdc6cc3} }, +/**/ {{0xdb1ace69, 0x4002032c} }, +/**/ {{0x3ed33616, 0xbbe5ebf8} },}, +/**/ {{{0x0508b34c, 0x3fdb0000} }, +/**/ {{0xa27e8d37, 0x3fdcb985} }, +/**/ {{0xd4459a2b, 0x4001d30a} }, +/**/ {{0xae61e2d1, 0xbbd01432} },}, +/**/ {{{0x0a84710c, 0x3fdb4000} }, +/**/ {{0xc3e50155, 0x3fdd068c} }, +/**/ {{0x775034dd, 0x4001a3bd} }, +/**/ {{0x58e0e228, 0xbbe80b1e} },}, +/**/ {{{0xf692e9d8, 0x3fdb7fff} }, +/**/ {{0xc49d6627, 0x3fdd53d9} }, +/**/ {{0xfe18066a, 0x4001753e} }, +/**/ {{0xf760d33e, 0xbbb004c8} },}, +/**/ {{{0x0280f14d, 0x3fdbc000} }, +/**/ {{0xe4e81013, 0x3fdda16d} }, +/**/ {{0xa38ea052, 0x40014789} }, +/**/ {{0x27c9c4ea, 0x3be848bc} },}, +/**/ {{{0x001121d1, 0x3fdc0000} }, +/**/ {{0xeac018f0, 0x3fddef49} }, +/**/ {{0x20b8be0c, 0x40011a98} }, +/**/ {{0xd0d6010e, 0xbbe1527e} },}, +/**/ {{{0xfef662aa, 0x3fdc3fff} }, +/**/ {{0xea0c7070, 0x3fde3d6e} }, +/**/ {{0x32f46ccd, 0x4000ee65} }, +/**/ {{0x189a000d, 0x3be8d241} },}, +/**/ {{{0x09845818, 0x3fdc8000} }, +/**/ {{0xf36a8b1b, 0x3fde8bdd} }, +/**/ {{0xcac73476, 0x4000c2eb} }, +/**/ {{0x12bed284, 0x3bd221f7} },}, +/**/ {{{0xfb0493bf, 0x3fdcbfff} }, +/**/ {{0xe0c60d10, 0x3fdeda97} }, +/**/ {{0x251c7836, 0x40009827} }, +/**/ {{0x6eec41b7, 0xbbe0bd54} },}, +/**/ {{{0xfd52961f, 0x3fdcffff} }, +/**/ {{0xefb3e44b, 0x3fdf299d} }, +/**/ {{0x74e459f5, 0x40006e12} }, +/**/ {{0xe969c82f, 0xbbd93f77} },}, +/**/ {{{0xfe2319a4, 0x3fdd3fff} }, +/**/ {{0x17139490, 0x3fdf78f1} }, +/**/ {{0x3e737e94, 0x400044a9} }, +/**/ {{0x49594b7a, 0xbb91e7cc} },}, +/**/ {{{0xfa4de596, 0x3fdd7fff} }, +/**/ {{0x638f49e8, 0x3fdfc892} }, +/**/ {{0x231057a5, 0x40001be7} }, +/**/ {{0xf5af9f5f, 0x3bd482b0} },}, +/**/ {{{0xfe729a69, 0x3fddbfff} }, +/**/ {{0x7c6ab019, 0x3fe00c41} }, +/**/ {{0xbf612660, 0x3fffe78f} }, +/**/ {{0x00da681e, 0x3bea5cda} },}, +/**/ {{{0x09d66802, 0x3fde0000} }, +/**/ {{0xf6b883cf, 0x3fe03461} }, +/**/ {{0xbc05a87c, 0x3fff988e} }, +/**/ {{0xf2372669, 0xbbe06c33} },}, +/**/ {{{0xfb211657, 0x3fde3fff} }, +/**/ {{0x191db8e8, 0x3fe05cab} }, +/**/ {{0x7bcfe6be, 0x3fff4ac3} }, +/**/ {{0x5ed8d35b, 0xbbd5d51f} },}, +/**/ {{{0x0a3f068a, 0x3fde8000} }, +/**/ {{0x95fb54f0, 0x3fe0851d} }, +/**/ {{0x144ca408, 0x3ffefe26} }, +/**/ {{0xa2c169c5, 0xbbc7c894} },}, +/**/ {{{0x01adb060, 0x3fdec000} }, +/**/ {{0xdc7b54f9, 0x3fe0adb9} }, +/**/ {{0x5ebe52a7, 0x3ffeb2af} }, +/**/ {{0x312c5ffd, 0x3bd4e740} },}, +/**/ {{{0xff5c0d01, 0x3fdeffff} }, +/**/ {{0x92550a8d, 0x3fe0d680} }, +/**/ {{0x0d71fdf0, 0x3ffe6858} }, +/**/ {{0x96b35499, 0x3bddd8a6} },}, +/**/ {{{0xf93d5fcc, 0x3fdf3fff} }, +/**/ {{0x45cb4374, 0x3fe0ff72} }, +/**/ {{0x3cce5040, 0x3ffe1f19} }, +/**/ {{0x7c1efab4, 0xbbc9f0ec} },}, +/**/ {{{0xfa0dd18f, 0x3fdf7fff} }, +/**/ {{0x944dd508, 0x3fe1288f} }, +/**/ {{0x298b874d, 0x3ffdd6ec} }, +/**/ {{0x9642a0a6, 0x3bea6ebd} },}, +/**/ {{{0xfd3a9f1a, 0x3fdfbfff} }, +/**/ {{0x13750f3e, 0x3fe151d9} }, +/**/ {{0x5806a27e, 0x3ffd8fca} }, +/**/ {{0xfc65ac7a, 0x3bda2a03} },}, +/**/ {{{0xfc481400, 0x3fdfffff} }, +/**/ {{0x598944ca, 0x3fe17b4f} }, +/**/ {{0x82532170, 0x3ffd49ad} }, +/**/ {{0x3d236dc3, 0x3bc4412e} },}, +/**/ {{{0xff53786c, 0x3fe01fff} }, +/**/ {{0x07d83d47, 0x3fe1a4f3} }, +/**/ {{0x851bffeb, 0x3ffd048f} }, +/**/ {{0x29f81b14, 0x3bd1589d} },}, +/**/ {{{0xfee301b7, 0x3fe03fff} }, +/**/ {{0xb8a6a382, 0x3fe1cec4} }, +/**/ {{0x7c519db6, 0x3ffcc06a} }, +/**/ {{0x5b24d6b2, 0x3bd370e6} },}, +/**/ {{{0x006e36bf, 0x3fe06000} }, +/**/ {{0x114eb8be, 0x3fe1f8c5} }, +/**/ {{0xa34d6786, 0x3ffc7d38} }, +/**/ {{0x4b98c1d4, 0xbbea92de} },}, +/**/ {{{0xfd60aa43, 0x3fe07fff} }, +/**/ {{0xabeccecb, 0x3fe222f4} }, +/**/ {{0x77342ac4, 0x3ffc3af4} }, +/**/ {{0x03a5c2c2, 0xbbdd47f6} },}, +/**/ {{{0x037762e8, 0x3fe0a000} }, +/**/ {{0x3f99efe8, 0x3fe24d54} }, +/**/ {{0x75f54fab, 0x3ffbf998} }, +/**/ {{0x15771a46, 0x3bedf7f4} },}, +/**/ {{{0xff1c6921, 0x3fe0bfff} }, +/**/ {{0x598e35d0, 0x3fe277e4} }, +/**/ {{0x8addd186, 0x3ffbb91f} }, +/**/ {{0x5e0e5a73, 0x3be0f16c} },}, +/**/ {{{0xff07154b, 0x3fe0dfff} }, +/**/ {{0xb6bc3986, 0x3fe2a2a5} }, +/**/ {{0x8301646d, 0x3ffb7984} }, +/**/ {{0xbbaa5310, 0xbbf02dd0} },}, +/**/ {{{0x02fcdda4, 0x3fe10000} }, +/**/ {{0x02a59f1e, 0x3fe2cd99} }, +/**/ {{0x705219bf, 0x3ffb3ac2} }, +/**/ {{0x112fa616, 0xbbe59357} },}, +/**/ {{{0x01ce1140, 0x3fe12000} }, +/**/ {{0xdf0a67c2, 0x3fe2f8be} }, +/**/ {{0x9ab8ae2a, 0x3ffafcd4} }, +/**/ {{0x9303f346, 0x3be2c542} },}, +/**/ {{{0x04d0f355, 0x3fe14000} }, +/**/ {{0x08fcc7bf, 0x3fe32418} }, +/**/ {{0x497b9a36, 0x3ffabfb6} }, +/**/ {{0xb5a59234, 0x3bebc044} },}, +/**/ {{{0x00fb0c8a, 0x3fe16000} }, +/**/ {{0x2471618b, 0x3fe34fa5} }, +/**/ {{0x0d26d117, 0x3ffa8363} }, +/**/ {{0x3f7bb7c9, 0xbbdbfbb2} },}, +/**/ {{{0x026f10b3, 0x3fe18000} }, +/**/ {{0xf7579056, 0x3fe37b66} }, +/**/ {{0x6b4cf4b1, 0x3ffa47d6} }, +/**/ {{0xaf0b5de9, 0x3bf0f6b4} },}, +/**/ {{{0xfd0978f8, 0x3fe19fff} }, +/**/ {{0x290cc78c, 0x3fe3a75e} }, +/**/ {{0x36c21315, 0x3ffa0d0c} }, +/**/ {{0xa296b262, 0x3beb2129} },}, +/**/ {{{0xfd94840b, 0x3fe1bfff} }, +/**/ {{0x85b4e4a4, 0x3fe3d38b} }, +/**/ {{0x32f2ecef, 0x3ff9d300} }, +/**/ {{0xb9bb7d74, 0xbbdbab1a} },}, +/**/ {{{0xfbda1ea1, 0x3fe1dfff} }, +/**/ {{0xbf3cee2f, 0x3fe3ffef} }, +/**/ {{0x6770fed8, 0x3ff999ae} }, +/**/ {{0xb4ace9a4, 0x3bda0bdc} },}, +/**/ {{{0xfc989533, 0x3fe1ffff} }, +/**/ {{0x9c27900c, 0x3fe42c8b} }, +/**/ {{0xe0d9f1ac, 0x3ff96112} }, +/**/ {{0x2fa2d81a, 0xbbee19eb} },}, +/**/ {{{0x012b8d26, 0x3fe22000} }, +/**/ {{0xe11975ca, 0x3fe4595f} }, +/**/ {{0xcdaa4e80, 0x3ff92929} }, +/**/ {{0xacc82d4b, 0x3bf23382} },}, +/**/ {{{0x04f4d6af, 0x3fe24000} }, +/**/ {{0x4d224131, 0x3fe4866d} }, +/**/ {{0x815c34e8, 0x3ff8f1ef} }, +/**/ {{0x3b740a99, 0xbbd0c6ff} },}, +/**/ {{{0xfcc07bda, 0x3fe25fff} }, +/**/ {{0x98b7d010, 0x3fe4b3b4} }, +/**/ {{0x73e7ffa1, 0x3ff8bb60} }, +/**/ 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{{0xe802df72, 0xbbca5294} },}, +/**/ {{{0xfc5609a9, 0x3fe6dfff} }, +/**/ {{0xfaed6ff1, 0x3febc68a} }, +/**/ {{0x1533411e, 0x3ff26ef8} }, +/**/ {{0xf51bc566, 0xbbf89153} },}, +/**/ {{{0xfc4eef86, 0x3fe6ffff} }, +/**/ {{0xc62205fe, 0x3febfed7} }, +/**/ {{0x0e70978c, 0x3ff249e6} }, +/**/ {{0xa2b9ff56, 0x3bc39021} },}, +/**/ {{{0x004d98b3, 0x3fe72000} }, +/**/ {{0x716968ad, 0x3fec3787} }, +/**/ {{0x61be7751, 0x3ff22528} }, +/**/ {{0x74ee2211, 0x3befc9c5} },}, +/**/ {{{0xfc155075, 0x3fe73fff} }, +/**/ {{0x5ec6fd4e, 0x3fec709b} }, +/**/ {{0xb5d53311, 0x3ff200bd} }, +/**/ {{0xa269ae63, 0x3be28a4d} },}, +/**/ {{{0x0498c203, 0x3fe76000} }, +/**/ {{0x323d08c1, 0x3fecaa15} }, +/**/ {{0x93433f65, 0x3ff1dca4} }, +/**/ {{0x14a28fb7, 0x3bf8cae4} },}, +/**/ {{{0xff1e5636, 0x3fe77fff} }, +/**/ {{0x4147c12c, 0x3fece3f6} }, +/**/ {{0xbfe294a8, 0x3ff1b8db} }, +/**/ {{0x4b56a744, 0xbbe7e19c} },}, +/**/ {{{0x0226d45a, 0x3fe7a000} }, +/**/ {{0x4120eb7f, 0x3fed1e40} }, +/**/ {{0xd15f8278, 0x3ff19561} }, +/**/ {{0x032c5d4c, 0x3be64b28} },}, +/**/ {{{0x0250a5aa, 0x3fe7c000} }, +/**/ {{0xb112a1e1, 0x3fed58f4} }, +/**/ {{0x8a59d565, 0x3ff17235} }, +/**/ {{0xb8dc7867, 0xbbe716de} },}, +/**/ {{{0x0482f82e, 0x3fe7e000} }, +/**/ {{0x3576bdf0, 0x3fed9415} }, +/**/ {{0xa22a1c5b, 0x3ff14f55} }, +/**/ {{0xe1305604, 0x3bf207e1} },}, +/**/ {{{0x0205003e, 0x3fe80000} }, +/**/ {{0x64d69ff7, 0x3fedcfa3} }, +/**/ {{0xe37eb26f, 0x3ff12cc0} }, +/**/ {{0xe32395f8, 0xbbd52ec6} },}, +/**/ {{{0xfbf99411, 0x3fe81fff} }, +/**/ {{0xebf98f51, 0x3fee0ba0} }, +/**/ {{0x16ddd5d6, 0x3ff10a76} }, +/**/ {{0x59866045, 0xbbece0d6} },}, +/**/ {{{0x0248e3a3, 0x3fe84000} }, +/**/ {{0x9bb7f565, 0x3fee480f} }, +/**/ {{0xfb84e05c, 0x3ff0e873} }, +/**/ {{0x1595df92, 0x3bf4e5e8} },}, +/**/ {{{0x0145c157, 0x3fe86000} }, +/**/ {{0x0a10b3ab, 0x3fee84f1} }, +/**/ {{0x7cbd7b1e, 0x3ff0c6b9} }, +/**/ {{0xd5f121d0, 0xbbe19de6} },}, +/**/ {{{0x022631b9, 0x3fe88000} }, +/**/ {{0x0be1f047, 0x3feec247} }, +/**/ {{0x6d0b3ee6, 0x3ff0a545} }, +/**/ {{0xa3ba2c6f, 0xbbc272b1} },}, +/**/ {{{0x045f7828, 0x3fe8a000} }, +/**/ {{0x6c45ba1c, 0x3fef0013} }, +/**/ {{0xaf2a0f09, 0x3ff08416} }, +/**/ {{0x5b63c799, 0x3be82b56} },}, +/**/ {{{0xffc686cf, 0x3fe8bfff} }, +/**/ {{0xf03c824b, 0x3fef3e57} }, +/**/ {{0x33502220, 0x3ff0632c} }, +/**/ {{0x2dbeeb25, 0xbbd039ad} },}, +/**/ {{{0xfd8644c6, 0x3fe8dfff} }, +/**/ {{0x8774261d, 0x3fef7d16} }, +/**/ {{0xdd5b3019, 0x3ff04284} }, +/**/ {{0xe1eba933, 0x3bd79f33} },}, +/**/ {{{0xfe4e7937, 0x3fe8ffff} }, +/**/ {{0x1a99a641, 0x3fefbc51} }, +/**/ {{0x9f69840b, 0x3ff0221f} }, +/**/ {{0x7beee018, 0xbbea9e84} },}, +/**/ {{{0x0435251f, 0x3fe92000} }, +/**/ {{0x9eb22390, 0x3feffc09} }, +/**/ {{0x6f7c51e8, 0x3ff001fb} }, +/**/ {{0x31032e0a, 0xbb5a12e7} },}, + }; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/w_exp_compat.c b/REORG.TODO/sysdeps/ieee754/dbl-64/w_exp_compat.c new file mode 100644 index 0000000000..e61e03b335 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/w_exp_compat.c @@ -0,0 +1,38 @@ +/* Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@gmail.com>, 2011. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* wrapper exp */ +double +__exp (double x) +{ + double z = __ieee754_exp (x); + if (__builtin_expect (!isfinite (z) || z == 0, 0) + && isfinite (x) && _LIB_VERSION != _IEEE_) + return __kernel_standard (x, x, 6 + !!signbit (x)); + + return z; +} +hidden_def (__exp) +weak_alias (__exp, exp) +#ifdef NO_LONG_DOUBLE +strong_alias (__exp, __expl) +weak_alias (__exp, expl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_acosh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_acosh.c new file mode 100644 index 0000000000..ccccdaf106 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_acosh.c @@ -0,0 +1,67 @@ +/* Optimized for 64-bit by Ulrich Drepper <drepper@gmail.com>, 2012 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include <math.h> +#include <math_private.h> + +static const double +one = 1.0, +ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + +double +__ieee754_acosh (double x) +{ + int64_t hx; + EXTRACT_WORDS64 (hx, x); + + if (hx > INT64_C (0x4000000000000000)) + { + if (__glibc_unlikely (hx >= INT64_C (0x41b0000000000000))) + { + /* x > 2**28 */ + if (hx >= INT64_C (0x7ff0000000000000)) + /* x is inf of NaN */ + return x + x; + else + return __ieee754_log (x) + ln2;/* acosh(huge)=log(2x) */ + } + + /* 2**28 > x > 2 */ + double t = x * x; + return __ieee754_log (2.0 * x - one / (x + __ieee754_sqrt (t - one))); + } + else if (__glibc_likely (hx > INT64_C (0x3ff0000000000000))) + { + /* 1<x<2 */ + double t = x - one; + return __log1p (t + __ieee754_sqrt (2.0 * t + t * t)); + } + else if (__glibc_likely (hx == INT64_C (0x3ff0000000000000))) + return 0.0; /* acosh(1) = 0 */ + else /* x < 1 */ + return (x - x) / (x - x); +} +strong_alias (__ieee754_acosh, __acosh_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_cosh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_cosh.c new file mode 100644 index 0000000000..fca80b13f9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_cosh.c @@ -0,0 +1,84 @@ +/* Optimized by Ulrich Drepper <drepper@gmail.com>, 2011 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : cosh(x) := ------------------- + * 2 + * 22 <= x <= lnovft : cosh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + +#include <math.h> +#include <math_private.h> + +static const double one = 1.0, half=0.5, huge = 1.0e300; + +double +__ieee754_cosh (double x) +{ + double t,w; + int32_t ix; + + /* High word of |x|. */ + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + /* |x| in [0,22] */ + if (ix < 0x40360000) { + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3fd62e43) { + if (ix<0x3c800000) /* cosh(tiny) = 1 */ + return one; + t = __expm1(fabs(x)); + w = one+t; + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + t = __ieee754_exp(fabs(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862e42) return half*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + int64_t fix; + EXTRACT_WORDS64(fix, x); + fix &= UINT64_C(0x7fffffffffffffff); + if (fix <= UINT64_C(0x408633ce8fb9f87d)) { + w = __ieee754_exp(half*fabs(x)); + t = half*w; + return t*w; + } + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x*x; + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} +strong_alias (__ieee754_cosh, __cosh_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_fmod.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_fmod.c new file mode 100644 index 0000000000..f686bb6706 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_fmod.c @@ -0,0 +1,105 @@ +/* Rewritten for 64-bit machines by Ulrich Drepper <drepper@gmail.com>. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __ieee754_fmod(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +static const double one = 1.0, Zero[] = {0.0, -0.0,}; + +double +__ieee754_fmod (double x, double y) +{ + int32_t n,ix,iy; + int64_t hx,hy,hz,sx,i; + + EXTRACT_WORDS64(hx,x); + EXTRACT_WORDS64(hy,y); + sx = hx&UINT64_C(0x8000000000000000); /* sign of x */ + hx ^=sx; /* |x| */ + hy &= UINT64_C(0x7fffffffffffffff); /* |y| */ + + /* purge off exception values */ + if(__builtin_expect(hy==0 + || hx >= UINT64_C(0x7ff0000000000000) + || hy > UINT64_C(0x7ff0000000000000), 0)) + /* y=0,or x not finite or y is NaN */ + return (x*y)/(x*y); + if(__builtin_expect(hx<=hy, 0)) { + if(hx<hy) return x; /* |x|<|y| return x */ + return Zero[(uint64_t)sx>>63]; /* |x|=|y| return x*0*/ + } + + /* determine ix = ilogb(x) */ + if(__builtin_expect(hx<UINT64_C(0x0010000000000000), 0)) { + /* subnormal x */ + for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; + } else ix = (hx>>52)-1023; + + /* determine iy = ilogb(y) */ + if(__builtin_expect(hy<UINT64_C(0x0010000000000000), 0)) { /* subnormal y */ + for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; + } else iy = (hy>>52)-1023; + + /* set up hx, hy and align y to x */ + if(__builtin_expect(ix >= -1022, 1)) + hx = UINT64_C(0x0010000000000000)|(UINT64_C(0x000fffffffffffff)&hx); + else { /* subnormal x, shift x to normal */ + n = -1022-ix; + hx<<=n; + } + if(__builtin_expect(iy >= -1022, 1)) + hy = UINT64_C(0x0010000000000000)|(UINT64_C(0x000fffffffffffff)&hy); + else { /* subnormal y, shift y to normal */ + n = -1022-iy; + hy<<=n; + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy; + if(hz<0){hx = hx+hx;} + else { + if(hz==0) /* return sign(x)*0 */ + return Zero[(uint64_t)sx>>63]; + hx = hz+hz; + } + } + hz=hx-hy; + if(hz>=0) {hx=hz;} + + /* convert back to floating value and restore the sign */ + if(hx==0) /* return sign(x)*0 */ + return Zero[(uint64_t)sx>>63]; + while(hx<UINT64_C(0x0010000000000000)) { /* normalize x */ + hx = hx+hx; + iy -= 1; + } + if(__builtin_expect(iy>= -1022, 1)) { /* normalize output */ + hx = ((hx-UINT64_C(0x0010000000000000))|((uint64_t)(iy+1023)<<52)); + INSERT_WORDS64(x,hx|sx); + } else { /* subnormal output */ + n = -1022 - iy; + hx>>=n; + INSERT_WORDS64(x,hx|sx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} +strong_alias (__ieee754_fmod, __fmod_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c new file mode 100644 index 0000000000..4f5a81669e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c @@ -0,0 +1,87 @@ +/* @(#)e_log10.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_log10(x) + * Return the base 10 logarithm of x + * + * Method : + * Let log10_2hi = leading 40 bits of log10(2) and + * log10_2lo = log10(2) - log10_2hi, + * ivln10 = 1/log(10) rounded. + * Then + * n = ilogb(x), + * if(n<0) n = n+1; + * x = scalbn(x,-n); + * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) + * + * Note 1: + * To guarantee log10(10**n)=n, where 10**n is normal, the rounding + * mode must set to Round-to-Nearest. + * Note 2: + * [1/log(10)] rounded to 53 bits has error .198 ulps; + * log10 is monotonic at all binary break points. + * + * Special cases: + * log10(x) is NaN with signal if x < 0; + * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; + * log10(NaN) is that NaN with no signal; + * log10(10**N) = N for N=0,1,...,22. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +static const double two54 = 1.80143985094819840000e+16; /* 0x4350000000000000 */ +static const double ivln10 = 4.34294481903251816668e-01; /* 0x3FDBCB7B1526E50E */ +static const double log10_2hi = 3.01029995663611771306e-01; /* 0x3FD34413509F6000 */ +static const double log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF311F12B36 */ + +double +__ieee754_log10 (double x) +{ + double y, z; + int64_t i, hx; + int32_t k; + + EXTRACT_WORDS64 (hx, x); + + k = 0; + if (hx < INT64_C(0x0010000000000000)) + { /* x < 2**-1022 */ + if (__glibc_unlikely ((hx & UINT64_C(0x7fffffffffffffff)) == 0)) + return -two54 / (x - x); /* log(+-0)=-inf */ + if (__glibc_unlikely (hx < 0)) + return (x - x) / (x - x); /* log(-#) = NaN */ + k -= 54; + x *= two54; /* subnormal number, scale up x */ + EXTRACT_WORDS64 (hx, x); + } + /* scale up resulted in a NaN number */ + if (__glibc_unlikely (hx >= UINT64_C(0x7ff0000000000000))) + return x + x; + k += (hx >> 52) - 1023; + i = ((uint64_t) k & UINT64_C(0x8000000000000000)) >> 63; + hx = (hx & UINT64_C(0x000fffffffffffff)) | ((0x3ff - i) << 52); + y = (double) (k + i); + INSERT_WORDS64 (x, hx); + z = y * log10_2lo + ivln10 * __ieee754_log (x); + return z + y * log10_2hi; +} + +strong_alias (__ieee754_log10, __log10_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c new file mode 100644 index 0000000000..5ccb78cf03 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c @@ -0,0 +1,128 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_log2(x) + * Return the logarithm to base 2 of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k + log(1+f). + * = k+(f-(hfsq-(s*(hfsq+R)))) + * + * Special cases: + * log2(x) is NaN with signal if x < 0 (including -INF) ; + * log2(+INF) is +INF; log(0) is -INF with signal; + * log2(NaN) is that NaN with no signal. + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <math.h> +#include <math_private.h> + +static const double ln2 = 0.69314718055994530942; +static const double two54 = 1.80143985094819840000e+16; /* 4350000000000000 */ +static const double Lg1 = 6.666666666666735130e-01; /* 3FE5555555555593 */ +static const double Lg2 = 3.999999999940941908e-01; /* 3FD999999997FA04 */ +static const double Lg3 = 2.857142874366239149e-01; /* 3FD2492494229359 */ +static const double Lg4 = 2.222219843214978396e-01; /* 3FCC71C51D8E78AF */ +static const double Lg5 = 1.818357216161805012e-01; /* 3FC7466496CB03DE */ +static const double Lg6 = 1.531383769920937332e-01; /* 3FC39A09D078C69F */ +static const double Lg7 = 1.479819860511658591e-01; /* 3FC2F112DF3E5244 */ + +static const double zero = 0.0; + +double +__ieee754_log2 (double x) +{ + double hfsq, f, s, z, R, w, t1, t2, dk; + int64_t hx, i, j; + int32_t k; + + EXTRACT_WORDS64 (hx, x); + + k = 0; + if (hx < INT64_C(0x0010000000000000)) + { /* x < 2**-1022 */ + if (__glibc_unlikely ((hx & UINT64_C(0x7fffffffffffffff)) == 0)) + return -two54 / (x - x); /* log(+-0)=-inf */ + if (__glibc_unlikely (hx < 0)) + return (x - x) / (x - x); /* log(-#) = NaN */ + k -= 54; + x *= two54; /* subnormal number, scale up x */ + EXTRACT_WORDS64 (hx, x); + } + if (__glibc_unlikely (hx >= UINT64_C(0x7ff0000000000000))) + return x + x; + k += (hx >> 52) - 1023; + hx &= UINT64_C(0x000fffffffffffff); + i = (hx + UINT64_C(0x95f6400000000)) & UINT64_C(0x10000000000000); + /* normalize x or x/2 */ + INSERT_WORDS64 (x, hx | (i ^ UINT64_C(0x3ff0000000000000))); + k += (i >> 52); + dk = (double) k; + f = x - 1.0; + if ((UINT64_C(0x000fffffffffffff) & (2 + hx)) < 3) + { /* |f| < 2**-20 */ + if (f == zero) + return dk; + R = f * f * (0.5 - 0.33333333333333333 * f); + return dk - (R - f) / ln2; + } + s = f / (2.0 + f); + z = s * s; + i = hx - UINT64_C(0x6147a00000000); + w = z * z; + j = UINT64_C(0x6b85100000000) - hx; + t1 = w * (Lg2 + w * (Lg4 + w * Lg6)); + t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7))); + i |= j; + R = t2 + t1; + if (i > 0) + { + hfsq = 0.5 * f * f; + return dk - ((hfsq - (s * (hfsq + R))) - f) / ln2; + } + else + { + return dk - ((s * (f - R)) - f) / ln2; + } +} + +strong_alias (__ieee754_log2, __log2_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_ceil.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_ceil.c new file mode 100644 index 0000000000..faaaf90208 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_ceil.c @@ -0,0 +1,54 @@ +/* @(#)s_ceil.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * ceil(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + */ + +#include <math.h> +#include <math_private.h> + +double +__ceil(double x) +{ + int64_t i0,i; + int32_t j0; + EXTRACT_WORDS64(i0,x); + j0 = ((i0>>52)&0x7ff)-0x3ff; + if(j0<=51) { + if(j0<0) { + /* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=INT64_C(0x8000000000000000);} + else if(i0!=0) { i0=INT64_C(0x3ff0000000000000);} + } else { + i = INT64_C(0x000fffffffffffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(i0>0) i0 += UINT64_C(0x0010000000000000)>>j0; + i0 &= (~i); + } + } else { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + INSERT_WORDS64(x,i0); + return x; +} +#ifndef __ceil +weak_alias (__ceil, ceil) +# ifdef NO_LONG_DOUBLE +strong_alias (__ceil, __ceill) +weak_alias (__ceil, ceill) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_finite.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_finite.c new file mode 100644 index 0000000000..ef51608f6e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_finite.c @@ -0,0 +1,42 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * finite(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <shlib-compat.h> +#include <stdint.h> + +#undef __finite +int +__finite(double x) +{ + int64_t lx; + EXTRACT_WORDS64(lx,x); + return (int)((uint64_t)((lx&INT64_C(0x7ff0000000000000))-INT64_C(0x7ff0000000000000))>>63); +} +hidden_def (__finite) +weak_alias (__finite, finite) +#ifdef NO_LONG_DOUBLE +# ifdef LDBL_CLASSIFY_COMPAT +# if SHLIB_COMPAT (libc, GLIBC_2_0, GLIBC_2_23) +compat_symbol (libc, __finite, __finitel, GLIBC_2_0); +# endif +# if SHLIB_COMPAT (libm, GLIBC_2_1, GLIBC_2_23) +compat_symbol (libm, __finite, __finitel, GLIBC_2_1); +# endif +# endif +weak_alias (__finite, finitel) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_floor.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_floor.c new file mode 100644 index 0000000000..1b99fffc30 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_floor.c @@ -0,0 +1,74 @@ +/* Round double to integer away from zero. + Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 2011. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* Based on a version which carries the following copyright: */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +/* + * floor(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + */ + + +double +__floor (double x) +{ + int64_t i0; + EXTRACT_WORDS64(i0,x); + int32_t j0 = ((i0>>52)&0x7ff)-0x3ff; + if(__builtin_expect(j0<52, 1)) { + if(j0<0) { + /* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=0;} + else if((i0&0x7fffffffffffffffl)!=0) + { i0=0xbff0000000000000l;} + } else { + uint64_t i = (0x000fffffffffffffl)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(i0<0) i0 += (0x0010000000000000l)>>j0; + i0 &= (~i); + } + INSERT_WORDS64(x,i0); + } else if (j0==0x400) + return x+x; /* inf or NaN */ + return x; +} +#ifndef __floor +weak_alias (__floor, floor) +# ifdef NO_LONG_DOUBLE +strong_alias (__floor, __floorl) +weak_alias (__floor, floorl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_frexp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_frexp.c new file mode 100644 index 0000000000..5e8bc64711 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_frexp.c @@ -0,0 +1,69 @@ +/* Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@gmail.com>, 2011. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <inttypes.h> +#include <math.h> +#include <math_private.h> + +/* + * for non-zero, finite x + * x = frexp(arg,&exp); + * return a double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg + * with *exp=0. + */ + + +double +__frexp (double x, int *eptr) +{ + int64_t ix; + EXTRACT_WORDS64 (ix, x); + int32_t ex = 0x7ff & (ix >> 52); + int e = 0; + + if (__glibc_likely (ex != 0x7ff && x != 0.0)) + { + /* Not zero and finite. */ + e = ex - 1022; + if (__glibc_unlikely (ex == 0)) + { + /* Subnormal. */ + x *= 0x1p54; + EXTRACT_WORDS64 (ix, x); + ex = 0x7ff & (ix >> 52); + e = ex - 1022 - 54; + } + + ix = (ix & INT64_C (0x800fffffffffffff)) | INT64_C (0x3fe0000000000000); + INSERT_WORDS64 (x, ix); + } + else + /* Quiet signaling NaNs. */ + x += x; + + *eptr = e; + return x; +} +weak_alias (__frexp, frexp) +#ifdef NO_LONG_DOUBLE +strong_alias (__frexp, __frexpl) +weak_alias (__frexp, frexpl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_getpayload.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_getpayload.c new file mode 100644 index 0000000000..fbcd75b8bd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_getpayload.c @@ -0,0 +1,33 @@ +/* Get NaN payload. dbl-64/wordsize-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +double +getpayload (const double *x) +{ + uint64_t ix; + EXTRACT_WORDS64 (ix, *x); + ix &= 0x7ffffffffffffULL; + return (double) ix; +} +#ifdef NO_LONG_DOUBLE +weak_alias (getpayload, getpayloadl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_isinf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_isinf.c new file mode 100644 index 0000000000..951fb73239 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_isinf.c @@ -0,0 +1,33 @@ +/* + * Written by J.T. Conklin <jtc@netbsd.org>. + * Changed to return -1 for -Inf by Ulrich Drepper <drepper@cygnus.com>. + * Public domain. + */ + +/* + * isinf(x) returns 1 is x is inf, -1 if x is -inf, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <shlib-compat.h> + +int +__isinf (double x) +{ + int64_t ix; + EXTRACT_WORDS64(ix,x); + int64_t t = ix & UINT64_C(0x7fffffffffffffff); + t ^= UINT64_C(0x7ff0000000000000); + t |= -t; + return ~(t >> 63) & (ix >> 62); +} +hidden_def (__isinf) +weak_alias (__isinf, isinf) +#ifdef NO_LONG_DOUBLE +# if defined LDBL_CLASSIFY_COMPAT && SHLIB_COMPAT (libc, GLIBC_2_0, GLIBC_2_23) +compat_symbol (libc, __isinf, __isinfl, GLIBC_2_0); +# endif +weak_alias (__isinf, isinfl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_isnan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_isnan.c new file mode 100644 index 0000000000..bcff9e3b67 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_isnan.c @@ -0,0 +1,39 @@ +/* @(#)s_isnan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * isnan(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <shlib-compat.h> +#include <stdint.h> + +#undef __isnan +int __isnan(double x) +{ + int64_t hx; + EXTRACT_WORDS64(hx,x); + hx &= UINT64_C(0x7fffffffffffffff); + hx = UINT64_C(0x7ff0000000000000) - hx; + return (int)(((uint64_t)hx)>>63); +} +hidden_def (__isnan) +weak_alias (__isnan, isnan) +#ifdef NO_LONG_DOUBLE +# if defined LDBL_CLASSIFY_COMPAT && SHLIB_COMPAT (libc, GLIBC_2_0, GLIBC_2_23) +compat_symbol (libc, __isnan, __isnanl, GLIBC_2_0); +# endif +weak_alias (__isnan, isnanl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_issignaling.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_issignaling.c new file mode 100644 index 0000000000..117f64bede --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_issignaling.c @@ -0,0 +1,43 @@ +/* Test for signaling NaN. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> + +int +__issignaling (double x) +{ + u_int64_t xi; + EXTRACT_WORDS64 (xi, x); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* We only have to care about the high-order bit of x's significand, because + having it set (sNaN) already makes the significand different from that + used to designate infinity. */ + return (xi & UINT64_C (0x7ff8000000000000)) == UINT64_C (0x7ff8000000000000); +#else + /* To keep the following comparison simple, toggle the quiet/signaling bit, + so that it is set for sNaNs. This is inverse to IEEE 754-2008 (as well as + common practice for IEEE 754-1985). */ + xi ^= UINT64_C (0x0008000000000000); + /* We have to compare for greater (instead of greater or equal), because x's + significand being all-zero designates infinity not NaN. */ + return (xi & UINT64_C (0x7fffffffffffffff)) > UINT64_C (0x7ff8000000000000); +#endif +} +libm_hidden_def (__issignaling) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_llround.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_llround.c new file mode 100644 index 0000000000..86a791111e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_llround.c @@ -0,0 +1,82 @@ +/* Round double value to long long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define lround __hidden_lround +#define __lround __hidden___lround + +#include <math.h> +#include <sysdep.h> + +#include <math_private.h> + + +long long int +__llround (double x) +{ + int32_t j0; + int64_t i0; + long long int result; + int sign; + + EXTRACT_WORDS64 (i0, x); + j0 = ((i0 >> 52) & 0x7ff) - 0x3ff; + sign = i0 < 0 ? -1 : 1; + i0 &= UINT64_C(0xfffffffffffff); + i0 |= UINT64_C(0x10000000000000); + + if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else if (j0 >= 52) + result = i0 << (j0 - 52); + else + { + i0 += UINT64_C(0x8000000000000) >> j0; + + result = i0 >> (52 - j0); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long long int) x; + } + + return sign * result; +} + +weak_alias (__llround, llround) +#ifdef NO_LONG_DOUBLE +strong_alias (__llround, __llroundl) +weak_alias (__llround, llroundl) +#endif + +/* long has the same width as long long on LP64 machines, so use an alias. */ +#undef lround +#undef __lround +#ifdef _LP64 +strong_alias (__llround, __lround) +weak_alias (__llround, lround) +# ifdef NO_LONG_DOUBLE +strong_alias (__llround, __lroundl) +weak_alias (__llround, lroundl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_logb.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_logb.c new file mode 100644 index 0000000000..c65cd52208 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_logb.c @@ -0,0 +1,48 @@ +/* Compute radix independent exponent. + Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@gmail.com>, 2011. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +double +__logb (double x) +{ + int64_t ix, ex; + + EXTRACT_WORDS64 (ix, x); + ix &= UINT64_C(0x7fffffffffffffff); + if (ix == 0) + return -1.0 / fabs (x); + ex = ix >> 52; + if (ex == 0x7ff) + return x * x; + if (__glibc_unlikely (ex == 0)) + { + int m = __builtin_clzll (ix); + ex -= m - 12; + } + return (double) (ex - 1023); +} +weak_alias (__logb, logb) +#ifdef NO_LONG_DOUBLE +strong_alias (__logb, __logbl) +weak_alias (__logb, logbl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_lround.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_lround.c new file mode 100644 index 0000000000..02b01aa00d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_lround.c @@ -0,0 +1,89 @@ +/* Round double value to long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> + +/* For LP64, lround is an alias for llround. */ +#ifndef _LP64 + +long int +__lround (double x) +{ + int32_t j0; + int64_t i0; + long int result; + int sign; + + EXTRACT_WORDS64 (i0, x); + j0 = ((i0 >> 52) & 0x7ff) - 0x3ff; + sign = i0 < 0 ? -1 : 1; + i0 &= UINT64_C(0xfffffffffffff); + i0 |= UINT64_C(0x10000000000000); + + if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else if (j0 >= 52) + result = i0 << (j0 - 52); + else + { + i0 += UINT64_C(0x8000000000000) >> j0; + + result = i0 >> (52 - j0); +#ifdef FE_INVALID + if (sizeof (long int) == 4 + && sign == 1 + && result == LONG_MIN) + /* Rounding brought the value out of range. */ + feraiseexcept (FE_INVALID); +#endif + } + } + else + { + /* The number is too large. Unless it rounds to LONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ +#ifdef FE_INVALID + if (sizeof (long int) == 4 + && x <= (double) LONG_MIN - 0.5) + { + /* If truncation produces LONG_MIN, the cast will not raise + the exception, but may raise "inexact". */ + feraiseexcept (FE_INVALID); + return LONG_MIN; + } +#endif + return (long int) x; + } + + return sign * result; +} + +weak_alias (__lround, lround) +# ifdef NO_LONG_DOUBLE +strong_alias (__lround, __lroundl) +weak_alias (__lround, lroundl) +# endif + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_modf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_modf.c new file mode 100644 index 0000000000..c309e56272 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_modf.c @@ -0,0 +1,66 @@ +/* Rewritten for 64-bit machines by Ulrich Drepper <drepper@gmail.com>. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * modf(double x, double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +static const double one = 1.0; + +double +__modf(double x, double *iptr) +{ + int64_t i0; + int32_t j0; + EXTRACT_WORDS64(i0,x); + j0 = ((i0>>52)&0x7ff)-0x3ff; /* exponent of x */ + if(j0<52) { /* integer part in x */ + if(j0<0) { /* |x|<1 */ + /* *iptr = +-0 */ + INSERT_WORDS64(*iptr,i0&UINT64_C(0x8000000000000000)); + return x; + } else { + uint64_t i = UINT64_C(0x000fffffffffffff)>>j0; + if((i0&i)==0) { /* x is integral */ + *iptr = x; + /* return +-0 */ + INSERT_WORDS64(x,i0&UINT64_C(0x8000000000000000)); + return x; + } else { + INSERT_WORDS64(*iptr,i0&(~i)); + return x - *iptr; + } + } + } else { /* no fraction part */ + *iptr = x*one; + /* We must handle NaNs separately. */ + if (j0 == 0x400 && (i0 & UINT64_C(0xfffffffffffff))) + return x*one; + INSERT_WORDS64(x,i0&UINT64_C(0x8000000000000000)); /* return +-0 */ + return x; + } +} +weak_alias (__modf, modf) +#ifdef NO_LONG_DOUBLE +strong_alias (__modf, __modfl) +weak_alias (__modf, modfl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_nearbyint.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_nearbyint.c new file mode 100644 index 0000000000..8293819981 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_nearbyint.c @@ -0,0 +1,66 @@ +/* Adapted for use as nearbyint by Ulrich Drepper <drepper@cygnus.com>. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include <fenv.h> +#include <math.h> +#include <math_private.h> + +static const double +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +double +__nearbyint(double x) +{ + fenv_t env; + int64_t i0,sx; + int32_t j0; + EXTRACT_WORDS64(i0,x); + sx = (i0>>63)&1; + j0 = ((i0>>52)&0x7ff)-0x3ff; + if(__builtin_expect(j0<52, 1)) { + if(j0<0) { + libc_feholdexcept (&env); + double w = TWO52[sx]+x; + double t = w-TWO52[sx]; + math_opt_barrier(t); + libc_fesetenv (&env); + return __copysign (t, x); + } + } else { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + libc_feholdexcept (&env); + double w = TWO52[sx]+x; + double t = w-TWO52[sx]; + math_opt_barrier (t); + libc_fesetenv (&env); + return t; +} +weak_alias (__nearbyint, nearbyint) +#ifdef NO_LONG_DOUBLE +strong_alias (__nearbyint, __nearbyintl) +weak_alias (__nearbyint, nearbyintl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_remquo.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_remquo.c new file mode 100644 index 0000000000..37a823c075 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_remquo.c @@ -0,0 +1,114 @@ +/* Compute remainder and a congruent to the quotient. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> +#include <stdint.h> + +static const double zero = 0.0; + + +double +__remquo (double x, double y, int *quo) +{ + int64_t hx, hy; + uint64_t sx, qs; + int cquo; + + EXTRACT_WORDS64 (hx, x); + EXTRACT_WORDS64 (hy, y); + sx = hx & UINT64_C(0x8000000000000000); + qs = sx ^ (hy & UINT64_C(0x8000000000000000)); + hy &= UINT64_C(0x7fffffffffffffff); + hx &= UINT64_C(0x7fffffffffffffff); + + /* Purge off exception values. */ + if (__glibc_unlikely (hy == 0)) + return (x * y) / (x * y); /* y = 0 */ + if (__builtin_expect (hx >= UINT64_C(0x7ff0000000000000) /* x not finite */ + || hy > UINT64_C(0x7ff0000000000000), 0))/* y is NaN */ + return (x * y) / (x * y); + + if (hy <= UINT64_C(0x7fbfffffffffffff)) + x = __ieee754_fmod (x, 8 * y); /* now x < 8y */ + + if (__glibc_unlikely (hx == hy)) + { + *quo = qs ? -1 : 1; + return zero * x; + } + + x = fabs (x); + INSERT_WORDS64 (y, hy); + cquo = 0; + + if (hy <= UINT64_C(0x7fcfffffffffffff) && x >= 4 * y) + { + x -= 4 * y; + cquo += 4; + } + if (hy <= UINT64_C(0x7fdfffffffffffff) && x >= 2 * y) + { + x -= 2 * y; + cquo += 2; + } + + if (hy < UINT64_C(0x0020000000000000)) + { + if (x + x > y) + { + x -= y; + ++cquo; + if (x + x >= y) + { + x -= y; + ++cquo; + } + } + } + else + { + double y_half = 0.5 * y; + if (x > y_half) + { + x -= y; + ++cquo; + if (x >= y_half) + { + x -= y; + ++cquo; + } + } + } + + *quo = qs ? -cquo : cquo; + + /* Ensure correct sign of zero result in round-downward mode. */ + if (x == 0.0) + x = 0.0; + if (sx) + x = -x; + return x; +} +weak_alias (__remquo, remquo) +#ifdef NO_LONG_DOUBLE +strong_alias (__remquo, __remquol) +weak_alias (__remquo, remquol) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_rint.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_rint.c new file mode 100644 index 0000000000..87b2339d43 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_rint.c @@ -0,0 +1,60 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include <math.h> +#include <math_private.h> + +static const double +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +double +__rint(double x) +{ + int64_t i0,sx; + int32_t j0; + EXTRACT_WORDS64(i0,x); + sx = (i0>>63)&1; + j0 = ((i0>>52)&0x7ff)-0x3ff; + if(j0<52) { + if(j0<0) { + double w = TWO52[sx]+x; + double t = w-TWO52[sx]; + EXTRACT_WORDS64(i0,t); + INSERT_WORDS64(t,(i0&UINT64_C(0x7fffffffffffffff))|(sx<<63)); + return t; + } + } else { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + double w = TWO52[sx]+x; + return w-TWO52[sx]; +} +#ifndef __rint +weak_alias (__rint, rint) +# ifdef NO_LONG_DOUBLE +strong_alias (__rint, __rintl) +weak_alias (__rint, rintl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_round.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_round.c new file mode 100644 index 0000000000..0e3738b6ef --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_round.c @@ -0,0 +1,68 @@ +/* Round double to integer away from zero. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> +#include <stdint.h> + + +double +__round (double x) +{ + int64_t i0, j0; + + EXTRACT_WORDS64 (i0, x); + j0 = ((i0 >> 52) & 0x7ff) - 0x3ff; + if (__glibc_likely (j0 < 52)) + { + if (j0 < 0) + { + i0 &= UINT64_C(0x8000000000000000); + if (j0 == -1) + i0 |= UINT64_C(0x3ff0000000000000); + } + else + { + uint64_t i = UINT64_C(0x000fffffffffffff) >> j0; + if ((i0 & i) == 0) + /* X is integral. */ + return x; + + i0 += UINT64_C(0x0008000000000000) >> j0; + i0 &= ~i; + } + } + else + { + if (j0 == 0x400) + /* Inf or NaN. */ + return x + x; + else + return x; + } + + INSERT_WORDS64 (x, i0); + return x; +} +weak_alias (__round, round) +#ifdef NO_LONG_DOUBLE +strong_alias (__round, __roundl) +weak_alias (__round, roundl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_roundeven.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_roundeven.c new file mode 100644 index 0000000000..d13ee25cea --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_roundeven.c @@ -0,0 +1,72 @@ +/* Round to nearest integer value, rounding halfway cases to even. + dbl-64/wordsize-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +#define BIAS 0x3ff +#define MANT_DIG 53 +#define MAX_EXP (2 * BIAS + 1) + +double +roundeven (double x) +{ + uint64_t ix, ux; + EXTRACT_WORDS64 (ix, x); + ux = ix & 0x7fffffffffffffffULL; + int exponent = ux >> (MANT_DIG - 1); + if (exponent >= BIAS + MANT_DIG - 1) + { + /* Integer, infinity or NaN. */ + if (exponent == MAX_EXP) + /* Infinity or NaN; quiet signaling NaNs. */ + return x + x; + else + return x; + } + else if (exponent >= BIAS) + { + /* At least 1; not necessarily an integer. Locate the bits with + exponents 0 and -1 (when the unbiased exponent is 0, the bit + with exponent 0 is implicit, but as the bias is odd it is OK + to take it from the low bit of the exponent). */ + int int_pos = (BIAS + MANT_DIG - 1) - exponent; + int half_pos = int_pos - 1; + uint64_t half_bit = 1ULL << half_pos; + uint64_t int_bit = 1ULL << int_pos; + if ((ix & (int_bit | (half_bit - 1))) != 0) + /* Carry into the exponent works correctly. No need to test + whether HALF_BIT is set. */ + ix += half_bit; + ix &= ~(int_bit - 1); + } + else if (exponent == BIAS - 1 && ux > 0x3fe0000000000000ULL) + /* Interval (0.5, 1). */ + ix = (ix & 0x8000000000000000ULL) | 0x3ff0000000000000ULL; + else + /* Rounds to 0. */ + ix &= 0x8000000000000000ULL; + INSERT_WORDS64 (x, ix); + return x; +} +hidden_def (roundeven) +#ifdef NO_LONG_DOUBLE +weak_alias (roundeven, roundevenl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_scalbln.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_scalbln.c new file mode 100644 index 0000000000..8dce51e928 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_scalbln.c @@ -0,0 +1,60 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ +huge = 1.0e+300, +tiny = 1.0e-300; + +double +__scalbln (double x, long int n) +{ + int64_t ix; + int64_t k; + EXTRACT_WORDS64(ix,x); + k = (ix >> 52) & 0x7ff; /* extract exponent */ + if (__builtin_expect(k==0, 0)) { /* 0 or subnormal x */ + if ((ix & UINT64_C(0xfffffffffffff))==0) return x; /* +-0 */ + x *= two54; + EXTRACT_WORDS64(ix,x); + k = ((ix >> 52) & 0x7ff) - 54; + } + if (__builtin_expect(k==0x7ff, 0)) return x+x; /* NaN or Inf */ + if (__builtin_expect(n< -50000, 0)) + return tiny*__copysign(tiny,x); /*underflow*/ + if (__builtin_expect(n> 50000 || k+n > 0x7fe, 0)) + return huge*__copysign(huge,x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k+n; + if (__builtin_expect(k > 0, 1)) /* normal result */ + {INSERT_WORDS64(x,(ix&UINT64_C(0x800fffffffffffff))|(k<<52)); + return x;} + if (k <= -54) + return tiny*__copysign(tiny,x); /*underflow*/ + k += 54; /* subnormal result */ + INSERT_WORDS64(x,(ix&INT64_C(0x800fffffffffffff))|(k<<52)); + return x*twom54; +} +#ifdef NO_LONG_DOUBLE +strong_alias (__scalbln, __scalblnl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_scalbn.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_scalbn.c new file mode 100644 index 0000000000..d517a919c8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_scalbn.c @@ -0,0 +1,60 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ +huge = 1.0e+300, +tiny = 1.0e-300; + +double +__scalbn (double x, int n) +{ + int64_t ix; + int64_t k; + EXTRACT_WORDS64(ix,x); + k = (ix >> 52) & 0x7ff; /* extract exponent */ + if (__builtin_expect(k==0, 0)) { /* 0 or subnormal x */ + if ((ix & UINT64_C(0xfffffffffffff))==0) return x; /* +-0 */ + x *= two54; + EXTRACT_WORDS64(ix,x); + k = ((ix >> 52) & 0x7ff) - 54; + } + if (__builtin_expect(k==0x7ff, 0)) return x+x; /* NaN or Inf */ + if (__builtin_expect(n< -50000, 0)) + return tiny*__copysign(tiny,x); /*underflow*/ + if (__builtin_expect(n> 50000 || k+n > 0x7fe, 0)) + return huge*__copysign(huge,x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k+n; + if (__builtin_expect(k > 0, 1)) /* normal result */ + {INSERT_WORDS64(x,(ix&UINT64_C(0x800fffffffffffff))|(k<<52)); + return x;} + if (k <= -54) + return tiny*__copysign(tiny,x); /*underflow*/ + k += 54; /* subnormal result */ + INSERT_WORDS64(x,(ix&INT64_C(0x800fffffffffffff))|(k<<52)); + return x*twom54; +} +#ifdef NO_LONG_DOUBLE +strong_alias (__scalbn, __scalbnl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_setpayload_main.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_setpayload_main.c new file mode 100644 index 0000000000..d4f6d55432 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_setpayload_main.c @@ -0,0 +1,53 @@ +/* Set NaN payload. dbl-64/wordsize-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +#define SET_HIGH_BIT (HIGH_ORDER_BIT_IS_SET_FOR_SNAN ? SIG : !SIG) +#define BIAS 0x3ff +#define PAYLOAD_DIG 51 +#define EXPLICIT_MANT_DIG 52 + +int +FUNC (double *x, double payload) +{ + uint64_t ix; + EXTRACT_WORDS64 (ix, payload); + int exponent = ix >> EXPLICIT_MANT_DIG; + /* Test if argument is (a) negative or too large; (b) too small, + except for 0 when allowed; (c) not an integer. */ + if (exponent >= BIAS + PAYLOAD_DIG + || (exponent < BIAS && !(SET_HIGH_BIT && ix == 0)) + || (ix & ((1ULL << (BIAS + EXPLICIT_MANT_DIG - exponent)) - 1)) != 0) + { + INSERT_WORDS64 (*x, 0); + return 1; + } + if (ix != 0) + { + ix &= (1ULL << EXPLICIT_MANT_DIG) - 1; + ix |= 1ULL << EXPLICIT_MANT_DIG; + ix >>= BIAS + EXPLICIT_MANT_DIG - exponent; + } + ix |= 0x7ff0000000000000ULL | (SET_HIGH_BIT ? 0x8000000000000ULL : 0); + INSERT_WORDS64 (*x, ix); + return 0; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c new file mode 100644 index 0000000000..1e8d57f32b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c @@ -0,0 +1,50 @@ +/* Total order operation. dbl-64/wordsize-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalorder (double x, double y) +{ + int64_t ix, iy; + EXTRACT_WORDS64 (ix, x); + EXTRACT_WORDS64 (iy, y); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the arguments interpreted as + sign-magnitude integers. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if ((ix & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL + && (iy & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL) + { + ix ^= 0x0008000000000000ULL; + iy ^= 0x0008000000000000ULL; + } +#endif + uint64_t ix_sign = ix >> 63; + uint64_t iy_sign = iy >> 63; + ix ^= ix_sign >> 1; + iy ^= iy_sign >> 1; + return ix <= iy; +} +#ifdef NO_LONG_DOUBLE +weak_alias (totalorder, totalorderl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_totalordermag.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_totalordermag.c new file mode 100644 index 0000000000..47a077f18b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_totalordermag.c @@ -0,0 +1,47 @@ +/* Total order operation on absolute values. dbl-64/wordsize-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalordermag (double x, double y) +{ + uint64_t ix, iy; + EXTRACT_WORDS64 (ix, x); + EXTRACT_WORDS64 (iy, y); + ix &= 0x7fffffffffffffffULL; + iy &= 0x7fffffffffffffffULL; +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the absolute values of the + arguments. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if (ix > 0x7ff0000000000000ULL && iy > 0x7ff0000000000000ULL) + { + ix ^= 0x0008000000000000ULL; + iy ^= 0x0008000000000000ULL; + } +#endif + return ix <= iy; +} +#ifdef NO_LONG_DOUBLE +weak_alias (totalordermag, totalordermagl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_trunc.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_trunc.c new file mode 100644 index 0000000000..050ec0016a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_trunc.c @@ -0,0 +1,57 @@ +/* Truncate argument to nearest integral value not larger than the argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +double +__trunc (double x) +{ + int64_t i0, j0; + int64_t sx; + + EXTRACT_WORDS64 (i0, x); + sx = i0 & UINT64_C(0x8000000000000000); + j0 = ((i0 >> 52) & 0x7ff) - 0x3ff; + if (j0 < 52) + { + if (j0 < 0) + /* The magnitude of the number is < 1 so the result is +-0. */ + INSERT_WORDS64 (x, sx); + else + INSERT_WORDS64 (x, sx | (i0 & ~(UINT64_C(0x000fffffffffffff) >> j0))); + } + else + { + if (j0 == 0x400) + /* x is inf or NaN. */ + return x + x; + } + + return x; +} +#ifndef __trunc +weak_alias (__trunc, trunc) +# ifdef NO_LONG_DOUBLE +strong_alias (__trunc, __truncl) +weak_alias (__trunc, truncl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1.c b/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1.c new file mode 100644 index 0000000000..70d33de74c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1.c @@ -0,0 +1,75 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_split.h> +#include <stdlib.h> + +/* Calculate X + Y exactly and store the result in *HI + *LO. It is + given that |X| >= |Y| and the values are small enough that no + overflow occurs. */ + +static inline void +add_split (double *hi, double *lo, double x, double y) +{ + /* Apply Dekker's algorithm. */ + *hi = x + y; + *lo = (x - *hi) + y; +} + +/* Compare absolute values of floating-point values pointed to by P + and Q for qsort. */ + +static int +compare (const void *p, const void *q) +{ + double pd = fabs (*(const double *) p); + double qd = fabs (*(const double *) q); + if (pd < qd) + return -1; + else if (pd == qd) + return 0; + else + return 1; +} + +/* Return X^2 + Y^2 - 1, computed without large cancellation error. + It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >= + 0.5. */ + +double +__x2y2m1 (double x, double y) +{ + double vals[5]; + SET_RESTORE_ROUND (FE_TONEAREST); + mul_split (&vals[1], &vals[0], x, x); + mul_split (&vals[3], &vals[2], y, y); + vals[4] = -1.0; + qsort (vals, 5, sizeof (double), compare); + /* Add up the values so that each element of VALS has absolute value + at most equal to the last set bit of the next nonzero + element. */ + for (size_t i = 0; i <= 3; i++) + { + add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); + qsort (vals + i + 1, 4 - i, sizeof (double), compare); + } + /* Now any error from this addition will be small. */ + return vals[4] + vals[3] + vals[2] + vals[1] + vals[0]; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1f.c b/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1f.c new file mode 100644 index 0000000000..17bc435a62 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1f.c @@ -0,0 +1,32 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Return X^2 + Y^2 - 1, computed without large cancellation error. + It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >= + 0.5. */ + +float +__x2y2m1f (float x, float y) +{ + double dx = x, dy = y; + return (float) ((dx - 1) * (dx + 1) + dy * dy); +} diff --git a/REORG.TODO/sysdeps/ieee754/float128/Makeconfig b/REORG.TODO/sysdeps/ieee754/float128/Makeconfig new file mode 100644 index 0000000000..6c385d2df2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/Makeconfig @@ -0,0 +1,3 @@ +# Include this earlier so it can be used earlier in Makefiles, +# and sysdep/ makefiles. +float128-fcts = yes diff --git a/REORG.TODO/sysdeps/ieee754/float128/Makefile b/REORG.TODO/sysdeps/ieee754/float128/Makefile new file mode 100644 index 0000000000..c07586c1b6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/Makefile @@ -0,0 +1,3 @@ +ifeq ($(subdir),stdlib) +routines += float1282mpn strfromf128 +endif diff --git a/REORG.TODO/sysdeps/ieee754/float128/Versions b/REORG.TODO/sysdeps/ieee754/float128/Versions new file mode 100644 index 0000000000..caf206475c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/Versions @@ -0,0 +1,150 @@ +%include <float128-abi.h> +%ifndef FLOAT128_VERSION +% error "float128-abi.h must define FLOAT128_VERSION" +%endif +libc { + FLOAT128_VERSION { + strfromf128; + } +} +libm { + FLOAT128_VERSION { + __acosf128_finite; + __acoshf128_finite; + __asinf128_finite; + __atan2f128_finite; + __atanhf128_finite; + __coshf128_finite; + __exp10f128_finite; + __exp2f128_finite; + __expf128_finite; + __finitef128; + __fmodf128_finite; + __fpclassifyf128; + __gammaf128_r_finite; + __hypotf128_finite; + __iseqsigf128; + __isinff128; + __isnanf128; + __issignalingf128; + __j0f128_finite; + __j1f128_finite; + __jnf128_finite; + __lgammaf128_r_finite; + __log10f128_finite; + __log2f128_finite; + __logf128_finite; + __powf128_finite; + __remainderf128_finite; + __signbitf128; + __sinhf128_finite; + __sqrtf128_finite; + __y0f128_finite; + __y1f128_finite; + __ynf128_finite; + acosf128; + acoshf128; + asinf128; + asinhf128; + atan2f128; + atanf128; + atanhf128; + cabsf128; + cacosf128; + cacoshf128; + canonicalizef128; + cargf128; + casinf128; + casinhf128; + catanf128; + catanhf128; + cbrtf128; + ccosf128; + ccoshf128; + ceilf128; + cexpf128; + cimagf128; + clog10f128; + clogf128; + conjf128; + copysignf128; + cosf128; + coshf128; + cpowf128; + cprojf128; + crealf128; + csinf128; + csinhf128; + csqrtf128; + ctanf128; + ctanhf128; + erfcf128; + erff128; + exp10f128; + exp2f128; + expf128; + expm1f128; + fabsf128; + fdimf128; + floorf128; + fmaf128; + fmaxf128; + fmaxmagf128; + fminf128; + fminmagf128; + fmodf128; + frexpf128; + fromfpf128; + fromfpxf128; + getpayloadf128; + hypotf128; + ilogbf128; + j0f128; + j1f128; + jnf128; + ldexpf128; + lgammaf128; + lgammaf128_r; + llogbf128; + llrintf128; + llroundf128; + log10f128; + log1pf128; + log2f128; + logbf128; + logf128; + lrintf128; + lroundf128; + modff128; + nanf128; + nearbyintf128; + nextafterf128; + nextdownf128; + nextupf128; + powf128; + remainderf128; + remquof128; + rintf128; + roundevenf128; + roundf128; + scalblnf128; + scalbnf128; + setpayloadf128; + setpayloadsigf128; + sincosf128; + sinf128; + sinhf128; + sqrtf128; + tanf128; + tanhf128; + tgammaf128; + totalorderf128; + totalordermagf128; + truncf128; + ufromfpf128; + ufromfpxf128; + y0f128; + y1f128; + ynf128; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_acosf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_acosf128.c new file mode 100644 index 0000000000..7ddf7dcdf1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_acosf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_acosl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_acoshf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_acoshf128.c new file mode 100644 index 0000000000..f6dd40cd88 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_acoshf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_acoshl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_asinf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_asinf128.c new file mode 100644 index 0000000000..133ab8d875 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_asinf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_asinl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_atan2f128.c b/REORG.TODO/sysdeps/ieee754/float128/e_atan2f128.c new file mode 100644 index 0000000000..9aa740f770 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_atan2f128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_atan2l.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_atanhf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_atanhf128.c new file mode 100644 index 0000000000..f26c8d54d2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_atanhf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_atanhl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_coshf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_coshf128.c new file mode 100644 index 0000000000..2abf067f64 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_coshf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_coshl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_exp10f128.c b/REORG.TODO/sysdeps/ieee754/float128/e_exp10f128.c new file mode 100644 index 0000000000..b3468d256b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_exp10f128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_exp10l.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_expf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_expf128.c new file mode 100644 index 0000000000..b727b17cc9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_expf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_expl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_fmodf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_fmodf128.c new file mode 100644 index 0000000000..ed8a7491ed --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_fmodf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_fmodl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_gammaf128_r.c b/REORG.TODO/sysdeps/ieee754/float128/e_gammaf128_r.c new file mode 100644 index 0000000000..895ac6374d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_gammaf128_r.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_gammal_r.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_hypotf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_hypotf128.c new file mode 100644 index 0000000000..1f06555505 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_hypotf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_hypotl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_ilogbf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_ilogbf128.c new file mode 100644 index 0000000000..2861801854 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_ilogbf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_ilogbl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_j0f128.c b/REORG.TODO/sysdeps/ieee754/float128/e_j0f128.c new file mode 100644 index 0000000000..b624b5c596 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_j0f128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_j0l.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_j1f128.c b/REORG.TODO/sysdeps/ieee754/float128/e_j1f128.c new file mode 100644 index 0000000000..445428e742 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_j1f128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_j1l.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_jnf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_jnf128.c new file mode 100644 index 0000000000..7854e11a1a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_jnf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_jnl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_lgammaf128_r.c b/REORG.TODO/sysdeps/ieee754/float128/e_lgammaf128_r.c new file mode 100644 index 0000000000..3517ac32af --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_lgammaf128_r.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_lgammal_r.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_log10f128.c b/REORG.TODO/sysdeps/ieee754/float128/e_log10f128.c new file mode 100644 index 0000000000..1c3341e412 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_log10f128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_log10l.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_log2f128.c b/REORG.TODO/sysdeps/ieee754/float128/e_log2f128.c new file mode 100644 index 0000000000..36becaadc4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_log2f128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_log2l.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_logf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_logf128.c new file mode 100644 index 0000000000..b0c9975caf --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_logf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_logl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_powf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_powf128.c new file mode 100644 index 0000000000..3afaf7f6a6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_powf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_powl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_rem_pio2f128.c b/REORG.TODO/sysdeps/ieee754/float128/e_rem_pio2f128.c new file mode 100644 index 0000000000..86c2ca1024 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_rem_pio2f128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_rem_pio2l.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_remainderf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_remainderf128.c new file mode 100644 index 0000000000..90c18f8493 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_remainderf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_remainderl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_scalbf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_scalbf128.c new file mode 100644 index 0000000000..067b724164 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_scalbf128.c @@ -0,0 +1 @@ +/* Not defined for _FloatN types. */ diff --git a/REORG.TODO/sysdeps/ieee754/float128/e_sinhf128.c b/REORG.TODO/sysdeps/ieee754/float128/e_sinhf128.c new file mode 100644 index 0000000000..42a54e0015 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/e_sinhf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/e_sinhl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/float1282mpn.c b/REORG.TODO/sysdeps/ieee754/float128/float1282mpn.c new file mode 100644 index 0000000000..f012ccf0a6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/float1282mpn.c @@ -0,0 +1,20 @@ +/* Convert a _Float128 type to multiprecision. + Copyright (C) 2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float128_private.h> +#include "../ldbl-128/ldbl2mpn.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/float128_private.h b/REORG.TODO/sysdeps/ieee754/float128/float128_private.h new file mode 100644 index 0000000000..1e00853c83 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/float128_private.h @@ -0,0 +1,326 @@ +/* _Float128 overrides for building ldbl-128 as _Float128. + Copyright (C) 2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* This must be included before the function renames below. */ +#include <gmp.h> +#include <math.h> +#undef HUGE_VALL +#define HUGE_VALL HUGE_VAL_F128 +#include <math/mul_splitl.h> + +/* Renames derived from math_private.h. */ +#include <math_private.h> +#include <ieee754_float128.h> +#define ieee854_long_double_shape_type ieee854_float128_shape_type +#define ieee854_long_double ieee854_float128 + +#undef GET_LDOUBLE_LSW64 +#undef GET_LDOUBLE_MSW64 +#undef GET_LDOUBLE_WORDS64 +#undef SET_LDOUBLE_LSW64 +#undef SET_LDOUBLE_MSW64 +#undef SET_LDOUBLE_WORDS64 +#define GET_LDOUBLE_LSW64(x,y) GET_FLOAT128_LSW64 (x, y) +#define GET_LDOUBLE_MSW64(x,y) GET_FLOAT128_MSW64 (x, y) +#define GET_LDOUBLE_WORDS64(x,y,z) GET_FLOAT128_WORDS64 (x, y, z) +#define SET_LDOUBLE_LSW64(x,y) SET_FLOAT128_LSW64 (x, y) +#define SET_LDOUBLE_MSW64(x,y) SET_FLOAT128_MSW64 (x, y) +#define SET_LDOUBLE_WORDS64(x,y,z) SET_FLOAT128_WORDS64 (x, y, z) + +#undef IEEE854_LONG_DOUBLE_BIAS +#define IEEE854_LONG_DOUBLE_BIAS IEEE854_FLOAT128_BIAS + +#ifdef SET_RESTORE_ROUNDF128 +# undef SET_RESTORE_ROUNDL +# define SET_RESTORE_ROUNDL() SET_RESTORE_ROUNDF128() +#endif + + +/* misc macros from the header below. */ +#include <fix-fp-int-convert-overflow.h> +#undef FIX_LDBL_LONG_CONVERT_OVERFLOW +#undef FIX_LDBL_LLONG_CONVERT_OVERFLOW +#define FIX_LDBL_LONG_CONVERT_OVERFLOW FIX_FLT128_LONG_CONVERT_OVERFLOW +#define FIX_LDBL_LLONG_CONVERT_OVERFLOW FIX_FLT128_LLONG_CONVERT_OVERFLOW + + +/* float.h constants. */ +#include <float.h> +#undef LDBL_DIG +#undef LDBL_EPSILON +#undef LDBL_MANT_DIG +#undef LDBL_MAX +#undef LDBL_MAX_10_EXP +#undef LDBL_MAX_EXP +#undef LDBL_MIN +#undef LDBL_MIN_10_EXP +#undef LDBL_MIN_EXP +#undef LDBL_TRUE_MIN +#define LDBL_DIG FLT128_DIG +#define LDBL_EPSILON FLT128_EPSILON +#define LDBL_MANT_DIG FLT128_MANT_DIG +#define LDBL_MAX FLT128_MAX +#define LDBL_MAX_10_EXP FLT128_MAX_10_EXP +#define LDBL_MAX_EXP FLT128_MAX_EXP +#define LDBL_MIN FLT128_MIN +#define LDBL_MIN_10_EXP FLT128_MIN_10_EXP +#define LDBL_MIN_EXP FLT128_MIN_EXP +#define LDBL_TRUE_MIN FLT128_TRUE_MIN + + +/* math.h GNU constants. */ +#undef M_El +#undef M_LOG2El +#undef M_LOG10El +#undef M_LN2l +#undef M_LN10l +#undef M_PIl +#undef M_PI_2l +#undef M_PI_4l +#undef M_1_PIl +#undef M_2_PIl +#undef M_2_SQRTPIl +#undef M_SQRT2l +#undef M_SQRT1_2l +#define M_El M_Ef128 +#define M_LOG2El M_LOG2Ef128 +#define M_LOG10El M_LOG10Ef128 +#define M_LN2l M_LN2f128 +#define M_LN10l M_LN10f128 +#define M_PIl M_PIf128 +#define M_PI_2l M_PI_2f128 +#define M_PI_4l M_PI_4f128 +#define M_1_PIl M_1_PIf128 +#define M_2_PIl M_2_PIf128 +#define M_2_SQRTPIl M_2_SQRTPIf128 +#define M_SQRT2l M_SQRT2f128 +#define M_SQRT1_2l M_SQRT1_2f128 + + +/* IEEE function renames. */ +#define __ieee754_acoshl __ieee754_acoshf128 +#define __ieee754_acosl __ieee754_acosf128 +#define __ieee754_asinhl __ieee754_asinhf128 +#define __ieee754_asinl __ieee754_asinf128 +#define __ieee754_atan2l __ieee754_atan2f128 +#define __ieee754_atanhl __ieee754_atanhf128 +#define __ieee754_coshl __ieee754_coshf128 +#define __ieee754_cosl __ieee754_cosf128 +#define __ieee754_exp10l __ieee754_exp10f128 +#define __ieee754_exp2l __ieee754_exp2f128 +#define __ieee754_expl __ieee754_expf128 +#define __ieee754_fmodl __ieee754_fmodf128 +#define __ieee754_gammal_r __ieee754_gammaf128_r +#define __ieee754_hypotl __ieee754_hypotf128 +#define __ieee754_ilogbl __ieee754_ilogbf128 +#define __ieee754_j0l __ieee754_j0f128 +#define __ieee754_j1l __ieee754_j1f128 +#define __ieee754_jnl __ieee754_jnf128 +#define __ieee754_lgammal_r __ieee754_lgammaf128_r +#define __ieee754_log10l __ieee754_log10f128 +#define __ieee754_log2l __ieee754_log2f128 +#define __ieee754_logl __ieee754_logf128 +#define __ieee754_powl __ieee754_powf128 +#define __ieee754_rem_pio2l __ieee754_rem_pio2f128 +#define __ieee754_remainderl __ieee754_remainderf128 +#define __ieee754_sinhl __ieee754_sinhf128 +#define __ieee754_sqrtl __ieee754_sqrtf128 +#define __ieee754_y0l __ieee754_y0f128 +#define __ieee754_y1l __ieee754_y1f128 +#define __ieee754_ynl __ieee754_ynf128 + + +/* finite math entry points. */ +#define __acoshl_finite __acoshf128_finite +#define __acosl_finite __acosf128_finite +#define __asinl_finite __asinf128_finite +#define __atan2l_finite __atan2f128_finite +#define __atanhl_finite __atanhf128_finite +#define __coshl_finite __coshf128_finite +#define __cosl_finite __cosf128_finite +#define __exp10l_finite __exp10f128_finite +#define __exp2l_finite __exp2f128_finite +#define __expl_finite __expf128_finite +#define __fmodl_finite __fmodf128_finite +#define __hypotl_finite __hypotf128_finite +#define __ilogbl_finite __ilogbf128_finite +#define __j0l_finite __j0f128_finite +#define __j1l_finite __j1f128_finite +#define __jnl_finite __jnf128_finite +#define __lgammal_r_finite __lgammaf128_r_finite +#define __log10l_finite __log10f128_finite +#define __log2l_finite __log2f128_finite +#define __logl_finite __logf128_finite +#define __powl_finite __powf128_finite +#define __remainderl_finite __remainderf128_finite +#define __sinhl_finite __sinhf128_finite +#define __y0l_finite __y0f128_finite +#define __y1l_finite __y1f128_finite +#define __ynl_finite __ynf128_finite + + +/* internal function names. */ +#define __asinhl __asinhf128 +#define __atanl __atanf128 +#define __cbrtl __cbrtf128 +#define __ceill __ceilf128 +#define __copysignl __copysignf128 +#define __cosl __cosf128 +#define __erfcl __erfcf128 +#define __erfl __erff128 +#define __expl __expf128 +#define __expm1l __expm1f128 +#define __fabsl __fabsf128 +#define __fdiml __fdimf128 +#define __finitel __finitef128 +#define __floorl __floorf128 +#define __fmal __fmaf128 +#define __fmaxl __fmaxf128 +#define __fminl __fminf128 +#define __fpclassifyl __fpclassifyf128 +#define __frexpl __frexpf128 +#define __gammal_r_finite __gammaf128_r_finite +#define __isinfl __isinff128 +#define __isnanl __isnanf128 +#define __issignalingl __issignalingf128 +#define __ldexpl __ldexpf128 +#define __llrintl __llrintf128 +#define __llroundl __llroundf128 +#define __log1pl __log1pf128 +#define __logbl __logbf128 +#define __logl __logf128 +#define __lrintl __lrintf128 +#define __lroundl __lroundf128 +#define __modfl __modff128 +#define __nearbyintl __nearbyintf128 +#define __nextafterl __nextafterf128 +#define __nextdownl __nextdownf128 +#define __nextupl __nextupf128 +#define __remquol __remquof128 +#define __rintl __rintf128 +#define __roundl __roundf128 +#define __scalblnl __scalblnf128 +#define __scalbnl __scalbnf128 +#define __signbitl __signbitf128 +#define __sincosl __sincosf128 +#define __sinl __sinf128 +#define __sqrtl __sqrtf128 +#define __tanhl __tanhf128 +#define __tanl __tanf128 +#define __truncl __truncf128 +#define __x2y2m1l __x2y2m1f128 + +/* __nexttowardf128 is not _Float128 API. */ +#define __nexttowardl __nexttowardf128_do_not_use +#define nexttowardl nexttowardf128_do_not_use + + +/* public entry points. */ +#define asinhl asinhf128 +#define atanl atanf128 +#define cbrtl cbrtf128 +#define ceill ceilf128 +#define copysignl copysignf128 +#define cosl cosf128 +#define erfcl erfcf128 +#define erfl erff128 +#define expl expf128 +#define expm1l expm1f128 +#define fabsl fabsf128 +#define fdiml fdimf128 +#define finitel finitef128_do_not_use +#define floorl floorf128 +#define fmal fmaf128 +#define fmaxl fmaxf128 +#define fminl fminf128 +#define frexpl frexpf128 +#define getpayloadl getpayloadf128 +#define isinfl isinff128_do_not_use +#define isnanl isnanf128_do_not_use +#define ldexpl ldexpf128 +#define llrintl llrintf128 +#define llroundl llroundf128 +#define log1pl log1pf128 +#define logbl logbf128 +#define logl logf128 +#define lrintl lrintf128 +#define lroundl lroundf128 +#define modfl modff128 +#define nanl nanf128 +#define nearbyintl nearbyintf128 +#define nextafterl nextafterf128 +#define nextdownl nextdownf128 +#define nextupl nextupf128 +#define remquol remquof128 +#define rintl rintf128 +#define roundevenl roundevenf128 +#define roundl roundf128 +#define scalbnl scalbnf128 +#define sincosl sincosf128 +#define sinl sinf128 +#define sqrtl sqrtf128 +#define tanhl tanhf128 +#define tanl tanf128 +#define totalorderl totalorderf128 +#define totalordermagl totalordermagf128 +#define truncl truncf128 + + +/* misc internal renames. */ +#define __builtin_fmal __builtin_fmaf128 +#define __expl_table __expf128_table +#define __gamma_productl __gamma_productf128 +#define __kernel_cosl __kernel_cosf128 +#define __kernel_rem_pio2l __kernel_rem_pio2f128 +#define __kernel_sincosl __kernel_sincosf128 +#define __kernel_sinl __kernel_sinf128 +#define __kernel_tanl __kernel_tanf128 +#define __lgamma_negl __lgamma_negf128 +#define __lgamma_productl __lgamma_productf128 +#define __mpn_extract_long_double __mpn_extract_float128 +#define __sincosl_table __sincosf128_table +#define mul_splitl mul_splitf128 + +/* Builtin renames. */ +#define __builtin_copysignl __builtin_copysignf128 +#define __builtin_signbitl __builtin_signbit + +/* Get the constant suffix from bits/floatn-compat.h. */ +#define L(x) __f128 (x) + +static inline void +mul_splitf128 (_Float128 *hi, _Float128 *lo, _Float128 x, _Float128 y) +{ +#ifdef __FP_FAST_FMAF128 + /* Fast built-in fused multiply-add. */ + *hi = x * y; + *lo = __builtin_fmal (x, y, -*hi); +#else + /* Apply Dekker's algorithm. */ + *hi = x * y; +# define C ((1LL << (FLT128_MANT_DIG + 1) / 2) + 1) + _Float128 x1 = x * C; + _Float128 y1 = y * C; +# undef C + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + _Float128 x2 = x - x1; + _Float128 y2 = y - y1; + *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2; +#endif +} diff --git a/REORG.TODO/sysdeps/ieee754/float128/gamma_productf128.c b/REORG.TODO/sysdeps/ieee754/float128/gamma_productf128.c new file mode 100644 index 0000000000..be2271f12f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/gamma_productf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/gamma_productl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/ieee754_float128.h b/REORG.TODO/sysdeps/ieee754/float128/ieee754_float128.h new file mode 100644 index 0000000000..e8e7211d88 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/ieee754_float128.h @@ -0,0 +1,140 @@ +/* _Float128 IEEE like macros. + Copyright (C) 2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ +#ifndef _IEEE754_FLOAT128_H +#define _IEEE754_FLOAT128_H + +#include <endian.h> +#include <stdint.h> + +# if __FLOAT_WORD_ORDER == BIG_ENDIAN +# define __FLT_EORDER2(t, a, b) t a; t b; +# define __FLT_EORDER4(t, a, b, c, d) \ + t a; t b; t c; t d; +# define __FLT_EORDER6(t, a, b, c, d, e, f) \ + t a; t b; t c; t d; t e; t f; +# define __FLT_EORDER7(t, a, b, c, d, e, f, g) \ + t a; t b; t c; t d; t e; t f; t g; +# else +# define __FLT_EORDER2(t, a, b) \ + t b; t a; +# define __FLT_EORDER4(t, a, b, c, d) \ + t d; t c; t b; t a; +# define __FLT_EORDER6(t, a, b, c, d, e, f) \ + t f; t e; t d; t c; t b; t a; +# define __FLT_EORDER7(t, a, b, c, d, e, f, g) \ + t g; t f; t e; t d; t c; t b; t a; +# endif + +/* A union which permits us to convert between _Float128 and + four 32 bit ints or two 64 bit ints. */ + +typedef union +{ + _Float128 value; + struct + { + __FLT_EORDER2 (uint64_t, msw, lsw); + } parts64; + struct + { + __FLT_EORDER4 (uint32_t, w0, w1, w2, w3); + } parts32; +} ieee854_float128_shape_type; + +/* Get two 64 bit ints from a _Float128. */ + +# define GET_FLOAT128_WORDS64(ix0,ix1,d) \ +do { \ + ieee854_float128_shape_type qw_u; \ + qw_u.value = (d); \ + (ix0) = qw_u.parts64.msw; \ + (ix1) = qw_u.parts64.lsw; \ +} while (0) + +/* Set a _Float128 from two 64 bit ints. */ + +# define SET_FLOAT128_WORDS64(d,ix0,ix1) \ +do { \ + ieee854_float128_shape_type qw_u; \ + qw_u.parts64.msw = (ix0); \ + qw_u.parts64.lsw = (ix1); \ + (d) = qw_u.value; \ +} while (0) + +/* Get the more significant 64 bits of a _Float128 mantissa. */ + +# define GET_FLOAT128_MSW64(v,d) \ +do { \ + ieee854_float128_shape_type sh_u; \ + sh_u.value = (d); \ + (v) = sh_u.parts64.msw; \ +} while (0) + +/* Set the more significant 64 bits of a _Float128 mantissa from an int. */ + +# define SET_FLOAT128_MSW64(d,v) \ +do { \ + ieee854_float128_shape_type sh_u; \ + sh_u.value = (d); \ + sh_u.parts64.msw = (v); \ + (d) = sh_u.value; \ +} while (0) + +/* Get the least significant 64 bits of a _Float128 mantissa. */ + +# define GET_FLOAT128_LSW64(v,d) \ +do { \ + ieee854_float128_shape_type sh_u; \ + sh_u.value = (d); \ + (v) = sh_u.parts64.lsw; \ +} while (0) + +/* Likewise, some helper macros which are exposed via ieee754.h for + C99 real types, but not _Float128. */ + +union ieee854_float128 + { + _Float128 d; + + /* This is the IEEE 854 quad-precision format. */ + struct + { + __FLT_EORDER6 (unsigned int, negative:1, + exponent:15, + mantissa0:16, + mantissa1:32, + mantissa2:32, + mantissa3:32) + } ieee; + + /* This format makes it easier to see if a NaN is a signalling NaN. */ + struct + { + __FLT_EORDER7 (unsigned int, negative:1, + exponent:15, + quiet_nan:1, + mantissa0:15, + mantissa1:32, + mantissa2:32, + mantissa3:32) + } ieee_nan; + }; + +#define IEEE854_FLOAT128_BIAS 0x3fff /* Added to exponent. */ + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/float128/k_cosf128.c b/REORG.TODO/sysdeps/ieee754/float128/k_cosf128.c new file mode 100644 index 0000000000..9db0906e9a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/k_cosf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/k_cosl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/k_sincosf128.c b/REORG.TODO/sysdeps/ieee754/float128/k_sincosf128.c new file mode 100644 index 0000000000..14c0f1eccf --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/k_sincosf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/k_sincosl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/k_sinf128.c b/REORG.TODO/sysdeps/ieee754/float128/k_sinf128.c new file mode 100644 index 0000000000..f3acf1cfe1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/k_sinf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/k_sinl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/k_tanf128.c b/REORG.TODO/sysdeps/ieee754/float128/k_tanf128.c new file mode 100644 index 0000000000..ca6be539f7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/k_tanf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/k_tanl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/lgamma_negf128.c b/REORG.TODO/sysdeps/ieee754/float128/lgamma_negf128.c new file mode 100644 index 0000000000..9c16f93025 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/lgamma_negf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/lgamma_negl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/lgamma_productf128.c b/REORG.TODO/sysdeps/ieee754/float128/lgamma_productf128.c new file mode 100644 index 0000000000..5efe5dd576 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/lgamma_productf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/lgamma_productl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_asinhf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_asinhf128.c new file mode 100644 index 0000000000..7b93d8cf3a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_asinhf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_asinhl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_atanf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_atanf128.c new file mode 100644 index 0000000000..9b4d7ecec3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_atanf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_atanl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_cbrtf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_cbrtf128.c new file mode 100644 index 0000000000..3bd5797373 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_cbrtf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_cbrtl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_ceilf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_ceilf128.c new file mode 100644 index 0000000000..0af15f5f03 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_ceilf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_ceill.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_copysignf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_copysignf128.c new file mode 100644 index 0000000000..808f7abbc0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_copysignf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_copysignl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_cosf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_cosf128.c new file mode 100644 index 0000000000..8ba552695c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_cosf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_cosl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_erff128.c b/REORG.TODO/sysdeps/ieee754/float128/s_erff128.c new file mode 100644 index 0000000000..ac16ad6665 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_erff128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_erfl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_expm1f128.c b/REORG.TODO/sysdeps/ieee754/float128/s_expm1f128.c new file mode 100644 index 0000000000..ea28d89db4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_expm1f128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_expm1l.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_fabsf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_fabsf128.c new file mode 100644 index 0000000000..79ba47c3fd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_fabsf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_fabsl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_finitef128.c b/REORG.TODO/sysdeps/ieee754/float128/s_finitef128.c new file mode 100644 index 0000000000..801de88e32 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_finitef128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_finitel.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_floorf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_floorf128.c new file mode 100644 index 0000000000..18298436a1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_floorf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_floorl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_fmaf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_fmaf128.c new file mode 100644 index 0000000000..6497895c8d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_fmaf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_fmal.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_fpclassifyf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_fpclassifyf128.c new file mode 100644 index 0000000000..15131dc4a2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_fpclassifyf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_fpclassifyl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_frexpf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_frexpf128.c new file mode 100644 index 0000000000..7b040b3e33 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_frexpf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_frexpl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_fromfpf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_fromfpf128.c new file mode 100644 index 0000000000..891de3d448 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_fromfpf128.c @@ -0,0 +1,5 @@ +#define UNSIGNED 0 +#define INEXACT 0 +#define FUNC fromfpf128 +#include <float128_private.h> +#include "../ldbl-128/s_fromfpl_main.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_fromfpxf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_fromfpxf128.c new file mode 100644 index 0000000000..21676fab03 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_fromfpxf128.c @@ -0,0 +1,5 @@ +#define UNSIGNED 0 +#define INEXACT 1 +#define FUNC fromfpxf128 +#include <float128_private.h> +#include "../ldbl-128/s_fromfpl_main.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_getpayloadf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_getpayloadf128.c new file mode 100644 index 0000000000..2e2607a81b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_getpayloadf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_getpayloadl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_isinff128.c b/REORG.TODO/sysdeps/ieee754/float128/s_isinff128.c new file mode 100644 index 0000000000..62cc424b16 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_isinff128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_isinfl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_isnanf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_isnanf128.c new file mode 100644 index 0000000000..efba24059a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_isnanf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_isnanl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_issignalingf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_issignalingf128.c new file mode 100644 index 0000000000..1d4599544f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_issignalingf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_issignalingl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_llrintf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_llrintf128.c new file mode 100644 index 0000000000..bb9ca580cd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_llrintf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_llrintl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_llroundf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_llroundf128.c new file mode 100644 index 0000000000..be54a90608 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_llroundf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_llroundl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_log1pf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_log1pf128.c new file mode 100644 index 0000000000..48bb84f987 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_log1pf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_log1pl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_logbf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_logbf128.c new file mode 100644 index 0000000000..167384a8d4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_logbf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_logbl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_lrintf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_lrintf128.c new file mode 100644 index 0000000000..1cfa9d7ca4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_lrintf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_lrintl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_lroundf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_lroundf128.c new file mode 100644 index 0000000000..13ba9f220d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_lroundf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_lroundl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_modff128.c b/REORG.TODO/sysdeps/ieee754/float128/s_modff128.c new file mode 100644 index 0000000000..4618c6c380 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_modff128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_modfl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_nearbyintf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_nearbyintf128.c new file mode 100644 index 0000000000..e61a3b3bfb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_nearbyintf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_nearbyintl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_nextafterf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_nextafterf128.c new file mode 100644 index 0000000000..2c43a00384 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_nextafterf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_nextafterl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_nexttowardf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_nexttowardf128.c new file mode 100644 index 0000000000..006e4c98b1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_nexttowardf128.c @@ -0,0 +1 @@ +/* This function does not exist for _FloatN types. */ diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_nextupf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_nextupf128.c new file mode 100644 index 0000000000..7d5d0b8c72 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_nextupf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_nextupl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_remquof128.c b/REORG.TODO/sysdeps/ieee754/float128/s_remquof128.c new file mode 100644 index 0000000000..1cef61ab1b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_remquof128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_remquol.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_rintf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_rintf128.c new file mode 100644 index 0000000000..2adb95f360 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_rintf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_rintl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_roundevenf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_roundevenf128.c new file mode 100644 index 0000000000..5a9b3f395f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_roundevenf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_roundevenl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_roundf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_roundf128.c new file mode 100644 index 0000000000..1eb36f2a5e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_roundf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_roundl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_scalblnf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_scalblnf128.c new file mode 100644 index 0000000000..999223c517 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_scalblnf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_scalblnl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_scalbnf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_scalbnf128.c new file mode 100644 index 0000000000..0e7ab2663b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_scalbnf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_scalbnl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_setpayloadf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_setpayloadf128.c new file mode 100644 index 0000000000..63e046a269 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_setpayloadf128.c @@ -0,0 +1,4 @@ +#include <float128_private.h> +#define SIG 0 +#define FUNC setpayloadf128 +#include "../ldbl-128/s_setpayloadl_main.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_setpayloadsigf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_setpayloadsigf128.c new file mode 100644 index 0000000000..85b2c4a1a8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_setpayloadsigf128.c @@ -0,0 +1,4 @@ +#include <float128_private.h> +#define SIG 1 +#define FUNC setpayloadsigf128 +#include "../ldbl-128/s_setpayloadl_main.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_signbitf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_signbitf128.c new file mode 100644 index 0000000000..71c1ca3a34 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_signbitf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_signbitl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_significandf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_significandf128.c new file mode 100644 index 0000000000..067b724164 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_significandf128.c @@ -0,0 +1 @@ +/* Not defined for _FloatN types. */ diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_sincosf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_sincosf128.c new file mode 100644 index 0000000000..472adde17f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_sincosf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_sincosl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_sinf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_sinf128.c new file mode 100644 index 0000000000..d79a1163a5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_sinf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_sinl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_tanf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_tanf128.c new file mode 100644 index 0000000000..382961aada --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_tanf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_tanl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_tanhf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_tanhf128.c new file mode 100644 index 0000000000..e02c9a6005 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_tanhf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_tanhl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_totalorderf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_totalorderf128.c new file mode 100644 index 0000000000..1b115d8307 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_totalorderf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_totalorderl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_totalordermagf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_totalordermagf128.c new file mode 100644 index 0000000000..e44c657275 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_totalordermagf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_totalordermagl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_truncf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_truncf128.c new file mode 100644 index 0000000000..474d9dc77e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_truncf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/s_truncl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_ufromfpf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_ufromfpf128.c new file mode 100644 index 0000000000..0cd2281035 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_ufromfpf128.c @@ -0,0 +1,5 @@ +#define UNSIGNED 1 +#define INEXACT 0 +#define FUNC ufromfpf128 +#include <float128_private.h> +#include "../ldbl-128/s_fromfpl_main.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/s_ufromfpxf128.c b/REORG.TODO/sysdeps/ieee754/float128/s_ufromfpxf128.c new file mode 100644 index 0000000000..c0cd7e3bc8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/s_ufromfpxf128.c @@ -0,0 +1,5 @@ +#define UNSIGNED 1 +#define INEXACT 1 +#define FUNC ufromfpxf128 +#include <float128_private.h> +#include "../ldbl-128/s_fromfpl_main.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/strfromf128.c b/REORG.TODO/sysdeps/ieee754/float128/strfromf128.c new file mode 100644 index 0000000000..597c7e62f9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/strfromf128.c @@ -0,0 +1,25 @@ +/* Definitions for strfromf128. Implementation in stdlib/strfrom-skeleton.c. + + Copyright (C) 2017 Free Software Foundation, Inc. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define FLOAT _Float128 +#define STRFROM strfromf128 + +#include <bits/floatn.h> +#include <float128_private.h> + +#include <stdlib/strfrom-skeleton.c> diff --git a/REORG.TODO/sysdeps/ieee754/float128/t_sincosf128.c b/REORG.TODO/sysdeps/ieee754/float128/t_sincosf128.c new file mode 100644 index 0000000000..7e699d3c8e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/t_sincosf128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/t_sincosl.c" diff --git a/REORG.TODO/sysdeps/ieee754/float128/x2y2m1f128.c b/REORG.TODO/sysdeps/ieee754/float128/x2y2m1f128.c new file mode 100644 index 0000000000..68880792e6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/float128/x2y2m1f128.c @@ -0,0 +1,2 @@ +#include <float128_private.h> +#include "../ldbl-128/x2y2m1l.c" diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_acosf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_acosf.c new file mode 100644 index 0000000000..6f792f6604 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_acosf.c @@ -0,0 +1,78 @@ +/* e_acosf.c -- float version of e_acos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +pi = 3.1415925026e+00, /* 0x40490fda */ +pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ +pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ +pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ +pS1 = -3.2556581497e-01, /* 0xbea6b090 */ +pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ +pS3 = -4.0055535734e-02, /* 0xbd241146 */ +pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ +pS5 = 3.4793309169e-05, /* 0x3811ef08 */ +qS1 = -2.4033949375e+00, /* 0xc019d139 */ +qS2 = 2.0209457874e+00, /* 0x4001572d */ +qS3 = -6.8828397989e-01, /* 0xbf303361 */ +qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ + +float +__ieee754_acosf(float x) +{ + float z,p,q,r,w,s,c,df; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix==0x3f800000) { /* |x|==1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */ + } else if(ix>0x3f800000) { /* |x| >= 1 */ + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3f000000) { /* |x| < 0.5 */ + if(ix<=0x32800000) return pio2_hi+pio2_lo;/*if|x|<=2**-26*/ + z = x*x; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*(float)0.5; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + s = __ieee754_sqrtf(z); + r = p/q; + w = r*s-pio2_lo; + return pi - (float)2.0*(s+w); + } else { /* x > 0.5 */ + int32_t idf; + z = (one-x)*(float)0.5; + s = __ieee754_sqrtf(z); + df = s; + GET_FLOAT_WORD(idf,df); + SET_FLOAT_WORD(df,idf&0xfffff000); + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + w = r*s+c; + return (float)2.0*(df+w); + } +} +strong_alias (__ieee754_acosf, __acosf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_acoshf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_acoshf.c new file mode 100644 index 0000000000..aabfb85df7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_acoshf.c @@ -0,0 +1,49 @@ +/* e_acoshf.c -- float version of e_acosh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_acoshf.c,v 1.5 1995/05/12 04:57:20 jtc Exp $"; +#endif + +#include <math.h> +#include <math_private.h> + +static const float +one = 1.0, +ln2 = 6.9314718246e-01; /* 0x3f317218 */ + +float __ieee754_acoshf(float x) +{ + float t; + int32_t hx; + GET_FLOAT_WORD(hx,x); + if(hx<0x3f800000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x4d800000) { /* x > 2**28 */ + if(hx >=0x7f800000) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_logf(x)+ln2; /* acosh(huge)=log(2x) */ + } else if (hx==0x3f800000) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_logf((float)2.0*x-one/(x+__ieee754_sqrtf(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return __log1pf(t+__ieee754_sqrtf((float)2.0*t+t*t)); + } +} +strong_alias (__ieee754_acoshf, __acoshf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_asinf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_asinf.c new file mode 100644 index 0000000000..2ca2dbcb28 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_asinf.c @@ -0,0 +1,104 @@ +/* e_asinf.c -- float version of e_asin.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + Modifications for single precision expansion are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_asinf.c,v 1.5 1995/05/12 04:57:25 jtc Exp $"; +#endif + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +huge = 1.000e+30, + +pio2_hi = 1.57079637050628662109375f, +pio2_lo = -4.37113900018624283e-8f, +pio4_hi = 0.785398185253143310546875f, + +/* asin x = x + x^3 p(x^2) + -0.5 <= x <= 0.5; + Peak relative error 4.8e-9 */ +p0 = 1.666675248e-1f, +p1 = 7.495297643e-2f, +p2 = 4.547037598e-2f, +p3 = 2.417951451e-2f, +p4 = 4.216630880e-2f; + +float __ieee754_asinf(float x) +{ + float t,w,p,q,c,r,s; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix==0x3f800000) { + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + } else if(ix> 0x3f800000) { /* |x|>= 1 */ + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3f000000) { /* |x|<0.5 */ + if(ix<0x32000000) { /* if |x| < 2**-27 */ + math_check_force_underflow (x); + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } else { + t = x*x; + w = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4)))); + return x+x*w; + } + } + /* 1> |x|>= 0.5 */ + w = one-fabsf(x); + t = w*0.5f; + p = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4)))); + s = __ieee754_sqrtf(t); + if(ix>=0x3F79999A) { /* if |x| > 0.975 */ + t = pio2_hi-(2.0f*(s+s*p)-pio2_lo); + } else { + int32_t iw; + w = s; + GET_FLOAT_WORD(iw,w); + SET_FLOAT_WORD(w,iw&0xfffff000); + c = (t-w*w)/(s+w); + r = p; + p = 2.0f*s*r-(pio2_lo-2.0f*c); + q = pio4_hi-2.0f*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; +} +strong_alias (__ieee754_asinf, __asinf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_atan2f.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_atan2f.c new file mode 100644 index 0000000000..29eefc0dd6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_atan2f.c @@ -0,0 +1,94 @@ +/* e_atan2f.c -- float version of e_atan2.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + +static const float +tiny = 1.0e-30, +zero = 0.0, +pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */ +pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */ +pi = 3.1415927410e+00, /* 0x40490fdb */ +pi_lo = -8.7422776573e-08; /* 0xb3bbbd2e */ + +float +__ieee754_atan2f (float y, float x) +{ + float z; + int32_t k,m,hx,hy,ix,iy; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + GET_FLOAT_WORD(hy,y); + iy = hy&0x7fffffff; + if((ix>0x7f800000)|| + (iy>0x7f800000)) /* x or y is NaN */ + return x+y; + if(hx==0x3f800000) return __atanf(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if(iy==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7f800000) { + if(iy==0x7f800000) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>23; + if(k > 60) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**60 */ + else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ + else z=__atanf(fabsf(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: { + u_int32_t zh; + GET_FLOAT_WORD(zh,z); + SET_FLOAT_WORD(z,zh ^ 0x80000000); + } + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} +strong_alias (__ieee754_atan2f, __atan2f_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_atanhf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_atanhf.c new file mode 100644 index 0000000000..feb6beeec7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_atanhf.c @@ -0,0 +1,74 @@ +/* Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@gmail.com>, 2011. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + + +/* __ieee754_atanh(x) + Method : + 1.Reduced x to positive by atanh(-x) = -atanh(x) + 2.For x>=0.5 + 1 2x x + atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + 2 1 - x 1 - x + + For x<0.5 + atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) + + Special cases: + atanh(x) is NaN if |x| > 1 with signal; + atanh(NaN) is that NaN with no signal; + atanh(+-1) is +-INF with signal. + + */ + +#include <float.h> +#include <inttypes.h> +#include <math.h> +#include <math_private.h> + +static const float huge = 1e30; + +float +__ieee754_atanhf (float x) +{ + float xa = fabsf (x); + float t; + if (isless (xa, 0.5f)) + { + if (__glibc_unlikely (xa < 0x1.0p-28f)) + { + math_force_eval (huge + x); + math_check_force_underflow (x); + return x; + } + + t = xa + xa; + t = 0.5f * __log1pf (t + t * xa / (1.0f - xa)); + } + else if (__glibc_likely (isless (xa, 1.0f))) + t = 0.5f * __log1pf ((xa + xa) / (1.0f - xa)); + else + { + if (isgreater (xa, 1.0f)) + return (x - x) / (x - x); + + return x / 0.0f; + } + + return __copysignf (t, x); +} +strong_alias (__ieee754_atanhf, __atanhf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_coshf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_coshf.c new file mode 100644 index 0000000000..7b223758e1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_coshf.c @@ -0,0 +1,63 @@ +/* e_coshf.c -- float version of e_cosh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Optimizations by Ulrich Drepper <drepper@gmail.com>, 2011 + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + +static const float huge = 1.0e30; +static const float one = 1.0, half=0.5; + +float +__ieee754_coshf (float x) +{ + float t,w; + int32_t ix; + + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + + /* |x| in [0,22] */ + if (ix < 0x41b00000) { + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3eb17218) { + if (ix<0x24000000) return one; /* cosh(tiny) = 1 */ + t = __expm1f(fabsf(x)); + w = one+t; + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + t = __ieee754_expf(fabsf(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x42b17180) return half*__ieee754_expf(fabsf(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x42b2d4fc) { + w = __ieee754_expf(half*fabsf(x)); + t = half*w; + return t*w; + } + + /* x is INF or NaN */ + if(ix>=0x7f800000) return x*x; + + /* |x| > overflowthresold, cosh(x) overflow */ + return math_narrow_eval (huge*huge); +} +strong_alias (__ieee754_coshf, __coshf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_exp2f.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_exp2f.c new file mode 100644 index 0000000000..567d3ff6d0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_exp2f.c @@ -0,0 +1,132 @@ +/* Single-precision floating point 2^x. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* The basic design here is from + Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical + Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft., + 17 (1), March 1991, pp. 26-45. + It has been slightly modified to compute 2^x instead of e^x, and for + single-precision. + */ +#ifndef _GNU_SOURCE +# define _GNU_SOURCE +#endif +#include <stdlib.h> +#include <float.h> +#include <ieee754.h> +#include <math.h> +#include <fenv.h> +#include <inttypes.h> +#include <math_private.h> + +#include "t_exp2f.h" + +static const float TWOM100 = 7.88860905e-31; +static const float TWO127 = 1.7014118346e+38; + +float +__ieee754_exp2f (float x) +{ + static const float himark = (float) FLT_MAX_EXP; + static const float lomark = (float) (FLT_MIN_EXP - FLT_MANT_DIG - 1); + + /* Check for usual case. */ + if (isless (x, himark) && isgreaterequal (x, lomark)) + { + static const float THREEp14 = 49152.0; + int tval, unsafe; + float rx, x22, result; + union ieee754_float ex2_u, scale_u; + + if (fabsf (x) < FLT_EPSILON / 4.0f) + return 1.0f + x; + + { + SET_RESTORE_ROUND_NOEXF (FE_TONEAREST); + + /* 1. Argument reduction. + Choose integers ex, -128 <= t < 128, and some real + -1/512 <= x1 <= 1/512 so that + x = ex + t/512 + x1. + + First, calculate rx = ex + t/256. */ + rx = x + THREEp14; + rx -= THREEp14; + x -= rx; /* Compute x=x1. */ + /* Compute tval = (ex*256 + t)+128. + Now, t = (tval mod 256)-128 and ex=tval/256 [that's mod, NOT %; + and /-round-to-nearest not the usual c integer /]. */ + tval = (int) (rx * 256.0f + 128.0f); + + /* 2. Adjust for accurate table entry. + Find e so that + x = ex + t/256 + e + x2 + where -7e-4 < e < 7e-4, and + (float)(2^(t/256+e)) + is accurate to one part in 2^-64. */ + + /* 'tval & 255' is the same as 'tval%256' except that it's always + positive. + Compute x = x2. */ + x -= __exp2f_deltatable[tval & 255]; + + /* 3. Compute ex2 = 2^(t/255+e+ex). */ + ex2_u.f = __exp2f_atable[tval & 255]; + tval >>= 8; + /* x2 is an integer multiple of 2^-30; avoid intermediate + underflow from the calculation of x22 * x. */ + unsafe = abs(tval) >= -FLT_MIN_EXP - 32; + ex2_u.ieee.exponent += tval >> unsafe; + scale_u.f = 1.0; + scale_u.ieee.exponent += tval - (tval >> unsafe); + + /* 4. Approximate 2^x2 - 1, using a second-degree polynomial, + with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14] + less than 1.3e-10. */ + + x22 = (.24022656679f * x + .69314736128f) * ex2_u.f; + } + + /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */ + result = x22 * x + ex2_u.f; + + if (!unsafe) + return result; + else + { + result *= scale_u.f; + math_check_force_underflow_nonneg (result); + return result; + } + } + /* Exceptional cases: */ + else if (isless (x, himark)) + { + if (isinf (x)) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TWOM100 * TWOM100; + } + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO127*x; +} +strong_alias (__ieee754_exp2f, __exp2f_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_expf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_expf.c new file mode 100644 index 0000000000..782072f213 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_expf.c @@ -0,0 +1,133 @@ +/* Single-precision floating point e^x. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* How this works: + + The input value, x, is written as + + x = n * ln(2) + t/512 + delta[t] + x; + + where: + - n is an integer, 127 >= n >= -150; + - t is an integer, 177 >= t >= -177 + - delta is based on a table entry, delta[t] < 2^-28 + - x is whatever is left, |x| < 2^-10 + + Then e^x is approximated as + + e^x = 2^n ( e^(t/512 + delta[t]) + + ( e^(t/512 + delta[t]) + * ( p(x + delta[t] + n * ln(2)) - delta ) ) ) + + where + - p(x) is a polynomial approximating e(x)-1; + - e^(t/512 + delta[t]) is obtained from a table. + + The table used is the same one as for the double precision version; + since we have the table, we might as well use it. + + It turns out to be faster to do calculations in double precision than + to perform an 'accurate table method' expf, because of the range reduction + overhead (compare exp2f). + */ +#include <float.h> +#include <ieee754.h> +#include <math.h> +#include <fenv.h> +#include <inttypes.h> +#include <math_private.h> + +extern const float __exp_deltatable[178]; +extern const double __exp_atable[355] /* __attribute__((mode(DF))) */; + +static const float TWOM100 = 7.88860905e-31; +static const float TWO127 = 1.7014118346e+38; + +float +__ieee754_expf (float x) +{ + static const float himark = 88.72283935546875; + static const float lomark = -103.972084045410; + /* Check for usual case. */ + if (isless (x, himark) && isgreater (x, lomark)) + { + static const float THREEp42 = 13194139533312.0; + static const float THREEp22 = 12582912.0; + /* 1/ln(2). */ +#undef M_1_LN2 + static const float M_1_LN2 = 1.44269502163f; + /* ln(2) */ +#undef M_LN2 + static const double M_LN2 = .6931471805599452862; + + int tval; + double x22, t, result, dx; + float n, delta; + union ieee754_double ex2_u; + + { + SET_RESTORE_ROUND_NOEXF (FE_TONEAREST); + + /* Calculate n. */ + n = x * M_1_LN2 + THREEp22; + n -= THREEp22; + dx = x - n*M_LN2; + + /* Calculate t/512. */ + t = dx + THREEp42; + t -= THREEp42; + dx -= t; + + /* Compute tval = t. */ + tval = (int) (t * 512.0); + + if (t >= 0) + delta = - __exp_deltatable[tval]; + else + delta = __exp_deltatable[-tval]; + + /* Compute ex2 = 2^n e^(t/512+delta[t]). */ + ex2_u.d = __exp_atable[tval+177]; + ex2_u.ieee.exponent += (int) n; + + /* Approximate e^(dx+delta) - 1, using a second-degree polynomial, + with maximum error in [-2^-10-2^-28,2^-10+2^-28] + less than 5e-11. */ + x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta; + } + + /* Return result. */ + result = x22 * ex2_u.d + ex2_u.d; + return (float) result; + } + /* Exceptional cases: */ + else if (isless (x, himark)) + { + if (isinf (x)) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TWOM100 * TWOM100; + } + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO127*x; +} +strong_alias (__ieee754_expf, __expf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_fmodf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_fmodf.c new file mode 100644 index 0000000000..8d8fad4eb5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_fmodf.c @@ -0,0 +1,102 @@ +/* e_fmodf.c -- float version of e_fmod.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __ieee754_fmodf(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include <math.h> +#include <math_private.h> + +static const float one = 1.0, Zero[] = {0.0, -0.0,}; + +float +__ieee754_fmodf (float x, float y) +{ + int32_t n,hx,hy,hz,ix,iy,sx,i; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + sx = hx&0x80000000; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if(hy==0||(hx>=0x7f800000)|| /* y=0,or x not finite */ + (hy>0x7f800000)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx<hy) return x; /* |x|<|y| return x */ + if(hx==hy) + return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/ + + /* determine ix = ilogb(x) */ + if(hx<0x00800000) { /* subnormal x */ + for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1; + } else ix = (hx>>23)-127; + + /* determine iy = ilogb(y) */ + if(hy<0x00800000) { /* subnormal y */ + for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1; + } else iy = (hy>>23)-127; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -126) + hx = 0x00800000|(0x007fffff&hx); + else { /* subnormal x, shift x to normal */ + n = -126-ix; + hx = hx<<n; + } + if(iy >= -126) + hy = 0x00800000|(0x007fffff&hy); + else { /* subnormal y, shift y to normal */ + n = -126-iy; + hy = hy<<n; + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy; + if(hz<0){hx = hx+hx;} + else { + if(hz==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + hx = hz+hz; + } + } + hz=hx-hy; + if(hz>=0) {hx=hz;} + + /* convert back to floating value and restore the sign */ + if(hx==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + while(hx<0x00800000) { /* normalize x */ + hx = hx+hx; + iy -= 1; + } + if(iy>= -126) { /* normalize output */ + hx = ((hx-0x00800000)|((iy+127)<<23)); + SET_FLOAT_WORD(x,hx|sx); + } else { /* subnormal output */ + n = -126 - iy; + hx >>= n; + SET_FLOAT_WORD(x,hx|sx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} +strong_alias (__ieee754_fmodf, __fmodf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_gammaf_r.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_gammaf_r.c new file mode 100644 index 0000000000..1157dec2fe --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_gammaf_r.c @@ -0,0 +1,212 @@ +/* Implementation of gamma function according to ISO C. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const float gamma_coeff[] = + { + 0x1.555556p-4f, + -0xb.60b61p-12f, + 0x3.403404p-12f, + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 42, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static float +gammaf_positive (float x, int *exp2_adj) +{ + int local_signgam; + if (x < 0.5f) + { + *exp2_adj = 0; + return __ieee754_expf (__ieee754_lgammaf_r (x + 1, &local_signgam)) / x; + } + else if (x <= 1.5f) + { + *exp2_adj = 0; + return __ieee754_expf (__ieee754_lgammaf_r (x, &local_signgam)); + } + else if (x < 2.5f) + { + *exp2_adj = 0; + float x_adj = x - 1; + return (__ieee754_expf (__ieee754_lgammaf_r (x_adj, &local_signgam)) + * x_adj); + } + else + { + float eps = 0; + float x_eps = 0; + float x_adj = x; + float prod = 1; + if (x < 4.0f) + { + /* Adjust into the range for applying Stirling's + approximation. */ + float n = __ceilf (4.0f - x); + x_adj = math_narrow_eval (x + n); + x_eps = (x - (x_adj - n)); + prod = __gamma_productf (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + float exp_adj = -eps; + float x_adj_int = __roundf (x_adj); + float x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + float x_adj_mant = __frexpf (x_adj, &x_adj_log2); + if (x_adj_mant < (float) M_SQRT1_2) + { + x_adj_log2--; + x_adj_mant *= 2.0f; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + float ret = (__ieee754_powf (x_adj_mant, x_adj) + * __ieee754_exp2f (x_adj_log2 * x_adj_frac) + * __ieee754_expf (-x_adj) + * __ieee754_sqrtf (2 * (float) M_PI / x_adj) + / prod); + exp_adj += x_eps * __ieee754_logf (x_adj); + float bsum = gamma_coeff[NCOEFF - 1]; + float x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1f (exp_adj); + } +} + +float +__ieee754_gammaf_r (float x, int *signgamp) +{ + int32_t hx; + float ret; + + GET_FLOAT_WORD (hx, x); + + if (__glibc_unlikely ((hx & 0x7fffffff) == 0)) + { + /* Return value for x == 0 is Inf with divide by zero exception. */ + *signgamp = 0; + return 1.0 / x; + } + if (__builtin_expect (hx < 0, 0) + && (u_int32_t) hx < 0xff800000 && __rintf (x) == x) + { + /* Return value for integer x < 0 is NaN with invalid exception. */ + *signgamp = 0; + return (x - x) / (x - x); + } + if (__glibc_unlikely (hx == 0xff800000)) + { + /* x == -Inf. According to ISO this is NaN. */ + *signgamp = 0; + return x - x; + } + if (__glibc_unlikely ((hx & 0x7f800000) == 0x7f800000)) + { + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ + *signgamp = 0; + return x + x; + } + + if (x >= 36.0f) + { + /* Overflow. */ + *signgamp = 0; + ret = math_narrow_eval (FLT_MAX * FLT_MAX); + return ret; + } + else + { + SET_RESTORE_ROUNDF (FE_TONEAREST); + if (x > 0.0f) + { + *signgamp = 0; + int exp2_adj; + float tret = gammaf_positive (x, &exp2_adj); + ret = __scalbnf (tret, exp2_adj); + } + else if (x >= -FLT_EPSILON / 4.0f) + { + *signgamp = 0; + ret = 1.0f / x; + } + else + { + float tx = __truncf (x); + *signgamp = (tx == 2.0f * __truncf (tx / 2.0f)) ? -1 : 1; + if (x <= -42.0f) + /* Underflow. */ + ret = FLT_MIN * FLT_MIN; + else + { + float frac = tx - x; + if (frac > 0.5f) + frac = 1.0f - frac; + float sinpix = (frac <= 0.25f + ? __sinf ((float) M_PI * frac) + : __cosf ((float) M_PI * (0.5f - frac))); + int exp2_adj; + float tret = (float) M_PI / (-x * sinpix + * gammaf_positive (-x, &exp2_adj)); + ret = __scalbnf (tret, -exp2_adj); + math_check_force_underflow_nonneg (ret); + } + } + ret = math_narrow_eval (ret); + } + if (isinf (ret) && x != 0) + { + if (*signgamp < 0) + { + ret = math_narrow_eval (-__copysignf (FLT_MAX, ret) * FLT_MAX); + ret = -ret; + } + else + ret = math_narrow_eval (__copysignf (FLT_MAX, ret) * FLT_MAX); + return ret; + } + else if (ret == 0) + { + if (*signgamp < 0) + { + ret = math_narrow_eval (-__copysignf (FLT_MIN, ret) * FLT_MIN); + ret = -ret; + } + else + ret = math_narrow_eval (__copysignf (FLT_MIN, ret) * FLT_MIN); + return ret; + } + else + return ret; +} +strong_alias (__ieee754_gammaf_r, __gammaf_r_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_hypotf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_hypotf.c new file mode 100644 index 0000000000..fda2651a84 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_hypotf.c @@ -0,0 +1,45 @@ +/* e_hypotf.c -- float version of e_hypot.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + +float +__ieee754_hypotf(float x, float y) +{ + double d_x, d_y; + int32_t ha, hb; + + GET_FLOAT_WORD(ha,x); + ha &= 0x7fffffff; + GET_FLOAT_WORD(hb,y); + hb &= 0x7fffffff; + if (ha == 0x7f800000 && !issignaling (y)) + return fabsf(x); + else if (hb == 0x7f800000 && !issignaling (x)) + return fabsf(y); + else if (ha > 0x7f800000 || hb > 0x7f800000) + return fabsf(x) * fabsf(y); + else if (ha == 0) + return fabsf(y); + else if (hb == 0) + return fabsf(x); + + d_x = (double) x; + d_y = (double) y; + + return (float) __ieee754_sqrt(d_x * d_x + d_y * d_y); +} +strong_alias (__ieee754_hypotf, __hypotf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_ilogbf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_ilogbf.c new file mode 100644 index 0000000000..1ae344ea39 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_ilogbf.c @@ -0,0 +1,44 @@ +/* s_ilogbf.c -- float version of s_ilogb.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_ilogbf.c,v 1.4 1995/05/10 20:47:31 jtc Exp $"; +#endif + +#include <limits.h> +#include <math.h> +#include <math_private.h> + +int __ieee754_ilogbf(float x) +{ + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + hx &= 0x7fffffff; + if(hx<0x00800000) { + if(hx==0) + return FP_ILOGB0; /* ilogb(0) = FP_ILOGB0 */ + else /* subnormal x */ + for (ix = -126,hx<<=8; hx>0; hx<<=1) ix -=1; + return ix; + } + else if (hx<0x7f800000) return (hx>>23)-127; + else if (FP_ILOGBNAN != INT_MAX) { + /* ISO C99 requires ilogbf(+-Inf) == INT_MAX. */ + if (hx==0x7f800000) + return INT_MAX; + } + return FP_ILOGBNAN; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_j0f.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_j0f.c new file mode 100644 index 0000000000..b783dd069d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_j0f.c @@ -0,0 +1,337 @@ +/* e_j0f.c -- float version of e_j0.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + +static float pzerof(float), qzerof(float); + +static const float +huge = 1e30, +one = 1.0, +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +tpi = 6.3661974669e-01, /* 0x3f22f983 */ + /* R0/S0 on [0, 2.00] */ +R02 = 1.5625000000e-02, /* 0x3c800000 */ +R03 = -1.8997929874e-04, /* 0xb947352e */ +R04 = 1.8295404516e-06, /* 0x35f58e88 */ +R05 = -4.6183270541e-09, /* 0xb19eaf3c */ +S01 = 1.5619102865e-02, /* 0x3c7fe744 */ +S02 = 1.1692678527e-04, /* 0x38f53697 */ +S03 = 5.1354652442e-07, /* 0x3509daa6 */ +S04 = 1.1661400734e-09; /* 0x30a045e8 */ + +static const float zero = 0.0; + +float +__ieee754_j0f(float x) +{ + float z, s,c,ss,cc,r,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return one/(x*x); + x = fabsf(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + __sincosf (x, &s, &c); + ss = s-c; + cc = s+c; + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = -__cosf(x+x); + if ((s*c)<zero) cc = z/ss; + else ss = z/cc; + } + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(x); + else { + u = pzerof(x); v = qzerof(x); + z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(x); + } + return z; + } + if(ix<0x39000000) { /* |x| < 2**-13 */ + math_force_eval(huge+x); /* raise inexact if x != 0 */ + if(ix<0x32000000) return one; /* |x|<2**-27 */ + else return one - (float)0.25*x*x; + } + z = x*x; + r = z*(R02+z*(R03+z*(R04+z*R05))); + s = one+z*(S01+z*(S02+z*(S03+z*S04))); + if(ix < 0x3F800000) { /* |x| < 1.00 */ + return one + z*((float)-0.25+(r/s)); + } else { + u = (float)0.5*x; + return((one+u)*(one-u)+z*(r/s)); + } +} +strong_alias (__ieee754_j0f, __j0f_finite) + +static const float +u00 = -7.3804296553e-02, /* 0xbd9726b5 */ +u01 = 1.7666645348e-01, /* 0x3e34e80d */ +u02 = -1.3818567619e-02, /* 0xbc626746 */ +u03 = 3.4745343146e-04, /* 0x39b62a69 */ +u04 = -3.8140706238e-06, /* 0xb67ff53c */ +u05 = 1.9559013964e-08, /* 0x32a802ba */ +u06 = -3.9820518410e-11, /* 0xae2f21eb */ +v01 = 1.2730483897e-02, /* 0x3c509385 */ +v02 = 7.6006865129e-05, /* 0x389f65e0 */ +v03 = 2.5915085189e-07, /* 0x348b216c */ +v04 = 4.4111031494e-10; /* 0x2ff280c2 */ + +float +__ieee754_y0f(float x) +{ + float z, s,c,ss,cc,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0, y0(0) is -inf. */ + if(ix>=0x7f800000) return one/(x+x*x); + if(ix==0) return -1/zero; /* -inf and divide by zero exception. */ + if(hx<0) return zero/(zero*x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + __sincosf (x, &s, &c); + ss = s-c; + cc = s+c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = -__cosf(x+x); + if ((s*c)<zero) cc = z/ss; + else ss = z/cc; + } + if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x); + else { + u = pzerof(x); v = qzerof(x); + z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x); + } + return z; + } + if(ix<=0x39800000) { /* x < 2**-13 */ + return(u00 + tpi*__ieee754_logf(x)); + } + z = x*x; + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); + return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x))); +} +strong_alias (__ieee754_y0f, __y0f_finite) + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + -7.0312500000e-02, /* 0xbd900000 */ + -8.0816707611e+00, /* 0xc1014e86 */ + -2.5706311035e+02, /* 0xc3808814 */ + -2.4852163086e+03, /* 0xc51b5376 */ + -5.2530439453e+03, /* 0xc5a4285a */ +}; +static const float pS8[5] = { + 1.1653436279e+02, /* 0x42e91198 */ + 3.8337448730e+03, /* 0x456f9beb */ + 4.0597855469e+04, /* 0x471e95db */ + 1.1675296875e+05, /* 0x47e4087c */ + 4.7627726562e+04, /* 0x473a0bba */ +}; +static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -1.1412546255e-11, /* 0xad48c58a */ + -7.0312492549e-02, /* 0xbd8fffff */ + -4.1596107483e+00, /* 0xc0851b88 */ + -6.7674766541e+01, /* 0xc287597b */ + -3.3123129272e+02, /* 0xc3a59d9b */ + -3.4643338013e+02, /* 0xc3ad3779 */ +}; +static const float pS5[5] = { + 6.0753936768e+01, /* 0x42730408 */ + 1.0512523193e+03, /* 0x44836813 */ + 5.9789707031e+03, /* 0x45bad7c4 */ + 9.6254453125e+03, /* 0x461665c8 */ + 2.4060581055e+03, /* 0x451660ee */ +}; + +static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + -2.5470459075e-09, /* 0xb12f081b */ + -7.0311963558e-02, /* 0xbd8fffb8 */ + -2.4090321064e+00, /* 0xc01a2d95 */ + -2.1965976715e+01, /* 0xc1afba52 */ + -5.8079170227e+01, /* 0xc2685112 */ + -3.1447946548e+01, /* 0xc1fb9565 */ +}; +static const float pS3[5] = { + 3.5856033325e+01, /* 0x420f6c94 */ + 3.6151397705e+02, /* 0x43b4c1ca */ + 1.1936077881e+03, /* 0x44953373 */ + 1.1279968262e+03, /* 0x448cffe6 */ + 1.7358093262e+02, /* 0x432d94b8 */ +}; + +static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -8.8753431271e-08, /* 0xb3be98b7 */ + -7.0303097367e-02, /* 0xbd8ffb12 */ + -1.4507384300e+00, /* 0xbfb9b1cc */ + -7.6356959343e+00, /* 0xc0f4579f */ + -1.1193166733e+01, /* 0xc1331736 */ + -3.2336456776e+00, /* 0xc04ef40d */ +}; +static const float pS2[5] = { + 2.2220300674e+01, /* 0x41b1c32d */ + 1.3620678711e+02, /* 0x430834f0 */ + 2.7047027588e+02, /* 0x43873c32 */ + 1.5387539673e+02, /* 0x4319e01a */ + 1.4657617569e+01, /* 0x416a859a */ +}; + +static float +pzerof(float x) +{ + const float *p,*q; + float z,r,s; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + /* ix >= 0x40000000 for all calls to this function. */ + if(ix>=0x41000000) {p = pR8; q= pS8;} + else if(ix>=0x40f71c58){p = pR5; q= pS5;} + else if(ix>=0x4036db68){p = pR3; q= pS3;} + else {p = pR2; q= pS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + 7.3242187500e-02, /* 0x3d960000 */ + 1.1768206596e+01, /* 0x413c4a93 */ + 5.5767340088e+02, /* 0x440b6b19 */ + 8.8591972656e+03, /* 0x460a6cca */ + 3.7014625000e+04, /* 0x471096a0 */ +}; +static const float qS8[6] = { + 1.6377603149e+02, /* 0x4323c6aa */ + 8.0983447266e+03, /* 0x45fd12c2 */ + 1.4253829688e+05, /* 0x480b3293 */ + 8.0330925000e+05, /* 0x49441ed4 */ + 8.4050156250e+05, /* 0x494d3359 */ + -3.4389928125e+05, /* 0xc8a7eb69 */ +}; + +static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.8408595828e-11, /* 0x2da1ec79 */ + 7.3242180049e-02, /* 0x3d95ffff */ + 5.8356351852e+00, /* 0x40babd86 */ + 1.3511157227e+02, /* 0x43071c90 */ + 1.0272437744e+03, /* 0x448067cd */ + 1.9899779053e+03, /* 0x44f8bf4b */ +}; +static const float qS5[6] = { + 8.2776611328e+01, /* 0x42a58da0 */ + 2.0778142090e+03, /* 0x4501dd07 */ + 1.8847289062e+04, /* 0x46933e94 */ + 5.6751113281e+04, /* 0x475daf1d */ + 3.5976753906e+04, /* 0x470c88c1 */ + -5.3543427734e+03, /* 0xc5a752be */ +}; + +static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + 4.3774099900e-09, /* 0x3196681b */ + 7.3241114616e-02, /* 0x3d95ff70 */ + 3.3442313671e+00, /* 0x405607e3 */ + 4.2621845245e+01, /* 0x422a7cc5 */ + 1.7080809021e+02, /* 0x432acedf */ + 1.6673394775e+02, /* 0x4326bbe4 */ +}; +static const float qS3[6] = { + 4.8758872986e+01, /* 0x42430916 */ + 7.0968920898e+02, /* 0x44316c1c */ + 3.7041481934e+03, /* 0x4567825f */ + 6.4604252930e+03, /* 0x45c9e367 */ + 2.5163337402e+03, /* 0x451d4557 */ + -1.4924745178e+02, /* 0xc3153f59 */ +}; + +static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.5044444979e-07, /* 0x342189db */ + 7.3223426938e-02, /* 0x3d95f62a */ + 1.9981917143e+00, /* 0x3fffc4bf */ + 1.4495602608e+01, /* 0x4167edfd */ + 3.1666231155e+01, /* 0x41fd5471 */ + 1.6252708435e+01, /* 0x4182058c */ +}; +static const float qS2[6] = { + 3.0365585327e+01, /* 0x41f2ecb8 */ + 2.6934811401e+02, /* 0x4386ac8f */ + 8.4478375244e+02, /* 0x44533229 */ + 8.8293585205e+02, /* 0x445cbbe5 */ + 2.1266638184e+02, /* 0x4354aa98 */ + -5.3109550476e+00, /* 0xc0a9f358 */ +}; + +static float +qzerof(float x) +{ + const float *p,*q; + float s,r,z; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + /* ix >= 0x40000000 for all calls to this function. */ + if(ix>=0x41000000) {p = qR8; q= qS8;} + else if(ix>=0x40f71c58){p = qR5; q= qS5;} + else if(ix>=0x4036db68){p = qR3; q= qS3;} + else {p = qR2; q= qS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (-(float).125 + r/s)/x; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_j1f.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_j1f.c new file mode 100644 index 0000000000..805a87d85b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_j1f.c @@ -0,0 +1,347 @@ +/* e_j1f.c -- float version of e_j1.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static float ponef(float), qonef(float); + +static const float +huge = 1e30, +one = 1.0, +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +tpi = 6.3661974669e-01, /* 0x3f22f983 */ + /* R0/S0 on [0,2] */ +r00 = -6.2500000000e-02, /* 0xbd800000 */ +r01 = 1.4070566976e-03, /* 0x3ab86cfd */ +r02 = -1.5995563444e-05, /* 0xb7862e36 */ +r03 = 4.9672799207e-08, /* 0x335557d2 */ +s01 = 1.9153760746e-02, /* 0x3c9ce859 */ +s02 = 1.8594678841e-04, /* 0x3942fab6 */ +s03 = 1.1771846857e-06, /* 0x359dffc2 */ +s04 = 5.0463624390e-09, /* 0x31ad6446 */ +s05 = 1.2354227016e-11; /* 0x2d59567e */ + +static const float zero = 0.0; + +float +__ieee754_j1f(float x) +{ + float z, s,c,ss,cc,r,u,v,y; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(__builtin_expect(ix>=0x7f800000, 0)) return one/x; + y = fabsf(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + __sincosf (y, &s, &c); + ss = -s-c; + cc = s-c; + if(ix<0x7f000000) { /* make sure y+y not overflow */ + z = __cosf(y+y); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* + * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) + * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) + */ + if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(y); + else { + u = ponef(y); v = qonef(y); + z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(y); + } + if(hx<0) return -z; + else return z; + } + if(__builtin_expect(ix<0x32000000, 0)) { /* |x|<2**-27 */ + if(huge+x>one) { /* inexact if x!=0 necessary */ + float ret = math_narrow_eval ((float) 0.5 * x); + math_check_force_underflow (ret); + if (ret == 0 && x != 0) + __set_errno (ERANGE); + return ret; + } + } + z = x*x; + r = z*(r00+z*(r01+z*(r02+z*r03))); + s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); + r *= x; + return(x*(float)0.5+r/s); +} +strong_alias (__ieee754_j1f, __j1f_finite) + +static const float U0[5] = { + -1.9605709612e-01, /* 0xbe48c331 */ + 5.0443872809e-02, /* 0x3d4e9e3c */ + -1.9125689287e-03, /* 0xbafaaf2a */ + 2.3525259166e-05, /* 0x37c5581c */ + -9.1909917899e-08, /* 0xb3c56003 */ +}; +static const float V0[5] = { + 1.9916731864e-02, /* 0x3ca3286a */ + 2.0255257550e-04, /* 0x3954644b */ + 1.3560879779e-06, /* 0x35b602d4 */ + 6.2274145840e-09, /* 0x31d5f8eb */ + 1.6655924903e-11, /* 0x2d9281cf */ +}; + +float +__ieee754_y1f(float x) +{ + float z, s,c,ss,cc,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if(__builtin_expect(ix>=0x7f800000, 0)) return one/(x+x*x); + if(__builtin_expect(ix==0, 0)) + return -1/zero; /* -inf and divide by zero exception. */ + if(__builtin_expect(hx<0, 0)) return zero/(zero*x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + SET_RESTORE_ROUNDF (FE_TONEAREST); + __sincosf (x, &s, &c); + ss = -s-c; + cc = s-c; + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = __cosf(x+x); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x); + else { + u = ponef(x); v = qonef(x); + z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x); + } + return z; + } + if(__builtin_expect(ix<=0x33000000, 0)) { /* x < 2**-25 */ + z = -tpi / x; + if (isinf (z)) + __set_errno (ERANGE); + return z; + } + z = x*x; + u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); + v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); + return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x)); +} +strong_alias (__ieee754_y1f, __y1f_finite) + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + 1.1718750000e-01, /* 0x3df00000 */ + 1.3239480972e+01, /* 0x4153d4ea */ + 4.1205184937e+02, /* 0x43ce06a3 */ + 3.8747453613e+03, /* 0x45722bed */ + 7.9144794922e+03, /* 0x45f753d6 */ +}; +static const float ps8[5] = { + 1.1420736694e+02, /* 0x42e46a2c */ + 3.6509309082e+03, /* 0x45642ee5 */ + 3.6956207031e+04, /* 0x47105c35 */ + 9.7602796875e+04, /* 0x47bea166 */ + 3.0804271484e+04, /* 0x46f0a88b */ +}; + +static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.3199052094e-11, /* 0x2d68333f */ + 1.1718749255e-01, /* 0x3defffff */ + 6.8027510643e+00, /* 0x40d9b023 */ + 1.0830818176e+02, /* 0x42d89dca */ + 5.1763616943e+02, /* 0x440168b7 */ + 5.2871520996e+02, /* 0x44042dc6 */ +}; +static const float ps5[5] = { + 5.9280597687e+01, /* 0x426d1f55 */ + 9.9140142822e+02, /* 0x4477d9b1 */ + 5.3532670898e+03, /* 0x45a74a23 */ + 7.8446904297e+03, /* 0x45f52586 */ + 1.5040468750e+03, /* 0x44bc0180 */ +}; + +static const float pr3[6] = { + 3.0250391081e-09, /* 0x314fe10d */ + 1.1718686670e-01, /* 0x3defffab */ + 3.9329774380e+00, /* 0x407bb5e7 */ + 3.5119403839e+01, /* 0x420c7a45 */ + 9.1055007935e+01, /* 0x42b61c2a */ + 4.8559066772e+01, /* 0x42423c7c */ +}; +static const float ps3[5] = { + 3.4791309357e+01, /* 0x420b2a4d */ + 3.3676245117e+02, /* 0x43a86198 */ + 1.0468714600e+03, /* 0x4482dbe3 */ + 8.9081134033e+02, /* 0x445eb3ed */ + 1.0378793335e+02, /* 0x42cf936c */ +}; + +static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.0771083225e-07, /* 0x33e74ea8 */ + 1.1717621982e-01, /* 0x3deffa16 */ + 2.3685150146e+00, /* 0x401795c0 */ + 1.2242610931e+01, /* 0x4143e1bc */ + 1.7693971634e+01, /* 0x418d8d41 */ + 5.0735230446e+00, /* 0x40a25a4d */ +}; +static const float ps2[5] = { + 2.1436485291e+01, /* 0x41ab7dec */ + 1.2529022980e+02, /* 0x42fa9499 */ + 2.3227647400e+02, /* 0x436846c7 */ + 1.1767937469e+02, /* 0x42eb5bd7 */ + 8.3646392822e+00, /* 0x4105d590 */ +}; + +static float +ponef(float x) +{ + const float *p,*q; + float z,r,s; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + /* ix >= 0x40000000 for all calls to this function. */ + if(ix>=0x41000000) {p = pr8; q= ps8;} + else if(ix>=0x40f71c58){p = pr5; q= ps5;} + else if(ix>=0x4036db68){p = pr3; q= ps3;} + else {p = pr2; q= ps2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + -1.0253906250e-01, /* 0xbdd20000 */ + -1.6271753311e+01, /* 0xc1822c8d */ + -7.5960174561e+02, /* 0xc43de683 */ + -1.1849806641e+04, /* 0xc639273a */ + -4.8438511719e+04, /* 0xc73d3683 */ +}; +static const float qs8[6] = { + 1.6139537048e+02, /* 0x43216537 */ + 7.8253862305e+03, /* 0x45f48b17 */ + 1.3387534375e+05, /* 0x4802bcd6 */ + 7.1965775000e+05, /* 0x492fb29c */ + 6.6660125000e+05, /* 0x4922be94 */ + -2.9449025000e+05, /* 0xc88fcb48 */ +}; + +static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -2.0897993405e-11, /* 0xadb7d219 */ + -1.0253904760e-01, /* 0xbdd1fffe */ + -8.0564479828e+00, /* 0xc100e736 */ + -1.8366960144e+02, /* 0xc337ab6b */ + -1.3731937256e+03, /* 0xc4aba633 */ + -2.6124443359e+03, /* 0xc523471c */ +}; +static const float qs5[6] = { + 8.1276550293e+01, /* 0x42a28d98 */ + 1.9917987061e+03, /* 0x44f8f98f */ + 1.7468484375e+04, /* 0x468878f8 */ + 4.9851425781e+04, /* 0x4742bb6d */ + 2.7948074219e+04, /* 0x46da5826 */ + -4.7191835938e+03, /* 0xc5937978 */ +}; + +static const float qr3[6] = { + -5.0783124372e-09, /* 0xb1ae7d4f */ + -1.0253783315e-01, /* 0xbdd1ff5b */ + -4.6101160049e+00, /* 0xc0938612 */ + -5.7847221375e+01, /* 0xc267638e */ + -2.2824453735e+02, /* 0xc3643e9a */ + -2.1921012878e+02, /* 0xc35b35cb */ +}; +static const float qs3[6] = { + 4.7665153503e+01, /* 0x423ea91e */ + 6.7386511230e+02, /* 0x4428775e */ + 3.3801528320e+03, /* 0x45534272 */ + 5.5477290039e+03, /* 0x45ad5dd5 */ + 1.9031191406e+03, /* 0x44ede3d0 */ + -1.3520118713e+02, /* 0xc3073381 */ +}; + +static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -1.7838172539e-07, /* 0xb43f8932 */ + -1.0251704603e-01, /* 0xbdd1f475 */ + -2.7522056103e+00, /* 0xc0302423 */ + -1.9663616180e+01, /* 0xc19d4f16 */ + -4.2325313568e+01, /* 0xc2294d1f */ + -2.1371921539e+01, /* 0xc1aaf9b2 */ +}; +static const float qs2[6] = { + 2.9533363342e+01, /* 0x41ec4454 */ + 2.5298155212e+02, /* 0x437cfb47 */ + 7.5750280762e+02, /* 0x443d602e */ + 7.3939318848e+02, /* 0x4438d92a */ + 1.5594900513e+02, /* 0x431bf2f2 */ + -4.9594988823e+00, /* 0xc09eb437 */ +}; + +static float +qonef(float x) +{ + const float *p,*q; + float s,r,z; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + /* ix >= 0x40000000 for all calls to this function. */ + if(ix>=0x40200000) {p = qr8; q= qs8;} + else if(ix>=0x40f71c58){p = qr5; q= qs5;} + else if(ix>=0x4036db68){p = qr3; q= qs3;} + else {p = qr2; q= qs2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return ((float).375 + r/s)/x; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_jnf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_jnf.c new file mode 100644 index 0000000000..4e634778d3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_jnf.c @@ -0,0 +1,233 @@ +/* e_jnf.c -- float version of e_jn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const float +two = 2.0000000000e+00, /* 0x40000000 */ +one = 1.0000000000e+00; /* 0x3F800000 */ + +static const float zero = 0.0000000000e+00; + +float +__ieee754_jnf(int n, float x) +{ + float ret; + { + int32_t i,hx,ix, sgn; + float a, b, temp, di; + float z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if J(n,NaN) is NaN */ + if(__builtin_expect(ix>0x7f800000, 0)) return x+x; + if(n<0){ + n = -n; + x = -x; + hx ^= 0x80000000; + } + if(n==0) return(__ieee754_j0f(x)); + if(n==1) return(__ieee754_j1f(x)); + sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ + x = fabsf(x); + SET_RESTORE_ROUNDF (FE_TONEAREST); + if(__builtin_expect(ix==0||ix>=0x7f800000, 0)) /* if x is 0 or inf */ + return sgn == 1 ? -zero : zero; + else if((float)n<=x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + a = __ieee754_j0f(x); + b = __ieee754_j1f(x); + for(i=1;i<n;i++){ + temp = b; + b = b*((double)(i+i)/x) - a; /* avoid underflow */ + a = temp; + } + } else { + if(ix<0x30800000) { /* x < 2**-29 */ + /* x is tiny, return the first Taylor expansion of J(n,x) + * J(n,x) = 1/n!*(x/2)^n - ... + */ + if(n>33) /* underflow */ + b = zero; + else { + temp = x*(float)0.5; b = temp; + for (a=one,i=2;i<=n;i++) { + a *= (float)i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b/a; + } + } else { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + float t,v; + float q0,q1,h,tmp; int32_t k,m; + w = (n+n)/(float)x; h = (float)2.0/(float)x; + q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1; + while(q1<(float)1.0e9) { + k += 1; z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n+n; + for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two/x; + tmp = tmp*__ieee754_logf(fabsf(v*tmp)); + if(tmp<(float)8.8721679688e+01) { + for(i=n-1,di=(float)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + } + } else { + for(i=n-1,di=(float)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if(b>(float)1e10) { + a /= b; + t /= b; + b = one; + } + } + } + /* j0() and j1() suffer enormous loss of precision at and + * near zero; however, we know that their zero points never + * coincide, so just choose the one further away from zero. + */ + z = __ieee754_j0f (x); + w = __ieee754_j1f (x); + if (fabsf (z) >= fabsf (w)) + b = (t * z / b); + else + b = (t * w / a); + } + } + if(sgn==1) ret = -b; else ret = b; + ret = math_narrow_eval (ret); + } + if (ret == 0) + { + ret = math_narrow_eval (__copysignf (FLT_MIN, ret) * FLT_MIN); + __set_errno (ERANGE); + } + else + math_check_force_underflow (ret); + return ret; +} +strong_alias (__ieee754_jnf, __jnf_finite) + +float +__ieee754_ynf(int n, float x) +{ + float ret; + { + int32_t i,hx,ix; + u_int32_t ib; + int32_t sign; + float a, b, temp; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if(__builtin_expect(ix>0x7f800000, 0)) return x+x; + if(__builtin_expect(ix==0, 0)) + return -HUGE_VALF+x; /* -inf and overflow exception. */ + if(__builtin_expect(hx<0, 0)) return zero/(zero*x); + sign = 1; + if(n<0){ + n = -n; + sign = 1 - ((n&1)<<1); + } + if(n==0) return(__ieee754_y0f(x)); + SET_RESTORE_ROUNDF (FE_TONEAREST); + if(n==1) { + ret = sign*__ieee754_y1f(x); + goto out; + } + if(__builtin_expect(ix==0x7f800000, 0)) return zero; + + a = __ieee754_y0f(x); + b = __ieee754_y1f(x); + /* quit if b is -inf */ + GET_FLOAT_WORD(ib,b); + for(i=1;i<n&&ib!=0xff800000;i++){ + temp = b; + b = ((double)(i+i)/x)*b - a; + GET_FLOAT_WORD(ib,b); + a = temp; + } + /* If B is +-Inf, set up errno accordingly. */ + if (! isfinite (b)) + __set_errno (ERANGE); + if(sign>0) ret = b; else ret = -b; + } + out: + if (isinf (ret)) + ret = __copysignf (FLT_MAX, ret) * FLT_MAX; + return ret; +} +strong_alias (__ieee754_ynf, __ynf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_lgammaf_r.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_lgammaf_r.c new file mode 100644 index 0000000000..1b30dcd84d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_lgammaf_r.c @@ -0,0 +1,246 @@ +/* e_lgammaf_r.c -- float version of e_lgamma_r.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> +#include <libc-diag.h> + +static const float +two23= 8.3886080000e+06, /* 0x4b000000 */ +half= 5.0000000000e-01, /* 0x3f000000 */ +one = 1.0000000000e+00, /* 0x3f800000 */ +pi = 3.1415927410e+00, /* 0x40490fdb */ +a0 = 7.7215664089e-02, /* 0x3d9e233f */ +a1 = 3.2246702909e-01, /* 0x3ea51a66 */ +a2 = 6.7352302372e-02, /* 0x3d89f001 */ +a3 = 2.0580807701e-02, /* 0x3ca89915 */ +a4 = 7.3855509982e-03, /* 0x3bf2027e */ +a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ +a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ +a7 = 5.1006977446e-04, /* 0x3a05b634 */ +a8 = 2.2086278477e-04, /* 0x39679767 */ +a9 = 1.0801156895e-04, /* 0x38e28445 */ +a10 = 2.5214456400e-05, /* 0x37d383a2 */ +a11 = 4.4864096708e-05, /* 0x383c2c75 */ +tc = 1.4616321325e+00, /* 0x3fbb16c3 */ +tf = -1.2148628384e-01, /* 0xbdf8cdcd */ +/* tt = -(tail of tf) */ +tt = 6.6971006518e-09, /* 0x31e61c52 */ +t0 = 4.8383611441e-01, /* 0x3ef7b95e */ +t1 = -1.4758771658e-01, /* 0xbe17213c */ +t2 = 6.4624942839e-02, /* 0x3d845a15 */ +t3 = -3.2788541168e-02, /* 0xbd064d47 */ +t4 = 1.7970675603e-02, /* 0x3c93373d */ +t5 = -1.0314224288e-02, /* 0xbc28fcfe */ +t6 = 6.1005386524e-03, /* 0x3bc7e707 */ +t7 = -3.6845202558e-03, /* 0xbb7177fe */ +t8 = 2.2596477065e-03, /* 0x3b141699 */ +t9 = -1.4034647029e-03, /* 0xbab7f476 */ +t10 = 8.8108185446e-04, /* 0x3a66f867 */ +t11 = -5.3859531181e-04, /* 0xba0d3085 */ +t12 = 3.1563205994e-04, /* 0x39a57b6b */ +t13 = -3.1275415677e-04, /* 0xb9a3f927 */ +t14 = 3.3552918467e-04, /* 0x39afe9f7 */ +u0 = -7.7215664089e-02, /* 0xbd9e233f */ +u1 = 6.3282704353e-01, /* 0x3f2200f4 */ +u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ +u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ +u4 = 2.2896373272e-01, /* 0x3e6a7578 */ +u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ +v1 = 2.4559779167e+00, /* 0x401d2ebe */ +v2 = 2.1284897327e+00, /* 0x4008392d */ +v3 = 7.6928514242e-01, /* 0x3f44efdf */ +v4 = 1.0422264785e-01, /* 0x3dd572af */ +v5 = 3.2170924824e-03, /* 0x3b52d5db */ +s0 = -7.7215664089e-02, /* 0xbd9e233f */ +s1 = 2.1498242021e-01, /* 0x3e5c245a */ +s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ +s3 = 1.4635047317e-01, /* 0x3e15dce6 */ +s4 = 2.6642270386e-02, /* 0x3cda40e4 */ +s5 = 1.8402845599e-03, /* 0x3af135b4 */ +s6 = 3.1947532989e-05, /* 0x3805ff67 */ +r1 = 1.3920053244e+00, /* 0x3fb22d3b */ +r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ +r3 = 1.7193385959e-01, /* 0x3e300f6e */ +r4 = 1.8645919859e-02, /* 0x3c98bf54 */ +r5 = 7.7794247773e-04, /* 0x3a4beed6 */ +r6 = 7.3266842264e-06, /* 0x36f5d7bd */ +w0 = 4.1893854737e-01, /* 0x3ed67f1d */ +w1 = 8.3333335817e-02, /* 0x3daaaaab */ +w2 = -2.7777778450e-03, /* 0xbb360b61 */ +w3 = 7.9365057172e-04, /* 0x3a500cfd */ +w4 = -5.9518753551e-04, /* 0xba1c065c */ +w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ +w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ + +static const float zero= 0.0000000000e+00; + +static float +sin_pif(float x) +{ + float y,z; + int n,ix; + + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = __floorf(y); + if(z!=y) { /* inexact anyway */ + y *= (float)0.5; + y = (float)2.0*(y - __floorf(y)); /* y = |x| mod 2.0 */ + n = (int) (y*(float)4.0); + } else { + if(ix>=0x4b800000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x4b000000) z = y+two23; /* exact */ + GET_FLOAT_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sinf(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break; + case 3: + case 4: y = __kernel_sinf(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break; + default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break; + } + return -y; +} + + +float +__ieee754_lgammaf_r(float x, int *signgamp) +{ + float t,y,z,nadj,p,p1,p2,p3,q,r,w; + int i,hx,ix; + + GET_FLOAT_WORD(hx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + *signgamp = 1; + ix = hx&0x7fffffff; + if(__builtin_expect(ix>=0x7f800000, 0)) return x*x; + if(__builtin_expect(ix==0, 0)) + { + if (hx < 0) + *signgamp = -1; + return one/fabsf(x); + } + if(__builtin_expect(ix<0x30800000, 0)) { + /* |x|<2**-30, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -__ieee754_logf(-x); + } else return -__ieee754_logf(x); + } + if(hx<0) { + if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ + return __fabsf (x)/zero; + if (ix > 0x40000000 /* X < 2.0f. */ + && ix < 0x41700000 /* X > -15.0f. */) + return __lgamma_negf (x, signgamp); + t = sin_pif(x); + if(t==zero) return one/fabsf(t); /* -integer */ + nadj = __ieee754_logf(pi/fabsf(t*x)); + if(t<zero) *signgamp = -1; + x = -x; + } + + /* purge off 1 and 2 */ + if (ix==0x3f800000||ix==0x40000000) r = 0; + /* for x < 2.0 */ + else if(ix<0x40000000) { + if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ + r = -__ieee754_logf(x); + if(ix>=0x3f3b4a20) {y = one-x; i= 0;} + else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-(float)0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-(float)0.5*y + p1/p2); + } + } + else if(ix<0x41000000) { /* x < 8.0 */ + i = (int)x; + t = zero; + y = x-(float)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+(float)6.0); /* FALLTHRU */ + case 6: z *= (y+(float)5.0); /* FALLTHRU */ + case 5: z *= (y+(float)4.0); /* FALLTHRU */ + case 4: z *= (y+(float)3.0); /* FALLTHRU */ + case 3: z *= (y+(float)2.0); /* FALLTHRU */ + r += __ieee754_logf(z); break; + } + /* 8.0 <= x < 2**26 */ + } else if (ix < 0x4c800000) { + t = __ieee754_logf(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**26 <= x <= inf */ + r = math_narrow_eval (x*(__ieee754_logf(x)-one)); + /* NADJ is set for negative arguments but not otherwise, + resulting in warnings that it may be used uninitialized + although in the cases where it is used it has always been + set. */ + DIAG_PUSH_NEEDS_COMMENT; + DIAG_IGNORE_NEEDS_COMMENT (4.9, "-Wmaybe-uninitialized"); + if(hx<0) r = nadj - r; + DIAG_POP_NEEDS_COMMENT; + return r; +} +strong_alias (__ieee754_lgammaf_r, __lgammaf_r_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_log10f.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_log10f.c new file mode 100644 index 0000000000..aa21bbc9c5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_log10f.c @@ -0,0 +1,54 @@ +/* e_log10f.c -- float version of e_log10.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> +#include <fix-int-fp-convert-zero.h> + +static const float +two25 = 3.3554432000e+07, /* 0x4c000000 */ +ivln10 = 4.3429449201e-01, /* 0x3ede5bd9 */ +log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */ +log10_2lo = 7.9034151668e-07; /* 0x355427db */ + +float +__ieee754_log10f(float x) +{ + float y,z; + int32_t i,k,hx; + + GET_FLOAT_WORD(hx,x); + + k=0; + if (hx < 0x00800000) { /* x < 2**-126 */ + if (__builtin_expect((hx&0x7fffffff)==0, 0)) + return -two25/__fabsf (x); /* log(+-0)=-inf */ + if (__builtin_expect(hx<0, 0)) + return (x-x)/(x-x); /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(hx,x); + } + if (__builtin_expect(hx >= 0x7f800000, 0)) return x+x; + k += (hx>>23)-127; + i = ((u_int32_t)k&0x80000000)>>31; + hx = (hx&0x007fffff)|((0x7f-i)<<23); + y = (float)(k+i); + if (FIX_INT_FP_CONVERT_ZERO && y == 0.0f) + y = 0.0f; + SET_FLOAT_WORD(x,hx); + z = y*log10_2lo + ivln10*__ieee754_logf(x); + return z+y*log10_2hi; +} +strong_alias (__ieee754_log10f, __log10f_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_log2f.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_log2f.c new file mode 100644 index 0000000000..782d901094 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_log2f.c @@ -0,0 +1,86 @@ +/* e_logf.c -- float version of e_log.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * adapted for log2 by Ulrich Drepper <drepper@cygnus.com> + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + +#include <math.h> +#include <math_private.h> +#include <fix-int-fp-convert-zero.h> + +static const float +ln2 = 0.69314718055994530942, +two25 = 3.355443200e+07, /* 0x4c000000 */ +Lg1 = 6.6666668653e-01, /* 3F2AAAAB */ +Lg2 = 4.0000000596e-01, /* 3ECCCCCD */ +Lg3 = 2.8571429849e-01, /* 3E924925 */ +Lg4 = 2.2222198546e-01, /* 3E638E29 */ +Lg5 = 1.8183572590e-01, /* 3E3A3325 */ +Lg6 = 1.5313838422e-01, /* 3E1CD04F */ +Lg7 = 1.4798198640e-01; /* 3E178897 */ + +static const float zero = 0.0; + +float +__ieee754_log2f(float x) +{ + float hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,ix,i,j; + + GET_FLOAT_WORD(ix,x); + + k=0; + if (ix < 0x00800000) { /* x < 2**-126 */ + if (__builtin_expect((ix&0x7fffffff)==0, 0)) + return -two25/__fabsf (x); /* log(+-0)=-inf */ + if (__builtin_expect(ix<0, 0)) + return (x-x)/(x-x); /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(ix,x); + } + if (__builtin_expect(ix >= 0x7f800000, 0)) return x+x; + k += (ix>>23)-127; + ix &= 0x007fffff; + i = (ix+(0x95f64<<3))&0x800000; + SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ + k += (i>>23); + dk = (float)k; + f = x-(float)1.0; + if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */ + if(f==zero) + { + if (FIX_INT_FP_CONVERT_ZERO && dk == 0.0f) + dk = 0.0f; + return dk; + } + R = f*f*((float)0.5-(float)0.33333333333333333*f); + return dk-(R-f)/ln2; + } + s = f/((float)2.0+f); + z = s*s; + i = ix-(0x6147a<<3); + w = z*z; + j = (0x6b851<<3)-ix; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=(float)0.5*f*f; + return dk-((hfsq-(s*(hfsq+R)))-f)/ln2; + } else { + return dk-((s*(f-R))-f)/ln2; + } +} +strong_alias (__ieee754_log2f, __log2f_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_logf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_logf.c new file mode 100644 index 0000000000..cf75e11781 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_logf.c @@ -0,0 +1,85 @@ +/* e_logf.c -- float version of e_log.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + +static const float +ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ +ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ +two25 = 3.355443200e+07, /* 0x4c000000 */ +Lg1 = 6.6666668653e-01, /* 3F2AAAAB */ +Lg2 = 4.0000000596e-01, /* 3ECCCCCD */ +Lg3 = 2.8571429849e-01, /* 3E924925 */ +Lg4 = 2.2222198546e-01, /* 3E638E29 */ +Lg5 = 1.8183572590e-01, /* 3E3A3325 */ +Lg6 = 1.5313838422e-01, /* 3E1CD04F */ +Lg7 = 1.4798198640e-01; /* 3E178897 */ + +static const float zero = 0.0; + +float +__ieee754_logf(float x) +{ + float hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,ix,i,j; + + GET_FLOAT_WORD(ix,x); + + k=0; + if (ix < 0x00800000) { /* x < 2**-126 */ + if (__builtin_expect((ix&0x7fffffff)==0, 0)) + return -two25/zero; /* log(+-0)=-inf */ + if (__builtin_expect(ix<0, 0)) + return (x-x)/(x-x); /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(ix,x); + } + if (__builtin_expect(ix >= 0x7f800000, 0)) return x+x; + k += (ix>>23)-127; + ix &= 0x007fffff; + i = (ix+(0x95f64<<3))&0x800000; + SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ + k += (i>>23); + f = x-(float)1.0; + if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */ + if(f==zero) { + if(k==0) return zero; else {dk=(float)k; + return dk*ln2_hi+dk*ln2_lo;} + } + R = f*f*((float)0.5-(float)0.33333333333333333*f); + if(k==0) return f-R; else {dk=(float)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/((float)2.0+f); + dk = (float)k; + z = s*s; + i = ix-(0x6147a<<3); + w = z*z; + j = (0x6b851<<3)-ix; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=(float)0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} +strong_alias (__ieee754_logf, __logf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_powf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_powf.c new file mode 100644 index 0000000000..13b49def8e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_powf.c @@ -0,0 +1,258 @@ +/* e_powf.c -- float version of e_pow.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + +static const float huge = 1.0e+30, tiny = 1.0e-30; + +static const float +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ +dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ +zero = 0.0, +one = 1.0, +two = 2.0, +two24 = 16777216.0, /* 0x4b800000 */ + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 6.0000002384e-01, /* 0x3f19999a */ +L2 = 4.2857143283e-01, /* 0x3edb6db7 */ +L3 = 3.3333334327e-01, /* 0x3eaaaaab */ +L4 = 2.7272811532e-01, /* 0x3e8ba305 */ +L5 = 2.3066075146e-01, /* 0x3e6c3255 */ +L6 = 2.0697501302e-01, /* 0x3e53f142 */ +P1 = 1.6666667163e-01, /* 0x3e2aaaab */ +P2 = -2.7777778450e-03, /* 0xbb360b61 */ +P3 = 6.6137559770e-05, /* 0x388ab355 */ +P4 = -1.6533901999e-06, /* 0xb5ddea0e */ +P5 = 4.1381369442e-08, /* 0x3331bb4c */ +lg2 = 6.9314718246e-01, /* 0x3f317218 */ +lg2_h = 6.93145752e-01, /* 0x3f317200 */ +lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ +ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ +cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ +cp_h = 0xf.64p-4, /* cp high 12 bits. */ +cp_l = -0x7.b11e3p-16, /* 2/(3ln2) - cp_h. */ +ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ +ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ +ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ + +float +__ieee754_powf(float x, float y) +{ + float z,ax,z_h,z_l,p_h,p_l; + float y1,t1,t2,r,s,t,u,v,w; + int32_t i,j,k,yisint,n; + int32_t hx,hy,ix,iy,is; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if(iy==0 && !issignaling (x)) return one; + + /* x==+-1 */ + if(x == 1.0 && !issignaling (y)) return one; + if(x == -1.0 && isinf(y)) return one; + + /* +-NaN return x+y */ + if(__builtin_expect(ix > 0x7f800000 || + iy > 0x7f800000, 0)) + return x+y; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x4b800000) yisint = 2; /* even integer y */ + else if(iy>=0x3f800000) { + k = (iy>>23)-0x7f; /* exponent */ + j = iy>>(23-k); + if((j<<(23-k))==iy) yisint = 2-(j&1); + } + } + + /* special value of y */ + if (__builtin_expect(iy==0x7f800000, 0)) { /* y is +-inf */ + if (ix==0x3f800000) + return y - y; /* inf**+-1 is NaN */ + else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3f800000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3f000000) { /* y is 0.5 */ + if(__builtin_expect(hx>=0, 1)) /* x >= +0 */ + return __ieee754_sqrtf(x); + } + + ax = fabsf(x); + /* special value of x */ + if(__builtin_expect(ix==0x7f800000||ix==0||ix==0x3f800000, 0)){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3f800000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } else if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + + /* (x<0)**(non-int) is NaN */ + if(__builtin_expect(((((u_int32_t)hx>>31)-1)|yisint)==0, 0)) + return (x-x)/(x-x); + + /* |y| is huge */ + if(__builtin_expect(iy>0x4d000000, 0)) { /* if |y| > 2**27 */ + /* over/underflow if x is not close to one */ + if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny; + if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny; + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + t = ax-1; /* t has 20 trailing zeros */ + w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25)); + u = ivln2_h*t; /* ivln2_h has 16 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = v-(t1-u); + } else { + float s2,s_h,s_l,t_h,t_l; + /* Avoid internal underflow for tiny y. The exact value + of y does not matter if |y| <= 2**-32. */ + if (iy < 0x2f800000) + SET_FLOAT_WORD (y, (hy & 0x80000000) | 0x2f800000); + n = 0; + /* take care subnormal number */ + if(ix<0x00800000) + {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); } + n += ((ix)>>23)-0x7f; + j = ix&0x007fffff; + /* determine interval */ + ix = j|0x3f800000; /* normalize ix */ + if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */ + else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */ + else {k=0;n+=1;ix -= 0x00800000;} + SET_FLOAT_WORD(ax,ix); + + /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ + u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ + v = one/(ax+bp[k]); + s = u*v; + s_h = s; + GET_FLOAT_WORD(is,s_h); + SET_FLOAT_WORD(s_h,is&0xfffff000); + /* t_h=ax+bp[k] High */ + SET_FLOAT_WORD (t_h, + ((((ix>>1)|0x20000000)+0x00400000+(k<<21)) + & 0xfffff000)); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = s*s; + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+s); + s2 = s_h*s_h; + t_h = (float)3.0+s2+r; + GET_FLOAT_WORD(is,t_h); + SET_FLOAT_WORD(t_h,is&0xfffff000); + t_l = r-((t_h-(float)3.0)-s2); + /* u+v = s*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*s; + /* 2/(3log2)*(s+...) */ + p_h = u+v; + GET_FLOAT_WORD(is,p_h); + SET_FLOAT_WORD(p_h,is&0xfffff000); + p_l = v-(p_h-u); + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l*p_h+p_l*cp+dp_l[k]; + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (float)n; + t1 = (((z_h+z_l)+dp_h[k])+t); + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) + s = -one; /* (-ve)**(odd int) */ + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + GET_FLOAT_WORD(is,y); + SET_FLOAT_WORD(y1,is&0xfffff000); + p_l = (y-y1)*t1+y*t2; + p_h = y1*t1; + z = p_l+p_h; + GET_FLOAT_WORD(j,z); + if (__builtin_expect(j>0x43000000, 0)) /* if z > 128 */ + return s*huge*huge; /* overflow */ + else if (__builtin_expect(j==0x43000000, 0)) { /* if z == 128 */ + if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ + } + else if (__builtin_expect((j&0x7fffffff)>0x43160000, 0))/* z <= -150 */ + return s*tiny*tiny; /* underflow */ + else if (__builtin_expect((u_int32_t) j==0xc3160000, 0)){/* z == -150*/ + if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>23)-0x7f; + n = 0; + if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00800000>>(k+1)); + k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */ + SET_FLOAT_WORD(t,n&~(0x007fffff>>k)); + n = ((n&0x007fffff)|0x00800000)>>(23-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + GET_FLOAT_WORD(is,t); + SET_FLOAT_WORD(t,is&0xfffff000); + u = t*lg2_h; + v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + GET_FLOAT_WORD(j,z); + j += (n<<23); + if((j>>23)<=0) /* subnormal output */ + { + z = __scalbnf (z, n); + float force_underflow = z * z; + math_force_eval (force_underflow); + } + else SET_FLOAT_WORD(z,j); + return s*z; +} +strong_alias (__ieee754_powf, __powf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_rem_pio2f.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_rem_pio2f.c new file mode 100644 index 0000000000..c4d28c8657 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_rem_pio2f.c @@ -0,0 +1,179 @@ +/* e_rem_pio2f.c -- float version of e_rem_pio2.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp $"; +#endif + +/* __ieee754_rem_pio2f(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2f() + */ + +#include <math.h> +#include <math_private.h> + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +static const int32_t two_over_pi[] = { +0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, +0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, +0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63, +0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A, +0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09, +0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, +0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44, +0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41, +0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C, +0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, +0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11, +0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF, +0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E, +0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, +0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92, +0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08, +0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0, +0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, +0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85, +0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80, +0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA, +0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, +}; + +/* This array is like the one in e_rem_pio2.c, but the numbers are + single precision and the last 8 bits are forced to 0. */ +static const int32_t npio2_hw[] = { +0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, +0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, +0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, +0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, +0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, +0x4242c700, 0x42490f00 +}; + +/* + * invpio2: 24 bits of 2/pi + * pio2_1: first 17 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 17 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 17 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +static const float +zero = 0.0000000000e+00, /* 0x00000000 */ +half = 5.0000000000e-01, /* 0x3f000000 */ +two8 = 2.5600000000e+02, /* 0x43800000 */ +invpio2 = 6.3661980629e-01, /* 0x3f22f984 */ +pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */ +pio2_1t = 1.0804334124e-05, /* 0x37354443 */ +pio2_2 = 1.0804273188e-05, /* 0x37354400 */ +pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */ +pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */ +pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ + +int32_t __ieee754_rem_pio2f(float x, float *y) +{ + float z,w,t,r,fn; + float tx[3]; + int32_t e0,i,j,nx,n,ix,hx; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ + {y[0] = x; y[1] = 0; return 0;} + if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ + if(hx>0) { + z = x - pio2_1; + if((ix&0xffffffc0)!=0x3fc90fc0) { /* 24+24 bit pi OK */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + } else { /* near pi/2, use 24+24+24 bit pi */ + z -= pio2_2; + y[0] = z - pio2_2t; + y[1] = (z-y[0])-pio2_2t; + } + return 1; + } else { /* negative x */ + z = x + pio2_1; + if((ix&0xffffffc0)!=0x3fc90fc0) { /* 24+24 bit pi OK */ + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + } else { /* near pi/2, use 24+24+24 bit pi */ + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z-y[0])+pio2_2t; + } + return -1; + } + } + if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */ + t = fabsf(x); + n = (int32_t) (t*invpio2+half); + fn = (float)n; + r = t-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 40 bit */ + if(n<32&&(int32_t)(ix&0xffffff00)!=npio2_hw[n-1]) { + y[0] = r-w; /* quick check no cancellation */ + } else { + u_int32_t high; + j = ix>>23; + y[0] = r-w; + GET_FLOAT_WORD(high,y[0]); + i = j-((high>>23)&0xff); + if(i>8) { /* 2nd iteration needed, good to 57 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + GET_FLOAT_WORD(high,y[0]); + i = j-((high>>23)&0xff); + if(i>25) { /* 3rd iteration need, 74 bits acc */ + t = r; /* will cover all possible cases */ + w = fn*pio2_3; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + else return n; + } + /* + * all other (large) arguments + */ + if(ix>=0x7f800000) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-7) */ + e0 = (ix>>23)-134; /* e0 = ilogb(z)-7; */ + SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23))); + for(i=0;i<2;i++) { + tx[i] = (float)((int32_t)(z)); + z = (z-tx[i])*two8; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi); + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + return n; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_remainderf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_remainderf.c new file mode 100644 index 0000000000..cc0167862e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_remainderf.c @@ -0,0 +1,62 @@ +/* e_remainderf.c -- float version of e_remainder.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + +static const float zero = 0.0; + + +float +__ieee754_remainderf(float x, float p) +{ + int32_t hx,hp; + u_int32_t sx; + float p_half; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hp,p); + sx = hx&0x80000000; + hp &= 0x7fffffff; + hx &= 0x7fffffff; + + /* purge off exception values */ + if(hp==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7f800000)|| /* x not finite */ + ((hp>0x7f800000))) /* p is NaN */ + return (x*p)/(x*p); + + + if (hp<=0x7effffff) x = __ieee754_fmodf(x,p+p); /* now x < 2p */ + if ((hx-hp)==0) return zero*x; + x = fabsf(x); + p = fabsf(p); + if (hp<0x01000000) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = (float)0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_FLOAT_WORD(hx,x); + SET_FLOAT_WORD(x,hx^sx); + return x; +} +strong_alias (__ieee754_remainderf, __remainderf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_sinhf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_sinhf.c new file mode 100644 index 0000000000..6100d95c55 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_sinhf.c @@ -0,0 +1,60 @@ +/* e_sinhf.c -- float version of e_sinh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const float one = 1.0, shuge = 1.0e37; + +float +__ieee754_sinhf(float x) +{ + float t,w,h; + int32_t ix,jx; + + GET_FLOAT_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(__builtin_expect(ix>=0x7f800000, 0)) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x41b00000) { /* |x|<22 */ + if (__builtin_expect(ix<0x31800000, 0)) { /* |x|<2**-28 */ + math_check_force_underflow (x); + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + } + t = __expm1f(fabsf(x)); + if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x42b17180) return h*__ieee754_expf(fabsf(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x42b2d4fc) { + w = __ieee754_expf((float)0.5*fabsf(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return math_narrow_eval (x*shuge); +} +strong_alias (__ieee754_sinhf, __sinhf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_sqrtf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_sqrtf.c new file mode 100644 index 0000000000..c02206ac01 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_sqrtf.c @@ -0,0 +1,86 @@ +/* e_sqrtf.c -- float version of e_sqrt.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + +static const float one = 1.0, tiny=1.0e-30; + +float +__ieee754_sqrtf(float x) +{ + float z; + int32_t sign = (int)0x80000000; + int32_t ix,s,q,m,t,i; + u_int32_t r; + + GET_FLOAT_WORD(ix,x); + + /* take care of Inf and NaN */ + if((ix&0x7f800000)==0x7f800000) { + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + } + /* take care of zero */ + if(ix<=0) { + if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } + /* normalize x */ + m = (ix>>23); + if(m==0) { /* subnormal x */ + for(i=0;(ix&0x00800000)==0;i++) ix<<=1; + m -= i-1; + } + m -= 127; /* unbias exponent */ + ix = (ix&0x007fffff)|0x00800000; + if(m&1) /* odd m, double x to make it even */ + ix += ix; + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix += ix; + q = s = 0; /* q = sqrt(x) */ + r = 0x01000000; /* r = moving bit from right to left */ + + while(r!=0) { + t = s+r; + if(t<=ix) { + s = t+r; + ix -= t; + q += r; + } + ix += ix; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if(ix!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (z>one) + q += 2; + else + q += (q&1); + } + } + ix = (q>>1)+0x3f000000; + ix += (m <<23); + SET_FLOAT_WORD(z,ix); + return z; +} +strong_alias (__ieee754_sqrtf, __sqrtf_finite) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/k_cosf.c b/REORG.TODO/sysdeps/ieee754/flt-32/k_cosf.c new file mode 100644 index 0000000000..63ca822f8c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/k_cosf.c @@ -0,0 +1,55 @@ +/* k_cosf.c -- float version of k_cos.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_cosf.c,v 1.4 1995/05/10 20:46:23 jtc Exp $"; +#endif + +#include <math.h> +#include <math_private.h> + +static const float +one = 1.0000000000e+00, /* 0x3f800000 */ +C1 = 4.1666667908e-02, /* 0x3d2aaaab */ +C2 = -1.3888889225e-03, /* 0xbab60b61 */ +C3 = 2.4801587642e-05, /* 0x37d00d01 */ +C4 = -2.7557314297e-07, /* 0xb493f27c */ +C5 = 2.0875723372e-09, /* 0x310f74f6 */ +C6 = -1.1359647598e-11; /* 0xad47d74e */ + +float __kernel_cosf(float x, float y) +{ + float a,hz,z,r,qx; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* ix = |x|'s high word*/ + if(ix<0x32000000) { /* if x < 2**27 */ + if(((int)x)==0) return one; /* generate inexact */ + } + z = x*x; + r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); + if(ix < 0x3e99999a) /* if |x| < 0.3 */ + return one - ((float)0.5*z - (z*r - x*y)); + else { + if(ix > 0x3f480000) { /* x > 0.78125 */ + qx = (float)0.28125; + } else { + SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */ + } + hz = (float)0.5*z-qx; + a = one-qx; + return a - (hz - (z*r-x*y)); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/k_rem_pio2f.c b/REORG.TODO/sysdeps/ieee754/flt-32/k_rem_pio2f.c new file mode 100644 index 0000000000..a8d5b216e6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/k_rem_pio2f.c @@ -0,0 +1,208 @@ +/* k_rem_pio2f.c -- float version of k_rem_pio2.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_rem_pio2f.c,v 1.4 1995/05/10 20:46:28 jtc Exp $"; +#endif + +#include <math.h> +#include <math_private.h> +#include <libc-diag.h> + +/* In the float version, the input parameter x contains 8 bit + integers, not 24 bit integers. 113 bit precision is not supported. */ + +static const int init_jk[] = {4,7,9}; /* initial value for jk */ + +static const float PIo2[] = { + 1.5703125000e+00, /* 0x3fc90000 */ + 4.5776367188e-04, /* 0x39f00000 */ + 2.5987625122e-05, /* 0x37da0000 */ + 7.5437128544e-08, /* 0x33a20000 */ + 6.0026650317e-11, /* 0x2e840000 */ + 7.3896444519e-13, /* 0x2b500000 */ + 5.3845816694e-15, /* 0x27c20000 */ + 5.6378512969e-18, /* 0x22d00000 */ + 8.3009228831e-20, /* 0x1fc40000 */ + 3.2756352257e-22, /* 0x1bc60000 */ + 6.3331015649e-25, /* 0x17440000 */ +}; + +static const float +zero = 0.0, +one = 1.0, +two8 = 2.5600000000e+02, /* 0x43800000 */ +twon8 = 3.9062500000e-03; /* 0x3b800000 */ + +int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2) +{ + int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; + float z,fw,f[20],fq[20],q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx-1; + jv = (e0-3)/8; if(jv<0) jv=0; + q0 = e0-8*(jv+1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv-jx; m = jx+jk; + for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i=0;i<=jk;i++) { + for(j=0,fw=0.0;j<=jx;j++) + fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + + jz = jk; +recompute: + /* distill q[] into iq[] reversingly */ + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (float)((int32_t)(twon8* z)); + iq[i] = (int32_t)(z-two8*fw); + z = q[j-1]+fw; + } + + /* compute n */ + z = __scalbnf(z,q0); /* actual value of z */ + z -= (float)8.0*__floorf(z*(float)0.125); /* trim off integer >= 8 */ + n = (int32_t) z; + z -= (float)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + i = (iq[jz-1]>>(8-q0)); n += i; + iq[jz-1] -= i<<(8-q0); + ih = iq[jz-1]>>(7-q0); + } + else if(q0==0) ih = iq[jz-1]>>7; + else if(z>=(float)0.5) ih=2; + + if(ih>0) { /* q > 0.5 */ + n += 1; carry = 0; + for(i=0;i<jz ;i++) { /* compute 1-q */ + j = iq[i]; + if(carry==0) { + if(j!=0) { + carry = 1; iq[i] = 0x100- j; + } + } else iq[i] = 0xff - j; + } + if(q0>0) { /* rare case: chance is 1 in 12 */ + switch(q0) { + case 1: + iq[jz-1] &= 0x7f; break; + case 2: + iq[jz-1] &= 0x3f; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= __scalbnf(one,q0); + } + } + + /* check if recomputation is needed */ + if(z==zero) { + j = 0; + for (i=jz-1;i>=jk;i--) j |= iq[i]; + if(j==0) { /* need recomputation */ + /* On s390x gcc 6.1 -O3 produces the warning "array subscript is + below array bounds [-Werror=array-bounds]". Only + __ieee754_rem_pio2f calls __kernel_rem_pio2f for normal + numbers and |x| ~> 2^7*(pi/2). Thus x can't be zero and + ipio2 is not zero, too. Thus not all iq[] values can't be + zero. */ + DIAG_PUSH_NEEDS_COMMENT; + DIAG_IGNORE_NEEDS_COMMENT (6.1, "-Warray-bounds"); + for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ + DIAG_POP_NEEDS_COMMENT; + + for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ + f[jx+i] = (float) ipio2[jv+i]; + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } + + /* chop off zero terms */ + if(z==(float)0.0) { + jz -= 1; q0 -= 8; + while(iq[jz]==0) { jz--; q0-=8;} + } else { /* break z into 8-bit if necessary */ + z = __scalbnf(z,-q0); + if(z>=two8) { + fw = (float)((int32_t)(twon8*z)); + iq[jz] = (int32_t)(z-two8*fw); + jz += 1; q0 += 8; + iq[jz] = (int32_t) fw; + } else iq[jz] = (int32_t) z ; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = __scalbnf(one,q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(float)iq[i]; fw*=twon8; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for(i=jz;i>=0;i--) { + for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; + fq[jz-i] = fw; + } + + /* compress fq[] into y[] */ + switch(prec) { + case 0: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + break; + case 1: + case 2:; + float fv = 0.0; + for (i=jz;i>=0;i--) fv = math_narrow_eval (fv + fq[i]); + y[0] = (ih==0)? fv: -fv; + fv = math_narrow_eval (fq[0]-fv); + for (i=1;i<=jz;i++) fv = math_narrow_eval (fv + fq[i]); + y[1] = (ih==0)? fv: -fv; + break; + case 3: /* painful */ + for (i=jz;i>0;i--) { + float fv = math_narrow_eval (fq[i-1]+fq[i]); + fq[i] += fq[i-1]-fv; + fq[i-1] = fv; + } + for (i=jz;i>1;i--) { + float fv = math_narrow_eval (fq[i-1]+fq[i]); + fq[i] += fq[i-1]-fv; + fq[i-1] = fv; + } + for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; + if(ih==0) { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } else { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n&7; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/k_sinf.c b/REORG.TODO/sysdeps/ieee754/flt-32/k_sinf.c new file mode 100644 index 0000000000..a195d59466 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/k_sinf.c @@ -0,0 +1,50 @@ +/* k_sinf.c -- float version of k_sin.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_sinf.c,v 1.4 1995/05/10 20:46:33 jtc Exp $"; +#endif + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const float +half = 5.0000000000e-01,/* 0x3f000000 */ +S1 = -1.6666667163e-01, /* 0xbe2aaaab */ +S2 = 8.3333337680e-03, /* 0x3c088889 */ +S3 = -1.9841270114e-04, /* 0xb9500d01 */ +S4 = 2.7557314297e-06, /* 0x3638ef1b */ +S5 = -2.5050759689e-08, /* 0xb2d72f34 */ +S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */ + +float __kernel_sinf(float x, float y, int iy) +{ + float z,r,v; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* high word of x */ + if(ix<0x32000000) /* |x| < 2**-27 */ + { + math_check_force_underflow (x); + if ((int) x == 0) + return x; /* generate inexact */ + } + z = x*x; + v = z*x; + r = S2+z*(S3+z*(S4+z*(S5+z*S6))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/k_tanf.c b/REORG.TODO/sysdeps/ieee754/flt-32/k_tanf.c new file mode 100644 index 0000000000..9f0e55860f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/k_tanf.c @@ -0,0 +1,101 @@ +/* k_tanf.c -- float version of k_tan.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_tanf.c,v 1.4 1995/05/10 20:46:39 jtc Exp $"; +#endif + +#include <float.h> +#include <math.h> +#include <math_private.h> +static const float +one = 1.0000000000e+00, /* 0x3f800000 */ +pio4 = 7.8539812565e-01, /* 0x3f490fda */ +pio4lo= 3.7748947079e-08, /* 0x33222168 */ +T[] = { + 3.3333334327e-01, /* 0x3eaaaaab */ + 1.3333334029e-01, /* 0x3e088889 */ + 5.3968254477e-02, /* 0x3d5d0dd1 */ + 2.1869488060e-02, /* 0x3cb327a4 */ + 8.8632395491e-03, /* 0x3c11371f */ + 3.5920790397e-03, /* 0x3b6b6916 */ + 1.4562094584e-03, /* 0x3abede48 */ + 5.8804126456e-04, /* 0x3a1a26c8 */ + 2.4646313977e-04, /* 0x398137b9 */ + 7.8179444245e-05, /* 0x38a3f445 */ + 7.1407252108e-05, /* 0x3895c07a */ + -1.8558637748e-05, /* 0xb79bae5f */ + 2.5907305826e-05, /* 0x37d95384 */ +}; + +float __kernel_tanf(float x, float y, int iy) +{ + float z,r,v,w,s; + int32_t ix,hx; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; /* high word of |x| */ + if(ix<0x39000000) /* x < 2**-13 */ + {if((int)x==0) { /* generate inexact */ + if((ix|(iy+1))==0) return one/fabsf(x); + else if (iy == 1) + { + math_check_force_underflow (x); + return x; + } + else + return -one / x; + } + } + if(ix>=0x3f2ca140) { /* |x|>=0.6744 */ + if(hx<0) {x = -x; y = -y;} + z = pio4-x; + w = pio4lo-y; + x = z+w; y = 0.0; + if (fabsf (x) < 0x1p-13f) + return (1 - ((hx >> 30) & 2)) * iy * (1.0f - 2 * iy * x); + } + z = x*x; + w = z*z; + /* Break x^5*(T[1]+x^2*T[2]+...) into + * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) + */ + r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); + v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); + s = z*x; + r = y + z*(s*(r+v)+y); + r += T[0]*s; + w = x+r; + if(ix>=0x3f2ca140) { + v = (float)iy; + return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r))); + } + if(iy==1) return w; + else { /* if allow error up to 2 ulp, + simply return -1.0/(x+r) here */ + /* compute -1.0/(x+r) accurately */ + float a,t; + int32_t i; + z = w; + GET_FLOAT_WORD(i,z); + SET_FLOAT_WORD(z,i&0xfffff000); + v = r-(z - x); /* z+v = r+x */ + t = a = -(float)1.0/w; /* a = -1.0/w */ + GET_FLOAT_WORD(i,t); + SET_FLOAT_WORD(t,i&0xfffff000); + s = (float)1.0+t*z; + return t+a*(s+t*v); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/lgamma_negf.c b/REORG.TODO/sysdeps/ieee754/flt-32/lgamma_negf.c new file mode 100644 index 0000000000..71bcbb0f9d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/lgamma_negf.c @@ -0,0 +1,280 @@ +/* lgammaf expanding around zeros. + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const float lgamma_zeros[][2] = + { + { -0x2.74ff94p+0f, 0x1.3fe0f2p-24f }, + { -0x2.bf682p+0f, -0x1.437b2p-24f }, + { -0x3.24c1b8p+0f, 0x6.c34cap-28f }, + { -0x3.f48e2cp+0f, 0x1.707a04p-24f }, + { -0x4.0a13ap+0f, 0x1.e99aap-24f }, + { -0x4.fdd5ep+0f, 0x1.64454p-24f }, + { -0x5.021a98p+0f, 0x2.03d248p-24f }, + { -0x5.ffa4cp+0f, 0x2.9b82fcp-24f }, + { -0x6.005ac8p+0f, -0x1.625f24p-24f }, + { -0x6.fff3p+0f, 0x2.251e44p-24f }, + { -0x7.000dp+0f, 0x8.48078p-28f }, + { -0x7.fffe6p+0f, 0x1.fa98c4p-28f }, + { -0x8.0001ap+0f, -0x1.459fcap-28f }, + { -0x8.ffffdp+0f, -0x1.c425e8p-24f }, + { -0x9.00003p+0f, 0x1.c44b82p-24f }, + { -0xap+0f, 0x4.9f942p-24f }, + { -0xap+0f, -0x4.9f93b8p-24f }, + { -0xbp+0f, 0x6.b9916p-28f }, + { -0xbp+0f, -0x6.b9915p-28f }, + { -0xcp+0f, 0x8.f76c8p-32f }, + { -0xcp+0f, -0x8.f76c7p-32f }, + { -0xdp+0f, 0xb.09231p-36f }, + { -0xdp+0f, -0xb.09231p-36f }, + { -0xep+0f, 0xc.9cba5p-40f }, + { -0xep+0f, -0xc.9cba5p-40f }, + { -0xfp+0f, 0xd.73f9fp-44f }, + }; + +static const float e_hi = 0x2.b7e15p+0f, e_lo = 0x1.628aeep-24f; + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) in Stirling's + approximation to lgamma function. */ + +static const float lgamma_coeff[] = + { + 0x1.555556p-4f, + -0xb.60b61p-12f, + 0x3.403404p-12f, + }; + +#define NCOEFF (sizeof (lgamma_coeff) / sizeof (lgamma_coeff[0])) + +/* Polynomial approximations to (|gamma(x)|-1)(x-n)/(x-x0), where n is + the integer end-point of the half-integer interval containing x and + x0 is the zero of lgamma in that half-integer interval. Each + polynomial is expressed in terms of x-xm, where xm is the midpoint + of the interval for which the polynomial applies. */ + +static const float poly_coeff[] = + { + /* Interval [-2.125, -2] (polynomial degree 5). */ + -0x1.0b71c6p+0f, + -0xc.73a1ep-4f, + -0x1.ec8462p-4f, + -0xe.37b93p-4f, + -0x1.02ed36p-4f, + -0xe.cbe26p-4f, + /* Interval [-2.25, -2.125] (polynomial degree 5). */ + -0xf.29309p-4f, + -0xc.a5cfep-4f, + 0x3.9c93fcp-4f, + -0x1.02a2fp+0f, + 0x9.896bep-4f, + -0x1.519704p+0f, + /* Interval [-2.375, -2.25] (polynomial degree 5). */ + -0xd.7d28dp-4f, + -0xe.6964cp-4f, + 0xb.0d4f1p-4f, + -0x1.9240aep+0f, + 0x1.dadabap+0f, + -0x3.1778c4p+0f, + /* Interval [-2.5, -2.375] (polynomial degree 6). */ + -0xb.74ea2p-4f, + -0x1.2a82cp+0f, + 0x1.880234p+0f, + -0x3.320c4p+0f, + 0x5.572a38p+0f, + -0x9.f92bap+0f, + 0x1.1c347ep+4f, + /* Interval [-2.625, -2.5] (polynomial degree 6). */ + -0x3.d10108p-4f, + 0x1.cd5584p+0f, + 0x3.819c24p+0f, + 0x6.84cbb8p+0f, + 0xb.bf269p+0f, + 0x1.57fb12p+4f, + 0x2.7b9854p+4f, + /* Interval [-2.75, -2.625] (polynomial degree 6). */ + -0x6.b5d25p-4f, + 0x1.28d604p+0f, + 0x1.db6526p+0f, + 0x2.e20b38p+0f, + 0x4.44c378p+0f, + 0x6.62a08p+0f, + 0x9.6db3ap+0f, + /* Interval [-2.875, -2.75] (polynomial degree 5). */ + -0x8.a41b2p-4f, + 0xc.da87fp-4f, + 0x1.147312p+0f, + 0x1.7617dap+0f, + 0x1.d6c13p+0f, + 0x2.57a358p+0f, + /* Interval [-3, -2.875] (polynomial degree 5). */ + -0xa.046d6p-4f, + 0x9.70b89p-4f, + 0xa.a89a6p-4f, + 0xd.2f2d8p-4f, + 0xd.e32b4p-4f, + 0xf.fb741p-4f, + }; + +static const size_t poly_deg[] = + { + 5, + 5, + 5, + 6, + 6, + 6, + 5, + 5, + }; + +static const size_t poly_end[] = + { + 5, + 11, + 17, + 24, + 31, + 38, + 44, + 50, + }; + +/* Compute sin (pi * X) for -0.25 <= X <= 0.5. */ + +static float +lg_sinpi (float x) +{ + if (x <= 0.25f) + return __sinf ((float) M_PI * x); + else + return __cosf ((float) M_PI * (0.5f - x)); +} + +/* Compute cos (pi * X) for -0.25 <= X <= 0.5. */ + +static float +lg_cospi (float x) +{ + if (x <= 0.25f) + return __cosf ((float) M_PI * x); + else + return __sinf ((float) M_PI * (0.5f - x)); +} + +/* Compute cot (pi * X) for -0.25 <= X <= 0.5. */ + +static float +lg_cotpi (float x) +{ + return lg_cospi (x) / lg_sinpi (x); +} + +/* Compute lgamma of a negative argument -15 < X < -2, setting + *SIGNGAMP accordingly. */ + +float +__lgamma_negf (float x, int *signgamp) +{ + /* Determine the half-integer region X lies in, handle exact + integers and determine the sign of the result. */ + int i = __floorf (-2 * x); + if ((i & 1) == 0 && i == -2 * x) + return 1.0f / 0.0f; + float xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2); + i -= 4; + *signgamp = ((i & 2) == 0 ? -1 : 1); + + SET_RESTORE_ROUNDF (FE_TONEAREST); + + /* Expand around the zero X0 = X0_HI + X0_LO. */ + float x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1]; + float xdiff = x - x0_hi - x0_lo; + + /* For arguments in the range -3 to -2, use polynomial + approximations to an adjusted version of the gamma function. */ + if (i < 2) + { + int j = __floorf (-8 * x) - 16; + float xm = (-33 - 2 * j) * 0.0625f; + float x_adj = x - xm; + size_t deg = poly_deg[j]; + size_t end = poly_end[j]; + float g = poly_coeff[end]; + for (size_t j = 1; j <= deg; j++) + g = g * x_adj + poly_coeff[end - j]; + return __log1pf (g * xdiff / (x - xn)); + } + + /* The result we want is log (sinpi (X0) / sinpi (X)) + + log (gamma (1 - X0) / gamma (1 - X)). */ + float x_idiff = fabsf (xn - x), x0_idiff = fabsf (xn - x0_hi - x0_lo); + float log_sinpi_ratio; + if (x0_idiff < x_idiff * 0.5f) + /* Use log not log1p to avoid inaccuracy from log1p of arguments + close to -1. */ + log_sinpi_ratio = __ieee754_logf (lg_sinpi (x0_idiff) + / lg_sinpi (x_idiff)); + else + { + /* Use log1p not log to avoid inaccuracy from log of arguments + close to 1. X0DIFF2 has positive sign if X0 is further from + XN than X is from XN, negative sign otherwise. */ + float x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * 0.5f; + float sx0d2 = lg_sinpi (x0diff2); + float cx0d2 = lg_cospi (x0diff2); + log_sinpi_ratio = __log1pf (2 * sx0d2 + * (-sx0d2 + cx0d2 * lg_cotpi (x_idiff))); + } + + float log_gamma_ratio; + float y0 = math_narrow_eval (1 - x0_hi); + float y0_eps = -x0_hi + (1 - y0) - x0_lo; + float y = math_narrow_eval (1 - x); + float y_eps = -x + (1 - y); + /* We now wish to compute LOG_GAMMA_RATIO + = log (gamma (Y0 + Y0_EPS) / gamma (Y + Y_EPS)). XDIFF + accurately approximates the difference Y0 + Y0_EPS - Y - + Y_EPS. Use Stirling's approximation. */ + float log_gamma_high + = (xdiff * __log1pf ((y0 - e_hi - e_lo + y0_eps) / e_hi) + + (y - 0.5f + y_eps) * __log1pf (xdiff / y)); + /* Compute the sum of (B_2k / 2k(2k-1))(Y0^-(2k-1) - Y^-(2k-1)). */ + float y0r = 1 / y0, yr = 1 / y; + float y0r2 = y0r * y0r, yr2 = yr * yr; + float rdiff = -xdiff / (y * y0); + float bterm[NCOEFF]; + float dlast = rdiff, elast = rdiff * yr * (yr + y0r); + bterm[0] = dlast * lgamma_coeff[0]; + for (size_t j = 1; j < NCOEFF; j++) + { + float dnext = dlast * y0r2 + elast; + float enext = elast * yr2; + bterm[j] = dnext * lgamma_coeff[j]; + dlast = dnext; + elast = enext; + } + float log_gamma_low = 0; + for (size_t j = 0; j < NCOEFF; j++) + log_gamma_low += bterm[NCOEFF - 1 - j]; + log_gamma_ratio = log_gamma_high + log_gamma_low; + + return log_sinpi_ratio + log_gamma_ratio; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/lgamma_productf.c b/REORG.TODO/sysdeps/ieee754/flt-32/lgamma_productf.c new file mode 100644 index 0000000000..1cc8931700 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/lgamma_productf.c @@ -0,0 +1 @@ +/* Not needed. */ diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/mpn2flt.c b/REORG.TODO/sysdeps/ieee754/flt-32/mpn2flt.c new file mode 100644 index 0000000000..abf6510f4e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/mpn2flt.c @@ -0,0 +1,41 @@ +/* Copyright (C) 1995-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include <ieee754.h> +#include <float.h> + +/* Convert a multi-precision integer of the needed number of bits (24 for + float) and an integral power of two to a `float' in IEEE754 single- + precision format. */ + +float +__mpn_construct_float (mp_srcptr frac_ptr, int expt, int sign) +{ + union ieee754_float u; + + u.ieee.negative = sign; + u.ieee.exponent = expt + IEEE754_FLOAT_BIAS; +#if BITS_PER_MP_LIMB > FLT_MANT_DIG + u.ieee.mantissa = frac_ptr[0] & (((mp_limb_t) 1 << FLT_MANT_DIG) - 1); +#else + #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif + + return u.f; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_asinhf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_asinhf.c new file mode 100644 index 0000000000..da9cafb600 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_asinhf.c @@ -0,0 +1,50 @@ +/* s_asinhf.c -- float version of s_asinh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +ln2 = 6.9314718246e-01, /* 0x3f317218 */ +huge= 1.0000000000e+30; + +float +__asinhf(float x) +{ + float w; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(__builtin_expect(ix< 0x38000000, 0)) { /* |x|<2**-14 */ + math_check_force_underflow (x); + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(__builtin_expect(ix>0x47000000, 0)) { /* |x| > 2**14 */ + if(ix>=0x7f800000) return x+x; /* x is inf or NaN */ + w = __ieee754_logf(fabsf(x))+ln2; + } else { + float xa = fabsf(x); + if (ix>0x40000000) { /* 2**14 > |x| > 2.0 */ + w = __ieee754_logf(2.0f*xa+one/(__ieee754_sqrtf(xa*xa+one)+xa)); + } else { /* 2.0 > |x| > 2**-14 */ + float t = xa*xa; + w =__log1pf(xa+t/(one+__ieee754_sqrtf(one+t))); + } + } + return __copysignf(w, x); +} +weak_alias (__asinhf, asinhf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_atanf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_atanf.c new file mode 100644 index 0000000000..e322a1d41f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_atanf.c @@ -0,0 +1,101 @@ +/* s_atanf.c -- float version of s_atan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_atanf.c,v 1.4 1995/05/10 20:46:47 jtc Exp $"; +#endif + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const float atanhi[] = { + 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ + 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ + 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ + 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ +}; + +static const float atanlo[] = { + 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ + 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ + 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ + 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ +}; + +static const float aT[] = { + 3.3333334327e-01, /* 0x3eaaaaaa */ + -2.0000000298e-01, /* 0xbe4ccccd */ + 1.4285714924e-01, /* 0x3e124925 */ + -1.1111110449e-01, /* 0xbde38e38 */ + 9.0908870101e-02, /* 0x3dba2e6e */ + -7.6918758452e-02, /* 0xbd9d8795 */ + 6.6610731184e-02, /* 0x3d886b35 */ + -5.8335702866e-02, /* 0xbd6ef16b */ + 4.9768779427e-02, /* 0x3d4bda59 */ + -3.6531571299e-02, /* 0xbd15a221 */ + 1.6285819933e-02, /* 0x3c8569d7 */ +}; + +static const float +one = 1.0, +huge = 1.0e30; + +float __atanf(float x) +{ + float w,s1,s2,z; + int32_t ix,hx,id; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x4c000000) { /* if |x| >= 2^25 */ + if(ix>0x7f800000) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+atanlo[3]; + else return -atanhi[3]-atanlo[3]; + } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ + if (ix < 0x31000000) { /* |x| < 2^-29 */ + math_check_force_underflow (x); + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabsf(x); + if (ix < 0x3f980000) { /* |x| < 1.1875 */ + if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = ((float)2.0*x-one)/((float)2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x401c0000) { /* |x| < 2.4375 */ + id = 2; x = (x-(float)1.5)/(one+(float)1.5*x); + } else { /* 2.4375 <= |x| < 2^66 */ + id = 3; x = -(float)1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ + s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); + s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +} +weak_alias (__atanf, atanf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_cbrtf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_cbrtf.c new file mode 100644 index 0000000000..1ac294c189 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_cbrtf.c @@ -0,0 +1,63 @@ +/* Compute cubic root of float value. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Dirk Alboth <dirka@uni-paderborn.de> and + Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + + +#define CBRT2 1.2599210498948731648 /* 2^(1/3) */ +#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */ + +static const double factor[5] = +{ + 1.0 / SQR_CBRT2, + 1.0 / CBRT2, + 1.0, + CBRT2, + SQR_CBRT2 +}; + + +float +__cbrtf (float x) +{ + float xm, ym, u, t2; + int xe; + + /* Reduce X. XM now is an range 1.0 to 0.5. */ + xm = __frexpf (fabsf (x), &xe); + + /* If X is not finite or is null return it (with raising exceptions + if necessary. + Note: *Our* version of `frexp' sets XE to zero if the argument is + Inf or NaN. This is not portable but faster. */ + if (xe == 0 && fpclassify (x) <= FP_ZERO) + return x + x; + + u = (0.492659620528969547 + (0.697570460207922770 + - 0.191502161678719066 * xm) * xm); + + t2 = u * u * u; + + ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3]; + + return __ldexpf (x > 0.0 ? ym : -ym, xe / 3); +} +weak_alias (__cbrtf, cbrtf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_ceilf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_ceilf.c new file mode 100644 index 0000000000..bff26c33cb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_ceilf.c @@ -0,0 +1,48 @@ +/* s_ceilf.c -- float version of s_ceil.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + + +float +__ceilf(float x) +{ + int32_t i0,j0; + u_int32_t i; + + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { + /* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;} + else if(i0!=0) { i0=0x3f800000;} + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(i0>0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } else { + if(__builtin_expect(j0==0x80, 0)) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} +#ifndef __ceilf +weak_alias (__ceilf, ceilf) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_copysignf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_copysignf.c new file mode 100644 index 0000000000..1621836065 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_copysignf.c @@ -0,0 +1,37 @@ +/* s_copysignf.c -- float version of s_copysign.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_copysignf.c,v 1.4 1995/05/10 20:46:59 jtc Exp $"; +#endif + +/* + * copysignf(float x, float y) + * copysignf(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include <math.h> +#include <math_private.h> + +float __copysignf(float x, float y) +{ + u_int32_t ix,iy; + GET_FLOAT_WORD(ix,x); + GET_FLOAT_WORD(iy,y); + SET_FLOAT_WORD(x,(ix&0x7fffffff)|(iy&0x80000000)); + return x; +} +weak_alias (__copysignf, copysignf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_cosf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_cosf.c new file mode 100644 index 0000000000..0affd406bb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_cosf.c @@ -0,0 +1,63 @@ +/* s_cosf.c -- float version of s_cos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_cosf.c,v 1.4 1995/05/10 20:47:03 jtc Exp $"; +#endif + +#include <errno.h> +#include <math.h> +#include <math_private.h> + +#ifndef COSF +# define COSF_FUNC __cosf +#else +# define COSF_FUNC COSF +#endif + +float COSF_FUNC(float x) +{ + float y[2],z=0.0; + int32_t n,ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fd8) return __kernel_cosf(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) { + if (ix == 0x7f800000) + __set_errno (EDOM); + return x-x; + } + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,y); + switch(n&3) { + case 0: return __kernel_cosf(y[0],y[1]); + case 1: return -__kernel_sinf(y[0],y[1],1); + case 2: return -__kernel_cosf(y[0],y[1]); + default: + return __kernel_sinf(y[0],y[1],1); + } + } +} + +#ifndef COSF +weak_alias (__cosf, cosf) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_erff.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_erff.c new file mode 100644 index 0000000000..c8b6287503 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_erff.c @@ -0,0 +1,230 @@ +/* s_erff.c -- float version of s_erf.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_erff.c,v 1.4 1995/05/10 20:47:07 jtc Exp $"; +#endif + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <fix-int-fp-convert-zero.h> + +static const float +tiny = 1e-30, +half= 5.0000000000e-01, /* 0x3F000000 */ +one = 1.0000000000e+00, /* 0x3F800000 */ +two = 2.0000000000e+00, /* 0x40000000 */ + /* c = (subfloat)0.84506291151 */ +erx = 8.4506291151e-01, /* 0x3f58560b */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx = 1.2837916613e-01, /* 0x3e0375d4 */ +pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ +pp1 = -3.2504209876e-01, /* 0xbea66beb */ +pp2 = -2.8481749818e-02, /* 0xbce9528f */ +pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ +pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ +qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ +qq2 = 6.5022252500e-02, /* 0x3d852a63 */ +qq3 = 5.0813062117e-03, /* 0x3ba68116 */ +qq4 = 1.3249473704e-04, /* 0x390aee49 */ +qq5 = -3.9602282413e-06, /* 0xb684e21a */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ +pa1 = 4.1485610604e-01, /* 0x3ed46805 */ +pa2 = -3.7220788002e-01, /* 0xbebe9208 */ +pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ +pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ +pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ +pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ +qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ +qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ +qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ +qa4 = 1.2617121637e-01, /* 0x3e013307 */ +qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ +qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +ra0 = -9.8649440333e-03, /* 0xbc21a093 */ +ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ +ra2 = -1.0558626175e+01, /* 0xc128f022 */ +ra3 = -6.2375331879e+01, /* 0xc2798057 */ +ra4 = -1.6239666748e+02, /* 0xc322658c */ +ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ +ra6 = -8.1287437439e+01, /* 0xc2a2932b */ +ra7 = -9.8143291473e+00, /* 0xc11d077e */ +sa1 = 1.9651271820e+01, /* 0x419d35ce */ +sa2 = 1.3765776062e+02, /* 0x4309a863 */ +sa3 = 4.3456588745e+02, /* 0x43d9486f */ +sa4 = 6.4538726807e+02, /* 0x442158c9 */ +sa5 = 4.2900814819e+02, /* 0x43d6810b */ +sa6 = 1.0863500214e+02, /* 0x42d9451f */ +sa7 = 6.5702495575e+00, /* 0x40d23f7c */ +sa8 = -6.0424413532e-02, /* 0xbd777f97 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ +rb0 = -9.8649431020e-03, /* 0xbc21a092 */ +rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ +rb2 = -1.7757955551e+01, /* 0xc18e104b */ +rb3 = -1.6063638306e+02, /* 0xc320a2ea */ +rb4 = -6.3756646729e+02, /* 0xc41f6441 */ +rb5 = -1.0250950928e+03, /* 0xc480230b */ +rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ +sb1 = 3.0338060379e+01, /* 0x41f2b459 */ +sb2 = 3.2579251099e+02, /* 0x43a2e571 */ +sb3 = 1.5367296143e+03, /* 0x44c01759 */ +sb4 = 3.1998581543e+03, /* 0x4547fdbb */ +sb5 = 2.5530502930e+03, /* 0x451f90ce */ +sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ +sb7 = -2.2440952301e+01; /* 0xc1b38712 */ + +float __erff(float x) +{ + int32_t hx,ix,i; + float R,S,P,Q,s,y,z,r; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) { /* erf(nan)=nan */ + i = ((u_int32_t)hx>>31)<<1; + return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ + } + + if(ix < 0x3f580000) { /* |x|<0.84375 */ + if(ix < 0x31800000) { /* |x|<2**-28 */ + if (ix < 0x04000000) + { + /* Avoid spurious underflow. */ + float ret = 0.0625f * (16.0f * x + (16.0f * efx) * x); + math_check_force_underflow (ret); + return ret; + } + return x + efx*x; + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + return x + x*y; + } + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ + s = fabsf(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) return erx + P/Q; else return -erx - P/Q; + } + if (ix >= 0x40c00000) { /* inf>|x|>=6 */ + if(hx>=0) return one-tiny; else return tiny-one; + } + x = fabsf(x); + s = one/(x*x); + if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/0.35 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(z,ix&0xfffff000); + r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S); + if(hx>=0) return one-r/x; else return r/x-one; +} +weak_alias (__erff, erff) + +float __erfcf(float x) +{ + int32_t hx,ix; + float R,S,P,Q,s,y,z,r; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + float ret = (float)(((u_int32_t)hx>>31)<<1)+one/x; + if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0f) + return 0.0f; + return ret; + } + + if(ix < 0x3f580000) { /* |x|<0.84375 */ + if(ix < 0x32800000) /* |x|<2**-26 */ + return one-x; + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + if(hx < 0x3e800000) { /* x<1/4 */ + return one-(x+x*y); + } else { + r = x*y; + r += (x-half); + return half - r ; + } + } + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ + s = fabsf(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + if (ix < 0x41e00000) { /* |x|<28 */ + x = fabsf(x); + s = one/(x*x); + if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/.35 ~ 2.857143 */ + if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(z,ix&0xffffe000); + r = __ieee754_expf(-z*z-(float)0.5625)* + __ieee754_expf((z-x)*(z+x)+R/S); + if(hx>0) { + float ret = math_narrow_eval (r/x); + if (ret == 0) + __set_errno (ERANGE); + return ret; + } else + return two-r/x; + } else { + if(hx>0) { + __set_errno (ERANGE); + return tiny*tiny; + } else + return two-tiny; + } +} +weak_alias (__erfcf, erfcf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_expm1f.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_expm1f.c new file mode 100644 index 0000000000..c515d25e28 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_expm1f.c @@ -0,0 +1,130 @@ +/* s_expm1f.c -- float version of s_expm1.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const float huge = 1.0e+30; +static const float tiny = 1.0e-30; + +static const float +one = 1.0, +o_threshold = 8.8721679688e+01,/* 0x42b17180 */ +ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ +ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ +invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ + /* scaled coefficients related to expm1 */ +Q1 = -3.3333335072e-02, /* 0xbd088889 */ +Q2 = 1.5873016091e-03, /* 0x3ad00d01 */ +Q3 = -7.9365076090e-05, /* 0xb8a670cd */ +Q4 = 4.0082177293e-06, /* 0x36867e54 */ +Q5 = -2.0109921195e-07; /* 0xb457edbb */ + +float +__expm1f(float x) +{ + float y,hi,lo,c,t,e,hxs,hfx,r1; + int32_t k,xsb; + u_int32_t hx; + + GET_FLOAT_WORD(hx,x); + xsb = hx&0x80000000; /* sign bit of x */ + if(xsb==0) y=x; else y= -x; /* y = |x| */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ + if(hx >= 0x42b17218) { /* if |x|>=88.721... */ + if(hx>0x7f800000) + return x+x; /* NaN */ + if(hx==0x7f800000) + return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ + if(x > o_threshold) { + __set_errno (ERANGE); + return huge*huge; /* overflow */ + } + } + if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ + math_force_eval(x+tiny);/* raise inexact */ + return tiny-one; /* return -1 */ + } + } + + /* argument reduction */ + if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ + if(xsb==0) + {hi = x - ln2_hi; lo = ln2_lo; k = 1;} + else + {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} + } else { + k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); + t = k; + hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ + lo = t*ln2_lo; + } + x = hi - lo; + c = (hi-x)-lo; + } + else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ + math_check_force_underflow (x); + t = huge+x; /* return x with inexact flags when x!=0 */ + return x - (t-(huge+x)); + } + else k = 0; + + /* x is now in primary range */ + hfx = (float)0.5*x; + hxs = x*hfx; + r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); + t = (float)3.0-r1*hfx; + e = hxs*((r1-t)/((float)6.0 - x*t)); + if(k==0) return x - (x*e-hxs); /* c is 0 */ + else { + e = (x*(e-c)-c); + e -= hxs; + if(k== -1) return (float)0.5*(x-e)-(float)0.5; + if(k==1) { + if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); + else return one+(float)2.0*(x-e); + } + if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ + int32_t i; + y = one-(e-x); + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + return y-one; + } + t = one; + if(k<23) { + int32_t i; + SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ + y = t-(e-x); + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + } else { + int32_t i; + SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ + y = x-(e+t); + y += one; + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + } + } + return y; +} +weak_alias (__expm1f, expm1f) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_fabsf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_fabsf.c new file mode 100644 index 0000000000..297abe64bd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_fabsf.c @@ -0,0 +1,30 @@ +/* s_fabsf.c -- float version of s_fabs.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_fabsf.c,v 1.4 1995/05/10 20:47:15 jtc Exp $"; +#endif + +/* + * fabsf(x) returns the absolute value of x. + */ + +#include <math.h> + +float __fabsf(float x) +{ + return __builtin_fabsf (x); +} +weak_alias (__fabsf, fabsf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_finitef.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_finitef.c new file mode 100644 index 0000000000..4c5b339235 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_finitef.c @@ -0,0 +1,41 @@ +/* s_finitef.c -- float version of s_finite.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_finitef.c,v 1.4 1995/05/10 20:47:18 jtc Exp $"; +#endif + +/* + * finitef(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> + +#undef __finitef + +#ifndef FINITEF +# define FINITEF __finitef +#endif + +int FINITEF(float x) +{ + int32_t ix; + GET_FLOAT_WORD(ix,x); + return (int)((u_int32_t)((ix&0x7f800000)-0x7f800000)>>31); +} +hidden_def (__finitef) +weak_alias (__finitef, finitef) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_floorf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_floorf.c new file mode 100644 index 0000000000..69160e5e10 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_floorf.c @@ -0,0 +1,54 @@ +/* s_floorf.c -- float version of s_floor.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * floorf(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + */ + +#include <math.h> +#include <math_private.h> + +float +__floorf(float x) +{ + int32_t i0,j0; + u_int32_t i; + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { + /* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=0;} + else if((i0&0x7fffffff)!=0) + { i0=0xbf800000;} + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(i0<0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } else { + if(__builtin_expect(j0==0x80, 0)) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} +#ifndef __floorf +weak_alias (__floorf, floorf) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_fpclassifyf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_fpclassifyf.c new file mode 100644 index 0000000000..8a67c6fc0e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_fpclassifyf.c @@ -0,0 +1,42 @@ +/* Return classification value corresponding to argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +int +__fpclassifyf (float x) +{ + u_int32_t wx; + int retval = FP_NORMAL; + + GET_FLOAT_WORD (wx, x); + wx &= 0x7fffffff; + if (wx == 0) + retval = FP_ZERO; + else if (wx < 0x800000) + retval = FP_SUBNORMAL; + else if (wx >= 0x7f800000) + retval = wx > 0x7f800000 ? FP_NAN : FP_INFINITE; + + return retval; +} +libm_hidden_def (__fpclassifyf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_frexpf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_frexpf.c new file mode 100644 index 0000000000..005367cf58 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_frexpf.c @@ -0,0 +1,44 @@ +/* s_frexpf.c -- float version of s_frexp.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_frexpf.c,v 1.5 1995/05/10 20:47:26 jtc Exp $"; +#endif + +#include <math.h> +#include <math_private.h> + +static const float +two25 = 3.3554432000e+07; /* 0x4c000000 */ + +float __frexpf(float x, int *eptr) +{ + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + *eptr = 0; + if(ix>=0x7f800000||(ix==0)) return x + x; /* 0,inf,nan */ + if (ix<0x00800000) { /* subnormal */ + x *= two25; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + *eptr = -25; + } + *eptr += (ix>>23)-126; + hx = (hx&0x807fffff)|0x3f000000; + SET_FLOAT_WORD(x,hx); + return x; +} +weak_alias (__frexpf, frexpf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_fromfpf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_fromfpf.c new file mode 100644 index 0000000000..68d4c80a17 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_fromfpf.c @@ -0,0 +1,4 @@ +#define UNSIGNED 0 +#define INEXACT 0 +#define FUNC fromfpf +#include <s_fromfpf_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_fromfpf_main.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_fromfpf_main.c new file mode 100644 index 0000000000..3a4ad80e55 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_fromfpf_main.c @@ -0,0 +1,82 @@ +/* Round to integer type. flt-32 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <fenv.h> +#include <math.h> +#include <math_private.h> +#include <stdbool.h> +#include <stdint.h> + +#define BIAS 0x7f +#define MANT_DIG 24 + +#if UNSIGNED +# define RET_TYPE uintmax_t +#else +# define RET_TYPE intmax_t +#endif + +#include <fromfp.h> + +RET_TYPE +FUNC (float x, int round, unsigned int width) +{ + if (width > INTMAX_WIDTH) + width = INTMAX_WIDTH; + uint32_t ix; + GET_FLOAT_WORD (ix, x); + bool negative = (ix & 0x80000000) != 0; + if (width == 0) + return fromfp_domain_error (negative, width); + ix &= 0x7fffffff; + if (ix == 0) + return 0; + int exponent = ix >> (MANT_DIG - 1); + exponent -= BIAS; + int max_exponent = fromfp_max_exponent (negative, width); + if (exponent > max_exponent) + return fromfp_domain_error (negative, width); + + ix &= ((1U << (MANT_DIG - 1)) - 1); + ix |= 1U << (MANT_DIG - 1); + uintmax_t uret; + bool half_bit, more_bits; + if (exponent >= MANT_DIG - 1) + { + uret = ix; + uret <<= exponent - (MANT_DIG - 1); + half_bit = false; + more_bits = false; + } + else if (exponent >= -1) + { + uint32_t h = 1U << (MANT_DIG - 2 - exponent); + half_bit = (ix & h) != 0; + more_bits = (ix & (h - 1)) != 0; + uret = ix >> (MANT_DIG - 1 - exponent); + } + else + { + uret = 0; + half_bit = false; + more_bits = true; + } + return fromfp_round_and_return (negative, uret, half_bit, more_bits, round, + exponent, max_exponent, width); +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_fromfpxf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_fromfpxf.c new file mode 100644 index 0000000000..9d0fcbc8cc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_fromfpxf.c @@ -0,0 +1,4 @@ +#define UNSIGNED 0 +#define INEXACT 1 +#define FUNC fromfpxf +#include <s_fromfpf_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_getpayloadf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_getpayloadf.c new file mode 100644 index 0000000000..90cfcc53b9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_getpayloadf.c @@ -0,0 +1,33 @@ +/* Get NaN payload. flt-32 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fix-int-fp-convert-zero.h> +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +float +getpayloadf (const float *x) +{ + uint32_t ix; + GET_FLOAT_WORD (ix, *x); + ix &= 0x3fffff; + if (FIX_INT_FP_CONVERT_ZERO && ix == 0) + return 0.0f; + return (float) ix; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_isinff.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_isinff.c new file mode 100644 index 0000000000..6eec050bb5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_isinff.c @@ -0,0 +1,29 @@ +/* + * Written by J.T. Conklin <jtc@netbsd.org>. + * Public domain. + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_isinff.c,v 1.3 1995/05/11 23:20:21 jtc Exp $"; +#endif + +/* + * isinff(x) returns 1 if x is inf, -1 if x is -inf, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> + +int +__isinff (float x) +{ + int32_t ix,t; + GET_FLOAT_WORD(ix,x); + t = ix & 0x7fffffff; + t ^= 0x7f800000; + t |= -t; + return ~(t >> 31) & (ix >> 30); +} +hidden_def (__isinff) +weak_alias (__isinff, isinff) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_isnanf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_isnanf.c new file mode 100644 index 0000000000..820b31a2b4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_isnanf.c @@ -0,0 +1,38 @@ +/* s_isnanf.c -- float version of s_isnan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993, 2011 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_isnanf.c,v 1.4 1995/05/10 20:47:38 jtc Exp $"; +#endif + +/* + * isnanf(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> + +#undef __isnanf +int __isnanf(float x) +{ + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + ix = 0x7f800000 - ix; + return (int)(((u_int32_t)(ix))>>31); +} +hidden_def (__isnanf) +weak_alias (__isnanf, isnanf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_issignalingf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_issignalingf.c new file mode 100644 index 0000000000..cd9830eae2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_issignalingf.c @@ -0,0 +1,43 @@ +/* Test for signaling NaN. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> + +int +__issignalingf (float x) +{ + u_int32_t xi; + GET_FLOAT_WORD (xi, x); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* We only have to care about the high-order bit of x's significand, because + having it set (sNaN) already makes the significand different from that + used to designate infinity. */ + return (xi & 0x7fc00000) == 0x7fc00000; +#else + /* To keep the following comparison simple, toggle the quiet/signaling bit, + so that it is set for sNaNs. This is inverse to IEEE 754-2008 (as well as + common practice for IEEE 754-1985). */ + xi ^= 0x00400000; + /* We have to compare for greater (instead of greater or equal), because x's + significand being all-zero designates infinity not NaN. */ + return (xi & 0x7fffffff) > 0x7fc00000; +#endif +} +libm_hidden_def (__issignalingf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_llrintf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_llrintf.c new file mode 100644 index 0000000000..e0ffbfee82 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_llrintf.c @@ -0,0 +1,86 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + +static const float two23[2] = +{ + 8.3886080000e+06, /* 0x4B000000 */ + -8.3886080000e+06, /* 0xCB000000 */ +}; + + +long long int +__llrintf (float x) +{ + int32_t j0; + u_int32_t i0; + float w; + float t; + long long int result; + int sx; + + GET_FLOAT_WORD (i0, x); + + sx = i0 >> 31; + j0 = ((i0 >> 23) & 0xff) - 0x7f; + i0 &= 0x7fffff; + i0 |= 0x800000; + + if (j0 < (int32_t) (sizeof (long long int) * 8) - 1) + { + if (j0 >= 23) + result = (long long int) i0 << (j0 - 23); + else + { + w = math_narrow_eval (two23[sx] + x); + t = w - two23[sx]; + GET_FLOAT_WORD (i0, t); + j0 = ((i0 >> 23) & 0xff) - 0x7f; + i0 &= 0x7fffff; + i0 |= 0x800000; + + result = (j0 < 0 ? 0 : i0 >> (23 - j0)); + } + } + else + { +#ifdef FE_INVALID + /* The number is too large. Unless it rounds to LLONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ + if (FIX_FLT_LLONG_CONVERT_OVERFLOW && x != (float) LLONG_MIN) + { + feraiseexcept (FE_INVALID); + return sx == 0 ? LLONG_MAX : LLONG_MIN; + } +#endif + return (long long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__llrintf, llrintf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_llroundf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_llroundf.c new file mode 100644 index 0000000000..faee87b879 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_llroundf.c @@ -0,0 +1,73 @@ +/* Round float value to long long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + + +long long int +__llroundf (float x) +{ + int32_t j0; + u_int32_t i; + long long int result; + int sign; + + GET_FLOAT_WORD (i, x); + j0 = ((i >> 23) & 0xff) - 0x7f; + sign = (i & 0x80000000) != 0 ? -1 : 1; + i &= 0x7fffff; + i |= 0x800000; + + if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else if (j0 >= 23) + result = (long long int) i << (j0 - 23); + else + { + i += 0x400000 >> j0; + + result = i >> (23 - j0); + } + } + else + { +#ifdef FE_INVALID + /* The number is too large. Unless it rounds to LLONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ + if (FIX_FLT_LLONG_CONVERT_OVERFLOW && x != (float) LLONG_MIN) + { + feraiseexcept (FE_INVALID); + return sign == 1 ? LLONG_MAX : LLONG_MIN; + } +#endif + return (long long int) x; + } + + return sign * result; +} + +weak_alias (__llroundf, llroundf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_log1pf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_log1pf.c new file mode 100644 index 0000000000..ade60a2e27 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_log1pf.c @@ -0,0 +1,102 @@ +/* s_log1pf.c -- float version of s_log1p.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const float +ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ +ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ +two25 = 3.355443200e+07, /* 0x4c000000 */ +Lp1 = 6.6666668653e-01, /* 3F2AAAAB */ +Lp2 = 4.0000000596e-01, /* 3ECCCCCD */ +Lp3 = 2.8571429849e-01, /* 3E924925 */ +Lp4 = 2.2222198546e-01, /* 3E638E29 */ +Lp5 = 1.8183572590e-01, /* 3E3A3325 */ +Lp6 = 1.5313838422e-01, /* 3E1CD04F */ +Lp7 = 1.4798198640e-01; /* 3E178897 */ + +static const float zero = 0.0; + +float +__log1pf(float x) +{ + float hfsq,f,c,s,z,R,u; + int32_t k,hx,hu,ax; + + GET_FLOAT_WORD(hx,x); + ax = hx&0x7fffffff; + + k = 1; + if (hx < 0x3ed413d7) { /* x < 0.41422 */ + if(ax>=0x3f800000) { /* x <= -1.0 */ + if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=-inf */ + else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ + } + if(ax<0x31000000) { /* |x| < 2**-29 */ + math_force_eval(two25+x); /* raise inexact */ + if (ax<0x24800000) /* |x| < 2**-54 */ + { + math_check_force_underflow (x); + return x; + } + else + return x - x*x*(float)0.5; + } + if(hx>0||hx<=((int32_t)0xbe95f61f)) { + k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */ + } + if (hx >= 0x7f800000) return x+x; + if(k!=0) { + if(hx<0x5a000000) { + u = (float)1.0+x; + GET_FLOAT_WORD(hu,u); + k = (hu>>23)-127; + /* correction term */ + c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); + c /= u; + } else { + u = x; + GET_FLOAT_WORD(hu,u); + k = (hu>>23)-127; + c = 0; + } + hu &= 0x007fffff; + if(hu<0x3504f7) { + SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ + } else { + k += 1; + SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ + hu = (0x00800000-hu)>>2; + } + f = u-(float)1.0; + } + hfsq=(float)0.5*f*f; + if(hu==0) { /* |f| < 2**-20 */ + if(f==zero) { + if(k==0) return zero; + else {c += k*ln2_lo; return k*ln2_hi+c;} + } + R = hfsq*((float)1.0-(float)0.66666666666666666*f); + if(k==0) return f-R; else + return k*ln2_hi-((R-(k*ln2_lo+c))-f); + } + s = f/((float)2.0+f); + z = s*s; + R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_logbf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_logbf.c new file mode 100644 index 0000000000..9ae20e332a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_logbf.c @@ -0,0 +1,41 @@ +/* s_logbf.c -- float version of s_logb.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> +#include <fix-int-fp-convert-zero.h> + +float +__logbf (float x) +{ + int32_t ix, rix; + + GET_FLOAT_WORD (ix, x); + ix &= 0x7fffffff; /* high |x| */ + if (ix == 0) + return (float) -1.0 / fabsf (x); + if (ix >= 0x7f800000) + return x * x; + if (__glibc_unlikely ((rix = ix >> 23) == 0)) + { + /* POSIX specifies that denormal number is treated as + though it were normalized. */ + rix -= __builtin_clz (ix) - 9; + } + if (FIX_INT_FP_CONVERT_ZERO && rix == 127) + return 0.0f; + return (float) (rix - 127); +} +weak_alias (__logbf, logbf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_lrintf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_lrintf.c new file mode 100644 index 0000000000..a1ed720c0f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_lrintf.c @@ -0,0 +1,86 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + +static const float two23[2] = +{ + 8.3886080000e+06, /* 0x4B000000 */ + -8.3886080000e+06, /* 0xCB000000 */ +}; + + +long int +__lrintf (float x) +{ + int32_t j0; + u_int32_t i0; + float w; + float t; + long int result; + int sx; + + GET_FLOAT_WORD (i0, x); + + sx = i0 >> 31; + j0 = ((i0 >> 23) & 0xff) - 0x7f; + i0 &= 0x7fffff; + i0 |= 0x800000; + + if (j0 < (int32_t) (sizeof (long int) * 8) - 1) + { + if (j0 >= 23) + result = (long int) i0 << (j0 - 23); + else + { + w = math_narrow_eval (two23[sx] + x); + t = w - two23[sx]; + GET_FLOAT_WORD (i0, t); + j0 = ((i0 >> 23) & 0xff) - 0x7f; + i0 &= 0x7fffff; + i0 |= 0x800000; + + result = (j0 < 0 ? 0 : i0 >> (23 - j0)); + } + } + else + { +#ifdef FE_INVALID + /* The number is too large. Unless it rounds to LONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ + if (FIX_FLT_LONG_CONVERT_OVERFLOW && x != (float) LONG_MIN) + { + feraiseexcept (FE_INVALID); + return sx == 0 ? LONG_MAX : LONG_MIN; + } +#endif + return (long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__lrintf, lrintf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_lroundf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_lroundf.c new file mode 100644 index 0000000000..81cb7ab10f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_lroundf.c @@ -0,0 +1,73 @@ +/* Round float value to long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + + +long int +__lroundf (float x) +{ + int32_t j0; + u_int32_t i; + long int result; + int sign; + + GET_FLOAT_WORD (i, x); + j0 = ((i >> 23) & 0xff) - 0x7f; + sign = (i & 0x80000000) != 0 ? -1 : 1; + i &= 0x7fffff; + i |= 0x800000; + + if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else if (j0 >= 23) + result = (long int) i << (j0 - 23); + else + { + i += 0x400000 >> j0; + + result = i >> (23 - j0); + } + } + else + { +#ifdef FE_INVALID + /* The number is too large. Unless it rounds to LONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ + if (FIX_FLT_LONG_CONVERT_OVERFLOW && x != (float) LONG_MIN) + { + feraiseexcept (FE_INVALID); + return sign == 1 ? LONG_MAX : LONG_MIN; + } +#endif + return (long int) x; + } + + return sign * result; +} + +weak_alias (__lroundf, lroundf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_modff.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_modff.c new file mode 100644 index 0000000000..23f6a902b3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_modff.c @@ -0,0 +1,54 @@ +/* s_modff.c -- float version of s_modf.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + +static const float one = 1.0; + +float +__modff(float x, float *iptr) +{ + int32_t i0,j0; + u_int32_t i; + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; /* exponent of x */ + if(__builtin_expect(j0<23, 1)) { /* integer part in x */ + if(j0<0) { /* |x|<1 */ + SET_FLOAT_WORD(*iptr,i0&0x80000000); /* *iptr = +-0 */ + return x; + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) { /* x is integral */ + u_int32_t ix; + *iptr = x; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x80000000); /* return +-0 */ + return x; + } else { + SET_FLOAT_WORD(*iptr,i0&(~i)); + return x - *iptr; + } + } + } else { /* no fraction part */ + *iptr = x*one; + /* We must handle NaNs separately. */ + if (j0 == 0x80 && (i0 & 0x7fffff)) + return x*one; + SET_FLOAT_WORD(x,i0&0x80000000); /* return +-0 */ + return x; + } +} +weak_alias (__modff, modff) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_nearbyintf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_nearbyintf.c new file mode 100644 index 0000000000..5aebefafcf --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_nearbyintf.c @@ -0,0 +1,59 @@ +/* s_rintf.c -- float version of s_rint.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ +/* Adapted for use as nearbyint by Ulrich Drepper <drepper@cygnus.com>. */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + +#include <fenv.h> +#include <math.h> +#include <math_private.h> + +static const float +TWO23[2]={ + 8.3886080000e+06, /* 0x4b000000 */ + -8.3886080000e+06, /* 0xcb000000 */ +}; + +float +__nearbyintf(float x) +{ + fenv_t env; + int32_t i0,j0,sx; + float w,t; + GET_FLOAT_WORD(i0,x); + sx = (i0>>31)&1; + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { + libc_feholdexceptf (&env); + w = TWO23[sx]+x; + t = w-TWO23[sx]; + math_force_eval (t); + libc_fesetenvf (&env); + GET_FLOAT_WORD(i0,t); + SET_FLOAT_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } + } else { + if(__builtin_expect(j0==0x80, 0)) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + libc_feholdexceptf (&env); + w = TWO23[sx]+x; + t = w-TWO23[sx]; + math_force_eval (t); + libc_fesetenvf (&env); + return t; +} +weak_alias (__nearbyintf, nearbyintf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_nextafterf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_nextafterf.c new file mode 100644 index 0000000000..625d54b768 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_nextafterf.c @@ -0,0 +1,73 @@ +/* s_nextafterf.c -- float version of s_nextafter.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_nextafterf.c,v 1.4 1995/05/10 20:48:01 jtc Exp $"; +#endif + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <float.h> + +float __nextafterf(float x, float y) +{ + int32_t hx,hy,ix,iy; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffff; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + (iy>0x7f800000)) /* y is nan */ + return x+y; + if(x==y) return y; /* x=y, return y */ + if(ix==0) { /* x == 0 */ + float u; + SET_FLOAT_WORD(x,(hy&0x80000000)|1);/* return +-minsubnormal */ + u = math_opt_barrier (x); + u = u*u; + math_force_eval (u); /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if(hx>hy) { /* x > y, x -= ulp */ + hx -= 1; + } else { /* x < y, x += ulp */ + hx += 1; + } + } else { /* x < 0 */ + if(hy>=0||hx>hy){ /* x < y, x -= ulp */ + hx -= 1; + } else { /* x > y, x += ulp */ + hx += 1; + } + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) { + float u = x+x; /* overflow */ + math_force_eval (u); + __set_errno (ERANGE); + } + if(hy<0x00800000) { + float u = x*x; /* underflow */ + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + SET_FLOAT_WORD(x,hx); + return x; +} +weak_alias (__nextafterf, nextafterf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_nextupf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_nextupf.c new file mode 100644 index 0000000000..bbabdf1bd6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_nextupf.c @@ -0,0 +1,46 @@ +/* Return the least floating-point number greater than X. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* Return the least floating-point number greater than X. */ +float +__nextupf (float x) +{ + int32_t hx, ix; + + GET_FLOAT_WORD (hx, x); + ix = hx & 0x7fffffff; + if (ix == 0) + return FLT_TRUE_MIN; + if (ix > 0x7f800000) /* x is nan. */ + return x + x; + if (hx >= 0) + { /* x > 0. */ + if (isinf (x)) + return x; + hx += 1; + } + else + hx -= 1; + SET_FLOAT_WORD (x, hx); + return x; +} + +weak_alias (__nextupf, nextupf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_remquof.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_remquof.c new file mode 100644 index 0000000000..8e398dc6c5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_remquof.c @@ -0,0 +1,110 @@ +/* Compute remainder and a congruent to the quotient. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +static const float zero = 0.0; + + +float +__remquof (float x, float y, int *quo) +{ + int32_t hx,hy; + u_int32_t sx; + int cquo, qs; + + GET_FLOAT_WORD (hx, x); + GET_FLOAT_WORD (hy, y); + sx = hx & 0x80000000; + qs = sx ^ (hy & 0x80000000); + hy &= 0x7fffffff; + hx &= 0x7fffffff; + + /* Purge off exception values. */ + if (hy == 0) + return (x * y) / (x * y); /* y = 0 */ + if ((hx >= 0x7f800000) /* x not finite */ + || (hy > 0x7f800000)) /* y is NaN */ + return (x * y) / (x * y); + + if (hy <= 0x7dffffff) + x = __ieee754_fmodf (x, 8 * y); /* now x < 8y */ + + if ((hx - hy) == 0) + { + *quo = qs ? -1 : 1; + return zero * x; + } + + x = fabsf (x); + y = fabsf (y); + cquo = 0; + + if (hy <= 0x7e7fffff && x >= 4 * y) + { + x -= 4 * y; + cquo += 4; + } + if (hy <= 0x7effffff && x >= 2 * y) + { + x -= 2 * y; + cquo += 2; + } + + if (hy < 0x01000000) + { + if (x + x > y) + { + x -= y; + ++cquo; + if (x + x >= y) + { + x -= y; + ++cquo; + } + } + } + else + { + float y_half = 0.5 * y; + if (x > y_half) + { + x -= y; + ++cquo; + if (x >= y_half) + { + x -= y; + ++cquo; + } + } + } + + *quo = qs ? -cquo : cquo; + + /* Ensure correct sign of zero result in round-downward mode. */ + if (x == 0.0f) + x = 0.0f; + if (sx) + x = -x; + return x; +} +weak_alias (__remquof, remquof) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_rintf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_rintf.c new file mode 100644 index 0000000000..8a907488f7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_rintf.c @@ -0,0 +1,50 @@ +/* s_rintf.c -- float version of s_rint.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + +static const float +TWO23[2]={ + 8.3886080000e+06, /* 0x4b000000 */ + -8.3886080000e+06, /* 0xcb000000 */ +}; + +float +__rintf(float x) +{ + int32_t i0,j0,sx; + float w,t; + GET_FLOAT_WORD(i0,x); + sx = (i0>>31)&1; + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { + w = TWO23[sx]+x; + t = w-TWO23[sx]; + GET_FLOAT_WORD(i0,t); + SET_FLOAT_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + w = TWO23[sx]+x; + return w-TWO23[sx]; +} +#ifndef __rintf +weak_alias (__rintf, rintf) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_roundevenf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_roundevenf.c new file mode 100644 index 0000000000..4a8c2624bb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_roundevenf.c @@ -0,0 +1,68 @@ +/* Round to nearest integer value, rounding halfway cases to even. + flt-32 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +#define BIAS 0x7f +#define MANT_DIG 24 +#define MAX_EXP (2 * BIAS + 1) + +float +roundevenf (float x) +{ + uint32_t ix, ux; + GET_FLOAT_WORD (ix, x); + ux = ix & 0x7fffffff; + int exponent = ux >> (MANT_DIG - 1); + if (exponent >= BIAS + MANT_DIG - 1) + { + /* Integer, infinity or NaN. */ + if (exponent == MAX_EXP) + /* Infinity or NaN; quiet signaling NaNs. */ + return x + x; + else + return x; + } + else if (exponent >= BIAS) + { + /* At least 1; not necessarily an integer. Locate the bits with + exponents 0 and -1 (when the unbiased exponent is 0, the bit + with exponent 0 is implicit, but as the bias is odd it is OK + to take it from the low bit of the exponent). */ + int int_pos = (BIAS + MANT_DIG - 1) - exponent; + int half_pos = int_pos - 1; + uint32_t half_bit = 1U << half_pos; + uint32_t int_bit = 1U << int_pos; + if ((ix & (int_bit | (half_bit - 1))) != 0) + /* Carry into the exponent works correctly. No need to test + whether HALF_BIT is set. */ + ix += half_bit; + ix &= ~(int_bit - 1); + } + else if (exponent == BIAS - 1 && ux > 0x3f000000) + /* Interval (0.5, 1). */ + ix = (ix & 0x80000000) | 0x3f800000; + else + /* Rounds to 0. */ + ix &= 0x80000000; + SET_FLOAT_WORD (x, ix); + return x; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_roundf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_roundf.c new file mode 100644 index 0000000000..7ea0d97756 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_roundf.c @@ -0,0 +1,63 @@ +/* Round float to integer away from zero. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +float +__roundf (float x) +{ + int32_t i0, j0; + + GET_FLOAT_WORD (i0, x); + j0 = ((i0 >> 23) & 0xff) - 0x7f; + if (j0 < 23) + { + if (j0 < 0) + { + i0 &= 0x80000000; + if (j0 == -1) + i0 |= 0x3f800000; + } + else + { + u_int32_t i = 0x007fffff >> j0; + if ((i0 & i) == 0) + /* X is integral. */ + return x; + + i0 += 0x00400000 >> j0; + i0 &= ~i; + } + } + else + { + if (j0 == 0x80) + /* Inf or NaN. */ + return x + x; + else + return x; + } + + SET_FLOAT_WORD (x, i0); + return x; +} +weak_alias (__roundf, roundf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_scalblnf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_scalblnf.c new file mode 100644 index 0000000000..ad3c586b33 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_scalblnf.c @@ -0,0 +1,52 @@ +/* s_scalbnf.c -- float version of s_scalbn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + +static const float +two25 = 3.355443200e+07, /* 0x4c000000 */ +twom25 = 2.9802322388e-08, /* 0x33000000 */ +huge = 1.0e+30, +tiny = 1.0e-30; + +float +__scalblnf (float x, long int n) +{ + int32_t k,ix; + GET_FLOAT_WORD(ix,x); + k = (ix&0x7f800000)>>23; /* extract exponent */ + if (__builtin_expect(k==0, 0)) { /* 0 or subnormal x */ + if ((ix&0x7fffffff)==0) return x; /* +-0 */ + x *= two25; + GET_FLOAT_WORD(ix,x); + k = ((ix&0x7f800000)>>23) - 25; + } + if (__builtin_expect(k==0xff, 0)) return x+x; /* NaN or Inf */ + if (__builtin_expect(n< -50000, 0)) + return tiny*copysignf(tiny,x); /*underflow*/ + if (__builtin_expect(n> 50000 || k+n > 0xfe, 0)) + return huge*copysignf(huge,x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k+n; + if (__builtin_expect(k > 0, 1)) /* normal result */ + {SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); return x;} + if (k <= -25) + return tiny*copysignf(tiny,x); /*underflow*/ + k += 25; /* subnormal result */ + SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); + return x*twom25; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_scalbnf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_scalbnf.c new file mode 100644 index 0000000000..f36ae241b2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_scalbnf.c @@ -0,0 +1,52 @@ +/* s_scalbnf.c -- float version of s_scalbn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> + +static const float +two25 = 3.355443200e+07, /* 0x4c000000 */ +twom25 = 2.9802322388e-08, /* 0x33000000 */ +huge = 1.0e+30, +tiny = 1.0e-30; + +float +__scalbnf (float x, int n) +{ + int32_t k,ix; + GET_FLOAT_WORD(ix,x); + k = (ix&0x7f800000)>>23; /* extract exponent */ + if (__builtin_expect(k==0, 0)) { /* 0 or subnormal x */ + if ((ix&0x7fffffff)==0) return x; /* +-0 */ + x *= two25; + GET_FLOAT_WORD(ix,x); + k = ((ix&0x7f800000)>>23) - 25; + } + if (__builtin_expect(k==0xff, 0)) return x+x; /* NaN or Inf */ + if (__builtin_expect(n< -50000, 0)) + return tiny*__copysignf(tiny,x); /*underflow*/ + if (__builtin_expect(n> 50000 || k+n > 0xfe, 0)) + return huge*__copysignf(huge,x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k+n; + if (__builtin_expect(k > 0, 1)) /* normal result */ + {SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); return x;} + if (k <= -25) + return tiny*__copysignf(tiny,x); /*underflow*/ + k += 25; /* subnormal result */ + SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); + return x*twom25; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_setpayloadf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_setpayloadf.c new file mode 100644 index 0000000000..86dfda9aa6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_setpayloadf.c @@ -0,0 +1,3 @@ +#define SIG 0 +#define FUNC setpayloadf +#include <s_setpayloadf_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_setpayloadf_main.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_setpayloadf_main.c new file mode 100644 index 0000000000..8b046d6547 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_setpayloadf_main.c @@ -0,0 +1,53 @@ +/* Set NaN payload. flt-32 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +#define SET_HIGH_BIT (HIGH_ORDER_BIT_IS_SET_FOR_SNAN ? SIG : !SIG) +#define BIAS 0x7f +#define PAYLOAD_DIG 22 +#define EXPLICIT_MANT_DIG 23 + +int +FUNC (float *x, float payload) +{ + uint32_t ix; + GET_FLOAT_WORD (ix, payload); + int exponent = ix >> EXPLICIT_MANT_DIG; + /* Test if argument is (a) negative or too large; (b) too small, + except for 0 when allowed; (c) not an integer. */ + if (exponent >= BIAS + PAYLOAD_DIG + || (exponent < BIAS && !(SET_HIGH_BIT && ix == 0)) + || (ix & ((1U << (BIAS + EXPLICIT_MANT_DIG - exponent)) - 1)) != 0) + { + SET_FLOAT_WORD (*x, 0); + return 1; + } + if (ix != 0) + { + ix &= (1U << EXPLICIT_MANT_DIG) - 1; + ix |= 1U << EXPLICIT_MANT_DIG; + ix >>= BIAS + EXPLICIT_MANT_DIG - exponent; + } + ix |= 0x7f800000 | (SET_HIGH_BIT ? 0x400000 : 0); + SET_FLOAT_WORD (*x, ix); + return 0; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_setpayloadsigf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_setpayloadsigf.c new file mode 100644 index 0000000000..f7b335dac7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_setpayloadsigf.c @@ -0,0 +1,3 @@ +#define SIG 1 +#define FUNC setpayloadsigf +#include <s_setpayloadf_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_signbitf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_signbitf.c new file mode 100644 index 0000000000..0f7e23d7f9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_signbitf.c @@ -0,0 +1,26 @@ +/* Return nonzero value if number is negative. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +int +__signbitf (float x) +{ + return __builtin_signbitf (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_sincosf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_sincosf.c new file mode 100644 index 0000000000..3ab92ee0ba --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_sincosf.c @@ -0,0 +1,84 @@ +/* Compute sine and cosine of argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <math.h> + +#include <math_private.h> + +#ifndef SINCOSF +# define SINCOSF_FUNC __sincosf +#else +# define SINCOSF_FUNC SINCOSF +#endif + +void +SINCOSF_FUNC (float x, float *sinx, float *cosx) +{ + int32_t ix; + + /* High word of x. */ + GET_FLOAT_WORD (ix, x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if (ix <= 0x3f490fd8) + { + *sinx = __kernel_sinf (x, 0.0, 0); + *cosx = __kernel_cosf (x, 0.0); + } + else if (ix>=0x7f800000) + { + /* sin(Inf or NaN) is NaN */ + *sinx = *cosx = x - x; + if (ix == 0x7f800000) + __set_errno (EDOM); + } + else + { + /* Argument reduction needed. */ + float y[2]; + int n; + + n = __ieee754_rem_pio2f (x, y); + switch (n & 3) + { + case 0: + *sinx = __kernel_sinf (y[0], y[1], 1); + *cosx = __kernel_cosf (y[0], y[1]); + break; + case 1: + *sinx = __kernel_cosf (y[0], y[1]); + *cosx = -__kernel_sinf (y[0], y[1], 1); + break; + case 2: + *sinx = -__kernel_sinf (y[0], y[1], 1); + *cosx = -__kernel_cosf (y[0], y[1]); + break; + default: + *sinx = -__kernel_cosf (y[0], y[1]); + *cosx = __kernel_sinf (y[0], y[1], 1); + break; + } + } +} + +#ifndef SINCOSF +weak_alias (__sincosf, sincosf) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_sinf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_sinf.c new file mode 100644 index 0000000000..916e345571 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_sinf.c @@ -0,0 +1,63 @@ +/* s_sinf.c -- float version of s_sin.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_sinf.c,v 1.4 1995/05/10 20:48:16 jtc Exp $"; +#endif + +#include <errno.h> +#include <math.h> +#include <math_private.h> + +#ifndef SINF +# define SINF_FUNC __sinf +#else +# define SINF_FUNC SINF +#endif + +float SINF_FUNC(float x) +{ + float y[2],z=0.0; + int32_t n, ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) { + if (ix == 0x7f800000) + __set_errno (EDOM); + return x-x; + } + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,y); + switch(n&3) { + case 0: return __kernel_sinf(y[0],y[1],1); + case 1: return __kernel_cosf(y[0],y[1]); + case 2: return -__kernel_sinf(y[0],y[1],1); + default: + return -__kernel_cosf(y[0],y[1]); + } + } +} + +#ifndef SINF +weak_alias (__sinf, sinf) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_tanf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_tanf.c new file mode 100644 index 0000000000..685df8fa35 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_tanf.c @@ -0,0 +1,49 @@ +/* s_tanf.c -- float version of s_tan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_tanf.c,v 1.4 1995/05/10 20:48:20 jtc Exp $"; +#endif + +#include <errno.h> +#include <math.h> +#include <math_private.h> + +float __tanf(float x) +{ + float y[2],z=0.0; + int32_t n, ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fda) return __kernel_tanf(x,z,1); + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) { + if (ix==0x7f800000) + __set_errno (EDOM); + return x-x; /* NaN */ + } + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,y); + return __kernel_tanf(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} +weak_alias (__tanf, tanf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_tanhf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_tanhf.c new file mode 100644 index 0000000000..f70702b29c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_tanhf.c @@ -0,0 +1,62 @@ +/* s_tanhf.c -- float version of s_tanh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_tanhf.c,v 1.4 1995/05/10 20:48:24 jtc Exp $"; +#endif + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const float one=1.0, two=2.0, tiny = 1.0e-30; + +float __tanhf(float x) +{ + float t,z; + int32_t jx,ix; + + GET_FLOAT_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x41b00000) { /* |x|<22 */ + if (ix == 0) + return x; /* x == +-0 */ + if (ix<0x24000000) /* |x|<2**-55 */ + { + math_check_force_underflow (x); + return x*(one+x); /* tanh(small) = small */ + } + if (ix>=0x3f800000) { /* |x|>=1 */ + t = __expm1f(two*fabsf(x)); + z = one - two/(t+two); + } else { + t = __expm1f(-two*fabsf(x)); + z= -t/(t+two); + } + /* |x| > 22, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (jx>=0)? z: -z; +} +weak_alias (__tanhf, tanhf) diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_totalorderf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_totalorderf.c new file mode 100644 index 0000000000..f592b051db --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_totalorderf.c @@ -0,0 +1,46 @@ +/* Total order operation. flt-32 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalorderf (float x, float y) +{ + int32_t ix, iy; + GET_FLOAT_WORD (ix, x); + GET_FLOAT_WORD (iy, y); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the arguments interpreted as + sign-magnitude integers. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if ((ix & 0x7fffffff) > 0x7f800000 && (iy & 0x7fffffff) > 0x7f800000) + { + ix ^= 0x00400000; + iy ^= 0x00400000; + } +#endif + uint32_t ix_sign = ix >> 31; + uint32_t iy_sign = iy >> 31; + ix ^= ix_sign >> 1; + iy ^= iy_sign >> 1; + return ix <= iy; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_totalordermagf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_totalordermagf.c new file mode 100644 index 0000000000..cac7601e12 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_totalordermagf.c @@ -0,0 +1,44 @@ +/* Total order operation on absolute values. flt-32 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalordermagf (float x, float y) +{ + uint32_t ix, iy; + GET_FLOAT_WORD (ix, x); + GET_FLOAT_WORD (iy, y); + ix &= 0x7fffffff; + iy &= 0x7fffffff; +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the absolute values of the + arguments. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if (ix > 0x7f800000 && iy > 0x7f800000) + { + ix ^= 0x00400000; + iy ^= 0x00400000; + } +#endif + return ix <= iy; +} diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_truncf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_truncf.c new file mode 100644 index 0000000000..2edb03c16f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_truncf.c @@ -0,0 +1,53 @@ +/* Truncate argument to nearest integral value not larger than the argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +float +__truncf (float x) +{ + int32_t i0, j0; + int sx; + + GET_FLOAT_WORD (i0, x); + sx = i0 & 0x80000000; + j0 = ((i0 >> 23) & 0xff) - 0x7f; + if (j0 < 23) + { + if (j0 < 0) + /* The magnitude of the number is < 1 so the result is +-0. */ + SET_FLOAT_WORD (x, sx); + else + SET_FLOAT_WORD (x, sx | (i0 & ~(0x007fffff >> j0))); + } + else + { + if (j0 == 0x80) + /* x is inf or NaN. */ + return x + x; + } + + return x; +} +#ifndef __truncf +weak_alias (__truncf, truncf) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_ufromfpf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_ufromfpf.c new file mode 100644 index 0000000000..e6ffdf3374 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_ufromfpf.c @@ -0,0 +1,4 @@ +#define UNSIGNED 1 +#define INEXACT 0 +#define FUNC ufromfpf +#include <s_fromfpf_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/s_ufromfpxf.c b/REORG.TODO/sysdeps/ieee754/flt-32/s_ufromfpxf.c new file mode 100644 index 0000000000..97aa6890f0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/s_ufromfpxf.c @@ -0,0 +1,4 @@ +#define UNSIGNED 1 +#define INEXACT 1 +#define FUNC ufromfpxf +#include <s_fromfpf_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/t_exp2f.h b/REORG.TODO/sysdeps/ieee754/flt-32/t_exp2f.h new file mode 100644 index 0000000000..aecabcc372 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/t_exp2f.h @@ -0,0 +1,351 @@ +/* Accurate tables for exp2f(). + Copyright (C) 1998-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* This table has the property that, for all integers -128 <= i <= 127, + exp(i/256.0 + __exp2f_deltatable[i-128]) == __exp2f_atable[i+128] + r + for some -2^-35 < r < 2^-35 (abs(r) < 2^-36 if i <= 0); and that + __exp2f_deltatable[i+128] == t * 2^-30 + for integer t so that abs(t) <= 43447 * 2^0. */ + +#define W30 (9.31322575e-10) +static const float __exp2f_deltatable[256] = { + -810*W30, 283*W30, -1514*W30, 1304*W30, + -1148*W30, -98*W30, -744*W30, -156*W30, + -419*W30, -155*W30, 474*W30, 167*W30, + -1984*W30, -826*W30, 692*W30, 781*W30, + -578*W30, -411*W30, -129*W30, -1500*W30, + 654*W30, -141*W30, -816*W30, -53*W30, + 148*W30, 493*W30, -2214*W30, 760*W30, + 260*W30, 750*W30, -1300*W30, 1424*W30, + -1445*W30, -339*W30, -680*W30, -349*W30, + -922*W30, 531*W30, 193*W30, -2892*W30, + 290*W30, -2145*W30, -276*W30, 485*W30, + -695*W30, 215*W30, -7093*W30, 412*W30, + -4596*W30, 367*W30, 592*W30, -615*W30, + -97*W30, -1066*W30, 972*W30, -226*W30, + -625*W30, -374*W30, -5647*W30, -180*W30, + 20349*W30, -447*W30, 111*W30, -4164*W30, + -87*W30, -21*W30, -251*W30, 66*W30, + -517*W30, 2093*W30, -263*W30, 182*W30, + -601*W30, 475*W30, -483*W30, -1251*W30, + -373*W30, 1471*W30, -92*W30, -215*W30, + -97*W30, -190*W30, 0*W30, -290*W30, + -2647*W30, 1940*W30, -582*W30, 28*W30, + 833*W30, 1493*W30, 34*W30, 321*W30, + 3327*W30, -35*W30, 177*W30, -135*W30, + -796*W30, -428*W30, 129*W30, 9332*W30, + -12*W30, -69*W30, -1743*W30, 6508*W30, + -60*W30, 359*W30, 43447*W30, 15*W30, + -23*W30, -305*W30, -375*W30, -652*W30, + 667*W30, 269*W30, -1575*W30, 185*W30, + -329*W30, 200*W30, 6002*W30, 163*W30, + -647*W30, 19*W30, -603*W30, -755*W30, + 742*W30, -438*W30, 3587*W30, 2560*W30, + 0*W30, -520*W30, -241*W30, -299*W30, + -1270*W30, -991*W30, -1138*W30, 255*W30, + -1192*W30, 1722*W30, 1023*W30, 3700*W30, + -1388*W30, -1551*W30, -2549*W30, 27*W30, + 282*W30, 673*W30, 113*W30, 1561*W30, + 72*W30, 873*W30, 87*W30, -395*W30, + -433*W30, 629*W30, 3440*W30, -284*W30, + -592*W30, -103*W30, -46*W30, -3844*W30, + 1712*W30, 303*W30, 1555*W30, -631*W30, + -1400*W30, -961*W30, -854*W30, -276*W30, + 407*W30, 833*W30, -345*W30, -1501*W30, + 121*W30, -1581*W30, 400*W30, 150*W30, + 1224*W30, -139*W30, -563*W30, 879*W30, + 933*W30, 2939*W30, 788*W30, 211*W30, + 530*W30, -192*W30, 706*W30, -13347*W30, + 1065*W30, 3*W30, 111*W30, -208*W30, + -360*W30, -532*W30, -291*W30, 483*W30, + 987*W30, -33*W30, -1373*W30, -166*W30, + -1174*W30, -3955*W30, 1601*W30, -280*W30, + 1405*W30, 600*W30, -1659*W30, -23*W30, + 390*W30, 449*W30, 570*W30, -13143*W30, + -9*W30, -1646*W30, 1201*W30, 294*W30, + 2181*W30, -1173*W30, 1388*W30, -4504*W30, + 190*W30, -2304*W30, 211*W30, 239*W30, + 48*W30, -817*W30, 1018*W30, 1828*W30, + -663*W30, 1408*W30, 408*W30, -36*W30, + 1295*W30, -230*W30, 1341*W30, 9*W30, + 40*W30, 705*W30, 186*W30, 376*W30, + 557*W30, 5866*W30, 363*W30, -1558*W30, + 718*W30, 669*W30, 1369*W30, -2972*W30, + -468*W30, -121*W30, -219*W30, 667*W30, + 29954*W30, 366*W30, 48*W30, -203*W30 +}; + +static const float __exp2f_atable[256] /* __attribute__((mode(SF))) */ = { + 0.707106411447, /* 0x0.b504ecfff */ + 0.709024071690, /* 0x0.b58299fff */ + 0.710945606239, /* 0x0.b60088000 */ + 0.712874472142, /* 0x0.b67ef1000 */ + 0.714806139464, /* 0x0.b6fd88fff */ + 0.716744661340, /* 0x0.b77c94000 */ + 0.718687653549, /* 0x0.b7fbea000 */ + 0.720636486992, /* 0x0.b87ba1fff */ + 0.722590208040, /* 0x0.b8fbabfff */ + 0.724549472323, /* 0x0.b97c12fff */ + 0.726514220228, /* 0x0.b9fcd5fff */ + 0.728483855735, /* 0x0.ba7deb000 */ + 0.730457961549, /* 0x0.baff4afff */ + 0.732438981522, /* 0x0.bb811efff */ + 0.734425544748, /* 0x0.bc0350000 */ + 0.736416816713, /* 0x0.bc85d0000 */ + 0.738412797450, /* 0x0.bd089efff */ + 0.740414917465, /* 0x0.bd8bd4fff */ + 0.742422521111, /* 0x0.be0f66fff */ + 0.744434773914, /* 0x0.be9346fff */ + 0.746454179287, /* 0x0.bf179f000 */ + 0.748477637755, /* 0x0.bf9c3afff */ + 0.750506639473, /* 0x0.c02133fff */ + 0.752541840064, /* 0x0.c0a694fff */ + 0.754582285889, /* 0x0.c12c4e000 */ + 0.756628334525, /* 0x0.c1b265000 */ + 0.758678436269, /* 0x0.c238bffff */ + 0.760736882681, /* 0x0.c2bfa6fff */ + 0.762799203401, /* 0x0.c346cf000 */ + 0.764867603790, /* 0x0.c3ce5d000 */ + 0.766940355298, /* 0x0.c45633fff */ + 0.769021093841, /* 0x0.c4de90fff */ + 0.771104693409, /* 0x0.c5671dfff */ + 0.773195922364, /* 0x0.c5f02afff */ + 0.775292098512, /* 0x0.c6798afff */ + 0.777394294745, /* 0x0.c70350000 */ + 0.779501736166, /* 0x0.c78d6d000 */ + 0.781615912910, /* 0x0.c817fafff */ + 0.783734917628, /* 0x0.c8a2d9fff */ + 0.785858273516, /* 0x0.c92e02000 */ + 0.787990570071, /* 0x0.c9b9c0000 */ + 0.790125787245, /* 0x0.ca45aefff */ + 0.792268991467, /* 0x0.cad223fff */ + 0.794417440881, /* 0x0.cb5ef0fff */ + 0.796570718287, /* 0x0.cbec0efff */ + 0.798730909811, /* 0x0.cc79a0fff */ + 0.800892710672, /* 0x0.cd074dfff */ + 0.803068041795, /* 0x0.cd95ddfff */ + 0.805242776881, /* 0x0.ce2464000 */ + 0.807428598393, /* 0x0.ceb3a3fff */ + 0.809617877002, /* 0x0.cf431dfff */ + 0.811812341211, /* 0x0.cfd2eefff */ + 0.814013659956, /* 0x0.d06333000 */ + 0.816220164311, /* 0x0.d0f3ce000 */ + 0.818434238424, /* 0x0.d184e7fff */ + 0.820652604094, /* 0x0.d21649fff */ + 0.822877407074, /* 0x0.d2a818000 */ + 0.825108587751, /* 0x0.d33a51000 */ + 0.827342867839, /* 0x0.d3ccbdfff */ + 0.829588949684, /* 0x0.d45ff1000 */ + 0.831849217401, /* 0x0.d4f411fff */ + 0.834093391880, /* 0x0.d58724fff */ + 0.836355149750, /* 0x0.d61b5f000 */ + 0.838620424257, /* 0x0.d6afd3fff */ + 0.840896368027, /* 0x0.d744fc000 */ + 0.843176305293, /* 0x0.d7da66fff */ + 0.845462262643, /* 0x0.d87037000 */ + 0.847754716864, /* 0x0.d90673fff */ + 0.850052893157, /* 0x0.d99d10fff */ + 0.852359056469, /* 0x0.da3433fff */ + 0.854668736446, /* 0x0.dacb91fff */ + 0.856986224651, /* 0x0.db6373000 */ + 0.859309315673, /* 0x0.dbfbb1fff */ + 0.861639738080, /* 0x0.dc946bfff */ + 0.863975346095, /* 0x0.dd2d7d000 */ + 0.866317391394, /* 0x0.ddc6f9fff */ + 0.868666708472, /* 0x0.de60f1000 */ + 0.871022939695, /* 0x0.defb5c000 */ + 0.873383641229, /* 0x0.df9611fff */ + 0.875751554968, /* 0x0.e03141000 */ + 0.878126025200, /* 0x0.e0ccde000 */ + 0.880506813521, /* 0x0.e168e4fff */ + 0.882894217966, /* 0x0.e2055afff */ + 0.885287821299, /* 0x0.e2a239000 */ + 0.887686729423, /* 0x0.e33f6ffff */ + 0.890096127973, /* 0x0.e3dd56fff */ + 0.892507970338, /* 0x0.e47b67000 */ + 0.894928157336, /* 0x0.e51a03000 */ + 0.897355020043, /* 0x0.e5b90efff */ + 0.899788379682, /* 0x0.e65888000 */ + 0.902227103705, /* 0x0.e6f85afff */ + 0.904673457151, /* 0x0.e798ae000 */ + 0.907128036008, /* 0x0.e8398afff */ + 0.909585535528, /* 0x0.e8da99000 */ + 0.912051796915, /* 0x0.e97c3a000 */ + 0.914524436003, /* 0x0.ea1e46000 */ + 0.917003571999, /* 0x0.eac0bf000 */ + 0.919490039339, /* 0x0.eb63b2fff */ + 0.921983361257, /* 0x0.ec071a000 */ + 0.924488604054, /* 0x0.ecab48fff */ + 0.926989555360, /* 0x0.ed4f30000 */ + 0.929502844812, /* 0x0.edf3e6000 */ + 0.932021975503, /* 0x0.ee98fdfff */ + 0.934553921208, /* 0x0.ef3eecfff */ + 0.937083780759, /* 0x0.efe4b8fff */ + 0.939624726786, /* 0x0.f08b3f000 */ + 0.942198514924, /* 0x0.f133ebfff */ + 0.944726586343, /* 0x0.f1d99a000 */ + 0.947287976728, /* 0x0.f28176fff */ + 0.949856162070, /* 0x0.f329c5fff */ + 0.952431440345, /* 0x0.f3d28bfff */ + 0.955013573175, /* 0x0.f47bc5000 */ + 0.957603693021, /* 0x0.f52584000 */ + 0.960199773321, /* 0x0.f5cfa7000 */ + 0.962801992906, /* 0x0.f67a31000 */ + 0.965413510788, /* 0x0.f72556fff */ + 0.968030691152, /* 0x0.f7d0dc000 */ + 0.970655620084, /* 0x0.f87ce2fff */ + 0.973290979849, /* 0x0.f92998fff */ + 0.975926160805, /* 0x0.f9d64bfff */ + 0.978571653370, /* 0x0.fa83ac000 */ + 0.981225252139, /* 0x0.fb3193fff */ + 0.983885228626, /* 0x0.fbdfe6fff */ + 0.986552715296, /* 0x0.fc8eb7fff */ + 0.989228487027, /* 0x0.fd3e14000 */ + 0.991909801964, /* 0x0.fdedcd000 */ + 0.994601726545, /* 0x0.fe9e38000 */ + 0.997297704209, /* 0x0.ff4ee6fff */ + 1.000000000000, /* 0x1.000000000 */ + 1.002710938457, /* 0x1.00b1aa000 */ + 1.005429744692, /* 0x1.0163d7ffe */ + 1.008155703526, /* 0x1.02167dffe */ + 1.010888457284, /* 0x1.02c995fff */ + 1.013629436498, /* 0x1.037d38000 */ + 1.016377568250, /* 0x1.043152000 */ + 1.019134163841, /* 0x1.04e5f9ffe */ + 1.021896362316, /* 0x1.059b00000 */ + 1.024668931945, /* 0x1.0650b3ffe */ + 1.027446627635, /* 0x1.0706be001 */ + 1.030234098408, /* 0x1.07bd6bffe */ + 1.033023953416, /* 0x1.087441ffe */ + 1.035824656494, /* 0x1.092bce000 */ + 1.038632392900, /* 0x1.09e3d0001 */ + 1.041450142840, /* 0x1.0a9c79ffe */ + 1.044273972530, /* 0x1.0b558a001 */ + 1.047105550795, /* 0x1.0c0f1c001 */ + 1.049944162390, /* 0x1.0cc924001 */ + 1.052791833895, /* 0x1.0d83c4001 */ + 1.055645227426, /* 0x1.0e3ec3fff */ + 1.058507919326, /* 0x1.0efa60001 */ + 1.061377286898, /* 0x1.0fb66bfff */ + 1.064254641510, /* 0x1.1072fdffe */ + 1.067140102389, /* 0x1.113018000 */ + 1.070034146304, /* 0x1.11edc1fff */ + 1.072937250162, /* 0x1.12ac04001 */ + 1.075843691823, /* 0x1.136a7dfff */ + 1.078760385496, /* 0x1.1429a3ffe */ + 1.081685543070, /* 0x1.14e958000 */ + 1.084618330005, /* 0x1.15a98c000 */ + 1.087556362176, /* 0x1.166a18001 */ + 1.090508937863, /* 0x1.172b98001 */ + 1.093464612954, /* 0x1.17ed4bfff */ + 1.096430182434, /* 0x1.18afa5ffe */ + 1.099401354802, /* 0x1.19725e000 */ + 1.102381587017, /* 0x1.1a35adfff */ + 1.105370759965, /* 0x1.1af994000 */ + 1.108367800686, /* 0x1.1bbdfdffe */ + 1.111373305331, /* 0x1.1c82f6000 */ + 1.114387035385, /* 0x1.1d4878001 */ + 1.117408752440, /* 0x1.1e0e7ffff */ + 1.120437502874, /* 0x1.1ed4fe000 */ + 1.123474478729, /* 0x1.1f9c06000 */ + 1.126521706601, /* 0x1.2063ba001 */ + 1.129574775716, /* 0x1.212bd0001 */ + 1.132638812065, /* 0x1.21f49e000 */ + 1.135709524130, /* 0x1.22bddbffe */ + 1.138789534565, /* 0x1.2387b5fff */ + 1.141876101508, /* 0x1.2451fe000 */ + 1.144971728301, /* 0x1.251cddffe */ + 1.148077130296, /* 0x1.25e861ffe */ + 1.151189923305, /* 0x1.26b462001 */ + 1.154312610610, /* 0x1.278107ffe */ + 1.157440662410, /* 0x1.284e08001 */ + 1.160578370109, /* 0x1.291baa001 */ + 1.163725256932, /* 0x1.29e9e6000 */ + 1.166879892324, /* 0x1.2ab8a3ffe */ + 1.170044302935, /* 0x1.2b8805fff */ + 1.173205971694, /* 0x1.2c5739ffe */ + 1.176397800428, /* 0x1.2d2867ffe */ + 1.179586529747, /* 0x1.2df962001 */ + 1.182784795737, /* 0x1.2ecafbffe */ + 1.185991406414, /* 0x1.2f9d21ffe */ + 1.189206838636, /* 0x1.306fdc001 */ + 1.192430973067, /* 0x1.314328000 */ + 1.195664167430, /* 0x1.32170c001 */ + 1.198906540890, /* 0x1.32eb8a001 */ + 1.202157497408, /* 0x1.33c098000 */ + 1.205416083326, /* 0x1.349625fff */ + 1.208683252332, /* 0x1.356c43fff */ + 1.211961269402, /* 0x1.364318001 */ + 1.215246438983, /* 0x1.371a64000 */ + 1.218539118740, /* 0x1.37f22dffe */ + 1.221847295770, /* 0x1.38cafc000 */ + 1.225158572187, /* 0x1.39a3fdfff */ + 1.228481650325, /* 0x1.3a7dc5ffe */ + 1.231811761846, /* 0x1.3b5803fff */ + 1.235149741144, /* 0x1.3c32c5ffe */ + 1.238499879811, /* 0x1.3d0e53ffe */ + 1.241858124726, /* 0x1.3dea69fff */ + 1.245225191102, /* 0x1.3ec713fff */ + 1.248601436624, /* 0x1.3fa458000 */ + 1.251975655584, /* 0x1.40817a001 */ + 1.255380749731, /* 0x1.4160a2001 */ + 1.258783102010, /* 0x1.423f9bffe */ + 1.262198328973, /* 0x1.431f6e000 */ + 1.265619754780, /* 0x1.43ffa7fff */ + 1.269052743928, /* 0x1.44e0a4001 */ + 1.272490739830, /* 0x1.45c1f4000 */ + 1.275942921659, /* 0x1.46a432001 */ + 1.279397487615, /* 0x1.478697ffe */ + 1.282870173427, /* 0x1.486a2dffe */ + 1.286346316319, /* 0x1.494dfdffe */ + 1.289836049094, /* 0x1.4a32b2001 */ + 1.293333172770, /* 0x1.4b17e1ffe */ + 1.296839594835, /* 0x1.4bfdadfff */ + 1.300354957560, /* 0x1.4ce40fffe */ + 1.303882122055, /* 0x1.4dcb38001 */ + 1.307417988757, /* 0x1.4eb2f1ffe */ + 1.310960650439, /* 0x1.4f9b1dfff */ + 1.314516782746, /* 0x1.50842bfff */ + 1.318079948424, /* 0x1.516daffff */ + 1.321653246888, /* 0x1.5257de000 */ + 1.325237751030, /* 0x1.5342c8001 */ + 1.328829526907, /* 0x1.542e2c000 */ + 1.332433700535, /* 0x1.551a5fffe */ + 1.336045145966, /* 0x1.56070dffe */ + 1.339667558645, /* 0x1.56f473ffe */ + 1.343300342533, /* 0x1.57e287ffe */ + 1.346941947961, /* 0x1.58d130001 */ + 1.350594043714, /* 0x1.59c087ffe */ + 1.354256033883, /* 0x1.5ab085fff */ + 1.357932448365, /* 0x1.5ba175ffe */ + 1.361609339707, /* 0x1.5c926dfff */ + 1.365299344044, /* 0x1.5d8441ffe */ + 1.369003057507, /* 0x1.5e76fc001 */ + 1.372714757920, /* 0x1.5f6a3c000 */ + 1.376437187179, /* 0x1.605e2fffe */ + 1.380165219333, /* 0x1.615282001 */ + 1.383909463864, /* 0x1.6247e3ffe */ + 1.387661933907, /* 0x1.633dd0000 */ + 1.391424179060, /* 0x1.64345fffe */ + 1.395197510706, /* 0x1.652ba9fff */ + 1.399006724329, /* 0x1.66254dffe */ + 1.402773022651, /* 0x1.671c22000 */ + 1.406576037403, /* 0x1.68155dfff */ + 1.410389423392, /* 0x1.690f48001 */ +}; diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/w_expf_compat.c b/REORG.TODO/sysdeps/ieee754/flt-32/w_expf_compat.c new file mode 100644 index 0000000000..b2be6aa7e1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/w_expf_compat.c @@ -0,0 +1,34 @@ +/* Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@gmail.com>, 2011. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* wrapper expf */ +float +__expf (float x) +{ + float z = __ieee754_expf (x); + if (__builtin_expect (!isfinite (z) || z == 0, 0) + && isfinite (x) && _LIB_VERSION != _IEEE_) + return __kernel_standard_f (x, x, 106 + !!signbit (x)); + + return z; +} +hidden_def (__expf) +weak_alias (__expf, expf) diff --git a/REORG.TODO/sysdeps/ieee754/ieee754.h b/REORG.TODO/sysdeps/ieee754/ieee754.h new file mode 100644 index 0000000000..5c00d6377a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ieee754.h @@ -0,0 +1,198 @@ +/* Copyright (C) 1992-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _IEEE754_H + +#define _IEEE754_H 1 +#include <features.h> + +#include <endian.h> + +__BEGIN_DECLS + +union ieee754_float + { + float f; + + /* This is the IEEE 754 single-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:8; + unsigned int mantissa:23; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + unsigned int mantissa:23; + unsigned int exponent:8; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee; + + /* This format makes it easier to see if a NaN is a signalling NaN. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:8; + unsigned int quiet_nan:1; + unsigned int mantissa:22; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + unsigned int mantissa:22; + unsigned int quiet_nan:1; + unsigned int exponent:8; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee_nan; + }; + +#define IEEE754_FLOAT_BIAS 0x7f /* Added to exponent. */ + + +union ieee754_double + { + double d; + + /* This is the IEEE 754 double-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:11; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:20; + unsigned int mantissa1:32; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN +# if __FLOAT_WORD_ORDER == __BIG_ENDIAN + unsigned int mantissa0:20; + unsigned int exponent:11; + unsigned int negative:1; + unsigned int mantissa1:32; +# else + /* Together these comprise the mantissa. */ + unsigned int mantissa1:32; + unsigned int mantissa0:20; + unsigned int exponent:11; + unsigned int negative:1; +# endif +#endif /* Little endian. */ + } ieee; + + /* This format makes it easier to see if a NaN is a signalling NaN. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:11; + unsigned int quiet_nan:1; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:19; + unsigned int mantissa1:32; +#else +# if __FLOAT_WORD_ORDER == __BIG_ENDIAN + unsigned int mantissa0:19; + unsigned int quiet_nan:1; + unsigned int exponent:11; + unsigned int negative:1; + unsigned int mantissa1:32; +# else + /* Together these comprise the mantissa. */ + unsigned int mantissa1:32; + unsigned int mantissa0:19; + unsigned int quiet_nan:1; + unsigned int exponent:11; + unsigned int negative:1; +# endif +#endif + } ieee_nan; + }; + +#define IEEE754_DOUBLE_BIAS 0x3ff /* Added to exponent. */ + + +union ieee854_long_double + { + long double d; + + /* This is the IEEE 854 double-extended-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:15; + unsigned int empty:16; + unsigned int mantissa0:32; + unsigned int mantissa1:32; +#endif +#if __BYTE_ORDER == __LITTLE_ENDIAN +# if __FLOAT_WORD_ORDER == __BIG_ENDIAN + unsigned int exponent:15; + unsigned int negative:1; + unsigned int empty:16; + unsigned int mantissa0:32; + unsigned int mantissa1:32; +# else + unsigned int mantissa1:32; + unsigned int mantissa0:32; + unsigned int exponent:15; + unsigned int negative:1; + unsigned int empty:16; +# endif +#endif + } ieee; + + /* This is for NaNs in the IEEE 854 double-extended-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:15; + unsigned int empty:16; + unsigned int one:1; + unsigned int quiet_nan:1; + unsigned int mantissa0:30; + unsigned int mantissa1:32; +#endif +#if __BYTE_ORDER == __LITTLE_ENDIAN +# if __FLOAT_WORD_ORDER == __BIG_ENDIAN + unsigned int exponent:15; + unsigned int negative:1; + unsigned int empty:16; + unsigned int mantissa0:30; + unsigned int quiet_nan:1; + unsigned int one:1; + unsigned int mantissa1:32; +# else + unsigned int mantissa1:32; + unsigned int mantissa0:30; + unsigned int quiet_nan:1; + unsigned int one:1; + unsigned int exponent:15; + unsigned int negative:1; + unsigned int empty:16; +# endif +#endif + } ieee_nan; + }; + +#define IEEE854_LONG_DOUBLE_BIAS 0x3fff + +__END_DECLS + +#endif /* ieee754.h */ diff --git a/REORG.TODO/sysdeps/ieee754/k_standard.c b/REORG.TODO/sysdeps/ieee754/k_standard.c new file mode 100644 index 0000000000..b100b3e351 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/k_standard.c @@ -0,0 +1,943 @@ +/* @(#)k_standard.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_standard.c,v 1.6 1995/05/10 20:46:35 jtc Exp $"; +#endif + +#include <math.h> +#include <math_private.h> +#include <errno.h> + +#include <assert.h> + +#ifndef _USE_WRITE +#include <stdio.h> /* fputs(), stderr */ +#define WRITE2(u,v) fputs(u, stderr) +#else /* !defined(_USE_WRITE) */ +#include <unistd.h> /* write */ +#define WRITE2(u,v) write(2, u, v) +#undef fflush +#endif /* !defined(_USE_WRITE) */ + +/* XXX gcc versions until now don't delay the 0.0/0.0 division until + runtime but produce NaN at compile time. This is wrong since the + exceptions are not set correctly. */ +#if 0 +static const double zero = 0.0; /* used as const */ +#else +static double zero = 0.0; /* used as const */ +#endif + +/* + * Standard conformance (non-IEEE) on exception cases. + * Mapping: + * 1 -- acos(|x|>1) + * 2 -- asin(|x|>1) + * 3 -- atan2(+-0,+-0) + * 4 -- hypot overflow + * 5 -- cosh overflow + * 6 -- exp overflow + * 7 -- exp underflow + * 8 -- y0(0) + * 9 -- y0(-ve) + * 10-- y1(0) + * 11-- y1(-ve) + * 12-- yn(0) + * 13-- yn(-ve) + * 14-- lgamma(finite) overflow + * 15-- lgamma(-integer) + * 16-- log(0) + * 17-- log(x<0) + * 18-- log10(0) + * 19-- log10(x<0) + * 21-- pow(x,y) overflow + * 22-- pow(x,y) underflow + * 23-- pow(0,negative) + * 24-- pow(neg,non-integral) + * 25-- sinh(finite) overflow + * 26-- sqrt(negative) + * 27-- fmod(x,0) + * 28-- remainder(x,0) + * 29-- acosh(x<1) + * 30-- atanh(|x|>1) + * 31-- atanh(|x|=1) + * 32-- scalb overflow + * 33-- scalb underflow + * 34-- j0(|x|>X_TLOSS) + * 35-- y0(x>X_TLOSS) + * 36-- j1(|x|>X_TLOSS) + * 37-- y1(x>X_TLOSS) + * 38-- jn(|x|>X_TLOSS, n) + * 39-- yn(x>X_TLOSS, n) + * 40-- tgamma(finite) overflow + * 41-- tgamma(-integer) + * 43-- +0**neg + * 44-- exp2 overflow + * 45-- exp2 underflow + * 46-- exp10 overflow + * 47-- exp10 underflow + * 48-- log2(0) + * 49-- log2(x<0) + * 50-- tgamma(+-0) + */ + + +double +__kernel_standard(double x, double y, int type) +{ + struct exception exc; +#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */ +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + + /* The SVID struct exception uses a field "char *name;". */ +#define CSTR(func) ((char *) (type < 100 \ + ? func \ + : (type < 200 ? func "f" : func "l"))) + +#ifdef _USE_WRITE + (void) fflush(stdout); +#endif + exc.arg1 = x; + exc.arg2 = y; + switch(type) { + case 1: + case 101: + case 201: + /* acos(|x|>1) */ + exc.type = DOMAIN; + exc.name = CSTR ("acos"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = NAN; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if(_LIB_VERSION == _SVID_) { + (void) WRITE2("acos: DOMAIN error\n", 19); + } + __set_errno (EDOM); + } + break; + case 2: + case 102: + case 202: + /* asin(|x|>1) */ + exc.type = DOMAIN; + exc.name = CSTR ("asin"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = NAN; + if(_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if(_LIB_VERSION == _SVID_) { + (void) WRITE2("asin: DOMAIN error\n", 19); + } + __set_errno (EDOM); + } + break; + case 3: + case 103: + case 203: + /* atan2(+-0,+-0) */ + exc.arg1 = y; + exc.arg2 = x; + exc.type = DOMAIN; + exc.name = CSTR ("atan2"); + assert (_LIB_VERSION == _SVID_); + exc.retval = HUGE; + if(_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if(_LIB_VERSION == _SVID_) { + (void) WRITE2("atan2: DOMAIN error\n", 20); + } + __set_errno (EDOM); + } + break; + case 4: + case 104: + case 204: + /* hypot(finite,finite) overflow */ + exc.type = OVERFLOW; + exc.name = CSTR ("hypot"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 5: + case 105: + case 205: + /* cosh(finite) overflow */ + exc.type = OVERFLOW; + exc.name = CSTR ("cosh"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 6: + case 106: + case 206: + /* exp(finite) overflow */ + exc.type = OVERFLOW; + exc.name = CSTR ("exp"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 7: + case 107: + case 207: + /* exp(finite) underflow */ + exc.type = UNDERFLOW; + exc.name = CSTR ("exp"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 8: + case 108: + case 208: + /* y0(0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = CSTR ("y0"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y0: DOMAIN error\n", 17); + } + __set_errno (EDOM); + } + break; + case 9: + case 109: + case 209: + /* y0(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = CSTR ("y0"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = NAN; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y0: DOMAIN error\n", 17); + } + __set_errno (EDOM); + } + break; + case 10: + case 110: + case 210: + /* y1(0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = CSTR ("y1"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y1: DOMAIN error\n", 17); + } + __set_errno (EDOM); + } + break; + case 11: + case 111: + case 211: + /* y1(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = CSTR ("y1"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = NAN; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y1: DOMAIN error\n", 17); + } + __set_errno (EDOM); + } + break; + case 12: + case 112: + case 212: + /* yn(n,0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = CSTR ("yn"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = ((x < 0 && ((int) x & 1) != 0) + ? HUGE_VAL + : -HUGE_VAL); + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("yn: DOMAIN error\n", 17); + } + __set_errno (EDOM); + } + break; + case 13: + case 113: + case 213: + /* yn(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = CSTR ("yn"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = NAN; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("yn: DOMAIN error\n", 17); + } + __set_errno (EDOM); + } + break; + case 14: + case 114: + case 214: + /* lgamma(finite) overflow */ + exc.type = OVERFLOW; + exc.name = CSTR ("lgamma"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 15: + case 115: + case 215: + /* lgamma(-integer) or lgamma(0) */ + exc.type = SING; + exc.name = CSTR ("lgamma"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("lgamma: SING error\n", 19); + } + __set_errno (EDOM); + } + break; + case 16: + case 116: + case 216: + /* log(0) */ + exc.type = SING; + exc.name = CSTR ("log"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log: SING error\n", 16); + } + __set_errno (EDOM); + } + break; + case 17: + case 117: + case 217: + /* log(x<0) */ + exc.type = DOMAIN; + exc.name = CSTR ("log"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = NAN; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log: DOMAIN error\n", 18); + } + __set_errno (EDOM); + } + break; + case 18: + case 118: + case 218: + /* log10(0) */ + exc.type = SING; + exc.name = CSTR ("log10"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log10: SING error\n", 18); + } + __set_errno (EDOM); + } + break; + case 19: + case 119: + case 219: + /* log10(x<0) */ + exc.type = DOMAIN; + exc.name = CSTR ("log10"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = NAN; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log10: DOMAIN error\n", 20); + } + __set_errno (EDOM); + } + break; + case 21: + case 121: + case 221: + /* pow(x,y) overflow */ + exc.type = OVERFLOW; + exc.name = CSTR ("pow"); + if (_LIB_VERSION == _SVID_) { + exc.retval = HUGE; + y *= 0.5; + if(x<zero&&__rint(y)!=y) exc.retval = -HUGE; + } else { + exc.retval = HUGE_VAL; + y *= 0.5; + if(x<zero&&__rint(y)!=y) exc.retval = -HUGE_VAL; + } + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 22: + case 122: + case 222: + /* pow(x,y) underflow */ + exc.type = UNDERFLOW; + exc.name = CSTR ("pow"); + exc.retval = zero; + y *= 0.5; + if (x < zero && __rint (y) != y) + exc.retval = -zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 23: + case 123: + case 223: + /* -0**neg */ + exc.type = DOMAIN; + exc.name = CSTR ("pow"); + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("pow(0,neg): DOMAIN error\n", 25); + } + __set_errno (EDOM); + } + break; + case 43: + case 143: + case 243: + /* +0**neg */ + exc.type = DOMAIN; + exc.name = CSTR ("pow"); + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("pow(0,neg): DOMAIN error\n", 25); + } + __set_errno (EDOM); + } + break; + case 24: + case 124: + case 224: + /* neg**non-integral */ + exc.type = DOMAIN; + exc.name = CSTR ("pow"); + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = zero/zero; /* X/Open allow NaN */ + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("neg**non-integral: DOMAIN error\n", 32); + } + __set_errno (EDOM); + } + break; + case 25: + case 125: + case 225: + /* sinh(finite) overflow */ + exc.type = OVERFLOW; + exc.name = CSTR ("sinh"); + if (_LIB_VERSION == _SVID_) + exc.retval = ( (x>zero) ? HUGE : -HUGE); + else + exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL); + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 26: + case 126: + case 226: + /* sqrt(x<0) */ + exc.type = DOMAIN; + exc.name = CSTR ("sqrt"); + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("sqrt: DOMAIN error\n", 19); + } + __set_errno (EDOM); + } + break; + case 27: + case 127: + case 227: + /* fmod(x,0) */ + exc.type = DOMAIN; + exc.name = CSTR ("fmod"); + if (_LIB_VERSION == _SVID_) + exc.retval = x; + else + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("fmod: DOMAIN error\n", 20); + } + __set_errno (EDOM); + } + break; + case 28: + case 128: + case 228: + /* remainder(x,0) */ + exc.type = DOMAIN; + exc.name = CSTR ("remainder"); + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("remainder: DOMAIN error\n", 24); + } + __set_errno (EDOM); + } + break; + case 29: + case 129: + case 229: + /* acosh(x<1) */ + exc.type = DOMAIN; + exc.name = CSTR ("acosh"); + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("acosh: DOMAIN error\n", 20); + } + __set_errno (EDOM); + } + break; + case 30: + case 130: + case 230: + /* atanh(|x|>1) */ + exc.type = DOMAIN; + exc.name = CSTR ("atanh"); + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("atanh: DOMAIN error\n", 20); + } + __set_errno (EDOM); + } + break; + case 31: + case 131: + case 231: + /* atanh(|x|=1) */ + exc.type = SING; + exc.name = CSTR ("atanh"); + exc.retval = x/zero; /* sign(x)*inf */ + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("atanh: SING error\n", 18); + } + __set_errno (EDOM); + } + break; + case 32: + case 132: + case 232: + /* scalb overflow; SVID also returns +-HUGE_VAL */ + exc.type = OVERFLOW; + exc.name = CSTR ("scalb"); + exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 33: + case 133: + case 233: + /* scalb underflow */ + exc.type = UNDERFLOW; + exc.name = CSTR ("scalb"); + exc.retval = __copysign(zero,x); + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 34: + case 134: + case 234: + /* j0(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = CSTR ("j0"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + __set_errno (ERANGE); + } + break; + case 35: + case 135: + case 235: + /* y0(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = CSTR ("y0"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + __set_errno (ERANGE); + } + break; + case 36: + case 136: + case 236: + /* j1(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = CSTR ("j1"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + __set_errno (ERANGE); + } + break; + case 37: + case 137: + case 237: + /* y1(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = CSTR ("y1"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + __set_errno (ERANGE); + } + break; + case 38: + case 138: + case 238: + /* jn(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = CSTR ("jn"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + __set_errno (ERANGE); + } + break; + case 39: + case 139: + case 239: + /* yn(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = CSTR ("yn"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + __set_errno (ERANGE); + } + break; + case 40: + case 140: + case 240: + /* tgamma(finite) overflow */ + exc.type = OVERFLOW; + exc.name = CSTR ("tgamma"); + exc.retval = __copysign (HUGE_VAL, x); + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 41: + case 141: + case 241: + /* tgamma(-integer) */ + exc.type = SING; + exc.name = CSTR ("tgamma"); + exc.retval = NAN; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("tgamma: SING error\n", 18); + exc.retval = HUGE_VAL; + } + __set_errno (EDOM); + } + break; + + case 44: + case 144: + case 244: + /* exp(finite) overflow */ + exc.type = OVERFLOW; + exc.name = CSTR ("exp2"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 45: + case 145: + case 245: + /* exp(finite) underflow */ + exc.type = UNDERFLOW; + exc.name = CSTR ("exp2"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + + case 46: + case 146: + case 246: + /* exp(finite) overflow */ + exc.type = OVERFLOW; + exc.name = CSTR ("exp10"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 47: + case 147: + case 247: + /* exp(finite) underflow */ + exc.type = UNDERFLOW; + exc.name = CSTR ("exp10"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 48: + case 148: + case 248: + /* log2(0) */ + exc.type = SING; + exc.name = CSTR ("log2"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (EDOM); + } + break; + case 49: + case 149: + case 249: + /* log2(x<0) */ + exc.type = DOMAIN; + exc.name = CSTR ("log2"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = NAN; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + __set_errno (EDOM); + } + break; + case 50: + case 150: + case 250: + /* tgamma(+-0) */ + exc.type = SING; + exc.name = CSTR ("tgamma"); + exc.retval = __copysign (HUGE_VAL, x); + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) + (void) WRITE2("tgamma: SING error\n", 18); + __set_errno (ERANGE); + } + break; + + /* #### Last used is 50/150/250 ### */ + } + return exc.retval; +} diff --git a/REORG.TODO/sysdeps/ieee754/k_standardf.c b/REORG.TODO/sysdeps/ieee754/k_standardf.c new file mode 100644 index 0000000000..678b38d91a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/k_standardf.c @@ -0,0 +1,31 @@ +/* Implement __kernel_standard_f. + Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + + +/* Handle errors for a libm function as specified by TYPE (see + comments in k_standard.c for details), with arguments X and Y, + returning the appropriate return value for that function. */ + +float +__kernel_standard_f (float x, float y, int type) +{ + return __kernel_standard (x, y, type); +} diff --git a/REORG.TODO/sysdeps/ieee754/k_standardl.c b/REORG.TODO/sysdeps/ieee754/k_standardl.c new file mode 100644 index 0000000000..08d789f942 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/k_standardl.c @@ -0,0 +1,107 @@ +/* Implement __kernel_standard_l. + Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. + + Parts based on k_standard.c from fdlibm: */ + +/* @(#)k_standard.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> +#include <fenv.h> +#include <float.h> +#include <errno.h> + + +static double zero = 0.0; + +/* Handle errors for a libm function as specified by TYPE (see + comments in k_standard.c for details), with arguments X and Y, + returning the appropriate return value for that function. */ + +long double +__kernel_standard_l (long double x, long double y, int type) +{ + double dx, dy; + struct exception exc; + fenv_t env; + + feholdexcept (&env); + dx = x; + dy = y; + math_force_eval (dx); + math_force_eval (dy); + fesetenv (&env); + + switch (type) + { + case 221: + /* powl (x, y) overflow. */ + exc.arg1 = dx; + exc.arg2 = dy; + exc.type = OVERFLOW; + exc.name = (char *) "powl"; + if (_LIB_VERSION == _SVID_) + { + exc.retval = HUGE; + y *= 0.5; + if (x < zero && __rintl (y) != y) + exc.retval = -HUGE; + } + else + { + exc.retval = HUGE_VAL; + y *= 0.5; + if (x < zero && __rintl (y) != y) + exc.retval = -HUGE_VAL; + } + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr (&exc)) + __set_errno (ERANGE); + return exc.retval; + + case 222: + /* powl (x, y) underflow. */ + exc.arg1 = dx; + exc.arg2 = dy; + exc.type = UNDERFLOW; + exc.name = (char *) "powl"; + exc.retval = zero; + y *= 0.5; + if (x < zero && __rintl (y) != y) + exc.retval = -zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr (&exc)) + __set_errno (ERANGE); + return exc.retval; + + default: + return __kernel_standard (dx, dy, type); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/Makefile b/REORG.TODO/sysdeps/ieee754/ldbl-128/Makefile new file mode 100644 index 0000000000..8fd6dad343 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/Makefile @@ -0,0 +1 @@ +long-double-fcts = yes diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/bits/long-double.h b/REORG.TODO/sysdeps/ieee754/ldbl-128/bits/long-double.h new file mode 100644 index 0000000000..baddb2a905 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/bits/long-double.h @@ -0,0 +1,20 @@ +/* Properties of long double type. ldbl-128 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* long double is distinct from double, so there is nothing to + define here. */ diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_acoshl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_acoshl.c new file mode 100644 index 0000000000..7c79d437a2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_acoshl.c @@ -0,0 +1,61 @@ +/* e_acoshl.c -- long double version of e_acosh.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_acoshl(x) + * Method : + * Based on + * acoshl(x) = logl [ x + sqrtl(x*x-1) ] + * we have + * acoshl(x) := logl(x)+ln2, if x is large; else + * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else + * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acoshl(x) is NaN with signal if x<1. + * acoshl(NaN) is NaN without signal. + */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 +one = 1.0, +ln2 = L(0.6931471805599453094172321214581766); + +_Float128 +__ieee754_acoshl(_Float128 x) +{ + _Float128 t; + u_int64_t lx; + int64_t hx; + GET_LDOUBLE_WORDS64(hx,lx,x); + if(hx<0x3fff000000000000LL) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x4035000000000000LL) { /* x > 2**54 */ + if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */ + } else if(((hx-0x3fff000000000000LL)|lx)==0) { + return 0; /* acosh(1) = 0 */ + } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_logl(2*x-one/(x+__ieee754_sqrtl(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return __log1pl(t+__sqrtl(2*t+t*t)); + } +} +strong_alias (__ieee754_acoshl, __acoshl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_acosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_acosl.c new file mode 100644 index 0000000000..342ea5f47d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_acosl.c @@ -0,0 +1,319 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_acosl(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x| <= 0.375 + * acos(x) = pi/2 - asin(x) + * Between .375 and .5 the approximation is + * acos(0.4375 + x) = acos(0.4375) + x P(x) / Q(x) + * Between .5 and .625 the approximation is + * acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x) + * For x > 0.625, + * acos(x) = 2 asin(sqrt((1-x)/2)) + * computed with an extended precision square root in the leading term. + * For x < -0.625 + * acos(x) = pi - 2 asin(sqrt((1-|x|)/2)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Functions needed: __ieee754_sqrtl. + */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 + one = 1, + pio2_hi = L(1.5707963267948966192313216916397514420986), + pio2_lo = L(4.3359050650618905123985220130216759843812E-35), + + /* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x) + -0.0625 <= x <= 0.0625 + peak relative error 3.3e-35 */ + + rS0 = L(5.619049346208901520945464704848780243887E0), + rS1 = L(-4.460504162777731472539175700169871920352E1), + rS2 = L(1.317669505315409261479577040530751477488E2), + rS3 = L(-1.626532582423661989632442410808596009227E2), + rS4 = L(3.144806644195158614904369445440583873264E1), + rS5 = L(9.806674443470740708765165604769099559553E1), + rS6 = L(-5.708468492052010816555762842394927806920E1), + rS7 = L(-1.396540499232262112248553357962639431922E1), + rS8 = L(1.126243289311910363001762058295832610344E1), + rS9 = L(4.956179821329901954211277873774472383512E-1), + rS10 = L(-3.313227657082367169241333738391762525780E-1), + + sS0 = L(-4.645814742084009935700221277307007679325E0), + sS1 = L(3.879074822457694323970438316317961918430E1), + sS2 = L(-1.221986588013474694623973554726201001066E2), + sS3 = L(1.658821150347718105012079876756201905822E2), + sS4 = L(-4.804379630977558197953176474426239748977E1), + sS5 = L(-1.004296417397316948114344573811562952793E2), + sS6 = L(7.530281592861320234941101403870010111138E1), + sS7 = L(1.270735595411673647119592092304357226607E1), + sS8 = L(-1.815144839646376500705105967064792930282E1), + sS9 = L(-7.821597334910963922204235247786840828217E-2), + /* 1.000000000000000000000000000000000000000E0 */ + + acosr5625 = L(9.7338991014954640492751132535550279812151E-1), + pimacosr5625 = L(2.1682027434402468335351320579240000860757E0), + + /* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x) + -0.0625 <= x <= 0.0625 + peak relative error 2.1e-35 */ + + P0 = L(2.177690192235413635229046633751390484892E0), + P1 = L(-2.848698225706605746657192566166142909573E1), + P2 = L(1.040076477655245590871244795403659880304E2), + P3 = L(-1.400087608918906358323551402881238180553E2), + P4 = L(2.221047917671449176051896400503615543757E1), + P5 = L(9.643714856395587663736110523917499638702E1), + P6 = L(-5.158406639829833829027457284942389079196E1), + P7 = L(-1.578651828337585944715290382181219741813E1), + P8 = L(1.093632715903802870546857764647931045906E1), + P9 = L(5.448925479898460003048760932274085300103E-1), + P10 = L(-3.315886001095605268470690485170092986337E-1), + Q0 = L(-1.958219113487162405143608843774587557016E0), + Q1 = L(2.614577866876185080678907676023269360520E1), + Q2 = L(-9.990858606464150981009763389881793660938E1), + Q3 = L(1.443958741356995763628660823395334281596E2), + Q4 = L(-3.206441012484232867657763518369723873129E1), + Q5 = L(-1.048560885341833443564920145642588991492E2), + Q6 = L(6.745883931909770880159915641984874746358E1), + Q7 = L(1.806809656342804436118449982647641392951E1), + Q8 = L(-1.770150690652438294290020775359580915464E1), + Q9 = L(-5.659156469628629327045433069052560211164E-1), + /* 1.000000000000000000000000000000000000000E0 */ + + acosr4375 = L(1.1179797320499710475919903296900511518755E0), + pimacosr4375 = L(2.0236129215398221908706530535894517323217E0), + + /* asin(x) = x + x^3 pS(x^2) / qS(x^2) + 0 <= x <= 0.5 + peak relative error 1.9e-35 */ + pS0 = L(-8.358099012470680544198472400254596543711E2), + pS1 = L(3.674973957689619490312782828051860366493E3), + pS2 = L(-6.730729094812979665807581609853656623219E3), + pS3 = L(6.643843795209060298375552684423454077633E3), + pS4 = L(-3.817341990928606692235481812252049415993E3), + pS5 = L(1.284635388402653715636722822195716476156E3), + pS6 = L(-2.410736125231549204856567737329112037867E2), + pS7 = L(2.219191969382402856557594215833622156220E1), + pS8 = L(-7.249056260830627156600112195061001036533E-1), + pS9 = L(1.055923570937755300061509030361395604448E-3), + + qS0 = L(-5.014859407482408326519083440151745519205E3), + qS1 = L(2.430653047950480068881028451580393430537E4), + qS2 = L(-4.997904737193653607449250593976069726962E4), + qS3 = L(5.675712336110456923807959930107347511086E4), + qS4 = L(-3.881523118339661268482937768522572588022E4), + qS5 = L(1.634202194895541569749717032234510811216E4), + qS6 = L(-4.151452662440709301601820849901296953752E3), + qS7 = L(5.956050864057192019085175976175695342168E2), + qS8 = L(-4.175375777334867025769346564600396877176E1); + /* 1.000000000000000000000000000000000000000E0 */ + +_Float128 +__ieee754_acosl (_Float128 x) +{ + _Float128 z, r, w, p, q, s, t, f2; + int32_t ix, sign; + ieee854_long_double_shape_type u; + + u.value = x; + sign = u.parts32.w0; + ix = sign & 0x7fffffff; + u.parts32.w0 = ix; /* |x| */ + if (ix >= 0x3fff0000) /* |x| >= 1 */ + { + if (ix == 0x3fff0000 + && (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0) + { /* |x| == 1 */ + if ((sign & 0x80000000) == 0) + return 0.0; /* acos(1) = 0 */ + else + return (2.0 * pio2_hi) + (2.0 * pio2_lo); /* acos(-1)= pi */ + } + return (x - x) / (x - x); /* acos(|x| > 1) is NaN */ + } + else if (ix < 0x3ffe0000) /* |x| < 0.5 */ + { + if (ix < 0x3f8e0000) /* |x| < 2**-113 */ + return pio2_hi + pio2_lo; + if (ix < 0x3ffde000) /* |x| < .4375 */ + { + /* Arcsine of x. */ + z = x * x; + p = (((((((((pS9 * z + + pS8) * z + + pS7) * z + + pS6) * z + + pS5) * z + + pS4) * z + + pS3) * z + + pS2) * z + + pS1) * z + + pS0) * z; + q = (((((((( z + + qS8) * z + + qS7) * z + + qS6) * z + + qS5) * z + + qS4) * z + + qS3) * z + + qS2) * z + + qS1) * z + + qS0; + r = x + x * p / q; + z = pio2_hi - (r - pio2_lo); + return z; + } + /* .4375 <= |x| < .5 */ + t = u.value - L(0.4375); + p = ((((((((((P10 * t + + P9) * t + + P8) * t + + P7) * t + + P6) * t + + P5) * t + + P4) * t + + P3) * t + + P2) * t + + P1) * t + + P0) * t; + + q = (((((((((t + + Q9) * t + + Q8) * t + + Q7) * t + + Q6) * t + + Q5) * t + + Q4) * t + + Q3) * t + + Q2) * t + + Q1) * t + + Q0; + r = p / q; + if (sign & 0x80000000) + r = pimacosr4375 - r; + else + r = acosr4375 + r; + return r; + } + else if (ix < 0x3ffe4000) /* |x| < 0.625 */ + { + t = u.value - L(0.5625); + p = ((((((((((rS10 * t + + rS9) * t + + rS8) * t + + rS7) * t + + rS6) * t + + rS5) * t + + rS4) * t + + rS3) * t + + rS2) * t + + rS1) * t + + rS0) * t; + + q = (((((((((t + + sS9) * t + + sS8) * t + + sS7) * t + + sS6) * t + + sS5) * t + + sS4) * t + + sS3) * t + + sS2) * t + + sS1) * t + + sS0; + if (sign & 0x80000000) + r = pimacosr5625 - p / q; + else + r = acosr5625 + p / q; + return r; + } + else + { /* |x| >= .625 */ + z = (one - u.value) * 0.5; + s = __ieee754_sqrtl (z); + /* Compute an extended precision square root from + the Newton iteration s -> 0.5 * (s + z / s). + The change w from s to the improved value is + w = 0.5 * (s + z / s) - s = (s^2 + z)/2s - s = (z - s^2)/2s. + Express s = f1 + f2 where f1 * f1 is exactly representable. + w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s . + s + w has extended precision. */ + u.value = s; + u.parts32.w2 = 0; + u.parts32.w3 = 0; + f2 = s - u.value; + w = z - u.value * u.value; + w = w - 2.0 * u.value * f2; + w = w - f2 * f2; + w = w / (2.0 * s); + /* Arcsine of s. */ + p = (((((((((pS9 * z + + pS8) * z + + pS7) * z + + pS6) * z + + pS5) * z + + pS4) * z + + pS3) * z + + pS2) * z + + pS1) * z + + pS0) * z; + q = (((((((( z + + qS8) * z + + qS7) * z + + qS6) * z + + qS5) * z + + qS4) * z + + qS3) * z + + qS2) * z + + qS1) * z + + qS0; + r = s + (w + s * p / q); + + if (sign & 0x80000000) + w = pio2_hi + (pio2_lo - r); + else + w = r; + return 2.0 * w; + } +} +strong_alias (__ieee754_acosl, __acosl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_asinl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_asinl.c new file mode 100644 index 0000000000..1edf1c05a1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_asinl.c @@ -0,0 +1,258 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under the + following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_asin(x) + * Method : + * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... + * we approximate asin(x) on [0,0.5] by + * asin(x) = x + x*x^2*R(x^2) + * Between .5 and .625 the approximation is + * asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x) + * For x in [0.625,1] + * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) + * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; + * then for x>0.98 + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) + * For x<=0.98, let pio4_hi = pio2_hi/2, then + * f = hi part of s; + * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) + * and + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const _Float128 + one = 1, + huge = L(1.0e+4932), + pio2_hi = L(1.5707963267948966192313216916397514420986), + pio2_lo = L(4.3359050650618905123985220130216759843812E-35), + pio4_hi = L(7.8539816339744830961566084581987569936977E-1), + + /* coefficient for R(x^2) */ + + /* asin(x) = x + x^3 pS(x^2) / qS(x^2) + 0 <= x <= 0.5 + peak relative error 1.9e-35 */ + pS0 = L(-8.358099012470680544198472400254596543711E2), + pS1 = L(3.674973957689619490312782828051860366493E3), + pS2 = L(-6.730729094812979665807581609853656623219E3), + pS3 = L(6.643843795209060298375552684423454077633E3), + pS4 = L(-3.817341990928606692235481812252049415993E3), + pS5 = L(1.284635388402653715636722822195716476156E3), + pS6 = L(-2.410736125231549204856567737329112037867E2), + pS7 = L(2.219191969382402856557594215833622156220E1), + pS8 = L(-7.249056260830627156600112195061001036533E-1), + pS9 = L(1.055923570937755300061509030361395604448E-3), + + qS0 = L(-5.014859407482408326519083440151745519205E3), + qS1 = L(2.430653047950480068881028451580393430537E4), + qS2 = L(-4.997904737193653607449250593976069726962E4), + qS3 = L(5.675712336110456923807959930107347511086E4), + qS4 = L(-3.881523118339661268482937768522572588022E4), + qS5 = L(1.634202194895541569749717032234510811216E4), + qS6 = L(-4.151452662440709301601820849901296953752E3), + qS7 = L(5.956050864057192019085175976175695342168E2), + qS8 = L(-4.175375777334867025769346564600396877176E1), + /* 1.000000000000000000000000000000000000000E0 */ + + /* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x) + -0.0625 <= x <= 0.0625 + peak relative error 3.3e-35 */ + rS0 = L(-5.619049346208901520945464704848780243887E0), + rS1 = L(4.460504162777731472539175700169871920352E1), + rS2 = L(-1.317669505315409261479577040530751477488E2), + rS3 = L(1.626532582423661989632442410808596009227E2), + rS4 = L(-3.144806644195158614904369445440583873264E1), + rS5 = L(-9.806674443470740708765165604769099559553E1), + rS6 = L(5.708468492052010816555762842394927806920E1), + rS7 = L(1.396540499232262112248553357962639431922E1), + rS8 = L(-1.126243289311910363001762058295832610344E1), + rS9 = L(-4.956179821329901954211277873774472383512E-1), + rS10 = L(3.313227657082367169241333738391762525780E-1), + + sS0 = L(-4.645814742084009935700221277307007679325E0), + sS1 = L(3.879074822457694323970438316317961918430E1), + sS2 = L(-1.221986588013474694623973554726201001066E2), + sS3 = L(1.658821150347718105012079876756201905822E2), + sS4 = L(-4.804379630977558197953176474426239748977E1), + sS5 = L(-1.004296417397316948114344573811562952793E2), + sS6 = L(7.530281592861320234941101403870010111138E1), + sS7 = L(1.270735595411673647119592092304357226607E1), + sS8 = L(-1.815144839646376500705105967064792930282E1), + sS9 = L(-7.821597334910963922204235247786840828217E-2), + /* 1.000000000000000000000000000000000000000E0 */ + + asinr5625 = L(5.9740641664535021430381036628424864397707E-1); + + + +_Float128 +__ieee754_asinl (_Float128 x) +{ + _Float128 t, w, p, q, c, r, s; + int32_t ix, sign, flag; + ieee854_long_double_shape_type u; + + flag = 0; + u.value = x; + sign = u.parts32.w0; + ix = sign & 0x7fffffff; + u.parts32.w0 = ix; /* |x| */ + if (ix >= 0x3fff0000) /* |x|>= 1 */ + { + if (ix == 0x3fff0000 + && (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0) + /* asin(1)=+-pi/2 with inexact */ + return x * pio2_hi + x * pio2_lo; + return (x - x) / (x - x); /* asin(|x|>1) is NaN */ + } + else if (ix < 0x3ffe0000) /* |x| < 0.5 */ + { + if (ix < 0x3fc60000) /* |x| < 2**-57 */ + { + math_check_force_underflow (x); + _Float128 force_inexact = huge + x; + math_force_eval (force_inexact); + return x; /* return x with inexact if x!=0 */ + } + else + { + t = x * x; + /* Mark to use pS, qS later on. */ + flag = 1; + } + } + else if (ix < 0x3ffe4000) /* 0.625 */ + { + t = u.value - 0.5625; + p = ((((((((((rS10 * t + + rS9) * t + + rS8) * t + + rS7) * t + + rS6) * t + + rS5) * t + + rS4) * t + + rS3) * t + + rS2) * t + + rS1) * t + + rS0) * t; + + q = ((((((((( t + + sS9) * t + + sS8) * t + + sS7) * t + + sS6) * t + + sS5) * t + + sS4) * t + + sS3) * t + + sS2) * t + + sS1) * t + + sS0; + t = asinr5625 + p / q; + if ((sign & 0x80000000) == 0) + return t; + else + return -t; + } + else + { + /* 1 > |x| >= 0.625 */ + w = one - u.value; + t = w * 0.5; + } + + p = (((((((((pS9 * t + + pS8) * t + + pS7) * t + + pS6) * t + + pS5) * t + + pS4) * t + + pS3) * t + + pS2) * t + + pS1) * t + + pS0) * t; + + q = (((((((( t + + qS8) * t + + qS7) * t + + qS6) * t + + qS5) * t + + qS4) * t + + qS3) * t + + qS2) * t + + qS1) * t + + qS0; + + if (flag) /* 2^-57 < |x| < 0.5 */ + { + w = p / q; + return x + x * w; + } + + s = __ieee754_sqrtl (t); + if (ix >= 0x3ffef333) /* |x| > 0.975 */ + { + w = p / q; + t = pio2_hi - (2.0 * (s + s * w) - pio2_lo); + } + else + { + u.value = s; + u.parts32.w3 = 0; + u.parts32.w2 = 0; + w = u.value; + c = (t - w * w) / (s + w); + r = p / q; + p = 2.0 * s * r - (pio2_lo - 2.0 * c); + q = pio4_hi - 2.0 * w; + t = pio4_hi - (p - q); + } + + if ((sign & 0x80000000) == 0) + return t; + else + return -t; +} +strong_alias (__ieee754_asinl, __asinl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_atan2l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_atan2l.c new file mode 100644 index 0000000000..faecd1a63b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_atan2l.c @@ -0,0 +1,122 @@ +/* e_atan2l.c -- long double version of e_atan2.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_atan2l(y,x) + * Method : + * 1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * + * Special cases: + * + * ATAN2((anything), NaN ) is NaN; + * ATAN2(NAN , (anything) ) is NaN; + * ATAN2(+-0, +(anything but NaN)) is +-0 ; + * ATAN2(+-0, -(anything but NaN)) is +-pi ; + * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; + * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; + * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; + * ATAN2(+-INF,+INF ) is +-pi/4 ; + * ATAN2(+-INF,-INF ) is +-3pi/4; + * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 +tiny = L(1.0e-4900), +zero = 0.0, +pi_o_4 = L(7.85398163397448309615660845819875699e-01), /* 3ffe921fb54442d18469898cc51701b8 */ +pi_o_2 = L(1.57079632679489661923132169163975140e+00), /* 3fff921fb54442d18469898cc51701b8 */ +pi = L(3.14159265358979323846264338327950280e+00), /* 4000921fb54442d18469898cc51701b8 */ +pi_lo = L(8.67181013012378102479704402604335225e-35); /* 3f8dcd129024e088a67cc74020bbea64 */ + +_Float128 +__ieee754_atan2l(_Float128 y, _Float128 x) +{ + _Float128 z; + int64_t k,m,hx,hy,ix,iy; + u_int64_t lx,ly; + + GET_LDOUBLE_WORDS64(hx,lx,x); + ix = hx&0x7fffffffffffffffLL; + GET_LDOUBLE_WORDS64(hy,ly,y); + iy = hy&0x7fffffffffffffffLL; + if(((ix|((lx|-lx)>>63))>0x7fff000000000000LL)|| + ((iy|((ly|-ly)>>63))>0x7fff000000000000LL)) /* x or y is NaN */ + return x+y; + if(((hx-0x3fff000000000000LL)|lx)==0) return __atanl(y); /* x=1.0L */ + m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if((iy|ly)==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7fff000000000000LL) { + if(iy==0x7fff000000000000LL) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return 3*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7fff000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>48; + if(k > 120) z=pi_o_2+L(0.5)*pi_lo; /* |y/x| > 2**120 */ + else if(hx<0&&k<-120) z=0; /* |y|/x < -2**120 */ + else z=__atanl(fabsl(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: { + u_int64_t zh; + GET_LDOUBLE_MSW64(zh,z); + SET_LDOUBLE_MSW64(z,zh ^ 0x8000000000000000ULL); + } + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} +strong_alias (__ieee754_atan2l, __atan2l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_atanhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_atanhl.c new file mode 100644 index 0000000000..3905af4dfc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_atanhl.c @@ -0,0 +1,74 @@ +/* s_atanhl.c -- long double version of s_atan.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_atanhl(x) + * Method : + * 1.Reduced x to positive by atanh(-x) = -atanh(x) + * 2.For x>=0.5 + * 1 2x x + * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x)) + * + * Special cases: + * atanhl(x) is NaN if |x| > 1 with signal; + * atanhl(NaN) is that NaN with no signal; + * atanhl(+-1) is +-INF with signal. + * + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const _Float128 one = 1, huge = L(1e4900); + +static const _Float128 zero = 0; + +_Float128 +__ieee754_atanhl(_Float128 x) +{ + _Float128 t; + u_int32_t jx, ix; + ieee854_long_double_shape_type u; + + u.value = x; + jx = u.parts32.w0; + ix = jx & 0x7fffffff; + u.parts32.w0 = ix; + if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */ + { + if (u.value == one) + return x/zero; + else + return (x-x)/(x-x); + } + if(ix<0x3fc60000 && (huge+x)>zero) /* x < 2^-57 */ + { + math_check_force_underflow (x); + return x; + } + + if(ix<0x3ffe0000) { /* x < 0.5 */ + t = u.value+u.value; + t = 0.5*__log1pl(t+t*u.value/(one-u.value)); + } else + t = 0.5*__log1pl((u.value+u.value)/(one-u.value)); + if(jx & 0x80000000) return -t; else return t; +} +strong_alias (__ieee754_atanhl, __atanhl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_coshl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_coshl.c new file mode 100644 index 0000000000..70a2fe3e84 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_coshl.c @@ -0,0 +1,110 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Changes for 128-bit long double are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_coshl(x) + * Method : + * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (coshl(x) = coshl(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : coshl(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : coshl(x) := ------------------- + * 2 + * 22 <= x <= lnovft : coshl(x) := expl(x)/2 + * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2) + * ln2ovft < x : coshl(x) := huge*huge (overflow) + * + * Special cases: + * coshl(x) is |x| if x is +INF, -INF, or NaN. + * only coshl(0)=1 is exact for finite x. + */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 one = 1.0, half = 0.5, huge = L(1.0e4900), +ovf_thresh = L(1.1357216553474703894801348310092223067821E4); + +_Float128 +__ieee754_coshl (_Float128 x) +{ + _Float128 t, w; + int32_t ex; + ieee854_long_double_shape_type u; + + u.value = x; + ex = u.parts32.w0 & 0x7fffffff; + + /* Absolute value of x. */ + u.parts32.w0 = ex; + + /* x is INF or NaN */ + if (ex >= 0x7fff0000) + return x * x; + + /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ + if (ex < 0x3ffd62e4) /* 0.3465728759765625 */ + { + if (ex < 0x3fb80000) /* |x| < 2^-116 */ + return one; /* cosh(tiny) = 1 */ + t = __expm1l (u.value); + w = one + t; + + return one + (t * t) / (w + w); + } + + /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */ + if (ex < 0x40044000) + { + t = __ieee754_expl (u.value); + return half * t + half / t; + } + + /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ + if (ex <= 0x400c62e3) /* 11356.375 */ + return half * __ieee754_expl (u.value); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (u.value <= ovf_thresh) + { + w = __ieee754_expl (half * u.value); + t = half * w; + return t * w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge * huge; +} +strong_alias (__ieee754_coshl, __coshl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_exp10l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_exp10l.c new file mode 100644 index 0000000000..05a470fa39 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_exp10l.c @@ -0,0 +1,49 @@ +/* Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +static const _Float128 log10_high = L(0x2.4d763776aaa2bp0); +static const _Float128 log10_low = L(0x5.ba95b58ae0b4c28a38a3fb3e7698p-60); + +_Float128 +__ieee754_exp10l (_Float128 arg) +{ + ieee854_long_double_shape_type u; + _Float128 arg_high, arg_low; + _Float128 exp_high, exp_low; + + if (!isfinite (arg)) + return __ieee754_expl (arg); + if (arg < LDBL_MIN_10_EXP - LDBL_DIG - 10) + return LDBL_MIN * LDBL_MIN; + else if (arg > LDBL_MAX_10_EXP + 1) + return LDBL_MAX * LDBL_MAX; + else if (fabsl (arg) < L(0x1p-116)) + return 1; + + u.value = arg; + u.parts64.lsw &= 0xfe00000000000000LL; + arg_high = u.value; + arg_low = arg - arg_high; + exp_high = arg_high * log10_high; + exp_low = arg_high * log10_low + arg_low * M_LN10l; + return __ieee754_expl (exp_high) * __ieee754_expl (exp_low); +} +strong_alias (__ieee754_exp10l, __exp10l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_expl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_expl.c new file mode 100644 index 0000000000..15639d1da1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_expl.c @@ -0,0 +1,253 @@ +/* Quad-precision floating point e^x. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + Partly based on double-precision code + by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* The basic design here is from + Abraham Ziv, "Fast Evaluation of Elementary Mathematical Functions with + Correctly Rounded Last Bit", ACM Trans. Math. Soft., 17 (3), September 1991, + pp. 410-423. + + We work with number pairs where the first number is the high part and + the second one is the low part. Arithmetic with the high part numbers must + be exact, without any roundoff errors. + + The input value, X, is written as + X = n * ln(2)_0 + arg1[t1]_0 + arg2[t2]_0 + x + - n * ln(2)_1 + arg1[t1]_1 + arg2[t2]_1 + xl + + where: + - n is an integer, 16384 >= n >= -16495; + - ln(2)_0 is the first 93 bits of ln(2), and |ln(2)_0-ln(2)-ln(2)_1| < 2^-205 + - t1 is an integer, 89 >= t1 >= -89 + - t2 is an integer, 65 >= t2 >= -65 + - |arg1[t1]-t1/256.0| < 2^-53 + - |arg2[t2]-t2/32768.0| < 2^-53 + - x + xl is whatever is left, |x + xl| < 2^-16 + 2^-53 + + Then e^x is approximated as + + e^x = 2^n_1 ( 2^n_0 e^(arg1[t1]_0 + arg1[t1]_1) e^(arg2[t2]_0 + arg2[t2]_1) + + 2^n_0 e^(arg1[t1]_0 + arg1[t1]_1) e^(arg2[t2]_0 + arg2[t2]_1) + * p (x + xl + n * ln(2)_1)) + where: + - p(x) is a polynomial approximating e(x)-1 + - e^(arg1[t1]_0 + arg1[t1]_1) is obtained from a table + - e^(arg2[t2]_0 + arg2[t2]_1) likewise + - n_1 + n_0 = n, so that |n_0| < -LDBL_MIN_EXP-1. + + If it happens that n_1 == 0 (this is the usual case), that multiplication + is omitted. + */ + +#ifndef _GNU_SOURCE +#define _GNU_SOURCE +#endif +#include <float.h> +#include <ieee754.h> +#include <math.h> +#include <fenv.h> +#include <inttypes.h> +#include <math_private.h> +#include <stdlib.h> +#include "t_expl.h" + +static const _Float128 C[] = { +/* Smallest integer x for which e^x overflows. */ +#define himark C[0] + L(11356.523406294143949491931077970765), + +/* Largest integer x for which e^x underflows. */ +#define lomark C[1] +L(-11433.4627433362978788372438434526231), + +/* 3x2^96 */ +#define THREEp96 C[2] + L(59421121885698253195157962752.0), + +/* 3x2^103 */ +#define THREEp103 C[3] + L(30423614405477505635920876929024.0), + +/* 3x2^111 */ +#define THREEp111 C[4] + L(7788445287802241442795744493830144.0), + +/* 1/ln(2) */ +#define M_1_LN2 C[5] + L(1.44269504088896340735992468100189204), + +/* first 93 bits of ln(2) */ +#define M_LN2_0 C[6] + L(0.693147180559945309417232121457981864), + +/* ln2_0 - ln(2) */ +#define M_LN2_1 C[7] +L(-1.94704509238074995158795957333327386E-31), + +/* very small number */ +#define TINY C[8] + L(1.0e-4900), + +/* 2^16383 */ +#define TWO16383 C[9] + L(5.94865747678615882542879663314003565E+4931), + +/* 256 */ +#define TWO8 C[10] + 256, + +/* 32768 */ +#define TWO15 C[11] + 32768, + +/* Chebyshev polynom coefficients for (exp(x)-1)/x */ +#define P1 C[12] +#define P2 C[13] +#define P3 C[14] +#define P4 C[15] +#define P5 C[16] +#define P6 C[17] + L(0.5), + L(1.66666666666666666666666666666666683E-01), + L(4.16666666666666666666654902320001674E-02), + L(8.33333333333333333333314659767198461E-03), + L(1.38888888889899438565058018857254025E-03), + L(1.98412698413981650382436541785404286E-04), +}; + +_Float128 +__ieee754_expl (_Float128 x) +{ + /* Check for usual case. */ + if (isless (x, himark) && isgreater (x, lomark)) + { + int tval1, tval2, unsafe, n_i; + _Float128 x22, n, t, result, xl; + union ieee854_long_double ex2_u, scale_u; + fenv_t oldenv; + + feholdexcept (&oldenv); +#ifdef FE_TONEAREST + fesetround (FE_TONEAREST); +#endif + + /* Calculate n. */ + n = x * M_1_LN2 + THREEp111; + n -= THREEp111; + x = x - n * M_LN2_0; + xl = n * M_LN2_1; + + /* Calculate t/256. */ + t = x + THREEp103; + t -= THREEp103; + + /* Compute tval1 = t. */ + tval1 = (int) (t * TWO8); + + x -= __expl_table[T_EXPL_ARG1+2*tval1]; + xl -= __expl_table[T_EXPL_ARG1+2*tval1+1]; + + /* Calculate t/32768. */ + t = x + THREEp96; + t -= THREEp96; + + /* Compute tval2 = t. */ + tval2 = (int) (t * TWO15); + + x -= __expl_table[T_EXPL_ARG2+2*tval2]; + xl -= __expl_table[T_EXPL_ARG2+2*tval2+1]; + + x = x + xl; + + /* Compute ex2 = 2^n_0 e^(argtable[tval1]) e^(argtable[tval2]). */ + ex2_u.d = __expl_table[T_EXPL_RES1 + tval1] + * __expl_table[T_EXPL_RES2 + tval2]; + n_i = (int)n; + /* 'unsafe' is 1 iff n_1 != 0. */ + unsafe = abs(n_i) >= 15000; + ex2_u.ieee.exponent += n_i >> unsafe; + + /* Compute scale = 2^n_1. */ + scale_u.d = 1; + scale_u.ieee.exponent += n_i - (n_i >> unsafe); + + /* Approximate e^x2 - 1, using a seventh-degree polynomial, + with maximum error in [-2^-16-2^-53,2^-16+2^-53] + less than 4.8e-39. */ + x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6))))); + + /* Return result. */ + fesetenv (&oldenv); + + result = x22 * ex2_u.d + ex2_u.d; + + /* Now we can test whether the result is ultimate or if we are unsure. + In the later case we should probably call a mpn based routine to give + the ultimate result. + Empirically, this routine is already ultimate in about 99.9986% of + cases, the test below for the round to nearest case will be false + in ~ 99.9963% of cases. + Without proc2 routine maximum error which has been seen is + 0.5000262 ulp. + + union ieee854_long_double ex3_u; + + #ifdef FE_TONEAREST + fesetround (FE_TONEAREST); + #endif + ex3_u.d = (result - ex2_u.d) - x22 * ex2_u.d; + ex2_u.d = result; + ex3_u.ieee.exponent += LDBL_MANT_DIG + 15 + IEEE854_LONG_DOUBLE_BIAS + - ex2_u.ieee.exponent; + n_i = abs (ex3_u.d); + n_i = (n_i + 1) / 2; + fesetenv (&oldenv); + #ifdef FE_TONEAREST + if (fegetround () == FE_TONEAREST) + n_i -= 0x4000; + #endif + if (!n_i) { + return __ieee754_expl_proc2 (origx); + } + */ + if (!unsafe) + return result; + else + { + result *= scale_u.d; + math_check_force_underflow_nonneg (result); + return result; + } + } + /* Exceptional cases: */ + else if (isless (x, himark)) + { + if (isinf (x)) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TINY * TINY; + } + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO16383*x; +} +strong_alias (__ieee754_expl, __expl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_fmodl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_fmodl.c new file mode 100644 index 0000000000..f27cd4f8ff --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_fmodl.c @@ -0,0 +1,131 @@ +/* e_fmodl.c -- long double version of e_fmod.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ +/* + * ==================================================== + * Copyright (C) 1993, 2011 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __ieee754_fmodl(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 one = 1.0, Zero[] = {0.0, -0.0,}; + +_Float128 +__ieee754_fmodl (_Float128 x, _Float128 y) +{ + int64_t n,hx,hy,hz,ix,iy,sx,i; + u_int64_t lx,ly,lz; + + GET_LDOUBLE_WORDS64(hx,lx,x); + GET_LDOUBLE_WORDS64(hy,ly,y); + sx = hx&0x8000000000000000ULL; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffffffffffffLL; /* |y| */ + + /* purge off exception values */ + if((hy|ly)==0||(hx>=0x7fff000000000000LL)|| /* y=0,or x not finite */ + ((hy|((ly|-ly)>>63))>0x7fff000000000000LL)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx<=hy) { + if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */ + if(lx==ly) + return Zero[(u_int64_t)sx>>63]; /* |x|=|y| return x*0*/ + } + + /* determine ix = ilogb(x) */ + if(hx<0x0001000000000000LL) { /* subnormal x */ + if(hx==0) { + for (ix = -16431, i=lx; i>0; i<<=1) ix -=1; + } else { + for (ix = -16382, i=hx<<15; i>0; i<<=1) ix -=1; + } + } else ix = (hx>>48)-0x3fff; + + /* determine iy = ilogb(y) */ + if(hy<0x0001000000000000LL) { /* subnormal y */ + if(hy==0) { + for (iy = -16431, i=ly; i>0; i<<=1) iy -=1; + } else { + for (iy = -16382, i=hy<<15; i>0; i<<=1) iy -=1; + } + } else iy = (hy>>48)-0x3fff; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -16382) + hx = 0x0001000000000000LL|(0x0000ffffffffffffLL&hx); + else { /* subnormal x, shift x to normal */ + n = -16382-ix; + if(n<=63) { + hx = (hx<<n)|(lx>>(64-n)); + lx <<= n; + } else { + hx = lx<<(n-64); + lx = 0; + } + } + if(iy >= -16382) + hy = 0x0001000000000000LL|(0x0000ffffffffffffLL&hy); + else { /* subnormal y, shift y to normal */ + n = -16382-iy; + if(n<=63) { + hy = (hy<<n)|(ly>>(64-n)); + ly <<= n; + } else { + hy = ly<<(n-64); + ly = 0; + } + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; + if(hz<0){hx = hx+hx+(lx>>63); lx = lx+lx;} + else { + if((hz|lz)==0) /* return sign(x)*0 */ + return Zero[(u_int64_t)sx>>63]; + hx = hz+hz+(lz>>63); lx = lz+lz; + } + } + hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; + if(hz>=0) {hx=hz;lx=lz;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) /* return sign(x)*0 */ + return Zero[(u_int64_t)sx>>63]; + while(hx<0x0001000000000000LL) { /* normalize x */ + hx = hx+hx+(lx>>63); lx = lx+lx; + iy -= 1; + } + if(iy>= -16382) { /* normalize output */ + hx = ((hx-0x0001000000000000LL)|((iy+16383)<<48)); + SET_LDOUBLE_WORDS64(x,hx|sx,lx); + } else { /* subnormal output */ + n = -16382 - iy; + if(n<=48) { + lx = (lx>>n)|((u_int64_t)hx<<(64-n)); + hx >>= n; + } else if (n<=63) { + lx = (hx<<(64-n))|(lx>>n); hx = sx; + } else { + lx = hx>>(n-64); hx = sx; + } + SET_LDOUBLE_WORDS64(x,hx|sx,lx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} +strong_alias (__ieee754_fmodl, __fmodl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_gammal_r.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_gammal_r.c new file mode 100644 index 0000000000..3a5317ade1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_gammal_r.c @@ -0,0 +1,218 @@ +/* Implementation of gamma function according to ISO C. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const _Float128 gamma_coeff[] = + { + L(0x1.5555555555555555555555555555p-4), + L(-0xb.60b60b60b60b60b60b60b60b60b8p-12), + L(0x3.4034034034034034034034034034p-12), + L(-0x2.7027027027027027027027027028p-12), + L(0x3.72a3c5631fe46ae1d4e700dca8f2p-12), + L(-0x7.daac36664f1f207daac36664f1f4p-12), + L(0x1.a41a41a41a41a41a41a41a41a41ap-8), + L(-0x7.90a1b2c3d4e5f708192a3b4c5d7p-8), + L(0x2.dfd2c703c0cfff430edfd2c703cp-4), + L(-0x1.6476701181f39edbdb9ce625987dp+0), + L(0xd.672219167002d3a7a9c886459cp+0), + L(-0x9.cd9292e6660d55b3f712eb9e07c8p+4), + L(0x8.911a740da740da740da740da741p+8), + L(-0x8.d0cc570e255bf59ff6eec24b49p+12), + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 1775, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static _Float128 +gammal_positive (_Float128 x, int *exp2_adj) +{ + int local_signgam; + if (x < L(0.5)) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x; + } + else if (x <= L(1.5)) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam)); + } + else if (x < L(12.5)) + { + /* Adjust into the range for using exp (lgamma). */ + *exp2_adj = 0; + _Float128 n = __ceill (x - L(1.5)); + _Float128 x_adj = x - n; + _Float128 eps; + _Float128 prod = __gamma_productl (x_adj, 0, n, &eps); + return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam)) + * prod * (1 + eps)); + } + else + { + _Float128 eps = 0; + _Float128 x_eps = 0; + _Float128 x_adj = x; + _Float128 prod = 1; + if (x < 24) + { + /* Adjust into the range for applying Stirling's + approximation. */ + _Float128 n = __ceill (24 - x); + x_adj = x + n; + x_eps = (x - (x_adj - n)); + prod = __gamma_productl (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + _Float128 exp_adj = -eps; + _Float128 x_adj_int = __roundl (x_adj); + _Float128 x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + _Float128 x_adj_mant = __frexpl (x_adj, &x_adj_log2); + if (x_adj_mant < M_SQRT1_2l) + { + x_adj_log2--; + x_adj_mant *= 2; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + _Float128 ret = (__ieee754_powl (x_adj_mant, x_adj) + * __ieee754_exp2l (x_adj_log2 * x_adj_frac) + * __ieee754_expl (-x_adj) + * __ieee754_sqrtl (2 * M_PIl / x_adj) + / prod); + exp_adj += x_eps * __ieee754_logl (x_adj); + _Float128 bsum = gamma_coeff[NCOEFF - 1]; + _Float128 x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1l (exp_adj); + } +} + +_Float128 +__ieee754_gammal_r (_Float128 x, int *signgamp) +{ + int64_t hx; + u_int64_t lx; + _Float128 ret; + + GET_LDOUBLE_WORDS64 (hx, lx, x); + + if (((hx & 0x7fffffffffffffffLL) | lx) == 0) + { + /* Return value for x == 0 is Inf with divide by zero exception. */ + *signgamp = 0; + return 1.0 / x; + } + if (hx < 0 && (u_int64_t) hx < 0xffff000000000000ULL && __rintl (x) == x) + { + /* Return value for integer x < 0 is NaN with invalid exception. */ + *signgamp = 0; + return (x - x) / (x - x); + } + if (hx == 0xffff000000000000ULL && lx == 0) + { + /* x == -Inf. According to ISO this is NaN. */ + *signgamp = 0; + return x - x; + } + if ((hx & 0x7fff000000000000ULL) == 0x7fff000000000000ULL) + { + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ + *signgamp = 0; + return x + x; + } + + if (x >= 1756) + { + /* Overflow. */ + *signgamp = 0; + return LDBL_MAX * LDBL_MAX; + } + else + { + SET_RESTORE_ROUNDL (FE_TONEAREST); + if (x > 0) + { + *signgamp = 0; + int exp2_adj; + ret = gammal_positive (x, &exp2_adj); + ret = __scalbnl (ret, exp2_adj); + } + else if (x >= -LDBL_EPSILON / 4) + { + *signgamp = 0; + ret = 1 / x; + } + else + { + _Float128 tx = __truncl (x); + *signgamp = (tx == 2 * __truncl (tx / 2)) ? -1 : 1; + if (x <= -1775) + /* Underflow. */ + ret = LDBL_MIN * LDBL_MIN; + else + { + _Float128 frac = tx - x; + if (frac > L(0.5)) + frac = 1 - frac; + _Float128 sinpix = (frac <= L(0.25) + ? __sinl (M_PIl * frac) + : __cosl (M_PIl * (L(0.5) - frac))); + int exp2_adj; + ret = M_PIl / (-x * sinpix + * gammal_positive (-x, &exp2_adj)); + ret = __scalbnl (ret, -exp2_adj); + math_check_force_underflow_nonneg (ret); + } + } + } + if (isinf (ret) && x != 0) + { + if (*signgamp < 0) + return -(-__copysignl (LDBL_MAX, ret) * LDBL_MAX); + else + return __copysignl (LDBL_MAX, ret) * LDBL_MAX; + } + else if (ret == 0) + { + if (*signgamp < 0) + return -(-__copysignl (LDBL_MIN, ret) * LDBL_MIN); + else + return __copysignl (LDBL_MIN, ret) * LDBL_MIN; + } + else + return ret; +} +strong_alias (__ieee754_gammal_r, __gammal_r_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_hypotl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_hypotl.c new file mode 100644 index 0000000000..6c4e178fbe --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_hypotl.c @@ -0,0 +1,140 @@ +/* e_hypotl.c -- long double version of e_hypot.c. + * Conversion to long double by Jakub Jelinek, jakub@redhat.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_hypotl(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrtl(2)/2 ulp, than + * sqrtl(z) has error less than 1 ulp (exercise). + * + * So, compute sqrtl(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 64 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1, + * y1= y with lower 64 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypotl(x,y) is INF if x or y is +INF or -INF; else + * hypotl(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypotl(x,y) returns sqrtl(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include <math.h> +#include <math_private.h> + +_Float128 +__ieee754_hypotl(_Float128 x, _Float128 y) +{ + _Float128 a,b,t1,t2,y1,y2,w; + int64_t j,k,ha,hb; + + GET_LDOUBLE_MSW64(ha,x); + ha &= 0x7fffffffffffffffLL; + GET_LDOUBLE_MSW64(hb,y); + hb &= 0x7fffffffffffffffLL; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + SET_LDOUBLE_MSW64(a,ha); /* a <- |a| */ + SET_LDOUBLE_MSW64(b,hb); /* b <- |b| */ + if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */ + k=0; + if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */ + if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */ + u_int64_t low; + w = a+b; /* for sNaN */ + if (issignaling (a) || issignaling (b)) + return w; + GET_LDOUBLE_LSW64(low,a); + if(((ha&0xffffffffffffLL)|low)==0) w = a; + GET_LDOUBLE_LSW64(low,b); + if(((hb^0x7fff000000000000LL)|low)==0) w = b; + return w; + } + /* scale a and b by 2**-9600 */ + ha -= 0x2580000000000000LL; + hb -= 0x2580000000000000LL; k += 9600; + SET_LDOUBLE_MSW64(a,ha); + SET_LDOUBLE_MSW64(b,hb); + } + if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */ + if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */ + u_int64_t low; + GET_LDOUBLE_LSW64(low,b); + if((hb|low)==0) return a; + t1=0; + SET_LDOUBLE_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */ + b *= t1; + a *= t1; + k -= 16382; + GET_LDOUBLE_MSW64 (ha, a); + GET_LDOUBLE_MSW64 (hb, b); + if (hb > ha) + { + t1 = a; + a = b; + b = t1; + j = ha; + ha = hb; + hb = j; + } + } else { /* scale a and b by 2^9600 */ + ha += 0x2580000000000000LL; /* a *= 2^9600 */ + hb += 0x2580000000000000LL; /* b *= 2^9600 */ + k -= 9600; + SET_LDOUBLE_MSW64(a,ha); + SET_LDOUBLE_MSW64(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + t1 = 0; + SET_LDOUBLE_MSW64(t1,ha); + t2 = a-t1; + w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + y1 = 0; + SET_LDOUBLE_MSW64(y1,hb); + y2 = b - y1; + t1 = 0; + SET_LDOUBLE_MSW64(t1,ha+0x0001000000000000LL); + t2 = a - t1; + w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + u_int64_t high; + t1 = 1; + GET_LDOUBLE_MSW64(high,t1); + SET_LDOUBLE_MSW64(t1,high+(k<<48)); + w *= t1; + math_check_force_underflow_nonneg (w); + return w; + } else return w; +} +strong_alias (__ieee754_hypotl, __hypotl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_ilogbl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_ilogbl.c new file mode 100644 index 0000000000..9effe6386a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_ilogbl.c @@ -0,0 +1,56 @@ +/* s_ilogbl.c -- long double version of s_ilogb.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* ilogbl(long double x) + * return the binary exponent of non-zero x + * ilogbl(0) = FP_ILOGB0 + * ilogbl(NaN) = FP_ILOGBNAN (no signal is raised) + * ilogbl(+-Inf) = INT_MAX (no signal is raised) + */ + +#include <limits.h> +#include <math.h> +#include <math_private.h> + +int __ieee754_ilogbl (_Float128 x) +{ + int64_t hx,lx; + int ix; + + GET_LDOUBLE_WORDS64(hx,lx,x); + hx &= 0x7fffffffffffffffLL; + if(hx <= 0x0001000000000000LL) { + if((hx|lx)==0) + return FP_ILOGB0; /* ilogbl(0) = FP_ILOGB0 */ + else /* subnormal x */ + if(hx==0) { + for (ix = -16431; lx>0; lx<<=1) ix -=1; + } else { + for (ix = -16382, hx<<=15; hx>0; hx<<=1) ix -=1; + } + return ix; + } + else if (hx<0x7fff000000000000LL) return (hx>>48)-0x3fff; + else if (FP_ILOGBNAN != INT_MAX) { + /* ISO C99 requires ilogbl(+-Inf) == INT_MAX. */ + if (((hx^0x7fff000000000000LL)|lx) == 0) + return INT_MAX; + } + return FP_ILOGBNAN; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_j0l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_j0l.c new file mode 100644 index 0000000000..fb8d3518ce --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_j0l.c @@ -0,0 +1,937 @@ +/* j0l.c + * + * Bessel function of order zero + * + * + * + * SYNOPSIS: + * + * long double x, y, j0l(); + * + * y = j0l( x ); + * + * + * + * DESCRIPTION: + * + * Returns Bessel function of first kind, order zero of the argument. + * + * The domain is divided into two major intervals [0, 2] and + * (2, infinity). In the first interval the rational approximation + * is J0(x) = 1 - x^2 / 4 + x^4 R(x^2) + * The second interval is further partitioned into eight equal segments + * of 1/x. + * + * J0(x) = sqrt(2/(pi x)) (P0(x) cos(X) - Q0(x) sin(X)), + * X = x - pi/4, + * + * and the auxiliary functions are given by + * + * J0(x)cos(X) + Y0(x)sin(X) = sqrt( 2/(pi x)) P0(x), + * P0(x) = 1 + 1/x^2 R(1/x^2) + * + * Y0(x)cos(X) - J0(x)sin(X) = sqrt( 2/(pi x)) Q0(x), + * Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + * + * + * + * ACCURACY: + * + * Absolute error: + * arithmetic domain # trials peak rms + * IEEE 0, 30 100000 1.7e-34 2.4e-35 + * + * + */ + +/* y0l.c + * + * Bessel function of the second kind, order zero + * + * + * + * SYNOPSIS: + * + * double x, y, y0l(); + * + * y = y0l( x ); + * + * + * + * DESCRIPTION: + * + * Returns Bessel function of the second kind, of order + * zero, of the argument. + * + * The approximation is the same as for J0(x), and + * Y0(x) = sqrt(2/(pi x)) (P0(x) sin(X) + Q0(x) cos(X)). + * + * ACCURACY: + * + * Absolute error, when y0(x) < 1; else relative error: + * + * arithmetic domain # trials peak rms + * IEEE 0, 30 100000 3.0e-34 2.7e-35 + * + */ + +/* Copyright 2001 by Stephen L. Moshier (moshier@na-net.ornl.gov). + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* 1 / sqrt(pi) */ +static const _Float128 ONEOSQPI = L(5.6418958354775628694807945156077258584405E-1); +/* 2 / pi */ +static const _Float128 TWOOPI = L(6.3661977236758134307553505349005744813784E-1); +static const _Float128 zero = 0; + +/* J0(x) = 1 - x^2/4 + x^2 x^2 R(x^2) + Peak relative error 3.4e-37 + 0 <= x <= 2 */ +#define NJ0_2N 6 +static const _Float128 J0_2N[NJ0_2N + 1] = { + L(3.133239376997663645548490085151484674892E16), + L(-5.479944965767990821079467311839107722107E14), + L(6.290828903904724265980249871997551894090E12), + L(-3.633750176832769659849028554429106299915E10), + L(1.207743757532429576399485415069244807022E8), + L(-2.107485999925074577174305650549367415465E5), + L(1.562826808020631846245296572935547005859E2), +}; +#define NJ0_2D 6 +static const _Float128 J0_2D[NJ0_2D + 1] = { + L(2.005273201278504733151033654496928968261E18), + L(2.063038558793221244373123294054149790864E16), + L(1.053350447931127971406896594022010524994E14), + L(3.496556557558702583143527876385508882310E11), + L(8.249114511878616075860654484367133976306E8), + L(1.402965782449571800199759247964242790589E6), + L(1.619910762853439600957801751815074787351E3), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2), + 0 <= 1/x <= .0625 + Peak relative error 3.3e-36 */ +#define NP16_IN 9 +static const _Float128 P16_IN[NP16_IN + 1] = { + L(-1.901689868258117463979611259731176301065E-16), + L(-1.798743043824071514483008340803573980931E-13), + L(-6.481746687115262291873324132944647438959E-11), + L(-1.150651553745409037257197798528294248012E-8), + L(-1.088408467297401082271185599507222695995E-6), + L(-5.551996725183495852661022587879817546508E-5), + L(-1.477286941214245433866838787454880214736E-3), + L(-1.882877976157714592017345347609200402472E-2), + L(-9.620983176855405325086530374317855880515E-2), + L(-1.271468546258855781530458854476627766233E-1), +}; +#define NP16_ID 9 +static const _Float128 P16_ID[NP16_ID + 1] = { + L(2.704625590411544837659891569420764475007E-15), + L(2.562526347676857624104306349421985403573E-12), + L(9.259137589952741054108665570122085036246E-10), + L(1.651044705794378365237454962653430805272E-7), + L(1.573561544138733044977714063100859136660E-5), + L(8.134482112334882274688298469629884804056E-4), + L(2.219259239404080863919375103673593571689E-2), + L(2.976990606226596289580242451096393862792E-1), + L(1.713895630454693931742734911930937246254E0), + L(3.231552290717904041465898249160757368855E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + 0.0625 <= 1/x <= 0.125 + Peak relative error 2.4e-35 */ +#define NP8_16N 10 +static const _Float128 P8_16N[NP8_16N + 1] = { + L(-2.335166846111159458466553806683579003632E-15), + L(-1.382763674252402720401020004169367089975E-12), + L(-3.192160804534716696058987967592784857907E-10), + L(-3.744199606283752333686144670572632116899E-8), + L(-2.439161236879511162078619292571922772224E-6), + L(-9.068436986859420951664151060267045346549E-5), + L(-1.905407090637058116299757292660002697359E-3), + L(-2.164456143936718388053842376884252978872E-2), + L(-1.212178415116411222341491717748696499966E-1), + L(-2.782433626588541494473277445959593334494E-1), + L(-1.670703190068873186016102289227646035035E-1), +}; +#define NP8_16D 10 +static const _Float128 P8_16D[NP8_16D + 1] = { + L(3.321126181135871232648331450082662856743E-14), + L(1.971894594837650840586859228510007703641E-11), + L(4.571144364787008285981633719513897281690E-9), + L(5.396419143536287457142904742849052402103E-7), + L(3.551548222385845912370226756036899901549E-5), + L(1.342353874566932014705609788054598013516E-3), + L(2.899133293006771317589357444614157734385E-2), + L(3.455374978185770197704507681491574261545E-1), + L(2.116616964297512311314454834712634820514E0), + L(5.850768316827915470087758636881584174432E0), + L(5.655273858938766830855753983631132928968E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + 0.125 <= 1/x <= 0.1875 + Peak relative error 2.7e-35 */ +#define NP5_8N 10 +static const _Float128 P5_8N[NP5_8N + 1] = { + L(-1.270478335089770355749591358934012019596E-12), + L(-4.007588712145412921057254992155810347245E-10), + L(-4.815187822989597568124520080486652009281E-8), + L(-2.867070063972764880024598300408284868021E-6), + L(-9.218742195161302204046454768106063638006E-5), + L(-1.635746821447052827526320629828043529997E-3), + L(-1.570376886640308408247709616497261011707E-2), + L(-7.656484795303305596941813361786219477807E-2), + L(-1.659371030767513274944805479908858628053E-1), + L(-1.185340550030955660015841796219919804915E-1), + L(-8.920026499909994671248893388013790366712E-3), +}; +#define NP5_8D 9 +static const _Float128 P5_8D[NP5_8D + 1] = { + L(1.806902521016705225778045904631543990314E-11), + L(5.728502760243502431663549179135868966031E-9), + L(6.938168504826004255287618819550667978450E-7), + L(4.183769964807453250763325026573037785902E-5), + L(1.372660678476925468014882230851637878587E-3), + L(2.516452105242920335873286419212708961771E-2), + L(2.550502712902647803796267951846557316182E-1), + L(1.365861559418983216913629123778747617072E0), + L(3.523825618308783966723472468855042541407E0), + L(3.656365803506136165615111349150536282434E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + Peak relative error 3.5e-35 + 0.1875 <= 1/x <= 0.25 */ +#define NP4_5N 9 +static const _Float128 P4_5N[NP4_5N + 1] = { + L(-9.791405771694098960254468859195175708252E-10), + L(-1.917193059944531970421626610188102836352E-7), + L(-1.393597539508855262243816152893982002084E-5), + L(-4.881863490846771259880606911667479860077E-4), + L(-8.946571245022470127331892085881699269853E-3), + L(-8.707474232568097513415336886103899434251E-2), + L(-4.362042697474650737898551272505525973766E-1), + L(-1.032712171267523975431451359962375617386E0), + L(-9.630502683169895107062182070514713702346E-1), + L(-2.251804386252969656586810309252357233320E-1), +}; +#define NP4_5D 9 +static const _Float128 P4_5D[NP4_5D + 1] = { + L(1.392555487577717669739688337895791213139E-8), + L(2.748886559120659027172816051276451376854E-6), + L(2.024717710644378047477189849678576659290E-4), + L(7.244868609350416002930624752604670292469E-3), + L(1.373631762292244371102989739300382152416E-1), + L(1.412298581400224267910294815260613240668E0), + L(7.742495637843445079276397723849017617210E0), + L(2.138429269198406512028307045259503811861E1), + L(2.651547684548423476506826951831712762610E1), + L(1.167499382465291931571685222882909166935E1), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + Peak relative error 2.3e-36 + 0.25 <= 1/x <= 0.3125 */ +#define NP3r2_4N 9 +static const _Float128 P3r2_4N[NP3r2_4N + 1] = { + L(-2.589155123706348361249809342508270121788E-8), + L(-3.746254369796115441118148490849195516593E-6), + L(-1.985595497390808544622893738135529701062E-4), + L(-5.008253705202932091290132760394976551426E-3), + L(-6.529469780539591572179155511840853077232E-2), + L(-4.468736064761814602927408833818990271514E-1), + L(-1.556391252586395038089729428444444823380E0), + L(-2.533135309840530224072920725976994981638E0), + L(-1.605509621731068453869408718565392869560E0), + L(-2.518966692256192789269859830255724429375E-1), +}; +#define NP3r2_4D 9 +static const _Float128 P3r2_4D[NP3r2_4D + 1] = { + L(3.682353957237979993646169732962573930237E-7), + L(5.386741661883067824698973455566332102029E-5), + L(2.906881154171822780345134853794241037053E-3), + L(7.545832595801289519475806339863492074126E-2), + L(1.029405357245594877344360389469584526654E0), + L(7.565706120589873131187989560509757626725E0), + L(2.951172890699569545357692207898667665796E1), + L(5.785723537170311456298467310529815457536E1), + L(5.095621464598267889126015412522773474467E1), + L(1.602958484169953109437547474953308401442E1), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + Peak relative error 1.0e-35 + 0.3125 <= 1/x <= 0.375 */ +#define NP2r7_3r2N 9 +static const _Float128 P2r7_3r2N[NP2r7_3r2N + 1] = { + L(-1.917322340814391131073820537027234322550E-7), + L(-1.966595744473227183846019639723259011906E-5), + L(-7.177081163619679403212623526632690465290E-4), + L(-1.206467373860974695661544653741899755695E-2), + L(-1.008656452188539812154551482286328107316E-1), + L(-4.216016116408810856620947307438823892707E-1), + L(-8.378631013025721741744285026537009814161E-1), + L(-6.973895635309960850033762745957946272579E-1), + L(-1.797864718878320770670740413285763554812E-1), + L(-4.098025357743657347681137871388402849581E-3), +}; +#define NP2r7_3r2D 8 +static const _Float128 P2r7_3r2D[NP2r7_3r2D + 1] = { + L(2.726858489303036441686496086962545034018E-6), + L(2.840430827557109238386808968234848081424E-4), + L(1.063826772041781947891481054529454088832E-2), + L(1.864775537138364773178044431045514405468E-1), + L(1.665660052857205170440952607701728254211E0), + L(7.723745889544331153080842168958348568395E0), + L(1.810726427571829798856428548102077799835E1), + L(1.986460672157794440666187503833545388527E1), + L(8.645503204552282306364296517220055815488E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + Peak relative error 1.3e-36 + 0.3125 <= 1/x <= 0.4375 */ +#define NP2r3_2r7N 9 +static const _Float128 P2r3_2r7N[NP2r3_2r7N + 1] = { + L(-1.594642785584856746358609622003310312622E-6), + L(-1.323238196302221554194031733595194539794E-4), + L(-3.856087818696874802689922536987100372345E-3), + L(-5.113241710697777193011470733601522047399E-2), + L(-3.334229537209911914449990372942022350558E-1), + L(-1.075703518198127096179198549659283422832E0), + L(-1.634174803414062725476343124267110981807E0), + L(-1.030133247434119595616826842367268304880E0), + L(-1.989811539080358501229347481000707289391E-1), + L(-3.246859189246653459359775001466924610236E-3), +}; +#define NP2r3_2r7D 8 +static const _Float128 P2r3_2r7D[NP2r3_2r7D + 1] = { + L(2.267936634217251403663034189684284173018E-5), + L(1.918112982168673386858072491437971732237E-3), + L(5.771704085468423159125856786653868219522E-2), + L(8.056124451167969333717642810661498890507E-1), + L(5.687897967531010276788680634413789328776E0), + L(2.072596760717695491085444438270778394421E1), + L(3.801722099819929988585197088613160496684E1), + L(3.254620235902912339534998592085115836829E1), + L(1.104847772130720331801884344645060675036E1), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + Peak relative error 1.2e-35 + 0.4375 <= 1/x <= 0.5 */ +#define NP2_2r3N 8 +static const _Float128 P2_2r3N[NP2_2r3N + 1] = { + L(-1.001042324337684297465071506097365389123E-4), + L(-6.289034524673365824853547252689991418981E-3), + L(-1.346527918018624234373664526930736205806E-1), + L(-1.268808313614288355444506172560463315102E0), + L(-5.654126123607146048354132115649177406163E0), + L(-1.186649511267312652171775803270911971693E1), + L(-1.094032424931998612551588246779200724257E1), + L(-3.728792136814520055025256353193674625267E0), + L(-3.000348318524471807839934764596331810608E-1), +}; +#define NP2_2r3D 8 +static const _Float128 P2_2r3D[NP2_2r3D + 1] = { + L(1.423705538269770974803901422532055612980E-3), + L(9.171476630091439978533535167485230575894E-2), + L(2.049776318166637248868444600215942828537E0), + L(2.068970329743769804547326701946144899583E1), + L(1.025103500560831035592731539565060347709E2), + L(2.528088049697570728252145557167066708284E2), + L(2.992160327587558573740271294804830114205E2), + L(1.540193761146551025832707739468679973036E2), + L(2.779516701986912132637672140709452502650E1), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + Peak relative error 2.2e-35 + 0 <= 1/x <= .0625 */ +#define NQ16_IN 10 +static const _Float128 Q16_IN[NQ16_IN + 1] = { + L(2.343640834407975740545326632205999437469E-18), + L(2.667978112927811452221176781536278257448E-15), + L(1.178415018484555397390098879501969116536E-12), + L(2.622049767502719728905924701288614016597E-10), + L(3.196908059607618864801313380896308968673E-8), + L(2.179466154171673958770030655199434798494E-6), + L(8.139959091628545225221976413795645177291E-5), + L(1.563900725721039825236927137885747138654E-3), + L(1.355172364265825167113562519307194840307E-2), + L(3.928058355906967977269780046844768588532E-2), + L(1.107891967702173292405380993183694932208E-2), +}; +#define NQ16_ID 9 +static const _Float128 Q16_ID[NQ16_ID + 1] = { + L(3.199850952578356211091219295199301766718E-17), + L(3.652601488020654842194486058637953363918E-14), + L(1.620179741394865258354608590461839031281E-11), + L(3.629359209474609630056463248923684371426E-9), + L(4.473680923894354600193264347733477363305E-7), + L(3.106368086644715743265603656011050476736E-5), + L(1.198239259946770604954664925153424252622E-3), + L(2.446041004004283102372887804475767568272E-2), + L(2.403235525011860603014707768815113698768E-1), + L(9.491006790682158612266270665136910927149E-1), + /* 1.000000000000000000000000000000000000000E0 */ + }; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + Peak relative error 5.1e-36 + 0.0625 <= 1/x <= 0.125 */ +#define NQ8_16N 11 +static const _Float128 Q8_16N[NQ8_16N + 1] = { + L(1.001954266485599464105669390693597125904E-17), + L(7.545499865295034556206475956620160007849E-15), + L(2.267838684785673931024792538193202559922E-12), + L(3.561909705814420373609574999542459912419E-10), + L(3.216201422768092505214730633842924944671E-8), + L(1.731194793857907454569364622452058554314E-6), + L(5.576944613034537050396518509871004586039E-5), + L(1.051787760316848982655967052985391418146E-3), + L(1.102852974036687441600678598019883746959E-2), + L(5.834647019292460494254225988766702933571E-2), + L(1.290281921604364618912425380717127576529E-1), + L(7.598886310387075708640370806458926458301E-2), +}; +#define NQ8_16D 11 +static const _Float128 Q8_16D[NQ8_16D + 1] = { + L(1.368001558508338469503329967729951830843E-16), + L(1.034454121857542147020549303317348297289E-13), + L(3.128109209247090744354764050629381674436E-11), + L(4.957795214328501986562102573522064468671E-9), + L(4.537872468606711261992676606899273588899E-7), + L(2.493639207101727713192687060517509774182E-5), + L(8.294957278145328349785532236663051405805E-4), + L(1.646471258966713577374948205279380115839E-2), + L(1.878910092770966718491814497982191447073E-1), + L(1.152641605706170353727903052525652504075E0), + L(3.383550240669773485412333679367792932235E0), + L(3.823875252882035706910024716609908473970E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + Peak relative error 3.9e-35 + 0.125 <= 1/x <= 0.1875 */ +#define NQ5_8N 10 +static const _Float128 Q5_8N[NQ5_8N + 1] = { + L(1.750399094021293722243426623211733898747E-13), + L(6.483426211748008735242909236490115050294E-11), + L(9.279430665656575457141747875716899958373E-9), + L(6.696634968526907231258534757736576340266E-7), + L(2.666560823798895649685231292142838188061E-5), + L(6.025087697259436271271562769707550594540E-4), + L(7.652807734168613251901945778921336353485E-3), + L(5.226269002589406461622551452343519078905E-2), + L(1.748390159751117658969324896330142895079E-1), + L(2.378188719097006494782174902213083589660E-1), + L(8.383984859679804095463699702165659216831E-2), +}; +#define NQ5_8D 10 +static const _Float128 Q5_8D[NQ5_8D + 1] = { + L(2.389878229704327939008104855942987615715E-12), + L(8.926142817142546018703814194987786425099E-10), + L(1.294065862406745901206588525833274399038E-7), + L(9.524139899457666250828752185212769682191E-6), + L(3.908332488377770886091936221573123353489E-4), + L(9.250427033957236609624199884089916836748E-3), + L(1.263420066165922645975830877751588421451E-1), + L(9.692527053860420229711317379861733180654E-1), + L(3.937813834630430172221329298841520707954E0), + L(7.603126427436356534498908111445191312181E0), + L(5.670677653334105479259958485084550934305E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + Peak relative error 3.2e-35 + 0.1875 <= 1/x <= 0.25 */ +#define NQ4_5N 10 +static const _Float128 Q4_5N[NQ4_5N + 1] = { + L(2.233870042925895644234072357400122854086E-11), + L(5.146223225761993222808463878999151699792E-9), + L(4.459114531468296461688753521109797474523E-7), + L(1.891397692931537975547242165291668056276E-5), + L(4.279519145911541776938964806470674565504E-4), + L(5.275239415656560634702073291768904783989E-3), + L(3.468698403240744801278238473898432608887E-2), + L(1.138773146337708415188856882915457888274E-1), + L(1.622717518946443013587108598334636458955E-1), + L(7.249040006390586123760992346453034628227E-2), + L(1.941595365256460232175236758506411486667E-3), +}; +#define NQ4_5D 9 +static const _Float128 Q4_5D[NQ4_5D + 1] = { + L(3.049977232266999249626430127217988047453E-10), + L(7.120883230531035857746096928889676144099E-8), + L(6.301786064753734446784637919554359588859E-6), + L(2.762010530095069598480766869426308077192E-4), + L(6.572163250572867859316828886203406361251E-3), + L(8.752566114841221958200215255461843397776E-2), + L(6.487654992874805093499285311075289932664E-1), + L(2.576550017826654579451615283022812801435E0), + L(5.056392229924022835364779562707348096036E0), + L(4.179770081068251464907531367859072157773E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + Peak relative error 1.4e-36 + 0.25 <= 1/x <= 0.3125 */ +#define NQ3r2_4N 10 +static const _Float128 Q3r2_4N[NQ3r2_4N + 1] = { + L(6.126167301024815034423262653066023684411E-10), + L(1.043969327113173261820028225053598975128E-7), + L(6.592927270288697027757438170153763220190E-6), + L(2.009103660938497963095652951912071336730E-4), + L(3.220543385492643525985862356352195896964E-3), + L(2.774405975730545157543417650436941650990E-2), + L(1.258114008023826384487378016636555041129E-1), + L(2.811724258266902502344701449984698323860E-1), + L(2.691837665193548059322831687432415014067E-1), + L(7.949087384900985370683770525312735605034E-2), + L(1.229509543620976530030153018986910810747E-3), +}; +#define NQ3r2_4D 9 +static const _Float128 Q3r2_4D[NQ3r2_4D + 1] = { + L(8.364260446128475461539941389210166156568E-9), + L(1.451301850638956578622154585560759862764E-6), + L(9.431830010924603664244578867057141839463E-5), + L(3.004105101667433434196388593004526182741E-3), + L(5.148157397848271739710011717102773780221E-2), + L(4.901089301726939576055285374953887874895E-1), + L(2.581760991981709901216967665934142240346E0), + L(7.257105880775059281391729708630912791847E0), + L(1.006014717326362868007913423810737369312E1), + L(5.879416600465399514404064187445293212470E0), + /* 1.000000000000000000000000000000000000000E0*/ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + Peak relative error 3.8e-36 + 0.3125 <= 1/x <= 0.375 */ +#define NQ2r7_3r2N 9 +static const _Float128 Q2r7_3r2N[NQ2r7_3r2N + 1] = { + L(7.584861620402450302063691901886141875454E-8), + L(9.300939338814216296064659459966041794591E-6), + L(4.112108906197521696032158235392604947895E-4), + L(8.515168851578898791897038357239630654431E-3), + L(8.971286321017307400142720556749573229058E-2), + L(4.885856732902956303343015636331874194498E-1), + L(1.334506268733103291656253500506406045846E0), + L(1.681207956863028164179042145803851824654E0), + L(8.165042692571721959157677701625853772271E-1), + L(9.805848115375053300608712721986235900715E-2), +}; +#define NQ2r7_3r2D 9 +static const _Float128 Q2r7_3r2D[NQ2r7_3r2D + 1] = { + L(1.035586492113036586458163971239438078160E-6), + L(1.301999337731768381683593636500979713689E-4), + L(5.993695702564527062553071126719088859654E-3), + L(1.321184892887881883489141186815457808785E-1), + L(1.528766555485015021144963194165165083312E0), + L(9.561463309176490874525827051566494939295E0), + L(3.203719484883967351729513662089163356911E1), + L(5.497294687660930446641539152123568668447E1), + L(4.391158169390578768508675452986948391118E1), + L(1.347836630730048077907818943625789418378E1), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + Peak relative error 2.2e-35 + 0.375 <= 1/x <= 0.4375 */ +#define NQ2r3_2r7N 9 +static const _Float128 Q2r3_2r7N[NQ2r3_2r7N + 1] = { + L(4.455027774980750211349941766420190722088E-7), + L(4.031998274578520170631601850866780366466E-5), + L(1.273987274325947007856695677491340636339E-3), + L(1.818754543377448509897226554179659122873E-2), + L(1.266748858326568264126353051352269875352E-1), + L(4.327578594728723821137731555139472880414E-1), + L(6.892532471436503074928194969154192615359E-1), + L(4.490775818438716873422163588640262036506E-1), + L(8.649615949297322440032000346117031581572E-2), + L(7.261345286655345047417257611469066147561E-4), +}; +#define NQ2r3_2r7D 8 +static const _Float128 Q2r3_2r7D[NQ2r3_2r7D + 1] = { + L(6.082600739680555266312417978064954793142E-6), + L(5.693622538165494742945717226571441747567E-4), + L(1.901625907009092204458328768129666975975E-2), + L(2.958689532697857335456896889409923371570E-1), + L(2.343124711045660081603809437993368799568E0), + L(9.665894032187458293568704885528192804376E0), + L(2.035273104990617136065743426322454881353E1), + L(2.044102010478792896815088858740075165531E1), + L(8.445937177863155827844146643468706599304E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + Peak relative error 3.1e-36 + 0.4375 <= 1/x <= 0.5 */ +#define NQ2_2r3N 9 +static const _Float128 Q2_2r3N[NQ2_2r3N + 1] = { + L(2.817566786579768804844367382809101929314E-6), + L(2.122772176396691634147024348373539744935E-4), + L(5.501378031780457828919593905395747517585E-3), + L(6.355374424341762686099147452020466524659E-2), + L(3.539652320122661637429658698954748337223E-1), + L(9.571721066119617436343740541777014319695E-1), + L(1.196258777828426399432550698612171955305E0), + L(6.069388659458926158392384709893753793967E-1), + L(9.026746127269713176512359976978248763621E-2), + L(5.317668723070450235320878117210807236375E-4), +}; +#define NQ2_2r3D 8 +static const _Float128 Q2_2r3D[NQ2_2r3D + 1] = { + L(3.846924354014260866793741072933159380158E-5), + L(3.017562820057704325510067178327449946763E-3), + L(8.356305620686867949798885808540444210935E-2), + L(1.068314930499906838814019619594424586273E0), + L(6.900279623894821067017966573640732685233E0), + L(2.307667390886377924509090271780839563141E1), + L(3.921043465412723970791036825401273528513E1), + L(3.167569478939719383241775717095729233436E1), + L(1.051023841699200920276198346301543665909E1), + /* 1.000000000000000000000000000000000000000E0*/ +}; + + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static _Float128 +neval (_Float128 x, const _Float128 *p, int n) +{ + _Float128 y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static _Float128 +deval (_Float128 x, const _Float128 *p, int n) +{ + _Float128 y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Bessel function of the first kind, order zero. */ + +_Float128 +__ieee754_j0l (_Float128 x) +{ + _Float128 xx, xinv, z, p, q, c, s, cc, ss; + + if (! isfinite (x)) + { + if (x != x) + return x + x; + else + return 0; + } + if (x == 0) + return 1; + + xx = fabsl (x); + if (xx <= 2) + { + if (xx < L(0x1p-57)) + return 1; + /* 0 <= x <= 2 */ + z = xx * xx; + p = z * z * neval (z, J0_2N, NJ0_2N) / deval (z, J0_2D, NJ0_2D); + p -= L(0.25) * z; + p += 1; + return p; + } + + /* X = x - pi/4 + cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4) + = 1/sqrt(2) * (cos(x) + sin(x)) + sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4) + = 1/sqrt(2) * (sin(x) - cos(x)) + sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + cf. Fdlibm. */ + __sincosl (xx, &s, &c); + ss = s - c; + cc = s + c; + if (xx <= LDBL_MAX / 2) + { + z = -__cosl (xx + xx); + if ((s * c) < 0) + cc = z / ss; + else + ss = z / cc; + } + + if (xx > L(0x1p256)) + return ONEOSQPI * cc / __ieee754_sqrtl (xx); + + xinv = 1 / xx; + z = xinv * xinv; + if (xinv <= 0.25) + { + if (xinv <= 0.125) + { + if (xinv <= 0.0625) + { + p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID); + q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID); + } + else + { + p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D); + q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D); + } + } + else if (xinv <= 0.1875) + { + p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D); + q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D); + } + else + { + p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D); + q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D); + } + } /* .25 */ + else /* if (xinv <= 0.5) */ + { + if (xinv <= 0.375) + { + if (xinv <= 0.3125) + { + p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D); + q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D); + } + else + { + p = neval (z, P2r7_3r2N, NP2r7_3r2N) + / deval (z, P2r7_3r2D, NP2r7_3r2D); + q = neval (z, Q2r7_3r2N, NQ2r7_3r2N) + / deval (z, Q2r7_3r2D, NQ2r7_3r2D); + } + } + else if (xinv <= 0.4375) + { + p = neval (z, P2r3_2r7N, NP2r3_2r7N) + / deval (z, P2r3_2r7D, NP2r3_2r7D); + q = neval (z, Q2r3_2r7N, NQ2r3_2r7N) + / deval (z, Q2r3_2r7D, NQ2r3_2r7D); + } + else + { + p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D); + q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D); + } + } + p = 1 + z * p; + q = z * xinv * q; + q = q - L(0.125) * xinv; + z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx); + return z; +} +strong_alias (__ieee754_j0l, __j0l_finite) + + +/* Y0(x) = 2/pi * log(x) * J0(x) + R(x^2) + Peak absolute error 1.7e-36 (relative where Y0 > 1) + 0 <= x <= 2 */ +#define NY0_2N 7 +static _Float128 Y0_2N[NY0_2N + 1] = { + L(-1.062023609591350692692296993537002558155E19), + L(2.542000883190248639104127452714966858866E19), + L(-1.984190771278515324281415820316054696545E18), + L(4.982586044371592942465373274440222033891E16), + L(-5.529326354780295177243773419090123407550E14), + L(3.013431465522152289279088265336861140391E12), + L(-7.959436160727126750732203098982718347785E9), + L(8.230845651379566339707130644134372793322E6), +}; +#define NY0_2D 7 +static _Float128 Y0_2D[NY0_2D + 1] = { + L(1.438972634353286978700329883122253752192E20), + L(1.856409101981569254247700169486907405500E18), + L(1.219693352678218589553725579802986255614E16), + L(5.389428943282838648918475915779958097958E13), + L(1.774125762108874864433872173544743051653E11), + L(4.522104832545149534808218252434693007036E8), + L(8.872187401232943927082914504125234454930E5), + L(1.251945613186787532055610876304669413955E3), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +static const _Float128 U0 = L(-7.3804295108687225274343927948483016310862e-02); + +/* Bessel function of the second kind, order zero. */ + +_Float128 + __ieee754_y0l(_Float128 x) +{ + _Float128 xx, xinv, z, p, q, c, s, cc, ss; + + if (! isfinite (x)) + return 1 / (x + x * x); + if (x <= 0) + { + if (x < 0) + return (zero / (zero * x)); + return -1 / zero; /* -inf and divide by zero exception. */ + } + xx = fabsl (x); + if (xx <= 0x1p-57) + return U0 + TWOOPI * __ieee754_logl (x); + if (xx <= 2) + { + /* 0 <= x <= 2 */ + z = xx * xx; + p = neval (z, Y0_2N, NY0_2N) / deval (z, Y0_2D, NY0_2D); + p = TWOOPI * __ieee754_logl (x) * __ieee754_j0l (x) + p; + return p; + } + + /* X = x - pi/4 + cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4) + = 1/sqrt(2) * (cos(x) + sin(x)) + sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4) + = 1/sqrt(2) * (sin(x) - cos(x)) + sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + cf. Fdlibm. */ + __sincosl (x, &s, &c); + ss = s - c; + cc = s + c; + if (xx <= LDBL_MAX / 2) + { + z = -__cosl (x + x); + if ((s * c) < 0) + cc = z / ss; + else + ss = z / cc; + } + + if (xx > L(0x1p256)) + return ONEOSQPI * ss / __ieee754_sqrtl (x); + + xinv = 1 / xx; + z = xinv * xinv; + if (xinv <= 0.25) + { + if (xinv <= 0.125) + { + if (xinv <= 0.0625) + { + p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID); + q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID); + } + else + { + p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D); + q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D); + } + } + else if (xinv <= 0.1875) + { + p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D); + q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D); + } + else + { + p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D); + q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D); + } + } /* .25 */ + else /* if (xinv <= 0.5) */ + { + if (xinv <= 0.375) + { + if (xinv <= 0.3125) + { + p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D); + q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D); + } + else + { + p = neval (z, P2r7_3r2N, NP2r7_3r2N) + / deval (z, P2r7_3r2D, NP2r7_3r2D); + q = neval (z, Q2r7_3r2N, NQ2r7_3r2N) + / deval (z, Q2r7_3r2D, NQ2r7_3r2D); + } + } + else if (xinv <= 0.4375) + { + p = neval (z, P2r3_2r7N, NP2r3_2r7N) + / deval (z, P2r3_2r7D, NP2r3_2r7D); + q = neval (z, Q2r3_2r7N, NQ2r3_2r7N) + / deval (z, Q2r3_2r7D, NQ2r3_2r7D); + } + else + { + p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D); + q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D); + } + } + p = 1 + z * p; + q = z * xinv * q; + q = q - L(0.125) * xinv; + z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (x); + return z; +} +strong_alias (__ieee754_y0l, __y0l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_j1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_j1l.c new file mode 100644 index 0000000000..6fc69faa3c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_j1l.c @@ -0,0 +1,961 @@ +/* j1l.c + * + * Bessel function of order one + * + * + * + * SYNOPSIS: + * + * long double x, y, j1l(); + * + * y = j1l( x ); + * + * + * + * DESCRIPTION: + * + * Returns Bessel function of first kind, order one of the argument. + * + * The domain is divided into two major intervals [0, 2] and + * (2, infinity). In the first interval the rational approximation is + * J1(x) = .5x + x x^2 R(x^2) + * + * The second interval is further partitioned into eight equal segments + * of 1/x. + * J1(x) = sqrt(2/(pi x)) (P1(x) cos(X) - Q1(x) sin(X)), + * X = x - 3 pi / 4, + * + * and the auxiliary functions are given by + * + * J1(x)cos(X) + Y1(x)sin(X) = sqrt( 2/(pi x)) P1(x), + * P1(x) = 1 + 1/x^2 R(1/x^2) + * + * Y1(x)cos(X) - J1(x)sin(X) = sqrt( 2/(pi x)) Q1(x), + * Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)). + * + * + * + * ACCURACY: + * + * Absolute error: + * arithmetic domain # trials peak rms + * IEEE 0, 30 100000 2.8e-34 2.7e-35 + * + * + */ + +/* y1l.c + * + * Bessel function of the second kind, order one + * + * + * + * SYNOPSIS: + * + * double x, y, y1l(); + * + * y = y1l( x ); + * + * + * + * DESCRIPTION: + * + * Returns Bessel function of the second kind, of order + * one, of the argument. + * + * The domain is divided into two major intervals [0, 2] and + * (2, infinity). In the first interval the rational approximation is + * Y1(x) = 2/pi * (log(x) * J1(x) - 1/x) + x R(x^2) . + * In the second interval the approximation is the same as for J1(x), and + * Y1(x) = sqrt(2/(pi x)) (P1(x) sin(X) + Q1(x) cos(X)), + * X = x - 3 pi / 4. + * + * ACCURACY: + * + * Absolute error, when y0(x) < 1; else relative error: + * + * arithmetic domain # trials peak rms + * IEEE 0, 30 100000 2.7e-34 2.9e-35 + * + */ + +/* Copyright 2001 by Stephen L. Moshier (moshier@na-net.onrl.gov). + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* 1 / sqrt(pi) */ +static const _Float128 ONEOSQPI = L(5.6418958354775628694807945156077258584405E-1); +/* 2 / pi */ +static const _Float128 TWOOPI = L(6.3661977236758134307553505349005744813784E-1); +static const _Float128 zero = 0; + +/* J1(x) = .5x + x x^2 R(x^2) + Peak relative error 1.9e-35 + 0 <= x <= 2 */ +#define NJ0_2N 6 +static const _Float128 J0_2N[NJ0_2N + 1] = { + L(-5.943799577386942855938508697619735179660E16), + L(1.812087021305009192259946997014044074711E15), + L(-2.761698314264509665075127515729146460895E13), + L(2.091089497823600978949389109350658815972E11), + L(-8.546413231387036372945453565654130054307E8), + L(1.797229225249742247475464052741320612261E6), + L(-1.559552840946694171346552770008812083969E3) +}; +#define NJ0_2D 6 +static const _Float128 J0_2D[NJ0_2D + 1] = { + L(9.510079323819108569501613916191477479397E17), + L(1.063193817503280529676423936545854693915E16), + L(5.934143516050192600795972192791775226920E13), + L(2.168000911950620999091479265214368352883E11), + L(5.673775894803172808323058205986256928794E8), + L(1.080329960080981204840966206372671147224E6), + L(1.411951256636576283942477881535283304912E3), + /* 1.000000000000000000000000000000000000000E0L */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + 0 <= 1/x <= .0625 + Peak relative error 3.6e-36 */ +#define NP16_IN 9 +static const _Float128 P16_IN[NP16_IN + 1] = { + L(5.143674369359646114999545149085139822905E-16), + L(4.836645664124562546056389268546233577376E-13), + L(1.730945562285804805325011561498453013673E-10), + L(3.047976856147077889834905908605310585810E-8), + L(2.855227609107969710407464739188141162386E-6), + L(1.439362407936705484122143713643023998457E-4), + L(3.774489768532936551500999699815873422073E-3), + L(4.723962172984642566142399678920790598426E-2), + L(2.359289678988743939925017240478818248735E-1), + L(3.032580002220628812728954785118117124520E-1), +}; +#define NP16_ID 9 +static const _Float128 P16_ID[NP16_ID + 1] = { + L(4.389268795186898018132945193912677177553E-15), + L(4.132671824807454334388868363256830961655E-12), + L(1.482133328179508835835963635130894413136E-9), + L(2.618941412861122118906353737117067376236E-7), + L(2.467854246740858470815714426201888034270E-5), + L(1.257192927368839847825938545925340230490E-3), + L(3.362739031941574274949719324644120720341E-2), + L(4.384458231338934105875343439265370178858E-1), + L(2.412830809841095249170909628197264854651E0), + L(4.176078204111348059102962617368214856874E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + 0.0625 <= 1/x <= 0.125 + Peak relative error 1.9e-36 */ +#define NP8_16N 11 +static const _Float128 P8_16N[NP8_16N + 1] = { + L(2.984612480763362345647303274082071598135E-16), + L(1.923651877544126103941232173085475682334E-13), + L(4.881258879388869396043760693256024307743E-11), + L(6.368866572475045408480898921866869811889E-9), + L(4.684818344104910450523906967821090796737E-7), + L(2.005177298271593587095982211091300382796E-5), + L(4.979808067163957634120681477207147536182E-4), + L(6.946005761642579085284689047091173581127E-3), + L(5.074601112955765012750207555985299026204E-2), + L(1.698599455896180893191766195194231825379E-1), + L(1.957536905259237627737222775573623779638E-1), + L(2.991314703282528370270179989044994319374E-2), +}; +#define NP8_16D 10 +static const _Float128 P8_16D[NP8_16D + 1] = { + L(2.546869316918069202079580939942463010937E-15), + L(1.644650111942455804019788382157745229955E-12), + L(4.185430770291694079925607420808011147173E-10), + L(5.485331966975218025368698195861074143153E-8), + L(4.062884421686912042335466327098932678905E-6), + L(1.758139661060905948870523641319556816772E-4), + L(4.445143889306356207566032244985607493096E-3), + L(6.391901016293512632765621532571159071158E-2), + L(4.933040207519900471177016015718145795434E-1), + L(1.839144086168947712971630337250761842976E0), + L(2.715120873995490920415616716916149586579E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + 0.125 <= 1/x <= 0.1875 + Peak relative error 1.3e-36 */ +#define NP5_8N 10 +static const _Float128 P5_8N[NP5_8N + 1] = { + L(2.837678373978003452653763806968237227234E-12), + L(9.726641165590364928442128579282742354806E-10), + L(1.284408003604131382028112171490633956539E-7), + L(8.524624695868291291250573339272194285008E-6), + L(3.111516908953172249853673787748841282846E-4), + L(6.423175156126364104172801983096596409176E-3), + L(7.430220589989104581004416356260692450652E-2), + L(4.608315409833682489016656279567605536619E-1), + L(1.396870223510964882676225042258855977512E0), + L(1.718500293904122365894630460672081526236E0), + L(5.465927698800862172307352821870223855365E-1) +}; +#define NP5_8D 10 +static const _Float128 P5_8D[NP5_8D + 1] = { + L(2.421485545794616609951168511612060482715E-11), + L(8.329862750896452929030058039752327232310E-9), + L(1.106137992233383429630592081375289010720E-6), + L(7.405786153760681090127497796448503306939E-5), + L(2.740364785433195322492093333127633465227E-3), + L(5.781246470403095224872243564165254652198E-2), + L(6.927711353039742469918754111511109983546E-1), + L(4.558679283460430281188304515922826156690E0), + L(1.534468499844879487013168065728837900009E1), + L(2.313927430889218597919624843161569422745E1), + L(1.194506341319498844336768473218382828637E1), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + Peak relative error 1.4e-36 + 0.1875 <= 1/x <= 0.25 */ +#define NP4_5N 10 +static const _Float128 P4_5N[NP4_5N + 1] = { + L(1.846029078268368685834261260420933914621E-10), + L(3.916295939611376119377869680335444207768E-8), + L(3.122158792018920627984597530935323997312E-6), + L(1.218073444893078303994045653603392272450E-4), + L(2.536420827983485448140477159977981844883E-3), + L(2.883011322006690823959367922241169171315E-2), + L(1.755255190734902907438042414495469810830E-1), + L(5.379317079922628599870898285488723736599E-1), + L(7.284904050194300773890303361501726561938E-1), + L(3.270110346613085348094396323925000362813E-1), + L(1.804473805689725610052078464951722064757E-2), +}; +#define NP4_5D 9 +static const _Float128 P4_5D[NP4_5D + 1] = { + L(1.575278146806816970152174364308980863569E-9), + L(3.361289173657099516191331123405675054321E-7), + L(2.704692281550877810424745289838790693708E-5), + L(1.070854930483999749316546199273521063543E-3), + L(2.282373093495295842598097265627962125411E-2), + L(2.692025460665354148328762368240343249830E-1), + L(1.739892942593664447220951225734811133759E0), + L(5.890727576752230385342377570386657229324E0), + L(9.517442287057841500750256954117735128153E0), + L(6.100616353935338240775363403030137736013E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + Peak relative error 3.0e-36 + 0.25 <= 1/x <= 0.3125 */ +#define NP3r2_4N 9 +static const _Float128 P3r2_4N[NP3r2_4N + 1] = { + L(8.240803130988044478595580300846665863782E-8), + L(1.179418958381961224222969866406483744580E-5), + L(6.179787320956386624336959112503824397755E-4), + L(1.540270833608687596420595830747166658383E-2), + L(1.983904219491512618376375619598837355076E-1), + L(1.341465722692038870390470651608301155565E0), + L(4.617865326696612898792238245990854646057E0), + L(7.435574801812346424460233180412308000587E0), + L(4.671327027414635292514599201278557680420E0), + L(7.299530852495776936690976966995187714739E-1), +}; +#define NP3r2_4D 9 +static const _Float128 P3r2_4D[NP3r2_4D + 1] = { + L(7.032152009675729604487575753279187576521E-7), + L(1.015090352324577615777511269928856742848E-4), + L(5.394262184808448484302067955186308730620E-3), + L(1.375291438480256110455809354836988584325E-1), + L(1.836247144461106304788160919310404376670E0), + L(1.314378564254376655001094503090935880349E1), + L(4.957184590465712006934452500894672343488E1), + L(9.287394244300647738855415178790263465398E1), + L(7.652563275535900609085229286020552768399E1), + L(2.147042473003074533150718117770093209096E1), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + Peak relative error 1.0e-35 + 0.3125 <= 1/x <= 0.375 */ +#define NP2r7_3r2N 9 +static const _Float128 P2r7_3r2N[NP2r7_3r2N + 1] = { + L(4.599033469240421554219816935160627085991E-7), + L(4.665724440345003914596647144630893997284E-5), + L(1.684348845667764271596142716944374892756E-3), + L(2.802446446884455707845985913454440176223E-2), + L(2.321937586453963310008279956042545173930E-1), + L(9.640277413988055668692438709376437553804E-1), + L(1.911021064710270904508663334033003246028E0), + L(1.600811610164341450262992138893970224971E0), + L(4.266299218652587901171386591543457861138E-1), + L(1.316470424456061252962568223251247207325E-2), +}; +#define NP2r7_3r2D 8 +static const _Float128 P2r7_3r2D[NP2r7_3r2D + 1] = { + L(3.924508608545520758883457108453520099610E-6), + L(4.029707889408829273226495756222078039823E-4), + L(1.484629715787703260797886463307469600219E-2), + L(2.553136379967180865331706538897231588685E-1), + L(2.229457223891676394409880026887106228740E0), + L(1.005708903856384091956550845198392117318E1), + L(2.277082659664386953166629360352385889558E1), + L(2.384726835193630788249826630376533988245E1), + L(9.700989749041320895890113781610939632410E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + Peak relative error 1.7e-36 + 0.3125 <= 1/x <= 0.4375 */ +#define NP2r3_2r7N 9 +static const _Float128 P2r3_2r7N[NP2r3_2r7N + 1] = { + L(3.916766777108274628543759603786857387402E-6), + L(3.212176636756546217390661984304645137013E-4), + L(9.255768488524816445220126081207248947118E-3), + L(1.214853146369078277453080641911700735354E-1), + L(7.855163309847214136198449861311404633665E-1), + L(2.520058073282978403655488662066019816540E0), + L(3.825136484837545257209234285382183711466E0), + L(2.432569427554248006229715163865569506873E0), + L(4.877934835018231178495030117729800489743E-1), + L(1.109902737860249670981355149101343427885E-2), +}; +#define NP2r3_2r7D 8 +static const _Float128 P2r3_2r7D[NP2r3_2r7D + 1] = { + L(3.342307880794065640312646341190547184461E-5), + L(2.782182891138893201544978009012096558265E-3), + L(8.221304931614200702142049236141249929207E-2), + L(1.123728246291165812392918571987858010949E0), + L(7.740482453652715577233858317133423434590E0), + L(2.737624677567945952953322566311201919139E1), + L(4.837181477096062403118304137851260715475E1), + L(3.941098643468580791437772701093795299274E1), + L(1.245821247166544627558323920382547533630E1), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + Peak relative error 1.7e-35 + 0.4375 <= 1/x <= 0.5 */ +#define NP2_2r3N 8 +static const _Float128 P2_2r3N[NP2_2r3N + 1] = { + L(3.397930802851248553545191160608731940751E-4), + L(2.104020902735482418784312825637833698217E-2), + L(4.442291771608095963935342749477836181939E-1), + L(4.131797328716583282869183304291833754967E0), + L(1.819920169779026500146134832455189917589E1), + L(3.781779616522937565300309684282401791291E1), + L(3.459605449728864218972931220783543410347E1), + L(1.173594248397603882049066603238568316561E1), + L(9.455702270242780642835086549285560316461E-1), +}; +#define NP2_2r3D 8 +static const _Float128 P2_2r3D[NP2_2r3D + 1] = { + L(2.899568897241432883079888249845707400614E-3), + L(1.831107138190848460767699919531132426356E-1), + L(3.999350044057883839080258832758908825165E0), + L(3.929041535867957938340569419874195303712E1), + L(1.884245613422523323068802689915538908291E2), + L(4.461469948819229734353852978424629815929E2), + L(5.004998753999796821224085972610636347903E2), + L(2.386342520092608513170837883757163414100E2), + L(3.791322528149347975999851588922424189957E1), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + Peak relative error 8.0e-36 + 0 <= 1/x <= .0625 */ +#define NQ16_IN 10 +static const _Float128 Q16_IN[NQ16_IN + 1] = { + L(-3.917420835712508001321875734030357393421E-18), + L(-4.440311387483014485304387406538069930457E-15), + L(-1.951635424076926487780929645954007139616E-12), + L(-4.318256438421012555040546775651612810513E-10), + L(-5.231244131926180765270446557146989238020E-8), + L(-3.540072702902043752460711989234732357653E-6), + L(-1.311017536555269966928228052917534882984E-4), + L(-2.495184669674631806622008769674827575088E-3), + L(-2.141868222987209028118086708697998506716E-2), + L(-6.184031415202148901863605871197272650090E-2), + L(-1.922298704033332356899546792898156493887E-2), +}; +#define NQ16_ID 9 +static const _Float128 Q16_ID[NQ16_ID + 1] = { + L(3.820418034066293517479619763498400162314E-17), + L(4.340702810799239909648911373329149354911E-14), + L(1.914985356383416140706179933075303538524E-11), + L(4.262333682610888819476498617261895474330E-9), + L(5.213481314722233980346462747902942182792E-7), + L(3.585741697694069399299005316809954590558E-5), + L(1.366513429642842006385029778105539457546E-3), + L(2.745282599850704662726337474371355160594E-2), + L(2.637644521611867647651200098449903330074E-1), + L(1.006953426110765984590782655598680488746E0), + /* 1.000000000000000000000000000000000000000E0 */ + }; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + Peak relative error 1.9e-36 + 0.0625 <= 1/x <= 0.125 */ +#define NQ8_16N 11 +static const _Float128 Q8_16N[NQ8_16N + 1] = { + L(-2.028630366670228670781362543615221542291E-17), + L(-1.519634620380959966438130374006858864624E-14), + L(-4.540596528116104986388796594639405114524E-12), + L(-7.085151756671466559280490913558388648274E-10), + L(-6.351062671323970823761883833531546885452E-8), + L(-3.390817171111032905297982523519503522491E-6), + L(-1.082340897018886970282138836861233213972E-4), + L(-2.020120801187226444822977006648252379508E-3), + L(-2.093169910981725694937457070649605557555E-2), + L(-1.092176538874275712359269481414448063393E-1), + L(-2.374790947854765809203590474789108718733E-1), + L(-1.365364204556573800719985118029601401323E-1), +}; +#define NQ8_16D 11 +static const _Float128 Q8_16D[NQ8_16D + 1] = { + L(1.978397614733632533581207058069628242280E-16), + L(1.487361156806202736877009608336766720560E-13), + L(4.468041406888412086042576067133365913456E-11), + L(7.027822074821007443672290507210594648877E-9), + L(6.375740580686101224127290062867976007374E-7), + L(3.466887658320002225888644977076410421940E-5), + L(1.138625640905289601186353909213719596986E-3), + L(2.224470799470414663443449818235008486439E-2), + L(2.487052928527244907490589787691478482358E-1), + L(1.483927406564349124649083853892380899217E0), + L(4.182773513276056975777258788903489507705E0), + L(4.419665392573449746043880892524360870944E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + Peak relative error 1.5e-35 + 0.125 <= 1/x <= 0.1875 */ +#define NQ5_8N 10 +static const _Float128 Q5_8N[NQ5_8N + 1] = { + L(-3.656082407740970534915918390488336879763E-13), + L(-1.344660308497244804752334556734121771023E-10), + L(-1.909765035234071738548629788698150760791E-8), + L(-1.366668038160120210269389551283666716453E-6), + L(-5.392327355984269366895210704976314135683E-5), + L(-1.206268245713024564674432357634540343884E-3), + L(-1.515456784370354374066417703736088291287E-2), + L(-1.022454301137286306933217746545237098518E-1), + L(-3.373438906472495080504907858424251082240E-1), + L(-4.510782522110845697262323973549178453405E-1), + L(-1.549000892545288676809660828213589804884E-1), +}; +#define NQ5_8D 10 +static const _Float128 Q5_8D[NQ5_8D + 1] = { + L(3.565550843359501079050699598913828460036E-12), + L(1.321016015556560621591847454285330528045E-9), + L(1.897542728662346479999969679234270605975E-7), + L(1.381720283068706710298734234287456219474E-5), + L(5.599248147286524662305325795203422873725E-4), + L(1.305442352653121436697064782499122164843E-2), + L(1.750234079626943298160445750078631894985E-1), + L(1.311420542073436520965439883806946678491E0), + L(5.162757689856842406744504211089724926650E0), + L(9.527760296384704425618556332087850581308E0), + L(6.604648207463236667912921642545100248584E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + Peak relative error 1.3e-35 + 0.1875 <= 1/x <= 0.25 */ +#define NQ4_5N 10 +static const _Float128 Q4_5N[NQ4_5N + 1] = { + L(-4.079513568708891749424783046520200903755E-11), + L(-9.326548104106791766891812583019664893311E-9), + L(-8.016795121318423066292906123815687003356E-7), + L(-3.372350544043594415609295225664186750995E-5), + L(-7.566238665947967882207277686375417983917E-4), + L(-9.248861580055565402130441618521591282617E-3), + L(-6.033106131055851432267702948850231270338E-2), + L(-1.966908754799996793730369265431584303447E-1), + L(-2.791062741179964150755788226623462207560E-1), + L(-1.255478605849190549914610121863534191666E-1), + L(-4.320429862021265463213168186061696944062E-3), +}; +#define NQ4_5D 9 +static const _Float128 Q4_5D[NQ4_5D + 1] = { + L(3.978497042580921479003851216297330701056E-10), + L(9.203304163828145809278568906420772246666E-8), + L(8.059685467088175644915010485174545743798E-6), + L(3.490187375993956409171098277561669167446E-4), + L(8.189109654456872150100501732073810028829E-3), + L(1.072572867311023640958725265762483033769E-1), + L(7.790606862409960053675717185714576937994E-1), + L(3.016049768232011196434185423512777656328E0), + L(5.722963851442769787733717162314477949360E0), + L(4.510527838428473279647251350931380867663E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + Peak relative error 2.1e-35 + 0.25 <= 1/x <= 0.3125 */ +#define NQ3r2_4N 9 +static const _Float128 Q3r2_4N[NQ3r2_4N + 1] = { + L(-1.087480809271383885936921889040388133627E-8), + L(-1.690067828697463740906962973479310170932E-6), + L(-9.608064416995105532790745641974762550982E-5), + L(-2.594198839156517191858208513873961837410E-3), + L(-3.610954144421543968160459863048062977822E-2), + L(-2.629866798251843212210482269563961685666E-1), + L(-9.709186825881775885917984975685752956660E-1), + L(-1.667521829918185121727268867619982417317E0), + L(-1.109255082925540057138766105229900943501E0), + L(-1.812932453006641348145049323713469043328E-1), +}; +#define NQ3r2_4D 9 +static const _Float128 Q3r2_4D[NQ3r2_4D + 1] = { + L(1.060552717496912381388763753841473407026E-7), + L(1.676928002024920520786883649102388708024E-5), + L(9.803481712245420839301400601140812255737E-4), + L(2.765559874262309494758505158089249012930E-2), + L(4.117921827792571791298862613287549140706E-1), + L(3.323769515244751267093378361930279161413E0), + L(1.436602494405814164724810151689705353670E1), + L(3.163087869617098638064881410646782408297E1), + L(3.198181264977021649489103980298349589419E1), + L(1.203649258862068431199471076202897823272E1), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + Peak relative error 1.6e-36 + 0.3125 <= 1/x <= 0.375 */ +#define NQ2r7_3r2N 9 +static const _Float128 Q2r7_3r2N[NQ2r7_3r2N + 1] = { + L(-1.723405393982209853244278760171643219530E-7), + L(-2.090508758514655456365709712333460087442E-5), + L(-9.140104013370974823232873472192719263019E-4), + L(-1.871349499990714843332742160292474780128E-2), + L(-1.948930738119938669637865956162512983416E-1), + L(-1.048764684978978127908439526343174139788E0), + L(-2.827714929925679500237476105843643064698E0), + L(-3.508761569156476114276988181329773987314E0), + L(-1.669332202790211090973255098624488308989E0), + L(-1.930796319299022954013840684651016077770E-1), +}; +#define NQ2r7_3r2D 9 +static const _Float128 Q2r7_3r2D[NQ2r7_3r2D + 1] = { + L(1.680730662300831976234547482334347983474E-6), + L(2.084241442440551016475972218719621841120E-4), + L(9.445316642108367479043541702688736295579E-3), + L(2.044637889456631896650179477133252184672E-1), + L(2.316091982244297350829522534435350078205E0), + L(1.412031891783015085196708811890448488865E1), + L(4.583830154673223384837091077279595496149E1), + L(7.549520609270909439885998474045974122261E1), + L(5.697605832808113367197494052388203310638E1), + L(1.601496240876192444526383314589371686234E1), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + Peak relative error 9.5e-36 + 0.375 <= 1/x <= 0.4375 */ +#define NQ2r3_2r7N 9 +static const _Float128 Q2r3_2r7N[NQ2r3_2r7N + 1] = { + L(-8.603042076329122085722385914954878953775E-7), + L(-7.701746260451647874214968882605186675720E-5), + L(-2.407932004380727587382493696877569654271E-3), + L(-3.403434217607634279028110636919987224188E-2), + L(-2.348707332185238159192422084985713102877E-1), + L(-7.957498841538254916147095255700637463207E-1), + L(-1.258469078442635106431098063707934348577E0), + L(-8.162415474676345812459353639449971369890E-1), + L(-1.581783890269379690141513949609572806898E-1), + L(-1.890595651683552228232308756569450822905E-3), +}; +#define NQ2r3_2r7D 8 +static const _Float128 Q2r3_2r7D[NQ2r3_2r7D + 1] = { + L(8.390017524798316921170710533381568175665E-6), + L(7.738148683730826286477254659973968763659E-4), + L(2.541480810958665794368759558791634341779E-2), + L(3.878879789711276799058486068562386244873E-1), + L(3.003783779325811292142957336802456109333E0), + L(1.206480374773322029883039064575464497400E1), + L(2.458414064785315978408974662900438351782E1), + L(2.367237826273668567199042088835448715228E1), + L(9.231451197519171090875569102116321676763E0), + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + Peak relative error 1.4e-36 + 0.4375 <= 1/x <= 0.5 */ +#define NQ2_2r3N 9 +static const _Float128 Q2_2r3N[NQ2_2r3N + 1] = { + L(-5.552507516089087822166822364590806076174E-6), + L(-4.135067659799500521040944087433752970297E-4), + L(-1.059928728869218962607068840646564457980E-2), + L(-1.212070036005832342565792241385459023801E-1), + L(-6.688350110633603958684302153362735625156E-1), + L(-1.793587878197360221340277951304429821582E0), + L(-2.225407682237197485644647380483725045326E0), + L(-1.123402135458940189438898496348239744403E0), + L(-1.679187241566347077204805190763597299805E-1), + L(-1.458550613639093752909985189067233504148E-3), +}; +#define NQ2_2r3D 8 +static const _Float128 Q2_2r3D[NQ2_2r3D + 1] = { + L(5.415024336507980465169023996403597916115E-5), + L(4.179246497380453022046357404266022870788E-3), + L(1.136306384261959483095442402929502368598E-1), + L(1.422640343719842213484515445393284072830E0), + L(8.968786703393158374728850922289204805764E0), + L(2.914542473339246127533384118781216495934E1), + L(4.781605421020380669870197378210457054685E1), + L(3.693865837171883152382820584714795072937E1), + L(1.153220502744204904763115556224395893076E1), + /* 1.000000000000000000000000000000000000000E0 */ +}; + + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static _Float128 +neval (_Float128 x, const _Float128 *p, int n) +{ + _Float128 y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static _Float128 +deval (_Float128 x, const _Float128 *p, int n) +{ + _Float128 y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Bessel function of the first kind, order one. */ + +_Float128 +__ieee754_j1l (_Float128 x) +{ + _Float128 xx, xinv, z, p, q, c, s, cc, ss; + + if (! isfinite (x)) + { + if (x != x) + return x + x; + else + return 0; + } + if (x == 0) + return x; + xx = fabsl (x); + if (xx <= L(0x1p-58)) + { + _Float128 ret = x * L(0.5); + math_check_force_underflow (ret); + if (ret == 0) + __set_errno (ERANGE); + return ret; + } + if (xx <= 2) + { + /* 0 <= x <= 2 */ + z = xx * xx; + p = xx * z * neval (z, J0_2N, NJ0_2N) / deval (z, J0_2D, NJ0_2D); + p += L(0.5) * xx; + if (x < 0) + p = -p; + return p; + } + + /* X = x - 3 pi/4 + cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4) + = 1/sqrt(2) * (-cos(x) + sin(x)) + sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4) + = -1/sqrt(2) * (sin(x) + cos(x)) + cf. Fdlibm. */ + __sincosl (xx, &s, &c); + ss = -s - c; + cc = s - c; + if (xx <= LDBL_MAX / 2) + { + z = __cosl (xx + xx); + if ((s * c) > 0) + cc = z / ss; + else + ss = z / cc; + } + + if (xx > L(0x1p256)) + { + z = ONEOSQPI * cc / __ieee754_sqrtl (xx); + if (x < 0) + z = -z; + return z; + } + + xinv = 1 / xx; + z = xinv * xinv; + if (xinv <= 0.25) + { + if (xinv <= 0.125) + { + if (xinv <= 0.0625) + { + p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID); + q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID); + } + else + { + p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D); + q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D); + } + } + else if (xinv <= 0.1875) + { + p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D); + q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D); + } + else + { + p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D); + q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D); + } + } /* .25 */ + else /* if (xinv <= 0.5) */ + { + if (xinv <= 0.375) + { + if (xinv <= 0.3125) + { + p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D); + q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D); + } + else + { + p = neval (z, P2r7_3r2N, NP2r7_3r2N) + / deval (z, P2r7_3r2D, NP2r7_3r2D); + q = neval (z, Q2r7_3r2N, NQ2r7_3r2N) + / deval (z, Q2r7_3r2D, NQ2r7_3r2D); + } + } + else if (xinv <= 0.4375) + { + p = neval (z, P2r3_2r7N, NP2r3_2r7N) + / deval (z, P2r3_2r7D, NP2r3_2r7D); + q = neval (z, Q2r3_2r7N, NQ2r3_2r7N) + / deval (z, Q2r3_2r7D, NQ2r3_2r7D); + } + else + { + p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D); + q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D); + } + } + p = 1 + z * p; + q = z * q; + q = q * xinv + L(0.375) * xinv; + z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx); + if (x < 0) + z = -z; + return z; +} +strong_alias (__ieee754_j1l, __j1l_finite) + + +/* Y1(x) = 2/pi * (log(x) * J1(x) - 1/x) + x R(x^2) + Peak relative error 6.2e-38 + 0 <= x <= 2 */ +#define NY0_2N 7 +static _Float128 Y0_2N[NY0_2N + 1] = { + L(-6.804415404830253804408698161694720833249E19), + L(1.805450517967019908027153056150465849237E19), + L(-8.065747497063694098810419456383006737312E17), + L(1.401336667383028259295830955439028236299E16), + L(-1.171654432898137585000399489686629680230E14), + L(5.061267920943853732895341125243428129150E11), + L(-1.096677850566094204586208610960870217970E9), + L(9.541172044989995856117187515882879304461E5), +}; +#define NY0_2D 7 +static _Float128 Y0_2D[NY0_2D + 1] = { + L(3.470629591820267059538637461549677594549E20), + L(4.120796439009916326855848107545425217219E18), + L(2.477653371652018249749350657387030814542E16), + L(9.954678543353888958177169349272167762797E13), + L(2.957927997613630118216218290262851197754E11), + L(6.748421382188864486018861197614025972118E8), + L(1.173453425218010888004562071020305709319E6), + L(1.450335662961034949894009554536003377187E3), + /* 1.000000000000000000000000000000000000000E0 */ +}; + + +/* Bessel function of the second kind, order one. */ + +_Float128 +__ieee754_y1l (_Float128 x) +{ + _Float128 xx, xinv, z, p, q, c, s, cc, ss; + + if (! isfinite (x)) + return 1 / (x + x * x); + if (x <= 0) + { + if (x < 0) + return (zero / (zero * x)); + return -1 / zero; /* -inf and divide by zero exception. */ + } + xx = fabsl (x); + if (xx <= 0x1p-114) + { + z = -TWOOPI / x; + if (isinf (z)) + __set_errno (ERANGE); + return z; + } + if (xx <= 2) + { + /* 0 <= x <= 2 */ + SET_RESTORE_ROUNDL (FE_TONEAREST); + z = xx * xx; + p = xx * neval (z, Y0_2N, NY0_2N) / deval (z, Y0_2D, NY0_2D); + p = -TWOOPI / xx + p; + p = TWOOPI * __ieee754_logl (x) * __ieee754_j1l (x) + p; + return p; + } + + /* X = x - 3 pi/4 + cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4) + = 1/sqrt(2) * (-cos(x) + sin(x)) + sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4) + = -1/sqrt(2) * (sin(x) + cos(x)) + cf. Fdlibm. */ + __sincosl (xx, &s, &c); + ss = -s - c; + cc = s - c; + if (xx <= LDBL_MAX / 2) + { + z = __cosl (xx + xx); + if ((s * c) > 0) + cc = z / ss; + else + ss = z / cc; + } + + if (xx > L(0x1p256)) + return ONEOSQPI * ss / __ieee754_sqrtl (xx); + + xinv = 1 / xx; + z = xinv * xinv; + if (xinv <= 0.25) + { + if (xinv <= 0.125) + { + if (xinv <= 0.0625) + { + p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID); + q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID); + } + else + { + p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D); + q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D); + } + } + else if (xinv <= 0.1875) + { + p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D); + q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D); + } + else + { + p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D); + q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D); + } + } /* .25 */ + else /* if (xinv <= 0.5) */ + { + if (xinv <= 0.375) + { + if (xinv <= 0.3125) + { + p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D); + q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D); + } + else + { + p = neval (z, P2r7_3r2N, NP2r7_3r2N) + / deval (z, P2r7_3r2D, NP2r7_3r2D); + q = neval (z, Q2r7_3r2N, NQ2r7_3r2N) + / deval (z, Q2r7_3r2D, NQ2r7_3r2D); + } + } + else if (xinv <= 0.4375) + { + p = neval (z, P2r3_2r7N, NP2r3_2r7N) + / deval (z, P2r3_2r7D, NP2r3_2r7D); + q = neval (z, Q2r3_2r7N, NQ2r3_2r7N) + / deval (z, Q2r3_2r7D, NQ2r3_2r7D); + } + else + { + p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D); + q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D); + } + } + p = 1 + z * p; + q = z * q; + q = q * xinv + L(0.375) * xinv; + z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (xx); + return z; +} +strong_alias (__ieee754_y1l, __y1l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_jnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_jnl.c new file mode 100644 index 0000000000..470631e600 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_jnl.c @@ -0,0 +1,419 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Modifications for 128-bit long double are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* + * __ieee754_jn(n, x), __ieee754_yn(n, x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for n<x, forward recursion us used starting + * from values of j0(x) and j1(x). + * for n>x, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const _Float128 + invsqrtpi = L(5.6418958354775628694807945156077258584405E-1), + two = 2, + one = 1, + zero = 0; + + +_Float128 +__ieee754_jnl (int n, _Float128 x) +{ + u_int32_t se; + int32_t i, ix, sgn; + _Float128 a, b, temp, di, ret; + _Float128 z, w; + ieee854_long_double_shape_type u; + + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + + u.value = x; + se = u.parts32.w0; + ix = se & 0x7fffffff; + + /* if J(n,NaN) is NaN */ + if (ix >= 0x7fff0000) + { + if ((u.parts32.w0 & 0xffff) | u.parts32.w1 | u.parts32.w2 | u.parts32.w3) + return x + x; + } + + if (n < 0) + { + n = -n; + x = -x; + se ^= 0x80000000; + } + if (n == 0) + return (__ieee754_j0l (x)); + if (n == 1) + return (__ieee754_j1l (x)); + sgn = (n & 1) & (se >> 31); /* even n -- 0, odd n -- sign(x) */ + x = fabsl (x); + + { + SET_RESTORE_ROUNDL (FE_TONEAREST); + if (x == 0 || ix >= 0x7fff0000) /* if x is 0 or inf */ + return sgn == 1 ? -zero : zero; + else if ((_Float128) n <= x) + { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + if (ix >= 0x412D0000) + { /* x > 2**302 */ + + /* ??? Could use an expansion for large x here. */ + + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + _Float128 s; + _Float128 c; + __sincosl (x, &s, &c); + switch (n & 3) + { + case 0: + temp = c + s; + break; + case 1: + temp = -c + s; + break; + case 2: + temp = -c - s; + break; + case 3: + temp = c - s; + break; + } + b = invsqrtpi * temp / __ieee754_sqrtl (x); + } + else + { + a = __ieee754_j0l (x); + b = __ieee754_j1l (x); + for (i = 1; i < n; i++) + { + temp = b; + b = b * ((_Float128) (i + i) / x) - a; /* avoid underflow */ + a = temp; + } + } + } + else + { + if (ix < 0x3fc60000) + { /* x < 2**-57 */ + /* x is tiny, return the first Taylor expansion of J(n,x) + * J(n,x) = 1/n!*(x/2)^n - ... + */ + if (n >= 400) /* underflow, result < 10^-4952 */ + b = zero; + else + { + temp = x * 0.5; + b = temp; + for (a = one, i = 2; i <= n; i++) + { + a *= (_Float128) i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b / a; + } + } + else + { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + _Float128 t, v; + _Float128 q0, q1, h, tmp; + int32_t k, m; + w = (n + n) / (_Float128) x; + h = 2 / (_Float128) x; + q0 = w; + z = w + h; + q1 = w * z - 1; + k = 1; + while (q1 < L(1.0e17)) + { + k += 1; + z += h; + tmp = z * q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n + n; + for (t = zero, i = 2 * (n + k); i >= m; i -= 2) + t = one / (i / x - t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two / x; + tmp = tmp * __ieee754_logl (fabsl (v * tmp)); + + if (tmp < L(1.1356523406294143949491931077970765006170e+04)) + { + for (i = n - 1, di = (_Float128) (i + i); i > 0; i--) + { + temp = b; + b *= di; + b = b / x - a; + a = temp; + di -= two; + } + } + else + { + for (i = n - 1, di = (_Float128) (i + i); i > 0; i--) + { + temp = b; + b *= di; + b = b / x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if (b > L(1e100)) + { + a /= b; + t /= b; + b = one; + } + } + } + /* j0() and j1() suffer enormous loss of precision at and + * near zero; however, we know that their zero points never + * coincide, so just choose the one further away from zero. + */ + z = __ieee754_j0l (x); + w = __ieee754_j1l (x); + if (fabsl (z) >= fabsl (w)) + b = (t * z / b); + else + b = (t * w / a); + } + } + if (sgn == 1) + ret = -b; + else + ret = b; + } + if (ret == 0) + { + ret = __copysignl (LDBL_MIN, ret) * LDBL_MIN; + __set_errno (ERANGE); + } + else + math_check_force_underflow (ret); + return ret; +} +strong_alias (__ieee754_jnl, __jnl_finite) + +_Float128 +__ieee754_ynl (int n, _Float128 x) +{ + u_int32_t se; + int32_t i, ix; + int32_t sign; + _Float128 a, b, temp, ret; + ieee854_long_double_shape_type u; + + u.value = x; + se = u.parts32.w0; + ix = se & 0x7fffffff; + + /* if Y(n,NaN) is NaN */ + if (ix >= 0x7fff0000) + { + if ((u.parts32.w0 & 0xffff) | u.parts32.w1 | u.parts32.w2 | u.parts32.w3) + return x + x; + } + if (x <= 0) + { + if (x == 0) + return ((n < 0 && (n & 1) != 0) ? 1 : -1) / L(0.0); + if (se & 0x80000000) + return zero / (zero * x); + } + sign = 1; + if (n < 0) + { + n = -n; + sign = 1 - ((n & 1) << 1); + } + if (n == 0) + return (__ieee754_y0l (x)); + { + SET_RESTORE_ROUNDL (FE_TONEAREST); + if (n == 1) + { + ret = sign * __ieee754_y1l (x); + goto out; + } + if (ix >= 0x7fff0000) + return zero; + if (ix >= 0x412D0000) + { /* x > 2**302 */ + + /* ??? See comment above on the possible futility of this. */ + + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + _Float128 s; + _Float128 c; + __sincosl (x, &s, &c); + switch (n & 3) + { + case 0: + temp = s - c; + break; + case 1: + temp = -s - c; + break; + case 2: + temp = -s + c; + break; + case 3: + temp = s + c; + break; + } + b = invsqrtpi * temp / __ieee754_sqrtl (x); + } + else + { + a = __ieee754_y0l (x); + b = __ieee754_y1l (x); + /* quit if b is -inf */ + u.value = b; + se = u.parts32.w0 & 0xffff0000; + for (i = 1; i < n && se != 0xffff0000; i++) + { + temp = b; + b = ((_Float128) (i + i) / x) * b - a; + u.value = b; + se = u.parts32.w0 & 0xffff0000; + a = temp; + } + } + /* If B is +-Inf, set up errno accordingly. */ + if (! isfinite (b)) + __set_errno (ERANGE); + if (sign > 0) + ret = b; + else + ret = -b; + } + out: + if (isinf (ret)) + ret = __copysignl (LDBL_MAX, ret) * LDBL_MAX; + return ret; +} +strong_alias (__ieee754_ynl, __ynl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_lgammal_r.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_lgammal_r.c new file mode 100644 index 0000000000..bef2601bce --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_lgammal_r.c @@ -0,0 +1,1046 @@ +/* lgammal + * + * Natural logarithm of gamma function + * + * + * + * SYNOPSIS: + * + * long double x, y, lgammal(); + * extern int sgngam; + * + * y = lgammal(x); + * + * + * + * DESCRIPTION: + * + * Returns the base e (2.718...) logarithm of the absolute + * value of the gamma function of the argument. + * The sign (+1 or -1) of the gamma function is returned in a + * global (extern) variable named sgngam. + * + * The positive domain is partitioned into numerous segments for approximation. + * For x > 10, + * log gamma(x) = (x - 0.5) log(x) - x + log sqrt(2 pi) + 1/x R(1/x^2) + * Near the minimum at x = x0 = 1.46... the approximation is + * log gamma(x0 + z) = log gamma(x0) + z^2 P(z)/Q(z) + * for small z. + * Elsewhere between 0 and 10, + * log gamma(n + z) = log gamma(n) + z P(z)/Q(z) + * for various selected n and small z. + * + * The cosecant reflection formula is employed for negative arguments. + * + * + * + * ACCURACY: + * + * + * arithmetic domain # trials peak rms + * Relative error: + * IEEE 10, 30 100000 3.9e-34 9.8e-35 + * IEEE 0, 10 100000 3.8e-34 5.3e-35 + * Absolute error: + * IEEE -10, 0 100000 8.0e-34 8.0e-35 + * IEEE -30, -10 100000 4.4e-34 1.0e-34 + * IEEE -100, 100 100000 1.0e-34 + * + * The absolute error criterion is the same as relative error + * when the function magnitude is greater than one but it is absolute + * when the magnitude is less than one. + * + */ + +/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov> + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +static const _Float128 PIL = L(3.1415926535897932384626433832795028841972E0); +#if LDBL_MANT_DIG == 106 +static const _Float128 MAXLGM = L(0x5.d53649e2d469dbc1f01e99fd66p+1012); +#else +static const _Float128 MAXLGM = L(1.0485738685148938358098967157129705071571E4928); +#endif +static const _Float128 one = 1; +static const _Float128 huge = LDBL_MAX; + +/* log gamma(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x P(1/x^2) + 1/x <= 0.0741 (x >= 13.495...) + Peak relative error 1.5e-36 */ +static const _Float128 ls2pi = L(9.1893853320467274178032973640561763986140E-1); +#define NRASY 12 +static const _Float128 RASY[NRASY + 1] = +{ + L(8.333333333333333333333333333310437112111E-2), + L(-2.777777777777777777777774789556228296902E-3), + L(7.936507936507936507795933938448586499183E-4), + L(-5.952380952380952041799269756378148574045E-4), + L(8.417508417507928904209891117498524452523E-4), + L(-1.917526917481263997778542329739806086290E-3), + L(6.410256381217852504446848671499409919280E-3), + L(-2.955064066900961649768101034477363301626E-2), + L(1.796402955865634243663453415388336954675E-1), + L(-1.391522089007758553455753477688592767741E0), + L(1.326130089598399157988112385013829305510E1), + L(-1.420412699593782497803472576479997819149E2), + L(1.218058922427762808938869872528846787020E3) +}; + + +/* log gamma(x+13) = log gamma(13) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 12.5 <= x+13 <= 13.5 + Peak relative error 1.1e-36 */ +static const _Float128 lgam13a = L(1.9987213134765625E1); +static const _Float128 lgam13b = L(1.3608962611495173623870550785125024484248E-6); +#define NRN13 7 +static const _Float128 RN13[NRN13 + 1] = +{ + L(8.591478354823578150238226576156275285700E11), + L(2.347931159756482741018258864137297157668E11), + L(2.555408396679352028680662433943000804616E10), + L(1.408581709264464345480765758902967123937E9), + L(4.126759849752613822953004114044451046321E7), + L(6.133298899622688505854211579222889943778E5), + L(3.929248056293651597987893340755876578072E3), + L(6.850783280018706668924952057996075215223E0) +}; +#define NRD13 6 +static const _Float128 RD13[NRD13 + 1] = +{ + L(3.401225382297342302296607039352935541669E11), + L(8.756765276918037910363513243563234551784E10), + L(8.873913342866613213078554180987647243903E9), + L(4.483797255342763263361893016049310017973E8), + L(1.178186288833066430952276702931512870676E7), + L(1.519928623743264797939103740132278337476E5), + L(7.989298844938119228411117593338850892311E2) + /* 1.0E0L */ +}; + + +/* log gamma(x+12) = log gamma(12) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 11.5 <= x+12 <= 12.5 + Peak relative error 4.1e-36 */ +static const _Float128 lgam12a = L(1.75023040771484375E1); +static const _Float128 lgam12b = L(3.7687254483392876529072161996717039575982E-6); +#define NRN12 7 +static const _Float128 RN12[NRN12 + 1] = +{ + L(4.709859662695606986110997348630997559137E11), + L(1.398713878079497115037857470168777995230E11), + L(1.654654931821564315970930093932954900867E10), + L(9.916279414876676861193649489207282144036E8), + L(3.159604070526036074112008954113411389879E7), + L(5.109099197547205212294747623977502492861E5), + L(3.563054878276102790183396740969279826988E3), + L(6.769610657004672719224614163196946862747E0) +}; +#define NRD12 6 +static const _Float128 RD12[NRD12 + 1] = +{ + L(1.928167007860968063912467318985802726613E11), + L(5.383198282277806237247492369072266389233E10), + L(5.915693215338294477444809323037871058363E9), + L(3.241438287570196713148310560147925781342E8), + L(9.236680081763754597872713592701048455890E6), + L(1.292246897881650919242713651166596478850E5), + L(7.366532445427159272584194816076600211171E2) + /* 1.0E0L */ +}; + + +/* log gamma(x+11) = log gamma(11) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 10.5 <= x+11 <= 11.5 + Peak relative error 1.8e-35 */ +static const _Float128 lgam11a = L(1.5104400634765625E1); +static const _Float128 lgam11b = L(1.1938309890295225709329251070371882250744E-5); +#define NRN11 7 +static const _Float128 RN11[NRN11 + 1] = +{ + L(2.446960438029415837384622675816736622795E11), + L(7.955444974446413315803799763901729640350E10), + L(1.030555327949159293591618473447420338444E10), + L(6.765022131195302709153994345470493334946E8), + L(2.361892792609204855279723576041468347494E7), + L(4.186623629779479136428005806072176490125E5), + L(3.202506022088912768601325534149383594049E3), + L(6.681356101133728289358838690666225691363E0) +}; +#define NRD11 6 +static const _Float128 RD11[NRD11 + 1] = +{ + L(1.040483786179428590683912396379079477432E11), + L(3.172251138489229497223696648369823779729E10), + L(3.806961885984850433709295832245848084614E9), + L(2.278070344022934913730015420611609620171E8), + L(7.089478198662651683977290023829391596481E6), + L(1.083246385105903533237139380509590158658E5), + L(6.744420991491385145885727942219463243597E2) + /* 1.0E0L */ +}; + + +/* log gamma(x+10) = log gamma(10) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 9.5 <= x+10 <= 10.5 + Peak relative error 5.4e-37 */ +static const _Float128 lgam10a = L(1.280181884765625E1); +static const _Float128 lgam10b = L(8.6324252196112077178745667061642811492557E-6); +#define NRN10 7 +static const _Float128 RN10[NRN10 + 1] = +{ + L(-1.239059737177249934158597996648808363783E14), + L(-4.725899566371458992365624673357356908719E13), + L(-7.283906268647083312042059082837754850808E12), + L(-5.802855515464011422171165179767478794637E11), + L(-2.532349691157548788382820303182745897298E10), + L(-5.884260178023777312587193693477072061820E8), + L(-6.437774864512125749845840472131829114906E6), + L(-2.350975266781548931856017239843273049384E4) +}; +#define NRD10 7 +static const _Float128 RD10[NRD10 + 1] = +{ + L(-5.502645997581822567468347817182347679552E13), + L(-1.970266640239849804162284805400136473801E13), + L(-2.819677689615038489384974042561531409392E12), + L(-2.056105863694742752589691183194061265094E11), + L(-8.053670086493258693186307810815819662078E9), + L(-1.632090155573373286153427982504851867131E8), + L(-1.483575879240631280658077826889223634921E6), + L(-4.002806669713232271615885826373550502510E3) + /* 1.0E0L */ +}; + + +/* log gamma(x+9) = log gamma(9) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 8.5 <= x+9 <= 9.5 + Peak relative error 3.6e-36 */ +static const _Float128 lgam9a = L(1.06045989990234375E1); +static const _Float128 lgam9b = L(3.9037218127284172274007216547549861681400E-6); +#define NRN9 7 +static const _Float128 RN9[NRN9 + 1] = +{ + L(-4.936332264202687973364500998984608306189E13), + L(-2.101372682623700967335206138517766274855E13), + L(-3.615893404644823888655732817505129444195E12), + L(-3.217104993800878891194322691860075472926E11), + L(-1.568465330337375725685439173603032921399E10), + L(-4.073317518162025744377629219101510217761E8), + L(-4.983232096406156139324846656819246974500E6), + L(-2.036280038903695980912289722995505277253E4) +}; +#define NRD9 7 +static const _Float128 RD9[NRD9 + 1] = +{ + L(-2.306006080437656357167128541231915480393E13), + L(-9.183606842453274924895648863832233799950E12), + L(-1.461857965935942962087907301194381010380E12), + L(-1.185728254682789754150068652663124298303E11), + L(-5.166285094703468567389566085480783070037E9), + L(-1.164573656694603024184768200787835094317E8), + L(-1.177343939483908678474886454113163527909E6), + L(-3.529391059783109732159524500029157638736E3) + /* 1.0E0L */ +}; + + +/* log gamma(x+8) = log gamma(8) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 7.5 <= x+8 <= 8.5 + Peak relative error 2.4e-37 */ +static const _Float128 lgam8a = L(8.525146484375E0); +static const _Float128 lgam8b = L(1.4876690414300165531036347125050759667737E-5); +#define NRN8 8 +static const _Float128 RN8[NRN8 + 1] = +{ + L(6.600775438203423546565361176829139703289E11), + L(3.406361267593790705240802723914281025800E11), + L(7.222460928505293914746983300555538432830E10), + L(8.102984106025088123058747466840656458342E9), + L(5.157620015986282905232150979772409345927E8), + L(1.851445288272645829028129389609068641517E7), + L(3.489261702223124354745894067468953756656E5), + L(2.892095396706665774434217489775617756014E3), + L(6.596977510622195827183948478627058738034E0) +}; +#define NRD8 7 +static const _Float128 RD8[NRD8 + 1] = +{ + L(3.274776546520735414638114828622673016920E11), + L(1.581811207929065544043963828487733970107E11), + L(3.108725655667825188135393076860104546416E10), + L(3.193055010502912617128480163681842165730E9), + L(1.830871482669835106357529710116211541839E8), + L(5.790862854275238129848491555068073485086E6), + L(9.305213264307921522842678835618803553589E4), + L(6.216974105861848386918949336819572333622E2) + /* 1.0E0L */ +}; + + +/* log gamma(x+7) = log gamma(7) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 6.5 <= x+7 <= 7.5 + Peak relative error 3.2e-36 */ +static const _Float128 lgam7a = L(6.5792388916015625E0); +static const _Float128 lgam7b = L(1.2320408538495060178292903945321122583007E-5); +#define NRN7 8 +static const _Float128 RN7[NRN7 + 1] = +{ + L(2.065019306969459407636744543358209942213E11), + L(1.226919919023736909889724951708796532847E11), + L(2.996157990374348596472241776917953749106E10), + L(3.873001919306801037344727168434909521030E9), + L(2.841575255593761593270885753992732145094E8), + L(1.176342515359431913664715324652399565551E7), + L(2.558097039684188723597519300356028511547E5), + L(2.448525238332609439023786244782810774702E3), + L(6.460280377802030953041566617300902020435E0) +}; +#define NRD7 7 +static const _Float128 RD7[NRD7 + 1] = +{ + L(1.102646614598516998880874785339049304483E11), + L(6.099297512712715445879759589407189290040E10), + L(1.372898136289611312713283201112060238351E10), + L(1.615306270420293159907951633566635172343E9), + L(1.061114435798489135996614242842561967459E8), + L(3.845638971184305248268608902030718674691E6), + L(7.081730675423444975703917836972720495507E4), + L(5.423122582741398226693137276201344096370E2) + /* 1.0E0L */ +}; + + +/* log gamma(x+6) = log gamma(6) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 5.5 <= x+6 <= 6.5 + Peak relative error 6.2e-37 */ +static const _Float128 lgam6a = L(4.7874908447265625E0); +static const _Float128 lgam6b = L(8.9805548349424770093452324304839959231517E-7); +#define NRN6 8 +static const _Float128 RN6[NRN6 + 1] = +{ + L(-3.538412754670746879119162116819571823643E13), + L(-2.613432593406849155765698121483394257148E13), + L(-8.020670732770461579558867891923784753062E12), + L(-1.322227822931250045347591780332435433420E12), + L(-1.262809382777272476572558806855377129513E11), + L(-7.015006277027660872284922325741197022467E9), + L(-2.149320689089020841076532186783055727299E8), + L(-3.167210585700002703820077565539658995316E6), + L(-1.576834867378554185210279285358586385266E4) +}; +#define NRD6 8 +static const _Float128 RD6[NRD6 + 1] = +{ + L(-2.073955870771283609792355579558899389085E13), + L(-1.421592856111673959642750863283919318175E13), + L(-4.012134994918353924219048850264207074949E12), + L(-6.013361045800992316498238470888523722431E11), + L(-5.145382510136622274784240527039643430628E10), + L(-2.510575820013409711678540476918249524123E9), + L(-6.564058379709759600836745035871373240904E7), + L(-7.861511116647120540275354855221373571536E5), + L(-2.821943442729620524365661338459579270561E3) + /* 1.0E0L */ +}; + + +/* log gamma(x+5) = log gamma(5) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 4.5 <= x+5 <= 5.5 + Peak relative error 3.4e-37 */ +static const _Float128 lgam5a = L(3.17803955078125E0); +static const _Float128 lgam5b = L(1.4279566695619646941601297055408873990961E-5); +#define NRN5 9 +static const _Float128 RN5[NRN5 + 1] = +{ + L(2.010952885441805899580403215533972172098E11), + L(1.916132681242540921354921906708215338584E11), + L(7.679102403710581712903937970163206882492E10), + L(1.680514903671382470108010973615268125169E10), + L(2.181011222911537259440775283277711588410E9), + L(1.705361119398837808244780667539728356096E8), + L(7.792391565652481864976147945997033946360E6), + L(1.910741381027985291688667214472560023819E5), + L(2.088138241893612679762260077783794329559E3), + L(6.330318119566998299106803922739066556550E0) +}; +#define NRD5 8 +static const _Float128 RD5[NRD5 + 1] = +{ + L(1.335189758138651840605141370223112376176E11), + L(1.174130445739492885895466097516530211283E11), + L(4.308006619274572338118732154886328519910E10), + L(8.547402888692578655814445003283720677468E9), + L(9.934628078575618309542580800421370730906E8), + L(6.847107420092173812998096295422311820672E7), + L(2.698552646016599923609773122139463150403E6), + L(5.526516251532464176412113632726150253215E4), + L(4.772343321713697385780533022595450486932E2) + /* 1.0E0L */ +}; + + +/* log gamma(x+4) = log gamma(4) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 3.5 <= x+4 <= 4.5 + Peak relative error 6.7e-37 */ +static const _Float128 lgam4a = L(1.791748046875E0); +static const _Float128 lgam4b = L(1.1422353055000812477358380702272722990692E-5); +#define NRN4 9 +static const _Float128 RN4[NRN4 + 1] = +{ + L(-1.026583408246155508572442242188887829208E13), + L(-1.306476685384622809290193031208776258809E13), + L(-7.051088602207062164232806511992978915508E12), + L(-2.100849457735620004967624442027793656108E12), + L(-3.767473790774546963588549871673843260569E11), + L(-4.156387497364909963498394522336575984206E10), + L(-2.764021460668011732047778992419118757746E9), + L(-1.036617204107109779944986471142938641399E8), + L(-1.895730886640349026257780896972598305443E6), + L(-1.180509051468390914200720003907727988201E4) +}; +#define NRD4 9 +static const _Float128 RD4[NRD4 + 1] = +{ + L(-8.172669122056002077809119378047536240889E12), + L(-9.477592426087986751343695251801814226960E12), + L(-4.629448850139318158743900253637212801682E12), + L(-1.237965465892012573255370078308035272942E12), + L(-1.971624313506929845158062177061297598956E11), + L(-1.905434843346570533229942397763361493610E10), + L(-1.089409357680461419743730978512856675984E9), + L(-3.416703082301143192939774401370222822430E7), + L(-4.981791914177103793218433195857635265295E5), + L(-2.192507743896742751483055798411231453733E3) + /* 1.0E0L */ +}; + + +/* log gamma(x+3) = log gamma(3) + x P(x)/Q(x) + -0.25 <= x <= 0.5 + 2.75 <= x+3 <= 3.5 + Peak relative error 6.0e-37 */ +static const _Float128 lgam3a = L(6.93145751953125E-1); +static const _Float128 lgam3b = L(1.4286068203094172321214581765680755001344E-6); + +#define NRN3 9 +static const _Float128 RN3[NRN3 + 1] = +{ + L(-4.813901815114776281494823863935820876670E11), + L(-8.425592975288250400493910291066881992620E11), + L(-6.228685507402467503655405482985516909157E11), + L(-2.531972054436786351403749276956707260499E11), + L(-6.170200796658926701311867484296426831687E10), + L(-9.211477458528156048231908798456365081135E9), + L(-8.251806236175037114064561038908691305583E8), + L(-4.147886355917831049939930101151160447495E7), + L(-1.010851868928346082547075956946476932162E6), + L(-8.333374463411801009783402800801201603736E3) +}; +#define NRD3 9 +static const _Float128 RD3[NRD3 + 1] = +{ + L(-5.216713843111675050627304523368029262450E11), + L(-8.014292925418308759369583419234079164391E11), + L(-5.180106858220030014546267824392678611990E11), + L(-1.830406975497439003897734969120997840011E11), + L(-3.845274631904879621945745960119924118925E10), + L(-4.891033385370523863288908070309417710903E9), + L(-3.670172254411328640353855768698287474282E8), + L(-1.505316381525727713026364396635522516989E7), + L(-2.856327162923716881454613540575964890347E5), + L(-1.622140448015769906847567212766206894547E3) + /* 1.0E0L */ +}; + + +/* log gamma(x+2.5) = log gamma(2.5) + x P(x)/Q(x) + -0.125 <= x <= 0.25 + 2.375 <= x+2.5 <= 2.75 */ +static const _Float128 lgam2r5a = L(2.8466796875E-1); +static const _Float128 lgam2r5b = L(1.4901722919159632494669682701924320137696E-5); +#define NRN2r5 8 +static const _Float128 RN2r5[NRN2r5 + 1] = +{ + L(-4.676454313888335499356699817678862233205E9), + L(-9.361888347911187924389905984624216340639E9), + L(-7.695353600835685037920815799526540237703E9), + L(-3.364370100981509060441853085968900734521E9), + L(-8.449902011848163568670361316804900559863E8), + L(-1.225249050950801905108001246436783022179E8), + L(-9.732972931077110161639900388121650470926E6), + L(-3.695711763932153505623248207576425983573E5), + L(-4.717341584067827676530426007495274711306E3) +}; +#define NRD2r5 8 +static const _Float128 RD2r5[NRD2r5 + 1] = +{ + L(-6.650657966618993679456019224416926875619E9), + L(-1.099511409330635807899718829033488771623E10), + L(-7.482546968307837168164311101447116903148E9), + L(-2.702967190056506495988922973755870557217E9), + L(-5.570008176482922704972943389590409280950E8), + L(-6.536934032192792470926310043166993233231E7), + L(-4.101991193844953082400035444146067511725E6), + L(-1.174082735875715802334430481065526664020E5), + L(-9.932840389994157592102947657277692978511E2) + /* 1.0E0L */ +}; + + +/* log gamma(x+2) = x P(x)/Q(x) + -0.125 <= x <= +0.375 + 1.875 <= x+2 <= 2.375 + Peak relative error 4.6e-36 */ +#define NRN2 9 +static const _Float128 RN2[NRN2 + 1] = +{ + L(-3.716661929737318153526921358113793421524E9), + L(-1.138816715030710406922819131397532331321E10), + L(-1.421017419363526524544402598734013569950E10), + L(-9.510432842542519665483662502132010331451E9), + L(-3.747528562099410197957514973274474767329E9), + L(-8.923565763363912474488712255317033616626E8), + L(-1.261396653700237624185350402781338231697E8), + L(-9.918402520255661797735331317081425749014E6), + L(-3.753996255897143855113273724233104768831E5), + L(-4.778761333044147141559311805999540765612E3) +}; +#define NRD2 9 +static const _Float128 RD2[NRD2 + 1] = +{ + L(-8.790916836764308497770359421351673950111E9), + L(-2.023108608053212516399197678553737477486E10), + L(-1.958067901852022239294231785363504458367E10), + L(-1.035515043621003101254252481625188704529E10), + L(-3.253884432621336737640841276619272224476E9), + L(-6.186383531162456814954947669274235815544E8), + L(-6.932557847749518463038934953605969951466E7), + L(-4.240731768287359608773351626528479703758E6), + L(-1.197343995089189188078944689846348116630E5), + L(-1.004622911670588064824904487064114090920E3) +/* 1.0E0 */ +}; + + +/* log gamma(x+1.75) = log gamma(1.75) + x P(x)/Q(x) + -0.125 <= x <= +0.125 + 1.625 <= x+1.75 <= 1.875 + Peak relative error 9.2e-37 */ +static const _Float128 lgam1r75a = L(-8.441162109375E-2); +static const _Float128 lgam1r75b = L(1.0500073264444042213965868602268256157604E-5); +#define NRN1r75 8 +static const _Float128 RN1r75[NRN1r75 + 1] = +{ + L(-5.221061693929833937710891646275798251513E7), + L(-2.052466337474314812817883030472496436993E8), + L(-2.952718275974940270675670705084125640069E8), + L(-2.132294039648116684922965964126389017840E8), + L(-8.554103077186505960591321962207519908489E7), + L(-1.940250901348870867323943119132071960050E7), + L(-2.379394147112756860769336400290402208435E6), + L(-1.384060879999526222029386539622255797389E5), + L(-2.698453601378319296159355612094598695530E3) +}; +#define NRD1r75 8 +static const _Float128 RD1r75[NRD1r75 + 1] = +{ + L(-2.109754689501705828789976311354395393605E8), + L(-5.036651829232895725959911504899241062286E8), + L(-4.954234699418689764943486770327295098084E8), + L(-2.589558042412676610775157783898195339410E8), + L(-7.731476117252958268044969614034776883031E7), + L(-1.316721702252481296030801191240867486965E7), + L(-1.201296501404876774861190604303728810836E6), + L(-5.007966406976106636109459072523610273928E4), + L(-6.155817990560743422008969155276229018209E2) + /* 1.0E0L */ +}; + + +/* log gamma(x+x0) = y0 + x^2 P(x)/Q(x) + -0.0867 <= x <= +0.1634 + 1.374932... <= x+x0 <= 1.625032... + Peak relative error 4.0e-36 */ +static const _Float128 x0a = L(1.4616241455078125); +static const _Float128 x0b = L(7.9994605498412626595423257213002588621246E-6); +static const _Float128 y0a = L(-1.21490478515625E-1); +static const _Float128 y0b = L(4.1879797753919044854428223084178486438269E-6); +#define NRN1r5 8 +static const _Float128 RN1r5[NRN1r5 + 1] = +{ + L(6.827103657233705798067415468881313128066E5), + L(1.910041815932269464714909706705242148108E6), + L(2.194344176925978377083808566251427771951E6), + L(1.332921400100891472195055269688876427962E6), + L(4.589080973377307211815655093824787123508E5), + L(8.900334161263456942727083580232613796141E4), + L(9.053840838306019753209127312097612455236E3), + L(4.053367147553353374151852319743594873771E2), + L(5.040631576303952022968949605613514584950E0) +}; +#define NRD1r5 8 +static const _Float128 RD1r5[NRD1r5 + 1] = +{ + L(1.411036368843183477558773688484699813355E6), + L(4.378121767236251950226362443134306184849E6), + L(5.682322855631723455425929877581697918168E6), + L(3.999065731556977782435009349967042222375E6), + L(1.653651390456781293163585493620758410333E6), + L(4.067774359067489605179546964969435858311E5), + L(5.741463295366557346748361781768833633256E4), + L(4.226404539738182992856094681115746692030E3), + L(1.316980975410327975566999780608618774469E2), + /* 1.0E0L */ +}; + + +/* log gamma(x+1.25) = log gamma(1.25) + x P(x)/Q(x) + -.125 <= x <= +.125 + 1.125 <= x+1.25 <= 1.375 + Peak relative error = 4.9e-36 */ +static const _Float128 lgam1r25a = L(-9.82818603515625E-2); +static const _Float128 lgam1r25b = L(1.0023929749338536146197303364159774377296E-5); +#define NRN1r25 9 +static const _Float128 RN1r25[NRN1r25 + 1] = +{ + L(-9.054787275312026472896002240379580536760E4), + L(-8.685076892989927640126560802094680794471E4), + L(2.797898965448019916967849727279076547109E5), + L(6.175520827134342734546868356396008898299E5), + L(5.179626599589134831538516906517372619641E5), + L(2.253076616239043944538380039205558242161E5), + L(5.312653119599957228630544772499197307195E4), + L(6.434329437514083776052669599834938898255E3), + L(3.385414416983114598582554037612347549220E2), + L(4.907821957946273805080625052510832015792E0) +}; +#define NRD1r25 8 +static const _Float128 RD1r25[NRD1r25 + 1] = +{ + L(3.980939377333448005389084785896660309000E5), + L(1.429634893085231519692365775184490465542E6), + L(2.145438946455476062850151428438668234336E6), + L(1.743786661358280837020848127465970357893E6), + L(8.316364251289743923178092656080441655273E5), + L(2.355732939106812496699621491135458324294E5), + L(3.822267399625696880571810137601310855419E4), + L(3.228463206479133236028576845538387620856E3), + L(1.152133170470059555646301189220117965514E2) + /* 1.0E0L */ +}; + + +/* log gamma(x + 1) = x P(x)/Q(x) + 0.0 <= x <= +0.125 + 1.0 <= x+1 <= 1.125 + Peak relative error 1.1e-35 */ +#define NRN1 8 +static const _Float128 RN1[NRN1 + 1] = +{ + L(-9.987560186094800756471055681088744738818E3), + L(-2.506039379419574361949680225279376329742E4), + L(-1.386770737662176516403363873617457652991E4), + L(1.439445846078103202928677244188837130744E4), + L(2.159612048879650471489449668295139990693E4), + L(1.047439813638144485276023138173676047079E4), + L(2.250316398054332592560412486630769139961E3), + L(1.958510425467720733041971651126443864041E2), + L(4.516830313569454663374271993200291219855E0) +}; +#define NRD1 7 +static const _Float128 RD1[NRD1 + 1] = +{ + L(1.730299573175751778863269333703788214547E4), + L(6.807080914851328611903744668028014678148E4), + L(1.090071629101496938655806063184092302439E5), + L(9.124354356415154289343303999616003884080E4), + L(4.262071638655772404431164427024003253954E4), + L(1.096981664067373953673982635805821283581E4), + L(1.431229503796575892151252708527595787588E3), + L(7.734110684303689320830401788262295992921E1) + /* 1.0E0 */ +}; + + +/* log gamma(x + 1) = x P(x)/Q(x) + -0.125 <= x <= 0 + 0.875 <= x+1 <= 1.0 + Peak relative error 7.0e-37 */ +#define NRNr9 8 +static const _Float128 RNr9[NRNr9 + 1] = +{ + L(4.441379198241760069548832023257571176884E5), + L(1.273072988367176540909122090089580368732E6), + L(9.732422305818501557502584486510048387724E5), + L(-5.040539994443998275271644292272870348684E5), + L(-1.208719055525609446357448132109723786736E6), + L(-7.434275365370936547146540554419058907156E5), + L(-2.075642969983377738209203358199008185741E5), + L(-2.565534860781128618589288075109372218042E4), + L(-1.032901669542994124131223797515913955938E3), +}; +#define NRDr9 8 +static const _Float128 RDr9[NRDr9 + 1] = +{ + L(-7.694488331323118759486182246005193998007E5), + L(-3.301918855321234414232308938454112213751E6), + L(-5.856830900232338906742924836032279404702E6), + L(-5.540672519616151584486240871424021377540E6), + L(-3.006530901041386626148342989181721176919E6), + L(-9.350378280513062139466966374330795935163E5), + L(-1.566179100031063346901755685375732739511E5), + L(-1.205016539620260779274902967231510804992E4), + L(-2.724583156305709733221564484006088794284E2) +/* 1.0E0 */ +}; + + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static _Float128 +neval (_Float128 x, const _Float128 *p, int n) +{ + _Float128 y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static _Float128 +deval (_Float128 x, const _Float128 *p, int n) +{ + _Float128 y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +_Float128 +__ieee754_lgammal_r (_Float128 x, int *signgamp) +{ + _Float128 p, q, w, z, nx; + int i, nn; + + *signgamp = 1; + + if (! isfinite (x)) + return x * x; + + if (x == 0) + { + if (signbit (x)) + *signgamp = -1; + } + + if (x < 0) + { + if (x < -2 && x > (LDBL_MANT_DIG == 106 ? -48 : -50)) + return __lgamma_negl (x, signgamp); + q = -x; + p = __floorl (q); + if (p == q) + return (one / __fabsl (p - p)); + _Float128 halfp = p * L(0.5); + if (halfp == __floorl (halfp)) + *signgamp = -1; + else + *signgamp = 1; + if (q < L(0x1p-120)) + return -__logl (q); + z = q - p; + if (z > L(0.5)) + { + p += 1; + z = p - q; + } + z = q * __sinl (PIL * z); + w = __ieee754_lgammal_r (q, &i); + z = __logl (PIL / z) - w; + return (z); + } + + if (x < L(13.5)) + { + p = 0; + nx = __floorl (x + L(0.5)); + nn = nx; + switch (nn) + { + case 0: + /* log gamma (x + 1) = log(x) + log gamma(x) */ + if (x < L(0x1p-120)) + return -__logl (x); + else if (x <= 0.125) + { + p = x * neval (x, RN1, NRN1) / deval (x, RD1, NRD1); + } + else if (x <= 0.375) + { + z = x - L(0.25); + p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25); + p += lgam1r25b; + p += lgam1r25a; + } + else if (x <= 0.625) + { + z = x + (1 - x0a); + z = z - x0b; + p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); + p = p * z * z; + p = p + y0b; + p = p + y0a; + } + else if (x <= 0.875) + { + z = x - L(0.75); + p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75); + p += lgam1r75b; + p += lgam1r75a; + } + else + { + z = x - 1; + p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); + } + p = p - __logl (x); + break; + + case 1: + if (x < L(0.875)) + { + if (x <= 0.625) + { + z = x + (1 - x0a); + z = z - x0b; + p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); + p = p * z * z; + p = p + y0b; + p = p + y0a; + } + else if (x <= 0.875) + { + z = x - L(0.75); + p = z * neval (z, RN1r75, NRN1r75) + / deval (z, RD1r75, NRD1r75); + p += lgam1r75b; + p += lgam1r75a; + } + else + { + z = x - 1; + p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); + } + p = p - __logl (x); + } + else if (x < 1) + { + z = x - 1; + p = z * neval (z, RNr9, NRNr9) / deval (z, RDr9, NRDr9); + } + else if (x == 1) + p = 0; + else if (x <= L(1.125)) + { + z = x - 1; + p = z * neval (z, RN1, NRN1) / deval (z, RD1, NRD1); + } + else if (x <= 1.375) + { + z = x - L(1.25); + p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25); + p += lgam1r25b; + p += lgam1r25a; + } + else + { + /* 1.375 <= x+x0 <= 1.625 */ + z = x - x0a; + z = z - x0b; + p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); + p = p * z * z; + p = p + y0b; + p = p + y0a; + } + break; + + case 2: + if (x < L(1.625)) + { + z = x - x0a; + z = z - x0b; + p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); + p = p * z * z; + p = p + y0b; + p = p + y0a; + } + else if (x < L(1.875)) + { + z = x - L(1.75); + p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75); + p += lgam1r75b; + p += lgam1r75a; + } + else if (x == 2) + p = 0; + else if (x < L(2.375)) + { + z = x - 2; + p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); + } + else + { + z = x - L(2.5); + p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5); + p += lgam2r5b; + p += lgam2r5a; + } + break; + + case 3: + if (x < 2.75) + { + z = x - L(2.5); + p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5); + p += lgam2r5b; + p += lgam2r5a; + } + else + { + z = x - 3; + p = z * neval (z, RN3, NRN3) / deval (z, RD3, NRD3); + p += lgam3b; + p += lgam3a; + } + break; + + case 4: + z = x - 4; + p = z * neval (z, RN4, NRN4) / deval (z, RD4, NRD4); + p += lgam4b; + p += lgam4a; + break; + + case 5: + z = x - 5; + p = z * neval (z, RN5, NRN5) / deval (z, RD5, NRD5); + p += lgam5b; + p += lgam5a; + break; + + case 6: + z = x - 6; + p = z * neval (z, RN6, NRN6) / deval (z, RD6, NRD6); + p += lgam6b; + p += lgam6a; + break; + + case 7: + z = x - 7; + p = z * neval (z, RN7, NRN7) / deval (z, RD7, NRD7); + p += lgam7b; + p += lgam7a; + break; + + case 8: + z = x - 8; + p = z * neval (z, RN8, NRN8) / deval (z, RD8, NRD8); + p += lgam8b; + p += lgam8a; + break; + + case 9: + z = x - 9; + p = z * neval (z, RN9, NRN9) / deval (z, RD9, NRD9); + p += lgam9b; + p += lgam9a; + break; + + case 10: + z = x - 10; + p = z * neval (z, RN10, NRN10) / deval (z, RD10, NRD10); + p += lgam10b; + p += lgam10a; + break; + + case 11: + z = x - 11; + p = z * neval (z, RN11, NRN11) / deval (z, RD11, NRD11); + p += lgam11b; + p += lgam11a; + break; + + case 12: + z = x - 12; + p = z * neval (z, RN12, NRN12) / deval (z, RD12, NRD12); + p += lgam12b; + p += lgam12a; + break; + + case 13: + z = x - 13; + p = z * neval (z, RN13, NRN13) / deval (z, RD13, NRD13); + p += lgam13b; + p += lgam13a; + break; + } + return p; + } + + if (x > MAXLGM) + return (*signgamp * huge * huge); + + if (x > L(0x1p120)) + return x * (__logl (x) - 1); + q = ls2pi - x; + q = (x - L(0.5)) * __logl (x) + q; + if (x > L(1.0e18)) + return (q); + + p = 1 / (x * x); + q += neval (p, RASY, NRASY) / x; + return (q); +} +strong_alias (__ieee754_lgammal_r, __lgammal_r_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_log10l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_log10l.c new file mode 100644 index 0000000000..c992f6e5ee --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_log10l.c @@ -0,0 +1,259 @@ +/* log10l.c + * + * Common logarithm, 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log10l(); + * + * y = log10l( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base 10 logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the logarithm + * of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(x-1)/x+1), + * + * log(x) = z + z^3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.5, 2.0 30000 2.3e-34 4.9e-35 + * IEEE exp(+-10000) 30000 1.0e-34 4.1e-35 + * + * In the tests over the interval exp(+-10000), the logarithms + * of the random arguments were uniformly distributed over + * [-10000, +10000]. + * + */ + +/* + Cephes Math Library Release 2.2: January, 1991 + Copyright 1984, 1991 by Stephen L. Moshier + Adapted for glibc November, 2001 + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see <http://www.gnu.org/licenses/>. + */ + +#include <math.h> +#include <math_private.h> + +/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 5.3e-37, + * relative peak error spread = 2.3e-14 + */ +static const _Float128 P[13] = +{ + L(1.313572404063446165910279910527789794488E4), + L(7.771154681358524243729929227226708890930E4), + L(2.014652742082537582487669938141683759923E5), + L(3.007007295140399532324943111654767187848E5), + L(2.854829159639697837788887080758954924001E5), + L(1.797628303815655343403735250238293741397E5), + L(7.594356839258970405033155585486712125861E4), + L(2.128857716871515081352991964243375186031E4), + L(3.824952356185897735160588078446136783779E3), + L(4.114517881637811823002128927449878962058E2), + L(2.321125933898420063925789532045674660756E1), + L(4.998469661968096229986658302195402690910E-1), + L(1.538612243596254322971797716843006400388E-6) +}; +static const _Float128 Q[12] = +{ + L(3.940717212190338497730839731583397586124E4), + L(2.626900195321832660448791748036714883242E5), + L(7.777690340007566932935753241556479363645E5), + L(1.347518538384329112529391120390701166528E6), + L(1.514882452993549494932585972882995548426E6), + L(1.158019977462989115839826904108208787040E6), + L(6.132189329546557743179177159925690841200E5), + L(2.248234257620569139969141618556349415120E5), + L(5.605842085972455027590989944010492125825E4), + L(9.147150349299596453976674231612674085381E3), + L(9.104928120962988414618126155557301584078E2), + L(4.839208193348159620282142911143429644326E1) +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 1.1e-35, + * relative peak error spread 1.1e-9 + */ +static const _Float128 R[6] = +{ + L(1.418134209872192732479751274970992665513E5), + L(-8.977257995689735303686582344659576526998E4), + L(2.048819892795278657810231591630928516206E4), + L(-2.024301798136027039250415126250455056397E3), + L(8.057002716646055371965756206836056074715E1), + L(-8.828896441624934385266096344596648080902E-1) +}; +static const _Float128 S[6] = +{ + L(1.701761051846631278975701529965589676574E6), + L(-1.332535117259762928288745111081235577029E6), + L(4.001557694070773974936904547424676279307E5), + L(-5.748542087379434595104154610899551484314E4), + L(3.998526750980007367835804959888064681098E3), + L(-1.186359407982897997337150403816839480438E2) +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const _Float128 +/* log10(2) */ +L102A = L(0.3125), +L102B = L(-1.14700043360188047862611052755069732318101185E-2), +/* log10(e) */ +L10EA = L(0.5), +L10EB = L(-6.570551809674817234887108108339491770560299E-2), +/* sqrt(2)/2 */ +SQRTH = L(7.071067811865475244008443621048490392848359E-1); + + + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static _Float128 +neval (_Float128 x, const _Float128 *p, int n) +{ + _Float128 y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static _Float128 +deval (_Float128 x, const _Float128 *p, int n) +{ + _Float128 y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + + +_Float128 +__ieee754_log10l (_Float128 x) +{ + _Float128 z; + _Float128 y; + int e; + int64_t hx, lx; + +/* Test for domain */ + GET_LDOUBLE_WORDS64 (hx, lx, x); + if (((hx & 0x7fffffffffffffffLL) | lx) == 0) + return (-1 / __fabsl (x)); /* log10l(+-0)=-inf */ + if (hx < 0) + return (x - x) / (x - x); + if (hx >= 0x7fff000000000000LL) + return (x + x); + + if (x == 1) + return 0; + +/* separate mantissa from exponent */ + +/* Note, frexp is used so that denormal numbers + * will be handled properly. + */ + x = __frexpl (x, &e); + + +/* logarithm using log(x) = z + z**3 P(z)/Q(z), + * where z = 2(x-1)/x+1) + */ + if ((e > 2) || (e < -2)) + { + if (x < SQRTH) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - L(0.5); + y = L(0.5) * z + L(0.5); + } + else + { /* 2 (x-1)/(x+1) */ + z = x - L(0.5); + z -= L(0.5); + y = L(0.5) * x + L(0.5); + } + x = z / y; + z = x * x; + y = x * (z * neval (z, R, 5) / deval (z, S, 5)); + goto done; + } + + +/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ + + if (x < SQRTH) + { + e -= 1; + x = 2.0 * x - 1; /* 2x - 1 */ + } + else + { + x = x - 1; + } + z = x * x; + y = x * (z * neval (x, P, 12) / deval (x, Q, 11)); + y = y - 0.5 * z; + +done: + + /* Multiply log of fraction by log10(e) + * and base 2 exponent by log10(2). + */ + z = y * L10EB; + z += x * L10EB; + z += e * L102B; + z += y * L10EA; + z += x * L10EA; + z += e * L102A; + return (z); +} +strong_alias (__ieee754_log10l, __log10l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_log2l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_log2l.c new file mode 100644 index 0000000000..cf4a380f16 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_log2l.c @@ -0,0 +1,252 @@ +/* log2l.c + * Base 2 logarithm, 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log2l(); + * + * y = log2l( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base 2 logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the (natural) + * logarithm of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(x-1)/x+1), + * + * log(x) = z + z^3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.5, 2.0 100,000 2.6e-34 4.9e-35 + * IEEE exp(+-10000) 100,000 9.6e-35 4.0e-35 + * + * In the tests over the interval exp(+-10000), the logarithms + * of the random arguments were uniformly distributed over + * [-10000, +10000]. + * + */ + +/* + Cephes Math Library Release 2.2: January, 1991 + Copyright 1984, 1991 by Stephen L. Moshier + Adapted for glibc November, 2001 + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see <http://www.gnu.org/licenses/>. + */ + +#include <math.h> +#include <math_private.h> + +/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 5.3e-37, + * relative peak error spread = 2.3e-14 + */ +static const _Float128 P[13] = +{ + L(1.313572404063446165910279910527789794488E4), + L(7.771154681358524243729929227226708890930E4), + L(2.014652742082537582487669938141683759923E5), + L(3.007007295140399532324943111654767187848E5), + L(2.854829159639697837788887080758954924001E5), + L(1.797628303815655343403735250238293741397E5), + L(7.594356839258970405033155585486712125861E4), + L(2.128857716871515081352991964243375186031E4), + L(3.824952356185897735160588078446136783779E3), + L(4.114517881637811823002128927449878962058E2), + L(2.321125933898420063925789532045674660756E1), + L(4.998469661968096229986658302195402690910E-1), + L(1.538612243596254322971797716843006400388E-6) +}; +static const _Float128 Q[12] = +{ + L(3.940717212190338497730839731583397586124E4), + L(2.626900195321832660448791748036714883242E5), + L(7.777690340007566932935753241556479363645E5), + L(1.347518538384329112529391120390701166528E6), + L(1.514882452993549494932585972882995548426E6), + L(1.158019977462989115839826904108208787040E6), + L(6.132189329546557743179177159925690841200E5), + L(2.248234257620569139969141618556349415120E5), + L(5.605842085972455027590989944010492125825E4), + L(9.147150349299596453976674231612674085381E3), + L(9.104928120962988414618126155557301584078E2), + L(4.839208193348159620282142911143429644326E1) +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 1.1e-35, + * relative peak error spread 1.1e-9 + */ +static const _Float128 R[6] = +{ + L(1.418134209872192732479751274970992665513E5), + L(-8.977257995689735303686582344659576526998E4), + L(2.048819892795278657810231591630928516206E4), + L(-2.024301798136027039250415126250455056397E3), + L(8.057002716646055371965756206836056074715E1), + L(-8.828896441624934385266096344596648080902E-1) +}; +static const _Float128 S[6] = +{ + L(1.701761051846631278975701529965589676574E6), + L(-1.332535117259762928288745111081235577029E6), + L(4.001557694070773974936904547424676279307E5), + L(-5.748542087379434595104154610899551484314E4), + L(3.998526750980007367835804959888064681098E3), + L(-1.186359407982897997337150403816839480438E2) +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const _Float128 +/* log2(e) - 1 */ +LOG2EA = L(4.4269504088896340735992468100189213742664595E-1), +/* sqrt(2)/2 */ +SQRTH = L(7.071067811865475244008443621048490392848359E-1); + + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static _Float128 +neval (_Float128 x, const _Float128 *p, int n) +{ + _Float128 y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static _Float128 +deval (_Float128 x, const _Float128 *p, int n) +{ + _Float128 y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + + +_Float128 +__ieee754_log2l (_Float128 x) +{ + _Float128 z; + _Float128 y; + int e; + int64_t hx, lx; + +/* Test for domain */ + GET_LDOUBLE_WORDS64 (hx, lx, x); + if (((hx & 0x7fffffffffffffffLL) | lx) == 0) + return (-1 / __fabsl (x)); /* log2l(+-0)=-inf */ + if (hx < 0) + return (x - x) / (x - x); + if (hx >= 0x7fff000000000000LL) + return (x + x); + + if (x == 1) + return 0; + +/* separate mantissa from exponent */ + +/* Note, frexp is used so that denormal numbers + * will be handled properly. + */ + x = __frexpl (x, &e); + + +/* logarithm using log(x) = z + z**3 P(z)/Q(z), + * where z = 2(x-1)/x+1) + */ + if ((e > 2) || (e < -2)) + { + if (x < SQRTH) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - L(0.5); + y = L(0.5) * z + L(0.5); + } + else + { /* 2 (x-1)/(x+1) */ + z = x - L(0.5); + z -= L(0.5); + y = L(0.5) * x + L(0.5); + } + x = z / y; + z = x * x; + y = x * (z * neval (z, R, 5) / deval (z, S, 5)); + goto done; + } + + +/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ + + if (x < SQRTH) + { + e -= 1; + x = 2.0 * x - 1; /* 2x - 1 */ + } + else + { + x = x - 1; + } + z = x * x; + y = x * (z * neval (x, P, 12) / deval (x, Q, 11)); + y = y - 0.5 * z; + +done: + +/* Multiply log of fraction by log2(e) + * and base 2 exponent by 1 + */ + z = y * LOG2EA; + z += x * LOG2EA; + z += y; + z += x; + z += e; + return (z); +} +strong_alias (__ieee754_log2l, __log2l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_logl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_logl.c new file mode 100644 index 0000000000..8672047e43 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_logl.c @@ -0,0 +1,282 @@ +/* logll.c + * + * Natural logarithm for 128-bit long double precision. + * + * + * + * SYNOPSIS: + * + * long double x, y, logl(); + * + * y = logl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base e (2.718...) logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. Use of a lookup table increases the speed of the routine. + * The program uses logarithms tabulated at intervals of 1/128 to + * cover the domain from approximately 0.7 to 1.4. + * + * On the interval [-1/128, +1/128] the logarithm of 1+x is approximated by + * log(1+x) = x - 0.5 x^2 + x^3 P(x) . + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.875, 1.125 100000 1.2e-34 4.1e-35 + * IEEE 0.125, 8 100000 1.2e-34 4.1e-35 + * + * + * WARNING: + * + * This program uses integer operations on bit fields of floating-point + * numbers. It does not work with data structures other than the + * structure assumed. + * + */ + +/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov> + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* log(1+x) = x - .5 x^2 + x^3 l(x) + -.0078125 <= x <= +.0078125 + peak relative error 1.2e-37 */ +static const _Float128 +l3 = L(3.333333333333333333333333333333336096926E-1), +l4 = L(-2.499999999999999999999999999486853077002E-1), +l5 = L(1.999999999999999999999999998515277861905E-1), +l6 = L(-1.666666666666666666666798448356171665678E-1), +l7 = L(1.428571428571428571428808945895490721564E-1), +l8 = L(-1.249999999999999987884655626377588149000E-1), +l9 = L(1.111111111111111093947834982832456459186E-1), +l10 = L(-1.000000000000532974938900317952530453248E-1), +l11 = L(9.090909090915566247008015301349979892689E-2), +l12 = L(-8.333333211818065121250921925397567745734E-2), +l13 = L(7.692307559897661630807048686258659316091E-2), +l14 = L(-7.144242754190814657241902218399056829264E-2), +l15 = L(6.668057591071739754844678883223432347481E-2); + +/* Lookup table of ln(t) - (t-1) + t = 0.5 + (k+26)/128) + k = 0, ..., 91 */ +static const _Float128 logtbl[92] = { +L(-5.5345593589352099112142921677820359632418E-2), +L(-5.2108257402767124761784665198737642086148E-2), +L(-4.8991686870576856279407775480686721935120E-2), +L(-4.5993270766361228596215288742353061431071E-2), +L(-4.3110481649613269682442058976885699556950E-2), +L(-4.0340872319076331310838085093194799765520E-2), +L(-3.7682072451780927439219005993827431503510E-2), +L(-3.5131785416234343803903228503274262719586E-2), +L(-3.2687785249045246292687241862699949178831E-2), +L(-3.0347913785027239068190798397055267411813E-2), +L(-2.8110077931525797884641940838507561326298E-2), +L(-2.5972247078357715036426583294246819637618E-2), +L(-2.3932450635346084858612873953407168217307E-2), +L(-2.1988775689981395152022535153795155900240E-2), +L(-2.0139364778244501615441044267387667496733E-2), +L(-1.8382413762093794819267536615342902718324E-2), +L(-1.6716169807550022358923589720001638093023E-2), +L(-1.5138929457710992616226033183958974965355E-2), +L(-1.3649036795397472900424896523305726435029E-2), +L(-1.2244881690473465543308397998034325468152E-2), +L(-1.0924898127200937840689817557742469105693E-2), +L(-9.6875626072830301572839422532631079809328E-3), +L(-8.5313926245226231463436209313499745894157E-3), +L(-7.4549452072765973384933565912143044991706E-3), +L(-6.4568155251217050991200599386801665681310E-3), +L(-5.5356355563671005131126851708522185605193E-3), +L(-4.6900728132525199028885749289712348829878E-3), +L(-3.9188291218610470766469347968659624282519E-3), +L(-3.2206394539524058873423550293617843896540E-3), +L(-2.5942708080877805657374888909297113032132E-3), +L(-2.0385211375711716729239156839929281289086E-3), +L(-1.5522183228760777967376942769773768850872E-3), +L(-1.1342191863606077520036253234446621373191E-3), +L(-7.8340854719967065861624024730268350459991E-4), +L(-4.9869831458030115699628274852562992756174E-4), +L(-2.7902661731604211834685052867305795169688E-4), +L(-1.2335696813916860754951146082826952093496E-4), +L(-3.0677461025892873184042490943581654591817E-5), +#define ZERO logtbl[38] + L(0.0000000000000000000000000000000000000000E0), +L(-3.0359557945051052537099938863236321874198E-5), +L(-1.2081346403474584914595395755316412213151E-4), +L(-2.7044071846562177120083903771008342059094E-4), +L(-4.7834133324631162897179240322783590830326E-4), +L(-7.4363569786340080624467487620270965403695E-4), +L(-1.0654639687057968333207323853366578860679E-3), +L(-1.4429854811877171341298062134712230604279E-3), +L(-1.8753781835651574193938679595797367137975E-3), +L(-2.3618380914922506054347222273705859653658E-3), +L(-2.9015787624124743013946600163375853631299E-3), +L(-3.4938307889254087318399313316921940859043E-3), +L(-4.1378413103128673800485306215154712148146E-3), +L(-4.8328735414488877044289435125365629849599E-3), +L(-5.5782063183564351739381962360253116934243E-3), +L(-6.3731336597098858051938306767880719015261E-3), +L(-7.2169643436165454612058905294782949315193E-3), +L(-8.1090214990427641365934846191367315083867E-3), +L(-9.0486422112807274112838713105168375482480E-3), +L(-1.0035177140880864314674126398350812606841E-2), +L(-1.1067990155502102718064936259435676477423E-2), +L(-1.2146457974158024928196575103115488672416E-2), +L(-1.3269969823361415906628825374158424754308E-2), +L(-1.4437927104692837124388550722759686270765E-2), +L(-1.5649743073340777659901053944852735064621E-2), +L(-1.6904842527181702880599758489058031645317E-2), +L(-1.8202661505988007336096407340750378994209E-2), +L(-1.9542647000370545390701192438691126552961E-2), +L(-2.0924256670080119637427928803038530924742E-2), +L(-2.2346958571309108496179613803760727786257E-2), +L(-2.3810230892650362330447187267648486279460E-2), +L(-2.5313561699385640380910474255652501521033E-2), +L(-2.6856448685790244233704909690165496625399E-2), +L(-2.8438398935154170008519274953860128449036E-2), +L(-3.0058928687233090922411781058956589863039E-2), +L(-3.1717563112854831855692484086486099896614E-2), +L(-3.3413836095418743219397234253475252001090E-2), +L(-3.5147290019036555862676702093393332533702E-2), +L(-3.6917475563073933027920505457688955423688E-2), +L(-3.8723951502862058660874073462456610731178E-2), +L(-4.0566284516358241168330505467000838017425E-2), +L(-4.2444048996543693813649967076598766917965E-2), +L(-4.4356826869355401653098777649745233339196E-2), +L(-4.6304207416957323121106944474331029996141E-2), +L(-4.8285787106164123613318093945035804818364E-2), +L(-5.0301169421838218987124461766244507342648E-2), +L(-5.2349964705088137924875459464622098310997E-2), +L(-5.4431789996103111613753440311680967840214E-2), +L(-5.6546268881465384189752786409400404404794E-2), +L(-5.8693031345788023909329239565012647817664E-2), +L(-6.0871713627532018185577188079210189048340E-2), +L(-6.3081958078862169742820420185833800925568E-2), +L(-6.5323413029406789694910800219643791556918E-2), +L(-6.7595732653791419081537811574227049288168E-2) +}; + +/* ln(2) = ln2a + ln2b with extended precision. */ +static const _Float128 + ln2a = L(6.93145751953125e-1), + ln2b = L(1.4286068203094172321214581765680755001344E-6); + +_Float128 +__ieee754_logl(_Float128 x) +{ + _Float128 z, y, w; + ieee854_long_double_shape_type u, t; + unsigned int m; + int k, e; + + u.value = x; + m = u.parts32.w0; + + /* Check for IEEE special cases. */ + k = m & 0x7fffffff; + /* log(0) = -infinity. */ + if ((k | u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0) + { + return L(-0.5) / ZERO; + } + /* log ( x < 0 ) = NaN */ + if (m & 0x80000000) + { + return (x - x) / ZERO; + } + /* log (infinity or NaN) */ + if (k >= 0x7fff0000) + { + return x + x; + } + + /* Extract exponent and reduce domain to 0.703125 <= u < 1.40625 */ + u.value = __frexpl (x, &e); + m = u.parts32.w0 & 0xffff; + m |= 0x10000; + /* Find lookup table index k from high order bits of the significand. */ + if (m < 0x16800) + { + k = (m - 0xff00) >> 9; + /* t is the argument 0.5 + (k+26)/128 + of the nearest item to u in the lookup table. */ + t.parts32.w0 = 0x3fff0000 + (k << 9); + t.parts32.w1 = 0; + t.parts32.w2 = 0; + t.parts32.w3 = 0; + u.parts32.w0 += 0x10000; + e -= 1; + k += 64; + } + else + { + k = (m - 0xfe00) >> 10; + t.parts32.w0 = 0x3ffe0000 + (k << 10); + t.parts32.w1 = 0; + t.parts32.w2 = 0; + t.parts32.w3 = 0; + } + /* On this interval the table is not used due to cancellation error. */ + if ((x <= L(1.0078125)) && (x >= L(0.9921875))) + { + if (x == 1) + return 0; + z = x - 1; + k = 64; + t.value = 1; + e = 0; + } + else + { + /* log(u) = log( t u/t ) = log(t) + log(u/t) + log(t) is tabulated in the lookup table. + Express log(u/t) = log(1+z), where z = u/t - 1 = (u-t)/t. + cf. Cody & Waite. */ + z = (u.value - t.value) / t.value; + } + /* Series expansion of log(1+z). */ + w = z * z; + y = ((((((((((((l15 * z + + l14) * z + + l13) * z + + l12) * z + + l11) * z + + l10) * z + + l9) * z + + l8) * z + + l7) * z + + l6) * z + + l5) * z + + l4) * z + + l3) * z * w; + y -= 0.5 * w; + y += e * ln2b; /* Base 2 exponent offset times ln(2). */ + y += z; + y += logtbl[k-26]; /* log(t) - (t-1) */ + y += (t.value - 1); + y += e * ln2a; + return y; +} +strong_alias (__ieee754_logl, __logl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_powl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_powl.c new file mode 100644 index 0000000000..a344840090 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_powl.c @@ -0,0 +1,451 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Expansions and modifications for 128-bit long double are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_powl(x,y) return x**y + * + * n + * Method: Let x = 2 * (1+f) + * 1. Compute and return log2(x) in two pieces: + * log2(x) = w1 + w2, + * where w1 has 113-53 = 60 bit trailing zeros. + * 2. Perform y*log2(x) = n+y' by simulating muti-precision + * arithmetic, where |y'|<=0.5. + * 3. Return x**y = 2**n*exp(y'*log2) + * + * Special cases: + * 1. (anything) ** 0 is 1 + * 2. (anything) ** 1 is itself + * 3. (anything) ** NAN is NAN + * 4. NAN ** (anything except 0) is NAN + * 5. +-(|x| > 1) ** +INF is +INF + * 6. +-(|x| > 1) ** -INF is +0 + * 7. +-(|x| < 1) ** +INF is +0 + * 8. +-(|x| < 1) ** -INF is +INF + * 9. +-1 ** +-INF is NAN + * 10. +0 ** (+anything except 0, NAN) is +0 + * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 12. +0 ** (-anything except 0, NAN) is +INF + * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 15. +INF ** (+anything except 0,NAN) is +INF + * 16. +INF ** (-anything except 0,NAN) is +0 + * 17. -INF ** (anything) = -0 ** (-anything) + * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * + */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 bp[] = { + 1, + L(1.5), +}; + +/* log_2(1.5) */ +static const _Float128 dp_h[] = { + 0.0, + L(5.8496250072115607565592654282227158546448E-1) +}; + +/* Low part of log_2(1.5) */ +static const _Float128 dp_l[] = { + 0.0, + L(1.0579781240112554492329533686862998106046E-16) +}; + +static const _Float128 zero = 0, + one = 1, + two = 2, + two113 = L(1.0384593717069655257060992658440192E34), + huge = L(1.0e3000), + tiny = L(1.0e-3000); + +/* 3/2 log x = 3 z + z^3 + z^3 (z^2 R(z^2)) + z = (x-1)/(x+1) + 1 <= x <= 1.25 + Peak relative error 2.3e-37 */ +static const _Float128 LN[] = +{ + L(-3.0779177200290054398792536829702930623200E1), + L(6.5135778082209159921251824580292116201640E1), + L(-4.6312921812152436921591152809994014413540E1), + L(1.2510208195629420304615674658258363295208E1), + L(-9.9266909031921425609179910128531667336670E-1) +}; +static const _Float128 LD[] = +{ + L(-5.129862866715009066465422805058933131960E1), + L(1.452015077564081884387441590064272782044E2), + L(-1.524043275549860505277434040464085593165E2), + L(7.236063513651544224319663428634139768808E1), + L(-1.494198912340228235853027849917095580053E1) + /* 1.0E0 */ +}; + +/* exp(x) = 1 + x - x / (1 - 2 / (x - x^2 R(x^2))) + 0 <= x <= 0.5 + Peak relative error 5.7e-38 */ +static const _Float128 PN[] = +{ + L(5.081801691915377692446852383385968225675E8), + L(9.360895299872484512023336636427675327355E6), + L(4.213701282274196030811629773097579432957E4), + L(5.201006511142748908655720086041570288182E1), + L(9.088368420359444263703202925095675982530E-3), +}; +static const _Float128 PD[] = +{ + L(3.049081015149226615468111430031590411682E9), + L(1.069833887183886839966085436512368982758E8), + L(8.259257717868875207333991924545445705394E5), + L(1.872583833284143212651746812884298360922E3), + /* 1.0E0 */ +}; + +static const _Float128 + /* ln 2 */ + lg2 = L(6.9314718055994530941723212145817656807550E-1), + lg2_h = L(6.9314718055994528622676398299518041312695E-1), + lg2_l = L(2.3190468138462996154948554638754786504121E-17), + ovt = L(8.0085662595372944372e-0017), + /* 2/(3*log(2)) */ + cp = L(9.6179669392597560490661645400126142495110E-1), + cp_h = L(9.6179669392597555432899980587535537779331E-1), + cp_l = L(5.0577616648125906047157785230014751039424E-17); + +_Float128 +__ieee754_powl (_Float128 x, _Float128 y) +{ + _Float128 z, ax, z_h, z_l, p_h, p_l; + _Float128 y1, t1, t2, r, s, sgn, t, u, v, w; + _Float128 s2, s_h, s_l, t_h, t_l, ay; + int32_t i, j, k, yisint, n; + u_int32_t ix, iy; + int32_t hx, hy; + ieee854_long_double_shape_type o, p, q; + + p.value = x; + hx = p.parts32.w0; + ix = hx & 0x7fffffff; + + q.value = y; + hy = q.parts32.w0; + iy = hy & 0x7fffffff; + + + /* y==zero: x**0 = 1 */ + if ((iy | q.parts32.w1 | q.parts32.w2 | q.parts32.w3) == 0 + && !issignaling (x)) + return one; + + /* 1.0**y = 1; -1.0**+-Inf = 1 */ + if (x == one && !issignaling (y)) + return one; + if (x == -1 && iy == 0x7fff0000 + && (q.parts32.w1 | q.parts32.w2 | q.parts32.w3) == 0) + return one; + + /* +-NaN return x+y */ + if ((ix > 0x7fff0000) + || ((ix == 0x7fff0000) + && ((p.parts32.w1 | p.parts32.w2 | p.parts32.w3) != 0)) + || (iy > 0x7fff0000) + || ((iy == 0x7fff0000) + && ((q.parts32.w1 | q.parts32.w2 | q.parts32.w3) != 0))) + return x + y; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if (hx < 0) + { + if (iy >= 0x40700000) /* 2^113 */ + yisint = 2; /* even integer y */ + else if (iy >= 0x3fff0000) /* 1.0 */ + { + if (__floorl (y) == y) + { + z = 0.5 * y; + if (__floorl (z) == z) + yisint = 2; + else + yisint = 1; + } + } + } + + /* special value of y */ + if ((q.parts32.w1 | q.parts32.w2 | q.parts32.w3) == 0) + { + if (iy == 0x7fff0000) /* y is +-inf */ + { + if (((ix - 0x3fff0000) | p.parts32.w1 | p.parts32.w2 | p.parts32.w3) + == 0) + return y - y; /* +-1**inf is NaN */ + else if (ix >= 0x3fff0000) /* (|x|>1)**+-inf = inf,0 */ + return (hy >= 0) ? y : zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy < 0) ? -y : zero; + } + if (iy == 0x3fff0000) + { /* y is +-1 */ + if (hy < 0) + return one / x; + else + return x; + } + if (hy == 0x40000000) + return x * x; /* y is 2 */ + if (hy == 0x3ffe0000) + { /* y is 0.5 */ + if (hx >= 0) /* x >= +0 */ + return __ieee754_sqrtl (x); + } + } + + ax = fabsl (x); + /* special value of x */ + if ((p.parts32.w1 | p.parts32.w2 | p.parts32.w3) == 0) + { + if (ix == 0x7fff0000 || ix == 0 || ix == 0x3fff0000) + { + z = ax; /*x is +-0,+-inf,+-1 */ + if (hy < 0) + z = one / z; /* z = (1/|x|) */ + if (hx < 0) + { + if (((ix - 0x3fff0000) | yisint) == 0) + { + z = (z - z) / (z - z); /* (-1)**non-int is NaN */ + } + else if (yisint == 1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + } + + /* (x<0)**(non-int) is NaN */ + if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0) + return (x - x) / (x - x); + + /* sgn (sign of result -ve**odd) = -1 else = 1 */ + sgn = one; + if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0) + sgn = -one; /* (-ve)**(odd int) */ + + /* |y| is huge. + 2^-16495 = 1/2 of smallest representable value. + If (1 - 1/131072)^y underflows, y > 1.4986e9 */ + if (iy > 0x401d654b) + { + /* if (1 - 2^-113)^y underflows, y > 1.1873e38 */ + if (iy > 0x407d654b) + { + if (ix <= 0x3ffeffff) + return (hy < 0) ? huge * huge : tiny * tiny; + if (ix >= 0x3fff0000) + return (hy > 0) ? huge * huge : tiny * tiny; + } + /* over/underflow if x is not close to one */ + if (ix < 0x3ffeffff) + return (hy < 0) ? sgn * huge * huge : sgn * tiny * tiny; + if (ix > 0x3fff0000) + return (hy > 0) ? sgn * huge * huge : sgn * tiny * tiny; + } + + ay = y > 0 ? y : -y; + if (ay < 0x1p-128) + y = y < 0 ? -0x1p-128 : 0x1p-128; + + n = 0; + /* take care subnormal number */ + if (ix < 0x00010000) + { + ax *= two113; + n -= 113; + o.value = ax; + ix = o.parts32.w0; + } + n += ((ix) >> 16) - 0x3fff; + j = ix & 0x0000ffff; + /* determine interval */ + ix = j | 0x3fff0000; /* normalize ix */ + if (j <= 0x3988) + k = 0; /* |x|<sqrt(3/2) */ + else if (j < 0xbb67) + k = 1; /* |x|<sqrt(3) */ + else + { + k = 0; + n += 1; + ix -= 0x00010000; + } + + o.value = ax; + o.parts32.w0 = ix; + ax = o.value; + + /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ + u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ + v = one / (ax + bp[k]); + s = u * v; + s_h = s; + + o.value = s_h; + o.parts32.w3 = 0; + o.parts32.w2 &= 0xf8000000; + s_h = o.value; + /* t_h=ax+bp[k] High */ + t_h = ax + bp[k]; + o.value = t_h; + o.parts32.w3 = 0; + o.parts32.w2 &= 0xf8000000; + t_h = o.value; + t_l = ax - (t_h - bp[k]); + s_l = v * ((u - s_h * t_h) - s_h * t_l); + /* compute log(ax) */ + s2 = s * s; + u = LN[0] + s2 * (LN[1] + s2 * (LN[2] + s2 * (LN[3] + s2 * LN[4]))); + v = LD[0] + s2 * (LD[1] + s2 * (LD[2] + s2 * (LD[3] + s2 * (LD[4] + s2)))); + r = s2 * s2 * u / v; + r += s_l * (s_h + s); + s2 = s_h * s_h; + t_h = 3.0 + s2 + r; + o.value = t_h; + o.parts32.w3 = 0; + o.parts32.w2 &= 0xf8000000; + t_h = o.value; + t_l = r - ((t_h - 3.0) - s2); + /* u+v = s*(1+...) */ + u = s_h * t_h; + v = s_l * t_h + t_l * s; + /* 2/(3log2)*(s+...) */ + p_h = u + v; + o.value = p_h; + o.parts32.w3 = 0; + o.parts32.w2 &= 0xf8000000; + p_h = o.value; + p_l = v - (p_h - u); + z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l * p_h + p_l * cp + dp_l[k]; + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (_Float128) n; + t1 = (((z_h + z_l) + dp_h[k]) + t); + o.value = t1; + o.parts32.w3 = 0; + o.parts32.w2 &= 0xf8000000; + t1 = o.value; + t2 = z_l - (((t1 - t) - dp_h[k]) - z_h); + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + y1 = y; + o.value = y1; + o.parts32.w3 = 0; + o.parts32.w2 &= 0xf8000000; + y1 = o.value; + p_l = (y - y1) * t1 + y * t2; + p_h = y1 * t1; + z = p_l + p_h; + o.value = z; + j = o.parts32.w0; + if (j >= 0x400d0000) /* z >= 16384 */ + { + /* if z > 16384 */ + if (((j - 0x400d0000) | o.parts32.w1 | o.parts32.w2 | o.parts32.w3) != 0) + return sgn * huge * huge; /* overflow */ + else + { + if (p_l + ovt > z - p_h) + return sgn * huge * huge; /* overflow */ + } + } + else if ((j & 0x7fffffff) >= 0x400d01b9) /* z <= -16495 */ + { + /* z < -16495 */ + if (((j - 0xc00d01bc) | o.parts32.w1 | o.parts32.w2 | o.parts32.w3) + != 0) + return sgn * tiny * tiny; /* underflow */ + else + { + if (p_l <= z - p_h) + return sgn * tiny * tiny; /* underflow */ + } + } + /* compute 2**(p_h+p_l) */ + i = j & 0x7fffffff; + k = (i >> 16) - 0x3fff; + n = 0; + if (i > 0x3ffe0000) + { /* if |z| > 0.5, set n = [z+0.5] */ + n = __floorl (z + L(0.5)); + t = n; + p_h -= t; + } + t = p_l + p_h; + o.value = t; + o.parts32.w3 = 0; + o.parts32.w2 &= 0xf8000000; + t = o.value; + u = t * lg2_h; + v = (p_l - (t - p_h)) * lg2 + t * lg2_l; + z = u + v; + w = v - (z - u); + /* exp(z) */ + t = z * z; + u = PN[0] + t * (PN[1] + t * (PN[2] + t * (PN[3] + t * PN[4]))); + v = PD[0] + t * (PD[1] + t * (PD[2] + t * (PD[3] + t))); + t1 = z - t * u / v; + r = (z * t1) / (t1 - two) - (w + z * w); + z = one - (r - z); + o.value = z; + j = o.parts32.w0; + j += (n << 16); + if ((j >> 16) <= 0) + { + z = __scalbnl (z, n); /* subnormal output */ + _Float128 force_underflow = z * z; + math_force_eval (force_underflow); + } + else + { + o.parts32.w0 = j; + z = o.value; + } + return sgn * z; +} +strong_alias (__ieee754_powl, __powl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_rem_pio2l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_rem_pio2l.c new file mode 100644 index 0000000000..21b440762f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_rem_pio2l.c @@ -0,0 +1,273 @@ +/* Quad-precision floating point argument reduction. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* + * Table of constants for 2/pi, 5628 hexadecimal digits of 2/pi + */ +static const int32_t two_over_pi[] = { +0xa2f983, 0x6e4e44, 0x1529fc, 0x2757d1, 0xf534dd, 0xc0db62, +0x95993c, 0x439041, 0xfe5163, 0xabdebb, 0xc561b7, 0x246e3a, +0x424dd2, 0xe00649, 0x2eea09, 0xd1921c, 0xfe1deb, 0x1cb129, +0xa73ee8, 0x8235f5, 0x2ebb44, 0x84e99c, 0x7026b4, 0x5f7e41, +0x3991d6, 0x398353, 0x39f49c, 0x845f8b, 0xbdf928, 0x3b1ff8, +0x97ffde, 0x05980f, 0xef2f11, 0x8b5a0a, 0x6d1f6d, 0x367ecf, +0x27cb09, 0xb74f46, 0x3f669e, 0x5fea2d, 0x7527ba, 0xc7ebe5, +0xf17b3d, 0x0739f7, 0x8a5292, 0xea6bfb, 0x5fb11f, 0x8d5d08, +0x560330, 0x46fc7b, 0x6babf0, 0xcfbc20, 0x9af436, 0x1da9e3, +0x91615e, 0xe61b08, 0x659985, 0x5f14a0, 0x68408d, 0xffd880, +0x4d7327, 0x310606, 0x1556ca, 0x73a8c9, 0x60e27b, 0xc08c6b, +0x47c419, 0xc367cd, 0xdce809, 0x2a8359, 0xc4768b, 0x961ca6, +0xddaf44, 0xd15719, 0x053ea5, 0xff0705, 0x3f7e33, 0xe832c2, +0xde4f98, 0x327dbb, 0xc33d26, 0xef6b1e, 0x5ef89f, 0x3a1f35, +0xcaf27f, 0x1d87f1, 0x21907c, 0x7c246a, 0xfa6ed5, 0x772d30, +0x433b15, 0xc614b5, 0x9d19c3, 0xc2c4ad, 0x414d2c, 0x5d000c, +0x467d86, 0x2d71e3, 0x9ac69b, 0x006233, 0x7cd2b4, 0x97a7b4, +0xd55537, 0xf63ed7, 0x1810a3, 0xfc764d, 0x2a9d64, 0xabd770, +0xf87c63, 0x57b07a, 0xe71517, 0x5649c0, 0xd9d63b, 0x3884a7, +0xcb2324, 0x778ad6, 0x23545a, 0xb91f00, 0x1b0af1, 0xdfce19, +0xff319f, 0x6a1e66, 0x615799, 0x47fbac, 0xd87f7e, 0xb76522, +0x89e832, 0x60bfe6, 0xcdc4ef, 0x09366c, 0xd43f5d, 0xd7de16, +0xde3b58, 0x929bde, 0x2822d2, 0xe88628, 0x4d58e2, 0x32cac6, +0x16e308, 0xcb7de0, 0x50c017, 0xa71df3, 0x5be018, 0x34132e, +0x621283, 0x014883, 0x5b8ef5, 0x7fb0ad, 0xf2e91e, 0x434a48, +0xd36710, 0xd8ddaa, 0x425fae, 0xce616a, 0xa4280a, 0xb499d3, +0xf2a606, 0x7f775c, 0x83c2a3, 0x883c61, 0x78738a, 0x5a8caf, +0xbdd76f, 0x63a62d, 0xcbbff4, 0xef818d, 0x67c126, 0x45ca55, +0x36d9ca, 0xd2a828, 0x8d61c2, 0x77c912, 0x142604, 0x9b4612, +0xc459c4, 0x44c5c8, 0x91b24d, 0xf31700, 0xad43d4, 0xe54929, +0x10d5fd, 0xfcbe00, 0xcc941e, 0xeece70, 0xf53e13, 0x80f1ec, +0xc3e7b3, 0x28f8c7, 0x940593, 0x3e71c1, 0xb3092e, 0xf3450b, +0x9c1288, 0x7b20ab, 0x9fb52e, 0xc29247, 0x2f327b, 0x6d550c, +0x90a772, 0x1fe76b, 0x96cb31, 0x4a1679, 0xe27941, 0x89dff4, +0x9794e8, 0x84e6e2, 0x973199, 0x6bed88, 0x365f5f, 0x0efdbb, +0xb49a48, 0x6ca467, 0x427271, 0x325d8d, 0xb8159f, 0x09e5bc, +0x25318d, 0x3974f7, 0x1c0530, 0x010c0d, 0x68084b, 0x58ee2c, +0x90aa47, 0x02e774, 0x24d6bd, 0xa67df7, 0x72486e, 0xef169f, +0xa6948e, 0xf691b4, 0x5153d1, 0xf20acf, 0x339820, 0x7e4bf5, +0x6863b2, 0x5f3edd, 0x035d40, 0x7f8985, 0x295255, 0xc06437, +0x10d86d, 0x324832, 0x754c5b, 0xd4714e, 0x6e5445, 0xc1090b, +0x69f52a, 0xd56614, 0x9d0727, 0x50045d, 0xdb3bb4, 0xc576ea, +0x17f987, 0x7d6b49, 0xba271d, 0x296996, 0xacccc6, 0x5414ad, +0x6ae290, 0x89d988, 0x50722c, 0xbea404, 0x940777, 0x7030f3, +0x27fc00, 0xa871ea, 0x49c266, 0x3de064, 0x83dd97, 0x973fa3, +0xfd9443, 0x8c860d, 0xde4131, 0x9d3992, 0x8c70dd, 0xe7b717, +0x3bdf08, 0x2b3715, 0xa0805c, 0x93805a, 0x921110, 0xd8e80f, +0xaf806c, 0x4bffdb, 0x0f9038, 0x761859, 0x15a562, 0xbbcb61, +0xb989c7, 0xbd4010, 0x04f2d2, 0x277549, 0xf6b6eb, 0xbb22db, +0xaa140a, 0x2f2689, 0x768364, 0x333b09, 0x1a940e, 0xaa3a51, +0xc2a31d, 0xaeedaf, 0x12265c, 0x4dc26d, 0x9c7a2d, 0x9756c0, +0x833f03, 0xf6f009, 0x8c402b, 0x99316d, 0x07b439, 0x15200c, +0x5bc3d8, 0xc492f5, 0x4badc6, 0xa5ca4e, 0xcd37a7, 0x36a9e6, +0x9492ab, 0x6842dd, 0xde6319, 0xef8c76, 0x528b68, 0x37dbfc, +0xaba1ae, 0x3115df, 0xa1ae00, 0xdafb0c, 0x664d64, 0xb705ed, +0x306529, 0xbf5657, 0x3aff47, 0xb9f96a, 0xf3be75, 0xdf9328, +0x3080ab, 0xf68c66, 0x15cb04, 0x0622fa, 0x1de4d9, 0xa4b33d, +0x8f1b57, 0x09cd36, 0xe9424e, 0xa4be13, 0xb52333, 0x1aaaf0, +0xa8654f, 0xa5c1d2, 0x0f3f0b, 0xcd785b, 0x76f923, 0x048b7b, +0x721789, 0x53a6c6, 0xe26e6f, 0x00ebef, 0x584a9b, 0xb7dac4, +0xba66aa, 0xcfcf76, 0x1d02d1, 0x2df1b1, 0xc1998c, 0x77adc3, +0xda4886, 0xa05df7, 0xf480c6, 0x2ff0ac, 0x9aecdd, 0xbc5c3f, +0x6dded0, 0x1fc790, 0xb6db2a, 0x3a25a3, 0x9aaf00, 0x9353ad, +0x0457b6, 0xb42d29, 0x7e804b, 0xa707da, 0x0eaa76, 0xa1597b, +0x2a1216, 0x2db7dc, 0xfde5fa, 0xfedb89, 0xfdbe89, 0x6c76e4, +0xfca906, 0x70803e, 0x156e85, 0xff87fd, 0x073e28, 0x336761, +0x86182a, 0xeabd4d, 0xafe7b3, 0x6e6d8f, 0x396795, 0x5bbf31, +0x48d784, 0x16df30, 0x432dc7, 0x356125, 0xce70c9, 0xb8cb30, +0xfd6cbf, 0xa200a4, 0xe46c05, 0xa0dd5a, 0x476f21, 0xd21262, +0x845cb9, 0x496170, 0xe0566b, 0x015299, 0x375550, 0xb7d51e, +0xc4f133, 0x5f6e13, 0xe4305d, 0xa92e85, 0xc3b21d, 0x3632a1, +0xa4b708, 0xd4b1ea, 0x21f716, 0xe4698f, 0x77ff27, 0x80030c, +0x2d408d, 0xa0cd4f, 0x99a520, 0xd3a2b3, 0x0a5d2f, 0x42f9b4, +0xcbda11, 0xd0be7d, 0xc1db9b, 0xbd17ab, 0x81a2ca, 0x5c6a08, +0x17552e, 0x550027, 0xf0147f, 0x8607e1, 0x640b14, 0x8d4196, +0xdebe87, 0x2afdda, 0xb6256b, 0x34897b, 0xfef305, 0x9ebfb9, +0x4f6a68, 0xa82a4a, 0x5ac44f, 0xbcf82d, 0x985ad7, 0x95c7f4, +0x8d4d0d, 0xa63a20, 0x5f57a4, 0xb13f14, 0x953880, 0x0120cc, +0x86dd71, 0xb6dec9, 0xf560bf, 0x11654d, 0x6b0701, 0xacb08c, +0xd0c0b2, 0x485551, 0x0efb1e, 0xc37295, 0x3b06a3, 0x3540c0, +0x7bdc06, 0xcc45e0, 0xfa294e, 0xc8cad6, 0x41f3e8, 0xde647c, +0xd8649b, 0x31bed9, 0xc397a4, 0xd45877, 0xc5e369, 0x13daf0, +0x3c3aba, 0x461846, 0x5f7555, 0xf5bdd2, 0xc6926e, 0x5d2eac, +0xed440e, 0x423e1c, 0x87c461, 0xe9fd29, 0xf3d6e7, 0xca7c22, +0x35916f, 0xc5e008, 0x8dd7ff, 0xe26a6e, 0xc6fdb0, 0xc10893, +0x745d7c, 0xb2ad6b, 0x9d6ecd, 0x7b723e, 0x6a11c6, 0xa9cff7, +0xdf7329, 0xbac9b5, 0x5100b7, 0x0db2e2, 0x24ba74, 0x607de5, +0x8ad874, 0x2c150d, 0x0c1881, 0x94667e, 0x162901, 0x767a9f, +0xbefdfd, 0xef4556, 0x367ed9, 0x13d9ec, 0xb9ba8b, 0xfc97c4, +0x27a831, 0xc36ef1, 0x36c594, 0x56a8d8, 0xb5a8b4, 0x0ecccf, +0x2d8912, 0x34576f, 0x89562c, 0xe3ce99, 0xb920d6, 0xaa5e6b, +0x9c2a3e, 0xcc5f11, 0x4a0bfd, 0xfbf4e1, 0x6d3b8e, 0x2c86e2, +0x84d4e9, 0xa9b4fc, 0xd1eeef, 0xc9352e, 0x61392f, 0x442138, +0xc8d91b, 0x0afc81, 0x6a4afb, 0xd81c2f, 0x84b453, 0x8c994e, +0xcc2254, 0xdc552a, 0xd6c6c0, 0x96190b, 0xb8701a, 0x649569, +0x605a26, 0xee523f, 0x0f117f, 0x11b5f4, 0xf5cbfc, 0x2dbc34, +0xeebc34, 0xcc5de8, 0x605edd, 0x9b8e67, 0xef3392, 0xb817c9, +0x9b5861, 0xbc57e1, 0xc68351, 0x103ed8, 0x4871dd, 0xdd1c2d, +0xa118af, 0x462c21, 0xd7f359, 0x987ad9, 0xc0549e, 0xfa864f, +0xfc0656, 0xae79e5, 0x362289, 0x22ad38, 0xdc9367, 0xaae855, +0x382682, 0x9be7ca, 0xa40d51, 0xb13399, 0x0ed7a9, 0x480569, +0xf0b265, 0xa7887f, 0x974c88, 0x36d1f9, 0xb39221, 0x4a827b, +0x21cf98, 0xdc9f40, 0x5547dc, 0x3a74e1, 0x42eb67, 0xdf9dfe, +0x5fd45e, 0xa4677b, 0x7aacba, 0xa2f655, 0x23882b, 0x55ba41, +0x086e59, 0x862a21, 0x834739, 0xe6e389, 0xd49ee5, 0x40fb49, +0xe956ff, 0xca0f1c, 0x8a59c5, 0x2bfa94, 0xc5c1d3, 0xcfc50f, +0xae5adb, 0x86c547, 0x624385, 0x3b8621, 0x94792c, 0x876110, +0x7b4c2a, 0x1a2c80, 0x12bf43, 0x902688, 0x893c78, 0xe4c4a8, +0x7bdbe5, 0xc23ac4, 0xeaf426, 0x8a67f7, 0xbf920d, 0x2ba365, +0xb1933d, 0x0b7cbd, 0xdc51a4, 0x63dd27, 0xdde169, 0x19949a, +0x9529a8, 0x28ce68, 0xb4ed09, 0x209f44, 0xca984e, 0x638270, +0x237c7e, 0x32b90f, 0x8ef5a7, 0xe75614, 0x08f121, 0x2a9db5, +0x4d7e6f, 0x5119a5, 0xabf9b5, 0xd6df82, 0x61dd96, 0x023616, +0x9f3ac4, 0xa1a283, 0x6ded72, 0x7a8d39, 0xa9b882, 0x5c326b, +0x5b2746, 0xed3400, 0x7700d2, 0x55f4fc, 0x4d5901, 0x8071e0, +0xe13f89, 0xb295f3, 0x64a8f1, 0xaea74b, 0x38fc4c, 0xeab2bb, +0x47270b, 0xabc3a7, 0x34ba60, 0x52dd34, 0xf8563a, 0xeb7e8a, +0x31bb36, 0x5895b7, 0x47f7a9, 0x94c3aa, 0xd39225, 0x1e7f3e, +0xd8974e, 0xbba94f, 0xd8ae01, 0xe661b4, 0x393d8e, 0xa523aa, +0x33068e, 0x1633b5, 0x3bb188, 0x1d3a9d, 0x4013d0, 0xcc1be5, +0xf862e7, 0x3bf28f, 0x39b5bf, 0x0bc235, 0x22747e, 0xa247c0, +0xd52d1f, 0x19add3, 0x9094df, 0x9311d0, 0xb42b25, 0x496db2, +0xe264b2, 0x5ef135, 0x3bc6a4, 0x1a4ad0, 0xaac92e, 0x64e886, +0x573091, 0x982cfb, 0x311b1a, 0x08728b, 0xbdcee1, 0x60e142, +0xeb641d, 0xd0bba3, 0xe559d4, 0x597b8c, 0x2a4483, 0xf332ba, +0xf84867, 0x2c8d1b, 0x2fa9b0, 0x50f3dd, 0xf9f573, 0xdb61b4, +0xfe233e, 0x6c41a6, 0xeea318, 0x775a26, 0xbc5e5c, 0xcea708, +0x94dc57, 0xe20196, 0xf1e839, 0xbe4851, 0x5d2d2f, 0x4e9555, +0xd96ec2, 0xe7d755, 0x6304e0, 0xc02e0e, 0xfc40a0, 0xbbf9b3, +0x7125a7, 0x222dfb, 0xf619d8, 0x838c1c, 0x6619e6, 0xb20d55, +0xbb5137, 0x79e809, 0xaf9149, 0x0d73de, 0x0b0da5, 0xce7f58, +0xac1934, 0x724667, 0x7a1a13, 0x9e26bc, 0x4555e7, 0x585cb5, +0x711d14, 0x486991, 0x480d60, 0x56adab, 0xd62f64, 0x96ee0c, +0x212ff3, 0x5d6d88, 0xa67684, 0x95651e, 0xab9e0a, 0x4ddefe, +0x571010, 0x836a39, 0xf8ea31, 0x9e381d, 0xeac8b1, 0xcac96b, +0x37f21e, 0xd505e9, 0x984743, 0x9fc56c, 0x0331b7, 0x3b8bf8, +0x86e56a, 0x8dc343, 0x6230e7, 0x93cfd5, 0x6a8f2d, 0x733005, +0x1af021, 0xa09fcb, 0x7415a1, 0xd56b23, 0x6ff725, 0x2f4bc7, +0xb8a591, 0x7fac59, 0x5c55de, 0x212c38, 0xb13296, 0x5cff50, +0x366262, 0xfa7b16, 0xf4d9a6, 0x2acfe7, 0xf07403, 0xd4d604, +0x6fd916, 0x31b1bf, 0xcbb450, 0x5bd7c8, 0x0ce194, 0x6bd643, +0x4fd91c, 0xdf4543, 0x5f3453, 0xe2b5aa, 0xc9aec8, 0x131485, +0xf9d2bf, 0xbadb9e, 0x76f5b9, 0xaf15cf, 0xca3182, 0x14b56d, +0xe9fe4d, 0x50fc35, 0xf5aed5, 0xa2d0c1, 0xc96057, 0x192eb6, +0xe91d92, 0x07d144, 0xaea3c6, 0x343566, 0x26d5b4, 0x3161e2, +0x37f1a2, 0x209eff, 0x958e23, 0x493798, 0x35f4a6, 0x4bdc02, +0xc2be13, 0xbe80a0, 0x0b72a3, 0x115c5f, 0x1e1bd1, 0x0db4d3, +0x869e85, 0x96976b, 0x2ac91f, 0x8a26c2, 0x3070f0, 0x041412, +0xfc9fa5, 0xf72a38, 0x9c6878, 0xe2aa76, 0x50cfe1, 0x559274, +0x934e38, 0x0a92f7, 0x5533f0, 0xa63db4, 0x399971, 0xe2b755, +0xa98a7c, 0x008f19, 0xac54d2, 0x2ea0b4, 0xf5f3e0, 0x60c849, +0xffd269, 0xae52ce, 0x7a5fdd, 0xe9ce06, 0xfb0ae8, 0xa50cce, +0xea9d3e, 0x3766dd, 0xb834f5, 0x0da090, 0x846f88, 0x4ae3d5, +0x099a03, 0x2eae2d, 0xfcb40a, 0xfb9b33, 0xe281dd, 0x1b16ba, +0xd8c0af, 0xd96b97, 0xb52dc9, 0x9c277f, 0x5951d5, 0x21ccd6, +0xb6496b, 0x584562, 0xb3baf2, 0xa1a5c4, 0x7ca2cf, 0xa9b93d, +0x7b7b89, 0x483d38, +}; + +static const _Float128 c[] = { +/* 113 bits of pi/2 */ +#define PI_2_1 c[0] + L(0x1.921fb54442d18469898cc51701b8p+0), + +/* pi/2 - PI_2_1 */ +#define PI_2_1t c[1] + L(0x3.9a252049c1114cf98e804177d4c8p-116), +}; + +int32_t __ieee754_rem_pio2l(_Float128 x, _Float128 *y) +{ + _Float128 z, w, t; + double tx[8]; + int64_t exp, n, ix, hx; + u_int64_t lx; + + GET_LDOUBLE_WORDS64 (hx, lx, x); + ix = hx & 0x7fffffffffffffffLL; + if (ix <= 0x3ffe921fb54442d1LL) /* x in <-pi/4, pi/4> */ + { + y[0] = x; + y[1] = 0; + return 0; + } + + if (ix < 0x40002d97c7f3321dLL) /* |x| in <pi/4, 3pi/4) */ + { + if (hx > 0) + { + /* 113 + 113 bit PI is ok */ + z = x - PI_2_1; + y[0] = z - PI_2_1t; + y[1] = (z - y[0]) - PI_2_1t; + return 1; + } + else + { + /* 113 + 113 bit PI is ok */ + z = x + PI_2_1; + y[0] = z + PI_2_1t; + y[1] = (z - y[0]) + PI_2_1t; + return -1; + } + } + + if (ix >= 0x7fff000000000000LL) /* x is +=oo or NaN */ + { + y[0] = x - x; + y[1] = y[0]; + return 0; + } + + /* Handle large arguments. + We split the 113 bits of the mantissa into 5 24bit integers + stored in a double array. */ + exp = (ix >> 48) - 16383 - 23; + + /* This is faster than doing this in floating point, because we + have to convert it to integers anyway and like this we can keep + both integer and floating point units busy. */ + tx [0] = (double)(((ix >> 25) & 0x7fffff) | 0x800000); + tx [1] = (double)((ix >> 1) & 0xffffff); + tx [2] = (double)(((ix << 23) | (lx >> 41)) & 0xffffff); + tx [3] = (double)((lx >> 17) & 0xffffff); + tx [4] = (double)((lx << 7) & 0xffffff); + + n = __kernel_rem_pio2 (tx, tx + 5, exp, ((lx << 7) & 0xffffff) ? 5 : 4, + 3, two_over_pi); + + /* The result is now stored in 3 double values, we need to convert it into + two long double values. */ + t = (_Float128) tx [6] + (_Float128) tx [7]; + w = (_Float128) tx [5]; + + if (hx >= 0) + { + y[0] = w + t; + y[1] = t - (y[0] - w); + return n; + } + else + { + y[0] = -(w + t); + y[1] = -t - (y[0] + w); + return -n; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_remainderl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_remainderl.c new file mode 100644 index 0000000000..c1c196ca9a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_remainderl.c @@ -0,0 +1,71 @@ +/* e_fmodl.c -- long double version of e_fmod.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_remainderl(x,p) + * Return : + * returns x REM p = x - [x/p]*p as if in infinite + * precise arithmetic, where [x/p] is the (infinite bit) + * integer nearest x/p (in half way case choose the even one). + * Method : + * Based on fmodl() return x-[x/p]chopped*p exactlp. + */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 zero = 0; + + +_Float128 +__ieee754_remainderl(_Float128 x, _Float128 p) +{ + int64_t hx,hp; + u_int64_t sx,lx,lp; + _Float128 p_half; + + GET_LDOUBLE_WORDS64(hx,lx,x); + GET_LDOUBLE_WORDS64(hp,lp,p); + sx = hx&0x8000000000000000ULL; + hp &= 0x7fffffffffffffffLL; + hx &= 0x7fffffffffffffffLL; + + /* purge off exception values */ + if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7fff000000000000LL)|| /* x not finite */ + ((hp>=0x7fff000000000000LL)&& /* p is NaN */ + (((hp-0x7fff000000000000LL)|lp)!=0))) + return (x*p)/(x*p); + + + if (hp<=0x7ffdffffffffffffLL) x = __ieee754_fmodl(x,p+p); /* now x < 2p */ + if (((hx-hp)|(lx-lp))==0) return zero*x; + x = fabsl(x); + p = fabsl(p); + if (hp<0x0002000000000000LL) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = L(0.5)*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_LDOUBLE_MSW64(hx,x); + SET_LDOUBLE_MSW64(x,hx^sx); + return x; +} +strong_alias (__ieee754_remainderl, __remainderl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_sinhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_sinhl.c new file mode 100644 index 0000000000..a2b30c2190 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_sinhl.c @@ -0,0 +1,117 @@ +/* e_sinhl.c -- long double version of e_sinh.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Changes for 128-bit long double are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_sinhl(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x) + * 2 + * + * 25 <= x <= lnovft : sinhl(x) := expl(x)/2 + * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2) + * ln2ovft < x : sinhl(x) := x*shuge (overflow) + * + * Special cases: + * sinhl(x) is |x| if x is +INF, -INF, or NaN. + * only sinhl(0)=0 is exact for finite x. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const _Float128 one = 1.0, shuge = L(1.0e4931), +ovf_thresh = L(1.1357216553474703894801348310092223067821E4); + +_Float128 +__ieee754_sinhl (_Float128 x) +{ + _Float128 t, w, h; + u_int32_t jx, ix; + ieee854_long_double_shape_type u; + + /* Words of |x|. */ + u.value = x; + jx = u.parts32.w0; + ix = jx & 0x7fffffff; + + /* x is INF or NaN */ + if (ix >= 0x7fff0000) + return x + x; + + h = 0.5; + if (jx & 0x80000000) + h = -h; + + /* Absolute value of x. */ + u.parts32.w0 = ix; + + /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix <= 0x40044000) + { + if (ix < 0x3fc60000) /* |x| < 2^-57 */ + { + math_check_force_underflow (x); + if (shuge + x > one) + return x; /* sinh(tiny) = tiny with inexact */ + } + t = __expm1l (u.value); + if (ix < 0x3fff0000) + return h * (2.0 * t - t * t / (t + one)); + return h * (t + t / (t + one)); + } + + /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix <= 0x400c62e3) /* 11356.375 */ + return h * __ieee754_expl (u.value); + + /* |x| in [log(maxdouble), overflowthreshold] + Overflow threshold is log(2 * maxdouble). */ + if (u.value <= ovf_thresh) + { + w = __ieee754_expl (0.5 * u.value); + t = h * w; + return t * w; + } + + /* |x| > overflowthreshold, sinhl(x) overflow */ + return x * shuge; +} +strong_alias (__ieee754_sinhl, __sinhl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/gamma_productl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/gamma_productl.c new file mode 100644 index 0000000000..319a45119e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/gamma_productl.c @@ -0,0 +1,45 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_splitl.h> + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +_Float128 +__gamma_productl (_Float128 x, _Float128 x_eps, int n, _Float128 *eps) +{ + SET_RESTORE_ROUNDL (FE_TONEAREST); + _Float128 ret = x; + *eps = x_eps / x; + for (int i = 1; i < n; i++) + { + *eps += x_eps / (x + i); + _Float128 lo; + mul_splitl (&ret, &lo, ret, x + i); + *eps += lo / ret; + } + return ret; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/ieee754.h b/REORG.TODO/sysdeps/ieee754/ldbl-128/ieee754.h new file mode 100644 index 0000000000..94662a350f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/ieee754.h @@ -0,0 +1,170 @@ +/* Copyright (C) 1992-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _IEEE754_H + +#define _IEEE754_H 1 +#include <features.h> + +#include <endian.h> + +__BEGIN_DECLS + +union ieee754_float + { + float f; + + /* This is the IEEE 754 single-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:8; + unsigned int mantissa:23; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + unsigned int mantissa:23; + unsigned int exponent:8; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee; + + /* This format makes it easier to see if a NaN is a signalling NaN. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:8; + unsigned int quiet_nan:1; + unsigned int mantissa:22; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + unsigned int mantissa:22; + unsigned int quiet_nan:1; + unsigned int exponent:8; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee_nan; + }; + +#define IEEE754_FLOAT_BIAS 0x7f /* Added to exponent. */ + + +union ieee754_double + { + double d; + + /* This is the IEEE 754 double-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:11; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:20; + unsigned int mantissa1:32; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + /* Together these comprise the mantissa. */ + unsigned int mantissa1:32; + unsigned int mantissa0:20; + unsigned int exponent:11; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee; + + /* This format makes it easier to see if a NaN is a signalling NaN. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:11; + unsigned int quiet_nan:1; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:19; + unsigned int mantissa1:32; +#else + /* Together these comprise the mantissa. */ + unsigned int mantissa1:32; + unsigned int mantissa0:19; + unsigned int quiet_nan:1; + unsigned int exponent:11; + unsigned int negative:1; +#endif + } ieee_nan; + }; + +#define IEEE754_DOUBLE_BIAS 0x3ff /* Added to exponent. */ + + +union ieee854_long_double + { + long double d; + + /* This is the IEEE 854 quad-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:15; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:16; + unsigned int mantissa1:32; + unsigned int mantissa2:32; + unsigned int mantissa3:32; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + /* Together these comprise the mantissa. */ + unsigned int mantissa3:32; + unsigned int mantissa2:32; + unsigned int mantissa1:32; + unsigned int mantissa0:16; + unsigned int exponent:15; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee; + + /* This format makes it easier to see if a NaN is a signalling NaN. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:15; + unsigned int quiet_nan:1; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:15; + unsigned int mantissa1:32; + unsigned int mantissa2:32; + unsigned int mantissa3:32; +#else + /* Together these comprise the mantissa. */ + unsigned int mantissa3:32; + unsigned int mantissa2:32; + unsigned int mantissa1:32; + unsigned int mantissa0:15; + unsigned int quiet_nan:1; + unsigned int exponent:15; + unsigned int negative:1; +#endif + } ieee_nan; + }; + +#define IEEE854_LONG_DOUBLE_BIAS 0x3fff /* Added to exponent. */ + +__END_DECLS + +#endif /* ieee754.h */ diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/k_cosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/k_cosl.c new file mode 100644 index 0000000000..b7c606379e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/k_cosl.c @@ -0,0 +1,131 @@ +/* Quad-precision floating point cosine on <-pi/4,pi/4>. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 c[] = { +#define ONE c[0] + L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */ + +/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) + x in <0,1/256> */ +#define SCOS1 c[1] +#define SCOS2 c[2] +#define SCOS3 c[3] +#define SCOS4 c[4] +#define SCOS5 c[5] +L(-5.00000000000000000000000000000000000E-01), /* bffe0000000000000000000000000000 */ + L(4.16666666666666666666666666556146073E-02), /* 3ffa5555555555555555555555395023 */ +L(-1.38888888888888888888309442601939728E-03), /* bff56c16c16c16c16c16a566e42c0375 */ + L(2.48015873015862382987049502531095061E-05), /* 3fefa01a01a019ee02dcf7da2d6d5444 */ +L(-2.75573112601362126593516899592158083E-07), /* bfe927e4f5dce637cb0b54908754bde0 */ + +/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) + x in <0,0.1484375> */ +#define COS1 c[6] +#define COS2 c[7] +#define COS3 c[8] +#define COS4 c[9] +#define COS5 c[10] +#define COS6 c[11] +#define COS7 c[12] +#define COS8 c[13] +L(-4.99999999999999999999999999999999759E-01), /* bffdfffffffffffffffffffffffffffb */ + L(4.16666666666666666666666666651287795E-02), /* 3ffa5555555555555555555555516f30 */ +L(-1.38888888888888888888888742314300284E-03), /* bff56c16c16c16c16c16c16a463dfd0d */ + L(2.48015873015873015867694002851118210E-05), /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ +L(-2.75573192239858811636614709689300351E-07), /* bfe927e4fb7789f5aa8142a22044b51f */ + L(2.08767569877762248667431926878073669E-09), /* 3fe21eed8eff881d1e9262d7adff4373 */ +L(-1.14707451049343817400420280514614892E-11), /* bfda9397496922a9601ed3d4ca48944b */ + L(4.77810092804389587579843296923533297E-14), /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ + +/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) + x in <0,1/256> */ +#define SSIN1 c[14] +#define SSIN2 c[15] +#define SSIN3 c[16] +#define SSIN4 c[17] +#define SSIN5 c[18] +L(-1.66666666666666666666666666666666659E-01), /* bffc5555555555555555555555555555 */ + L(8.33333333333333333333333333146298442E-03), /* 3ff81111111111111111111110fe195d */ +L(-1.98412698412698412697726277416810661E-04), /* bff2a01a01a01a01a019e7121e080d88 */ + L(2.75573192239848624174178393552189149E-06), /* 3fec71de3a556c640c6aaa51aa02ab41 */ +L(-2.50521016467996193495359189395805639E-08), /* bfe5ae644ee90c47dc71839de75b2787 */ +}; + +#define SINCOSL_COS_HI 0 +#define SINCOSL_COS_LO 1 +#define SINCOSL_SIN_HI 2 +#define SINCOSL_SIN_LO 3 +extern const _Float128 __sincosl_table[]; + +_Float128 +__kernel_cosl(_Float128 x, _Float128 y) +{ + _Float128 h, l, z, sin_l, cos_l_m1; + int64_t ix; + u_int32_t tix, hix, index; + GET_LDOUBLE_MSW64 (ix, x); + tix = ((u_int64_t)ix) >> 32; + tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ + if (tix < 0x3ffc3000) /* |x| < 0.1484375 */ + { + /* Argument is small enough to approximate it by a Chebyshev + polynomial of degree 16. */ + if (tix < 0x3fc60000) /* |x| < 2^-57 */ + if (!((int)x)) return ONE; /* generate inexact */ + z = x * x; + return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ + z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); + } + else + { + /* So that we don't have to use too large polynomial, we find + l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 + possible values for h. We look up cosl(h) and sinl(h) in + pre-computed tables, compute cosl(l) and sinl(l) using a + Chebyshev polynomial of degree 10(11) and compute + cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ + index = 0x3ffe - (tix >> 16); + hix = (tix + (0x200 << index)) & (0xfffffc00 << index); + if (signbit (x)) + { + x = -x; + y = -y; + } + switch (index) + { + case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; + case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; + default: + case 2: index = (hix - 0x3ffc3000) >> 10; break; + } + + SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0); + l = y - (h - x); + z = l * l; + sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); + cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); + return __sincosl_table [index + SINCOSL_COS_HI] + + (__sincosl_table [index + SINCOSL_COS_LO] + - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l + - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1)); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/k_sincosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/k_sincosl.c new file mode 100644 index 0000000000..03710f9e3a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/k_sincosl.c @@ -0,0 +1,170 @@ +/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const _Float128 c[] = { +#define ONE c[0] + L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */ + +/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) + x in <0,1/256> */ +#define SCOS1 c[1] +#define SCOS2 c[2] +#define SCOS3 c[3] +#define SCOS4 c[4] +#define SCOS5 c[5] +L(-5.00000000000000000000000000000000000E-01), /* bffe0000000000000000000000000000 */ + L(4.16666666666666666666666666556146073E-02), /* 3ffa5555555555555555555555395023 */ +L(-1.38888888888888888888309442601939728E-03), /* bff56c16c16c16c16c16a566e42c0375 */ + L(2.48015873015862382987049502531095061E-05), /* 3fefa01a01a019ee02dcf7da2d6d5444 */ +L(-2.75573112601362126593516899592158083E-07), /* bfe927e4f5dce637cb0b54908754bde0 */ + +/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) + x in <0,0.1484375> */ +#define COS1 c[6] +#define COS2 c[7] +#define COS3 c[8] +#define COS4 c[9] +#define COS5 c[10] +#define COS6 c[11] +#define COS7 c[12] +#define COS8 c[13] +L(-4.99999999999999999999999999999999759E-01), /* bffdfffffffffffffffffffffffffffb */ + L(4.16666666666666666666666666651287795E-02), /* 3ffa5555555555555555555555516f30 */ +L(-1.38888888888888888888888742314300284E-03), /* bff56c16c16c16c16c16c16a463dfd0d */ + L(2.48015873015873015867694002851118210E-05), /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ +L(-2.75573192239858811636614709689300351E-07), /* bfe927e4fb7789f5aa8142a22044b51f */ + L(2.08767569877762248667431926878073669E-09), /* 3fe21eed8eff881d1e9262d7adff4373 */ +L(-1.14707451049343817400420280514614892E-11), /* bfda9397496922a9601ed3d4ca48944b */ + L(4.77810092804389587579843296923533297E-14), /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ + +/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) + x in <0,1/256> */ +#define SSIN1 c[14] +#define SSIN2 c[15] +#define SSIN3 c[16] +#define SSIN4 c[17] +#define SSIN5 c[18] +L(-1.66666666666666666666666666666666659E-01), /* bffc5555555555555555555555555555 */ + L(8.33333333333333333333333333146298442E-03), /* 3ff81111111111111111111110fe195d */ +L(-1.98412698412698412697726277416810661E-04), /* bff2a01a01a01a01a019e7121e080d88 */ + L(2.75573192239848624174178393552189149E-06), /* 3fec71de3a556c640c6aaa51aa02ab41 */ +L(-2.50521016467996193495359189395805639E-08), /* bfe5ae644ee90c47dc71839de75b2787 */ + +/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) + x in <0,0.1484375> */ +#define SIN1 c[19] +#define SIN2 c[20] +#define SIN3 c[21] +#define SIN4 c[22] +#define SIN5 c[23] +#define SIN6 c[24] +#define SIN7 c[25] +#define SIN8 c[26] +L(-1.66666666666666666666666666666666538e-01), /* bffc5555555555555555555555555550 */ + L(8.33333333333333333333333333307532934e-03), /* 3ff811111111111111111111110e7340 */ +L(-1.98412698412698412698412534478712057e-04), /* bff2a01a01a01a01a01a019e7a626296 */ + L(2.75573192239858906520896496653095890e-06), /* 3fec71de3a556c7338fa38527474b8f5 */ +L(-2.50521083854417116999224301266655662e-08), /* bfe5ae64567f544e16c7de65c2ea551f */ + L(1.60590438367608957516841576404938118e-10), /* 3fde6124613a811480538a9a41957115 */ +L(-7.64716343504264506714019494041582610e-13), /* bfd6ae7f3d5aef30c7bc660b060ef365 */ + L(2.81068754939739570236322404393398135e-15), /* 3fce9510115aabf87aceb2022a9a9180 */ +}; + +#define SINCOSL_COS_HI 0 +#define SINCOSL_COS_LO 1 +#define SINCOSL_SIN_HI 2 +#define SINCOSL_SIN_LO 3 +extern const _Float128 __sincosl_table[]; + +void +__kernel_sincosl(_Float128 x, _Float128 y, _Float128 *sinx, _Float128 *cosx, int iy) +{ + _Float128 h, l, z, sin_l, cos_l_m1; + int64_t ix; + u_int32_t tix, hix, index; + GET_LDOUBLE_MSW64 (ix, x); + tix = ((u_int64_t)ix) >> 32; + tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ + if (tix < 0x3ffc3000) /* |x| < 0.1484375 */ + { + /* Argument is small enough to approximate it by a Chebyshev + polynomial of degree 16(17). */ + if (tix < 0x3fc60000) /* |x| < 2^-57 */ + { + math_check_force_underflow (x); + if (!((int)x)) /* generate inexact */ + { + *sinx = x; + *cosx = ONE; + return; + } + } + z = x * x; + *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ + z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); + *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ + z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); + } + else + { + /* So that we don't have to use too large polynomial, we find + l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 + possible values for h. We look up cosl(h) and sinl(h) in + pre-computed tables, compute cosl(l) and sinl(l) using a + Chebyshev polynomial of degree 10(11) and compute + sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and + cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ + index = 0x3ffe - (tix >> 16); + hix = (tix + (0x200 << index)) & (0xfffffc00 << index); + if (signbit (x)) + { + x = -x; + y = -y; + } + switch (index) + { + case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; + case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; + default: + case 2: index = (hix - 0x3ffc3000) >> 10; break; + } + + SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0); + if (iy) + l = y - (h - x); + else + l = x - h; + z = l * l; + sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); + cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); + z = __sincosl_table [index + SINCOSL_SIN_HI] + + (__sincosl_table [index + SINCOSL_SIN_LO] + + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1) + + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l)); + *sinx = (ix < 0) ? -z : z; + *cosx = __sincosl_table [index + SINCOSL_COS_HI] + + (__sincosl_table [index + SINCOSL_COS_LO] + - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l + - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1)); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/k_sinl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/k_sinl.c new file mode 100644 index 0000000000..4107eeb9f9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/k_sinl.c @@ -0,0 +1,135 @@ +/* Quad-precision floating point sine on <-pi/4,pi/4>. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const _Float128 c[] = { +#define ONE c[0] + L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */ + +/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) + x in <0,1/256> */ +#define SCOS1 c[1] +#define SCOS2 c[2] +#define SCOS3 c[3] +#define SCOS4 c[4] +#define SCOS5 c[5] +L(-5.00000000000000000000000000000000000E-01), /* bffe0000000000000000000000000000 */ + L(4.16666666666666666666666666556146073E-02), /* 3ffa5555555555555555555555395023 */ +L(-1.38888888888888888888309442601939728E-03), /* bff56c16c16c16c16c16a566e42c0375 */ + L(2.48015873015862382987049502531095061E-05), /* 3fefa01a01a019ee02dcf7da2d6d5444 */ +L(-2.75573112601362126593516899592158083E-07), /* bfe927e4f5dce637cb0b54908754bde0 */ + +/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) + x in <0,0.1484375> */ +#define SIN1 c[6] +#define SIN2 c[7] +#define SIN3 c[8] +#define SIN4 c[9] +#define SIN5 c[10] +#define SIN6 c[11] +#define SIN7 c[12] +#define SIN8 c[13] +L(-1.66666666666666666666666666666666538e-01), /* bffc5555555555555555555555555550 */ + L(8.33333333333333333333333333307532934e-03), /* 3ff811111111111111111111110e7340 */ +L(-1.98412698412698412698412534478712057e-04), /* bff2a01a01a01a01a01a019e7a626296 */ + L(2.75573192239858906520896496653095890e-06), /* 3fec71de3a556c7338fa38527474b8f5 */ +L(-2.50521083854417116999224301266655662e-08), /* bfe5ae64567f544e16c7de65c2ea551f */ + L(1.60590438367608957516841576404938118e-10), /* 3fde6124613a811480538a9a41957115 */ +L(-7.64716343504264506714019494041582610e-13), /* bfd6ae7f3d5aef30c7bc660b060ef365 */ + L(2.81068754939739570236322404393398135e-15), /* 3fce9510115aabf87aceb2022a9a9180 */ + +/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) + x in <0,1/256> */ +#define SSIN1 c[14] +#define SSIN2 c[15] +#define SSIN3 c[16] +#define SSIN4 c[17] +#define SSIN5 c[18] +L(-1.66666666666666666666666666666666659E-01), /* bffc5555555555555555555555555555 */ + L(8.33333333333333333333333333146298442E-03), /* 3ff81111111111111111111110fe195d */ +L(-1.98412698412698412697726277416810661E-04), /* bff2a01a01a01a01a019e7121e080d88 */ + L(2.75573192239848624174178393552189149E-06), /* 3fec71de3a556c640c6aaa51aa02ab41 */ +L(-2.50521016467996193495359189395805639E-08), /* bfe5ae644ee90c47dc71839de75b2787 */ +}; + +#define SINCOSL_COS_HI 0 +#define SINCOSL_COS_LO 1 +#define SINCOSL_SIN_HI 2 +#define SINCOSL_SIN_LO 3 +extern const _Float128 __sincosl_table[]; + +_Float128 +__kernel_sinl(_Float128 x, _Float128 y, int iy) +{ + _Float128 h, l, z, sin_l, cos_l_m1; + int64_t ix; + u_int32_t tix, hix, index; + GET_LDOUBLE_MSW64 (ix, x); + tix = ((u_int64_t)ix) >> 32; + tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ + if (tix < 0x3ffc3000) /* |x| < 0.1484375 */ + { + /* Argument is small enough to approximate it by a Chebyshev + polynomial of degree 17. */ + if (tix < 0x3fc60000) /* |x| < 2^-57 */ + { + math_check_force_underflow (x); + if (!((int)x)) return x; /* generate inexact */ + } + z = x * x; + return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ + z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); + } + else + { + /* So that we don't have to use too large polynomial, we find + l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 + possible values for h. We look up cosl(h) and sinl(h) in + pre-computed tables, compute cosl(l) and sinl(l) using a + Chebyshev polynomial of degree 10(11) and compute + sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */ + index = 0x3ffe - (tix >> 16); + hix = (tix + (0x200 << index)) & (0xfffffc00 << index); + x = fabsl (x); + switch (index) + { + case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; + case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; + default: + case 2: index = (hix - 0x3ffc3000) >> 10; break; + } + + SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0); + if (iy) + l = (ix < 0 ? -y : y) - (h - x); + else + l = x - h; + z = l * l; + sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); + cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); + z = __sincosl_table [index + SINCOSL_SIN_HI] + + (__sincosl_table [index + SINCOSL_SIN_LO] + + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1) + + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l)); + return (ix < 0) ? -z : z; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/k_tanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/k_tanl.c new file mode 100644 index 0000000000..e79023c69a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/k_tanl.c @@ -0,0 +1,168 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __kernel_tanl( x, y, k ) + * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input k indicates whether tan (if k=1) or + * -1/tan (if k= -1) is returned. + * + * Algorithm + * 1. Since tan(-x) = -tan(x), we need only to consider positive x. + * 2. if x < 2^-57, return x with inexact if x!=0. + * 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2) + * on [0,0.67433]. + * + * Note: tan(x+y) = tan(x) + tan'(x)*y + * ~ tan(x) + (1+x*x)*y + * Therefore, for better accuracy in computing tan(x+y), let + * r = x^3 * R(x^2) + * then + * tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y)) + * + * 4. For x in [0.67433,pi/4], let y = pi/4 - x, then + * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) + * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <libc-diag.h> + +static const _Float128 + one = 1, + pio4hi = L(7.8539816339744830961566084581987569936977E-1), + pio4lo = L(2.1679525325309452561992610065108379921906E-35), + + /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2) + 0 <= x <= 0.6743316650390625 + Peak relative error 8.0e-36 */ + TH = L(3.333333333333333333333333333333333333333E-1), + T0 = L(-1.813014711743583437742363284336855889393E7), + T1 = L(1.320767960008972224312740075083259247618E6), + T2 = L(-2.626775478255838182468651821863299023956E4), + T3 = L(1.764573356488504935415411383687150199315E2), + T4 = L(-3.333267763822178690794678978979803526092E-1), + + U0 = L(-1.359761033807687578306772463253710042010E8), + U1 = L(6.494370630656893175666729313065113194784E7), + U2 = L(-4.180787672237927475505536849168729386782E6), + U3 = L(8.031643765106170040139966622980914621521E4), + U4 = L(-5.323131271912475695157127875560667378597E2); + /* 1.000000000000000000000000000000000000000E0 */ + + +_Float128 +__kernel_tanl (_Float128 x, _Float128 y, int iy) +{ + _Float128 z, r, v, w, s; + int32_t ix, sign; + ieee854_long_double_shape_type u, u1; + + u.value = x; + ix = u.parts32.w0 & 0x7fffffff; + if (ix < 0x3fc60000) /* x < 2**-57 */ + { + if ((int) x == 0) + { /* generate inexact */ + if ((ix | u.parts32.w1 | u.parts32.w2 | u.parts32.w3 + | (iy + 1)) == 0) + return one / fabsl (x); + else if (iy == 1) + { + math_check_force_underflow (x); + return x; + } + else + return -one / x; + } + } + if (ix >= 0x3ffe5942) /* |x| >= 0.6743316650390625 */ + { + if ((u.parts32.w0 & 0x80000000) != 0) + { + x = -x; + y = -y; + sign = -1; + } + else + sign = 1; + z = pio4hi - x; + w = pio4lo - y; + x = z + w; + y = 0.0; + } + z = x * x; + r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4))); + v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z)))); + r = r / v; + + s = z * x; + r = y + z * (s * r + y); + r += TH * s; + w = x + r; + if (ix >= 0x3ffe5942) + { + v = (_Float128) iy; + w = (v - 2.0 * (x - (w * w / (w + v) - r))); + /* SIGN is set for arguments that reach this code, but not + otherwise, resulting in warnings that it may be used + uninitialized although in the cases where it is used it has + always been set. */ + DIAG_PUSH_NEEDS_COMMENT; + DIAG_IGNORE_NEEDS_COMMENT (5, "-Wmaybe-uninitialized"); + if (sign < 0) + w = -w; + DIAG_POP_NEEDS_COMMENT; + return w; + } + if (iy == 1) + return w; + else + { /* if allow error up to 2 ulp, + simply return -1.0/(x+r) here */ + /* compute -1.0/(x+r) accurately */ + u1.value = w; + u1.parts32.w2 = 0; + u1.parts32.w3 = 0; + v = r - (u1.value - x); /* u1+v = r+x */ + z = -1.0 / w; + u.value = z; + u.parts32.w2 = 0; + u.parts32.w3 = 0; + s = 1.0 + u.value * u1.value; + return u.value + z * (s + u.value * v); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/ldbl2mpn.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/ldbl2mpn.c new file mode 100644 index 0000000000..1c79a5dbe5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/ldbl2mpn.c @@ -0,0 +1,140 @@ +/* Copyright (C) 1995-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include "longlong.h" +#include <ieee754.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <stdlib.h> + +/* Convert a `long double' in IEEE854 quad-precision format to a + multi-precision integer representing the significand scaled up by its + number of bits (113 for long double) and an integral power of two + (MPN frexpl). */ + +mp_size_t +__mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size, + int *expt, int *is_neg, + _Float128 value) +{ + union ieee854_long_double u; + u.d = value; + + *is_neg = u.ieee.negative; + *expt = (int) u.ieee.exponent - IEEE854_LONG_DOUBLE_BIAS; + +#if BITS_PER_MP_LIMB == 32 + res_ptr[0] = u.ieee.mantissa3; /* Low-order 32 bits of fraction. */ + res_ptr[1] = u.ieee.mantissa2; + res_ptr[2] = u.ieee.mantissa1; + res_ptr[3] = u.ieee.mantissa0; /* High-order 32 bits. */ + #define N 4 +#elif BITS_PER_MP_LIMB == 64 + /* Hopefully the compiler will combine the two bitfield extracts + and this composition into just the original quadword extract. */ + res_ptr[0] = ((mp_limb_t) u.ieee.mantissa2 << 32) | u.ieee.mantissa3; + res_ptr[1] = ((mp_limb_t) u.ieee.mantissa0 << 32) | u.ieee.mantissa1; + #define N 2 +#else + #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif +/* The format does not fill the last limb. There are some zeros. */ +#define NUM_LEADING_ZEROS (BITS_PER_MP_LIMB \ + - (LDBL_MANT_DIG - ((N - 1) * BITS_PER_MP_LIMB))) + + if (u.ieee.exponent == 0) + { + /* A biased exponent of zero is a special case. + Either it is a zero or it is a denormal number. */ + if (res_ptr[0] == 0 && res_ptr[1] == 0 + && res_ptr[N - 2] == 0 && res_ptr[N - 1] == 0) /* Assumes N<=4. */ + /* It's zero. */ + *expt = 0; + else + { + /* It is a denormal number, meaning it has no implicit leading + one bit, and its exponent is in fact the format minimum. */ + int cnt; + +#if N == 2 + if (res_ptr[N - 1] != 0) + { + count_leading_zeros (cnt, res_ptr[N - 1]); + cnt -= NUM_LEADING_ZEROS; + res_ptr[N - 1] = res_ptr[N - 1] << cnt + | (res_ptr[0] >> (BITS_PER_MP_LIMB - cnt)); + res_ptr[0] <<= cnt; + *expt = LDBL_MIN_EXP - 1 - cnt; + } + else + { + count_leading_zeros (cnt, res_ptr[0]); + if (cnt >= NUM_LEADING_ZEROS) + { + res_ptr[N - 1] = res_ptr[0] << (cnt - NUM_LEADING_ZEROS); + res_ptr[0] = 0; + } + else + { + res_ptr[N - 1] = res_ptr[0] >> (NUM_LEADING_ZEROS - cnt); + res_ptr[0] <<= BITS_PER_MP_LIMB - (NUM_LEADING_ZEROS - cnt); + } + *expt = LDBL_MIN_EXP - 1 + - (BITS_PER_MP_LIMB - NUM_LEADING_ZEROS) - cnt; + } +#else + int j, k, l; + + for (j = N - 1; j > 0; j--) + if (res_ptr[j] != 0) + break; + + count_leading_zeros (cnt, res_ptr[j]); + cnt -= NUM_LEADING_ZEROS; + l = N - 1 - j; + if (cnt < 0) + { + cnt += BITS_PER_MP_LIMB; + l--; + } + if (!cnt) + for (k = N - 1; k >= l; k--) + res_ptr[k] = res_ptr[k-l]; + else + { + for (k = N - 1; k > l; k--) + res_ptr[k] = res_ptr[k-l] << cnt + | res_ptr[k-l-1] >> (BITS_PER_MP_LIMB - cnt); + res_ptr[k--] = res_ptr[0] << cnt; + } + + for (; k >= 0; k--) + res_ptr[k] = 0; + *expt = LDBL_MIN_EXP - 1 - l * BITS_PER_MP_LIMB - cnt; +#endif + } + } + else + /* Add the implicit leading one bit for a normalized number. */ + res_ptr[N - 1] |= (mp_limb_t) 1 << (LDBL_MANT_DIG - 1 + - ((N - 1) * BITS_PER_MP_LIMB)); + + return N; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/lgamma_negl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/lgamma_negl.c new file mode 100644 index 0000000000..17dc4f5bfe --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/lgamma_negl.c @@ -0,0 +1,551 @@ +/* lgammal expanding around zeros. + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const _Float128 lgamma_zeros[][2] = + { + { L(-0x2.74ff92c01f0d82abec9f315f1a08p+0), L(0xe.d3ccb7fb2658634a2b9f6b2ba81p-116) }, + { L(-0x2.bf6821437b20197995a4b4641eaep+0), L(-0xb.f4b00b4829f961e428533e6ad048p-116) }, + { L(-0x3.24c1b793cb35efb8be699ad3d9bap+0), L(-0x6.5454cb7fac60e3f16d9d7840c2ep-116) }, + { L(-0x3.f48e2a8f85fca170d4561291236cp+0), L(-0xc.320a4887d1cb4c711828a75d5758p-116) }, + { L(-0x4.0a139e16656030c39f0b0de18114p+0), L(0x1.53e84029416e1242006b2b3d1cfp-112) }, + { L(-0x4.fdd5de9bbabf3510d0aa40769884p+0), L(-0x1.01d7d78125286f78d1e501f14966p-112) }, + { L(-0x5.021a95fc2db6432a4c56e595394cp+0), L(-0x1.ecc6af0430d4fe5746fa7233356fp-112) }, + { L(-0x5.ffa4bd647d0357dd4ed62cbd31ecp+0), L(-0x1.f8e3f8e5deba2d67dbd70dd96ce1p-112) }, + { L(-0x6.005ac9625f233b607c2d96d16384p+0), L(-0x1.cb86ac569340cf1e5f24df7aab7bp-112) }, + { L(-0x6.fff2fddae1bbff3d626b65c23fd4p+0), L(0x1.e0bfcff5c457ebcf4d3ad9674167p-112) }, + { L(-0x7.000cff7b7f87adf4482dcdb98784p+0), L(0x1.54d99e35a74d6407b80292df199fp-112) }, + { L(-0x7.fffe5fe05673c3ca9e82b522b0ccp+0), L(0x1.62d177c832e0eb42c2faffd1b145p-112) }, + { L(-0x8.0001a01459fc9f60cb3cec1cec88p+0), L(0x2.8998835ac7277f7bcef67c47f188p-112) }, + { L(-0x8.ffffd1c425e80ffc864e95749258p+0), L(-0x1.e7e20210e7f81cf781b44e9d2b02p-112) }, + { L(-0x9.00002e3bb47d86d6d843fedc352p+0), L(0x2.14852f613a16291751d2ab751f7ep-112) }, + { L(-0x9.fffffb606bdfdcd062ae77a50548p+0), L(0x3.962d1490cc2e8f031c7007eaa1ap-116) }, + { L(-0xa.0000049f93bb9927b45d95e1544p+0), L(-0x1.e03086db9146a9287bd4f2172d5ap-112) }, + { L(-0xa.ffffff9466e9f1b36dacd2adbd18p+0), L(-0xd.05a4e458062f3f95345a4d9c9b6p-116) }, + { L(-0xb.0000006b9915315d965a6ffea41p+0), L(0x1.b415c6fff233e7b7fdc3a094246fp-112) }, + { L(-0xb.fffffff7089387387de41acc3d4p+0), L(0x3.687427c6373bd74a10306e10a28ep-112) }, + { L(-0xc.00000008f76c7731567c0f0250fp+0), L(-0x3.87920df5675833859190eb128ef6p-112) }, + { L(-0xc.ffffffff4f6dcf617f97a5ffc758p+0), L(0x2.ab72d76f32eaee2d1a42ed515d3ap-116) }, + { L(-0xd.00000000b092309c06683dd1b9p+0), L(-0x3.e3700857a15c19ac5a611de9688ap-112) }, + { L(-0xd.fffffffff36345ab9e184a3e09dp+0), L(-0x1.176dc48e47f62d917973dd44e553p-112) }, + { L(-0xe.000000000c9cba545e94e75ec57p+0), L(-0x1.8f753e2501e757a17cf2ecbeeb89p-112) }, + { L(-0xe.ffffffffff28c060c6604ef3037p+0), L(-0x1.f89d37357c9e3dc17c6c6e63becap-112) }, + { L(-0xf.0000000000d73f9f399bd0e420f8p+0), L(-0x5.e9ee31b0b890744fc0e3fbc01048p-116) }, + { L(-0xf.fffffffffff28c060c6621f512e8p+0), L(0xd.1b2eec9d960bd9adc5be5f5fa5p-116) }, + { L(-0x1.000000000000d73f9f399da1424cp+4), L(0x6.c46e0e88305d2800f0e414c506a8p-116) }, + { L(-0x1.0ffffffffffff3569c47e7a93e1cp+4), L(-0x4.6a08a2e008a998ebabb8087efa2cp-112) }, + { L(-0x1.1000000000000ca963b818568887p+4), L(-0x6.ca5a3a64ec15db0a95caf2c9ffb4p-112) }, + { L(-0x1.1fffffffffffff4bec3ce234132dp+4), L(-0x8.b2b726187c841cb92cd5221e444p-116) }, + { L(-0x1.20000000000000b413c31dcbeca5p+4), L(0x3.c4d005344b6cd0e7231120294abcp-112) }, + { L(-0x1.2ffffffffffffff685b25cbf5f54p+4), L(-0x5.ced932e38485f7dd296b8fa41448p-112) }, + { L(-0x1.30000000000000097a4da340a0acp+4), L(0x7.e484e0e0ffe38d406ebebe112f88p-112) }, + { L(-0x1.3fffffffffffffff86af516ff7f7p+4), L(-0x6.bd67e720d57854502b7db75e1718p-112) }, + { L(-0x1.40000000000000007950ae900809p+4), L(0x6.bec33375cac025d9c073168c5d9p-112) }, + { L(-0x1.4ffffffffffffffffa391c4248c3p+4), L(0x5.c63022b62b5484ba346524db607p-112) }, + { L(-0x1.500000000000000005c6e3bdb73dp+4), L(-0x5.c62f55ed5322b2685c5e9a51e6a8p-112) }, + { L(-0x1.5fffffffffffffffffbcc71a492p+4), L(-0x1.eb5aeb96c74d7ad25e060528fb5p-112) }, + { L(-0x1.6000000000000000004338e5b6ep+4), L(0x1.eb5aec04b2f2eb663e4e3d8a018cp-112) }, + { L(-0x1.6ffffffffffffffffffd13c97d9dp+4), L(-0x3.8fcc4d08d6fe5aa56ab04307ce7ep-112) }, + { L(-0x1.70000000000000000002ec368263p+4), L(0x3.8fcc4d090cee2f5d0b69a99c353cp-112) }, + { L(-0x1.7fffffffffffffffffffe0d30fe7p+4), L(0x7.2f577cca4b4c8cb1dc14001ac5ecp-112) }, + { L(-0x1.800000000000000000001f2cf019p+4), L(-0x7.2f577cca4b3442e35f0040b3b9e8p-112) }, + { L(-0x1.8ffffffffffffffffffffec0c332p+4), L(-0x2.e9a0572b1bb5b95f346a92d67a6p-112) }, + { L(-0x1.90000000000000000000013f3ccep+4), L(0x2.e9a0572b1bb5c371ddb3561705ap-112) }, + { L(-0x1.9ffffffffffffffffffffff3b8bdp+4), L(-0x1.cad8d32e386fd783e97296d63dcbp-116) }, + { L(-0x1.a0000000000000000000000c4743p+4), L(0x1.cad8d32e386fd7c1ab8c1fe34c0ep-116) }, + { L(-0x1.afffffffffffffffffffffff8b95p+4), L(-0x3.8f48cc5737d5979c39db806c5406p-112) }, + { L(-0x1.b00000000000000000000000746bp+4), L(0x3.8f48cc5737d5979c3b3a6bda06f6p-112) }, + { L(-0x1.bffffffffffffffffffffffffbd8p+4), L(0x6.2898d42174dcf171470d8c8c6028p-112) }, + { L(-0x1.c000000000000000000000000428p+4), L(-0x6.2898d42174dcf171470d18ba412cp-112) }, + { L(-0x1.cfffffffffffffffffffffffffdbp+4), L(-0x4.c0ce9794ea50a839e311320bde94p-112) }, + { L(-0x1.d000000000000000000000000025p+4), L(0x4.c0ce9794ea50a839e311322f7cf8p-112) }, + { L(-0x1.dfffffffffffffffffffffffffffp+4), L(0x3.932c5047d60e60caded4c298a174p-112) }, + { L(-0x1.e000000000000000000000000001p+4), L(-0x3.932c5047d60e60caded4c298973ap-112) }, + { L(-0x1.fp+4), L(0xa.1a6973c1fade2170f7237d35fe3p-116) }, + { L(-0x1.fp+4), L(-0xa.1a6973c1fade2170f7237d35fe08p-116) }, + { L(-0x2p+4), L(0x5.0d34b9e0fd6f10b87b91be9aff1p-120) }, + { L(-0x2p+4), L(-0x5.0d34b9e0fd6f10b87b91be9aff0cp-120) }, + { L(-0x2.1p+4), L(0x2.73024a9ba1aa36a7059bff52e844p-124) }, + { L(-0x2.1p+4), L(-0x2.73024a9ba1aa36a7059bff52e844p-124) }, + { L(-0x2.2p+4), L(0x1.2710231c0fd7a13f8a2b4af9d6b7p-128) }, + { L(-0x2.2p+4), L(-0x1.2710231c0fd7a13f8a2b4af9d6b7p-128) }, + { L(-0x2.3p+4), L(0x8.6e2ce38b6c8f9419e3fad3f0312p-136) }, + { L(-0x2.3p+4), L(-0x8.6e2ce38b6c8f9419e3fad3f0312p-136) }, + { L(-0x2.4p+4), L(0x3.bf30652185952560d71a254e4eb8p-140) }, + { L(-0x2.4p+4), L(-0x3.bf30652185952560d71a254e4eb8p-140) }, + { L(-0x2.5p+4), L(0x1.9ec8d1c94e85af4c78b15c3d89d3p-144) }, + { L(-0x2.5p+4), L(-0x1.9ec8d1c94e85af4c78b15c3d89d3p-144) }, + { L(-0x2.6p+4), L(0xa.ea565ce061d57489e9b85276274p-152) }, + { L(-0x2.6p+4), L(-0xa.ea565ce061d57489e9b85276274p-152) }, + { L(-0x2.7p+4), L(0x4.7a6512692eb37804111dabad30ecp-156) }, + { L(-0x2.7p+4), L(-0x4.7a6512692eb37804111dabad30ecp-156) }, + { L(-0x2.8p+4), L(0x1.ca8ed42a12ae3001a07244abad2bp-160) }, + { L(-0x2.8p+4), L(-0x1.ca8ed42a12ae3001a07244abad2bp-160) }, + { L(-0x2.9p+4), L(0xb.2f30e1ce812063f12e7e8d8d96e8p-168) }, + { L(-0x2.9p+4), L(-0xb.2f30e1ce812063f12e7e8d8d96e8p-168) }, + { L(-0x2.ap+4), L(0x4.42bd49d4c37a0db136489772e428p-172) }, + { L(-0x2.ap+4), L(-0x4.42bd49d4c37a0db136489772e428p-172) }, + { L(-0x2.bp+4), L(0x1.95db45257e5122dcbae56def372p-176) }, + { L(-0x2.bp+4), L(-0x1.95db45257e5122dcbae56def372p-176) }, + { L(-0x2.cp+4), L(0x9.3958d81ff63527ecf993f3fb6f48p-184) }, + { L(-0x2.cp+4), L(-0x9.3958d81ff63527ecf993f3fb6f48p-184) }, + { L(-0x2.dp+4), L(0x3.47970e4440c8f1c058bd238c9958p-188) }, + { L(-0x2.dp+4), L(-0x3.47970e4440c8f1c058bd238c9958p-188) }, + { L(-0x2.ep+4), L(0x1.240804f65951062ca46e4f25c608p-192) }, + { L(-0x2.ep+4), L(-0x1.240804f65951062ca46e4f25c608p-192) }, + { L(-0x2.fp+4), L(0x6.36a382849fae6de2d15362d8a394p-200) }, + { L(-0x2.fp+4), L(-0x6.36a382849fae6de2d15362d8a394p-200) }, + { L(-0x3p+4), L(0x2.123680d6dfe4cf4b9b1bcb9d8bdcp-204) }, + { L(-0x3p+4), L(-0x2.123680d6dfe4cf4b9b1bcb9d8bdcp-204) }, + { L(-0x3.1p+4), L(0xa.d21786ff5842eca51fea0870919p-212) }, + { L(-0x3.1p+4), L(-0xa.d21786ff5842eca51fea0870919p-212) }, + { L(-0x3.2p+4), L(0x3.766dedc259af040be140a68a6c04p-216) }, + }; + +static const _Float128 e_hi = L(0x2.b7e151628aed2a6abf7158809cf4p+0); +static const _Float128 e_lo = L(0xf.3c762e7160f38b4da56a784d9048p-116); + + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) in Stirling's + approximation to lgamma function. */ + +static const _Float128 lgamma_coeff[] = + { + L(0x1.5555555555555555555555555555p-4), + L(-0xb.60b60b60b60b60b60b60b60b60b8p-12), + L(0x3.4034034034034034034034034034p-12), + L(-0x2.7027027027027027027027027028p-12), + L(0x3.72a3c5631fe46ae1d4e700dca8f2p-12), + L(-0x7.daac36664f1f207daac36664f1f4p-12), + L(0x1.a41a41a41a41a41a41a41a41a41ap-8), + L(-0x7.90a1b2c3d4e5f708192a3b4c5d7p-8), + L(0x2.dfd2c703c0cfff430edfd2c703cp-4), + L(-0x1.6476701181f39edbdb9ce625987dp+0), + L(0xd.672219167002d3a7a9c886459cp+0), + L(-0x9.cd9292e6660d55b3f712eb9e07c8p+4), + L(0x8.911a740da740da740da740da741p+8), + L(-0x8.d0cc570e255bf59ff6eec24b49p+12), + L(0xa.8d1044d3708d1c219ee4fdc446ap+16), + L(-0xe.8844d8a169abbc406169abbc406p+20), + L(0x1.6d29a0f6433b79890cede62433b8p+28), + L(-0x2.88a233b3c8cddaba9809357125d8p+32), + L(0x5.0dde6f27500939a85c40939a85c4p+36), + L(-0xb.4005bde03d4642a243581714af68p+40), + L(0x1.bc8cd6f8f1f755c78753cdb5d5c9p+48), + L(-0x4.bbebb143bb94de5a0284fa7ec424p+52), + L(0xe.2e1337f5af0bed90b6b0a352d4fp+56), + L(-0x2.e78250162b62405ad3e4bfe61b38p+64), + L(0xa.5f7eef9e71ac7c80326ab4cc8bfp+68), + L(-0x2.83be0395e550213369924971b21ap+76), + L(0xa.8ebfe48da17dd999790760b0cep+80), + }; + +#define NCOEFF (sizeof (lgamma_coeff) / sizeof (lgamma_coeff[0])) + +/* Polynomial approximations to (|gamma(x)|-1)(x-n)/(x-x0), where n is + the integer end-point of the half-integer interval containing x and + x0 is the zero of lgamma in that half-integer interval. Each + polynomial is expressed in terms of x-xm, where xm is the midpoint + of the interval for which the polynomial applies. */ + +static const _Float128 poly_coeff[] = + { + /* Interval [-2.125, -2] (polynomial degree 23). */ + L(-0x1.0b71c5c54d42eb6c17f30b7aa8f5p+0), + L(-0xc.73a1dc05f34951602554c6d7506p-4), + L(-0x1.ec841408528b51473e6c425ee5ffp-4), + L(-0xe.37c9da26fc3c9a3c1844c8c7f1cp-4), + L(-0x1.03cd87c519305703b021fa33f827p-4), + L(-0xe.ae9ada65e09aa7f1c75216128f58p-4), + L(0x9.b11855a4864b5731cf85736015a8p-8), + L(-0xe.f28c133e697a95c28607c9701dep-4), + L(0x2.6ec14a1c586a72a7cc33ee569d6ap-4), + L(-0xf.57cab973e14464a262fc24723c38p-4), + L(0x4.5b0fc25f16e52997b2886bbae808p-4), + L(-0xf.f50e59f1a9b56e76e988dac9ccf8p-4), + L(0x6.5f5eae15e9a93369e1d85146c6fcp-4), + L(-0x1.0d2422daac459e33e0994325ed23p+0), + L(0x8.82000a0e7401fb1117a0e6606928p-4), + L(-0x1.1f492f178a3f1b19f58a2ca68e55p+0), + L(0xa.cb545f949899a04c160b19389abp-4), + L(-0x1.36165a1b155ba3db3d1b77caf498p+0), + L(0xd.44c5d5576f74302e5cf79e183eep-4), + L(-0x1.51f22e0cdd33d3d481e326c02f3ep+0), + L(0xf.f73a349c08244ac389c007779bfp-4), + L(-0x1.73317bf626156ba716747c4ca866p+0), + L(0x1.379c3c97b9bc71e1c1c4802dd657p+0), + L(-0x1.a72a351c54f902d483052000f5dfp+0), + /* Interval [-2.25, -2.125] (polynomial degree 24). */ + L(-0xf.2930890d7d675a80c36afb0fd5e8p-4), + L(-0xc.a5cfde054eab5c6770daeca577f8p-4), + L(0x3.9c9e0fdebb07cdf89c61d41c9238p-4), + L(-0x1.02a5ad35605fcf4af65a6dbacb84p+0), + L(0x9.6e9b1185bb48be9de1918e00a2e8p-4), + L(-0x1.4d8332f3cfbfa116fd611e9ce90dp+0), + L(0x1.1c0c8cb4d9f4b1d490e1a41fae4dp+0), + L(-0x1.c9a6f5ae9130cd0299e293a42714p+0), + L(0x1.d7e9307fd58a2ea997f29573a112p+0), + L(-0x2.921cb3473d96178ca2a11d2a8d46p+0), + L(0x2.e8d59113b6f3409ff8db226e9988p+0), + L(-0x3.cbab931625a1ae2b26756817f264p+0), + L(0x4.7d9f0f05d5296d18663ca003912p+0), + L(-0x5.ade9cba12a14ea485667b7135bbp+0), + L(0x6.dc983a5da74fb48e767b7fec0a3p+0), + L(-0x8.8d9ed454ae31d9e138dd8ee0d1a8p+0), + L(0xa.6fa099d4e7c202e0c0fd6ed8492p+0), + L(-0xc.ebc552a8090a0f0115e92d4ebbc8p+0), + L(0xf.d695e4772c0d829b53fba9ca5568p+0), + L(-0x1.38c32ae38e5e9eb79b2a4c5570a9p+4), + L(0x1.8035145646cfab49306d0999a51bp+4), + L(-0x1.d930adbb03dd342a4c2a8c4e1af6p+4), + L(0x2.45c2edb1b4943ddb3686cd9c6524p+4), + L(-0x2.e818ebbfafe2f916fa21abf7756p+4), + L(0x3.9804ce51d0fb9a430a711fd7307p+4), + /* Interval [-2.375, -2.25] (polynomial degree 25). */ + L(-0xd.7d28d505d6181218a25f31d5e45p-4), + L(-0xe.69649a3040985140cdf946829fap-4), + L(0xb.0d74a2827d053a8d44595012484p-4), + L(-0x1.924b0922853617cac181afbc08ddp+0), + L(0x1.d49b12bccf0a568582e2d3c410f3p+0), + L(-0x3.0898bb7d8c4093e636279c791244p+0), + L(0x4.207a6cac711cb53868e8a5057eep+0), + L(-0x6.39ee63ea4fb1dcab0c9144bf3ddcp+0), + L(0x8.e2e2556a797b649bf3f53bd26718p+0), + L(-0xd.0e83ac82552ef12af508589e7a8p+0), + L(0x1.2e4525e0ce6670563c6484a82b05p+4), + L(-0x1.b8e350d6a8f2b222fa390a57c23dp+4), + L(0x2.805cd69b919087d8a80295892c2cp+4), + L(-0x3.a42585424a1b7e64c71743ab014p+4), + L(0x5.4b4f409f98de49f7bfb03c05f984p+4), + L(-0x7.b3c5827fbe934bc820d6832fb9fcp+4), + L(0xb.33b7b90cc96c425526e0d0866e7p+4), + L(-0x1.04b77047ac4f59ee3775ca10df0dp+8), + L(0x1.7b366f5e94a34f41386eac086313p+8), + L(-0x2.2797338429385c9849ca6355bfc2p+8), + L(0x3.225273cf92a27c9aac1b35511256p+8), + L(-0x4.8f078aa48afe6cb3a4e89690f898p+8), + L(0x6.9f311d7b6654fc1d0b5195141d04p+8), + L(-0x9.a0c297b6b4621619ca9bacc48ed8p+8), + L(0xe.ce1f06b6f90d92138232a76e4cap+8), + L(-0x1.5b0e6806fa064daf011613e43b17p+12), + /* Interval [-2.5, -2.375] (polynomial degree 27). */ + L(-0xb.74ea1bcfff94b2c01afba9daa7d8p-4), + L(-0x1.2a82bd590c37538cab143308de4dp+0), + L(0x1.88020f828b966fec66b8649fd6fcp+0), + L(-0x3.32279f040eb694970e9db24863dcp+0), + L(0x5.57ac82517767e68a721005853864p+0), + L(-0x9.c2aedcfe22833de43834a0a6cc4p+0), + L(0x1.12c132f1f5577f99e1a0ed3538e1p+4), + L(-0x1.ea94e26628a3de3597f7bb55a948p+4), + L(0x3.66b4ac4fa582f58b59f96b2f7c7p+4), + L(-0x6.0cf746a9cf4cba8c39afcc73fc84p+4), + L(0xa.c102ef2c20d75a342197df7fedf8p+4), + L(-0x1.31ebff06e8f14626782df58db3b6p+8), + L(0x2.1fd6f0c0e710994e059b9dbdb1fep+8), + L(-0x3.c6d76040407f447f8b5074f07706p+8), + L(0x6.b6d18e0d8feb4c2ef5af6a40ed18p+8), + L(-0xb.efaf542c529f91e34217f24ae6a8p+8), + L(0x1.53852d873210e7070f5d9eb2296p+12), + L(-0x2.5b977c0ddc6d540717173ac29fc8p+12), + L(0x4.310d452ae05100eff1e02343a724p+12), + L(-0x7.73a5d8f20c4f986a7dd1912b2968p+12), + L(0xd.3f5ea2484f3fca15eab1f4d1a218p+12), + L(-0x1.78d18aac156d1d93a2ffe7e08d3fp+16), + L(0x2.9df49ca75e5b567f5ea3e47106cp+16), + L(-0x4.a7149af8961a08aa7c3233b5bb94p+16), + L(0x8.3db10ffa742c707c25197d989798p+16), + L(-0xe.a26d6dd023cadd02041a049ec368p+16), + L(0x1.c825d90514e7c57c7fa5316f947cp+20), + L(-0x3.34bb81e5a0952df8ca1abdc6684cp+20), + /* Interval [-2.625, -2.5] (polynomial degree 28). */ + L(-0x3.d10108c27ebafad533c20eac32bp-4), + L(0x1.cd557caff7d2b2085f41dbec5106p+0), + L(0x3.819b4856d399520dad9776ea2cacp+0), + L(0x6.8505cbad03dc34c5e42e8b12eb78p+0), + L(0xb.c1b2e653a9e38f82b399c94e7f08p+0), + L(0x1.50a53a38f148138105124df65419p+4), + L(0x2.57ae00cbe5232cbeeed34d89727ap+4), + L(0x4.2b156301b8604db85a601544bfp+4), + L(0x7.6989ed23ca3ca7579b3462592b5cp+4), + L(0xd.2dd2976557939517f831f5552cc8p+4), + L(0x1.76e1c3430eb860969bce40cd494p+8), + L(0x2.9a77bf5488742466db3a2c7c1ec6p+8), + L(0x4.a0d62ed7266e8eb36f725a8ebcep+8), + L(0x8.3a6184dd3021067df2f8b91e99c8p+8), + L(0xe.a0ade1538245bf55d39d7e436b1p+8), + L(0x1.a01359fae8617b5826dd74428e9p+12), + L(0x2.e3b0a32caae77251169acaca1ad4p+12), + L(0x5.2301257c81589f62b38fb5993ee8p+12), + L(0x9.21c9275db253d4e719b73b18cb9p+12), + L(0x1.03c104bc96141cda3f3fa4b112bcp+16), + L(0x1.cdc8ed65119196a08b0c78f1445p+16), + L(0x3.34f31d2eaacf34382cdb0073572ap+16), + L(0x5.b37628cadf12bf0000907d0ef294p+16), + L(0xa.22d8b332c0b1e6a616f425dfe5ap+16), + L(0x1.205b01444804c3ff922cd78b4c42p+20), + L(0x1.fe8f0cea9d1e0ff25be2470b4318p+20), + L(0x3.8872aebeb368399aee02b39340aep+20), + L(0x6.ebd560d351e84e26a4381f5b293cp+20), + L(0xc.c3644d094b0dae2fbcbf682cd428p+20), + /* Interval [-2.75, -2.625] (polynomial degree 26). */ + L(-0x6.b5d252a56e8a75458a27ed1c2dd4p-4), + L(0x1.28d60383da3ac721aed3c5794da9p+0), + L(0x1.db6513ada8a66ea77d87d9a8827bp+0), + L(0x2.e217118f9d348a27f7506a707e6ep+0), + L(0x4.450112c5cbf725a0fb9802396c9p+0), + L(0x6.4af99151eae7810a75df2a0303c4p+0), + L(0x9.2db598b4a97a7f69aeef32aec758p+0), + L(0xd.62bef9c22471f5ee47ea1b9c0b5p+0), + L(0x1.379f294e412bd62328326d4222f9p+4), + L(0x1.c5827349d8865f1e8825c37c31c6p+4), + L(0x2.93a7e7a75b7568cc8cbe8c016c12p+4), + L(0x3.bf9bb882afe57edb383d41879d3ap+4), + L(0x5.73c737828cee095c43a5566731c8p+4), + L(0x7.ee4653493a7f81e0442062b3823cp+4), + L(0xb.891c6b83fc8b55bd973b5d962d6p+4), + L(0x1.0c775d7de3bf9b246c0208e0207ep+8), + L(0x1.867ee43ec4bd4f4fd56abc05110ap+8), + L(0x2.37fe9ba6695821e9822d8c8af0a6p+8), + L(0x3.3a2c667e37c942f182cd3223a936p+8), + L(0x4.b1b500eb59f3f782c7ccec88754p+8), + L(0x6.d3efd3b65b3d0d8488d30b79fa4cp+8), + L(0x9.ee8224e65bed5ced8b75eaec609p+8), + L(0xe.72416e510cca77d53fc615c1f3dp+8), + L(0x1.4fb538b0a2dfe567a8904b7e0445p+12), + L(0x1.e7f56a9266cf525a5b8cf4cb76cep+12), + L(0x2.f0365c983f68c597ee49d099cce8p+12), + L(0x4.53aa229e1b9f5b5e59625265951p+12), + /* Interval [-2.875, -2.75] (polynomial degree 24). */ + L(-0x8.a41b1e4f36ff88dc820815607d68p-4), + L(0xc.da87d3b69dc0f2f9c6f368b8ca1p-4), + L(0x1.1474ad5c36158a7bea04fd2f98c6p+0), + L(0x1.761ecb90c555df6555b7dba955b6p+0), + L(0x1.d279bff9ae291caf6c4b4bcb3202p+0), + L(0x2.4e5d00559a6e2b9b5d7fe1f6689cp+0), + L(0x2.d57545a75cee8743ae2b17bc8d24p+0), + L(0x3.8514eee3aac88b89bec2307021bap+0), + L(0x4.5235e3b6e1891ffeb87fed9f8a24p+0), + L(0x5.562acdb10eef3c9a773b3e27a864p+0), + L(0x6.8ec8965c76efe03c26bff60b1194p+0), + L(0x8.15251aca144877af32658399f9b8p+0), + L(0x9.f08d56aba174d844138af782c0f8p+0), + L(0xc.3dbbeda2679e8a1346ccc3f6da88p+0), + L(0xf.0f5bfd5eacc26db308ffa0556fa8p+0), + L(0x1.28a6ccd84476fbc713d6bab49ac9p+4), + L(0x1.6d0a3ae2a3b1c8ff400641a3a21fp+4), + L(0x1.c15701b28637f87acfb6a91d33b5p+4), + L(0x2.28fbe0eccf472089b017651ca55ep+4), + L(0x2.a8a453004f6e8ffaacd1603bc3dp+4), + L(0x3.45ae4d9e1e7cd1a5dba0e4ec7f6cp+4), + L(0x4.065fbfacb7fad3e473cb577a61e8p+4), + L(0x4.f3d1473020927acac1944734a39p+4), + L(0x6.54bb091245815a36fb74e314dd18p+4), + L(0x7.d7f445129f7fb6c055e582d3f6ep+4), + /* Interval [-3, -2.875] (polynomial degree 23). */ + L(-0xa.046d667e468f3e44dcae1afcc648p-4), + L(0x9.70b88dcc006c214d8d996fdf5ccp-4), + L(0xa.a8a39421c86d3ff24931a0929fp-4), + L(0xd.2f4d1363f324da2b357c8b6ec94p-4), + L(0xd.ca9aa1a3a5c00de11bf60499a97p-4), + L(0xf.cf09c31eeb52a45dfa7ebe3778dp-4), + L(0x1.04b133a39ed8a09691205660468bp+0), + L(0x1.22b547a06edda944fcb12fd9b5ecp+0), + L(0x1.2c57fce7db86a91df09602d344b3p+0), + L(0x1.4aade4894708f84795212fe257eep+0), + L(0x1.579c8b7b67ec4afed5b28c8bf787p+0), + L(0x1.776820e7fc80ae5284239733078ap+0), + L(0x1.883ab28c7301fde4ca6b8ec26ec8p+0), + L(0x1.aa2ef6e1ae52eb42c9ee83b206e3p+0), + L(0x1.bf4ad50f0a9a9311300cf0c51ee7p+0), + L(0x1.e40206e0e96b1da463814dde0d09p+0), + L(0x1.fdcbcffef3a21b29719c2bd9feb1p+0), + L(0x2.25e2e8948939c4d42cf108fae4bep+0), + L(0x2.44ce14d2b59c1c0e6bf2cfa81018p+0), + L(0x2.70ee80bbd0387162be4861c43622p+0), + L(0x2.954b64d2c2ebf3489b949c74476p+0), + L(0x2.c616e133a811c1c9446105208656p+0), + L(0x3.05a69dfe1a9ba1079f90fcf26bd4p+0), + L(0x3.410d2ad16a0506de29736e6aafdap+0), + }; + +static const size_t poly_deg[] = + { + 23, + 24, + 25, + 27, + 28, + 26, + 24, + 23, + }; + +static const size_t poly_end[] = + { + 23, + 48, + 74, + 102, + 131, + 158, + 183, + 207, + }; + +/* Compute sin (pi * X) for -0.25 <= X <= 0.5. */ + +static _Float128 +lg_sinpi (_Float128 x) +{ + if (x <= L(0.25)) + return __sinl (M_PIl * x); + else + return __cosl (M_PIl * (L(0.5) - x)); +} + +/* Compute cos (pi * X) for -0.25 <= X <= 0.5. */ + +static _Float128 +lg_cospi (_Float128 x) +{ + if (x <= L(0.25)) + return __cosl (M_PIl * x); + else + return __sinl (M_PIl * (L(0.5) - x)); +} + +/* Compute cot (pi * X) for -0.25 <= X <= 0.5. */ + +static _Float128 +lg_cotpi (_Float128 x) +{ + return lg_cospi (x) / lg_sinpi (x); +} + +/* Compute lgamma of a negative argument -50 < X < -2, setting + *SIGNGAMP accordingly. */ + +_Float128 +__lgamma_negl (_Float128 x, int *signgamp) +{ + /* Determine the half-integer region X lies in, handle exact + integers and determine the sign of the result. */ + int i = __floorl (-2 * x); + if ((i & 1) == 0 && i == -2 * x) + return L(1.0) / L(0.0); + _Float128 xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2); + i -= 4; + *signgamp = ((i & 2) == 0 ? -1 : 1); + + SET_RESTORE_ROUNDL (FE_TONEAREST); + + /* Expand around the zero X0 = X0_HI + X0_LO. */ + _Float128 x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1]; + _Float128 xdiff = x - x0_hi - x0_lo; + + /* For arguments in the range -3 to -2, use polynomial + approximations to an adjusted version of the gamma function. */ + if (i < 2) + { + int j = __floorl (-8 * x) - 16; + _Float128 xm = (-33 - 2 * j) * L(0.0625); + _Float128 x_adj = x - xm; + size_t deg = poly_deg[j]; + size_t end = poly_end[j]; + _Float128 g = poly_coeff[end]; + for (size_t j = 1; j <= deg; j++) + g = g * x_adj + poly_coeff[end - j]; + return __log1pl (g * xdiff / (x - xn)); + } + + /* The result we want is log (sinpi (X0) / sinpi (X)) + + log (gamma (1 - X0) / gamma (1 - X)). */ + _Float128 x_idiff = fabsl (xn - x), x0_idiff = fabsl (xn - x0_hi - x0_lo); + _Float128 log_sinpi_ratio; + if (x0_idiff < x_idiff * L(0.5)) + /* Use log not log1p to avoid inaccuracy from log1p of arguments + close to -1. */ + log_sinpi_ratio = __ieee754_logl (lg_sinpi (x0_idiff) + / lg_sinpi (x_idiff)); + else + { + /* Use log1p not log to avoid inaccuracy from log of arguments + close to 1. X0DIFF2 has positive sign if X0 is further from + XN than X is from XN, negative sign otherwise. */ + _Float128 x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * L(0.5); + _Float128 sx0d2 = lg_sinpi (x0diff2); + _Float128 cx0d2 = lg_cospi (x0diff2); + log_sinpi_ratio = __log1pl (2 * sx0d2 + * (-sx0d2 + cx0d2 * lg_cotpi (x_idiff))); + } + + _Float128 log_gamma_ratio; + _Float128 y0 = 1 - x0_hi; + _Float128 y0_eps = -x0_hi + (1 - y0) - x0_lo; + _Float128 y = 1 - x; + _Float128 y_eps = -x + (1 - y); + /* We now wish to compute LOG_GAMMA_RATIO + = log (gamma (Y0 + Y0_EPS) / gamma (Y + Y_EPS)). XDIFF + accurately approximates the difference Y0 + Y0_EPS - Y - + Y_EPS. Use Stirling's approximation. First, we may need to + adjust into the range where Stirling's approximation is + sufficiently accurate. */ + _Float128 log_gamma_adj = 0; + if (i < 20) + { + int n_up = (21 - i) / 2; + _Float128 ny0, ny0_eps, ny, ny_eps; + ny0 = y0 + n_up; + ny0_eps = y0 - (ny0 - n_up) + y0_eps; + y0 = ny0; + y0_eps = ny0_eps; + ny = y + n_up; + ny_eps = y - (ny - n_up) + y_eps; + y = ny; + y_eps = ny_eps; + _Float128 prodm1 = __lgamma_productl (xdiff, y - n_up, y_eps, n_up); + log_gamma_adj = -__log1pl (prodm1); + } + _Float128 log_gamma_high + = (xdiff * __log1pl ((y0 - e_hi - e_lo + y0_eps) / e_hi) + + (y - L(0.5) + y_eps) * __log1pl (xdiff / y) + log_gamma_adj); + /* Compute the sum of (B_2k / 2k(2k-1))(Y0^-(2k-1) - Y^-(2k-1)). */ + _Float128 y0r = 1 / y0, yr = 1 / y; + _Float128 y0r2 = y0r * y0r, yr2 = yr * yr; + _Float128 rdiff = -xdiff / (y * y0); + _Float128 bterm[NCOEFF]; + _Float128 dlast = rdiff, elast = rdiff * yr * (yr + y0r); + bterm[0] = dlast * lgamma_coeff[0]; + for (size_t j = 1; j < NCOEFF; j++) + { + _Float128 dnext = dlast * y0r2 + elast; + _Float128 enext = elast * yr2; + bterm[j] = dnext * lgamma_coeff[j]; + dlast = dnext; + elast = enext; + } + _Float128 log_gamma_low = 0; + for (size_t j = 0; j < NCOEFF; j++) + log_gamma_low += bterm[NCOEFF - 1 - j]; + log_gamma_ratio = log_gamma_high + log_gamma_low; + + return log_sinpi_ratio + log_gamma_ratio; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/lgamma_productl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/lgamma_productl.c new file mode 100644 index 0000000000..212c26a960 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/lgamma_productl.c @@ -0,0 +1,52 @@ +/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), .... + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_splitl.h> + +/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS + + 1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that + all the values X + 1, ..., X + N - 1 are exactly representable, and + X_EPS / X is small enough that factors quadratic in it can be + neglected. */ + +_Float128 +__lgamma_productl (_Float128 t, _Float128 x, _Float128 x_eps, int n) +{ + _Float128 ret = 0, ret_eps = 0; + for (int i = 0; i < n; i++) + { + _Float128 xi = x + i; + _Float128 quot = t / xi; + _Float128 mhi, mlo; + mul_splitl (&mhi, &mlo, quot, xi); + _Float128 quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi); + /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */ + _Float128 rhi, rlo; + mul_splitl (&rhi, &rlo, ret, quot); + _Float128 rpq = ret + quot; + _Float128 rpq_eps = (ret - rpq) + quot; + _Float128 nret = rpq + rhi; + _Float128 nret_eps = (rpq - nret) + rhi; + ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot + + quot_lo + quot_lo * (ret + ret_eps)); + ret = nret; + } + return ret + ret_eps; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/math_ldbl.h b/REORG.TODO/sysdeps/ieee754/ldbl-128/math_ldbl.h new file mode 100644 index 0000000000..bb5cce2a36 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/math_ldbl.h @@ -0,0 +1,120 @@ +/* Manipulation of the bit representation of 'long double' quantities. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_LDBL_H_ +#define _MATH_LDBL_H_ 1 + +#include <stdint.h> +#include <endian.h> + +/* A union which permits us to convert between a long double and + four 32 bit ints or two 64 bit ints. */ + +#if __FLOAT_WORD_ORDER == __BIG_ENDIAN + +typedef union +{ + long double value; + struct + { + uint64_t msw; + uint64_t lsw; + } parts64; + struct + { + uint32_t w0, w1, w2, w3; + } parts32; +} ieee854_long_double_shape_type; + +#endif + +#if __FLOAT_WORD_ORDER == __LITTLE_ENDIAN + +typedef union +{ + long double value; + struct + { + uint64_t lsw; + uint64_t msw; + } parts64; + struct + { + uint32_t w3, w2, w1, w0; + } parts32; +} ieee854_long_double_shape_type; + +#endif + +/* Get two 64 bit ints from a long double. */ + +#define GET_LDOUBLE_WORDS64(ix0,ix1,d) \ +do { \ + ieee854_long_double_shape_type qw_u; \ + qw_u.value = (d); \ + (ix0) = qw_u.parts64.msw; \ + (ix1) = qw_u.parts64.lsw; \ +} while (0) + +/* Set a long double from two 64 bit ints. */ + +#define SET_LDOUBLE_WORDS64(d,ix0,ix1) \ +do { \ + ieee854_long_double_shape_type qw_u; \ + qw_u.parts64.msw = (ix0); \ + qw_u.parts64.lsw = (ix1); \ + (d) = qw_u.value; \ +} while (0) + +/* Get the more significant 64 bits of a long double mantissa. */ + +#define GET_LDOUBLE_MSW64(v,d) \ +do { \ + ieee854_long_double_shape_type sh_u; \ + sh_u.value = (d); \ + (v) = sh_u.parts64.msw; \ +} while (0) + +/* Set the more significant 64 bits of a long double mantissa from an int. */ + +#define SET_LDOUBLE_MSW64(d,v) \ +do { \ + ieee854_long_double_shape_type sh_u; \ + sh_u.value = (d); \ + sh_u.parts64.msw = (v); \ + (d) = sh_u.value; \ +} while (0) + +/* Get the least significant 64 bits of a long double mantissa. */ + +#define GET_LDOUBLE_LSW64(v,d) \ +do { \ + ieee854_long_double_shape_type sh_u; \ + sh_u.value = (d); \ + (v) = sh_u.parts64.lsw; \ +} while (0) + +/* + On a platform already supporting a binary128 long double, + _Float128 will alias to long double. This transformation + makes aliasing *l functions to *f128 trivial. +*/ +#define _Float128 long double +#define L(x) x##L + +#endif /* math_ldbl.h */ diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/mpn2ldbl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/mpn2ldbl.c new file mode 100644 index 0000000000..625186fdc2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/mpn2ldbl.c @@ -0,0 +1,52 @@ +/* Copyright (C) 1995-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include <ieee754.h> +#include <float.h> +#include <math.h> + +/* Convert a multi-precision integer of the needed number of bits (113 for + long double) and an integral power of two to a `long double' in IEEE854 + quad-precision format. */ + +long double +__mpn_construct_long_double (mp_srcptr frac_ptr, int expt, int sign) +{ + union ieee854_long_double u; + + u.ieee.negative = sign; + u.ieee.exponent = expt + IEEE854_LONG_DOUBLE_BIAS; +#if BITS_PER_MP_LIMB == 32 + u.ieee.mantissa3 = frac_ptr[0]; + u.ieee.mantissa2 = frac_ptr[1]; + u.ieee.mantissa1 = frac_ptr[2]; + u.ieee.mantissa0 = frac_ptr[3] & (((mp_limb_t) 1 + << (LDBL_MANT_DIG - 96)) - 1); +#elif BITS_PER_MP_LIMB == 64 + u.ieee.mantissa3 = frac_ptr[0] & (((mp_limb_t) 1 << 32) - 1); + u.ieee.mantissa2 = frac_ptr[0] >> 32; + u.ieee.mantissa1 = frac_ptr[1] & (((mp_limb_t) 1 << 32) - 1); + u.ieee.mantissa0 = (frac_ptr[1] >> 32) & (((mp_limb_t) 1 + << (LDBL_MANT_DIG - 96)) - 1); +#else + #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif + + return u.d; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/printf_fphex.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/printf_fphex.c new file mode 100644 index 0000000000..294464ecff --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/printf_fphex.c @@ -0,0 +1,25 @@ +/* Print floating point number in hexadecimal notation according to + ISO C99. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <ldbl-128/printf_fphex_macros.h> +#define PRINT_FPHEX_LONG_DOUBLE \ + PRINT_FPHEX (long double, fpnum.ldbl, ieee854_long_double, \ + IEEE854_LONG_DOUBLE_BIAS) + +#include <stdio-common/printf_fphex.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/printf_fphex_macros.h b/REORG.TODO/sysdeps/ieee754/ldbl-128/printf_fphex_macros.h new file mode 100644 index 0000000000..86681c4c1e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/printf_fphex_macros.h @@ -0,0 +1,104 @@ +/* Macro to print floating point numbers in hexadecimal notation. + Copyright (C) 2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define PRINT_FPHEX(FLOAT, VAR, IEEE854_UNION, IEEE854_BIAS) \ +do { \ + /* We have 112 bits of mantissa plus one implicit digit. Since \ + 112 bits are representable without rest using hexadecimal \ + digits we use only the implicit digits for the number before \ + the decimal point. */ \ + unsigned long long int num0, num1; \ + union IEEE854_UNION u; \ + u.d = VAR; \ + \ + assert (sizeof (FLOAT) == 16); \ + \ + num0 = (((unsigned long long int) u.ieee.mantissa0) << 32 \ + | u.ieee.mantissa1); \ + num1 = (((unsigned long long int) u.ieee.mantissa2) << 32 \ + | u.ieee.mantissa3); \ + \ + zero_mantissa = (num0|num1) == 0; \ + \ + if (sizeof (unsigned long int) > 6) \ + { \ + numstr = _itoa_word (num1, numbuf + sizeof numbuf, 16, \ + info->spec == 'A'); \ + wnumstr = _itowa_word (num1, \ + wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t),\ + 16, info->spec == 'A'); \ + } \ + else \ + { \ + numstr = _itoa (num1, numbuf + sizeof numbuf, 16, \ + info->spec == 'A'); \ + wnumstr = _itowa (num1, \ + wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t), \ + 16, info->spec == 'A'); \ + } \ + \ + while (numstr > numbuf + (sizeof numbuf - 64 / 4)) \ + { \ + *--numstr = '0'; \ + *--wnumstr = L'0'; \ + } \ + \ + if (sizeof (unsigned long int) > 6) \ + { \ + numstr = _itoa_word (num0, numstr, 16, info->spec == 'A'); \ + wnumstr = _itowa_word (num0, wnumstr, 16, info->spec == 'A'); \ + } \ + else \ + { \ + numstr = _itoa (num0, numstr, 16, info->spec == 'A'); \ + wnumstr = _itowa (num0, wnumstr, 16, info->spec == 'A'); \ + } \ + \ + /* Fill with zeroes. */ \ + while (numstr > numbuf + (sizeof numbuf - 112 / 4)) \ + { \ + *--numstr = '0'; \ + *--wnumstr = L'0'; \ + } \ + \ + leading = u.ieee.exponent == 0 ? '0' : '1'; \ + \ + exponent = u.ieee.exponent; \ + \ + if (exponent == 0) \ + { \ + if (zero_mantissa) \ + expnegative = 0; \ + else \ + { \ + /* This is a denormalized number. */ \ + expnegative = 1; \ + exponent = IEEE854_BIAS - 1; \ + } \ + } \ + else if (exponent >= IEEE854_BIAS) \ + { \ + expnegative = 0; \ + exponent -= IEEE854_BIAS; \ + } \ + else \ + { \ + expnegative = 1; \ + exponent = -(exponent - IEEE854_BIAS); \ + } \ +} while (0) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_asinhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_asinhl.c new file mode 100644 index 0000000000..83efb34447 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_asinhl.c @@ -0,0 +1,79 @@ +/* s_asinhl.c -- long double version of s_asinh.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* asinhl(x) + * Method : + * Based on + * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ] + * we have + * asinhl(x) := x if 1+x*x=1, + * := signl(x)*(logl(x)+ln2)) for large |x|, else + * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else + * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2))) + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const _Float128 + one = 1, + ln2 = L(6.931471805599453094172321214581765681e-1), + huge = L(1.0e+4900); + +_Float128 +__asinhl (_Float128 x) +{ + _Float128 t, w; + int32_t ix, sign; + ieee854_long_double_shape_type u; + + u.value = x; + sign = u.parts32.w0; + ix = sign & 0x7fffffff; + if (ix == 0x7fff0000) + return x + x; /* x is inf or NaN */ + if (ix < 0x3fc70000) + { /* |x| < 2^ -56 */ + math_check_force_underflow (x); + if (huge + x > one) + return x; /* return x inexact except 0 */ + } + u.parts32.w0 = ix; + if (ix > 0x40350000) + { /* |x| > 2 ^ 54 */ + w = __ieee754_logl (u.value) + ln2; + } + else if (ix >0x40000000) + { /* 2^ 54 > |x| > 2.0 */ + t = u.value; + w = __ieee754_logl (2.0 * t + one / (__ieee754_sqrtl (x * x + one) + t)); + } + else + { /* 2.0 > |x| > 2 ^ -56 */ + t = x * x; + w = __log1pl (u.value + t / (one + __ieee754_sqrtl (one + t))); + } + if (sign & 0x80000000) + return -w; + else + return w; +} +weak_alias (__asinhl, asinhl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_atanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_atanl.c new file mode 100644 index 0000000000..6f2cd549ec --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_atanl.c @@ -0,0 +1,253 @@ +/* s_atanl.c + * + * Inverse circular tangent for 128-bit long double precision + * (arctangent) + * + * + * + * SYNOPSIS: + * + * long double x, y, atanl(); + * + * y = atanl( x ); + * + * + * + * DESCRIPTION: + * + * Returns radian angle between -pi/2 and +pi/2 whose tangent is x. + * + * The function uses a rational approximation of the form + * t + t^3 P(t^2)/Q(t^2), optimized for |t| < 0.09375. + * + * The argument is reduced using the identity + * arctan x - arctan u = arctan ((x-u)/(1 + ux)) + * and an 83-entry lookup table for arctan u, with u = 0, 1/8, ..., 10.25. + * Use of the table improves the execution speed of the routine. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -19, 19 4e5 1.7e-34 5.4e-35 + * + * + * WARNING: + * + * This program uses integer operations on bit fields of floating-point + * numbers. It does not work with data structures other than the + * structure assumed. + * + */ + +/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov> + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + + +#include <float.h> +#include <math.h> +#include <math_private.h> + +/* arctan(k/8), k = 0, ..., 82 */ +static const _Float128 atantbl[84] = { + L(0.0000000000000000000000000000000000000000E0), + L(1.2435499454676143503135484916387102557317E-1), /* arctan(0.125) */ + L(2.4497866312686415417208248121127581091414E-1), + L(3.5877067027057222039592006392646049977698E-1), + L(4.6364760900080611621425623146121440202854E-1), + L(5.5859931534356243597150821640166127034645E-1), + L(6.4350110879328438680280922871732263804151E-1), + L(7.1882999962162450541701415152590465395142E-1), + L(7.8539816339744830961566084581987572104929E-1), + L(8.4415398611317100251784414827164750652594E-1), + L(8.9605538457134395617480071802993782702458E-1), + L(9.4200004037946366473793717053459358607166E-1), + L(9.8279372324732906798571061101466601449688E-1), + L(1.0191413442663497346383429170230636487744E0), + L(1.0516502125483736674598673120862998296302E0), + L(1.0808390005411683108871567292171998202703E0), + L(1.1071487177940905030170654601785370400700E0), + L(1.1309537439791604464709335155363278047493E0), + L(1.1525719972156675180401498626127513797495E0), + L(1.1722738811284763866005949441337046149712E0), + L(1.1902899496825317329277337748293183376012E0), + L(1.2068173702852525303955115800565576303133E0), + L(1.2220253232109896370417417439225704908830E0), + L(1.2360594894780819419094519711090786987027E0), + L(1.2490457723982544258299170772810901230778E0), + L(1.2610933822524404193139408812473357720101E0), + L(1.2722973952087173412961937498224804940684E0), + L(1.2827408797442707473628852511364955306249E0), + L(1.2924966677897852679030914214070816845853E0), + L(1.3016288340091961438047858503666855921414E0), + L(1.3101939350475556342564376891719053122733E0), + L(1.3182420510168370498593302023271362531155E0), + L(1.3258176636680324650592392104284756311844E0), + L(1.3329603993374458675538498697331558093700E0), + L(1.3397056595989995393283037525895557411039E0), + L(1.3460851583802539310489409282517796256512E0), + L(1.3521273809209546571891479413898128509842E0), + L(1.3578579772154994751124898859640585287459E0), + L(1.3633001003596939542892985278250991189943E0), + L(1.3684746984165928776366381936948529556191E0), + L(1.3734007669450158608612719264449611486510E0), + L(1.3780955681325110444536609641291551522494E0), + L(1.3825748214901258580599674177685685125566E0), + L(1.3868528702577214543289381097042486034883E0), + L(1.3909428270024183486427686943836432060856E0), + L(1.3948567013423687823948122092044222644895E0), + L(1.3986055122719575950126700816114282335732E0), + L(1.4021993871854670105330304794336492676944E0), + L(1.4056476493802697809521934019958079881002E0), + L(1.4089588955564736949699075250792569287156E0), + L(1.4121410646084952153676136718584891599630E0), + L(1.4152014988178669079462550975833894394929E0), + L(1.4181469983996314594038603039700989523716E0), + L(1.4209838702219992566633046424614466661176E0), + L(1.4237179714064941189018190466107297503086E0), + L(1.4263547484202526397918060597281265695725E0), + L(1.4288992721907326964184700745371983590908E0), + L(1.4313562697035588982240194668401779312122E0), + L(1.4337301524847089866404719096698873648610E0), + L(1.4360250423171655234964275337155008780675E0), + L(1.4382447944982225979614042479354815855386E0), + L(1.4403930189057632173997301031392126865694E0), + L(1.4424730991091018200252920599377292525125E0), + L(1.4444882097316563655148453598508037025938E0), + L(1.4464413322481351841999668424758804165254E0), + L(1.4483352693775551917970437843145232637695E0), + L(1.4501726582147939000905940595923466567576E0), + L(1.4519559822271314199339700039142990228105E0), + L(1.4536875822280323362423034480994649820285E0), + L(1.4553696664279718992423082296859928222270E0), + L(1.4570043196511885530074841089245667532358E0), + L(1.4585935117976422128825857356750737658039E0), + L(1.4601391056210009726721818194296893361233E0), + L(1.4616428638860188872060496086383008594310E0), + L(1.4631064559620759326975975316301202111560E0), + L(1.4645314639038178118428450961503371619177E0), + L(1.4659193880646627234129855241049975398470E0), + L(1.4672716522843522691530527207287398276197E0), + L(1.4685896086876430842559640450619880951144E0), + L(1.4698745421276027686510391411132998919794E0), + L(1.4711276743037345918528755717617308518553E0), + L(1.4723501675822635384916444186631899205983E0), + L(1.4735431285433308455179928682541563973416E0), /* arctan(10.25) */ + L(1.5707963267948966192313216916397514420986E0) /* pi/2 */ +}; + + +/* arctan t = t + t^3 p(t^2) / q(t^2) + |t| <= 0.09375 + peak relative error 5.3e-37 */ + +static const _Float128 + p0 = L(-4.283708356338736809269381409828726405572E1), + p1 = L(-8.636132499244548540964557273544599863825E1), + p2 = L(-5.713554848244551350855604111031839613216E1), + p3 = L(-1.371405711877433266573835355036413750118E1), + p4 = L(-8.638214309119210906997318946650189640184E-1), + q0 = L(1.285112506901621042780814422948906537959E2), + q1 = L(3.361907253914337187957855834229672347089E2), + q2 = L(3.180448303864130128268191635189365331680E2), + q3 = L(1.307244136980865800160844625025280344686E2), + q4 = L(2.173623741810414221251136181221172551416E1); + /* q5 = 1.000000000000000000000000000000000000000E0 */ + +static const _Float128 huge = L(1.0e4930); + +_Float128 +__atanl (_Float128 x) +{ + int k, sign; + _Float128 t, u, p, q; + ieee854_long_double_shape_type s; + + s.value = x; + k = s.parts32.w0; + if (k & 0x80000000) + sign = 1; + else + sign = 0; + + /* Check for IEEE special cases. */ + k &= 0x7fffffff; + if (k >= 0x7fff0000) + { + /* NaN. */ + if ((k & 0xffff) | s.parts32.w1 | s.parts32.w2 | s.parts32.w3) + return (x + x); + + /* Infinity. */ + if (sign) + return -atantbl[83]; + else + return atantbl[83]; + } + + if (k <= 0x3fc50000) /* |x| < 2**-58 */ + { + math_check_force_underflow (x); + /* Raise inexact. */ + if (huge + x > 0.0) + return x; + } + + if (k >= 0x40720000) /* |x| > 2**115 */ + { + /* Saturate result to {-,+}pi/2 */ + if (sign) + return -atantbl[83]; + else + return atantbl[83]; + } + + if (sign) + x = -x; + + if (k >= 0x40024800) /* 10.25 */ + { + k = 83; + t = -1.0/x; + } + else + { + /* Index of nearest table element. + Roundoff to integer is asymmetrical to avoid cancellation when t < 0 + (cf. fdlibm). */ + k = 8.0 * x + 0.25; + u = L(0.125) * k; + /* Small arctan argument. */ + t = (x - u) / (1.0 + x * u); + } + + /* Arctan of small argument t. */ + u = t * t; + p = ((((p4 * u) + p3) * u + p2) * u + p1) * u + p0; + q = ((((u + q4) * u + q3) * u + q2) * u + q1) * u + q0; + u = t * u * p / q + t; + + /* arctan x = arctan u + arctan t */ + u = atantbl[k] + u; + if (sign) + return (-u); + else + return u; +} + +weak_alias (__atanl, atanl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_cbrtl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_cbrtl.c new file mode 100644 index 0000000000..eb88d29fc9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_cbrtl.c @@ -0,0 +1,135 @@ +/* cbrtl.c + * + * Cube root, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, cbrtl(); + * + * y = cbrtl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the cube root of the argument, which may be negative. + * + * Range reduction involves determining the power of 2 of + * the argument. A polynomial of degree 2 applied to the + * mantissa, and multiplication by the cube root of 1, 2, or 4 + * approximates the root to within about 0.1%. Then Newton's + * iteration is used three times to converge to an accurate + * result. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -8,8 100000 1.3e-34 3.9e-35 + * IEEE exp(+-707) 100000 1.3e-34 4.3e-35 + * + */ + +/* +Cephes Math Library Release 2.2: January, 1991 +Copyright 1984, 1991 by Stephen L. Moshier +Adapted for glibc October, 2001. + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + + +#include <math.h> +#include <math_private.h> + +static const _Float128 CBRT2 = L(1.259921049894873164767210607278228350570251); +static const _Float128 CBRT4 = L(1.587401051968199474751705639272308260391493); +static const _Float128 CBRT2I = L(0.7937005259840997373758528196361541301957467); +static const _Float128 CBRT4I = L(0.6299605249474365823836053036391141752851257); + + +_Float128 +__cbrtl (_Float128 x) +{ + int e, rem, sign; + _Float128 z; + + if (!isfinite (x)) + return x + x; + + if (x == 0) + return (x); + + if (x > 0) + sign = 1; + else + { + sign = -1; + x = -x; + } + + z = x; + /* extract power of 2, leaving mantissa between 0.5 and 1 */ + x = __frexpl (x, &e); + + /* Approximate cube root of number between .5 and 1, + peak relative error = 1.2e-6 */ + x = ((((L(1.3584464340920900529734e-1) * x + - L(6.3986917220457538402318e-1)) * x + + L(1.2875551670318751538055e0)) * x + - L(1.4897083391357284957891e0)) * x + + L(1.3304961236013647092521e0)) * x + L(3.7568280825958912391243e-1); + + /* exponent divided by 3 */ + if (e >= 0) + { + rem = e; + e /= 3; + rem -= 3 * e; + if (rem == 1) + x *= CBRT2; + else if (rem == 2) + x *= CBRT4; + } + else + { /* argument less than 1 */ + e = -e; + rem = e; + e /= 3; + rem -= 3 * e; + if (rem == 1) + x *= CBRT2I; + else if (rem == 2) + x *= CBRT4I; + e = -e; + } + + /* multiply by power of 2 */ + x = __ldexpl (x, e); + + /* Newton iteration */ + x -= (x - (z / (x * x))) * L(0.3333333333333333333333333333333333333333); + x -= (x - (z / (x * x))) * L(0.3333333333333333333333333333333333333333); + x -= (x - (z / (x * x))) * L(0.3333333333333333333333333333333333333333); + + if (sign < 0) + x = -x; + return (x); +} + +weak_alias (__cbrtl, cbrtl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_ceill.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_ceill.c new file mode 100644 index 0000000000..8034795072 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_ceill.c @@ -0,0 +1,66 @@ +/* s_ceill.c -- long double version of s_ceil.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * ceill(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + */ + +#include <math.h> +#include <math_private.h> + +_Float128 __ceill(_Float128 x) +{ + int64_t i0,i1,j0; + u_int64_t i,j; + GET_LDOUBLE_WORDS64(i0,i1,x); + j0 = ((i0>>48)&0x7fff)-0x3fff; + if(j0<48) { + if(j0<0) { + /* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x8000000000000000ULL;i1=0;} + else if((i0|i1)!=0) { i0=0x3fff000000000000ULL;i1=0;} + } else { + i = (0x0000ffffffffffffULL)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(i0>0) i0 += (0x0001000000000000LL)>>j0; + i0 &= (~i); i1=0; + } + } else if (j0>111) { + if(j0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = -1ULL>>(j0-48); + if((i1&i)==0) return x; /* x is integral */ + if(i0>0) { + if(j0==48) i0+=1; + else { + j = i1+(1LL<<(112-j0)); + if(j<i1) i0 +=1 ; /* got a carry */ + i1=j; + } + } + i1 &= (~i); + } + SET_LDOUBLE_WORDS64(x,i0,i1); + return x; +} +weak_alias (__ceill, ceill) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_copysignl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_copysignl.c new file mode 100644 index 0000000000..8ee85ea8f7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_copysignl.c @@ -0,0 +1,38 @@ +/* s_copysignl.c -- long double version of s_copysign.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * copysignl(long double x, long double y) + * copysignl(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include <math.h> +#include <math_private.h> + +_Float128 __copysignl(_Float128 x, _Float128 y) +{ + u_int64_t hx,hy; + GET_LDOUBLE_MSW64(hx,x); + GET_LDOUBLE_MSW64(hy,y); + SET_LDOUBLE_MSW64(x,(hx&0x7fffffffffffffffULL) + |(hy&0x8000000000000000ULL)); + return x; +} +weak_alias (__copysignl, copysignl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_cosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_cosl.c new file mode 100644 index 0000000000..ed3e77d0db --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_cosl.c @@ -0,0 +1,86 @@ +/* s_cosl.c -- long double version of s_cos.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* cosl(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sinl ... sine function on [-pi/4,pi/4] + * __kernel_cosl ... cosine function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> + +_Float128 __cosl(_Float128 x) +{ + _Float128 y[2],z=0; + int64_t n, ix; + + /* High word of x. */ + GET_LDOUBLE_MSW64(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if(ix <= 0x3ffe921fb54442d1LL) + return __kernel_cosl(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7fff000000000000LL) { + if (ix == 0x7fff000000000000LL) { + GET_LDOUBLE_LSW64(n,x); + if (n == 0) + __set_errno (EDOM); + } + return x-x; + } + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + switch(n&3) { + case 0: return __kernel_cosl(y[0],y[1]); + case 1: return -__kernel_sinl(y[0],y[1],1); + case 2: return -__kernel_cosl(y[0],y[1]); + default: + return __kernel_sinl(y[0],y[1],1); + } + } +} +weak_alias (__cosl, cosl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_erfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_erfl.c new file mode 100644 index 0000000000..e5dfae9636 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_erfl.c @@ -0,0 +1,948 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Modifications and expansions for 128-bit long double are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. erf(x) = x + x*R(x^2) for |x| in [0, 7/8] + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. + * + * 1a. erf(x) = 1 - erfc(x), for |x| > 1.0 + * erfc(x) = 1 - erf(x) if |x| < 1/4 + * + * 2. For |x| in [7/8, 1], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(s + c) = sign(x) * (c + P1(s)/Q1(s)) + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * + * 3. For x in [1/4, 5/4], + * erfc(s + const) = erfc(const) + s P1(s)/Q1(s) + * for const = 1/4, 3/8, ..., 9/8 + * and 0 <= s <= 1/8 . + * + * 4. For x in [5/4, 107], + * erfc(x) = (1/x)*exp(-x*x-0.5625 + R(z)) + * z=1/x^2 + * The interval is partitioned into several segments + * of width 1/8 in 1/x. + * + * Note1: + * To compute exp(-x*x-0.5625+R/S), let s be a single + * precision number and s := x; then + * -x*x = -s*s + (s-x)*(s+x) + * exp(-x*x-0.5626+R/S) = + * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); + * Note2: + * Here 4 and 5 make use of the asymptotic series + * exp(-x*x) + * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) + * x*sqrt(pi) + * + * 5. For inf > x >= 107 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static _Float128 +neval (_Float128 x, const _Float128 *p, int n) +{ + _Float128 y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static _Float128 +deval (_Float128 x, const _Float128 *p, int n) +{ + _Float128 y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + + +static const _Float128 +tiny = L(1e-4931), + one = 1, + two = 2, + /* 2/sqrt(pi) - 1 */ + efx = L(1.2837916709551257389615890312154517168810E-1); + + +/* erf(x) = x + x R(x^2) + 0 <= x <= 7/8 + Peak relative error 1.8e-35 */ +#define NTN1 8 +static const _Float128 TN1[NTN1 + 1] = +{ + L(-3.858252324254637124543172907442106422373E10), + L(9.580319248590464682316366876952214879858E10), + L(1.302170519734879977595901236693040544854E10), + L(2.922956950426397417800321486727032845006E9), + L(1.764317520783319397868923218385468729799E8), + L(1.573436014601118630105796794840834145120E7), + L(4.028077380105721388745632295157816229289E5), + L(1.644056806467289066852135096352853491530E4), + L(3.390868480059991640235675479463287886081E1) +}; +#define NTD1 8 +static const _Float128 TD1[NTD1 + 1] = +{ + L(-3.005357030696532927149885530689529032152E11), + L(-1.342602283126282827411658673839982164042E11), + L(-2.777153893355340961288511024443668743399E10), + L(-3.483826391033531996955620074072768276974E9), + L(-2.906321047071299585682722511260895227921E8), + L(-1.653347985722154162439387878512427542691E7), + L(-6.245520581562848778466500301865173123136E5), + L(-1.402124304177498828590239373389110545142E4), + L(-1.209368072473510674493129989468348633579E2) +/* 1.0E0 */ +}; + + +/* erf(z+1) = erf_const + P(z)/Q(z) + -.125 <= z <= 0 + Peak relative error 7.3e-36 */ +static const _Float128 erf_const = L(0.845062911510467529296875); +#define NTN2 8 +static const _Float128 TN2[NTN2 + 1] = +{ + L(-4.088889697077485301010486931817357000235E1), + L(7.157046430681808553842307502826960051036E3), + L(-2.191561912574409865550015485451373731780E3), + L(2.180174916555316874988981177654057337219E3), + L(2.848578658049670668231333682379720943455E2), + L(1.630362490952512836762810462174798925274E2), + L(6.317712353961866974143739396865293596895E0), + L(2.450441034183492434655586496522857578066E1), + L(5.127662277706787664956025545897050896203E-1) +}; +#define NTD2 8 +static const _Float128 TD2[NTD2 + 1] = +{ + L(1.731026445926834008273768924015161048885E4), + L(1.209682239007990370796112604286048173750E4), + L(1.160950290217993641320602282462976163857E4), + L(5.394294645127126577825507169061355698157E3), + L(2.791239340533632669442158497532521776093E3), + L(8.989365571337319032943005387378993827684E2), + L(2.974016493766349409725385710897298069677E2), + L(6.148192754590376378740261072533527271947E1), + L(1.178502892490738445655468927408440847480E1) + /* 1.0E0 */ +}; + + +/* erfc(x + 0.25) = erfc(0.25) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.4e-35 */ +#define NRNr13 8 +static const _Float128 RNr13[NRNr13 + 1] = +{ + L(-2.353707097641280550282633036456457014829E3), + L(3.871159656228743599994116143079870279866E2), + L(-3.888105134258266192210485617504098426679E2), + L(-2.129998539120061668038806696199343094971E1), + L(-8.125462263594034672468446317145384108734E1), + L(8.151549093983505810118308635926270319660E0), + L(-5.033362032729207310462422357772568553670E0), + L(-4.253956621135136090295893547735851168471E-2), + L(-8.098602878463854789780108161581050357814E-2) +}; +#define NRDr13 7 +static const _Float128 RDr13[NRDr13 + 1] = +{ + L(2.220448796306693503549505450626652881752E3), + L(1.899133258779578688791041599040951431383E2), + L(1.061906712284961110196427571557149268454E3), + L(7.497086072306967965180978101974566760042E1), + L(2.146796115662672795876463568170441327274E2), + L(1.120156008362573736664338015952284925592E1), + L(2.211014952075052616409845051695042741074E1), + L(6.469655675326150785692908453094054988938E-1) + /* 1.0E0 */ +}; +/* erfc(0.25) = C13a + C13b to extra precision. */ +static const _Float128 C13a = L(0.723663330078125); +static const _Float128 C13b = L(1.0279753638067014931732235184287934646022E-5); + + +/* erfc(x + 0.375) = erfc(0.375) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.2e-35 */ +#define NRNr14 8 +static const _Float128 RNr14[NRNr14 + 1] = +{ + L(-2.446164016404426277577283038988918202456E3), + L(6.718753324496563913392217011618096698140E2), + L(-4.581631138049836157425391886957389240794E2), + L(-2.382844088987092233033215402335026078208E1), + L(-7.119237852400600507927038680970936336458E1), + L(1.313609646108420136332418282286454287146E1), + L(-6.188608702082264389155862490056401365834E0), + L(-2.787116601106678287277373011101132659279E-2), + L(-2.230395570574153963203348263549700967918E-2) +}; +#define NRDr14 7 +static const _Float128 RDr14[NRDr14 + 1] = +{ + L(2.495187439241869732696223349840963702875E3), + L(2.503549449872925580011284635695738412162E2), + L(1.159033560988895481698051531263861842461E3), + L(9.493751466542304491261487998684383688622E1), + L(2.276214929562354328261422263078480321204E2), + L(1.367697521219069280358984081407807931847E1), + L(2.276988395995528495055594829206582732682E1), + L(7.647745753648996559837591812375456641163E-1) + /* 1.0E0 */ +}; +/* erfc(0.375) = C14a + C14b to extra precision. */ +static const _Float128 C14a = L(0.5958709716796875); +static const _Float128 C14b = L(1.2118885490201676174914080878232469565953E-5); + +/* erfc(x + 0.5) = erfc(0.5) + x R(x) + 0 <= x < 0.125 + Peak relative error 4.7e-36 */ +#define NRNr15 8 +static const _Float128 RNr15[NRNr15 + 1] = +{ + L(-2.624212418011181487924855581955853461925E3), + L(8.473828904647825181073831556439301342756E2), + L(-5.286207458628380765099405359607331669027E2), + L(-3.895781234155315729088407259045269652318E1), + L(-6.200857908065163618041240848728398496256E1), + L(1.469324610346924001393137895116129204737E1), + L(-6.961356525370658572800674953305625578903E0), + L(5.145724386641163809595512876629030548495E-3), + L(1.990253655948179713415957791776180406812E-2) +}; +#define NRDr15 7 +static const _Float128 RDr15[NRDr15 + 1] = +{ + L(2.986190760847974943034021764693341524962E3), + L(5.288262758961073066335410218650047725985E2), + L(1.363649178071006978355113026427856008978E3), + L(1.921707975649915894241864988942255320833E2), + L(2.588651100651029023069013885900085533226E2), + L(2.628752920321455606558942309396855629459E1), + L(2.455649035885114308978333741080991380610E1), + L(1.378826653595128464383127836412100939126E0) + /* 1.0E0 */ +}; +/* erfc(0.5) = C15a + C15b to extra precision. */ +static const _Float128 C15a = L(0.4794921875); +static const _Float128 C15b = L(7.9346869534623172533461080354712635484242E-6); + +/* erfc(x + 0.625) = erfc(0.625) + x R(x) + 0 <= x < 0.125 + Peak relative error 5.1e-36 */ +#define NRNr16 8 +static const _Float128 RNr16[NRNr16 + 1] = +{ + L(-2.347887943200680563784690094002722906820E3), + L(8.008590660692105004780722726421020136482E2), + L(-5.257363310384119728760181252132311447963E2), + L(-4.471737717857801230450290232600243795637E1), + L(-4.849540386452573306708795324759300320304E1), + L(1.140885264677134679275986782978655952843E1), + L(-6.731591085460269447926746876983786152300E0), + L(1.370831653033047440345050025876085121231E-1), + L(2.022958279982138755020825717073966576670E-2), +}; +#define NRDr16 7 +static const _Float128 RDr16[NRDr16 + 1] = +{ + L(3.075166170024837215399323264868308087281E3), + L(8.730468942160798031608053127270430036627E2), + L(1.458472799166340479742581949088453244767E3), + L(3.230423687568019709453130785873540386217E2), + L(2.804009872719893612081109617983169474655E2), + L(4.465334221323222943418085830026979293091E1), + L(2.612723259683205928103787842214809134746E1), + L(2.341526751185244109722204018543276124997E0), + /* 1.0E0 */ +}; +/* erfc(0.625) = C16a + C16b to extra precision. */ +static const _Float128 C16a = L(0.3767547607421875); +static const _Float128 C16b = L(4.3570693945275513594941232097252997287766E-6); + +/* erfc(x + 0.75) = erfc(0.75) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.7e-35 */ +#define NRNr17 8 +static const _Float128 RNr17[NRNr17 + 1] = +{ + L(-1.767068734220277728233364375724380366826E3), + L(6.693746645665242832426891888805363898707E2), + L(-4.746224241837275958126060307406616817753E2), + L(-2.274160637728782675145666064841883803196E1), + L(-3.541232266140939050094370552538987982637E1), + L(6.988950514747052676394491563585179503865E0), + L(-5.807687216836540830881352383529281215100E0), + L(3.631915988567346438830283503729569443642E-1), + L(-1.488945487149634820537348176770282391202E-2) +}; +#define NRDr17 7 +static const _Float128 RDr17[NRDr17 + 1] = +{ + L(2.748457523498150741964464942246913394647E3), + L(1.020213390713477686776037331757871252652E3), + L(1.388857635935432621972601695296561952738E3), + L(3.903363681143817750895999579637315491087E2), + L(2.784568344378139499217928969529219886578E2), + L(5.555800830216764702779238020065345401144E1), + L(2.646215470959050279430447295801291168941E1), + L(2.984905282103517497081766758550112011265E0), + /* 1.0E0 */ +}; +/* erfc(0.75) = C17a + C17b to extra precision. */ +static const _Float128 C17a = L(0.2888336181640625); +static const _Float128 C17b = L(1.0748182422368401062165408589222625794046E-5); + + +/* erfc(x + 0.875) = erfc(0.875) + x R(x) + 0 <= x < 0.125 + Peak relative error 2.2e-35 */ +#define NRNr18 8 +static const _Float128 RNr18[NRNr18 + 1] = +{ + L(-1.342044899087593397419622771847219619588E3), + L(6.127221294229172997509252330961641850598E2), + L(-4.519821356522291185621206350470820610727E2), + L(1.223275177825128732497510264197915160235E1), + L(-2.730789571382971355625020710543532867692E1), + L(4.045181204921538886880171727755445395862E0), + L(-4.925146477876592723401384464691452700539E0), + L(5.933878036611279244654299924101068088582E-1), + L(-5.557645435858916025452563379795159124753E-2) +}; +#define NRDr18 7 +static const _Float128 RDr18[NRDr18 + 1] = +{ + L(2.557518000661700588758505116291983092951E3), + L(1.070171433382888994954602511991940418588E3), + L(1.344842834423493081054489613250688918709E3), + L(4.161144478449381901208660598266288188426E2), + L(2.763670252219855198052378138756906980422E2), + L(5.998153487868943708236273854747564557632E1), + L(2.657695108438628847733050476209037025318E1), + L(3.252140524394421868923289114410336976512E0), + /* 1.0E0 */ +}; +/* erfc(0.875) = C18a + C18b to extra precision. */ +static const _Float128 C18a = L(0.215911865234375); +static const _Float128 C18b = L(1.3073705765341685464282101150637224028267E-5); + +/* erfc(x + 1.0) = erfc(1.0) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.6e-35 */ +#define NRNr19 8 +static const _Float128 RNr19[NRNr19 + 1] = +{ + L(-1.139180936454157193495882956565663294826E3), + L(6.134903129086899737514712477207945973616E2), + L(-4.628909024715329562325555164720732868263E2), + L(4.165702387210732352564932347500364010833E1), + L(-2.286979913515229747204101330405771801610E1), + L(1.870695256449872743066783202326943667722E0), + L(-4.177486601273105752879868187237000032364E0), + L(7.533980372789646140112424811291782526263E-1), + L(-8.629945436917752003058064731308767664446E-2) +}; +#define NRDr19 7 +static const _Float128 RDr19[NRDr19 + 1] = +{ + L(2.744303447981132701432716278363418643778E3), + L(1.266396359526187065222528050591302171471E3), + L(1.466739461422073351497972255511919814273E3), + L(4.868710570759693955597496520298058147162E2), + L(2.993694301559756046478189634131722579643E2), + L(6.868976819510254139741559102693828237440E1), + L(2.801505816247677193480190483913753613630E1), + L(3.604439909194350263552750347742663954481E0), + /* 1.0E0 */ +}; +/* erfc(1.0) = C19a + C19b to extra precision. */ +static const _Float128 C19a = L(0.15728759765625); +static const _Float128 C19b = L(1.1609394035130658779364917390740703933002E-5); + +/* erfc(x + 1.125) = erfc(1.125) + x R(x) + 0 <= x < 0.125 + Peak relative error 3.6e-36 */ +#define NRNr20 8 +static const _Float128 RNr20[NRNr20 + 1] = +{ + L(-9.652706916457973956366721379612508047640E2), + L(5.577066396050932776683469951773643880634E2), + L(-4.406335508848496713572223098693575485978E2), + L(5.202893466490242733570232680736966655434E1), + L(-1.931311847665757913322495948705563937159E1), + L(-9.364318268748287664267341457164918090611E-2), + L(-3.306390351286352764891355375882586201069E0), + L(7.573806045289044647727613003096916516475E-1), + L(-9.611744011489092894027478899545635991213E-2) +}; +#define NRDr20 7 +static const _Float128 RDr20[NRDr20 + 1] = +{ + L(3.032829629520142564106649167182428189014E3), + L(1.659648470721967719961167083684972196891E3), + L(1.703545128657284619402511356932569292535E3), + L(6.393465677731598872500200253155257708763E2), + L(3.489131397281030947405287112726059221934E2), + L(8.848641738570783406484348434387611713070E1), + L(3.132269062552392974833215844236160958502E1), + L(4.430131663290563523933419966185230513168E0) + /* 1.0E0 */ +}; +/* erfc(1.125) = C20a + C20b to extra precision. */ +static const _Float128 C20a = L(0.111602783203125); +static const _Float128 C20b = L(8.9850951672359304215530728365232161564636E-6); + +/* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2)) + 7/8 <= 1/x < 1 + Peak relative error 1.4e-35 */ +#define NRNr8 9 +static const _Float128 RNr8[NRNr8 + 1] = +{ + L(3.587451489255356250759834295199296936784E1), + L(5.406249749087340431871378009874875889602E2), + L(2.931301290625250886238822286506381194157E3), + L(7.359254185241795584113047248898753470923E3), + L(9.201031849810636104112101947312492532314E3), + L(5.749697096193191467751650366613289284777E3), + L(1.710415234419860825710780802678697889231E3), + L(2.150753982543378580859546706243022719599E2), + L(8.740953582272147335100537849981160931197E0), + L(4.876422978828717219629814794707963640913E-2) +}; +#define NRDr8 8 +static const _Float128 RDr8[NRDr8 + 1] = +{ + L(6.358593134096908350929496535931630140282E1), + L(9.900253816552450073757174323424051765523E2), + L(5.642928777856801020545245437089490805186E3), + L(1.524195375199570868195152698617273739609E4), + L(2.113829644500006749947332935305800887345E4), + L(1.526438562626465706267943737310282977138E4), + L(5.561370922149241457131421914140039411782E3), + L(9.394035530179705051609070428036834496942E2), + L(6.147019596150394577984175188032707343615E1) + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2)) + 0.75 <= 1/x <= 0.875 + Peak relative error 2.0e-36 */ +#define NRNr7 9 +static const _Float128 RNr7[NRNr7 + 1] = +{ + L(1.686222193385987690785945787708644476545E1), + L(1.178224543567604215602418571310612066594E3), + L(1.764550584290149466653899886088166091093E4), + L(1.073758321890334822002849369898232811561E5), + L(3.132840749205943137619839114451290324371E5), + L(4.607864939974100224615527007793867585915E5), + L(3.389781820105852303125270837910972384510E5), + L(1.174042187110565202875011358512564753399E5), + L(1.660013606011167144046604892622504338313E4), + L(6.700393957480661937695573729183733234400E2) +}; +#define NRDr7 9 +static const _Float128 RDr7[NRDr7 + 1] = +{ +L(-1.709305024718358874701575813642933561169E3), +L(-3.280033887481333199580464617020514788369E4), +L(-2.345284228022521885093072363418750835214E5), +L(-8.086758123097763971926711729242327554917E5), +L(-1.456900414510108718402423999575992450138E6), +L(-1.391654264881255068392389037292702041855E6), +L(-6.842360801869939983674527468509852583855E5), +L(-1.597430214446573566179675395199807533371E5), +L(-1.488876130609876681421645314851760773480E4), +L(-3.511762950935060301403599443436465645703E2) + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 5/8 <= 1/x < 3/4 + Peak relative error 1.9e-35 */ +#define NRNr6 9 +static const _Float128 RNr6[NRNr6 + 1] = +{ + L(1.642076876176834390623842732352935761108E0), + L(1.207150003611117689000664385596211076662E2), + L(2.119260779316389904742873816462800103939E3), + L(1.562942227734663441801452930916044224174E4), + L(5.656779189549710079988084081145693580479E4), + L(1.052166241021481691922831746350942786299E5), + L(9.949798524786000595621602790068349165758E4), + L(4.491790734080265043407035220188849562856E4), + L(8.377074098301530326270432059434791287601E3), + L(4.506934806567986810091824791963991057083E2) +}; +#define NRDr6 9 +static const _Float128 RDr6[NRDr6 + 1] = +{ +L(-1.664557643928263091879301304019826629067E2), +L(-3.800035902507656624590531122291160668452E3), +L(-3.277028191591734928360050685359277076056E4), +L(-1.381359471502885446400589109566587443987E5), +L(-3.082204287382581873532528989283748656546E5), +L(-3.691071488256738343008271448234631037095E5), +L(-2.300482443038349815750714219117566715043E5), +L(-6.873955300927636236692803579555752171530E4), +L(-8.262158817978334142081581542749986845399E3), +L(-2.517122254384430859629423488157361983661E2) + /* 1.00 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/2 <= 1/x < 5/8 + Peak relative error 4.6e-36 */ +#define NRNr5 10 +static const _Float128 RNr5[NRNr5 + 1] = +{ +L(-3.332258927455285458355550878136506961608E-3), +L(-2.697100758900280402659586595884478660721E-1), +L(-6.083328551139621521416618424949137195536E0), +L(-6.119863528983308012970821226810162441263E1), +L(-3.176535282475593173248810678636522589861E2), +L(-8.933395175080560925809992467187963260693E2), +L(-1.360019508488475978060917477620199499560E3), +L(-1.075075579828188621541398761300910213280E3), +L(-4.017346561586014822824459436695197089916E2), +L(-5.857581368145266249509589726077645791341E1), +L(-2.077715925587834606379119585995758954399E0) +}; +#define NRDr5 9 +static const _Float128 RDr5[NRDr5 + 1] = +{ + L(3.377879570417399341550710467744693125385E-1), + L(1.021963322742390735430008860602594456187E1), + L(1.200847646592942095192766255154827011939E2), + L(7.118915528142927104078182863387116942836E2), + L(2.318159380062066469386544552429625026238E3), + L(4.238729853534009221025582008928765281620E3), + L(4.279114907284825886266493994833515580782E3), + L(2.257277186663261531053293222591851737504E3), + L(5.570475501285054293371908382916063822957E2), + L(5.142189243856288981145786492585432443560E1) + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 3/8 <= 1/x < 1/2 + Peak relative error 2.0e-36 */ +#define NRNr4 10 +static const _Float128 RNr4[NRNr4 + 1] = +{ + L(3.258530712024527835089319075288494524465E-3), + L(2.987056016877277929720231688689431056567E-1), + L(8.738729089340199750734409156830371528862E0), + L(1.207211160148647782396337792426311125923E2), + L(8.997558632489032902250523945248208224445E2), + L(3.798025197699757225978410230530640879762E3), + L(9.113203668683080975637043118209210146846E3), + L(1.203285891339933238608683715194034900149E4), + L(8.100647057919140328536743641735339740855E3), + L(2.383888249907144945837976899822927411769E3), + L(2.127493573166454249221983582495245662319E2) +}; +#define NRDr4 10 +static const _Float128 RDr4[NRDr4 + 1] = +{ +L(-3.303141981514540274165450687270180479586E-1), +L(-1.353768629363605300707949368917687066724E1), +L(-2.206127630303621521950193783894598987033E2), +L(-1.861800338758066696514480386180875607204E3), +L(-8.889048775872605708249140016201753255599E3), +L(-2.465888106627948210478692168261494857089E4), +L(-3.934642211710774494879042116768390014289E4), +L(-3.455077258242252974937480623730228841003E4), +L(-1.524083977439690284820586063729912653196E4), +L(-2.810541887397984804237552337349093953857E3), +L(-1.343929553541159933824901621702567066156E2) + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/4 <= 1/x < 3/8 + Peak relative error 8.4e-37 */ +#define NRNr3 11 +static const _Float128 RNr3[NRNr3 + 1] = +{ +L(-1.952401126551202208698629992497306292987E-6), +L(-2.130881743066372952515162564941682716125E-4), +L(-8.376493958090190943737529486107282224387E-3), +L(-1.650592646560987700661598877522831234791E-1), +L(-1.839290818933317338111364667708678163199E0), +L(-1.216278715570882422410442318517814388470E1), +L(-4.818759344462360427612133632533779091386E1), +L(-1.120994661297476876804405329172164436784E2), +L(-1.452850765662319264191141091859300126931E2), +L(-9.485207851128957108648038238656777241333E1), +L(-2.563663855025796641216191848818620020073E1), +L(-1.787995944187565676837847610706317833247E0) +}; +#define NRDr3 10 +static const _Float128 RDr3[NRDr3 + 1] = +{ + L(1.979130686770349481460559711878399476903E-4), + L(1.156941716128488266238105813374635099057E-2), + L(2.752657634309886336431266395637285974292E-1), + L(3.482245457248318787349778336603569327521E0), + L(2.569347069372696358578399521203959253162E1), + L(1.142279000180457419740314694631879921561E2), + L(3.056503977190564294341422623108332700840E2), + L(4.780844020923794821656358157128719184422E2), + L(4.105972727212554277496256802312730410518E2), + L(1.724072188063746970865027817017067646246E2), + L(2.815939183464818198705278118326590370435E1) + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/8 <= 1/x < 1/4 + Peak relative error 1.5e-36 */ +#define NRNr2 11 +static const _Float128 RNr2[NRNr2 + 1] = +{ +L(-2.638914383420287212401687401284326363787E-8), +L(-3.479198370260633977258201271399116766619E-6), +L(-1.783985295335697686382487087502222519983E-4), +L(-4.777876933122576014266349277217559356276E-3), +L(-7.450634738987325004070761301045014986520E-2), +L(-7.068318854874733315971973707247467326619E-1), +L(-4.113919921935944795764071670806867038732E0), +L(-1.440447573226906222417767283691888875082E1), +L(-2.883484031530718428417168042141288943905E1), +L(-2.990886974328476387277797361464279931446E1), +L(-1.325283914915104866248279787536128997331E1), +L(-1.572436106228070195510230310658206154374E0) +}; +#define NRDr2 10 +static const _Float128 RDr2[NRDr2 + 1] = +{ + L(2.675042728136731923554119302571867799673E-6), + L(2.170997868451812708585443282998329996268E-4), + L(7.249969752687540289422684951196241427445E-3), + L(1.302040375859768674620410563307838448508E-1), + L(1.380202483082910888897654537144485285549E0), + L(8.926594113174165352623847870299170069350E0), + L(3.521089584782616472372909095331572607185E1), + L(8.233547427533181375185259050330809105570E1), + L(1.072971579885803033079469639073292840135E2), + L(6.943803113337964469736022094105143158033E1), + L(1.775695341031607738233608307835017282662E1) + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/128 <= 1/x < 1/8 + Peak relative error 2.2e-36 */ +#define NRNr1 9 +static const _Float128 RNr1[NRNr1 + 1] = +{ +L(-4.250780883202361946697751475473042685782E-8), +L(-5.375777053288612282487696975623206383019E-6), +L(-2.573645949220896816208565944117382460452E-4), +L(-6.199032928113542080263152610799113086319E-3), +L(-8.262721198693404060380104048479916247786E-2), +L(-6.242615227257324746371284637695778043982E-1), +L(-2.609874739199595400225113299437099626386E0), +L(-5.581967563336676737146358534602770006970E0), +L(-5.124398923356022609707490956634280573882E0), +L(-1.290865243944292370661544030414667556649E0) +}; +#define NRDr1 8 +static const _Float128 RDr1[NRDr1 + 1] = +{ + L(4.308976661749509034845251315983612976224E-6), + L(3.265390126432780184125233455960049294580E-4), + L(9.811328839187040701901866531796570418691E-3), + L(1.511222515036021033410078631914783519649E-1), + L(1.289264341917429958858379585970225092274E0), + L(6.147640356182230769548007536914983522270E0), + L(1.573966871337739784518246317003956180750E1), + L(1.955534123435095067199574045529218238263E1), + L(9.472613121363135472247929109615785855865E0) + /* 1.0E0 */ +}; + + +_Float128 +__erfl (_Float128 x) +{ + _Float128 a, y, z; + int32_t i, ix, sign; + ieee854_long_double_shape_type u; + + u.value = x; + sign = u.parts32.w0; + ix = sign & 0x7fffffff; + + if (ix >= 0x7fff0000) + { /* erf(nan)=nan */ + i = ((sign & 0xffff0000) >> 31) << 1; + return (_Float128) (1 - i) + one / x; /* erf(+-inf)=+-1 */ + } + + if (ix >= 0x3fff0000) /* |x| >= 1.0 */ + { + if (ix >= 0x40030000 && sign > 0) + return one; /* x >= 16, avoid spurious underflow from erfc. */ + y = __erfcl (x); + return (one - y); + /* return (one - __erfcl (x)); */ + } + u.parts32.w0 = ix; + a = u.value; + z = x * x; + if (ix < 0x3ffec000) /* a < 0.875 */ + { + if (ix < 0x3fc60000) /* |x|<2**-57 */ + { + if (ix < 0x00080000) + { + /* Avoid spurious underflow. */ + _Float128 ret = 0.0625 * (16.0 * x + (16.0 * efx) * x); + math_check_force_underflow (ret); + return ret; + } + return x + efx * x; + } + y = a + a * neval (z, TN1, NTN1) / deval (z, TD1, NTD1); + } + else + { + a = a - one; + y = erf_const + neval (a, TN2, NTN2) / deval (a, TD2, NTD2); + } + + if (sign & 0x80000000) /* x < 0 */ + y = -y; + return( y ); +} + +weak_alias (__erfl, erfl) +_Float128 +__erfcl (_Float128 x) +{ + _Float128 y, z, p, r; + int32_t i, ix, sign; + ieee854_long_double_shape_type u; + + u.value = x; + sign = u.parts32.w0; + ix = sign & 0x7fffffff; + u.parts32.w0 = ix; + + if (ix >= 0x7fff0000) + { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (_Float128) (((u_int32_t) sign >> 31) << 1) + one / x; + } + + if (ix < 0x3ffd0000) /* |x| <1/4 */ + { + if (ix < 0x3f8d0000) /* |x|<2**-114 */ + return one - x; + return one - __erfl (x); + } + if (ix < 0x3fff4000) /* 1.25 */ + { + x = u.value; + i = 8.0 * x; + switch (i) + { + case 2: + z = x - L(0.25); + y = C13b + z * neval (z, RNr13, NRNr13) / deval (z, RDr13, NRDr13); + y += C13a; + break; + case 3: + z = x - L(0.375); + y = C14b + z * neval (z, RNr14, NRNr14) / deval (z, RDr14, NRDr14); + y += C14a; + break; + case 4: + z = x - L(0.5); + y = C15b + z * neval (z, RNr15, NRNr15) / deval (z, RDr15, NRDr15); + y += C15a; + break; + case 5: + z = x - L(0.625); + y = C16b + z * neval (z, RNr16, NRNr16) / deval (z, RDr16, NRDr16); + y += C16a; + break; + case 6: + z = x - L(0.75); + y = C17b + z * neval (z, RNr17, NRNr17) / deval (z, RDr17, NRDr17); + y += C17a; + break; + case 7: + z = x - L(0.875); + y = C18b + z * neval (z, RNr18, NRNr18) / deval (z, RDr18, NRDr18); + y += C18a; + break; + case 8: + z = x - 1; + y = C19b + z * neval (z, RNr19, NRNr19) / deval (z, RDr19, NRDr19); + y += C19a; + break; + default: /* i == 9. */ + z = x - L(1.125); + y = C20b + z * neval (z, RNr20, NRNr20) / deval (z, RDr20, NRDr20); + y += C20a; + break; + } + if (sign & 0x80000000) + y = 2 - y; + return y; + } + /* 1.25 < |x| < 107 */ + if (ix < 0x4005ac00) + { + /* x < -9 */ + if ((ix >= 0x40022000) && (sign & 0x80000000)) + return two - tiny; + + x = fabsl (x); + z = one / (x * x); + i = 8.0 / x; + switch (i) + { + default: + case 0: + p = neval (z, RNr1, NRNr1) / deval (z, RDr1, NRDr1); + break; + case 1: + p = neval (z, RNr2, NRNr2) / deval (z, RDr2, NRDr2); + break; + case 2: + p = neval (z, RNr3, NRNr3) / deval (z, RDr3, NRDr3); + break; + case 3: + p = neval (z, RNr4, NRNr4) / deval (z, RDr4, NRDr4); + break; + case 4: + p = neval (z, RNr5, NRNr5) / deval (z, RDr5, NRDr5); + break; + case 5: + p = neval (z, RNr6, NRNr6) / deval (z, RDr6, NRDr6); + break; + case 6: + p = neval (z, RNr7, NRNr7) / deval (z, RDr7, NRDr7); + break; + case 7: + p = neval (z, RNr8, NRNr8) / deval (z, RDr8, NRDr8); + break; + } + u.value = x; + u.parts32.w3 = 0; + u.parts32.w2 &= 0xfe000000; + z = u.value; + r = __ieee754_expl (-z * z - 0.5625) * + __ieee754_expl ((z - x) * (z + x) + p); + if ((sign & 0x80000000) == 0) + { + _Float128 ret = r / x; + if (ret == 0) + __set_errno (ERANGE); + return ret; + } + else + return two - r / x; + } + else + { + if ((sign & 0x80000000) == 0) + { + __set_errno (ERANGE); + return tiny * tiny; + } + else + return two - tiny; + } +} + +weak_alias (__erfcl, erfcl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_expm1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_expm1l.c new file mode 100644 index 0000000000..46d078b77b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_expm1l.c @@ -0,0 +1,166 @@ +/* expm1l.c + * + * Exponential function, minus 1 + * 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, expm1l(); + * + * y = expm1l( x ); + * + * + * + * DESCRIPTION: + * + * Returns e (2.71828...) raised to the x power, minus one. + * + * Range reduction is accomplished by separating the argument + * into an integer k and fraction f such that + * + * x k f + * e = 2 e. + * + * An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1 + * in the basic range [-0.5 ln 2, 0.5 ln 2]. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -79,+MAXLOG 100,000 1.7e-34 4.5e-35 + * + */ + +/* Copyright 2001 by Stephen L. Moshier + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + + + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x) + -.5 ln 2 < x < .5 ln 2 + Theoretical peak relative error = 8.1e-36 */ + +static const _Float128 + P0 = L(2.943520915569954073888921213330863757240E8), + P1 = L(-5.722847283900608941516165725053359168840E7), + P2 = L(8.944630806357575461578107295909719817253E6), + P3 = L(-7.212432713558031519943281748462837065308E5), + P4 = L(4.578962475841642634225390068461943438441E4), + P5 = L(-1.716772506388927649032068540558788106762E3), + P6 = L(4.401308817383362136048032038528753151144E1), + P7 = L(-4.888737542888633647784737721812546636240E-1), + Q0 = L(1.766112549341972444333352727998584753865E9), + Q1 = L(-7.848989743695296475743081255027098295771E8), + Q2 = L(1.615869009634292424463780387327037251069E8), + Q3 = L(-2.019684072836541751428967854947019415698E7), + Q4 = L(1.682912729190313538934190635536631941751E6), + Q5 = L(-9.615511549171441430850103489315371768998E4), + Q6 = L(3.697714952261803935521187272204485251835E3), + Q7 = L(-8.802340681794263968892934703309274564037E1), + /* Q8 = 1.000000000000000000000000000000000000000E0 */ +/* C1 + C2 = ln 2 */ + + C1 = L(6.93145751953125E-1), + C2 = L(1.428606820309417232121458176568075500134E-6), +/* ln 2^-114 */ + minarg = L(-7.9018778583833765273564461846232128760607E1), big = L(1e4932); + + +_Float128 +__expm1l (_Float128 x) +{ + _Float128 px, qx, xx; + int32_t ix, sign; + ieee854_long_double_shape_type u; + int k; + + /* Detect infinity and NaN. */ + u.value = x; + ix = u.parts32.w0; + sign = ix & 0x80000000; + ix &= 0x7fffffff; + if (!sign && ix >= 0x40060000) + { + /* If num is positive and exp >= 6 use plain exp. */ + return __expl (x); + } + if (ix >= 0x7fff0000) + { + /* Infinity (which must be negative infinity). */ + if (((ix & 0xffff) | u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0) + return -1; + /* NaN. Invalid exception if signaling. */ + return x + x; + } + + /* expm1(+- 0) = +- 0. */ + if ((ix == 0) && (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0) + return x; + + /* Minimum value. */ + if (x < minarg) + return (4.0/big - 1); + + /* Avoid internal underflow when result does not underflow, while + ensuring underflow (without returning a zero of the wrong sign) + when the result does underflow. */ + if (fabsl (x) < L(0x1p-113)) + { + math_check_force_underflow (x); + return x; + } + + /* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */ + xx = C1 + C2; /* ln 2. */ + px = __floorl (0.5 + x / xx); + k = px; + /* remainder times ln 2 */ + x -= px * C1; + x -= px * C2; + + /* Approximate exp(remainder ln 2). */ + px = (((((((P7 * x + + P6) * x + + P5) * x + P4) * x + P3) * x + P2) * x + P1) * x + P0) * x; + + qx = (((((((x + + Q7) * x + + Q6) * x + Q5) * x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0; + + xx = x * x; + qx = x + (0.5 * xx + xx * px / qx); + + /* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2). + + We have qx = exp(remainder ln 2) - 1, so + exp(x) - 1 = 2^k (qx + 1) - 1 + = 2^k qx + 2^k - 1. */ + + px = __ldexpl (1, k); + x = px * qx + (px - 1.0); + return x; +} +libm_hidden_def (__expm1l) +weak_alias (__expm1l, expm1l) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fabsl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fabsl.c new file mode 100644 index 0000000000..0ce6f734cf --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fabsl.c @@ -0,0 +1,34 @@ +/* s_fabsl.c -- long double version of s_fabs.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * fabsl(x) returns the absolute value of x. + */ + +#include <math.h> +#include <math_private.h> + +_Float128 __fabsl(_Float128 x) +{ + u_int64_t hx; + GET_LDOUBLE_MSW64(hx,x); + SET_LDOUBLE_MSW64(x,hx&0x7fffffffffffffffLL); + return x; +} +weak_alias (__fabsl, fabsl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_finitel.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_finitel.c new file mode 100644 index 0000000000..7c699688fe --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_finitel.c @@ -0,0 +1,36 @@ +/* s_finitel.c -- long double version of s_finite.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * finitel(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> + +int __finitel(_Float128 x) +{ + int64_t hx; + GET_LDOUBLE_MSW64(hx,x); + return (int)((u_int64_t)((hx&0x7fff000000000000LL) + -0x7fff000000000000LL)>>63); +} +mathx_hidden_def (__finitel) +weak_alias (__finitel, finitel) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_floorl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_floorl.c new file mode 100644 index 0000000000..13ad0848a4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_floorl.c @@ -0,0 +1,67 @@ +/* s_floorl.c -- long double version of s_floor.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * floorl(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + */ + +#include <math.h> +#include <math_private.h> + +_Float128 __floorl(_Float128 x) +{ + int64_t i0,i1,j0; + u_int64_t i,j; + GET_LDOUBLE_WORDS64(i0,i1,x); + j0 = ((i0>>48)&0x7fff)-0x3fff; + if(j0<48) { + if(j0<0) { + /* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=i1=0;} + else if(((i0&0x7fffffffffffffffLL)|i1)!=0) + { i0=0xbfff000000000000ULL;i1=0;} + } else { + i = (0x0000ffffffffffffULL)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(i0<0) i0 += (0x0001000000000000LL)>>j0; + i0 &= (~i); i1=0; + } + } else if (j0>111) { + if(j0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = -1ULL>>(j0-48); + if((i1&i)==0) return x; /* x is integral */ + if(i0<0) { + if(j0==48) i0+=1; + else { + j = i1+(1LL<<(112-j0)); + if(j<i1) i0 +=1 ; /* got a carry */ + i1=j; + } + } + i1 &= (~i); + } + SET_LDOUBLE_WORDS64(x,i0,i1); + return x; +} +weak_alias (__floorl, floorl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fma.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fma.c new file mode 100644 index 0000000000..13da2904f4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fma.c @@ -0,0 +1,55 @@ +/* Compute x * y + z as ternary operation. + Copyright (C) 2010-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <fenv.h> +#include <ieee754.h> + +/* This implementation relies on long double being more than twice as + precise as double and uses rounding to odd in order to avoid problems + with double rounding. + See a paper by Boldo and Melquiond: + http://www.lri.fr/~melquion/doc/08-tc.pdf */ + +double +__fma (double x, double y, double z) +{ + fenv_t env; + /* Multiplication is always exact. */ + long double temp = (long double) x * (long double) y; + + /* Ensure correct sign of an exact zero result by performing the + addition in the original rounding mode in that case. */ + if (temp == -z) + return (double) temp + z; + + union ieee854_long_double u; + feholdexcept (&env); + fesetround (FE_TOWARDZERO); + /* Perform addition with round to odd. */ + u.d = temp + (long double) z; + if ((u.ieee.mantissa3 & 1) == 0 && u.ieee.exponent != 0x7fff) + u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* And finally truncation with round to nearest. */ + return (double) u.d; +} +#ifndef __fma +weak_alias (__fma, fma) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fmal.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fmal.c new file mode 100644 index 0000000000..40c4e73d2b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fmal.c @@ -0,0 +1,298 @@ +/* Compute x * y + z as ternary operation. + Copyright (C) 2010-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <fenv.h> +#include <ieee754.h> +#include <math_private.h> +#include <tininess.h> + +/* This implementation uses rounding to odd to avoid problems with + double rounding. See a paper by Boldo and Melquiond: + http://www.lri.fr/~melquion/doc/08-tc.pdf */ + +_Float128 +__fmal (_Float128 x, _Float128 y, _Float128 z) +{ + union ieee854_long_double u, v, w; + int adjust = 0; + u.d = x; + v.d = y; + w.d = z; + if (__builtin_expect (u.ieee.exponent + v.ieee.exponent + >= 0x7fff + IEEE854_LONG_DOUBLE_BIAS + - LDBL_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0) + || __builtin_expect (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0) + || __builtin_expect (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent + v.ieee.exponent + <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG, 0)) + { + /* If z is Inf, but x and y are finite, the result should be + z rather than NaN. */ + if (w.ieee.exponent == 0x7fff + && u.ieee.exponent != 0x7fff + && v.ieee.exponent != 0x7fff) + return (z + x) + y; + /* If z is zero and x are y are nonzero, compute the result + as x * y to avoid the wrong sign of a zero result if x * y + underflows to 0. */ + if (z == 0 && x != 0 && y != 0) + return x * y; + /* If x or y or z is Inf/NaN, or if x * y is zero, compute as + x * y + z. */ + if (u.ieee.exponent == 0x7fff + || v.ieee.exponent == 0x7fff + || w.ieee.exponent == 0x7fff + || x == 0 + || y == 0) + return x * y + z; + /* If fma will certainly overflow, compute as x * y. */ + if (u.ieee.exponent + v.ieee.exponent + > 0x7fff + IEEE854_LONG_DOUBLE_BIAS) + return x * y; + /* If x * y is less than 1/4 of LDBL_TRUE_MIN, neither the + result nor whether there is underflow depends on its exact + value, only on its sign. */ + if (u.ieee.exponent + v.ieee.exponent + < IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2) + { + int neg = u.ieee.negative ^ v.ieee.negative; + _Float128 tiny = neg ? L(-0x1p-16494) : L(0x1p-16494); + if (w.ieee.exponent >= 3) + return tiny + z; + /* Scaling up, adding TINY and scaling down produces the + correct result, because in round-to-nearest mode adding + TINY has no effect and in other modes double rounding is + harmless. But it may not produce required underflow + exceptions. */ + v.d = z * L(0x1p114) + tiny; + if (TININESS_AFTER_ROUNDING + ? v.ieee.exponent < 115 + : (w.ieee.exponent == 0 + || (w.ieee.exponent == 1 + && w.ieee.negative != neg + && w.ieee.mantissa3 == 0 + && w.ieee.mantissa2 == 0 + && w.ieee.mantissa1 == 0 + && w.ieee.mantissa0 == 0))) + { + _Float128 force_underflow = x * y; + math_force_eval (force_underflow); + } + return v.d * L(0x1p-114); + } + if (u.ieee.exponent + v.ieee.exponent + >= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG) + { + /* Compute 1p-113 times smaller result and multiply + at the end. */ + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent -= LDBL_MANT_DIG; + else + v.ieee.exponent -= LDBL_MANT_DIG; + /* If x + y exponent is very large and z exponent is very small, + it doesn't matter if we don't adjust it. */ + if (w.ieee.exponent > LDBL_MANT_DIG) + w.ieee.exponent -= LDBL_MANT_DIG; + adjust = 1; + } + else if (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG) + { + /* Similarly. + If z exponent is very large and x and y exponents are + very small, adjust them up to avoid spurious underflows, + rather than down. */ + if (u.ieee.exponent + v.ieee.exponent + <= IEEE854_LONG_DOUBLE_BIAS + 2 * LDBL_MANT_DIG) + { + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent += 2 * LDBL_MANT_DIG + 2; + else + v.ieee.exponent += 2 * LDBL_MANT_DIG + 2; + } + else if (u.ieee.exponent > v.ieee.exponent) + { + if (u.ieee.exponent > LDBL_MANT_DIG) + u.ieee.exponent -= LDBL_MANT_DIG; + } + else if (v.ieee.exponent > LDBL_MANT_DIG) + v.ieee.exponent -= LDBL_MANT_DIG; + w.ieee.exponent -= LDBL_MANT_DIG; + adjust = 1; + } + else if (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG) + { + u.ieee.exponent -= LDBL_MANT_DIG; + if (v.ieee.exponent) + v.ieee.exponent += LDBL_MANT_DIG; + else + v.d *= L(0x1p113); + } + else if (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG) + { + v.ieee.exponent -= LDBL_MANT_DIG; + if (u.ieee.exponent) + u.ieee.exponent += LDBL_MANT_DIG; + else + u.d *= L(0x1p113); + } + else /* if (u.ieee.exponent + v.ieee.exponent + <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) */ + { + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent += 2 * LDBL_MANT_DIG + 2; + else + v.ieee.exponent += 2 * LDBL_MANT_DIG + 2; + if (w.ieee.exponent <= 4 * LDBL_MANT_DIG + 6) + { + if (w.ieee.exponent) + w.ieee.exponent += 2 * LDBL_MANT_DIG + 2; + else + w.d *= L(0x1p228); + adjust = -1; + } + /* Otherwise x * y should just affect inexact + and nothing else. */ + } + x = u.d; + y = v.d; + z = w.d; + } + + /* Ensure correct sign of exact 0 + 0. */ + if (__glibc_unlikely ((x == 0 || y == 0) && z == 0)) + { + x = math_opt_barrier (x); + return x * y + z; + } + + fenv_t env; + feholdexcept (&env); + fesetround (FE_TONEAREST); + + /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ +#define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) + _Float128 x1 = x * C; + _Float128 y1 = y * C; + _Float128 m1 = x * y; + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + _Float128 x2 = x - x1; + _Float128 y2 = y - y1; + _Float128 m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2; + + /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */ + _Float128 a1 = z + m1; + _Float128 t1 = a1 - z; + _Float128 t2 = a1 - t1; + t1 = m1 - t1; + t2 = z - t2; + _Float128 a2 = t1 + t2; + /* Ensure the arithmetic is not scheduled after feclearexcept call. */ + math_force_eval (m2); + math_force_eval (a2); + feclearexcept (FE_INEXACT); + + /* If the result is an exact zero, ensure it has the correct sign. */ + if (a1 == 0 && m2 == 0) + { + feupdateenv (&env); + /* Ensure that round-to-nearest value of z + m1 is not reused. */ + z = math_opt_barrier (z); + return z + m1; + } + + fesetround (FE_TOWARDZERO); + /* Perform m2 + a2 addition with round to odd. */ + u.d = a2 + m2; + + if (__glibc_likely (adjust == 0)) + { + if ((u.ieee.mantissa3 & 1) == 0 && u.ieee.exponent != 0x7fff) + u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Result is a1 + u.d. */ + return a1 + u.d; + } + else if (__glibc_likely (adjust > 0)) + { + if ((u.ieee.mantissa3 & 1) == 0 && u.ieee.exponent != 0x7fff) + u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Result is a1 + u.d, scaled up. */ + return (a1 + u.d) * L(0x1p113); + } + else + { + if ((u.ieee.mantissa3 & 1) == 0) + u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0; + v.d = a1 + u.d; + /* Ensure the addition is not scheduled after fetestexcept call. */ + math_force_eval (v.d); + int j = fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Ensure the following computations are performed in default rounding + mode instead of just reusing the round to zero computation. */ + asm volatile ("" : "=m" (u) : "m" (u)); + /* If a1 + u.d is exact, the only rounding happens during + scaling down. */ + if (j == 0) + return v.d * L(0x1p-228); + /* If result rounded to zero is not subnormal, no double + rounding will occur. */ + if (v.ieee.exponent > 228) + return (a1 + u.d) * L(0x1p-228); + /* If v.d * 0x1p-228L with round to zero is a subnormal above + or equal to LDBL_MIN / 2, then v.d * 0x1p-228L shifts mantissa + down just by 1 bit, which means v.ieee.mantissa3 |= j would + change the round bit, not sticky or guard bit. + v.d * 0x1p-228L never normalizes by shifting up, + so round bit plus sticky bit should be already enough + for proper rounding. */ + if (v.ieee.exponent == 228) + { + /* If the exponent would be in the normal range when + rounding to normal precision with unbounded exponent + range, the exact result is known and spurious underflows + must be avoided on systems detecting tininess after + rounding. */ + if (TININESS_AFTER_ROUNDING) + { + w.d = a1 + u.d; + if (w.ieee.exponent == 229) + return w.d * L(0x1p-228); + } + /* v.ieee.mantissa3 & 2 is LSB bit of the result before rounding, + v.ieee.mantissa3 & 1 is the round bit and j is our sticky + bit. */ + w.d = 0; + w.ieee.mantissa3 = ((v.ieee.mantissa3 & 3) << 1) | j; + w.ieee.negative = v.ieee.negative; + v.ieee.mantissa3 &= ~3U; + v.d *= L(0x1p-228); + w.d *= L(0x1p-2); + return v.d + w.d; + } + v.ieee.mantissa3 |= j; + return v.d * L(0x1p-228); + } +} +weak_alias (__fmal, fmal) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c new file mode 100644 index 0000000000..daa7d79ec2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c @@ -0,0 +1,44 @@ +/* Return classification value corresponding to argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +int +__fpclassifyl (_Float128 x) +{ + u_int64_t hx, lx; + int retval = FP_NORMAL; + + GET_LDOUBLE_WORDS64 (hx, lx, x); + lx |= (hx & 0x0000ffffffffffffLL); + hx &= 0x7fff000000000000LL; + if ((hx | lx) == 0) + retval = FP_ZERO; + else if (hx == 0) + retval = FP_SUBNORMAL; + else if (hx == 0x7fff000000000000LL) + retval = lx != 0 ? FP_NAN : FP_INFINITE; + + return retval; +} +libm_hidden_def (__fpclassifyl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_frexpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_frexpl.c new file mode 100644 index 0000000000..47a171f551 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_frexpl.c @@ -0,0 +1,54 @@ +/* s_frexpl.c -- long double version of s_frexp.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * for non-zero x + * x = frexpl(arg,&exp); + * return a long double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexpl(arg,&exp) returns arg + * with *exp=0. + */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 +two114 = L(2.0769187434139310514121985316880384E+34); /* 0x4071000000000000, 0 */ + +_Float128 __frexpl(_Float128 x, int *eptr) +{ + u_int64_t hx, lx, ix; + GET_LDOUBLE_WORDS64(hx,lx,x); + ix = 0x7fffffffffffffffULL&hx; + *eptr = 0; + if(ix>=0x7fff000000000000ULL||((ix|lx)==0)) return x + x;/* 0,inf,nan */ + if (ix<0x0001000000000000ULL) { /* subnormal */ + x *= two114; + GET_LDOUBLE_MSW64(hx,x); + ix = hx&0x7fffffffffffffffULL; + *eptr = -114; + } + *eptr += (ix>>48)-16382; + hx = (hx&0x8000ffffffffffffULL) | 0x3ffe000000000000ULL; + SET_LDOUBLE_MSW64(x,hx); + return x; +} +weak_alias (__frexpl, frexpl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fromfpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fromfpl.c new file mode 100644 index 0000000000..e323b4c25b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fromfpl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 0 +#define INEXACT 0 +#define FUNC fromfpl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fromfpl_main.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fromfpl_main.c new file mode 100644 index 0000000000..7dc507111b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fromfpl_main.c @@ -0,0 +1,90 @@ +/* Round to integer type. ldbl-128 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <fenv.h> +#include <math.h> +#include <math_private.h> +#include <stdbool.h> +#include <stdint.h> + +#define BIAS 0x3fff +#define MANT_DIG 113 + +#if UNSIGNED +# define RET_TYPE uintmax_t +#else +# define RET_TYPE intmax_t +#endif + +#include <fromfp.h> + +RET_TYPE +FUNC (_Float128 x, int round, unsigned int width) +{ + if (width > INTMAX_WIDTH) + width = INTMAX_WIDTH; + uint64_t hx, lx; + GET_LDOUBLE_WORDS64 (hx, lx, x); + bool negative = (hx & 0x8000000000000000ULL) != 0; + if (width == 0) + return fromfp_domain_error (negative, width); + hx &= 0x7fffffffffffffffULL; + if ((hx | lx) == 0) + return 0; + int exponent = hx >> (MANT_DIG - 1 - 64); + exponent -= BIAS; + int max_exponent = fromfp_max_exponent (negative, width); + if (exponent > max_exponent) + return fromfp_domain_error (negative, width); + + hx &= ((1ULL << (MANT_DIG - 1 - 64)) - 1); + hx |= 1ULL << (MANT_DIG - 1 - 64); + uintmax_t uret; + bool half_bit, more_bits; + /* The exponent is at most 63, so we are shifting right by at least + 49 bits. */ + if (exponent >= -1) + { + int shift = MANT_DIG - 1 - exponent; + if (shift <= 64) + { + uint64_t h = 1ULL << (shift - 1); + half_bit = (lx & h) != 0; + more_bits = (lx & (h - 1)) != 0; + uret = hx << (64 - shift); + if (shift != 64) + uret |= lx >> shift; + } + else + { + uint64_t h = 1ULL << (shift - 1 - 64); + half_bit = (hx & h) != 0; + more_bits = ((hx & (h - 1)) | lx) != 0; + uret = hx >> (shift - 64); + } + } + else + { + uret = 0; + half_bit = false; + more_bits = true; + } + return fromfp_round_and_return (negative, uret, half_bit, more_bits, round, + exponent, max_exponent, width); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fromfpxl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fromfpxl.c new file mode 100644 index 0000000000..2f3189d7de --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_fromfpxl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 0 +#define INEXACT 1 +#define FUNC fromfpxl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_getpayloadl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_getpayloadl.c new file mode 100644 index 0000000000..d384645532 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_getpayloadl.c @@ -0,0 +1,57 @@ +/* Get NaN payload. ldbl-128 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +_Float128 +getpayloadl (const _Float128 *x) +{ + uint64_t hx, lx; + GET_LDOUBLE_WORDS64 (hx, lx, *x); + hx &= 0x7fffffffffffULL; + /* Construct the representation of the return value directly, since + 128-bit integers may not be available. */ + int lz; + if (hx == 0) + { + if (lx == 0) + return 0.0L; + else + lz = __builtin_clzll (lx) + 64; + } + else + lz = __builtin_clzll (hx); + int shift = lz - 15; + if (shift >= 64) + { + hx = lx << (shift - 64); + lx = 0; + } + else + { + /* 2 <= SHIFT <= 63. */ + hx = (hx << shift) | (lx >> (64 - shift)); + lx <<= shift; + } + hx = (hx & 0xffffffffffffULL) | ((0x3fffULL + 127 - lz) << 48); + _Float128 ret; + SET_LDOUBLE_WORDS64 (ret, hx, lx); + return ret; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_isinfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_isinfl.c new file mode 100644 index 0000000000..a41e8cf44b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_isinfl.c @@ -0,0 +1,29 @@ +/* + * Written by J.T. Conklin <jtc@netbsd.org>. + * Change for long double by Jakub Jelinek <jj@ultra.linux.cz> + * Public domain. + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * isinfl(x) returns 1 if x is inf, -1 if x is -inf, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> + +int +__isinfl (_Float128 x) +{ + int64_t hx,lx; + GET_LDOUBLE_WORDS64(hx,lx,x); + lx |= (hx & 0x7fffffffffffffffLL) ^ 0x7fff000000000000LL; + lx |= -lx; + return ~(lx >> 63) & (hx >> 62); +} +mathx_hidden_def (__isinfl) +weak_alias (__isinfl, isinfl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_isnanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_isnanl.c new file mode 100644 index 0000000000..80f97fea4c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_isnanl.c @@ -0,0 +1,38 @@ +/* s_isnanl.c -- long double version of s_isnan.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * isnanl(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> + +int __isnanl(_Float128 x) +{ + int64_t hx,lx; + GET_LDOUBLE_WORDS64(hx,lx,x); + hx &= 0x7fffffffffffffffLL; + hx |= (u_int64_t)(lx|(-lx))>>63; + hx = 0x7fff000000000000LL - hx; + return (int)((u_int64_t)hx>>63); +} +mathx_hidden_def (__isnanl) +weak_alias (__isnanl, isnanl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_issignalingl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_issignalingl.c new file mode 100644 index 0000000000..02d6a0ae07 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_issignalingl.c @@ -0,0 +1,46 @@ +/* Test for signaling NaN. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> + +int +__issignalingl (_Float128 x) +{ + u_int64_t hxi, lxi __attribute__ ((unused)); + GET_LDOUBLE_WORDS64 (hxi, lxi, x); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* We only have to care about the high-order bit of x's significand, because + having it set (sNaN) already makes the significand different from that + used to designate infinity. */ + return ((hxi & UINT64_C (0x7fff800000000000)) + == UINT64_C (0x7fff800000000000)); +#else + /* To keep the following comparison simple, toggle the quiet/signaling bit, + so that it is set for sNaNs. This is inverse to IEEE 754-2008 (as well as + common practice for IEEE 754-1985). */ + hxi ^= UINT64_C (0x0000800000000000); + /* If lxi != 0, then set any suitable bit of the significand in hxi. */ + hxi |= (lxi | -lxi) >> 63; + /* We have to compare for greater (instead of greater or equal), because x's + significand being all-zero designates infinity not NaN. */ + return (hxi & UINT64_C (0x7fffffffffffffff)) > UINT64_C (0x7fff800000000000); +#endif +} +libm_hidden_def (__issignalingl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_llrintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_llrintl.c new file mode 100644 index 0000000000..d08a90a1b3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_llrintl.c @@ -0,0 +1,108 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + +static const _Float128 two112[2] = +{ + L(5.19229685853482762853049632922009600E+33), /* 0x406F000000000000, 0 */ + L(-5.19229685853482762853049632922009600E+33) /* 0xC06F000000000000, 0 */ +}; + +long long int +__llrintl (_Float128 x) +{ + int32_t j0; + u_int64_t i0,i1; + _Float128 w; + _Float128 t; + long long int result; + int sx; + + GET_LDOUBLE_WORDS64 (i0, i1, x); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + sx = i0 >> 63; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { +#if defined FE_INVALID || defined FE_INEXACT + /* X < LLONG_MAX + 1 implied by J0 < 63. */ + if (x > (_Float128) LLONG_MAX) + { + /* In the event of overflow we must raise the "invalid" + exception, but not "inexact". */ + t = __nearbyintl (x); + feraiseexcept (t == LLONG_MAX ? FE_INEXACT : FE_INVALID); + } + else +#endif + { + w = two112[sx] + x; + t = w - two112[sx]; + } + GET_LDOUBLE_WORDS64 (i0, i1, t); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + if (j0 < 0) + result = 0; + else if (j0 <= 48) + result = i0 >> (48 - j0); + else + result = ((long long int) i0 << (j0 - 48)) | (i1 >> (112 - j0)); + } + else + { + /* The number is too large. Unless it rounds to LLONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ +#if defined FE_INVALID || defined FE_INEXACT + if (x < (_Float128) LLONG_MIN + && x > (_Float128) LLONG_MIN - 1) + { + /* If truncation produces LLONG_MIN, the cast will not raise + the exception, but may raise "inexact". */ + t = __nearbyintl (x); + feraiseexcept (t == LLONG_MIN ? FE_INEXACT : FE_INVALID); + return LLONG_MIN; + } + else if (FIX_LDBL_LLONG_CONVERT_OVERFLOW && x != (_Float128) LLONG_MIN) + { + feraiseexcept (FE_INVALID); + return sx == 0 ? LLONG_MAX : LLONG_MIN; + } + +#endif + return (long long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__llrintl, llrintl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_llroundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_llroundl.c new file mode 100644 index 0000000000..bb0b5bcf4b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_llroundl.c @@ -0,0 +1,102 @@ +/* Round long double value to long long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + +long long int +__llroundl (_Float128 x) +{ + int64_t j0; + u_int64_t i1, i0; + long long int result; + int sign; + + GET_LDOUBLE_WORDS64 (i0, i1, x); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + sign = (i0 & 0x8000000000000000ULL) != 0 ? -1 : 1; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + if (j0 < 48) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + i0 += 0x0000800000000000LL >> j0; + result = i0 >> (48 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 >= 112) + result = ((long long int) i0 << (j0 - 48)) | (i1 << (j0 - 112)); + else + { + u_int64_t j = i1 + (0x8000000000000000ULL >> (j0 - 48)); + if (j < i1) + ++i0; + + if (j0 == 48) + result = (long long int) i0; + else + { + result = ((long long int) i0 << (j0 - 48)) | (j >> (112 - j0)); +#ifdef FE_INVALID + if (sign == 1 && result == LLONG_MIN) + /* Rounding brought the value out of range. */ + feraiseexcept (FE_INVALID); +#endif + } + } + } + else + { + /* The number is too large. Unless it rounds to LLONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ +#ifdef FE_INVALID + if (FIX_LDBL_LLONG_CONVERT_OVERFLOW + && !(sign == -1 && x > (_Float128) LLONG_MIN - L(0.5))) + { + feraiseexcept (FE_INVALID); + return sign == 1 ? LLONG_MAX : LLONG_MIN; + } + else if (!FIX_LDBL_LLONG_CONVERT_OVERFLOW + && x <= (_Float128) LLONG_MIN - L(0.5)) + { + /* If truncation produces LLONG_MIN, the cast will not raise + the exception, but may raise "inexact". */ + feraiseexcept (FE_INVALID); + return LLONG_MIN; + } +#endif + return (long long int) x; + } + + return sign * result; +} + +weak_alias (__llroundl, llroundl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_log1pl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_log1pl.c new file mode 100644 index 0000000000..b8b2ffeba1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_log1pl.c @@ -0,0 +1,256 @@ +/* log1pl.c + * + * Relative error logarithm + * Natural logarithm of 1+x, 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log1pl(); + * + * y = log1pl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base e (2.718...) logarithm of 1+x. + * + * The argument 1+x is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the logarithm + * of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(w-1)/(w+1), + * + * log(w) = z + z^3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -1, 8 100000 1.9e-34 4.3e-35 + */ + +/* Copyright 2001 by Stephen L. Moshier + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + + +#include <float.h> +#include <math.h> +#include <math_private.h> + +/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x) + * 1/sqrt(2) <= 1+x < sqrt(2) + * Theoretical peak relative error = 5.3e-37, + * relative peak error spread = 2.3e-14 + */ +static const _Float128 + P12 = L(1.538612243596254322971797716843006400388E-6), + P11 = L(4.998469661968096229986658302195402690910E-1), + P10 = L(2.321125933898420063925789532045674660756E1), + P9 = L(4.114517881637811823002128927449878962058E2), + P8 = L(3.824952356185897735160588078446136783779E3), + P7 = L(2.128857716871515081352991964243375186031E4), + P6 = L(7.594356839258970405033155585486712125861E4), + P5 = L(1.797628303815655343403735250238293741397E5), + P4 = L(2.854829159639697837788887080758954924001E5), + P3 = L(3.007007295140399532324943111654767187848E5), + P2 = L(2.014652742082537582487669938141683759923E5), + P1 = L(7.771154681358524243729929227226708890930E4), + P0 = L(1.313572404063446165910279910527789794488E4), + /* Q12 = 1.000000000000000000000000000000000000000E0L, */ + Q11 = L(4.839208193348159620282142911143429644326E1), + Q10 = L(9.104928120962988414618126155557301584078E2), + Q9 = L(9.147150349299596453976674231612674085381E3), + Q8 = L(5.605842085972455027590989944010492125825E4), + Q7 = L(2.248234257620569139969141618556349415120E5), + Q6 = L(6.132189329546557743179177159925690841200E5), + Q5 = L(1.158019977462989115839826904108208787040E6), + Q4 = L(1.514882452993549494932585972882995548426E6), + Q3 = L(1.347518538384329112529391120390701166528E6), + Q2 = L(7.777690340007566932935753241556479363645E5), + Q1 = L(2.626900195321832660448791748036714883242E5), + Q0 = L(3.940717212190338497730839731583397586124E4); + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 1.1e-35, + * relative peak error spread 1.1e-9 + */ +static const _Float128 + R5 = L(-8.828896441624934385266096344596648080902E-1), + R4 = L(8.057002716646055371965756206836056074715E1), + R3 = L(-2.024301798136027039250415126250455056397E3), + R2 = L(2.048819892795278657810231591630928516206E4), + R1 = L(-8.977257995689735303686582344659576526998E4), + R0 = L(1.418134209872192732479751274970992665513E5), + /* S6 = 1.000000000000000000000000000000000000000E0L, */ + S5 = L(-1.186359407982897997337150403816839480438E2), + S4 = L(3.998526750980007367835804959888064681098E3), + S3 = L(-5.748542087379434595104154610899551484314E4), + S2 = L(4.001557694070773974936904547424676279307E5), + S1 = L(-1.332535117259762928288745111081235577029E6), + S0 = L(1.701761051846631278975701529965589676574E6); + +/* C1 + C2 = ln 2 */ +static const _Float128 C1 = L(6.93145751953125E-1); +static const _Float128 C2 = L(1.428606820309417232121458176568075500134E-6); + +static const _Float128 sqrth = L(0.7071067811865475244008443621048490392848); +/* ln (2^16384 * (1 - 2^-113)) */ +static const _Float128 zero = 0; + +_Float128 +__log1pl (_Float128 xm1) +{ + _Float128 x, y, z, r, s; + ieee854_long_double_shape_type u; + int32_t hx; + int e; + + /* Test for NaN or infinity input. */ + u.value = xm1; + hx = u.parts32.w0; + if ((hx & 0x7fffffff) >= 0x7fff0000) + return xm1 + fabsl (xm1); + + /* log1p(+- 0) = +- 0. */ + if (((hx & 0x7fffffff) == 0) + && (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0) + return xm1; + + if ((hx & 0x7fffffff) < 0x3f8e0000) + { + math_check_force_underflow (xm1); + if ((int) xm1 == 0) + return xm1; + } + + if (xm1 >= L(0x1p113)) + x = xm1; + else + x = xm1 + 1; + + /* log1p(-1) = -inf */ + if (x <= 0) + { + if (x == 0) + return (-1 / zero); /* log1p(-1) = -inf */ + else + return (zero / (x - x)); + } + + /* Separate mantissa from exponent. */ + + /* Use frexp used so that denormal numbers will be handled properly. */ + x = __frexpl (x, &e); + + /* Logarithm using log(x) = z + z^3 P(z^2)/Q(z^2), + where z = 2(x-1)/x+1). */ + if ((e > 2) || (e < -2)) + { + if (x < sqrth) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - L(0.5); + y = L(0.5) * z + L(0.5); + } + else + { /* 2 (x-1)/(x+1) */ + z = x - L(0.5); + z -= L(0.5); + y = L(0.5) * x + L(0.5); + } + x = z / y; + z = x * x; + r = ((((R5 * z + + R4) * z + + R3) * z + + R2) * z + + R1) * z + + R0; + s = (((((z + + S5) * z + + S4) * z + + S3) * z + + S2) * z + + S1) * z + + S0; + z = x * (z * r / s); + z = z + e * C2; + z = z + x; + z = z + e * C1; + return (z); + } + + + /* Logarithm using log(1+x) = x - .5x^2 + x^3 P(x)/Q(x). */ + + if (x < sqrth) + { + e -= 1; + if (e != 0) + x = 2 * x - 1; /* 2x - 1 */ + else + x = xm1; + } + else + { + if (e != 0) + x = x - 1; + else + x = xm1; + } + z = x * x; + r = (((((((((((P12 * x + + P11) * x + + P10) * x + + P9) * x + + P8) * x + + P7) * x + + P6) * x + + P5) * x + + P4) * x + + P3) * x + + P2) * x + + P1) * x + + P0; + s = (((((((((((x + + Q11) * x + + Q10) * x + + Q9) * x + + Q8) * x + + Q7) * x + + Q6) * x + + Q5) * x + + Q4) * x + + Q3) * x + + Q2) * x + + Q1) * x + + Q0; + y = x * (z * r / s); + y = y + e * C2; + z = y - L(0.5) * z; + z = z + x; + z = z + e * C1; + return (z); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_logbl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_logbl.c new file mode 100644 index 0000000000..24baae64fa --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_logbl.c @@ -0,0 +1,54 @@ +/* s_logbl.c -- long double version of s_logb.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * long double logbl(x) + * IEEE 754 logb. Included to pass IEEE test suite. Not recommend. + * Use ilogb instead. + */ + +#include <math.h> +#include <math_private.h> + +_Float128 +__logbl (_Float128 x) +{ + int64_t lx, hx, ex; + + GET_LDOUBLE_WORDS64 (hx, lx, x); + hx &= 0x7fffffffffffffffLL; /* high |x| */ + if ((hx | lx) == 0) + return -1.0 / fabsl (x); + if (hx >= 0x7fff000000000000LL) + return x * x; + if ((ex = hx >> 48) == 0) /* IEEE 754 logb */ + { + /* POSIX specifies that denormal number is treated as + though it were normalized. */ + int ma; + if (hx == 0) + ma = __builtin_clzll (lx) + 64; + else + ma = __builtin_clzll (hx); + ex -= ma - 16; + } + return (_Float128) (ex - 16383); +} + +weak_alias (__logbl, logbl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_lrintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_lrintl.c new file mode 100644 index 0000000000..c690ddc8b8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_lrintl.c @@ -0,0 +1,137 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + +static const _Float128 two112[2] = +{ + L(5.19229685853482762853049632922009600E+33), /* 0x406F000000000000, 0 */ + L(-5.19229685853482762853049632922009600E+33) /* 0xC06F000000000000, 0 */ +}; + +long int +__lrintl (_Float128 x) +{ + int32_t j0; + u_int64_t i0,i1; + _Float128 w; + _Float128 t; + long int result; + int sx; + + GET_LDOUBLE_WORDS64 (i0, i1, x); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + sx = i0 >> 63; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 < 48) + { +#if defined FE_INVALID || defined FE_INEXACT + /* X < LONG_MAX + 1 implied by J0 < 31. */ + if (sizeof (long int) == 4 + && x > (_Float128) LONG_MAX) + { + /* In the event of overflow we must raise the "invalid" + exception, but not "inexact". */ + t = __nearbyintl (x); + feraiseexcept (t == LONG_MAX ? FE_INEXACT : FE_INVALID); + } + else +#endif + { + w = two112[sx] + x; + t = w - two112[sx]; + } + GET_LDOUBLE_WORDS64 (i0, i1, t); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + result = (j0 < 0 ? 0 : i0 >> (48 - j0)); + } + else if (j0 >= 112) + result = ((long int) i0 << (j0 - 48)) | (i1 << (j0 - 112)); + else + { +#if defined FE_INVALID || defined FE_INEXACT + /* X < LONG_MAX + 1 implied by J0 < 63. */ + if (sizeof (long int) == 8 + && x > (_Float128) LONG_MAX) + { + /* In the event of overflow we must raise the "invalid" + exception, but not "inexact". */ + t = __nearbyintl (x); + feraiseexcept (t == LONG_MAX ? FE_INEXACT : FE_INVALID); + } + else +#endif + { + w = two112[sx] + x; + t = w - two112[sx]; + } + GET_LDOUBLE_WORDS64 (i0, i1, t); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + if (j0 == 48) + result = (long int) i0; + else + result = ((long int) i0 << (j0 - 48)) | (i1 >> (112 - j0)); + } + } + else + { + /* The number is too large. Unless it rounds to LONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ +#if defined FE_INVALID || defined FE_INEXACT + if (x < (_Float128) LONG_MIN + && x > (_Float128) LONG_MIN - 1) + { + /* If truncation produces LONG_MIN, the cast will not raise + the exception, but may raise "inexact". */ + t = __nearbyintl (x); + feraiseexcept (t == LONG_MIN ? FE_INEXACT : FE_INVALID); + return LONG_MIN; + } + else if (FIX_LDBL_LONG_CONVERT_OVERFLOW && x != (_Float128) LONG_MIN) + { + feraiseexcept (FE_INVALID); + return sx == 0 ? LONG_MAX : LONG_MIN; + } + +#endif + return (long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__lrintl, lrintl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_lroundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_lroundl.c new file mode 100644 index 0000000000..419112519d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_lroundl.c @@ -0,0 +1,113 @@ +/* Round long double value to long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + +long int +__lroundl (_Float128 x) +{ + int64_t j0; + u_int64_t i1, i0; + long int result; + int sign; + + GET_LDOUBLE_WORDS64 (i0, i1, x); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + sign = (i0 & 0x8000000000000000ULL) != 0 ? -1 : 1; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 < 48) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + i0 += 0x0000800000000000LL >> j0; + result = i0 >> (48 - j0); +#ifdef FE_INVALID + if (sizeof (long int) == 4 + && sign == 1 + && result == LONG_MIN) + /* Rounding brought the value out of range. */ + feraiseexcept (FE_INVALID); +#endif + } + } + else if (j0 >= 112) + result = ((long int) i0 << (j0 - 48)) | (i1 << (j0 - 112)); + else + { + u_int64_t j = i1 + (0x8000000000000000ULL >> (j0 - 48)); + if (j < i1) + ++i0; + + if (j0 == 48) + result = (long int) i0; + else + { + result = ((long int) i0 << (j0 - 48)) | (j >> (112 - j0)); +#ifdef FE_INVALID + if (sizeof (long int) == 8 + && sign == 1 + && result == LONG_MIN) + /* Rounding brought the value out of range. */ + feraiseexcept (FE_INVALID); +#endif + } + } + } + else + { + /* The number is too large. Unless it rounds to LONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ +#ifdef FE_INVALID + if (FIX_LDBL_LONG_CONVERT_OVERFLOW + && !(sign == -1 && x > (_Float128) LONG_MIN - L(0.5))) + { + feraiseexcept (FE_INVALID); + return sign == 1 ? LONG_MAX : LONG_MIN; + } + else if (!FIX_LDBL_LONG_CONVERT_OVERFLOW + && x <= (_Float128) LONG_MIN - L(0.5)) + { + /* If truncation produces LONG_MIN, the cast will not raise + the exception, but may raise "inexact". */ + feraiseexcept (FE_INVALID); + return LONG_MIN; + } +#endif + /* The number is too large. It is left implementation defined + what happens. */ + return (long int) x; + } + + return sign * result; +} + +weak_alias (__lroundl, lroundl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_modfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_modfl.c new file mode 100644 index 0000000000..01e150b24f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_modfl.c @@ -0,0 +1,79 @@ +/* s_modfl.c -- long double version of s_modf.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * modfl(long double x, long double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 one = 1.0; + +_Float128 __modfl(_Float128 x, _Float128 *iptr) +{ + int64_t i0,i1,j0; + u_int64_t i; + GET_LDOUBLE_WORDS64(i0,i1,x); + j0 = ((i0>>48)&0x7fff)-0x3fff; /* exponent of x */ + if(j0<48) { /* integer part in high x */ + if(j0<0) { /* |x|<1 */ + /* *iptr = +-0 */ + SET_LDOUBLE_WORDS64(*iptr,i0&0x8000000000000000ULL,0); + return x; + } else { + i = (0x0000ffffffffffffLL)>>j0; + if(((i0&i)|i1)==0) { /* x is integral */ + *iptr = x; + /* return +-0 */ + SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0); + return x; + } else { + SET_LDOUBLE_WORDS64(*iptr,i0&(~i),0); + return x - *iptr; + } + } + } else if (j0>111) { /* no fraction part */ + *iptr = x*one; + /* We must handle NaNs separately. */ + if (j0 == 0x4000 && ((i0 & 0x0000ffffffffffffLL) | i1)) + return x*one; + /* return +-0 */ + SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0); + return x; + } else { /* fraction part in low x */ + i = -1ULL>>(j0-48); + if((i1&i)==0) { /* x is integral */ + *iptr = x; + /* return +-0 */ + SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0); + return x; + } else { + SET_LDOUBLE_WORDS64(*iptr,i0,i1&(~i)); + return x - *iptr; + } + } +} +weak_alias (__modfl, modfl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nearbyintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nearbyintl.c new file mode 100644 index 0000000000..1565a8183f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nearbyintl.c @@ -0,0 +1,67 @@ +/* s_nearbyintl.c -- long double version of s_nearbyint.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * nearbyintl(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rintl(x). + */ + +#include <fenv.h> +#include <math.h> +#include <math_private.h> + +static const _Float128 +TWO112[2]={ + L(5.19229685853482762853049632922009600E+33), /* 0x406F000000000000, 0 */ + L(-5.19229685853482762853049632922009600E+33) /* 0xC06F000000000000, 0 */ +}; + +_Float128 __nearbyintl(_Float128 x) +{ + fenv_t env; + int64_t i0,j0,sx; + u_int64_t i1 __attribute__ ((unused)); + _Float128 w,t; + GET_LDOUBLE_WORDS64(i0,i1,x); + sx = (((u_int64_t)i0)>>63); + j0 = ((i0>>48)&0x7fff)-0x3fff; + if(j0<112) { + if(j0<0) { + feholdexcept (&env); + w = TWO112[sx]+x; + t = w-TWO112[sx]; + math_force_eval (t); + fesetenv (&env); + GET_LDOUBLE_MSW64(i0,t); + SET_LDOUBLE_MSW64(t,(i0&0x7fffffffffffffffLL)|(sx<<63)); + return t; + } + } else { + if(j0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + feholdexcept (&env); + w = TWO112[sx]+x; + t = w-TWO112[sx]; + math_force_eval (t); + fesetenv (&env); + return t; +} +weak_alias (__nearbyintl, nearbyintl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nextafterl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nextafterl.c new file mode 100644 index 0000000000..d29f58a7e0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nextafterl.c @@ -0,0 +1,86 @@ +/* s_nextafterl.c -- long double version of s_nextafter.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* IEEE functions + * nextafterl(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> + +_Float128 __nextafterl(_Float128 x, _Float128 y) +{ + int64_t hx,hy,ix,iy; + u_int64_t lx,ly; + + GET_LDOUBLE_WORDS64(hx,lx,x); + GET_LDOUBLE_WORDS64(hy,ly,y); + ix = hx&0x7fffffffffffffffLL; /* |x| */ + iy = hy&0x7fffffffffffffffLL; /* |y| */ + + if(((ix>=0x7fff000000000000LL)&&((ix-0x7fff000000000000LL)|lx)!=0) || /* x is nan */ + ((iy>=0x7fff000000000000LL)&&((iy-0x7fff000000000000LL)|ly)!=0)) /* y is nan */ + return x+y; + if(x==y) return y; /* x=y, return y */ + if((ix|lx)==0) { /* x == 0 */ + _Float128 u; + SET_LDOUBLE_WORDS64(x,hy&0x8000000000000000ULL,1);/* return +-minsubnormal */ + u = math_opt_barrier (x); + u = u * u; + math_force_eval (u); /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */ + if(lx==0) hx--; + lx--; + } else { /* x < y, x += ulp */ + lx++; + if(lx==0) hx++; + } + } else { /* x < 0 */ + if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */ + if(lx==0) hx--; + lx--; + } else { /* x > y, x += ulp */ + lx++; + if(lx==0) hx++; + } + } + hy = hx&0x7fff000000000000LL; + if(hy==0x7fff000000000000LL) { + _Float128 u = x + x; /* overflow */ + math_force_eval (u); + __set_errno (ERANGE); + } + if(hy==0) { + _Float128 u = x*x; /* underflow */ + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + SET_LDOUBLE_WORDS64(x,hx,lx); + return x; +} +weak_alias (__nextafterl, nextafterl) +strong_alias (__nextafterl, __nexttowardl) +weak_alias (__nextafterl, nexttowardl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nexttoward.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nexttoward.c new file mode 100644 index 0000000000..4343fe83f8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nexttoward.c @@ -0,0 +1,89 @@ +/* s_nexttoward.c + * Conversion from s_nextafter.c by Ulrich Drepper, Cygnus Support, + * drepper@cygnus.com and Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* IEEE functions + * nexttoward(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <float.h> + +double __nexttoward(double x, long double y) +{ + int32_t hx,ix; + int64_t hy,iy; + u_int32_t lx; + u_int64_t ly; + + EXTRACT_WORDS(hx,lx,x); + GET_LDOUBLE_WORDS64(hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffffffffffffLL; /* |y| */ + + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ + ((iy>=0x7fff000000000000LL)&&((iy-0x7fff000000000000LL)|ly)!=0)) + /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if((ix|lx)==0) { /* x == 0 */ + double u; + INSERT_WORDS(x,(u_int32_t)((hy>>32)&0x80000000),1);/* return +-minsub */ + u = math_opt_barrier (x); + u = u * u; + math_force_eval (u); /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if (x > y) { /* x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } else { /* x < 0 */ + if (x < y) { /* x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } + hy = hx&0x7ff00000; + if(hy>=0x7ff00000) { + double u = x+x; /* overflow */ + math_force_eval (u); + __set_errno (ERANGE); + } + if(hy<0x00100000) { + double u = x*x; /* underflow */ + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + INSERT_WORDS(x,hx,lx); + return x; +} +weak_alias (__nexttoward, nexttoward) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nexttowardf.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nexttowardf.c new file mode 100644 index 0000000000..8703359d4f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nexttowardf.c @@ -0,0 +1,76 @@ +/* s_nexttowardf.c -- float version of s_nextafter.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com + * and Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +#include <errno.h> +#include <math.h> +#include <math_private.h> + +float __nexttowardf(float x, long double y) +{ + int32_t hx,ix; + int64_t hy,iy; + u_int64_t ly; + + GET_FLOAT_WORD(hx,x); + GET_LDOUBLE_WORDS64(hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffffffffffffLL; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + ((iy>=0x7fff000000000000LL)&&((iy-0x7fff000000000000LL)|ly)!=0)) + /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if(ix==0) { /* x == 0 */ + float u; + SET_FLOAT_WORD(x,(u_int32_t)((hy>>32)&0x80000000)|1);/* return +-minsub*/ + u = math_opt_barrier (x); + u = u * u; + math_force_eval (u); /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if(x > y) { /* x -= ulp */ + hx -= 1; + } else { /* x < y, x += ulp */ + hx += 1; + } + } else { /* x < 0 */ + if(x < y) { /* x < y, x -= ulp */ + hx -= 1; + } else { /* x > y, x += ulp */ + hx += 1; + } + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) { + float u = x+x; /* overflow */ + math_force_eval (u); + __set_errno (ERANGE); + } + if(hy<0x00800000) { + float u = x*x; /* underflow */ + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + SET_FLOAT_WORD(x,hx); + return x; +} +weak_alias (__nexttowardf, nexttowardf) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nextupl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nextupl.c new file mode 100644 index 0000000000..85f43b4eb0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_nextupl.c @@ -0,0 +1,56 @@ +/* Return the least floating-point number greater than X. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* Return the least floating-point number greater than X. */ +_Float128 +__nextupl (_Float128 x) +{ + int64_t hx, ix; + u_int64_t lx; + + GET_LDOUBLE_WORDS64 (hx, lx, x); + ix = hx & 0x7fffffffffffffffLL; + + /* x is nan. */ + if (((ix >= 0x7fff000000000000LL) + && ((ix - 0x7fff000000000000LL) | lx) != 0)) + return x + x; + if ((ix | lx) == 0) + return LDBL_TRUE_MIN; + if (hx >= 0) + { /* x > 0. */ + if (isinf (x)) + return x; + lx++; + if (lx == 0) + hx++; + } + else + { /* x < 0. */ + if (lx == 0) + hx--; + lx--; + } + SET_LDOUBLE_WORDS64 (x, hx, lx); + return x; +} + +weak_alias (__nextupl, nextupl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_remquol.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_remquol.c new file mode 100644 index 0000000000..d360f82dba --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_remquol.c @@ -0,0 +1,112 @@ +/* Compute remainder and a congruent to the quotient. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +static const _Float128 zero = 0.0; + + +_Float128 +__remquol (_Float128 x, _Float128 y, int *quo) +{ + int64_t hx,hy; + u_int64_t sx,lx,ly,qs; + int cquo; + + GET_LDOUBLE_WORDS64 (hx, lx, x); + GET_LDOUBLE_WORDS64 (hy, ly, y); + sx = hx & 0x8000000000000000ULL; + qs = sx ^ (hy & 0x8000000000000000ULL); + hy &= 0x7fffffffffffffffLL; + hx &= 0x7fffffffffffffffLL; + + /* Purge off exception values. */ + if ((hy | ly) == 0) + return (x * y) / (x * y); /* y = 0 */ + if ((hx >= 0x7fff000000000000LL) /* x not finite */ + || ((hy >= 0x7fff000000000000LL) /* y is NaN */ + && (((hy - 0x7fff000000000000LL) | ly) != 0))) + return (x * y) / (x * y); + + if (hy <= 0x7ffbffffffffffffLL) + x = __ieee754_fmodl (x, 8 * y); /* now x < 8y */ + + if (((hx - hy) | (lx - ly)) == 0) + { + *quo = qs ? -1 : 1; + return zero * x; + } + + x = fabsl (x); + y = fabsl (y); + cquo = 0; + + if (hy <= 0x7ffcffffffffffffLL && x >= 4 * y) + { + x -= 4 * y; + cquo += 4; + } + if (hy <= 0x7ffdffffffffffffLL && x >= 2 * y) + { + x -= 2 * y; + cquo += 2; + } + + if (hy < 0x0002000000000000LL) + { + if (x + x > y) + { + x -= y; + ++cquo; + if (x + x >= y) + { + x -= y; + ++cquo; + } + } + } + else + { + _Float128 y_half = L(0.5) * y; + if (x > y_half) + { + x -= y; + ++cquo; + if (x >= y_half) + { + x -= y; + ++cquo; + } + } + } + + *quo = qs ? -cquo : cquo; + + /* Ensure correct sign of zero result in round-downward mode. */ + if (x == 0) + x = 0; + if (sx) + x = -x; + return x; +} +weak_alias (__remquol, remquol) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_rintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_rintl.c new file mode 100644 index 0000000000..410951626b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_rintl.c @@ -0,0 +1,62 @@ +/* s_rintl.c -- long double version of s_rint.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * rintl(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rintl(x). + */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 +TWO112[2]={ + 5.19229685853482762853049632922009600E+33L, /* 0x406F000000000000, 0 */ + -5.19229685853482762853049632922009600E+33L /* 0xC06F000000000000, 0 */ +}; + +_Float128 __rintl(_Float128 x) +{ + int64_t i0,j0,sx; + u_int64_t i1 __attribute__ ((unused)); + _Float128 w,t; + GET_LDOUBLE_WORDS64(i0,i1,x); + sx = (((u_int64_t)i0)>>63); + j0 = ((i0>>48)&0x7fff)-0x3fff; + if(j0<112) { + if(j0<0) { + w = TWO112[sx]+x; + t = w-TWO112[sx]; + GET_LDOUBLE_MSW64(i0,t); + SET_LDOUBLE_MSW64(t,(i0&0x7fffffffffffffffLL)|(sx<<63)); + return t; + } + } else { + if(j0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + w = TWO112[sx]+x; + return w-TWO112[sx]; +} +weak_alias (__rintl, rintl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_roundevenl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_roundevenl.c new file mode 100644 index 0000000000..93b895546a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_roundevenl.c @@ -0,0 +1,102 @@ +/* Round to nearest integer value, rounding halfway cases to even. + ldbl-128 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +#define BIAS 0x3fff +#define MANT_DIG 113 +#define MAX_EXP (2 * BIAS + 1) + +_Float128 +roundevenl (_Float128 x) +{ + uint64_t hx, lx, uhx; + GET_LDOUBLE_WORDS64 (hx, lx, x); + uhx = hx & 0x7fffffffffffffffULL; + int exponent = uhx >> (MANT_DIG - 1 - 64); + if (exponent >= BIAS + MANT_DIG - 1) + { + /* Integer, infinity or NaN. */ + if (exponent == MAX_EXP) + /* Infinity or NaN; quiet signaling NaNs. */ + return x + x; + else + return x; + } + else if (exponent >= BIAS + MANT_DIG - 64) + { + /* Not necessarily an integer; integer bit is in low word. + Locate the bits with exponents 0 and -1. */ + int int_pos = (BIAS + MANT_DIG - 1) - exponent; + int half_pos = int_pos - 1; + uint64_t half_bit = 1ULL << half_pos; + uint64_t int_bit = 1ULL << int_pos; + if ((lx & (int_bit | (half_bit - 1))) != 0) + { + /* Carry into the exponent works correctly. No need to test + whether HALF_BIT is set. */ + lx += half_bit; + hx += lx < half_bit; + } + lx &= ~(int_bit - 1); + } + else if (exponent == BIAS + MANT_DIG - 65) + { + /* Not necessarily an integer; integer bit is bottom of high + word, half bit is top of low word. */ + if (((hx & 1) | (lx & 0x7fffffffffffffffULL)) != 0) + { + lx += 0x8000000000000000ULL; + hx += lx < 0x8000000000000000ULL; + } + lx = 0; + } + else if (exponent >= BIAS) + { + /* At least 1; not necessarily an integer, integer bit and half + bit are in the high word. Locate the bits with exponents 0 + and -1 (when the unbiased exponent is 0, the bit with + exponent 0 is implicit, but as the bias is odd it is OK to + take it from the low bit of the exponent). */ + int int_pos = (BIAS + MANT_DIG - 65) - exponent; + int half_pos = int_pos - 1; + uint64_t half_bit = 1ULL << half_pos; + uint64_t int_bit = 1ULL << int_pos; + if (((hx & (int_bit | (half_bit - 1))) | lx) != 0) + hx += half_bit; + hx &= ~(int_bit - 1); + lx = 0; + } + else if (exponent == BIAS - 1 && (uhx > 0x3ffe000000000000ULL || lx != 0)) + { + /* Interval (0.5, 1). */ + hx = (hx & 0x8000000000000000ULL) | 0x3fff000000000000ULL; + lx = 0; + } + else + { + /* Rounds to 0. */ + hx &= 0x8000000000000000ULL; + lx = 0; + } + SET_LDOUBLE_WORDS64 (x, hx, lx); + return x; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_roundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_roundl.c new file mode 100644 index 0000000000..078d9b9c45 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_roundl.c @@ -0,0 +1,80 @@ +/* Round long double to integer away from zero. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +_Float128 +__roundl (_Float128 x) +{ + int32_t j0; + u_int64_t i1, i0; + + GET_LDOUBLE_WORDS64 (i0, i1, x); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + if (j0 < 48) + { + if (j0 < 0) + { + i0 &= 0x8000000000000000ULL; + if (j0 == -1) + i0 |= 0x3fff000000000000LL; + i1 = 0; + } + else + { + u_int64_t i = 0x0000ffffffffffffLL >> j0; + if (((i0 & i) | i1) == 0) + /* X is integral. */ + return x; + + i0 += 0x0000800000000000LL >> j0; + i0 &= ~i; + i1 = 0; + } + } + else if (j0 > 111) + { + if (j0 == 0x4000) + /* Inf or NaN. */ + return x + x; + else + return x; + } + else + { + u_int64_t i = -1ULL >> (j0 - 48); + if ((i1 & i) == 0) + /* X is integral. */ + return x; + + u_int64_t j = i1 + (1LL << (111 - j0)); + if (j < i1) + i0 += 1; + i1 = j; + i1 &= ~i; + } + + SET_LDOUBLE_WORDS64 (x, i0, i1); + return x; +} +weak_alias (__roundl, roundl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_scalblnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_scalblnl.c new file mode 100644 index 0000000000..5864eaf93c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_scalblnl.c @@ -0,0 +1,62 @@ +/* s_scalblnl.c -- long double version of s_scalbn.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* @(#)s_scalbn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * scalblnl (long double x, long int n) + * scalblnl(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 +two114 = L(2.0769187434139310514121985316880384E+34), /* 0x4071000000000000, 0 */ +twom114 = L(4.8148248609680896326399448564623183E-35), /* 0x3F8D000000000000, 0 */ +huge = L(1.0E+4900), +tiny = L(1.0E-4900); + +_Float128 __scalblnl (_Float128 x, long int n) +{ + int64_t k,hx,lx; + GET_LDOUBLE_WORDS64(hx,lx,x); + k = (hx>>48)&0x7fff; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffffffffffffULL))==0) return x; /* +-0 */ + x *= two114; + GET_LDOUBLE_MSW64(hx,x); + k = ((hx>>48)&0x7fff) - 114; + } + if (k==0x7fff) return x+x; /* NaN or Inf */ + if (n< -50000) return tiny*__copysignl(tiny,x); /*underflow*/ + if (n> 50000 || k+n > 0x7ffe) + return huge*__copysignl(huge,x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k+n; + if (k > 0) /* normal result */ + {SET_LDOUBLE_MSW64(x,(hx&0x8000ffffffffffffULL)|(k<<48)); return x;} + if (k <= -114) + return tiny*__copysignl(tiny,x); /*underflow*/ + k += 114; /* subnormal result */ + SET_LDOUBLE_MSW64(x,(hx&0x8000ffffffffffffULL)|(k<<48)); + return x*twom114; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_scalbnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_scalbnl.c new file mode 100644 index 0000000000..e6fe796079 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_scalbnl.c @@ -0,0 +1,62 @@ +/* s_scalbnl.c -- long double version of s_scalbn.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* @(#)s_scalbn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * scalbnl (long double x, int n) + * scalbnl(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 +two114 = L(2.0769187434139310514121985316880384E+34), /* 0x4071000000000000, 0 */ +twom114 = L(4.8148248609680896326399448564623183E-35), /* 0x3F8D000000000000, 0 */ +huge = L(1.0E+4900), +tiny = L(1.0E-4900); + +_Float128 __scalbnl (_Float128 x, int n) +{ + int64_t k,hx,lx; + GET_LDOUBLE_WORDS64(hx,lx,x); + k = (hx>>48)&0x7fff; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffffffffffffULL))==0) return x; /* +-0 */ + x *= two114; + GET_LDOUBLE_MSW64(hx,x); + k = ((hx>>48)&0x7fff) - 114; + } + if (k==0x7fff) return x+x; /* NaN or Inf */ + if (n< -50000) return tiny*__copysignl(tiny,x); /*underflow*/ + if (n> 50000 || k+n > 0x7ffe) + return huge*__copysignl(huge,x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k+n; + if (k > 0) /* normal result */ + {SET_LDOUBLE_MSW64(x,(hx&0x8000ffffffffffffULL)|(k<<48)); return x;} + if (k <= -114) + return tiny*__copysignl(tiny,x); /*underflow*/ + k += 114; /* subnormal result */ + SET_LDOUBLE_MSW64(x,(hx&0x8000ffffffffffffULL)|(k<<48)); + return x*twom114; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_setpayloadl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_setpayloadl.c new file mode 100644 index 0000000000..1aba33e6e2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_setpayloadl.c @@ -0,0 +1,3 @@ +#define SIG 0 +#define FUNC setpayloadl +#include <s_setpayloadl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_setpayloadl_main.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_setpayloadl_main.c new file mode 100644 index 0000000000..5646634db2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_setpayloadl_main.c @@ -0,0 +1,69 @@ +/* Set NaN payload. ldbl-128 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +#define SET_HIGH_BIT (HIGH_ORDER_BIT_IS_SET_FOR_SNAN ? SIG : !SIG) +#define BIAS 0x3fff +#define PAYLOAD_DIG 111 +#define EXPLICIT_MANT_DIG 112 + +int +FUNC (_Float128 *x, _Float128 payload) +{ + uint64_t hx, lx; + GET_LDOUBLE_WORDS64 (hx, lx, payload); + int exponent = hx >> (EXPLICIT_MANT_DIG - 64); + /* Test if argument is (a) negative or too large; (b) too small, + except for 0 when allowed; (c) not an integer. */ + if (exponent >= BIAS + PAYLOAD_DIG + || (exponent < BIAS && !(SET_HIGH_BIT && hx == 0 && lx == 0))) + { + SET_LDOUBLE_WORDS64 (*x, 0, 0); + return 1; + } + int shift = BIAS + EXPLICIT_MANT_DIG - exponent; + if (shift < 64 + ? (lx & ((1ULL << shift) - 1)) != 0 + : (lx != 0 || (hx & ((1ULL << (shift - 64)) - 1)) != 0)) + { + SET_LDOUBLE_WORDS64 (*x, 0, 0); + return 1; + } + if (exponent != 0) + { + hx &= (1ULL << (EXPLICIT_MANT_DIG - 64)) - 1; + hx |= 1ULL << (EXPLICIT_MANT_DIG - 64); + if (shift >= 64) + { + lx = hx >> (shift - 64); + hx = 0; + } + else if (shift != 0) + { + lx = (lx >> shift) | (hx << (64 - shift)); + hx >>= shift; + } + } + hx |= 0x7fff000000000000ULL | (SET_HIGH_BIT ? 0x800000000000ULL : 0); + SET_LDOUBLE_WORDS64 (*x, hx, lx); + return 0; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_setpayloadsigl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_setpayloadsigl.c new file mode 100644 index 0000000000..d97e2c8206 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_setpayloadsigl.c @@ -0,0 +1,3 @@ +#define SIG 1 +#define FUNC setpayloadsigl +#include <s_setpayloadl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_signbitl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_signbitl.c new file mode 100644 index 0000000000..062b47f55b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_signbitl.c @@ -0,0 +1,27 @@ +/* Return nonzero value if number is negative. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +int +__signbitl (_Float128 x) +{ + return __builtin_signbitl (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_sincosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_sincosl.c new file mode 100644 index 0000000000..34ca6ee03b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_sincosl.c @@ -0,0 +1,73 @@ +/* Compute sine and cosine of argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <math.h> + +#include <math_private.h> + +void +__sincosl (_Float128 x, _Float128 *sinx, _Float128 *cosx) +{ + int64_t ix; + + /* High word of x. */ + GET_LDOUBLE_MSW64 (ix, x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if (ix <= 0x3ffe921fb54442d1LL) + __kernel_sincosl (x, 0, sinx, cosx, 0); + else if (ix >= 0x7fff000000000000LL) + { + /* sin(Inf or NaN) is NaN */ + *sinx = *cosx = x - x; + if (isinf (x)) + __set_errno (EDOM); + } + else + { + /* Argument reduction needed. */ + _Float128 y[2]; + int n; + + n = __ieee754_rem_pio2l (x, y); + switch (n & 3) + { + case 0: + __kernel_sincosl (y[0], y[1], sinx, cosx, 1); + break; + case 1: + __kernel_sincosl (y[0], y[1], cosx, sinx, 1); + *cosx = -*cosx; + break; + case 2: + __kernel_sincosl (y[0], y[1], sinx, cosx, 1); + *sinx = -*sinx; + *cosx = -*cosx; + break; + default: + __kernel_sincosl (y[0], y[1], cosx, sinx, 1); + *sinx = -*sinx; + break; + } + } +} +weak_alias (__sincosl, sincosl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_sinl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_sinl.c new file mode 100644 index 0000000000..887e45dbfa --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_sinl.c @@ -0,0 +1,86 @@ +/* s_sinl.c -- long double version of s_sin.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* sinl(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sinl ... sine function on [-pi/4,pi/4] + * __kernel_cosl ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> + +_Float128 __sinl(_Float128 x) +{ + _Float128 y[2],z=0; + int64_t n, ix; + + /* High word of x. */ + GET_LDOUBLE_MSW64(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if(ix <= 0x3ffe921fb54442d1LL) + return __kernel_sinl(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7fff000000000000LL) { + if (ix == 0x7fff000000000000LL) { + GET_LDOUBLE_LSW64(n,x); + if (n == 0) + __set_errno (EDOM); + } + return x-x; + } + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + switch(n&3) { + case 0: return __kernel_sinl(y[0],y[1],1); + case 1: return __kernel_cosl(y[0],y[1]); + case 2: return -__kernel_sinl(y[0],y[1],1); + default: + return -__kernel_cosl(y[0],y[1]); + } + } +} +weak_alias (__sinl, sinl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_tanhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_tanhl.c new file mode 100644 index 0000000000..0db8f5f775 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_tanhl.c @@ -0,0 +1,100 @@ +/* s_tanhl.c -- long double version of s_tanh.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Changes for 128-bit long double contributed by + Stephen L. Moshier <moshier@na-net.ornl.gov> */ + +/* tanhl(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanhl(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x). + * 2. 0 <= x <= 2**-57 : tanhl(x) := x*(one+x) + * -t + * 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x) + * t + 2 + * 2 + * 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x) + * t + 2 + * 40.0 < x <= INF : tanhl(x) := 1. + * + * Special cases: + * tanhl(NaN) is NaN; + * only tanhl(0)=0 is exact for finite argument. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const _Float128 one = 1.0, two = 2.0, tiny = L(1.0e-4900); + +_Float128 +__tanhl (_Float128 x) +{ + _Float128 t, z; + u_int32_t jx, ix; + ieee854_long_double_shape_type u; + + /* Words of |x|. */ + u.value = x; + jx = u.parts32.w0; + ix = jx & 0x7fffffff; + /* x is INF or NaN */ + if (ix >= 0x7fff0000) + { + /* for NaN it's not important which branch: tanhl(NaN) = NaN */ + if (jx & 0x80000000) + return one / x - one; /* tanhl(-inf)= -1; */ + else + return one / x + one; /* tanhl(+inf)=+1 */ + } + + /* |x| < 40 */ + if (ix < 0x40044000) + { + if (u.value == 0) + return x; /* x == +- 0 */ + if (ix < 0x3fc60000) /* |x| < 2^-57 */ + { + math_check_force_underflow (x); + return x * (one + tiny); /* tanh(small) = small */ + } + u.parts32.w0 = ix; /* Absolute value of x. */ + if (ix >= 0x3fff0000) + { /* |x| >= 1 */ + t = __expm1l (two * u.value); + z = one - two / (t + two); + } + else + { + t = __expm1l (-two * u.value); + z = -t / (t + two); + } + /* |x| > 40, return +-1 */ + } + else + { + z = one - tiny; /* raised inexact flag */ + } + return (jx & 0x80000000) ? -z : z; +} +weak_alias (__tanhl, tanhl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_tanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_tanl.c new file mode 100644 index 0000000000..cd7b258616 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_tanl.c @@ -0,0 +1,80 @@ +/* s_tanl.c -- long double version of s_tan.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* @(#)s_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* tanl(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tanl ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> + +_Float128 __tanl(_Float128 x) +{ + _Float128 y[2],z=0; + int64_t n, ix; + + /* High word of x. */ + GET_LDOUBLE_MSW64(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if(ix <= 0x3ffe921fb54442d1LL) return __kernel_tanl(x,z,1); + + /* tanl(Inf or NaN) is NaN */ + else if (ix>=0x7fff000000000000LL) { + if (ix == 0x7fff000000000000LL) { + GET_LDOUBLE_LSW64(n,x); + if (n == 0) + __set_errno (EDOM); + } + return x-x; /* NaN */ + } + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} +weak_alias (__tanl, tanl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_totalorderl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_totalorderl.c new file mode 100644 index 0000000000..ca7b3102e1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_totalorderl.c @@ -0,0 +1,54 @@ +/* Total order operation. ldbl-128 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalorderl (_Float128 x, _Float128 y) +{ + int64_t hx, hy; + uint64_t lx, ly; + GET_LDOUBLE_WORDS64 (hx, lx, x); + GET_LDOUBLE_WORDS64 (hy, ly, y); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + uint64_t uhx = hx & 0x7fffffffffffffffULL; + uint64_t uhy = hy & 0x7fffffffffffffffULL; + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the arguments interpreted as + sign-magnitude integers. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if ((uhx > 0x7fff000000000000ULL || (uhx == 0x7fff000000000000ULL + && lx != 0)) + && (uhy > 0x7fff000000000000ULL || (uhy == 0x7fff000000000000ULL + && ly != 0))) + { + hx ^= 0x0000800000000000ULL; + hy ^= 0x0000800000000000ULL; + } +#endif + uint64_t hx_sign = hx >> 63; + uint64_t hy_sign = hy >> 63; + hx ^= hx_sign >> 1; + lx ^= hx_sign; + hy ^= hy_sign >> 1; + ly ^= hy_sign; + return hx < hy || (hx == hy && lx <= ly); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_totalordermagl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_totalordermagl.c new file mode 100644 index 0000000000..41b969d811 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_totalordermagl.c @@ -0,0 +1,48 @@ +/* Total order operation on absolute values. ldbl-128 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalordermagl (_Float128 x, _Float128 y) +{ + uint64_t hx, hy; + uint64_t lx, ly; + GET_LDOUBLE_WORDS64 (hx, lx, x); + GET_LDOUBLE_WORDS64 (hy, ly, y); + hx &= 0x7fffffffffffffffULL; + hy &= 0x7fffffffffffffffULL; +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the absolute values of the + arguments. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if ((hx > 0x7fff000000000000ULL || (hx == 0x7fff000000000000ULL + && lx != 0)) + && (hy > 0x7fff000000000000ULL || (hy == 0x7fff000000000000ULL + && ly != 0))) + { + hx ^= 0x0000800000000000ULL; + hy ^= 0x0000800000000000ULL; + } +#endif + return hx < hy || (hx == hy && lx <= ly); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_truncl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_truncl.c new file mode 100644 index 0000000000..6d1a11e7c4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_truncl.c @@ -0,0 +1,56 @@ +/* Truncate argument to nearest integral value not larger than the argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +_Float128 +__truncl (_Float128 x) +{ + int32_t j0; + u_int64_t i0, i1, sx; + + GET_LDOUBLE_WORDS64 (i0, i1, x); + sx = i0 & 0x8000000000000000ULL; + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + if (j0 < 48) + { + if (j0 < 0) + /* The magnitude of the number is < 1 so the result is +-0. */ + SET_LDOUBLE_WORDS64 (x, sx, 0); + else + SET_LDOUBLE_WORDS64 (x, i0 & ~(0x0000ffffffffffffLL >> j0), 0); + } + else if (j0 > 111) + { + if (j0 == 0x4000) + /* x is inf or NaN. */ + return x + x; + } + else + { + SET_LDOUBLE_WORDS64 (x, i0, i1 & ~(0xffffffffffffffffULL >> (j0 - 48))); + } + + return x; +} +weak_alias (__truncl, truncl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_ufromfpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_ufromfpl.c new file mode 100644 index 0000000000..c686daa4a7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_ufromfpl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 1 +#define INEXACT 0 +#define FUNC ufromfpl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_ufromfpxl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_ufromfpxl.c new file mode 100644 index 0000000000..906066c83c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_ufromfpxl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 1 +#define INEXACT 1 +#define FUNC ufromfpxl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/strtod_nan_ldouble.h b/REORG.TODO/sysdeps/ieee754/ldbl-128/strtod_nan_ldouble.h new file mode 100644 index 0000000000..142393d787 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/strtod_nan_ldouble.h @@ -0,0 +1,33 @@ +/* Convert string for NaN payload to corresponding NaN. For ldbl-128. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define FLOAT long double +#define SET_MANTISSA(flt, mant) \ + do \ + { \ + union ieee854_long_double u; \ + u.d = (flt); \ + u.ieee_nan.mantissa0 = 0; \ + u.ieee_nan.mantissa1 = 0; \ + u.ieee_nan.mantissa2 = (mant) >> 32; \ + u.ieee_nan.mantissa3 = (mant); \ + if ((u.ieee.mantissa0 | u.ieee.mantissa1 \ + | u.ieee.mantissa2 | u.ieee.mantissa3) != 0) \ + (flt) = u.d; \ + } \ + while (0) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/strtold_l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/strtold_l.c new file mode 100644 index 0000000000..4a8b14c4bb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/strtold_l.c @@ -0,0 +1,37 @@ +/* Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +/* The actual implementation for all floating point sizes is in strtod.c. + These macros tell it to produce the `long double' version, `strtold'. */ + +#define FLOAT long double +#define FLT LDBL +#ifdef USE_WIDE_CHAR +# define STRTOF wcstold_l +# define __STRTOF __wcstold_l +# define STRTOF_NAN __wcstold_nan +#else +# define STRTOF strtold_l +# define __STRTOF __strtold_l +# define STRTOF_NAN __strtold_nan +#endif +#define MPN2FLOAT __mpn_construct_long_double +#define FLOAT_HUGE_VAL HUGE_VALL + +#include <strtod_l.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/t_expl.h b/REORG.TODO/sysdeps/ieee754/ldbl-128/t_expl.h new file mode 100644 index 0000000000..2b1b647db9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/t_expl.h @@ -0,0 +1,970 @@ +/* Accurate table for expl(). + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __expl_table basically consists of four tables, T_EXPL_ARG{1,2} and + T_EXPL_RES{1,2}. All tables use positive and negative indexes, the 0 points + are marked by T_EXPL_* defines. + For ARG1 and RES1 tables lets B be 89 and S 256.0, for ARG2 and RES2 B is 65 + and S 32768.0. + These table have the property that, for all integers -B <= i <= B + expl(__expl_table[T_EXPL_ARGN+2*i]+__expl_table[T_EXPL_ARGN+2*i+1]+r) == + __expl_table[T_EXPL_RESN+i], __expl_table[T_EXPL_RESN+i] is some exact number + with the low 58 bits of the mantissa 0, + __expl_table[T_EXPL_ARGN+2*i] == i/S+s + where absl(s) <= 2^-54 and absl(r) <= 2^-212. */ + +static const _Float128 __expl_table [] = { + L(-3.47656250000000000584188889839535373E-01), /* bffd640000000000002b1b04213cf000 */ + L(6.90417668990715641167244540876988960E-32), /* 3f97667c3fdb588a6ae1af8748357a17 */ + L(-3.43749999999999981853132895957607418E-01), /* bffd5ffffffffffffac4ff5f4050b000 */ + L(-7.16021898043268093462818380603370350E-33), /* bf94296c8219427edc1431ac2498583e */ + L(-3.39843750000000013418643523138766329E-01), /* bffd5c000000000003de1f027a30e000 */ + L(8.16920774283317801641347327589583265E-32), /* 3f97a82b65774bdca1b4440d749ed8d3 */ + L(-3.35937500000000014998092453039303051E-01), /* bffd5800000000000452a9f4d8857000 */ + L(-6.55865578425428447938248396879359670E-32), /* bf97548b7d240f3d034b395e6eecfac8 */ + L(-3.32031250000000000981984049529998541E-01), /* bffd540000000000004875277cda5000 */ + L(6.91213046334032232108944519541512737E-32), /* 3f9766e5f925338a19045c94443b66e1 */ + L(-3.28124999999999986646017645350399708E-01), /* bffd4ffffffffffffc26a667bf44d000 */ + L(-6.16281060996110316602421505683742661E-32), /* bf973ffdcdcffb6fbffc86b2b8d42f5d */ + L(-3.24218749999999991645717430645867963E-01), /* bffd4bfffffffffffd97901063e48000 */ + L(-7.90797211087760527593856542417304137E-32), /* bf979a9afaaca1ada6a8ed1c80584d60 */ + L(-3.20312499999999998918211610690789652E-01), /* bffd47ffffffffffffb02d9856d71000 */ + L(8.64024799457616856987630373786503376E-32), /* 3f97c0a098623f95579d5d9b2b67342d */ + L(-3.16406249999999998153974811017181883E-01), /* bffd43ffffffffffff77c991f1076000 */ + L(-2.73176610180696076418536105483668404E-32), /* bf961baeccb32f9b1fcbb8e60468e95a */ + L(-3.12500000000000011420976192575972779E-01), /* bffd400000000000034ab8240483d000 */ + L(7.16573502812389453744433792609989420E-32), /* 3f977410f4c2cfc4335f28446c0fb363 */ + L(-3.08593750000000001735496343854851414E-01), /* bffd3c000000000000800e995c176000 */ + L(-1.56292999645122272621237565671593071E-32), /* bf95449b9cbdaff6ac1246adb2c826ac */ + L(-3.04687499999999982592401295899221626E-01), /* bffd37fffffffffffafb8bc1e061a000 */ + L(6.48993208584888904958594509625158417E-32), /* 3f9750f9fe8366d82d77afa0031a92e1 */ + L(-3.00781249999999999230616898937763959E-01), /* bffd33ffffffffffffc73ac39da54000 */ + L(6.57082437496961397305801409357792029E-32), /* 3f97552d3cb598ea80135cf3feb27ec4 */ + L(-2.96874999999999998788769281703245722E-01), /* bffd2fffffffffffffa6a07fa5021000 */ + L(-3.26588297198283968096426564544269170E-32), /* bf9653260fc1802f46b629aee171809b */ + L(-2.92968750000000015318089182805941695E-01), /* bffd2c0000000000046a468614bd6000 */ + L(-1.73291974845198589684358727559290718E-32), /* bf9567e9d158f52e483c8d8dcb5961dd */ + L(-2.89062500000000007736778942676309681E-01), /* bffd280000000000023adf9f4c3d3000 */ + L(-6.83629745986675744404029225571026236E-32), /* bf9762f5face6281c1daf1c6aedbdb45 */ + L(-2.85156250000000001367091555763661937E-01), /* bffd2400000000000064dfa11e3fb000 */ + L(-5.44898442619766878281110054067026237E-32), /* bf971aed6d2db9f542986a785edae072 */ + L(-2.81249999999999986958718100227029406E-01), /* bffd1ffffffffffffc3db9265ca9d000 */ + L(1.13007318374506125723591889451107046E-32), /* 3f94d569fe387f456a97902907ac3856 */ + L(-2.77343750000000000356078829380495179E-01), /* bffd1c0000000000001a462390083000 */ + L(-4.98979365468978332358409063436543102E-32), /* bf970315bbf3e0d14b5c94c900702d4c */ + L(-2.73437499999999990276993957508540484E-01), /* bffd17fffffffffffd32919bcdc94000 */ + L(-8.79390484115892344533724650295100871E-32), /* bf97c89b0b89cc19c3ab2b60da9bbbc3 */ + L(-2.69531250000000002434203866460082225E-01), /* bffd14000000000000b39ccf9e130000 */ + L(9.44060754687026590886751809927191596E-32), /* 3f97ea2f32cfecca5c64a26137a9210f */ + L(-2.65624999999999997296320716986257179E-01), /* bffd0fffffffffffff3880f13a2bc000 */ + L(2.07142664067265697791007875348396921E-32), /* 3f95ae37ee685b9122fbe377bd205ee4 */ + L(-2.61718750000000010237478733739017956E-01), /* bffd0c000000000002f3648179d40000 */ + L(-6.10552936159265665298996309192680256E-32), /* bf973d0467d31e407515a3cca0f3b4e2 */ + L(-2.57812500000000011948220522778370303E-01), /* bffd08000000000003719f81275bd000 */ + L(6.72477169058908902499239631466443836E-32), /* 3f975d2b8c475d3160cf72d227d8e6f9 */ + L(-2.53906249999999991822993360536596860E-01), /* bffd03fffffffffffda4a4b62f818000 */ + L(-2.44868296623215865054704392917190994E-32), /* bf95fc92516c6d057d29fc2528855976 */ + L(-2.49999999999999986862019457428548084E-01), /* bffcfffffffffffff86d2d20d5ff4000 */ + L(-3.85302898949105073614122724961613078E-32), /* bf96901f147cb7d643af71b6129ce929 */ + L(-2.46093750000000000237554160737318435E-01), /* bffcf8000000000000230e8ade26b000 */ + L(-1.52823675242678363494345369284988589E-32), /* bf953d6700c5f3fc303f79d0ec8c680a */ + L(-2.42187500000000003023380963205457065E-01), /* bffcf0000000000001be2c1a78bb0000 */ + L(-7.78402037952209709489481182714311699E-34), /* bf9102ab1f3998e887f0ee4cf940faa5 */ + L(-2.38281249999999995309623303145485725E-01), /* bffce7fffffffffffd4bd2940f43f000 */ + L(-3.54307216794236899443913216397197696E-32), /* bf966fef03ab69c3f289436205b21d02 */ + L(-2.34374999999999998425804947623207526E-01), /* bffcdfffffffffffff17b097a6092000 */ + L(-2.86038428948386602859761879407549696E-32), /* bf96290a0eba0131efe3a05fe188f2e3 */ + L(-2.30468749999999993822207406785200832E-01), /* bffcd7fffffffffffc70519834eae000 */ + L(-2.54339521031747516806893838749365762E-32), /* bf96081f0ad7f9107ae6cddb32c178ab */ + L(-2.26562499999999997823524030344489884E-01), /* bffccffffffffffffebecf10093df000 */ + L(4.31904611473158635644635628922959401E-32), /* 3f96c083f0b1faa7c4c686193e38d67c */ + L(-2.22656250000000004835132405125162742E-01), /* bffcc8000000000002c98a233f19f000 */ + L(2.54709791629335691650310168420597566E-33), /* 3f92a735903f5eed07a716ab931e20d9 */ + L(-2.18749999999999988969454021829236626E-01), /* bffcbffffffffffff9a42dc14ce36000 */ + L(-3.77236096429336082213752014054909454E-32), /* bf9687be8e5b2fca54d3e81157eac660 */ + L(-2.14843750000000010613256919115758495E-01), /* bffcb80000000000061e3d828ecac000 */ + L(-4.55194148712216691177097854305964738E-32), /* bf96d8b35c776aa3e1a4768271380503 */ + L(-2.10937499999999993204656148110447201E-01), /* bffcaffffffffffffc152f2aea118000 */ + L(-2.95044199165561453749332254271716417E-32), /* bf96326433b00b2439094d9bef22ddd1 */ + L(-2.07031250000000012233944895423355677E-01), /* bffca80000000000070d695ee0e94000 */ + L(1.93146788688385419095981415411012357E-32), /* 3f959126729135a5e390d4bb802a0bde */ + L(-2.03125000000000008030983633336321863E-01), /* bffca0000000000004a129fbc51af000 */ + L(2.37361904671826193563212931215900137E-32), /* 3f95ecfb3c4ba1b97ea3ad45cbb1e68a */ + L(-1.99218750000000001763815712796132779E-01), /* bffc98000000000001044b12d9950000 */ + L(-3.63171243370923753295192486732883239E-33), /* bf932db5fb3f27c38e0fa7bbcfc64f55 */ + L(-1.95312500000000004883660234506677272E-01), /* bffc90000000000002d0b3779d1f9000 */ + L(-3.19989507343607877747980892249711601E-33), /* bf9309d63de96bb3ef744c865f22f1bd */ + L(-1.91406250000000013720152363227519348E-01), /* bffc88000000000007e8bcb387121000 */ + L(-1.89295754093147174148371614722178860E-32), /* bf958926e2e67dfe812c508290add2e7 */ + L(-1.87500000000000000182342082774432620E-01), /* bffc800000000000001ae8b06a39f000 */ + L(-2.96812835183184815200854214892983927E-32), /* bf96343a62d156bbe71f55d14ca4b6e5 */ + L(-1.83593750000000012410147185883290345E-01), /* bffc78000000000007276a1adda8d000 */ + L(-2.02191931237489669058466239995304587E-32), /* bf95a3efab92d26ec2df90df036a117f */ + L(-1.79687499999999997439177363346082917E-01), /* bffc6ffffffffffffe8616db2927d000 */ + L(-9.92752326937775530007399526834009465E-33), /* bf949c5f88ed17041e1a3f1829d543cd */ + L(-1.75781249999999995824373974504785174E-01), /* bffc67fffffffffffd97c94f13ea3000 */ + L(1.44184772065335613487885714828816178E-32), /* 3f952b75c63476e7fcc2f5841c27bcce */ + L(-1.71874999999999986685050259043077809E-01), /* bffc5ffffffffffff8530f6bc531a000 */ + L(-3.49007014971241147689894940544402482E-32), /* bf966a6dfaa012aea8ffe6d90b02330f */ + L(-1.67968749999999997316058782350439701E-01), /* bffc57fffffffffffe73eb914f2aa000 */ + L(3.34025733574205019081305778794376391E-32), /* 3f965adf4572561fd5456a6c13d8babf */ + L(-1.64062499999999993322730602128318480E-01), /* bffc4ffffffffffffc269be4f68f3000 */ + L(-1.83345916769684984022099095506340635E-32), /* bf957ccb69026cb2f6024c211576d5f4 */ + L(-1.60156249999999992419000744447607979E-01), /* bffc47fffffffffffba13df21784a000 */ + L(2.73442789798110494773517431626534726E-32), /* 3f961bf58ff22c9b30f1e2b39f26d7d5 */ + L(-1.56249999999999987665010524130393080E-01), /* bffc3ffffffffffff8e3ad45e7508000 */ + L(2.02695576464836145806428118889332191E-32), /* 3f95a4fb7435a4a2f71de81eb8ae75d1 */ + L(-1.52343749999999989905291167951491803E-01), /* bffc37fffffffffffa2e48aecfc24000 */ + L(-3.61436631548815190395331054871041524E-32), /* bf967756567ebd108075ae527cc2e7f0 */ + L(-1.48437500000000006686107754967759751E-01), /* bffc30000000000003dab20261b3c000 */ + L(-2.15524270159131591469319477922198390E-32), /* bf95bfa05b82ef3a708c4f0395e9fcf6 */ + L(-1.44531250000000005132889939177166485E-01), /* bffc28000000000002f57b1969e7b000 */ + L(2.74741116529653547935086189244019604E-32), /* 3f961d4eb77c1185d34fe1b04a3f3cf5 */ + L(-1.40625000000000000707469094533647325E-01), /* bffc2000000000000068676d3d5c4000 */ + L(4.40607097220049957013547629906723266E-33), /* 3f936e0ac425daf795b42913cf0ef881 */ + L(-1.36718749999999995713752139187543306E-01), /* bffc17fffffffffffd87762255991000 */ + L(-3.73751317180116492404578048203389108E-32), /* bf9684202491e9cbb7ceb67d9ff7e0c9 */ + L(-1.32812500000000007198453630478482191E-01), /* bffc10000000000004264de3a4379000 */ + L(-3.97050085179660203884930593717220728E-32), /* bf969c52048de14be3c9c1971e50869c */ + L(-1.28906250000000006070486371645733082E-01), /* bffc080000000000037fd87db2cb0000 */ + L(3.59610068058504988294019521946586131E-32), /* 3f967570c10687cb8e9ebd0b280abf5a */ + L(-1.25000000000000003700729208608337966E-01), /* bffc00000000000002222198bbc74000 */ + L(3.23464851393124362331846965931995969E-33), /* 3f930cb95da3bfc847e593716c91d57a */ + L(-1.21093750000000013729038501177102555E-01), /* bffbf000000000000fd418d1f5fda000 */ + L(2.45242487730722066611358741283977619E-32), /* 3f95fd5945ad86a464292e26ac192a84 */ + L(-1.17187499999999999765305306880205578E-01), /* bffbdfffffffffffffbabaf869845000 */ + L(-1.14557520298960389903199646350205537E-32), /* bf94dbda735322179d9bcf392e1dd06d */ + L(-1.13281250000000009579647893740755690E-01), /* bffbd000000000000b0b69bae7ab9000 */ + L(2.37873962873837390105423621772752350E-32), /* 3f95ee0b7e0bd5ac1f6fab1e2a71abc3 */ + L(-1.09375000000000008981153004560108539E-01), /* bffbc000000000000a5ac4bc1d2c3000 */ + L(1.53152444860014076105003555837231015E-32), /* 3f953e15ce931e12ef9a152522e32bdd */ + L(-1.05468749999999992399063850363228723E-01), /* bffbaffffffffffff73c998091408000 */ + L(-8.75920903597804862471749360196688834E-33), /* bf946bd7e310a01bae5687ebdc47fcc5 */ + L(-1.01562500000000007685885179918350550E-01), /* bffba0000000000008dc7910a648c000 */ + L(-4.63820993797174451904075397785059501E-33), /* bf938153d0e54001a472da180fb5e8aa */ + L(-9.76562499999999887262211517861331814E-02), /* bffb8ffffffffffff300915aa6fd6000 */ + L(-2.63767025974952608658936466715705903E-33), /* bf92b64215bb8d520be5404620d38088 */ + L(-9.37499999999999939650246024457439795E-02), /* bffb7ffffffffffff90aca26bd0fc000 */ + L(-1.72047822349322956713582039121348377E-32), /* bf9565545015c5b9b56d02cfefca2c7d */ + L(-8.98437500000000033088896383977486369E-02), /* bffb70000000000003d09ca1e3cbe000 */ + L(3.04831994420989436248526129869697270E-33), /* 3f92fa7d30d2ed90e7ebbd6231fd08b1 */ + L(-8.59374999999999947312400115121319225E-02), /* bffb5ffffffffffff9ecefc03376e000 */ + L(1.50416954438393392150792422537312281E-32), /* 3f9538675ee99bd722fad0023c09c915 */ + L(-8.20312500000000054182280847004695514E-02), /* bffb500000000000063f2dbd40200000 */ + L(2.68399664523430004488075638997207289E-33), /* 3f92bdf49766629882c49a3da88928ed */ + L(-7.81250000000000114767533968079748798E-02), /* bffb4000000000000d3b56f81ba70000 */ + L(1.72318124201659121296305402819694281E-32), /* 3f9565e407aaabfb359e8a567d760de3 */ + L(-7.42187500000000035531829472486812869E-02), /* bffb3000000000000418b6e9b5388000 */ + L(2.09401756478514117051383998628099655E-32), /* 3f95b2e91221fcd74be0a86d8ad658d2 */ + L(-7.03124999999999987474933134860732535E-02), /* bffb1ffffffffffffe8e53453d2ac000 */ + L(2.28515798224350800271565551341211666E-32), /* 3f95da9bd6adf00894f05b5cc5530125 */ + L(-6.64062500000000042267533361089054159E-02), /* bffb10000000000004df8473dbcf2000 */ + L(1.97576478800281368377376002585430031E-32), /* 3f959a59acbddb2f53bd3096b66370e9 */ + L(-6.25000000000000066329769382774201686E-02), /* bffb00000000000007a5b5914e336000 */ + L(-1.46422615813786836245343723048221678E-33), /* bf91e69295f069fc0c4a9db181ea25a3 */ + L(-5.85937500000000002823707957982406053E-02), /* bffae0000000000000a6aeab10592000 */ + L(9.25637741701318872896718218457555829E-33), /* 3f94807eb021f1f40a37d4015b1eb76b */ + L(-5.46875000000000081586888005226044448E-02), /* bffac0000000000012d00a3171e3a000 */ + L(-4.87144542459404765480424673678105050E-33), /* bf9394b42faba6b7036fe7b36269daf3 */ + L(-5.07812499999999927720348253140567013E-02), /* bffa9fffffffffffef555cc8dd914000 */ + L(-3.01901021987395945826043649523451725E-33), /* bf92f59e7e3025691f290f8f67277faf */ + L(-4.68749999999999935349476738962633103E-02), /* bffa7ffffffffffff117b4ea2b876000 */ + L(1.21521638219189777347767475937119750E-32), /* 3f94f8c7f88c5b56674b94d984ac8ecb */ + L(-4.29687500000000056305562847814228219E-02), /* bffa6000000000000cfbb19be30c0000 */ + L(-1.18643699217679276275559592978275214E-32), /* bf94ecd39f0833a876550e83eb012b99 */ + L(-3.90624999999999962692914526031373542E-02), /* bffa3ffffffffffff765c743922f9000 */ + L(-4.91277156857520035712509544689973679E-33), /* bf939823189996193872e58ac0dececb */ + L(-3.51562500000000108152468207687602886E-02), /* bffa20000000000018f031e41177f000 */ + L(1.18599806302656253755207072755609820E-32), /* 3f94eca4f23e787fab73ce8f6b9b8d64 */ + L(-3.12500000000000077376981036742289578E-02), /* bffa00000000000011d787e0b386f000 */ + L(9.97730386477005171963635210799577079E-33), /* 3f949e70e498c46a0173ac0d46c699fc */ + L(-2.73437500000000139436129596418623235E-02), /* bff9c00000000000404db66e70a08000 */ + L(2.25755321633070123579875157841633859E-33), /* 3f927719b1a93074bdf9f3c2cb784785 */ + L(-2.34375000000000088003629211828324876E-02), /* bff98000000000002895a27d45feb000 */ + L(2.84374279216848803102126617873942975E-33), /* 3f92d87f70e749d6da6c260b68dc210b */ + L(-1.95312500000000107408831063404855424E-02), /* bff9400000000000318898ba69f71000 */ + L(2.47348089686935458989103979140011912E-33), /* 3f929afa3de45086fe909fdddb41edce */ + L(-1.56250000000000081443917555362290635E-02), /* bff9000000000000258f335e9cdd6000 */ + L(-2.43379314483517422161458863218426254E-33), /* bf9294621c8a9ccacf2b020ec19cad27 */ + L(-1.17187500000000051490597418161403184E-02), /* bff88000000000002f7ddfa26221f000 */ + L(1.83405297208145390679150568810924707E-33), /* 3f9230bbfc5d5fe1b534fbcda0465bb9 */ + L(-7.81249999999999715861805208310174953E-03), /* bff7ffffffffffffcb95f3fff157d000 */ + L(3.51548384878710915171654413641872451E-34), /* 3f8fd349b76c22966f77a39fc37ed704 */ + L(-3.90625000000000309326013918295097128E-03), /* bff7000000000000390f820c8e153000 */ + L(6.38058004651791109324060099097251911E-36), /* 3f8a0f665d3ac25a1ac94d688273dbcd */ +#define T_EXPL_ARG1 (2*89) + L(0.00000000000000000000000000000000000E+00), /* 00000000000000000000000000000000 */ + L(0.00000000000000000000000000000000000E+00), /* 00000000000000000000000000000000 */ + L(3.90625000000000245479958859972588985E-03), /* 3ff70000000000002d48769ac9874000 */ + L(-6.58439598384342854976169982902779828E-36), /* bf8a1811b923e6c626b07ef29761482a */ + L(7.81250000000001311374391093664996358E-03), /* 3ff800000000000078f3f3cd89111000 */ + L(2.60265650555493781464273319671555602E-33), /* 3f92b070c3b635b87af426735a71fc87 */ + L(1.17187500000000269581156218247101912E-02), /* 3ff8800000000000f8a50d02fe20d000 */ + L(1.00961747974945520631836275894919326E-33), /* 3f914f80c1a4f8042044fe3b757b030b */ + L(1.56249999999999797878275270751825475E-02), /* 3ff8ffffffffffff45935b69da62e000 */ + L(2.03174577741375590087897353146748580E-33), /* 3f925194e863496e0f6e91cbf6b22e26 */ + L(1.95312499999999760319884511789111533E-02), /* 3ff93fffffffffff917790ff9a8f4000 */ + L(4.62788519658803722282100289809515007E-33), /* 3f9380783ba81295feeb3e4879d7d52d */ + L(2.34374999999999822953909016349145918E-02), /* 3ff97fffffffffffae5a163bd3cd5000 */ + L(-3.19499956304699705390404384504876533E-33), /* bf93096e2037ced8194cf344c692f8d6 */ + L(2.73437500000000137220327275871555682E-02), /* 3ff9c000000000003f481dea5dd51000 */ + L(-2.25757776523031994464630107442723424E-33), /* bf92771abcf988a02b414bf2614e3734 */ + L(3.12499999999999790857640618332718621E-02), /* 3ff9ffffffffffff9f8cd40b51509000 */ + L(-4.22479470489989916319395454536511458E-33), /* bf935efb7245612f371deca17cb7b30c */ + L(3.51562499999999840753382405747597346E-02), /* 3ffa1fffffffffffdb47bd275f722000 */ + L(1.08459658374118041980976756063083500E-34), /* 3f8e2055d18b7117c9db1c318b1e889b */ + L(3.90624999999999989384433621470426757E-02), /* 3ffa3ffffffffffffd8d5e18b042e000 */ + L(-7.41674226146122000759491297811091830E-33), /* bf94341454e48029e5b0205d91baffdc */ + L(4.29687500000000107505739500500200462E-02), /* 3ffa60000000000018ca04cd9085c000 */ + L(-4.74689012756713017494437969420919847E-34), /* bf903b7c268103c6f7fbaaa24142e287 */ + L(4.68749999999999978700749928325717352E-02), /* 3ffa7ffffffffffffb16b6d5479e3000 */ + L(-1.06208165308448830117773486334902917E-32), /* bf94b92be4b3b5b5a596a0a5187cc955 */ + L(5.07812499999999815072625435955786253E-02), /* 3ffa9fffffffffffd55bd086d5cbc000 */ + L(-9.37038897148383660401929567549111394E-33), /* bf94853b111b0175b491c80d00419416 */ + L(5.46874999999999809511553152189867394E-02), /* 3ffabfffffffffffd4138bfa74a61000 */ + L(1.06642963074562437340498606682822123E-32), /* 3f94bafa3fe991b39255d563dfa05d89 */ + L(5.85937500000000184331996330905145551E-02), /* 3ffae000000000002a810a5f2f8bf000 */ + L(-1.76639977694797200820296641773791945E-34), /* bf8ed596f07ce4408f1705c8ec16864c */ + L(6.25000000000000021544696744852045001E-02), /* 3ffb000000000000027be32045e2b000 */ + L(1.68616371995798354366633034788947149E-32), /* 3f955e33d7440794d8a1b25233d086ab */ + L(6.64062499999999965563110718495802889E-02), /* 3ffb0ffffffffffffc079a38a3fed000 */ + L(-1.82463217667830160048872113565316215E-32), /* bf957af6163bcdb97cefab44a942482a */ + L(7.03124999999999759989183341261898222E-02), /* 3ffb1fffffffffffe454218acea05000 */ + L(-1.07843770101525495515646940862541503E-32), /* bf94bff72aada26d94e76e71c07e0580 */ + L(7.42187499999999898968873730710101412E-02), /* 3ffb2ffffffffffff45a166496dc1000 */ + L(1.28629441689592874462780757154138223E-32), /* 3f950b2724597b8b93ce1e9d1cf4d035 */ + L(7.81249999999999957198938523510804668E-02), /* 3ffb3ffffffffffffb10bc52adbc5000 */ + L(1.13297573459968118467100063135856856E-33), /* 3f91787eea895b3c245899cf34ad0abd */ + L(8.20312500000000199911640621145851159E-02), /* 3ffb500000000000170c59a661a89000 */ + L(-1.51161335208135146756554123073528707E-32), /* bf9539f326c5ca84e7db5401566f3775 */ + L(8.59375000000000134175373433347670743E-02), /* 3ffb6000000000000f78287547af0000 */ + L(1.09763629458404270323909815379924900E-32), /* 3f94c7f0b61b6e3e27d44b9f5bbc7e9d */ + L(8.98437500000000036533922600308306335E-02), /* 3ffb70000000000004364a83b7a14000 */ + L(3.11459653680110433194288029777718358E-33), /* 3f9302c0248136d65cebeab69488d949 */ + L(9.37500000000000184977946245216914691E-02), /* 3ffb800000000000155395d870b17000 */ + L(-4.66656154468277949130395786965043927E-33), /* bf9383aec9b993b6db492b1ede786d8a */ + L(9.76562500000000237839723100419376084E-02), /* 3ffb9000000000001b6bca237f6c4000 */ + L(-1.03028043424658760249140747856831301E-32), /* bf94abf6352e3d2bb398e47919a343fb */ + L(1.01562500000000012345545575236836572E-01), /* 3ffba000000000000e3bc30cd9a1f000 */ + L(2.15755372310795701322789783729456319E-32), /* 3f95c01b3b819edd9d07548fafd61550 */ + L(1.05468749999999976493840484471911438E-01), /* 3ffbafffffffffffe4e634cd77985000 */ + L(1.78771847038773333029677216592309083E-32), /* 3f95734b6ae650f33dd43c49a1df9fc0 */ + L(1.09375000000000002267015055992785402E-01), /* 3ffbc00000000000029d1ad08de7b000 */ + L(6.23263106693943817730045115112427717E-33), /* 3f9402e4b39ce2198a45e1d045868cd6 */ + L(1.13281250000000022354208618429577398E-01), /* 3ffbd0000000000019c5cc3f9d2b5000 */ + L(5.40514416644786448581426756221178868E-33), /* 3f93c10ab4021472c662f69435de9269 */ + L(1.17187500000000013252367133076817603E-01), /* 3ffbe000000000000f47688cc561b000 */ + L(-7.12412585457324989451327215568641325E-33), /* bf9427ecb343a8d1758990565fcfbf45 */ + L(1.21093750000000020759863992944300792E-01), /* 3ffbf0000000000017ef3af97bf04000 */ + L(6.26591408357572503875647872077266444E-33), /* 3f940446a09a2da771b45fc075514d12 */ + L(1.25000000000000004739659392396765618E-01), /* 3ffc00000000000002bb7344ecd89000 */ + L(-1.55611398459729463981000080101758830E-32), /* bf95433135febefa9e6aa4db39e263d2 */ + L(1.28906249999999982360888081057894783E-01), /* 3ffc07fffffffffff5d4ed3154361000 */ + L(-1.77531518652835570781208599686606474E-32), /* bf9570b7f225ea076f97f418d11359c1 */ + L(1.32812500000000010568583998727400436E-01), /* 3ffc1000000000000617a5d09526a000 */ + L(2.12104021624990594668286391598300893E-32), /* 3f95b885d767a1048d93055927a27adc */ + L(1.36718749999999998434125157367005292E-01), /* 3ffc17ffffffffffff18eaebc7970000 */ + L(2.50454798592543203967309921276955297E-32), /* 3f9604164e5598528a76faff26cd1c97 */ + L(1.40625000000000015550032422969330356E-01), /* 3ffc20000000000008f6c79d8928c000 */ + L(7.80972982879849783680252962992639832E-33), /* 3f9444674acf2b3225c7647e0d95edf3 */ + L(1.44531250000000012402535562111122522E-01), /* 3ffc28000000000007264a8bc1ff1000 */ + L(2.79662468716455159585514763921671876E-32), /* 3f96226b095bd78aa650faf95a221993 */ + L(1.48437500000000007761020440087419948E-01), /* 3ffc3000000000000479530ff8fe3000 */ + L(2.15518492972728435680556239996258527E-32), /* 3f95bf9d49295e73a957906a029768cb */ + L(1.52343750000000001733189947520484032E-01), /* 3ffc38000000000000ffc6109f71f000 */ + L(8.34032236093545825619420380704500188E-33), /* 3f945a71851226a1d0ce5e656693153e */ + L(1.56249999999999988073295321246958484E-01), /* 3ffc3ffffffffffff91fedd62ae0f000 */ + L(2.44119337150624789345260194989620908E-32), /* 3f95fb041a57bc1c1280680ac1620bea */ + L(1.60156250000000002076894210913572460E-01), /* 3ffc48000000000001327ed84a199000 */ + L(-7.36124501128859978061216696286151753E-33), /* bf9431c62f01e59d2c1e00f195a0037f */ + L(1.64062500000000000950861276373482172E-01), /* 3ffc500000000000008c5285fba85000 */ + L(-4.80566184447001164583855800470217373E-33), /* bf938f3d1fcafd390f22f80e6c19421f */ + L(1.67968749999999989878071706155265999E-01), /* 3ffc57fffffffffffa2a445c548c5000 */ + L(-4.42154428718618459799673088733365064E-32), /* bf96cb28cf1c1b28006d53ffe633b22a */ + L(1.71874999999999999459734108403218175E-01), /* 3ffc5fffffffffffffb04554e9dd4000 */ + L(-3.29736288190321377985697972236270628E-32), /* bf96566af0ebc852e84be12859b24a31 */ + L(1.75781249999999997987525759778901845E-01), /* 3ffc67fffffffffffed702df6ffff000 */ + L(-1.28800728638468399687523924685844352E-32), /* bf950b8236b88ca0c1b739dc91a7e3fc */ + L(1.79687500000000004929565820437175783E-01), /* 3ffc70000000000002d779bb32d2e000 */ + L(1.60624461317978482424582320675174225E-32), /* 3f954d9a9cc0c963fd081f3dc922d04e */ + L(1.83593750000000016873727045739708856E-01), /* 3ffc78000000000009ba1f6263c9a000 */ + L(-3.83390389582056606880506003118452558E-32), /* bf968e22a5d826f77f19ee788474df22 */ + L(1.87500000000000013443068740761666872E-01), /* 3ffc80000000000007bfd8c72a1bf000 */ + L(-2.74141662712926256150154726565203091E-32), /* bf961caf5ac59c7f941f928e324c2cc1 */ + L(1.91406249999999981494101786848611970E-01), /* 3ffc87fffffffffff55502eeae001000 */ + L(3.68992437075565165346469517256118001E-32), /* 3f967f2f03f9096793372a27b92ad79d */ + L(1.95312499999999989069921848800501648E-01), /* 3ffc8ffffffffffff9b3015280394000 */ + L(3.69712249337856518452988332367785220E-32), /* 3f967fee5fdb5bd501ff93516999faa0 */ + L(1.99218750000000021148042946919300804E-01), /* 3ffc9800000000000c30e67939095000 */ + L(2.50142536781142175091322844848566649E-32), /* 3f9603c34ae58e10b300b07137ee618a */ + L(2.03124999999999977732559198825437141E-01), /* 3ffc9ffffffffffff329e7df079e4000 */ + L(-2.41951877287895024779300892731537816E-32), /* bf95f683aefe6965f080df8f59dd34a1 */ + L(2.07031249999999996744030653771913124E-01), /* 3ffca7fffffffffffe1f80f4b73ca000 */ + L(-1.94346475904454000031592792989765585E-32), /* bf9593a44f87870a3d100d498501ecc7 */ + L(2.10937500000000000251399259834392298E-01), /* 3ffcb000000000000025199873310000 */ + L(-1.33528748788094249098998693871759411E-33), /* bf91bbb9b25c813668d6103d08acac35 */ + L(2.14843749999999993936323609611875097E-01), /* 3ffcb7fffffffffffc8128c866236000 */ + L(1.14839877977014974625242788556545292E-32), /* 3f94dd06b4655c9b83a1305b240e7a42 */ + L(2.18750000000000015181732784749663837E-01), /* 3ffcc0000000000008c06da5fff24000 */ + L(1.42689085313142539755499441881408391E-32), /* 3f95285a87dfa7ea7dad5b3be8c669f4 */ + L(2.22656249999999992172647770539596569E-01), /* 3ffcc7fffffffffffb7ce2fe531f6000 */ + L(-3.34421462850496887359128610229650547E-32), /* bf965b487962b5c2d9056ca6ac0c2e5c */ + L(2.26562499999999989595607223847082419E-01), /* 3ffccffffffffffffa0095277be5c000 */ + L(-3.08983588107248752517344356508205569E-32), /* bf9640dded57157f8eded311213bdbcd */ + L(2.30468749999999979130462438434567117E-01), /* 3ffcd7fffffffffff3f8332996560000 */ + L(-3.01407539802851697849105682795217019E-32), /* bf9638ffde35dbdfe1a1ffe45185de5d */ + L(2.34375000000000012194252337217891971E-01), /* 3ffce0000000000007078dd402c86000 */ + L(-8.46879710915628592284714319904522657E-33), /* bf945fc7b29a2ac6c9eff9eb258a510f */ + L(2.38281249999999982991877076137149870E-01), /* 3ffce7fffffffffff6320b486eece000 */ + L(-2.93563878880439245627127095245798544E-32), /* bf9630daaa4f40ff05caf29ace2ea7d4 */ + L(2.42187499999999981447559841442773990E-01), /* 3ffceffffffffffff54e24a09a8d5000 */ + L(-4.56766746558806021264215486909850481E-32), /* bf96da556dee11f3113e5a3467b908e6 */ + L(2.46093749999999991067720539980207318E-01), /* 3ffcf7fffffffffffad9d405dcb5d000 */ + L(2.14033004219908074003010247652128251E-32), /* 3f95bc8776e8f9ae098884aa664cc3df */ + L(2.50000000000000016613825838126835953E-01), /* 3ffd00000000000004c9e24c12bb3000 */ + L(2.57617532593749185996714235009382870E-32), /* 3f960b867cc01178c0ec68226c6cb47d */ + L(2.53906250000000013372004437827044321E-01), /* 3ffd04000000000003daae05b3168000 */ + L(7.20177123439204414298152646284640101E-32), /* 3f9775eff59ddad7e7530b83934af87f */ + L(2.57812499999999995765234725413886085E-01), /* 3ffd07fffffffffffec7878bad9d5000 */ + L(6.51253187532920882777046064603770602E-32), /* 3f975226659ca241402e71c2011583b0 */ + L(2.61718750000000007647689994011222248E-01), /* 3ffd0c000000000002344cc793a0f000 */ + L(3.02370610028725823590045201871491395E-32), /* 3f9639ffe55fa2fa011674448b4e5b96 */ + L(2.65624999999999986893899042596554269E-01), /* 3ffd0ffffffffffffc38f0c0a1e9f000 */ + L(-2.07683715950724761146070082510569258E-32), /* bf95af579a92e872fef81abfdf06bae8 */ + L(2.69531249999999979842788204900639327E-01), /* 3ffd13fffffffffffa30a908d67db000 */ + L(8.71465252506557329027658736641075706E-32), /* 3f97c47d99e19830447a42b1c0ffac61 */ + L(2.73437500000000006712165837793818271E-01), /* 3ffd18000000000001ef453a58edb000 */ + L(-6.62704045767568912140550474455810301E-32), /* bf9758187a204dcb06ece46588aeeaba */ + L(2.77343749999999994411329302988535617E-01), /* 3ffd1bfffffffffffe63a0fec9c9e000 */ + L(-4.87273466291944117406493607771338767E-32), /* bf96fa0381b0844a0be46bac2d673f0c */ + L(2.81250000000000012677892447379453135E-01), /* 3ffd20000000000003a7769e125d6000 */ + L(-8.55871796664700790726282049552906783E-32), /* bf97bc64e01332cf7616b0091b8dff2c */ + L(2.85156249999999998558643013736363981E-01), /* 3ffd23ffffffffffff95a5894bccf000 */ + L(-1.33068334720606220176455289635046875E-32), /* bf95145f43290ecf5b7adcb24697bc73 */ + L(2.89062500000000008831431235621753924E-01), /* 3ffd280000000000028ba504fac59000 */ + L(-9.34157398616814623985483776710704237E-32), /* bf97e50ad1115b941fcb5f0c88a428f7 */ + L(2.92968750000000019840235286110877063E-01), /* 3ffd2c000000000005b7f372d184f000 */ + L(4.99302093775173155906059132992249671E-33), /* 3f939ecdcfb97bad3f8dbec5df5ec67d */ + L(2.96875000000000015867911730971630513E-01), /* 3ffd3000000000000492d860c79db000 */ + L(7.86107787827057767235127454590866211E-33), /* 3f944689517ee8f16cdb97d6a6938f32 */ + L(3.00781250000000015814100002286124758E-01), /* 3ffd340000000000048edfe73a17d000 */ + L(-1.65419431293024229981937172317171504E-32), /* bf9557900e3efca16c89646b57f68dc0 */ + L(3.04687499999999985213157159965287195E-01), /* 3ffd37fffffffffffbbcec6f99b36000 */ + L(9.68753602893894024018934325652944198E-32), /* 3f97f70170e5458660c33a7e8d43d049 */ + L(3.08593749999999989969324338045156215E-01), /* 3ffd3bfffffffffffd1bdde4d0fb1000 */ + L(7.10268609610294706092252562643261106E-32), /* 3f9770cae45cdf615010401a4b37d8d4 */ + L(3.12500000000000002971606591018488854E-01), /* 3ffd40000000000000db440fbc06b000 */ + L(6.38924218802905979887732294952782964E-32), /* 3f974bbf988bb5622bd8fbaa46e8b811 */ + L(3.16406250000000006594921047402056305E-01), /* 3ffd44000000000001e69e8954814000 */ + L(3.96079878754651470094149874444850097E-32), /* 3f969b5017b9fa7a1e86975258c73d3d */ + L(3.20312500000000006713799366908329147E-01), /* 3ffd48000000000001ef64159c065000 */ + L(-1.86401314975634286055150437995880517E-32), /* bf958323f0434911794e5fb8bfe136ba */ + L(3.24218749999999987061246567584951210E-01), /* 3ffd4bfffffffffffc4549db9b928000 */ + L(-3.18643523744758601387071062700407431E-32), /* bf964ae5fa7e26c2c3981bed12e14372 */ + L(3.28124999999999991782776266707412953E-01), /* 3ffd4ffffffffffffda1ad0840ca8000 */ + L(-4.46964199751314296839915534813144652E-32), /* bf96d0277729ffd74727150df6d15547 */ + L(3.32031250000000000393816557756032682E-01), /* 3ffd540000000000001d0efc04fad000 */ + L(-9.03246333902065439930373230002688649E-33), /* bf947731a008748cc6dee948839ef7ae */ + L(3.35937499999999983810482995064392173E-01), /* 3ffd57fffffffffffb556cab8ae61000 */ + L(5.27742727066129518825981597650621794E-32), /* 3f9712050a6ddbf1cabf1b971f4b5d0b */ + L(3.39843750000000004310441349760912471E-01), /* 3ffd5c0000000000013e0def5ddc4000 */ + L(-3.85927263474732591932884416445586106E-32), /* bf9690c51088ef3db9ca000829c450c2 */ + L(3.43749999999999990248130003997484364E-01), /* 3ffd5ffffffffffffd3070624a0af000 */ + L(9.62005170171527308106468341512327487E-34), /* 3f913fae595cea84432eb01430817fca */ + L(3.47656250000000004085726414568625697E-01), /* 3ffd640000000000012d79309e291000 */ + L(-6.59664093705705297250259434519072507E-32), /* bf97568465eafb0e662e64a5dbfaf35f */ + + L(-1.98364257812501251077851763965418372E-03), /* bff6040000000001cd90f658cf0b1000 */ + L(-3.71984513103117734260309047540278737E-34), /* bf8fee73c54483194782aac4a6154d11 */ + L(-1.95312500000000378520649630233891879E-03), /* bff60000000000008ba643bb5e2e8000 */ + L(-1.12194202736719050440745599339855038E-34), /* bf8e2a436aeff7bc529873354f47a3f5 */ + L(-1.92260742187499397430259771221991482E-03), /* bff5f7fffffffffe4361cb51170da000 */ + L(-2.30068299876822157331268484824540848E-34), /* bf8f31d02f85cfe8c0cc02276ce0f437 */ + L(-1.89208984375001137424603270262074989E-03), /* bff5f0000000000347456ed490c23000 */ + L(-1.15012507244426243338260435466985403E-34), /* bf8e31c174d5677a937a34ad8d2a70b4 */ + L(-1.86157226562500172319250342061336738E-03), /* bff5e800000000007f262fa3617b4000 */ + L(-3.12438344643346437509767736937785561E-34), /* bf8f9f4d426a2457c273d34ef7d9bde9 */ + L(-1.83105468749999505256246872355430379E-03), /* bff5dffffffffffe92f18c1c2b6fa000 */ + L(-5.91130415288336591179087455220308942E-35), /* bf8d3a4c80b42dc036bae446c9807f78 */ + L(-1.80053710937499445182387245573120522E-03), /* bff5d7fffffffffe669dea82b4a4c000 */ + L(-1.92396289352411531324908916321392100E-34), /* bf8eff7a2123fb573ba9778550d669bd */ + L(-1.77001953125000387737631542516323906E-03), /* bff5d000000000011e19915c3ddb7000 */ + L(7.91101758977203355387806553469731354E-36), /* 3f8a507f5a70faaccf469e3461873dea */ + L(-1.73950195312500034854670281415554486E-03), /* bff5c8000000000019b7dc6ef97bd000 */ + L(1.55906551582436824067407021178835755E-34), /* 3f8e9e7880333e34955aebcde3cfb053 */ + L(-1.70898437499998955782591472611429852E-03), /* bff5bffffffffffcfd80e88aa6b96000 */ + L(8.22951661962611381718215899498500357E-35), /* 3f8db58e6031a779b59f6ece191de7cc */ + L(-1.67846679687500586652037711131708544E-03), /* bff5b80000000001b0df6fd21c133000 */ + L(-8.96642618848426299713145894522897419E-35), /* bf8ddcbcab46d531801bfae4121f2f8a */ + L(-1.64794921875000109499161354039904782E-03), /* bff5b0000000000050cbce8915575000 */ + L(-2.88077905394253859590587789680486639E-34), /* bf8f7eebd4dd860ef73b674d5e707959 */ + L(-1.61743164062501133830507079150388351E-03), /* bff5a80000000003449e8700c3e82000 */ + L(-3.68271725851639066312899986829350273E-34), /* bf8fe9845fe20a5fe74059e0cae185d6 */ + L(-1.58691406249999015546015764131101956E-03), /* bff59ffffffffffd2999e668cdd28000 */ + L(8.48197657099957029953716507898788812E-35), /* 3f8dc2faaebb97392e451b07b28c4b12 */ + L(-1.55639648437500317366570219290722587E-03), /* bff5980000000000ea2cd9a40d256000 */ + L(-3.45156704719737676412949957712570373E-36), /* bf8925a079505516c8e317ac1ff53255 */ + L(-1.52587890625000568759013197767046039E-03), /* bff5900000000001a3ab8a3f6b698000 */ + L(-1.01902948542497496574967177677556729E-34), /* bf8e0ee78d94d9b5ad3d63ae35c9b554 */ + L(-1.49536132812500945889014955936485340E-03), /* bff5880000000002b9f1621b57743000 */ + L(-3.32264697086631598830366079048117140E-34), /* bf8fb9a7d14c32289204fbb0c9eb20e0 */ + L(-1.46484374999999931883259902869504725E-03), /* bff57fffffffffffcdbd1c90e1b4a000 */ + L(-1.76487524793892929381101031660811433E-34), /* bf8ed52f2f724bc1ae870b18356337b4 */ + L(-1.43432617187498876325946983333888768E-03), /* bff577fffffffffcc2dff8faa5570000 */ + L(-3.54550084538495708816233114576143814E-34), /* bf8fd74724576915868c1e8ce9f430f1 */ + L(-1.40380859374999215367421282192718062E-03), /* bff56ffffffffffdbd0b18aac65ed000 */ + L(-1.90585907028351204486765167064669639E-34), /* bf8efaaa0c0e23e50c11b2120348054f */ + L(-1.37329101562499692341771212945644892E-03), /* bff567ffffffffff1cfd00f1b0577000 */ + L(-3.59631150411372589637918252836880320E-34), /* bf8fde08239ac74942a46298ea4fb715 */ + L(-1.34277343749999137467356674296739172E-03), /* bff55ffffffffffd839030b05d53d000 */ + L(-1.49571076125940368185068762485268117E-35), /* bf8b3e1a3d5c684b27a9f835b1d8d3c9 */ + L(-1.31225585937499247038404301859788734E-03), /* bff557fffffffffdd469936e691e3000 */ + L(3.10375845385355395586146533282311300E-34), /* 3f8f9c8f6d63b7a4145716ffd92491fb */ + L(-1.28173828124999024755581675764821898E-03), /* bff54ffffffffffd306589b0ab21d000 */ + L(-1.98541096105909793397376077900810019E-34), /* bf8f07e808bbb1e35106c294ffbb9687 */ + L(-1.25122070312500340204619591143332523E-03), /* bff5480000000000fb06d5f16ad2c000 */ + L(3.62884195935761446237911443317457521E-34), /* 3f8fe25b17d623178a386a6fa6c5afb2 */ + L(-1.22070312499999591578388993012071279E-03), /* bff53ffffffffffed2a356c440074000 */ + L(-2.96756662615653130862526710937493307E-35), /* bf8c3b90d8ff2a991e5bd16718fb0645 */ + L(-1.19018554687498821966212632349422735E-03), /* bff537fffffffffc9ac3b585dda89000 */ + L(1.44659971891167323357060028901142644E-34), /* 3f8e809279ab249edf1dad9fe13fb0bf */ + L(-1.15966796875000160938908064907298384E-03), /* bff530000000000076c0800db9639000 */ + L(2.50088010538742402346270685365928513E-34), /* 3f8f4c6c8a483b60201d30c1a83c3cb7 */ + L(-1.12915039062500267151512523291939657E-03), /* bff5280000000000c51f7e7315137000 */ + L(7.56402096465615210500092443924888831E-35), /* 3f8d922c1e485d99aea2668ed32b55a6 */ + L(-1.09863281249998665006360103291051571E-03), /* bff51ffffffffffc26f2d4c9ce2ba000 */ + L(1.43982174467233642713619821353592061E-34), /* 3f8e7ec530b3d92b6303bec1c81214d1 */ + L(-1.06811523437500522742248711752028025E-03), /* bff518000000000181b7380f10446000 */ + L(5.41265133745862349181293024531133174E-35), /* 3f8d1fc9313d018b30e790e06b6be723 */ + L(-1.03759765624999980942114138999770552E-03), /* bff50ffffffffffff1f01130490e1000 */ + L(1.21525139612685854366189534669623436E-34), /* 3f8e4311b96b6fcde412caf3f0d86fb9 */ + L(-1.00708007812499602697537601515759439E-03), /* bff507fffffffffedad7afcce7051000 */ + L(1.00020246351201558505328236381833392E-34), /* 3f8e09e640992512b1300744a7e984ed */ + L(-9.76562499999992592487302113340463694E-04), /* bff4fffffffffffbbad8151f8adf6000 */ + L(-1.64984406575162932060422892046851002E-34), /* bf8eb69a919986e8054b86fc34300f24 */ + L(-9.46044921874989085824996924138179594E-04), /* bff4effffffffff9b55a204fd9792000 */ + L(-9.29539174108308550334255350011347171E-35), /* bf8dee3a50ed896b4656fa577a1df3d7 */ + L(-9.15527343750013735214860599791540029E-04), /* bff4e00000000007eaf5bf103f82d000 */ + L(3.07557018309280519949818825519490586E-35), /* 3f8c470cfbef77d32c74cb8042f6ee81 */ + L(-8.85009765625012292294986105781516428E-04), /* bff4d000000000071605c65403b97000 */ + L(4.77499983783821950338363358545463558E-35), /* 3f8cfbc3dc18884c4c4f9e07d90d7bd3 */ + L(-8.54492187499986941239470706817188192E-04), /* bff4bffffffffff878ddf9cab264a000 */ + L(-1.60128240346239526958630011447901568E-34), /* bf8ea9b1a21e19e2d5bd84b0fbffcf95 */ + L(-8.23974609374996290174598690241743810E-04), /* bff4affffffffffddc86c249ebe06000 */ + L(1.61677540391961912631535763471935882E-34), /* 3f8eadd00841366b0dc2bc262c2c8c36 */ + L(-7.93457031249988696952538334288757473E-04), /* bff49ffffffffff97bf6f0aa85a5f000 */ + L(1.22318577008381887076634753347515709E-34), /* 3f8e452db5b5d250878f71040da06d14 */ + L(-7.62939453124996723316499040007097041E-04), /* bff48ffffffffffe1c7265b431108000 */ + L(-1.03845161748762410745671891558398468E-34), /* bf8e14115ad884c96d1a820c73647220 */ + L(-7.32421874999998242520117923997325794E-04), /* bff47ffffffffffefca4498b7aa8a000 */ + L(5.64005211953031009549514026639438083E-35), /* 3f8d2be06950f68f1a6d8ff829a6928e */ + L(-7.01904296874999772890934814265622012E-04), /* bff46fffffffffffde7c0fe5d8041000 */ + L(5.90245467325173644235991233229525762E-35), /* 3f8d39d40cc49002189243c194b1db0e */ + L(-6.71386718750008699269643939210658742E-04), /* bff460000000000503c91d798b60c000 */ + L(-5.20515801723324452151498579012322191E-35), /* bf8d14c0f08a6a9285b32b8bda003eb5 */ + L(-6.40869140625005499535275057463709988E-04), /* bff45000000000032b969184e9751000 */ + L(-6.69469163285461870099846471658294534E-35), /* bf8d63f36bab7b24d936c9380e3d3fa6 */ + L(-6.10351562499999293780097329596079841E-04), /* bff43fffffffffff97c7c433e35ed000 */ + L(-1.16941808547394177991845382085515086E-34), /* bf8e36e27886f10b234a7dd8fc588bf0 */ + L(-5.79833984375000068291972326409994795E-04), /* bff43000000000000a13ff6dcf2bf000 */ + L(1.17885044988246219185041488459766001E-34), /* 3f8e3964677e001a00412aab52790842 */ + L(-5.49316406249990904622170867910987793E-04), /* bff41ffffffffffac1c25739c716b000 */ + L(-3.31875702128137033065075734368960972E-35), /* bf8c60e928d8982c3c99aef4f885a121 */ + L(-5.18798828125011293653756992177727236E-04), /* bff410000000000682a62cff36775000 */ + L(-5.69971237642088463334239430962628187E-35), /* bf8d2f0c76f8757d61cd1abc7ea7d066 */ + L(-4.88281249999990512232251384917893121E-04), /* bff3fffffffffff50fb48992320df000 */ + L(1.02144616714408655325510171265051108E-35), /* 3f8ab279a3626612710b9b3ac71734ac */ + L(-4.57763671874997554564967307956493434E-04), /* bff3dffffffffffd2e3c272e3cca9000 */ + L(-8.25484058867957231164162481843653503E-35), /* bf8db6e71158e7bf93e2e683f07aa841 */ + L(-4.27246093749991203999790346349633286E-04), /* bff3bffffffffff5dbe103cba0eb2000 */ + L(-3.51191203319375193921924105905691755E-35), /* bf8c757356d0f3dd7fbefc0dd419ab50 */ + L(-3.96728515624986649402960638705483281E-04), /* bff39ffffffffff09b996882706ec000 */ + L(-5.51925962073095883016589497244931171E-36), /* bf89d586d49f22289cfc860bebb99056 */ + L(-3.66210937499999945095511981300980754E-04), /* bff37fffffffffffefcb88bfc7df6000 */ + L(-2.11696465278144529364423332249588595E-35), /* bf8bc23a84d28e5496c874ef9833be25 */ + L(-3.35693359374992480958458008559640163E-04), /* bff35ffffffffff754c548a8798f2000 */ + L(-8.58941791799705081104736787493668352E-35), /* bf8dc8b1192fb7c3662826d43acb7c68 */ + L(-3.05175781250009811036303273640122156E-04), /* bff340000000000b4fb4f1aad1c76000 */ + L(-8.61173897858769926480551302277426632E-35), /* bf8dc9e0eabb1c0b33051011b64769fa */ + L(-2.74658203124987298321920308390303850E-04), /* bff31ffffffffff15b2056ac252fd000 */ + L(3.35152809454778381053519808988046631E-37), /* 3f85c82fb59ff8d7c80d44e635420ab1 */ + L(-2.44140624999999992770514819575735516E-04), /* bff2fffffffffffffbbb82d6a7636000 */ + L(3.54445837111124472730013879165516908E-35), /* 3f8c78e955b01378be647b1c92aa9a77 */ + L(-2.13623046875012756463165168672749438E-04), /* bff2c0000000001d6a1635fea6bbf000 */ + L(1.50050816288650121729916777279129473E-35), /* 3f8b3f1f6f616a61129a58e131cbd31d */ + L(-1.83105468749991323078784464300306893E-04), /* bff27fffffffffebfe0cbd0c82399000 */ + L(-9.14919506501448661140572099029756008E-37), /* bf873754bacaa9d9513b6127e791eb47 */ + L(-1.52587890625013337032336300236461546E-04), /* bff240000000001ec0cb57f2cc995000 */ + L(2.84906084373176180870418394956384516E-35), /* 3f8c2ef6d03a7e6ab087c4f099e4de89 */ + L(-1.22070312499990746786116828458007518E-04), /* bff1ffffffffffd553bbb49f35a34000 */ + L(6.71618008964968339584520728412444537E-36), /* 3f8a1dacb99c60071fc9cd2349495bf0 */ + L(-9.15527343750029275602791047595142231E-05), /* bff180000000000d8040cd6ecde28000 */ + L(-1.95753652091078750312541716951402172E-35), /* bf8ba0526cfb24d8d59122f1c7a09a14 */ + L(-6.10351562499913258461494008080572701E-05), /* bff0ffffffffffaffebbb92d7f6a9000 */ + L(5.69868489273961111703398456218119973E-36), /* 3f89e4ca5df09ef4a4386dd5b3bf0331 */ + L(-3.05175781250092882818419203884960853E-05), /* bff0000000000055ab55de88fac1d000 */ + L(9.03341100018476837609128961872915953E-36), /* 3f8a803d229fa3a0e834a63abb06662b */ +#define T_EXPL_ARG2 (2*T_EXPL_ARG1 + 2 + 2*65) + L(0.00000000000000000000000000000000000E+00), /* 00000000000000000000000000000000 */ + L(0.00000000000000000000000000000000000E+00), /* 00000000000000000000000000000000 */ + L(3.05175781249814607084128277672749162E-05), /* 3feffffffffffeaa02abb9102f499000 */ + L(1.00271855391179733380665816525889949E-36), /* 3f8755351afa042ac3f58114824d4c10 */ + L(6.10351562500179243748093427073421439E-05), /* 3ff1000000000052a95de07a4c26d000 */ + L(1.67231624299180373502350811501181670E-36), /* 3f881c87a53691cae9d77f4e40d66616 */ + L(9.15527343749970728685313252158399200E-05), /* 3ff17ffffffffff28040cc2acde28000 */ + L(2.43665747834893104318707597514407880E-36), /* 3f889e9366c7c6c6a2ecb78dc9b0509e */ + L(1.22070312500027751961838150070880064E-04), /* 3ff200000000003ffddde6c153b53000 */ + L(-1.73322146370624186623546452226755405E-35), /* bf8b709d8d658ed5dbbe943de56ee84e */ + L(1.52587890624995916105682628143179430E-04), /* 3ff23ffffffffff6954b56e285d23000 */ + L(1.23580432650945898349135528000443828E-35), /* 3f8b06d396601dde16de7d7bc27346e6 */ + L(1.83105468750008670314358488289621794E-04), /* 3ff2800000000013fe0cdc8c823b7000 */ + L(4.30446229148833293310207915930740796E-35), /* 3f8cc9ba9bfe554a4f7f2fece291eb23 */ + L(2.13623046875005741337455947623248132E-04), /* 3ff2c0000000000d3d1662de21a3f000 */ + L(-3.96110759869520786681660669615255057E-35), /* bf8ca5379b04ff4a31aab0ceacc917e6 */ + L(2.44140624999981493573336463433440506E-04), /* 3ff2ffffffffffd553bbdf48e0534000 */ + L(-1.39617373942387888957350179316792928E-35), /* bf8b28eeedc286015802b63f96b8c5cd */ + L(2.74658203124984920706309918754626834E-04), /* 3ff31fffffffffee9d60c8439ec1d000 */ + L(-3.16168080483901830349738314447356223E-36), /* bf890cf74f81c77a611abc1243812444 */ + L(3.05175781250008648918265055410966055E-04), /* 3ff3400000000009f8b5c9a346636000 */ + L(8.54421306185008998867856704677221443E-35), /* 3f8dc649cd40922fc08adc6b6b20ead0 */ + L(3.35693359374988945462612499316774515E-04), /* 3ff35ffffffffff34146c540f15b2000 */ + L(7.96443137431639500475160850431097078E-35), /* 3f8da77638ed3148fc4d99d1c9e13446 */ + L(3.66210937500027690542093987739604535E-04), /* 3ff380000000001fecce34bea89c4000 */ + L(2.14507323877752361258862577769090367E-35), /* 3f8bc834e554d38894cf91957b0253d3 */ + L(3.96728515625003928083564943615052121E-04), /* 3ff3a00000000004875d9a4acf6ab000 */ + L(4.88358523466632050664019922448605508E-35), /* 3f8d03a7eaeef1a9f78c71a12c44dd28 */ + L(4.27246093750017799227172345607351585E-04), /* 3ff3c00000000014856794c3ee850000 */ + L(6.66520494592631402182216588784828935E-35), /* 3f8d6262118fcdb59b8f16108f5f1a6c */ + L(4.57763671875002108342364320152138181E-04), /* 3ff3e000000000026e45d855410b9000 */ + L(7.21799615960261390920033272189522298E-35), /* 3f8d7fc645cff8879462296af975c9fd */ + L(4.88281249999999768797631616370963356E-04), /* 3ff3ffffffffffffbbc2d7cc004df000 */ + L(-5.30564629906905979452258114088325361E-35), /* bf8d1a18b71929a30d67a217a27ae851 */ + L(5.18798828124997339054881383202487041E-04), /* 3ff40ffffffffffe775055eea5851000 */ + L(-4.03682911253647925867848180522846377E-35), /* bf8cad44f0f3e5199d8a589d9332acad */ + L(5.49316406249980511907933706754958501E-04), /* 3ff41ffffffffff4c410b29bb62fb000 */ + L(-2.08166843948323917121806956728438051E-35), /* bf8bbab8cf691403249fe5b699e25143 */ + L(5.79833984374989593561576568548497165E-04), /* 3ff42ffffffffffa0047df328d817000 */ + L(-1.72745033420153042445343706432627539E-34), /* bf8ecb3c2d7d3a9e6e960576be901fdf */ + L(6.10351562500008540711511259540838154E-04), /* 3ff4400000000004ec62f54f8c271000 */ + L(7.41889382604319545724663095428976499E-35), /* 3f8d8a74c002c81a47c93b8e05d15f8e */ + L(6.40869140625020444702875407535884986E-04), /* 3ff450000000000bc91b09718515d000 */ + L(-4.47321009727305792048065440180490107E-35), /* bf8cdbac5c8fe70822081d8993eb5cb6 */ + L(6.71386718750007531635964622352684074E-04), /* 3ff460000000000457792973db05c000 */ + L(5.13698959677949336513874456684462092E-35), /* 3f8d112114436949c5ef38d8049004ab */ + L(7.01904296875006634673332887754430334E-04), /* 3ff4700000000003d31adf2cb8b1d000 */ + L(-8.25665755717729437292989870760751482E-35), /* bf8db6ffcc8ef71f8e648e3a8b160f5a */ + L(7.32421874999998244664170215504673504E-04), /* 3ff47ffffffffffefcf5498bd5c8a000 */ + L(-5.64005234937832153139057628112753364E-35), /* bf8d2be06a1dfe90e7bf90fba7c12a98 */ + L(7.62939453125017456345986752604096408E-04), /* 3ff490000000000a101a1b093d4a8000 */ + L(-1.11084094120417622468550608896588329E-34), /* bf8e274feabd2d94f6694507a46accb1 */ + L(7.93457031249987558617598988993908016E-04), /* 3ff49ffffffffff8d3f9dcab74bbf000 */ + L(-1.22966480225449015129079129940978828E-34), /* bf8e46e6a65eef8fa9e42eddf3da305e */ + L(8.23974609374997378723747633335135819E-04), /* 3ff4affffffffffe7d2afbaa55b26000 */ + L(-1.62270010016794279091906973366704963E-34), /* bf8eaf633f057ebdb664a34566401c4e */ + L(8.54492187500023938282350821569920958E-04), /* 3ff4c0000000000dccaabce399e59000 */ + L(-1.39076361712838158775374263169606160E-34), /* bf8e71ba779364b3bbdba7841f2c4ca1 */ + L(8.85009765624987932362186815286691297E-04), /* 3ff4cffffffffff90b218886edc2a000 */ + L(4.07328275060905585228261577392403980E-35), /* 3f8cb1254dbb6ea4b8cfa5ed4cf28d24 */ + L(9.15527343749975579461305518559161974E-04), /* 3ff4dffffffffff1ec2a21f25df33000 */ + L(1.16855112459192484947855553716334015E-35), /* 3f8af10bf319e9f5270cf249eeffbe5c */ + L(9.46044921875016761584725882821122521E-04), /* 3ff4f00000000009a992c46c16d71000 */ + L(9.51660680007524262741115611071680436E-35), /* 3f8df9fd56e81f8edf133843910ee831 */ + L(9.76562499999974118878133088548272636E-04), /* 3ff4fffffffffff1149edc46a6df6000 */ + L(-5.65271128977550656964071208289181661E-36), /* bf89e0e12689dd721aa2314c81eb6429 */ + L(1.00708007812498671732140389760347830E-03), /* 3ff507fffffffffc2be94b90ed091000 */ + L(-1.43355074891483635310132767255371379E-34), /* bf8e7d1a688c247b16022daab1316d55 */ + L(1.03759765625002637786192745235343007E-03), /* 3ff51000000000079a57b966bc158000 */ + L(2.95905815240957629366749917020106928E-34), /* 3f8f895387fc73bb38f8a1b254c01a60 */ + L(1.06811523437500860568717813047520763E-03), /* 3ff51800000000027afcd5b35f5e6000 */ + L(-5.98328495358586628195372356742878314E-35), /* bf8d3e204130013bf6328f1b70ff8c76 */ + L(1.09863281250001439958487251556220070E-03), /* 3ff5200000000004268077c6c66bd000 */ + L(2.41371837889426603334113000868144760E-34), /* 3f8f40d6948edf864054ccf151f9815e */ + L(1.12915039062501298413451613770002366E-03), /* 3ff5280000000003be0f5dd8fe81b000 */ + L(-1.28815268997394164973472617519705703E-34), /* bf8e567321172ea089dce4bc8354ecb7 */ + L(1.15966796874997272036339054191407232E-03), /* 3ff52ffffffffff8231e3bcfff1e8000 */ + L(1.02996064554316248496839462594377804E-34), /* 3f8e11cf7d402789244f68e2d4f985b1 */ + L(1.19018554687502744121802585360546796E-03), /* 3ff5380000000007e8cdf3f8f6c20000 */ + L(-1.43453217726255628994625761307322163E-34), /* bf8e7d5d3370d85a374f5f4802fc517a */ + L(1.22070312499997743541996266398850614E-03), /* 3ff53ffffffffff97f0722561f454000 */ + L(-1.41086259180534339713692694428211646E-34), /* bf8e77125519ff76244dfec5fbd58402 */ + L(1.25122070312501024092560690174507039E-03), /* 3ff5480000000002f3a59d8820691000 */ + L(3.84102646020099293168698506729765213E-34), /* 3f8ffe8f5b86f9c3569c8f26e19b1f50 */ + L(1.28173828124997986521442660131425390E-03), /* 3ff54ffffffffffa3250a764439d9000 */ + L(1.44644589735033114377952806106652650E-34), /* 3f8e808801b80dcf38323cdbfdca2549 */ + L(1.31225585937501665804856968749058137E-03), /* 3ff5580000000004cd25a414c6d62000 */ + L(1.67474574742200577294563576414361377E-34), /* 3f8ebd394a151dbda4f81d5d83c0f1e9 */ + L(1.34277343749997290265837386401818888E-03), /* 3ff55ffffffffff83091b042cfd59000 */ + L(-1.55650565030381326742591837551559103E-34), /* bf8e9dca490d7fecfadba9625ffb91c5 */ + L(1.37329101562497720784949380297774268E-03), /* 3ff567fffffffff96e3c7312f5ccf000 */ + L(1.65279335325630026116581677369221748E-34), /* 3f8eb763496f5bd7404f2298b402074f */ + L(1.40380859374999099958354100336136647E-03), /* 3ff56ffffffffffd67e2f09f2a381000 */ + L(1.89919944388961890195706641264717076E-34), /* 3f8ef8e4d0ffdfeba982aa8829501389 */ + L(1.43432617187497484122173130998160625E-03), /* 3ff577fffffffff8bf9c1d71af8a8000 */ + L(2.57638517142061429772064578590009568E-34), /* 3f8f5675d82c1cc4ada70fd3a957b89a */ + L(1.46484374999999929342158925502052945E-03), /* 3ff57fffffffffffcbdd1c7671b46000 */ + L(1.76487201934184070490166772482073801E-34), /* 3f8ed52ef732458f6e4c5c07504f33cc */ + L(1.49536132812502318451070466256902933E-03), /* 3ff5880000000006aeb7066c8ad43000 */ + L(2.38068367275295804321313550609246656E-34), /* 3f8f3c7277ae6fc390ace5e06c0b025b */ + L(1.52587890625000448053340248672949543E-03), /* 3ff59000000000014a9ae2104b3bc000 */ + L(1.01174455568392813258454590274740959E-34), /* 3f8e0cf7c434762991bb38e12acee215 */ + L(1.55639648437501113499837053523090913E-03), /* 3ff5980000000003359e2c204355e000 */ + L(-2.82398418808099749023517211651363693E-35), /* bf8c2c4c2971d88caa95e15fb1ccb1a1 */ + L(1.58691406249999937955142588308171026E-03), /* 3ff59fffffffffffd2380ecbc87c2000 */ + L(-1.27361695572422741562701199136538047E-34), /* bf8e5295e0e206dfb0f0266c07225448 */ + L(1.61743164062498000531048954475329309E-03), /* 3ff5a7fffffffffa3ca6fe61ed94c000 */ + L(-1.22606548862580061633942923016222044E-34), /* bf8e45f1b17bb61039d21a351bb207b8 */ + L(1.64794921875001835451453858682255576E-03), /* 3ff5b000000000054a52fa20f6565000 */ + L(1.39132339594152335892305491425264583E-34), /* 3f8e71e0904c5449b414ee49b191cef2 */ + L(1.67846679687501263995029340691547953E-03), /* 3ff5b80000000003a4a9e912c910b000 */ + L(6.67245854693585315412242764786197029E-35), /* 3f8d62c4ccac1e7511a617d469468ccd */ + L(1.70898437500002646861403514115369655E-03), /* 3ff5c00000000007a109fbaa7e015000 */ + L(6.87367172354719289559624829652240928E-36), /* 3f8a245fa835eceb42bae8128d9336db */ + L(1.73950195312501174308226096992992128E-03), /* 3ff5c80000000003627c8d637a005000 */ + L(-2.20824271875474985927385878948759352E-34), /* bf8f25869b1cbefb25e735992f232f57 */ + L(1.77001953124997491747605207736194513E-03), /* 3ff5cffffffffff8c53c84b6883b8000 */ + L(3.43123048533596296514343180408963705E-34), /* 3f8fc816b91d173ddadbbf09b1287906 */ + L(1.80053710937497698911127570705069398E-03), /* 3ff5d7fffffffff95e1899f4a8430000 */ + L(3.99231237340890073475077494556136100E-35), /* 3f8ca889148f62fa854da5674df41279 */ + L(1.83105468750002267094899598630423914E-03), /* 3ff5e0000000000688d21e62ba674000 */ + L(-3.22274595655810623999007524769365273E-34), /* bf8fac605cb9ae01eb719675ced25560 */ + L(1.86157226562500499224728040579690330E-03), /* 3ff5e80000000001705ce28a6d89e000 */ + L(3.07094985075881613489605622068441083E-34), /* 3f8f98330225ec7e2c8f3c0d1c432b91 */ + L(1.89208984374998234666824993196980949E-03), /* 3ff5effffffffffae969fdc7cd8cf000 */ + L(-3.06287628722973914692165056776495733E-34), /* bf8f9720477d9cfa10e464df7f91020c */ + L(1.92260742187501225343755557292811682E-03), /* 3ff5f800000000038824e428ed49a000 */ + L(6.30049124729794620592961282769623368E-35), /* 3f8d4efdd7cd4336d88a6aa49e1e96bc */ + L(1.95312499999998514894032051116231258E-03), /* 3ff5fffffffffffbb82f6a04f1ae0000 */ + L(-6.14610057507500948543216998736262902E-35), /* bf8d46c862d39255370e7974d48daa7e */ + L(1.98364257812501222021119324146882732E-03), /* 3ff6040000000001c2d8a1aa5188d000 */ + L(3.71942298418113774118754986159801984E-34), /* 3f8fee6567d9940495519ffe62cbc9a4 */ + + L(7.06341639425619532977052017486130353E-01), /* 3ffe69a59c8245a9ac00000000000000 */ + L(7.09106182437398424589503065362805501E-01), /* 3ffe6b0ff72deb89d000000000000000 */ + L(7.11881545564596485142772053222870454E-01), /* 3ffe6c7bbce9a6d93000000000000000 */ + L(7.14667771155948150507697391731198877E-01), /* 3ffe6de8ef213d71e000000000000000 */ + L(7.17464901725936049503573599395167548E-01), /* 3ffe6f578f41e1a9e400000000000000 */ + L(7.20272979955439790478166628417966422E-01), /* 3ffe70c79eba33c06c00000000000000 */ + L(7.23092048692387218133958981525211129E-01), /* 3ffe72391efa434c7400000000000000 */ + L(7.25922150952408251622927082280511968E-01), /* 3ffe73ac117390acd800000000000000 */ + L(7.28763329919491220643124052003258839E-01), /* 3ffe752077990e79d000000000000000 */ + L(7.31615628946641782803794740175362676E-01), /* 3ffe769652df22f7e000000000000000 */ + L(7.34479091556544505525749855223693885E-01), /* 3ffe780da4bba98c4800000000000000 */ + L(7.37353761442226890432394270646909717E-01), /* 3ffe79866ea5f432d400000000000000 */ + L(7.40239682467726090031590047146892175E-01), /* 3ffe7b00b216ccf53000000000000000 */ + L(7.43136898668758316688354170764796436E-01), /* 3ffe7c7c70887763c000000000000000 */ + L(7.46045454253390638577059235103661194E-01), /* 3ffe7df9ab76b20fd000000000000000 */ + L(7.48965393602715662213498148958024103E-01), /* 3ffe7f78645eb8076400000000000000 */ + L(7.51896761271528629722027403659012634E-01), /* 3ffe80f89cbf42526400000000000000 */ + L(7.54839601989007347171423134568613023E-01), /* 3ffe827a561889716000000000000000 */ + L(7.57793960659394638668118204805068672E-01), /* 3ffe83fd91ec46ddc000000000000000 */ + L(7.60759882362683631518152083117456641E-01), /* 3ffe858251bdb68b8c00000000000000 */ + L(7.63737412355305483879774897104653064E-01), /* 3ffe87089711986c9400000000000000 */ + L(7.66726596070820082262642358728044201E-01), /* 3ffe8890636e31f54400000000000000 */ + L(7.69727479120609181517664865168626420E-01), /* 3ffe8a19b85b4fa2d800000000000000 */ + L(7.72740107294572486917871856348938309E-01), /* 3ffe8ba4976246833800000000000000 */ + L(7.75764526561826289752232810315035749E-01), /* 3ffe8d31020df5be4400000000000000 */ + L(7.78800783071404878477039801509818062E-01), /* 3ffe8ebef9eac820b000000000000000 */ + L(7.81848923152964780936002853195532225E-01), /* 3ffe904e8086b5a87800000000000000 */ + L(7.84908993317491698871180005880887620E-01), /* 3ffe91df97714512d800000000000000 */ + L(7.87981040258010162480317717381694820E-01), /* 3ffe9372403b8d6bcc00000000000000 */ + L(7.91065110850296016042904057030682452E-01), /* 3ffe95067c78379f2800000000000000 */ + L(7.94161252153591734614934694036492147E-01), /* 3ffe969c4dbb800b4800000000000000 */ + L(7.97269511411324433014513601847284008E-01), /* 3ffe9833b59b38154400000000000000 */ + L(8.00389936051826789142893403550260700E-01), /* 3ffe99ccb5aec7bec800000000000000 */ + L(8.03522573689060742863077280162542593E-01), /* 3ffe9b674f8f2f3d7c00000000000000 */ + L(8.06667472123343942680406826184480451E-01), /* 3ffe9d0384d70893f800000000000000 */ + L(8.09824679342079301047618855591281317E-01), /* 3ffe9ea15722892c7800000000000000 */ + L(8.12994243520486992160556383169023320E-01), /* 3ffea040c80f8374f000000000000000 */ + L(8.16176213022339780422953481320291758E-01), /* 3ffea1e1d93d687d0000000000000000 */ + L(8.19370636400700819157449927843117621E-01), /* 3ffea3848c4d49954c00000000000000 */ + L(8.22577562398664585696650419777142815E-01), /* 3ffea528e2e1d9f09800000000000000 */ + L(8.25797039950100647542896581398963463E-01), /* 3ffea6cede9f70467c00000000000000 */ + L(8.29029118180400342863478613253391813E-01), /* 3ffea876812c0877bc00000000000000 */ + L(8.32273846407226292054559735333896242E-01), /* 3ffeaa1fcc2f45343800000000000000 */ + L(8.35531274141265073440720811959181447E-01), /* 3ffeabcac15271a2a400000000000000 */ + L(8.38801451086982535754188461396552157E-01), /* 3ffead7762408309bc00000000000000 */ + L(8.42084427143382358016410194068157580E-01), /* 3ffeaf25b0a61a7b4c00000000000000 */ + L(8.45380252404767357221615498019673396E-01), /* 3ffeb0d5ae318680c400000000000000 */ + L(8.48688977161503960155997106085123960E-01), /* 3ffeb2875c92c4c99400000000000000 */ + L(8.52010651900789478530029441571969073E-01), /* 3ffeb43abd7b83db1c00000000000000 */ + L(8.55345327307422548246407245642330963E-01), /* 3ffeb5efd29f24c26400000000000000 */ + L(8.58693054264576483003423845730139874E-01), /* 3ffeb7a69db2bcc77800000000000000 */ + L(8.62053883854575708767242758767679334E-01), /* 3ffeb95f206d17228000000000000000 */ + L(8.65427867359675251357487013592617586E-01), /* 3ffebb195c86b6b29000000000000000 */ + L(8.68815056262843166123843730019871145E-01), /* 3ffebcd553b9d7b62000000000000000 */ + L(8.72215502248546159513864495238522068E-01), /* 3ffebe9307c271855000000000000000 */ + L(8.75629257203538208242932228131394368E-01), /* 3ffec0527a5e384ddc00000000000000 */ + L(8.79056373217652342599848225290770642E-01), /* 3ffec213ad4c9ed0d800000000000000 */ + L(8.82496902584595399599010079327854328E-01), /* 3ffec3d6a24ed8221800000000000000 */ + L(8.85950897802745995779361010136199184E-01), /* 3ffec59b5b27d9696800000000000000 */ + L(8.89418411575955636383383762222365476E-01), /* 3ffec761d99c5ba58800000000000000 */ + L(8.92899496814352794382685374330321793E-01), /* 3ffec92a1f72dd70d400000000000000 */ + L(8.96394206635150403439382671422208659E-01), /* 3ffecaf42e73a4c7d800000000000000 */ + L(8.99902594363456265202927397695020773E-01), /* 3ffeccc00868c0d18800000000000000 */ + L(9.03424713533086704009278378180169966E-01), /* 3ffece8daf1e0ba94c00000000000000 */ + L(9.06960617887383580004723171441582963E-01), /* 3ffed05d24612c2af000000000000000 */ + L(9.10510361380034133338412516422977205E-01), /* 3ffed22e6a0197c02c00000000000000 */ + L(9.14073998175894436579724811053893063E-01), /* 3ffed40181d094303400000000000000 */ + L(9.17651582651815816982221463149471674E-01), /* 3ffed5d66da13970f400000000000000 */ + L(9.21243169397474526149949269893113524E-01), /* 3ffed7ad2f48737a2000000000000000 */ + L(9.24848813216204823639543519675498828E-01), /* 3ffed985c89d041a3000000000000000 */ + L(9.28468569125835141431224428743007593E-01), /* 3ffedb603b7784cd1800000000000000 */ + L(9.32102492359527579068867453315760940E-01), /* 3ffedd3c89b26894e000000000000000 */ + L(9.35750638366620729469147477175283711E-01), /* 3ffedf1ab529fdd41c00000000000000 */ + L(9.39413062813475779888605643463961314E-01), /* 3ffee0fabfbc702a3c00000000000000 */ + L(9.43089821584325888048638830696290825E-01), /* 3ffee2dcab49ca51b400000000000000 */ + L(9.46780970782128888929563004239753354E-01), /* 3ffee4c079b3f8000400000000000000 */ + L(9.50486566729423443256052905780961737E-01), /* 3ffee6a62cdec7c7b000000000000000 */ + L(9.54206665969188322362626308859034907E-01), /* 3ffee88dc6afecfbfc00000000000000 */ + L(9.57941325265705301283958306157728657E-01), /* 3ffeea77490f0196b000000000000000 */ + L(9.61690601605425299247542625380447134E-01), /* 3ffeec62b5e5881fb000000000000000 */ + L(9.65454552197837823079851204965962097E-01), /* 3ffeee500f1eed967000000000000000 */ + L(9.69233234476344074348475032820715569E-01), /* 3ffef03f56a88b5d7800000000000000 */ + L(9.73026706099133165128733935489435680E-01), /* 3ffef2308e71a927a800000000000000 */ + L(9.76835024950062025261843245971249416E-01), /* 3ffef423b86b7ee79000000000000000 */ + L(9.80658249139538557015427500118676107E-01), /* 3ffef618d68936c09c00000000000000 */ + L(9.84496437005408397968864164795377292E-01), /* 3ffef80feabfeefa4800000000000000 */ + L(9.88349647113845042323276857132441364E-01), /* 3ffefa08f706bbf53800000000000000 */ + L(9.92217938260243514925207364285597578E-01), /* 3ffefc03fd56aa225000000000000000 */ + L(9.96101369470117486981664001177705359E-01), /* 3ffefe00ffaabffbbc00000000000000 */ +#define T_EXPL_RES1 (T_EXPL_ARG2 + 2 + 2*65 + 89) + L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */ + L(1.00391388933834757590801700644078664E+00), /* 3fff0100802ab5577800000000000000 */ + L(1.00784309720644799091004983893071767E+00), /* 3fff0202015600445c00000000000000 */ + L(1.01178768355933151879000320150225889E+00), /* 3fff0304848362076c00000000000000 */ + L(1.01574770858668572692806719715008512E+00), /* 3fff04080ab55de39000000000000000 */ + L(1.01972323271377413034244341361045372E+00), /* 3fff050c94ef7a206c00000000000000 */ + L(1.02371431660235789884438872832106426E+00), /* 3fff06122436410dd000000000000000 */ + L(1.02772102115162167201845022646011785E+00), /* 3fff0718b98f42085000000000000000 */ + L(1.03174340749910264936062276319717057E+00), /* 3fff08205601127ec800000000000000 */ + L(1.03578153702162378824169763902318664E+00), /* 3fff0928fa934ef90800000000000000 */ + L(1.03983547133622999947277776300325058E+00), /* 3fff0a32a84e9c1f5800000000000000 */ + L(1.04390527230112850620713516036630608E+00), /* 3fff0b3d603ca7c32800000000000000 */ + L(1.04799100201663270004459604933799710E+00), /* 3fff0c49236829e8bc00000000000000 */ + L(1.05209272282610977189420964350574650E+00), /* 3fff0d55f2dce5d1e800000000000000 */ + L(1.05621049731693195106174698594259098E+00), /* 3fff0e63cfa7ab09d000000000000000 */ + L(1.06034438832143151909548350886325352E+00), /* 3fff0f72bad65671b800000000000000 */ + L(1.06449445891785943185681162503897212E+00), /* 3fff1082b577d34ed800000000000000 */ + L(1.06866077243134810492719566354935523E+00), /* 3fff1193c09c1c595c00000000000000 */ + L(1.07284339243487741866189821848820429E+00), /* 3fff12a5dd543ccc4c00000000000000 */ + L(1.07704238275024494209120007326419000E+00), /* 3fff13b90cb25176a400000000000000 */ + L(1.08125780744903959851299646288680378E+00), /* 3fff14cd4fc989cd6400000000000000 */ + L(1.08548973085361949442173568058933597E+00), /* 3fff15e2a7ae28fecc00000000000000 */ + L(1.08973821753809324563988525369495619E+00), /* 3fff16f9157587069400000000000000 */ + L(1.09400333232930546678574046381982043E+00), /* 3fff18109a3611c35000000000000000 */ + L(1.09828514030782586896606289883493446E+00), /* 3fff192937074e0cd800000000000000 */ + L(1.10258370680894224324930519287590869E+00), /* 3fff1a42ed01d8cbc800000000000000 */ + L(1.10689909742365749645287564817408565E+00), /* 3fff1b5dbd3f68122400000000000000 */ + L(1.11123137799969046168868658241990488E+00), /* 3fff1c79a8dacc350c00000000000000 */ + L(1.11558061464248076122274255794764031E+00), /* 3fff1d96b0eff0e79400000000000000 */ + L(1.11994687371619722204840741142106708E+00), /* 3fff1eb4d69bde569c00000000000000 */ + L(1.12433022184475073235176978414529003E+00), /* 3fff1fd41afcba45e800000000000000 */ + L(1.12873072591281087273529237791080959E+00), /* 3fff20f47f31c92e4800000000000000 */ + L(1.13314845306682632219974493636982515E+00), /* 3fff2216045b6f5cd000000000000000 */ + L(1.13758347071604959399593326452304609E+00), /* 3fff2338ab9b32134800000000000000 */ + L(1.14203584653356560174586320499656722E+00), /* 3fff245c7613b8a9b000000000000000 */ + L(1.14650564845732405583333957110880874E+00), /* 3fff258164e8cdb0d800000000000000 */ + L(1.15099294469117646722011727433709893E+00), /* 3fff26a7793f60164400000000000000 */ + L(1.15549780370591653744227755851170514E+00), /* 3fff27ceb43d84490400000000000000 */ + L(1.16002029424032515603215642840950750E+00), /* 3fff28f7170a755fd800000000000000 */ + L(1.16456048530221917269855680387991015E+00), /* 3fff2a20a2ce96406400000000000000 */ + L(1.16911844616950438835445424956560601E+00), /* 3fff2b4b58b372c79400000000000000 */ + L(1.17369424639123270948104504896036815E+00), /* 3fff2c7739e3c0f32c00000000000000 */ + L(1.17828795578866324378353169777255971E+00), /* 3fff2da4478b620c7400000000000000 */ + L(1.18289964445632783673900689791480545E+00), /* 3fff2ed282d763d42400000000000000 */ + L(1.18752938276310060494722620205720887E+00), /* 3fff3001ecf601af7000000000000000 */ + L(1.19217724135327157730657177125976887E+00), /* 3fff31328716a5d63c00000000000000 */ + L(1.19684329114762477708211463323095813E+00), /* 3fff32645269ea829000000000000000 */ + L(1.20152760334452030077656559114984702E+00), /* 3fff339750219b212c00000000000000 */ + L(1.20623024942098072687102217059873510E+00), /* 3fff34cb8170b5835400000000000000 */ + L(1.21095130113378179892436037334846333E+00), /* 3fff3600e78b6b11d000000000000000 */ + L(1.21569083052054743854242246925423387E+00), /* 3fff373783a722012400000000000000 */ + L(1.22044890990084875515009343871497549E+00), /* 3fff386f56fa7686e800000000000000 */ + L(1.22522561187730755216662714701669756E+00), /* 3fff39a862bd3c106400000000000000 */ + L(1.23002100933670455162882717559114099E+00), /* 3fff3ae2a8287e7a8000000000000000 */ + L(1.23483517545109100499445276000187732E+00), /* 3fff3c1e2876834aa800000000000000 */ + L(1.23966818367890557750499169742397498E+00), /* 3fff3d5ae4e2cae92c00000000000000 */ + L(1.24452010776609517384017067342938390E+00), /* 3fff3e98deaa11dcbc00000000000000 */ + L(1.24939102174724003813111039562500082E+00), /* 3fff3fd8170a52071800000000000000 */ + L(1.25428099994668373895478907797951251E+00), /* 3fff41188f42c3e32000000000000000 */ + L(1.25919011697966698459794088194030337E+00), /* 3fff425a4893dfc3f800000000000000 */ + L(1.26411844775346637881341393949696794E+00), /* 3fff439d443f5f159000000000000000 */ + L(1.26906606746853711786826579555054195E+00), /* 3fff44e183883d9e4800000000000000 */ + L(1.27403305161966090564007458851847332E+00), /* 3fff462707b2bac20c00000000000000 */ + L(1.27901947599709753244923149395617656E+00), /* 3fff476dd2045ac67800000000000000 */ + L(1.28402541668774150540599521264084615E+00), /* 3fff48b5e3c3e8186800000000000000 */ + L(1.28905095007628295311619126550795045E+00), /* 3fff49ff3e397492bc00000000000000 */ + L(1.29409615284637330434591717676084954E+00), /* 3fff4b49e2ae5ac67400000000000000 */ + L(1.29916110198179535206719492634874769E+00), /* 3fff4c95d26d3f440800000000000000 */ + L(1.30424587476763775839572190307080746E+00), /* 3fff4de30ec211e60000000000000000 */ + L(1.30935054879147461104338390214252286E+00), /* 3fff4f3198fa0f1cf800000000000000 */ + L(1.31447520194454914310711046709911898E+00), /* 3fff50817263c13cd000000000000000 */ + L(1.31961991242296217130558488861424848E+00), /* 3fff51d29c4f01cb3000000000000000 */ + L(1.32478475872886558573071624778094701E+00), /* 3fff5325180cfacf7800000000000000 */ + L(1.32996981967165983640200010995613411E+00), /* 3fff5478e6f02823d000000000000000 */ + L(1.33517517436919680440254865061433520E+00), /* 3fff55ce0a4c58c7bc00000000000000 */ + L(1.34040090224898678084031189428060316E+00), /* 3fff57248376b033d800000000000000 */ + L(1.34564708304941055283521222918352578E+00), /* 3fff587c53c5a7af0400000000000000 */ + L(1.35091379682093615244298234756570309E+00), /* 3fff59d57c910fa4e000000000000000 */ + L(1.35620112392734021300455538039386738E+00), /* 3fff5b2fff3210fd9400000000000000 */ + L(1.36150914504693443252136830778908916E+00), /* 3fff5c8bdd032e770800000000000000 */ + L(1.36683794117379636690046140756749082E+00), /* 3fff5de9176045ff5400000000000000 */ + L(1.37218759361900544124779344201670028E+00), /* 3fff5f47afa69210a800000000000000 */ + L(1.37755818401188367960941150158760138E+00), /* 3fff60a7a734ab0e8800000000000000 */ + L(1.38294979430124120867162673675920814E+00), /* 3fff6208ff6a88a46000000000000000 */ + L(1.38836250675662681297595213436579797E+00), /* 3fff636bb9a983258400000000000000 */ + L(1.39379640396958309755959248832368758E+00), /* 3fff64cfd75454ee7c00000000000000 */ + L(1.39925156885490681313299887733592186E+00), /* 3fff663559cf1bc7c400000000000000 */ + L(1.40472808465191417726103395580139477E+00), /* 3fff679c427f5a49f400000000000000 */ + L(1.41022603492571069194738697660795879E+00), /* 3fff690492cbf9432c00000000000000 */ + L(1.41574550356846662335641440222389065E+00), /* 3fff6a6e4c1d491e1800000000000000 */ + + L(9.98018323540573404351050612604012713E-01), /* 3ffefefc41f8d4bdb000000000000000 */ + L(9.98048781107475468932221929208026268E-01), /* 3ffeff003ff556aa8800000000000000 */ + L(9.98079239603882895082165305211674422E-01), /* 3ffeff043df9d4986000000000000000 */ + L(9.98109699029824021243584297735651489E-01), /* 3ffeff083c064e972c00000000000000 */ + L(9.98140159385327269125909310787392315E-01), /* 3ffeff0c3a1ac4b6ec00000000000000 */ + L(9.98170620670420977171843901487591211E-01), /* 3ffeff10383737079400000000000000 */ + L(9.98201082885133511579667242585856002E-01), /* 3ffeff14365ba5991c00000000000000 */ + L(9.98231546029493238547658506831794512E-01), /* 3ffeff183488107b7c00000000000000 */ + L(9.98262010103528552029672482603928074E-01), /* 3ffeff1c32bc77beb000000000000000 */ + L(9.98292475107267818223988342651864514E-01), /* 3ffeff2030f8db72b000000000000000 */ + L(9.98322941040739375573309644096298143E-01), /* 3ffeff242f3d3ba77000000000000000 */ + L(9.98353407903971645787066790944663808E-01), /* 3ffeff282d89986cf000000000000000 */ + L(9.98383875696992967307963340317655820E-01), /* 3ffeff2c2bddf1d32400000000000000 */ + L(9.98414344419831761845429696222709026E-01), /* 3ffeff302a3a47ea0c00000000000000 */ + L(9.98444814072516340086593800151604228E-01), /* 3ffeff34289e9ac19800000000000000 */ + L(9.98475284655075123740886056111776270E-01), /* 3ffeff38270aea69c800000000000000 */ + L(9.98505756167536479006585636852832977E-01), /* 3ffeff3c257f36f29400000000000000 */ + L(9.98536228609928799837547330753295682E-01), /* 3ffeff4023fb806bf800000000000000 */ + L(9.98566701982280452432050310562772211E-01), /* 3ffeff44227fc6e5ec00000000000000 */ + L(9.98597176284619802988373749030870385E-01), /* 3ffeff48210c0a706800000000000000 */ + L(9.98627651516975245460372434536111541E-01), /* 3ffeff4c1fa04b1b6800000000000000 */ + L(9.98658127679375173801901155457017012E-01), /* 3ffeff501e3c88f6e800000000000000 */ + L(9.98688604771847954211239084543194622E-01), /* 3ffeff541ce0c412e000000000000000 */ + L(9.98719082794421980642241010173165705E-01), /* 3ffeff581b8cfc7f4c00000000000000 */ + L(9.98749561747125619293186105096538085E-01), /* 3ffeff5c1a41324c2400000000000000 */ + L(9.98780041629987291873504773320746608E-01), /* 3ffeff6018fd65896800000000000000 */ + L(9.98810522443035364581476187595399097E-01), /* 3ffeff6417c196471000000000000000 */ + L(9.98841004186298203615379520670103375E-01), /* 3ffeff68168dc4951400000000000000 */ + L(9.98871486859804230684645176552294288E-01), /* 3ffeff6c1561f0837400000000000000 */ + L(9.98901970463581839743127943620493170E-01), /* 3ffeff70143e1a222c00000000000000 */ + L(9.98932454997659369233531378995394334E-01), /* 3ffeff74132241813000000000000000 */ + L(9.98962940462065268620861502313346136E-01), /* 3ffeff78120e66b08400000000000000 */ + L(9.98993426856827904103397486323956400E-01), /* 3ffeff7c110289c02000000000000000 */ + L(9.99023914181975669634994119405746460E-01), /* 3ffeff800ffeaac00000000000000000 */ + L(9.99054402437536959169506189937237650E-01), /* 3ffeff840f02c9c02000000000000000 */ + L(9.99084891623540138905212870668037795E-01), /* 3ffeff880e0ee6d07800000000000000 */ + L(9.99115381740013658307120181234495249E-01), /* 3ffeff8c0d2302010c00000000000000 */ + L(9.99145872786985911329082910015131347E-01), /* 3ffeff900c3f1b61d800000000000000 */ + L(9.99176364764485236413804614130640402E-01), /* 3ffeff940b633302d000000000000000 */ + L(9.99206857672540083026291313217370771E-01), /* 3ffeff980a8f48f3f800000000000000 */ + L(9.99237351511178817364822180024930276E-01), /* 3ffeff9c09c35d454800000000000000 */ + L(9.99267846280429861138827618560753763E-01), /* 3ffeffa008ff7006c000000000000000 */ + L(9.99298341980321608302162417203362565E-01), /* 3ffeffa4084381485c00000000000000 */ + L(9.99328838610882452808681364331278019E-01), /* 3ffeffa8078f911a1800000000000000 */ + L(9.99359336172140816367814863951934967E-01), /* 3ffeffac06e39f8bf400000000000000 */ + L(9.99389834664125092933417704443854745E-01), /* 3ffeffb0063facadec00000000000000 */ + L(9.99420334086863676459344674185558688E-01), /* 3ffeffb405a3b88ffc00000000000000 */ + L(9.99450834440384988655026177184481639E-01), /* 3ffeffb8050fc3422400000000000000 */ + L(9.99481335724717395718741386190231424E-01), /* 3ffeffbc0483ccd45c00000000000000 */ + L(9.99511837939889374871071936468069907E-01), /* 3ffeffc003ffd556ac00000000000000 */ + L(9.99542341085929264554721385138691403E-01), /* 3ffeffc40383dcd90800000000000000 */ + L(9.99572845162865514234695751838444266E-01), /* 3ffeffc8030fe36b7400000000000000 */ + L(9.99603350170726517864849824945849832E-01), /* 3ffeffcc02a3e91dec00000000000000 */ + L(9.99633856109540669399038392839429434E-01), /* 3ffeffd0023fee006c00000000000000 */ + L(9.99664362979336418302267475155531429E-01), /* 3ffeffd401e3f222f800000000000000 */ + L(9.99694870780142130772816244643763639E-01), /* 3ffeffd8018ff5958800000000000000 */ + L(9.99725379511986284031266336569387931E-01), /* 3ffeffdc0143f8682400000000000000 */ + L(9.99755889174897216520321308053098619E-01), /* 3ffeffe000fffaaac000000000000000 */ + L(9.99786399768903377704987178731244057E-01), /* 3ffeffe400c3fc6d6000000000000000 */ + L(9.99816911294033217050269968240172602E-01), /* 3ffeffe8008ffdc00800000000000000 */ + L(9.99847423750315072998873233700578567E-01), /* 3ffeffec0063feb2ac00000000000000 */ + L(9.99877937137777450526954226006637327E-01), /* 3ffefff0003fff555800000000000000 */ + L(9.99908451456448688077216502279043198E-01), /* 3ffefff40023ffb80000000000000000 */ + L(9.99938966706357262870241697783058044E-01), /* 3ffefff8000fffeaac00000000000000 */ + L(9.99969482887531541104308985268289689E-01), /* 3ffefffc0003fffd5400000000000000 */ +#define T_EXPL_RES2 (T_EXPL_RES1 + 1 + 89 + 65) + L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */ + L(1.00003051804379100575559391472779680E+00), /* 3fff0002000200015400000000000000 */ + L(1.00006103701893306334724798034585547E+00), /* 3fff00040008000aac00000000000000 */ + L(1.00009155692545448346209013834595680E+00), /* 3fff0006001200240000000000000000 */ + L(1.00012207776338379883185325525118969E+00), /* 3fff0008002000555800000000000000 */ + L(1.00015259953274932014366527255333494E+00), /* 3fff000a003200a6ac00000000000000 */ + L(1.00018312223357958012925905677548144E+00), /* 3fff000c004801200400000000000000 */ + L(1.00021364586590294498691378066723701E+00), /* 3fff000e006201c95c00000000000000 */ + L(1.00024417042974783642605984823603649E+00), /* 3fff0010008002aab400000000000000 */ + L(1.00027469592514273166727889474714175E+00), /* 3fff001200a203cc1000000000000000 */ + L(1.00030522235211605242000132420798764E+00), /* 3fff001400c805357000000000000000 */ + L(1.00033574971069616488250630936818197E+00), /* 3fff001600f206eed000000000000000 */ + L(1.00036627800091160178652671675081365E+00), /* 3fff0018012009003800000000000000 */ + L(1.00039680722279067381919048784766346E+00), /* 3fff001a01520b71a000000000000000 */ + L(1.00042733737636191371223048918182030E+00), /* 3fff001c01880e4b1000000000000000 */ + L(1.00045786846165368766392589350289200E+00), /* 3fff001e01c211948400000000000000 */ + L(1.00048840047869447289485833607614040E+00), /* 3fff0020020015560000000000000000 */ + L(1.00051893342751269111445822090900037E+00), /* 3fff0022024219978400000000000000 */ + L(1.00054946730813676403215595200890675E+00), /* 3fff002402881e611000000000000000 */ + L(1.00058000212059516886853316464112140E+00), /* 3fff002602d223baa800000000000000 */ + L(1.00061053786491632733302026281307917E+00), /* 3fff0028032029ac4c00000000000000 */ + L(1.00064107454112866113504765053221490E+00), /* 3fff002a0372303dfc00000000000000 */ + L(1.00067161214926059198404573180596344E+00), /* 3fff002c03c83777b800000000000000 */ + L(1.00070215068934059710059614189958666E+00), /* 3fff002e04223f618400000000000000 */ + L(1.00073269016139709819412928482051939E+00), /* 3fff0030048048036000000000000000 */ + L(1.00076323056545857248522679583402351E+00), /* 3fff003204e251655000000000000000 */ + L(1.00079377190155338617216784768970683E+00), /* 3fff003405485b8f5000000000000000 */ + L(1.00082431416971007198668530691065826E+00), /* 3fff003605b266896800000000000000 */ + L(1.00085485736995705163820957750431262E+00), /* 3fff00380620725b9800000000000000 */ + L(1.00088540150232269132501983222027775E+00), /* 3fff003a06927f0ddc00000000000000 */ + L(1.00091594656683552377884893758164253E+00), /* 3fff003c07088ca83c00000000000000 */ + L(1.00094649256352402622027852885366883E+00), /* 3fff003e07829b32bc00000000000000 */ + L(1.00097703949241650933643654752813745E+00), /* 3fff00400800aab55400000000000000 */ + L(1.00100758735354156137020709138596430E+00), /* 3fff00420882bb381000000000000000 */ + L(1.00103813614692760403102056443458423E+00), /* 3fff00440908ccc2f000000000000000 */ + L(1.00106868587260300351715613942360505E+00), /* 3fff00460992df5df000000000000000 */ + L(1.00109923653059629256034668287611566E+00), /* 3fff00480a20f3111800000000000000 */ + L(1.00112978812093589287002259879955091E+00), /* 3fff004a0ab307e46800000000000000 */ + L(1.00116034064365022615561429120134562E+00), /* 3fff004c0b491ddfe000000000000000 */ + L(1.00119089409876788066000585786241572E+00), /* 3fff004e0be3350b8c00000000000000 */ + L(1.00122144848631711155917400901671499E+00), /* 3fff00500c814d6f6000000000000000 */ + L(1.00125200380632656260715407370298635E+00), /* 3fff00520d2367136c00000000000000 */ + L(1.00128256005882454449107399341301061E+00), /* 3fff00540dc981ffa800000000000000 */ + L(1.00131311724383964545381786592770368E+00), /* 3fff00560e739e3c2000000000000000 */ + L(1.00134367536140017618251363273884635E+00), /* 3fff00580f21bbd0cc00000000000000 */ + L(1.00137423441153472492004539162735455E+00), /* 3fff005a0fd3dac5b800000000000000 */ + L(1.00140479439427171337584354660066310E+00), /* 3fff005c1089fb22e400000000000000 */ + L(1.00143535530963956325933850166620687E+00), /* 3fff005e11441cf05000000000000000 */ + L(1.00146591715766680730226312334707472E+00), /* 3fff0060120240360400000000000000 */ + L(1.00149647993838186721404781565070152E+00), /* 3fff006212c464fc0000000000000000 */ + L(1.00152704365181316470412298258452211E+00), /* 3fff0064138a8b4a4400000000000000 */ + L(1.00155760829798923250422149067162536E+00), /* 3fff00661454b328d800000000000000 */ + L(1.00158817387693849232377374391944613E+00), /* 3fff00681522dc9fbc00000000000000 */ + L(1.00161874038868942138336137759324629E+00), /* 3fff006a15f507b6f400000000000000 */ + L(1.00164930783327055241471725821611471E+00), /* 3fff006c16cb34768800000000000000 */ + L(1.00167987621071025161612055853765924E+00), /* 3fff006e17a562e67400000000000000 */ + L(1.00171044552103705171930414508096874E+00), /* 3fff00701883930ec000000000000000 */ + L(1.00174101576427937443369842185347807E+00), /* 3fff00721965c4f76c00000000000000 */ + L(1.00177158694046569697988502412044909E+00), /* 3fff00741a4bf8a87c00000000000000 */ + L(1.00180215904962455208959681840497069E+00), /* 3fff00761b362e29f800000000000000 */ + L(1.00183273209178441698341543997230474E+00), /* 3fff00781c246583e400000000000000 */ + L(1.00186330606697365785962006157205906E+00), /* 3fff007a1d169ebe3c00000000000000 */ + L(1.00189388097522080744994354972732253E+00), /* 3fff007c1e0cd9e10800000000000000 */ + L(1.00192445681655439848611877096118405E+00), /* 3fff007e1f0716f45000000000000000 */ + L(1.00195503359100279716642489802325144E+00), /* 3fff0080200556001000000000000000 */ + L(1.00198561129859459173374602869444061E+00), /* 3fff00822107970c5400000000000000 */ +}; diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/t_sincosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/t_sincosl.c new file mode 100644 index 0000000000..601662c399 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/t_sincosl.c @@ -0,0 +1,696 @@ +/* Quad-precision floating point sine and cosine tables. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* For 0.1484375 + n/128.0, n=0..82 this table contains + first 113 bits of cosine, then at least 113 additional + bits and the same for sine. + 0.1484375+82.0/128.0 is the smallest number among above defined numbers + larger than pi/4. + Computed using gmp. + */ + +/* Include to grab typedefs and wrappers for _Float128 and such. */ +#include <math_private.h> + +const _Float128 __sincosl_table[] = { + +/* x = 1.48437500000000000000000000000000000e-01L 3ffc3000000000000000000000000000 */ +/* cos(x) = 0.fd2f5320e1b790209b4dda2f98f79caaa7b873aff1014b0fbc5243766d03cb006bc837c4358 */ + L(9.89003367927322909016887196069562069e-01), /* 3ffefa5ea641c36f2041369bb45f31ef */ + L(2.15663692029265697782289400027743703e-35), /* 3f8bcaaa7b873aff1014b0fbc5243767 */ +/* sin(x) = 0.25dc50bc95711d0d9787d108fd438cf5959ee0bfb7a1e36e8b1a112968f356657420e9cc9ea */ + L(1.47892995873409608580026675734609314e-01), /* 3ffc2ee285e4ab88e86cbc3e8847ea1c */ + L(9.74950446464233268291647449768590886e-36), /* 3f8a9eb2b3dc17f6f43c6dd16342252d */ + +/* x = 1.56250000000000000000000000000000000e-01 3ffc4000000000000000000000000000 */ +/* cos(x) = 0.fce1a053e621438b6d60c76e8c45bf0a9dc71aa16f922acc10e95144ec796a249813c9cb649 */ + L(9.87817783816471944100503034363211317e-01), /* 3ffef9c340a7cc428716dac18edd188b */ + L(4.74271307836705897892468107620526395e-35), /* 3f8cf854ee38d50b7c915660874a8a27 */ +/* sin(x) = 0.27d66258bacd96a3eb335b365c87d59438c5142bb56a489e9b8db9d36234ffdebb6bdc22d8e */ + L(1.55614992773556041209920643203516258e-01), /* 3ffc3eb312c5d66cb51f599ad9b2e43f */ +L(-7.83989563419287980121718050629497270e-36), /* bf8a4d78e75d7a8952b6ec2c8e48c594 */ + +/* x = 1.64062500000000000000000000000000000e-01 3ffc5000000000000000000000000000 */ +/* cos(x) = 0.fc8ffa01ba6807417e05962b0d9fdf1fddb0cc4c07d22e19e08019bffa50a6c7acdb40307a3 */ + L(9.86571908399497588757337407495308409e-01), /* 3ffef91ff40374d00e82fc0b2c561b40 */ +L(-2.47327949936985362476252401212720725e-35), /* bf8c070112799d9fc16e8f30fbff3200 */ +/* sin(x) = 0.29cfd49b8be4f665276cab01cbf0426934906c3dd105473b226e410b1450f62e53ff7c6cce1 */ + L(1.63327491736612850846866172454354370e-01), /* 3ffc4e7ea4dc5f27b3293b65580e5f82 */ + L(1.81380344301155485770367902300754350e-36), /* 3f88349a48361ee882a39d913720858a */ + +/* x = 1.71875000000000000000000000000000000e-01 3ffc6000000000000000000000000000 */ +/* cos(x) = 0.fc3a6170f767ac735d63d99a9d439e1db5e59d3ef153a4265d5855850ed82b536bf361b80e3 */ + L(9.85265817718213816204294709759578994e-01), /* 3ffef874c2e1eecf58e6bac7b3353a87 */ + L(2.26568029505818066141517497778527952e-35), /* 3f8be1db5e59d3ef153a4265d5855851 */ +/* sin(x) = 0.2bc89f9f424de5485de7ce03b2514952b9faf5648c3244d4736feb95dbb9da49f3b58a9253b */ + L(1.71030022031395019281347969239834331e-01), /* 3ffc5e44fcfa126f2a42ef3e701d928a */ + L(7.01395875187487608875416030203241317e-36), /* 3f8a2a573f5eac9186489a8e6dfd72bb */ + +/* x = 1.79687500000000000000000000000000000e-01 3ffc7000000000000000000000000000 */ +/* cos(x) = 0.fbe0d7f7fef11e70aa43b8abf4f6a457cea20c8f3f676b47781f9821bbe9ce04b3c7b981c0b */ + L(9.83899591489663972178309351416487245e-01), /* 3ffef7c1afeffde23ce154877157e9ed */ + L(2.73414318948066207810486330723761265e-35), /* 3f8c22be75106479fb3b5a3bc0fcc10e */ +/* sin(x) = 0.2dc0bb80b49a97ffb34e8dd1f8db9df7af47ed2dcf58b12c8e7827e048cae929da02c04ecac */ + L(1.78722113535153659375356241864180724e-01), /* 3ffc6e05dc05a4d4bffd9a746e8fc6dd */ +L(-1.52906926517265103202547561260594148e-36), /* bf8804285c09691853a769b8c3ec0fdc */ + +/* x = 1.87500000000000000000000000000000000e-01 3ffc8000000000000000000000000000 */ +/* cos(x) = 0.fb835efcf670dd2ce6fe7924697eea13ea358867e9cdb3899b783f4f9f43aa5626e8b67b3bc */ + L(9.82473313101255257487327683243622495e-01), /* 3ffef706bdf9ece1ba59cdfcf248d2fe */ +L(-1.64924358891557584625463868014230342e-35), /* bf8b5ec15ca779816324c766487c0b06 */ +/* sin(x) = 0.2fb8205f75e56a2b56a1c4792f856258769af396e0189ef72c05e4df59a6b00e4b44a6ea515 */ + L(1.86403296762269884552379983103205261e-01), /* 3ffc7dc102fbaf2b515ab50e23c97c2b */ + L(1.76460304806826780010586715975331753e-36), /* 3f882c3b4d79cb700c4f7b9602f26fad */ + +/* x = 1.95312500000000000000000000000000000e-01 3ffc9000000000000000000000000000 */ +/* cos(x) = 0.fb21f7f5c156696b00ac1fe28ac5fd76674a92b4df80d9c8a46c684399005deccc41386257c */ + L(9.80987069605669190469329896435309665e-01), /* 3ffef643efeb82acd2d601583fc5158c */ +L(-1.90899259410096419886996331536278461e-36), /* bf8844cc5ab6a5903f931badc9cbde34 */ +/* sin(x) = 0.31aec65df552876f82ece9a2356713246eba6799983d7011b0b3698d6e1da919c15d57c30c1 */ + L(1.94073102892909791156055200214145404e-01), /* 3ffc8d7632efaa943b7c17674d11ab39 */ +L(-9.67304741051998267208945242944928999e-36), /* bf8a9b7228b30cccf851fdc9e992ce52 */ + +/* x = 2.03125000000000000000000000000000000e-01 3ffca000000000000000000000000000 */ +/* cos(x) = 0.fabca467fb3cb8f1d069f01d8ea33ade5bfd68296ecd1cc9f7b7609bbcf3676e726c3301334 */ + L(9.79440951715548359998530954502987493e-01), /* 3ffef57948cff67971e3a0d3e03b1d46 */ + L(4.42878056591560757066844797290067990e-35), /* 3f8cd6f2dfeb414b7668e64fbdbb04de */ +/* sin(x) = 0.33a4a5a19d86246710f602c44df4fa513f4639ce938477aeeabb82e8e0a7ed583a188879fd4 */ + L(2.01731063801638804725038151164000971e-01), /* 3ffc9d252d0cec31233887b016226fa8 */ +L(-4.27513434754966978435151290617384120e-36), /* bf896bb02e718c5b1ee21445511f45c8 */ + +/* x = 2.10937500000000000000000000000000000e-01 3ffcb000000000000000000000000000 */ +/* cos(x) = 0.fa5365e8f1d3ca27be1db5d76ae64d983d7470a4ab0f4ccf65a2b8c67a380df949953a09bc1 */ + L(9.77835053797959793331971572944454549e-01), /* 3ffef4a6cbd1e3a7944f7c3b6baed5cd */ +L(-3.79207422905180416937210853779192702e-35), /* bf8c933e145c7adaa7859984d2ea39cc */ +/* sin(x) = 0.3599b652f40ec999df12a0a4c8561de159c98d4e54555de518b97f48886f715d8df5f4f093e */ + L(2.09376712085993643711890752724881652e-01), /* 3ffcaccdb297a0764ccef895052642b1 */ +L(-1.59470287344329449965314638482515925e-36), /* bf880f531b3958d5d5510d73a3405bbc */ + +/* x = 2.18750000000000000000000000000000000e-01 3ffcc000000000000000000000000000 */ +/* cos(x) = 0.f9e63e1d9e8b6f6f2e296bae5b5ed9c11fd7fa2fe11e09fc7bde901abed24b6365e72f7db4e */ + L(9.76169473868635276723989035435135534e-01), /* 3ffef3cc7c3b3d16dede5c52d75cb6be */ +L(-2.87727974249481583047944860626985460e-35), /* bf8c31f701402e80f70fb01c210b7f2a */ +/* sin(x) = 0.378df09db8c332ce0d2b53d865582e4526ea336c768f68c32b496c6d11c1cd241bb9f1da523 */ + L(2.17009581095010156760578095826055396e-01), /* 3ffcbc6f84edc6199670695a9ec32ac1 */ + L(1.07356488794216831812829549198201194e-35), /* 3f8ac8a4dd466d8ed1ed1865692d8da2 */ + +/* x = 2.26562500000000000000000000000000000e-01 3ffcd000000000000000000000000000 */ +/* cos(x) = 0.f9752eba9fff6b98842beadab054a932fb0f8d5b875ae63d6b2288d09b148921aeb6e52f61b */ + L(9.74444313585988980349711056045434344e-01), /* 3ffef2ea5d753ffed7310857d5b560a9 */ + L(3.09947905955053419304514538592548333e-35), /* 3f8c4997d87c6adc3ad731eb59144685 */ +/* sin(x) = 0.39814cb10513453cb97b21bc1ca6a337b150c21a675ab85503bc09a436a10ab1473934e20c8 */ + L(2.24629204957705292350428549796424820e-01), /* 3ffccc0a6588289a29e5cbd90de0e535 */ + L(2.42061510849297469844695751870058679e-36), /* 3f889bd8a8610d33ad5c2a81de04d21b */ + +/* x = 2.34375000000000000000000000000000000e-01 3ffce000000000000000000000000000 */ +/* cos(x) = 0.f90039843324f9b940416c1984b6cbed1fc733d97354d4265788a86150493ce657cae032674 */ + L(9.72659678244912752670913058267565260e-01), /* 3ffef20073086649f3728082d833096e */ +L(-3.91759231819314904966076958560252735e-35), /* bf8ca09701c6613465595ecd43babcf5 */ +/* sin(x) = 0.3b73c2bf6b4b9f668ef9499c81f0d965087f1753fa64b086e58cb8470515c18c1412f8c2e02 */ + L(2.32235118611511462413930877746235872e-01), /* 3ffcdb9e15fb5a5cfb3477ca4ce40f87 */ +L(-4.96930483364191020075024624332928910e-36), /* bf89a6bde03a2b0166d3de469cd1ee3f */ + +/* x = 2.42187500000000000000000000000000000e-01 3ffcf000000000000000000000000000 */ +/* cos(x) = 0.f887604e2c39dbb20e4ec5825059a789ffc95b275ad9954078ba8a28d3fcfe9cc2c1d49697b */ + L(9.70815676770349462947490545785046027e-01), /* 3ffef10ec09c5873b7641c9d8b04a0b3 */ + L(2.97458820972393859125277682021202860e-35), /* 3f8c3c4ffe4ad93ad6ccaa03c5d45147 */ +/* sin(x) = 0.3d654aff15cb457a0fca854698aba33039a8a40626609204472d9d40309b626eccc6dff0ffa */ + L(2.39826857830661564441369251810886574e-01), /* 3ffceb2a57f8ae5a2bd07e542a34c55d */ + L(2.39867036569896287240938444445071448e-36), /* 3f88981cd45203133049022396cea018 */ + +/* x = 2.50000000000000000000000000000000000e-01 3ffd0000000000000000000000000000 */ +/* cos(x) = 0.f80aa4fbef750ba783d33cb95f94f8a41426dbe79edc4a023ef9ec13c944551c0795b84fee1 */ + L(9.68912421710644784144595449494189205e-01), /* 3ffef01549f7deea174f07a67972bf2a */ +L(-5.53634706113461989398873287749326500e-36), /* bf89d6faf649061848ed7f704184fb0e */ +/* sin(x) = 0.3f55dda9e62aed7513bd7b8e6a3d1635dd5676648d7db525898d7086af9330f03c7f285442a */ + L(2.47403959254522929596848704849389203e-01), /* 3ffcfaaeed4f31576ba89debdc7351e9 */ +L(-7.36487001108599532943597115275811618e-36), /* bf8a39445531336e50495b4ece51ef2a */ + +/* x = 2.57812500000000000000000000000000000e-01 3ffd0800000000000000000000000000 */ +/* cos(x) = 0.f78a098069792daabc9ee42591b7c5a68cb1ab822aeb446b3311b4ba5371b8970e2c1547ad7 */ + L(9.66950029230677822008341623610531503e-01), /* 3ffeef141300d2f25b55793dc84b2370 */ +L(-4.38972214432792412062088059990480514e-35), /* bf8cd2cb9a72a3eea8a5dca667725a2d */ +/* sin(x) = 0.414572fd94556e6473d620271388dd47c0ba050cdb5270112e3e370e8c4705ae006426fb5d5 */ + L(2.54965960415878467487556574864872628e-01), /* 3ffd0515cbf65155b991cf58809c4e23 */ + L(2.20280377918534721005071688328074154e-35), /* 3f8bd47c0ba050cdb5270112e3e370e9 */ + +/* x = 2.65625000000000000000000000000000000e-01 3ffd1000000000000000000000000000 */ +/* cos(x) = 0.f7058fde0788dfc805b8fe88789e4f4253e3c50afe8b22f41159620ab5940ff7df9557c0d1f */ + L(9.64928619104771009581074665315748371e-01), /* 3ffeee0b1fbc0f11bf900b71fd10f13d */ +L(-3.66685832670820775002475545602761113e-35), /* bf8c85ed60e1d7a80ba6e85f7534efaa */ +/* sin(x) = 0.4334033bcd90d6604f5f36c1d4b84451a87150438275b77470b50e5b968fa7962b5ffb379b7 */ + L(2.62512399769153281450949626395692931e-01), /* 3ffd0cd00cef364359813d7cdb0752e1 */ + L(3.24923677072031064673177178571821843e-36), /* 3f89146a1c5410e09d6ddd1c2d4396e6 */ + +/* x = 2.73437500000000000000000000000000000e-01 3ffd1800000000000000000000000000 */ +/* cos(x) = 0.f67d3a26af7d07aa4bd6d42af8c0067fefb96d5b46c031eff53627f215ea3242edc3f2e13eb */ + L(9.62848314709379699899701093480214365e-01), /* 3ffeecfa744d5efa0f5497ada855f180 */ + L(4.88986966383343450799422013051821394e-36), /* 3f899ffbee5b56d1b00c7bfd4d89fc85 */ +/* sin(x) = 0.452186aa5377ab20bbf2524f52e3a06a969f47166ab88cf88c111ad12c55941021ef3317a1a */ + L(2.70042816718585031552755063618827102e-01), /* 3ffd14861aa94ddeac82efc9493d4b8f */ +L(-2.37608892440611310321138680065803162e-35), /* bf8bf956960b8e99547730773eee52ed */ + +/* x = 2.81250000000000000000000000000000000e-01 3ffd2000000000000000000000000000 */ +/* cos(x) = 0.f5f10a7bb77d3dfa0c1da8b57842783280d01ce3c0f82bae3b9d623c168d2e7c29977994451 */ + L(9.60709243015561903066659350581313472e-01), /* 3ffeebe214f76efa7bf4183b516af085 */ +L(-5.87011558231583960712013351601221840e-36), /* bf89f35fcbf8c70fc1f5147118a770fa */ +/* sin(x) = 0.470df5931ae1d946076fe0dcff47fe31bb2ede618ebc607821f8462b639e1f4298b5ae87fd3 */ + L(2.77556751646336325922023446828128568e-01), /* 3ffd1c37d64c6b8765181dbf8373fd20 */ +L(-1.35848595468998128214344668770082997e-36), /* bf87ce44d1219e71439f87de07b9d49c */ + +/* x = 2.89062500000000000000000000000000000e-01 3ffd2800000000000000000000000000 */ +/* cos(x) = 0.f561030ddd7a78960ea9f4a32c6521554995667f5547bafee9ec48b3155cdb0f7fd00509713 */ + L(9.58511534581228627301969408154919822e-01), /* 3ffeeac2061bbaf4f12c1d53e94658ca */ + L(2.50770779371636481145735089393154404e-35), /* 3f8c0aaa4cab33faaa3dd7f74f624599 */ +/* sin(x) = 0.48f948446abcd6b0f7fccb100e7a1b26eccad880b0d24b59948c7cdd49514d44b933e6985c2 */ + L(2.85053745940547424587763033323252561e-01), /* 3ffd23e52111aaf35ac3dff32c4039e8 */ + L(2.04269325885902918802700123680403749e-35), /* 3f8bb26eccad880b0d24b59948c7cdd5 */ + +/* x = 2.96875000000000000000000000000000000e-01 3ffd3000000000000000000000000000 */ +/* cos(x) = 0.f4cd261d3e6c15bb369c8758630d2ac00b7ace2a51c0631bfeb39ed158ba924cc91e259c195 */ + L(9.56255323543175296975599942263028361e-01), /* 3ffee99a4c3a7cd82b766d390eb0c61a */ + L(3.21616572190865997051103645135837207e-35), /* 3f8c56005bd671528e0318dff59cf68b */ +/* sin(x) = 0.4ae37710fad27c8aa9c4cf96c03519b9ce07dc08a1471775499f05c29f86190aaebaeb9716e */ + L(2.92533342023327543624702326493913423e-01), /* 3ffd2b8ddc43eb49f22aa7133e5b00d4 */ + L(1.93539408668704450308003687950685128e-35), /* 3f8b9b9ce07dc08a1471775499f05c2a */ + +/* x = 3.04687500000000000000000000000000000e-01 3ffd3800000000000000000000000000 */ +/* cos(x) = 0.f43575f94d4f6b272f5fb76b14d2a64ab52df1ee8ddf7c651034e5b2889305a9ea9015d758a */ + L(9.53940747608894733981324795987611623e-01), /* 3ffee86aebf29a9ed64e5ebf6ed629a5 */ + L(2.88075689052478602008395972924657164e-35), /* 3f8c3255a96f8f746efbe32881a72d94 */ +/* sin(x) = 0.4ccc7a50127e1de0cb6b40c302c651f7bded4f9e7702b0471ae0288d091a37391950907202f */ + L(2.99995083378683051163248282011699944e-01), /* 3ffd3331e94049f877832dad030c0b19 */ + L(1.35174265535697850139283361475571050e-35), /* 3f8b1f7bded4f9e7702b0471ae0288d1 */ + +/* x = 3.12500000000000000000000000000000000e-01 3ffd4000000000000000000000000000 */ +/* cos(x) = 0.f399f500c9e9fd37ae9957263dab8877102beb569f101ee4495350868e5847d181d50d3cca2 */ + L(9.51567948048172202145488217364270962e-01), /* 3ffee733ea0193d3fa6f5d32ae4c7b57 */ + L(6.36842628598115658308749288799884606e-36), /* 3f8a0ee2057d6ad3e203dc892a6a10d2 */ +/* sin(x) = 0.4eb44a5da74f600207aaa090f0734e288603ffadb3eb2542a46977b105f8547128036dcf7f0 */ + L(3.07438514580380850670502958201982091e-01), /* 3ffd3ad129769d3d80081eaa8243c1cd */ + L(1.06515172423204645839241099453417152e-35), /* 3f8ac510c07ff5b67d64a8548d2ef621 */ + +/* x = 3.20312500000000000000000000000000000e-01 3ffd4800000000000000000000000000 */ +/* cos(x) = 0.f2faa5a1b74e82fd61fa05f9177380e8e69b7b15a945e8e5ae1124bf3d12b0617e03af4fab5 */ + L(9.49137069684463027665847421762105623e-01), /* 3ffee5f54b436e9d05fac3f40bf22ee7 */ + L(6.84433965991637152250309190468859701e-37), /* 3f86d1cd36f62b528bd1cb5c22497e7a */ +/* sin(x) = 0.509adf9a7b9a5a0f638a8fa3a60a199418859f18b37169a644fdb986c21ecb00133853bc35b */ + L(3.14863181319745250865036315126939016e-01), /* 3ffd426b7e69ee69683d8e2a3e8e9828 */ + L(1.92431240212432926993057705062834160e-35), /* 3f8b99418859f18b37169a644fdb986c */ + +/* x = 3.28125000000000000000000000000000000e-01 3ffd5000000000000000000000000000 */ +/* cos(x) = 0.f2578a595224dd2e6bfa2eb2f99cc674f5ea6f479eae2eb580186897ae3f893df1113ca06b8 */ + L(9.46648260886053321846099507295532976e-01), /* 3ffee4af14b2a449ba5cd7f45d65f33a */ +L(-4.32906339663000890941529420498824645e-35), /* bf8ccc5850ac85c30a8e8a53ff3cbb43 */ +/* sin(x) = 0.5280326c3cf481823ba6bb08eac82c2093f2bce3c4eb4ee3dec7df41c92c8a4226098616075 */ + L(3.22268630433386625687745919893188031e-01), /* 3ffd4a00c9b0f3d20608ee9aec23ab21 */ +L(-1.49505897804759263483853908335500228e-35), /* bf8b3df6c0d431c3b14b11c213820be3 */ + +/* x = 3.35937500000000000000000000000000000e-01 3ffd5800000000000000000000000000 */ +/* cos(x) = 0.f1b0a5b406b526d886c55feadc8d0dcc8eb9ae2ac707051771b48e05b25b000009660bdb3e3 */ + L(9.44101673557004345630017691253124860e-01), /* 3ffee3614b680d6a4db10d8abfd5b91a */ + L(1.03812535240120229609822461172145584e-35), /* 3f8ab991d735c558e0e0a2ee3691c0b6 */ +/* sin(x) = 0.54643b3da29de9b357155eef0f332fb3e66c83bf4dddd9491c5eb8e103ccd92d6175220ed51 */ + L(3.29654409930860171914317725126463176e-01), /* 3ffd5190ecf68a77a6cd5c557bbc3ccd */ +L(-1.22606996784743214973082192294232854e-35), /* bf8b04c19937c40b22226b6e3a1471f0 */ + +/* x = 3.43750000000000000000000000000000000e-01 3ffd6000000000000000000000000000 */ +/* cos(x) = 0.f105fa4d66b607a67d44e042725204435142ac8ad54dfb0907a4f6b56b06d98ee60f19e557a */ + L(9.41497463127881068644511236053670815e-01), /* 3ffee20bf49acd6c0f4cfa89c084e4a4 */ + L(3.20709366603165602071590241054884900e-36), /* 3f8910d450ab22b5537ec241e93dad5b */ +/* sin(x) = 0.5646f27e8bd65cbe3a5d61ff06572290ee826d9674a00246b05ae26753cdfc90d9ce81a7d02 */ + L(3.37020069022253076261281754173810024e-01), /* 3ffd591bc9fa2f5972f8e97587fc195d */ +L(-2.21435756148839473677777545049890664e-35), /* bf8bd6f117d92698b5ffdb94fa51d98b */ + +/* x = 3.51562500000000000000000000000000000e-01 3ffd6800000000000000000000000000 */ +/* cos(x) = 0.f0578ad01ede707fa39c09dc6b984afef74f3dc8d0efb0f4c5a6b13771145b3e0446fe33887 */ + L(9.38835788546265488632578305984712554e-01), /* 3ffee0af15a03dbce0ff473813b8d731 */ +L(-3.98758068773974031348585072752245458e-35), /* bf8ca808458611b978827859d2ca7644 */ +/* sin(x) = 0.582850a41e1dd46c7f602ea244cdbbbfcdfa8f3189be794dda427ce090b5f85164f1f80ac13 */ + L(3.44365158145698408207172046472223747e-01), /* 3ffd60a14290787751b1fd80ba891337 */ +L(-3.19791885005480924937758467594051927e-36), /* bf89100c815c339d9061ac896f60c7dc */ + +/* x = 3.59375000000000000000000000000000000e-01 3ffd7000000000000000000000000000 */ +/* cos(x) = 0.efa559f5ec3aec3a4eb03319278a2d41fcf9189462261125fe6147b078f1daa0b06750a1654 */ + L(9.36116812267055290294237411019508588e-01), /* 3ffedf4ab3ebd875d8749d6066324f14 */ + L(3.40481591236710658435409862439032162e-35), /* 3f8c6a0fe7c8c4a31130892ff30a3d84 */ +/* sin(x) = 0.5a084e28e35fda2776dfdbbb5531d74ced2b5d17c0b1afc4647529d50c295e36d8ceec126c1 */ + L(3.51689228994814059222584896955547016e-01), /* 3ffd682138a38d7f689ddb7f6eed54c7 */ + L(1.75293433418270210567525412802083294e-35), /* 3f8b74ced2b5d17c0b1afc4647529d51 */ + +/* x = 3.67187500000000000000000000000000000e-01 3ffd7800000000000000000000000000 */ +/* cos(x) = 0.eeef6a879146af0bf9b95ea2ea0ac0d3e2e4d7e15d93f48cbd41bf8e4fded40bef69e19eafa */ + L(9.33340700242548435655299229469995527e-01), /* 3ffeddded50f228d5e17f372bd45d416 */ +L(-4.75255707251679831124800898831382223e-35), /* bf8cf960e8d940f513605b9a15f2038e */ +/* sin(x) = 0.5be6e38ce8095542bc14ee9da0d36483e6734bcab2e07624188af5653f114eeb46738fa899d */ + L(3.58991834546065053677710299152868941e-01), /* 3ffd6f9b8e33a025550af053ba76834e */ +L(-2.06772389262723368139416970257112089e-35), /* bf8bb7c198cb4354d1f89dbe7750a9ac */ + +/* x = 3.75000000000000000000000000000000000e-01 3ffd8000000000000000000000000000 */ +/* cos(x) = 0.ee35bf5ccac89052cd91ddb734d3a47e262e3b609db604e217053803be0091e76daf28a89b7 */ + L(9.30507621912314291149476792229555481e-01), /* 3ffedc6b7eb9959120a59b23bb6e69a7 */ + L(2.74541088551732982573335285685416092e-35), /* 3f8c23f13171db04edb02710b829c01e */ +/* sin(x) = 0.5dc40955d9084f48a94675a2498de5d851320ff5528a6afb3f2e24de240fce6cbed1ba0ccd6 */ + L(3.66272529086047561372909351716264177e-01), /* 3ffd7710255764213d22a519d6892638 */ +L(-1.96768433534936592675897818253108989e-35), /* bf8ba27aecdf00aad759504c0d1db21e */ + +/* x = 3.82812500000000000000000000000000000e-01 3ffd8800000000000000000000000000 */ +/* cos(x) = 0.ed785b5c44741b4493c56bcb9d338a151c6f6b85d8f8aca658b28572c162b199680eb9304da */ + L(9.27617750192851909628030798799961350e-01), /* 3ffedaf0b6b888e83689278ad7973a67 */ + L(7.58520371916345756281201167126854712e-36), /* 3f8a42a38ded70bb1f1594cb1650ae58 */ +/* sin(x) = 0.5f9fb80f21b53649c432540a50e22c53057ff42ae0fdf1307760dc0093f99c8efeb2fbd7073 */ + L(3.73530868238692946416839752660848112e-01), /* 3ffd7e7ee03c86d4d92710c950294389 */ +L(-1.48023494778986556048879113411517128e-35), /* bf8b3acfa800bd51f020ecf889f23ff7 */ + +/* x = 3.90625000000000000000000000000000000e-01 3ffd9000000000000000000000000000 */ +/* cos(x) = 0.ecb7417b8d4ee3fec37aba4073aa48f1f14666006fb431d9671303c8100d10190ec8179c41d */ + L(9.24671261467036098502113014560138771e-01), /* 3ffed96e82f71a9dc7fd86f57480e755 */ +L(-4.14187124860031825108649347251175815e-35), /* bf8cb87075cccffc825e7134c767e1bf */ +/* sin(x) = 0.6179e84a09a5258a40e9b5face03e525f8b5753cd0105d93fe6298010c3458e84d75fe420e9 */ + L(3.80766408992390192057200703388896675e-01), /* 3ffd85e7a1282694962903a6d7eb3810 */ +L(-2.02009541175208636336924533372496107e-35), /* bf8bada074a8ac32fefa26c019d67fef */ + +/* x = 3.98437500000000000000000000000000000e-01 3ffd9800000000000000000000000000 */ +/* cos(x) = 0.ebf274bf0bda4f62447e56a093626798d3013b5942b1abfd155aacc9dc5c6d0806a20d6b9c1 */ + L(9.21668335573351918175411368202712714e-01), /* 3ffed7e4e97e17b49ec488fcad4126c5 */ +L(-1.83587995433957622948710263541479322e-35), /* bf8b8672cfec4a6bd4e5402eaa553362 */ +/* sin(x) = 0.6352929dd264bd44a02ea766325d8aa8bd9695fc8def3caefba5b94c9a3c873f7b2d3776ead */ + L(3.87978709727025046051079690813741960e-01), /* 3ffd8d4a4a774992f51280ba9d98c976 */ + L(8.01904783870935075844443278617586301e-36), /* 3f8a5517b2d2bf91bde795df74b72993 */ + +/* x = 4.06250000000000000000000000000000000e-01 3ffda000000000000000000000000000 */ +/* cos(x) = 0.eb29f839f201fd13b93796827916a78f15c85230a4e8ea4b21558265a14367e1abb4c30695a */ + L(9.18609155794918267837824977718549863e-01), /* 3ffed653f073e403fa27726f2d04f22d */ + L(2.97608282778274433460057745798409849e-35), /* 3f8c3c78ae429185274752590aac132d */ +/* sin(x) = 0.6529afa7d51b129631ec197c0a840a11d7dc5368b0a47956feb285caa8371c4637ef17ef01b */ + L(3.95167330240934236244832640419653657e-01), /* 3ffd94a6be9f546c4a58c7b065f02a10 */ + L(7.57560031388312550940040194042627704e-36), /* 3f8a423afb8a6d16148f2adfd650b955 */ + +/* x = 4.14062500000000000000000000000000000e-01 3ffda800000000000000000000000000 */ +/* cos(x) = 0.ea5dcf0e30cf03e6976ef0b1ec26515fba47383855c3b4055a99b5e86824b2cd1a691fdca7b */ + L(9.15493908848301228563917732180221882e-01), /* 3ffed4bb9e1c619e07cd2edde163d84d */ +L(-3.50775517955306954815090901168305659e-35), /* bf8c75022dc63e3d51e25fd52b3250bd */ +/* sin(x) = 0.66ff380ba0144109e39a320b0a3fa5fd65ea0585bcbf9b1a769a9b0334576c658139e1a1cbe */ + L(4.02331831777773111217105598880982387e-01), /* 3ffd9bfce02e805104278e68c82c28ff */ +L(-1.95678722882848174723569916504871563e-35), /* bf8ba029a15fa7a434064e5896564fcd */ + +/* x = 4.21875000000000000000000000000000000e-01 3ffdb000000000000000000000000000 */ +/* cos(x) = 0.e98dfc6c6be031e60dd3089cbdd18a75b1f6b2c1e97f79225202f03dbea45b07a5ec4efc062 */ + L(9.12322784872117846492029542047341734e-01), /* 3ffed31bf8d8d7c063cc1ba611397ba3 */ + L(7.86903886556373674267948132178845568e-36), /* 3f8a4eb63ed6583d2fef244a405e07b8 */ +/* sin(x) = 0.68d32473143327973bc712bcc4ccddc47630d755850c0655243b205934dc49ffed8eb76adcb */ + L(4.09471777053295066122694027011452236e-01), /* 3ffda34c91cc50cc9e5cef1c4af31333 */ + L(2.23945241468457597921655785729821354e-35), /* 3f8bdc47630d755850c0655243b20593 */ + +/* x = 4.29687500000000000000000000000000000e-01 3ffdb800000000000000000000000000 */ +/* cos(x) = 0.e8ba8393eca7821aa563d83491b6101189b3b101c3677f73d7bad7c10f9ee02b7ab4009739a */ + L(9.09095977415431051650381735684476417e-01), /* 3ffed1750727d94f04354ac7b069236c */ + L(1.20886014028444155733776025085677953e-35), /* 3f8b01189b3b101c3677f73d7bad7c11 */ +/* sin(x) = 0.6aa56d8e8249db4eb60a761fe3f9e559be456b9e13349ca99b0bfb787f22b95db3b70179615 */ + L(4.16586730282041119259112448831069657e-01), /* 3ffdaa95b63a09276d3ad829d87f8fe8 */ +L(-2.00488106831998813675438269796963612e-35), /* bf8baa641ba9461eccb635664f404878 */ + +/* x = 4.37500000000000000000000000000000000e-01 3ffdc000000000000000000000000000 */ +/* cos(x) = 0.e7e367d2956cfb16b6aa11e5419cd0057f5c132a6455bf064297e6a76fe2b72bb630d6d50ff */ + L(9.05813683425936420744516660652700258e-01), /* 3ffecfc6cfa52ad9f62d6d5423ca833a */ +L(-3.60950307605941169775676563004467163e-35), /* bf8c7fd4051f66acdd5207cdeb40cac5 */ +/* sin(x) = 0.6c760c14c8585a51dbd34660ae6c52ac7036a0b40887a0b63724f8b4414348c3063a637f457 */ + L(4.23676257203938010361683988031102480e-01), /* 3ffdb1d83053216169476f4d1982b9b1 */ + L(1.40484456388654470329473096579312595e-35), /* 3f8b2ac7036a0b40887a0b63724f8b44 */ + +/* x = 4.45312500000000000000000000000000000e-01 3ffdc800000000000000000000000000 */ +/* cos(x) = 0.e708ac84d4172a3e2737662213429e14021074d7e702e77d72a8f1101a7e70410df8273e9aa */ + L(9.02476103237941504925183272675895999e-01), /* 3ffece115909a82e547c4e6ecc442685 */ + L(2.26282899501344419018306295680210602e-35), /* 3f8be14021074d7e702e77d72a8f1102 */ +/* sin(x) = 0.6e44f8c36eb10a1c752d093c00f4d47ba446ac4c215d26b0316442f168459e677d06e7249e3 */ + L(4.30739925110803197216321517850849190e-01), /* 3ffdb913e30dbac42871d4b424f003d3 */ + L(1.54096780001629398850891218396761548e-35), /* 3f8b47ba446ac4c215d26b0316442f17 */ + +/* x = 4.53125000000000000000000000000000000e-01 3ffdd000000000000000000000000000 */ +/* cos(x) = 0.e62a551594b970a770b15d41d4c0e483e47aca550111df6966f9e7ac3a94ae49e6a71eb031e */ + L(8.99083440560138456216544929209379307e-01), /* 3ffecc54aa2b2972e14ee162ba83a982 */ +L(-2.06772615490904370666670275154751976e-35), /* bf8bb7c1b8535aafeee209699061853c */ +/* sin(x) = 0.70122c5ec5028c8cff33abf4fd340ccc382e038379b09cf04f9a52692b10b72586060cbb001 */ + L(4.37777302872755132861618974702796680e-01), /* 3ffdc048b17b140a3233fcceafd3f4d0 */ + L(9.62794364503442612477117426033922467e-36), /* 3f8a998705c0706f36139e09f34a4d25 */ + +/* x = 4.60937500000000000000000000000000000e-01 3ffdd800000000000000000000000000 */ +/* cos(x) = 0.e54864fe33e8575cabf5bd0e5cf1b1a8bc7c0d5f61702450fa6b6539735820dd2603ae355d5 */ + L(8.95635902463170698900570000446256350e-01), /* 3ffeca90c9fc67d0aeb957eb7a1cb9e3 */ + L(3.73593741659866883088620495542311808e-35), /* 3f8c8d45e3e06afb0b812287d35b29cc */ +/* sin(x) = 0.71dd9fb1ff4677853acb970a9f6729c6e3aac247b1c57cea66c77413f1f98e8b9e98e49d851 */ + L(4.44787960964527211433056012529525211e-01), /* 3ffdc7767ec7fd19de14eb2e5c2a7d9d */ +L(-1.67187936511493678007508371613954899e-35), /* bf8b6391c553db84e3a831599388bec1 */ + +/* x = 4.68750000000000000000000000000000000e-01 3ffde000000000000000000000000000 */ +/* cos(x) = 0.e462dfc670d421ab3d1a15901228f146a0547011202bf5ab01f914431859aef577966bc4fa4 */ + L(8.92133699366994404723900253723788575e-01), /* 3ffec8c5bf8ce1a843567a342b202452 */ +L(-1.10771937602567314732693079264692504e-35), /* bf8ad72bf571fddbfa814a9fc0dd779d */ +/* sin(x) = 0.73a74b8f52947b681baf6928eb3fb021769bf4779bad0e3aa9b1cdb75ec60aad9fc63ff19d5 */ + L(4.51771471491683776581688750134062870e-01), /* 3ffdce9d2e3d4a51eda06ebda4a3acff */ +L(-1.19387223016472295893794387275284505e-35), /* bf8afbd12c81710c8a5e38aac9c64914 */ + +/* x = 4.76562500000000000000000000000000000e-01 3ffde800000000000000000000000000 */ +/* cos(x) = 0.e379c9045f29d517c4808aa497c2057b2b3d109e76c0dc302d4d0698b36e3f0bdbf33d8e952 */ + L(8.88577045028035543317609023116020980e-01), /* 3ffec6f39208be53aa2f890115492f84 */ + L(4.12354278954664731443813655177022170e-36), /* 3f895ecacf44279db0370c0b5341a62d */ +/* sin(x) = 0.756f28d011d98528a44a75fc29c779bd734ecdfb582fdb74b68a4c4c4be54cfd0b2d3ad292f */ + L(4.58727408216736592377295028972874773e-01), /* 3ffdd5bca340476614a29129d7f0a71e */ +L(-4.70946994194182908929251719575431779e-36), /* bf8990a32c4c8129f40922d25d6ceced */ + +/* x = 4.84375000000000000000000000000000000e-01 3ffdf000000000000000000000000000 */ +/* cos(x) = 0.e28d245c58baef72225e232abc003c4366acd9eb4fc2808c2ab7fe7676cf512ac7f945ae5fb */ + L(8.84966156526143291697296536966647926e-01), /* 3ffec51a48b8b175dee444bc46557800 */ + L(4.53370570288325630442037826313462165e-35), /* 3f8ce21b3566cf5a7e14046155bff3b4 */ +/* sin(x) = 0.77353054ca72690d4c6e171fd99e6b39fa8e1ede5f052fd2964534c75340970a3a9cd3c5c32 */ + L(4.65655346585160182681199512507546779e-01), /* 3ffddcd4c15329c9a43531b85c7f667a */ +L(-1.56282598978971872478619772155305961e-35), /* bf8b4c60571e121a0fad02d69bacb38b */ + +/* x = 4.92187500000000000000000000000000000e-01 3ffdf800000000000000000000000000 */ +/* cos(x) = 0.e19cf580eeec046aa1422fa74807ecefb2a1911c94e7b5f20a00f70022d940193691e5bd790 */ + L(8.81301254251340599140161908298100173e-01), /* 3ffec339eb01ddd808d542845f4e9010 */ +L(-1.43419192312116687783945619009629445e-35), /* bf8b3104d5e6ee36b184a0df5ff08ffe */ +/* sin(x) = 0.78f95b0560a9a3bd6df7bd981dc38c61224d08bc20631ea932e605e53b579e9e0767dfcbbcb */ + L(4.72554863751304451146551317808516942e-01), /* 3ffde3e56c1582a68ef5b7def660770e */ + L(9.31324774957768018850224267625371204e-36), /* 3f8a8c2449a117840c63d5265cc0bca7 */ + +/* x = 5.00000000000000000000000000000000000e-01 3ffe0000000000000000000000000000 */ +/* cos(x) = 0.e0a94032dbea7cedbddd9da2fafad98556566b3a89f43eabd72350af3e8b19e801204d8fe2e */ + L(8.77582561890372716116281582603829681e-01), /* 3ffec1528065b7d4f9db7bbb3b45f5f6 */ +L(-2.89484960181363924855192538540698851e-35), /* bf8c33d54d4ca62bb05e0aa146e57a86 */ +/* sin(x) = 0.7abba1d12c17bfa1d92f0d93f60ded9992f45b4fcaf13cd58b303693d2a0db47db35ae8a3a9 */ + L(4.79425538604203000273287935215571402e-01), /* 3ffdeaee8744b05efe8764bc364fd838 */ +L(-1.38426977616718318950175848639381926e-35), /* bf8b2666d0ba4b0350ec32a74cfc96c3 */ + +/* x = 5.07812500000000000000000000000000000e-01 3ffe0400000000000000000000000000 */ +/* cos(x) = 0.dfb20840f3a9b36f7ae2c515342890b5ec583b8366cc2b55029e95094d31112383f2553498b */ + L(8.73810306413054508282556837071377159e-01), /* 3ffebf641081e75366def5c58a2a6851 */ + L(1.25716864497849302237218128599994785e-35), /* 3f8b0b5ec583b8366cc2b55029e95095 */ +/* sin(x) = 0.7c7bfdaf13e5ed17212f8a7525bfb113aba6c0741b5362bb8d59282a850b63716bca0c910f0 */ + L(4.86266951793275574311011306895834993e-01), /* 3ffdf1eff6bc4f97b45c84be29d496ff */ +L(-1.12269393250914752644352376448094271e-35), /* bf8add8a8b27f17c9593a88e54dafaaf */ + +/* x = 5.15625000000000000000000000000000000e-01 3ffe0800000000000000000000000000 */ +/* cos(x) = 0.deb7518814a7a931bbcc88c109cd41c50bf8bb48f20ae8c36628d1d3d57574f7dc58f27d91c */ + L(8.69984718058417388828915599901466243e-01), /* 3ffebd6ea310294f526377991182139b */ +L(-4.68168638300575626782741319792183837e-35), /* bf8cf1d7a03a25b86fa8b9e4ceb97161 */ +/* sin(x) = 0.7e3a679daaf25c676542bcb4028d0964172961c921823a4ef0c3a9070d886dbd073f6283699 */ + L(4.93078685753923057265136552753487121e-01), /* 3ffdf8e99e76abc9719d950af2d00a34 */ + L(7.06498693112535056352301101088624950e-36), /* 3f8a2c82e52c3924304749de187520e2 */ + +/* x = 5.23437500000000000000000000000000000e-01 3ffe0c00000000000000000000000000 */ +/* cos(x) = 0.ddb91ff318799172bd2452d0a3889f5169c64a0094bcf0b8aa7dcf0d7640a2eba68955a80be */ + L(8.66106030320656714696616831654267220e-01), /* 3ffebb723fe630f322e57a48a5a14711 */ + L(2.35610597588322493119667003904687628e-35), /* 3f8bf5169c64a0094bcf0b8aa7dcf0d7 */ +/* sin(x) = 0.7ff6d8a34bd5e8fa54c97482db5159df1f24e8038419c0b448b9eea8939b5d4dfcf40900257 */ + L(4.99860324733013463819556536946425724e-01), /* 3ffdffdb628d2f57a3e95325d20b6d45 */ + L(1.94636052312235297538564591686645139e-35), /* 3f8b9df1f24e8038419c0b448b9eea89 */ + +/* x = 5.31250000000000000000000000000000000e-01 3ffe1000000000000000000000000000 */ +/* cos(x) = 0.dcb7777ac420705168f31e3eb780ce9c939ecada62843b54522f5407eb7f21e556059fcd734 */ + L(8.62174479934880504367162510253324274e-01), /* 3ffeb96eeef58840e0a2d1e63c7d6f02 */ +L(-3.71556818317533582234562471835771823e-35), /* bf8c8b1b6309a92cebde255d6e855fc1 */ +/* sin(x) = 0.81b149ce34caa5a4e650f8d09fd4d6aa74206c32ca951a93074c83b2d294d25dbb0f7fdfad2 */ + L(5.06611454814257367642296000893867192e-01), /* 3ffe0362939c69954b49cca1f1a13faa */ +L(-3.10963699824274155702706043065967062e-35), /* bf8c4aac5efc9e69ab572b67c59be269 */ + +/* x = 5.39062500000000000000000000000000000e-01 3ffe1400000000000000000000000000 */ +/* cos(x) = 0.dbb25c25b8260c14f6e7bc98ec991b70c65335198b0ab628bad20cc7b229d4dd62183cfa055 */ + L(8.58190306862660347046629564970494649e-01), /* 3ffeb764b84b704c1829edcf7931d932 */ + L(2.06439574601190798155563653000684861e-35), /* 3f8bb70c65335198b0ab628bad20cc7b */ +/* sin(x) = 0.8369b434a372da7eb5c8a71fe36ce1e0b2b493f6f5cb2e38bcaec2a556b3678c401940d1c3c */ + L(5.13331663943471218288801270215706878e-01), /* 3ffe06d3686946e5b4fd6b914e3fc6da */ +L(-2.26614796466671970772244932848067224e-35), /* bf8be1f4d4b6c090a34d1c743513d5ab */ + +/* x = 5.46875000000000000000000000000000000e-01 3ffe1800000000000000000000000000 */ +/* cos(x) = 0.daa9d20860827063fde51c09e855e9932e1b17143e7244fd267a899d41ae1f3bc6a0ec42e27 */ + L(8.54153754277385385143451785105103176e-01), /* 3ffeb553a410c104e0c7fbca3813d0ac */ +L(-1.68707534013095152873222061722573172e-35), /* bf8b66cd1e4e8ebc18dbb02d9857662c */ +/* sin(x) = 0.852010f4f0800521378bd8dd614753d080c2e9e0775ffc609947b9132f5357404f464f06a58 */ + L(5.20020541953727004760213699874674730e-01), /* 3ffe0a4021e9e1000a426f17b1bac28f */ +L(-3.32415021330884924833711842866896734e-35), /* bf8c617bf9e8b0fc45001cfb35c23767 */ + +/* x = 5.54687500000000000000000000000000000e-01 3ffe1c00000000000000000000000000 */ +/* cos(x) = 0.d99ddd44e44a43d4d4a3a3ed95204106fd54d78e8c7684545c0da0b7c2c72be7a89b7c182ad */ + L(8.50065068549420263957072899177793617e-01), /* 3ffeb33bba89c89487a9a94747db2a41 */ +L(-4.73753917078785974356016104842568442e-35), /* bf8cf7c81559438b9c4bdd5d1f92fa42 */ +/* sin(x) = 0.86d45935ab396cb4e421e822dee54f3562dfcefeaa782184c23401d231f5ad981a1cc195b18 */ + L(5.26677680590386730710789410624833901e-01), /* 3ffe0da8b26b5672d969c843d045bdcb */ +L(-3.67066148195515214077582496518566735e-35), /* bf8c8654e901880aac3ef3d9ee5ff16e */ + +/* x = 5.62500000000000000000000000000000000e-01 3ffe2000000000000000000000000000 */ +/* cos(x) = 0.d88e820b1526311dd561efbc0c1a9a5375eb26f65d246c5744b13ca26a7e0fd42556da843c8 */ + L(8.45924499231067954459723078597493262e-01), /* 3ffeb11d04162a4c623baac3df781835 */ + L(1.98054947141989878179164342925274053e-35), /* 3f8ba5375eb26f65d246c5744b13ca27 */ +/* sin(x) = 0.88868625b4e1dbb2313310133022527200c143a5cb16637cb7daf8ade82459ff2e98511f40f */ + L(5.33302673536020173329131103308161529e-01), /* 3ffe110d0c4b69c3b764626620266045 */ +L(-3.42715291319551615996993795226755157e-35), /* bf8c6c6ff9f5e2d1a74ce41a41283a91 */ + +/* x = 5.70312500000000000000000000000000000e-01 3ffe2400000000000000000000000000 */ +/* cos(x) = 0.d77bc4985e93a607c9d868b906bbc6bbe3a04258814acb0358468b826fc91bd4d814827f65e */ + L(8.41732299041338366963111794309701085e-01), /* 3ffeaef78930bd274c0f93b0d1720d78 */ +L(-4.30821936750410026005408345400225948e-35), /* bf8cca20e2fded3bf5a9a7e53dcba3ed */ +/* sin(x) = 0.8a3690fc5bfc11bf9535e2739a8512f448a41251514bbed7fc18d530f9b4650fcbb2861b0aa */ + L(5.39895116435204405041660709903993340e-01), /* 3ffe146d21f8b7f8237f2a6bc4e7350a */ + L(1.42595803521626714477253741404712093e-35), /* 3f8b2f448a41251514bbed7fc18d5310 */ + +/* x = 5.78125000000000000000000000000000000e-01 3ffe2800000000000000000000000000 */ +/* cos(x) = 0.d665a937b4ef2b1f6d51bad6d988a4419c1d7051faf31a9efa151d7631117efac03713f950a */ + L(8.37488723850523685315353348917240617e-01), /* 3ffeaccb526f69de563edaa375adb311 */ + L(2.72761997872084533045777718677326179e-35), /* 3f8c220ce0eb828fd798d4f7d0a8ebb2 */ +/* sin(x) = 0.8be472f9776d809af2b88171243d63d66dfceeeb739cc894e023fbc165a0e3f26ff729c5d57 */ + L(5.46454606919203564403349553749411001e-01), /* 3ffe17c8e5f2eedb0135e57102e2487b */ +L(-2.11870230730160315420936523771864858e-35), /* bf8bc29920311148c63376b1fdc043ea */ + +/* x = 5.85937500000000000000000000000000000e-01 3ffe2c00000000000000000000000000 */ +/* cos(x) = 0.d54c3441844897fc8f853f0655f1ba695eba9fbfd7439dbb1171d862d9d9146ca5136f825ac */ + L(8.33194032664581363070224042208032321e-01), /* 3ffeaa98688308912ff91f0a7e0cabe3 */ + L(4.39440050052045486567668031751259899e-35), /* 3f8cd34af5d4fdfeba1cedd88b8ec317 */ +/* sin(x) = 0.8d902565817ee7839bce3cd128060119492cd36d42d82ada30d7f8bde91324808377ddbf5d4 */ + L(5.52980744630527369849695082681623667e-01), /* 3ffe1b204acb02fdcf07379c79a2500c */ + L(8.26624790417342895897164123189984127e-37), /* 3f8719492cd36d42d82ada30d7f8bde9 */ + +/* x = 5.93750000000000000000000000000000000e-01 3ffe3000000000000000000000000000 */ +/* cos(x) = 0.d42f6a1b9f0168cdf031c2f63c8d9304d86f8d34cb1d5fccb68ca0f2241427fc18d1fd5bbdf */ + L(8.28848487609325734810171790119116638e-01), /* 3ffea85ed4373e02d19be06385ec791b */ + L(1.43082508100496581719048175506239770e-35), /* 3f8b304d86f8d34cb1d5fccb68ca0f22 */ +/* sin(x) = 0.8f39a191b2ba6122a3fa4f41d5a3ffd421417d46f19a22230a14f7fcc8fce5c75b4b28b29d1 */ + L(5.59473131247366877384844006003116688e-01), /* 3ffe1e7343236574c24547f49e83ab48 */ +L(-1.28922620524163922306886952100992796e-37), /* bf845ef5f415c8732eeee7af584019b8 */ + +/* x = 6.01562500000000000000000000000000000e-01 3ffe3400000000000000000000000000 */ +/* cos(x) = 0.d30f4f392c357ab0661c5fa8a7d9b26627846fef214b1d19a22379ff9eddba087cf410eb097 */ + L(8.24452353914429207485643598212356053e-01), /* 3ffea61e9e72586af560cc38bf514fb3 */ + L(3.79160239225080026987031418939026741e-35), /* 3f8c93313c237f790a58e8cd111bcffd */ +/* sin(x) = 0.90e0e0d81ca678796cc92c8ea8c2815bc72ca78abe571bfa8576aacc571e096a33237e0e830 */ + L(5.65931370507905990773159095689276114e-01), /* 3ffe21c1c1b0394cf0f2d992591d5185 */ + L(1.02202775968053982310991962521535027e-36), /* 3f875bc72ca78abe571bfa8576aacc57 */ + +/* x = 6.09375000000000000000000000000000000e-01 3ffe3800000000000000000000000000 */ +/* cos(x) = 0.d1ebe81a95ee752e48a26bcd32d6e922d7eb44b8ad2232f6930795e84b56317269b9dd1dfa6 */ + L(8.20005899897234008255550633876556043e-01), /* 3ffea3d7d0352bdcea5c9144d79a65ae */ +L(-1.72008811955230823416724332297991247e-35), /* bf8b6dd2814bb4752ddcd096cf86a17b */ +/* sin(x) = 0.9285dc9bc45dd9ea3d02457bcce59c4175aab6ff7929a8d287195525fdace200dba032874fb */ + L(5.72355068234507240384953706824503608e-01), /* 3ffe250bb93788bbb3d47a048af799cb */ + L(2.12572273479933123944580199464514529e-35), /* 3f8bc4175aab6ff7929a8d2871955260 */ + +/* x = 6.17187500000000000000000000000000000e-01 3ffe3c00000000000000000000000000 */ +/* cos(x) = 0.d0c5394d772228195e25736c03574707de0af1ca344b13bd3914bfe27518e9e426f5deff1e1 */ + L(8.15509396946375476876345384201386217e-01), /* 3ffea18a729aee445032bc4ae6d806af */ +L(-4.28589138410712954051679139949341961e-35), /* bf8cc7c10fa871ae5da76216375a00ec */ +/* sin(x) = 0.94288e48bd0335fc41c4cbd2920497a8f5d1d8185c99fa0081f90c27e2a53ffdd208a0dbe69 */ + L(5.78743832357770354521111378581385347e-01), /* 3ffe28511c917a066bf8838997a52409 */ + L(1.77998063432551282609698670002456093e-35), /* 3f8b7a8f5d1d8185c99fa0081f90c27e */ + +/* x = 6.25000000000000000000000000000000000e-01 3ffe4000000000000000000000000000 */ +/* cos(x) = 0.cf9b476c897c25c5bfe750dd3f308eaf7bcc1ed00179a256870f4200445043dcdb1974b5878 */ + L(8.10963119505217902189534803941080724e-01), /* 3ffe9f368ed912f84b8b7fcea1ba7e61 */ + L(1.10481292856794436426051402418804358e-35), /* 3f8ad5ef7983da002f344ad0e1e84009 */ +/* sin(x) = 0.95c8ef544210ec0b91c49bd2aa09e8515fa61a156ebb10f5f8c232a6445b61ebf3c2ec268f9 */ + L(5.85097272940462154805399314150080459e-01), /* 3ffe2b91dea88421d817238937a55414 */ +L(-1.78164576278056195136525335403380464e-35), /* bf8b7aea059e5ea9144ef0a073dcd59c */ + +/* x = 6.32812500000000000000000000000000000e-01 3ffe4400000000000000000000000000 */ +/* cos(x) = 0.ce6e171f92f2e27f32225327ec440ddaefae248413efc0e58ceee1ae369aabe73f88c87ed1a */ + L(8.06367345055103913698795406077297399e-01), /* 3ffe9cdc2e3f25e5c4fe6444a64fd888 */ + L(1.04235088143133625463876245029180850e-35), /* 3f8abb5df5c490827df81cb19ddc35c7 */ +/* sin(x) = 0.9766f93cd18413a6aafc1cfc6fc28abb6817bf94ce349901ae3f48c3215d3eb60acc5f78903 */ + L(5.91415002201316315087000225758031236e-01), /* 3ffe2ecdf279a308274d55f839f8df85 */ + L(8.07390238063560077355762466502569603e-36), /* 3f8a576d02f7f299c6932035c7e91864 */ + +/* x = 6.40625000000000000000000000000000000e-01 3ffe4800000000000000000000000000 */ +/* cos(x) = 0.cd3dad1b5328a2e459f993f4f5108819faccbc4eeba9604e81c7adad51cc8a2561631a06826 */ + L(8.01722354098418450607492605652964208e-01), /* 3ffe9a7b5a36a65145c8b3f327e9ea21 */ + L(6.09487851305233089325627939458963741e-36), /* 3f8a033f599789dd752c09d038f5b5aa */ +/* sin(x) = 0.9902a58a45e27bed68412b426b675ed503f54d14c8172e0d373f42cadf04daf67319a7f94be */ + L(5.97696634538701531238647618967334337e-01), /* 3ffe32054b148bc4f7dad0825684d6cf */ +L(-2.49527608940873714527427941350461554e-35), /* bf8c0957e0559759bf468f964605e9a9 */ + +/* x = 6.48437500000000000000000000000000000e-01 3ffe4c00000000000000000000000000 */ +/* cos(x) = 0.cc0a0e21709883a3ff00911e11a07ee3bd7ea2b04e081be99be0264791170761ae64b8b744a */ + L(7.97028430141468342004642741431945296e-01), /* 3ffe98141c42e1310747fe01223c2341 */ +L(-8.35364432831812599727083251866305534e-37), /* bf871c42815d4fb1f7e416641fd9b86f */ +/* sin(x) = 0.9a9bedcdf01b38d993f3d7820781de292033ead73b89e28f39313dbe3a6e463f845b5fa8490 */ + L(6.03941786554156657267270287527367726e-01), /* 3ffe3537db9be03671b327e7af040f04 */ +L(-2.54578992328947177770363936132309779e-35), /* bf8c0eb6fe60a94623b0eb863676120e */ + +/* x = 6.56250000000000000000000000000000000e-01 3ffe5000000000000000000000000000 */ +/* cos(x) = 0.cad33f00658fe5e8204bbc0f3a66a0e6a773f87987a780b243d7be83b3db1448ca0e0e62787 */ + L(7.92285859677178543141501323781709399e-01), /* 3ffe95a67e00cb1fcbd04097781e74cd */ + L(2.47519558228473167879248891673807645e-35), /* 3f8c07353b9fc3cc3d3c05921ebdf41e */ +/* sin(x) = 0.9c32cba2b14156ef05256c4f857991ca6a547cd7ceb1ac8a8e62a282bd7b9183648a462bd04 */ + L(6.10150077075791371273742393566183220e-01), /* 3ffe386597456282adde0a4ad89f0af3 */ + L(1.33842237929938963780969418369150532e-35), /* 3f8b1ca6a547cd7ceb1ac8a8e62a282c */ + +/* x = 6.64062500000000000000000000000000000e-01 3ffe5400000000000000000000000000 */ +/* cos(x) = 0.c99944936cf48c8911ff93fe64b3ddb7981e414bdaf6aae1203577de44878c62bc3bc9cf7b9 */ + L(7.87494932167606083931328295965533034e-01), /* 3ffe93328926d9e9191223ff27fcc968 */ +L(-2.57915385618070637156514241185180920e-35), /* bf8c12433f0df5a1284aa8f6fe54410e */ +/* sin(x) = 0.9dc738ad14204e689ac582d0f85826590feece34886cfefe2e08cf2bb8488d55424dc9d3525 */ + L(6.16321127181550943005700433761731837e-01), /* 3ffe3b8e715a28409cd1358b05a1f0b0 */ + L(2.88497530050197716298085892460478666e-35), /* 3f8c32c87f7671a44367f7f17046795e */ + +/* x = 6.71875000000000000000000000000000000e-01 3ffe5800000000000000000000000000 */ +/* cos(x) = 0.c85c23c26ed7b6f014ef546c47929682122876bfbf157de0aff3c4247d820c746e32cd4174f */ + L(7.82655940026272796930787447428139026e-01), /* 3ffe90b84784ddaf6de029dea8d88f25 */ + L(1.69332045679237919427807771288506254e-35), /* 3f8b682122876bfbf157de0aff3c4248 */ +/* sin(x) = 0.9f592e9b66a9cf906a3c7aa3c10199849040c45ec3f0a747597311038101780c5f266059dbf */ + L(6.22454560222343683041926705090443330e-01), /* 3ffe3eb25d36cd539f20d478f5478203 */ + L(1.91974786921147072717621236192269859e-35), /* 3f8b9849040c45ec3f0a747597311038 */ + +/* x = 6.79687500000000000000000000000000000e-01 3ffe5c00000000000000000000000000 */ +/* cos(x) = 0.c71be181ecd6875ce2da5615a03cca207d9adcb9dfb0a1d6c40a4f0056437f1a59ccddd06ee */ + L(7.77769178600317903122203513685412863e-01), /* 3ffe8e37c303d9ad0eb9c5b4ac2b407a */ +L(-4.05296033424632846931240580239929672e-35), /* bf8caefc13291a31027af149dfad87fd */ +/* sin(x) = 0.a0e8a725d33c828c11fa50fd9e9a15ffecfad43f3e534358076b9b0f6865694842b1e8c67dc */ + L(6.28550001845029662028004327939032867e-01), /* 3ffe41d14e4ba679051823f4a1fb3d34 */ + L(1.65507421184028099672784511397428852e-35), /* 3f8b5ffecfad43f3e534358076b9b0f7 */ + +/* x = 6.87500000000000000000000000000000000e-01 3ffe6000000000000000000000000000 */ +/* cos(x) = 0.c5d882d2ee48030c7c07d28e981e34804f82ed4cf93655d2365389b716de6ad44676a1cc5da */ + L(7.72834946152471544810851845913425178e-01), /* 3ffe8bb105a5dc900618f80fa51d303c */ + L(3.94975229341211664237241534741146939e-35), /* 3f8ca4027c176a67c9b2ae91b29c4db9 */ +/* sin(x) = 0.a2759c0e79c35582527c32b55f5405c182c66160cb1d9eb7bb0b7cdf4ad66f317bda4332914 */ + L(6.34607080015269296850309914203671436e-01), /* 3ffe44eb381cf386ab04a4f8656abea8 */ + L(4.33025916939968369326060156455927002e-36), /* 3f897060b1985832c767adeec2df37d3 */ + +/* x = 6.95312500000000000000000000000000000e-01 3ffe6400000000000000000000000000 */ +/* cos(x) = 0.c4920cc2ec38fb891b38827db08884fc66371ac4c2052ca8885b981bbcfd3bb7b093ee31515 */ + L(7.67853543842850365879920759114193964e-01), /* 3ffe89241985d871f712367104fb6111 */ + L(3.75100035267325597157244776081706979e-36), /* 3f893f198dc6b130814b2a2216e606ef */ +/* sin(x) = 0.a400072188acf49cd6b173825e038346f105e1301afe642bcc364cea455e21e506e3e927ed8 */ + L(6.40625425040230409188409779413961021e-01), /* 3ffe48000e431159e939ad62e704bc07 */ + L(2.46542747294664049615806500747173281e-36), /* 3f88a37882f0980d7f3215e61b267523 */ + +/* x = 7.03125000000000000000000000000000000e-01 3ffe6800000000000000000000000000 */ +/* cos(x) = 0.c348846bbd3631338ffe2bfe9dd1381a35b4e9c0c51b4c13fe376bad1bf5caacc4542be0aa9 */ + L(7.62825275710576250507098753625429792e-01), /* 3ffe869108d77a6c62671ffc57fd3ba2 */ + L(4.22067411888601505004748939382325080e-35), /* 3f8cc0d1ada74e0628da609ff1bb5d69 */ +/* sin(x) = 0.a587e23555bb08086d02b9c662cdd29316c3e9bd08d93793634a21b1810cce73bdb97a99b9e */ + L(6.46604669591152370524042159882800763e-01), /* 3ffe4b0fc46aab761010da05738cc59c */ +L(-3.41742981816219412415674365946079826e-35), /* bf8c6b6749e0b217b9364364e5aef274 */ + +/* x = 7.10937500000000000000000000000000000e-01 3ffe6c00000000000000000000000000 */ +/* cos(x) = 0.c1fbeef380e4ffdd5a613ec8722f643ffe814ec2343e53adb549627224fdc9f2a7b77d3d69f */ + L(7.57750448655219342240234832230493361e-01), /* 3ffe83f7dde701c9ffbab4c27d90e45f */ +L(-2.08767968311222650582659938787920125e-35), /* bf8bbc0017eb13dcbc1ac524ab69d8de */ +/* sin(x) = 0.a70d272a76a8d4b6da0ec90712bb748b96dabf88c3079246f3db7eea6e58ead4ed0e2843303 */ + L(6.52544448725765956407573982284767763e-01), /* 3ffe4e1a4e54ed51a96db41d920e2577 */ +L(-8.61758060284379660697102362141557170e-36), /* bf8a6e8d24a80ee79f0db721849022b2 */ + +/* x = 7.18750000000000000000000000000000000e-01 3ffe7000000000000000000000000000 */ +/* cos(x) = 0.c0ac518c8b6ae710ba37a3eeb90cb15aebcb8bed4356fb507a48a6e97de9aa6d9660116b436 */ + L(7.52629372418066476054541324847143116e-01), /* 3ffe8158a31916d5ce21746f47dd7219 */ + L(3.71306958657663189665450864311104571e-35), /* 3f8c8ad75e5c5f6a1ab7da83d245374c */ +/* sin(x) = 0.a88fcfebd9a8dd47e2f3c76ef9e2439920f7e7fbe735f8bcc985491ec6f12a2d4214f8cfa99 */ + L(6.58444399910567541589583954884041989e-01), /* 3ffe511f9fd7b351ba8fc5e78eddf3c5 */ +L(-4.54412944084300330523721391865787219e-35), /* bf8ce336f840c020c6503a19b3d5b70a */ + +/* x = 7.26562500000000000000000000000000000e-01 3ffe7400000000000000000000000000 */ +/* cos(x) = 0.bf59b17550a4406875969296567cf3e3b4e483061877c02811c6cae85fad5a6c3da58f49292 */ + L(7.47462359563216166669700384714767552e-01), /* 3ffe7eb362eaa14880d0eb2d252cacfa */ +L(-9.11094340926220027288083639048016945e-36), /* bf8a8389636f9f3cf107fafdc726a2f4 */ +/* sin(x) = 0.aa0fd66eddb921232c28520d3911b8a03193b47f187f1471ac216fbcd5bb81029294d3a73f1 */ + L(6.64304163042946276515506587432846246e-01), /* 3ffe541facddbb7242465850a41a7223 */ + L(4.26004843895378210155889028714676019e-35), /* 3f8cc5018c9da3f8c3f8a38d610b7de7 */ + +/* x = 7.34375000000000000000000000000000000e-01 3ffe7800000000000000000000000000 */ +/* cos(x) = 0.be0413f84f2a771c614946a88cbf4da1d75a5560243de8f2283fefa0ea4a48468a52d51d8b3 */ + L(7.42249725458501306991347253449610537e-01), /* 3ffe7c0827f09e54ee38c2928d51197f */ +L(-3.78925270049800913539923473871287550e-35), /* bf8c92f1452d54fede10b86ebe0082f9 */ +/* sin(x) = 0.ab8d34b36acd987210ed343ec65d7e3adc2e7109fce43d55c8d57dfdf55b9e01d2cc1f1b9ec */ + L(6.70123380473162894654531583500648495e-01), /* 3ffe571a6966d59b30e421da687d8cbb */ +L(-1.33165852952743729897634069393684656e-36), /* bf87c523d18ef6031bc2aa372a82020b */ + +/* x = 7.42187500000000000000000000000000000e-01 3ffe7c00000000000000000000000000 */ +/* cos(x) = 0.bcab7e6bfb2a14a9b122c574a376bec98ab14808c64a4e731b34047e217611013ac99c0f25d */ + L(7.36991788256240741057089385586450844e-01), /* 3ffe7956fcd7f654295362458ae946ed */ + L(4.72358938637974850573747497460125519e-35), /* 3f8cf64c558a404632527398d9a023f1 */ +/* sin(x) = 0.ad07e4c409d08c4fa3a9057bb0ac24b8636e74e76f51e09bd6b2319707cbd9f5e254643897a */ + L(6.75901697026178809189642203142423973e-01), /* 3ffe5a0fc98813a1189f47520af76158 */ + L(2.76252586616364878801928456702948857e-35), /* 3f8c25c31b73a73b7a8f04deb5918cb8 */ + +/* x = 7.50000000000000000000000000000000000e-01 3ffe8000000000000000000000000000 */ +/* cos(x) = 0.bb4ff632a908f73ec151839cb9d993b4e0bfb8f20e7e44e6e4aee845e35575c3106dbe6fd06 */ + L(7.31688868873820886311838753000084529e-01), /* 3ffe769fec655211ee7d82a3073973b3 */ + L(1.48255637548931697184991710293198620e-35), /* 3f8b3b4e0bfb8f20e7e44e6e4aee845e */ +/* sin(x) = 0.ae7fe0b5fc786b2d966e1d6af140a488476747c2646425fc7533f532cd044cb10a971a49a6a */ + L(6.81638760023334166733241952779893908e-01), /* 3ffe5cffc16bf8f0d65b2cdc3ad5e281 */ + L(2.74838775935027549024224114338667371e-35), /* 3f8c24423b3a3e1323212fe3a99fa996 */ + +/* x = 7.57812500000000000000000000000000000e-01 3ffe8400000000000000000000000000 */ +/* cos(x) = 0.b9f180ba77dd0751628e135a9508299012230f14becacdd14c3f8862d122de5b56d55b53360 */ + L(7.26341290974108590410147630237598973e-01), /* 3ffe73e30174efba0ea2c51c26b52a10 */ + L(3.12683579338351123545814364980658990e-35), /* 3f8c4c80911878a5f6566e8a61fc4317 */ +/* sin(x) = 0.aff522a954f2ba16d9defdc416e33f5e9a5dfd5a6c228e0abc4d521327ff6e2517a7b3851dd */ + L(6.87334219303873534951703613035647220e-01), /* 3ffe5fea4552a9e5742db3bdfb882dc6 */ + L(4.76739454455410744997012795035529128e-35), /* 3f8cfaf4d2efead361147055e26a9099 */ + +/* x = 7.65625000000000000000000000000000000e-01 3ffe8800000000000000000000000000 */ +/* cos(x) = 0.b890237d3bb3c284b614a0539016bfa1053730bbdf940fa895e185f8e58884d3dda15e63371 */ + L(7.20949380945696418043812784148447688e-01), /* 3ffe712046fa776785096c2940a7202d */ + L(4.78691285733673379499536326050811832e-35), /* 3f8cfd0829b985defca07d44af0c2fc7 */ +/* sin(x) = 0.b167a4c90d63c4244cf5493b7cc23bd3c3c1225e078baa0c53d6d400b926281f537a1a260e6 */ + L(6.92987727246317910281815490823048210e-01), /* 3ffe62cf49921ac7884899ea9276f984 */ + L(4.50089871077663557180849219529189918e-35), /* 3f8cde9e1e0912f03c5d50629eb6a006 */ + +/* x = 7.73437500000000000000000000000000000e-01 3ffe8c00000000000000000000000000 */ +/* cos(x) = 0.b72be40067aaf2c050dbdb7a14c3d7d4f203f6b3f0224a4afe55d6ec8e92b508fd5c5984b3b */ + L(7.15513467882981573520620561289896903e-01), /* 3ffe6e57c800cf55e580a1b7b6f42988 */ +L(-3.02191815581445336509438104625489192e-35), /* bf8c41586fe04a607eedada80d51489c */ +/* sin(x) = 0.b2d7614b1f3aaa24df2d6e20a77e1ca3e6d838c03e29c1bcb026e6733324815fadc9eb89674 */ + L(6.98598938789681741301929277107891591e-01), /* 3ffe65aec2963e755449be5adc414efc */ + L(2.15465226809256290914423429408722521e-35), /* 3f8bca3e6d838c03e29c1bcb026e6733 */ + +/* x = 7.81250000000000000000000000000000000e-01 3ffe9000000000000000000000000000 */ +/* cos(x) = 0.b5c4c7d4f7dae915ac786ccf4b1a498d3e73b6e5e74fe7519d9c53ee6d6b90e881bddfc33e1 */ + L(7.10033883566079674974121643959490219e-01), /* 3ffe6b898fa9efb5d22b58f0d99e9635 */ +L(-4.09623224763692443220896752907902465e-35), /* bf8cb3960c6248d0c580c573131d608d */ +/* sin(x) = 0.b44452709a59752905913765434a59d111f0433eb2b133f7d103207e2aeb4aae111ddc385b3 */ + L(7.04167511454533672780059509973942844e-01), /* 3ffe6888a4e134b2ea520b226eca8695 */ +L(-2.87259372740393348676633610275598640e-35), /* bf8c3177707de60a6a76604177e6fc0f */ + +/* x = 7.89062500000000000000000000000000000e-01 3ffe9400000000000000000000000000 */ +/* cos(x) = 0.b45ad4975b1294cadca4cf40ec8f22a68cd14b175835239a37e63acb85e8e9505215df18140 */ + L(7.04510962440574606164129481545916976e-01), /* 3ffe68b5a92eb6252995b9499e81d91e */ + L(2.60682037357042658395360726992048803e-35), /* 3f8c1534668a58bac1a91cd1bf31d65c */ +/* sin(x) = 0.b5ae7285bc10cf515753847e8f8b7a30e0a580d929d770103509880680f7b8b0e8ad23b65d8 */ + L(7.09693105363899724959669028139035515e-01), /* 3ffe6b5ce50b78219ea2aea708fd1f17 */ +L(-4.37026016974122945368562319136420097e-36), /* bf8973c7d69fc9b58a23fbf2bd9dfe60 */ +}; diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/w_expl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/w_expl_compat.c new file mode 100644 index 0000000000..c32616e504 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/w_expl_compat.c @@ -0,0 +1,42 @@ +/* w_expl.c -- long double version of w_exp.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * wrapper expl(x) + */ + +#include <math.h> +#include <math_private.h> + +long double __expl(long double x) /* wrapper exp */ +{ +#ifdef _IEEE_LIBM + return __ieee754_expl(x); +#else + long double z = __ieee754_expl (x); + if (__glibc_unlikely (!isfinite (z) || z == 0) + && isfinite (x) && _LIB_VERSION != _IEEE_) + return __kernel_standard_l (x, x, 206 + !!signbit (x)); + + return z; +#endif +} +hidden_def (__expl) +weak_alias (__expl, expl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/x2y2m1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/x2y2m1l.c new file mode 100644 index 0000000000..d3f88331b5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/x2y2m1l.c @@ -0,0 +1,76 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_splitl.h> +#include <stdlib.h> + + +/* Calculate X + Y exactly and store the result in *HI + *LO. It is + given that |X| >= |Y| and the values are small enough that no + overflow occurs. */ + +static inline void +add_split (_Float128 *hi, _Float128 *lo, _Float128 x, _Float128 y) +{ + /* Apply Dekker's algorithm. */ + *hi = x + y; + *lo = (x - *hi) + y; +} + +/* Compare absolute values of floating-point values pointed to by P + and Q for qsort. */ + +static int +compare (const void *p, const void *q) +{ + _Float128 pld = fabsl (*(const _Float128 *) p); + _Float128 qld = fabsl (*(const _Float128 *) q); + if (pld < qld) + return -1; + else if (pld == qld) + return 0; + else + return 1; +} + +/* Return X^2 + Y^2 - 1, computed without large cancellation error. + It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >= + 0.5. */ + +_Float128 +__x2y2m1l (_Float128 x, _Float128 y) +{ + _Float128 vals[5]; + SET_RESTORE_ROUNDL (FE_TONEAREST); + mul_splitl (&vals[1], &vals[0], x, x); + mul_splitl (&vals[3], &vals[2], y, y); + vals[4] = -1; + qsort (vals, 5, sizeof (_Float128), compare); + /* Add up the values so that each element of VALS has absolute value + at most equal to the last set bit of the next nonzero + element. */ + for (size_t i = 0; i <= 3; i++) + { + add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); + qsort (vals + i + 1, 4 - i, sizeof (_Float128), compare); + } + /* Now any error from this addition will be small. */ + return vals[4] + vals[3] + vals[2] + vals[1] + vals[0]; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/Makefile b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/Makefile new file mode 100644 index 0000000000..bdba6cc6b5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/Makefile @@ -0,0 +1,16 @@ +# The`long double' type is a distinct type we support if +# -mlong-double-128 option is used (or when it becomes a default +# when -mlong-double-64 is not used). +long-double-fcts = yes +sysdep-CFLAGS += -mlong-double-128 + +ifeq ($(subdir),stdlib) +tests += tst-strtold-ldbl-128ibm +$(objpfx)tst-strtold-ldbl-128ibm: $(libm) +endif + +ifeq ($(subdir),math) +tests += test-fmodl-ldbl-128ibm test-remainderl-ldbl-128ibm \ + test-remquol-ldbl-128ibm test-canonical-ldbl-128ibm \ + test-totalorderl-ldbl-128ibm +endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/bits/iscanonical.h b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/bits/iscanonical.h new file mode 100644 index 0000000000..7ddb368d26 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/bits/iscanonical.h @@ -0,0 +1,41 @@ +/* Define iscanonical macro. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_H +# error "Never use <bits/iscanonical.h> directly; include <math.h> instead." +#endif + +#ifdef __NO_LONG_DOUBLE_MATH +# define iscanonical(x) ((void) (__typeof (x)) (x), 1) +#else +extern int __iscanonicall (long double __x) + __THROW __attribute__ ((__const__)); +# define __iscanonicalf(x) ((void) (__typeof (x)) (x), 1) +# define __iscanonical(x) ((void) (__typeof (x)) (x), 1) +# if __HAVE_DISTINCT_FLOAT128 +# define __iscanonicalf128(x) ((void) (__typeof (x)) (x), 1) +# endif + +/* Return nonzero value if X is canonical. In IEEE interchange binary + formats, all values are canonical, but the argument must still be + converted to its semantic type for any exceptions arising from the + conversion, before being discarded; in IBM long double, there are + encodings that are not consistently handled as corresponding to any + particular value of the type, and we return 0 for those. */ +# define iscanonical(x) __MATH_TG ((x), __iscanonical, (x)) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c new file mode 100644 index 0000000000..cab1da9995 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c @@ -0,0 +1,62 @@ +/* @(#)e_acosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include <math.h> +#include <math_private.h> + +static const long double +one = 1.0L, +ln2 = M_LN2l; + +long double +__ieee754_acoshl(long double x) +{ + long double t; + int64_t hx; + uint64_t lx; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + if(hx<0x3ff0000000000000LL) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x4370000000000000LL) { /* x >= 2**56 */ + if(hx >=0x7ff0000000000000LL) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_logl(x)+ln2; /* acosh(huge)=log(2x) */ + } else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x4000000000000000LL) { /* 2**56 > x > 2 */ + t=x*x; + return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return __log1pl(t+__ieee754_sqrtl(2.0*t+t*t)); + } +} +strong_alias (__ieee754_acoshl, __acoshl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_acosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_acosl.c new file mode 100644 index 0000000000..5974ee1338 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_acosl.c @@ -0,0 +1,316 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_acosl(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x| <= 0.375 + * acos(x) = pi/2 - asin(x) + * Between .375 and .5 the approximation is + * acos(0.4375 + x) = acos(0.4375) + x P(x) / Q(x) + * Between .5 and .625 the approximation is + * acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x) + * For x > 0.625, + * acos(x) = 2 asin(sqrt((1-x)/2)) + * computed with an extended precision square root in the leading term. + * For x < -0.625 + * acos(x) = pi - 2 asin(sqrt((1-|x|)/2)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Functions needed: __ieee754_sqrtl. + */ + +#include <math.h> +#include <math_private.h> + +static const long double + one = 1.0L, + pio2_hi = 1.5707963267948966192313216916397514420986L, + pio2_lo = 4.3359050650618905123985220130216759843812E-35L, + + /* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x) + -0.0625 <= x <= 0.0625 + peak relative error 3.3e-35 */ + + rS0 = 5.619049346208901520945464704848780243887E0L, + rS1 = -4.460504162777731472539175700169871920352E1L, + rS2 = 1.317669505315409261479577040530751477488E2L, + rS3 = -1.626532582423661989632442410808596009227E2L, + rS4 = 3.144806644195158614904369445440583873264E1L, + rS5 = 9.806674443470740708765165604769099559553E1L, + rS6 = -5.708468492052010816555762842394927806920E1L, + rS7 = -1.396540499232262112248553357962639431922E1L, + rS8 = 1.126243289311910363001762058295832610344E1L, + rS9 = 4.956179821329901954211277873774472383512E-1L, + rS10 = -3.313227657082367169241333738391762525780E-1L, + + sS0 = -4.645814742084009935700221277307007679325E0L, + sS1 = 3.879074822457694323970438316317961918430E1L, + sS2 = -1.221986588013474694623973554726201001066E2L, + sS3 = 1.658821150347718105012079876756201905822E2L, + sS4 = -4.804379630977558197953176474426239748977E1L, + sS5 = -1.004296417397316948114344573811562952793E2L, + sS6 = 7.530281592861320234941101403870010111138E1L, + sS7 = 1.270735595411673647119592092304357226607E1L, + sS8 = -1.815144839646376500705105967064792930282E1L, + sS9 = -7.821597334910963922204235247786840828217E-2L, + /* 1.000000000000000000000000000000000000000E0 */ + + acosr5625 = 9.7338991014954640492751132535550279812151E-1L, + pimacosr5625 = 2.1682027434402468335351320579240000860757E0L, + + /* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x) + -0.0625 <= x <= 0.0625 + peak relative error 2.1e-35 */ + + P0 = 2.177690192235413635229046633751390484892E0L, + P1 = -2.848698225706605746657192566166142909573E1L, + P2 = 1.040076477655245590871244795403659880304E2L, + P3 = -1.400087608918906358323551402881238180553E2L, + P4 = 2.221047917671449176051896400503615543757E1L, + P5 = 9.643714856395587663736110523917499638702E1L, + P6 = -5.158406639829833829027457284942389079196E1L, + P7 = -1.578651828337585944715290382181219741813E1L, + P8 = 1.093632715903802870546857764647931045906E1L, + P9 = 5.448925479898460003048760932274085300103E-1L, + P10 = -3.315886001095605268470690485170092986337E-1L, + Q0 = -1.958219113487162405143608843774587557016E0L, + Q1 = 2.614577866876185080678907676023269360520E1L, + Q2 = -9.990858606464150981009763389881793660938E1L, + Q3 = 1.443958741356995763628660823395334281596E2L, + Q4 = -3.206441012484232867657763518369723873129E1L, + Q5 = -1.048560885341833443564920145642588991492E2L, + Q6 = 6.745883931909770880159915641984874746358E1L, + Q7 = 1.806809656342804436118449982647641392951E1L, + Q8 = -1.770150690652438294290020775359580915464E1L, + Q9 = -5.659156469628629327045433069052560211164E-1L, + /* 1.000000000000000000000000000000000000000E0 */ + + acosr4375 = 1.1179797320499710475919903296900511518755E0L, + pimacosr4375 = 2.0236129215398221908706530535894517323217E0L, + + /* asin(x) = x + x^3 pS(x^2) / qS(x^2) + 0 <= x <= 0.5 + peak relative error 1.9e-35 */ + pS0 = -8.358099012470680544198472400254596543711E2L, + pS1 = 3.674973957689619490312782828051860366493E3L, + pS2 = -6.730729094812979665807581609853656623219E3L, + pS3 = 6.643843795209060298375552684423454077633E3L, + pS4 = -3.817341990928606692235481812252049415993E3L, + pS5 = 1.284635388402653715636722822195716476156E3L, + pS6 = -2.410736125231549204856567737329112037867E2L, + pS7 = 2.219191969382402856557594215833622156220E1L, + pS8 = -7.249056260830627156600112195061001036533E-1L, + pS9 = 1.055923570937755300061509030361395604448E-3L, + + qS0 = -5.014859407482408326519083440151745519205E3L, + qS1 = 2.430653047950480068881028451580393430537E4L, + qS2 = -4.997904737193653607449250593976069726962E4L, + qS3 = 5.675712336110456923807959930107347511086E4L, + qS4 = -3.881523118339661268482937768522572588022E4L, + qS5 = 1.634202194895541569749717032234510811216E4L, + qS6 = -4.151452662440709301601820849901296953752E3L, + qS7 = 5.956050864057192019085175976175695342168E2L, + qS8 = -4.175375777334867025769346564600396877176E1L; + /* 1.000000000000000000000000000000000000000E0 */ + +long double +__ieee754_acosl (long double x) +{ + long double a, z, r, w, p, q, s, t, f2; + + if (__glibc_unlikely (isnan (x))) + return x + x; + a = __builtin_fabsl (x); + if (a == 1.0L) + { + if (x > 0.0L) + return 0.0; /* acos(1) = 0 */ + else + return (2.0 * pio2_hi) + (2.0 * pio2_lo); /* acos(-1)= pi */ + } + else if (a > 1.0L) + { + return (x - x) / (x - x); /* acos(|x| > 1) is NaN */ + } + if (a < 0.5L) + { + if (a < 0x1p-106L) + return pio2_hi + pio2_lo; + if (a < 0.4375L) + { + /* Arcsine of x. */ + z = x * x; + p = (((((((((pS9 * z + + pS8) * z + + pS7) * z + + pS6) * z + + pS5) * z + + pS4) * z + + pS3) * z + + pS2) * z + + pS1) * z + + pS0) * z; + q = (((((((( z + + qS8) * z + + qS7) * z + + qS6) * z + + qS5) * z + + qS4) * z + + qS3) * z + + qS2) * z + + qS1) * z + + qS0; + r = x + x * p / q; + z = pio2_hi - (r - pio2_lo); + return z; + } + /* .4375 <= |x| < .5 */ + t = a - 0.4375L; + p = ((((((((((P10 * t + + P9) * t + + P8) * t + + P7) * t + + P6) * t + + P5) * t + + P4) * t + + P3) * t + + P2) * t + + P1) * t + + P0) * t; + + q = (((((((((t + + Q9) * t + + Q8) * t + + Q7) * t + + Q6) * t + + Q5) * t + + Q4) * t + + Q3) * t + + Q2) * t + + Q1) * t + + Q0; + r = p / q; + if (x < 0.0L) + r = pimacosr4375 - r; + else + r = acosr4375 + r; + return r; + } + else if (a < 0.625L) + { + t = a - 0.5625L; + p = ((((((((((rS10 * t + + rS9) * t + + rS8) * t + + rS7) * t + + rS6) * t + + rS5) * t + + rS4) * t + + rS3) * t + + rS2) * t + + rS1) * t + + rS0) * t; + + q = (((((((((t + + sS9) * t + + sS8) * t + + sS7) * t + + sS6) * t + + sS5) * t + + sS4) * t + + sS3) * t + + sS2) * t + + sS1) * t + + sS0; + if (x < 0.0L) + r = pimacosr5625 - p / q; + else + r = acosr5625 + p / q; + return r; + } + else + { /* |x| >= .625 */ + double shi, slo; + + z = (one - a) * 0.5; + s = __ieee754_sqrtl (z); + /* Compute an extended precision square root from + the Newton iteration s -> 0.5 * (s + z / s). + The change w from s to the improved value is + w = 0.5 * (s + z / s) - s = (s^2 + z)/2s - s = (z - s^2)/2s. + Express s = f1 + f2 where f1 * f1 is exactly representable. + w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s . + s + w has extended precision. */ + ldbl_unpack (s, &shi, &slo); + a = shi; + f2 = slo; + w = z - a * a; + w = w - 2.0 * a * f2; + w = w - f2 * f2; + w = w / (2.0 * s); + /* Arcsine of s. */ + p = (((((((((pS9 * z + + pS8) * z + + pS7) * z + + pS6) * z + + pS5) * z + + pS4) * z + + pS3) * z + + pS2) * z + + pS1) * z + + pS0) * z; + q = (((((((( z + + qS8) * z + + qS7) * z + + qS6) * z + + qS5) * z + + qS4) * z + + qS3) * z + + qS2) * z + + qS1) * z + + qS0; + r = s + (w + s * p / q); + + if (x < 0.0L) + w = pio2_hi + (pio2_lo - r); + else + w = r; + return 2.0 * w; + } +} +strong_alias (__ieee754_acosl, __acosl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_asinl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_asinl.c new file mode 100644 index 0000000000..6ed5e8d68d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_asinl.c @@ -0,0 +1,250 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under the + following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_asin(x) + * Method : + * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... + * we approximate asin(x) on [0,0.5] by + * asin(x) = x + x*x^2*R(x^2) + * Between .5 and .625 the approximation is + * asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x) + * For x in [0.625,1] + * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) + * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; + * then for x>0.98 + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) + * For x<=0.98, let pio4_hi = pio2_hi/2, then + * f = hi part of s; + * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) + * and + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + + +#include <float.h> +#include <math.h> +#include <math_private.h> +long double sqrtl (long double); + +static const long double + one = 1.0L, + huge = 1.0e+300L, + pio2_hi = 1.5707963267948966192313216916397514420986L, + pio2_lo = 4.3359050650618905123985220130216759843812E-35L, + pio4_hi = 7.8539816339744830961566084581987569936977E-1L, + + /* coefficient for R(x^2) */ + + /* asin(x) = x + x^3 pS(x^2) / qS(x^2) + 0 <= x <= 0.5 + peak relative error 1.9e-35 */ + pS0 = -8.358099012470680544198472400254596543711E2L, + pS1 = 3.674973957689619490312782828051860366493E3L, + pS2 = -6.730729094812979665807581609853656623219E3L, + pS3 = 6.643843795209060298375552684423454077633E3L, + pS4 = -3.817341990928606692235481812252049415993E3L, + pS5 = 1.284635388402653715636722822195716476156E3L, + pS6 = -2.410736125231549204856567737329112037867E2L, + pS7 = 2.219191969382402856557594215833622156220E1L, + pS8 = -7.249056260830627156600112195061001036533E-1L, + pS9 = 1.055923570937755300061509030361395604448E-3L, + + qS0 = -5.014859407482408326519083440151745519205E3L, + qS1 = 2.430653047950480068881028451580393430537E4L, + qS2 = -4.997904737193653607449250593976069726962E4L, + qS3 = 5.675712336110456923807959930107347511086E4L, + qS4 = -3.881523118339661268482937768522572588022E4L, + qS5 = 1.634202194895541569749717032234510811216E4L, + qS6 = -4.151452662440709301601820849901296953752E3L, + qS7 = 5.956050864057192019085175976175695342168E2L, + qS8 = -4.175375777334867025769346564600396877176E1L, + /* 1.000000000000000000000000000000000000000E0 */ + + /* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x) + -0.0625 <= x <= 0.0625 + peak relative error 3.3e-35 */ + rS0 = -5.619049346208901520945464704848780243887E0L, + rS1 = 4.460504162777731472539175700169871920352E1L, + rS2 = -1.317669505315409261479577040530751477488E2L, + rS3 = 1.626532582423661989632442410808596009227E2L, + rS4 = -3.144806644195158614904369445440583873264E1L, + rS5 = -9.806674443470740708765165604769099559553E1L, + rS6 = 5.708468492052010816555762842394927806920E1L, + rS7 = 1.396540499232262112248553357962639431922E1L, + rS8 = -1.126243289311910363001762058295832610344E1L, + rS9 = -4.956179821329901954211277873774472383512E-1L, + rS10 = 3.313227657082367169241333738391762525780E-1L, + + sS0 = -4.645814742084009935700221277307007679325E0L, + sS1 = 3.879074822457694323970438316317961918430E1L, + sS2 = -1.221986588013474694623973554726201001066E2L, + sS3 = 1.658821150347718105012079876756201905822E2L, + sS4 = -4.804379630977558197953176474426239748977E1L, + sS5 = -1.004296417397316948114344573811562952793E2L, + sS6 = 7.530281592861320234941101403870010111138E1L, + sS7 = 1.270735595411673647119592092304357226607E1L, + sS8 = -1.815144839646376500705105967064792930282E1L, + sS9 = -7.821597334910963922204235247786840828217E-2L, + /* 1.000000000000000000000000000000000000000E0 */ + + asinr5625 = 5.9740641664535021430381036628424864397707E-1L; + + + +long double +__ieee754_asinl (long double x) +{ + long double a, t, w, p, q, c, r, s; + int flag; + + if (__glibc_unlikely (isnan (x))) + return x + x; + flag = 0; + a = __builtin_fabsl (x); + if (a == 1.0L) /* |x|>= 1 */ + return x * pio2_hi + x * pio2_lo; /* asin(1)=+-pi/2 with inexact */ + else if (a >= 1.0L) + return (x - x) / (x - x); /* asin(|x|>1) is NaN */ + else if (a < 0.5L) + { + if (a < 6.938893903907228e-18L) /* |x| < 2**-57 */ + { + math_check_force_underflow (x); + long double force_inexact = huge + x; + math_force_eval (force_inexact); + return x; /* return x with inexact if x!=0 */ + } + else + { + t = x * x; + /* Mark to use pS, qS later on. */ + flag = 1; + } + } + else if (a < 0.625L) + { + t = a - 0.5625; + p = ((((((((((rS10 * t + + rS9) * t + + rS8) * t + + rS7) * t + + rS6) * t + + rS5) * t + + rS4) * t + + rS3) * t + + rS2) * t + + rS1) * t + + rS0) * t; + + q = ((((((((( t + + sS9) * t + + sS8) * t + + sS7) * t + + sS6) * t + + sS5) * t + + sS4) * t + + sS3) * t + + sS2) * t + + sS1) * t + + sS0; + t = asinr5625 + p / q; + if (x > 0.0L) + return t; + else + return -t; + } + else + { + /* 1 > |x| >= 0.625 */ + w = one - a; + t = w * 0.5; + } + + p = (((((((((pS9 * t + + pS8) * t + + pS7) * t + + pS6) * t + + pS5) * t + + pS4) * t + + pS3) * t + + pS2) * t + + pS1) * t + + pS0) * t; + + q = (((((((( t + + qS8) * t + + qS7) * t + + qS6) * t + + qS5) * t + + qS4) * t + + qS3) * t + + qS2) * t + + qS1) * t + + qS0; + + if (flag) /* 2^-57 < |x| < 0.5 */ + { + w = p / q; + return x + x * w; + } + + s = __ieee754_sqrtl (t); + if (a > 0.975L) + { + w = p / q; + t = pio2_hi - (2.0 * (s + s * w) - pio2_lo); + } + else + { + w = ldbl_high (s); + c = (t - w * w) / (s + w); + r = p / q; + p = 2.0 * s * r - (pio2_lo - 2.0 * c); + q = pio4_hi - 2.0 * w; + t = pio4_hi - (p - q); + } + + if (x > 0.0L) + return t; + else + return -t; +} +strong_alias (__ieee754_asinl, __asinl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_atan2l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_atan2l.c new file mode 100644 index 0000000000..b625323df3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_atan2l.c @@ -0,0 +1,122 @@ +/* e_atan2l.c -- long double version of e_atan2.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_atan2l(y,x) + * Method : + * 1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * + * Special cases: + * + * ATAN2((anything), NaN ) is NaN; + * ATAN2(NAN , (anything) ) is NaN; + * ATAN2(+-0, +(anything but NaN)) is +-0 ; + * ATAN2(+-0, -(anything but NaN)) is +-pi ; + * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; + * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; + * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; + * ATAN2(+-INF,+INF ) is +-pi/4 ; + * ATAN2(+-INF,-INF ) is +-3pi/4; + * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <math.h> +#include <math_private.h> + +static const long double +tiny = 1.0e-300L, +zero = 0.0, +pi_o_4 = 7.85398163397448309615660845819875699e-01L, /* 3ffe921fb54442d18469898cc51701b8 */ +pi_o_2 = 1.57079632679489661923132169163975140e+00L, /* 3fff921fb54442d18469898cc51701b8 */ +pi = 3.14159265358979323846264338327950280e+00L, /* 4000921fb54442d18469898cc51701b8 */ +pi_lo = 8.67181013012378102479704402604335225e-35L; /* 3f8dcd129024e088a67cc74020bbea64 */ + +long double +__ieee754_atan2l(long double y, long double x) +{ + long double z; + int64_t k,m,hx,hy,ix,iy; + uint64_t lx; + double xhi, xlo, yhi; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + ix = hx&0x7fffffffffffffffLL; + yhi = ldbl_high (y); + EXTRACT_WORDS64 (hy, yhi); + iy = hy&0x7fffffffffffffffLL; + if(((ix)>0x7ff0000000000000LL)|| + ((iy)>0x7ff0000000000000LL)) /* x or y is NaN */ + return x+y; + if(((hx-0x3ff0000000000000LL))==0 + && (lx&0x7fffffffffffffff)==0) return __atanl(y); /* x=1.0L */ + m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if(iy==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7ff0000000000000LL) { + if(iy==0x7ff0000000000000LL) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return 3.0L*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3.0L*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7ff0000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>52; + if(k > 120) z=pi_o_2+0.5L*pi_lo; /* |y/x| > 2**120 */ + else if(hx<0&&k<-120) z=0.0L; /* |y|/x < -2**120 */ + else z=__atanl(fabsl(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: return -z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} +strong_alias (__ieee754_atan2l, __atan2l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_atanhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_atanhl.c new file mode 100644 index 0000000000..b576f42030 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_atanhl.c @@ -0,0 +1,71 @@ +/* @(#)e_atanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_atanh(x) + * Method : + * 1.Reduced x to positive by atanh(-x) = -atanh(x) + * 2.For x>=0.5 + * 1 2x x + * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) + * + * Special cases: + * atanh(x) is NaN if |x| > 1 with signal; + * atanh(NaN) is that NaN with no signal; + * atanh(+-1) is +-INF with signal. + * + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double one = 1.0L, huge = 1e300L; + +static const long double zero = 0.0L; + +long double +__ieee754_atanhl(long double x) +{ + long double t; + int64_t hx,ix; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + ix = hx&0x7fffffffffffffffLL; + if (ix >= 0x3ff0000000000000LL) { /* |x|>=1 */ + if (ix > 0x3ff0000000000000LL) + return (x-x)/(x-x); + t = fabsl (x); + if (t > one) + return (x-x)/(x-x); + if (t == one) + return x/zero; + } + if(ix<0x3c70000000000000LL&&(huge+x)>zero) /* x<2**-56 */ + { + math_check_force_underflow (x); + return x; + } + x = fabsl (x); + if(ix<0x3fe0000000000000LL) { /* x < 0.5 */ + t = x+x; + t = 0.5*__log1pl(t+t*x/(one-x)); + } else + t = 0.5*__log1pl((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} +strong_alias (__ieee754_atanhl, __atanhl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_coshl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_coshl.c new file mode 100644 index 0000000000..327b2ab960 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_coshl.c @@ -0,0 +1,81 @@ +/* @(#)e_cosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 40 : cosh(x) := ------------------- + * 2 + * 40 <= x <= lnovft : cosh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + +#include <math.h> +#include <math_private.h> + +static const long double one = 1.0L, half=0.5L, huge = 1.0e300L; + +long double +__ieee754_coshl (long double x) +{ + long double t,w; + int64_t ix; + double xhi; + + /* High word of |x|. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + ix &= 0x7fffffffffffffffLL; + + /* x is INF or NaN */ + if(ix>=0x7ff0000000000000LL) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3fd62e42fefa39efLL) { + if (ix<0x3c80000000000000LL) return one; /* cosh(tiny) = 1 */ + t = __expm1l(fabsl(x)); + w = one+t; + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x4044000000000000LL) { + t = __ieee754_expl(fabsl(x)); + return half*t+half/t; + } + + /* |x| in [40, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862e42fefa39efLL) return half*__ieee754_expl(fabsl(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix < 0x408633ce8fb9f87fLL) { + w = __ieee754_expl(half*fabsl(x)); + t = half*w; + return t*w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} +strong_alias (__ieee754_coshl, __coshl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_exp10l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_exp10l.c new file mode 100644 index 0000000000..6c3b6f5589 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_exp10l.c @@ -0,0 +1,48 @@ +/* Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +static const long double log10_high = 0x2.4d763776aaap+0L; +static const long double log10_low = 0x2.b05ba95b58ae0b4c28a38a3fb4p-48L; + +long double +__ieee754_exp10l (long double arg) +{ + union ibm_extended_long_double u; + long double arg_high, arg_low; + long double exp_high, exp_low; + + if (!isfinite (arg)) + return __ieee754_expl (arg); + if (arg < LDBL_MIN_10_EXP - LDBL_DIG - 10) + return LDBL_MIN * LDBL_MIN; + else if (arg > LDBL_MAX_10_EXP + 1) + return LDBL_MAX * LDBL_MAX; + else if (fabsl (arg) < 0x1p-109L) + return 1.0L; + + u.ld = arg; + arg_high = u.d[0].d; + arg_low = u.d[1].d; + exp_high = arg_high * log10_high; + exp_low = arg_high * log10_low + arg_low * M_LN10l; + return __ieee754_expl (exp_high) * __ieee754_expl (exp_low); +} +strong_alias (__ieee754_exp10l, __exp10l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_expl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_expl.c new file mode 100644 index 0000000000..10df6bb7d5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_expl.c @@ -0,0 +1,256 @@ +/* Quad-precision floating point e^x. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + Partly based on double-precision code + by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* The basic design here is from + Abraham Ziv, "Fast Evaluation of Elementary Mathematical Functions with + Correctly Rounded Last Bit", ACM Trans. Math. Soft., 17 (3), September 1991, + pp. 410-423. + + We work with number pairs where the first number is the high part and + the second one is the low part. Arithmetic with the high part numbers must + be exact, without any roundoff errors. + + The input value, X, is written as + X = n * ln(2)_0 + arg1[t1]_0 + arg2[t2]_0 + x + - n * ln(2)_1 + arg1[t1]_1 + arg2[t2]_1 + xl + + where: + - n is an integer, 16384 >= n >= -16495; + - ln(2)_0 is the first 93 bits of ln(2), and |ln(2)_0-ln(2)-ln(2)_1| < 2^-205 + - t1 is an integer, 89 >= t1 >= -89 + - t2 is an integer, 65 >= t2 >= -65 + - |arg1[t1]-t1/256.0| < 2^-53 + - |arg2[t2]-t2/32768.0| < 2^-53 + - x + xl is whatever is left, |x + xl| < 2^-16 + 2^-53 + + Then e^x is approximated as + + e^x = 2^n_1 ( 2^n_0 e^(arg1[t1]_0 + arg1[t1]_1) e^(arg2[t2]_0 + arg2[t2]_1) + + 2^n_0 e^(arg1[t1]_0 + arg1[t1]_1) e^(arg2[t2]_0 + arg2[t2]_1) + * p (x + xl + n * ln(2)_1)) + where: + - p(x) is a polynomial approximating e(x)-1 + - e^(arg1[t1]_0 + arg1[t1]_1) is obtained from a table + - e^(arg2[t2]_0 + arg2[t2]_1) likewise + - n_1 + n_0 = n, so that |n_0| < -LDBL_MIN_EXP-1. + + If it happens that n_1 == 0 (this is the usual case), that multiplication + is omitted. + */ + +#ifndef _GNU_SOURCE +#define _GNU_SOURCE +#endif +#include <float.h> +#include <ieee754.h> +#include <math.h> +#include <fenv.h> +#include <inttypes.h> +#include <math_private.h> + +#define _Float128 long double +#define L(x) x ## L + +#include <sysdeps/ieee754/ldbl-128/t_expl.h> + +static const long double C[] = { +/* Smallest integer x for which e^x overflows. */ +#define himark C[0] + 709.78271289338399678773454114191496482L, + +/* Largest integer x for which e^x underflows. */ +#define lomark C[1] +-744.44007192138126231410729844608163411L, + +/* 3x2^96 */ +#define THREEp96 C[2] + 59421121885698253195157962752.0L, + +/* 3x2^103 */ +#define THREEp103 C[3] + 30423614405477505635920876929024.0L, + +/* 3x2^111 */ +#define THREEp111 C[4] + 7788445287802241442795744493830144.0L, + +/* 1/ln(2) */ +#define M_1_LN2 C[5] + 1.44269504088896340735992468100189204L, + +/* first 93 bits of ln(2) */ +#define M_LN2_0 C[6] + 0.693147180559945309417232121457981864L, + +/* ln2_0 - ln(2) */ +#define M_LN2_1 C[7] +-1.94704509238074995158795957333327386E-31L, + +/* very small number */ +#define TINY C[8] + 1.0e-308L, + +/* 2^16383 */ +#define TWO1023 C[9] + 8.988465674311579538646525953945123668E+307L, + +/* 256 */ +#define TWO8 C[10] + 256.0L, + +/* 32768 */ +#define TWO15 C[11] + 32768.0L, + +/* Chebyshev polynom coefficients for (exp(x)-1)/x */ +#define P1 C[12] +#define P2 C[13] +#define P3 C[14] +#define P4 C[15] +#define P5 C[16] +#define P6 C[17] + 0.5L, + 1.66666666666666666666666666666666683E-01L, + 4.16666666666666666666654902320001674E-02L, + 8.33333333333333333333314659767198461E-03L, + 1.38888888889899438565058018857254025E-03L, + 1.98412698413981650382436541785404286E-04L, +}; + +long double +__ieee754_expl (long double x) +{ + long double result, x22; + union ibm_extended_long_double ex2_u, scale_u; + int unsafe; + + /* Check for usual case. */ + if (isless (x, himark) && isgreater (x, lomark)) + { + int tval1, tval2, n_i, exponent2; + long double n, xl; + + SET_RESTORE_ROUND (FE_TONEAREST); + + n = __roundl (x*M_1_LN2); + x = x-n*M_LN2_0; + xl = n*M_LN2_1; + + tval1 = __roundl (x*TWO8); + x -= __expl_table[T_EXPL_ARG1+2*tval1]; + xl -= __expl_table[T_EXPL_ARG1+2*tval1+1]; + + tval2 = __roundl (x*TWO15); + x -= __expl_table[T_EXPL_ARG2+2*tval2]; + xl -= __expl_table[T_EXPL_ARG2+2*tval2+1]; + + x = x + xl; + + /* Compute ex2 = 2^n_0 e^(argtable[tval1]) e^(argtable[tval2]). */ + ex2_u.ld = (__expl_table[T_EXPL_RES1 + tval1] + * __expl_table[T_EXPL_RES2 + tval2]); + n_i = (int)n; + /* 'unsafe' is 1 iff n_1 != 0. */ + unsafe = fabsl(n_i) >= -LDBL_MIN_EXP - 1; + ex2_u.d[0].ieee.exponent += n_i >> unsafe; + /* Fortunately, there are no subnormal lowpart doubles in + __expl_table, only normal values and zeros. + But after scaling it can be subnormal. */ + exponent2 = ex2_u.d[1].ieee.exponent + (n_i >> unsafe); + if (ex2_u.d[1].ieee.exponent == 0) + /* assert ((ex2_u.d[1].ieee.mantissa0|ex2_u.d[1].ieee.mantissa1) == 0) */; + else if (exponent2 > 0) + ex2_u.d[1].ieee.exponent = exponent2; + else if (exponent2 <= -54) + { + ex2_u.d[1].ieee.exponent = 0; + ex2_u.d[1].ieee.mantissa0 = 0; + ex2_u.d[1].ieee.mantissa1 = 0; + } + else + { + static const double + two54 = 1.80143985094819840000e+16, /* 4350000000000000 */ + twom54 = 5.55111512312578270212e-17; /* 3C90000000000000 */ + ex2_u.d[1].d *= two54; + ex2_u.d[1].ieee.exponent += n_i >> unsafe; + ex2_u.d[1].d *= twom54; + } + + /* Compute scale = 2^n_1. */ + scale_u.ld = 1.0L; + scale_u.d[0].ieee.exponent += n_i - (n_i >> unsafe); + + /* Approximate e^x2 - 1, using a seventh-degree polynomial, + with maximum error in [-2^-16-2^-53,2^-16+2^-53] + less than 4.8e-39. */ + x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6))))); + + /* Now we can test whether the result is ultimate or if we are unsure. + In the later case we should probably call a mpn based routine to give + the ultimate result. + Empirically, this routine is already ultimate in about 99.9986% of + cases, the test below for the round to nearest case will be false + in ~ 99.9963% of cases. + Without proc2 routine maximum error which has been seen is + 0.5000262 ulp. + + union ieee854_long_double ex3_u; + + #ifdef FE_TONEAREST + fesetround (FE_TONEAREST); + #endif + ex3_u.d = (result - ex2_u.d) - x22 * ex2_u.d; + ex2_u.d = result; + ex3_u.ieee.exponent += LDBL_MANT_DIG + 15 + IEEE854_LONG_DOUBLE_BIAS + - ex2_u.ieee.exponent; + n_i = abs (ex3_u.d); + n_i = (n_i + 1) / 2; + fesetenv (&oldenv); + #ifdef FE_TONEAREST + if (fegetround () == FE_TONEAREST) + n_i -= 0x4000; + #endif + if (!n_i) { + return __ieee754_expl_proc2 (origx); + } + */ + } + /* Exceptional cases: */ + else if (isless (x, himark)) + { + if (isinf (x)) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TINY * TINY; + } + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO1023*x; + + result = x22 * ex2_u.ld + ex2_u.ld; + if (!unsafe) + return result; + return result * scale_u.ld; +} +strong_alias (__ieee754_expl, __expl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c new file mode 100644 index 0000000000..5284fd0fd5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c @@ -0,0 +1,149 @@ +/* e_fmodl.c -- long double version of e_fmod.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __ieee754_fmodl(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include <math.h> +#include <math_private.h> +#include <ieee754.h> + +static const long double one = 1.0, Zero[] = {0.0, -0.0,}; + +long double +__ieee754_fmodl (long double x, long double y) +{ + int64_t hx, hy, hz, sx, sy; + uint64_t lx, ly, lz; + int n, ix, iy; + double xhi, xlo, yhi, ylo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS64 (hy, yhi); + EXTRACT_WORDS64 (ly, ylo); + sx = hx&0x8000000000000000ULL; /* sign of x */ + hx ^= sx; /* |x| */ + sy = hy&0x8000000000000000ULL; /* sign of y */ + hy ^= sy; /* |y| */ + + /* purge off exception values */ + if(__builtin_expect(hy==0 || + (hx>=0x7ff0000000000000LL)|| /* y=0,or x not finite */ + (hy>0x7ff0000000000000LL),0)) /* or y is NaN */ + return (x*y)/(x*y); + if (__glibc_unlikely (hx <= hy)) + { + /* If |x| < |y| return x. */ + if (hx < hy) + return x; + /* At this point the absolute value of the high doubles of + x and y must be equal. */ + if ((lx & 0x7fffffffffffffffLL) == 0 + && (ly & 0x7fffffffffffffffLL) == 0) + /* Both low parts are zero. The result should be an + appropriately signed zero, but the subsequent logic + could treat them as unequal, depending on the signs + of the low parts. */ + return Zero[(uint64_t) sx >> 63]; + /* If the low double of y is the same sign as the high + double of y (ie. the low double increases |y|)... */ + if (((ly ^ sy) & 0x8000000000000000LL) == 0 + /* ... then a different sign low double to high double + for x or same sign but lower magnitude... */ + && (int64_t) (lx ^ sx) < (int64_t) (ly ^ sy)) + /* ... means |x| < |y|. */ + return x; + /* If the low double of x differs in sign to the high + double of x (ie. the low double decreases |x|)... */ + if (((lx ^ sx) & 0x8000000000000000LL) != 0 + /* ... then a different sign low double to high double + for y with lower magnitude (we've already caught + the same sign for y case above)... */ + && (int64_t) (lx ^ sx) > (int64_t) (ly ^ sy)) + /* ... means |x| < |y|. */ + return x; + /* If |x| == |y| return x*0. */ + if ((lx ^ sx) == (ly ^ sy)) + return Zero[(uint64_t) sx >> 63]; + } + + /* Make the IBM extended format 105 bit mantissa look like the ieee854 112 + bit mantissa so the following operations will give the correct + result. */ + ldbl_extract_mantissa(&hx, &lx, &ix, x); + ldbl_extract_mantissa(&hy, &ly, &iy, y); + + if (__glibc_unlikely (ix == -IEEE754_DOUBLE_BIAS)) + { + /* subnormal x, shift x to normal. */ + while ((hx & (1LL << 48)) == 0) + { + hx = (hx << 1) | (lx >> 63); + lx = lx << 1; + ix -= 1; + } + } + + if (__glibc_unlikely (iy == -IEEE754_DOUBLE_BIAS)) + { + /* subnormal y, shift y to normal. */ + while ((hy & (1LL << 48)) == 0) + { + hy = (hy << 1) | (ly >> 63); + ly = ly << 1; + iy -= 1; + } + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; + if(hz<0){hx = hx+hx+(lx>>63); lx = lx+lx;} + else { + if((hz|lz)==0) /* return sign(x)*0 */ + return Zero[(u_int64_t)sx>>63]; + hx = hz+hz+(lz>>63); lx = lz+lz; + } + } + hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; + if(hz>=0) {hx=hz;lx=lz;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) /* return sign(x)*0 */ + return Zero[(u_int64_t)sx>>63]; + while(hx<0x0001000000000000LL) { /* normalize x */ + hx = hx+hx+(lx>>63); lx = lx+lx; + iy -= 1; + } + if(__builtin_expect(iy>= -1022,0)) { /* normalize output */ + x = ldbl_insert_mantissa((sx>>63), iy, hx, lx); + } else { /* subnormal output */ + n = -1022 - iy; + /* We know 1 <= N <= 52, and that there are no nonzero + bits in places below 2^-1074. */ + lx = (lx >> n) | ((u_int64_t) hx << (64 - n)); + hx >>= n; + x = ldbl_insert_mantissa((sx>>63), -1023, hx, lx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} +strong_alias (__ieee754_fmodl, __fmodl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c new file mode 100644 index 0000000000..81dbe42c79 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c @@ -0,0 +1,218 @@ +/* Implementation of gamma function according to ISO C. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const long double gamma_coeff[] = + { + 0x1.555555555555555555555555558p-4L, + -0xb.60b60b60b60b60b60b60b60b6p-12L, + 0x3.4034034034034034034034034p-12L, + -0x2.7027027027027027027027027p-12L, + 0x3.72a3c5631fe46ae1d4e700dca9p-12L, + -0x7.daac36664f1f207daac36664f2p-12L, + 0x1.a41a41a41a41a41a41a41a41a4p-8L, + -0x7.90a1b2c3d4e5f708192a3b4c5ep-8L, + 0x2.dfd2c703c0cfff430edfd2c704p-4L, + -0x1.6476701181f39edbdb9ce625988p+0L, + 0xd.672219167002d3a7a9c886459cp+0L, + -0x9.cd9292e6660d55b3f712eb9e08p+4L, + 0x8.911a740da740da740da740da74p+8L, + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 191, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static long double +gammal_positive (long double x, int *exp2_adj) +{ + int local_signgam; + if (x < 0.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x; + } + else if (x <= 1.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam)); + } + else if (x < 11.5L) + { + /* Adjust into the range for using exp (lgamma). */ + *exp2_adj = 0; + long double n = __ceill (x - 1.5L); + long double x_adj = x - n; + long double eps; + long double prod = __gamma_productl (x_adj, 0, n, &eps); + return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam)) + * prod * (1.0L + eps)); + } + else + { + long double eps = 0; + long double x_eps = 0; + long double x_adj = x; + long double prod = 1; + if (x < 23.0L) + { + /* Adjust into the range for applying Stirling's + approximation. */ + long double n = __ceill (23.0L - x); + x_adj = x + n; + x_eps = (x - (x_adj - n)); + prod = __gamma_productl (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + long double exp_adj = -eps; + long double x_adj_int = __roundl (x_adj); + long double x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + long double x_adj_mant = __frexpl (x_adj, &x_adj_log2); + if (x_adj_mant < M_SQRT1_2l) + { + x_adj_log2--; + x_adj_mant *= 2.0L; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + long double ret = (__ieee754_powl (x_adj_mant, x_adj) + * __ieee754_exp2l (x_adj_log2 * x_adj_frac) + * __ieee754_expl (-x_adj) + * __ieee754_sqrtl (2 * M_PIl / x_adj) + / prod); + exp_adj += x_eps * __ieee754_logl (x_adj); + long double bsum = gamma_coeff[NCOEFF - 1]; + long double x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1l (exp_adj); + } +} + +long double +__ieee754_gammal_r (long double x, int *signgamp) +{ + int64_t hx; + double xhi; + long double ret; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + + if ((hx & 0x7fffffffffffffffLL) == 0) + { + /* Return value for x == 0 is Inf with divide by zero exception. */ + *signgamp = 0; + return 1.0 / x; + } + if (hx < 0 && (u_int64_t) hx < 0xfff0000000000000ULL && __rintl (x) == x) + { + /* Return value for integer x < 0 is NaN with invalid exception. */ + *signgamp = 0; + return (x - x) / (x - x); + } + if (hx == 0xfff0000000000000ULL) + { + /* x == -Inf. According to ISO this is NaN. */ + *signgamp = 0; + return x - x; + } + if ((hx & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL) + { + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ + *signgamp = 0; + return x + x; + } + + if (x >= 172.0L) + { + /* Overflow. */ + *signgamp = 0; + return LDBL_MAX * LDBL_MAX; + } + else + { + SET_RESTORE_ROUNDL (FE_TONEAREST); + if (x > 0.0L) + { + *signgamp = 0; + int exp2_adj; + ret = gammal_positive (x, &exp2_adj); + ret = __scalbnl (ret, exp2_adj); + } + else if (x >= -0x1p-110L) + { + *signgamp = 0; + ret = 1.0L / x; + } + else + { + long double tx = __truncl (x); + *signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1; + if (x <= -191.0L) + /* Underflow. */ + ret = LDBL_MIN * LDBL_MIN; + else + { + long double frac = tx - x; + if (frac > 0.5L) + frac = 1.0L - frac; + long double sinpix = (frac <= 0.25L + ? __sinl (M_PIl * frac) + : __cosl (M_PIl * (0.5L - frac))); + int exp2_adj; + ret = M_PIl / (-x * sinpix + * gammal_positive (-x, &exp2_adj)); + ret = __scalbnl (ret, -exp2_adj); + math_check_force_underflow_nonneg (ret); + } + } + } + if (isinf (ret) && x != 0) + { + if (*signgamp < 0) + return -(-__copysignl (LDBL_MAX, ret) * LDBL_MAX); + else + return __copysignl (LDBL_MAX, ret) * LDBL_MAX; + } + else if (ret == 0) + { + if (*signgamp < 0) + return -(-__copysignl (LDBL_MIN, ret) * LDBL_MIN); + else + return __copysignl (LDBL_MIN, ret) * LDBL_MIN; + } + else + return ret; +} +strong_alias (__ieee754_gammal_r, __gammal_r_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c new file mode 100644 index 0000000000..de5a66ab05 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c @@ -0,0 +1,138 @@ +/* @(#)e_hypotl.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_hypotl(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrtl(2)/2 ulp, than + * sqrtl(z) has error less than 1 ulp (exercise). + * + * So, compute sqrtl(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 53 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 53 bits cleared, t2 = 2x-t1, + * y1= y with lower 53 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypotl(x,y) is INF if x or y is +INF or -INF; else + * hypotl(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypotl(x,y) returns sqrtl(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include <math.h> +#include <math_private.h> + +long double +__ieee754_hypotl(long double x, long double y) +{ + long double a,b,a1,a2,b1,b2,w,kld; + int64_t j,k,ha,hb; + double xhi, yhi, hi, lo; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ha, xhi); + yhi = ldbl_high (y); + EXTRACT_WORDS64 (hb, yhi); + ha &= 0x7fffffffffffffffLL; + hb &= 0x7fffffffffffffffLL; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + a = fabsl(a); /* a <- |a| */ + b = fabsl(b); /* b <- |b| */ + if((ha-hb)>0x0780000000000000LL) {return a+b;} /* x/y > 2**120 */ + k=0; + kld = 1.0L; + if(ha > 0x5f30000000000000LL) { /* a>2**500 */ + if(ha >= 0x7ff0000000000000LL) { /* Inf or NaN */ + w = a+b; /* for sNaN */ + if (issignaling (a) || issignaling (b)) + return w; + if(ha == 0x7ff0000000000000LL) + w = a; + if(hb == 0x7ff0000000000000LL) + w = b; + return w; + } + /* scale a and b by 2**-600 */ + a *= 0x1p-600L; + b *= 0x1p-600L; + k = 600; + kld = 0x1p+600L; + } + else if(hb < 0x23d0000000000000LL) { /* b < 2**-450 */ + if(hb <= 0x000fffffffffffffLL) { /* subnormal b or 0 */ + if(hb==0) return a; + a *= 0x1p+1022L; + b *= 0x1p+1022L; + k = -1022; + kld = 0x1p-1022L; + } else { /* scale a and b by 2^600 */ + a *= 0x1p+600L; + b *= 0x1p+600L; + k = -600; + kld = 0x1p-600L; + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + ldbl_unpack (a, &hi, &lo); + a1 = hi; + a2 = lo; + /* a*a + b*b + = (a1+a2)*a + b*b + = a1*a + a2*a + b*b + = a1*(a1+a2) + a2*a + b*b + = a1*a1 + a1*a2 + a2*a + b*b + = a1*a1 + a2*(a+a1) + b*b */ + w = __ieee754_sqrtl(a1*a1-(b*(-b)-a2*(a+a1))); + } else { + a = a+a; + ldbl_unpack (b, &hi, &lo); + b1 = hi; + b2 = lo; + ldbl_unpack (a, &hi, &lo); + a1 = hi; + a2 = lo; + /* a*a + b*b + = a*a + (a-b)*(a-b) - (a-b)*(a-b) + b*b + = a*a + w*w - (a*a - 2*a*b + b*b) + b*b + = w*w + 2*a*b + = w*w + (a1+a2)*b + = w*w + a1*b + a2*b + = w*w + a1*(b1+b2) + a2*b + = w*w + a1*b1 + a1*b2 + a2*b */ + w = __ieee754_sqrtl(a1*b1-(w*(-w)-(a1*b2+a2*b))); + } + if(k!=0) + { + w *= kld; + math_check_force_underflow_nonneg (w); + return w; + } + else + return w; +} +strong_alias (__ieee754_hypotl, __hypotl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_ilogbl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_ilogbl.c new file mode 100644 index 0000000000..4088238f30 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_ilogbl.c @@ -0,0 +1,70 @@ +/* s_ilogbl.c -- long double version of s_ilogb.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* ilogbl(long double x) + * return the binary exponent of non-zero x + * ilogbl(0) = FP_ILOGB0 + * ilogbl(NaN) = FP_ILOGBNAN (no signal is raised) + * ilogbl(+-Inf) = INT_MAX (no signal is raised) + */ + +#include <limits.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +int __ieee754_ilogbl(long double x) +{ + int64_t hx, hxs; + int ix; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + hxs = hx; + hx &= 0x7fffffffffffffffLL; + if(hx <= 0x0010000000000000LL) { + if(hx==0) + return FP_ILOGB0; /* ilogbl(0) = FP_ILOGB0 */ + else /* subnormal x */ + for (ix = -1022, hx<<=11; hx>0; hx<<=1) ix -=1; + return ix; + } + else if (hx < 0x7ff0000000000000LL) + { + int hexp = (hx >> 52) - 0x3ff; + /* If the high part is a power of 2, and the low part is + nonzero with the opposite sign, the low part affects + the exponent. */ + if ((hx & 0x000fffffffffffffLL) == 0) + { + int64_t lx; + EXTRACT_WORDS64 (lx, xlo); + if ((hxs ^ lx) < 0 && (lx & 0x7fffffffffffffffLL) != 0) + hexp--; + } + return hexp; + } + else if (FP_ILOGBNAN != INT_MAX) { + /* ISO C99 requires ilogbl(+-Inf) == INT_MAX. */ + if (hx==0x7ff0000000000000LL) + return INT_MAX; + } + return FP_ILOGBNAN; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_j0l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_j0l.c new file mode 100644 index 0000000000..00bce29284 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_j0l.c @@ -0,0 +1,5 @@ +/* Looks like we can use ieee854 e_j0l.c as is for IBM extended format. */ +#define _Float128 long double +#define L(x) x ## L +#include <sysdeps/ieee754/ldbl-128/e_j0l.c> + diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_j1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_j1l.c new file mode 100644 index 0000000000..da9fd9eeca --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_j1l.c @@ -0,0 +1,4 @@ +/* Looks like we can use ieee854 e_j1l.c as is for IBM extended format. */ +#define _Float128 long double +#define L(x) x ## L +#include <sysdeps/ieee754/ldbl-128/e_j1l.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_jnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_jnl.c new file mode 100644 index 0000000000..4a8ccb044e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_jnl.c @@ -0,0 +1,421 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Modifications for 128-bit long double are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* + * __ieee754_jn(n, x), __ieee754_yn(n, x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for n<x, forward recursion us used starting + * from values of j0(x) and j1(x). + * for n>x, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double + invsqrtpi = 5.6418958354775628694807945156077258584405E-1L, + two = 2.0e0L, + one = 1.0e0L, + zero = 0.0L; + + +long double +__ieee754_jnl (int n, long double x) +{ + uint32_t se, lx; + int32_t i, ix, sgn; + long double a, b, temp, di, ret; + long double z, w; + double xhi; + + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + + xhi = ldbl_high (x); + EXTRACT_WORDS (se, lx, xhi); + ix = se & 0x7fffffff; + + /* if J(n,NaN) is NaN */ + if (ix >= 0x7ff00000) + { + if (((ix - 0x7ff00000) | lx) != 0) + return x + x; + } + + if (n < 0) + { + n = -n; + x = -x; + se ^= 0x80000000; + } + if (n == 0) + return (__ieee754_j0l (x)); + if (n == 1) + return (__ieee754_j1l (x)); + sgn = (n & 1) & (se >> 31); /* even n -- 0, odd n -- sign(x) */ + x = fabsl (x); + + { + SET_RESTORE_ROUNDL (FE_TONEAREST); + if (x == 0.0L || ix >= 0x7ff00000) /* if x is 0 or inf */ + return sgn == 1 ? -zero : zero; + else if ((long double) n <= x) + { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + if (ix >= 0x52d00000) + { /* x > 2**302 */ + + /* ??? Could use an expansion for large x here. */ + + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + long double s; + long double c; + __sincosl (x, &s, &c); + switch (n & 3) + { + case 0: + temp = c + s; + break; + case 1: + temp = -c + s; + break; + case 2: + temp = -c - s; + break; + case 3: + temp = c - s; + break; + } + b = invsqrtpi * temp / __ieee754_sqrtl (x); + } + else + { + a = __ieee754_j0l (x); + b = __ieee754_j1l (x); + for (i = 1; i < n; i++) + { + temp = b; + b = b * ((long double) (i + i) / x) - a; /* avoid underflow */ + a = temp; + } + } + } + else + { + if (ix < 0x3e100000) + { /* x < 2**-29 */ + /* x is tiny, return the first Taylor expansion of J(n,x) + * J(n,x) = 1/n!*(x/2)^n - ... + */ + if (n >= 33) /* underflow, result < 10^-300 */ + b = zero; + else + { + temp = x * 0.5; + b = temp; + for (a = one, i = 2; i <= n; i++) + { + a *= (long double) i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b / a; + } + } + else + { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + long double t, v; + long double q0, q1, h, tmp; + int32_t k, m; + w = (n + n) / (long double) x; + h = 2.0L / (long double) x; + q0 = w; + z = w + h; + q1 = w * z - 1.0L; + k = 1; + while (q1 < 1.0e17L) + { + k += 1; + z += h; + tmp = z * q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n + n; + for (t = zero, i = 2 * (n + k); i >= m; i -= 2) + t = one / (i / x - t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two / x; + tmp = tmp * __ieee754_logl (fabsl (v * tmp)); + + if (tmp < 1.1356523406294143949491931077970765006170e+04L) + { + for (i = n - 1, di = (long double) (i + i); i > 0; i--) + { + temp = b; + b *= di; + b = b / x - a; + a = temp; + di -= two; + } + } + else + { + for (i = n - 1, di = (long double) (i + i); i > 0; i--) + { + temp = b; + b *= di; + b = b / x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if (b > 1e100L) + { + a /= b; + t /= b; + b = one; + } + } + } + /* j0() and j1() suffer enormous loss of precision at and + * near zero; however, we know that their zero points never + * coincide, so just choose the one further away from zero. + */ + z = __ieee754_j0l (x); + w = __ieee754_j1l (x); + if (fabsl (z) >= fabsl (w)) + b = (t * z / b); + else + b = (t * w / a); + } + } + if (sgn == 1) + ret = -b; + else + ret = b; + } + if (ret == 0) + { + ret = __copysignl (LDBL_MIN, ret) * LDBL_MIN; + __set_errno (ERANGE); + } + else + math_check_force_underflow (ret); + return ret; +} +strong_alias (__ieee754_jnl, __jnl_finite) + +long double +__ieee754_ynl (int n, long double x) +{ + uint32_t se, lx; + int32_t i, ix; + int32_t sign; + long double a, b, temp, ret; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS (se, lx, xhi); + ix = se & 0x7fffffff; + + /* if Y(n,NaN) is NaN */ + if (ix >= 0x7ff00000) + { + if (((ix - 0x7ff00000) | lx) != 0) + return x + x; + } + if (x <= 0.0L) + { + if (x == 0.0L) + return ((n < 0 && (n & 1) != 0) ? 1.0L : -1.0L) / 0.0L; + if (se & 0x80000000) + return zero / (zero * x); + } + sign = 1; + if (n < 0) + { + n = -n; + sign = 1 - ((n & 1) << 1); + } + if (n == 0) + return (__ieee754_y0l (x)); + { + SET_RESTORE_ROUNDL (FE_TONEAREST); + if (n == 1) + { + ret = sign * __ieee754_y1l (x); + goto out; + } + if (ix >= 0x7ff00000) + return zero; + if (ix >= 0x52D00000) + { /* x > 2**302 */ + + /* ??? See comment above on the possible futility of this. */ + + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + long double s; + long double c; + __sincosl (x, &s, &c); + switch (n & 3) + { + case 0: + temp = s - c; + break; + case 1: + temp = -s - c; + break; + case 2: + temp = -s + c; + break; + case 3: + temp = s + c; + break; + } + b = invsqrtpi * temp / __ieee754_sqrtl (x); + } + else + { + a = __ieee754_y0l (x); + b = __ieee754_y1l (x); + /* quit if b is -inf */ + xhi = ldbl_high (b); + GET_HIGH_WORD (se, xhi); + se &= 0xfff00000; + for (i = 1; i < n && se != 0xfff00000; i++) + { + temp = b; + b = ((long double) (i + i) / x) * b - a; + xhi = ldbl_high (b); + GET_HIGH_WORD (se, xhi); + se &= 0xfff00000; + a = temp; + } + } + /* If B is +-Inf, set up errno accordingly. */ + if (! isfinite (b)) + __set_errno (ERANGE); + if (sign > 0) + ret = b; + else + ret = -b; + } + out: + if (isinf (ret)) + ret = __copysignl (LDBL_MAX, ret) * LDBL_MAX; + return ret; +} +strong_alias (__ieee754_ynl, __ynl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c new file mode 100644 index 0000000000..8ac8283bd8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c @@ -0,0 +1,5 @@ +/* Looks like we can use ieee854 e_lgammal_r.c as is for IBM extended format. */ +#define _Float128 long double +#define L(x) x ## L +#include <sysdeps/ieee754/ldbl-128/e_lgammal_r.c> + diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_log10l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_log10l.c new file mode 100644 index 0000000000..1fbfa48e13 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_log10l.c @@ -0,0 +1,261 @@ +/* log10l.c + * + * Common logarithm, 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log10l(); + * + * y = log10l( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base 10 logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the logarithm + * of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(x-1)/x+1), + * + * log(x) = z + z^3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.5, 2.0 30000 2.3e-34 4.9e-35 + * IEEE exp(+-10000) 30000 1.0e-34 4.1e-35 + * + * In the tests over the interval exp(+-10000), the logarithms + * of the random arguments were uniformly distributed over + * [-10000, +10000]. + * + */ + +/* + Cephes Math Library Release 2.2: January, 1991 + Copyright 1984, 1991 by Stephen L. Moshier + Adapted for glibc November, 2001 + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see <http://www.gnu.org/licenses/>. + */ + +#include <math.h> +#include <math_private.h> + +/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 5.3e-37, + * relative peak error spread = 2.3e-14 + */ +static const long double P[13] = +{ + 1.313572404063446165910279910527789794488E4L, + 7.771154681358524243729929227226708890930E4L, + 2.014652742082537582487669938141683759923E5L, + 3.007007295140399532324943111654767187848E5L, + 2.854829159639697837788887080758954924001E5L, + 1.797628303815655343403735250238293741397E5L, + 7.594356839258970405033155585486712125861E4L, + 2.128857716871515081352991964243375186031E4L, + 3.824952356185897735160588078446136783779E3L, + 4.114517881637811823002128927449878962058E2L, + 2.321125933898420063925789532045674660756E1L, + 4.998469661968096229986658302195402690910E-1L, + 1.538612243596254322971797716843006400388E-6L +}; +static const long double Q[12] = +{ + 3.940717212190338497730839731583397586124E4L, + 2.626900195321832660448791748036714883242E5L, + 7.777690340007566932935753241556479363645E5L, + 1.347518538384329112529391120390701166528E6L, + 1.514882452993549494932585972882995548426E6L, + 1.158019977462989115839826904108208787040E6L, + 6.132189329546557743179177159925690841200E5L, + 2.248234257620569139969141618556349415120E5L, + 5.605842085972455027590989944010492125825E4L, + 9.147150349299596453976674231612674085381E3L, + 9.104928120962988414618126155557301584078E2L, + 4.839208193348159620282142911143429644326E1L +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 1.1e-35, + * relative peak error spread 1.1e-9 + */ +static const long double R[6] = +{ + 1.418134209872192732479751274970992665513E5L, + -8.977257995689735303686582344659576526998E4L, + 2.048819892795278657810231591630928516206E4L, + -2.024301798136027039250415126250455056397E3L, + 8.057002716646055371965756206836056074715E1L, + -8.828896441624934385266096344596648080902E-1L +}; +static const long double S[6] = +{ + 1.701761051846631278975701529965589676574E6L, + -1.332535117259762928288745111081235577029E6L, + 4.001557694070773974936904547424676279307E5L, + -5.748542087379434595104154610899551484314E4L, + 3.998526750980007367835804959888064681098E3L, + -1.186359407982897997337150403816839480438E2L +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const long double +/* log10(2) */ +L102A = 0.3125L, +L102B = -1.14700043360188047862611052755069732318101185E-2L, +/* log10(e) */ +L10EA = 0.5L, +L10EB = -6.570551809674817234887108108339491770560299E-2L, +/* sqrt(2)/2 */ +SQRTH = 7.071067811865475244008443621048490392848359E-1L; + + + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +neval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +deval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + + +long double +__ieee754_log10l (long double x) +{ + long double z; + long double y; + int e; + int64_t hx; + double xhi; + +/* Test for domain */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + if ((hx & 0x7fffffffffffffffLL) == 0) + return (-1.0L / __fabsl (x)); /* log10l(+-0)=-inf */ + if (hx < 0) + return (x - x) / (x - x); + if (hx >= 0x7ff0000000000000LL) + return (x + x); + + if (x == 1.0L) + return 0.0L; + +/* separate mantissa from exponent */ + +/* Note, frexp is used so that denormal numbers + * will be handled properly. + */ + x = __frexpl (x, &e); + + +/* logarithm using log(x) = z + z**3 P(z)/Q(z), + * where z = 2(x-1)/x+1) + */ + if ((e > 2) || (e < -2)) + { + if (x < SQRTH) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } + else + { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } + x = z / y; + z = x * x; + y = x * (z * neval (z, R, 5) / deval (z, S, 5)); + goto done; + } + + +/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ + + if (x < SQRTH) + { + e -= 1; + x = 2.0 * x - 1.0L; /* 2x - 1 */ + } + else + { + x = x - 1.0L; + } + z = x * x; + y = x * (z * neval (x, P, 12) / deval (x, Q, 11)); + y = y - 0.5 * z; + +done: + + /* Multiply log of fraction by log10(e) + * and base 2 exponent by log10(2). + */ + z = y * L10EB; + z += x * L10EB; + z += e * L102B; + z += y * L10EA; + z += x * L10EA; + z += e * L102A; + return (z); +} +strong_alias (__ieee754_log10l, __log10l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_log2l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_log2l.c new file mode 100644 index 0000000000..c820dacf08 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_log2l.c @@ -0,0 +1,254 @@ +/* log2l.c + * Base 2 logarithm, 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log2l(); + * + * y = log2l( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base 2 logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the (natural) + * logarithm of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(x-1)/x+1), + * + * log(x) = z + z^3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.5, 2.0 100,000 2.6e-34 4.9e-35 + * IEEE exp(+-10000) 100,000 9.6e-35 4.0e-35 + * + * In the tests over the interval exp(+-10000), the logarithms + * of the random arguments were uniformly distributed over + * [-10000, +10000]. + * + */ + +/* + Cephes Math Library Release 2.2: January, 1991 + Copyright 1984, 1991 by Stephen L. Moshier + Adapted for glibc November, 2001 + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see <http://www.gnu.org/licenses/>. + */ + +#include <math.h> +#include <math_private.h> + +/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 5.3e-37, + * relative peak error spread = 2.3e-14 + */ +static const long double P[13] = +{ + 1.313572404063446165910279910527789794488E4L, + 7.771154681358524243729929227226708890930E4L, + 2.014652742082537582487669938141683759923E5L, + 3.007007295140399532324943111654767187848E5L, + 2.854829159639697837788887080758954924001E5L, + 1.797628303815655343403735250238293741397E5L, + 7.594356839258970405033155585486712125861E4L, + 2.128857716871515081352991964243375186031E4L, + 3.824952356185897735160588078446136783779E3L, + 4.114517881637811823002128927449878962058E2L, + 2.321125933898420063925789532045674660756E1L, + 4.998469661968096229986658302195402690910E-1L, + 1.538612243596254322971797716843006400388E-6L +}; +static const long double Q[12] = +{ + 3.940717212190338497730839731583397586124E4L, + 2.626900195321832660448791748036714883242E5L, + 7.777690340007566932935753241556479363645E5L, + 1.347518538384329112529391120390701166528E6L, + 1.514882452993549494932585972882995548426E6L, + 1.158019977462989115839826904108208787040E6L, + 6.132189329546557743179177159925690841200E5L, + 2.248234257620569139969141618556349415120E5L, + 5.605842085972455027590989944010492125825E4L, + 9.147150349299596453976674231612674085381E3L, + 9.104928120962988414618126155557301584078E2L, + 4.839208193348159620282142911143429644326E1L +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 1.1e-35, + * relative peak error spread 1.1e-9 + */ +static const long double R[6] = +{ + 1.418134209872192732479751274970992665513E5L, + -8.977257995689735303686582344659576526998E4L, + 2.048819892795278657810231591630928516206E4L, + -2.024301798136027039250415126250455056397E3L, + 8.057002716646055371965756206836056074715E1L, + -8.828896441624934385266096344596648080902E-1L +}; +static const long double S[6] = +{ + 1.701761051846631278975701529965589676574E6L, + -1.332535117259762928288745111081235577029E6L, + 4.001557694070773974936904547424676279307E5L, + -5.748542087379434595104154610899551484314E4L, + 3.998526750980007367835804959888064681098E3L, + -1.186359407982897997337150403816839480438E2L +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const long double +/* log2(e) - 1 */ +LOG2EA = 4.4269504088896340735992468100189213742664595E-1L, +/* sqrt(2)/2 */ +SQRTH = 7.071067811865475244008443621048490392848359E-1L; + + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +neval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +deval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + + +long double +__ieee754_log2l (long double x) +{ + long double z; + long double y; + int e; + int64_t hx; + double xhi; + +/* Test for domain */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + if ((hx & 0x7fffffffffffffffLL) == 0) + return (-1.0L / __fabsl (x)); /* log2l(+-0)=-inf */ + if (hx < 0) + return (x - x) / (x - x); + if (hx >= 0x7ff0000000000000LL) + return (x + x); + + if (x == 1.0L) + return 0.0L; + +/* separate mantissa from exponent */ + +/* Note, frexp is used so that denormal numbers + * will be handled properly. + */ + x = __frexpl (x, &e); + + +/* logarithm using log(x) = z + z**3 P(z)/Q(z), + * where z = 2(x-1)/x+1) + */ + if ((e > 2) || (e < -2)) + { + if (x < SQRTH) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } + else + { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } + x = z / y; + z = x * x; + y = x * (z * neval (z, R, 5) / deval (z, S, 5)); + goto done; + } + + +/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ + + if (x < SQRTH) + { + e -= 1; + x = 2.0 * x - 1.0L; /* 2x - 1 */ + } + else + { + x = x - 1.0L; + } + z = x * x; + y = x * (z * neval (x, P, 12) / deval (x, Q, 11)); + y = y - 0.5 * z; + +done: + +/* Multiply log of fraction by log2(e) + * and base 2 exponent by 1 + */ + z = y * LOG2EA; + z += x * LOG2EA; + z += y; + z += x; + z += e; + return (z); +} +strong_alias (__ieee754_log2l, __log2l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_logl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_logl.c new file mode 100644 index 0000000000..c44feca65b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_logl.c @@ -0,0 +1,300 @@ +/* logll.c + * + * Natural logarithm for 128-bit long double precision. + * + * + * + * SYNOPSIS: + * + * long double x, y, logl(); + * + * y = logl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base e (2.718...) logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. Use of a lookup table increases the speed of the routine. + * The program uses logarithms tabulated at intervals of 1/128 to + * cover the domain from approximately 0.7 to 1.4. + * + * On the interval [-1/128, +1/128] the logarithm of 1+x is approximated by + * log(1+x) = x - 0.5 x^2 + x^3 P(x) . + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.875, 1.125 100000 1.2e-34 4.1e-35 + * IEEE 0.125, 8 100000 1.2e-34 4.1e-35 + * + * + * WARNING: + * + * This program uses integer operations on bit fields of floating-point + * numbers. It does not work with data structures other than the + * structure assumed. + * + */ + +/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov> + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* log(1+x) = x - .5 x^2 + x^3 l(x) + -.0078125 <= x <= +.0078125 + peak relative error 1.2e-37 */ +static const long double +l3 = 3.333333333333333333333333333333336096926E-1L, +l4 = -2.499999999999999999999999999486853077002E-1L, +l5 = 1.999999999999999999999999998515277861905E-1L, +l6 = -1.666666666666666666666798448356171665678E-1L, +l7 = 1.428571428571428571428808945895490721564E-1L, +l8 = -1.249999999999999987884655626377588149000E-1L, +l9 = 1.111111111111111093947834982832456459186E-1L, +l10 = -1.000000000000532974938900317952530453248E-1L, +l11 = 9.090909090915566247008015301349979892689E-2L, +l12 = -8.333333211818065121250921925397567745734E-2L, +l13 = 7.692307559897661630807048686258659316091E-2L, +l14 = -7.144242754190814657241902218399056829264E-2L, +l15 = 6.668057591071739754844678883223432347481E-2L; + +/* Lookup table of ln(t) - (t-1) + t = 0.5 + (k+26)/128) + k = 0, ..., 91 */ +static const long double logtbl[92] = { +-5.5345593589352099112142921677820359632418E-2L, +-5.2108257402767124761784665198737642086148E-2L, +-4.8991686870576856279407775480686721935120E-2L, +-4.5993270766361228596215288742353061431071E-2L, +-4.3110481649613269682442058976885699556950E-2L, +-4.0340872319076331310838085093194799765520E-2L, +-3.7682072451780927439219005993827431503510E-2L, +-3.5131785416234343803903228503274262719586E-2L, +-3.2687785249045246292687241862699949178831E-2L, +-3.0347913785027239068190798397055267411813E-2L, +-2.8110077931525797884641940838507561326298E-2L, +-2.5972247078357715036426583294246819637618E-2L, +-2.3932450635346084858612873953407168217307E-2L, +-2.1988775689981395152022535153795155900240E-2L, +-2.0139364778244501615441044267387667496733E-2L, +-1.8382413762093794819267536615342902718324E-2L, +-1.6716169807550022358923589720001638093023E-2L, +-1.5138929457710992616226033183958974965355E-2L, +-1.3649036795397472900424896523305726435029E-2L, +-1.2244881690473465543308397998034325468152E-2L, +-1.0924898127200937840689817557742469105693E-2L, +-9.6875626072830301572839422532631079809328E-3L, +-8.5313926245226231463436209313499745894157E-3L, +-7.4549452072765973384933565912143044991706E-3L, +-6.4568155251217050991200599386801665681310E-3L, +-5.5356355563671005131126851708522185605193E-3L, +-4.6900728132525199028885749289712348829878E-3L, +-3.9188291218610470766469347968659624282519E-3L, +-3.2206394539524058873423550293617843896540E-3L, +-2.5942708080877805657374888909297113032132E-3L, +-2.0385211375711716729239156839929281289086E-3L, +-1.5522183228760777967376942769773768850872E-3L, +-1.1342191863606077520036253234446621373191E-3L, +-7.8340854719967065861624024730268350459991E-4L, +-4.9869831458030115699628274852562992756174E-4L, +-2.7902661731604211834685052867305795169688E-4L, +-1.2335696813916860754951146082826952093496E-4L, +-3.0677461025892873184042490943581654591817E-5L, +#define ZERO logtbl[38] + 0.0000000000000000000000000000000000000000E0L, +-3.0359557945051052537099938863236321874198E-5L, +-1.2081346403474584914595395755316412213151E-4L, +-2.7044071846562177120083903771008342059094E-4L, +-4.7834133324631162897179240322783590830326E-4L, +-7.4363569786340080624467487620270965403695E-4L, +-1.0654639687057968333207323853366578860679E-3L, +-1.4429854811877171341298062134712230604279E-3L, +-1.8753781835651574193938679595797367137975E-3L, +-2.3618380914922506054347222273705859653658E-3L, +-2.9015787624124743013946600163375853631299E-3L, +-3.4938307889254087318399313316921940859043E-3L, +-4.1378413103128673800485306215154712148146E-3L, +-4.8328735414488877044289435125365629849599E-3L, +-5.5782063183564351739381962360253116934243E-3L, +-6.3731336597098858051938306767880719015261E-3L, +-7.2169643436165454612058905294782949315193E-3L, +-8.1090214990427641365934846191367315083867E-3L, +-9.0486422112807274112838713105168375482480E-3L, +-1.0035177140880864314674126398350812606841E-2L, +-1.1067990155502102718064936259435676477423E-2L, +-1.2146457974158024928196575103115488672416E-2L, +-1.3269969823361415906628825374158424754308E-2L, +-1.4437927104692837124388550722759686270765E-2L, +-1.5649743073340777659901053944852735064621E-2L, +-1.6904842527181702880599758489058031645317E-2L, +-1.8202661505988007336096407340750378994209E-2L, +-1.9542647000370545390701192438691126552961E-2L, +-2.0924256670080119637427928803038530924742E-2L, +-2.2346958571309108496179613803760727786257E-2L, +-2.3810230892650362330447187267648486279460E-2L, +-2.5313561699385640380910474255652501521033E-2L, +-2.6856448685790244233704909690165496625399E-2L, +-2.8438398935154170008519274953860128449036E-2L, +-3.0058928687233090922411781058956589863039E-2L, +-3.1717563112854831855692484086486099896614E-2L, +-3.3413836095418743219397234253475252001090E-2L, +-3.5147290019036555862676702093393332533702E-2L, +-3.6917475563073933027920505457688955423688E-2L, +-3.8723951502862058660874073462456610731178E-2L, +-4.0566284516358241168330505467000838017425E-2L, +-4.2444048996543693813649967076598766917965E-2L, +-4.4356826869355401653098777649745233339196E-2L, +-4.6304207416957323121106944474331029996141E-2L, +-4.8285787106164123613318093945035804818364E-2L, +-5.0301169421838218987124461766244507342648E-2L, +-5.2349964705088137924875459464622098310997E-2L, +-5.4431789996103111613753440311680967840214E-2L, +-5.6546268881465384189752786409400404404794E-2L, +-5.8693031345788023909329239565012647817664E-2L, +-6.0871713627532018185577188079210189048340E-2L, +-6.3081958078862169742820420185833800925568E-2L, +-6.5323413029406789694910800219643791556918E-2L, +-6.7595732653791419081537811574227049288168E-2L +}; + +/* ln(2) = ln2a + ln2b with extended precision. */ +static const long double + ln2a = 6.93145751953125e-1L, + ln2b = 1.4286068203094172321214581765680755001344E-6L; + +static const long double + ldbl_epsilon = 0x1p-106L; + +long double +__ieee754_logl(long double x) +{ + long double z, y, w, t; + unsigned int m; + int k, e; + double xhi; + uint32_t hx, lx; + + xhi = ldbl_high (x); + EXTRACT_WORDS (hx, lx, xhi); + m = hx; + + /* Check for IEEE special cases. */ + k = m & 0x7fffffff; + /* log(0) = -infinity. */ + if ((k | lx) == 0) + { + return -0.5L / ZERO; + } + /* log ( x < 0 ) = NaN */ + if (m & 0x80000000) + { + return (x - x) / ZERO; + } + /* log (infinity or NaN) */ + if (k >= 0x7ff00000) + { + return x + x; + } + + /* On this interval the table is not used due to cancellation error. */ + if ((x <= 1.0078125L) && (x >= 0.9921875L)) + { + if (x == 1.0L) + return 0.0L; + z = x - 1.0L; + k = 64; + t = 1.0L; + e = 0; + } + else + { + /* Extract exponent and reduce domain to 0.703125 <= u < 1.40625 */ + unsigned int w0; + e = (int) (m >> 20) - (int) 0x3fe; + if (e == -1022) + { + x *= 0x1p106L; + xhi = ldbl_high (x); + EXTRACT_WORDS (hx, lx, xhi); + m = hx; + e = (int) (m >> 20) - (int) 0x3fe - 106; + } + m &= 0xfffff; + w0 = m | 0x3fe00000; + m |= 0x100000; + /* Find lookup table index k from high order bits of the significand. */ + if (m < 0x168000) + { + k = (m - 0xff000) >> 13; + /* t is the argument 0.5 + (k+26)/128 + of the nearest item to u in the lookup table. */ + INSERT_WORDS (xhi, 0x3ff00000 + (k << 13), 0); + t = xhi; + w0 += 0x100000; + e -= 1; + k += 64; + } + else + { + k = (m - 0xfe000) >> 14; + INSERT_WORDS (xhi, 0x3fe00000 + (k << 14), 0); + t = xhi; + } + x = __scalbnl (x, ((int) ((w0 - hx) * 2)) >> 21); + /* log(u) = log( t u/t ) = log(t) + log(u/t) + log(t) is tabulated in the lookup table. + Express log(u/t) = log(1+z), where z = u/t - 1 = (u-t)/t. + cf. Cody & Waite. */ + z = (x - t) / t; + } + /* Series expansion of log(1+z). */ + w = z * z; + /* Avoid spurious underflows. */ + if (__glibc_unlikely (fabsl (z) <= ldbl_epsilon)) + y = 0.0L; + else + { + y = ((((((((((((l15 * z + + l14) * z + + l13) * z + + l12) * z + + l11) * z + + l10) * z + + l9) * z + + l8) * z + + l7) * z + + l6) * z + + l5) * z + + l4) * z + + l3) * z * w; + y -= 0.5 * w; + } + y += e * ln2b; /* Base 2 exponent offset times ln(2). */ + y += z; + y += logtbl[k-26]; /* log(t) - (t-1) */ + y += (t - 1.0L); + y += e * ln2a; + return y; +} +strong_alias (__ieee754_logl, __logl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_powl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_powl.c new file mode 100644 index 0000000000..d6fbef6997 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_powl.c @@ -0,0 +1,415 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Expansions and modifications for 128-bit long double are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_powl(x,y) return x**y + * + * n + * Method: Let x = 2 * (1+f) + * 1. Compute and return log2(x) in two pieces: + * log2(x) = w1 + w2, + * where w1 has 113-53 = 60 bit trailing zeros. + * 2. Perform y*log2(x) = n+y' by simulating muti-precision + * arithmetic, where |y'|<=0.5. + * 3. Return x**y = 2**n*exp(y'*log2) + * + * Special cases: + * 1. (anything) ** 0 is 1 + * 2. (anything) ** 1 is itself + * 3. (anything) ** NAN is NAN + * 4. NAN ** (anything except 0) is NAN + * 5. +-(|x| > 1) ** +INF is +INF + * 6. +-(|x| > 1) ** -INF is +0 + * 7. +-(|x| < 1) ** +INF is +0 + * 8. +-(|x| < 1) ** -INF is +INF + * 9. +-1 ** +-INF is NAN + * 10. +0 ** (+anything except 0, NAN) is +0 + * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 12. +0 ** (-anything except 0, NAN) is +INF + * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 15. +INF ** (+anything except 0,NAN) is +INF + * 16. +INF ** (-anything except 0,NAN) is +0 + * 17. -INF ** (anything) = -0 ** (-anything) + * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * + */ + +#include <math.h> +#include <math_private.h> + +static const long double bp[] = { + 1.0L, + 1.5L, +}; + +/* log_2(1.5) */ +static const long double dp_h[] = { + 0.0, + 5.8496250072115607565592654282227158546448E-1L +}; + +/* Low part of log_2(1.5) */ +static const long double dp_l[] = { + 0.0, + 1.0579781240112554492329533686862998106046E-16L +}; + +static const long double zero = 0.0L, + one = 1.0L, + two = 2.0L, + two113 = 1.0384593717069655257060992658440192E34L, + huge = 1.0e300L, + tiny = 1.0e-300L; + +/* 3/2 log x = 3 z + z^3 + z^3 (z^2 R(z^2)) + z = (x-1)/(x+1) + 1 <= x <= 1.25 + Peak relative error 2.3e-37 */ +static const long double LN[] = +{ + -3.0779177200290054398792536829702930623200E1L, + 6.5135778082209159921251824580292116201640E1L, + -4.6312921812152436921591152809994014413540E1L, + 1.2510208195629420304615674658258363295208E1L, + -9.9266909031921425609179910128531667336670E-1L +}; +static const long double LD[] = +{ + -5.129862866715009066465422805058933131960E1L, + 1.452015077564081884387441590064272782044E2L, + -1.524043275549860505277434040464085593165E2L, + 7.236063513651544224319663428634139768808E1L, + -1.494198912340228235853027849917095580053E1L + /* 1.0E0 */ +}; + +/* exp(x) = 1 + x - x / (1 - 2 / (x - x^2 R(x^2))) + 0 <= x <= 0.5 + Peak relative error 5.7e-38 */ +static const long double PN[] = +{ + 5.081801691915377692446852383385968225675E8L, + 9.360895299872484512023336636427675327355E6L, + 4.213701282274196030811629773097579432957E4L, + 5.201006511142748908655720086041570288182E1L, + 9.088368420359444263703202925095675982530E-3L, +}; +static const long double PD[] = +{ + 3.049081015149226615468111430031590411682E9L, + 1.069833887183886839966085436512368982758E8L, + 8.259257717868875207333991924545445705394E5L, + 1.872583833284143212651746812884298360922E3L, + /* 1.0E0 */ +}; + +static const long double + /* ln 2 */ + lg2 = 6.9314718055994530941723212145817656807550E-1L, + lg2_h = 6.9314718055994528622676398299518041312695E-1L, + lg2_l = 2.3190468138462996154948554638754786504121E-17L, + ovt = 8.0085662595372944372e-0017L, + /* 2/(3*log(2)) */ + cp = 9.6179669392597560490661645400126142495110E-1L, + cp_h = 9.6179669392597555432899980587535537779331E-1L, + cp_l = 5.0577616648125906047157785230014751039424E-17L; + +long double +__ieee754_powl (long double x, long double y) +{ + long double z, ax, z_h, z_l, p_h, p_l; + long double y1, t1, t2, r, s, sgn, t, u, v, w; + long double s2, s_h, s_l, t_h, t_l, ay; + int32_t i, j, k, yisint, n; + uint32_t ix, iy; + int32_t hx, hy, hax; + double ohi, xhi, xlo, yhi, ylo; + uint32_t lx, ly, lj; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS (hx, lx, xhi); + ix = hx & 0x7fffffff; + + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS (hy, ly, yhi); + iy = hy & 0x7fffffff; + + /* y==zero: x**0 = 1 */ + if ((iy | ly) == 0 && !issignaling (x)) + return one; + + /* 1.0**y = 1; -1.0**+-Inf = 1 */ + if (x == one && !issignaling (y)) + return one; + if (x == -1.0L && ((iy - 0x7ff00000) | ly) == 0) + return one; + + /* +-NaN return x+y */ + if ((ix >= 0x7ff00000 && ((ix - 0x7ff00000) | lx) != 0) + || (iy >= 0x7ff00000 && ((iy - 0x7ff00000) | ly) != 0)) + return x + y; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if (hx < 0) + { + uint32_t low_ye; + + GET_HIGH_WORD (low_ye, ylo); + if ((low_ye & 0x7fffffff) >= 0x43400000) /* Low part >= 2^53 */ + yisint = 2; /* even integer y */ + else if (iy >= 0x3ff00000) /* 1.0 */ + { + if (__floorl (y) == y) + { + z = 0.5 * y; + if (__floorl (z) == z) + yisint = 2; + else + yisint = 1; + } + } + } + + ax = fabsl (x); + + /* special value of y */ + if (ly == 0) + { + if (iy == 0x7ff00000) /* y is +-inf */ + { + if (ax > one) + /* (|x|>1)**+-inf = inf,0 */ + return (hy >= 0) ? y : zero; + else + /* (|x|<1)**-,+inf = inf,0 */ + return (hy < 0) ? -y : zero; + } + if (ylo == 0.0) + { + if (iy == 0x3ff00000) + { /* y is +-1 */ + if (hy < 0) + return one / x; + else + return x; + } + if (hy == 0x40000000) + return x * x; /* y is 2 */ + if (hy == 0x3fe00000) + { /* y is 0.5 */ + if (hx >= 0) /* x >= +0 */ + return __ieee754_sqrtl (x); + } + } + } + + /* special value of x */ + if (lx == 0) + { + if (ix == 0x7ff00000 || ix == 0 || (ix == 0x3ff00000 && xlo == 0.0)) + { + z = ax; /*x is +-0,+-inf,+-1 */ + if (hy < 0) + z = one / z; /* z = (1/|x|) */ + if (hx < 0) + { + if (((ix - 0x3ff00000) | yisint) == 0) + { + z = (z - z) / (z - z); /* (-1)**non-int is NaN */ + } + else if (yisint == 1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + } + + /* (x<0)**(non-int) is NaN */ + if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0) + return (x - x) / (x - x); + + /* sgn (sign of result -ve**odd) = -1 else = 1 */ + sgn = one; + if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0) + sgn = -one; /* (-ve)**(odd int) */ + + /* |y| is huge. + 2^-16495 = 1/2 of smallest representable value. + If (1 - 1/131072)^y underflows, y > 1.4986e9 */ + if (iy > 0x41d654b0) + { + /* if (1 - 2^-113)^y underflows, y > 1.1873e38 */ + if (iy > 0x47d654b0) + { + if (ix <= 0x3fefffff) + return (hy < 0) ? sgn * huge * huge : sgn * tiny * tiny; + if (ix >= 0x3ff00000) + return (hy > 0) ? sgn * huge * huge : sgn * tiny * tiny; + } + /* over/underflow if x is not close to one */ + if (ix < 0x3fefffff) + return (hy < 0) ? sgn * huge * huge : sgn * tiny * tiny; + if (ix > 0x3ff00000) + return (hy > 0) ? sgn * huge * huge : sgn * tiny * tiny; + } + + ay = y > 0 ? y : -y; + if (ay < 0x1p-117) + y = y < 0 ? -0x1p-117 : 0x1p-117; + + n = 0; + /* take care subnormal number */ + if (ix < 0x00100000) + { + ax *= two113; + n -= 113; + ohi = ldbl_high (ax); + GET_HIGH_WORD (ix, ohi); + } + n += ((ix) >> 20) - 0x3ff; + j = ix & 0x000fffff; + /* determine interval */ + ix = j | 0x3ff00000; /* normalize ix */ + if (j <= 0x39880) + k = 0; /* |x|<sqrt(3/2) */ + else if (j < 0xbb670) + k = 1; /* |x|<sqrt(3) */ + else + { + k = 0; + n += 1; + ix -= 0x00100000; + } + + ohi = ldbl_high (ax); + GET_HIGH_WORD (hax, ohi); + ax = __scalbnl (ax, ((int) ((ix - hax) * 2)) >> 21); + + /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ + u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ + v = one / (ax + bp[k]); + s = u * v; + s_h = ldbl_high (s); + + /* t_h=ax+bp[k] High */ + t_h = ax + bp[k]; + t_h = ldbl_high (t_h); + t_l = ax - (t_h - bp[k]); + s_l = v * ((u - s_h * t_h) - s_h * t_l); + /* compute log(ax) */ + s2 = s * s; + u = LN[0] + s2 * (LN[1] + s2 * (LN[2] + s2 * (LN[3] + s2 * LN[4]))); + v = LD[0] + s2 * (LD[1] + s2 * (LD[2] + s2 * (LD[3] + s2 * (LD[4] + s2)))); + r = s2 * s2 * u / v; + r += s_l * (s_h + s); + s2 = s_h * s_h; + t_h = 3.0 + s2 + r; + t_h = ldbl_high (t_h); + t_l = r - ((t_h - 3.0) - s2); + /* u+v = s*(1+...) */ + u = s_h * t_h; + v = s_l * t_h + t_l * s; + /* 2/(3log2)*(s+...) */ + p_h = u + v; + p_h = ldbl_high (p_h); + p_l = v - (p_h - u); + z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l * p_h + p_l * cp + dp_l[k]; + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (long double) n; + t1 = (((z_h + z_l) + dp_h[k]) + t); + t1 = ldbl_high (t1); + t2 = z_l - (((t1 - t) - dp_h[k]) - z_h); + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + y1 = ldbl_high (y); + p_l = (y - y1) * t1 + y * t2; + p_h = y1 * t1; + z = p_l + p_h; + ohi = ldbl_high (z); + EXTRACT_WORDS (j, lj, ohi); + if (j >= 0x40d00000) /* z >= 16384 */ + { + /* if z > 16384 */ + if (((j - 0x40d00000) | lj) != 0) + return sgn * huge * huge; /* overflow */ + else + { + if (p_l + ovt > z - p_h) + return sgn * huge * huge; /* overflow */ + } + } + else if ((j & 0x7fffffff) >= 0x40d01b90) /* z <= -16495 */ + { + /* z < -16495 */ + if (((j - 0xc0d01bc0) | lj) != 0) + return sgn * tiny * tiny; /* underflow */ + else + { + if (p_l <= z - p_h) + return sgn * tiny * tiny; /* underflow */ + } + } + /* compute 2**(p_h+p_l) */ + i = j & 0x7fffffff; + k = (i >> 20) - 0x3ff; + n = 0; + if (i > 0x3fe00000) + { /* if |z| > 0.5, set n = [z+0.5] */ + n = __floorl (z + 0.5L); + t = n; + p_h -= t; + } + t = p_l + p_h; + t = ldbl_high (t); + u = t * lg2_h; + v = (p_l - (t - p_h)) * lg2 + t * lg2_l; + z = u + v; + w = v - (z - u); + /* exp(z) */ + t = z * z; + u = PN[0] + t * (PN[1] + t * (PN[2] + t * (PN[3] + t * PN[4]))); + v = PD[0] + t * (PD[1] + t * (PD[2] + t * (PD[3] + t))); + t1 = z - t * u / v; + r = (z * t1) / (t1 - two) - (w + z * w); + z = one - (r - z); + z = __scalbnl (sgn * z, n); + math_check_force_underflow (z); + return z; +} +strong_alias (__ieee754_powl, __powl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c new file mode 100644 index 0000000000..5aa2c1c007 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c @@ -0,0 +1,279 @@ +/* Quad-precision floating point argument reduction. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <ieee754.h> + +/* + * Table of constants for 2/pi, 5628 hexadecimal digits of 2/pi + */ +static const int32_t two_over_pi[] = { +0xa2f983, 0x6e4e44, 0x1529fc, 0x2757d1, 0xf534dd, 0xc0db62, +0x95993c, 0x439041, 0xfe5163, 0xabdebb, 0xc561b7, 0x246e3a, +0x424dd2, 0xe00649, 0x2eea09, 0xd1921c, 0xfe1deb, 0x1cb129, +0xa73ee8, 0x8235f5, 0x2ebb44, 0x84e99c, 0x7026b4, 0x5f7e41, +0x3991d6, 0x398353, 0x39f49c, 0x845f8b, 0xbdf928, 0x3b1ff8, +0x97ffde, 0x05980f, 0xef2f11, 0x8b5a0a, 0x6d1f6d, 0x367ecf, +0x27cb09, 0xb74f46, 0x3f669e, 0x5fea2d, 0x7527ba, 0xc7ebe5, +0xf17b3d, 0x0739f7, 0x8a5292, 0xea6bfb, 0x5fb11f, 0x8d5d08, +0x560330, 0x46fc7b, 0x6babf0, 0xcfbc20, 0x9af436, 0x1da9e3, +0x91615e, 0xe61b08, 0x659985, 0x5f14a0, 0x68408d, 0xffd880, +0x4d7327, 0x310606, 0x1556ca, 0x73a8c9, 0x60e27b, 0xc08c6b, +0x47c419, 0xc367cd, 0xdce809, 0x2a8359, 0xc4768b, 0x961ca6, +0xddaf44, 0xd15719, 0x053ea5, 0xff0705, 0x3f7e33, 0xe832c2, +0xde4f98, 0x327dbb, 0xc33d26, 0xef6b1e, 0x5ef89f, 0x3a1f35, +0xcaf27f, 0x1d87f1, 0x21907c, 0x7c246a, 0xfa6ed5, 0x772d30, +0x433b15, 0xc614b5, 0x9d19c3, 0xc2c4ad, 0x414d2c, 0x5d000c, +0x467d86, 0x2d71e3, 0x9ac69b, 0x006233, 0x7cd2b4, 0x97a7b4, +0xd55537, 0xf63ed7, 0x1810a3, 0xfc764d, 0x2a9d64, 0xabd770, +0xf87c63, 0x57b07a, 0xe71517, 0x5649c0, 0xd9d63b, 0x3884a7, +0xcb2324, 0x778ad6, 0x23545a, 0xb91f00, 0x1b0af1, 0xdfce19, +0xff319f, 0x6a1e66, 0x615799, 0x47fbac, 0xd87f7e, 0xb76522, +0x89e832, 0x60bfe6, 0xcdc4ef, 0x09366c, 0xd43f5d, 0xd7de16, +0xde3b58, 0x929bde, 0x2822d2, 0xe88628, 0x4d58e2, 0x32cac6, +0x16e308, 0xcb7de0, 0x50c017, 0xa71df3, 0x5be018, 0x34132e, +0x621283, 0x014883, 0x5b8ef5, 0x7fb0ad, 0xf2e91e, 0x434a48, +0xd36710, 0xd8ddaa, 0x425fae, 0xce616a, 0xa4280a, 0xb499d3, +0xf2a606, 0x7f775c, 0x83c2a3, 0x883c61, 0x78738a, 0x5a8caf, +0xbdd76f, 0x63a62d, 0xcbbff4, 0xef818d, 0x67c126, 0x45ca55, +0x36d9ca, 0xd2a828, 0x8d61c2, 0x77c912, 0x142604, 0x9b4612, +0xc459c4, 0x44c5c8, 0x91b24d, 0xf31700, 0xad43d4, 0xe54929, +0x10d5fd, 0xfcbe00, 0xcc941e, 0xeece70, 0xf53e13, 0x80f1ec, +0xc3e7b3, 0x28f8c7, 0x940593, 0x3e71c1, 0xb3092e, 0xf3450b, +0x9c1288, 0x7b20ab, 0x9fb52e, 0xc29247, 0x2f327b, 0x6d550c, +0x90a772, 0x1fe76b, 0x96cb31, 0x4a1679, 0xe27941, 0x89dff4, +0x9794e8, 0x84e6e2, 0x973199, 0x6bed88, 0x365f5f, 0x0efdbb, +0xb49a48, 0x6ca467, 0x427271, 0x325d8d, 0xb8159f, 0x09e5bc, +0x25318d, 0x3974f7, 0x1c0530, 0x010c0d, 0x68084b, 0x58ee2c, +0x90aa47, 0x02e774, 0x24d6bd, 0xa67df7, 0x72486e, 0xef169f, +0xa6948e, 0xf691b4, 0x5153d1, 0xf20acf, 0x339820, 0x7e4bf5, +0x6863b2, 0x5f3edd, 0x035d40, 0x7f8985, 0x295255, 0xc06437, +0x10d86d, 0x324832, 0x754c5b, 0xd4714e, 0x6e5445, 0xc1090b, +0x69f52a, 0xd56614, 0x9d0727, 0x50045d, 0xdb3bb4, 0xc576ea, +0x17f987, 0x7d6b49, 0xba271d, 0x296996, 0xacccc6, 0x5414ad, +0x6ae290, 0x89d988, 0x50722c, 0xbea404, 0x940777, 0x7030f3, +0x27fc00, 0xa871ea, 0x49c266, 0x3de064, 0x83dd97, 0x973fa3, +0xfd9443, 0x8c860d, 0xde4131, 0x9d3992, 0x8c70dd, 0xe7b717, +0x3bdf08, 0x2b3715, 0xa0805c, 0x93805a, 0x921110, 0xd8e80f, +0xaf806c, 0x4bffdb, 0x0f9038, 0x761859, 0x15a562, 0xbbcb61, +0xb989c7, 0xbd4010, 0x04f2d2, 0x277549, 0xf6b6eb, 0xbb22db, +0xaa140a, 0x2f2689, 0x768364, 0x333b09, 0x1a940e, 0xaa3a51, +0xc2a31d, 0xaeedaf, 0x12265c, 0x4dc26d, 0x9c7a2d, 0x9756c0, +0x833f03, 0xf6f009, 0x8c402b, 0x99316d, 0x07b439, 0x15200c, +0x5bc3d8, 0xc492f5, 0x4badc6, 0xa5ca4e, 0xcd37a7, 0x36a9e6, +0x9492ab, 0x6842dd, 0xde6319, 0xef8c76, 0x528b68, 0x37dbfc, +0xaba1ae, 0x3115df, 0xa1ae00, 0xdafb0c, 0x664d64, 0xb705ed, +0x306529, 0xbf5657, 0x3aff47, 0xb9f96a, 0xf3be75, 0xdf9328, +0x3080ab, 0xf68c66, 0x15cb04, 0x0622fa, 0x1de4d9, 0xa4b33d, +0x8f1b57, 0x09cd36, 0xe9424e, 0xa4be13, 0xb52333, 0x1aaaf0, +0xa8654f, 0xa5c1d2, 0x0f3f0b, 0xcd785b, 0x76f923, 0x048b7b, +0x721789, 0x53a6c6, 0xe26e6f, 0x00ebef, 0x584a9b, 0xb7dac4, +0xba66aa, 0xcfcf76, 0x1d02d1, 0x2df1b1, 0xc1998c, 0x77adc3, +0xda4886, 0xa05df7, 0xf480c6, 0x2ff0ac, 0x9aecdd, 0xbc5c3f, +0x6dded0, 0x1fc790, 0xb6db2a, 0x3a25a3, 0x9aaf00, 0x9353ad, +0x0457b6, 0xb42d29, 0x7e804b, 0xa707da, 0x0eaa76, 0xa1597b, +0x2a1216, 0x2db7dc, 0xfde5fa, 0xfedb89, 0xfdbe89, 0x6c76e4, +0xfca906, 0x70803e, 0x156e85, 0xff87fd, 0x073e28, 0x336761, +0x86182a, 0xeabd4d, 0xafe7b3, 0x6e6d8f, 0x396795, 0x5bbf31, +0x48d784, 0x16df30, 0x432dc7, 0x356125, 0xce70c9, 0xb8cb30, +0xfd6cbf, 0xa200a4, 0xe46c05, 0xa0dd5a, 0x476f21, 0xd21262, +0x845cb9, 0x496170, 0xe0566b, 0x015299, 0x375550, 0xb7d51e, +0xc4f133, 0x5f6e13, 0xe4305d, 0xa92e85, 0xc3b21d, 0x3632a1, +0xa4b708, 0xd4b1ea, 0x21f716, 0xe4698f, 0x77ff27, 0x80030c, +0x2d408d, 0xa0cd4f, 0x99a520, 0xd3a2b3, 0x0a5d2f, 0x42f9b4, +0xcbda11, 0xd0be7d, 0xc1db9b, 0xbd17ab, 0x81a2ca, 0x5c6a08, +0x17552e, 0x550027, 0xf0147f, 0x8607e1, 0x640b14, 0x8d4196, +0xdebe87, 0x2afdda, 0xb6256b, 0x34897b, 0xfef305, 0x9ebfb9, +0x4f6a68, 0xa82a4a, 0x5ac44f, 0xbcf82d, 0x985ad7, 0x95c7f4, +0x8d4d0d, 0xa63a20, 0x5f57a4, 0xb13f14, 0x953880, 0x0120cc, +0x86dd71, 0xb6dec9, 0xf560bf, 0x11654d, 0x6b0701, 0xacb08c, +0xd0c0b2, 0x485551, 0x0efb1e, 0xc37295, 0x3b06a3, 0x3540c0, +0x7bdc06, 0xcc45e0, 0xfa294e, 0xc8cad6, 0x41f3e8, 0xde647c, +0xd8649b, 0x31bed9, 0xc397a4, 0xd45877, 0xc5e369, 0x13daf0, +0x3c3aba, 0x461846, 0x5f7555, 0xf5bdd2, 0xc6926e, 0x5d2eac, +0xed440e, 0x423e1c, 0x87c461, 0xe9fd29, 0xf3d6e7, 0xca7c22, +0x35916f, 0xc5e008, 0x8dd7ff, 0xe26a6e, 0xc6fdb0, 0xc10893, +0x745d7c, 0xb2ad6b, 0x9d6ecd, 0x7b723e, 0x6a11c6, 0xa9cff7, +0xdf7329, 0xbac9b5, 0x5100b7, 0x0db2e2, 0x24ba74, 0x607de5, +0x8ad874, 0x2c150d, 0x0c1881, 0x94667e, 0x162901, 0x767a9f, +0xbefdfd, 0xef4556, 0x367ed9, 0x13d9ec, 0xb9ba8b, 0xfc97c4, +0x27a831, 0xc36ef1, 0x36c594, 0x56a8d8, 0xb5a8b4, 0x0ecccf, +0x2d8912, 0x34576f, 0x89562c, 0xe3ce99, 0xb920d6, 0xaa5e6b, +0x9c2a3e, 0xcc5f11, 0x4a0bfd, 0xfbf4e1, 0x6d3b8e, 0x2c86e2, +0x84d4e9, 0xa9b4fc, 0xd1eeef, 0xc9352e, 0x61392f, 0x442138, +0xc8d91b, 0x0afc81, 0x6a4afb, 0xd81c2f, 0x84b453, 0x8c994e, +0xcc2254, 0xdc552a, 0xd6c6c0, 0x96190b, 0xb8701a, 0x649569, +0x605a26, 0xee523f, 0x0f117f, 0x11b5f4, 0xf5cbfc, 0x2dbc34, +0xeebc34, 0xcc5de8, 0x605edd, 0x9b8e67, 0xef3392, 0xb817c9, +0x9b5861, 0xbc57e1, 0xc68351, 0x103ed8, 0x4871dd, 0xdd1c2d, +0xa118af, 0x462c21, 0xd7f359, 0x987ad9, 0xc0549e, 0xfa864f, +0xfc0656, 0xae79e5, 0x362289, 0x22ad38, 0xdc9367, 0xaae855, +0x382682, 0x9be7ca, 0xa40d51, 0xb13399, 0x0ed7a9, 0x480569, +0xf0b265, 0xa7887f, 0x974c88, 0x36d1f9, 0xb39221, 0x4a827b, +0x21cf98, 0xdc9f40, 0x5547dc, 0x3a74e1, 0x42eb67, 0xdf9dfe, +0x5fd45e, 0xa4677b, 0x7aacba, 0xa2f655, 0x23882b, 0x55ba41, +0x086e59, 0x862a21, 0x834739, 0xe6e389, 0xd49ee5, 0x40fb49, +0xe956ff, 0xca0f1c, 0x8a59c5, 0x2bfa94, 0xc5c1d3, 0xcfc50f, +0xae5adb, 0x86c547, 0x624385, 0x3b8621, 0x94792c, 0x876110, +0x7b4c2a, 0x1a2c80, 0x12bf43, 0x902688, 0x893c78, 0xe4c4a8, +0x7bdbe5, 0xc23ac4, 0xeaf426, 0x8a67f7, 0xbf920d, 0x2ba365, +0xb1933d, 0x0b7cbd, 0xdc51a4, 0x63dd27, 0xdde169, 0x19949a, +0x9529a8, 0x28ce68, 0xb4ed09, 0x209f44, 0xca984e, 0x638270, +0x237c7e, 0x32b90f, 0x8ef5a7, 0xe75614, 0x08f121, 0x2a9db5, +0x4d7e6f, 0x5119a5, 0xabf9b5, 0xd6df82, 0x61dd96, 0x023616, +0x9f3ac4, 0xa1a283, 0x6ded72, 0x7a8d39, 0xa9b882, 0x5c326b, +0x5b2746, 0xed3400, 0x7700d2, 0x55f4fc, 0x4d5901, 0x8071e0, +0xe13f89, 0xb295f3, 0x64a8f1, 0xaea74b, 0x38fc4c, 0xeab2bb, +0x47270b, 0xabc3a7, 0x34ba60, 0x52dd34, 0xf8563a, 0xeb7e8a, +0x31bb36, 0x5895b7, 0x47f7a9, 0x94c3aa, 0xd39225, 0x1e7f3e, +0xd8974e, 0xbba94f, 0xd8ae01, 0xe661b4, 0x393d8e, 0xa523aa, +0x33068e, 0x1633b5, 0x3bb188, 0x1d3a9d, 0x4013d0, 0xcc1be5, +0xf862e7, 0x3bf28f, 0x39b5bf, 0x0bc235, 0x22747e, 0xa247c0, +0xd52d1f, 0x19add3, 0x9094df, 0x9311d0, 0xb42b25, 0x496db2, +0xe264b2, 0x5ef135, 0x3bc6a4, 0x1a4ad0, 0xaac92e, 0x64e886, +0x573091, 0x982cfb, 0x311b1a, 0x08728b, 0xbdcee1, 0x60e142, +0xeb641d, 0xd0bba3, 0xe559d4, 0x597b8c, 0x2a4483, 0xf332ba, +0xf84867, 0x2c8d1b, 0x2fa9b0, 0x50f3dd, 0xf9f573, 0xdb61b4, +0xfe233e, 0x6c41a6, 0xeea318, 0x775a26, 0xbc5e5c, 0xcea708, +0x94dc57, 0xe20196, 0xf1e839, 0xbe4851, 0x5d2d2f, 0x4e9555, +0xd96ec2, 0xe7d755, 0x6304e0, 0xc02e0e, 0xfc40a0, 0xbbf9b3, +0x7125a7, 0x222dfb, 0xf619d8, 0x838c1c, 0x6619e6, 0xb20d55, +0xbb5137, 0x79e809, 0xaf9149, 0x0d73de, 0x0b0da5, 0xce7f58, +0xac1934, 0x724667, 0x7a1a13, 0x9e26bc, 0x4555e7, 0x585cb5, +0x711d14, 0x486991, 0x480d60, 0x56adab, 0xd62f64, 0x96ee0c, +0x212ff3, 0x5d6d88, 0xa67684, 0x95651e, 0xab9e0a, 0x4ddefe, +0x571010, 0x836a39, 0xf8ea31, 0x9e381d, 0xeac8b1, 0xcac96b, +0x37f21e, 0xd505e9, 0x984743, 0x9fc56c, 0x0331b7, 0x3b8bf8, +0x86e56a, 0x8dc343, 0x6230e7, 0x93cfd5, 0x6a8f2d, 0x733005, +0x1af021, 0xa09fcb, 0x7415a1, 0xd56b23, 0x6ff725, 0x2f4bc7, +0xb8a591, 0x7fac59, 0x5c55de, 0x212c38, 0xb13296, 0x5cff50, +0x366262, 0xfa7b16, 0xf4d9a6, 0x2acfe7, 0xf07403, 0xd4d604, +0x6fd916, 0x31b1bf, 0xcbb450, 0x5bd7c8, 0x0ce194, 0x6bd643, +0x4fd91c, 0xdf4543, 0x5f3453, 0xe2b5aa, 0xc9aec8, 0x131485, +0xf9d2bf, 0xbadb9e, 0x76f5b9, 0xaf15cf, 0xca3182, 0x14b56d, +0xe9fe4d, 0x50fc35, 0xf5aed5, 0xa2d0c1, 0xc96057, 0x192eb6, +0xe91d92, 0x07d144, 0xaea3c6, 0x343566, 0x26d5b4, 0x3161e2, +0x37f1a2, 0x209eff, 0x958e23, 0x493798, 0x35f4a6, 0x4bdc02, +0xc2be13, 0xbe80a0, 0x0b72a3, 0x115c5f, 0x1e1bd1, 0x0db4d3, +0x869e85, 0x96976b, 0x2ac91f, 0x8a26c2, 0x3070f0, 0x041412, +0xfc9fa5, 0xf72a38, 0x9c6878, 0xe2aa76, 0x50cfe1, 0x559274, +0x934e38, 0x0a92f7, 0x5533f0, 0xa63db4, 0x399971, 0xe2b755, +0xa98a7c, 0x008f19, 0xac54d2, 0x2ea0b4, 0xf5f3e0, 0x60c849, +0xffd269, 0xae52ce, 0x7a5fdd, 0xe9ce06, 0xfb0ae8, 0xa50cce, +0xea9d3e, 0x3766dd, 0xb834f5, 0x0da090, 0x846f88, 0x4ae3d5, +0x099a03, 0x2eae2d, 0xfcb40a, 0xfb9b33, 0xe281dd, 0x1b16ba, +0xd8c0af, 0xd96b97, 0xb52dc9, 0x9c277f, 0x5951d5, 0x21ccd6, +0xb6496b, 0x584562, 0xb3baf2, 0xa1a5c4, 0x7ca2cf, 0xa9b93d, +0x7b7b89, 0x483d38, +}; + +static const long double c[] = { +/* 106 bits of pi/2 */ +#define PI_2_1 c[0] + 0x1.921fb54442d18469898cc517018p+0L, + +/* pi/2 - PI_2_1 */ +#define PI_2_1t c[1] + 0x3.839a252049c1114cf98e804178p-108L, +}; + +int32_t __ieee754_rem_pio2l(long double x, long double *y) +{ + long double z, w, t; + double tx[8]; + int exp; + int64_t n, ix, hx, ixd; + u_int64_t lxd; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + ix = hx & 0x7fffffffffffffffLL; + if (ix <= 0x3fe921fb54442d10LL) /* x in <-pi/4, pi/4> */ + { + y[0] = x; + y[1] = 0; + return 0; + } + + if (ix < 0x4002d97c7f3321d0LL) /* |x| in <pi/4, 3pi/4) */ + { + if (hx > 0) + { + /* 106 + 106 bit PI is ok */ + z = x - PI_2_1; + y[0] = z - PI_2_1t; + y[1] = (z - y[0]) - PI_2_1t; + return 1; + } + else + { + /* 106 + 106 bit PI is ok */ + z = x + PI_2_1; + y[0] = z + PI_2_1t; + y[1] = (z - y[0]) + PI_2_1t; + return -1; + } + } + + if (ix >= 0x7ff0000000000000LL) /* x is +=oo or NaN */ + { + y[0] = x - x; + y[1] = y[0]; + return 0; + } + + /* Handle large arguments. + We split the 113 bits of the mantissa into 5 24bit integers + stored in a double array. */ + /* Make the IBM extended format 105 bit mantissa look like the ieee854 112 + bit mantissa so the next operation will give the correct result. */ + ldbl_extract_mantissa (&ixd, &lxd, &exp, x); + exp = exp - 23; + /* This is faster than doing this in floating point, because we + have to convert it to integers anyway and like this we can keep + both integer and floating point units busy. */ + tx [0] = (double)(((ixd >> 25) & 0x7fffff) | 0x800000); + tx [1] = (double)((ixd >> 1) & 0xffffff); + tx [2] = (double)(((ixd << 23) | (lxd >> 41)) & 0xffffff); + tx [3] = (double)((lxd >> 17) & 0xffffff); + tx [4] = (double)((lxd << 7) & 0xffffff); + + n = __kernel_rem_pio2 (tx, tx + 5, exp, ((lxd << 7) & 0xffffff) ? 5 : 4, + 3, two_over_pi); + + /* The result is now stored in 3 double values, we need to convert it into + two long double values. */ + t = (long double) tx [6] + (long double) tx [7]; + w = (long double) tx [5]; + + if (hx >= 0) + { + y[0] = w + t; + y[1] = t - (y[0] - w); + return n; + } + else + { + y[0] = -(w + t); + y[1] = -t - (y[0] + w); + return -n; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c new file mode 100644 index 0000000000..68b8fb3519 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c @@ -0,0 +1,81 @@ +/* e_fmodl.c -- long double version of e_fmod.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_remainderl(x,p) + * Return : + * returns x REM p = x - [x/p]*p as if in infinite + * precise arithmetic, where [x/p] is the (infinite bit) + * integer nearest x/p (in half way case choose the even one). + * Method : + * Based on fmodl() return x-[x/p]chopped*p exactlp. + */ + +#include <math.h> +#include <math_private.h> + +static const long double zero = 0.0L; + + +long double +__ieee754_remainderl(long double x, long double p) +{ + int64_t hx,hp; + u_int64_t sx,lx,lp; + long double p_half; + double xhi, xlo, phi, plo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + ldbl_unpack (p, &phi, &plo); + EXTRACT_WORDS64 (hp, phi); + EXTRACT_WORDS64 (lp, plo); + sx = hx&0x8000000000000000ULL; + lp ^= hp & 0x8000000000000000ULL; + hp &= 0x7fffffffffffffffLL; + lx ^= sx; + hx &= 0x7fffffffffffffffLL; + if (lp == 0x8000000000000000ULL) + lp = 0; + if (lx == 0x8000000000000000ULL) + lx = 0; + + /* purge off exception values */ + if(hp==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7ff0000000000000LL)|| /* x not finite */ + (hp>0x7ff0000000000000LL)) /* p is NaN */ + return (x*p)/(x*p); + + + if (hp<=0x7fdfffffffffffffLL) x = __ieee754_fmodl(x,p+p); /* now x < 2p */ + if (((hx-hp)|(lx-lp))==0) return zero*x; + x = fabsl(x); + p = fabsl(p); + if (hp<0x0020000000000000LL) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = 0.5L*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + if (sx) + x = -x; + return x; +} +strong_alias (__ieee754_remainderl, __remainderl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c new file mode 100644 index 0000000000..67d9d24ce7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c @@ -0,0 +1,79 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + +/* __ieee754_sinh(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinh(-x) = -sinh(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 40 : sinh(x) := --------------, E=expm1(x) + * 2 + * + * 40 <= x <= lnovft : sinh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : sinh(x) := x*shuge (overflow) + * + * Special cases: + * sinh(x) is |x| if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite x. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double one = 1.0, shuge = 1.0e307; + +long double +__ieee754_sinhl(long double x) +{ + long double t,w,h; + int64_t ix,jx; + double xhi; + + /* High word of |x|. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (jx, xhi); + ix = jx&0x7fffffffffffffffLL; + + /* x is INF or NaN */ + if(ix>=0x7ff0000000000000LL) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x4044000000000000LL) { /* |x|<40 */ + if (ix<0x3c90000000000000LL) { /* |x|<2**-54 */ + math_check_force_underflow (x); + if(shuge+x>one) return x;/* sinhl(tiny) = tiny with inexact */ + } + t = __expm1l(fabsl(x)); + if(ix<0x3ff0000000000000LL) return h*(2.0*t-t*t/(t+one)); + w = t/(t+one); + return h*(t+w); + } + + /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x40862e42fefa39efLL) return h*__ieee754_expl(fabsl(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix <= 0x408633ce8fb9f87eLL) { + w = __ieee754_expl(0.5*fabsl(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} +strong_alias (__ieee754_sinhl, __sinhl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c new file mode 100644 index 0000000000..8089090533 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c @@ -0,0 +1,102 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*********************************************************************/ +/* MODULE_NAME: uroot.c */ +/* */ +/* FUNCTION: usqrt */ +/* */ +/* FILES NEEDED: dla.h endian.h mydefs.h uroot.h */ +/* uroot.tbl */ +/* */ +/* An ultimate sqrt routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of square */ +/* root of x. */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/*********************************************************************/ + +#include <math_private.h> + +typedef union {int64_t i[2]; long double x; double d[2]; } mynumber; + +static const double + t512 = 0x1p512, + tm256 = 0x1p-256, + two54 = 0x1p54, /* 0x4350000000000000 */ + twom54 = 0x1p-54; /* 0x3C90000000000000 */ + +/*********************************************************************/ +/* An ultimate sqrt routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of square */ +/* root of x. */ +/*********************************************************************/ +long double __ieee754_sqrtl(long double x) +{ + static const long double big = 134217728.0, big1 = 134217729.0; + long double t,s,i; + mynumber a,c; + uint64_t k, l; + int64_t m, n; + double d; + + a.x=x; + k=a.i[0] & INT64_C(0x7fffffffffffffff); + /*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/ + if (k>INT64_C(0x000fffff00000000) && k<INT64_C(0x7ff0000000000000)) { + if (x < 0) return (big1-big1)/(big-big); + l = (k&INT64_C(0x001fffffffffffff))|INT64_C(0x3fe0000000000000); + if ((a.i[1] & INT64_C(0x7fffffffffffffff)) != 0) { + n = (int64_t) ((l - k) * 2) >> 53; + m = (a.i[1] >> 52) & 0x7ff; + if (m == 0) { + a.d[1] *= two54; + m = ((a.i[1] >> 52) & 0x7ff) - 54; + } + m += n; + if (m > 0) + a.i[1] = (a.i[1] & INT64_C(0x800fffffffffffff)) | (m << 52); + else if (m <= -54) { + a.i[1] &= INT64_C(0x8000000000000000); + } else { + m += 54; + a.i[1] = (a.i[1] & INT64_C(0x800fffffffffffff)) | (m << 52); + a.d[1] *= twom54; + } + } + a.i[0] = l; + s = a.x; + d = __ieee754_sqrt (a.d[0]); + c.i[0] = INT64_C(0x2000000000000000)+((k&INT64_C(0x7fe0000000000000))>>1); + c.i[1] = 0; + i = d; + t = 0.5L * (i + s / i); + i = 0.5L * (t + s / t); + return c.x * i; + } + else { + if (k>=INT64_C(0x7ff0000000000000)) + /* sqrt (-Inf) = NaN, sqrt (NaN) = NaN, sqrt (+Inf) = +Inf. */ + return x * x + x; + if (x == 0) return x; + if (x < 0) return (big1-big1)/(big-big); + return tm256*__ieee754_sqrtl(x*t512); + } +} +strong_alias (__ieee754_sqrtl, __sqrtl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c new file mode 100644 index 0000000000..7e71cb008a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c @@ -0,0 +1,42 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +long double +__gamma_productl (long double x, long double x_eps, int n, long double *eps) +{ + long double ret = x; + *eps = x_eps / x; + for (int i = 1; i < n; i++) + { + *eps += x_eps / (x + i); + ret *= x + i; + /* FIXME: no error estimates for the multiplication. */ + } + return ret; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/ieee754.h b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/ieee754.h new file mode 100644 index 0000000000..7e31128996 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/ieee754.h @@ -0,0 +1,133 @@ +/* Copyright (C) 1992-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _IEEE754_H + +#define _IEEE754_H 1 +#include <features.h> + +#include <endian.h> + +__BEGIN_DECLS + +union ieee754_float + { + float f; + + /* This is the IEEE 754 single-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:8; + unsigned int mantissa:23; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + unsigned int mantissa:23; + unsigned int exponent:8; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee; + + /* This format makes it easier to see if a NaN is a signalling NaN. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:8; + unsigned int quiet_nan:1; + unsigned int mantissa:22; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + unsigned int mantissa:22; + unsigned int quiet_nan:1; + unsigned int exponent:8; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee_nan; + }; + +#define IEEE754_FLOAT_BIAS 0x7f /* Added to exponent. */ + + +union ieee754_double + { + double d; + + /* This is the IEEE 754 double-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:11; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:20; + unsigned int mantissa1:32; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + /* Together these comprise the mantissa. */ + unsigned int mantissa1:32; + unsigned int mantissa0:20; + unsigned int exponent:11; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee; + + /* This format makes it easier to see if a NaN is a signalling NaN. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:11; + unsigned int quiet_nan:1; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:19; + unsigned int mantissa1:32; +#else + /* Together these comprise the mantissa. */ + unsigned int mantissa1:32; + unsigned int mantissa0:19; + unsigned int quiet_nan:1; + unsigned int exponent:11; + unsigned int negative:1; +#endif + } ieee_nan; + }; + +#define IEEE754_DOUBLE_BIAS 0x3ff /* Added to exponent. */ + + +/* IBM extended format for long double. + + Each long double is made up of two IEEE doubles. The value of the + long double is the sum of the values of the two parts. The most + significant part is required to be the value of the long double + rounded to the nearest double, as specified by IEEE. For Inf + values, the least significant part is required to be one of +0.0 or + -0.0. No other requirements are made; so, for example, 1.0 may be + represented as (1.0, +0.0) or (1.0, -0.0), and the low part of a + NaN is don't-care. */ + +union ibm_extended_long_double + { + long double ld; + union ieee754_double d[2]; + }; + +__END_DECLS + +#endif /* ieee754.h */ diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/include/bits/iscanonical.h b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/include/bits/iscanonical.h new file mode 100644 index 0000000000..bee080bd29 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/include/bits/iscanonical.h @@ -0,0 +1,5 @@ +#include_next <bits/iscanonical.h> + +#ifndef _ISOMAC +libm_hidden_proto (__iscanonicall) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_cosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_cosl.c new file mode 100644 index 0000000000..0010d6274a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_cosl.c @@ -0,0 +1,153 @@ +/* Quad-precision floating point cosine on <-pi/4,pi/4>. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +static const long double c[] = { +#define ONE c[0] + 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */ + +/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) + x in <0,1/256> */ +#define SCOS1 c[1] +#define SCOS2 c[2] +#define SCOS3 c[3] +#define SCOS4 c[4] +#define SCOS5 c[5] +-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */ + 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */ +-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */ + 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ +-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */ + +/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) + x in <0,0.1484375> */ +#define COS1 c[6] +#define COS2 c[7] +#define COS3 c[8] +#define COS4 c[9] +#define COS5 c[10] +#define COS6 c[11] +#define COS7 c[12] +#define COS8 c[13] +-4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */ + 4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */ +-1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */ + 2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ +-2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */ + 2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */ +-1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */ + 4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ + +/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) + x in <0,1/256> */ +#define SSIN1 c[14] +#define SSIN2 c[15] +#define SSIN3 c[16] +#define SSIN4 c[17] +#define SSIN5 c[18] +-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */ + 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */ +-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */ + 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */ +-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */ +}; + +#define SINCOSL_COS_HI 0 +#define SINCOSL_COS_LO 1 +#define SINCOSL_SIN_HI 2 +#define SINCOSL_SIN_LO 3 +extern const long double __sincosl_table[]; + +long double +__kernel_cosl(long double x, long double y) +{ + long double h, l, z, sin_l, cos_l_m1; + int64_t ix; + uint32_t tix, hix, index; + double xhi, hhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + tix = ((u_int64_t)ix) >> 32; + tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ + if (tix < 0x3fc30000) /* |x| < 0.1484375 */ + { + /* Argument is small enough to approximate it by a Chebyshev + polynomial of degree 16. */ + if (tix < 0x3c600000) /* |x| < 2^-57 */ + if (!((int)x)) return ONE; /* generate inexact */ + z = x * x; + return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ + z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); + } + else + { + /* So that we don't have to use too large polynomial, we find + l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 + possible values for h. We look up cosl(h) and sinl(h) in + pre-computed tables, compute cosl(l) and sinl(l) using a + Chebyshev polynomial of degree 10(11) and compute + cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ + int six = tix; + tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000; + index = 0x3ffe - (tix >> 16); + hix = (tix + (0x200 << index)) & (0xfffffc00 << index); + x = fabsl (x); + switch (index) + { + case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; + case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; + default: + case 2: index = (hix - 0x3ffc3000) >> 10; break; + } + hix = (hix << 4) & 0x3fffffff; +/* + The following should work for double but generates the wrong index. + For now the code above converts double to ieee extended to compute + the index back to double for the h value. + + index = 0x3fe - (tix >> 20); + hix = (tix + (0x200 << index)) & (0xfffffc00 << index); + if (signbit (x)) + { + x = -x; + y = -y; + } + switch (index) + { + case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break; + case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break; + default: + case 2: index = (hix - 0x3fc30000) >> 14; break; + } +*/ + INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32); + h = hhi; + l = y - (h - x); + z = l * l; + sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); + cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); + return __sincosl_table [index + SINCOSL_COS_HI] + + (__sincosl_table [index + SINCOSL_COS_LO] + - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l + - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1)); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_sincosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_sincosl.c new file mode 100644 index 0000000000..14b0359c15 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_sincosl.c @@ -0,0 +1,193 @@ +/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double c[] = { +#define ONE c[0] + 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */ + +/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) + x in <0,1/256> */ +#define SCOS1 c[1] +#define SCOS2 c[2] +#define SCOS3 c[3] +#define SCOS4 c[4] +#define SCOS5 c[5] +-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */ + 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */ +-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */ + 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ +-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */ + +/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) + x in <0,0.1484375> */ +#define COS1 c[6] +#define COS2 c[7] +#define COS3 c[8] +#define COS4 c[9] +#define COS5 c[10] +#define COS6 c[11] +#define COS7 c[12] +#define COS8 c[13] +-4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */ + 4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */ +-1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */ + 2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ +-2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */ + 2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */ +-1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */ + 4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ + +/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) + x in <0,1/256> */ +#define SSIN1 c[14] +#define SSIN2 c[15] +#define SSIN3 c[16] +#define SSIN4 c[17] +#define SSIN5 c[18] +-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */ + 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */ +-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */ + 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */ +-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */ + +/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) + x in <0,0.1484375> */ +#define SIN1 c[19] +#define SIN2 c[20] +#define SIN3 c[21] +#define SIN4 c[22] +#define SIN5 c[23] +#define SIN6 c[24] +#define SIN7 c[25] +#define SIN8 c[26] +-1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */ + 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */ +-1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */ + 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */ +-2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */ + 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */ +-7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */ + 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */ +}; + +#define SINCOSL_COS_HI 0 +#define SINCOSL_COS_LO 1 +#define SINCOSL_SIN_HI 2 +#define SINCOSL_SIN_LO 3 +extern const long double __sincosl_table[]; + +void +__kernel_sincosl(long double x, long double y, long double *sinx, long double *cosx, int iy) +{ + long double h, l, z, sin_l, cos_l_m1; + int64_t ix; + uint32_t tix, hix, index; + double xhi, hhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + tix = ((uint64_t)ix) >> 32; + tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ + if (tix < 0x3fc30000) /* |x| < 0.1484375 */ + { + /* Argument is small enough to approximate it by a Chebyshev + polynomial of degree 16(17). */ + if (tix < 0x3c600000) /* |x| < 2^-57 */ + { + math_check_force_underflow (x); + if (!((int)x)) /* generate inexact */ + { + *sinx = x; + *cosx = ONE; + return; + } + } + z = x * x; + *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ + z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); + *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ + z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); + } + else + { + /* So that we don't have to use too large polynomial, we find + l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 + possible values for h. We look up cosl(h) and sinl(h) in + pre-computed tables, compute cosl(l) and sinl(l) using a + Chebyshev polynomial of degree 10(11) and compute + sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and + cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ + int six = tix; + tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000; + index = 0x3ffe - (tix >> 16); + hix = (tix + (0x200 << index)) & (0xfffffc00 << index); + x = fabsl (x); + switch (index) + { + case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; + case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; + default: + case 2: index = (hix - 0x3ffc3000) >> 10; break; + } + hix = (hix << 4) & 0x3fffffff; +/* + The following should work for double but generates the wrong index. + For now the code above converts double to ieee extended to compute + the index back to double for the h value. + + + index = 0x3fe - (tix >> 20); + hix = (tix + (0x2000 << index)) & (0xffffc000 << index); + if (signbit (x)) + { + x = -x; + y = -y; + } + switch (index) + { + case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break; + case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break; + default: + case 2: index = (hix - 0x3fc30000) >> 14; break; + } +*/ + INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32); + h = hhi; + if (iy) + l = y - (h - x); + else + l = x - h; + z = l * l; + sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); + cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); + z = __sincosl_table [index + SINCOSL_SIN_HI] + + (__sincosl_table [index + SINCOSL_SIN_LO] + + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1) + + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l)); + *sinx = (ix < 0) ? -z : z; + *cosx = __sincosl_table [index + SINCOSL_COS_HI] + + (__sincosl_table [index + SINCOSL_COS_LO] + - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l + - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1)); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_sinl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_sinl.c new file mode 100644 index 0000000000..2138ccf13b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_sinl.c @@ -0,0 +1,157 @@ +/* Quad-precision floating point sine on <-pi/4,pi/4>. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double c[] = { +#define ONE c[0] + 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */ + +/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) + x in <0,1/256> */ +#define SCOS1 c[1] +#define SCOS2 c[2] +#define SCOS3 c[3] +#define SCOS4 c[4] +#define SCOS5 c[5] +-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */ + 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */ +-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */ + 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ +-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */ + +/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) + x in <0,0.1484375> */ +#define SIN1 c[6] +#define SIN2 c[7] +#define SIN3 c[8] +#define SIN4 c[9] +#define SIN5 c[10] +#define SIN6 c[11] +#define SIN7 c[12] +#define SIN8 c[13] +-1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */ + 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */ +-1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */ + 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */ +-2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */ + 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */ +-7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */ + 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */ + +/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) + x in <0,1/256> */ +#define SSIN1 c[14] +#define SSIN2 c[15] +#define SSIN3 c[16] +#define SSIN4 c[17] +#define SSIN5 c[18] +-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */ + 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */ +-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */ + 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */ +-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */ +}; + +#define SINCOSL_COS_HI 0 +#define SINCOSL_COS_LO 1 +#define SINCOSL_SIN_HI 2 +#define SINCOSL_SIN_LO 3 +extern const long double __sincosl_table[]; + +long double +__kernel_sinl(long double x, long double y, int iy) +{ + long double h, l, z, sin_l, cos_l_m1; + int64_t ix; + u_int32_t tix, hix, index; + double xhi, hhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + tix = ((u_int64_t)ix) >> 32; + tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ + if (tix < 0x3fc30000) /* |x| < 0.1484375 */ + { + /* Argument is small enough to approximate it by a Chebyshev + polynomial of degree 17. */ + if (tix < 0x3c600000) /* |x| < 2^-57 */ + { + math_check_force_underflow (x); + if (!((int)x)) return x; /* generate inexact */ + } + z = x * x; + return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ + z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); + } + else + { + /* So that we don't have to use too large polynomial, we find + l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 + possible values for h. We look up cosl(h) and sinl(h) in + pre-computed tables, compute cosl(l) and sinl(l) using a + Chebyshev polynomial of degree 10(11) and compute + sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */ + int six = tix; + tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000; + index = 0x3ffe - (tix >> 16); + hix = (tix + (0x200 << index)) & (0xfffffc00 << index); + x = fabsl (x); + switch (index) + { + case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; + case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; + default: + case 2: index = (hix - 0x3ffc3000) >> 10; break; + } + hix = (hix << 4) & 0x3fffffff; +/* + The following should work for double but generates the wrong index. + For now the code above converts double to ieee extended to compute + the index back to double for the h value. + + index = 0x3fe - (tix >> 20); + hix = (tix + (0x2000 << index)) & (0xffffc000 << index); + x = fabsl (x); + switch (index) + { + case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break; + case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break; + default: + case 2: index = (hix - 0x3fc30000) >> 14; break; + } +*/ + INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32); + h = hhi; + if (iy) + l = (ix < 0 ? -y : y) - (h - x); + else + l = x - h; + z = l * l; + sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); + cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); + z = __sincosl_table [index + SINCOSL_SIN_HI] + + (__sincosl_table [index + SINCOSL_SIN_LO] + + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1) + + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l)); + return (ix < 0) ? -z : z; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_tanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_tanl.c new file mode 100644 index 0000000000..232e00c345 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_tanl.c @@ -0,0 +1,166 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __kernel_tanl( x, y, k ) + * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input k indicates whether tan (if k=1) or + * -1/tan (if k= -1) is returned. + * + * Algorithm + * 1. Since tan(-x) = -tan(x), we need only to consider positive x. + * 2. if x < 2^-57, return x with inexact if x!=0. + * 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2) + * on [0,0.67433]. + * + * Note: tan(x+y) = tan(x) + tan'(x)*y + * ~ tan(x) + (1+x*x)*y + * Therefore, for better accuracy in computing tan(x+y), let + * r = x^3 * R(x^2) + * then + * tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y)) + * + * 4. For x in [0.67433,pi/4], let y = pi/4 - x, then + * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) + * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <libc-diag.h> + +static const long double + one = 1.0L, + pio4hi = 7.8539816339744830961566084581987569936977E-1L, + pio4lo = 2.1679525325309452561992610065108379921906E-35L, + + /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2) + 0 <= x <= 0.6743316650390625 + Peak relative error 8.0e-36 */ + TH = 3.333333333333333333333333333333333333333E-1L, + T0 = -1.813014711743583437742363284336855889393E7L, + T1 = 1.320767960008972224312740075083259247618E6L, + T2 = -2.626775478255838182468651821863299023956E4L, + T3 = 1.764573356488504935415411383687150199315E2L, + T4 = -3.333267763822178690794678978979803526092E-1L, + + U0 = -1.359761033807687578306772463253710042010E8L, + U1 = 6.494370630656893175666729313065113194784E7L, + U2 = -4.180787672237927475505536849168729386782E6L, + U3 = 8.031643765106170040139966622980914621521E4L, + U4 = -5.323131271912475695157127875560667378597E2L; + /* 1.000000000000000000000000000000000000000E0 */ + + +long double +__kernel_tanl (long double x, long double y, int iy) +{ + long double z, r, v, w, s; + int32_t ix, sign, hx, lx; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS (hx, lx, xhi); + ix = hx & 0x7fffffff; + if (ix < 0x3c600000) /* x < 2**-57 */ + { + if ((int) x == 0) /* generate inexact */ + { + if ((ix | lx | (iy + 1)) == 0) + return one / fabs (x); + else if (iy == 1) + { + math_check_force_underflow (x); + return x; + } + else + return -one / x; + } + } + if (ix >= 0x3fe59420) /* |x| >= 0.6743316650390625 */ + { + if ((hx & 0x80000000) != 0) + { + x = -x; + y = -y; + sign = -1; + } + else + sign = 1; + z = pio4hi - x; + w = pio4lo - y; + x = z + w; + y = 0.0; + } + z = x * x; + r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4))); + v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z)))); + r = r / v; + + s = z * x; + r = y + z * (s * r + y); + r += TH * s; + w = x + r; + if (ix >= 0x3fe59420) + { + v = (long double) iy; + w = (v - 2.0 * (x - (w * w / (w + v) - r))); + /* SIGN is set for arguments that reach this code, but not + otherwise, resulting in warnings that it may be used + uninitialized although in the cases where it is used it has + always been set. */ + DIAG_PUSH_NEEDS_COMMENT; + DIAG_IGNORE_NEEDS_COMMENT (5, "-Wmaybe-uninitialized"); + if (sign < 0) + w = -w; + DIAG_POP_NEEDS_COMMENT; + return w; + } + if (iy == 1) + return w; + else + { /* if allow error up to 2 ulp, + simply return -1.0/(x+r) here */ + /* compute -1.0/(x+r) accurately */ + long double u1, z1; + + u1 = ldbl_high (w); + v = r - (u1 - x); /* u1+v = r+x */ + z = -1.0 / w; + z1 = ldbl_high (z); + s = 1.0 + z1 * u1; + return z1 + z * (s + z1 * v); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c new file mode 100644 index 0000000000..4146e5c2d4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c @@ -0,0 +1,197 @@ +/* Copyright (C) 1995-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include "longlong.h" +#include <ieee754.h> +#include <float.h> +#include <math.h> +#include <stdlib.h> + +/* Convert a `long double' in IBM extended format to a multi-precision + integer representing the significand scaled up by its number of + bits (106 for long double) and an integral power of two (MPN + frexpl). */ + + +/* When signs differ, the actual value is the difference between the + significant double and the less significant double. Sometimes a + bit can be lost when we borrow from the significant mantissa. */ +#define EXTRA_INTERNAL_PRECISION (7) + +mp_size_t +__mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size, + int *expt, int *is_neg, + long double value) +{ + union ibm_extended_long_double u; + unsigned long long hi, lo; + int ediff; + + u.ld = value; + + *is_neg = u.d[0].ieee.negative; + *expt = (int) u.d[0].ieee.exponent - IEEE754_DOUBLE_BIAS; + + lo = ((long long) u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1; + hi = ((long long) u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1; + + /* Hold 7 extra bits of precision in the mantissa. This allows + the normalizing shifts below to prevent losing precision when + the signs differ and the exponents are sufficiently far apart. */ + lo <<= EXTRA_INTERNAL_PRECISION; + + /* If the lower double is not a denormal or zero then set the hidden + 53rd bit. */ + if (u.d[1].ieee.exponent != 0) + lo |= 1ULL << (52 + EXTRA_INTERNAL_PRECISION); + else + lo = lo << 1; + + /* The lower double is normalized separately from the upper. We may + need to adjust the lower manitissa to reflect this. */ + ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53; + if (ediff > 0) + { + if (ediff < 64) + lo = lo >> ediff; + else + lo = 0; + } + else if (ediff < 0) + lo = lo << -ediff; + + /* The high double may be rounded and the low double reflects the + difference between the long double and the rounded high double + value. This is indicated by a differnce between the signs of the + high and low doubles. */ + if (u.d[0].ieee.negative != u.d[1].ieee.negative + && lo != 0) + { + lo = (1ULL << (53 + EXTRA_INTERNAL_PRECISION)) - lo; + if (hi == 0) + { + /* we have a borrow from the hidden bit, so shift left 1. */ + hi = 0x000ffffffffffffeLL | (lo >> (52 + EXTRA_INTERNAL_PRECISION)); + lo = 0x0fffffffffffffffLL & (lo << 1); + (*expt)--; + } + else + hi--; + } +#if BITS_PER_MP_LIMB == 32 + /* Combine the mantissas to be contiguous. */ + res_ptr[0] = lo >> EXTRA_INTERNAL_PRECISION; + res_ptr[1] = (hi << (53 - 32)) | (lo >> (32 + EXTRA_INTERNAL_PRECISION)); + res_ptr[2] = hi >> 11; + res_ptr[3] = hi >> (32 + 11); + #define N 4 +#elif BITS_PER_MP_LIMB == 64 + /* Combine the two mantissas to be contiguous. */ + res_ptr[0] = (hi << 53) | (lo >> EXTRA_INTERNAL_PRECISION); + res_ptr[1] = hi >> 11; + #define N 2 +#else + #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif +/* The format does not fill the last limb. There are some zeros. */ +#define NUM_LEADING_ZEROS (BITS_PER_MP_LIMB \ + - (LDBL_MANT_DIG - ((N - 1) * BITS_PER_MP_LIMB))) + + if (u.d[0].ieee.exponent == 0) + { + /* A biased exponent of zero is a special case. + Either it is a zero or it is a denormal number. */ + if (res_ptr[0] == 0 && res_ptr[1] == 0 + && res_ptr[N - 2] == 0 && res_ptr[N - 1] == 0) /* Assumes N<=4. */ + /* It's zero. */ + *expt = 0; + else + { + /* It is a denormal number, meaning it has no implicit leading + one bit, and its exponent is in fact the format minimum. We + use DBL_MIN_EXP instead of LDBL_MIN_EXP below because the + latter describes the properties of both parts together, but + the exponent is computed from the high part only. */ + int cnt; + +#if N == 2 + if (res_ptr[N - 1] != 0) + { + count_leading_zeros (cnt, res_ptr[N - 1]); + cnt -= NUM_LEADING_ZEROS; + res_ptr[N - 1] = res_ptr[N - 1] << cnt + | (res_ptr[0] >> (BITS_PER_MP_LIMB - cnt)); + res_ptr[0] <<= cnt; + *expt = DBL_MIN_EXP - 1 - cnt; + } + else + { + count_leading_zeros (cnt, res_ptr[0]); + if (cnt >= NUM_LEADING_ZEROS) + { + res_ptr[N - 1] = res_ptr[0] << (cnt - NUM_LEADING_ZEROS); + res_ptr[0] = 0; + } + else + { + res_ptr[N - 1] = res_ptr[0] >> (NUM_LEADING_ZEROS - cnt); + res_ptr[0] <<= BITS_PER_MP_LIMB - (NUM_LEADING_ZEROS - cnt); + } + *expt = DBL_MIN_EXP - 1 + - (BITS_PER_MP_LIMB - NUM_LEADING_ZEROS) - cnt; + } +#else + int j, k, l; + + for (j = N - 1; j > 0; j--) + if (res_ptr[j] != 0) + break; + + count_leading_zeros (cnt, res_ptr[j]); + cnt -= NUM_LEADING_ZEROS; + l = N - 1 - j; + if (cnt < 0) + { + cnt += BITS_PER_MP_LIMB; + l--; + } + if (!cnt) + for (k = N - 1; k >= l; k--) + res_ptr[k] = res_ptr[k-l]; + else + { + for (k = N - 1; k > l; k--) + res_ptr[k] = res_ptr[k-l] << cnt + | res_ptr[k-l-1] >> (BITS_PER_MP_LIMB - cnt); + res_ptr[k--] = res_ptr[0] << cnt; + } + + for (; k >= 0; k--) + res_ptr[k] = 0; + *expt = DBL_MIN_EXP - 1 - l * BITS_PER_MP_LIMB - cnt; +#endif + } + } + else + /* Add the implicit leading one bit for a normalized number. */ + res_ptr[N - 1] |= (mp_limb_t) 1 << (LDBL_MANT_DIG - 1 + - ((N - 1) * BITS_PER_MP_LIMB)); + + return N; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/lgamma_negl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/lgamma_negl.c new file mode 100644 index 0000000000..638812c50b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/lgamma_negl.c @@ -0,0 +1,532 @@ +/* lgammal expanding around zeros. + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double lgamma_zeros[][2] = + { + { -0x2.74ff92c01f0d82abec9f315f1ap+0L, -0x7.12c334804d9a79cb5d46094d46p-112L }, + { -0x2.bf6821437b20197995a4b4641fp+0L, 0x5.140b4ff4b7d6069e1bd7acc196p-108L }, + { -0x3.24c1b793cb35efb8be699ad3dap+0L, 0x4.59abab3480539f1c0e926287cp-108L }, + { -0x3.f48e2a8f85fca170d456129123p+0L, -0x6.cc320a4887d1cb4c711828a75ep-108L }, + { -0x4.0a139e16656030c39f0b0de182p+0L, 0xe.d53e84029416e1242006b2b3dp-108L }, + { -0x4.fdd5de9bbabf3510d0aa407698p+0L, -0x8.501d7d78125286f78d1e501f14p-108L }, + { -0x5.021a95fc2db6432a4c56e5953ap+0L, 0xb.2133950fbcf2b01a8b9058dcccp-108L }, + { -0x5.ffa4bd647d0357dd4ed62cbd32p+0L, 0x1.2071c071a2145d2982428f2269p-108L }, + { -0x6.005ac9625f233b607c2d96d164p+0L, 0x7.a347953a96cbf30e1a0db20856p-108L }, + { -0x6.fff2fddae1bbff3d626b65c24p+0L, 0x2.de0bfcff5c457ebcf4d3ad9674p-108L }, + { -0x7.000cff7b7f87adf4482dcdb988p+0L, 0x7.d54d99e35a74d6407b80292df2p-108L }, + { -0x7.fffe5fe05673c3ca9e82b522bp+0L, -0xc.a9d2e8837cd1f14bd3d05002e4p-108L }, + { -0x8.0001a01459fc9f60cb3cec1cecp+0L, -0x8.576677ca538d88084310983b8p-108L }, + { -0x8.ffffd1c425e80ffc864e957494p+0L, 0x1.a6181dfdef1807e3087e4bb163p-104L }, + { -0x9.00002e3bb47d86d6d843fedc34p+0L, -0x1.1deb7ad09ec5e9d6e8ae2d548bp-104L }, + { -0x9.fffffb606bdfdcd062ae77a504p+0L, -0x1.47c69d2eb6f33d170fce38ff818p-104L }, + { -0xa.0000049f93bb9927b45d95e154p+0L, -0x4.1e03086db9146a9287bd4f2172p-108L }, + { -0xa.ffffff9466e9f1b36dacd2adbcp+0L, -0x1.18d05a4e458062f3f95345a4dap-104L }, + { -0xb.0000006b9915315d965a6ffea4p+0L, -0xe.4bea39000dcc1848023c5f6bdcp-112L }, + { -0xb.fffffff7089387387de41acc3cp+0L, -0x1.3c978bd839c8c428b5efcf91ef8p-104L }, + { -0xc.00000008f76c7731567c0f025p+0L, -0xf.387920df5675833859190eb128p-108L }, + { -0xc.ffffffff4f6dcf617f97a5ffc8p+0L, 0xa.82ab72d76f32eaee2d1a42ed5p-108L }, + { -0xd.00000000b092309c06683dd1b8p+0L, -0x1.03e3700857a15c19ac5a611de98p-104L }, + { -0xd.fffffffff36345ab9e184a3e08p+0L, -0x1.d1176dc48e47f62d917973dd45p-104L }, + { -0xe.000000000c9cba545e94e75ec4p+0L, -0x1.718f753e2501e757a17cf2ecbfp-104L }, + { -0xe.ffffffffff28c060c6604ef304p+0L, 0x8.e0762c8ca8361c23e8393919c4p-108L }, + { -0xf.0000000000d73f9f399bd0e42p+0L, -0xf.85e9ee31b0b890744fc0e3fbcp-108L }, + { -0xf.fffffffffff28c060c6621f514p+0L, 0x1.18d1b2eec9d960bd9adc5be5f6p-104L }, + { -0x1.000000000000d73f9f399da1428p+4L, 0x3.406c46e0e88305d2800f0e414cp-104L }, + { -0x1.0ffffffffffff3569c47e7a93ep+4L, -0x1.c46a08a2e008a998ebabb8087fp-104L }, + { -0x1.1000000000000ca963b81856888p+4L, -0x7.6ca5a3a64ec15db0a95caf2cap-108L }, + { -0x1.1fffffffffffff4bec3ce23413p+4L, -0x2.d08b2b726187c841cb92cd5222p-104L }, + { -0x1.20000000000000b413c31dcbec8p+4L, -0x2.4c3b2ffacbb4932f18dceedfd7p-104L }, + { -0x1.2ffffffffffffff685b25cbf5f8p+4L, 0x2.ba3126cd1c7b7a0822d694705cp-104L }, + { -0x1.30000000000000097a4da340a08p+4L, -0x2.b81b7b1f1f001c72bf914141efp-104L }, + { -0x1.3fffffffffffffff86af516ff8p+4L, 0x8.9429818df2a87abafd48248a2p-108L }, + { -0x1.40000000000000007950ae9008p+4L, -0x8.9413ccc8a353fda263f8ce973cp-108L }, + { -0x1.4ffffffffffffffffa391c4249p+4L, 0x3.d5c63022b62b5484ba346524dbp-104L }, + { -0x1.500000000000000005c6e3bdb7p+4L, -0x3.d5c62f55ed5322b2685c5e9a52p-104L }, + { -0x1.5fffffffffffffffffbcc71a49p+4L, -0x2.01eb5aeb96c74d7ad25e060529p-104L }, + { -0x1.6000000000000000004338e5b7p+4L, 0x2.01eb5aec04b2f2eb663e4e3d8ap-104L }, + { -0x1.6ffffffffffffffffffd13c97d8p+4L, -0x1.d38fcc4d08d6fe5aa56ab04308p-104L }, + { -0x1.70000000000000000002ec36828p+4L, 0x1.d38fcc4d090cee2f5d0b69a99cp-104L }, + { -0x1.7fffffffffffffffffffe0d31p+4L, 0x1.972f577cca4b4c8cb1dc14001bp-104L }, + { -0x1.800000000000000000001f2cfp+4L, -0x1.972f577cca4b3442e35f0040b38p-104L }, + { -0x1.8ffffffffffffffffffffec0c3p+4L, -0x3.22e9a0572b1bb5b95f346a92d6p-104L }, + { -0x1.90000000000000000000013f3dp+4L, 0x3.22e9a0572b1bb5c371ddb35617p-104L }, + { -0x1.9ffffffffffffffffffffff3b88p+4L, -0x3.d01cad8d32e386fd783e97296dp-104L }, + { -0x1.a0000000000000000000000c478p+4L, 0x3.d01cad8d32e386fd7c1ab8c1fep-104L }, + { -0x1.afffffffffffffffffffffff8b8p+4L, -0x1.538f48cc5737d5979c39db806c8p-104L }, + { -0x1.b00000000000000000000000748p+4L, 0x1.538f48cc5737d5979c3b3a6bdap-104L }, + { -0x1.bffffffffffffffffffffffffcp+4L, 0x2.862898d42174dcf171470d8c8cp-104L }, + { -0x1.c0000000000000000000000004p+4L, -0x2.862898d42174dcf171470d18bap-104L }, + { -0x1.dp+4L, 0x2.4b3f31686b15af57c61ceecdf4p-104L }, + { -0x1.dp+4L, -0x2.4b3f31686b15af57c61ceecdd1p-104L }, + { -0x1.ep+4L, 0x1.3932c5047d60e60caded4c298ap-108L }, + { -0x1.ep+4L, -0x1.3932c5047d60e60caded4c29898p-108L }, + { -0x1.fp+4L, 0xa.1a6973c1fade2170f7237d36p-116L }, + { -0x1.fp+4L, -0xa.1a6973c1fade2170f7237d36p-116L }, + { -0x2p+4L, 0x5.0d34b9e0fd6f10b87b91be9bp-120L }, + { -0x2p+4L, -0x5.0d34b9e0fd6f10b87b91be9bp-120L }, + { -0x2.1p+4L, 0x2.73024a9ba1aa36a7059bff52e8p-124L }, + { -0x2.1p+4L, -0x2.73024a9ba1aa36a7059bff52e8p-124L }, + { -0x2.2p+4L, 0x1.2710231c0fd7a13f8a2b4af9d68p-128L }, + { -0x2.2p+4L, -0x1.2710231c0fd7a13f8a2b4af9d68p-128L }, + { -0x2.3p+4L, 0x8.6e2ce38b6c8f9419e3fad3f03p-136L }, + { -0x2.3p+4L, -0x8.6e2ce38b6c8f9419e3fad3f03p-136L }, + { -0x2.4p+4L, 0x3.bf30652185952560d71a254e4fp-140L }, + { -0x2.4p+4L, -0x3.bf30652185952560d71a254e4fp-140L }, + { -0x2.5p+4L, 0x1.9ec8d1c94e85af4c78b15c3d8ap-144L }, + { -0x2.5p+4L, -0x1.9ec8d1c94e85af4c78b15c3d8ap-144L }, + { -0x2.6p+4L, 0xa.ea565ce061d57489e9b8527628p-152L }, + { -0x2.6p+4L, -0xa.ea565ce061d57489e9b8527628p-152L }, + { -0x2.7p+4L, 0x4.7a6512692eb37804111dabad3p-156L }, + { -0x2.7p+4L, -0x4.7a6512692eb37804111dabad3p-156L }, + { -0x2.8p+4L, 0x1.ca8ed42a12ae3001a07244abadp-160L }, + { -0x2.8p+4L, -0x1.ca8ed42a12ae3001a07244abadp-160L }, + { -0x2.9p+4L, 0xb.2f30e1ce812063f12e7e8d8d98p-168L }, + { -0x2.9p+4L, -0xb.2f30e1ce812063f12e7e8d8d98p-168L }, + { -0x2.ap+4L, 0x4.42bd49d4c37a0db136489772e4p-172L }, + { -0x2.ap+4L, -0x4.42bd49d4c37a0db136489772e4p-172L }, + { -0x2.bp+4L, 0x1.95db45257e5122dcbae56def37p-176L }, + { -0x2.bp+4L, -0x1.95db45257e5122dcbae56def37p-176L }, + { -0x2.cp+4L, 0x9.3958d81ff63527ecf993f3fb7p-184L }, + { -0x2.cp+4L, -0x9.3958d81ff63527ecf993f3fb7p-184L }, + { -0x2.dp+4L, 0x3.47970e4440c8f1c058bd238c99p-188L }, + { -0x2.dp+4L, -0x3.47970e4440c8f1c058bd238c99p-188L }, + { -0x2.ep+4L, 0x1.240804f65951062ca46e4f25c6p-192L }, + { -0x2.ep+4L, -0x1.240804f65951062ca46e4f25c6p-192L }, + { -0x2.fp+4L, 0x6.36a382849fae6de2d15362d8a4p-200L }, + { -0x2.fp+4L, -0x6.36a382849fae6de2d15362d8a4p-200L }, + { -0x3p+4L, 0x2.123680d6dfe4cf4b9b1bcb9d8cp-204L }, + }; + +static const long double e_hi = 0x2.b7e151628aed2a6abf7158809dp+0L; +static const long double e_lo = -0xb.0c389d18e9f0c74b25a9587b28p-112L; + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) in Stirling's + approximation to lgamma function. */ + +static const long double lgamma_coeff[] = + { + 0x1.555555555555555555555555558p-4L, + -0xb.60b60b60b60b60b60b60b60b6p-12L, + 0x3.4034034034034034034034034p-12L, + -0x2.7027027027027027027027027p-12L, + 0x3.72a3c5631fe46ae1d4e700dca9p-12L, + -0x7.daac36664f1f207daac36664f2p-12L, + 0x1.a41a41a41a41a41a41a41a41a4p-8L, + -0x7.90a1b2c3d4e5f708192a3b4c5ep-8L, + 0x2.dfd2c703c0cfff430edfd2c704p-4L, + -0x1.6476701181f39edbdb9ce625988p+0L, + 0xd.672219167002d3a7a9c886459cp+0L, + -0x9.cd9292e6660d55b3f712eb9e08p+4L, + 0x8.911a740da740da740da740da74p+8L, + -0x8.d0cc570e255bf59ff6eec24b48p+12L, + 0xa.8d1044d3708d1c219ee4fdc448p+16L, + -0xe.8844d8a169abbc406169abbc4p+20L, + 0x1.6d29a0f6433b79890cede624338p+28L, + -0x2.88a233b3c8cddaba9809357126p+32L, + 0x5.0dde6f27500939a85c40939a86p+36L, + -0xb.4005bde03d4642a243581714bp+40L, + 0x1.bc8cd6f8f1f755c78753cdb5d6p+48L, + -0x4.bbebb143bb94de5a0284fa7ec4p+52L, + 0xe.2e1337f5af0bed90b6b0a352d4p+56L, + -0x2.e78250162b62405ad3e4bfe61bp+64L, + 0xa.5f7eef9e71ac7c80326ab4cc8cp+68L, + -0x2.83be0395e550213369924971b2p+76L, + }; + +#define NCOEFF (sizeof (lgamma_coeff) / sizeof (lgamma_coeff[0])) + +/* Polynomial approximations to (|gamma(x)|-1)(x-n)/(x-x0), where n is + the integer end-point of the half-integer interval containing x and + x0 is the zero of lgamma in that half-integer interval. Each + polynomial is expressed in terms of x-xm, where xm is the midpoint + of the interval for which the polynomial applies. */ + +static const long double poly_coeff[] = + { + /* Interval [-2.125, -2] (polynomial degree 21). */ + -0x1.0b71c5c54d42eb6c17f30b7aa9p+0L, + -0xc.73a1dc05f34951602554c6d76cp-4L, + -0x1.ec841408528b51473e6c42f1c58p-4L, + -0xe.37c9da26fc3c9a3c1844c04b84p-4L, + -0x1.03cd87c519305703b00b046ce4p-4L, + -0xe.ae9ada65e09aa7f1c817c91048p-4L, + 0x9.b11855a4864b571b6a4f571c88p-8L, + -0xe.f28c133e697a95ba2dabb97584p-4L, + 0x2.6ec14a1c586a7ddb6c4be90fe1p-4L, + -0xf.57cab973e14496f0900851c0d4p-4L, + 0x4.5b0fc25f16b0df37175495c70cp-4L, + -0xf.f50e59f1a8fb8c402091e3cd3cp-4L, + 0x6.5f5eae1681d1e50e575c3d4d36p-4L, + -0x1.0d2422dac7ea8a52db6bf0d14fp+0L, + 0x8.820008f221eae5a36e15913bacp-4L, + -0x1.1f492eec53b9481ea23a7e944ep+0L, + 0xa.cb55b4d662945e8cf1f81ee5b4p-4L, + -0x1.3616863983e131d7935700ccd48p+0L, + 0xd.43c783ebab66074d18709d5cap-4L, + -0x1.51d5dbc56bc85976871c6e51f78p+0L, + 0x1.06253af656eb6b2ed998387aabp+0L, + -0x1.7d910a0aadc63d7a1ef7690dbb8p+0L, + /* Interval [-2.25, -2.125] (polynomial degree 22). */ + -0xf.2930890d7d675a80c36afb0fd4p-4L, + -0xc.a5cfde054eab5c6770daeca684p-4L, + 0x3.9c9e0fdebb07cdf89c61d434adp-4L, + -0x1.02a5ad35605fcf4af65a67fe8a8p+0L, + 0x9.6e9b1185bb48be9de18d8bbeb8p-4L, + -0x1.4d8332f3cfbfa116fdf648372cp+0L, + 0x1.1c0c8cb4d9f4b1d495142b53ebp+0L, + -0x1.c9a6f5ae9130ccfb9b7e39136f8p+0L, + 0x1.d7e9307fd58a2e85209d0e83eap+0L, + -0x2.921cb3473d96462f22c171712fp+0L, + 0x2.e8d59113b6f3fc1ed3b556b62cp+0L, + -0x3.cbab931624e3b6cf299cea1213p+0L, + 0x4.7d9f0f05d2c4cf91e41ea1f048p+0L, + -0x5.ade9cba31affa276fe516135eep+0L, + 0x6.dc983a62cf6ddc935ae3c5b9ap+0L, + -0x8.8d9ed100b2a7813f82cbd83e3cp+0L, + 0xa.6fa0926892835a9a29c9b8db8p+0L, + -0xc.ebc90aff4ffe319d70bef0d61p+0L, + 0xf.d69cf50ab226bacece014c0b44p+0L, + -0x1.389964ac7cfef4578eec028e5c8p+4L, + 0x1.7ff0d2090164e25901f97cab3bp+4L, + -0x1.e9e6d282da6bd004619d073071p+4L, + 0x2.5d719ab6ad4be8b5c32b0fba2ap+4L, + /* Interval [-2.375, -2.25] (polynomial degree 24). */ + -0xd.7d28d505d6181218a25f31d5e4p-4L, + -0xe.69649a3040985140cdf946827cp-4L, + 0xb.0d74a2827d053a8d4459500f88p-4L, + -0x1.924b0922853617cac181b097e48p+0L, + 0x1.d49b12bccf0a568582e2dbf8ep+0L, + -0x3.0898bb7d8c4093e6360d26bbc5p+0L, + 0x4.207a6cac711cb538684f74619ep+0L, + -0x6.39ee63ea4fb1dcac86ab337e3cp+0L, + 0x8.e2e2556a797b64a1b9328a3978p+0L, + -0xd.0e83ac82552ee5596df1706ff4p+0L, + 0x1.2e4525e0ce666e48fac68ddcdep+4L, + -0x1.b8e350d6a8f6597ed2eb3c2eff8p+4L, + 0x2.805cd69b9197ee0089dd1b1c46p+4L, + -0x3.a42585423e4d00db075f2d687ep+4L, + 0x5.4b4f409f874e2a7dcd8aa4a62ap+4L, + -0x7.b3c5829962ca1b95535db9cc4ep+4L, + 0xb.33b7b928986ec6b219e2e15a98p+4L, + -0x1.04b76dec4115106bb16316d9cd8p+8L, + 0x1.7b366d8d46f179d5c5302d6534p+8L, + -0x2.2799846ddc54813d40da622b99p+8L, + 0x3.2253a862c1078a3ccabac65bebp+8L, + -0x4.8d92cebc90a4a29816f4952f4ep+8L, + 0x6.9ebb8f9d72c66c80c4f4492e7ap+8L, + -0xa.2850a483f9ba0e43f5848b5cd8p+8L, + 0xe.e1b6bdce83b27944edab8c428p+8L, + /* Interval [-2.5, -2.375] (polynomial degree 25). */ + -0xb.74ea1bcfff94b2c01afba9daa8p-4L, + -0x1.2a82bd590c37538cab143308e3p+0L, + 0x1.88020f828b966fec66b8648d16p+0L, + -0x3.32279f040eb694970e9db0308bp+0L, + 0x5.57ac82517767e68a72142041b4p+0L, + -0x9.c2aedcfe22833de438786dc658p+0L, + 0x1.12c132f1f5577f99dbfb7ecb408p+4L, + -0x1.ea94e26628a3de3557dc349db8p+4L, + 0x3.66b4ac4fa582f5cbe7e19d10c6p+4L, + -0x6.0cf746a9cf4cbcb0004cb01f66p+4L, + 0xa.c102ef2c20d5a313cbfd37f5b8p+4L, + -0x1.31ebff06e8f08f58d1c35eacfdp+8L, + 0x2.1fd6f0c0e788660ba1f1573722p+8L, + -0x3.c6d760404305e75356a86a11d6p+8L, + 0x6.b6d18e0c31a2ba4d5b5ac78676p+8L, + -0xb.efaf5426343e6b41a823ed6c44p+8L, + 0x1.53852db2fe01305b9f336d132d8p+12L, + -0x2.5b977cb2b568382e71ca93a36bp+12L, + 0x4.310d090a6119c7d85a2786a616p+12L, + -0x7.73a518387ef1d4d04917dfb25cp+12L, + 0xd.3f965798601aabd24bdaa6e68cp+12L, + -0x1.78db20b0b166480c93cf0031198p+16L, + 0x2.9be0068b65cf13bd1cf71f0eccp+16L, + -0x4.a221230466b9cd51d5b811d6b6p+16L, + 0x8.f6f8c13e2b52aa3e30a4ce6898p+16L, + -0x1.02145337ff16b44fa7c2adf7f28p+20L, + /* Interval [-2.625, -2.5] (polynomial degree 26). */ + -0x3.d10108c27ebafad533c20eac33p-4L, + 0x1.cd557caff7d2b2085f41dbec538p+0L, + 0x3.819b4856d399520dad9776ebb9p+0L, + 0x6.8505cbad03dc34c5e42e89c4b4p+0L, + 0xb.c1b2e653a9e38f82b3997134a8p+0L, + 0x1.50a53a38f1481381051544750ep+4L, + 0x2.57ae00cbe5232cbeef4e94eb2cp+4L, + 0x4.2b156301b8604db82856d5767p+4L, + 0x7.6989ed23ca3ca751fc9c32eb88p+4L, + 0xd.2dd29765579396f3a456772c44p+4L, + 0x1.76e1c3430eb8630991d1aa8a248p+8L, + 0x2.9a77bf548873743fe65d025f56p+8L, + 0x4.a0d62ed7266389753842d7be74p+8L, + 0x8.3a6184dd32d31ec73fc6f2d37cp+8L, + 0xe.a0ade153a3bf0247db49e11ae8p+8L, + 0x1.a01359fa74d4eaf8858bbc35f68p+12L, + 0x2.e3b0a32845cbc135bae4a5216cp+12L, + 0x5.23012653815fe88456170a7dc6p+12L, + 0x9.21c92dcde748ec199bc9c65738p+12L, + 0x1.03c0f3621b4c67d2d86e5e813d8p+16L, + 0x1.cdc884edcc9f5404f2708551cb8p+16L, + 0x3.35025f0b1624d1ffc86688bf03p+16L, + 0x5.b3bd9562ebf2409c5ce99929ep+16L, + 0xa.1a229b1986d9f89cb80abccfdp+16L, + 0x1.1e69136ebd520146d51837f3308p+20L, + 0x2.2d2738c72449db2524171b9271p+20L, + 0x4.036e80cc6621b836f94f426834p+20L, + /* Interval [-2.75, -2.625] (polynomial degree 24). */ + -0x6.b5d252a56e8a75458a27ed1c2ep-4L, + 0x1.28d60383da3ac721aed3c57949p+0L, + 0x1.db6513ada8a66ea77d87d9a796p+0L, + 0x2.e217118f9d348a27f7506c4b4fp+0L, + 0x4.450112c5cbf725a0fb982fc44cp+0L, + 0x6.4af99151eae7810a75a5fceac8p+0L, + 0x9.2db598b4a97a7f69ab7be31128p+0L, + 0xd.62bef9c22471f5f17955733c6p+0L, + 0x1.379f294e412bd6255506135f4a8p+4L, + 0x1.c5827349d8865d858d4f85f3c38p+4L, + 0x2.93a7e7a75b755bbea1785a1349p+4L, + 0x3.bf9bb882afed66a08b22ed7a45p+4L, + 0x5.73c737828d2044aca95fdef33ep+4L, + 0x7.ee46534920f1c81574db260f0ep+4L, + 0xb.891c6b837b513eaf1592fe78ccp+4L, + 0x1.0c775d815bf741526a3dd66ded8p+8L, + 0x1.867ee44cf11f26455a8924a56bp+8L, + 0x2.37fe968baa1018e55cae680f1dp+8L, + 0x3.3a2c557f686679eb5d8e960fd1p+8L, + 0x4.b1ba0539d4d80cc9174738b992p+8L, + 0x6.d3fd80155b6d2211956cb6bc5ap+8L, + 0x9.eb5a96b0ee3d9ca523f5fbc1fp+8L, + 0xe.6b37429c1acc7dc19ef312dda4p+8L, + 0x1.621132d6aa138b203a28e4792fp+12L, + 0x2.09610219270e2ce11a985d4d36p+12L, + /* Interval [-2.875, -2.75] (polynomial degree 23). */ + -0x8.a41b1e4f36ff88dc820815607cp-4L, + 0xc.da87d3b69dc0f2f9c6f368b8c8p-4L, + 0x1.1474ad5c36158a7bea04fd30b28p+0L, + 0x1.761ecb90c555df6555b7dbb9ce8p+0L, + 0x1.d279bff9ae291caf6c4b17497f8p+0L, + 0x2.4e5d00559a6e2b9b5d7e35b575p+0L, + 0x2.d57545a75cee8743b1ff6e22b8p+0L, + 0x3.8514eee3aac88b89d2d4ddef4ep+0L, + 0x4.5235e3b6e1891fd9c975383318p+0L, + 0x5.562acdb10eef3c14a780490e3cp+0L, + 0x6.8ec8965c76f0b261bc41b5e532p+0L, + 0x8.15251aca144a98a1e1c0981388p+0L, + 0x9.f08d56ab9e7eee9515a457214cp+0L, + 0xc.3dbbeda2620d5be4fe8621ce6p+0L, + 0xf.0f5bfd65b3feb6d745a2cdbf9cp+0L, + 0x1.28a6ccd8dd27fb90fcaa31d37dp+4L, + 0x1.6d0a3a3091c3d64cfd1a3c5769p+4L, + 0x1.c1570107e02d5ab0b8bea6d6c98p+4L, + 0x2.28fc9b295b583fa469de7acceap+4L, + 0x2.a8a4cac0217026bbdbce34f4adp+4L, + 0x3.4532c98bce75262ac0ede53edep+4L, + 0x4.062fd9ba18e00e55c25a4f0688p+4L, + 0x5.22e00e6d9846a3451fad5587f8p+4L, + 0x6.5d0f7ce92a0bf928d4a30e92c6p+4L, + /* Interval [-3, -2.875] (polynomial degree 22). */ + -0xa.046d667e468f3e44dcae1afcc8p-4L, + 0x9.70b88dcc006c214d8d996fdf7p-4L, + 0xa.a8a39421c86d3ff24931a093c4p-4L, + 0xd.2f4d1363f324da2b357c850124p-4L, + 0xd.ca9aa1a3a5c00de11bf5d7047p-4L, + 0xf.cf09c31eeb52a45dfb25e50ebcp-4L, + 0x1.04b133a39ed8a096914cc78812p+0L, + 0x1.22b547a06edda9447f516a2ee7p+0L, + 0x1.2c57fce7db86a91c8d0f12077b8p+0L, + 0x1.4aade4894708fb8b78365e9bf88p+0L, + 0x1.579c8b7b67ec5179ecc4e9c7dp+0L, + 0x1.776820e7fc7361c50e7ef40a88p+0L, + 0x1.883ab28c72ef238ada6c480ab18p+0L, + 0x1.aa2ef6e1d11b9fcea06a1dcab1p+0L, + 0x1.bf4ad50f2dd2aeb02395ea08648p+0L, + 0x1.e40206a5477615838e02279dfc8p+0L, + 0x1.fdcbcfd4b0777fb173b85d5b398p+0L, + 0x2.25e32b3b3c89e833029169a17bp+0L, + 0x2.44ce344ff0bda6570fe3d0a76dp+0L, + 0x2.70bfba6fa079faf2dbf31d2216p+0L, + 0x2.953e22a97725cc179ad21024fap+0L, + 0x2.d8ccc51524659a499eee0f267p+0L, + 0x3.080fbb09c14936c2171c8a51bcp+0L, + }; + +static const size_t poly_deg[] = + { + 21, + 22, + 24, + 25, + 26, + 24, + 23, + 22, + }; + +static const size_t poly_end[] = + { + 21, + 44, + 69, + 95, + 122, + 147, + 171, + 194, + }; + +/* Compute sin (pi * X) for -0.25 <= X <= 0.5. */ + +static long double +lg_sinpi (long double x) +{ + if (x <= 0.25L) + return __sinl (M_PIl * x); + else + return __cosl (M_PIl * (0.5L - x)); +} + +/* Compute cos (pi * X) for -0.25 <= X <= 0.5. */ + +static long double +lg_cospi (long double x) +{ + if (x <= 0.25L) + return __cosl (M_PIl * x); + else + return __sinl (M_PIl * (0.5L - x)); +} + +/* Compute cot (pi * X) for -0.25 <= X <= 0.5. */ + +static long double +lg_cotpi (long double x) +{ + return lg_cospi (x) / lg_sinpi (x); +} + +/* Compute lgamma of a negative argument -48 < X < -2, setting + *SIGNGAMP accordingly. */ + +long double +__lgamma_negl (long double x, int *signgamp) +{ + /* Determine the half-integer region X lies in, handle exact + integers and determine the sign of the result. */ + int i = __floorl (-2 * x); + if ((i & 1) == 0 && i == -2 * x) + return 1.0L / 0.0L; + long double xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2); + i -= 4; + *signgamp = ((i & 2) == 0 ? -1 : 1); + + SET_RESTORE_ROUNDL (FE_TONEAREST); + + /* Expand around the zero X0 = X0_HI + X0_LO. */ + long double x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1]; + long double xdiff = x - x0_hi - x0_lo; + + /* For arguments in the range -3 to -2, use polynomial + approximations to an adjusted version of the gamma function. */ + if (i < 2) + { + int j = __floorl (-8 * x) - 16; + long double xm = (-33 - 2 * j) * 0.0625L; + long double x_adj = x - xm; + size_t deg = poly_deg[j]; + size_t end = poly_end[j]; + long double g = poly_coeff[end]; + for (size_t j = 1; j <= deg; j++) + g = g * x_adj + poly_coeff[end - j]; + return __log1pl (g * xdiff / (x - xn)); + } + + /* The result we want is log (sinpi (X0) / sinpi (X)) + + log (gamma (1 - X0) / gamma (1 - X)). */ + long double x_idiff = fabsl (xn - x), x0_idiff = fabsl (xn - x0_hi - x0_lo); + long double log_sinpi_ratio; + if (x0_idiff < x_idiff * 0.5L) + /* Use log not log1p to avoid inaccuracy from log1p of arguments + close to -1. */ + log_sinpi_ratio = __ieee754_logl (lg_sinpi (x0_idiff) + / lg_sinpi (x_idiff)); + else + { + /* Use log1p not log to avoid inaccuracy from log of arguments + close to 1. X0DIFF2 has positive sign if X0 is further from + XN than X is from XN, negative sign otherwise. */ + long double x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * 0.5L; + long double sx0d2 = lg_sinpi (x0diff2); + long double cx0d2 = lg_cospi (x0diff2); + log_sinpi_ratio = __log1pl (2 * sx0d2 + * (-sx0d2 + cx0d2 * lg_cotpi (x_idiff))); + } + + long double log_gamma_ratio; + long double y0 = 1 - x0_hi; + long double y0_eps = -x0_hi + (1 - y0) - x0_lo; + long double y = 1 - x; + long double y_eps = -x + (1 - y); + /* We now wish to compute LOG_GAMMA_RATIO + = log (gamma (Y0 + Y0_EPS) / gamma (Y + Y_EPS)). XDIFF + accurately approximates the difference Y0 + Y0_EPS - Y - + Y_EPS. Use Stirling's approximation. First, we may need to + adjust into the range where Stirling's approximation is + sufficiently accurate. */ + long double log_gamma_adj = 0; + if (i < 18) + { + int n_up = (19 - i) / 2; + long double ny0, ny0_eps, ny, ny_eps; + ny0 = y0 + n_up; + ny0_eps = y0 - (ny0 - n_up) + y0_eps; + y0 = ny0; + y0_eps = ny0_eps; + ny = y + n_up; + ny_eps = y - (ny - n_up) + y_eps; + y = ny; + y_eps = ny_eps; + long double prodm1 = __lgamma_productl (xdiff, y - n_up, y_eps, n_up); + log_gamma_adj = -__log1pl (prodm1); + } + long double log_gamma_high + = (xdiff * __log1pl ((y0 - e_hi - e_lo + y0_eps) / e_hi) + + (y - 0.5L + y_eps) * __log1pl (xdiff / y) + log_gamma_adj); + /* Compute the sum of (B_2k / 2k(2k-1))(Y0^-(2k-1) - Y^-(2k-1)). */ + long double y0r = 1 / y0, yr = 1 / y; + long double y0r2 = y0r * y0r, yr2 = yr * yr; + long double rdiff = -xdiff / (y * y0); + long double bterm[NCOEFF]; + long double dlast = rdiff, elast = rdiff * yr * (yr + y0r); + bterm[0] = dlast * lgamma_coeff[0]; + for (size_t j = 1; j < NCOEFF; j++) + { + long double dnext = dlast * y0r2 + elast; + long double enext = elast * yr2; + bterm[j] = dnext * lgamma_coeff[j]; + dlast = dnext; + elast = enext; + } + long double log_gamma_low = 0; + for (size_t j = 0; j < NCOEFF; j++) + log_gamma_low += bterm[NCOEFF - 1 - j]; + log_gamma_ratio = log_gamma_high + log_gamma_low; + + return log_sinpi_ratio + log_gamma_ratio; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/lgamma_productl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/lgamma_productl.c new file mode 100644 index 0000000000..92c1cffd67 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/lgamma_productl.c @@ -0,0 +1,38 @@ +/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), .... + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS + + 1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that + all the values X + 1, ..., X + N - 1 are exactly representable, and + X_EPS / X is small enough that factors quadratic in it can be + neglected. */ + +long double +__lgamma_productl (long double t, long double x, long double x_eps, int n) +{ + long double x_full = x + x_eps; + long double ret = 0; + for (int i = 0; i < n; i++) + /* FIXME: no extra precision used. */ + ret += (t / (x_full + i)) * (1 + ret); + return ret; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h new file mode 100644 index 0000000000..8f2984e924 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h @@ -0,0 +1,290 @@ +/* Manipulation of the bit representation of 'long double' quantities. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_LDBL_H_ +#define _MATH_LDBL_H_ 1 + +#include <ieee754.h> +#include <stdint.h> + +/* To suit our callers we return *hi64 and *lo64 as if they came from + an ieee854 112 bit mantissa, that is, 48 bits in *hi64 (plus one + implicit bit) and 64 bits in *lo64. */ + +static inline void +ldbl_extract_mantissa (int64_t *hi64, uint64_t *lo64, int *exp, long double x) +{ + /* We have 105 bits of mantissa plus one implicit digit. Since + 106 bits are representable we use the first implicit digit for + the number before the decimal point and the second implicit bit + as bit 53 of the mantissa. */ + uint64_t hi, lo; + union ibm_extended_long_double u; + + u.ld = x; + *exp = u.d[0].ieee.exponent - IEEE754_DOUBLE_BIAS; + + lo = ((uint64_t) u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1; + hi = ((uint64_t) u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1; + + if (u.d[0].ieee.exponent != 0) + { + int ediff; + + /* If not a denormal or zero then we have an implicit 53rd bit. */ + hi |= (uint64_t) 1 << 52; + + if (u.d[1].ieee.exponent != 0) + lo |= (uint64_t) 1 << 52; + else + /* A denormal is to be interpreted as having a biased exponent + of 1. */ + lo = lo << 1; + + /* We are going to shift 4 bits out of hi later, because we only + want 48 bits in *hi64. That means we want 60 bits in lo, but + we currently only have 53. Shift the value up. */ + lo = lo << 7; + + /* The lower double is normalized separately from the upper. + We may need to adjust the lower mantissa to reflect this. + The difference between the exponents can be larger than 53 + when the low double is much less than 1ULP of the upper + (in which case there are significant bits, all 0's or all + 1's, between the two significands). The difference between + the exponents can be less than 53 when the upper double + exponent is nearing its minimum value (in which case the low + double is denormal ie. has an exponent of zero). */ + ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53; + if (ediff > 0) + { + if (ediff < 64) + lo = lo >> ediff; + else + lo = 0; + } + else if (ediff < 0) + lo = lo << -ediff; + + if (u.d[0].ieee.negative != u.d[1].ieee.negative + && lo != 0) + { + hi--; + lo = ((uint64_t) 1 << 60) - lo; + if (hi < (uint64_t) 1 << 52) + { + /* We have a borrow from the hidden bit, so shift left 1. */ + hi = (hi << 1) | (lo >> 59); + lo = (((uint64_t) 1 << 60) - 1) & (lo << 1); + *exp = *exp - 1; + } + } + } + else + /* If the larger magnitude double is denormal then the smaller + one must be zero. */ + hi = hi << 1; + + *lo64 = (hi << 60) | lo; + *hi64 = hi >> 4; +} + +static inline long double +ldbl_insert_mantissa (int sign, int exp, int64_t hi64, uint64_t lo64) +{ + union ibm_extended_long_double u; + int expnt2; + uint64_t hi, lo; + + u.d[0].ieee.negative = sign; + u.d[1].ieee.negative = sign; + u.d[0].ieee.exponent = exp + IEEE754_DOUBLE_BIAS; + u.d[1].ieee.exponent = 0; + expnt2 = exp - 53 + IEEE754_DOUBLE_BIAS; + + /* Expect 113 bits (112 bits + hidden) right justified in two longs. + The low order 53 bits (52 + hidden) go into the lower double */ + lo = (lo64 >> 7) & (((uint64_t) 1 << 53) - 1); + /* The high order 53 bits (52 + hidden) go into the upper double */ + hi = lo64 >> 60; + hi |= hi64 << 4; + + if (lo != 0) + { + int lzcount; + + /* hidden bit of low double controls rounding of the high double. + If hidden is '1' and either the explicit mantissa is non-zero + or hi is odd, then round up hi and adjust lo (2nd mantissa) + plus change the sign of the low double to compensate. */ + if ((lo & ((uint64_t) 1 << 52)) != 0 + && ((hi & 1) != 0 || (lo & (((uint64_t) 1 << 52) - 1)) != 0)) + { + hi++; + if ((hi & ((uint64_t) 1 << 53)) != 0) + { + hi = hi >> 1; + u.d[0].ieee.exponent++; + } + u.d[1].ieee.negative = !sign; + lo = ((uint64_t) 1 << 53) - lo; + } + + /* Normalize the low double. Shift the mantissa left until + the hidden bit is '1' and adjust the exponent accordingly. */ + + if (sizeof (lo) == sizeof (long)) + lzcount = __builtin_clzl (lo); + else if ((lo >> 32) != 0) + lzcount = __builtin_clzl ((long) (lo >> 32)); + else + lzcount = __builtin_clzl ((long) lo) + 32; + lzcount = lzcount - (64 - 53); + lo <<= lzcount; + expnt2 -= lzcount; + + if (expnt2 >= 1) + /* Not denormal. */ + u.d[1].ieee.exponent = expnt2; + else + { + /* Is denormal. Note that biased exponent of 0 is treated + as if it was 1, hence the extra shift. */ + if (expnt2 > -53) + lo >>= 1 - expnt2; + else + lo = 0; + } + } + else + u.d[1].ieee.negative = 0; + + u.d[1].ieee.mantissa1 = lo; + u.d[1].ieee.mantissa0 = lo >> 32; + u.d[0].ieee.mantissa1 = hi; + u.d[0].ieee.mantissa0 = hi >> 32; + return u.ld; +} + +/* Handy utility functions to pack/unpack/cononicalize and find the nearbyint + of long double implemented as double double. */ +static inline long double +default_ldbl_pack (double a, double aa) +{ + union ibm_extended_long_double u; + u.d[0].d = a; + u.d[1].d = aa; + return u.ld; +} + +static inline void +default_ldbl_unpack (long double l, double *a, double *aa) +{ + union ibm_extended_long_double u; + u.ld = l; + *a = u.d[0].d; + *aa = u.d[1].d; +} + +#ifndef ldbl_pack +# define ldbl_pack default_ldbl_pack +#endif +#ifndef ldbl_unpack +# define ldbl_unpack default_ldbl_unpack +#endif + +/* Extract high double. */ +#define ldbl_high(x) ((double) x) + +/* Convert a finite long double to canonical form. + Does not handle +/-Inf properly. */ +static inline void +ldbl_canonicalize (double *a, double *aa) +{ + double xh, xl; + + xh = *a + *aa; + xl = (*a - xh) + *aa; + *a = xh; + *aa = xl; +} + +/* Simple inline nearbyint (double) function. + Only works in the default rounding mode + but is useful in long double rounding functions. */ +static inline double +ldbl_nearbyint (double a) +{ + double two52 = 0x1p52; + + if (__glibc_likely ((__builtin_fabs (a) < two52))) + { + if (__glibc_likely ((a > 0.0))) + { + a += two52; + a -= two52; + } + else if (__glibc_likely ((a < 0.0))) + { + a = two52 - a; + a = -(a - two52); + } + } + return a; +} + +/* Canonicalize a result from an integer rounding function, in any + rounding mode. *A and *AA are finite and integers, with *A being + nonzero; if the result is not already canonical, *AA is plus or + minus a power of 2 that does not exceed the least set bit in + *A. */ +static inline void +ldbl_canonicalize_int (double *a, double *aa) +{ + /* Previously we used EXTRACT_WORDS64 from math_private.h, but in order + to avoid including internal headers we duplicate that code here. */ + uint64_t ax, aax; + union { double value; uint64_t word; } extractor; + extractor.value = *a; + ax = extractor.word; + extractor.value = *aa; + aax = extractor.word; + + int expdiff = ((ax >> 52) & 0x7ff) - ((aax >> 52) & 0x7ff); + if (expdiff <= 53) + { + if (expdiff == 53) + { + /* Half way between two double values; noncanonical iff the + low bit of A's mantissa is 1. */ + if ((ax & 1) != 0) + { + *a += 2 * *aa; + *aa = -*aa; + } + } + else + { + /* The sum can be represented in a single double. */ + *a += *aa; + *aa = 0; + } + } +} + +#endif /* math_ldbl.h */ diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c new file mode 100644 index 0000000000..92b28b8b5d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c @@ -0,0 +1,161 @@ +/* Copyright (C) 1995-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <ieee754.h> +#include <errno.h> +#include <float.h> +#include <math.h> + +/* Need to set this when including gmp headers after system headers. */ +#define HAVE_ALLOCA 1 + +#include "gmp.h" +#include "gmp-impl.h" + +/* Convert a multi-precision integer of the needed number of bits (106 + for long double) and an integral power of two to a `long double' in + IBM extended format. */ + +long double +__mpn_construct_long_double (mp_srcptr frac_ptr, int expt, int sign) +{ + union ibm_extended_long_double u; + unsigned long lzcount; + unsigned long long hi, lo; + int exponent2; + + u.d[0].ieee.negative = sign; + u.d[1].ieee.negative = sign; + u.d[0].ieee.exponent = expt + IEEE754_DOUBLE_BIAS; + u.d[1].ieee.exponent = 0; + exponent2 = expt - 53 + IEEE754_DOUBLE_BIAS; + +#if BITS_PER_MP_LIMB == 32 + /* The low order 53 bits (52 + hidden) go into the lower double */ + lo = frac_ptr[0]; + lo |= (frac_ptr[1] & ((1LL << (53 - 32)) - 1)) << 32; + /* The high order 53 bits (52 + hidden) go into the upper double */ + hi = (frac_ptr[1] >> (53 - 32)) & ((1 << 11) - 1); + hi |= ((unsigned long long) frac_ptr[2]) << 11; + hi |= ((unsigned long long) frac_ptr[3]) << (32 + 11); +#elif BITS_PER_MP_LIMB == 64 + /* The low order 53 bits (52 + hidden) go into the lower double */ + lo = frac_ptr[0] & (((mp_limb_t) 1 << 53) - 1); + /* The high order 53 bits (52 + hidden) go into the upper double */ + hi = (frac_ptr[0] >> 53) & (((mp_limb_t) 1 << 11) - 1); + hi |= (frac_ptr[1] << 11); +#else + #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif + + if ((hi & (1LL << 52)) == 0 && (hi | lo) != 0) + { + /* denormal number */ + unsigned long long val = hi ? hi : lo; + + if (sizeof (val) == sizeof (long)) + lzcount = __builtin_clzl (val); + else if ((val >> 32) != 0) + lzcount = __builtin_clzl ((long) (val >> 32)); + else + lzcount = __builtin_clzl ((long) val) + 32; + if (hi) + lzcount = lzcount - (64 - 53); + else + lzcount = lzcount + 53 - (64 - 53); + + if (lzcount > u.d[0].ieee.exponent) + { + lzcount = u.d[0].ieee.exponent; + u.d[0].ieee.exponent = 0; + exponent2 -= lzcount; + } + else + { + u.d[0].ieee.exponent -= (lzcount - 1); + exponent2 -= (lzcount - 1); + } + + if (lzcount <= 53) + { + hi = (hi << lzcount) | (lo >> (53 - lzcount)); + lo = (lo << lzcount) & ((1LL << 53) - 1); + } + else + { + hi = lo << (lzcount - 53); + lo = 0; + } + } + + if (lo != 0) + { + /* hidden bit of low double controls rounding of the high double. + If hidden is '1' and either the explicit mantissa is non-zero + or hi is odd, then round up hi and adjust lo (2nd mantissa) + plus change the sign of the low double to compensate. */ + if ((lo & (1LL << 52)) != 0 + && ((hi & 1) != 0 || (lo & ((1LL << 52) - 1)) != 0)) + { + hi++; + if ((hi & (1LL << 53)) != 0) + { + hi >>= 1; + u.d[0].ieee.exponent++; + if (u.d[0].ieee.exponent == IEEE754_DOUBLE_BIAS + DBL_MAX_EXP) + { + /* Overflow. The appropriate overflowed result must + be produced (if an infinity, that means the low + part must be zero). */ + __set_errno (ERANGE); + return (sign ? -LDBL_MAX : LDBL_MAX) * LDBL_MAX; + } + } + u.d[1].ieee.negative = !sign; + lo = (1LL << 53) - lo; + } + + /* Normalize the low double. Shift the mantissa left until + the hidden bit is '1' and adjust the exponent accordingly. */ + + if (sizeof (lo) == sizeof (long)) + lzcount = __builtin_clzl (lo); + else if ((lo >> 32) != 0) + lzcount = __builtin_clzl ((long) (lo >> 32)); + else + lzcount = __builtin_clzl ((long) lo) + 32; + lzcount = lzcount - (64 - 53); + lo <<= lzcount; + exponent2 -= lzcount; + + if (exponent2 > 0) + u.d[1].ieee.exponent = exponent2; + else if (exponent2 > -53) + lo >>= 1 - exponent2; + else + lo = 0; + } + else + u.d[1].ieee.negative = 0; + + u.d[1].ieee.mantissa1 = lo; + u.d[1].ieee.mantissa0 = lo >> 32; + u.d[0].ieee.mantissa1 = hi; + u.d[0].ieee.mantissa0 = hi >> 32; + + return u.ld; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c new file mode 100644 index 0000000000..2f87ec17cc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c @@ -0,0 +1,139 @@ +/* Print floating point number in hexadecimal notation according to ISO C99. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define PRINT_FPHEX_LONG_DOUBLE \ +do { \ + /* We have 105 bits of mantissa plus one implicit digit. Since \ + 106 bits are representable without rest using hexadecimal \ + digits we use only the implicit digits for the number before \ + the decimal point. */ \ + unsigned long long int num0, num1; \ + unsigned long long hi, lo; \ + int ediff; \ + union ibm_extended_long_double u; \ + u.ld = fpnum.ldbl; \ + \ + assert (sizeof (long double) == 16); \ + \ + lo = ((long long)u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1; \ + hi = ((long long)u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1; \ + lo <<= 7; /* pre-shift lo to match ieee854. */ \ + /* If the lower double is not a denormal or zero then set the hidden \ + 53rd bit. */ \ + if (u.d[1].ieee.exponent != 0) \ + lo |= (1ULL << (52 + 7)); \ + else \ + lo <<= 1; \ + /* The lower double is normalized separately from the upper. We \ + may need to adjust the lower manitissa to reflect this. */ \ + ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53; \ + if (ediff > 63) \ + lo = 0; \ + else if (ediff > 0) \ + lo = lo >> ediff; \ + else if (ediff < 0) \ + lo = lo << -ediff; \ + if (u.d[0].ieee.negative != u.d[1].ieee.negative \ + && lo != 0) \ + { \ + lo = (1ULL << 60) - lo; \ + if (hi == 0L) \ + { \ + /* we have a borrow from the hidden bit, so shift left 1. */ \ + hi = 0xffffffffffffeLL | (lo >> 59); \ + lo = 0xfffffffffffffffLL & (lo << 1); \ + u.d[0].ieee.exponent--; \ + } \ + else \ + hi--; \ + } \ + num1 = (hi << 60) | lo; \ + num0 = hi >> 4; \ + \ + zero_mantissa = (num0|num1) == 0; \ + \ + if (sizeof (unsigned long int) > 6) \ + { \ + numstr = _itoa_word (num1, numbuf + sizeof numbuf, 16, \ + info->spec == 'A'); \ + wnumstr = _itowa_word (num1, \ + wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t),\ + 16, info->spec == 'A'); \ + } \ + else \ + { \ + numstr = _itoa (num1, numbuf + sizeof numbuf, 16, \ + info->spec == 'A'); \ + wnumstr = _itowa (num1, \ + wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t), \ + 16, info->spec == 'A'); \ + } \ + \ + while (numstr > numbuf + (sizeof numbuf - 64 / 4)) \ + { \ + *--numstr = '0'; \ + *--wnumstr = L'0'; \ + } \ + \ + if (sizeof (unsigned long int) > 6) \ + { \ + numstr = _itoa_word (num0, numstr, 16, info->spec == 'A'); \ + wnumstr = _itowa_word (num0, wnumstr, 16, info->spec == 'A'); \ + } \ + else \ + { \ + numstr = _itoa (num0, numstr, 16, info->spec == 'A'); \ + wnumstr = _itowa (num0, wnumstr, 16, info->spec == 'A'); \ + } \ + \ + /* Fill with zeroes. */ \ + while (numstr > numbuf + (sizeof numbuf - 112 / 4)) \ + { \ + *--numstr = '0'; \ + *--wnumstr = L'0'; \ + } \ + \ + leading = u.d[0].ieee.exponent == 0 ? '0' : '1'; \ + \ + exponent = u.d[0].ieee.exponent; \ + \ + if (exponent == 0) \ + { \ + if (zero_mantissa) \ + expnegative = 0; \ + else \ + { \ + /* This is a denormalized number. */ \ + expnegative = 1; \ + exponent = IEEE754_DOUBLE_BIAS - 1; \ + } \ + } \ + else if (exponent >= IEEE754_DOUBLE_BIAS) \ + { \ + expnegative = 0; \ + exponent -= IEEE754_DOUBLE_BIAS; \ + } \ + else \ + { \ + expnegative = 1; \ + exponent = -(exponent - IEEE754_DOUBLE_BIAS); \ + } \ +} while (0) + +#include <stdio-common/printf_fphex.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_asinhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_asinhl.c new file mode 100644 index 0000000000..aa9a9ba213 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_asinhl.c @@ -0,0 +1,63 @@ +/* @(#)s_asinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $"; +#endif + +/* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +static const long double +one = 1.00000000000000000000e+00L, /* 0x3ff0000000000000, 0 */ +ln2 = 0.6931471805599453094172321214581766L, /* 0x3fe62e42fefa39ef, 0x3c7abc9e3b398040 */ +huge= 1.00000000000000000000e+300L; + +long double __asinhl(long double x) +{ + long double t,w; + int64_t hx,ix; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + ix = hx&0x7fffffffffffffffLL; + if(ix>=0x7ff0000000000000LL) return x+x; /* x is inf or NaN */ + if(ix< 0x3c70000000000000LL) { /* |x|<2**-56 */ + math_check_force_underflow (x); + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x4370000000000000LL) { /* |x| > 2**56 */ + w = __ieee754_logl(fabsl(x))+ln2; + } else if (ix>0x4000000000000000LL) { /* 2**56 >= |x| > 2.0 */ + t = fabs(x); + w = __ieee754_logl(2.0*t+one/(__ieee754_sqrtl(x*x+one)+t)); + } else { /* 2.0 >= |x| >= 2**-56 */ + t = x*x; + w =__log1pl(fabsl(x)+t/(one+__ieee754_sqrtl(one+t))); + } + if(hx>0) return w; else return -w; +} +long_double_symbol (libm, __asinhl, asinhl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_atanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_atanl.c new file mode 100644 index 0000000000..0560d820ae --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_atanl.c @@ -0,0 +1,250 @@ +/* s_atanl.c + * + * Inverse circular tangent for 128-bit long double precision + * (arctangent) + * + * + * + * SYNOPSIS: + * + * long double x, y, atanl(); + * + * y = atanl( x ); + * + * + * + * DESCRIPTION: + * + * Returns radian angle between -pi/2 and +pi/2 whose tangent is x. + * + * The function uses a rational approximation of the form + * t + t^3 P(t^2)/Q(t^2), optimized for |t| < 0.09375. + * + * The argument is reduced using the identity + * arctan x - arctan u = arctan ((x-u)/(1 + ux)) + * and an 83-entry lookup table for arctan u, with u = 0, 1/8, ..., 10.25. + * Use of the table improves the execution speed of the routine. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -19, 19 4e5 1.7e-34 5.4e-35 + * + * + * WARNING: + * + * This program uses integer operations on bit fields of floating-point + * numbers. It does not work with data structures other than the + * structure assumed. + * + */ + +/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov> + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +/* arctan(k/8), k = 0, ..., 82 */ +static const long double atantbl[84] = { + 0.0000000000000000000000000000000000000000E0L, + 1.2435499454676143503135484916387102557317E-1L, /* arctan(0.125) */ + 2.4497866312686415417208248121127581091414E-1L, + 3.5877067027057222039592006392646049977698E-1L, + 4.6364760900080611621425623146121440202854E-1L, + 5.5859931534356243597150821640166127034645E-1L, + 6.4350110879328438680280922871732263804151E-1L, + 7.1882999962162450541701415152590465395142E-1L, + 7.8539816339744830961566084581987572104929E-1L, + 8.4415398611317100251784414827164750652594E-1L, + 8.9605538457134395617480071802993782702458E-1L, + 9.4200004037946366473793717053459358607166E-1L, + 9.8279372324732906798571061101466601449688E-1L, + 1.0191413442663497346383429170230636487744E0L, + 1.0516502125483736674598673120862998296302E0L, + 1.0808390005411683108871567292171998202703E0L, + 1.1071487177940905030170654601785370400700E0L, + 1.1309537439791604464709335155363278047493E0L, + 1.1525719972156675180401498626127513797495E0L, + 1.1722738811284763866005949441337046149712E0L, + 1.1902899496825317329277337748293183376012E0L, + 1.2068173702852525303955115800565576303133E0L, + 1.2220253232109896370417417439225704908830E0L, + 1.2360594894780819419094519711090786987027E0L, + 1.2490457723982544258299170772810901230778E0L, + 1.2610933822524404193139408812473357720101E0L, + 1.2722973952087173412961937498224804940684E0L, + 1.2827408797442707473628852511364955306249E0L, + 1.2924966677897852679030914214070816845853E0L, + 1.3016288340091961438047858503666855921414E0L, + 1.3101939350475556342564376891719053122733E0L, + 1.3182420510168370498593302023271362531155E0L, + 1.3258176636680324650592392104284756311844E0L, + 1.3329603993374458675538498697331558093700E0L, + 1.3397056595989995393283037525895557411039E0L, + 1.3460851583802539310489409282517796256512E0L, + 1.3521273809209546571891479413898128509842E0L, + 1.3578579772154994751124898859640585287459E0L, + 1.3633001003596939542892985278250991189943E0L, + 1.3684746984165928776366381936948529556191E0L, + 1.3734007669450158608612719264449611486510E0L, + 1.3780955681325110444536609641291551522494E0L, + 1.3825748214901258580599674177685685125566E0L, + 1.3868528702577214543289381097042486034883E0L, + 1.3909428270024183486427686943836432060856E0L, + 1.3948567013423687823948122092044222644895E0L, + 1.3986055122719575950126700816114282335732E0L, + 1.4021993871854670105330304794336492676944E0L, + 1.4056476493802697809521934019958079881002E0L, + 1.4089588955564736949699075250792569287156E0L, + 1.4121410646084952153676136718584891599630E0L, + 1.4152014988178669079462550975833894394929E0L, + 1.4181469983996314594038603039700989523716E0L, + 1.4209838702219992566633046424614466661176E0L, + 1.4237179714064941189018190466107297503086E0L, + 1.4263547484202526397918060597281265695725E0L, + 1.4288992721907326964184700745371983590908E0L, + 1.4313562697035588982240194668401779312122E0L, + 1.4337301524847089866404719096698873648610E0L, + 1.4360250423171655234964275337155008780675E0L, + 1.4382447944982225979614042479354815855386E0L, + 1.4403930189057632173997301031392126865694E0L, + 1.4424730991091018200252920599377292525125E0L, + 1.4444882097316563655148453598508037025938E0L, + 1.4464413322481351841999668424758804165254E0L, + 1.4483352693775551917970437843145232637695E0L, + 1.4501726582147939000905940595923466567576E0L, + 1.4519559822271314199339700039142990228105E0L, + 1.4536875822280323362423034480994649820285E0L, + 1.4553696664279718992423082296859928222270E0L, + 1.4570043196511885530074841089245667532358E0L, + 1.4585935117976422128825857356750737658039E0L, + 1.4601391056210009726721818194296893361233E0L, + 1.4616428638860188872060496086383008594310E0L, + 1.4631064559620759326975975316301202111560E0L, + 1.4645314639038178118428450961503371619177E0L, + 1.4659193880646627234129855241049975398470E0L, + 1.4672716522843522691530527207287398276197E0L, + 1.4685896086876430842559640450619880951144E0L, + 1.4698745421276027686510391411132998919794E0L, + 1.4711276743037345918528755717617308518553E0L, + 1.4723501675822635384916444186631899205983E0L, + 1.4735431285433308455179928682541563973416E0L, /* arctan(10.25) */ + 1.5707963267948966192313216916397514420986E0L /* pi/2 */ +}; + + +/* arctan t = t + t^3 p(t^2) / q(t^2) + |t| <= 0.09375 + peak relative error 5.3e-37 */ + +static const long double + p0 = -4.283708356338736809269381409828726405572E1L, + p1 = -8.636132499244548540964557273544599863825E1L, + p2 = -5.713554848244551350855604111031839613216E1L, + p3 = -1.371405711877433266573835355036413750118E1L, + p4 = -8.638214309119210906997318946650189640184E-1L, + q0 = 1.285112506901621042780814422948906537959E2L, + q1 = 3.361907253914337187957855834229672347089E2L, + q2 = 3.180448303864130128268191635189365331680E2L, + q3 = 1.307244136980865800160844625025280344686E2L, + q4 = 2.173623741810414221251136181221172551416E1L; + /* q5 = 1.000000000000000000000000000000000000000E0 */ + + +long double +__atanl (long double x) +{ + int32_t k, sign, lx; + long double t, u, p, q; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS (k, lx, xhi); + sign = k & 0x80000000; + + /* Check for IEEE special cases. */ + k &= 0x7fffffff; + if (k >= 0x7ff00000) + { + /* NaN. */ + if (((k - 0x7ff00000) | lx) != 0) + return (x + x); + + /* Infinity. */ + if (sign) + return -atantbl[83]; + else + return atantbl[83]; + } + + if (k <= 0x3c800000) /* |x| <= 2**-55. */ + { + math_check_force_underflow (x); + /* Raise inexact. */ + if (1e300L + x > 0.0) + return x; + } + + if (k >= 0x46c00000) /* |x| >= 2**109. */ + { + /* Saturate result to {-,+}pi/2. */ + if (sign) + return -atantbl[83]; + else + return atantbl[83]; + } + + if (sign) + x = -x; + + if (k >= 0x40248000) /* 10.25 */ + { + k = 83; + t = -1.0/x; + } + else + { + /* Index of nearest table element. + Roundoff to integer is asymmetrical to avoid cancellation when t < 0 + (cf. fdlibm). */ + k = 8.0 * x + 0.25; + u = 0.125 * k; + /* Small arctan argument. */ + t = (x - u) / (1.0 + x * u); + } + + /* Arctan of small argument t. */ + u = t * t; + p = ((((p4 * u) + p3) * u + p2) * u + p1) * u + p0; + q = ((((u + q4) * u + q3) * u + q2) * u + q1) * u + q0; + u = t * u * p / q + t; + + /* arctan x = arctan u + arctan t */ + u = atantbl[k] + u; + if (sign) + return (-u); + else + return u; +} + +long_double_symbol (libm, __atanl, atanl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c new file mode 100644 index 0000000000..64bfc46414 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c @@ -0,0 +1,10 @@ +/* Looks like we can use ieee854 s_cbrtl.c as is for IBM extended format. */ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) + +#define _Float128 long double +#define L(x) x ## L + +#include <sysdeps/ieee754/ldbl-128/s_cbrtl.c> +long_double_symbol (libm, __cbrtl, cbrtl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ceill.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ceill.c new file mode 100644 index 0000000000..c451825c62 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ceill.c @@ -0,0 +1,62 @@ +/* Ceil (round to +inf) long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + + +long double +__ceill (long double x) +{ + double xh, xl, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Return Inf, Nan, +/-0 unchanged. */ + if (__builtin_expect (xh != 0.0 + && __builtin_isless (__builtin_fabs (xh), + __builtin_inf ()), 1)) + { + hi = __ceil (xh); + if (hi != xh) + { + /* The high part is not an integer; the low part does not + affect the result. */ + xh = hi; + xl = 0; + } + else + { + /* The high part is a nonzero integer. */ + lo = __ceil (xl); + xh = hi; + xl = lo; + ldbl_canonicalize_int (&xh, &xl); + } + } + else + /* Quiet signaling NaN arguments. */ + xh += xh; + + return ldbl_pack (xh, xl); +} + +long_double_symbol (libm, __ceill, ceill); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_copysignl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_copysignl.c new file mode 100644 index 0000000000..3b8ec1a74d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_copysignl.c @@ -0,0 +1,41 @@ +/* s_copysignl.c -- long double version of s_copysign.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * copysignl(long double x, long double y) + * copysignl(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __copysignl(long double x, long double y) +{ + if (signbit (x) != signbit (y)) + x = -x; + return x; +} + +#if IS_IN (libm) +long_double_symbol (libm, __copysignl, copysignl); +#else +long_double_symbol (libc, __copysignl, copysignl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_cosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_cosl.c new file mode 100644 index 0000000000..54c6cc77d2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_cosl.c @@ -0,0 +1,88 @@ +/* s_cosl.c -- long double version of s_cos.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* cosl(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sinl ... sine function on [-pi/4,pi/4] + * __kernel_cosl ... cosine function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __cosl(long double x) +{ + long double y[2],z=0.0L; + int64_t n, ix; + double xhi; + + /* High word of x. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if(ix <= 0x3fe921fb54442d18LL) + return __kernel_cosl(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7ff0000000000000LL) { + if (ix == 0x7ff0000000000000LL) + __set_errno (EDOM); + return x-x; + } + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + switch(n&3) { + case 0: + return __kernel_cosl(y[0],y[1]); + case 1: + return -__kernel_sinl(y[0],y[1],1); + case 2: + return -__kernel_cosl(y[0],y[1]); + default: + return __kernel_sinl(y[0],y[1],1); + } + } +} +long_double_symbol (libm, __cosl, cosl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_erfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_erfl.c new file mode 100644 index 0000000000..7b761b0afa --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_erfl.c @@ -0,0 +1,970 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Modifications and expansions for 128-bit long double are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. erf(x) = x + x*R(x^2) for |x| in [0, 7/8] + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. + * + * 1a. erf(x) = 1 - erfc(x), for |x| > 1.0 + * erfc(x) = 1 - erf(x) if |x| < 1/4 + * + * 2. For |x| in [7/8, 1], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(s + c) = sign(x) * (c + P1(s)/Q1(s)) + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * + * 3. For x in [1/4, 5/4], + * erfc(s + const) = erfc(const) + s P1(s)/Q1(s) + * for const = 1/4, 3/8, ..., 9/8 + * and 0 <= s <= 1/8 . + * + * 4. For x in [5/4, 107], + * erfc(x) = (1/x)*exp(-x*x-0.5625 + R(z)) + * z=1/x^2 + * The interval is partitioned into several segments + * of width 1/8 in 1/x. + * erf(x) = 1.0 - erfc(x) if x < 25.6283 else + * erf(x) = sign(x)*(1.0 - tiny) + * + * Note1: + * To compute exp(-x*x-0.5625+R/S), let s be a single + * precision number and s := x; then + * -x*x = -s*s + (s-x)*(s+x) + * exp(-x*x-0.5626+R/S) = + * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); + * Note2: + * Here 4 and 5 make use of the asymptotic series + * exp(-x*x) + * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) + * x*sqrt(pi) + * + * Note3: + * For x higher than 25.6283, erf(x) underflows. + * + * 5. For inf > x >= 107 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> +#include <fix-int-fp-convert-zero.h> + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +neval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +deval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + + +static const long double +tiny = 1e-300L, + one = 1.0L, + two = 2.0L, + /* 2/sqrt(pi) - 1 */ + efx = 1.2837916709551257389615890312154517168810E-1L; + + +/* erf(x) = x + x R(x^2) + 0 <= x <= 7/8 + Peak relative error 1.8e-35 */ +#define NTN1 8 +static const long double TN1[NTN1 + 1] = +{ + -3.858252324254637124543172907442106422373E10L, + 9.580319248590464682316366876952214879858E10L, + 1.302170519734879977595901236693040544854E10L, + 2.922956950426397417800321486727032845006E9L, + 1.764317520783319397868923218385468729799E8L, + 1.573436014601118630105796794840834145120E7L, + 4.028077380105721388745632295157816229289E5L, + 1.644056806467289066852135096352853491530E4L, + 3.390868480059991640235675479463287886081E1L +}; +#define NTD1 8 +static const long double TD1[NTD1 + 1] = +{ + -3.005357030696532927149885530689529032152E11L, + -1.342602283126282827411658673839982164042E11L, + -2.777153893355340961288511024443668743399E10L, + -3.483826391033531996955620074072768276974E9L, + -2.906321047071299585682722511260895227921E8L, + -1.653347985722154162439387878512427542691E7L, + -6.245520581562848778466500301865173123136E5L, + -1.402124304177498828590239373389110545142E4L, + -1.209368072473510674493129989468348633579E2L +/* 1.0E0 */ +}; + + +/* erf(z+1) = erf_const + P(z)/Q(z) + -.125 <= z <= 0 + Peak relative error 7.3e-36 */ +static const long double erf_const = 0.845062911510467529296875L; +#define NTN2 8 +static const long double TN2[NTN2 + 1] = +{ + -4.088889697077485301010486931817357000235E1L, + 7.157046430681808553842307502826960051036E3L, + -2.191561912574409865550015485451373731780E3L, + 2.180174916555316874988981177654057337219E3L, + 2.848578658049670668231333682379720943455E2L, + 1.630362490952512836762810462174798925274E2L, + 6.317712353961866974143739396865293596895E0L, + 2.450441034183492434655586496522857578066E1L, + 5.127662277706787664956025545897050896203E-1L +}; +#define NTD2 8 +static const long double TD2[NTD2 + 1] = +{ + 1.731026445926834008273768924015161048885E4L, + 1.209682239007990370796112604286048173750E4L, + 1.160950290217993641320602282462976163857E4L, + 5.394294645127126577825507169061355698157E3L, + 2.791239340533632669442158497532521776093E3L, + 8.989365571337319032943005387378993827684E2L, + 2.974016493766349409725385710897298069677E2L, + 6.148192754590376378740261072533527271947E1L, + 1.178502892490738445655468927408440847480E1L + /* 1.0E0 */ +}; + + +/* erfc(x + 0.25) = erfc(0.25) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.4e-35 */ +#define NRNr13 8 +static const long double RNr13[NRNr13 + 1] = +{ + -2.353707097641280550282633036456457014829E3L, + 3.871159656228743599994116143079870279866E2L, + -3.888105134258266192210485617504098426679E2L, + -2.129998539120061668038806696199343094971E1L, + -8.125462263594034672468446317145384108734E1L, + 8.151549093983505810118308635926270319660E0L, + -5.033362032729207310462422357772568553670E0L, + -4.253956621135136090295893547735851168471E-2L, + -8.098602878463854789780108161581050357814E-2L +}; +#define NRDr13 7 +static const long double RDr13[NRDr13 + 1] = +{ + 2.220448796306693503549505450626652881752E3L, + 1.899133258779578688791041599040951431383E2L, + 1.061906712284961110196427571557149268454E3L, + 7.497086072306967965180978101974566760042E1L, + 2.146796115662672795876463568170441327274E2L, + 1.120156008362573736664338015952284925592E1L, + 2.211014952075052616409845051695042741074E1L, + 6.469655675326150785692908453094054988938E-1L + /* 1.0E0 */ +}; +/* erfc(0.25) = C13a + C13b to extra precision. */ +static const long double C13a = 0.723663330078125L; +static const long double C13b = 1.0279753638067014931732235184287934646022E-5L; + + +/* erfc(x + 0.375) = erfc(0.375) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.2e-35 */ +#define NRNr14 8 +static const long double RNr14[NRNr14 + 1] = +{ + -2.446164016404426277577283038988918202456E3L, + 6.718753324496563913392217011618096698140E2L, + -4.581631138049836157425391886957389240794E2L, + -2.382844088987092233033215402335026078208E1L, + -7.119237852400600507927038680970936336458E1L, + 1.313609646108420136332418282286454287146E1L, + -6.188608702082264389155862490056401365834E0L, + -2.787116601106678287277373011101132659279E-2L, + -2.230395570574153963203348263549700967918E-2L +}; +#define NRDr14 7 +static const long double RDr14[NRDr14 + 1] = +{ + 2.495187439241869732696223349840963702875E3L, + 2.503549449872925580011284635695738412162E2L, + 1.159033560988895481698051531263861842461E3L, + 9.493751466542304491261487998684383688622E1L, + 2.276214929562354328261422263078480321204E2L, + 1.367697521219069280358984081407807931847E1L, + 2.276988395995528495055594829206582732682E1L, + 7.647745753648996559837591812375456641163E-1L + /* 1.0E0 */ +}; +/* erfc(0.375) = C14a + C14b to extra precision. */ +static const long double C14a = 0.5958709716796875L; +static const long double C14b = 1.2118885490201676174914080878232469565953E-5L; + +/* erfc(x + 0.5) = erfc(0.5) + x R(x) + 0 <= x < 0.125 + Peak relative error 4.7e-36 */ +#define NRNr15 8 +static const long double RNr15[NRNr15 + 1] = +{ + -2.624212418011181487924855581955853461925E3L, + 8.473828904647825181073831556439301342756E2L, + -5.286207458628380765099405359607331669027E2L, + -3.895781234155315729088407259045269652318E1L, + -6.200857908065163618041240848728398496256E1L, + 1.469324610346924001393137895116129204737E1L, + -6.961356525370658572800674953305625578903E0L, + 5.145724386641163809595512876629030548495E-3L, + 1.990253655948179713415957791776180406812E-2L +}; +#define NRDr15 7 +static const long double RDr15[NRDr15 + 1] = +{ + 2.986190760847974943034021764693341524962E3L, + 5.288262758961073066335410218650047725985E2L, + 1.363649178071006978355113026427856008978E3L, + 1.921707975649915894241864988942255320833E2L, + 2.588651100651029023069013885900085533226E2L, + 2.628752920321455606558942309396855629459E1L, + 2.455649035885114308978333741080991380610E1L, + 1.378826653595128464383127836412100939126E0L + /* 1.0E0 */ +}; +/* erfc(0.5) = C15a + C15b to extra precision. */ +static const long double C15a = 0.4794921875L; +static const long double C15b = 7.9346869534623172533461080354712635484242E-6L; + +/* erfc(x + 0.625) = erfc(0.625) + x R(x) + 0 <= x < 0.125 + Peak relative error 5.1e-36 */ +#define NRNr16 8 +static const long double RNr16[NRNr16 + 1] = +{ + -2.347887943200680563784690094002722906820E3L, + 8.008590660692105004780722726421020136482E2L, + -5.257363310384119728760181252132311447963E2L, + -4.471737717857801230450290232600243795637E1L, + -4.849540386452573306708795324759300320304E1L, + 1.140885264677134679275986782978655952843E1L, + -6.731591085460269447926746876983786152300E0L, + 1.370831653033047440345050025876085121231E-1L, + 2.022958279982138755020825717073966576670E-2L, +}; +#define NRDr16 7 +static const long double RDr16[NRDr16 + 1] = +{ + 3.075166170024837215399323264868308087281E3L, + 8.730468942160798031608053127270430036627E2L, + 1.458472799166340479742581949088453244767E3L, + 3.230423687568019709453130785873540386217E2L, + 2.804009872719893612081109617983169474655E2L, + 4.465334221323222943418085830026979293091E1L, + 2.612723259683205928103787842214809134746E1L, + 2.341526751185244109722204018543276124997E0L, + /* 1.0E0 */ +}; +/* erfc(0.625) = C16a + C16b to extra precision. */ +static const long double C16a = 0.3767547607421875L; +static const long double C16b = 4.3570693945275513594941232097252997287766E-6L; + +/* erfc(x + 0.75) = erfc(0.75) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.7e-35 */ +#define NRNr17 8 +static const long double RNr17[NRNr17 + 1] = +{ + -1.767068734220277728233364375724380366826E3L, + 6.693746645665242832426891888805363898707E2L, + -4.746224241837275958126060307406616817753E2L, + -2.274160637728782675145666064841883803196E1L, + -3.541232266140939050094370552538987982637E1L, + 6.988950514747052676394491563585179503865E0L, + -5.807687216836540830881352383529281215100E0L, + 3.631915988567346438830283503729569443642E-1L, + -1.488945487149634820537348176770282391202E-2L +}; +#define NRDr17 7 +static const long double RDr17[NRDr17 + 1] = +{ + 2.748457523498150741964464942246913394647E3L, + 1.020213390713477686776037331757871252652E3L, + 1.388857635935432621972601695296561952738E3L, + 3.903363681143817750895999579637315491087E2L, + 2.784568344378139499217928969529219886578E2L, + 5.555800830216764702779238020065345401144E1L, + 2.646215470959050279430447295801291168941E1L, + 2.984905282103517497081766758550112011265E0L, + /* 1.0E0 */ +}; +/* erfc(0.75) = C17a + C17b to extra precision. */ +static const long double C17a = 0.2888336181640625L; +static const long double C17b = 1.0748182422368401062165408589222625794046E-5L; + + +/* erfc(x + 0.875) = erfc(0.875) + x R(x) + 0 <= x < 0.125 + Peak relative error 2.2e-35 */ +#define NRNr18 8 +static const long double RNr18[NRNr18 + 1] = +{ + -1.342044899087593397419622771847219619588E3L, + 6.127221294229172997509252330961641850598E2L, + -4.519821356522291185621206350470820610727E2L, + 1.223275177825128732497510264197915160235E1L, + -2.730789571382971355625020710543532867692E1L, + 4.045181204921538886880171727755445395862E0L, + -4.925146477876592723401384464691452700539E0L, + 5.933878036611279244654299924101068088582E-1L, + -5.557645435858916025452563379795159124753E-2L +}; +#define NRDr18 7 +static const long double RDr18[NRDr18 + 1] = +{ + 2.557518000661700588758505116291983092951E3L, + 1.070171433382888994954602511991940418588E3L, + 1.344842834423493081054489613250688918709E3L, + 4.161144478449381901208660598266288188426E2L, + 2.763670252219855198052378138756906980422E2L, + 5.998153487868943708236273854747564557632E1L, + 2.657695108438628847733050476209037025318E1L, + 3.252140524394421868923289114410336976512E0L, + /* 1.0E0 */ +}; +/* erfc(0.875) = C18a + C18b to extra precision. */ +static const long double C18a = 0.215911865234375L; +static const long double C18b = 1.3073705765341685464282101150637224028267E-5L; + +/* erfc(x + 1.0) = erfc(1.0) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.6e-35 */ +#define NRNr19 8 +static const long double RNr19[NRNr19 + 1] = +{ + -1.139180936454157193495882956565663294826E3L, + 6.134903129086899737514712477207945973616E2L, + -4.628909024715329562325555164720732868263E2L, + 4.165702387210732352564932347500364010833E1L, + -2.286979913515229747204101330405771801610E1L, + 1.870695256449872743066783202326943667722E0L, + -4.177486601273105752879868187237000032364E0L, + 7.533980372789646140112424811291782526263E-1L, + -8.629945436917752003058064731308767664446E-2L +}; +#define NRDr19 7 +static const long double RDr19[NRDr19 + 1] = +{ + 2.744303447981132701432716278363418643778E3L, + 1.266396359526187065222528050591302171471E3L, + 1.466739461422073351497972255511919814273E3L, + 4.868710570759693955597496520298058147162E2L, + 2.993694301559756046478189634131722579643E2L, + 6.868976819510254139741559102693828237440E1L, + 2.801505816247677193480190483913753613630E1L, + 3.604439909194350263552750347742663954481E0L, + /* 1.0E0 */ +}; +/* erfc(1.0) = C19a + C19b to extra precision. */ +static const long double C19a = 0.15728759765625L; +static const long double C19b = 1.1609394035130658779364917390740703933002E-5L; + +/* erfc(x + 1.125) = erfc(1.125) + x R(x) + 0 <= x < 0.125 + Peak relative error 3.6e-36 */ +#define NRNr20 8 +static const long double RNr20[NRNr20 + 1] = +{ + -9.652706916457973956366721379612508047640E2L, + 5.577066396050932776683469951773643880634E2L, + -4.406335508848496713572223098693575485978E2L, + 5.202893466490242733570232680736966655434E1L, + -1.931311847665757913322495948705563937159E1L, + -9.364318268748287664267341457164918090611E-2L, + -3.306390351286352764891355375882586201069E0L, + 7.573806045289044647727613003096916516475E-1L, + -9.611744011489092894027478899545635991213E-2L +}; +#define NRDr20 7 +static const long double RDr20[NRDr20 + 1] = +{ + 3.032829629520142564106649167182428189014E3L, + 1.659648470721967719961167083684972196891E3L, + 1.703545128657284619402511356932569292535E3L, + 6.393465677731598872500200253155257708763E2L, + 3.489131397281030947405287112726059221934E2L, + 8.848641738570783406484348434387611713070E1L, + 3.132269062552392974833215844236160958502E1L, + 4.430131663290563523933419966185230513168E0L + /* 1.0E0 */ +}; +/* erfc(1.125) = C20a + C20b to extra precision. */ +static const long double C20a = 0.111602783203125L; +static const long double C20b = 8.9850951672359304215530728365232161564636E-6L; + +/* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2)) + 7/8 <= 1/x < 1 + Peak relative error 1.4e-35 */ +#define NRNr8 9 +static const long double RNr8[NRNr8 + 1] = +{ + 3.587451489255356250759834295199296936784E1L, + 5.406249749087340431871378009874875889602E2L, + 2.931301290625250886238822286506381194157E3L, + 7.359254185241795584113047248898753470923E3L, + 9.201031849810636104112101947312492532314E3L, + 5.749697096193191467751650366613289284777E3L, + 1.710415234419860825710780802678697889231E3L, + 2.150753982543378580859546706243022719599E2L, + 8.740953582272147335100537849981160931197E0L, + 4.876422978828717219629814794707963640913E-2L +}; +#define NRDr8 8 +static const long double RDr8[NRDr8 + 1] = +{ + 6.358593134096908350929496535931630140282E1L, + 9.900253816552450073757174323424051765523E2L, + 5.642928777856801020545245437089490805186E3L, + 1.524195375199570868195152698617273739609E4L, + 2.113829644500006749947332935305800887345E4L, + 1.526438562626465706267943737310282977138E4L, + 5.561370922149241457131421914140039411782E3L, + 9.394035530179705051609070428036834496942E2L, + 6.147019596150394577984175188032707343615E1L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2)) + 0.75 <= 1/x <= 0.875 + Peak relative error 2.0e-36 */ +#define NRNr7 9 +static const long double RNr7[NRNr7 + 1] = +{ + 1.686222193385987690785945787708644476545E1L, + 1.178224543567604215602418571310612066594E3L, + 1.764550584290149466653899886088166091093E4L, + 1.073758321890334822002849369898232811561E5L, + 3.132840749205943137619839114451290324371E5L, + 4.607864939974100224615527007793867585915E5L, + 3.389781820105852303125270837910972384510E5L, + 1.174042187110565202875011358512564753399E5L, + 1.660013606011167144046604892622504338313E4L, + 6.700393957480661937695573729183733234400E2L +}; +#define NRDr7 9 +static const long double RDr7[NRDr7 + 1] = +{ +-1.709305024718358874701575813642933561169E3L, +-3.280033887481333199580464617020514788369E4L, +-2.345284228022521885093072363418750835214E5L, +-8.086758123097763971926711729242327554917E5L, +-1.456900414510108718402423999575992450138E6L, +-1.391654264881255068392389037292702041855E6L, +-6.842360801869939983674527468509852583855E5L, +-1.597430214446573566179675395199807533371E5L, +-1.488876130609876681421645314851760773480E4L, +-3.511762950935060301403599443436465645703E2L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 5/8 <= 1/x < 3/4 + Peak relative error 1.9e-35 */ +#define NRNr6 9 +static const long double RNr6[NRNr6 + 1] = +{ + 1.642076876176834390623842732352935761108E0L, + 1.207150003611117689000664385596211076662E2L, + 2.119260779316389904742873816462800103939E3L, + 1.562942227734663441801452930916044224174E4L, + 5.656779189549710079988084081145693580479E4L, + 1.052166241021481691922831746350942786299E5L, + 9.949798524786000595621602790068349165758E4L, + 4.491790734080265043407035220188849562856E4L, + 8.377074098301530326270432059434791287601E3L, + 4.506934806567986810091824791963991057083E2L +}; +#define NRDr6 9 +static const long double RDr6[NRDr6 + 1] = +{ +-1.664557643928263091879301304019826629067E2L, +-3.800035902507656624590531122291160668452E3L, +-3.277028191591734928360050685359277076056E4L, +-1.381359471502885446400589109566587443987E5L, +-3.082204287382581873532528989283748656546E5L, +-3.691071488256738343008271448234631037095E5L, +-2.300482443038349815750714219117566715043E5L, +-6.873955300927636236692803579555752171530E4L, +-8.262158817978334142081581542749986845399E3L, +-2.517122254384430859629423488157361983661E2L + /* 1.00 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/2 <= 1/x < 5/8 + Peak relative error 4.6e-36 */ +#define NRNr5 10 +static const long double RNr5[NRNr5 + 1] = +{ +-3.332258927455285458355550878136506961608E-3L, +-2.697100758900280402659586595884478660721E-1L, +-6.083328551139621521416618424949137195536E0L, +-6.119863528983308012970821226810162441263E1L, +-3.176535282475593173248810678636522589861E2L, +-8.933395175080560925809992467187963260693E2L, +-1.360019508488475978060917477620199499560E3L, +-1.075075579828188621541398761300910213280E3L, +-4.017346561586014822824459436695197089916E2L, +-5.857581368145266249509589726077645791341E1L, +-2.077715925587834606379119585995758954399E0L +}; +#define NRDr5 9 +static const long double RDr5[NRDr5 + 1] = +{ + 3.377879570417399341550710467744693125385E-1L, + 1.021963322742390735430008860602594456187E1L, + 1.200847646592942095192766255154827011939E2L, + 7.118915528142927104078182863387116942836E2L, + 2.318159380062066469386544552429625026238E3L, + 4.238729853534009221025582008928765281620E3L, + 4.279114907284825886266493994833515580782E3L, + 2.257277186663261531053293222591851737504E3L, + 5.570475501285054293371908382916063822957E2L, + 5.142189243856288981145786492585432443560E1L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 3/8 <= 1/x < 1/2 + Peak relative error 2.0e-36 */ +#define NRNr4 10 +static const long double RNr4[NRNr4 + 1] = +{ + 3.258530712024527835089319075288494524465E-3L, + 2.987056016877277929720231688689431056567E-1L, + 8.738729089340199750734409156830371528862E0L, + 1.207211160148647782396337792426311125923E2L, + 8.997558632489032902250523945248208224445E2L, + 3.798025197699757225978410230530640879762E3L, + 9.113203668683080975637043118209210146846E3L, + 1.203285891339933238608683715194034900149E4L, + 8.100647057919140328536743641735339740855E3L, + 2.383888249907144945837976899822927411769E3L, + 2.127493573166454249221983582495245662319E2L +}; +#define NRDr4 10 +static const long double RDr4[NRDr4 + 1] = +{ +-3.303141981514540274165450687270180479586E-1L, +-1.353768629363605300707949368917687066724E1L, +-2.206127630303621521950193783894598987033E2L, +-1.861800338758066696514480386180875607204E3L, +-8.889048775872605708249140016201753255599E3L, +-2.465888106627948210478692168261494857089E4L, +-3.934642211710774494879042116768390014289E4L, +-3.455077258242252974937480623730228841003E4L, +-1.524083977439690284820586063729912653196E4L, +-2.810541887397984804237552337349093953857E3L, +-1.343929553541159933824901621702567066156E2L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/4 <= 1/x < 3/8 + Peak relative error 8.4e-37 */ +#define NRNr3 11 +static const long double RNr3[NRNr3 + 1] = +{ +-1.952401126551202208698629992497306292987E-6L, +-2.130881743066372952515162564941682716125E-4L, +-8.376493958090190943737529486107282224387E-3L, +-1.650592646560987700661598877522831234791E-1L, +-1.839290818933317338111364667708678163199E0L, +-1.216278715570882422410442318517814388470E1L, +-4.818759344462360427612133632533779091386E1L, +-1.120994661297476876804405329172164436784E2L, +-1.452850765662319264191141091859300126931E2L, +-9.485207851128957108648038238656777241333E1L, +-2.563663855025796641216191848818620020073E1L, +-1.787995944187565676837847610706317833247E0L +}; +#define NRDr3 10 +static const long double RDr3[NRDr3 + 1] = +{ + 1.979130686770349481460559711878399476903E-4L, + 1.156941716128488266238105813374635099057E-2L, + 2.752657634309886336431266395637285974292E-1L, + 3.482245457248318787349778336603569327521E0L, + 2.569347069372696358578399521203959253162E1L, + 1.142279000180457419740314694631879921561E2L, + 3.056503977190564294341422623108332700840E2L, + 4.780844020923794821656358157128719184422E2L, + 4.105972727212554277496256802312730410518E2L, + 1.724072188063746970865027817017067646246E2L, + 2.815939183464818198705278118326590370435E1L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/8 <= 1/x < 1/4 + Peak relative error 1.5e-36 */ +#define NRNr2 11 +static const long double RNr2[NRNr2 + 1] = +{ +-2.638914383420287212401687401284326363787E-8L, +-3.479198370260633977258201271399116766619E-6L, +-1.783985295335697686382487087502222519983E-4L, +-4.777876933122576014266349277217559356276E-3L, +-7.450634738987325004070761301045014986520E-2L, +-7.068318854874733315971973707247467326619E-1L, +-4.113919921935944795764071670806867038732E0L, +-1.440447573226906222417767283691888875082E1L, +-2.883484031530718428417168042141288943905E1L, +-2.990886974328476387277797361464279931446E1L, +-1.325283914915104866248279787536128997331E1L, +-1.572436106228070195510230310658206154374E0L +}; +#define NRDr2 10 +static const long double RDr2[NRDr2 + 1] = +{ + 2.675042728136731923554119302571867799673E-6L, + 2.170997868451812708585443282998329996268E-4L, + 7.249969752687540289422684951196241427445E-3L, + 1.302040375859768674620410563307838448508E-1L, + 1.380202483082910888897654537144485285549E0L, + 8.926594113174165352623847870299170069350E0L, + 3.521089584782616472372909095331572607185E1L, + 8.233547427533181375185259050330809105570E1L, + 1.072971579885803033079469639073292840135E2L, + 6.943803113337964469736022094105143158033E1L, + 1.775695341031607738233608307835017282662E1L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/128 <= 1/x < 1/8 + Peak relative error 2.2e-36 */ +#define NRNr1 9 +static const long double RNr1[NRNr1 + 1] = +{ +-4.250780883202361946697751475473042685782E-8L, +-5.375777053288612282487696975623206383019E-6L, +-2.573645949220896816208565944117382460452E-4L, +-6.199032928113542080263152610799113086319E-3L, +-8.262721198693404060380104048479916247786E-2L, +-6.242615227257324746371284637695778043982E-1L, +-2.609874739199595400225113299437099626386E0L, +-5.581967563336676737146358534602770006970E0L, +-5.124398923356022609707490956634280573882E0L, +-1.290865243944292370661544030414667556649E0L +}; +#define NRDr1 8 +static const long double RDr1[NRDr1 + 1] = +{ + 4.308976661749509034845251315983612976224E-6L, + 3.265390126432780184125233455960049294580E-4L, + 9.811328839187040701901866531796570418691E-3L, + 1.511222515036021033410078631914783519649E-1L, + 1.289264341917429958858379585970225092274E0L, + 6.147640356182230769548007536914983522270E0L, + 1.573966871337739784518246317003956180750E1L, + 1.955534123435095067199574045529218238263E1L, + 9.472613121363135472247929109615785855865E0L + /* 1.0E0 */ +}; + + +long double +__erfl (long double x) +{ + long double a, y, z; + int32_t i, ix, hx; + double xhi; + + xhi = ldbl_high (x); + GET_HIGH_WORD (hx, xhi); + ix = hx & 0x7fffffff; + + if (ix >= 0x7ff00000) + { /* erf(nan)=nan */ + i = ((uint32_t) hx >> 31) << 1; + return (long double) (1 - i) + one / x; /* erf(+-inf)=+-1 */ + } + + if (ix >= 0x3ff00000) /* |x| >= 1.0 */ + { + if (ix >= 0x4039A0DE) + { + /* __erfcl (x) underflows if x > 25.6283 */ + if ((hx & 0x80000000) == 0) + return one-tiny; + else + return tiny-one; + } + else + { + y = __erfcl (x); + return (one - y); + } + } + a = x; + if ((hx & 0x80000000) != 0) + a = -a; + z = x * x; + if (ix < 0x3fec0000) /* a < 0.875 */ + { + if (ix < 0x3c600000) /* |x|<2**-57 */ + { + if (ix < 0x00800000) + { + /* erf (-0) = -0. Unfortunately, for IBM extended double + 0.0625 * (16.0 * x + (16.0 * efx) * x) for x = -0 + evaluates to 0. */ + if (x == 0) + return x; + long double ret = 0.0625 * (16.0 * x + (16.0 * efx) * x); + math_check_force_underflow (ret); + return ret; + } + return x + efx * x; + } + y = a + a * neval (z, TN1, NTN1) / deval (z, TD1, NTD1); + } + else + { + a = a - one; + y = erf_const + neval (a, TN2, NTN2) / deval (a, TD2, NTD2); + } + + if (hx & 0x80000000) /* x < 0 */ + y = -y; + return( y ); +} + +long_double_symbol (libm, __erfl, erfl); +long double +__erfcl (long double x) +{ + long double y, z, p, r; + int32_t i, ix; + uint32_t hx; + double xhi; + + xhi = ldbl_high (x); + GET_HIGH_WORD (hx, xhi); + ix = hx & 0x7fffffff; + + if (ix >= 0x7ff00000) + { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + long double ret = (long double) ((hx >> 31) << 1) + one / x; + if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0L) + return 0.0L; + return ret; + } + + if (ix < 0x3fd00000) /* |x| <1/4 */ + { + if (ix < 0x38d00000) /* |x|<2**-114 */ + return one - x; + return one - __erfl (x); + } + if (ix < 0x3ff40000) /* 1.25 */ + { + if ((hx & 0x80000000) != 0) + x = -x; + i = 8.0 * x; + switch (i) + { + case 2: + z = x - 0.25L; + y = C13b + z * neval (z, RNr13, NRNr13) / deval (z, RDr13, NRDr13); + y += C13a; + break; + case 3: + z = x - 0.375L; + y = C14b + z * neval (z, RNr14, NRNr14) / deval (z, RDr14, NRDr14); + y += C14a; + break; + case 4: + z = x - 0.5L; + y = C15b + z * neval (z, RNr15, NRNr15) / deval (z, RDr15, NRDr15); + y += C15a; + break; + case 5: + z = x - 0.625L; + y = C16b + z * neval (z, RNr16, NRNr16) / deval (z, RDr16, NRDr16); + y += C16a; + break; + case 6: + z = x - 0.75L; + y = C17b + z * neval (z, RNr17, NRNr17) / deval (z, RDr17, NRDr17); + y += C17a; + break; + case 7: + z = x - 0.875L; + y = C18b + z * neval (z, RNr18, NRNr18) / deval (z, RDr18, NRDr18); + y += C18a; + break; + case 8: + z = x - 1.0L; + y = C19b + z * neval (z, RNr19, NRNr19) / deval (z, RDr19, NRDr19); + y += C19a; + break; + default: /* i == 9. */ + z = x - 1.125L; + y = C20b + z * neval (z, RNr20, NRNr20) / deval (z, RDr20, NRDr20); + y += C20a; + break; + } + if (hx & 0x80000000) + y = 2.0L - y; + return y; + } + /* 1.25 < |x| < 107 */ + if (ix < 0x405ac000) + { + /* x < -9 */ + if (hx >= 0xc0220000) + return two - tiny; + + if ((hx & 0x80000000) != 0) + x = -x; + z = one / (x * x); + i = 8.0 / x; + switch (i) + { + default: + case 0: + p = neval (z, RNr1, NRNr1) / deval (z, RDr1, NRDr1); + break; + case 1: + p = neval (z, RNr2, NRNr2) / deval (z, RDr2, NRDr2); + break; + case 2: + p = neval (z, RNr3, NRNr3) / deval (z, RDr3, NRDr3); + break; + case 3: + p = neval (z, RNr4, NRNr4) / deval (z, RDr4, NRDr4); + break; + case 4: + p = neval (z, RNr5, NRNr5) / deval (z, RDr5, NRDr5); + break; + case 5: + p = neval (z, RNr6, NRNr6) / deval (z, RDr6, NRDr6); + break; + case 6: + p = neval (z, RNr7, NRNr7) / deval (z, RDr7, NRDr7); + break; + case 7: + p = neval (z, RNr8, NRNr8) / deval (z, RDr8, NRDr8); + break; + } + z = (float) x; + r = __ieee754_expl (-z * z - 0.5625) * + __ieee754_expl ((z - x) * (z + x) + p); + if ((hx & 0x80000000) == 0) + { + long double ret = r / x; + if (ret == 0) + __set_errno (ERANGE); + return ret; + } + else + return two - r / x; + } + else + { + if ((hx & 0x80000000) == 0) + { + __set_errno (ERANGE); + return tiny * tiny; + } + else + return two - tiny; + } +} + +long_double_symbol (libm, __erfcl, erfcl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c new file mode 100644 index 0000000000..42d57c6eec --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c @@ -0,0 +1,152 @@ +/* expm1l.c + * + * Exponential function, minus 1 + * 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, expm1l(); + * + * y = expm1l( x ); + * + * + * + * DESCRIPTION: + * + * Returns e (2.71828...) raised to the x power, minus one. + * + * Range reduction is accomplished by separating the argument + * into an integer k and fraction f such that + * + * x k f + * e = 2 e. + * + * An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1 + * in the basic range [-0.5 ln 2, 0.5 ln 2]. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -79,+MAXLOG 100,000 1.7e-34 4.5e-35 + * + */ + +/* Copyright 2001 by Stephen L. Moshier + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x) + -.5 ln 2 < x < .5 ln 2 + Theoretical peak relative error = 8.1e-36 */ + +static const long double + P0 = 2.943520915569954073888921213330863757240E8L, + P1 = -5.722847283900608941516165725053359168840E7L, + P2 = 8.944630806357575461578107295909719817253E6L, + P3 = -7.212432713558031519943281748462837065308E5L, + P4 = 4.578962475841642634225390068461943438441E4L, + P5 = -1.716772506388927649032068540558788106762E3L, + P6 = 4.401308817383362136048032038528753151144E1L, + P7 = -4.888737542888633647784737721812546636240E-1L, + Q0 = 1.766112549341972444333352727998584753865E9L, + Q1 = -7.848989743695296475743081255027098295771E8L, + Q2 = 1.615869009634292424463780387327037251069E8L, + Q3 = -2.019684072836541751428967854947019415698E7L, + Q4 = 1.682912729190313538934190635536631941751E6L, + Q5 = -9.615511549171441430850103489315371768998E4L, + Q6 = 3.697714952261803935521187272204485251835E3L, + Q7 = -8.802340681794263968892934703309274564037E1L, + /* Q8 = 1.000000000000000000000000000000000000000E0 */ +/* C1 + C2 = ln 2 */ + + C1 = 6.93145751953125E-1L, + C2 = 1.428606820309417232121458176568075500134E-6L, +/* ln 2^-114 */ + minarg = -7.9018778583833765273564461846232128760607E1L, big = 1e290L; + + +long double +__expm1l (long double x) +{ + long double px, qx, xx; + int32_t ix, lx, sign; + int k; + double xhi; + + /* Detect infinity and NaN. */ + xhi = ldbl_high (x); + EXTRACT_WORDS (ix, lx, xhi); + sign = ix & 0x80000000; + ix &= 0x7fffffff; + if (!sign && ix >= 0x40600000) + return __expl (x); + if (ix >= 0x7ff00000) + { + /* Infinity (which must be negative infinity). */ + if (((ix - 0x7ff00000) | lx) == 0) + return -1.0L; + /* NaN. Invalid exception if signaling. */ + return x + x; + } + + /* expm1(+- 0) = +- 0. */ + if ((ix | lx) == 0) + return x; + + /* Minimum value. */ + if (x < minarg) + return (4.0/big - 1.0L); + + /* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */ + xx = C1 + C2; /* ln 2. */ + px = __floorl (0.5 + x / xx); + k = px; + /* remainder times ln 2 */ + x -= px * C1; + x -= px * C2; + + /* Approximate exp(remainder ln 2). */ + px = (((((((P7 * x + + P6) * x + + P5) * x + P4) * x + P3) * x + P2) * x + P1) * x + P0) * x; + + qx = (((((((x + + Q7) * x + + Q6) * x + Q5) * x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0; + + xx = x * x; + qx = x + (0.5 * xx + xx * px / qx); + + /* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2). + + We have qx = exp(remainder ln 2) - 1, so + exp(x) - 1 = 2^k (qx + 1) - 1 + = 2^k qx + 2^k - 1. */ + + px = __ldexpl (1.0L, k); + x = px * qx + (px - 1.0); + return x; +} +libm_hidden_def (__expm1l) +long_double_symbol (libm, __expm1l, expm1l); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fabsl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fabsl.c new file mode 100644 index 0000000000..c801c97065 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fabsl.c @@ -0,0 +1,44 @@ +/* s_fabsl.c -- long double version of s_fabs.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + + +/* + * fabsl(x) returns the absolute value of x. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __fabsl(long double x) +{ + u_int64_t hx, lx; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + lx = lx ^ ( hx & 0x8000000000000000LL ); + hx = hx & 0x7fffffffffffffffLL; + INSERT_WORDS64 (xhi, hx); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x; +} +long_double_symbol (libm, __fabsl, fabsl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_finitel.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_finitel.c new file mode 100644 index 0000000000..3b9e3de292 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_finitel.c @@ -0,0 +1,49 @@ +/* s_finitel.c -- long double version of s_finite.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * finitel(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +int +___finitel (long double x) +{ + uint64_t hx; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + hx &= 0x7ff0000000000000LL; + hx -= 0x7ff0000000000000LL; + return hx >> 63; +} +hidden_ver (___finitel, __finitel) +weak_alias (___finitel, ____finitel) +#if IS_IN (libm) +long_double_symbol (libm, ____finitel, finitel); +long_double_symbol (libm, ___finitel, __finitel); +#else +long_double_symbol (libc, ____finitel, finitel); +long_double_symbol (libc, ___finitel, __finitel); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_floorl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_floorl.c new file mode 100644 index 0000000000..6b837c7bcd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_floorl.c @@ -0,0 +1,62 @@ +/* Round to int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + + +long double +__floorl (long double x) +{ + double xh, xl, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Return Inf, Nan, +/-0 unchanged. */ + if (__builtin_expect (xh != 0.0 + && __builtin_isless (__builtin_fabs (xh), + __builtin_inf ()), 1)) + { + hi = __floor (xh); + if (hi != xh) + { + /* The high part is not an integer; the low part does not + affect the result. */ + xh = hi; + xl = 0; + } + else + { + /* The high part is a nonzero integer. */ + lo = __floor (xl); + xh = hi; + xl = lo; + ldbl_canonicalize_int (&xh, &xl); + } + } + else + /* Quiet signaling NaN arguments. */ + xh += xh; + + return ldbl_pack (xh, xl); +} + +long_double_symbol (libm, __floorl, floorl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fmal.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fmal.c new file mode 100644 index 0000000000..9098e79df9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fmal.c @@ -0,0 +1,257 @@ +/* Compute x * y + z as ternary operation. + Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by David Flaherty <flaherty@linux.vnet.ibm.com>. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> +#include <mul_split.h> +#include <stdlib.h> + +/* Calculate X + Y exactly and store the result in *HI + *LO. It is + given that |X| >= |Y| and the values are small enough that no + overflow occurs. */ + +static void +add_split (double *hi, double *lo, double x, double y) +{ + /* Apply Dekker's algorithm. */ + *hi = x + y; + *lo = (x - *hi) + y; +} + +/* Value with extended range, used in intermediate computations. */ +typedef struct +{ + /* Value in [0.5, 1), as from frexp, or 0. */ + double val; + /* Exponent of power of 2 it is multiplied by, or 0 for zero. */ + int exp; +} ext_val; + +/* Store D as an ext_val value. */ + +static void +store_ext_val (ext_val *v, double d) +{ + v->val = __frexp (d, &v->exp); +} + +/* Store X * Y as ext_val values *V0 and *V1. */ + +static void +mul_ext_val (ext_val *v0, ext_val *v1, double x, double y) +{ + int xexp, yexp; + x = __frexp (x, &xexp); + y = __frexp (y, &yexp); + double hi, lo; + mul_split (&hi, &lo, x, y); + store_ext_val (v0, hi); + if (hi != 0) + v0->exp += xexp + yexp; + store_ext_val (v1, lo); + if (lo != 0) + v1->exp += xexp + yexp; +} + +/* Compare absolute values of ext_val values pointed to by P and Q for + qsort. */ + +static int +compare (const void *p, const void *q) +{ + const ext_val *pe = p; + const ext_val *qe = q; + if (pe->val == 0) + return qe->val == 0 ? 0 : -1; + else if (qe->val == 0) + return 1; + else if (pe->exp < qe->exp) + return -1; + else if (pe->exp > qe->exp) + return 1; + else + { + double pd = fabs (pe->val); + double qd = fabs (qe->val); + if (pd < qd) + return -1; + else if (pd == qd) + return 0; + else + return 1; + } +} + +/* Calculate *X + *Y exactly, storing the high part in *X (rounded to + nearest) and the low part in *Y. It is given that |X| >= |Y|. */ + +static void +add_split_ext (ext_val *x, ext_val *y) +{ + int xexp = x->exp, yexp = y->exp; + if (y->val == 0 || xexp - yexp > 53) + return; + double hi = x->val; + double lo = __scalbn (y->val, yexp - xexp); + add_split (&hi, &lo, hi, lo); + store_ext_val (x, hi); + if (hi != 0) + x->exp += xexp; + store_ext_val (y, lo); + if (lo != 0) + y->exp += xexp; +} + +long double +__fmal (long double x, long double y, long double z) +{ + double xhi, xlo, yhi, ylo, zhi, zlo; + int64_t hx, hy, hz; + int xexp, yexp, zexp; + double scale_val; + int scale_exp; + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + xexp = (hx & 0x7ff0000000000000LL) >> 52; + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS64 (hy, yhi); + yexp = (hy & 0x7ff0000000000000LL) >> 52; + ldbl_unpack (z, &zhi, &zlo); + EXTRACT_WORDS64 (hz, zhi); + zexp = (hz & 0x7ff0000000000000LL) >> 52; + + /* If z is Inf or NaN, but x and y are finite, avoid any exceptions + from computing x * y. */ + if (zexp == 0x7ff && xexp != 0x7ff && yexp != 0x7ff) + return (z + x) + y; + + /* If z is zero and x are y are nonzero, compute the result as x * y + to avoid the wrong sign of a zero result if x * y underflows to + 0. */ + if (z == 0 && x != 0 && y != 0) + return x * y; + + /* If x or y or z is Inf/NaN, or if x * y is zero, compute as x * y + + z. */ + if (xexp == 0x7ff || yexp == 0x7ff || zexp == 0x7ff + || x == 0 || y == 0) + return (x * y) + z; + + { + SET_RESTORE_ROUND (FE_TONEAREST); + + ext_val vals[10]; + store_ext_val (&vals[0], zhi); + store_ext_val (&vals[1], zlo); + mul_ext_val (&vals[2], &vals[3], xhi, yhi); + mul_ext_val (&vals[4], &vals[5], xhi, ylo); + mul_ext_val (&vals[6], &vals[7], xlo, yhi); + mul_ext_val (&vals[8], &vals[9], xlo, ylo); + qsort (vals, 10, sizeof (ext_val), compare); + /* Add up the values so that each element of VALS has absolute + value at most equal to the last set bit of the next nonzero + element. */ + for (size_t i = 0; i <= 8; i++) + { + add_split_ext (&vals[i + 1], &vals[i]); + qsort (vals + i + 1, 9 - i, sizeof (ext_val), compare); + } + /* Add up the values in the other direction, so that each element + of VALS has absolute value less than 5ulp of the next + value. */ + size_t dstpos = 9; + for (size_t i = 1; i <= 9; i++) + { + if (vals[dstpos].val == 0) + { + vals[dstpos] = vals[9 - i]; + vals[9 - i].val = 0; + vals[9 - i].exp = 0; + } + else + { + add_split_ext (&vals[dstpos], &vals[9 - i]); + if (vals[9 - i].val != 0) + { + if (9 - i < dstpos - 1) + { + vals[dstpos - 1] = vals[9 - i]; + vals[9 - i].val = 0; + vals[9 - i].exp = 0; + } + dstpos--; + } + } + } + /* If the result is an exact zero, it results from adding two + values with opposite signs; recompute in the original rounding + mode. */ + if (vals[9].val == 0) + goto zero_out; + /* Adding the top three values will now give a result as accurate + as the underlying long double arithmetic. */ + add_split_ext (&vals[9], &vals[8]); + if (compare (&vals[8], &vals[7]) < 0) + { + ext_val tmp = vals[7]; + vals[7] = vals[8]; + vals[8] = tmp; + } + add_split_ext (&vals[8], &vals[7]); + add_split_ext (&vals[9], &vals[8]); + if (vals[9].exp > DBL_MAX_EXP || vals[9].exp < DBL_MIN_EXP) + { + /* Overflow or underflow, with the result depending on the + original rounding mode, but not on the low part computed + here. */ + scale_val = vals[9].val; + scale_exp = vals[9].exp; + goto scale_out; + } + double hi = __scalbn (vals[9].val, vals[9].exp); + double lo = __scalbn (vals[8].val, vals[8].exp); + /* It is possible that the low part became subnormal and was + rounded so that the result is no longer canonical. */ + ldbl_canonicalize (&hi, &lo); + long double ret = ldbl_pack (hi, lo); + math_check_force_underflow (ret); + return ret; + } + + scale_out: + scale_val = math_opt_barrier (scale_val); + scale_val = __scalbn (scale_val, scale_exp); + if (fabs (scale_val) == DBL_MAX) + return __copysignl (LDBL_MAX, scale_val); + math_check_force_underflow (scale_val); + return scale_val; + + zero_out:; + double zero = 0.0; + zero = math_opt_barrier (zero); + return zero - zero; +} +#if IS_IN (libm) +long_double_symbol (libm, __fmal, fmal); +#else +long_double_symbol (libc, __fmal, fmal); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c new file mode 100644 index 0000000000..82d520bc7f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c @@ -0,0 +1,97 @@ +/* Return classification value corresponding to argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> +#include <math_ldbl_opt.h> + + /* + * hx lx + * +NaN 7ffn nnnn nnnn nnnn xxxx xxxx xxxx xxxx + * -NaN fffn nnnn nnnn nnnn xxxx xxxx xxxx xxxx + * +Inf 7ff0 0000 0000 0000 xxxx xxxx xxxx xxxx + * -Inf fff0 0000 0000 0000 xxxx xxxx xxxx xxxx + * +0 0000 0000 0000 0000 xxxx xxxx xxxx xxxx + * -0 8000 0000 0000 0000 xxxx xxxx xxxx xxxx + * +normal 0360 0000 0000 0000 0000 0000 0000 0000 (smallest) + * -normal 8360 0000 0000 0000 0000 0000 0000 0000 (smallest) + * +normal 7fef ffff ffff ffff 7c8f ffff ffff fffe (largest) + * +normal ffef ffff ffff ffff fc8f ffff ffff fffe (largest) + * +denorm 0360 0000 0000 0000 8000 0000 0000 0001 (largest) + * -denorm 8360 0000 0000 0000 0000 0000 0000 0001 (largest) + * +denorm 000n nnnn nnnn nnnn xxxx xxxx xxxx xxxx + * -denorm 800n nnnn nnnn nnnn xxxx xxxx xxxx xxxx + */ + +int +___fpclassifyl (long double x) +{ + u_int64_t hx, lx; + int retval = FP_NORMAL; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + if ((hx & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL) { + /* +/-NaN or +/-Inf */ + if (hx & 0x000fffffffffffffULL) { + /* +/-NaN */ + retval = FP_NAN; + } else { + retval = FP_INFINITE; + } + } else { + /* +/-zero or +/- normal or +/- denormal */ + if (hx & 0x7fffffffffffffffULL) { + /* +/- normal or +/- denormal */ + if ((hx & 0x7ff0000000000000ULL) > 0x0360000000000000ULL) { + /* +/- normal */ + retval = FP_NORMAL; + } else { + if ((hx & 0x7ff0000000000000ULL) == 0x0360000000000000ULL) { + EXTRACT_WORDS64 (lx, xlo); + if ((lx & 0x7fffffffffffffff) /* lower is non-zero */ + && ((lx^hx) & 0x8000000000000000ULL)) { /* and sign differs */ + /* +/- denormal */ + retval = FP_SUBNORMAL; + } else { + /* +/- normal */ + retval = FP_NORMAL; + } + } else { + /* +/- denormal */ + retval = FP_SUBNORMAL; + } + } + } else { + /* +/- zero */ + retval = FP_ZERO; + } + } + + return retval; +} +long_double_symbol (libm, ___fpclassifyl, __fpclassifyl); +#ifdef __LONG_DOUBLE_MATH_OPTIONAL +libm_hidden_ver (___fpclassifyl, __fpclassifyl) +#else +libm_hidden_def (__fpclassifyl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c new file mode 100644 index 0000000000..210c5d2ed4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c @@ -0,0 +1,148 @@ +/* s_frexpl.c -- long double version of s_frexp.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * for non-zero x + * x = frexpl(arg,&exp); + * return a long double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexpl(arg,&exp) returns arg + * with *exp=0. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __frexpl(long double x, int *eptr) +{ + uint64_t hx, lx, ix, ixl; + int64_t explo, expon; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + ixl = 0x7fffffffffffffffULL & lx; + ix = 0x7fffffffffffffffULL & hx; + expon = 0; + if (ix >= 0x7ff0000000000000ULL || ix == 0) + { + /* 0,inf,nan. */ + *eptr = expon; + return x + x; + } + expon = ix >> 52; + if (expon == 0) + { + /* Denormal high double, the low double must be 0.0. */ + int cnt; + + /* Normalize. */ + if (sizeof (ix) == sizeof (long)) + cnt = __builtin_clzl (ix); + else if ((ix >> 32) != 0) + cnt = __builtin_clzl ((long) (ix >> 32)); + else + cnt = __builtin_clzl ((long) ix) + 32; + cnt = cnt - 12; + expon -= cnt; + ix <<= cnt + 1; + } + expon -= 1022; + ix &= 0x000fffffffffffffULL; + hx &= 0x8000000000000000ULL; + hx |= (1022LL << 52) | ix; + + if (ixl != 0) + { + /* If the high double is an exact power of two and the low + double has the opposite sign, then the exponent calculated + from the high double is one too big. */ + if (ix == 0 + && (int64_t) (hx ^ lx) < 0) + { + hx += 1LL << 52; + expon -= 1; + } + + explo = ixl >> 52; + if (explo == 0) + { + /* The low double started out as a denormal. Normalize its + mantissa and adjust the exponent. */ + int cnt; + + if (sizeof (ixl) == sizeof (long)) + cnt = __builtin_clzl (ixl); + else if ((ixl >> 32) != 0) + cnt = __builtin_clzl ((long) (ixl >> 32)); + else + cnt = __builtin_clzl ((long) ixl) + 32; + cnt = cnt - 12; + explo -= cnt; + ixl <<= cnt + 1; + } + + /* With variable precision we can't assume much about the + magnitude of the returned low double. It may even be a + denormal. */ + explo -= expon; + ixl &= 0x000fffffffffffffULL; + lx &= 0x8000000000000000ULL; + if (explo <= 0) + { + /* Handle denormal low double. */ + if (explo > -52) + { + ixl |= 1LL << 52; + ixl >>= 1 - explo; + } + else + { + ixl = 0; + lx = 0; + if ((hx & 0x7ff0000000000000ULL) == (1023LL << 52)) + { + /* Oops, the adjustment we made above for values a + little smaller than powers of two turned out to + be wrong since the returned low double will be + zero. This can happen if the input was + something weird like 0x1p1000 - 0x1p-1000. */ + hx -= 1LL << 52; + expon += 1; + } + } + explo = 0; + } + lx |= (explo << 52) | ixl; + } + + INSERT_WORDS64 (xhi, hx); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + *eptr = expon; + return x; +} +#if IS_IN (libm) +long_double_symbol (libm, __frexpl, frexpl); +#else +long_double_symbol (libc, __frexpl, frexpl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpl.c new file mode 100644 index 0000000000..e323b4c25b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 0 +#define INEXACT 0 +#define FUNC fromfpl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpl_main.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpl_main.c new file mode 100644 index 0000000000..8b9108e84d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpl_main.c @@ -0,0 +1,147 @@ +/* Round to integer type. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <fenv.h> +#include <math.h> +#include <math_private.h> +#include <stdbool.h> +#include <stdint.h> + +#define BIAS 0x3ff +#define MANT_DIG 53 + +#if UNSIGNED +# define RET_TYPE uintmax_t +#else +# define RET_TYPE intmax_t +#endif + +#include <fromfp.h> + +RET_TYPE +FUNC (long double x, int round, unsigned int width) +{ + double hi, lo; + if (width > INTMAX_WIDTH) + width = INTMAX_WIDTH; + uint64_t hx, lx; + ldbl_unpack (x, &hi, &lo); + EXTRACT_WORDS64 (hx, hi); + EXTRACT_WORDS64 (lx, lo); + bool negative = (hx & 0x8000000000000000ULL) != 0; + bool lo_negative = (lx & 0x8000000000000000ULL) != 0; + if (width == 0) + return fromfp_domain_error (negative, width); + hx &= 0x7fffffffffffffffULL; + lx &= 0x7fffffffffffffffULL; + if ((hx | lx) == 0) + return 0; + int hi_exponent = hx >> (MANT_DIG - 1); + hi_exponent -= BIAS; + int exponent = hi_exponent; + hx &= ((1ULL << (MANT_DIG - 1)) - 1); + if (hx == 0 && lx != 0 && lo_negative != negative) + exponent--; + int max_exponent = fromfp_max_exponent (negative, width); + if (exponent > max_exponent) + return fromfp_domain_error (negative, width); + int lo_exponent = lx >> (MANT_DIG - 1); + lo_exponent -= BIAS; + + /* Convert the high part to integer. */ + hx |= 1ULL << (MANT_DIG - 1); + uintmax_t uret; + bool half_bit, more_bits; + if (hi_exponent >= MANT_DIG - 1) + { + uret = hx; + uret <<= hi_exponent - (MANT_DIG - 1); + half_bit = false; + more_bits = false; + } + else if (hi_exponent >= -1) + { + uint64_t h = 1ULL << (MANT_DIG - 2 - hi_exponent); + half_bit = (hx & h) != 0; + more_bits = (hx & (h - 1)) != 0; + uret = hx >> (MANT_DIG - 1 - hi_exponent); + } + else + { + uret = 0; + half_bit = false; + more_bits = true; + } + + /* Likewise, the low part. */ + if (lx != 0) + { + uintmax_t lo_uret; + bool lo_half_bit, lo_more_bits; + lx &= ((1ULL << (MANT_DIG - 1)) - 1); + lx |= 1ULL << (MANT_DIG - 1); + /* The high part exponent is at most 64, so the low part + exponent is at most 11. */ + if (lo_exponent >= -1) + { + uint64_t h = 1ULL << (MANT_DIG - 2 - lo_exponent); + lo_half_bit = (lx & h) != 0; + lo_more_bits = (lx & (h - 1)) != 0; + lo_uret = lx >> (MANT_DIG - 1 - lo_exponent); + } + else + { + lo_uret = 0; + lo_half_bit = false; + lo_more_bits = true; + } + if (lo_negative == negative) + { + uret += lo_uret; + half_bit |= lo_half_bit; + more_bits |= lo_more_bits; + } + else + { + uret -= lo_uret; + if (lo_half_bit) + { + uret--; + half_bit = true; + } + if (lo_more_bits && !more_bits) + { + if (half_bit) + { + half_bit = false; + more_bits = true; + } + else + { + uret--; + half_bit = true; + more_bits = true; + } + } + } + } + + return fromfp_round_and_return (negative, uret, half_bit, more_bits, round, + exponent, max_exponent, width); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpxl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpxl.c new file mode 100644 index 0000000000..2f3189d7de --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpxl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 0 +#define INEXACT 1 +#define FUNC fromfpxl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_getpayloadl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_getpayloadl.c new file mode 100644 index 0000000000..420b17837e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_getpayloadl.c @@ -0,0 +1,34 @@ +/* Get NaN payload. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fix-int-fp-convert-zero.h> +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +long double +getpayloadl (const long double *x) +{ + double xhi = ldbl_high (*x); + uint64_t ix; + EXTRACT_WORDS64 (ix, xhi); + ix &= 0x7ffffffffffffULL; + if (FIX_INT_FP_CONVERT_ZERO && ix == 0) + return 0.0L; + return (long double) ix; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c new file mode 100644 index 0000000000..24999a920d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c @@ -0,0 +1,60 @@ +/* Test whether long double value is canonical. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +int +__iscanonicall (long double x) +{ + double xhi, xlo; + uint64_t hx, lx; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + int64_t ix = hx & 0x7fffffffffffffffULL; + int64_t iy = lx & 0x7fffffffffffffffULL; + int hexp = (ix & 0x7ff0000000000000LL) >> 52; + int lexp = (iy & 0x7ff0000000000000LL) >> 52; + + if (iy == 0) + /* Low part 0 is always OK. */ + return 1; + + if (hexp == 0x7ff) + /* If a NaN, the low part does not matter. If an infinity, the + low part must be 0, in which case we have already returned. */ + return ix != 0x7ff0000000000000LL; + + /* The high part is finite and the low part is nonzero. There must + be sufficient difference between the exponents. */ + bool low_p2; + if (lexp == 0) + { + /* Adjust the exponent for subnormal low part. */ + lexp = 12 - __builtin_clzll (iy); + low_p2 = iy == (1LL << (51 + lexp)); + } + else + low_p2 = (iy & 0xfffffffffffffLL) == 0; + int expdiff = hexp - lexp; + return expdiff > 53 || (expdiff == 53 && low_p2 && (ix & 1) == 0); +} +libm_hidden_def (__iscanonicall) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_isinfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_isinfl.c new file mode 100644 index 0000000000..730aa4d8d1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_isinfl.c @@ -0,0 +1,40 @@ +/* + * Written by J.T. Conklin <jtc@netbsd.org>. + * Change for long double by Jakub Jelinek <jj@ultra.linux.cz> + * Public domain. + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * isinfl(x) returns 1 if x is inf, -1 if x is -inf, else 0; + * no branching! + * slightly dodgy in relying on signed shift right copying sign bit + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +int +___isinfl (long double x) +{ + double xhi; + int64_t hx, mask; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + + mask = (hx & 0x7fffffffffffffffLL) ^ 0x7ff0000000000000LL; + mask |= -mask; + mask >>= 63; + return ~mask & (hx >> 62); +} +hidden_ver (___isinfl, __isinfl) +#if !IS_IN (libm) +weak_alias (___isinfl, ____isinfl) +long_double_symbol (libc, ___isinfl, isinfl); +long_double_symbol (libc, ____isinfl, __isinfl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_isnanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_isnanl.c new file mode 100644 index 0000000000..9980875df2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_isnanl.c @@ -0,0 +1,46 @@ +/* s_isnanl.c -- long double version of s_isnan.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * isnanl(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +int +___isnanl (long double x) +{ + uint64_t hx; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + hx &= 0x7fffffffffffffffLL; + hx = 0x7ff0000000000000LL - hx; + return (int) (hx >> 63); +} +hidden_ver (___isnanl, __isnanl) +#if !IS_IN (libm) +weak_alias (___isnanl, ____isnanl) +long_double_symbol (libc, ___isnanl, isnanl); +long_double_symbol (libc, ____isnanl, __isnanl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c new file mode 100644 index 0000000000..feb7edea5d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c @@ -0,0 +1,49 @@ +/* Test for signaling NaN. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> + +int +__issignalingl (long double x) +{ + uint64_t xi; + /* For inspecting NaN status, we only have to look at the first of the pair + of IEEE 754 64-bit precision numbers. */ + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (xi, xhi); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN +# error untested + /* We only have to care about the high-order bit of x's significand, because + having it set (sNaN) already makes the significand different from that + used to designate infinity. */ + return (xi & UINT64_C (0x7ff8000000000000)) == UINT64_C (0x7ff8000000000000); +#else + /* To keep the following comparison simple, toggle the quiet/signaling bit, + so that it is set for sNaNs. This is inverse to IEEE 754-2008 (as well as + common practice for IEEE 754-1985). */ + xi ^= UINT64_C (0x0008000000000000); + /* We have to compare for greater (instead of greater or equal), because x's + significand being all-zero designates infinity not NaN. */ + return (xi & UINT64_C (0x7fffffffffffffff)) > UINT64_C (0x7ff8000000000000); +#endif +} +libm_hidden_def (__issignalingl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_llrintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_llrintl.c new file mode 100644 index 0000000000..fbf38bf717 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_llrintl.c @@ -0,0 +1,140 @@ +/* Round to long long int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <fenv.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + + +long long +__llrintl (long double x) +{ + double xh, xl; + long long res, hi, lo; + int save_round; + + ldbl_unpack (x, &xh, &xl); + + /* Limit the range of values handled by the conversion to long long. + We do this because we aren't sure whether that conversion properly + raises FE_INVALID. */ + if (__builtin_expect + ((__builtin_fabs (xh) <= -(double) (-__LONG_LONG_MAX__ - 1)), 1) +#if !defined (FE_INVALID) + || 1 +#endif + ) + { + save_round = fegetround (); + + if (__glibc_unlikely ((xh == -(double) (-__LONG_LONG_MAX__ - 1)))) + { + /* When XH is 9223372036854775808.0, converting to long long will + overflow, resulting in an invalid operation. However, XL might + be negative and of sufficient magnitude that the overall long + double is in fact in range. Avoid raising an exception. In any + case we need to convert this value specially, because + the converted value is not exactly represented as a double + thus subtracting HI from XH suffers rounding error. */ + hi = __LONG_LONG_MAX__; + xh = 1.0; + } + else + { + hi = (long long) xh; + xh -= hi; + } + ldbl_canonicalize (&xh, &xl); + + lo = (long long) xh; + + /* Peg at max/min values, assuming that the above conversions do so. + Strictly speaking, we can return anything for values that overflow, + but this is more useful. */ + res = hi + lo; + + /* This is just sign(hi) == sign(lo) && sign(res) != sign(hi). */ + if (__glibc_unlikely (((~(hi ^ lo) & (res ^ hi)) < 0))) + goto overflow; + + xh -= lo; + ldbl_canonicalize (&xh, &xl); + + hi = res; + switch (save_round) + { + case FE_TONEAREST: + if (fabs (xh) < 0.5 + || (fabs (xh) == 0.5 + && ((xh > 0.0 && xl < 0.0) + || (xh < 0.0 && xl > 0.0) + || (xl == 0.0 && (res & 1) == 0)))) + return res; + + if (xh < 0.0) + res -= 1; + else + res += 1; + break; + + case FE_TOWARDZERO: + if (res > 0 && (xh < 0.0 || (xh == 0.0 && xl < 0.0))) + res -= 1; + else if (res < 0 && (xh > 0.0 || (xh == 0.0 && xl > 0.0))) + res += 1; + return res; + break; + + case FE_UPWARD: + if (xh > 0.0 || (xh == 0.0 && xl > 0.0)) + res += 1; + break; + + case FE_DOWNWARD: + if (xh < 0.0 || (xh == 0.0 && xl < 0.0)) + res -= 1; + break; + } + + if (__glibc_unlikely (((~(hi ^ (res - hi)) & (res ^ hi)) < 0))) + goto overflow; + + return res; + } + else + { + if (xh > 0.0) + hi = __LONG_LONG_MAX__; + else if (xh < 0.0) + hi = -__LONG_LONG_MAX__ - 1; + else + /* Nan */ + hi = 0; + } + +overflow: +#ifdef FE_INVALID + feraiseexcept (FE_INVALID); +#endif + return hi; +} + +long_double_symbol (libm, __llrintl, llrintl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_llroundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_llroundl.c new file mode 100644 index 0000000000..609cc864de --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_llroundl.c @@ -0,0 +1,120 @@ +/* Round to long long int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <fenv.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + +long long +__llroundl (long double x) +{ + double xh, xl; + long long res, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Limit the range of values handled by the conversion to long long. + We do this because we aren't sure whether that conversion properly + raises FE_INVALID. */ + if (__builtin_expect + ((__builtin_fabs (xh) <= -(double) (-__LONG_LONG_MAX__ - 1)), 1) +#if !defined (FE_INVALID) + || 1 +#endif + ) + { + if (__glibc_unlikely ((xh == -(double) (-__LONG_LONG_MAX__ - 1)))) + { + /* When XH is 9223372036854775808.0, converting to long long will + overflow, resulting in an invalid operation. However, XL might + be negative and of sufficient magnitude that the overall long + double is in fact in range. Avoid raising an exception. In any + case we need to convert this value specially, because + the converted value is not exactly represented as a double + thus subtracting HI from XH suffers rounding error. */ + hi = __LONG_LONG_MAX__; + xh = 1.0; + } + else + { + hi = (long long) xh; + xh -= hi; + } + ldbl_canonicalize (&xh, &xl); + + lo = (long long) xh; + + /* Peg at max/min values, assuming that the above conversions do so. + Strictly speaking, we can return anything for values that overflow, + but this is more useful. */ + res = hi + lo; + + /* This is just sign(hi) == sign(lo) && sign(res) != sign(hi). */ + if (__glibc_unlikely (((~(hi ^ lo) & (res ^ hi)) < 0))) + goto overflow; + + xh -= lo; + ldbl_canonicalize (&xh, &xl); + + hi = res; + if (xh > 0.5) + { + res += 1; + } + else if (xh == 0.5) + { + if (xl > 0.0 || (xl == 0.0 && res >= 0)) + res += 1; + } + else if (-xh > 0.5) + { + res -= 1; + } + else if (-xh == 0.5) + { + if (xl < 0.0 || (xl == 0.0 && res <= 0)) + res -= 1; + } + + if (__glibc_unlikely (((~(hi ^ (res - hi)) & (res ^ hi)) < 0))) + goto overflow; + + return res; + } + else + { + if (xh > 0.0) + hi = __LONG_LONG_MAX__; + else if (xh < 0.0) + hi = -__LONG_LONG_MAX__ - 1; + else + /* Nan */ + hi = 0; + } + +overflow: +#ifdef FE_INVALID + feraiseexcept (FE_INVALID); +#endif + return hi; +} + +long_double_symbol (libm, __llroundl, llroundl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_log1pl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_log1pl.c new file mode 100644 index 0000000000..5457892a98 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_log1pl.c @@ -0,0 +1,249 @@ +/* log1pl.c + * + * Relative error logarithm + * Natural logarithm of 1+x, 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log1pl(); + * + * y = log1pl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base e (2.718...) logarithm of 1+x. + * + * The argument 1+x is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the logarithm + * of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(w-1)/(w+1), + * + * log(w) = z + z^3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -1, 8 100000 1.9e-34 4.3e-35 + */ + +/* Copyright 2001 by Stephen L. Moshier + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x) + * 1/sqrt(2) <= 1+x < sqrt(2) + * Theoretical peak relative error = 5.3e-37, + * relative peak error spread = 2.3e-14 + */ +static const long double + P12 = 1.538612243596254322971797716843006400388E-6L, + P11 = 4.998469661968096229986658302195402690910E-1L, + P10 = 2.321125933898420063925789532045674660756E1L, + P9 = 4.114517881637811823002128927449878962058E2L, + P8 = 3.824952356185897735160588078446136783779E3L, + P7 = 2.128857716871515081352991964243375186031E4L, + P6 = 7.594356839258970405033155585486712125861E4L, + P5 = 1.797628303815655343403735250238293741397E5L, + P4 = 2.854829159639697837788887080758954924001E5L, + P3 = 3.007007295140399532324943111654767187848E5L, + P2 = 2.014652742082537582487669938141683759923E5L, + P1 = 7.771154681358524243729929227226708890930E4L, + P0 = 1.313572404063446165910279910527789794488E4L, + /* Q12 = 1.000000000000000000000000000000000000000E0L, */ + Q11 = 4.839208193348159620282142911143429644326E1L, + Q10 = 9.104928120962988414618126155557301584078E2L, + Q9 = 9.147150349299596453976674231612674085381E3L, + Q8 = 5.605842085972455027590989944010492125825E4L, + Q7 = 2.248234257620569139969141618556349415120E5L, + Q6 = 6.132189329546557743179177159925690841200E5L, + Q5 = 1.158019977462989115839826904108208787040E6L, + Q4 = 1.514882452993549494932585972882995548426E6L, + Q3 = 1.347518538384329112529391120390701166528E6L, + Q2 = 7.777690340007566932935753241556479363645E5L, + Q1 = 2.626900195321832660448791748036714883242E5L, + Q0 = 3.940717212190338497730839731583397586124E4L; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 1.1e-35, + * relative peak error spread 1.1e-9 + */ +static const long double + R5 = -8.828896441624934385266096344596648080902E-1L, + R4 = 8.057002716646055371965756206836056074715E1L, + R3 = -2.024301798136027039250415126250455056397E3L, + R2 = 2.048819892795278657810231591630928516206E4L, + R1 = -8.977257995689735303686582344659576526998E4L, + R0 = 1.418134209872192732479751274970992665513E5L, + /* S6 = 1.000000000000000000000000000000000000000E0L, */ + S5 = -1.186359407982897997337150403816839480438E2L, + S4 = 3.998526750980007367835804959888064681098E3L, + S3 = -5.748542087379434595104154610899551484314E4L, + S2 = 4.001557694070773974936904547424676279307E5L, + S1 = -1.332535117259762928288745111081235577029E6L, + S0 = 1.701761051846631278975701529965589676574E6L; + +/* C1 + C2 = ln 2 */ +static const long double C1 = 6.93145751953125E-1L; +static const long double C2 = 1.428606820309417232121458176568075500134E-6L; + +static const long double sqrth = 0.7071067811865475244008443621048490392848L; +/* ln (2^16384 * (1 - 2^-113)) */ +static const long double zero = 0.0L; + + +long double +__log1pl (long double xm1) +{ + long double x, y, z, r, s; + double xhi; + int32_t hx, lx; + int e; + + /* Test for NaN or infinity input. */ + xhi = ldbl_high (xm1); + EXTRACT_WORDS (hx, lx, xhi); + if (hx >= 0x7ff00000) + return xm1 + xm1; + + /* log1p(+- 0) = +- 0. */ + if (((hx & 0x7fffffff) | lx) == 0) + return xm1; + + if (xm1 >= 0x1p107L) + x = xm1; + else + x = xm1 + 1.0L; + + /* log1p(-1) = -inf */ + if (x <= 0.0L) + { + if (x == 0.0L) + return (-1.0L / 0.0L); + else + return (zero / (x - x)); + } + + /* Separate mantissa from exponent. */ + + /* Use frexp used so that denormal numbers will be handled properly. */ + x = __frexpl (x, &e); + + /* Logarithm using log(x) = z + z^3 P(z^2)/Q(z^2), + where z = 2(x-1)/x+1). */ + if ((e > 2) || (e < -2)) + { + if (x < sqrth) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } + else + { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } + x = z / y; + z = x * x; + r = ((((R5 * z + + R4) * z + + R3) * z + + R2) * z + + R1) * z + + R0; + s = (((((z + + S5) * z + + S4) * z + + S3) * z + + S2) * z + + S1) * z + + S0; + z = x * (z * r / s); + z = z + e * C2; + z = z + x; + z = z + e * C1; + return (z); + } + + + /* Logarithm using log(1+x) = x - .5x^2 + x^3 P(x)/Q(x). */ + + if (x < sqrth) + { + e -= 1; + if (e != 0) + x = 2.0L * x - 1.0L; /* 2x - 1 */ + else + x = xm1; + } + else + { + if (e != 0) + x = x - 1.0L; + else + x = xm1; + } + z = x * x; + r = (((((((((((P12 * x + + P11) * x + + P10) * x + + P9) * x + + P8) * x + + P7) * x + + P6) * x + + P5) * x + + P4) * x + + P3) * x + + P2) * x + + P1) * x + + P0; + s = (((((((((((x + + Q11) * x + + Q10) * x + + Q9) * x + + Q8) * x + + Q7) * x + + Q6) * x + + Q5) * x + + Q4) * x + + Q3) * x + + Q2) * x + + Q1) * x + + Q0; + y = x * (z * r / s); + y = y + e * C2; + z = y - 0.5L * z; + z = z + x; + z = z + e * C1; + return (z); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_logbl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_logbl.c new file mode 100644 index 0000000000..3c07c5e8e2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_logbl.c @@ -0,0 +1,63 @@ +/* s_logbl.c -- long double version of s_logb.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * long double logbl(x) + * IEEE 754 logb. Included to pass IEEE test suite. Not recommend. + * Use ilogb instead. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> +#include <fix-int-fp-convert-zero.h> + +long double +__logbl (long double x) +{ + int64_t hx, hxs, rhx; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + hxs = hx; + hx &= 0x7fffffffffffffffLL; /* high |x| */ + if (hx == 0) + return -1.0 / fabs (x); + if (hx >= 0x7ff0000000000000LL) + return x * x; + if (__glibc_unlikely ((rhx = hx >> 52) == 0)) + { + /* POSIX specifies that denormal number is treated as + though it were normalized. */ + rhx -= __builtin_clzll (hx) - 12; + } + else if ((hx & 0x000fffffffffffffLL) == 0) + { + /* If the high part is a power of 2, and the low part is nonzero + with the opposite sign, the low part affects the + exponent. */ + int64_t lx; + EXTRACT_WORDS64 (lx, xlo); + if ((hxs ^ lx) < 0 && (lx & 0x7fffffffffffffffLL) != 0) + rhx--; + } + if (FIX_INT_FP_CONVERT_ZERO && rhx == 1023) + return 0.0L; + return (long double) (rhx - 1023); +} +#ifndef __logbl +long_double_symbol (libm, __logbl, logbl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_lrintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_lrintl.c new file mode 100644 index 0000000000..b404cab8e3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_lrintl.c @@ -0,0 +1,155 @@ +/* Round to long int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <fenv.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + + +long +__lrintl (long double x) +{ + double xh, xl; + long res, hi, lo; + int save_round; + + ldbl_unpack (x, &xh, &xl); + + /* Limit the range of values handled by the conversion to long. + We do this because we aren't sure whether that conversion properly + raises FE_INVALID. */ + if ( +#if __LONG_MAX__ == 2147483647 + __builtin_expect + ((__builtin_fabs (xh) <= (double) __LONG_MAX__ + 2), 1) +#else + __builtin_expect + ((__builtin_fabs (xh) <= -(double) (-__LONG_MAX__ - 1)), 1) +#endif +#if !defined (FE_INVALID) + || 1 +#endif + ) + { + save_round = fegetround (); + +#if __LONG_MAX__ == 2147483647 + long long llhi = (long long) xh; + if (llhi != (long) llhi) + hi = llhi < 0 ? -__LONG_MAX__ - 1 : __LONG_MAX__; + else + hi = llhi; + xh -= hi; +#else + if (__glibc_unlikely ((xh == -(double) (-__LONG_MAX__ - 1)))) + { + /* When XH is 9223372036854775808.0, converting to long long will + overflow, resulting in an invalid operation. However, XL might + be negative and of sufficient magnitude that the overall long + double is in fact in range. Avoid raising an exception. In any + case we need to convert this value specially, because + the converted value is not exactly represented as a double + thus subtracting HI from XH suffers rounding error. */ + hi = __LONG_MAX__; + xh = 1.0; + } + else + { + hi = (long) xh; + xh -= hi; + } +#endif + ldbl_canonicalize (&xh, &xl); + + lo = (long) xh; + + /* Peg at max/min values, assuming that the above conversions do so. + Strictly speaking, we can return anything for values that overflow, + but this is more useful. */ + res = hi + lo; + + /* This is just sign(hi) == sign(lo) && sign(res) != sign(hi). */ + if (__glibc_unlikely (((~(hi ^ lo) & (res ^ hi)) < 0))) + goto overflow; + + xh -= lo; + ldbl_canonicalize (&xh, &xl); + + hi = res; + switch (save_round) + { + case FE_TONEAREST: + if (fabs (xh) < 0.5 + || (fabs (xh) == 0.5 + && ((xh > 0.0 && xl < 0.0) + || (xh < 0.0 && xl > 0.0) + || (xl == 0.0 && (res & 1) == 0)))) + return res; + + if (xh < 0.0) + res -= 1; + else + res += 1; + break; + + case FE_TOWARDZERO: + if (res > 0 && (xh < 0.0 || (xh == 0.0 && xl < 0.0))) + res -= 1; + else if (res < 0 && (xh > 0.0 || (xh == 0.0 && xl > 0.0))) + res += 1; + return res; + break; + + case FE_UPWARD: + if (xh > 0.0 || (xh == 0.0 && xl > 0.0)) + res += 1; + break; + + case FE_DOWNWARD: + if (xh < 0.0 || (xh == 0.0 && xl < 0.0)) + res -= 1; + break; + } + + if (__glibc_unlikely (((~(hi ^ (res - hi)) & (res ^ hi)) < 0))) + goto overflow; + + return res; + } + else + { + if (xh > 0.0) + hi = __LONG_MAX__; + else if (xh < 0.0) + hi = -__LONG_MAX__ - 1; + else + /* Nan */ + hi = 0; + } + +overflow: +#ifdef FE_INVALID + feraiseexcept (FE_INVALID); +#endif + return hi; +} + +long_double_symbol (libm, __lrintl, lrintl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_lroundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_lroundl.c new file mode 100644 index 0000000000..f9ae37e844 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_lroundl.c @@ -0,0 +1,135 @@ +/* Round to long int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <fenv.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + +long +__lroundl (long double x) +{ + double xh, xl; + long res, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Limit the range of values handled by the conversion to long. + We do this because we aren't sure whether that conversion properly + raises FE_INVALID. */ + if ( +#if __LONG_MAX__ == 2147483647 + __builtin_expect + ((__builtin_fabs (xh) <= (double) __LONG_MAX__ + 2), 1) +#else + __builtin_expect + ((__builtin_fabs (xh) <= -(double) (-__LONG_MAX__ - 1)), 1) +#endif +#if !defined (FE_INVALID) + || 1 +#endif + ) + { +#if __LONG_MAX__ == 2147483647 + long long llhi = (long long) xh; + if (llhi != (long) llhi) + hi = llhi < 0 ? -__LONG_MAX__ - 1 : __LONG_MAX__; + else + hi = llhi; + xh -= hi; +#else + if (__glibc_unlikely ((xh == -(double) (-__LONG_MAX__ - 1)))) + { + /* When XH is 9223372036854775808.0, converting to long long will + overflow, resulting in an invalid operation. However, XL might + be negative and of sufficient magnitude that the overall long + double is in fact in range. Avoid raising an exception. In any + case we need to convert this value specially, because + the converted value is not exactly represented as a double + thus subtracting HI from XH suffers rounding error. */ + hi = __LONG_MAX__; + xh = 1.0; + } + else + { + hi = (long) xh; + xh -= hi; + } +#endif + ldbl_canonicalize (&xh, &xl); + + lo = (long) xh; + + /* Peg at max/min values, assuming that the above conversions do so. + Strictly speaking, we can return anything for values that overflow, + but this is more useful. */ + res = hi + lo; + + /* This is just sign(hi) == sign(lo) && sign(res) != sign(hi). */ + if (__glibc_unlikely (((~(hi ^ lo) & (res ^ hi)) < 0))) + goto overflow; + + xh -= lo; + ldbl_canonicalize (&xh, &xl); + + hi = res; + if (xh > 0.5) + { + res += 1; + } + else if (xh == 0.5) + { + if (xl > 0.0 || (xl == 0.0 && res >= 0)) + res += 1; + } + else if (-xh > 0.5) + { + res -= 1; + } + else if (-xh == 0.5) + { + if (xl < 0.0 || (xl == 0.0 && res <= 0)) + res -= 1; + } + + if (__glibc_unlikely (((~(hi ^ (res - hi)) & (res ^ hi)) < 0))) + goto overflow; + + return res; + } + else + { + if (xh > 0.0) + hi = __LONG_MAX__; + else if (xh < 0.0) + hi = -__LONG_MAX__ - 1; + else + /* Nan */ + hi = 0; + } + +overflow: +#ifdef FE_INVALID + feraiseexcept (FE_INVALID); +#endif + return hi; +} + +long_double_symbol (libm, __lroundl, lroundl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_modfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_modfl.c new file mode 100644 index 0000000000..260cc3e33c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_modfl.c @@ -0,0 +1,96 @@ +/* s_modfl.c -- long double version of s_modf.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * modfl(long double x, long double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +static const long double one = 1.0; + +long double __modfl(long double x, long double *iptr) +{ + int64_t i0,i1,j0; + u_int64_t i; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (i0, xhi); + EXTRACT_WORDS64 (i1, xlo); + i1 &= 0x000fffffffffffffLL; + j0 = ((i0>>52)&0x7ff)-0x3ff; /* exponent of x */ + if(j0<52) { /* integer part in high x */ + if(j0<0) { /* |x|<1 */ + /* *iptr = +-0 */ + INSERT_WORDS64 (xhi, i0&0x8000000000000000ULL); + *iptr = xhi; + return x; + } else { + i = (0x000fffffffffffffLL)>>j0; + if(((i0&i)|(i1&0x7fffffffffffffffLL))==0) { /* x is integral */ + *iptr = x; + /* return +-0 */ + INSERT_WORDS64 (xhi, i0&0x8000000000000000ULL); + x = xhi; + return x; + } else { + INSERT_WORDS64 (xhi, i0&(~i)); + *iptr = xhi; + return x - *iptr; + } + } + } else if (j0>103) { /* no fraction part */ + *iptr = x*one; + /* We must handle NaNs separately. */ + if ((i0 & 0x7fffffffffffffffLL) > 0x7ff0000000000000LL) + return x*one; + /* return +-0 */ + INSERT_WORDS64 (xhi, i0&0x8000000000000000ULL); + x = xhi; + return x; + } else { /* fraction part in low x */ + i = -1ULL>>(j0-52); + if((i1&i)==0) { /* x is integral */ + *iptr = x; + /* return +-0 */ + INSERT_WORDS64 (xhi, i0&0x8000000000000000ULL); + x = xhi; + return x; + } else { + INSERT_WORDS64 (xhi, i0); + INSERT_WORDS64 (xlo, i1&(~i)); + *iptr = ldbl_pack (xhi, xlo); + return x - *iptr; + } + } +} +#if IS_IN (libm) +long_double_symbol (libm, __modfl, modfl); +#else +long_double_symbol (libc, __modfl, modfl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c new file mode 100644 index 0000000000..18b052cecb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c @@ -0,0 +1,21 @@ +/* Round to int long double floating-point values without raising inexact. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define USE_AS_NEARBYINTL +#include "s_rintl.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c new file mode 100644 index 0000000000..0d6469d548 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c @@ -0,0 +1,160 @@ +/* s_nextafterl.c -- long double version of s_nextafter.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* IEEE functions + * nextafterl(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __nextafterl(long double x, long double y) +{ + int64_t hx, hy, ihx, ihy, lx; + double xhi, xlo, yhi; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + yhi = ldbl_high (y); + EXTRACT_WORDS64 (hy, yhi); + ihx = hx&0x7fffffffffffffffLL; /* |hx| */ + ihy = hy&0x7fffffffffffffffLL; /* |hy| */ + + if((ihx>0x7ff0000000000000LL) || /* x is nan */ + (ihy>0x7ff0000000000000LL)) /* y is nan */ + return x+y; /* signal the nan */ + if(x==y) + return y; /* x=y, return y */ + if(ihx == 0) { /* x == 0 */ + long double u; /* return +-minsubnormal */ + hy = (hy & 0x8000000000000000ULL) | 1; + INSERT_WORDS64 (yhi, hy); + x = yhi; + u = math_opt_barrier (x); + u = u * u; + math_force_eval (u); /* raise underflow flag */ + return x; + } + + long double u; + if(x > y) { /* x > y, x -= ulp */ + /* This isn't the largest magnitude correctly rounded + long double as you can see from the lowest mantissa + bit being zero. It is however the largest magnitude + long double with a 106 bit mantissa, and nextafterl + is insane with variable precision. So to make + nextafterl sane we assume 106 bit precision. */ + if((hx==0xffefffffffffffffLL)&&(lx==0xfc8ffffffffffffeLL)) { + u = x+x; /* overflow, return -inf */ + math_force_eval (u); + __set_errno (ERANGE); + return y; + } + if (hx >= 0x7ff0000000000000LL) { + u = 0x1.fffffffffffff7ffffffffffff8p+1023L; + return u; + } + if(ihx <= 0x0360000000000000LL) { /* x <= LDBL_MIN */ + u = math_opt_barrier (x); + x -= LDBL_TRUE_MIN; + if (ihx < 0x0360000000000000LL + || (hx > 0 && lx <= 0) + || (hx < 0 && lx > 1)) { + u = u * u; + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + /* Avoid returning -0 in FE_DOWNWARD mode. */ + if (x == 0.0L) + return 0.0L; + return x; + } + /* If the high double is an exact power of two and the low + double is the opposite sign, then 1ulp is one less than + what we might determine from the high double. Similarly + if X is an exact power of two, and positive, because + making it a little smaller will result in the exponent + decreasing by one and normalisation of the mantissa. */ + if ((hx & 0x000fffffffffffffLL) == 0 + && ((lx != 0 && (hx ^ lx) < 0) + || (lx == 0 && hx >= 0))) + ihx -= 1LL << 52; + if (ihx < (106LL << 52)) { /* ulp will denormal */ + INSERT_WORDS64 (yhi, ihx & (0x7ffLL<<52)); + u = yhi * 0x1p-105; + } else { + INSERT_WORDS64 (yhi, (ihx & (0x7ffLL<<52))-(105LL<<52)); + u = yhi; + } + return x - u; + } else { /* x < y, x += ulp */ + if((hx==0x7fefffffffffffffLL)&&(lx==0x7c8ffffffffffffeLL)) { + u = x+x; /* overflow, return +inf */ + math_force_eval (u); + __set_errno (ERANGE); + return y; + } + if ((uint64_t) hx >= 0xfff0000000000000ULL) { + u = -0x1.fffffffffffff7ffffffffffff8p+1023L; + return u; + } + if(ihx <= 0x0360000000000000LL) { /* x <= LDBL_MIN */ + u = math_opt_barrier (x); + x += LDBL_TRUE_MIN; + if (ihx < 0x0360000000000000LL + || (hx > 0 && lx < 0 && lx != 0x8000000000000001LL) + || (hx < 0 && lx >= 0)) { + u = u * u; + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + if (x == 0.0L) /* handle negative LDBL_TRUE_MIN case */ + x = -0.0L; + return x; + } + /* If the high double is an exact power of two and the low + double is the opposite sign, then 1ulp is one less than + what we might determine from the high double. Similarly + if X is an exact power of two, and negative, because + making it a little larger will result in the exponent + decreasing by one and normalisation of the mantissa. */ + if ((hx & 0x000fffffffffffffLL) == 0 + && ((lx != 0 && (hx ^ lx) < 0) + || (lx == 0 && hx < 0))) + ihx -= 1LL << 52; + if (ihx < (106LL << 52)) { /* ulp will denormal */ + INSERT_WORDS64 (yhi, ihx & (0x7ffLL<<52)); + u = yhi * 0x1p-105; + } else { + INSERT_WORDS64 (yhi, (ihx & (0x7ffLL<<52))-(105LL<<52)); + u = yhi; + } + return x + u; + } +} +strong_alias (__nextafterl, __nexttowardl) +long_double_symbol (libm, __nextafterl, nextafterl); +long_double_symbol (libm, __nexttowardl, nexttowardl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c new file mode 100644 index 0000000000..d8f4fc6523 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c @@ -0,0 +1,90 @@ +/* s_nexttoward.c + * Conversion from s_nextafter.c by Ulrich Drepper, Cygnus Support, + * drepper@cygnus.com and Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* IEEE functions + * nexttoward(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> +#include <float.h> + +double __nexttoward(double x, long double y) +{ + int32_t hx,ix; + int64_t hy,iy; + uint32_t lx; + double yhi; + + EXTRACT_WORDS(hx,lx,x); + yhi = ldbl_high (y); + EXTRACT_WORDS64(hy,yhi); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffffffffffffLL; /* |y| */ + + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ + iy>0x7ff0000000000000LL) /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if((ix|lx)==0) { /* x == 0 */ + double u; + INSERT_WORDS(x,(uint32_t)((hy>>32)&0x80000000),1);/* return +-minsub */ + u = math_opt_barrier (x); + u = u * u; + math_force_eval (u); /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if (x > y) { /* x > 0 */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } else { /* x < 0 */ + if (x < y) { /* x < 0 */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } + hy = hx&0x7ff00000; + if(hy>=0x7ff00000) { + double u = x+x; /* overflow */ + math_force_eval (u); + __set_errno (ERANGE); + } + if(hy<0x00100000) { + double u = x*x; /* underflow */ + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + INSERT_WORDS(x,hx,lx); + return x; +} +long_double_symbol (libm, __nexttoward, nexttoward); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c new file mode 100644 index 0000000000..7c5d1cc112 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c @@ -0,0 +1,79 @@ +/* s_nexttowardf.c -- float version of s_nextafter.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com + * and Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> +#include <float.h> + +float __nexttowardf(float x, long double y) +{ + int32_t hx,ix; + int64_t hy,iy; + double yhi; + + GET_FLOAT_WORD(hx,x); + yhi = ldbl_high (y); + EXTRACT_WORDS64 (hy, yhi); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffffffffffffLL; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + (iy>0x7ff0000000000000LL)) + /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if(ix==0) { /* x == 0 */ + float u; + SET_FLOAT_WORD(x,(u_int32_t)((hy>>32)&0x80000000)|1);/* return +-minsub*/ + u = math_opt_barrier (x); + u = u * u; + math_force_eval (u); /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if(x > y) { /* x -= ulp */ + hx -= 1; + } else { /* x < y, x += ulp */ + hx += 1; + } + } else { /* x < 0 */ + if(x < y) { /* x -= ulp */ + hx -= 1; + } else { /* x > y, x += ulp */ + hx += 1; + } + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) { + float u = x+x; /* overflow */ + math_force_eval (u); + __set_errno (ERANGE); + } + if(hy<0x00800000) { /* underflow */ + float u = x*x; + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + SET_FLOAT_WORD(x,hx); + return x; +} +long_double_symbol (libm, __nexttowardf, nexttowardf); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nextupl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nextupl.c new file mode 100644 index 0000000000..bf74f0e1ab --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nextupl.c @@ -0,0 +1,78 @@ +/* Return the least floating-point number greater than X. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +/* Return the least floating-point number greater than X. */ +long double +__nextupl (long double x) +{ + int64_t hx, ihx, lx; + double xhi, xlo, yhi; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + ihx = hx & 0x7fffffffffffffffLL; + + if (ihx > 0x7ff0000000000000LL) /* x is nan. */ + return x + x; /* Signal the nan. */ + if (ihx == 0) + return LDBL_TRUE_MIN; + + long double u; + if ((hx == 0x7fefffffffffffffLL) && (lx == 0x7c8ffffffffffffeLL)) + return INFINITY; + if ((uint64_t) hx >= 0xfff0000000000000ULL) + { + u = -0x1.fffffffffffff7ffffffffffff8p+1023L; + return u; + } + if (ihx <= 0x0360000000000000LL) + { /* x <= LDBL_MIN. */ + x += LDBL_TRUE_MIN; + if (x == 0.0L) /* Handle negative LDBL_TRUE_MIN case. */ + x = -0.0L; + return x; + } + /* If the high double is an exact power of two and the low + double is the opposite sign, then 1ulp is one less than + what we might determine from the high double. Similarly + if X is an exact power of two, and negative, because + making it a little larger will result in the exponent + decreasing by one and normalisation of the mantissa. */ + if ((hx & 0x000fffffffffffffLL) == 0 + && ((lx != 0 && lx != 0x8000000000000000LL && (hx ^ lx) < 0) + || ((lx == 0 || lx == 0x8000000000000000LL) && hx < 0))) + ihx -= 1LL << 52; + if (ihx < (106LL << 52)) + { /* ulp will denormal. */ + INSERT_WORDS64 (yhi, ihx & (0x7ffLL << 52)); + u = yhi * 0x1p-105; + } + else + { + INSERT_WORDS64 (yhi, (ihx & (0x7ffLL << 52)) - (105LL << 52)); + u = yhi; + } + return x + u; +} + +weak_alias (__nextupl, nextupl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_remquol.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_remquol.c new file mode 100644 index 0000000000..9b6ec09d41 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_remquol.c @@ -0,0 +1,119 @@ +/* Compute remainder and a congruent to the quotient. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> +#include <math_ldbl_opt.h> + + +static const long double zero = 0.0; + + +long double +__remquol (long double x, long double y, int *quo) +{ + int64_t hx,hy; + u_int64_t sx,lx,ly,qs; + int cquo; + double xhi, xlo, yhi, ylo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS64 (hy, yhi); + EXTRACT_WORDS64 (ly, ylo); + sx = hx & 0x8000000000000000ULL; + qs = sx ^ (hy & 0x8000000000000000ULL); + ly ^= hy & 0x8000000000000000ULL; + hy &= 0x7fffffffffffffffLL; + lx ^= sx; + hx &= 0x7fffffffffffffffLL; + + /* Purge off exception values. */ + if (hy == 0) + return (x * y) / (x * y); /* y = 0 */ + if ((hx >= 0x7ff0000000000000LL) /* x not finite */ + || (hy > 0x7ff0000000000000LL)) /* y is NaN */ + return (x * y) / (x * y); + + if (hy <= 0x7fbfffffffffffffLL) + x = __ieee754_fmodl (x, 8 * y); /* now x < 8y */ + + if (((hx - hy) | (lx - ly)) == 0) + { + *quo = qs ? -1 : 1; + return zero * x; + } + + x = fabsl (x); + y = fabsl (y); + cquo = 0; + + if (hy <= 0x7fcfffffffffffffLL && x >= 4 * y) + { + x -= 4 * y; + cquo += 4; + } + if (hy <= 0x7fdfffffffffffffLL && x >= 2 * y) + { + x -= 2 * y; + cquo += 2; + } + + if (hy < 0x0020000000000000LL) + { + if (x + x > y) + { + x -= y; + ++cquo; + if (x + x >= y) + { + x -= y; + ++cquo; + } + } + } + else + { + long double y_half = 0.5L * y; + if (x > y_half) + { + x -= y; + ++cquo; + if (x >= y_half) + { + x -= y; + ++cquo; + } + } + } + + *quo = qs ? -cquo : cquo; + + /* Ensure correct sign of zero result in round-downward mode. */ + if (x == 0.0L) + x = 0.0L; + if (sx) + x = -x; + return x; +} +long_double_symbol (libm, __remquol, remquol); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_rintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_rintl.c new file mode 100644 index 0000000000..ea8c2bca0e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_rintl.c @@ -0,0 +1,129 @@ +/* Round to int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* This has been coded in assembler because GCC makes such a mess of it + when it's coded in C. */ + +#include <math.h> +#include <fenv.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + +#ifdef USE_AS_NEARBYINTL +# define rintl nearbyintl +# define __rintl __nearbyintl +#endif + + +long double +__rintl (long double x) +{ + double xh, xl, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Return Inf, Nan, +/-0 unchanged. */ + if (__builtin_expect (xh != 0.0 + && __builtin_isless (__builtin_fabs (xh), + __builtin_inf ()), 1)) + { + double orig_xh; + int save_round = fegetround (); + + /* Long double arithmetic, including the canonicalisation below, + only works in round-to-nearest mode. */ +#ifdef USE_AS_NEARBYINTL + SET_RESTORE_ROUND_NOEX (FE_TONEAREST); +#else + fesetround (FE_TONEAREST); +#endif + + /* Convert the high double to integer. */ + orig_xh = xh; + hi = ldbl_nearbyint (xh); + + /* Subtract integral high part from the value. If the low double + happens to be exactly 0.5 or -0.5, you might think that this + subtraction could result in an incorrect conversion. For + instance, subtracting an odd number would cause this function + to round in the wrong direction. However, if we have a + canonical long double with the low double 0.5 or -0.5, then the + high double must be even. */ + xh -= hi; + ldbl_canonicalize (&xh, &xl); + + /* Now convert the low double, adjusted for any remainder from the + high double. */ + lo = ldbl_nearbyint (xh); + + xh -= lo; + ldbl_canonicalize (&xh, &xl); + + switch (save_round) + { + case FE_TONEAREST: + if (xl > 0.0 && xh == 0.5) + lo += 1.0; + else if (xl < 0.0 && -xh == 0.5) + lo -= 1.0; + break; + + case FE_TOWARDZERO: + if (orig_xh < 0.0) + goto do_up; + /* Fall thru */ + + case FE_DOWNWARD: + if (xh < 0.0 || (xh == 0.0 && xl < 0.0)) + lo -= 1.0; + break; + + case FE_UPWARD: + do_up: + if (xh > 0.0 || (xh == 0.0 && xl > 0.0)) + lo += 1.0; + break; + } + + /* Ensure the final value is canonical. In certain cases, + rounding causes hi,lo calculated so far to be non-canonical. */ + xh = hi; + xl = lo; + ldbl_canonicalize (&xh, &xl); + + /* Ensure we return -0 rather than +0 when appropriate. */ + if (orig_xh < 0.0) + xh = -__builtin_fabs (xh); + +#ifdef USE_AS_NEARBYINTL + math_force_eval (xh); + math_force_eval (xl); +#else + fesetround (save_round); +#endif + } + else + /* Quiet signaling NaN arguments. */ + xh += xh; + + return ldbl_pack (xh, xl); +} + +long_double_symbol (libm, __rintl, rintl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_roundevenl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_roundevenl.c new file mode 100644 index 0000000000..f4221cda4b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_roundevenl.c @@ -0,0 +1,69 @@ +/* Round to nearest integer value, rounding halfway cases to even. + ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +long double +roundevenl (long double x) +{ + double xh, xl, hi; + + ldbl_unpack (x, &xh, &xl); + + if (xh != 0 && isfinite (xh)) + { + hi = roundeven (xh); + if (hi != xh) + { + /* The high part is not an integer; the low part only + affects the result if the high part is exactly half way + between two integers and the low part is nonzero in the + opposite direction to the rounding of the high part. */ + double diff = hi - xh; + if (fabs (diff) == 0.5) + { + if (xl < 0 && diff > 0) + xh = hi - 1; + else if (xl > 0 && diff < 0) + xh = hi + 1; + else + xh = hi; + } + else + xh = hi; + xl = 0; + } + else + { + /* The high part is a nonzero integer. Rounding the low + part to nearest, ties round to even, is always correct, + as a high part that is an odd integer together with a low + part with magnitude 0.5 is not a valid long double. */ + xl = roundeven (xl); + xh = hi; + ldbl_canonicalize_int (&xh, &xl); + } + } + else + /* Quiet signaling NaN arguments. */ + xh += xh; + + return ldbl_pack (xh, xl); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_roundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_roundl.c new file mode 100644 index 0000000000..0b70e24637 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_roundl.c @@ -0,0 +1,87 @@ +/* Round to int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* This has been coded in assembler because GCC makes such a mess of it + when it's coded in C. */ + +#include <math.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + + +long double +__roundl (long double x) +{ + double xh, xl, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Return Inf, Nan, +/-0 unchanged. */ + if (__builtin_expect (xh != 0.0 + && __builtin_isless (__builtin_fabs (xh), + __builtin_inf ()), 1)) + { + hi = __round (xh); + if (hi != xh) + { + /* The high part is not an integer; the low part only + affects the result if the high part is exactly half way + between two integers and the low part is nonzero with the + opposite sign. */ + if (fabs (hi - xh) == 0.5) + { + if (xh > 0 && xl < 0) + xh = hi - 1; + else if (xh < 0 && xl > 0) + xh = hi + 1; + else + xh = hi; + } + else + xh = hi; + xl = 0; + } + else + { + /* The high part is a nonzero integer. */ + lo = __round (xl); + if (fabs (lo - xl) == 0.5) + { + if (xh > 0 && xl < 0) + xl = lo + 1; + else if (xh < 0 && lo > 0) + xl = lo - 1; + else + xl = lo; + } + else + xl = lo; + xh = hi; + ldbl_canonicalize_int (&xh, &xl); + } + } + else + /* Quiet signaling NaN arguments. */ + xh += xh; + + return ldbl_pack (xh, xl); +} + +long_double_symbol (libm, __roundl, roundl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c new file mode 100644 index 0000000000..031635267f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c @@ -0,0 +1,104 @@ +/* s_scalblnl.c -- long double version of s_scalbln.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* @(#)s_scalbln.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * scalblnl (long double x, long int n) + * scalblnl(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +static const long double +twolm54 = 5.55111512312578270212e-17, /* 0x3C90000000000000, 0 */ +huge = 1.0E+300L, +tiny = 1.0E-300L; +static const double +two54 = 1.80143985094819840000e+16, /* 0x4350000000000000 */ +twom54 = 5.55111512312578270212e-17; /* 0x3C90000000000000 */ + +long double __scalblnl (long double x, long int n) +{ + int64_t k,l,hx,lx; + union { int64_t i; double d; } u; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + k = (hx>>52)&0x7ff; /* extract exponent */ + l = (lx>>52)&0x7ff; + if (k==0) { /* 0 or subnormal x */ + if ((hx&0x7fffffffffffffffULL)==0) return x; /* +-0 */ + u.i = hx; + u.d *= two54; + hx = u.i; + k = ((hx>>52)&0x7ff) - 54; + } + else if (k==0x7ff) return x+x; /* NaN or Inf */ + if (n< -50000) return tiny*__copysignl(tiny,x); /*underflow */ + if (n> 50000 || k+n > 0x7fe) + return huge*__copysignl(huge,x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k+n; + if (k > 0) { /* normal result */ + hx = (hx&0x800fffffffffffffULL)|(k<<52); + if ((lx & 0x7fffffffffffffffULL) == 0) { /* low part +-0 */ + INSERT_WORDS64 (xhi, hx); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x; + } + if (l == 0) { /* low part subnormal */ + u.i = lx; + u.d *= two54; + lx = u.i; + l = ((lx>>52)&0x7ff) - 54; + } + l = l + n; + if (l > 0) + lx = (lx&0x800fffffffffffffULL)|(l<<52); + else if (l <= -54) + lx = (lx&0x8000000000000000ULL); + else { + l += 54; + u.i = (lx&0x800fffffffffffffULL)|(l<<52); + u.d *= twom54; + lx = u.i; + } + INSERT_WORDS64 (xhi, hx); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x; + } + if (k <= -54) + return tiny*__copysignl(tiny,x); /*underflow*/ + k += 54; /* subnormal result */ + lx &= 0x8000000000000000ULL; + hx &= 0x800fffffffffffffULL; + INSERT_WORDS64 (xhi, hx|(k<<52)); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x*twolm54; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c new file mode 100644 index 0000000000..0c4508835e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c @@ -0,0 +1,104 @@ +/* s_scalbnl.c -- long double version of s_scalbn.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* @(#)s_scalbn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * scalbnl (long double x, int n) + * scalbnl(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +static const long double +twolm54 = 5.55111512312578270212e-17, /* 0x3C90000000000000, 0 */ +huge = 1.0E+300L, +tiny = 1.0E-300L; +static const double +two54 = 1.80143985094819840000e+16, /* 0x4350000000000000 */ +twom54 = 5.55111512312578270212e-17; /* 0x3C90000000000000 */ + +long double __scalbnl (long double x, int n) +{ + int64_t k,l,hx,lx; + union { int64_t i; double d; } u; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + k = (hx>>52)&0x7ff; /* extract exponent */ + l = (lx>>52)&0x7ff; + if (k==0) { /* 0 or subnormal x */ + if ((hx&0x7fffffffffffffffULL)==0) return x; /* +-0 */ + u.i = hx; + u.d *= two54; + hx = u.i; + k = ((hx>>52)&0x7ff) - 54; + } + else if (k==0x7ff) return x+x; /* NaN or Inf */ + if (n< -50000) return tiny*__copysignl(tiny,x); /*underflow */ + if (n> 50000 || k+n > 0x7fe) + return huge*__copysignl(huge,x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k+n; + if (k > 0) { /* normal result */ + hx = (hx&0x800fffffffffffffULL)|(k<<52); + if ((lx & 0x7fffffffffffffffULL) == 0) { /* low part +-0 */ + INSERT_WORDS64 (xhi, hx); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x; + } + if (l == 0) { /* low part subnormal */ + u.i = lx; + u.d *= two54; + lx = u.i; + l = ((lx>>52)&0x7ff) - 54; + } + l = l + n; + if (l > 0) + lx = (lx&0x800fffffffffffffULL)|(l<<52); + else if (l <= -54) + lx = (lx&0x8000000000000000ULL); + else { + l += 54; + u.i = (lx&0x800fffffffffffffULL)|(l<<52); + u.d *= twom54; + lx = u.i; + } + INSERT_WORDS64 (xhi, hx); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x; + } + if (k <= -54) + return tiny*__copysignl(tiny,x); /*underflow*/ + k += 54; /* subnormal result */ + lx &= 0x8000000000000000ULL; + hx &= 0x800fffffffffffffULL; + INSERT_WORDS64 (xhi, hx|(k<<52)); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x*twolm54; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl.c new file mode 100644 index 0000000000..1aba33e6e2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl.c @@ -0,0 +1,3 @@ +#define SIG 0 +#define FUNC setpayloadl +#include <s_setpayloadl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl_main.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl_main.c new file mode 100644 index 0000000000..9aa02cdf93 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl_main.c @@ -0,0 +1,60 @@ +/* Set NaN payload. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +#define SET_HIGH_BIT (HIGH_ORDER_BIT_IS_SET_FOR_SNAN ? SIG : !SIG) +#define BIAS 0x3ff +#define PAYLOAD_DIG 51 +#define EXPLICIT_MANT_DIG 52 + +int +FUNC (long double *x, long double payload) +{ + double hi, lo; + uint64_t hx, lx; + + ldbl_unpack (payload, &hi, &lo); + EXTRACT_WORDS64 (hx, hi); + EXTRACT_WORDS64 (lx, lo); + int exponent = hx >> EXPLICIT_MANT_DIG; + /* Test if argument is (a) negative or too large; (b) too small, + except for 0 when allowed; (c) not an integer. All valid + arguments have the low part zero. */ + if ((lx & 0x7fffffffffffffffULL) != 0 + || exponent >= BIAS + PAYLOAD_DIG + || (exponent < BIAS && !(SET_HIGH_BIT && hx == 0)) + || (hx & ((1ULL << (BIAS + EXPLICIT_MANT_DIG - exponent)) - 1)) != 0) + { + *x = 0.0L; + return 1; + } + if (hx != 0) + { + hx &= (1ULL << EXPLICIT_MANT_DIG) - 1; + hx |= 1ULL << EXPLICIT_MANT_DIG; + hx >>= BIAS + EXPLICIT_MANT_DIG - exponent; + } + hx |= 0x7ff0000000000000ULL | (SET_HIGH_BIT ? 0x8000000000000ULL : 0); + INSERT_WORDS64 (hi, hx); + *x = ldbl_pack (hi, 0.0); + return 0; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadsigl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadsigl.c new file mode 100644 index 0000000000..d97e2c8206 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadsigl.c @@ -0,0 +1,3 @@ +#define SIG 1 +#define FUNC setpayloadsigl +#include <s_setpayloadl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_signbitl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_signbitl.c new file mode 100644 index 0000000000..d6ceede69f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_signbitl.c @@ -0,0 +1,32 @@ +/* Return nonzero value if number is negative. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_ldbl_opt.h> + +int +___signbitl (long double x) +{ + return __builtin_signbitl (x); +} +#if IS_IN (libm) +long_double_symbol (libm, ___signbitl, __signbitl); +#else +long_double_symbol (libc, ___signbitl, __signbitl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_sincosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_sincosl.c new file mode 100644 index 0000000000..8329979931 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_sincosl.c @@ -0,0 +1,76 @@ +/* Compute sine and cosine of argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <math.h> + +#include <math_private.h> +#include <math_ldbl_opt.h> + +void +__sincosl (long double x, long double *sinx, long double *cosx) +{ + int64_t ix; + double xhi; + + /* High word of x. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if (ix <= 0x3fe921fb54442d10LL) + __kernel_sincosl (x, 0.0L, sinx, cosx, 0); + else if (ix >= 0x7ff0000000000000LL) + { + /* sin(Inf or NaN) is NaN */ + *sinx = *cosx = x - x; + if (isinf (x)) + __set_errno (EDOM); + } + else + { + /* Argument reduction needed. */ + long double y[2]; + int n; + + n = __ieee754_rem_pio2l (x, y); + switch (n & 3) + { + case 0: + __kernel_sincosl (y[0], y[1], sinx, cosx, 1); + break; + case 1: + __kernel_sincosl (y[0], y[1], cosx, sinx, 1); + *cosx = -*cosx; + break; + case 2: + __kernel_sincosl (y[0], y[1], sinx, cosx, 1); + *sinx = -*sinx; + *cosx = -*cosx; + break; + default: + __kernel_sincosl (y[0], y[1], cosx, sinx, 1); + *sinx = -*sinx; + break; + } + } +} +long_double_symbol (libm, __sincosl, sincosl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_sinl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_sinl.c new file mode 100644 index 0000000000..087921a913 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_sinl.c @@ -0,0 +1,85 @@ +/* s_sinl.c -- long double version of s_sin.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* sinl(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sinl ... sine function on [-pi/4,pi/4] + * __kernel_cosl ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __sinl(long double x) +{ + long double y[2],z=0.0L; + int64_t n, ix; + double xhi; + + /* High word of x. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if(ix <= 0x3fe921fb54442d10LL) + return __kernel_sinl(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7ff0000000000000LL) { + if (ix == 0x7ff0000000000000LL) + __set_errno (EDOM); + return x-x; + } + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + switch(n&3) { + case 0: return __kernel_sinl(y[0],y[1],1); + case 1: return __kernel_cosl(y[0],y[1]); + case 2: return -__kernel_sinl(y[0],y[1],1); + default: + return -__kernel_cosl(y[0],y[1]); + } + } +} +long_double_symbol (libm, __sinl, sinl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c new file mode 100644 index 0000000000..e6457a1c1c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c @@ -0,0 +1,87 @@ +/* @(#)s_tanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $"; +#endif + +/* Tanh(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanh(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanh(-x) = -tanh(x). + * 2. 0 <= x <= 2**-57 : tanh(x) := x*(one+x) + * -t + * 2**-57 < x <= 1 : tanh(x) := -----; t = expm1(-2x) + * t + 2 + * 2 + * 1 <= x <= 40.0 : tanh(x) := 1- ----- ; t=expm1(2x) + * t + 2 + * 40.0 < x <= INF : tanh(x) := 1. + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +static const long double one=1.0L, two=2.0L, tiny = 1.0e-300L; + +long double __tanhl(long double x) +{ + long double t,z; + int64_t jx,ix; + double xhi; + + /* High word of |x|. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (jx, xhi); + ix = jx&0x7fffffffffffffffLL; + + /* x is INF or NaN */ + if(ix>=0x7ff0000000000000LL) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 40 */ + if (ix < 0x4044000000000000LL) { /* |x|<40 */ + if (ix == 0) + return x; /* x == +-0 */ + if (ix<0x3c60000000000000LL) /* |x|<2**-57 */ + { + math_check_force_underflow (x); + return x; /* tanh(small) = small */ + } + if (ix>=0x3ff0000000000000LL) { /* |x|>=1 */ + t = __expm1l(two*fabsl(x)); + z = one - two/(t+two); + } else { + t = __expm1l(-two*fabsl(x)); + z= -t/(t+two); + } + /* |x| > 40, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (jx>=0)? z: -z; +} +long_double_symbol (libm, __tanhl, tanhl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_tanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_tanl.c new file mode 100644 index 0000000000..66b8a0621e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_tanl.c @@ -0,0 +1,79 @@ +/* s_tanl.c -- long double version of s_tan.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* @(#)s_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* tanl(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tanl ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __tanl(long double x) +{ + long double y[2],z=0.0L; + int64_t n, ix; + double xhi; + + /* High word of x. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if(ix <= 0x3fe921fb54442d10LL) return __kernel_tanl(x,z,1); + + /* tanl(Inf or NaN) is NaN */ + else if (ix>=0x7ff0000000000000LL) { + if (ix == 0x7ff0000000000000LL) + __set_errno (EDOM); + return x-x; /* NaN */ + } + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} +long_double_symbol (libm, __tanl, tanl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c new file mode 100644 index 0000000000..963376a7cf --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c @@ -0,0 +1,62 @@ +/* Total order operation. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalorderl (long double x, long double y) +{ + double xhi, xlo, yhi, ylo; + int64_t hx, hy, lx, ly; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS64 (hy, yhi); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN +# error not implemented +#endif + uint64_t hx_sign = hx >> 63; + uint64_t hy_sign = hy >> 63; + int64_t hx_adj = hx ^ (hx_sign >> 1); + int64_t hy_adj = hy ^ (hy_sign >> 1); + if (hx_adj < hy_adj) + return 1; + else if (hx_adj > hy_adj) + return 0; + + /* The high doubles are identical. If they are NaNs or both the low + parts are zero, the low parts are not significant (and if they + are infinities, both the low parts must be zero). */ + if ((hx & 0x7fffffffffffffffULL) >= 0x7ff0000000000000ULL) + return 1; + EXTRACT_WORDS64 (lx, xlo); + EXTRACT_WORDS64 (ly, ylo); + if (((lx | ly) & 0x7fffffffffffffffULL) == 0) + return 1; + + /* Otherwise compare the low parts. */ + uint64_t lx_sign = lx >> 63; + uint64_t ly_sign = ly >> 63; + lx ^= lx_sign >> 1; + ly ^= ly_sign >> 1; + return lx <= ly; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c new file mode 100644 index 0000000000..f7480909df --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c @@ -0,0 +1,64 @@ +/* Total order operation on absolute values. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalordermagl (long double x, long double y) +{ + double xhi, xlo, yhi, ylo; + int64_t hx, hy, lx, ly; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS64 (hy, yhi); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN +# error not implemented +#endif + uint64_t x_sign = hx & 0x8000000000000000ULL; + uint64_t y_sign = hy & 0x8000000000000000ULL; + hx ^= x_sign; + hy ^= y_sign; + if (hx < hy) + return 1; + else if (hx > hy) + return 0; + + /* The high doubles are identical. If they are NaNs or both the low + parts are zero, the low parts are not significant (and if they + are infinities, both the low parts must be zero). */ + if (hx >= 0x7ff0000000000000ULL) + return 1; + EXTRACT_WORDS64 (lx, xlo); + EXTRACT_WORDS64 (ly, ylo); + if (((lx | ly) & 0x7fffffffffffffffULL) == 0) + return 1; + lx ^= x_sign; + ly ^= y_sign; + + /* Otherwise compare the low parts. */ + uint64_t lx_sign = lx >> 63; + uint64_t ly_sign = ly >> 63; + lx ^= lx_sign >> 1; + ly ^= ly_sign >> 1; + return lx <= ly; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_truncl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_truncl.c new file mode 100644 index 0000000000..ecabf9d711 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_truncl.c @@ -0,0 +1,62 @@ +/* Truncate (toward zero) long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + + +long double +__truncl (long double x) +{ + double xh, xl, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Return Inf, Nan, +/-0 unchanged. */ + if (__builtin_expect (xh != 0.0 + && __builtin_isless (__builtin_fabs (xh), + __builtin_inf ()), 1)) + { + hi = __trunc (xh); + if (hi != xh) + { + /* The high part is not an integer; the low part does not + affect the result. */ + xh = hi; + xl = 0; + } + else + { + /* The high part is a nonzero integer. */ + lo = xh > 0 ? __floor (xl) : __ceil (xl); + xh = hi; + xl = lo; + ldbl_canonicalize_int (&xh, &xl); + } + } + else + /* Quiet signaling NaN arguments. */ + xh += xh; + + return ldbl_pack (xh, xl); +} + +long_double_symbol (libm, __truncl, truncl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ufromfpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ufromfpl.c new file mode 100644 index 0000000000..c686daa4a7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ufromfpl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 1 +#define INEXACT 0 +#define FUNC ufromfpl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ufromfpxl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ufromfpxl.c new file mode 100644 index 0000000000..906066c83c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ufromfpxl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 1 +#define INEXACT 1 +#define FUNC ufromfpxl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/strtod_nan_ldouble.h b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/strtod_nan_ldouble.h new file mode 100644 index 0000000000..198fe48f5c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/strtod_nan_ldouble.h @@ -0,0 +1,30 @@ +/* Convert string for NaN payload to corresponding NaN. For ldbl-128ibm. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define FLOAT long double +#define SET_MANTISSA(flt, mant) \ + do \ + { \ + union ibm_extended_long_double u; \ + u.ld = (flt); \ + u.d[0].ieee_nan.mantissa0 = (mant) >> 32; \ + u.d[0].ieee_nan.mantissa1 = (mant); \ + if ((u.d[0].ieee.mantissa0 | u.d[0].ieee.mantissa1) != 0) \ + (flt) = u.ld; \ + } \ + while (0) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/strtold_l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/strtold_l.c new file mode 100644 index 0000000000..37034cb254 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/strtold_l.c @@ -0,0 +1,60 @@ +/* Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <stdlib.h> +#include <wchar.h> +#include <xlocale.h> + +/* The actual implementation for all floating point sizes is in strtod.c. + These macros tell it to produce the `long double' version, `strtold'. */ + +#define FLOAT long double +#define FLT LDBL +#ifdef USE_WIDE_CHAR +extern long double ____new_wcstold_l (const wchar_t *, wchar_t **, __locale_t); +# define STRTOF __new_wcstold_l +# define __STRTOF ____new_wcstold_l +# define ____STRTOF_INTERNAL ____wcstold_l_internal +# define STRTOF_NAN __wcstold_nan +#else +extern long double ____new_strtold_l (const char *, char **, __locale_t); +# define STRTOF __new_strtold_l +# define __STRTOF ____new_strtold_l +# define ____STRTOF_INTERNAL ____strtold_l_internal +# define STRTOF_NAN __strtold_nan +#endif +extern __typeof (__STRTOF) STRTOF; +libc_hidden_proto (__STRTOF) +libc_hidden_proto (STRTOF) +#define MPN2FLOAT __mpn_construct_long_double +#define FLOAT_HUGE_VAL HUGE_VALL + +#include <strtod_l.c> + +#ifdef __LONG_DOUBLE_MATH_OPTIONAL +# include <math_ldbl_opt.h> +# ifdef USE_WIDE_CHAR +weak_alias (____new_wcstold_l, ___new_wcstold_l); +long_double_symbol (libc, ___new_wcstold_l, wcstold_l); +long_double_symbol (libc, ____new_wcstold_l, __wcstold_l); +# else +weak_alias (____new_strtold_l, ___new_strtold_l); +long_double_symbol (libc, ___new_strtold_l, strtold_l); +long_double_symbol (libc, ____new_strtold_l, __strtold_l); +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/t_sincosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/t_sincosl.c new file mode 100644 index 0000000000..22c59150be --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/t_sincosl.c @@ -0,0 +1,693 @@ +/* Quad-precision floating point sine and cosine tables. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* For 0.1484375 + n/128.0, n=0..82 this table contains + first 113 bits of cosine, then at least 113 additional + bits and the same for sine. + 0.1484375+82.0/128.0 is the smallest number among above defined numbers + larger than pi/4. + Computed using gmp. + */ + +const long double __sincosl_table[] = { + +/* x = 1.48437500000000000000000000000000000e-01L 3ffc3000000000000000000000000000 */ +/* cos(x) = 0.fd2f5320e1b790209b4dda2f98 f79caaa7b873aff1014b0fbc52 43766d03cb006bc837c4358 */ + 0x0.fd2f5320e1b790209b4dda2f98p0L, + 0x0.f79caaa7b873aff1014b0fbc52p-104L, +/* sin(x) = 0.25dc50bc95711d0d9787d108fd 438cf5959ee0bfb7a1e36e8b1a 112968f356657420e9cc9ea */ + 0x0.25dc50bc95711d0d9787d108fdp0L, + 0x0.438cf5959ee0bfb7a1e36e8b1ap-104L, + +/* x = 1.56250000000000000000000000000000000e-01 3ffc4000000000000000000000000000 */ +/* cos(x) = 0.fce1a053e621438b6d60c76e8c 45bf0a9dc71aa16f922acc10e9 5144ec796a249813c9cb649 */ + 0x0.fce1a053e621438b6d60c76e8cp0L, + 0x0.45bf0a9dc71aa16f922acc10e9p-104L, +/* sin(x) = 0.27d66258bacd96a3eb335b365c 87d59438c5142bb56a489e9b8d b9d36234ffdebb6bdc22d8e */ + 0x0.27d66258bacd96a3eb335b365cp0L, + 0x0.87d59438c5142bb56a489e9b8dp-104L, + +/* x = 1.64062500000000000000000000000000000e-01 3ffc5000000000000000000000000000 */ +/* cos(x) = 0.fc8ffa01ba6807417e05962b0d 9fdf1fddb0cc4c07d22e19e080 19bffa50a6c7acdb40307a3 */ + 0x0.fc8ffa01ba6807417e05962b0dp0L, + 0x0.9fdf1fddb0cc4c07d22e19e080p-104L, +/* sin(x) = 0.29cfd49b8be4f665276cab01cb f0426934906c3dd105473b226e 410b1450f62e53ff7c6cce1 */ + 0x0.29cfd49b8be4f665276cab01cbp0L, + 0x0.f0426934906c3dd105473b226ep-104L, + +/* x = 1.71875000000000000000000000000000000e-01 3ffc6000000000000000000000000000 */ +/* cos(x) = 0.fc3a6170f767ac735d63d99a9d 439e1db5e59d3ef153a4265d58 55850ed82b536bf361b80e3 */ + 0x0.fc3a6170f767ac735d63d99a9dp0L, + 0x0.439e1db5e59d3ef153a4265d58p-104L, +/* sin(x) = 0.2bc89f9f424de5485de7ce03b2 514952b9faf5648c3244d4736f eb95dbb9da49f3b58a9253b */ + 0x0.2bc89f9f424de5485de7ce03b2p0L, + 0x0.514952b9faf5648c3244d4736fp-104L, + +/* x = 1.79687500000000000000000000000000000e-01 3ffc7000000000000000000000000000 */ +/* cos(x) = 0.fbe0d7f7fef11e70aa43b8abf4 f6a457cea20c8f3f676b47781f 9821bbe9ce04b3c7b981c0b */ + 0x0.fbe0d7f7fef11e70aa43b8abf4p0L, + 0x0.f6a457cea20c8f3f676b47781fp-104L, +/* sin(x) = 0.2dc0bb80b49a97ffb34e8dd1f8 db9df7af47ed2dcf58b12c8e78 27e048cae929da02c04ecac */ + 0x0.2dc0bb80b49a97ffb34e8dd1f8p0L, + 0x0.db9df7af47ed2dcf58b12c8e78p-104L, + +/* x = 1.87500000000000000000000000000000000e-01 3ffc8000000000000000000000000000 */ +/* cos(x) = 0.fb835efcf670dd2ce6fe792469 7eea13ea358867e9cdb3899b78 3f4f9f43aa5626e8b67b3bc */ + 0x0.fb835efcf670dd2ce6fe792469p0L, + 0x0.7eea13ea358867e9cdb3899b78p-104L, +/* sin(x) = 0.2fb8205f75e56a2b56a1c4792f 856258769af396e0189ef72c05 e4df59a6b00e4b44a6ea515 */ + 0x0.2fb8205f75e56a2b56a1c4792fp0L, + 0x0.856258769af396e0189ef72c05p-104L, + +/* x = 1.95312500000000000000000000000000000e-01 3ffc9000000000000000000000000000 */ +/* cos(x) = 0.fb21f7f5c156696b00ac1fe28a c5fd76674a92b4df80d9c8a46c 684399005deccc41386257c */ + 0x0.fb21f7f5c156696b00ac1fe28ap0L, + 0x0.c5fd76674a92b4df80d9c8a46cp-104L, +/* sin(x) = 0.31aec65df552876f82ece9a235 6713246eba6799983d7011b0b3 698d6e1da919c15d57c30c1 */ + 0x0.31aec65df552876f82ece9a235p0L, + 0x0.6713246eba6799983d7011b0b3p-104L, + +/* x = 2.03125000000000000000000000000000000e-01 3ffca000000000000000000000000000 */ +/* cos(x) = 0.fabca467fb3cb8f1d069f01d8e a33ade5bfd68296ecd1cc9f7b7 609bbcf3676e726c3301334 */ + 0x0.fabca467fb3cb8f1d069f01d8ep0L, + 0x0.a33ade5bfd68296ecd1cc9f7b7p-104L, +/* sin(x) = 0.33a4a5a19d86246710f602c44d f4fa513f4639ce938477aeeabb 82e8e0a7ed583a188879fd4 */ + 0x0.33a4a5a19d86246710f602c44dp0L, + 0x0.f4fa513f4639ce938477aeeabbp-104L, + +/* x = 2.10937500000000000000000000000000000e-01 3ffcb000000000000000000000000000 */ +/* cos(x) = 0.fa5365e8f1d3ca27be1db5d76a e64d983d7470a4ab0f4ccf65a2 b8c67a380df949953a09bc1 */ + 0x0.fa5365e8f1d3ca27be1db5d76ap0L, + 0x0.e64d983d7470a4ab0f4ccf65a2p-104L, +/* sin(x) = 0.3599b652f40ec999df12a0a4c8 561de159c98d4e54555de518b9 7f48886f715d8df5f4f093e */ + 0x0.3599b652f40ec999df12a0a4c8p0L, + 0x0.561de159c98d4e54555de518b9p-104L, + +/* x = 2.18750000000000000000000000000000000e-01 3ffcc000000000000000000000000000 */ +/* cos(x) = 0.f9e63e1d9e8b6f6f2e296bae5b 5ed9c11fd7fa2fe11e09fc7bde 901abed24b6365e72f7db4e */ + 0x0.f9e63e1d9e8b6f6f2e296bae5bp0L, + 0x0.5ed9c11fd7fa2fe11e09fc7bdep-104L, +/* sin(x) = 0.378df09db8c332ce0d2b53d865 582e4526ea336c768f68c32b49 6c6d11c1cd241bb9f1da523 */ + 0x0.378df09db8c332ce0d2b53d865p0L, + 0x0.582e4526ea336c768f68c32b49p-104L, + +/* x = 2.26562500000000000000000000000000000e-01 3ffcd000000000000000000000000000 */ +/* cos(x) = 0.f9752eba9fff6b98842beadab0 54a932fb0f8d5b875ae63d6b22 88d09b148921aeb6e52f61b */ + 0x0.f9752eba9fff6b98842beadab0p0L, + 0x0.54a932fb0f8d5b875ae63d6b22p-104L, +/* sin(x) = 0.39814cb10513453cb97b21bc1c a6a337b150c21a675ab85503bc 09a436a10ab1473934e20c8 */ + 0x0.39814cb10513453cb97b21bc1cp0L, + 0x0.a6a337b150c21a675ab85503bcp-104L, + +/* x = 2.34375000000000000000000000000000000e-01 3ffce000000000000000000000000000 */ +/* cos(x) = 0.f90039843324f9b940416c1984 b6cbed1fc733d97354d4265788 a86150493ce657cae032674 */ + 0x0.f90039843324f9b940416c1984p0L, + 0x0.b6cbed1fc733d97354d4265788p-104L, +/* sin(x) = 0.3b73c2bf6b4b9f668ef9499c81 f0d965087f1753fa64b086e58c b8470515c18c1412f8c2e02 */ + 0x0.3b73c2bf6b4b9f668ef9499c81p0L, + 0x0.f0d965087f1753fa64b086e58cp-104L, + +/* x = 2.42187500000000000000000000000000000e-01 3ffcf000000000000000000000000000 */ +/* cos(x) = 0.f887604e2c39dbb20e4ec58250 59a789ffc95b275ad9954078ba 8a28d3fcfe9cc2c1d49697b */ + 0x0.f887604e2c39dbb20e4ec58250p0L, + 0x0.59a789ffc95b275ad9954078bap-104L, +/* sin(x) = 0.3d654aff15cb457a0fca854698 aba33039a8a40626609204472d 9d40309b626eccc6dff0ffa */ + 0x0.3d654aff15cb457a0fca854698p0L, + 0x0.aba33039a8a40626609204472dp-104L, + +/* x = 2.50000000000000000000000000000000000e-01 3ffd0000000000000000000000000000 */ +/* cos(x) = 0.f80aa4fbef750ba783d33cb95f 94f8a41426dbe79edc4a023ef9 ec13c944551c0795b84fee1 */ + 0x0.f80aa4fbef750ba783d33cb95fp0L, + 0x0.94f8a41426dbe79edc4a023ef9p-104L, +/* sin(x) = 0.3f55dda9e62aed7513bd7b8e6a 3d1635dd5676648d7db525898d 7086af9330f03c7f285442a */ + 0x0.3f55dda9e62aed7513bd7b8e6ap0L, + 0x0.3d1635dd5676648d7db525898dp-104L, + +/* x = 2.57812500000000000000000000000000000e-01 3ffd0800000000000000000000000000 */ +/* cos(x) = 0.f78a098069792daabc9ee42591 b7c5a68cb1ab822aeb446b3311 b4ba5371b8970e2c1547ad7 */ + 0x0.f78a098069792daabc9ee42591p0L, + 0x0.b7c5a68cb1ab822aeb446b3311p-104L, +/* sin(x) = 0.414572fd94556e6473d6202713 88dd47c0ba050cdb5270112e3e 370e8c4705ae006426fb5d5 */ + 0x0.414572fd94556e6473d6202713p0L, + 0x0.88dd47c0ba050cdb5270112e3ep-104L, + +/* x = 2.65625000000000000000000000000000000e-01 3ffd1000000000000000000000000000 */ +/* cos(x) = 0.f7058fde0788dfc805b8fe8878 9e4f4253e3c50afe8b22f41159 620ab5940ff7df9557c0d1f */ + 0x0.f7058fde0788dfc805b8fe8878p0L, + 0x0.9e4f4253e3c50afe8b22f41159p-104L, +/* sin(x) = 0.4334033bcd90d6604f5f36c1d4 b84451a87150438275b77470b5 0e5b968fa7962b5ffb379b7 */ + 0x0.4334033bcd90d6604f5f36c1d4p0L, + 0x0.b84451a87150438275b77470b5p-104L, + +/* x = 2.73437500000000000000000000000000000e-01 3ffd1800000000000000000000000000 */ +/* cos(x) = 0.f67d3a26af7d07aa4bd6d42af8 c0067fefb96d5b46c031eff536 27f215ea3242edc3f2e13eb */ + 0x0.f67d3a26af7d07aa4bd6d42af8p0L, + 0x0.c0067fefb96d5b46c031eff536p-104L, +/* sin(x) = 0.452186aa5377ab20bbf2524f52 e3a06a969f47166ab88cf88c11 1ad12c55941021ef3317a1a */ + 0x0.452186aa5377ab20bbf2524f52p0L, + 0x0.e3a06a969f47166ab88cf88c11p-104L, + +/* x = 2.81250000000000000000000000000000000e-01 3ffd2000000000000000000000000000 */ +/* cos(x) = 0.f5f10a7bb77d3dfa0c1da8b578 42783280d01ce3c0f82bae3b9d 623c168d2e7c29977994451 */ + 0x0.f5f10a7bb77d3dfa0c1da8b578p0L, + 0x0.42783280d01ce3c0f82bae3b9dp-104L, +/* sin(x) = 0.470df5931ae1d946076fe0dcff 47fe31bb2ede618ebc607821f8 462b639e1f4298b5ae87fd3 */ + 0x0.470df5931ae1d946076fe0dcffp0L, + 0x0.47fe31bb2ede618ebc607821f8p-104L, + +/* x = 2.89062500000000000000000000000000000e-01 3ffd2800000000000000000000000000 */ +/* cos(x) = 0.f561030ddd7a78960ea9f4a32c 6521554995667f5547bafee9ec 48b3155cdb0f7fd00509713 */ + 0x0.f561030ddd7a78960ea9f4a32cp0L, + 0x0.6521554995667f5547bafee9ecp-104L, +/* sin(x) = 0.48f948446abcd6b0f7fccb100e 7a1b26eccad880b0d24b59948c 7cdd49514d44b933e6985c2 */ + 0x0.48f948446abcd6b0f7fccb100ep0L, + 0x0.7a1b26eccad880b0d24b59948cp-104L, + +/* x = 2.96875000000000000000000000000000000e-01 3ffd3000000000000000000000000000 */ +/* cos(x) = 0.f4cd261d3e6c15bb369c875863 0d2ac00b7ace2a51c0631bfeb3 9ed158ba924cc91e259c195 */ + 0x0.f4cd261d3e6c15bb369c875863p0L, + 0x0.0d2ac00b7ace2a51c0631bfeb3p-104L, +/* sin(x) = 0.4ae37710fad27c8aa9c4cf96c0 3519b9ce07dc08a1471775499f 05c29f86190aaebaeb9716e */ + 0x0.4ae37710fad27c8aa9c4cf96c0p0L, + 0x0.3519b9ce07dc08a1471775499fp-104L, + +/* x = 3.04687500000000000000000000000000000e-01 3ffd3800000000000000000000000000 */ +/* cos(x) = 0.f43575f94d4f6b272f5fb76b14 d2a64ab52df1ee8ddf7c651034 e5b2889305a9ea9015d758a */ + 0x0.f43575f94d4f6b272f5fb76b14p0L, + 0x0.d2a64ab52df1ee8ddf7c651034p-104L, +/* sin(x) = 0.4ccc7a50127e1de0cb6b40c302 c651f7bded4f9e7702b0471ae0 288d091a37391950907202f */ + 0x0.4ccc7a50127e1de0cb6b40c302p0L, + 0x0.c651f7bded4f9e7702b0471ae0p-104L, + +/* x = 3.12500000000000000000000000000000000e-01 3ffd4000000000000000000000000000 */ +/* cos(x) = 0.f399f500c9e9fd37ae9957263d ab8877102beb569f101ee44953 50868e5847d181d50d3cca2 */ + 0x0.f399f500c9e9fd37ae9957263dp0L, + 0x0.ab8877102beb569f101ee44953p-104L, +/* sin(x) = 0.4eb44a5da74f600207aaa090f0 734e288603ffadb3eb2542a469 77b105f8547128036dcf7f0 */ + 0x0.4eb44a5da74f600207aaa090f0p0L, + 0x0.734e288603ffadb3eb2542a469p-104L, + +/* x = 3.20312500000000000000000000000000000e-01 3ffd4800000000000000000000000000 */ +/* cos(x) = 0.f2faa5a1b74e82fd61fa05f917 7380e8e69b7b15a945e8e5ae11 24bf3d12b0617e03af4fab5 */ + 0x0.f2faa5a1b74e82fd61fa05f917p0L, + 0x0.7380e8e69b7b15a945e8e5ae11p-104L, +/* sin(x) = 0.509adf9a7b9a5a0f638a8fa3a6 0a199418859f18b37169a644fd b986c21ecb00133853bc35b */ + 0x0.509adf9a7b9a5a0f638a8fa3a6p0L, + 0x0.0a199418859f18b37169a644fdp-104L, + +/* x = 3.28125000000000000000000000000000000e-01 3ffd5000000000000000000000000000 */ +/* cos(x) = 0.f2578a595224dd2e6bfa2eb2f9 9cc674f5ea6f479eae2eb58018 6897ae3f893df1113ca06b8 */ + 0x0.f2578a595224dd2e6bfa2eb2f9p0L, + 0x0.9cc674f5ea6f479eae2eb58018p-104L, +/* sin(x) = 0.5280326c3cf481823ba6bb08ea c82c2093f2bce3c4eb4ee3dec7 df41c92c8a4226098616075 */ + 0x0.5280326c3cf481823ba6bb08eap0L, + 0x0.c82c2093f2bce3c4eb4ee3dec7p-104L, + +/* x = 3.35937500000000000000000000000000000e-01 3ffd5800000000000000000000000000 */ +/* cos(x) = 0.f1b0a5b406b526d886c55feadc 8d0dcc8eb9ae2ac707051771b4 8e05b25b000009660bdb3e3 */ + 0x0.f1b0a5b406b526d886c55feadcp0L, + 0x0.8d0dcc8eb9ae2ac707051771b4p-104L, +/* sin(x) = 0.54643b3da29de9b357155eef0f 332fb3e66c83bf4dddd9491c5e b8e103ccd92d6175220ed51 */ + 0x0.54643b3da29de9b357155eef0fp0L, + 0x0.332fb3e66c83bf4dddd9491c5ep-104L, + +/* x = 3.43750000000000000000000000000000000e-01 3ffd6000000000000000000000000000 */ +/* cos(x) = 0.f105fa4d66b607a67d44e04272 5204435142ac8ad54dfb0907a4 f6b56b06d98ee60f19e557a */ + 0x0.f105fa4d66b607a67d44e04272p0L, + 0x0.5204435142ac8ad54dfb0907a4p-104L, +/* sin(x) = 0.5646f27e8bd65cbe3a5d61ff06 572290ee826d9674a00246b05a e26753cdfc90d9ce81a7d02 */ + 0x0.5646f27e8bd65cbe3a5d61ff06p0L, + 0x0.572290ee826d9674a00246b05ap-104L, + +/* x = 3.51562500000000000000000000000000000e-01 3ffd6800000000000000000000000000 */ +/* cos(x) = 0.f0578ad01ede707fa39c09dc6b 984afef74f3dc8d0efb0f4c5a6 b13771145b3e0446fe33887 */ + 0x0.f0578ad01ede707fa39c09dc6bp0L, + 0x0.984afef74f3dc8d0efb0f4c5a6p-104L, +/* sin(x) = 0.582850a41e1dd46c7f602ea244 cdbbbfcdfa8f3189be794dda42 7ce090b5f85164f1f80ac13 */ + 0x0.582850a41e1dd46c7f602ea244p0L, + 0x0.cdbbbfcdfa8f3189be794dda42p-104L, + +/* x = 3.59375000000000000000000000000000000e-01 3ffd7000000000000000000000000000 */ +/* cos(x) = 0.efa559f5ec3aec3a4eb0331927 8a2d41fcf9189462261125fe61 47b078f1daa0b06750a1654 */ + 0x0.efa559f5ec3aec3a4eb0331927p0L, + 0x0.8a2d41fcf9189462261125fe61p-104L, +/* sin(x) = 0.5a084e28e35fda2776dfdbbb55 31d74ced2b5d17c0b1afc46475 29d50c295e36d8ceec126c1 */ + 0x0.5a084e28e35fda2776dfdbbb55p0L, + 0x0.31d74ced2b5d17c0b1afc46475p-104L, + +/* x = 3.67187500000000000000000000000000000e-01 3ffd7800000000000000000000000000 */ +/* cos(x) = 0.eeef6a879146af0bf9b95ea2ea 0ac0d3e2e4d7e15d93f48cbd41 bf8e4fded40bef69e19eafa */ + 0x0.eeef6a879146af0bf9b95ea2eap0L, + 0x0.0ac0d3e2e4d7e15d93f48cbd41p-104L, +/* sin(x) = 0.5be6e38ce8095542bc14ee9da0 d36483e6734bcab2e07624188a f5653f114eeb46738fa899d */ + 0x0.5be6e38ce8095542bc14ee9da0p0L, + 0x0.d36483e6734bcab2e07624188ap-104L, + +/* x = 3.75000000000000000000000000000000000e-01 3ffd8000000000000000000000000000 */ +/* cos(x) = 0.ee35bf5ccac89052cd91ddb734 d3a47e262e3b609db604e21705 3803be0091e76daf28a89b7 */ + 0x0.ee35bf5ccac89052cd91ddb734p0L, + 0x0.d3a47e262e3b609db604e21705p-104L, +/* sin(x) = 0.5dc40955d9084f48a94675a249 8de5d851320ff5528a6afb3f2e 24de240fce6cbed1ba0ccd6 */ + 0x0.5dc40955d9084f48a94675a249p0L, + 0x0.8de5d851320ff5528a6afb3f2ep-104L, + +/* x = 3.82812500000000000000000000000000000e-01 3ffd8800000000000000000000000000 */ +/* cos(x) = 0.ed785b5c44741b4493c56bcb9d 338a151c6f6b85d8f8aca658b2 8572c162b199680eb9304da */ + 0x0.ed785b5c44741b4493c56bcb9dp0L, + 0x0.338a151c6f6b85d8f8aca658b2p-104L, +/* sin(x) = 0.5f9fb80f21b53649c432540a50 e22c53057ff42ae0fdf1307760 dc0093f99c8efeb2fbd7073 */ + 0x0.5f9fb80f21b53649c432540a50p0L, + 0x0.e22c53057ff42ae0fdf1307760p-104L, + +/* x = 3.90625000000000000000000000000000000e-01 3ffd9000000000000000000000000000 */ +/* cos(x) = 0.ecb7417b8d4ee3fec37aba4073 aa48f1f14666006fb431d96713 03c8100d10190ec8179c41d */ + 0x0.ecb7417b8d4ee3fec37aba4073p0L, + 0x0.aa48f1f14666006fb431d96713p-104L, +/* sin(x) = 0.6179e84a09a5258a40e9b5face 03e525f8b5753cd0105d93fe62 98010c3458e84d75fe420e9 */ + 0x0.6179e84a09a5258a40e9b5facep0L, + 0x0.03e525f8b5753cd0105d93fe62p-104L, + +/* x = 3.98437500000000000000000000000000000e-01 3ffd9800000000000000000000000000 */ +/* cos(x) = 0.ebf274bf0bda4f62447e56a093 626798d3013b5942b1abfd155a acc9dc5c6d0806a20d6b9c1 */ + 0x0.ebf274bf0bda4f62447e56a093p0L, + 0x0.626798d3013b5942b1abfd155ap-104L, +/* sin(x) = 0.6352929dd264bd44a02ea76632 5d8aa8bd9695fc8def3caefba5 b94c9a3c873f7b2d3776ead */ + 0x0.6352929dd264bd44a02ea76632p0L, + 0x0.5d8aa8bd9695fc8def3caefba5p-104L, + +/* x = 4.06250000000000000000000000000000000e-01 3ffda000000000000000000000000000 */ +/* cos(x) = 0.eb29f839f201fd13b937968279 16a78f15c85230a4e8ea4b2155 8265a14367e1abb4c30695a */ + 0x0.eb29f839f201fd13b937968279p0L, + 0x0.16a78f15c85230a4e8ea4b2155p-104L, +/* sin(x) = 0.6529afa7d51b129631ec197c0a 840a11d7dc5368b0a47956feb2 85caa8371c4637ef17ef01b */ + 0x0.6529afa7d51b129631ec197c0ap0L, + 0x0.840a11d7dc5368b0a47956feb2p-104L, + +/* x = 4.14062500000000000000000000000000000e-01 3ffda800000000000000000000000000 */ +/* cos(x) = 0.ea5dcf0e30cf03e6976ef0b1ec 26515fba47383855c3b4055a99 b5e86824b2cd1a691fdca7b */ + 0x0.ea5dcf0e30cf03e6976ef0b1ecp0L, + 0x0.26515fba47383855c3b4055a99p-104L, +/* sin(x) = 0.66ff380ba0144109e39a320b0a 3fa5fd65ea0585bcbf9b1a769a 9b0334576c658139e1a1cbe */ + 0x0.66ff380ba0144109e39a320b0ap0L, + 0x0.3fa5fd65ea0585bcbf9b1a769ap-104L, + +/* x = 4.21875000000000000000000000000000000e-01 3ffdb000000000000000000000000000 */ +/* cos(x) = 0.e98dfc6c6be031e60dd3089cbd d18a75b1f6b2c1e97f79225202 f03dbea45b07a5ec4efc062 */ + 0x0.e98dfc6c6be031e60dd3089cbdp0L, + 0x0.d18a75b1f6b2c1e97f79225202p-104L, +/* sin(x) = 0.68d32473143327973bc712bcc4 ccddc47630d755850c0655243b 205934dc49ffed8eb76adcb */ + 0x0.68d32473143327973bc712bcc4p0L, + 0x0.ccddc47630d755850c0655243bp-104L, + +/* x = 4.29687500000000000000000000000000000e-01 3ffdb800000000000000000000000000 */ +/* cos(x) = 0.e8ba8393eca7821aa563d83491 b6101189b3b101c3677f73d7ba d7c10f9ee02b7ab4009739a */ + 0x0.e8ba8393eca7821aa563d83491p0L, + 0x0.b6101189b3b101c3677f73d7bap-104L, +/* sin(x) = 0.6aa56d8e8249db4eb60a761fe3 f9e559be456b9e13349ca99b0b fb787f22b95db3b70179615 */ + 0x0.6aa56d8e8249db4eb60a761fe3p0L, + 0x0.f9e559be456b9e13349ca99b0bp-104L, + +/* x = 4.37500000000000000000000000000000000e-01 3ffdc000000000000000000000000000 */ +/* cos(x) = 0.e7e367d2956cfb16b6aa11e541 9cd0057f5c132a6455bf064297 e6a76fe2b72bb630d6d50ff */ + 0x0.e7e367d2956cfb16b6aa11e541p0L, + 0x0.9cd0057f5c132a6455bf064297p-104L, +/* sin(x) = 0.6c760c14c8585a51dbd34660ae 6c52ac7036a0b40887a0b63724 f8b4414348c3063a637f457 */ + 0x0.6c760c14c8585a51dbd34660aep0L, + 0x0.6c52ac7036a0b40887a0b63724p-104L, + +/* x = 4.45312500000000000000000000000000000e-01 3ffdc800000000000000000000000000 */ +/* cos(x) = 0.e708ac84d4172a3e2737662213 429e14021074d7e702e77d72a8 f1101a7e70410df8273e9aa */ + 0x0.e708ac84d4172a3e2737662213p0L, + 0x0.429e14021074d7e702e77d72a8p-104L, +/* sin(x) = 0.6e44f8c36eb10a1c752d093c00 f4d47ba446ac4c215d26b03164 42f168459e677d06e7249e3 */ + 0x0.6e44f8c36eb10a1c752d093c00p0L, + 0x0.f4d47ba446ac4c215d26b03164p-104L, + +/* x = 4.53125000000000000000000000000000000e-01 3ffdd000000000000000000000000000 */ +/* cos(x) = 0.e62a551594b970a770b15d41d4 c0e483e47aca550111df6966f9 e7ac3a94ae49e6a71eb031e */ + 0x0.e62a551594b970a770b15d41d4p0L, + 0x0.c0e483e47aca550111df6966f9p-104L, +/* sin(x) = 0.70122c5ec5028c8cff33abf4fd 340ccc382e038379b09cf04f9a 52692b10b72586060cbb001 */ + 0x0.70122c5ec5028c8cff33abf4fdp0L, + 0x0.340ccc382e038379b09cf04f9ap-104L, + +/* x = 4.60937500000000000000000000000000000e-01 3ffdd800000000000000000000000000 */ +/* cos(x) = 0.e54864fe33e8575cabf5bd0e5c f1b1a8bc7c0d5f61702450fa6b 6539735820dd2603ae355d5 */ + 0x0.e54864fe33e8575cabf5bd0e5cp0L, + 0x0.f1b1a8bc7c0d5f61702450fa6bp-104L, +/* sin(x) = 0.71dd9fb1ff4677853acb970a9f 6729c6e3aac247b1c57cea66c7 7413f1f98e8b9e98e49d851 */ + 0x0.71dd9fb1ff4677853acb970a9fp0L, + 0x0.6729c6e3aac247b1c57cea66c7p-104L, + +/* x = 4.68750000000000000000000000000000000e-01 3ffde000000000000000000000000000 */ +/* cos(x) = 0.e462dfc670d421ab3d1a159012 28f146a0547011202bf5ab01f9 14431859aef577966bc4fa4 */ + 0x0.e462dfc670d421ab3d1a159012p0L, + 0x0.28f146a0547011202bf5ab01f9p-104L, +/* sin(x) = 0.73a74b8f52947b681baf6928eb 3fb021769bf4779bad0e3aa9b1 cdb75ec60aad9fc63ff19d5 */ + 0x0.73a74b8f52947b681baf6928ebp0L, + 0x0.3fb021769bf4779bad0e3aa9b1p-104L, + +/* x = 4.76562500000000000000000000000000000e-01 3ffde800000000000000000000000000 */ +/* cos(x) = 0.e379c9045f29d517c4808aa497 c2057b2b3d109e76c0dc302d4d 0698b36e3f0bdbf33d8e952 */ + 0x0.e379c9045f29d517c4808aa497p0L, + 0x0.c2057b2b3d109e76c0dc302d4dp-104L, +/* sin(x) = 0.756f28d011d98528a44a75fc29 c779bd734ecdfb582fdb74b68a 4c4c4be54cfd0b2d3ad292f */ + 0x0.756f28d011d98528a44a75fc29p0L, + 0x0.c779bd734ecdfb582fdb74b68ap-104L, + +/* x = 4.84375000000000000000000000000000000e-01 3ffdf000000000000000000000000000 */ +/* cos(x) = 0.e28d245c58baef72225e232abc 003c4366acd9eb4fc2808c2ab7 fe7676cf512ac7f945ae5fb */ + 0x0.e28d245c58baef72225e232abcp0L, + 0x0.003c4366acd9eb4fc2808c2ab7p-104L, +/* sin(x) = 0.77353054ca72690d4c6e171fd9 9e6b39fa8e1ede5f052fd29645 34c75340970a3a9cd3c5c32 */ + 0x0.77353054ca72690d4c6e171fd9p0L, + 0x0.9e6b39fa8e1ede5f052fd29645p-104L, + +/* x = 4.92187500000000000000000000000000000e-01 3ffdf800000000000000000000000000 */ +/* cos(x) = 0.e19cf580eeec046aa1422fa748 07ecefb2a1911c94e7b5f20a00 f70022d940193691e5bd790 */ + 0x0.e19cf580eeec046aa1422fa748p0L, + 0x0.07ecefb2a1911c94e7b5f20a00p-104L, +/* sin(x) = 0.78f95b0560a9a3bd6df7bd981d c38c61224d08bc20631ea932e6 05e53b579e9e0767dfcbbcb */ + 0x0.78f95b0560a9a3bd6df7bd981dp0L, + 0x0.c38c61224d08bc20631ea932e6p-104L, + +/* x = 5.00000000000000000000000000000000000e-01 3ffe0000000000000000000000000000 */ +/* cos(x) = 0.e0a94032dbea7cedbddd9da2fa fad98556566b3a89f43eabd723 50af3e8b19e801204d8fe2e */ + 0x0.e0a94032dbea7cedbddd9da2fap0L, + 0x0.fad98556566b3a89f43eabd723p-104L, +/* sin(x) = 0.7abba1d12c17bfa1d92f0d93f6 0ded9992f45b4fcaf13cd58b30 3693d2a0db47db35ae8a3a9 */ + 0x0.7abba1d12c17bfa1d92f0d93f6p0L, + 0x0.0ded9992f45b4fcaf13cd58b30p-104L, + +/* x = 5.07812500000000000000000000000000000e-01 3ffe0400000000000000000000000000 */ +/* cos(x) = 0.dfb20840f3a9b36f7ae2c51534 2890b5ec583b8366cc2b55029e 95094d31112383f2553498b */ + 0x0.dfb20840f3a9b36f7ae2c51534p0L, + 0x0.2890b5ec583b8366cc2b55029ep-104L, +/* sin(x) = 0.7c7bfdaf13e5ed17212f8a7525 bfb113aba6c0741b5362bb8d59 282a850b63716bca0c910f0 */ + 0x0.7c7bfdaf13e5ed17212f8a7525p0L, + 0x0.bfb113aba6c0741b5362bb8d59p-104L, + +/* x = 5.15625000000000000000000000000000000e-01 3ffe0800000000000000000000000000 */ +/* cos(x) = 0.deb7518814a7a931bbcc88c109 cd41c50bf8bb48f20ae8c36628 d1d3d57574f7dc58f27d91c */ + 0x0.deb7518814a7a931bbcc88c109p0L, + 0x0.cd41c50bf8bb48f20ae8c36628p-104L, +/* sin(x) = 0.7e3a679daaf25c676542bcb402 8d0964172961c921823a4ef0c3 a9070d886dbd073f6283699 */ + 0x0.7e3a679daaf25c676542bcb402p0L, + 0x0.8d0964172961c921823a4ef0c3p-104L, + +/* x = 5.23437500000000000000000000000000000e-01 3ffe0c00000000000000000000000000 */ +/* cos(x) = 0.ddb91ff318799172bd2452d0a3 889f5169c64a0094bcf0b8aa7d cf0d7640a2eba68955a80be */ + 0x0.ddb91ff318799172bd2452d0a3p0L, + 0x0.889f5169c64a0094bcf0b8aa7dp-104L, +/* sin(x) = 0.7ff6d8a34bd5e8fa54c97482db 5159df1f24e8038419c0b448b9 eea8939b5d4dfcf40900257 */ + 0x0.7ff6d8a34bd5e8fa54c97482dbp0L, + 0x0.5159df1f24e8038419c0b448b9p-104L, + +/* x = 5.31250000000000000000000000000000000e-01 3ffe1000000000000000000000000000 */ +/* cos(x) = 0.dcb7777ac420705168f31e3eb7 80ce9c939ecada62843b54522f 5407eb7f21e556059fcd734 */ + 0x0.dcb7777ac420705168f31e3eb7p0L, + 0x0.80ce9c939ecada62843b54522fp-104L, +/* sin(x) = 0.81b149ce34caa5a4e650f8d09f d4d6aa74206c32ca951a93074c 83b2d294d25dbb0f7fdfad2 */ + 0x0.81b149ce34caa5a4e650f8d09fp0L, + 0x0.d4d6aa74206c32ca951a93074cp-104L, + +/* x = 5.39062500000000000000000000000000000e-01 3ffe1400000000000000000000000000 */ +/* cos(x) = 0.dbb25c25b8260c14f6e7bc98ec 991b70c65335198b0ab628bad2 0cc7b229d4dd62183cfa055 */ + 0x0.dbb25c25b8260c14f6e7bc98ecp0L, + 0x0.991b70c65335198b0ab628bad2p-104L, +/* sin(x) = 0.8369b434a372da7eb5c8a71fe3 6ce1e0b2b493f6f5cb2e38bcae c2a556b3678c401940d1c3c */ + 0x0.8369b434a372da7eb5c8a71fe3p0L, + 0x0.6ce1e0b2b493f6f5cb2e38bcaep-104L, + +/* x = 5.46875000000000000000000000000000000e-01 3ffe1800000000000000000000000000 */ +/* cos(x) = 0.daa9d20860827063fde51c09e8 55e9932e1b17143e7244fd267a 899d41ae1f3bc6a0ec42e27 */ + 0x0.daa9d20860827063fde51c09e8p0L, + 0x0.55e9932e1b17143e7244fd267ap-104L, +/* sin(x) = 0.852010f4f0800521378bd8dd61 4753d080c2e9e0775ffc609947 b9132f5357404f464f06a58 */ + 0x0.852010f4f0800521378bd8dd61p0L, + 0x0.4753d080c2e9e0775ffc609947p-104L, + +/* x = 5.54687500000000000000000000000000000e-01 3ffe1c00000000000000000000000000 */ +/* cos(x) = 0.d99ddd44e44a43d4d4a3a3ed95 204106fd54d78e8c7684545c0d a0b7c2c72be7a89b7c182ad */ + 0x0.d99ddd44e44a43d4d4a3a3ed95p0L, + 0x0.204106fd54d78e8c7684545c0dp-104L, +/* sin(x) = 0.86d45935ab396cb4e421e822de e54f3562dfcefeaa782184c234 01d231f5ad981a1cc195b18 */ + 0x0.86d45935ab396cb4e421e822dep0L, + 0x0.e54f3562dfcefeaa782184c234p-104L, + +/* x = 5.62500000000000000000000000000000000e-01 3ffe2000000000000000000000000000 */ +/* cos(x) = 0.d88e820b1526311dd561efbc0c 1a9a5375eb26f65d246c5744b1 3ca26a7e0fd42556da843c8 */ + 0x0.d88e820b1526311dd561efbc0cp0L, + 0x0.1a9a5375eb26f65d246c5744b1p-104L, +/* sin(x) = 0.88868625b4e1dbb23133101330 22527200c143a5cb16637cb7da f8ade82459ff2e98511f40f */ + 0x0.88868625b4e1dbb23133101330p0L, + 0x0.22527200c143a5cb16637cb7dap-104L, + +/* x = 5.70312500000000000000000000000000000e-01 3ffe2400000000000000000000000000 */ +/* cos(x) = 0.d77bc4985e93a607c9d868b906 bbc6bbe3a04258814acb035846 8b826fc91bd4d814827f65e */ + 0x0.d77bc4985e93a607c9d868b906p0L, + 0x0.bbc6bbe3a04258814acb035846p-104L, +/* sin(x) = 0.8a3690fc5bfc11bf9535e2739a 8512f448a41251514bbed7fc18 d530f9b4650fcbb2861b0aa */ + 0x0.8a3690fc5bfc11bf9535e2739ap0L, + 0x0.8512f448a41251514bbed7fc18p-104L, + +/* x = 5.78125000000000000000000000000000000e-01 3ffe2800000000000000000000000000 */ +/* cos(x) = 0.d665a937b4ef2b1f6d51bad6d9 88a4419c1d7051faf31a9efa15 1d7631117efac03713f950a */ + 0x0.d665a937b4ef2b1f6d51bad6d9p0L, + 0x0.88a4419c1d7051faf31a9efa15p-104L, +/* sin(x) = 0.8be472f9776d809af2b8817124 3d63d66dfceeeb739cc894e023 fbc165a0e3f26ff729c5d57 */ + 0x0.8be472f9776d809af2b8817124p0L, + 0x0.3d63d66dfceeeb739cc894e023p-104L, + +/* x = 5.85937500000000000000000000000000000e-01 3ffe2c00000000000000000000000000 */ +/* cos(x) = 0.d54c3441844897fc8f853f0655 f1ba695eba9fbfd7439dbb1171 d862d9d9146ca5136f825ac */ + 0x0.d54c3441844897fc8f853f0655p0L, + 0x0.f1ba695eba9fbfd7439dbb1171p-104L, +/* sin(x) = 0.8d902565817ee7839bce3cd128 060119492cd36d42d82ada30d7 f8bde91324808377ddbf5d4 */ + 0x0.8d902565817ee7839bce3cd128p0L, + 0x0.060119492cd36d42d82ada30d7p-104L, + +/* x = 5.93750000000000000000000000000000000e-01 3ffe3000000000000000000000000000 */ +/* cos(x) = 0.d42f6a1b9f0168cdf031c2f63c 8d9304d86f8d34cb1d5fccb68c a0f2241427fc18d1fd5bbdf */ + 0x0.d42f6a1b9f0168cdf031c2f63cp0L, + 0x0.8d9304d86f8d34cb1d5fccb68cp-104L, +/* sin(x) = 0.8f39a191b2ba6122a3fa4f41d5 a3ffd421417d46f19a22230a14 f7fcc8fce5c75b4b28b29d1 */ + 0x0.8f39a191b2ba6122a3fa4f41d5p0L, + 0x0.a3ffd421417d46f19a22230a14p-104L, + +/* x = 6.01562500000000000000000000000000000e-01 3ffe3400000000000000000000000000 */ +/* cos(x) = 0.d30f4f392c357ab0661c5fa8a7 d9b26627846fef214b1d19a223 79ff9eddba087cf410eb097 */ + 0x0.d30f4f392c357ab0661c5fa8a7p0L, + 0x0.d9b26627846fef214b1d19a223p-104L, +/* sin(x) = 0.90e0e0d81ca678796cc92c8ea8 c2815bc72ca78abe571bfa8576 aacc571e096a33237e0e830 */ + 0x0.90e0e0d81ca678796cc92c8ea8p0L, + 0x0.c2815bc72ca78abe571bfa8576p-104L, + +/* x = 6.09375000000000000000000000000000000e-01 3ffe3800000000000000000000000000 */ +/* cos(x) = 0.d1ebe81a95ee752e48a26bcd32 d6e922d7eb44b8ad2232f69307 95e84b56317269b9dd1dfa6 */ + 0x0.d1ebe81a95ee752e48a26bcd32p0L, + 0x0.d6e922d7eb44b8ad2232f69307p-104L, +/* sin(x) = 0.9285dc9bc45dd9ea3d02457bcc e59c4175aab6ff7929a8d28719 5525fdace200dba032874fb */ + 0x0.9285dc9bc45dd9ea3d02457bccp0L, + 0x0.e59c4175aab6ff7929a8d28719p-104L, + +/* x = 6.17187500000000000000000000000000000e-01 3ffe3c00000000000000000000000000 */ +/* cos(x) = 0.d0c5394d772228195e25736c03 574707de0af1ca344b13bd3914 bfe27518e9e426f5deff1e1 */ + 0x0.d0c5394d772228195e25736c03p0L, + 0x0.574707de0af1ca344b13bd3914p-104L, +/* sin(x) = 0.94288e48bd0335fc41c4cbd292 0497a8f5d1d8185c99fa0081f9 0c27e2a53ffdd208a0dbe69 */ + 0x0.94288e48bd0335fc41c4cbd292p0L, + 0x0.0497a8f5d1d8185c99fa0081f9p-104L, + +/* x = 6.25000000000000000000000000000000000e-01 3ffe4000000000000000000000000000 */ +/* cos(x) = 0.cf9b476c897c25c5bfe750dd3f 308eaf7bcc1ed00179a256870f 4200445043dcdb1974b5878 */ + 0x0.cf9b476c897c25c5bfe750dd3fp0L, + 0x0.308eaf7bcc1ed00179a256870fp-104L, +/* sin(x) = 0.95c8ef544210ec0b91c49bd2aa 09e8515fa61a156ebb10f5f8c2 32a6445b61ebf3c2ec268f9 */ + 0x0.95c8ef544210ec0b91c49bd2aap0L, + 0x0.09e8515fa61a156ebb10f5f8c2p-104L, + +/* x = 6.32812500000000000000000000000000000e-01 3ffe4400000000000000000000000000 */ +/* cos(x) = 0.ce6e171f92f2e27f32225327ec 440ddaefae248413efc0e58cee e1ae369aabe73f88c87ed1a */ + 0x0.ce6e171f92f2e27f32225327ecp0L, + 0x0.440ddaefae248413efc0e58ceep-104L, +/* sin(x) = 0.9766f93cd18413a6aafc1cfc6f c28abb6817bf94ce349901ae3f 48c3215d3eb60acc5f78903 */ + 0x0.9766f93cd18413a6aafc1cfc6fp0L, + 0x0.c28abb6817bf94ce349901ae3fp-104L, + +/* x = 6.40625000000000000000000000000000000e-01 3ffe4800000000000000000000000000 */ +/* cos(x) = 0.cd3dad1b5328a2e459f993f4f5 108819faccbc4eeba9604e81c7 adad51cc8a2561631a06826 */ + 0x0.cd3dad1b5328a2e459f993f4f5p0L, + 0x0.108819faccbc4eeba9604e81c7p-104L, +/* sin(x) = 0.9902a58a45e27bed68412b426b 675ed503f54d14c8172e0d373f 42cadf04daf67319a7f94be */ + 0x0.9902a58a45e27bed68412b426bp0L, + 0x0.675ed503f54d14c8172e0d373fp-104L, + +/* x = 6.48437500000000000000000000000000000e-01 3ffe4c00000000000000000000000000 */ +/* cos(x) = 0.cc0a0e21709883a3ff00911e11 a07ee3bd7ea2b04e081be99be0 264791170761ae64b8b744a */ + 0x0.cc0a0e21709883a3ff00911e11p0L, + 0x0.a07ee3bd7ea2b04e081be99be0p-104L, +/* sin(x) = 0.9a9bedcdf01b38d993f3d78207 81de292033ead73b89e28f3931 3dbe3a6e463f845b5fa8490 */ + 0x0.9a9bedcdf01b38d993f3d78207p0L, + 0x0.81de292033ead73b89e28f3931p-104L, + +/* x = 6.56250000000000000000000000000000000e-01 3ffe5000000000000000000000000000 */ +/* cos(x) = 0.cad33f00658fe5e8204bbc0f3a 66a0e6a773f87987a780b243d7 be83b3db1448ca0e0e62787 */ + 0x0.cad33f00658fe5e8204bbc0f3ap0L, + 0x0.66a0e6a773f87987a780b243d7p-104L, +/* sin(x) = 0.9c32cba2b14156ef05256c4f85 7991ca6a547cd7ceb1ac8a8e62 a282bd7b9183648a462bd04 */ + 0x0.9c32cba2b14156ef05256c4f85p0L, + 0x0.7991ca6a547cd7ceb1ac8a8e62p-104L, + +/* x = 6.64062500000000000000000000000000000e-01 3ffe5400000000000000000000000000 */ +/* cos(x) = 0.c99944936cf48c8911ff93fe64 b3ddb7981e414bdaf6aae12035 77de44878c62bc3bc9cf7b9 */ + 0x0.c99944936cf48c8911ff93fe64p0L, + 0x0.b3ddb7981e414bdaf6aae12035p-104L, +/* sin(x) = 0.9dc738ad14204e689ac582d0f8 5826590feece34886cfefe2e08 cf2bb8488d55424dc9d3525 */ + 0x0.9dc738ad14204e689ac582d0f8p0L, + 0x0.5826590feece34886cfefe2e08p-104L, + +/* x = 6.71875000000000000000000000000000000e-01 3ffe5800000000000000000000000000 */ +/* cos(x) = 0.c85c23c26ed7b6f014ef546c47 929682122876bfbf157de0aff3 c4247d820c746e32cd4174f */ + 0x0.c85c23c26ed7b6f014ef546c47p0L, + 0x0.929682122876bfbf157de0aff3p-104L, +/* sin(x) = 0.9f592e9b66a9cf906a3c7aa3c1 0199849040c45ec3f0a7475973 11038101780c5f266059dbf */ + 0x0.9f592e9b66a9cf906a3c7aa3c1p0L, + 0x0.0199849040c45ec3f0a7475973p-104L, + +/* x = 6.79687500000000000000000000000000000e-01 3ffe5c00000000000000000000000000 */ +/* cos(x) = 0.c71be181ecd6875ce2da5615a0 3cca207d9adcb9dfb0a1d6c40a 4f0056437f1a59ccddd06ee */ + 0x0.c71be181ecd6875ce2da5615a0p0L, + 0x0.3cca207d9adcb9dfb0a1d6c40ap-104L, +/* sin(x) = 0.a0e8a725d33c828c11fa50fd9e 9a15ffecfad43f3e534358076b 9b0f6865694842b1e8c67dc */ + 0x0.a0e8a725d33c828c11fa50fd9ep0L, + 0x0.9a15ffecfad43f3e534358076bp-104L, + +/* x = 6.87500000000000000000000000000000000e-01 3ffe6000000000000000000000000000 */ +/* cos(x) = 0.c5d882d2ee48030c7c07d28e98 1e34804f82ed4cf93655d23653 89b716de6ad44676a1cc5da */ + 0x0.c5d882d2ee48030c7c07d28e98p0L, + 0x0.1e34804f82ed4cf93655d23653p-104L, +/* sin(x) = 0.a2759c0e79c35582527c32b55f 5405c182c66160cb1d9eb7bb0b 7cdf4ad66f317bda4332914 */ + 0x0.a2759c0e79c35582527c32b55fp0L, + 0x0.5405c182c66160cb1d9eb7bb0bp-104L, + +/* x = 6.95312500000000000000000000000000000e-01 3ffe6400000000000000000000000000 */ +/* cos(x) = 0.c4920cc2ec38fb891b38827db0 8884fc66371ac4c2052ca8885b 981bbcfd3bb7b093ee31515 */ + 0x0.c4920cc2ec38fb891b38827db0p0L, + 0x0.8884fc66371ac4c2052ca8885bp-104L, +/* sin(x) = 0.a400072188acf49cd6b173825e 038346f105e1301afe642bcc36 4cea455e21e506e3e927ed8 */ + 0x0.a400072188acf49cd6b173825ep0L, + 0x0.038346f105e1301afe642bcc36p-104L, + +/* x = 7.03125000000000000000000000000000000e-01 3ffe6800000000000000000000000000 */ +/* cos(x) = 0.c348846bbd3631338ffe2bfe9d d1381a35b4e9c0c51b4c13fe37 6bad1bf5caacc4542be0aa9 */ + 0x0.c348846bbd3631338ffe2bfe9dp0L, + 0x0.d1381a35b4e9c0c51b4c13fe37p-104L, +/* sin(x) = 0.a587e23555bb08086d02b9c662 cdd29316c3e9bd08d93793634a 21b1810cce73bdb97a99b9e */ + 0x0.a587e23555bb08086d02b9c662p0L, + 0x0.cdd29316c3e9bd08d93793634ap-104L, + +/* x = 7.10937500000000000000000000000000000e-01 3ffe6c00000000000000000000000000 */ +/* cos(x) = 0.c1fbeef380e4ffdd5a613ec872 2f643ffe814ec2343e53adb549 627224fdc9f2a7b77d3d69f */ + 0x0.c1fbeef380e4ffdd5a613ec872p0L, + 0x0.2f643ffe814ec2343e53adb549p-104L, +/* sin(x) = 0.a70d272a76a8d4b6da0ec90712 bb748b96dabf88c3079246f3db 7eea6e58ead4ed0e2843303 */ + 0x0.a70d272a76a8d4b6da0ec90712p0L, + 0x0.bb748b96dabf88c3079246f3dbp-104L, + +/* x = 7.18750000000000000000000000000000000e-01 3ffe7000000000000000000000000000 */ +/* cos(x) = 0.c0ac518c8b6ae710ba37a3eeb9 0cb15aebcb8bed4356fb507a48 a6e97de9aa6d9660116b436 */ + 0x0.c0ac518c8b6ae710ba37a3eeb9p0L, + 0x0.0cb15aebcb8bed4356fb507a48p-104L, +/* sin(x) = 0.a88fcfebd9a8dd47e2f3c76ef9 e2439920f7e7fbe735f8bcc985 491ec6f12a2d4214f8cfa99 */ + 0x0.a88fcfebd9a8dd47e2f3c76ef9p0L, + 0x0.e2439920f7e7fbe735f8bcc985p-104L, + +/* x = 7.26562500000000000000000000000000000e-01 3ffe7400000000000000000000000000 */ +/* cos(x) = 0.bf59b17550a440687596929656 7cf3e3b4e483061877c02811c6 cae85fad5a6c3da58f49292 */ + 0x0.bf59b17550a440687596929656p0L, + 0x0.7cf3e3b4e483061877c02811c6p-104L, +/* sin(x) = 0.aa0fd66eddb921232c28520d39 11b8a03193b47f187f1471ac21 6fbcd5bb81029294d3a73f1 */ + 0x0.aa0fd66eddb921232c28520d39p0L, + 0x0.11b8a03193b47f187f1471ac21p-104L, + +/* x = 7.34375000000000000000000000000000000e-01 3ffe7800000000000000000000000000 */ +/* cos(x) = 0.be0413f84f2a771c614946a88c bf4da1d75a5560243de8f2283f efa0ea4a48468a52d51d8b3 */ + 0x0.be0413f84f2a771c614946a88cp0L, + 0x0.bf4da1d75a5560243de8f2283fp-104L, +/* sin(x) = 0.ab8d34b36acd987210ed343ec6 5d7e3adc2e7109fce43d55c8d5 7dfdf55b9e01d2cc1f1b9ec */ + 0x0.ab8d34b36acd987210ed343ec6p0L, + 0x0.5d7e3adc2e7109fce43d55c8d5p-104L, + +/* x = 7.42187500000000000000000000000000000e-01 3ffe7c00000000000000000000000000 */ +/* cos(x) = 0.bcab7e6bfb2a14a9b122c574a3 76bec98ab14808c64a4e731b34 047e217611013ac99c0f25d */ + 0x0.bcab7e6bfb2a14a9b122c574a3p0L, + 0x0.76bec98ab14808c64a4e731b34p-104L, +/* sin(x) = 0.ad07e4c409d08c4fa3a9057bb0 ac24b8636e74e76f51e09bd6b2 319707cbd9f5e254643897a */ + 0x0.ad07e4c409d08c4fa3a9057bb0p0L, + 0x0.ac24b8636e74e76f51e09bd6b2p-104L, + +/* x = 7.50000000000000000000000000000000000e-01 3ffe8000000000000000000000000000 */ +/* cos(x) = 0.bb4ff632a908f73ec151839cb9 d993b4e0bfb8f20e7e44e6e4ae e845e35575c3106dbe6fd06 */ + 0x0.bb4ff632a908f73ec151839cb9p0L, + 0x0.d993b4e0bfb8f20e7e44e6e4aep-104L, +/* sin(x) = 0.ae7fe0b5fc786b2d966e1d6af1 40a488476747c2646425fc7533 f532cd044cb10a971a49a6a */ + 0x0.ae7fe0b5fc786b2d966e1d6af1p0L, + 0x0.40a488476747c2646425fc7533p-104L, + +/* x = 7.57812500000000000000000000000000000e-01 3ffe8400000000000000000000000000 */ +/* cos(x) = 0.b9f180ba77dd0751628e135a95 08299012230f14becacdd14c3f 8862d122de5b56d55b53360 */ + 0x0.b9f180ba77dd0751628e135a95p0L, + 0x0.08299012230f14becacdd14c3fp-104L, +/* sin(x) = 0.aff522a954f2ba16d9defdc416 e33f5e9a5dfd5a6c228e0abc4d 521327ff6e2517a7b3851dd */ + 0x0.aff522a954f2ba16d9defdc416p0L, + 0x0.e33f5e9a5dfd5a6c228e0abc4dp-104L, + +/* x = 7.65625000000000000000000000000000000e-01 3ffe8800000000000000000000000000 */ +/* cos(x) = 0.b890237d3bb3c284b614a05390 16bfa1053730bbdf940fa895e1 85f8e58884d3dda15e63371 */ + 0x0.b890237d3bb3c284b614a05390p0L, + 0x0.16bfa1053730bbdf940fa895e1p-104L, +/* sin(x) = 0.b167a4c90d63c4244cf5493b7c c23bd3c3c1225e078baa0c53d6 d400b926281f537a1a260e6 */ + 0x0.b167a4c90d63c4244cf5493b7cp0L, + 0x0.c23bd3c3c1225e078baa0c53d6p-104L, + +/* x = 7.73437500000000000000000000000000000e-01 3ffe8c00000000000000000000000000 */ +/* cos(x) = 0.b72be40067aaf2c050dbdb7a14 c3d7d4f203f6b3f0224a4afe55 d6ec8e92b508fd5c5984b3b */ + 0x0.b72be40067aaf2c050dbdb7a14p0L, + 0x0.c3d7d4f203f6b3f0224a4afe55p-104L, +/* sin(x) = 0.b2d7614b1f3aaa24df2d6e20a7 7e1ca3e6d838c03e29c1bcb026 e6733324815fadc9eb89674 */ + 0x0.b2d7614b1f3aaa24df2d6e20a7p0L, + 0x0.7e1ca3e6d838c03e29c1bcb026p-104L, + +/* x = 7.81250000000000000000000000000000000e-01 3ffe9000000000000000000000000000 */ +/* cos(x) = 0.b5c4c7d4f7dae915ac786ccf4b 1a498d3e73b6e5e74fe7519d9c 53ee6d6b90e881bddfc33e1 */ + 0x0.b5c4c7d4f7dae915ac786ccf4bp0L, + 0x0.1a498d3e73b6e5e74fe7519d9cp-104L, +/* sin(x) = 0.b44452709a5975290591376543 4a59d111f0433eb2b133f7d103 207e2aeb4aae111ddc385b3 */ + 0x0.b44452709a5975290591376543p0L, + 0x0.4a59d111f0433eb2b133f7d103p-104L, + +/* x = 7.89062500000000000000000000000000000e-01 3ffe9400000000000000000000000000 */ +/* cos(x) = 0.b45ad4975b1294cadca4cf40ec 8f22a68cd14b175835239a37e6 3acb85e8e9505215df18140 */ + 0x0.b45ad4975b1294cadca4cf40ecp0L, + 0x0.8f22a68cd14b175835239a37e6p-104L, +/* sin(x) = 0.b5ae7285bc10cf515753847e8f 8b7a30e0a580d929d770103509 880680f7b8b0e8ad23b65d8 */ + 0x0.b5ae7285bc10cf515753847e8fp0L, + 0x0.8b7a30e0a580d929d770103509p-104L +}; diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c new file mode 100644 index 0000000000..75735db18e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c @@ -0,0 +1,230 @@ +/* Test iscanonical and canonicalizel for ldbl-128ibm. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_ldbl.h> +#include <stdbool.h> +#include <stdio.h> + +struct test +{ + double hi, lo; + bool canonical; +}; + +static const struct test tests[] = + { + { __builtin_nan (""), 0.0, true }, + { __builtin_nan (""), DBL_MAX, true }, + { __builtin_nan (""), __builtin_inf (), true }, + { __builtin_nan (""), __builtin_nan (""), true }, + { __builtin_nan (""), __builtin_nans (""), true }, + { __builtin_nans (""), 0.0, true }, + { __builtin_nans (""), DBL_MAX, true }, + { __builtin_nans (""), __builtin_inf (), true }, + { __builtin_nans (""), __builtin_nan (""), true }, + { __builtin_nans (""), __builtin_nans (""), true }, + { __builtin_inf (), 0.0, true }, + { __builtin_inf (), -0.0, true }, + { -__builtin_inf (), 0.0, true }, + { -__builtin_inf (), -0.0, true }, + { __builtin_inf (), DBL_TRUE_MIN, false }, + { __builtin_inf (), -DBL_TRUE_MIN, false }, + { -__builtin_inf (), DBL_TRUE_MIN, false }, + { -__builtin_inf (), -DBL_TRUE_MIN, false }, + { __builtin_inf (), DBL_MIN, false }, + { __builtin_inf (), -DBL_MIN, false }, + { -__builtin_inf (), DBL_MIN, false }, + { -__builtin_inf (), -DBL_MIN, false }, + { __builtin_inf (), __builtin_inf (), false }, + { __builtin_inf (), -__builtin_inf (), false }, + { -__builtin_inf (), __builtin_inf (), false }, + { -__builtin_inf (), -__builtin_inf (), false }, + { __builtin_inf (), __builtin_nan (""), false }, + { __builtin_inf (), -__builtin_nan (""), false }, + { -__builtin_inf (), __builtin_nan (""), false }, + { -__builtin_inf (), -__builtin_nan (""), false }, + { 0.0, 0.0, true }, + { 0.0, -0.0, true }, + { -0.0, 0.0, true }, + { -0.0, -0.0, true }, + { 0.0, DBL_TRUE_MIN, false }, + { 0.0, -DBL_TRUE_MIN, false }, + { -0.0, DBL_TRUE_MIN, false }, + { -0.0, -DBL_TRUE_MIN, false }, + { 0.0, DBL_MAX, false }, + { 0.0, -DBL_MAX, false }, + { -0.0, DBL_MAX, false }, + { -0.0, -DBL_MAX, false }, + { 0.0, __builtin_inf (), false }, + { 0.0, -__builtin_inf (), false }, + { -0.0, __builtin_inf (), false }, + { -0.0, -__builtin_inf (), false }, + { 0.0, __builtin_nan (""), false }, + { 0.0, -__builtin_nan (""), false }, + { -0.0, __builtin_nan (""), false }, + { -0.0, -__builtin_nan (""), false }, + { 1.0, 0.0, true }, + { 1.0, -0.0, true }, + { -1.0, 0.0, true }, + { -1.0, -0.0, true }, + { 1.0, DBL_TRUE_MIN, true }, + { 1.0, -DBL_TRUE_MIN, true }, + { -1.0, DBL_TRUE_MIN, true }, + { -1.0, -DBL_TRUE_MIN, true }, + { 1.0, DBL_MAX, false }, + { 1.0, -DBL_MAX, false }, + { -1.0, DBL_MAX, false }, + { -1.0, -DBL_MAX, false }, + { 1.0, __builtin_inf (), false }, + { 1.0, -__builtin_inf (), false }, + { -1.0, __builtin_inf (), false }, + { -1.0, -__builtin_inf (), false }, + { 1.0, __builtin_nan (""), false }, + { 1.0, -__builtin_nan (""), false }, + { -1.0, __builtin_nan (""), false }, + { -1.0, -__builtin_nan (""), false }, + { 0x1p1023, 0x1.1p969, true }, + { 0x1p1023, -0x1.1p969, true }, + { -0x1p1023, 0x1.1p969, true }, + { -0x1p1023, -0x1.1p969, true }, + { 0x1p1023, 0x1.1p970, false }, + { 0x1p1023, -0x1.1p970, false }, + { -0x1p1023, 0x1.1p970, false }, + { -0x1p1023, -0x1.1p970, false }, + { 0x1p1023, 0x1p970, true }, + { 0x1p1023, -0x1p970, true }, + { -0x1p1023, 0x1p970, true }, + { -0x1p1023, -0x1p970, true }, + { 0x1.0000000000001p1023, 0x1p970, false }, + { 0x1.0000000000001p1023, -0x1p970, false }, + { -0x1.0000000000001p1023, 0x1p970, false }, + { -0x1.0000000000001p1023, -0x1p970, false }, + { 0x1p-969, 0x1.1p-1023, true }, + { 0x1p-969, -0x1.1p-1023, true }, + { -0x1p-969, 0x1.1p-1023, true }, + { -0x1p-969, -0x1.1p-1023, true }, + { 0x1p-969, 0x1.1p-1022, false }, + { 0x1p-969, -0x1.1p-1022, false }, + { -0x1p-969, 0x1.1p-1022, false }, + { -0x1p-969, -0x1.1p-1022, false }, + { 0x1p-969, 0x1p-1022, true }, + { 0x1p-969, -0x1p-1022, true }, + { -0x1p-969, 0x1p-1022, true }, + { -0x1p-969, -0x1p-1022, true }, + { 0x1.0000000000001p-969, 0x1p-1022, false }, + { 0x1.0000000000001p-969, -0x1p-1022, false }, + { -0x1.0000000000001p-969, 0x1p-1022, false }, + { -0x1.0000000000001p-969, -0x1p-1022, false }, + { 0x1p-970, 0x1.1p-1024, true }, + { 0x1p-970, -0x1.1p-1024, true }, + { -0x1p-970, 0x1.1p-1024, true }, + { -0x1p-970, -0x1.1p-1024, true }, + { 0x1p-970, 0x1.1p-1023, false }, + { 0x1p-970, -0x1.1p-1023, false }, + { -0x1p-970, 0x1.1p-1023, false }, + { -0x1p-970, -0x1.1p-1023, false }, + { 0x1p-970, 0x1p-1023, true }, + { 0x1p-970, -0x1p-1023, true }, + { -0x1p-970, 0x1p-1023, true }, + { -0x1p-970, -0x1p-1023, true }, + { 0x1.0000000000001p-970, 0x1p-1023, false }, + { 0x1.0000000000001p-970, -0x1p-1023, false }, + { -0x1.0000000000001p-970, 0x1p-1023, false }, + { -0x1.0000000000001p-970, -0x1p-1023, false }, + { 0x1p-1000, 0x1.1p-1054, true }, + { 0x1p-1000, -0x1.1p-1054, true }, + { -0x1p-1000, 0x1.1p-1054, true }, + { -0x1p-1000, -0x1.1p-1054, true }, + { 0x1p-1000, 0x1.1p-1053, false }, + { 0x1p-1000, -0x1.1p-1053, false }, + { -0x1p-1000, 0x1.1p-1053, false }, + { -0x1p-1000, -0x1.1p-1053, false }, + { 0x1p-1000, 0x1p-1053, true }, + { 0x1p-1000, -0x1p-1053, true }, + { -0x1p-1000, 0x1p-1053, true }, + { -0x1p-1000, -0x1p-1053, true }, + { 0x1.0000000000001p-1000, 0x1p-1053, false }, + { 0x1.0000000000001p-1000, -0x1p-1053, false }, + { -0x1.0000000000001p-1000, 0x1p-1053, false }, + { -0x1.0000000000001p-1000, -0x1p-1053, false }, + { 0x1p-1021, 0x1p-1074, true }, + { 0x1p-1021, -0x1p-1074, true }, + { -0x1p-1021, 0x1p-1074, true }, + { -0x1p-1021, -0x1p-1074, true }, + { 0x1.0000000000001p-1021, 0x1p-1074, false }, + { 0x1.0000000000001p-1021, -0x1p-1074, false }, + { -0x1.0000000000001p-1021, 0x1p-1074, false }, + { -0x1.0000000000001p-1021, -0x1p-1074, false }, + { 0x1p-1022, 0x1p-1074, false }, + { 0x1p-1022, -0x1p-1074, false }, + { -0x1p-1022, 0x1p-1074, false }, + { -0x1p-1022, -0x1p-1074, false }, + }; + +static int +do_test (void) +{ + int result = 0; + + for (size_t i = 0; i < sizeof (tests) / sizeof (tests[0]); i++) + { + long double ld = ldbl_pack (tests[i].hi, tests[i].lo); + bool canonical = iscanonical (ld); + if (canonical == tests[i].canonical) + { + printf ("PASS: iscanonical test %zu\n", i); + long double ldc = 12345.0L; + bool canonicalize_ret = canonicalizel (&ldc, &ld); + if (canonicalize_ret == !canonical) + { + printf ("PASS: canonicalizel test %zu\n", i); + bool canon_ok; + if (!canonical) + canon_ok = ldc == 12345.0L; + else if (isnan (ld)) + canon_ok = isnan (ldc) && !issignaling (ldc); + else + canon_ok = ldc == ld; + if (canon_ok) + printf ("PASS: canonicalized value test %zu\n", i); + else + { + printf ("FAIL: canonicalized value test %zu\n", i); + result = 1; + } + } + else + { + printf ("FAIL: canonicalizel test %zu\n", i); + result = 1; + } + } + else + { + printf ("FAIL: iscanonical test %zu\n", i); + result = 1; + } + } + + return result; +} + +#define TEST_FUNCTION do_test () +#include "../test-skeleton.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-fmodl-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-fmodl-ldbl-128ibm.c new file mode 100644 index 0000000000..c9bfcfc5a8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-fmodl-ldbl-128ibm.c @@ -0,0 +1,21 @@ +/* Test for ldbl-128ibm fmodl handling of equal values (bug 19602). + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define FUNC fmodl +#define SETUP +#include "test-fmodrem-ldbl-128ibm.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-fmodrem-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-fmodrem-ldbl-128ibm.c new file mode 100644 index 0000000000..a7cc042a15 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-fmodrem-ldbl-128ibm.c @@ -0,0 +1,84 @@ +/* Test for ldbl-128ibm fmodl etc. handling of equal values. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <float.h> +#include <math.h> +#include <stdio.h> + +/* FUNC is defined to be the name of the function to test. */ +#define STRX(x) #x +#define STR(x) STRX (x) +#define SFUNC STR (FUNC) + +union u +{ + long double ld; + double d[2]; +}; + +volatile union u p1 = { .d = { DBL_MIN, 0.0 } }; +volatile union u p2 = { .d = { DBL_MIN, -0.0 } }; +volatile union u m1 = { .d = { -DBL_MIN, 0.0 } }; +volatile union u m2 = { .d = { -DBL_MIN, -0.0 } }; + +static int +test_func (const char *s, long double x, long double y, long double expected) +{ + volatile long double r; + r = FUNC (x, y); + if (r != expected || copysignl (1.0, r) != copysignl (1.0, expected)) + { + printf ("FAIL: " SFUNC " (%s)\n", s); + return 1; + } + else + { + printf ("PASS: " SFUNC " (%s)\n", s); + return 0; + } +} + +#define TEST_FUNC(a, b, e) test_func (#a ", " #b, a, b, e) + +static int +do_test (void) +{ + int result = 0; + SETUP; + result |= TEST_FUNC (p1.ld, p1.ld, 0.0L); + result |= TEST_FUNC (p1.ld, p2.ld, 0.0L); + result |= TEST_FUNC (p1.ld, m1.ld, 0.0L); + result |= TEST_FUNC (p1.ld, m2.ld, 0.0L); + result |= TEST_FUNC (p2.ld, p1.ld, 0.0L); + result |= TEST_FUNC (p2.ld, p2.ld, 0.0L); + result |= TEST_FUNC (p2.ld, m1.ld, 0.0L); + result |= TEST_FUNC (p2.ld, m2.ld, 0.0L); + result |= TEST_FUNC (m1.ld, p1.ld, -0.0L); + result |= TEST_FUNC (m1.ld, p2.ld, -0.0L); + result |= TEST_FUNC (m1.ld, m1.ld, -0.0L); + result |= TEST_FUNC (m1.ld, m2.ld, -0.0L); + result |= TEST_FUNC (m2.ld, p1.ld, -0.0L); + result |= TEST_FUNC (m2.ld, p2.ld, -0.0L); + result |= TEST_FUNC (m2.ld, m1.ld, -0.0L); + result |= TEST_FUNC (m2.ld, m2.ld, -0.0L); + return result; +} + +#define TEST_FUNCTION do_test () +#include "../../../test-skeleton.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-remainderl-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-remainderl-ldbl-128ibm.c new file mode 100644 index 0000000000..32b18be741 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-remainderl-ldbl-128ibm.c @@ -0,0 +1,21 @@ +/* Test for ldbl-128ibm remainderl handling of equal values (bug 19677). + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define FUNC remainderl +#define SETUP fesetround (FE_DOWNWARD) +#include "test-fmodrem-ldbl-128ibm.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-remquol-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-remquol-ldbl-128ibm.c new file mode 100644 index 0000000000..f0d48420b8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-remquol-ldbl-128ibm.c @@ -0,0 +1,30 @@ +/* Test for ldbl-128ibm remquol handling of equal values (bug 19677). + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +static long double +wrap_remquol (long double x, long double y) +{ + int quo; + return remquol (x, y, &quo); +} + +#define FUNC wrap_remquol +#define SETUP fesetround (FE_DOWNWARD) +#include "test-fmodrem-ldbl-128ibm.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c new file mode 100644 index 0000000000..eaada2f848 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c @@ -0,0 +1,73 @@ +/* Test totalorderl and totalordermagl for ldbl-128ibm. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_ldbl.h> +#include <stdbool.h> +#include <stdio.h> + +struct test +{ + double hi, lo1, lo2; +}; + +static const struct test tests[] = + { + { __builtin_nan (""), 1, __builtin_nans ("") }, + { -__builtin_nan (""), 1, __builtin_nans ("") }, + { __builtin_nans (""), 1, __builtin_nan ("") }, + { -__builtin_nans (""), 1, __builtin_nan ("") }, + { __builtin_inf (), 0.0, -0.0 }, + { -__builtin_inf (), 0.0, -0.0 }, + { 1.5, 0.0, -0.0 }, + }; + +static int +do_test (void) +{ + int result = 0; + + for (size_t i = 0; i < sizeof (tests) / sizeof (tests[0]); i++) + { + long double ldx = ldbl_pack (tests[i].hi, tests[i].lo1); + long double ldy = ldbl_pack (tests[i].hi, tests[i].lo2); + bool to1 = totalorderl (ldx, ldy); + bool to2 = totalorderl (ldy, ldx); + if (to1 && to2) + printf ("PASS: test %zu\n", i); + else + { + printf ("FAIL: test %zu\n", i); + result = 1; + } + to1 = totalordermagl (ldx, ldy); + to2 = totalordermagl (ldy, ldx); + if (to1 && to2) + printf ("PASS: test %zu (totalordermagl)\n", i); + else + { + printf ("FAIL: test %zu (totalordermagl)\n", i); + result = 1; + } + } + + return result; +} + +#define TEST_FUNCTION do_test () +#include "../test-skeleton.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/tst-strtold-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/tst-strtold-ldbl-128ibm.c new file mode 100644 index 0000000000..1181892165 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/tst-strtold-ldbl-128ibm.c @@ -0,0 +1,85 @@ +/* Test for ldbl-128ibm strtold overflow to infinity (bug 14551). + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <fenv.h> +#include <math.h> +#include <stdio.h> +#include <stdlib.h> + +static int +test_strtold_value (const char *s, double exp_hi, double exp_lo, int exp_exc, + int exp_errno) +{ + int result = 0; + union { long double ld; double d[2]; } x; + feclearexcept (FE_ALL_EXCEPT); + errno = 0; + x.ld = strtold (s, NULL); + int exc = fetestexcept (FE_ALL_EXCEPT); + int new_errno = errno; + printf ("strtold (\"%s\") returned (%a, %a), exceptions 0x%x, errno %d\n", + s, x.d[0], x.d[1], exc, new_errno); + if (x.d[0] == exp_hi) + printf ("PASS: strtold (\"%s\") high == %a\n", s, exp_hi); + else + { + printf ("FAIL: strtold (\"%s\") high == %a\n", s, exp_hi); + result = 1; + } + if (x.d[1] == exp_lo) + printf ("PASS: strtold (\"%s\") low == %a\n", s, exp_lo); + else + { + printf ("FAIL: strtold (\"%s\") low == %a\n", s, exp_lo); + result = 1; + } + if (exc == exp_exc) + printf ("PASS: strtold (\"%s\") exceptions 0x%x\n", s, exp_exc); + else + { + printf ("FAIL: strtold (\"%s\") exceptions 0x%x\n", s, exp_exc); + result = 1; + } + if (new_errno == exp_errno) + printf ("PASS: strtold (\"%s\") errno %d\n", s, exp_errno); + else + { + printf ("FAIL: strtold (\"%s\") errno %d\n", s, exp_errno); + result = 1; + } + return result; +} + +static int +do_test (void) +{ + int result = 0; + result |= test_strtold_value ("0x1.fffffffffffff8p+1023", INFINITY, 0, + FE_OVERFLOW | FE_INEXACT, ERANGE); + result |= test_strtold_value ("-0x1.fffffffffffff8p+1023", -INFINITY, 0, + FE_OVERFLOW | FE_INEXACT, ERANGE); + result |= test_strtold_value ("0x1.ffffffffffffffp+1023", INFINITY, 0, + FE_OVERFLOW | FE_INEXACT, ERANGE); + result |= test_strtold_value ("-0x1.ffffffffffffffp+1023", -INFINITY, 0, + FE_OVERFLOW | FE_INEXACT, ERANGE); + return result; +} + +#define TEST_FUNCTION do_test () +#include "../../../test-skeleton.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/w_expl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/w_expl_compat.c new file mode 100644 index 0000000000..c9d44b61dd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/w_expl_compat.c @@ -0,0 +1,21 @@ +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __expl(long double x) /* wrapper exp */ +{ + long double z; + z = __ieee754_expl(x); + if (_LIB_VERSION == _IEEE_) + return z; + if (isfinite(x)) + { + if (!isfinite (z)) + return __kernel_standard_l(x,x,206); /* exp overflow */ + else if (z == 0.0L) + return __kernel_standard_l(x,x,207); /* exp underflow */ + } + return z; +} +hidden_def (__expl) +long_double_symbol (libm, __expl, expl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c new file mode 100644 index 0000000000..0bdb9a1848 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c @@ -0,0 +1,93 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_split.h> +#include <stdlib.h> + +/* Calculate X + Y exactly and store the result in *HI + *LO. It is + given that |X| >= |Y| and the values are small enough that no + overflow occurs. */ + +static inline void +add_split (double *hi, double *lo, double x, double y) +{ + /* Apply Dekker's algorithm. */ + *hi = x + y; + *lo = (x - *hi) + y; +} + +/* Compare absolute values of floating-point values pointed to by P + and Q for qsort. */ + +static int +compare (const void *p, const void *q) +{ + double pd = fabs (*(const double *) p); + double qd = fabs (*(const double *) q); + if (pd < qd) + return -1; + else if (pd == qd) + return 0; + else + return 1; +} + +/* Return X^2 + Y^2 - 1, computed without large cancellation error. + It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >= + 0.5. */ + +long double +__x2y2m1l (long double x, long double y) +{ + double vals[13]; + SET_RESTORE_ROUND (FE_TONEAREST); + union ibm_extended_long_double xu, yu; + xu.ld = x; + yu.ld = y; + if (fabs (xu.d[1].d) < 0x1p-500) + xu.d[1].d = 0.0; + if (fabs (yu.d[1].d) < 0x1p-500) + yu.d[1].d = 0.0; + mul_split (&vals[1], &vals[0], xu.d[0].d, xu.d[0].d); + mul_split (&vals[3], &vals[2], xu.d[0].d, xu.d[1].d); + vals[2] *= 2.0; + vals[3] *= 2.0; + mul_split (&vals[5], &vals[4], xu.d[1].d, xu.d[1].d); + mul_split (&vals[7], &vals[6], yu.d[0].d, yu.d[0].d); + mul_split (&vals[9], &vals[8], yu.d[0].d, yu.d[1].d); + vals[8] *= 2.0; + vals[9] *= 2.0; + mul_split (&vals[11], &vals[10], yu.d[1].d, yu.d[1].d); + vals[12] = -1.0; + qsort (vals, 13, sizeof (double), compare); + /* Add up the values so that each element of VALS has absolute value + at most equal to the last set bit of the next nonzero + element. */ + for (size_t i = 0; i <= 11; i++) + { + add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); + qsort (vals + i + 1, 12 - i, sizeof (double), compare); + } + /* Now any error from this addition will be small. */ + long double retval = (long double) vals[12]; + for (size_t i = 11; i != (size_t) -1; i--) + retval += (long double) vals[i]; + return retval; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/e_ilogbl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/e_ilogbl.c new file mode 100644 index 0000000000..75a38e13ce --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/e_ilogbl.c @@ -0,0 +1,2 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/ldbl-128/e_ilogbl.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_asinhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_asinhl.c new file mode 100644 index 0000000000..4e8a541263 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_asinhl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_asinhl.c> +long_double_symbol (libm, __asinhl, asinhl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_atanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_atanl.c new file mode 100644 index 0000000000..c23d14aade --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_atanl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_atanl.c> +long_double_symbol (libm, __atanl, atanl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_cbrtl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_cbrtl.c new file mode 100644 index 0000000000..ace5645277 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_cbrtl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_cbrtl.c> +long_double_symbol (libm, __cbrtl, cbrtl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_ceill.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_ceill.c new file mode 100644 index 0000000000..a646494f14 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_ceill.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_ceill.c> +long_double_symbol (libm, __ceill, ceill); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_copysignl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_copysignl.c new file mode 100644 index 0000000000..211e7240ac --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_copysignl.c @@ -0,0 +1,9 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_copysignl.c> +#if IS_IN (libm) +long_double_symbol (libm, __copysignl, copysignl); +#else +long_double_symbol (libc, __copysignl, copysignl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_cosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_cosl.c new file mode 100644 index 0000000000..6a7e2e3162 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_cosl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_cosl.c> +long_double_symbol (libm, __cosl, cosl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_erfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_erfl.c new file mode 100644 index 0000000000..c5f9bb3ac4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_erfl.c @@ -0,0 +1,6 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_erfl.c> +long_double_symbol (libm, __erfl, erfl); +long_double_symbol (libm, __erfcl, erfcl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_expm1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_expm1l.c new file mode 100644 index 0000000000..4fb186127f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_expm1l.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_expm1l.c> +long_double_symbol (libm, __expm1l, expm1l); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_fabsl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_fabsl.c new file mode 100644 index 0000000000..93d81d98bc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_fabsl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_fabsl.c> +long_double_symbol (libm, __fabsl, fabsl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_finitel.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_finitel.c new file mode 100644 index 0000000000..c0862a7485 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_finitel.c @@ -0,0 +1,17 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#undef hidden_def +#define hidden_def(x) +#define __finitel(arg) ___finitel(arg) +#include <sysdeps/ieee754/ldbl-128/s_finitel.c> +#undef __finitel +hidden_ver (___finitel, __finitel) +_weak_alias (___finitel, ____finitel) +#if IS_IN (libm) +long_double_symbol (libm, ____finitel, finitel); +long_double_symbol (libm, ___finitel, __finitel); +#else +long_double_symbol (libc, ____finitel, finitel); +long_double_symbol (libc, ___finitel, __finitel); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_floorl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_floorl.c new file mode 100644 index 0000000000..953043035e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_floorl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_floorl.c> +long_double_symbol (libm, __floorl, floorl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_fmal.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_fmal.c new file mode 100644 index 0000000000..218aa52b35 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_fmal.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_fmal.c> +long_double_symbol (libm, __fmal, fmal); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_fpclassifyl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_fpclassifyl.c new file mode 100644 index 0000000000..a10b6c3a1a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_fpclassifyl.c @@ -0,0 +1,10 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#define __fpclassifyl ___fpclassifyl +#undef libm_hidden_def +#define libm_hidden_def(a) +#include <sysdeps/ieee754/ldbl-128/s_fpclassifyl.c> +#undef __fpclassifyl +long_double_symbol (libm, ___fpclassifyl, __fpclassifyl); +libm_hidden_ver (___fpclassifyl, __fpclassifyl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_frexpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_frexpl.c new file mode 100644 index 0000000000..c7b6aaaaee --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_frexpl.c @@ -0,0 +1,9 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_frexpl.c> +#if IS_IN (libm) +long_double_symbol (libm, __frexpl, frexpl); +#else +long_double_symbol (libc, __frexpl, frexpl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_isinfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_isinfl.c new file mode 100644 index 0000000000..6dab0e9223 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_isinfl.c @@ -0,0 +1,16 @@ +#include <math_ldbl_opt.h> +#if !IS_IN (libm) +# undef weak_alias +# define weak_alias(n,a) +# undef hidden_def +# define hidden_def(x) +# define __isinfl(arg) ___isinfl(arg) +#endif +#include <sysdeps/ieee754/ldbl-128/s_isinfl.c> +#if !IS_IN (libm) +# undef __isinfl +hidden_ver (___isinfl, __isinfl) +_weak_alias (___isinfl, ____isinfl) +long_double_symbol (libc, ____isinfl, isinfl); +long_double_symbol (libc, ___isinfl, __isinfl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_isnanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_isnanl.c new file mode 100644 index 0000000000..ad5ecc5281 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_isnanl.c @@ -0,0 +1,16 @@ +#include <math_ldbl_opt.h> +#if !IS_IN (libm) +# undef weak_alias +# define weak_alias(n,a) +# undef hidden_def +# define hidden_def(x) +# define __isnanl(arg) ___isnanl(arg) +#endif +#include <sysdeps/ieee754/ldbl-128/s_isnanl.c> +#if !IS_IN (libm) +# undef __isnanl +hidden_ver (___isnanl, __isnanl) +_weak_alias (___isnanl, ____isnanl) +long_double_symbol (libc, ____isnanl, isnanl); +long_double_symbol (libc, ___isnanl, __isnanl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_llrintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_llrintl.c new file mode 100644 index 0000000000..1515f3abd7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_llrintl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_llrintl.c> +long_double_symbol (libm, __llrintl, llrintl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_llroundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_llroundl.c new file mode 100644 index 0000000000..ca35dae491 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_llroundl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_llroundl.c> +long_double_symbol (libm, __llroundl, llroundl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_log1pl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_log1pl.c new file mode 100644 index 0000000000..11d56bfe9f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_log1pl.c @@ -0,0 +1,2 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/ldbl-128/s_log1pl.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_logbl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_logbl.c new file mode 100644 index 0000000000..8ba8179feb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_logbl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_logbl.c> +long_double_symbol (libm, __logbl, logbl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_lrintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_lrintl.c new file mode 100644 index 0000000000..56e69c94f9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_lrintl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_lrintl.c> +long_double_symbol (libm, __lrintl, lrintl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_lroundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_lroundl.c new file mode 100644 index 0000000000..d5429e2384 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_lroundl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_lroundl.c> +long_double_symbol (libm, __lroundl, lroundl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_modfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_modfl.c new file mode 100644 index 0000000000..fa4d3ad82a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_modfl.c @@ -0,0 +1,9 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_modfl.c> +#if IS_IN (libm) +long_double_symbol (libm, __modfl, modfl); +#else +long_double_symbol (libc, __modfl, modfl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_nearbyintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_nearbyintl.c new file mode 100644 index 0000000000..a6d0a313fd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_nearbyintl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_nearbyintl.c> +long_double_symbol (libm, __nearbyintl, nearbyintl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_nextafterl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_nextafterl.c new file mode 100644 index 0000000000..64c663eda3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_nextafterl.c @@ -0,0 +1,6 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_nextafterl.c> +long_double_symbol (libm, __nextafterl, nextafterl); +long_double_symbol (libm, __nexttowardl, nexttowardl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_nexttoward.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_nexttoward.c new file mode 100644 index 0000000000..2968503d2e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_nexttoward.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_nexttoward.c> +long_double_symbol (libm, __nexttoward, nexttoward); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_nexttowardf.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_nexttowardf.c new file mode 100644 index 0000000000..64b9c24465 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_nexttowardf.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_nexttowardf.c> +long_double_symbol (libm, __nexttowardf, nexttowardf); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_remquol.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_remquol.c new file mode 100644 index 0000000000..16f0eb16a4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_remquol.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_remquol.c> +long_double_symbol (libm, __remquol, remquol); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_rintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_rintl.c new file mode 100644 index 0000000000..19af9bbdcb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_rintl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_rintl.c> +long_double_symbol (libm, __rintl, rintl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_roundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_roundl.c new file mode 100644 index 0000000000..3fa99d6f2a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_roundl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_roundl.c> +long_double_symbol (libm, __roundl, roundl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_scalblnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_scalblnl.c new file mode 100644 index 0000000000..97181d29b9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_scalblnl.c @@ -0,0 +1,4 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_scalblnl.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_scalbnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_scalbnl.c new file mode 100644 index 0000000000..15af1b2849 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_scalbnl.c @@ -0,0 +1,4 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_scalbnl.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_signbitl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_signbitl.c new file mode 100644 index 0000000000..850db7386a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_signbitl.c @@ -0,0 +1,11 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#define __signbitl(arg) ___signbitl(arg) +#include <sysdeps/ieee754/ldbl-128/s_signbitl.c> +#undef __signbitl +#if IS_IN (libm) +long_double_symbol (libm, ___signbitl, __signbitl); +#else +long_double_symbol (libc, ___signbitl, __signbitl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_sincosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_sincosl.c new file mode 100644 index 0000000000..ce0d4e2887 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_sincosl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_sincosl.c> +long_double_symbol (libm, __sincosl, sincosl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_sinl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_sinl.c new file mode 100644 index 0000000000..ebc20affdb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_sinl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_sinl.c> +long_double_symbol (libm, __sinl, sinl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_tanhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_tanhl.c new file mode 100644 index 0000000000..ede93930cd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_tanhl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_tanhl.c> +long_double_symbol (libm, __tanhl, tanhl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_tanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_tanl.c new file mode 100644 index 0000000000..6e635dfdc9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_tanl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_tanl.c> +long_double_symbol (libm, __tanl, tanl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_truncl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_truncl.c new file mode 100644 index 0000000000..6311479d01 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/s_truncl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_truncl.c> +long_double_symbol (libm, __truncl, truncl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/strtold_l.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/strtold_l.c new file mode 100644 index 0000000000..37034cb254 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/strtold_l.c @@ -0,0 +1,60 @@ +/* Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <stdlib.h> +#include <wchar.h> +#include <xlocale.h> + +/* The actual implementation for all floating point sizes is in strtod.c. + These macros tell it to produce the `long double' version, `strtold'. */ + +#define FLOAT long double +#define FLT LDBL +#ifdef USE_WIDE_CHAR +extern long double ____new_wcstold_l (const wchar_t *, wchar_t **, __locale_t); +# define STRTOF __new_wcstold_l +# define __STRTOF ____new_wcstold_l +# define ____STRTOF_INTERNAL ____wcstold_l_internal +# define STRTOF_NAN __wcstold_nan +#else +extern long double ____new_strtold_l (const char *, char **, __locale_t); +# define STRTOF __new_strtold_l +# define __STRTOF ____new_strtold_l +# define ____STRTOF_INTERNAL ____strtold_l_internal +# define STRTOF_NAN __strtold_nan +#endif +extern __typeof (__STRTOF) STRTOF; +libc_hidden_proto (__STRTOF) +libc_hidden_proto (STRTOF) +#define MPN2FLOAT __mpn_construct_long_double +#define FLOAT_HUGE_VAL HUGE_VALL + +#include <strtod_l.c> + +#ifdef __LONG_DOUBLE_MATH_OPTIONAL +# include <math_ldbl_opt.h> +# ifdef USE_WIDE_CHAR +weak_alias (____new_wcstold_l, ___new_wcstold_l); +long_double_symbol (libc, ___new_wcstold_l, wcstold_l); +long_double_symbol (libc, ____new_wcstold_l, __wcstold_l); +# else +weak_alias (____new_strtold_l, ___new_strtold_l); +long_double_symbol (libc, ___new_strtold_l, strtold_l); +long_double_symbol (libc, ____new_strtold_l, __strtold_l); +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/w_expl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/w_expl_compat.c new file mode 100644 index 0000000000..37c153e2a4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/w_expl_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/w_expl_compat.c> +long_double_symbol (libm, __expl, expl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-64-128/w_scalblnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/w_scalblnl.c new file mode 100644 index 0000000000..fef2507cd5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-64-128/w_scalblnl.c @@ -0,0 +1,26 @@ +/* Wrapper for __scalblnl handles setting errno. + Copyright (C) 2014-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define declare_mgen_alias(from, to) +#include <math-type-macros-ldouble.h> +#include <w_scalbln_template.c> +#if IS_IN (libm) +long_double_symbol (libm, __w_scalblnl, scalblnl); +#else +long_double_symbol (libc, __w_scalblnl, scalblnl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/Makefile b/REORG.TODO/sysdeps/ieee754/ldbl-96/Makefile new file mode 100644 index 0000000000..279342acdf --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/Makefile @@ -0,0 +1,21 @@ +# Makefile for sysdeps/ieee754/ldbl-96. +# Copyright (C) 2016-2017 Free Software Foundation, Inc. +# This file is part of the GNU C Library. + +# The GNU C Library is free software; you can redistribute it and/or +# modify it under the terms of the GNU Lesser General Public +# License as published by the Free Software Foundation; either +# version 2.1 of the License, or (at your option) any later version. + +# The GNU C Library is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +# Lesser General Public License for more details. + +# You should have received a copy of the GNU Lesser General Public +# License along with the GNU C Library; if not, see +# <http://www.gnu.org/licenses/>. + +ifeq ($(subdir),math) +tests += test-canonical-ldbl-96 test-totalorderl-ldbl-96 +endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/bits/iscanonical.h b/REORG.TODO/sysdeps/ieee754/ldbl-96/bits/iscanonical.h new file mode 100644 index 0000000000..2c8b786183 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/bits/iscanonical.h @@ -0,0 +1,34 @@ +/* Define iscanonical macro. ldbl-96 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_H +# error "Never use <bits/iscanonical.h> directly; include <math.h> instead." +#endif + +extern int __iscanonicall (long double __x) + __THROW __attribute__ ((__const__)); +#define __iscanonicalf(x) ((void) (__typeof (x)) (x), 1) +#define __iscanonical(x) ((void) (__typeof (x)) (x), 1) + +/* Return nonzero value if X is canonical. In IEEE interchange binary + formats, all values are canonical, but the argument must still be + converted to its semantic type for any exceptions arising from the + conversion, before being discarded; in extended precision, there + are encodings that are not consistently handled as corresponding to + any particular value of the type, and we return 0 for those. */ +#define iscanonical(x) __MATH_TG ((x), __iscanonical, (x)) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/bits/long-double.h b/REORG.TODO/sysdeps/ieee754/ldbl-96/bits/long-double.h new file mode 100644 index 0000000000..bb06df077f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/bits/long-double.h @@ -0,0 +1,20 @@ +/* Properties of long double type. ldbl-96 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* long double is distinct from double, so there is nothing to + define here. */ diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/e_acoshl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_acoshl.c new file mode 100644 index 0000000000..cf9a6db0ef --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_acoshl.c @@ -0,0 +1,61 @@ +/* e_acoshl.c -- long double version of e_acosh.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_acoshl(x) + * Method : + * Based on + * acoshl(x) = logl [ x + sqrtl(x*x-1) ] + * we have + * acoshl(x) := logl(x)+ln2, if x is large; else + * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else + * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acoshl(x) is NaN with signal if x<1. + * acoshl(NaN) is NaN without signal. + */ + +#include <math.h> +#include <math_private.h> + +static const long double +one = 1.0, +ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */ + +long double +__ieee754_acoshl(long double x) +{ + long double t; + u_int32_t se,i0,i1; + GET_LDOUBLE_WORDS(se,i0,i1,x); + if(se<0x3fff || se & 0x8000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(se >=0x401d) { /* x > 2**30 */ + if(se >=0x7fff) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */ + } else if(((se-0x3fff)|(i0^0x80000000)|i1)==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (se > 0x4000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return __log1pl(t+__ieee754_sqrtl(2.0*t+t*t)); + } +} +strong_alias (__ieee754_acoshl, __acoshl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/e_asinl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_asinl.c new file mode 100644 index 0000000000..f52b931459 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_asinl.c @@ -0,0 +1,157 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_asin(x) + * Method : + * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... + * we approximate asin(x) on [0,0.5] by + * asin(x) = x + x*x^2*R(x^2) + * + * For x in [0.5,1] + * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) + * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; + * then for x>0.98 + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) + * For x<=0.98, let pio4_hi = pio2_hi/2, then + * f = hi part of s; + * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) + * and + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double + one = 1.0L, + huge = 1.0e+4932L, + pio2_hi = 0x1.921fb54442d1846ap+0L, /* pi/2 rounded to nearest to 64 + bits. */ + pio2_lo = -0x7.6733ae8fe47c65d8p-68L, /* pi/2 - pio2_hi rounded to + nearest to 64 bits. */ + pio4_hi = 0xc.90fdaa22168c235p-4L, /* pi/4 rounded to nearest to 64 + bits. */ + + /* coefficient for R(x^2) */ + + /* asin(x) = x + x^3 pS(x^2) / qS(x^2) + 0 <= x <= 0.5 + peak relative error 1.9e-21 */ + pS0 = -1.008714657938491626019651170502036851607E1L, + pS1 = 2.331460313214179572063441834101394865259E1L, + pS2 = -1.863169762159016144159202387315381830227E1L, + pS3 = 5.930399351579141771077475766877674661747E0L, + pS4 = -6.121291917696920296944056882932695185001E-1L, + pS5 = 3.776934006243367487161248678019350338383E-3L, + + qS0 = -6.052287947630949712886794360635592886517E1L, + qS1 = 1.671229145571899593737596543114258558503E2L, + qS2 = -1.707840117062586426144397688315411324388E2L, + qS3 = 7.870295154902110425886636075950077640623E1L, + qS4 = -1.568433562487314651121702982333303458814E1L; + /* 1.000000000000000000000000000000000000000E0 */ + +long double +__ieee754_asinl (long double x) +{ + long double t, w, p, q, c, r, s; + int32_t ix; + u_int32_t se, i0, i1, k; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + ix = (ix << 16) | (i0 >> 16); + if (ix >= 0x3fff8000) + { /* |x|>= 1 */ + if (ix == 0x3fff8000 && ((i0 - 0x80000000) | i1) == 0) + /* asin(1)=+-pi/2 with inexact */ + return x * pio2_hi + x * pio2_lo; + return (x - x) / (x - x); /* asin(|x|>1) is NaN */ + } + else if (ix < 0x3ffe8000) + { /* |x|<0.5 */ + if (ix < 0x3fde8000) + { /* if |x| < 2**-33 */ + math_check_force_underflow (x); + if (huge + x > one) + return x; /* return x with inexact if x!=0 */ + } + else + { + t = x * x; + p = + t * (pS0 + + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5))))); + q = qS0 + t * (qS1 + t * (qS2 + t * (qS3 + t * (qS4 + t)))); + w = p / q; + return x + x * w; + } + } + /* 1> |x|>= 0.5 */ + w = one - fabsl (x); + t = w * 0.5; + p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5))))); + q = qS0 + t * (qS1 + t * (qS2 + t * (qS3 + t * (qS4 + t)))); + s = __ieee754_sqrtl (t); + if (ix >= 0x3ffef999) + { /* if |x| > 0.975 */ + w = p / q; + t = pio2_hi - (2.0 * (s + s * w) - pio2_lo); + } + else + { + GET_LDOUBLE_WORDS (k, i0, i1, s); + i1 = 0; + SET_LDOUBLE_WORDS (w,k,i0,i1); + c = (t - w * w) / (s + w); + r = p / q; + p = 2.0 * s * r - (pio2_lo - 2.0 * c); + q = pio4_hi - 2.0 * w; + t = pio4_hi - (p - q); + } + if ((se & 0x8000) == 0) + return t; + else + return -t; +} +strong_alias (__ieee754_asinl, __asinl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/e_atanhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_atanhl.c new file mode 100644 index 0000000000..b99a83c6ee --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_atanhl.c @@ -0,0 +1,69 @@ +/* s_atanhl.c -- long double version of s_atan.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_atanhl(x) + * Method : + * 1.Reduced x to positive by atanh(-x) = -atanh(x) + * 2.For x>=0.5 + * 1 2x x + * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x)) + * + * Special cases: + * atanhl(x) is NaN if |x| > 1 with signal; + * atanhl(NaN) is that NaN with no signal; + * atanhl(+-1) is +-INF with signal. + * + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double one = 1.0, huge = 1e4900L; + +static const long double zero = 0.0; + +long double +__ieee754_atanhl(long double x) +{ + long double t; + int32_t ix; + u_int32_t se,i0,i1; + GET_LDOUBLE_WORDS(se,i0,i1,x); + ix = se&0x7fff; + if ((ix+((((i0&0x7fffffff)|i1)|(-((i0&0x7fffffff)|i1)))>>31))>0x3fff) + /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3fff) + return x/zero; + if(ix<0x3fdf) { + math_force_eval(huge+x); + math_check_force_underflow (x); + return x; /* x<2**-32 */ + } + SET_LDOUBLE_EXP(x,ix); + if(ix<0x3ffe) { /* x < 0.5 */ + t = x+x; + t = 0.5*__log1pl(t+t*x/(one-x)); + } else + t = 0.5*__log1pl((x+x)/(one-x)); + if(se<=0x7fff) return t; else return -t; +} +strong_alias (__ieee754_atanhl, __atanhl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/e_coshl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_coshl.c new file mode 100644 index 0000000000..dd22cae363 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_coshl.c @@ -0,0 +1,87 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $"; +#endif + +/* __ieee754_coshl(x) + * Method : + * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (coshl(x) = coshl(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : coshl(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : coshl(x) := ------------------- + * 2 + * 22 <= x <= lnovft : coshl(x) := expl(x)/2 + * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2) + * ln2ovft < x : coshl(x) := huge*huge (overflow) + * + * Special cases: + * coshl(x) is |x| if x is +INF, -INF, or NaN. + * only coshl(0)=1 is exact for finite x. + */ + +#include <math.h> +#include <math_private.h> + +static const long double one = 1.0, half=0.5, huge = 1.0e4900L; + +long double +__ieee754_coshl (long double x) +{ + long double t,w; + int32_t ex; + u_int32_t mx,lx; + + /* High word of |x|. */ + GET_LDOUBLE_WORDS(ex,mx,lx,x); + ex &= 0x7fff; + + /* |x| in [0,22] */ + if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) { + /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ + if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) { + if (ex<0x3fbc) return one; /* cosh(tiny) = 1 */ + t = __expm1l(fabsl(x)); + w = one+t; + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + t = __ieee754_expl(fabsl(x)); + return half*t+half/t; + } + + /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ + if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u)) + return half*__ieee754_expl(fabsl(x)); + + /* |x| in [log(maxdouble), log(2*maxdouble)) */ + if (ex == 0x400c && (mx < 0xb174ddc0u + || (mx == 0xb174ddc0u && lx < 0x31aec0ebu))) + { + w = __ieee754_expl(half*fabsl(x)); + t = half*w; + return t*w; + } + + /* x is INF or NaN */ + if(ex==0x7fff) return x*x; + + /* |x| >= log(2*maxdouble), cosh(x) overflow */ + return huge*huge; +} +strong_alias (__ieee754_coshl, __coshl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/e_gammal_r.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_gammal_r.c new file mode 100644 index 0000000000..7e42cc1161 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_gammal_r.c @@ -0,0 +1,210 @@ +/* Implementation of gamma function according to ISO C. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const long double gamma_coeff[] = + { + 0x1.5555555555555556p-4L, + -0xb.60b60b60b60b60bp-12L, + 0x3.4034034034034034p-12L, + -0x2.7027027027027028p-12L, + 0x3.72a3c5631fe46aep-12L, + -0x7.daac36664f1f208p-12L, + 0x1.a41a41a41a41a41ap-8L, + -0x7.90a1b2c3d4e5f708p-8L, + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 1766, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static long double +gammal_positive (long double x, int *exp2_adj) +{ + int local_signgam; + if (x < 0.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x; + } + else if (x <= 1.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam)); + } + else if (x < 7.5L) + { + /* Adjust into the range for using exp (lgamma). */ + *exp2_adj = 0; + long double n = __ceill (x - 1.5L); + long double x_adj = x - n; + long double eps; + long double prod = __gamma_productl (x_adj, 0, n, &eps); + return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam)) + * prod * (1.0L + eps)); + } + else + { + long double eps = 0; + long double x_eps = 0; + long double x_adj = x; + long double prod = 1; + if (x < 13.0L) + { + /* Adjust into the range for applying Stirling's + approximation. */ + long double n = __ceill (13.0L - x); + x_adj = x + n; + x_eps = (x - (x_adj - n)); + prod = __gamma_productl (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + long double exp_adj = -eps; + long double x_adj_int = __roundl (x_adj); + long double x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + long double x_adj_mant = __frexpl (x_adj, &x_adj_log2); + if (x_adj_mant < M_SQRT1_2l) + { + x_adj_log2--; + x_adj_mant *= 2.0L; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + long double ret = (__ieee754_powl (x_adj_mant, x_adj) + * __ieee754_exp2l (x_adj_log2 * x_adj_frac) + * __ieee754_expl (-x_adj) + * __ieee754_sqrtl (2 * M_PIl / x_adj) + / prod); + exp_adj += x_eps * __ieee754_logl (x_adj); + long double bsum = gamma_coeff[NCOEFF - 1]; + long double x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1l (exp_adj); + } +} + +long double +__ieee754_gammal_r (long double x, int *signgamp) +{ + u_int32_t es, hx, lx; + long double ret; + + GET_LDOUBLE_WORDS (es, hx, lx, x); + + if (__glibc_unlikely (((es & 0x7fff) | hx | lx) == 0)) + { + /* Return value for x == 0 is Inf with divide by zero exception. */ + *signgamp = 0; + return 1.0 / x; + } + if (__glibc_unlikely (es == 0xffffffff && ((hx & 0x7fffffff) | lx) == 0)) + { + /* x == -Inf. According to ISO this is NaN. */ + *signgamp = 0; + return x - x; + } + if (__glibc_unlikely ((es & 0x7fff) == 0x7fff)) + { + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ + *signgamp = 0; + return x + x; + } + if (__builtin_expect ((es & 0x8000) != 0, 0) && __rintl (x) == x) + { + /* Return value for integer x < 0 is NaN with invalid exception. */ + *signgamp = 0; + return (x - x) / (x - x); + } + + if (x >= 1756.0L) + { + /* Overflow. */ + *signgamp = 0; + return LDBL_MAX * LDBL_MAX; + } + else + { + SET_RESTORE_ROUNDL (FE_TONEAREST); + if (x > 0.0L) + { + *signgamp = 0; + int exp2_adj; + ret = gammal_positive (x, &exp2_adj); + ret = __scalbnl (ret, exp2_adj); + } + else if (x >= -LDBL_EPSILON / 4.0L) + { + *signgamp = 0; + ret = 1.0L / x; + } + else + { + long double tx = __truncl (x); + *signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1; + if (x <= -1766.0L) + /* Underflow. */ + ret = LDBL_MIN * LDBL_MIN; + else + { + long double frac = tx - x; + if (frac > 0.5L) + frac = 1.0L - frac; + long double sinpix = (frac <= 0.25L + ? __sinl (M_PIl * frac) + : __cosl (M_PIl * (0.5L - frac))); + int exp2_adj; + ret = M_PIl / (-x * sinpix + * gammal_positive (-x, &exp2_adj)); + ret = __scalbnl (ret, -exp2_adj); + math_check_force_underflow_nonneg (ret); + } + } + } + if (isinf (ret) && x != 0) + { + if (*signgamp < 0) + return -(-__copysignl (LDBL_MAX, ret) * LDBL_MAX); + else + return __copysignl (LDBL_MAX, ret) * LDBL_MAX; + } + else if (ret == 0) + { + if (*signgamp < 0) + return -(-__copysignl (LDBL_MIN, ret) * LDBL_MIN); + else + return __copysignl (LDBL_MIN, ret) * LDBL_MIN; + } + else + return ret; +} +strong_alias (__ieee754_gammal_r, __gammal_r_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/e_hypotl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_hypotl.c new file mode 100644 index 0000000000..6b55b6d8ee --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_hypotl.c @@ -0,0 +1,142 @@ +/* e_hypotl.c -- long double version of e_hypot.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_hypotl(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 32 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * y1= y with lower 32 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include <math.h> +#include <math_private.h> + +long double __ieee754_hypotl(long double x, long double y) +{ + long double a,b,t1,t2,y1,y2,w; + u_int32_t j,k,ea,eb; + + GET_LDOUBLE_EXP(ea,x); + ea &= 0x7fff; + GET_LDOUBLE_EXP(eb,y); + eb &= 0x7fff; + if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;} + SET_LDOUBLE_EXP(a,ea); /* a <- |a| */ + SET_LDOUBLE_EXP(b,eb); /* b <- |b| */ + if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */ + k=0; + if(__builtin_expect(ea > 0x5f3f,0)) { /* a>2**8000 */ + if(ea == 0x7fff) { /* Inf or NaN */ + u_int32_t exp __attribute__ ((unused)); + u_int32_t high,low; + w = a+b; /* for sNaN */ + if (issignaling (a) || issignaling (b)) + return w; + GET_LDOUBLE_WORDS(exp,high,low,a); + if(((high&0x7fffffff)|low)==0) w = a; + GET_LDOUBLE_WORDS(exp,high,low,b); + if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b; + return w; + } + /* scale a and b by 2**-9600 */ + ea -= 0x2580; eb -= 0x2580; k += 9600; + SET_LDOUBLE_EXP(a,ea); + SET_LDOUBLE_EXP(b,eb); + } + if(__builtin_expect(eb < 0x20bf, 0)) { /* b < 2**-8000 */ + if(eb == 0) { /* subnormal b or 0 */ + u_int32_t exp __attribute__ ((unused)); + u_int32_t high,low; + GET_LDOUBLE_WORDS(exp,high,low,b); + if((high|low)==0) return a; + SET_LDOUBLE_WORDS(t1, 0x7ffd, 0x80000000, 0); /* t1=2^16382 */ + b *= t1; + a *= t1; + k -= 16382; + GET_LDOUBLE_EXP (ea, a); + GET_LDOUBLE_EXP (eb, b); + if (eb > ea) + { + t1 = a; + a = b; + b = t1; + j = ea; + ea = eb; + eb = j; + } + } else { /* scale a and b by 2^9600 */ + ea += 0x2580; /* a *= 2^9600 */ + eb += 0x2580; /* b *= 2^9600 */ + k -= 9600; + SET_LDOUBLE_EXP(a,ea); + SET_LDOUBLE_EXP(b,eb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + u_int32_t high; + GET_LDOUBLE_MSW(high,a); + SET_LDOUBLE_WORDS(t1,ea,high,0); + t2 = a-t1; + w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + u_int32_t high; + GET_LDOUBLE_MSW(high,b); + a = a+a; + SET_LDOUBLE_WORDS(y1,eb,high,0); + y2 = b - y1; + GET_LDOUBLE_MSW(high,a); + SET_LDOUBLE_WORDS(t1,ea+1,high,0); + t2 = a - t1; + w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + u_int32_t exp; + t1 = 1.0; + GET_LDOUBLE_EXP(exp,t1); + SET_LDOUBLE_EXP(t1,exp+k); + w *= t1; + math_check_force_underflow_nonneg (w); + return w; + } else return w; +} +strong_alias (__ieee754_hypotl, __hypotl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/e_j0l.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_j0l.c new file mode 100644 index 0000000000..a536054cde --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_j0l.c @@ -0,0 +1,531 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_j0(x), __ieee754_y0(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j0(x): + * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... + * 2. Reduce x to |x| since j0(x)=j0(-x), and + * for x in (0,2) + * j0(x) = 1 - z/4 + z^2*R0/S0, where z = x*x; + * for x in (2,inf) + * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * as follow: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (cos(x) + sin(x)) + * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j0(nan)= nan + * j0(0) = 1 + * j0(inf) = 0 + * + * Method -- y0(x): + * 1. For x<2. + * Since + * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) + * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. + * We use the following function to approximate y0, + * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 + * + * Note: For tiny x, U/V = u0 and j0(x)~1, hence + * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) + * 2. For x>=2. + * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * by the method mentioned above. + * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. + */ + +#include <math.h> +#include <math_private.h> + +static long double pzero (long double), qzero (long double); + +static const long double + huge = 1e4930L, + one = 1.0L, + invsqrtpi = 5.6418958354775628694807945156077258584405e-1L, + tpi = 6.3661977236758134307553505349005744813784e-1L, + + /* J0(x) = 1 - x^2 / 4 + x^4 R0(x^2) / S0(x^2) + 0 <= x <= 2 + peak relative error 1.41e-22 */ + R[5] = { + 4.287176872744686992880841716723478740566E7L, + -6.652058897474241627570911531740907185772E5L, + 7.011848381719789863458364584613651091175E3L, + -3.168040850193372408702135490809516253693E1L, + 6.030778552661102450545394348845599300939E-2L, +}, + + S[4] = { + 2.743793198556599677955266341699130654342E9L, + 3.364330079384816249840086842058954076201E7L, + 1.924119649412510777584684927494642526573E5L, + 6.239282256012734914211715620088714856494E2L, + /* 1.000000000000000000000000000000000000000E0L,*/ +}; + +static const long double zero = 0.0; + +long double +__ieee754_j0l (long double x) +{ + long double z, s, c, ss, cc, r, u, v; + int32_t ix; + u_int32_t se; + + GET_LDOUBLE_EXP (se, x); + ix = se & 0x7fff; + if (__glibc_unlikely (ix >= 0x7fff)) + return one / (x * x); + x = fabsl (x); + if (ix >= 0x4000) /* |x| >= 2.0 */ + { + __sincosl (x, &s, &c); + ss = s - c; + cc = s + c; + if (ix < 0x7ffe) + { /* make sure x+x not overflow */ + z = -__cosl (x + x); + if ((s * c) < zero) + cc = z / ss; + else + ss = z / cc; + } + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if (__glibc_unlikely (ix > 0x4080)) /* 2^129 */ + z = (invsqrtpi * cc) / __ieee754_sqrtl (x); + else + { + u = pzero (x); + v = qzero (x); + z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrtl (x); + } + return z; + } + if (__glibc_unlikely (ix < 0x3fef)) /* |x| < 2**-16 */ + { + /* raise inexact if x != 0 */ + math_force_eval (huge + x); + if (ix < 0x3fde) /* |x| < 2^-33 */ + return one; + else + return one - 0.25 * x * x; + } + z = x * x; + r = z * (R[0] + z * (R[1] + z * (R[2] + z * (R[3] + z * R[4])))); + s = S[0] + z * (S[1] + z * (S[2] + z * (S[3] + z))); + if (ix < 0x3fff) + { /* |x| < 1.00 */ + return (one - 0.25 * z + z * (r / s)); + } + else + { + u = 0.5 * x; + return ((one + u) * (one - u) + z * (r / s)); + } +} +strong_alias (__ieee754_j0l, __j0l_finite) + + +/* y0(x) = 2/pi ln(x) J0(x) + U(x^2)/V(x^2) + 0 < x <= 2 + peak relative error 1.7e-21 */ +static const long double +U[6] = { + -1.054912306975785573710813351985351350861E10L, + 2.520192609749295139432773849576523636127E10L, + -1.856426071075602001239955451329519093395E9L, + 4.079209129698891442683267466276785956784E7L, + -3.440684087134286610316661166492641011539E5L, + 1.005524356159130626192144663414848383774E3L, +}; +static const long double +V[5] = { + 1.429337283720789610137291929228082613676E11L, + 2.492593075325119157558811370165695013002E9L, + 2.186077620785925464237324417623665138376E7L, + 1.238407896366385175196515057064384929222E5L, + 4.693924035211032457494368947123233101664E2L, + /* 1.000000000000000000000000000000000000000E0L */ +}; + +long double +__ieee754_y0l (long double x) +{ + long double z, s, c, ss, cc, u, v; + int32_t ix; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ + if (__glibc_unlikely (se & 0x8000)) + return zero / (zero * x); + if (__glibc_unlikely (ix >= 0x7fff)) + return one / (x + x * x); + if (__glibc_unlikely ((i0 | i1) == 0)) + return -HUGE_VALL + x; /* -inf and overflow exception. */ + if (ix >= 0x4000) + { /* |x| >= 2.0 */ + + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + __sincosl (x, &s, &c); + ss = s - c; + cc = s + c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if (ix < 0x7ffe) + { /* make sure x+x not overflow */ + z = -__cosl (x + x); + if ((s * c) < zero) + cc = z / ss; + else + ss = z / cc; + } + if (__glibc_unlikely (ix > 0x4080)) /* 1e39 */ + z = (invsqrtpi * ss) / __ieee754_sqrtl (x); + else + { + u = pzero (x); + v = qzero (x); + z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrtl (x); + } + return z; + } + if (__glibc_unlikely (ix <= 0x3fde)) /* x < 2^-33 */ + { + z = -7.380429510868722527629822444004602747322E-2L + + tpi * __ieee754_logl (x); + return z; + } + z = x * x; + u = U[0] + z * (U[1] + z * (U[2] + z * (U[3] + z * (U[4] + z * U[5])))); + v = V[0] + z * (V[1] + z * (V[2] + z * (V[3] + z * (V[4] + z)))); + return (u / v + tpi * (__ieee754_j0l (x) * __ieee754_logl (x))); +} +strong_alias (__ieee754_y0l, __y0l_finite) + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + s^2 R(s^2) / S(s^2) + */ +static const long double pR8[7] = { + /* 8 <= x <= inf + Peak relative error 4.62 */ + -4.094398895124198016684337960227780260127E-9L, + -8.929643669432412640061946338524096893089E-7L, + -6.281267456906136703868258380673108109256E-5L, + -1.736902783620362966354814353559382399665E-3L, + -1.831506216290984960532230842266070146847E-2L, + -5.827178869301452892963280214772398135283E-2L, + -2.087563267939546435460286895807046616992E-2L, +}; +static const long double pS8[6] = { + 5.823145095287749230197031108839653988393E-8L, + 1.279281986035060320477759999428992730280E-5L, + 9.132668954726626677174825517150228961304E-4L, + 2.606019379433060585351880541545146252534E-2L, + 2.956262215119520464228467583516287175244E-1L, + 1.149498145388256448535563278632697465675E0L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const long double pR5[7] = { + /* 4.54541015625 <= x <= 8 + Peak relative error 6.51E-22 */ + -2.041226787870240954326915847282179737987E-7L, + -2.255373879859413325570636768224534428156E-5L, + -7.957485746440825353553537274569102059990E-4L, + -1.093205102486816696940149222095559439425E-2L, + -5.657957849316537477657603125260701114646E-2L, + -8.641175552716402616180994954177818461588E-2L, + -1.354654710097134007437166939230619726157E-2L, +}; +static const long double pS5[6] = { + 2.903078099681108697057258628212823545290E-6L, + 3.253948449946735405975737677123673867321E-4L, + 1.181269751723085006534147920481582279979E-2L, + 1.719212057790143888884745200257619469363E-1L, + 1.006306498779212467670654535430694221924E0L, + 2.069568808688074324555596301126375951502E0L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const long double pR3[7] = { + /* 2.85711669921875 <= x <= 4.54541015625 + peak relative error 5.25e-21 */ + -5.755732156848468345557663552240816066802E-6L, + -3.703675625855715998827966962258113034767E-4L, + -7.390893350679637611641350096842846433236E-3L, + -5.571922144490038765024591058478043873253E-2L, + -1.531290690378157869291151002472627396088E-1L, + -1.193350853469302941921647487062620011042E-1L, + -8.567802507331578894302991505331963782905E-3L, +}; +static const long double pS3[6] = { + 8.185931139070086158103309281525036712419E-5L, + 5.398016943778891093520574483111255476787E-3L, + 1.130589193590489566669164765853409621081E-1L, + 9.358652328786413274673192987670237145071E-1L, + 3.091711512598349056276917907005098085273E0L, + 3.594602474737921977972586821673124231111E0L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const long double pR2[7] = { + /* 2 <= x <= 2.85711669921875 + peak relative error 2.64e-21 */ + -1.219525235804532014243621104365384992623E-4L, + -4.838597135805578919601088680065298763049E-3L, + -5.732223181683569266223306197751407418301E-2L, + -2.472947430526425064982909699406646503758E-1L, + -3.753373645974077960207588073975976327695E-1L, + -1.556241316844728872406672349347137975495E-1L, + -5.355423239526452209595316733635519506958E-3L, +}; +static const long double pS2[6] = { + 1.734442793664291412489066256138894953823E-3L, + 7.158111826468626405416300895617986926008E-2L, + 9.153839713992138340197264669867993552641E-1L, + 4.539209519433011393525841956702487797582E0L, + 8.868932430625331650266067101752626253644E0L, + 6.067161890196324146320763844772857713502E0L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + +static long double +pzero (long double x) +{ + const long double *p, *q; + long double z, r, s; + int32_t ix; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + /* ix >= 0x4000 for all calls to this function. */ + if (ix >= 0x4002) + { + p = pR8; + q = pS8; + } /* x >= 8 */ + else + { + i1 = (ix << 16) | (i0 >> 16); + if (i1 >= 0x40019174) /* x >= 4.54541015625 */ + { + p = pR5; + q = pS5; + } + else if (i1 >= 0x4000b6db) /* x >= 2.85711669921875 */ + { + p = pR3; + q = pS3; + } + else /* x >= 2 */ + { + p = pR2; + q = pS2; + } + } + z = one / (x * x); + r = + p[0] + z * (p[1] + + z * (p[2] + z * (p[3] + z * (p[4] + z * (p[5] + z * p[6]))))); + s = + q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * (q[5] + z))))); + return (one + z * r / s); +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate qzero by + * qzero(x) = s*(-.125 + R(s^2) / S(s^2)) + */ +static const long double qR8[7] = { + /* 8 <= x <= inf + peak relative error 2.23e-21 */ + 3.001267180483191397885272640777189348008E-10L, + 8.693186311430836495238494289942413810121E-8L, + 8.496875536711266039522937037850596580686E-6L, + 3.482702869915288984296602449543513958409E-4L, + 6.036378380706107692863811938221290851352E-3L, + 3.881970028476167836382607922840452192636E-2L, + 6.132191514516237371140841765561219149638E-2L, +}; +static const long double qS8[7] = { + 4.097730123753051126914971174076227600212E-9L, + 1.199615869122646109596153392152131139306E-6L, + 1.196337580514532207793107149088168946451E-4L, + 5.099074440112045094341500497767181211104E-3L, + 9.577420799632372483249761659674764460583E-2L, + 7.385243015344292267061953461563695918646E-1L, + 1.917266424391428937962682301561699055943E0L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const long double qR5[7] = { + /* 4.54541015625 <= x <= 8 + peak relative error 1.03e-21 */ + 3.406256556438974327309660241748106352137E-8L, + 4.855492710552705436943630087976121021980E-6L, + 2.301011739663737780613356017352912281980E-4L, + 4.500470249273129953870234803596619899226E-3L, + 3.651376459725695502726921248173637054828E-2L, + 1.071578819056574524416060138514508609805E-1L, + 7.458950172851611673015774675225656063757E-2L, +}; +static const long double qS5[7] = { + 4.650675622764245276538207123618745150785E-7L, + 6.773573292521412265840260065635377164455E-5L, + 3.340711249876192721980146877577806687714E-3L, + 7.036218046856839214741678375536970613501E-2L, + 6.569599559163872573895171876511377891143E-1L, + 2.557525022583599204591036677199171155186E0L, + 3.457237396120935674982927714210361269133E0L, + /* 1.000000000000000000000000000000000000000E0L,*/ +}; + +static const long double qR3[7] = { + /* 2.85711669921875 <= x <= 4.54541015625 + peak relative error 5.24e-21 */ + 1.749459596550816915639829017724249805242E-6L, + 1.446252487543383683621692672078376929437E-4L, + 3.842084087362410664036704812125005761859E-3L, + 4.066369994699462547896426554180954233581E-2L, + 1.721093619117980251295234795188992722447E-1L, + 2.538595333972857367655146949093055405072E-1L, + 8.560591367256769038905328596020118877936E-2L, +}; +static const long double qS3[7] = { + 2.388596091707517488372313710647510488042E-5L, + 2.048679968058758616370095132104333998147E-3L, + 5.824663198201417760864458765259945181513E-2L, + 6.953906394693328750931617748038994763958E-1L, + 3.638186936390881159685868764832961092476E0L, + 7.900169524705757837298990558459547842607E0L, + 5.992718532451026507552820701127504582907E0L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const long double qR2[7] = { + /* 2 <= x <= 2.85711669921875 + peak relative error 1.58e-21 */ + 6.306524405520048545426928892276696949540E-5L, + 3.209606155709930950935893996591576624054E-3L, + 5.027828775702022732912321378866797059604E-2L, + 3.012705561838718956481911477587757845163E-1L, + 6.960544893905752937420734884995688523815E-1L, + 5.431871999743531634887107835372232030655E-1L, + 9.447736151202905471899259026430157211949E-2L, +}; +static const long double qS2[7] = { + 8.610579901936193494609755345106129102676E-4L, + 4.649054352710496997203474853066665869047E-2L, + 8.104282924459837407218042945106320388339E-1L, + 5.807730930825886427048038146088828206852E0L, + 1.795310145936848873627710102199881642939E1L, + 2.281313316875375733663657188888110605044E1L, + 1.011242067883822301487154844458322200143E1L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + +static long double +qzero (long double x) +{ + const long double *p, *q; + long double s, r, z; + int32_t ix; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + /* ix >= 0x4000 for all calls to this function. */ + if (ix >= 0x4002) /* x >= 8 */ + { + p = qR8; + q = qS8; + } + else + { + i1 = (ix << 16) | (i0 >> 16); + if (i1 >= 0x40019174) /* x >= 4.54541015625 */ + { + p = qR5; + q = qS5; + } + else if (i1 >= 0x4000b6db) /* x >= 2.85711669921875 */ + { + p = qR3; + q = qS3; + } + else /* x >= 2 */ + { + p = qR2; + q = qS2; + } + } + z = one / (x * x); + r = + p[0] + z * (p[1] + + z * (p[2] + z * (p[3] + z * (p[4] + z * (p[5] + z * p[6]))))); + s = + q[0] + z * (q[1] + + z * (q[2] + + z * (q[3] + z * (q[4] + z * (q[5] + z * (q[6] + z)))))); + return (-.125 + z * r / s) / x; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/e_j1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_j1l.c new file mode 100644 index 0000000000..e8a7349cf4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_j1l.c @@ -0,0 +1,550 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_j1(x), __ieee754_y1(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j1(x): + * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... + * 2. Reduce x to |x| since j1(x)=-j1(-x), and + * for x in (0,2) + * j1(x) = x/2 + x*z*R0/S0, where z = x*x; + * for x in (2,inf) + * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * as follow: + * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (sin(x) + cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j1(nan)= nan + * j1(0) = 0 + * j1(inf) = 0 + * + * Method -- y1(x): + * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN + * 2. For x<2. + * Since + * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) + * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. + * We use the following function to approximate y1, + * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 + * Note: For tiny x, 1/x dominate y1 and hence + * y1(tiny) = -2/pi/tiny + * 3. For x>=2. + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * by method mentioned above. + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static long double pone (long double), qone (long double); + +static const long double + huge = 1e4930L, + one = 1.0L, + invsqrtpi = 5.6418958354775628694807945156077258584405e-1L, + tpi = 6.3661977236758134307553505349005744813784e-1L, + + /* J1(x) = .5 x + x x^2 R(x^2) / S(x^2) + 0 <= x <= 2 + Peak relative error 4.5e-21 */ +R[5] = { + -9.647406112428107954753770469290757756814E7L, + 2.686288565865230690166454005558203955564E6L, + -3.689682683905671185891885948692283776081E4L, + 2.195031194229176602851429567792676658146E2L, + -5.124499848728030297902028238597308971319E-1L, +}, + + S[4] = +{ + 1.543584977988497274437410333029029035089E9L, + 2.133542369567701244002565983150952549520E7L, + 1.394077011298227346483732156167414670520E5L, + 5.252401789085732428842871556112108446506E2L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const long double zero = 0.0; + + +long double +__ieee754_j1l (long double x) +{ + long double z, c, r, s, ss, cc, u, v, y; + int32_t ix; + u_int32_t se; + + GET_LDOUBLE_EXP (se, x); + ix = se & 0x7fff; + if (__glibc_unlikely (ix >= 0x7fff)) + return one / x; + y = fabsl (x); + if (ix >= 0x4000) + { /* |x| >= 2.0 */ + __sincosl (y, &s, &c); + ss = -s - c; + cc = s - c; + if (ix < 0x7ffe) + { /* make sure y+y not overflow */ + z = __cosl (y + y); + if ((s * c) > zero) + cc = z / ss; + else + ss = z / cc; + } + /* + * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) + * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) + */ + if (__glibc_unlikely (ix > 0x4080)) + z = (invsqrtpi * cc) / __ieee754_sqrtl (y); + else + { + u = pone (y); + v = qone (y); + z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrtl (y); + } + if (se & 0x8000) + return -z; + else + return z; + } + if (__glibc_unlikely (ix < 0x3fde)) /* |x| < 2^-33 */ + { + if (huge + x > one) /* inexact if x!=0 necessary */ + { + long double ret = 0.5 * x; + math_check_force_underflow (ret); + if (ret == 0 && x != 0) + __set_errno (ERANGE); + return ret; + } + } + z = x * x; + r = z * (R[0] + z * (R[1]+ z * (R[2] + z * (R[3] + z * R[4])))); + s = S[0] + z * (S[1] + z * (S[2] + z * (S[3] + z))); + r *= x; + return (x * 0.5 + r / s); +} +strong_alias (__ieee754_j1l, __j1l_finite) + + +/* Y1(x) = 2/pi * (log(x) * j1(x) - 1/x) + x R(x^2) + 0 <= x <= 2 + Peak relative error 2.3e-23 */ +static const long double U0[6] = { + -5.908077186259914699178903164682444848615E10L, + 1.546219327181478013495975514375773435962E10L, + -6.438303331169223128870035584107053228235E8L, + 9.708540045657182600665968063824819371216E6L, + -6.138043997084355564619377183564196265471E4L, + 1.418503228220927321096904291501161800215E2L, +}; +static const long double V0[5] = { + 3.013447341682896694781964795373783679861E11L, + 4.669546565705981649470005402243136124523E9L, + 3.595056091631351184676890179233695857260E7L, + 1.761554028569108722903944659933744317994E5L, + 5.668480419646516568875555062047234534863E2L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + + +long double +__ieee754_y1l (long double x) +{ + long double z, s, c, ss, cc, u, v; + int32_t ix; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if (__glibc_unlikely (se & 0x8000)) + return zero / (zero * x); + if (__glibc_unlikely (ix >= 0x7fff)) + return one / (x + x * x); + if (__glibc_unlikely ((i0 | i1) == 0)) + return -HUGE_VALL + x; /* -inf and overflow exception. */ + if (ix >= 0x4000) + { /* |x| >= 2.0 */ + __sincosl (x, &s, &c); + ss = -s - c; + cc = s - c; + if (ix < 0x7ffe) + { /* make sure x+x not overflow */ + z = __cosl (x + x); + if ((s * c) > zero) + cc = z / ss; + else + ss = z / cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if (__glibc_unlikely (ix > 0x4080)) + z = (invsqrtpi * ss) / __ieee754_sqrtl (x); + else + { + u = pone (x); + v = qone (x); + z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrtl (x); + } + return z; + } + if (__glibc_unlikely (ix <= 0x3fbe)) + { /* x < 2**-65 */ + z = -tpi / x; + if (isinf (z)) + __set_errno (ERANGE); + return z; + } + z = x * x; + u = U0[0] + z * (U0[1] + z * (U0[2] + z * (U0[3] + z * (U0[4] + z * U0[5])))); + v = V0[0] + z * (V0[1] + z * (V0[2] + z * (V0[3] + z * (V0[4] + z)))); + return (x * (u / v) + + tpi * (__ieee754_j1l (x) * __ieee754_logl (x) - one / x)); +} +strong_alias (__ieee754_y1l, __y1l_finite) + + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + */ + +/* J1(x) cosX + Y1(x) sinX = sqrt( 2/(pi x)) P1(x) + P1(x) = 1 + z^2 R(z^2), z=1/x + 8 <= x <= inf (0 <= z <= 0.125) + Peak relative error 5.2e-22 */ + +static const long double pr8[7] = { + 8.402048819032978959298664869941375143163E-9L, + 1.813743245316438056192649247507255996036E-6L, + 1.260704554112906152344932388588243836276E-4L, + 3.439294839869103014614229832700986965110E-3L, + 3.576910849712074184504430254290179501209E-2L, + 1.131111483254318243139953003461511308672E-1L, + 4.480715825681029711521286449131671880953E-2L, +}; +static const long double ps8[6] = { + 7.169748325574809484893888315707824924354E-8L, + 1.556549720596672576431813934184403614817E-5L, + 1.094540125521337139209062035774174565882E-3L, + 3.060978962596642798560894375281428805840E-2L, + 3.374146536087205506032643098619414507024E-1L, + 1.253830208588979001991901126393231302559E0L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + +/* J1(x) cosX + Y1(x) sinX = sqrt( 2/(pi x)) P1(x) + P1(x) = 1 + z^2 R(z^2), z=1/x + 4.54541015625 <= x <= 8 + Peak relative error 7.7e-22 */ +static const long double pr5[7] = { + 4.318486887948814529950980396300969247900E-7L, + 4.715341880798817230333360497524173929315E-5L, + 1.642719430496086618401091544113220340094E-3L, + 2.228688005300803935928733750456396149104E-2L, + 1.142773760804150921573259605730018327162E-1L, + 1.755576530055079253910829652698703791957E-1L, + 3.218803858282095929559165965353784980613E-2L, +}; +static const long double ps5[6] = { + 3.685108812227721334719884358034713967557E-6L, + 4.069102509511177498808856515005792027639E-4L, + 1.449728676496155025507893322405597039816E-2L, + 2.058869213229520086582695850441194363103E-1L, + 1.164890985918737148968424972072751066553E0L, + 2.274776933457009446573027260373361586841E0L, + /* 1.000000000000000000000000000000000000000E0L,*/ +}; + +/* J1(x) cosX + Y1(x) sinX = sqrt( 2/(pi x)) P1(x) + P1(x) = 1 + z^2 R(z^2), z=1/x + 2.85711669921875 <= x <= 4.54541015625 + Peak relative error 6.5e-21 */ +static const long double pr3[7] = { + 1.265251153957366716825382654273326407972E-5L, + 8.031057269201324914127680782288352574567E-4L, + 1.581648121115028333661412169396282881035E-2L, + 1.179534658087796321928362981518645033967E-1L, + 3.227936912780465219246440724502790727866E-1L, + 2.559223765418386621748404398017602935764E-1L, + 2.277136933287817911091370397134882441046E-2L, +}; +static const long double ps3[6] = { + 1.079681071833391818661952793568345057548E-4L, + 6.986017817100477138417481463810841529026E-3L, + 1.429403701146942509913198539100230540503E-1L, + 1.148392024337075609460312658938700765074E0L, + 3.643663015091248720208251490291968840882E0L, + 3.990702269032018282145100741746633960737E0L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + +/* J1(x) cosX + Y1(x) sinX = sqrt( 2/(pi x)) P1(x) + P1(x) = 1 + z^2 R(z^2), z=1/x + 2 <= x <= 2.85711669921875 + Peak relative error 3.5e-21 */ +static const long double pr2[7] = { + 2.795623248568412225239401141338714516445E-4L, + 1.092578168441856711925254839815430061135E-2L, + 1.278024620468953761154963591853679640560E-1L, + 5.469680473691500673112904286228351988583E-1L, + 8.313769490922351300461498619045639016059E-1L, + 3.544176317308370086415403567097130611468E-1L, + 1.604142674802373041247957048801599740644E-2L, +}; +static const long double ps2[6] = { + 2.385605161555183386205027000675875235980E-3L, + 9.616778294482695283928617708206967248579E-2L, + 1.195215570959693572089824415393951258510E0L, + 5.718412857897054829999458736064922974662E0L, + 1.065626298505499086386584642761602177568E1L, + 6.809140730053382188468983548092322151791E0L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + + +static long double +pone (long double x) +{ + const long double *p, *q; + long double z, r, s; + int32_t ix; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + /* ix >= 0x4000 for all calls to this function. */ + if (ix >= 0x4002) /* x >= 8 */ + { + p = pr8; + q = ps8; + } + else + { + i1 = (ix << 16) | (i0 >> 16); + if (i1 >= 0x40019174) /* x >= 4.54541015625 */ + { + p = pr5; + q = ps5; + } + else if (i1 >= 0x4000b6db) /* x >= 2.85711669921875 */ + { + p = pr3; + q = ps3; + } + else /* x >= 2 */ + { + p = pr2; + q = ps2; + } + } + z = one / (x * x); + r = p[0] + z * (p[1] + + z * (p[2] + z * (p[3] + z * (p[4] + z * (p[5] + z * p[6]))))); + s = q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * (q[5] + z))))); + return one + z * r / s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + */ + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = z(.375 + z^2 R(z^2)), z=1/x + 8 <= x <= inf + Peak relative error 8.3e-22 */ + +static const long double qr8[7] = { + -5.691925079044209246015366919809404457380E-10L, + -1.632587664706999307871963065396218379137E-7L, + -1.577424682764651970003637263552027114600E-5L, + -6.377627959241053914770158336842725291713E-4L, + -1.087408516779972735197277149494929568768E-2L, + -6.854943629378084419631926076882330494217E-2L, + -1.055448290469180032312893377152490183203E-1L, +}; +static const long double qs8[7] = { + 5.550982172325019811119223916998393907513E-9L, + 1.607188366646736068460131091130644192244E-6L, + 1.580792530091386496626494138334505893599E-4L, + 6.617859900815747303032860443855006056595E-3L, + 1.212840547336984859952597488863037659161E-1L, + 9.017885953937234900458186716154005541075E-1L, + 2.201114489712243262000939120146436167178E0L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = z(.375 + z^2 R(z^2)), z=1/x + 4.54541015625 <= x <= 8 + Peak relative error 4.1e-22 */ +static const long double qr5[7] = { + -6.719134139179190546324213696633564965983E-8L, + -9.467871458774950479909851595678622044140E-6L, + -4.429341875348286176950914275723051452838E-4L, + -8.539898021757342531563866270278505014487E-3L, + -6.818691805848737010422337101409276287170E-2L, + -1.964432669771684034858848142418228214855E-1L, + -1.333896496989238600119596538299938520726E-1L, +}; +static const long double qs5[7] = { + 6.552755584474634766937589285426911075101E-7L, + 9.410814032118155978663509073200494000589E-5L, + 4.561677087286518359461609153655021253238E-3L, + 9.397742096177905170800336715661091535805E-2L, + 8.518538116671013902180962914473967738771E-1L, + 3.177729183645800174212539541058292579009E0L, + 4.006745668510308096259753538973038902990E0L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = z(.375 + z^2 R(z^2)), z=1/x + 2.85711669921875 <= x <= 4.54541015625 + Peak relative error 2.2e-21 */ +static const long double qr3[7] = { + -3.618746299358445926506719188614570588404E-6L, + -2.951146018465419674063882650970344502798E-4L, + -7.728518171262562194043409753656506795258E-3L, + -8.058010968753999435006488158237984014883E-2L, + -3.356232856677966691703904770937143483472E-1L, + -4.858192581793118040782557808823460276452E-1L, + -1.592399251246473643510898335746432479373E-1L, +}; +static const long double qs3[7] = { + 3.529139957987837084554591421329876744262E-5L, + 2.973602667215766676998703687065066180115E-3L, + 8.273534546240864308494062287908662592100E-2L, + 9.613359842126507198241321110649974032726E-1L, + 4.853923697093974370118387947065402707519E0L, + 1.002671608961669247462020977417828796933E1L, + 7.028927383922483728931327850683151410267E0L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = z(.375 + z^2 R(z^2)), z=1/x + 2 <= x <= 2.85711669921875 + Peak relative error 6.9e-22 */ +static const long double qr2[7] = { + -1.372751603025230017220666013816502528318E-4L, + -6.879190253347766576229143006767218972834E-3L, + -1.061253572090925414598304855316280077828E-1L, + -6.262164224345471241219408329354943337214E-1L, + -1.423149636514768476376254324731437473915E0L, + -1.087955310491078933531734062917489870754E0L, + -1.826821119773182847861406108689273719137E-1L, +}; +static const long double qs2[7] = { + 1.338768933634451601814048220627185324007E-3L, + 7.071099998918497559736318523932241901810E-2L, + 1.200511429784048632105295629933382142221E0L, + 8.327301713640367079030141077172031825276E0L, + 2.468479301872299311658145549931764426840E1L, + 2.961179686096262083509383820557051621644E1L, + 1.201402313144305153005639494661767354977E1L, + /* 1.000000000000000000000000000000000000000E0L, */ +}; + + +static long double +qone (long double x) +{ + const long double *p, *q; + static long double s, r, z; + int32_t ix; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + /* ix >= 0x4000 for all calls to this function. */ + if (ix >= 0x4002) /* x >= 8 */ + { + p = qr8; + q = qs8; + } + else + { + i1 = (ix << 16) | (i0 >> 16); + if (i1 >= 0x40019174) /* x >= 4.54541015625 */ + { + p = qr5; + q = qs5; + } + else if (i1 >= 0x4000b6db) /* x >= 2.85711669921875 */ + { + p = qr3; + q = qs3; + } + else /* x >= 2 */ + { + p = qr2; + q = qs2; + } + } + z = one / (x * x); + r = + p[0] + z * (p[1] + + z * (p[2] + z * (p[3] + z * (p[4] + z * (p[5] + z * p[6]))))); + s = + q[0] + z * (q[1] + + z * (q[2] + + z * (q[3] + z * (q[4] + z * (q[5] + z * (q[6] + z)))))); + return (.375 + z * r / s) / x; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/e_jnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_jnl.c new file mode 100644 index 0000000000..92f96921a7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_jnl.c @@ -0,0 +1,404 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Modifications for long double are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* + * __ieee754_jn(n, x), __ieee754_yn(n, x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with overflow signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for n<x, forward recursion us used starting + * from values of j0(x) and j1(x). + * for n>x, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double + invsqrtpi = 5.64189583547756286948079e-1L, two = 2.0e0L, one = 1.0e0L; + +static const long double zero = 0.0L; + +long double +__ieee754_jnl (int n, long double x) +{ + u_int32_t se, i0, i1; + int32_t i, ix, sgn; + long double a, b, temp, di, ret; + long double z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + + /* if J(n,NaN) is NaN */ + if (__glibc_unlikely ((ix == 0x7fff) && ((i0 & 0x7fffffff) != 0))) + return x + x; + if (n < 0) + { + n = -n; + x = -x; + se ^= 0x8000; + } + if (n == 0) + return (__ieee754_j0l (x)); + if (n == 1) + return (__ieee754_j1l (x)); + sgn = (n & 1) & (se >> 15); /* even n -- 0, odd n -- sign(x) */ + x = fabsl (x); + { + SET_RESTORE_ROUNDL (FE_TONEAREST); + if (__glibc_unlikely ((ix | i0 | i1) == 0 || ix >= 0x7fff)) + /* if x is 0 or inf */ + return sgn == 1 ? -zero : zero; + else if ((long double) n <= x) + { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + if (ix >= 0x412D) + { /* x > 2**302 */ + + /* ??? This might be a futile gesture. + If x exceeds X_TLOSS anyway, the wrapper function + will set the result to zero. */ + + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + long double s; + long double c; + __sincosl (x, &s, &c); + switch (n & 3) + { + case 0: + temp = c + s; + break; + case 1: + temp = -c + s; + break; + case 2: + temp = -c - s; + break; + case 3: + temp = c - s; + break; + } + b = invsqrtpi * temp / __ieee754_sqrtl (x); + } + else + { + a = __ieee754_j0l (x); + b = __ieee754_j1l (x); + for (i = 1; i < n; i++) + { + temp = b; + b = b * ((long double) (i + i) / x) - a; /* avoid underflow */ + a = temp; + } + } + } + else + { + if (ix < 0x3fde) + { /* x < 2**-33 */ + /* x is tiny, return the first Taylor expansion of J(n,x) + * J(n,x) = 1/n!*(x/2)^n - ... + */ + if (n >= 400) /* underflow, result < 10^-4952 */ + b = zero; + else + { + temp = x * 0.5; + b = temp; + for (a = one, i = 2; i <= n; i++) + { + a *= (long double) i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b / a; + } + } + else + { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + long double t, v; + long double q0, q1, h, tmp; + int32_t k, m; + w = (n + n) / (long double) x; + h = 2.0L / (long double) x; + q0 = w; + z = w + h; + q1 = w * z - 1.0L; + k = 1; + while (q1 < 1.0e11L) + { + k += 1; + z += h; + tmp = z * q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n + n; + for (t = zero, i = 2 * (n + k); i >= m; i -= 2) + t = one / (i / x - t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two / x; + tmp = tmp * __ieee754_logl (fabsl (v * tmp)); + + if (tmp < 1.1356523406294143949491931077970765006170e+04L) + { + for (i = n - 1, di = (long double) (i + i); i > 0; i--) + { + temp = b; + b *= di; + b = b / x - a; + a = temp; + di -= two; + } + } + else + { + for (i = n - 1, di = (long double) (i + i); i > 0; i--) + { + temp = b; + b *= di; + b = b / x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if (b > 1e100L) + { + a /= b; + t /= b; + b = one; + } + } + } + /* j0() and j1() suffer enormous loss of precision at and + * near zero; however, we know that their zero points never + * coincide, so just choose the one further away from zero. + */ + z = __ieee754_j0l (x); + w = __ieee754_j1l (x); + if (fabsl (z) >= fabsl (w)) + b = (t * z / b); + else + b = (t * w / a); + } + } + if (sgn == 1) + ret = -b; + else + ret = b; + } + if (ret == 0) + { + ret = __copysignl (LDBL_MIN, ret) * LDBL_MIN; + __set_errno (ERANGE); + } + else + math_check_force_underflow (ret); + return ret; +} +strong_alias (__ieee754_jnl, __jnl_finite) + +long double +__ieee754_ynl (int n, long double x) +{ + u_int32_t se, i0, i1; + int32_t i, ix; + int32_t sign; + long double a, b, temp, ret; + + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + /* if Y(n,NaN) is NaN */ + if (__builtin_expect ((ix == 0x7fff) && ((i0 & 0x7fffffff) != 0), 0)) + return x + x; + if (__builtin_expect ((ix | i0 | i1) == 0, 0)) + /* -inf or inf and divide-by-zero exception. */ + return ((n < 0 && (n & 1) != 0) ? 1.0L : -1.0L) / 0.0L; + if (__builtin_expect (se & 0x8000, 0)) + return zero / (zero * x); + sign = 1; + if (n < 0) + { + n = -n; + sign = 1 - ((n & 1) << 1); + } + if (n == 0) + return (__ieee754_y0l (x)); + { + SET_RESTORE_ROUNDL (FE_TONEAREST); + if (n == 1) + { + ret = sign * __ieee754_y1l (x); + goto out; + } + if (__glibc_unlikely (ix == 0x7fff)) + return zero; + if (ix >= 0x412D) + { /* x > 2**302 */ + + /* ??? See comment above on the possible futility of this. */ + + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + long double s; + long double c; + __sincosl (x, &s, &c); + switch (n & 3) + { + case 0: + temp = s - c; + break; + case 1: + temp = -s - c; + break; + case 2: + temp = -s + c; + break; + case 3: + temp = s + c; + break; + } + b = invsqrtpi * temp / __ieee754_sqrtl (x); + } + else + { + a = __ieee754_y0l (x); + b = __ieee754_y1l (x); + /* quit if b is -inf */ + GET_LDOUBLE_WORDS (se, i0, i1, b); + /* Use 0xffffffff since GET_LDOUBLE_WORDS sign-extends SE. */ + for (i = 1; i < n && se != 0xffffffff; i++) + { + temp = b; + b = ((long double) (i + i) / x) * b - a; + GET_LDOUBLE_WORDS (se, i0, i1, b); + a = temp; + } + } + /* If B is +-Inf, set up errno accordingly. */ + if (! isfinite (b)) + __set_errno (ERANGE); + if (sign > 0) + ret = b; + else + ret = -b; + } + out: + if (isinf (ret)) + ret = __copysignl (LDBL_MAX, ret) * LDBL_MAX; + return ret; +} +strong_alias (__ieee754_ynl, __ynl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/e_lgammal_r.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_lgammal_r.c new file mode 100644 index 0000000000..4ecd63045f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_lgammal_r.c @@ -0,0 +1,439 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_lgammal_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: + * 1. Argument Reduction for 0 < x <= 8 + * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may + * reduce x to a number in [1.5,2.5] by + * lgamma(1+s) = log(s) + lgamma(s) + * for example, + * lgamma(7.3) = log(6.3) + lgamma(6.3) + * = log(6.3*5.3) + lgamma(5.3) + * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) + * 2. Polynomial approximation of lgamma around its + * minimun ymin=1.461632144968362245 to maintain monotonicity. + * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use + * Let z = x-ymin; + * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) + * 2. Rational approximation in the primary interval [2,3] + * We use the following approximation: + * s = x-2.0; + * lgamma(x) = 0.5*s + s*P(s)/Q(s) + * Our algorithms are based on the following observation + * + * zeta(2)-1 2 zeta(3)-1 3 + * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... + * 2 3 + * + * where Euler = 0.5771... is the Euler constant, which is very + * close to 0.5. + * + * 3. For x>=8, we have + * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... + * (better formula: + * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) + * Let z = 1/x, then we approximation + * f(z) = lgamma(x) - (x-0.5)(log(x)-1) + * by + * 3 5 11 + * w = w0 + w1*z + w2*z + w3*z + ... + w6*z + * + * 4. For negative x, since (G is gamma function) + * -x*G(-x)*G(x) = pi/sin(pi*x), + * we have + * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) + * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 + * Hence, for x<0, signgam = sign(sin(pi*x)) and + * lgamma(x) = log(|Gamma(x)|) + * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); + * Note: one should avoid compute pi*(-x) directly in the + * computation of sin(pi*(-x)). + * + * 5. Special Cases + * lgamma(2+s) ~ s*(1-Euler) for tiny s + * lgamma(1)=lgamma(2)=0 + * lgamma(x) ~ -log(x) for tiny x + * lgamma(0) = lgamma(inf) = inf + * lgamma(-integer) = +-inf + * + */ + +#include <math.h> +#include <math_private.h> +#include <libc-diag.h> + +static const long double + half = 0.5L, + one = 1.0L, + pi = 3.14159265358979323846264L, + two63 = 9.223372036854775808e18L, + + /* lgam(1+x) = 0.5 x + x a(x)/b(x) + -0.268402099609375 <= x <= 0 + peak relative error 6.6e-22 */ + a0 = -6.343246574721079391729402781192128239938E2L, + a1 = 1.856560238672465796768677717168371401378E3L, + a2 = 2.404733102163746263689288466865843408429E3L, + a3 = 8.804188795790383497379532868917517596322E2L, + a4 = 1.135361354097447729740103745999661157426E2L, + a5 = 3.766956539107615557608581581190400021285E0L, + + b0 = 8.214973713960928795704317259806842490498E3L, + b1 = 1.026343508841367384879065363925870888012E4L, + b2 = 4.553337477045763320522762343132210919277E3L, + b3 = 8.506975785032585797446253359230031874803E2L, + b4 = 6.042447899703295436820744186992189445813E1L, + /* b5 = 1.000000000000000000000000000000000000000E0 */ + + + tc = 1.4616321449683623412626595423257213284682E0L, + tf = -1.2148629053584961146050602565082954242826E-1,/* double precision */ +/* tt = (tail of tf), i.e. tf + tt has extended precision. */ + tt = 3.3649914684731379602768989080467587736363E-18L, + /* lgam ( 1.4616321449683623412626595423257213284682E0 ) = +-1.2148629053584960809551455717769158215135617312999903886372437313313530E-1 */ + + /* lgam (x + tc) = tf + tt + x g(x)/h(x) + - 0.230003726999612341262659542325721328468 <= x + <= 0.2699962730003876587373404576742786715318 + peak relative error 2.1e-21 */ + g0 = 3.645529916721223331888305293534095553827E-18L, + g1 = 5.126654642791082497002594216163574795690E3L, + g2 = 8.828603575854624811911631336122070070327E3L, + g3 = 5.464186426932117031234820886525701595203E3L, + g4 = 1.455427403530884193180776558102868592293E3L, + g5 = 1.541735456969245924860307497029155838446E2L, + g6 = 4.335498275274822298341872707453445815118E0L, + + h0 = 1.059584930106085509696730443974495979641E4L, + h1 = 2.147921653490043010629481226937850618860E4L, + h2 = 1.643014770044524804175197151958100656728E4L, + h3 = 5.869021995186925517228323497501767586078E3L, + h4 = 9.764244777714344488787381271643502742293E2L, + h5 = 6.442485441570592541741092969581997002349E1L, + /* h6 = 1.000000000000000000000000000000000000000E0 */ + + + /* lgam (x+1) = -0.5 x + x u(x)/v(x) + -0.100006103515625 <= x <= 0.231639862060546875 + peak relative error 1.3e-21 */ + u0 = -8.886217500092090678492242071879342025627E1L, + u1 = 6.840109978129177639438792958320783599310E2L, + u2 = 2.042626104514127267855588786511809932433E3L, + u3 = 1.911723903442667422201651063009856064275E3L, + u4 = 7.447065275665887457628865263491667767695E2L, + u5 = 1.132256494121790736268471016493103952637E2L, + u6 = 4.484398885516614191003094714505960972894E0L, + + v0 = 1.150830924194461522996462401210374632929E3L, + v1 = 3.399692260848747447377972081399737098610E3L, + v2 = 3.786631705644460255229513563657226008015E3L, + v3 = 1.966450123004478374557778781564114347876E3L, + v4 = 4.741359068914069299837355438370682773122E2L, + v5 = 4.508989649747184050907206782117647852364E1L, + /* v6 = 1.000000000000000000000000000000000000000E0 */ + + + /* lgam (x+2) = .5 x + x s(x)/r(x) + 0 <= x <= 1 + peak relative error 7.2e-22 */ + s0 = 1.454726263410661942989109455292824853344E6L, + s1 = -3.901428390086348447890408306153378922752E6L, + s2 = -6.573568698209374121847873064292963089438E6L, + s3 = -3.319055881485044417245964508099095984643E6L, + s4 = -7.094891568758439227560184618114707107977E5L, + s5 = -6.263426646464505837422314539808112478303E4L, + s6 = -1.684926520999477529949915657519454051529E3L, + + r0 = -1.883978160734303518163008696712983134698E7L, + r1 = -2.815206082812062064902202753264922306830E7L, + r2 = -1.600245495251915899081846093343626358398E7L, + r3 = -4.310526301881305003489257052083370058799E6L, + r4 = -5.563807682263923279438235987186184968542E5L, + r5 = -3.027734654434169996032905158145259713083E4L, + r6 = -4.501995652861105629217250715790764371267E2L, + /* r6 = 1.000000000000000000000000000000000000000E0 */ + + +/* lgam(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x w(1/x^2) + x >= 8 + Peak relative error 1.51e-21 + w0 = LS2PI - 0.5 */ + w0 = 4.189385332046727417803e-1L, + w1 = 8.333333333333331447505E-2L, + w2 = -2.777777777750349603440E-3L, + w3 = 7.936507795855070755671E-4L, + w4 = -5.952345851765688514613E-4L, + w5 = 8.412723297322498080632E-4L, + w6 = -1.880801938119376907179E-3L, + w7 = 4.885026142432270781165E-3L; + +static const long double zero = 0.0L; + +static long double +sin_pi (long double x) +{ + long double y, z; + int n, ix; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + ix = (ix << 16) | (i0 >> 16); + if (ix < 0x3ffd8000) /* 0.25 */ + return __sinl (pi * x); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = __floorl (y); + if (z != y) + { /* inexact anyway */ + y *= 0.5; + y = 2.0*(y - __floorl(y)); /* y = |x| mod 2.0 */ + n = (int) (y*4.0); + } + else + { + if (ix >= 0x403f8000) /* 2^64 */ + { + y = zero; n = 0; /* y must be even */ + } + else + { + if (ix < 0x403e8000) /* 2^63 */ + z = y + two63; /* exact */ + GET_LDOUBLE_WORDS (se, i0, i1, z); + n = i1 & 1; + y = n; + n <<= 2; + } + } + + switch (n) + { + case 0: + y = __sinl (pi * y); + break; + case 1: + case 2: + y = __cosl (pi * (half - y)); + break; + case 3: + case 4: + y = __sinl (pi * (one - y)); + break; + case 5: + case 6: + y = -__cosl (pi * (y - 1.5)); + break; + default: + y = __sinl (pi * (y - 2.0)); + break; + } + return -y; +} + + +long double +__ieee754_lgammal_r (long double x, int *signgamp) +{ + long double t, y, z, nadj, p, p1, p2, q, r, w; + int i, ix; + u_int32_t se, i0, i1; + + *signgamp = 1; + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + + if (__builtin_expect((ix | i0 | i1) == 0, 0)) + { + if (se & 0x8000) + *signgamp = -1; + return one / fabsl (x); + } + + ix = (ix << 16) | (i0 >> 16); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + if (__builtin_expect(ix >= 0x7fff0000, 0)) + return x * x; + + if (__builtin_expect(ix < 0x3fc08000, 0)) /* 2^-63 */ + { /* |x|<2**-63, return -log(|x|) */ + if (se & 0x8000) + { + *signgamp = -1; + return -__ieee754_logl (-x); + } + else + return -__ieee754_logl (x); + } + if (se & 0x8000) + { + if (x < -2.0L && x > -33.0L) + return __lgamma_negl (x, signgamp); + t = sin_pi (x); + if (t == zero) + return one / fabsl (t); /* -integer */ + nadj = __ieee754_logl (pi / fabsl (t * x)); + if (t < zero) + *signgamp = -1; + x = -x; + } + + /* purge off 1 and 2 */ + if ((((ix - 0x3fff8000) | i0 | i1) == 0) + || (((ix - 0x40008000) | i0 | i1) == 0)) + r = 0; + else if (ix < 0x40008000) /* 2.0 */ + { + /* x < 2.0 */ + if (ix <= 0x3ffee666) /* 8.99993896484375e-1 */ + { + /* lgamma(x) = lgamma(x+1) - log(x) */ + r = -__ieee754_logl (x); + if (ix >= 0x3ffebb4a) /* 7.31597900390625e-1 */ + { + y = x - one; + i = 0; + } + else if (ix >= 0x3ffced33)/* 2.31639862060546875e-1 */ + { + y = x - (tc - one); + i = 1; + } + else + { + /* x < 0.23 */ + y = x; + i = 2; + } + } + else + { + r = zero; + if (ix >= 0x3fffdda6) /* 1.73162841796875 */ + { + /* [1.7316,2] */ + y = x - 2.0; + i = 0; + } + else if (ix >= 0x3fff9da6)/* 1.23162841796875 */ + { + /* [1.23,1.73] */ + y = x - tc; + i = 1; + } + else + { + /* [0.9, 1.23] */ + y = x - one; + i = 2; + } + } + switch (i) + { + case 0: + p1 = a0 + y * (a1 + y * (a2 + y * (a3 + y * (a4 + y * a5)))); + p2 = b0 + y * (b1 + y * (b2 + y * (b3 + y * (b4 + y)))); + r += half * y + y * p1/p2; + break; + case 1: + p1 = g0 + y * (g1 + y * (g2 + y * (g3 + y * (g4 + y * (g5 + y * g6))))); + p2 = h0 + y * (h1 + y * (h2 + y * (h3 + y * (h4 + y * (h5 + y))))); + p = tt + y * p1/p2; + r += (tf + p); + break; + case 2: + p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * (u5 + y * u6)))))); + p2 = v0 + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * (v5 + y))))); + r += (-half * y + p1 / p2); + } + } + else if (ix < 0x40028000) /* 8.0 */ + { + /* x < 8.0 */ + i = (int) x; + t = zero; + y = x - (double) i; + p = y * + (s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6)))))); + q = r0 + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * (r6 + y)))))); + r = half * y + p / q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch (i) + { + case 7: + z *= (y + 6.0); /* FALLTHRU */ + case 6: + z *= (y + 5.0); /* FALLTHRU */ + case 5: + z *= (y + 4.0); /* FALLTHRU */ + case 4: + z *= (y + 3.0); /* FALLTHRU */ + case 3: + z *= (y + 2.0); /* FALLTHRU */ + r += __ieee754_logl (z); + break; + } + } + else if (ix < 0x40418000) /* 2^66 */ + { + /* 8.0 <= x < 2**66 */ + t = __ieee754_logl (x); + z = one / x; + y = z * z; + w = w0 + z * (w1 + + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * (w6 + y * w7)))))); + r = (x - half) * (t - one) + w; + } + else + /* 2**66 <= x <= inf */ + r = x * (__ieee754_logl (x) - one); + /* NADJ is set for negative arguments but not otherwise, resulting + in warnings that it may be used uninitialized although in the + cases where it is used it has always been set. */ + DIAG_PUSH_NEEDS_COMMENT; + DIAG_IGNORE_NEEDS_COMMENT (4.9, "-Wmaybe-uninitialized"); + if (se & 0x8000) + r = nadj - r; + DIAG_POP_NEEDS_COMMENT; + return r; +} +strong_alias (__ieee754_lgammal_r, __lgammal_r_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/e_rem_pio2l.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_rem_pio2l.c new file mode 100644 index 0000000000..43c5d91f0b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_rem_pio2l.c @@ -0,0 +1,236 @@ +/* Extended-precision floating point argument reduction. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Based on quad-precision code by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* Table of constants for 2/pi, 5628 hexadecimal digits of 2/pi. */ +static const int32_t two_over_pi[] = { +0xa2f983, 0x6e4e44, 0x1529fc, 0x2757d1, 0xf534dd, 0xc0db62, +0x95993c, 0x439041, 0xfe5163, 0xabdebb, 0xc561b7, 0x246e3a, +0x424dd2, 0xe00649, 0x2eea09, 0xd1921c, 0xfe1deb, 0x1cb129, +0xa73ee8, 0x8235f5, 0x2ebb44, 0x84e99c, 0x7026b4, 0x5f7e41, +0x3991d6, 0x398353, 0x39f49c, 0x845f8b, 0xbdf928, 0x3b1ff8, +0x97ffde, 0x05980f, 0xef2f11, 0x8b5a0a, 0x6d1f6d, 0x367ecf, +0x27cb09, 0xb74f46, 0x3f669e, 0x5fea2d, 0x7527ba, 0xc7ebe5, +0xf17b3d, 0x0739f7, 0x8a5292, 0xea6bfb, 0x5fb11f, 0x8d5d08, +0x560330, 0x46fc7b, 0x6babf0, 0xcfbc20, 0x9af436, 0x1da9e3, +0x91615e, 0xe61b08, 0x659985, 0x5f14a0, 0x68408d, 0xffd880, +0x4d7327, 0x310606, 0x1556ca, 0x73a8c9, 0x60e27b, 0xc08c6b, +0x47c419, 0xc367cd, 0xdce809, 0x2a8359, 0xc4768b, 0x961ca6, +0xddaf44, 0xd15719, 0x053ea5, 0xff0705, 0x3f7e33, 0xe832c2, +0xde4f98, 0x327dbb, 0xc33d26, 0xef6b1e, 0x5ef89f, 0x3a1f35, +0xcaf27f, 0x1d87f1, 0x21907c, 0x7c246a, 0xfa6ed5, 0x772d30, +0x433b15, 0xc614b5, 0x9d19c3, 0xc2c4ad, 0x414d2c, 0x5d000c, +0x467d86, 0x2d71e3, 0x9ac69b, 0x006233, 0x7cd2b4, 0x97a7b4, +0xd55537, 0xf63ed7, 0x1810a3, 0xfc764d, 0x2a9d64, 0xabd770, +0xf87c63, 0x57b07a, 0xe71517, 0x5649c0, 0xd9d63b, 0x3884a7, +0xcb2324, 0x778ad6, 0x23545a, 0xb91f00, 0x1b0af1, 0xdfce19, +0xff319f, 0x6a1e66, 0x615799, 0x47fbac, 0xd87f7e, 0xb76522, +0x89e832, 0x60bfe6, 0xcdc4ef, 0x09366c, 0xd43f5d, 0xd7de16, +0xde3b58, 0x929bde, 0x2822d2, 0xe88628, 0x4d58e2, 0x32cac6, +0x16e308, 0xcb7de0, 0x50c017, 0xa71df3, 0x5be018, 0x34132e, +0x621283, 0x014883, 0x5b8ef5, 0x7fb0ad, 0xf2e91e, 0x434a48, +0xd36710, 0xd8ddaa, 0x425fae, 0xce616a, 0xa4280a, 0xb499d3, +0xf2a606, 0x7f775c, 0x83c2a3, 0x883c61, 0x78738a, 0x5a8caf, +0xbdd76f, 0x63a62d, 0xcbbff4, 0xef818d, 0x67c126, 0x45ca55, +0x36d9ca, 0xd2a828, 0x8d61c2, 0x77c912, 0x142604, 0x9b4612, +0xc459c4, 0x44c5c8, 0x91b24d, 0xf31700, 0xad43d4, 0xe54929, +0x10d5fd, 0xfcbe00, 0xcc941e, 0xeece70, 0xf53e13, 0x80f1ec, +0xc3e7b3, 0x28f8c7, 0x940593, 0x3e71c1, 0xb3092e, 0xf3450b, +0x9c1288, 0x7b20ab, 0x9fb52e, 0xc29247, 0x2f327b, 0x6d550c, +0x90a772, 0x1fe76b, 0x96cb31, 0x4a1679, 0xe27941, 0x89dff4, +0x9794e8, 0x84e6e2, 0x973199, 0x6bed88, 0x365f5f, 0x0efdbb, +0xb49a48, 0x6ca467, 0x427271, 0x325d8d, 0xb8159f, 0x09e5bc, +0x25318d, 0x3974f7, 0x1c0530, 0x010c0d, 0x68084b, 0x58ee2c, +0x90aa47, 0x02e774, 0x24d6bd, 0xa67df7, 0x72486e, 0xef169f, +0xa6948e, 0xf691b4, 0x5153d1, 0xf20acf, 0x339820, 0x7e4bf5, +0x6863b2, 0x5f3edd, 0x035d40, 0x7f8985, 0x295255, 0xc06437, +0x10d86d, 0x324832, 0x754c5b, 0xd4714e, 0x6e5445, 0xc1090b, +0x69f52a, 0xd56614, 0x9d0727, 0x50045d, 0xdb3bb4, 0xc576ea, +0x17f987, 0x7d6b49, 0xba271d, 0x296996, 0xacccc6, 0x5414ad, +0x6ae290, 0x89d988, 0x50722c, 0xbea404, 0x940777, 0x7030f3, +0x27fc00, 0xa871ea, 0x49c266, 0x3de064, 0x83dd97, 0x973fa3, +0xfd9443, 0x8c860d, 0xde4131, 0x9d3992, 0x8c70dd, 0xe7b717, +0x3bdf08, 0x2b3715, 0xa0805c, 0x93805a, 0x921110, 0xd8e80f, +0xaf806c, 0x4bffdb, 0x0f9038, 0x761859, 0x15a562, 0xbbcb61, +0xb989c7, 0xbd4010, 0x04f2d2, 0x277549, 0xf6b6eb, 0xbb22db, +0xaa140a, 0x2f2689, 0x768364, 0x333b09, 0x1a940e, 0xaa3a51, +0xc2a31d, 0xaeedaf, 0x12265c, 0x4dc26d, 0x9c7a2d, 0x9756c0, +0x833f03, 0xf6f009, 0x8c402b, 0x99316d, 0x07b439, 0x15200c, +0x5bc3d8, 0xc492f5, 0x4badc6, 0xa5ca4e, 0xcd37a7, 0x36a9e6, +0x9492ab, 0x6842dd, 0xde6319, 0xef8c76, 0x528b68, 0x37dbfc, +0xaba1ae, 0x3115df, 0xa1ae00, 0xdafb0c, 0x664d64, 0xb705ed, +0x306529, 0xbf5657, 0x3aff47, 0xb9f96a, 0xf3be75, 0xdf9328, +0x3080ab, 0xf68c66, 0x15cb04, 0x0622fa, 0x1de4d9, 0xa4b33d, +0x8f1b57, 0x09cd36, 0xe9424e, 0xa4be13, 0xb52333, 0x1aaaf0, +0xa8654f, 0xa5c1d2, 0x0f3f0b, 0xcd785b, 0x76f923, 0x048b7b, +0x721789, 0x53a6c6, 0xe26e6f, 0x00ebef, 0x584a9b, 0xb7dac4, +0xba66aa, 0xcfcf76, 0x1d02d1, 0x2df1b1, 0xc1998c, 0x77adc3, +0xda4886, 0xa05df7, 0xf480c6, 0x2ff0ac, 0x9aecdd, 0xbc5c3f, +0x6dded0, 0x1fc790, 0xb6db2a, 0x3a25a3, 0x9aaf00, 0x9353ad, +0x0457b6, 0xb42d29, 0x7e804b, 0xa707da, 0x0eaa76, 0xa1597b, +0x2a1216, 0x2db7dc, 0xfde5fa, 0xfedb89, 0xfdbe89, 0x6c76e4, +0xfca906, 0x70803e, 0x156e85, 0xff87fd, 0x073e28, 0x336761, +0x86182a, 0xeabd4d, 0xafe7b3, 0x6e6d8f, 0x396795, 0x5bbf31, +0x48d784, 0x16df30, 0x432dc7, 0x356125, 0xce70c9, 0xb8cb30, +0xfd6cbf, 0xa200a4, 0xe46c05, 0xa0dd5a, 0x476f21, 0xd21262, +0x845cb9, 0x496170, 0xe0566b, 0x015299, 0x375550, 0xb7d51e, +0xc4f133, 0x5f6e13, 0xe4305d, 0xa92e85, 0xc3b21d, 0x3632a1, +0xa4b708, 0xd4b1ea, 0x21f716, 0xe4698f, 0x77ff27, 0x80030c, +0x2d408d, 0xa0cd4f, 0x99a520, 0xd3a2b3, 0x0a5d2f, 0x42f9b4, +0xcbda11, 0xd0be7d, 0xc1db9b, 0xbd17ab, 0x81a2ca, 0x5c6a08, +0x17552e, 0x550027, 0xf0147f, 0x8607e1, 0x640b14, 0x8d4196, +0xdebe87, 0x2afdda, 0xb6256b, 0x34897b, 0xfef305, 0x9ebfb9, +0x4f6a68, 0xa82a4a, 0x5ac44f, 0xbcf82d, 0x985ad7, 0x95c7f4, +0x8d4d0d, 0xa63a20, 0x5f57a4, 0xb13f14, 0x953880, 0x0120cc, +0x86dd71, 0xb6dec9, 0xf560bf, 0x11654d, 0x6b0701, 0xacb08c, +0xd0c0b2, 0x485551, 0x0efb1e, 0xc37295, 0x3b06a3, 0x3540c0, +0x7bdc06, 0xcc45e0, 0xfa294e, 0xc8cad6, 0x41f3e8, 0xde647c, +0xd8649b, 0x31bed9, 0xc397a4, 0xd45877, 0xc5e369, 0x13daf0, +0x3c3aba, 0x461846, 0x5f7555, 0xf5bdd2, 0xc6926e, 0x5d2eac, +0xed440e, 0x423e1c, 0x87c461, 0xe9fd29, 0xf3d6e7, 0xca7c22, +0x35916f, 0xc5e008, 0x8dd7ff, 0xe26a6e, 0xc6fdb0, 0xc10893, +0x745d7c, 0xb2ad6b, 0x9d6ecd, 0x7b723e, 0x6a11c6, 0xa9cff7, +0xdf7329, 0xbac9b5, 0x5100b7, 0x0db2e2, 0x24ba74, 0x607de5, +0x8ad874, 0x2c150d, 0x0c1881, 0x94667e, 0x162901, 0x767a9f, +0xbefdfd, 0xef4556, 0x367ed9, 0x13d9ec, 0xb9ba8b, 0xfc97c4, +0x27a831, 0xc36ef1, 0x36c594, 0x56a8d8, 0xb5a8b4, 0x0ecccf, +0x2d8912, 0x34576f, 0x89562c, 0xe3ce99, 0xb920d6, 0xaa5e6b, +0x9c2a3e, 0xcc5f11, 0x4a0bfd, 0xfbf4e1, 0x6d3b8e, 0x2c86e2, +0x84d4e9, 0xa9b4fc, 0xd1eeef, 0xc9352e, 0x61392f, 0x442138, +0xc8d91b, 0x0afc81, 0x6a4afb, 0xd81c2f, 0x84b453, 0x8c994e, +0xcc2254, 0xdc552a, 0xd6c6c0, 0x96190b, 0xb8701a, 0x649569, +0x605a26, 0xee523f, 0x0f117f, 0x11b5f4, 0xf5cbfc, 0x2dbc34, +0xeebc34, 0xcc5de8, 0x605edd, 0x9b8e67, 0xef3392, 0xb817c9, +0x9b5861, 0xbc57e1, 0xc68351, 0x103ed8, 0x4871dd, 0xdd1c2d, +0xa118af, 0x462c21, 0xd7f359, 0x987ad9, 0xc0549e, 0xfa864f, +0xfc0656, 0xae79e5, 0x362289, 0x22ad38, 0xdc9367, 0xaae855, +0x382682, 0x9be7ca, 0xa40d51, 0xb13399, 0x0ed7a9, 0x480569, +0xf0b265, 0xa7887f, 0x974c88, 0x36d1f9, 0xb39221, 0x4a827b, +0x21cf98, 0xdc9f40, 0x5547dc, 0x3a74e1, 0x42eb67, 0xdf9dfe, +0x5fd45e, 0xa4677b, 0x7aacba, 0xa2f655, 0x23882b, 0x55ba41, +0x086e59, 0x862a21, 0x834739, 0xe6e389, 0xd49ee5, 0x40fb49, +0xe956ff, 0xca0f1c, 0x8a59c5, 0x2bfa94, 0xc5c1d3, 0xcfc50f, +0xae5adb, 0x86c547, 0x624385, 0x3b8621, 0x94792c, 0x876110, +0x7b4c2a, 0x1a2c80, 0x12bf43, 0x902688, 0x893c78, 0xe4c4a8, +0x7bdbe5, 0xc23ac4, 0xeaf426, 0x8a67f7, 0xbf920d, 0x2ba365, +0xb1933d, 0x0b7cbd, 0xdc51a4, 0x63dd27, 0xdde169, 0x19949a, +0x9529a8, 0x28ce68, 0xb4ed09, 0x209f44, 0xca984e, 0x638270, +0x237c7e, 0x32b90f, 0x8ef5a7, 0xe75614, 0x08f121, 0x2a9db5, +0x4d7e6f, 0x5119a5, 0xabf9b5, 0xd6df82, 0x61dd96, 0x023616, +0x9f3ac4, 0xa1a283, 0x6ded72, 0x7a8d39, 0xa9b882, 0x5c326b, +0x5b2746, 0xed3400, 0x7700d2, 0x55f4fc, 0x4d5901, 0x8071e0, +0xe13f89, 0xb295f3, 0x64a8f1, 0xaea74b, 0x38fc4c, 0xeab2bb, +0x47270b, 0xabc3a7, 0x34ba60, 0x52dd34, 0xf8563a, 0xeb7e8a, +0x31bb36, 0x5895b7, 0x47f7a9, 0x94c3aa, 0xd39225, 0x1e7f3e, +0xd8974e, 0xbba94f, 0xd8ae01, 0xe661b4, 0x393d8e, 0xa523aa, +0x33068e, 0x1633b5, 0x3bb188, 0x1d3a9d, 0x4013d0, 0xcc1be5, +0xf862e7, 0x3bf28f, 0x39b5bf, 0x0bc235, 0x22747e, 0xa247c0, +0xd52d1f, 0x19add3, 0x9094df, 0x9311d0, 0xb42b25, 0x496db2, +0xe264b2, 0x5ef135, 0x3bc6a4, 0x1a4ad0, 0xaac92e, 0x64e886, +0x573091, 0x982cfb, 0x311b1a, 0x08728b, 0xbdcee1, 0x60e142, +0xeb641d, 0xd0bba3, 0xe559d4, 0x597b8c, 0x2a4483, 0xf332ba, +0xf84867, 0x2c8d1b, 0x2fa9b0, 0x50f3dd, 0xf9f573, 0xdb61b4, +0xfe233e, 0x6c41a6, 0xeea318, 0x775a26, 0xbc5e5c, 0xcea708, +0x94dc57, 0xe20196, 0xf1e839, 0xbe4851, 0x5d2d2f, 0x4e9555, +0xd96ec2, 0xe7d755, 0x6304e0, 0xc02e0e, 0xfc40a0, 0xbbf9b3, +0x7125a7, 0x222dfb, 0xf619d8, 0x838c1c, 0x6619e6, 0xb20d55, +0xbb5137, 0x79e809, 0xaf9149, 0x0d73de, 0x0b0da5, 0xce7f58, +0xac1934, 0x724667, 0x7a1a13, 0x9e26bc, 0x4555e7, 0x585cb5, +0x711d14, 0x486991, 0x480d60, 0x56adab, 0xd62f64, 0x96ee0c, +0x212ff3, 0x5d6d88, 0xa67684, 0x95651e, 0xab9e0a, 0x4ddefe, +0x571010, 0x836a39, 0xf8ea31, 0x9e381d, 0xeac8b1, 0xcac96b, +0x37f21e, 0xd505e9, 0x984743, 0x9fc56c, 0x0331b7, 0x3b8bf8, +0x86e56a, 0x8dc343, 0x6230e7, 0x93cfd5, 0x6a8f2d, 0x733005, +0x1af021, 0xa09fcb, 0x7415a1, 0xd56b23, 0x6ff725, 0x2f4bc7, +0xb8a591, 0x7fac59, 0x5c55de, 0x212c38, 0xb13296, 0x5cff50, +0x366262, 0xfa7b16, 0xf4d9a6, 0x2acfe7, 0xf07403, 0xd4d604, +0x6fd916, 0x31b1bf, 0xcbb450, 0x5bd7c8, 0x0ce194, 0x6bd643, +0x4fd91c, 0xdf4543, 0x5f3453, 0xe2b5aa, 0xc9aec8, 0x131485, +0xf9d2bf, 0xbadb9e, 0x76f5b9, 0xaf15cf, 0xca3182, 0x14b56d, +0xe9fe4d, 0x50fc35, 0xf5aed5, 0xa2d0c1, 0xc96057, 0x192eb6, +0xe91d92, 0x07d144, 0xaea3c6, 0x343566, 0x26d5b4, 0x3161e2, +0x37f1a2, 0x209eff, 0x958e23, 0x493798, 0x35f4a6, 0x4bdc02, +0xc2be13, 0xbe80a0, 0x0b72a3, 0x115c5f, 0x1e1bd1, 0x0db4d3, +0x869e85, 0x96976b, 0x2ac91f, 0x8a26c2, 0x3070f0, 0x041412, +0xfc9fa5, 0xf72a38, 0x9c6878, 0xe2aa76, 0x50cfe1, 0x559274, +0x934e38, 0x0a92f7, 0x5533f0, 0xa63db4, 0x399971, 0xe2b755, +0xa98a7c, 0x008f19, 0xac54d2, 0x2ea0b4, 0xf5f3e0, 0x60c849, +0xffd269, 0xae52ce, 0x7a5fdd, 0xe9ce06, 0xfb0ae8, 0xa50cce, +0xea9d3e, 0x3766dd, 0xb834f5, 0x0da090, 0x846f88, 0x4ae3d5, +0x099a03, 0x2eae2d, 0xfcb40a, 0xfb9b33, 0xe281dd, 0x1b16ba, +0xd8c0af, 0xd96b97, 0xb52dc9, 0x9c277f, 0x5951d5, 0x21ccd6, +0xb6496b, 0x584562, 0xb3baf2, 0xa1a5c4, 0x7ca2cf, 0xa9b93d, +0x7b7b89, 0x483d38, +}; + +int32_t +__ieee754_rem_pio2l (long double x, long double *y) +{ + double tx[3], ty[3]; + int32_t se, j0; + u_int32_t i0, i1; + int sx; + int n, exp; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + sx = (se >> 15) & 1; + j0 = (se & 0x7fff) - 0x3fff; + + if (j0 < -1) + { + /* |x| < pi/4. */ + y[0] = x; + y[1] = 0; + return 0; + } + + if (j0 >= 0x8000) + { + /* x is infinite or NaN. */ + y[0] = x - x; + y[1] = y[0]; + return 0; + } + + /* Split the 64 bits of the mantissa into three 24-bit integers + stored in a double array. */ + exp = j0 - 23; + tx[0] = (double) (i0 >> 8); + tx[1] = (double) (((i0 << 16) | (i1 >> 16)) & 0xffffff); + tx[2] = (double) ((i1 << 8) & 0xffffff); + + n = __kernel_rem_pio2 (tx, ty, exp, 3, 2, two_over_pi); + + /* The result is now stored in two double values, we need to convert + it into two long double values. */ + if (sx == 0) + { + y[0] = (long double) ty[0] + (long double) ty[1]; + y[1] = ty[1] - (y[0] - ty[0]); + return n; + } + else + { + y[0] = -((long double) ty[0] + (long double) ty[1]); + y[1] = -ty[1] - (y[0] + ty[0]); + return -n; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/e_sinhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_sinhl.c new file mode 100644 index 0000000000..095b142621 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_sinhl.c @@ -0,0 +1,87 @@ +/* e_asinhl.c -- long double version of e_asinh.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* __ieee754_sinhl(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x) + * 2 + * + * 25 <= x <= lnovft : sinhl(x) := expl(x)/2 + * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2) + * ln2ovft < x : sinhl(x) := x*shuge (overflow) + * + * Special cases: + * sinhl(x) is |x| if x is +INF, -INF, or NaN. + * only sinhl(0)=0 is exact for finite x. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double one = 1.0, shuge = 1.0e4931L; + +long double +__ieee754_sinhl(long double x) +{ + long double t,w,h; + u_int32_t jx,ix,i0,i1; + + /* Words of |x|. */ + GET_LDOUBLE_WORDS(jx,i0,i1,x); + ix = jx&0x7fff; + + /* x is INF or NaN */ + if(__builtin_expect(ix==0x7fff, 0)) return x+x; + + h = 0.5; + if (jx & 0x8000) h = -h; + /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x|<25 */ + if (ix<0x3fdf) { /* |x|<2**-32 */ + math_check_force_underflow (x); + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + } + t = __expm1l(fabsl(x)); + if(ix<0x3fff) return h*(2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7)) + return h*__ieee754_expl(fabsl(x)); + + /* |x| in [log(maxdouble), overflowthreshold] */ + if (ix<0x400c || (ix == 0x400c && (i0 < 0xb174ddc0 + || (i0 == 0xb174ddc0 + && i1 <= 0x31aec0ea)))) { + w = __ieee754_expl(0.5*fabsl(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthreshold, sinhl(x) overflow */ + return x*shuge; +} +strong_alias (__ieee754_sinhl, __sinhl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/gamma_product.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/gamma_product.c new file mode 100644 index 0000000000..31931bbd17 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/gamma_product.c @@ -0,0 +1,43 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +double +__gamma_product (double x, double x_eps, int n, double *eps) +{ + long double x_full = (long double) x + (long double) x_eps; + long double ret = x_full; + for (int i = 1; i < n; i++) + ret *= x_full + i; + + double fret = math_narrow_eval ((double) ret); + *eps = (ret - fret) / fret; + + return fret; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/gamma_productl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/gamma_productl.c new file mode 100644 index 0000000000..0f1ccc4a2d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/gamma_productl.c @@ -0,0 +1,45 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_splitl.h> + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +long double +__gamma_productl (long double x, long double x_eps, int n, long double *eps) +{ + SET_RESTORE_ROUNDL (FE_TONEAREST); + long double ret = x; + *eps = x_eps / x; + for (int i = 1; i < n; i++) + { + *eps += x_eps / (x + i); + long double lo; + mul_splitl (&ret, &lo, ret, x + i); + *eps += lo / ret; + } + return ret; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/include/bits/iscanonical.h b/REORG.TODO/sysdeps/ieee754/ldbl-96/include/bits/iscanonical.h new file mode 100644 index 0000000000..bee080bd29 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/include/bits/iscanonical.h @@ -0,0 +1,5 @@ +#include_next <bits/iscanonical.h> + +#ifndef _ISOMAC +libm_hidden_proto (__iscanonicall) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/k_cosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/k_cosl.c new file mode 100644 index 0000000000..8e3cd49f81 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/k_cosl.c @@ -0,0 +1,123 @@ +/* Extended-precision floating point cosine on <-pi/4,pi/4>. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Based on quad-precision cosine by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* The polynomials have not been optimized for extended-precision and + may contain more terms than needed. */ + +static const long double c[] = { +#define ONE c[0] + 1.00000000000000000000000000000000000E+00L, + +/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) + x in <0,1/256> */ +#define SCOS1 c[1] +#define SCOS2 c[2] +#define SCOS3 c[3] +#define SCOS4 c[4] +#define SCOS5 c[5] +-5.00000000000000000000000000000000000E-01L, + 4.16666666666666666666666666556146073E-02L, +-1.38888888888888888888309442601939728E-03L, + 2.48015873015862382987049502531095061E-05L, +-2.75573112601362126593516899592158083E-07L, + +/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) + x in <0,0.1484375> */ +#define COS1 c[6] +#define COS2 c[7] +#define COS3 c[8] +#define COS4 c[9] +#define COS5 c[10] +#define COS6 c[11] +#define COS7 c[12] +#define COS8 c[13] +-4.99999999999999999999999999999999759E-01L, + 4.16666666666666666666666666651287795E-02L, +-1.38888888888888888888888742314300284E-03L, + 2.48015873015873015867694002851118210E-05L, +-2.75573192239858811636614709689300351E-07L, + 2.08767569877762248667431926878073669E-09L, +-1.14707451049343817400420280514614892E-11L, + 4.77810092804389587579843296923533297E-14L, + +/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) + x in <0,1/256> */ +#define SSIN1 c[14] +#define SSIN2 c[15] +#define SSIN3 c[16] +#define SSIN4 c[17] +#define SSIN5 c[18] +-1.66666666666666666666666666666666659E-01L, + 8.33333333333333333333333333146298442E-03L, +-1.98412698412698412697726277416810661E-04L, + 2.75573192239848624174178393552189149E-06L, +-2.50521016467996193495359189395805639E-08L, +}; + +#define SINCOSL_COS_HI 0 +#define SINCOSL_COS_LO 1 +#define SINCOSL_SIN_HI 2 +#define SINCOSL_SIN_LO 3 +extern const long double __sincosl_table[]; + +long double +__kernel_cosl(long double x, long double y) +{ + long double h, l, z, sin_l, cos_l_m1; + int index; + + if (signbit (x)) + { + x = -x; + y = -y; + } + if (x < 0.1484375L) + { + /* Argument is small enough to approximate it by a Chebyshev + polynomial of degree 16. */ + if (x < 0x1p-33L) + if (!((int)x)) return ONE; /* generate inexact */ + z = x * x; + return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ + z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); + } + else + { + /* So that we don't have to use too large polynomial, we find + l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 + possible values for h. We look up cosl(h) and sinl(h) in + pre-computed tables, compute cosl(l) and sinl(l) using a + Chebyshev polynomial of degree 10(11) and compute + cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ + index = (int) (128 * (x - (0.1484375L - 1.0L / 256.0L))); + h = 0.1484375L + index / 128.0; + index *= 4; + l = y - (h - x); + z = l * l; + sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); + cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); + return __sincosl_table [index + SINCOSL_COS_HI] + + (__sincosl_table [index + SINCOSL_COS_LO] + - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l + - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1)); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/k_sinl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/k_sinl.c new file mode 100644 index 0000000000..d56023aa8d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/k_sinl.c @@ -0,0 +1,130 @@ +/* Quad-precision floating point sine on <-pi/4,pi/4>. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Based on quad-precision sine by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* The polynomials have not been optimized for extended-precision and + may contain more terms than needed. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +/* The polynomials have not been optimized for extended-precision and + may contain more terms than needed. */ + +static const long double c[] = { +#define ONE c[0] + 1.00000000000000000000000000000000000E+00L, + +/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) + x in <0,1/256> */ +#define SCOS1 c[1] +#define SCOS2 c[2] +#define SCOS3 c[3] +#define SCOS4 c[4] +#define SCOS5 c[5] +-5.00000000000000000000000000000000000E-01L, + 4.16666666666666666666666666556146073E-02L, +-1.38888888888888888888309442601939728E-03L, + 2.48015873015862382987049502531095061E-05L, +-2.75573112601362126593516899592158083E-07L, + +/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) + x in <0,0.1484375> */ +#define SIN1 c[6] +#define SIN2 c[7] +#define SIN3 c[8] +#define SIN4 c[9] +#define SIN5 c[10] +#define SIN6 c[11] +#define SIN7 c[12] +#define SIN8 c[13] +-1.66666666666666666666666666666666538e-01L, + 8.33333333333333333333333333307532934e-03L, +-1.98412698412698412698412534478712057e-04L, + 2.75573192239858906520896496653095890e-06L, +-2.50521083854417116999224301266655662e-08L, + 1.60590438367608957516841576404938118e-10L, +-7.64716343504264506714019494041582610e-13L, + 2.81068754939739570236322404393398135e-15L, + +/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) + x in <0,1/256> */ +#define SSIN1 c[14] +#define SSIN2 c[15] +#define SSIN3 c[16] +#define SSIN4 c[17] +#define SSIN5 c[18] +-1.66666666666666666666666666666666659E-01L, + 8.33333333333333333333333333146298442E-03L, +-1.98412698412698412697726277416810661E-04L, + 2.75573192239848624174178393552189149E-06L, +-2.50521016467996193495359189395805639E-08L, +}; + +#define SINCOSL_COS_HI 0 +#define SINCOSL_COS_LO 1 +#define SINCOSL_SIN_HI 2 +#define SINCOSL_SIN_LO 3 +extern const long double __sincosl_table[]; + +long double +__kernel_sinl(long double x, long double y, int iy) +{ + long double absx, h, l, z, sin_l, cos_l_m1; + int index; + + absx = fabsl (x); + if (absx < 0.1484375L) + { + /* Argument is small enough to approximate it by a Chebyshev + polynomial of degree 17. */ + if (absx < 0x1p-33L) + { + math_check_force_underflow (x); + if (!((int)x)) return x; /* generate inexact */ + } + z = x * x; + return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ + z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); + } + else + { + /* So that we don't have to use too large polynomial, we find + l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 + possible values for h. We look up cosl(h) and sinl(h) in + pre-computed tables, compute cosl(l) and sinl(l) using a + Chebyshev polynomial of degree 10(11) and compute + sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */ + index = (int) (128 * (absx - (0.1484375L - 1.0L / 256.0L))); + h = 0.1484375L + index / 128.0; + index *= 4; + if (iy) + l = (x < 0 ? -y : y) - (h - absx); + else + l = absx - h; + z = l * l; + sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); + cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); + z = __sincosl_table [index + SINCOSL_SIN_HI] + + (__sincosl_table [index + SINCOSL_SIN_LO] + + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1) + + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l)); + return (x < 0) ? -z : z; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/k_tanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/k_tanl.c new file mode 100644 index 0000000000..f8641d5ce4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/k_tanl.c @@ -0,0 +1,152 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __kernel_tanl( x, y, k ) + * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input k indicates whether tan (if k=1) or + * -1/tan (if k= -1) is returned. + * + * Algorithm + * 1. Since tan(-x) = -tan(x), we need only to consider positive x. + * 2. if x < 2^-33, return x with inexact if x!=0. + * 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2) + * on [0,0.67433]. + * + * Note: tan(x+y) = tan(x) + tan'(x)*y + * ~ tan(x) + (1+x*x)*y + * Therefore, for better accuracy in computing tan(x+y), let + * r = x^3 * R(x^2) + * then + * tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y)) + * + * 4. For x in [0.67433,pi/4], let y = pi/4 - x, then + * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) + * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <libc-diag.h> + +static const long double + one = 1.0L, + pio4hi = 0xc.90fdaa22168c235p-4L, + pio4lo = -0x3.b399d747f23e32ecp-68L, + + /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2) + 0 <= x <= 0.6743316650390625 + Peak relative error 8.0e-36 */ + TH = 3.333333333333333333333333333333333333333E-1L, + T0 = -1.813014711743583437742363284336855889393E7L, + T1 = 1.320767960008972224312740075083259247618E6L, + T2 = -2.626775478255838182468651821863299023956E4L, + T3 = 1.764573356488504935415411383687150199315E2L, + T4 = -3.333267763822178690794678978979803526092E-1L, + + U0 = -1.359761033807687578306772463253710042010E8L, + U1 = 6.494370630656893175666729313065113194784E7L, + U2 = -4.180787672237927475505536849168729386782E6L, + U3 = 8.031643765106170040139966622980914621521E4L, + U4 = -5.323131271912475695157127875560667378597E2L; + /* 1.000000000000000000000000000000000000000E0 */ + + +long double +__kernel_tanl (long double x, long double y, int iy) +{ + long double z, r, v, w, s; + long double absx = fabsl (x); + int sign; + + if (absx < 0x1p-33) + { + if ((int) x == 0) + { /* generate inexact */ + if (x == 0 && iy == -1) + return one / fabsl (x); + else if (iy == 1) + { + math_check_force_underflow_nonneg (absx); + return x; + } + else + return -one / x; + } + } + if (absx >= 0.6743316650390625L) + { + if (signbit (x)) + { + x = -x; + y = -y; + sign = -1; + } + else + sign = 1; + z = pio4hi - x; + w = pio4lo - y; + x = z + w; + y = 0.0; + } + z = x * x; + r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4))); + v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z)))); + r = r / v; + + s = z * x; + r = y + z * (s * r + y); + r += TH * s; + w = x + r; + if (absx >= 0.6743316650390625L) + { + v = (long double) iy; + w = (v - 2.0 * (x - (w * w / (w + v) - r))); + /* SIGN is set for arguments that reach this code, but not + otherwise, resulting in warnings that it may be used + uninitialized although in the cases where it is used it has + always been set. */ + DIAG_PUSH_NEEDS_COMMENT; + DIAG_IGNORE_NEEDS_COMMENT (4.8, "-Wmaybe-uninitialized"); + if (sign < 0) + w = -w; + DIAG_POP_NEEDS_COMMENT; + return w; + } + if (iy == 1) + return w; + else + return -1.0 / (x + r); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/ldbl2mpn.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/ldbl2mpn.c new file mode 100644 index 0000000000..425078e1de --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/ldbl2mpn.c @@ -0,0 +1,94 @@ +/* Copyright (C) 1995-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include "longlong.h" +#include <ieee754.h> +#include <float.h> +#include <math.h> +#include <stdlib.h> + +/* Convert a `long double' in IEEE854 standard double-precision format to a + multi-precision integer representing the significand scaled up by its + number of bits (64 for long double) and an integral power of two + (MPN frexpl). */ + +mp_size_t +__mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size, + int *expt, int *is_neg, + long double value) +{ + union ieee854_long_double u; + u.d = value; + + *is_neg = u.ieee.negative; + *expt = (int) u.ieee.exponent - IEEE854_LONG_DOUBLE_BIAS; + +#if BITS_PER_MP_LIMB == 32 + res_ptr[0] = u.ieee.mantissa1; /* Low-order 32 bits of fraction. */ + res_ptr[1] = u.ieee.mantissa0; /* High-order 32 bits. */ + #define N 2 +#elif BITS_PER_MP_LIMB == 64 + /* Hopefully the compiler will combine the two bitfield extracts + and this composition into just the original quadword extract. */ + res_ptr[0] = ((mp_limb_t) u.ieee.mantissa0 << 32) | u.ieee.mantissa1; + #define N 1 +#else + #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif + + if (u.ieee.exponent == 0) + { + /* A biased exponent of zero is a special case. + Either it is a zero or it is a denormal number. */ + if (res_ptr[0] == 0 && res_ptr[N - 1] == 0) /* Assumes N<=2. */ + /* It's zero. */ + *expt = 0; + else + { + /* It is a denormal number, meaning it has no implicit leading + one bit, and its exponent is in fact the format minimum. */ + int cnt; + + if (res_ptr[N - 1] != 0) + { + count_leading_zeros (cnt, res_ptr[N - 1]); + if (cnt != 0) + { +#if N == 2 + res_ptr[N - 1] = res_ptr[N - 1] << cnt + | (res_ptr[0] >> (BITS_PER_MP_LIMB - cnt)); + res_ptr[0] <<= cnt; +#else + res_ptr[N - 1] <<= cnt; +#endif + } + *expt = LDBL_MIN_EXP - 1 - cnt; + } + else + { + count_leading_zeros (cnt, res_ptr[0]); + res_ptr[N - 1] = res_ptr[0] << cnt; + res_ptr[0] = 0; + *expt = LDBL_MIN_EXP - 1 - BITS_PER_MP_LIMB - cnt; + } + } + } + + return N; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/lgamma_negl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/lgamma_negl.c new file mode 100644 index 0000000000..36beb764be --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/lgamma_negl.c @@ -0,0 +1,418 @@ +/* lgammal expanding around zeros. + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double lgamma_zeros[][2] = + { + { -0x2.74ff92c01f0d82acp+0L, 0x1.360cea0e5f8ed3ccp-68L }, + { -0x2.bf6821437b201978p+0L, -0x1.95a4b4641eaebf4cp-64L }, + { -0x3.24c1b793cb35efb8p+0L, -0xb.e699ad3d9ba6545p-68L }, + { -0x3.f48e2a8f85fca17p+0L, -0xd.4561291236cc321p-68L }, + { -0x4.0a139e16656030cp+0L, -0x3.9f0b0de18112ac18p-64L }, + { -0x4.fdd5de9bbabf351p+0L, -0xd.0aa4076988501d8p-68L }, + { -0x5.021a95fc2db64328p+0L, -0x2.4c56e595394decc8p-64L }, + { -0x5.ffa4bd647d0357ep+0L, 0x2.b129d342ce12071cp-64L }, + { -0x6.005ac9625f233b6p+0L, -0x7.c2d96d16385cb868p-68L }, + { -0x6.fff2fddae1bbff4p+0L, 0x2.9d949a3dc02de0cp-64L }, + { -0x7.000cff7b7f87adf8p+0L, 0x3.b7d23246787d54d8p-64L }, + { -0x7.fffe5fe05673c3c8p+0L, -0x2.9e82b522b0ca9d3p-64L }, + { -0x8.0001a01459fc9f6p+0L, -0xc.b3cec1cec857667p-68L }, + { -0x8.ffffd1c425e81p+0L, 0x3.79b16a8b6da6181cp-64L }, + { -0x9.00002e3bb47d86dp+0L, -0x6.d843fedc351deb78p-64L }, + { -0x9.fffffb606bdfdcdp+0L, -0x6.2ae77a50547c69dp-68L }, + { -0xa.0000049f93bb992p+0L, -0x7.b45d95e15441e03p-64L }, + { -0xa.ffffff9466e9f1bp+0L, -0x3.6dacd2adbd18d05cp-64L }, + { -0xb.0000006b9915316p+0L, 0x2.69a590015bf1b414p-64L }, + { -0xb.fffffff70893874p+0L, 0x7.821be533c2c36878p-64L }, + { -0xc.00000008f76c773p+0L, -0x1.567c0f0250f38792p-64L }, + { -0xc.ffffffff4f6dcf6p+0L, -0x1.7f97a5ffc757d548p-64L }, + { -0xd.00000000b09230ap+0L, 0x3.f997c22e46fc1c9p-64L }, + { -0xd.fffffffff36345bp+0L, 0x4.61e7b5c1f62ee89p-64L }, + { -0xe.000000000c9cba5p+0L, -0x4.5e94e75ec5718f78p-64L }, + { -0xe.ffffffffff28c06p+0L, -0xc.6604ef30371f89dp-68L }, + { -0xf.0000000000d73fap+0L, 0xc.6642f1bdf07a161p-68L }, + { -0xf.fffffffffff28cp+0L, -0x6.0c6621f512e72e5p-64L }, + { -0x1.000000000000d74p+4L, 0x6.0c6625ebdb406c48p-64L }, + { -0x1.0ffffffffffff356p+4L, -0x9.c47e7a93e1c46a1p-64L }, + { -0x1.1000000000000caap+4L, 0x9.c47e7a97778935ap-64L }, + { -0x1.1fffffffffffff4cp+4L, 0x1.3c31dcbecd2f74d4p-64L }, + { -0x1.20000000000000b4p+4L, -0x1.3c31dcbeca4c3b3p-64L }, + { -0x1.2ffffffffffffff6p+4L, -0x8.5b25cbf5f545ceep-64L }, + { -0x1.300000000000000ap+4L, 0x8.5b25cbf5f547e48p-64L }, + { -0x1.4p+4L, 0x7.950ae90080894298p-64L }, + { -0x1.4p+4L, -0x7.950ae9008089414p-64L }, + { -0x1.5p+4L, 0x5.c6e3bdb73d5c63p-68L }, + { -0x1.5p+4L, -0x5.c6e3bdb73d5c62f8p-68L }, + { -0x1.6p+4L, 0x4.338e5b6dfe14a518p-72L }, + { -0x1.6p+4L, -0x4.338e5b6dfe14a51p-72L }, + { -0x1.7p+4L, 0x2.ec368262c7033b3p-76L }, + { -0x1.7p+4L, -0x2.ec368262c7033b3p-76L }, + { -0x1.8p+4L, 0x1.f2cf01972f577ccap-80L }, + { -0x1.8p+4L, -0x1.f2cf01972f577ccap-80L }, + { -0x1.9p+4L, 0x1.3f3ccdd165fa8d4ep-84L }, + { -0x1.9p+4L, -0x1.3f3ccdd165fa8d4ep-84L }, + { -0x1.ap+4L, 0xc.4742fe35272cd1cp-92L }, + { -0x1.ap+4L, -0xc.4742fe35272cd1cp-92L }, + { -0x1.bp+4L, 0x7.46ac70b733a8c828p-96L }, + { -0x1.bp+4L, -0x7.46ac70b733a8c828p-96L }, + { -0x1.cp+4L, 0x4.2862898d42174ddp-100L }, + { -0x1.cp+4L, -0x4.2862898d42174ddp-100L }, + { -0x1.dp+4L, 0x2.4b3f31686b15af58p-104L }, + { -0x1.dp+4L, -0x2.4b3f31686b15af58p-104L }, + { -0x1.ep+4L, 0x1.3932c5047d60e60cp-108L }, + { -0x1.ep+4L, -0x1.3932c5047d60e60cp-108L }, + { -0x1.fp+4L, 0xa.1a6973c1fade217p-116L }, + { -0x1.fp+4L, -0xa.1a6973c1fade217p-116L }, + { -0x2p+4L, 0x5.0d34b9e0fd6f10b8p-120L }, + { -0x2p+4L, -0x5.0d34b9e0fd6f10b8p-120L }, + { -0x2.1p+4L, 0x2.73024a9ba1aa36a8p-124L }, + }; + +static const long double e_hi = 0x2.b7e151628aed2a6cp+0L; +static const long double e_lo = -0x1.408ea77f630b0c38p-64L; + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) in Stirling's + approximation to lgamma function. */ + +static const long double lgamma_coeff[] = + { + 0x1.5555555555555556p-4L, + -0xb.60b60b60b60b60bp-12L, + 0x3.4034034034034034p-12L, + -0x2.7027027027027028p-12L, + 0x3.72a3c5631fe46aep-12L, + -0x7.daac36664f1f208p-12L, + 0x1.a41a41a41a41a41ap-8L, + -0x7.90a1b2c3d4e5f708p-8L, + 0x2.dfd2c703c0cfff44p-4L, + -0x1.6476701181f39edcp+0L, + 0xd.672219167002d3ap+0L, + -0x9.cd9292e6660d55bp+4L, + 0x8.911a740da740da7p+8L, + -0x8.d0cc570e255bf5ap+12L, + 0xa.8d1044d3708d1c2p+16L, + -0xe.8844d8a169abbc4p+20L, + }; + +#define NCOEFF (sizeof (lgamma_coeff) / sizeof (lgamma_coeff[0])) + +/* Polynomial approximations to (|gamma(x)|-1)(x-n)/(x-x0), where n is + the integer end-point of the half-integer interval containing x and + x0 is the zero of lgamma in that half-integer interval. Each + polynomial is expressed in terms of x-xm, where xm is the midpoint + of the interval for which the polynomial applies. */ + +static const long double poly_coeff[] = + { + /* Interval [-2.125, -2] (polynomial degree 13). */ + -0x1.0b71c5c54d42eb6cp+0L, + -0xc.73a1dc05f349517p-4L, + -0x1.ec841408528b6baep-4L, + -0xe.37c9da26fc3b492p-4L, + -0x1.03cd87c5178991ap-4L, + -0xe.ae9ada65ece2f39p-4L, + 0x9.b1185505edac18dp-8L, + -0xe.f28c130b54d3cb2p-4L, + 0x2.6ec1666cf44a63bp-4L, + -0xf.57cb2774193bbd5p-4L, + 0x4.5ae64671a41b1c4p-4L, + -0xf.f48ea8b5bd3a7cep-4L, + 0x6.7d73788a8d30ef58p-4L, + -0x1.11e0e4b506bd272ep+0L, + /* Interval [-2.25, -2.125] (polynomial degree 13). */ + -0xf.2930890d7d675a8p-4L, + -0xc.a5cfde054eab5cdp-4L, + 0x3.9c9e0fdebb0676e4p-4L, + -0x1.02a5ad35605f0d8cp+0L, + 0x9.6e9b1185d0b92edp-4L, + -0x1.4d8332f3d6a3959p+0L, + 0x1.1c0c8cacd0ced3eap+0L, + -0x1.c9a6f592a67b1628p+0L, + 0x1.d7e9476f96aa4bd6p+0L, + -0x2.921cedb488bb3318p+0L, + 0x2.e8b3fd6ca193e4c8p+0L, + -0x3.cb69d9d6628e4a2p+0L, + 0x4.95f12c73b558638p+0L, + -0x5.d392d0b97c02ab6p+0L, + /* Interval [-2.375, -2.25] (polynomial degree 14). */ + -0xd.7d28d505d618122p-4L, + -0xe.69649a304098532p-4L, + 0xb.0d74a2827d055c5p-4L, + -0x1.924b09228531c00ep+0L, + 0x1.d49b12bccee4f888p+0L, + -0x3.0898bb7dbb21e458p+0L, + 0x4.207a6cad6fa10a2p+0L, + -0x6.39ee630b46093ad8p+0L, + 0x8.e2e25211a3fb5ccp+0L, + -0xd.0e85ccd8e79c08p+0L, + 0x1.2e45882bc17f9e16p+4L, + -0x1.b8b6e841815ff314p+4L, + 0x2.7ff8bf7504fa04dcp+4L, + -0x3.c192e9c903352974p+4L, + 0x5.8040b75f4ef07f98p+4L, + /* Interval [-2.5, -2.375] (polynomial degree 15). */ + -0xb.74ea1bcfff94b2cp-4L, + -0x1.2a82bd590c375384p+0L, + 0x1.88020f828b968634p+0L, + -0x3.32279f040eb80fa4p+0L, + 0x5.57ac825175943188p+0L, + -0x9.c2aedcfe10f129ep+0L, + 0x1.12c132f2df02881ep+4L, + -0x1.ea94e26c0b6ffa6p+4L, + 0x3.66b4a8bb0290013p+4L, + -0x6.0cf735e01f5990bp+4L, + 0xa.c10a8db7ae99343p+4L, + -0x1.31edb212b315feeap+8L, + 0x2.1f478592298b3ebp+8L, + -0x3.c546da5957ace6ccp+8L, + 0x7.0e3d2a02579ba4bp+8L, + -0xc.b1ea961c39302f8p+8L, + /* Interval [-2.625, -2.5] (polynomial degree 16). */ + -0x3.d10108c27ebafad4p-4L, + 0x1.cd557caff7d2b202p+0L, + 0x3.819b4856d3995034p+0L, + 0x6.8505cbad03dd3bd8p+0L, + 0xb.c1b2e653aa0b924p+0L, + 0x1.50a53a38f05f72d6p+4L, + 0x2.57ae00cbd06efb34p+4L, + 0x4.2b1563077a577e9p+4L, + 0x7.6989ed790138a7f8p+4L, + 0xd.2dd28417b4f8406p+4L, + 0x1.76e1b71f0710803ap+8L, + 0x2.9a7a096254ac032p+8L, + 0x4.a0e6109e2a039788p+8L, + 0x8.37ea17a93c877b2p+8L, + 0xe.9506a641143612bp+8L, + 0x1.b680ed4ea386d52p+12L, + 0x3.28a2130c8de0ae84p+12L, + /* Interval [-2.75, -2.625] (polynomial degree 15). */ + -0x6.b5d252a56e8a7548p-4L, + 0x1.28d60383da3ac72p+0L, + 0x1.db6513ada8a6703ap+0L, + 0x2.e217118f9d34aa7cp+0L, + 0x4.450112c5cbd6256p+0L, + 0x6.4af99151e972f92p+0L, + 0x9.2db598b5b183cd6p+0L, + 0xd.62bef9c9adcff6ap+0L, + 0x1.379f290d743d9774p+4L, + 0x1.c58271ff823caa26p+4L, + 0x2.93a871b87a06e73p+4L, + 0x3.bf9db66103d7ec98p+4L, + 0x5.73247c111fbf197p+4L, + 0x7.ec8b9973ba27d008p+4L, + 0xb.eca5f9619b39c03p+4L, + 0x1.18f2e46411c78b1cp+8L, + /* Interval [-2.875, -2.75] (polynomial degree 14). */ + -0x8.a41b1e4f36ff88ep-4L, + 0xc.da87d3b69dc0f34p-4L, + 0x1.1474ad5c36158ad2p+0L, + 0x1.761ecb90c5553996p+0L, + 0x1.d279bff9ae234f8p+0L, + 0x2.4e5d0055a16c5414p+0L, + 0x2.d57545a783902f8cp+0L, + 0x3.8514eec263aa9f98p+0L, + 0x4.5235e338245f6fe8p+0L, + 0x5.562b1ef200b256c8p+0L, + 0x6.8ec9782b93bd565p+0L, + 0x8.14baf4836483508p+0L, + 0x9.efaf35dc712ea79p+0L, + 0xc.8431f6a226507a9p+0L, + 0xf.80358289a768401p+0L, + /* Interval [-3, -2.875] (polynomial degree 13). */ + -0xa.046d667e468f3e4p-4L, + 0x9.70b88dcc006c216p-4L, + 0xa.a8a39421c86ce9p-4L, + 0xd.2f4d1363f321e89p-4L, + 0xd.ca9aa1a3ab2f438p-4L, + 0xf.cf09c31f05d02cbp-4L, + 0x1.04b133a195686a38p+0L, + 0x1.22b54799d0072024p+0L, + 0x1.2c5802b869a36ae8p+0L, + 0x1.4aadf23055d7105ep+0L, + 0x1.5794078dd45c55d6p+0L, + 0x1.7759069da18bcf0ap+0L, + 0x1.8e672cefa4623f34p+0L, + 0x1.b2acfa32c17145e6p+0L, + }; + +static const size_t poly_deg[] = + { + 13, + 13, + 14, + 15, + 16, + 15, + 14, + 13, + }; + +static const size_t poly_end[] = + { + 13, + 27, + 42, + 58, + 75, + 91, + 106, + 120, + }; + +/* Compute sin (pi * X) for -0.25 <= X <= 0.5. */ + +static long double +lg_sinpi (long double x) +{ + if (x <= 0.25L) + return __sinl (M_PIl * x); + else + return __cosl (M_PIl * (0.5L - x)); +} + +/* Compute cos (pi * X) for -0.25 <= X <= 0.5. */ + +static long double +lg_cospi (long double x) +{ + if (x <= 0.25L) + return __cosl (M_PIl * x); + else + return __sinl (M_PIl * (0.5L - x)); +} + +/* Compute cot (pi * X) for -0.25 <= X <= 0.5. */ + +static long double +lg_cotpi (long double x) +{ + return lg_cospi (x) / lg_sinpi (x); +} + +/* Compute lgamma of a negative argument -33 < X < -2, setting + *SIGNGAMP accordingly. */ + +long double +__lgamma_negl (long double x, int *signgamp) +{ + /* Determine the half-integer region X lies in, handle exact + integers and determine the sign of the result. */ + int i = __floorl (-2 * x); + if ((i & 1) == 0 && i == -2 * x) + return 1.0L / 0.0L; + long double xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2); + i -= 4; + *signgamp = ((i & 2) == 0 ? -1 : 1); + + SET_RESTORE_ROUNDL (FE_TONEAREST); + + /* Expand around the zero X0 = X0_HI + X0_LO. */ + long double x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1]; + long double xdiff = x - x0_hi - x0_lo; + + /* For arguments in the range -3 to -2, use polynomial + approximations to an adjusted version of the gamma function. */ + if (i < 2) + { + int j = __floorl (-8 * x) - 16; + long double xm = (-33 - 2 * j) * 0.0625L; + long double x_adj = x - xm; + size_t deg = poly_deg[j]; + size_t end = poly_end[j]; + long double g = poly_coeff[end]; + for (size_t j = 1; j <= deg; j++) + g = g * x_adj + poly_coeff[end - j]; + return __log1pl (g * xdiff / (x - xn)); + } + + /* The result we want is log (sinpi (X0) / sinpi (X)) + + log (gamma (1 - X0) / gamma (1 - X)). */ + long double x_idiff = fabsl (xn - x), x0_idiff = fabsl (xn - x0_hi - x0_lo); + long double log_sinpi_ratio; + if (x0_idiff < x_idiff * 0.5L) + /* Use log not log1p to avoid inaccuracy from log1p of arguments + close to -1. */ + log_sinpi_ratio = __ieee754_logl (lg_sinpi (x0_idiff) + / lg_sinpi (x_idiff)); + else + { + /* Use log1p not log to avoid inaccuracy from log of arguments + close to 1. X0DIFF2 has positive sign if X0 is further from + XN than X is from XN, negative sign otherwise. */ + long double x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * 0.5L; + long double sx0d2 = lg_sinpi (x0diff2); + long double cx0d2 = lg_cospi (x0diff2); + log_sinpi_ratio = __log1pl (2 * sx0d2 + * (-sx0d2 + cx0d2 * lg_cotpi (x_idiff))); + } + + long double log_gamma_ratio; + long double y0 = 1 - x0_hi; + long double y0_eps = -x0_hi + (1 - y0) - x0_lo; + long double y = 1 - x; + long double y_eps = -x + (1 - y); + /* We now wish to compute LOG_GAMMA_RATIO + = log (gamma (Y0 + Y0_EPS) / gamma (Y + Y_EPS)). XDIFF + accurately approximates the difference Y0 + Y0_EPS - Y - + Y_EPS. Use Stirling's approximation. First, we may need to + adjust into the range where Stirling's approximation is + sufficiently accurate. */ + long double log_gamma_adj = 0; + if (i < 8) + { + int n_up = (9 - i) / 2; + long double ny0, ny0_eps, ny, ny_eps; + ny0 = y0 + n_up; + ny0_eps = y0 - (ny0 - n_up) + y0_eps; + y0 = ny0; + y0_eps = ny0_eps; + ny = y + n_up; + ny_eps = y - (ny - n_up) + y_eps; + y = ny; + y_eps = ny_eps; + long double prodm1 = __lgamma_productl (xdiff, y - n_up, y_eps, n_up); + log_gamma_adj = -__log1pl (prodm1); + } + long double log_gamma_high + = (xdiff * __log1pl ((y0 - e_hi - e_lo + y0_eps) / e_hi) + + (y - 0.5L + y_eps) * __log1pl (xdiff / y) + log_gamma_adj); + /* Compute the sum of (B_2k / 2k(2k-1))(Y0^-(2k-1) - Y^-(2k-1)). */ + long double y0r = 1 / y0, yr = 1 / y; + long double y0r2 = y0r * y0r, yr2 = yr * yr; + long double rdiff = -xdiff / (y * y0); + long double bterm[NCOEFF]; + long double dlast = rdiff, elast = rdiff * yr * (yr + y0r); + bterm[0] = dlast * lgamma_coeff[0]; + for (size_t j = 1; j < NCOEFF; j++) + { + long double dnext = dlast * y0r2 + elast; + long double enext = elast * yr2; + bterm[j] = dnext * lgamma_coeff[j]; + dlast = dnext; + elast = enext; + } + long double log_gamma_low = 0; + for (size_t j = 0; j < NCOEFF; j++) + log_gamma_low += bterm[NCOEFF - 1 - j]; + log_gamma_ratio = log_gamma_high + log_gamma_low; + + return log_sinpi_ratio + log_gamma_ratio; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/lgamma_product.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/lgamma_product.c new file mode 100644 index 0000000000..46be5df762 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/lgamma_product.c @@ -0,0 +1,37 @@ +/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), .... + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS + + 1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that + all the values X + 1, ..., X + N - 1 are exactly representable, and + X_EPS / X is small enough that factors quadratic in it can be + neglected. */ + +double +__lgamma_product (double t, double x, double x_eps, int n) +{ + long double x_full = (long double) x + (long double) x_eps; + long double ret = 0; + for (int i = 0; i < n; i++) + ret += (t / (x_full + i)) * (1 + ret); + return ret; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/lgamma_productl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/lgamma_productl.c new file mode 100644 index 0000000000..cd6f2f3156 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/lgamma_productl.c @@ -0,0 +1,52 @@ +/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), .... + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_splitl.h> + +/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS + + 1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that + all the values X + 1, ..., X + N - 1 are exactly representable, and + X_EPS / X is small enough that factors quadratic in it can be + neglected. */ + +long double +__lgamma_productl (long double t, long double x, long double x_eps, int n) +{ + long double ret = 0, ret_eps = 0; + for (int i = 0; i < n; i++) + { + long double xi = x + i; + long double quot = t / xi; + long double mhi, mlo; + mul_splitl (&mhi, &mlo, quot, xi); + long double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi); + /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */ + long double rhi, rlo; + mul_splitl (&rhi, &rlo, ret, quot); + long double rpq = ret + quot; + long double rpq_eps = (ret - rpq) + quot; + long double nret = rpq + rhi; + long double nret_eps = (rpq - nret) + rhi; + ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot + + quot_lo + quot_lo * (ret + ret_eps)); + ret = nret; + } + return ret + ret_eps; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/math_ldbl.h b/REORG.TODO/sysdeps/ieee754/ldbl-96/math_ldbl.h new file mode 100644 index 0000000000..ef897065b7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/math_ldbl.h @@ -0,0 +1,120 @@ +/* Manipulation of the bit representation of 'long double' quantities. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_LDBL_H_ +#define _MATH_LDBL_H_ 1 + +#include <stdint.h> +#include <endian.h> + +/* A union which permits us to convert between a long double and + three 32 bit ints. */ + +#if __FLOAT_WORD_ORDER == __BIG_ENDIAN + +typedef union +{ + long double value; + struct + { + int sign_exponent:16; + unsigned int empty:16; + uint32_t msw; + uint32_t lsw; + } parts; +} ieee_long_double_shape_type; + +#endif + +#if __FLOAT_WORD_ORDER == __LITTLE_ENDIAN + +typedef union +{ + long double value; + struct + { + uint32_t lsw; + uint32_t msw; + int sign_exponent:16; + unsigned int empty:16; + } parts; +} ieee_long_double_shape_type; + +#endif + +/* Get three 32 bit ints from a double. */ + +#define GET_LDOUBLE_WORDS(exp,ix0,ix1,d) \ +do { \ + ieee_long_double_shape_type ew_u; \ + ew_u.value = (d); \ + (exp) = ew_u.parts.sign_exponent; \ + (ix0) = ew_u.parts.msw; \ + (ix1) = ew_u.parts.lsw; \ +} while (0) + +/* Set a double from two 32 bit ints. */ + +#define SET_LDOUBLE_WORDS(d,exp,ix0,ix1) \ +do { \ + ieee_long_double_shape_type iw_u; \ + iw_u.parts.sign_exponent = (exp); \ + iw_u.parts.msw = (ix0); \ + iw_u.parts.lsw = (ix1); \ + (d) = iw_u.value; \ +} while (0) + +/* Get the more significant 32 bits of a long double mantissa. */ + +#define GET_LDOUBLE_MSW(v,d) \ +do { \ + ieee_long_double_shape_type sh_u; \ + sh_u.value = (d); \ + (v) = sh_u.parts.msw; \ +} while (0) + +/* Set the more significant 32 bits of a long double mantissa from an int. */ + +#define SET_LDOUBLE_MSW(d,v) \ +do { \ + ieee_long_double_shape_type sh_u; \ + sh_u.value = (d); \ + sh_u.parts.msw = (v); \ + (d) = sh_u.value; \ +} while (0) + +/* Get int from the exponent of a long double. */ + +#define GET_LDOUBLE_EXP(exp,d) \ +do { \ + ieee_long_double_shape_type ge_u; \ + ge_u.value = (d); \ + (exp) = ge_u.parts.sign_exponent; \ +} while (0) + +/* Set exponent of a long double from an int. */ + +#define SET_LDOUBLE_EXP(d,exp) \ +do { \ + ieee_long_double_shape_type se_u; \ + se_u.value = (d); \ + se_u.parts.sign_exponent = (exp); \ + (d) = se_u.value; \ +} while (0) + +#endif /* math_ldbl.h */ diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/mpn2ldbl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/mpn2ldbl.c new file mode 100644 index 0000000000..715efb40b2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/mpn2ldbl.c @@ -0,0 +1,46 @@ +/* Copyright (C) 1995-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include <ieee754.h> +#include <float.h> +#include <math.h> + +/* Convert a multi-precision integer of the needed number of bits (64 for + long double) and an integral power of two to a `long double' in IEEE854 + extended-precision format. */ + +long double +__mpn_construct_long_double (mp_srcptr frac_ptr, int expt, int sign) +{ + union ieee854_long_double u; + + u.ieee.negative = sign; + u.ieee.exponent = expt + IEEE854_LONG_DOUBLE_BIAS; +#if BITS_PER_MP_LIMB == 32 + u.ieee.mantissa1 = frac_ptr[0]; + u.ieee.mantissa0 = frac_ptr[1]; +#elif BITS_PER_MP_LIMB == 64 + u.ieee.mantissa1 = frac_ptr[0] & (((mp_limb_t) 1 << 32) - 1); + u.ieee.mantissa0 = frac_ptr[0] >> 32; +#else + #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif + + return u.d; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/printf_fphex.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/printf_fphex.c new file mode 100644 index 0000000000..0df9462d91 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/printf_fphex.c @@ -0,0 +1,95 @@ +/* Print floating point number in hexadecimal notation according to ISO C99. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef LONG_DOUBLE_DENORM_BIAS +# define LONG_DOUBLE_DENORM_BIAS (IEEE854_LONG_DOUBLE_BIAS - 1) +#endif + +#define PRINT_FPHEX_LONG_DOUBLE \ +do { \ + /* The "strange" 80 bit format on ix86 and m68k has an explicit \ + leading digit in the 64 bit mantissa. */ \ + unsigned long long int num; \ + union ieee854_long_double u; \ + u.d = fpnum.ldbl; \ + \ + assert (sizeof (long double) == 12); \ + \ + num = (((unsigned long long int) u.ieee.mantissa0) << 32 \ + | u.ieee.mantissa1); \ + \ + zero_mantissa = num == 0; \ + \ + if (sizeof (unsigned long int) > 6) \ + { \ + numstr = _itoa_word (num, numbuf + sizeof numbuf, 16, \ + info->spec == 'A'); \ + wnumstr = _itowa_word (num, \ + wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t),\ + 16, info->spec == 'A'); \ + } \ + else \ + { \ + numstr = _itoa (num, numbuf + sizeof numbuf, 16, info->spec == 'A');\ + wnumstr = _itowa (num, \ + wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t), \ + 16, info->spec == 'A'); \ + } \ + \ + /* Fill with zeroes. */ \ + while (numstr > numbuf + (sizeof numbuf - 64 / 4)) \ + { \ + *--numstr = '0'; \ + *--wnumstr = L'0'; \ + } \ + \ + /* We use a full nibble for the leading digit. */ \ + leading = *numstr++; \ + wnumstr++; \ + \ + /* We have 3 bits from the mantissa in the leading nibble. \ + Therefore we are here using `IEEE854_LONG_DOUBLE_BIAS + 3'. */ \ + exponent = u.ieee.exponent; \ + \ + if (exponent == 0) \ + { \ + if (zero_mantissa) \ + expnegative = 0; \ + else \ + { \ + /* This is a denormalized number. */ \ + expnegative = 1; \ + /* This is a hook for the m68k long double format, where the \ + exponent bias is the same for normalized and denormalized \ + numbers. */ \ + exponent = LONG_DOUBLE_DENORM_BIAS + 3; \ + } \ + } \ + else if (exponent >= IEEE854_LONG_DOUBLE_BIAS + 3) \ + { \ + expnegative = 0; \ + exponent -= IEEE854_LONG_DOUBLE_BIAS + 3; \ + } \ + else \ + { \ + expnegative = 1; \ + exponent = -(exponent - (IEEE854_LONG_DOUBLE_BIAS + 3)); \ + } \ +} while (0) + +#include <stdio-common/printf_fphex.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_asinhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_asinhl.c new file mode 100644 index 0000000000..da49ea5988 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_asinhl.c @@ -0,0 +1,65 @@ +/* s_asinhl.c -- long double version of s_asinh.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* asinhl(x) + * Method : + * Based on + * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ] + * we have + * asinhl(x) := x if 1+x*x=1, + * := signl(x)*(logl(x)+ln2)) for large |x|, else + * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else + * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2))) + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double +one = 1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */ +ln2 = 6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */ +huge= 1.000000000000000000e+4900L; + +long double __asinhl(long double x) +{ + long double t,w; + int32_t hx,ix; + GET_LDOUBLE_EXP(hx,x); + ix = hx&0x7fff; + if(__builtin_expect(ix< 0x3fde, 0)) { /* |x|<2**-34 */ + math_check_force_underflow (x); + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(__builtin_expect(ix>0x4020,0)) { /* |x| > 2**34 */ + if(ix==0x7fff) return x+x; /* x is inf or NaN */ + w = __ieee754_logl(fabsl(x))+ln2; + } else { + long double xa = fabsl(x); + if (ix>0x4000) { /* 2**34 > |x| > 2.0 */ + w = __ieee754_logl(2.0*xa+one/(__ieee754_sqrtl(xa*xa+one)+xa)); + } else { /* 2.0 > |x| > 2**-28 */ + t = xa*xa; + w =__log1pl(xa+t/(one+__ieee754_sqrtl(one+t))); + } + } + return __copysignl(w, x); +} +weak_alias (__asinhl, asinhl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_cbrtl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_cbrtl.c new file mode 100644 index 0000000000..5712fce2e9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_cbrtl.c @@ -0,0 +1,70 @@ +/* Compute cubic root of double value. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Dirk Alboth <dirka@uni-paderborn.de> and + Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + + +#define CBRT2 1.2599210498948731648 /* 2^(1/3) */ +#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */ + +/* We don't use long double values here since U need not be computed + with full precision. */ +static const double factor[5] = +{ + 1.0 / SQR_CBRT2, + 1.0 / CBRT2, + 1.0, + CBRT2, + SQR_CBRT2 +}; + +static const long double third = 0.3333333333333333333333333L; + +long double +__cbrtl (long double x) +{ + long double xm, u; + int xe; + + /* Reduce X. XM now is an range 1.0 to 0.5. */ + xm = __frexpl (fabsl (x), &xe); + + /* If X is not finite or is null return it (with raising exceptions + if necessary. + Note: *Our* version of `frexp' sets XE to zero if the argument is + Inf or NaN. This is not portable but faster. */ + if (xe == 0 && fpclassify (x) <= FP_ZERO) + return x + x; + + u = (((-1.34661104733595206551E-1 * xm + + 5.46646013663955245034E-1) * xm + - 9.54382247715094465250E-1) * xm + + 1.13999833547172932737E0) * xm + + 4.02389795645447521269E-1; + + u *= factor[2 + xe % 3]; + u = __ldexpl (x > 0.0 ? u : -u, xe / 3); + + u -= (u - (x / (u * u))) * third; + u -= (u - (x / (u * u))) * third; + return u; +} +weak_alias (__cbrtl, cbrtl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_copysignl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_copysignl.c new file mode 100644 index 0000000000..b1c442452f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_copysignl.c @@ -0,0 +1,38 @@ +/* s_copysignl.c -- long double version of s_copysign.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * copysignl(long double x, long double y) + * copysignl(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include <math.h> +#include <math_private.h> + +long double __copysignl(long double x, long double y) +{ + u_int32_t es1,es2; + GET_LDOUBLE_EXP(es1,x); + GET_LDOUBLE_EXP(es2,y); + SET_LDOUBLE_EXP(x,(es1&0x7fff)|(es2&0x8000)); + return x; +} +weak_alias (__copysignl, copysignl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_cosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_cosl.c new file mode 100644 index 0000000000..8b0b7d3cc2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_cosl.c @@ -0,0 +1,88 @@ +/* s_cosl.c -- long double version of s_cos.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* cosl(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sinl ... sine function on [-pi/4,pi/4] + * __kernel_cosl ... cosine function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> + +long double __cosl(long double x) +{ + long double y[2],z=0.0; + int32_t n, se, i0, i1; + + /* High word of x. */ + GET_LDOUBLE_WORDS(se,i0,i1,x); + + /* |x| ~< pi/4 */ + se &= 0x7fff; + if(se < 0x3ffe || (se == 0x3ffe && i0 <= 0xc90fdaa2)) + return __kernel_cosl(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (se==0x7fff) { + if (i1 == 0 && i0 == 0x80000000) + __set_errno (EDOM); + return x-x; + } + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + switch(n&3) { + case 0: return __kernel_cosl(y[0],y[1]); + case 1: return -__kernel_sinl(y[0],y[1],1); + case 2: return -__kernel_cosl(y[0],y[1]); + default: + return __kernel_sinl(y[0],y[1],1); + } + } +} +weak_alias (__cosl, cosl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_erfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_erfl.c new file mode 100644 index 0000000000..d00adb1000 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_erfl.c @@ -0,0 +1,451 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. For |x| in [0, 0.84375] + * erf(x) = x + x*R(x^2) + * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] + * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. The interval is chosen because the fix + * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is + * near 0.6174), and by some experiment, 0.84375 is chosen to + * guarantee the error is less than one ulp for erf. + * + * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(x) = sign(x) * (c + P1(s)/Q1(s)) + * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 + * 1+(c+P1(s)/Q1(s)) if x < 0 + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * + * 3. For x in [1.25,1/0.35(~2.857143)], + * erfc(x) = (1/x)*exp(-x*x-0.5625+R1(z)/S1(z)) + * z=1/x^2 + * erf(x) = 1 - erfc(x) + * + * 4. For x in [1/0.35,107] + * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 + * = 2.0 - (1/x)*exp(-x*x-0.5625+R2(z)/S2(z)) + * if -6.666<x<0 + * = 2.0 - tiny (if x <= -6.666) + * z=1/x^2 + * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6.666, else + * erf(x) = sign(x)*(1.0 - tiny) + * Note1: + * To compute exp(-x*x-0.5625+R/S), let s be a single + * precision number and s := x; then + * -x*x = -s*s + (s-x)*(s+x) + * exp(-x*x-0.5626+R/S) = + * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); + * Note2: + * Here 4 and 5 make use of the asymptotic series + * exp(-x*x) + * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) + * x*sqrt(pi) + * + * 5. For inf > x >= 107 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double +tiny = 1e-4931L, + half = 0.5L, + one = 1.0L, + two = 2.0L, + /* c = (float)0.84506291151 */ + erx = 0.845062911510467529296875L, +/* + * Coefficients for approximation to erf on [0,0.84375] + */ + /* 2/sqrt(pi) - 1 */ + efx = 1.2837916709551257389615890312154517168810E-1L, + + pp[6] = { + 1.122751350964552113068262337278335028553E6L, + -2.808533301997696164408397079650699163276E6L, + -3.314325479115357458197119660818768924100E5L, + -6.848684465326256109712135497895525446398E4L, + -2.657817695110739185591505062971929859314E3L, + -1.655310302737837556654146291646499062882E2L, + }, + + qq[6] = { + 8.745588372054466262548908189000448124232E6L, + 3.746038264792471129367533128637019611485E6L, + 7.066358783162407559861156173539693900031E5L, + 7.448928604824620999413120955705448117056E4L, + 4.511583986730994111992253980546131408924E3L, + 1.368902937933296323345610240009071254014E2L, + /* 1.000000000000000000000000000000000000000E0 */ + }, + +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +/* erf(x+1) = 0.845062911510467529296875 + pa(x)/qa(x) + -0.15625 <= x <= +.25 + Peak relative error 8.5e-22 */ + + pa[8] = { + -1.076952146179812072156734957705102256059E0L, + 1.884814957770385593365179835059971587220E2L, + -5.339153975012804282890066622962070115606E1L, + 4.435910679869176625928504532109635632618E1L, + 1.683219516032328828278557309642929135179E1L, + -2.360236618396952560064259585299045804293E0L, + 1.852230047861891953244413872297940938041E0L, + 9.394994446747752308256773044667843200719E-2L, + }, + + qa[7] = { + 4.559263722294508998149925774781887811255E2L, + 3.289248982200800575749795055149780689738E2L, + 2.846070965875643009598627918383314457912E2L, + 1.398715859064535039433275722017479994465E2L, + 6.060190733759793706299079050985358190726E1L, + 2.078695677795422351040502569964299664233E1L, + 4.641271134150895940966798357442234498546E0L, + /* 1.000000000000000000000000000000000000000E0 */ + }, + +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +/* erfc(1/x) = x exp (-1/x^2 - 0.5625 + ra(x^2)/sa(x^2)) + 1/2.85711669921875 < 1/x < 1/1.25 + Peak relative error 3.1e-21 */ + + ra[] = { + 1.363566591833846324191000679620738857234E-1L, + 1.018203167219873573808450274314658434507E1L, + 1.862359362334248675526472871224778045594E2L, + 1.411622588180721285284945138667933330348E3L, + 5.088538459741511988784440103218342840478E3L, + 8.928251553922176506858267311750789273656E3L, + 7.264436000148052545243018622742770549982E3L, + 2.387492459664548651671894725748959751119E3L, + 2.220916652813908085449221282808458466556E2L, + }, + + sa[] = { + -1.382234625202480685182526402169222331847E1L, + -3.315638835627950255832519203687435946482E2L, + -2.949124863912936259747237164260785326692E3L, + -1.246622099070875940506391433635999693661E4L, + -2.673079795851665428695842853070996219632E4L, + -2.880269786660559337358397106518918220991E4L, + -1.450600228493968044773354186390390823713E4L, + -2.874539731125893533960680525192064277816E3L, + -1.402241261419067750237395034116942296027E2L, + /* 1.000000000000000000000000000000000000000E0 */ + }, +/* + * Coefficients for approximation to erfc in [1/.35,107] + */ +/* erfc(1/x) = x exp (-1/x^2 - 0.5625 + rb(x^2)/sb(x^2)) + 1/6.6666259765625 < 1/x < 1/2.85711669921875 + Peak relative error 4.2e-22 */ + rb[] = { + -4.869587348270494309550558460786501252369E-5L, + -4.030199390527997378549161722412466959403E-3L, + -9.434425866377037610206443566288917589122E-2L, + -9.319032754357658601200655161585539404155E-1L, + -4.273788174307459947350256581445442062291E0L, + -8.842289940696150508373541814064198259278E0L, + -7.069215249419887403187988144752613025255E0L, + -1.401228723639514787920274427443330704764E0L, + }, + + sb[] = { + 4.936254964107175160157544545879293019085E-3L, + 1.583457624037795744377163924895349412015E-1L, + 1.850647991850328356622940552450636420484E0L, + 9.927611557279019463768050710008450625415E0L, + 2.531667257649436709617165336779212114570E1L, + 2.869752886406743386458304052862814690045E1L, + 1.182059497870819562441683560749192539345E1L, + /* 1.000000000000000000000000000000000000000E0 */ + }, +/* erfc(1/x) = x exp (-1/x^2 - 0.5625 + rc(x^2)/sc(x^2)) + 1/107 <= 1/x <= 1/6.6666259765625 + Peak relative error 1.1e-21 */ + rc[] = { + -8.299617545269701963973537248996670806850E-5L, + -6.243845685115818513578933902532056244108E-3L, + -1.141667210620380223113693474478394397230E-1L, + -7.521343797212024245375240432734425789409E-1L, + -1.765321928311155824664963633786967602934E0L, + -1.029403473103215800456761180695263439188E0L, + }, + + sc[] = { + 8.413244363014929493035952542677768808601E-3L, + 2.065114333816877479753334599639158060979E-1L, + 1.639064941530797583766364412782135680148E0L, + 4.936788463787115555582319302981666347450E0L, + 5.005177727208955487404729933261347679090E0L, + /* 1.000000000000000000000000000000000000000E0 */ + }; + +long double +__erfl (long double x) +{ + long double R, S, P, Q, s, y, z, r; + int32_t ix, i; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + + if (ix >= 0x7fff) + { /* erf(nan)=nan */ + i = ((se & 0xffff) >> 15) << 1; + return (long double) (1 - i) + one / x; /* erf(+-inf)=+-1 */ + } + + ix = (ix << 16) | (i0 >> 16); + if (ix < 0x3ffed800) /* |x|<0.84375 */ + { + if (ix < 0x3fde8000) /* |x|<2**-33 */ + { + if (ix < 0x00080000) + { + /* Avoid spurious underflow. */ + long double ret = 0.0625 * (16.0 * x + (16.0 * efx) * x); + math_check_force_underflow (ret); + return ret; + } + return x + efx * x; + } + z = x * x; + r = pp[0] + z * (pp[1] + + z * (pp[2] + z * (pp[3] + z * (pp[4] + z * pp[5])))); + s = qq[0] + z * (qq[1] + + z * (qq[2] + z * (qq[3] + z * (qq[4] + z * (qq[5] + z))))); + y = r / s; + return x + x * y; + } + if (ix < 0x3fffa000) /* 1.25 */ + { /* 0.84375 <= |x| < 1.25 */ + s = fabsl (x) - one; + P = pa[0] + s * (pa[1] + s * (pa[2] + + s * (pa[3] + s * (pa[4] + s * (pa[5] + s * (pa[6] + s * pa[7])))))); + Q = qa[0] + s * (qa[1] + s * (qa[2] + + s * (qa[3] + s * (qa[4] + s * (qa[5] + s * (qa[6] + s)))))); + if ((se & 0x8000) == 0) + return erx + P / Q; + else + return -erx - P / Q; + } + if (ix >= 0x4001d555) /* 6.6666259765625 */ + { /* inf>|x|>=6.666 */ + if ((se & 0x8000) == 0) + return one - tiny; + else + return tiny - one; + } + x = fabsl (x); + s = one / (x * x); + if (ix < 0x4000b6db) /* 2.85711669921875 */ + { + R = ra[0] + s * (ra[1] + s * (ra[2] + s * (ra[3] + s * (ra[4] + + s * (ra[5] + s * (ra[6] + s * (ra[7] + s * ra[8]))))))); + S = sa[0] + s * (sa[1] + s * (sa[2] + s * (sa[3] + s * (sa[4] + + s * (sa[5] + s * (sa[6] + s * (sa[7] + s * (sa[8] + s)))))))); + } + else + { /* |x| >= 1/0.35 */ + R = rb[0] + s * (rb[1] + s * (rb[2] + s * (rb[3] + s * (rb[4] + + s * (rb[5] + s * (rb[6] + s * rb[7])))))); + S = sb[0] + s * (sb[1] + s * (sb[2] + s * (sb[3] + s * (sb[4] + + s * (sb[5] + s * (sb[6] + s)))))); + } + z = x; + GET_LDOUBLE_WORDS (i, i0, i1, z); + i1 = 0; + SET_LDOUBLE_WORDS (z, i, i0, i1); + r = + __ieee754_expl (-z * z - 0.5625) * __ieee754_expl ((z - x) * (z + x) + + R / S); + if ((se & 0x8000) == 0) + return one - r / x; + else + return r / x - one; +} + +weak_alias (__erfl, erfl) +long double +__erfcl (long double x) +{ + int32_t hx, ix; + long double R, S, P, Q, s, y, z, r; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + if (ix >= 0x7fff) + { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (long double) (((se & 0xffff) >> 15) << 1) + one / x; + } + + ix = (ix << 16) | (i0 >> 16); + if (ix < 0x3ffed800) /* |x|<0.84375 */ + { + if (ix < 0x3fbe0000) /* |x|<2**-65 */ + return one - x; + z = x * x; + r = pp[0] + z * (pp[1] + + z * (pp[2] + z * (pp[3] + z * (pp[4] + z * pp[5])))); + s = qq[0] + z * (qq[1] + + z * (qq[2] + z * (qq[3] + z * (qq[4] + z * (qq[5] + z))))); + y = r / s; + if (ix < 0x3ffd8000) /* x<1/4 */ + { + return one - (x + x * y); + } + else + { + r = x * y; + r += (x - half); + return half - r; + } + } + if (ix < 0x3fffa000) /* 1.25 */ + { /* 0.84375 <= |x| < 1.25 */ + s = fabsl (x) - one; + P = pa[0] + s * (pa[1] + s * (pa[2] + + s * (pa[3] + s * (pa[4] + s * (pa[5] + s * (pa[6] + s * pa[7])))))); + Q = qa[0] + s * (qa[1] + s * (qa[2] + + s * (qa[3] + s * (qa[4] + s * (qa[5] + s * (qa[6] + s)))))); + if ((se & 0x8000) == 0) + { + z = one - erx; + return z - P / Q; + } + else + { + z = erx + P / Q; + return one + z; + } + } + if (ix < 0x4005d600) /* 107 */ + { /* |x|<107 */ + x = fabsl (x); + s = one / (x * x); + if (ix < 0x4000b6db) /* 2.85711669921875 */ + { /* |x| < 1/.35 ~ 2.857143 */ + R = ra[0] + s * (ra[1] + s * (ra[2] + s * (ra[3] + s * (ra[4] + + s * (ra[5] + s * (ra[6] + s * (ra[7] + s * ra[8]))))))); + S = sa[0] + s * (sa[1] + s * (sa[2] + s * (sa[3] + s * (sa[4] + + s * (sa[5] + s * (sa[6] + s * (sa[7] + s * (sa[8] + s)))))))); + } + else if (ix < 0x4001d555) /* 6.6666259765625 */ + { /* 6.666 > |x| >= 1/.35 ~ 2.857143 */ + R = rb[0] + s * (rb[1] + s * (rb[2] + s * (rb[3] + s * (rb[4] + + s * (rb[5] + s * (rb[6] + s * rb[7])))))); + S = sb[0] + s * (sb[1] + s * (sb[2] + s * (sb[3] + s * (sb[4] + + s * (sb[5] + s * (sb[6] + s)))))); + } + else + { /* |x| >= 6.666 */ + if (se & 0x8000) + return two - tiny; /* x < -6.666 */ + + R = rc[0] + s * (rc[1] + s * (rc[2] + s * (rc[3] + + s * (rc[4] + s * rc[5])))); + S = sc[0] + s * (sc[1] + s * (sc[2] + s * (sc[3] + + s * (sc[4] + s)))); + } + z = x; + GET_LDOUBLE_WORDS (hx, i0, i1, z); + i1 = 0; + i0 &= 0xffffff00; + SET_LDOUBLE_WORDS (z, hx, i0, i1); + r = __ieee754_expl (-z * z - 0.5625) * + __ieee754_expl ((z - x) * (z + x) + R / S); + if ((se & 0x8000) == 0) + { + long double ret = r / x; + if (ret == 0) + __set_errno (ERANGE); + return ret; + } + else + return two - r / x; + } + else + { + if ((se & 0x8000) == 0) + { + __set_errno (ERANGE); + return tiny * tiny; + } + else + return two - tiny; + } +} + +weak_alias (__erfcl, erfcl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fma.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fma.c new file mode 100644 index 0000000000..370592074e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fma.c @@ -0,0 +1,101 @@ +/* Compute x * y + z as ternary operation. + Copyright (C) 2010-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <fenv.h> +#include <ieee754.h> +#include <math_private.h> + +/* This implementation uses rounding to odd to avoid problems with + double rounding. See a paper by Boldo and Melquiond: + http://www.lri.fr/~melquion/doc/08-tc.pdf */ + +double +__fma (double x, double y, double z) +{ + if (__glibc_unlikely (isinf (z))) + { + /* If z is Inf, but x and y are finite, the result should be + z rather than NaN. */ + if (isfinite (x) && isfinite (y)) + return (z + x) + y; + return (x * y) + z; + } + + /* Ensure correct sign of exact 0 + 0. */ + if (__glibc_unlikely ((x == 0 || y == 0) && z == 0)) + { + x = math_opt_barrier (x); + return x * y + z; + } + + fenv_t env; + feholdexcept (&env); + fesetround (FE_TONEAREST); + + /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ +#define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1) + long double x1 = (long double) x * C; + long double y1 = (long double) y * C; + long double m1 = (long double) x * y; + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + long double x2 = x - x1; + long double y2 = y - y1; + long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2; + + /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */ + long double a1 = z + m1; + long double t1 = a1 - z; + long double t2 = a1 - t1; + t1 = m1 - t1; + t2 = z - t2; + long double a2 = t1 + t2; + /* Ensure the arithmetic is not scheduled after feclearexcept call. */ + math_force_eval (m2); + math_force_eval (a2); + feclearexcept (FE_INEXACT); + + /* If the result is an exact zero, ensure it has the correct sign. */ + if (a1 == 0 && m2 == 0) + { + feupdateenv (&env); + /* Ensure that round-to-nearest value of z + m1 is not reused. */ + z = math_opt_barrier (z); + return z + m1; + } + + fesetround (FE_TOWARDZERO); + /* Perform m2 + a2 addition with round to odd. */ + a2 = a2 + m2; + + /* Add that to a1 again using rounding to odd. */ + union ieee854_long_double u; + u.d = a1 + a2; + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff) + u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + + /* Add finally round to double precision. */ + return u.d; +} +#ifndef __fma +weak_alias (__fma, fma) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fmal.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fmal.c new file mode 100644 index 0000000000..1f3fa1ea1e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fmal.c @@ -0,0 +1,296 @@ +/* Compute x * y + z as ternary operation. + Copyright (C) 2010-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <fenv.h> +#include <ieee754.h> +#include <math_private.h> +#include <tininess.h> + +/* This implementation uses rounding to odd to avoid problems with + double rounding. See a paper by Boldo and Melquiond: + http://www.lri.fr/~melquion/doc/08-tc.pdf */ + +long double +__fmal (long double x, long double y, long double z) +{ + union ieee854_long_double u, v, w; + int adjust = 0; + u.d = x; + v.d = y; + w.d = z; + if (__builtin_expect (u.ieee.exponent + v.ieee.exponent + >= 0x7fff + IEEE854_LONG_DOUBLE_BIAS + - LDBL_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0) + || __builtin_expect (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0) + || __builtin_expect (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent + v.ieee.exponent + <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG, 0)) + { + /* If z is Inf, but x and y are finite, the result should be + z rather than NaN. */ + if (w.ieee.exponent == 0x7fff + && u.ieee.exponent != 0x7fff + && v.ieee.exponent != 0x7fff) + return (z + x) + y; + /* If z is zero and x are y are nonzero, compute the result + as x * y to avoid the wrong sign of a zero result if x * y + underflows to 0. */ + if (z == 0 && x != 0 && y != 0) + return x * y; + /* If x or y or z is Inf/NaN, or if x * y is zero, compute as + x * y + z. */ + if (u.ieee.exponent == 0x7fff + || v.ieee.exponent == 0x7fff + || w.ieee.exponent == 0x7fff + || x == 0 + || y == 0) + return x * y + z; + /* If fma will certainly overflow, compute as x * y. */ + if (u.ieee.exponent + v.ieee.exponent + > 0x7fff + IEEE854_LONG_DOUBLE_BIAS) + return x * y; + /* If x * y is less than 1/4 of LDBL_TRUE_MIN, neither the + result nor whether there is underflow depends on its exact + value, only on its sign. */ + if (u.ieee.exponent + v.ieee.exponent + < IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2) + { + int neg = u.ieee.negative ^ v.ieee.negative; + long double tiny = neg ? -0x1p-16445L : 0x1p-16445L; + if (w.ieee.exponent >= 3) + return tiny + z; + /* Scaling up, adding TINY and scaling down produces the + correct result, because in round-to-nearest mode adding + TINY has no effect and in other modes double rounding is + harmless. But it may not produce required underflow + exceptions. */ + v.d = z * 0x1p65L + tiny; + if (TININESS_AFTER_ROUNDING + ? v.ieee.exponent < 66 + : (w.ieee.exponent == 0 + || (w.ieee.exponent == 1 + && w.ieee.negative != neg + && w.ieee.mantissa1 == 0 + && w.ieee.mantissa0 == 0x80000000))) + { + long double force_underflow = x * y; + math_force_eval (force_underflow); + } + return v.d * 0x1p-65L; + } + if (u.ieee.exponent + v.ieee.exponent + >= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG) + { + /* Compute 1p-64 times smaller result and multiply + at the end. */ + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent -= LDBL_MANT_DIG; + else + v.ieee.exponent -= LDBL_MANT_DIG; + /* If x + y exponent is very large and z exponent is very small, + it doesn't matter if we don't adjust it. */ + if (w.ieee.exponent > LDBL_MANT_DIG) + w.ieee.exponent -= LDBL_MANT_DIG; + adjust = 1; + } + else if (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG) + { + /* Similarly. + If z exponent is very large and x and y exponents are + very small, adjust them up to avoid spurious underflows, + rather than down. */ + if (u.ieee.exponent + v.ieee.exponent + <= IEEE854_LONG_DOUBLE_BIAS + 2 * LDBL_MANT_DIG) + { + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent += 2 * LDBL_MANT_DIG + 2; + else + v.ieee.exponent += 2 * LDBL_MANT_DIG + 2; + } + else if (u.ieee.exponent > v.ieee.exponent) + { + if (u.ieee.exponent > LDBL_MANT_DIG) + u.ieee.exponent -= LDBL_MANT_DIG; + } + else if (v.ieee.exponent > LDBL_MANT_DIG) + v.ieee.exponent -= LDBL_MANT_DIG; + w.ieee.exponent -= LDBL_MANT_DIG; + adjust = 1; + } + else if (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG) + { + u.ieee.exponent -= LDBL_MANT_DIG; + if (v.ieee.exponent) + v.ieee.exponent += LDBL_MANT_DIG; + else + v.d *= 0x1p64L; + } + else if (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG) + { + v.ieee.exponent -= LDBL_MANT_DIG; + if (u.ieee.exponent) + u.ieee.exponent += LDBL_MANT_DIG; + else + u.d *= 0x1p64L; + } + else /* if (u.ieee.exponent + v.ieee.exponent + <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) */ + { + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent += 2 * LDBL_MANT_DIG + 2; + else + v.ieee.exponent += 2 * LDBL_MANT_DIG + 2; + if (w.ieee.exponent <= 4 * LDBL_MANT_DIG + 6) + { + if (w.ieee.exponent) + w.ieee.exponent += 2 * LDBL_MANT_DIG + 2; + else + w.d *= 0x1p130L; + adjust = -1; + } + /* Otherwise x * y should just affect inexact + and nothing else. */ + } + x = u.d; + y = v.d; + z = w.d; + } + + /* Ensure correct sign of exact 0 + 0. */ + if (__glibc_unlikely ((x == 0 || y == 0) && z == 0)) + { + x = math_opt_barrier (x); + return x * y + z; + } + + fenv_t env; + feholdexcept (&env); + fesetround (FE_TONEAREST); + + /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ +#define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) + long double x1 = x * C; + long double y1 = y * C; + long double m1 = x * y; + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + long double x2 = x - x1; + long double y2 = y - y1; + long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2; + + /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */ + long double a1 = z + m1; + long double t1 = a1 - z; + long double t2 = a1 - t1; + t1 = m1 - t1; + t2 = z - t2; + long double a2 = t1 + t2; + /* Ensure the arithmetic is not scheduled after feclearexcept call. */ + math_force_eval (m2); + math_force_eval (a2); + feclearexcept (FE_INEXACT); + + /* If the result is an exact zero, ensure it has the correct sign. */ + if (a1 == 0 && m2 == 0) + { + feupdateenv (&env); + /* Ensure that round-to-nearest value of z + m1 is not reused. */ + z = math_opt_barrier (z); + return z + m1; + } + + fesetround (FE_TOWARDZERO); + /* Perform m2 + a2 addition with round to odd. */ + u.d = a2 + m2; + + if (__glibc_likely (adjust == 0)) + { + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff) + u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Result is a1 + u.d. */ + return a1 + u.d; + } + else if (__glibc_likely (adjust > 0)) + { + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff) + u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Result is a1 + u.d, scaled up. */ + return (a1 + u.d) * 0x1p64L; + } + else + { + if ((u.ieee.mantissa1 & 1) == 0) + u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; + v.d = a1 + u.d; + /* Ensure the addition is not scheduled after fetestexcept call. */ + math_force_eval (v.d); + int j = fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Ensure the following computations are performed in default rounding + mode instead of just reusing the round to zero computation. */ + asm volatile ("" : "=m" (u) : "m" (u)); + /* If a1 + u.d is exact, the only rounding happens during + scaling down. */ + if (j == 0) + return v.d * 0x1p-130L; + /* If result rounded to zero is not subnormal, no double + rounding will occur. */ + if (v.ieee.exponent > 130) + return (a1 + u.d) * 0x1p-130L; + /* If v.d * 0x1p-130L with round to zero is a subnormal above + or equal to LDBL_MIN / 2, then v.d * 0x1p-130L shifts mantissa + down just by 1 bit, which means v.ieee.mantissa1 |= j would + change the round bit, not sticky or guard bit. + v.d * 0x1p-130L never normalizes by shifting up, + so round bit plus sticky bit should be already enough + for proper rounding. */ + if (v.ieee.exponent == 130) + { + /* If the exponent would be in the normal range when + rounding to normal precision with unbounded exponent + range, the exact result is known and spurious underflows + must be avoided on systems detecting tininess after + rounding. */ + if (TININESS_AFTER_ROUNDING) + { + w.d = a1 + u.d; + if (w.ieee.exponent == 131) + return w.d * 0x1p-130L; + } + /* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding, + v.ieee.mantissa1 & 1 is the round bit and j is our sticky + bit. */ + w.d = 0.0L; + w.ieee.mantissa1 = ((v.ieee.mantissa1 & 3) << 1) | j; + w.ieee.negative = v.ieee.negative; + v.ieee.mantissa1 &= ~3U; + v.d *= 0x1p-130L; + w.d *= 0x1p-2L; + return v.d + w.d; + } + v.ieee.mantissa1 |= j; + return v.d * 0x1p-130L; + } +} +weak_alias (__fmal, fmal) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_frexpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_frexpl.c new file mode 100644 index 0000000000..799880f373 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_frexpl.c @@ -0,0 +1,61 @@ +/* s_frexpl.c -- long double version of s_frexp.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * for non-zero x + * x = frexpl(arg,&exp); + * return a long double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexpl(arg,&exp) returns arg + * with *exp=0. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double +#if LDBL_MANT_DIG == 64 +two65 = 3.68934881474191032320e+19L; /* 0x4040, 0x80000000, 0x00000000 */ +#else +# error "Cannot handle this MANT_DIG" +#endif + + +long double __frexpl(long double x, int *eptr) +{ + u_int32_t se, hx, ix, lx; + GET_LDOUBLE_WORDS(se,hx,lx,x); + ix = 0x7fff&se; + *eptr = 0; + if(ix==0x7fff||((ix|hx|lx)==0)) return x + x; /* 0,inf,nan */ + if (ix==0x0000) { /* subnormal */ + x *= two65; + GET_LDOUBLE_EXP(se,x); + ix = se&0x7fff; + *eptr = -65; + } + *eptr += ix-16382; + se = (se & 0x8000) | 0x3ffe; + SET_LDOUBLE_EXP(x,se); + return x; +} +weak_alias (__frexpl, frexpl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fromfpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fromfpl.c new file mode 100644 index 0000000000..e323b4c25b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fromfpl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 0 +#define INEXACT 0 +#define FUNC fromfpl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fromfpl_main.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fromfpl_main.c new file mode 100644 index 0000000000..05de1fa6c0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fromfpl_main.c @@ -0,0 +1,84 @@ +/* Round to integer type. ldbl-96 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <fenv.h> +#include <math.h> +#include <math_private.h> +#include <stdbool.h> +#include <stdint.h> + +#define BIAS 0x3fff +#define MANT_DIG 64 + +#if UNSIGNED +# define RET_TYPE uintmax_t +#else +# define RET_TYPE intmax_t +#endif + +#include <fromfp.h> + +RET_TYPE +FUNC (long double x, int round, unsigned int width) +{ + if (width > INTMAX_WIDTH) + width = INTMAX_WIDTH; + uint16_t se; + uint32_t hx, lx; + GET_LDOUBLE_WORDS (se, hx, lx, x); + bool negative = (se & 0x8000) != 0; + if (width == 0) + return fromfp_domain_error (negative, width); + if ((hx | lx) == 0) + return 0; + int exponent = se & 0x7fff; + exponent -= BIAS; + int max_exponent = fromfp_max_exponent (negative, width); + if (exponent > max_exponent) + return fromfp_domain_error (negative, width); + + uint64_t ix = (((uint64_t) hx) << 32) | lx; + uintmax_t uret; + bool half_bit, more_bits; + if (exponent >= MANT_DIG - 1) + { + uret = ix; + /* Exponent 63; no shifting required. */ + half_bit = false; + more_bits = false; + } + else if (exponent >= -1) + { + uint64_t h = 1ULL << (MANT_DIG - 2 - exponent); + half_bit = (ix & h) != 0; + more_bits = (ix & (h - 1)) != 0; + if (exponent == -1) + uret = 0; + else + uret = ix >> (MANT_DIG - 1 - exponent); + } + else + { + uret = 0; + half_bit = false; + more_bits = true; + } + return fromfp_round_and_return (negative, uret, half_bit, more_bits, round, + exponent, max_exponent, width); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fromfpxl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fromfpxl.c new file mode 100644 index 0000000000..2f3189d7de --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_fromfpxl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 0 +#define INEXACT 1 +#define FUNC fromfpxl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_getpayloadl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_getpayloadl.c new file mode 100644 index 0000000000..6efe97baee --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_getpayloadl.c @@ -0,0 +1,32 @@ +/* Get NaN payload. ldbl-96 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +long double +getpayloadl (const long double *x) +{ + uint16_t se __attribute__ ((unused)); + uint32_t hx, lx; + GET_LDOUBLE_WORDS (se, hx, lx, *x); + hx &= 0x3fffffff; + uint64_t ix = ((uint64_t) hx << 32) | lx; + return (long double) ix; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_iscanonicall.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_iscanonicall.c new file mode 100644 index 0000000000..820a45e3a8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_iscanonicall.c @@ -0,0 +1,44 @@ +/* Test whether long double value is canonical. ldbl-96 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <stdbool.h> +#include <stdint.h> + +int +__iscanonicall (long double x) +{ + uint32_t se, i0, i1 __attribute__ ((unused)); + + GET_LDOUBLE_WORDS (se, i0, i1, x); + int32_t ix = se & 0x7fff; + bool mant_high = (i0 & 0x80000000) != 0; + + if (LDBL_MIN_EXP == -16381) + /* Intel variant: the high mantissa bit should have a value + determined by the exponent. */ + return ix > 0 ? mant_high : !mant_high; + else + /* M68K variant: both values of the high bit are valid for the + greatest and smallest exponents, while other exponents require + the high bit to be set. */ + return ix == 0 || ix == 0x7fff || mant_high; +} +libm_hidden_def (__iscanonicall) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_issignalingl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_issignalingl.c new file mode 100644 index 0000000000..f659bb7b35 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_issignalingl.c @@ -0,0 +1,44 @@ +/* Test for signaling NaN. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> + +int +__issignalingl (long double x) +{ + u_int32_t exi, hxi, lxi; + GET_LDOUBLE_WORDS (exi, hxi, lxi, x); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN +# error not implemented +#else + /* To keep the following comparison simple, toggle the quiet/signaling bit, + so that it is set for sNaNs. This is inverse to IEEE 754-2008 (as well as + common practice for IEEE 754-1985). */ + hxi ^= 0x40000000; + /* If lxi != 0, then set any suitable bit of the significand in hxi. */ + hxi |= (lxi | -lxi) >> 31; + /* We do not recognize a pseudo NaN as sNaN; they're invalid on 80387 and + later. */ + /* We have to compare for greater (instead of greater or equal), because x's + significand being all-zero designates infinity not NaN. */ + return ((exi & 0x7fff) == 0x7fff) && (hxi > 0xc0000000); +#endif +} +libm_hidden_def (__issignalingl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_llrintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_llrintl.c new file mode 100644 index 0000000000..53d33c3999 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_llrintl.c @@ -0,0 +1,91 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> + +static const long double two63[2] = +{ + 9.223372036854775808000000e+18, /* 0x403E, 0x00000000, 0x00000000 */ + -9.223372036854775808000000e+18 /* 0xC03E, 0x00000000, 0x00000000 */ +}; + + +long long int +__llrintl (long double x) +{ + int32_t se,j0; + u_int32_t i0, i1; + long long int result; + long double w; + long double t; + int sx; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + + sx = (se >> 15) & 1; + j0 = (se & 0x7fff) - 0x3fff; + + if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 >= 63) + result = (((long long int) i0 << 32) | i1) << (j0 - 63); + else + { +#if defined FE_INVALID || defined FE_INEXACT + /* X < LLONG_MAX + 1 implied by J0 < 63. */ + if (x > (long double) LLONG_MAX) + { + /* In the event of overflow we must raise the "invalid" + exception, but not "inexact". */ + t = __nearbyintl (x); + feraiseexcept (t == LLONG_MAX ? FE_INEXACT : FE_INVALID); + } + else +#endif + { + w = two63[sx] + x; + t = w - two63[sx]; + } + GET_LDOUBLE_WORDS (se, i0, i1, t); + j0 = (se & 0x7fff) - 0x3fff; + + if (j0 < 0) + result = 0; + else if (j0 <= 31) + result = i0 >> (31 - j0); + else + result = ((long long int) i0 << (j0 - 31)) | (i1 >> (63 - j0)); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__llrintl, llrintl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_llroundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_llroundl.c new file mode 100644 index 0000000000..f113fabd1a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_llroundl.c @@ -0,0 +1,89 @@ +/* Round long double value to long long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> + + +long long int +__llroundl (long double x) +{ + int32_t j0; + u_int32_t se, i1, i0; + long long int result; + int sign; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + j0 = (se & 0x7fff) - 0x3fff; + sign = (se & 0x8000) != 0 ? -1 : 1; + + if (j0 < 31) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + u_int32_t j = i0 + (0x40000000 >> j0); + if (j < i0) + { + j >>= 1; + j |= 0x80000000; + ++j0; + } + + result = j >> (31 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 >= 63) + result = (((long long int) i0 << 32) | i1) << (j0 - 63); + else + { + u_int32_t j = i1 + (0x80000000 >> (j0 - 31)); + + result = (long long int) i0; + if (j < i1) + ++result; + + if (j0 > 31) + { + result = (result << (j0 - 31)) | (j >> (63 - j0)); +#ifdef FE_INVALID + if (sign == 1 && result == LLONG_MIN) + /* Rounding brought the value out of range. */ + feraiseexcept (FE_INVALID); +#endif + } + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long long int) x; + } + + return sign * result; +} + +weak_alias (__llroundl, llroundl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_lrintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_lrintl.c new file mode 100644 index 0000000000..02dafe67f3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_lrintl.c @@ -0,0 +1,126 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> + +static const long double two63[2] = +{ + 9.223372036854775808000000e+18, /* 0x403E, 0x00000000, 0x00000000 */ + -9.223372036854775808000000e+18 /* 0xC03E, 0x00000000, 0x00000000 */ +}; + + +long int +__lrintl (long double x) +{ + int32_t se,j0; + u_int32_t i0, i1; + long int result; + long double w; + long double t; + int sx; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + + sx = (se >> 15) & 1; + j0 = (se & 0x7fff) - 0x3fff; + + if (j0 < 31) + { +#if defined FE_INVALID || defined FE_INEXACT + /* X < LONG_MAX + 1 implied by J0 < 31. */ + if (sizeof (long int) == 4 + && x > (long double) LONG_MAX) + { + /* In the event of overflow we must raise the "invalid" + exception, but not "inexact". */ + t = __nearbyintl (x); + feraiseexcept (t == LONG_MAX ? FE_INEXACT : FE_INVALID); + } + else +#endif + { + w = two63[sx] + x; + t = w - two63[sx]; + } + GET_LDOUBLE_WORDS (se, i0, i1, t); + j0 = (se & 0x7fff) - 0x3fff; + + result = (j0 < 0 ? 0 : i0 >> (31 - j0)); + } + else if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 >= 63) + result = ((long int) i0 << (j0 - 31)) | (i1 << (j0 - 63)); + else + { +#if defined FE_INVALID || defined FE_INEXACT + /* X < LONG_MAX + 1 implied by J0 < 63. */ + if (sizeof (long int) == 8 + && x > (long double) LONG_MAX) + { + /* In the event of overflow we must raise the "invalid" + exception, but not "inexact". */ + t = __nearbyintl (x); + feraiseexcept (t == LONG_MAX ? FE_INEXACT : FE_INVALID); + } + else +#endif + { + w = two63[sx] + x; + t = w - two63[sx]; + } + GET_LDOUBLE_WORDS (se, i0, i1, t); + j0 = (se & 0x7fff) - 0x3fff; + + if (j0 == 31) + result = (long int) i0; + else + result = ((long int) i0 << (j0 - 31)) | (i1 >> (63 - j0)); + } + } + else + { + /* The number is too large. Unless it rounds to LONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ +#if defined FE_INVALID || defined FE_INEXACT + if (sizeof (long int) == 4 + && x < (long double) LONG_MIN + && x > (long double) LONG_MIN - 1.0L) + { + /* If truncation produces LONG_MIN, the cast will not raise + the exception, but may raise "inexact". */ + t = __nearbyintl (x); + feraiseexcept (t == LONG_MIN ? FE_INEXACT : FE_INVALID); + return LONG_MIN; + } +#endif + return (long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__lrintl, lrintl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_lroundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_lroundl.c new file mode 100644 index 0000000000..7f418e6142 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_lroundl.c @@ -0,0 +1,111 @@ +/* Round long double value to long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> + + +long int +__lroundl (long double x) +{ + int32_t j0; + u_int32_t se, i1, i0; + long int result; + int sign; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + j0 = (se & 0x7fff) - 0x3fff; + sign = (se & 0x8000) != 0 ? -1 : 1; + + if (j0 < 31) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + u_int32_t j = i0 + (0x40000000 >> j0); + if (j < i0) + { + j >>= 1; + j |= 0x80000000; + ++j0; + } + + result = j >> (31 - j0); +#ifdef FE_INVALID + if (sizeof (long int) == 4 + && sign == 1 + && result == LONG_MIN) + /* Rounding brought the value out of range. */ + feraiseexcept (FE_INVALID); +#endif + } + } + else if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 >= 63) + result = ((long int) i0 << (j0 - 31)) | (i1 << (j0 - 63)); + else + { + u_int32_t j = i1 + (0x80000000 >> (j0 - 31)); + unsigned long int ures = i0; + + if (j < i1) + ++ures; + + if (j0 == 31) + result = ures; + else + { + result = (ures << (j0 - 31)) | (j >> (63 - j0)); +#ifdef FE_INVALID + if (sizeof (long int) == 8 + && sign == 1 + && result == LONG_MIN) + /* Rounding brought the value out of range. */ + feraiseexcept (FE_INVALID); +#endif + } + } + } + else + { + /* The number is too large. Unless it rounds to LONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ +#ifdef FE_INVALID + if (sizeof (long int) == 4 + && x <= (long double) LONG_MIN - 0.5L) + { + /* If truncation produces LONG_MIN, the cast will not raise + the exception, but may raise "inexact". */ + feraiseexcept (FE_INVALID); + return LONG_MIN; + } +#endif + return (long int) x; + } + + return sign * result; +} + +weak_alias (__lroundl, lroundl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_modfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_modfl.c new file mode 100644 index 0000000000..e9401d0f5d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_modfl.c @@ -0,0 +1,73 @@ +/* s_modfl.c -- long double version of s_modf.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * modfl(long double x, long double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include <math.h> +#include <math_private.h> + +static const long double one = 1.0; + +long double +__modfl(long double x, long double *iptr) +{ + int32_t i0,i1,j0; + u_int32_t i,se; + GET_LDOUBLE_WORDS(se,i0,i1,x); + j0 = (se&0x7fff)-0x3fff; /* exponent of x */ + if(j0<32) { /* integer part in high x */ + if(j0<0) { /* |x|<1 */ + SET_LDOUBLE_WORDS(*iptr,se&0x8000,0,0); /* *iptr = +-0 */ + return x; + } else { + i = (0x7fffffff)>>j0; + if(((i0&i)|i1)==0) { /* x is integral */ + *iptr = x; + SET_LDOUBLE_WORDS(x,se&0x8000,0,0); /* return +-0 */ + return x; + } else { + SET_LDOUBLE_WORDS(*iptr,se,i0&(~i),0); + return x - *iptr; + } + } + } else if (__builtin_expect(j0>63, 0)) { /* no fraction part */ + *iptr = x*one; + /* We must handle NaNs separately. */ + if (j0 == 0x4000 && ((i0 & 0x7fffffff) | i1)) + return x*one; + SET_LDOUBLE_WORDS(x,se&0x8000,0,0); /* return +-0 */ + return x; + } else { /* fraction part in low x */ + i = ((u_int32_t)(0x7fffffff))>>(j0-32); + if((i1&i)==0) { /* x is integral */ + *iptr = x; + SET_LDOUBLE_WORDS(x,se&0x8000,0,0); /* return +-0 */ + return x; + } else { + SET_LDOUBLE_WORDS(*iptr,se,i0,i1&(~i)); + return x - *iptr; + } + } +} +weak_alias (__modfl, modfl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_nexttoward.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_nexttoward.c new file mode 100644 index 0000000000..3d0382eac9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_nexttoward.c @@ -0,0 +1,86 @@ +/* s_nexttoward.c + * Conversion from s_nextafter.c by Ulrich Drepper, Cygnus Support, + * drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* IEEE functions + * nexttoward(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <float.h> + +double __nexttoward(double x, long double y) +{ + int32_t hx,ix,iy; + u_int32_t lx,hy,ly,esy; + + EXTRACT_WORDS(hx,lx,x); + GET_LDOUBLE_WORDS(esy,hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = esy&0x7fff; /* |y| */ + + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ + ((iy>=0x7fff)&&(hy|ly)!=0)) /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if((ix|lx)==0) { /* x == 0 */ + double u; + INSERT_WORDS(x,(esy&0x8000)<<16,1); /* return +-minsub */ + u = math_opt_barrier (x); + u = u * u; + math_force_eval (u); /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if (x > y) { /* x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } else { /* x < 0 */ + if (x < y) { /* x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } + hy = hx&0x7ff00000; + if(hy>=0x7ff00000) { + double u = x+x; /* overflow */ + math_force_eval (u); + __set_errno (ERANGE); + } + if(hy<0x00100000) { + double u = x*x; /* underflow */ + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + INSERT_WORDS(x,hx,lx); + return x; +} +weak_alias (__nexttoward, nexttoward) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_nexttowardf.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_nexttowardf.c new file mode 100644 index 0000000000..ae7538942f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_nexttowardf.c @@ -0,0 +1,74 @@ +/* s_nexttowardf.c -- float version of s_nextafter.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <float.h> + +float __nexttowardf(float x, long double y) +{ + int32_t hx,ix,iy; + u_int32_t hy,ly,esy; + + GET_FLOAT_WORD(hx,x); + GET_LDOUBLE_WORDS(esy,hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = esy&0x7fff; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + (iy>=0x7fff&&((hy|ly)!=0))) /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if(ix==0) { /* x == 0 */ + float u; + SET_FLOAT_WORD(x,((esy&0x8000)<<16)|1);/* return +-minsub*/ + u = math_opt_barrier (x); + u = u * u; + math_force_eval (u); /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if(x > y) { /* x -= ulp */ + hx -= 1; + } else { /* x < y, x += ulp */ + hx += 1; + } + } else { /* x < 0 */ + if(x < y) { /* x -= ulp */ + hx -= 1; + } else { /* x > y, x += ulp */ + hx += 1; + } + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) { + float u = x+x; /* overflow */ + math_force_eval (u); + __set_errno (ERANGE); + } + if(hy<0x00800000) { + float u = x*x; /* underflow */ + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + SET_FLOAT_WORD(x,hx); + return x; +} +weak_alias (__nexttowardf, nexttowardf) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_nextupl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_nextupl.c new file mode 100644 index 0000000000..aa66eaf106 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_nextupl.c @@ -0,0 +1,84 @@ +/* Return the least floating-point number greater than X. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* Return the least floating-point number greater than X. */ +long double +__nextupl (long double x) +{ + u_int32_t hx, ix; + u_int32_t lx; + int32_t esx; + + GET_LDOUBLE_WORDS (esx, hx, lx, x); + ix = esx & 0x7fff; + + if (((ix == 0x7fff) && (((hx & 0x7fffffff) | lx) != 0))) /* x is nan. */ + return x + x; + if ((ix | hx | lx) == 0) + return LDBL_TRUE_MIN; + if (esx >= 0) + { /* x > 0. */ + if (isinf (x)) + return x; + lx += 1; + if (lx == 0) + { + hx += 1; +#if LDBL_MIN_EXP == -16381 + if (hx == 0 || (esx == 0 && hx == 0x80000000)) +#else + if (hx == 0) +#endif + { + esx += 1; + hx |= 0x80000000; + } + } + } + else + { /* x < 0. */ + if (lx == 0) + { +#if LDBL_MIN_EXP == -16381 + if (hx <= 0x80000000 && esx != 0xffff8000) + { + esx -= 1; + hx = hx - 1; + if ((esx & 0x7fff) > 0) + hx |= 0x80000000; + } + else + hx -= 1; +#else + if (ix != 0 && hx == 0x80000000) + hx = 0; + if (hx == 0) + esx -= 1; + hx -= 1; +#endif + } + lx -= 1; + } + SET_LDOUBLE_WORDS (x, esx, hx, lx); + return x; +} + +weak_alias (__nextupl, nextupl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_remquol.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_remquol.c new file mode 100644 index 0000000000..ee9a6a7d2a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_remquol.c @@ -0,0 +1,111 @@ +/* Compute remainder and a congruent to the quotient. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +static const long double zero = 0.0; + + +long double +__remquol (long double x, long double p, int *quo) +{ + int32_t ex,ep,hx,hp; + u_int32_t sx,lx,lp; + int cquo,qs; + + GET_LDOUBLE_WORDS (ex, hx, lx, x); + GET_LDOUBLE_WORDS (ep, hp, lp, p); + sx = ex & 0x8000; + qs = (sx ^ (ep & 0x8000)) >> 15; + ep &= 0x7fff; + ex &= 0x7fff; + + /* Purge off exception values. */ + if ((ep | hp | lp) == 0) + return (x * p) / (x * p); /* p = 0 */ + if ((ex == 0x7fff) /* x not finite */ + || ((ep == 0x7fff) /* p is NaN */ + && (((hp & 0x7fffffff) | lp) != 0))) + return (x * p) / (x * p); + + if (ep <= 0x7ffb) + x = __ieee754_fmodl (x, 8 * p); /* now x < 8p */ + + if (((ex - ep) | (hx - hp) | (lx - lp)) == 0) + { + *quo = qs ? -1 : 1; + return zero * x; + } + + x = fabsl (x); + p = fabsl (p); + cquo = 0; + + if (ep <= 0x7ffc && x >= 4 * p) + { + x -= 4 * p; + cquo += 4; + } + if (ep <= 0x7ffd && x >= 2 * p) + { + x -= 2 * p; + cquo += 2; + } + + if (ep < 0x0002) + { + if (x + x > p) + { + x -= p; + ++cquo; + if (x + x >= p) + { + x -= p; + ++cquo; + } + } + } + else + { + long double p_half = 0.5 * p; + if (x > p_half) + { + x -= p; + ++cquo; + if (x >= p_half) + { + x -= p; + ++cquo; + } + } + } + + *quo = qs ? -cquo : cquo; + + /* Ensure correct sign of zero result in round-downward mode. */ + if (x == 0.0L) + x = 0.0L; + if (sx) + x = -x; + return x; +} +weak_alias (__remquol, remquol) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_roundevenl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_roundevenl.c new file mode 100644 index 0000000000..dab6aa6558 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_roundevenl.c @@ -0,0 +1,124 @@ +/* Round to nearest integer value, rounding halfway cases to even. + ldbl-96 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +#define BIAS 0x3fff +#define MANT_DIG 64 +#define MAX_EXP (2 * BIAS + 1) + +long double +roundevenl (long double x) +{ + uint16_t se; + uint32_t hx, lx; + GET_LDOUBLE_WORDS (se, hx, lx, x); + int exponent = se & 0x7fff; + if (exponent >= BIAS + MANT_DIG - 1) + { + /* Integer, infinity or NaN. */ + if (exponent == MAX_EXP) + /* Infinity or NaN; quiet signaling NaNs. */ + return x + x; + else + return x; + } + else if (exponent >= BIAS + MANT_DIG - 32) + { + /* Not necessarily an integer; integer bit is in low word. + Locate the bits with exponents 0 and -1. */ + int int_pos = (BIAS + MANT_DIG - 1) - exponent; + int half_pos = int_pos - 1; + uint32_t half_bit = 1U << half_pos; + uint32_t int_bit = 1U << int_pos; + if ((lx & (int_bit | (half_bit - 1))) != 0) + { + /* No need to test whether HALF_BIT is set. */ + lx += half_bit; + if (lx < half_bit) + { + hx++; + if (hx == 0) + { + hx = 0x80000000; + se++; + } + } + } + lx &= ~(int_bit - 1); + } + else if (exponent == BIAS + MANT_DIG - 33) + { + /* Not necessarily an integer; integer bit is bottom of high + word, half bit is top of low word. */ + if (((hx & 1) | (lx & 0x7fffffff)) != 0) + { + lx += 0x80000000; + if (lx < 0x80000000) + { + hx++; + if (hx == 0) + { + hx = 0x80000000; + se++; + } + } + } + lx = 0; + } + else if (exponent >= BIAS) + { + /* At least 1; not necessarily an integer, integer bit and half + bit are in the high word. Locate the bits with exponents 0 + and -1. */ + int int_pos = (BIAS + MANT_DIG - 33) - exponent; + int half_pos = int_pos - 1; + uint32_t half_bit = 1U << half_pos; + uint32_t int_bit = 1U << int_pos; + if (((hx & (int_bit | (half_bit - 1))) | lx) != 0) + { + hx += half_bit; + if (hx < half_bit) + { + hx = 0x80000000; + se++; + } + } + hx &= ~(int_bit - 1); + lx = 0; + } + else if (exponent == BIAS - 1 && (hx > 0x80000000 || lx != 0)) + { + /* Interval (0.5, 1). */ + se = (se & 0x8000) | 0x3fff; + hx = 0x80000000; + lx = 0; + } + else + { + /* Rounds to 0. */ + se &= 0x8000; + hx = 0; + lx = 0; + } + SET_LDOUBLE_WORDS (x, se, hx, lx); + return x; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_roundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_roundl.c new file mode 100644 index 0000000000..d8918d2874 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_roundl.c @@ -0,0 +1,92 @@ +/* Round long double to integer away from zero. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +long double +__roundl (long double x) +{ + int32_t j0; + u_int32_t se, i1, i0; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + j0 = (se & 0x7fff) - 0x3fff; + if (j0 < 31) + { + if (j0 < 0) + { + se &= 0x8000; + i0 = i1 = 0; + if (j0 == -1) + { + se |= 0x3fff; + i0 = 0x80000000; + } + } + else + { + u_int32_t i = 0x7fffffff >> j0; + if (((i0 & i) | i1) == 0) + /* X is integral. */ + return x; + + u_int32_t j = i0 + (0x40000000 >> j0); + if (j < i0) + se += 1; + i0 = (j & ~i) | 0x80000000; + i1 = 0; + } + } + else if (j0 > 62) + { + if (j0 == 0x4000) + /* Inf or NaN. */ + return x + x; + else + return x; + } + else + { + u_int32_t i = 0xffffffff >> (j0 - 31); + if ((i1 & i) == 0) + /* X is integral. */ + return x; + + u_int32_t j = i1 + (1 << (62 - j0)); + if (j < i1) + { + u_int32_t k = i0 + 1; + if (k < i0) + { + se += 1; + k |= 0x80000000; + } + i0 = k; + } + i1 = j; + i1 &= ~i; + } + + SET_LDOUBLE_WORDS (x, se, i0, i1); + return x; +} +weak_alias (__roundl, roundl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_scalblnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_scalblnl.c new file mode 100644 index 0000000000..457e999c6c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_scalblnl.c @@ -0,0 +1,60 @@ +/* s_scalbnl.c -- long double version of s_scalbn.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbnl (long double x, int n) + * scalbnl(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> + +static const long double +two63 = 0x1p63L, +twom64 = 0x1p-64L, +huge = 1.0e+4900L, +tiny = 1.0e-4900L; + +long double +__scalblnl (long double x, long int n) +{ + int32_t k,es,hx,lx; + GET_LDOUBLE_WORDS(es,hx,lx,x); + k = es&0x7fff; /* extract exponent */ + if (__builtin_expect(k==0, 0)) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ + x *= two63; + GET_LDOUBLE_EXP(es,x); + k = (es&0x7fff) - 63; + } + if (__builtin_expect(k==0x7fff, 0)) return x+x; /* NaN or Inf */ + if (__builtin_expect(n< -50000, 0)) + return tiny*__copysignl(tiny,x); + if (__builtin_expect(n> 50000 || k+n > 0x7ffe, 0)) + return huge*__copysignl(huge,x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k+n; + if (__builtin_expect(k > 0, 1)) /* normal result */ + {SET_LDOUBLE_EXP(x,(es&0x8000)|k); return x;} + if (k <= -64) + return tiny*__copysignl(tiny,x); /*underflow*/ + k += 64; /* subnormal result */ + SET_LDOUBLE_EXP(x,(es&0x8000)|k); + return x*twom64; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_setpayloadl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_setpayloadl.c new file mode 100644 index 0000000000..1aba33e6e2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_setpayloadl.c @@ -0,0 +1,3 @@ +#define SIG 0 +#define FUNC setpayloadl +#include <s_setpayloadl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_setpayloadl_main.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_setpayloadl_main.c new file mode 100644 index 0000000000..c2fd0401d7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_setpayloadl_main.c @@ -0,0 +1,68 @@ +/* Set NaN payload. ldbl-96 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +#define SET_HIGH_BIT (HIGH_ORDER_BIT_IS_SET_FOR_SNAN ? SIG : !SIG) +#define BIAS 0x3fff +#define PAYLOAD_DIG 62 +#define EXPLICIT_MANT_DIG 63 + +int +FUNC (long double *x, long double payload) +{ + uint32_t hx, lx; + uint16_t exponent; + GET_LDOUBLE_WORDS (exponent, hx, lx, payload); + /* Test if argument is (a) negative or too large; (b) too small, + except for 0 when allowed; (c) not an integer. */ + if (exponent >= BIAS + PAYLOAD_DIG + || (exponent < BIAS && !(SET_HIGH_BIT + && exponent == 0 && hx == 0 && lx == 0))) + { + SET_LDOUBLE_WORDS (*x, 0, 0, 0); + return 1; + } + int shift = BIAS + EXPLICIT_MANT_DIG - exponent; + if (shift < 32 + ? (lx & ((1U << shift) - 1)) != 0 + : (lx != 0 || (hx & ((1U << (shift - 32)) - 1)) != 0)) + { + SET_LDOUBLE_WORDS (*x, 0, 0, 0); + return 1; + } + if (exponent != 0) + { + if (shift >= 32) + { + lx = hx >> (shift - 32); + hx = 0; + } + else if (shift != 0) + { + lx = (lx >> shift) | (hx << (32 - shift)); + hx >>= shift; + } + } + hx |= 0x80000000 | (SET_HIGH_BIT ? 0x40000000 : 0); + SET_LDOUBLE_WORDS (*x, 0x7fff, hx, lx); + return 0; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_setpayloadsigl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_setpayloadsigl.c new file mode 100644 index 0000000000..d97e2c8206 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_setpayloadsigl.c @@ -0,0 +1,3 @@ +#define SIG 1 +#define FUNC setpayloadsigl +#include <s_setpayloadl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_signbitl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_signbitl.c new file mode 100644 index 0000000000..d430eb8600 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_signbitl.c @@ -0,0 +1,26 @@ +/* Return nonzero value if number is negative. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +int +__signbitl (long double x) +{ + return __builtin_signbitl (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_sincosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_sincosl.c new file mode 100644 index 0000000000..7d33c97162 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_sincosl.c @@ -0,0 +1,76 @@ +/* Compute sine and cosine of argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <math.h> + +#include <math_private.h> + + +void +__sincosl (long double x, long double *sinx, long double *cosx) +{ + int32_t se, i0, i1 __attribute__ ((unused)); + + /* High word of x. */ + GET_LDOUBLE_WORDS (se, i0, i1, x); + + /* |x| ~< pi/4 */ + se &= 0x7fff; + if (se < 0x3ffe || (se == 0x3ffe && i0 <= 0xc90fdaa2)) + { + *sinx = __kernel_sinl (x, 0.0, 0); + *cosx = __kernel_cosl (x, 0.0); + } + else if (se == 0x7fff) + { + /* sin(Inf or NaN) is NaN */ + *sinx = *cosx = x - x; + if (isinf (x)) + __set_errno (EDOM); + } + else + { + /* Argument reduction needed. */ + long double y[2]; + int n; + + n = __ieee754_rem_pio2l (x, y); + switch (n & 3) + { + case 0: + *sinx = __kernel_sinl (y[0], y[1], 1); + *cosx = __kernel_cosl (y[0], y[1]); + break; + case 1: + *sinx = __kernel_cosl (y[0], y[1]); + *cosx = -__kernel_sinl (y[0], y[1], 1); + break; + case 2: + *sinx = -__kernel_sinl (y[0], y[1], 1); + *cosx = -__kernel_cosl (y[0], y[1]); + break; + default: + *sinx = -__kernel_cosl (y[0], y[1]); + *cosx = __kernel_sinl (y[0], y[1], 1); + break; + } + } +} +weak_alias (__sincosl, sincosl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_sinl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_sinl.c new file mode 100644 index 0000000000..11e1899822 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_sinl.c @@ -0,0 +1,88 @@ +/* s_sinl.c -- long double version of s_sin.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* sinl(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sinl ... sine function on [-pi/4,pi/4] + * __kernel_cosl ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> + +long double __sinl(long double x) +{ + long double y[2],z=0.0; + int32_t n, se, i0, i1; + + /* High word of x. */ + GET_LDOUBLE_WORDS(se,i0,i1,x); + + /* |x| ~< pi/4 */ + se &= 0x7fff; + if(se < 0x3ffe || (se == 0x3ffe && i0 <= 0xc90fdaa2)) + return __kernel_sinl(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (se==0x7fff) { + if (i1 == 0 && i0 == 0x80000000) + __set_errno (EDOM); + return x-x; + } + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + switch(n&3) { + case 0: return __kernel_sinl(y[0],y[1],1); + case 1: return __kernel_cosl(y[0],y[1]); + case 2: return -__kernel_sinl(y[0],y[1],1); + default: + return -__kernel_cosl(y[0],y[1]); + } + } +} +weak_alias (__sinl, sinl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_tanhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_tanhl.c new file mode 100644 index 0000000000..38edf9f75e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_tanhl.c @@ -0,0 +1,90 @@ +/* s_tanhl.c -- long double version of s_tanh.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* tanhl(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanhl(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x). + * 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x) + * -t + * 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x) + * t + 2 + * 2 + * 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x) + * t + 2 + * 23.0 < x <= INF : tanhl(x) := 1. + * + * Special cases: + * tanhl(NaN) is NaN; + * only tanhl(0)=0 is exact for finite argument. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double one=1.0, two=2.0, tiny = 1.0e-4900L; + +long double __tanhl(long double x) +{ + long double t,z; + int32_t se; + u_int32_t j0,j1,ix; + + /* High word of |x|. */ + GET_LDOUBLE_WORDS(se,j0,j1,x); + ix = se&0x7fff; + + /* x is INF or NaN */ + if(ix==0x7fff) { + /* for NaN it's not important which branch: tanhl(NaN) = NaN */ + if (se&0x8000) return one/x-one; /* tanhl(-inf)= -1; */ + else return one/x+one; /* tanhl(+inf)=+1 */ + } + + /* |x| < 23 */ + if (ix < 0x4003 || (ix == 0x4003 && j0 < 0xb8000000u)) {/* |x|<23 */ + if ((ix|j0|j1) == 0) + return x; /* x == +- 0 */ + if (ix<0x3fc8) /* |x|<2**-55 */ + { + math_check_force_underflow (x); + return x*(one+tiny); /* tanh(small) = small */ + } + if (ix>=0x3fff) { /* |x|>=1 */ + t = __expm1l(two*fabsl(x)); + z = one - two/(t+two); + } else { + t = __expm1l(-two*fabsl(x)); + z= -t/(t+two); + } + /* |x| > 23, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (se&0x8000)? -z: z; +} +weak_alias (__tanhl, tanhl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_tanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_tanl.c new file mode 100644 index 0000000000..3fbe4a8f6b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_tanl.c @@ -0,0 +1,81 @@ +/* s_tanl.c -- long double version of s_tan.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* tanl(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tanl ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> + +long double __tanl(long double x) +{ + long double y[2],z=0.0; + int32_t n, se, i0, i1; + + /* High word of x. */ + GET_LDOUBLE_WORDS(se,i0,i1,x); + + /* |x| ~< pi/4 */ + se &= 0x7fff; + if(se <= 0x3ffe) return __kernel_tanl(x,z,1); + + /* tan(Inf or NaN) is NaN */ + else if (se==0x7fff) { + if (i1 == 0 && i0 == 0x80000000) + __set_errno (EDOM); + return x-x; + } + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} +weak_alias (__tanl, tanl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_totalorderl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_totalorderl.c new file mode 100644 index 0000000000..16accad1ff --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_totalorderl.c @@ -0,0 +1,57 @@ +/* Total order operation. ldbl-96 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalorderl (long double x, long double y) +{ + int16_t expx, expy; + uint32_t hx, hy; + uint32_t lx, ly; + GET_LDOUBLE_WORDS (expx, hx, lx, x); + GET_LDOUBLE_WORDS (expy, hy, ly, y); + if (LDBL_MIN_EXP == -16382) + { + /* M68K variant: for the greatest exponent, the high mantissa + bit is not significant and both values of it are valid, so + set it before comparing. For the Intel variant, only one + value of the high mantissa bit is valid for each exponent, so + this is not necessary. */ + if ((expx & 0x7fff) == 0x7fff) + hx |= 0x80000000; + if ((expy & 0x7fff) == 0x7fff) + hy |= 0x80000000; + } +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN +# error not implemented +#endif + uint32_t x_sign = expx >> 15; + uint32_t y_sign = expy >> 15; + expx ^= x_sign >> 17; + hx ^= x_sign; + lx ^= x_sign; + expy ^= y_sign >> 17; + hy ^= y_sign; + ly ^= y_sign; + return expx < expy || (expx == expy && (hx < hy || (hx == hy && lx <= ly))); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_totalordermagl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_totalordermagl.c new file mode 100644 index 0000000000..6b370b2ade --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_totalordermagl.c @@ -0,0 +1,51 @@ +/* Total order operation on absolute values. ldbl-96 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalordermagl (long double x, long double y) +{ + uint16_t expx, expy; + uint32_t hx, hy; + uint32_t lx, ly; + GET_LDOUBLE_WORDS (expx, hx, lx, x); + GET_LDOUBLE_WORDS (expy, hy, ly, y); + expx &= 0x7fff; + expy &= 0x7fff; + if (LDBL_MIN_EXP == -16382) + { + /* M68K variant: for the greatest exponent, the high mantissa + bit is not significant and both values of it are valid, so + set it before comparing. For the Intel variant, only one + value of the high mantissa bit is valid for each exponent, so + this is not necessary. */ + if (expx == 0x7fff) + hx |= 0x80000000; + if (expy == 0x7fff) + hy |= 0x80000000; + } +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN +# error not implemented +#endif + return expx < expy || (expx == expy && (hx < hy || (hx == hy && lx <= ly))); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_ufromfpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_ufromfpl.c new file mode 100644 index 0000000000..c686daa4a7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_ufromfpl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 1 +#define INEXACT 0 +#define FUNC ufromfpl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/s_ufromfpxl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_ufromfpxl.c new file mode 100644 index 0000000000..906066c83c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/s_ufromfpxl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 1 +#define INEXACT 1 +#define FUNC ufromfpxl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/strtod_nan_ldouble.h b/REORG.TODO/sysdeps/ieee754/ldbl-96/strtod_nan_ldouble.h new file mode 100644 index 0000000000..e847b13b40 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/strtod_nan_ldouble.h @@ -0,0 +1,30 @@ +/* Convert string for NaN payload to corresponding NaN. For ldbl-96. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define FLOAT long double +#define SET_MANTISSA(flt, mant) \ + do \ + { \ + union ieee854_long_double u; \ + u.d = (flt); \ + u.ieee_nan.mantissa0 = (mant) >> 32; \ + u.ieee_nan.mantissa1 = (mant); \ + if ((u.ieee.mantissa0 | u.ieee.mantissa1) != 0) \ + (flt) = u.d; \ + } \ + while (0) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/strtold_l.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/strtold_l.c new file mode 100644 index 0000000000..251f91ba9d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/strtold_l.c @@ -0,0 +1,37 @@ +/* Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +/* The actual implementation for all floating point sizes is in strtod.c. + These macros tell it to produce the `long double' version, `strtold'. */ + +#define FLOAT long double +#define FLT LDBL +#ifdef USE_WIDE_CHAR +# define STRTOF wcstold_l +# define __STRTOF __wcstold_l +# define STRTOF_NAN __wcstold_nan +#else +# define STRTOF strtold_l +# define __STRTOF __strtold_l +# define STRTOF_NAN __strtold_nan +#endif +#define MPN2FLOAT __mpn_construct_long_double +#define FLOAT_HUGE_VAL HUGE_VALL + +#include <stdlib/strtod_l.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/t_sincosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/t_sincosl.c new file mode 100644 index 0000000000..77bf9cfdba --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/t_sincosl.c @@ -0,0 +1,483 @@ +/* Extended-precision floating point sine and cosine tables. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Based on quad-precision tables by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* For 0.1484375 + n/128.0, n=0..82 this table contains + first 64 bits of cosine, then at least 64 additional + bits and the same for sine. + 0.1484375+82.0/128.0 is the smallest number among above defined numbers + larger than pi/4. + Computed using MPFR: + + #include <stdio.h> + #include <mpfr.h> + + int + main (void) + { + int j; + mpfr_t t, b, i, rs, rc, ts, tc, tsl, tcl; + mpfr_init2 (b, 64); + mpfr_init2 (i, 64); + mpfr_init2 (t, 64); + mpfr_set_str (b, "0.1484375", 0, MPFR_RNDN); + mpfr_set_str (i, "0x1p-7", 0, MPFR_RNDN); + mpfr_init2 (rs, 300); + mpfr_init2 (rc, 300); + mpfr_init2 (ts, 64); + mpfr_init2 (tc, 64); + mpfr_init2 (tsl, 64); + mpfr_init2 (tcl, 64); + for (j = 0; j <= 82; j++) + { + mpfr_mul_ui (t, i, j, MPFR_RNDN); + mpfr_add (t, t, b, MPFR_RNDN); + printf (" /" "* x = 0.1484375 + %d/128. *" "/\n", j); + mpfr_cos (rc, t, MPFR_RNDN); + mpfr_sin (rs, t, MPFR_RNDN); + mpfr_set (tc, rc, MPFR_RNDN); + mpfr_set (ts, rs, MPFR_RNDN); + mpfr_sub (tcl, rc, tc, MPFR_RNDN); + mpfr_sub (tsl, rs, ts, MPFR_RNDN); + mpfr_printf (" %.17RaL,\n", tc); + mpfr_printf (" %.17RaL,\n", tcl); + mpfr_printf (" %.17RaL,\n", ts); + mpfr_printf (" %.17RaL,\n", tsl); + } + return 0; + } + +*/ + +const long double __sincosl_table[] = { + /* x = 0.1484375 + 0/128. */ + 0xf.d2f5320e1b7902100p-4L, + -0x6.4b225d06708635580p-68L, + 0x2.5dc50bc95711d0d80p-4L, + 0x1.787d108fd438cf5a0p-68L, + /* x = 0.1484375 + 1/128. */ + 0xf.ce1a053e621438b00p-4L, + 0x6.d60c76e8c45bf0a80p-68L, + 0x2.7d66258bacd96a400p-4L, + -0x1.4cca4c9a3782a6bc0p-68L, + /* x = 0.1484375 + 2/128. */ + 0xf.c8ffa01ba68074100p-4L, + 0x7.e05962b0d9fdf2000p-68L, + 0x2.9cfd49b8be4f66540p-4L, + -0x1.89354fe340fbd96c0p-68L, + /* x = 0.1484375 + 3/128. */ + 0xf.c3a6170f767ac7300p-4L, + 0x5.d63d99a9d439e1d80p-68L, + 0x2.bc89f9f424de54840p-4L, + 0x1.de7ce03b2514952c0p-68L, + /* x = 0.1484375 + 4/128. */ + 0xf.be0d7f7fef11e7100p-4L, + -0x5.5bc47540b095ba800p-68L, + 0x2.dc0bb80b49a97ffc0p-4L, + -0xc.b1722e07246208500p-72L, + /* x = 0.1484375 + 5/128. */ + 0xf.b835efcf670dd2d00p-4L, + -0x1.90186db968115ec20p-68L, + 0x2.fb8205f75e56a2b40p-4L, + 0x1.6a1c4792f85625880p-68L, + /* x = 0.1484375 + 6/128. */ + 0xf.b21f7f5c156696b00p-4L, + 0xa.c1fe28ac5fd766700p-76L, + 0x3.1aec65df552876f80p-4L, + 0x2.ece9a235671324700p-72L, + /* x = 0.1484375 + 7/128. */ + 0xf.abca467fb3cb8f200p-4L, + -0x2.f960fe2715cc521c0p-68L, + 0x3.3a4a5a19d86246700p-4L, + 0x1.0f602c44df4fa5140p-68L, + /* x = 0.1484375 + 8/128. */ + 0xf.a5365e8f1d3ca2800p-4L, + -0x4.1e24a289519b26800p-68L, + 0x3.599b652f40ec999c0p-4L, + 0x1.f12a0a4c8561de160p-68L, + /* x = 0.1484375 + 9/128. */ + 0xf.9e63e1d9e8b6f6f00p-4L, + 0x2.e296bae5b5ed9c100p-68L, + 0x3.78df09db8c332ce00p-4L, + 0xd.2b53d865582e45200p-72L, + /* x = 0.1484375 + 10/128. */ + 0xf.9752eba9fff6b9900p-4L, + -0x7.bd415254fab56cd00p-68L, + 0x3.9814cb10513453cc0p-4L, + -0x6.84de43e3595cc8500p-72L, + /* x = 0.1484375 + 11/128. */ + 0xf.90039843324f9b900p-4L, + 0x4.0416c1984b6cbed00p-68L, + 0x3.b73c2bf6b4b9f6680p-4L, + 0xe.f9499c81f0d965100p-72L, + /* x = 0.1484375 + 12/128. */ + 0xf.887604e2c39dbb200p-4L, + 0xe.4ec5825059a78a000p-72L, + 0x3.d654aff15cb457a00p-4L, + 0xf.ca854698aba330400p-72L, + /* x = 0.1484375 + 13/128. */ + 0xf.80aa4fbef750ba800p-4L, + -0x7.c2cc346a06b075c00p-68L, + 0x3.f55dda9e62aed7500p-4L, + 0x1.3bd7b8e6a3d1635e0p-68L, + /* x = 0.1484375 + 14/128. */ + 0xf.78a098069792dab00p-4L, + -0x4.3611bda6e483a5980p-68L, + 0x4.14572fd94556e6480p-4L, + -0xc.29dfd8ec7722b8400p-72L, + /* x = 0.1484375 + 15/128. */ + 0xf.7058fde0788dfc800p-4L, + 0x5.b8fe88789e4f42500p-72L, + 0x4.334033bcd90d66080p-4L, + -0x3.0a0c93e2b47bbae40p-68L, + /* x = 0.1484375 + 16/128. */ + 0xf.67d3a26af7d07aa00p-4L, + 0x4.bd6d42af8c0068000p-68L, + 0x4.52186aa5377ab2080p-4L, + 0x3.bf2524f52e3a06a80p-68L, + /* x = 0.1484375 + 17/128. */ + 0xf.5f10a7bb77d3dfa00p-4L, + 0xc.1da8b578427832800p-72L, + 0x4.70df5931ae1d94600p-4L, + 0x7.6fe0dcff47fe31b80p-72L, + /* x = 0.1484375 + 18/128. */ + 0xf.561030ddd7a789600p-4L, + 0xe.a9f4a32c652155500p-72L, + 0x4.8f948446abcd6b100p-4L, + -0x8.0334eff185e4d9100p-72L, + /* x = 0.1484375 + 19/128. */ + 0xf.4cd261d3e6c15bb00p-4L, + 0x3.69c8758630d2ac000p-68L, + 0x4.ae37710fad27c8a80p-4L, + 0x2.9c4cf96c03519b9c0p-68L, + /* x = 0.1484375 + 20/128. */ + 0xf.43575f94d4f6b2700p-4L, + 0x2.f5fb76b14d2a64ac0p-68L, + 0x4.ccc7a50127e1de100p-4L, + -0x3.494bf3cfd39ae0840p-68L, + /* x = 0.1484375 + 21/128. */ + 0xf.399f500c9e9fd3800p-4L, + -0x5.166a8d9c254778900p-68L, + 0x4.eb44a5da74f600200p-4L, + 0x7.aaa090f0734e28880p-72L, + /* x = 0.1484375 + 22/128. */ + 0xf.2faa5a1b74e82fd00p-4L, + 0x6.1fa05f9177380e900p-68L, + 0x5.09adf9a7b9a5a0f80p-4L, + -0x1.c75705c59f5e66be0p-68L, + /* x = 0.1484375 + 23/128. */ + 0xf.2578a595224dd2e00p-4L, + 0x6.bfa2eb2f99cc67500p-68L, + 0x5.280326c3cf4818200p-4L, + 0x3.ba6bb08eac82c2080p-68L, + /* x = 0.1484375 + 24/128. */ + 0xf.1b0a5b406b526d900p-4L, + -0x7.93aa0152372f23380p-68L, + 0x5.4643b3da29de9b380p-4L, + -0x2.8eaa110f0ccd04c00p-68L, + /* x = 0.1484375 + 25/128. */ + 0xf.105fa4d66b607a600p-4L, + 0x7.d44e0427252044380p-68L, + 0x5.646f27e8bd65cbe00p-4L, + 0x3.a5d61ff0657229100p-68L, + /* x = 0.1484375 + 26/128. */ + 0xf.0578ad01ede708000p-4L, + -0x5.c63f6239467b50100p-68L, + 0x5.82850a41e1dd46c80p-4L, + -0x9.fd15dbb3244403200p-76L, + /* x = 0.1484375 + 27/128. */ + 0xe.fa559f5ec3aec3a00p-4L, + 0x4.eb03319278a2d4200p-68L, + 0x5.a084e28e35fda2780p-4L, + -0x9.202444aace28b3100p-72L, + /* x = 0.1484375 + 28/128. */ + 0xe.eef6a879146af0c00p-4L, + -0x6.46a15d15f53f2c200p-72L, + 0x5.be6e38ce809554280p-4L, + 0x3.c14ee9da0d3648400p-68L, + /* x = 0.1484375 + 29/128. */ + 0xe.e35bf5ccac8905300p-4L, + -0x3.26e2248cb2c5b81c0p-68L, + 0x5.dc40955d9084f4880p-4L, + 0x2.94675a2498de5d840p-68L, + /* x = 0.1484375 + 30/128. */ + 0xe.d785b5c44741b4500p-4L, + -0x6.c3a943462cc75eb00p-68L, + 0x5.f9fb80f21b5364a00p-4L, + -0x3.bcdabf5af1dd3ad00p-68L, + /* x = 0.1484375 + 31/128. */ + 0xe.cb7417b8d4ee3ff00p-4L, + -0x3.c8545bf8c55b70e00p-68L, + 0x6.179e84a09a5258a80p-4L, + -0x3.f164a0531fc1ada00p-68L, + /* x = 0.1484375 + 32/128. */ + 0xe.bf274bf0bda4f6200p-4L, + 0x4.47e56a09362679900p-68L, + 0x6.352929dd264bd4480p-4L, + 0x2.02ea766325d8aa8c0p-68L, + /* x = 0.1484375 + 33/128. */ + 0xe.b29f839f201fd1400p-4L, + -0x4.6c8697d86e9587100p-68L, + 0x6.529afa7d51b129600p-4L, + 0x3.1ec197c0a840a11c0p-68L, + /* x = 0.1484375 + 34/128. */ + 0xe.a5dcf0e30cf03e700p-4L, + -0x6.8910f4e13d9aea080p-68L, + 0x6.6ff380ba014410a00p-4L, + -0x1.c65cdf4f5c05a02a0p-68L, + /* x = 0.1484375 + 35/128. */ + 0xe.98dfc6c6be031e600p-4L, + 0xd.d3089cbdd18a75b00p-72L, + 0x6.8d324731433279700p-4L, + 0x3.bc712bcc4ccddc480p-68L, + /* x = 0.1484375 + 36/128. */ + 0xe.8ba8393eca7821b00p-4L, + -0x5.a9c27cb6e49efee80p-68L, + 0x6.aa56d8e8249db4e80p-4L, + 0x3.60a761fe3f9e559c0p-68L, + /* x = 0.1484375 + 37/128. */ + 0xe.7e367d2956cfb1700p-4L, + -0x4.955ee1abe632ffa80p-68L, + 0x6.c760c14c8585a5200p-4L, + -0x2.42cb99f5193ad5380p-68L, + /* x = 0.1484375 + 38/128. */ + 0xe.708ac84d4172a3e00p-4L, + 0x2.737662213429e1400p-68L, + 0x6.e44f8c36eb10a1c80p-4L, + -0xa.d2f6c3ff0b2b84600p-72L, + /* x = 0.1484375 + 39/128. */ + 0xe.62a551594b970a700p-4L, + 0x7.0b15d41d4c0e48400p-68L, + 0x7.0122c5ec5028c8d00p-4L, + -0xc.c540b02cbf333c800p-76L, + /* x = 0.1484375 + 40/128. */ + 0xe.54864fe33e8575d00p-4L, + -0x5.40a42f1a30e4e5780p-68L, + 0x7.1dd9fb1ff46778500p-4L, + 0x3.acb970a9f6729c700p-68L, + /* x = 0.1484375 + 41/128. */ + 0xe.462dfc670d421ab00p-4L, + 0x3.d1a15901228f146c0p-68L, + 0x7.3a74b8f52947b6800p-4L, + 0x1.baf6928eb3fb02180p-68L, + /* x = 0.1484375 + 42/128. */ + 0xe.379c9045f29d51800p-4L, + -0x3.b7f755b683dfa84c0p-68L, + 0x7.56f28d011d9852880p-4L, + 0x2.44a75fc29c779bd80p-68L, + /* x = 0.1484375 + 43/128. */ + 0xe.28d245c58baef7200p-4L, + 0x2.25e232abc003c4380p-68L, + 0x7.7353054ca72690d80p-4L, + -0x3.391e8e0266194c600p-68L, + /* x = 0.1484375 + 44/128. */ + 0xe.19cf580eeec046b00p-4L, + -0x5.ebdd058b7f8131080p-68L, + 0x7.8f95b0560a9a3bd80p-4L, + -0x1.2084267e23c739ee0p-68L, + /* x = 0.1484375 + 45/128. */ + 0xe.0a94032dbea7cee00p-4L, + -0x4.222625d0505267a80p-68L, + 0x7.abba1d12c17bfa200p-4L, + -0x2.6d0f26c09f2126680p-68L, + /* x = 0.1484375 + 46/128. */ + 0xd.fb20840f3a9b36f00p-4L, + 0x7.ae2c515342890b600p-68L, + 0x7.c7bfdaf13e5ed1700p-4L, + 0x2.12f8a7525bfb113c0p-68L, + /* x = 0.1484375 + 47/128. */ + 0xd.eb7518814a7a93200p-4L, + -0x4.433773ef632be3b00p-68L, + 0x7.e3a679daaf25c6780p-4L, + -0x1.abd434bfd72f69be0p-68L, + /* x = 0.1484375 + 48/128. */ + 0xd.db91ff31879917300p-4L, + -0x4.2dbad2f5c7760ae80p-68L, + 0x7.ff6d8a34bd5e8fa80p-4L, + -0x2.b368b7d24aea62100p-68L, + /* x = 0.1484375 + 49/128. */ + 0xd.cb7777ac420705100p-4L, + 0x6.8f31e3eb780ce9c80p-68L, + 0x8.1b149ce34caa5a500p-4L, + -0x1.9af072f602b295580p-68L, + /* x = 0.1484375 + 50/128. */ + 0xd.bb25c25b8260c1500p-4L, + -0x9.1843671366e48f400p-72L, + 0x8.369b434a372da7f00p-4L, + -0x4.a3758e01c931e1f80p-68L, + /* x = 0.1484375 + 51/128. */ + 0xd.aa9d2086082706400p-4L, + -0x2.1ae3f617aa166cd00p-72L, + 0x8.52010f4f080052100p-4L, + 0x3.78bd8dd614753d080p-68L, + /* x = 0.1484375 + 52/128. */ + 0xd.99ddd44e44a43d500p-4L, + -0x2.b5c5c126adfbef900p-68L, + 0x8.6d45935ab396cb500p-4L, + -0x1.bde17dd211ab0caa0p-68L, + /* x = 0.1484375 + 53/128. */ + 0xd.88e820b1526311e00p-4L, + -0x2.a9e1043f3e565ac80p-68L, + 0x8.8868625b4e1dbb200p-4L, + 0x3.13310133022527200p-68L, + /* x = 0.1484375 + 54/128. */ + 0xd.77bc4985e93a60800p-4L, + -0x3.6279746f944394400p-68L, + 0x8.a3690fc5bfc11c000p-4L, + -0x6.aca1d8c657aed0b80p-68L, + /* x = 0.1484375 + 55/128. */ + 0xd.665a937b4ef2b1f00p-4L, + 0x6.d51bad6d988a44180p-68L, + 0x8.be472f9776d809b00p-4L, + -0xd.477e8edbc29c29900p-72L, + /* x = 0.1484375 + 56/128. */ + 0xd.54c3441844897fd00p-4L, + -0x7.07ac0f9aa0e459680p-68L, + 0x8.d902565817ee78400p-4L, + -0x6.431c32ed7f9fee680p-68L, + /* x = 0.1484375 + 57/128. */ + 0xd.42f6a1b9f0168ce00p-4L, + -0xf.ce3d09c3726cfb200p-72L, + 0x8.f39a191b2ba612300p-4L, + -0x5.c05b0be2a5c002c00p-68L, + /* x = 0.1484375 + 58/128. */ + 0xd.30f4f392c357ab000p-4L, + 0x6.61c5fa8a7d9b26600p-68L, + 0x9.0e0e0d81ca6787900p-4L, + 0x6.cc92c8ea8c2815c00p-68L, + /* x = 0.1484375 + 59/128. */ + 0xd.1ebe81a95ee752e00p-4L, + 0x4.8a26bcd32d6e92300p-68L, + 0x9.285dc9bc45dd9ea00p-4L, + 0x3.d02457bcce59c4180p-68L, + /* x = 0.1484375 + 60/128. */ + 0xd.0c5394d7722281900p-4L, + 0x5.e25736c0357470800p-68L, + 0x9.4288e48bd0335fc00p-4L, + 0x4.1c4cbd2920497a900p-68L, + /* x = 0.1484375 + 61/128. */ + 0xc.f9b476c897c25c600p-4L, + -0x4.018af22c0cf715080p-68L, + 0x9.5c8ef544210ec0c00p-4L, + -0x6.e3b642d55f617ae80p-68L, + /* x = 0.1484375 + 62/128. */ + 0xc.e6e171f92f2e27f00p-4L, + 0x3.2225327ec440ddb00p-68L, + 0x9.766f93cd18413a700p-4L, + -0x5.503e303903d754480p-68L, + /* x = 0.1484375 + 63/128. */ + 0xc.d3dad1b5328a2e400p-4L, + 0x5.9f993f4f510881a00p-68L, + 0x9.902a58a45e27bed00p-4L, + 0x6.8412b426b675ed500p-68L, + /* x = 0.1484375 + 64/128. */ + 0xc.c0a0e21709883a400p-4L, + -0xf.f6ee1ee5f811c4300p-76L, + 0x9.a9bedcdf01b38da00p-4L, + -0x6.c0c287df87e21d700p-68L, + /* x = 0.1484375 + 65/128. */ + 0xc.ad33f00658fe5e800p-4L, + 0x2.04bbc0f3a66a0e6c0p-68L, + 0x9.c32cba2b14156ef00p-4L, + 0x5.256c4f857991ca680p-72L, + /* x = 0.1484375 + 66/128. */ + 0xc.99944936cf48c8900p-4L, + 0x1.1ff93fe64b3ddb7a0p-68L, + 0x9.dc738ad14204e6900p-4L, + -0x6.53a7d2f07a7d9a700p-68L, + /* x = 0.1484375 + 67/128. */ + 0xc.85c23c26ed7b6f000p-4L, + 0x1.4ef546c4792968220p-68L, + 0x9.f592e9b66a9cf9000p-4L, + 0x6.a3c7aa3c101998480p-68L, + /* x = 0.1484375 + 68/128. */ + 0xc.71be181ecd6875d00p-4L, + -0x1.d25a9ea5fc335df80p-68L, + 0xa.0e8a725d33c828c00p-4L, + 0x1.1fa50fd9e9a15ffe0p-68L, + /* x = 0.1484375 + 69/128. */ + 0xc.5d882d2ee48030c00p-4L, + 0x7.c07d28e981e348080p-68L, + 0xa.2759c0e79c3558200p-4L, + 0x5.27c32b55f5405c180p-68L, + /* x = 0.1484375 + 70/128. */ + 0xc.4920cc2ec38fb8900p-4L, + 0x1.b38827db08884fc60p-68L, + 0xa.400072188acf49d00p-4L, + -0x2.94e8c7da1fc7cb900p-68L, + /* x = 0.1484375 + 71/128. */ + 0xc.348846bbd36313400p-4L, + -0x7.001d401622ec7e600p-68L, + 0xa.587e23555bb080800p-4L, + 0x6.d02b9c662cdd29300p-68L, + /* x = 0.1484375 + 72/128. */ + 0xc.1fbeef380e4ffdd00p-4L, + 0x5.a613ec8722f644000p-68L, + 0xa.70d272a76a8d4b700p-4L, + -0x2.5f136f8ed448b7480p-68L, + /* x = 0.1484375 + 73/128. */ + 0xc.0ac518c8b6ae71100p-4L, + -0x4.5c85c1146f34ea500p-68L, + 0xa.88fcfebd9a8dd4800p-4L, + -0x1.d0c3891061dbc66e0p-68L, + /* x = 0.1484375 + 74/128. */ + 0xb.f59b17550a4406800p-4L, + 0x7.5969296567cf3e380p-68L, + 0xa.a0fd66eddb9212300p-4L, + 0x2.c28520d3911b8a040p-68L, + /* x = 0.1484375 + 75/128. */ + 0xb.e0413f84f2a771c00p-4L, + 0x6.14946a88cbf4da200p-68L, + 0xa.b8d34b36acd987200p-4L, + 0x1.0ed343ec65d7e3ae0p-68L, + /* x = 0.1484375 + 76/128. */ + 0xb.cab7e6bfb2a14aa00p-4L, + -0x4.edd3a8b5c89413680p-68L, + 0xa.d07e4c409d08c5000p-4L, + -0x5.c56fa844f53db4780p-68L, + /* x = 0.1484375 + 77/128. */ + 0xb.b4ff632a908f73f00p-4L, + -0x3.eae7c6346266c4b00p-68L, + 0xa.e7fe0b5fc786b2e00p-4L, + -0x6.991e2950ebf5b7780p-68L, + /* x = 0.1484375 + 78/128. */ + 0xb.9f180ba77dd075100p-4L, + 0x6.28e135a9508299000p-68L, + 0xa.ff522a954f2ba1700p-4L, + -0x2.621023be91cc0a180p-68L, + /* x = 0.1484375 + 79/128. */ + 0xb.890237d3bb3c28500p-4L, + -0x4.9eb5fac6fe9405f00p-68L, + 0xb.167a4c90d63c42400p-4L, + 0x4.cf5493b7cc23bd400p-68L, + /* x = 0.1484375 + 80/128. */ + 0xb.72be40067aaf2c000p-4L, + 0x5.0dbdb7a14c3d7d500p-68L, + 0xb.2d7614b1f3aaa2500p-4L, + -0x2.0d291df5881e35c00p-68L, + /* x = 0.1484375 + 81/128. */ + 0xb.5c4c7d4f7dae91600p-4L, + -0x5.3879330b4e5b67300p-68L, + 0xb.44452709a59752900p-4L, + 0x5.913765434a59d1100p-72L, + /* x = 0.1484375 + 82/128. */ + 0xb.45ad4975b1294cb00p-4L, + -0x2.35b30bf1370dd5980p-68L, + 0xb.5ae7285bc10cf5100p-4L, + 0x5.753847e8f8b7a3100p-68L, +}; diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/test-canonical-ldbl-96.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/test-canonical-ldbl-96.c new file mode 100644 index 0000000000..3254097754 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/test-canonical-ldbl-96.c @@ -0,0 +1,141 @@ +/* Test iscanonical and canonicalizel for ldbl-96. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_ldbl.h> +#include <stdbool.h> +#include <stdint.h> +#include <stdio.h> + +struct test +{ + bool sign; + uint16_t exponent; + bool high; + uint64_t mantissa; + bool canonical; +}; + +#define M68K_VARIANT (LDBL_MIN_EXP == -16382) + +static const struct test tests[] = + { + { false, 0, true, 0, M68K_VARIANT }, + { true, 0, true, 0, M68K_VARIANT }, + { false, 0, true, 1, M68K_VARIANT }, + { true, 0, true, 1, M68K_VARIANT }, + { false, 0, true, 0x100000000ULL, M68K_VARIANT }, + { true, 0, true, 0x100000000ULL, M68K_VARIANT }, + { false, 0, false, 0, true }, + { true, 0, false, 0, true }, + { false, 0, false, 1, true }, + { true, 0, false, 1, true }, + { false, 0, false, 0x100000000ULL, true }, + { true, 0, false, 0x100000000ULL, true }, + { false, 1, true, 0, true }, + { true, 1, true, 0, true }, + { false, 1, true, 1, true }, + { true, 1, true, 1, true }, + { false, 1, true, 0x100000000ULL, true }, + { true, 1, true, 0x100000000ULL, true }, + { false, 1, false, 0, false }, + { true, 1, false, 0, false }, + { false, 1, false, 1, false }, + { true, 1, false, 1, false }, + { false, 1, false, 0x100000000ULL, false }, + { true, 1, false, 0x100000000ULL, false }, + { false, 0x7ffe, true, 0, true }, + { true, 0x7ffe, true, 0, true }, + { false, 0x7ffe, true, 1, true }, + { true, 0x7ffe, true, 1, true }, + { false, 0x7ffe, true, 0x100000000ULL, true }, + { true, 0x7ffe, true, 0x100000000ULL, true }, + { false, 0x7ffe, false, 0, false }, + { true, 0x7ffe, false, 0, false }, + { false, 0x7ffe, false, 1, false }, + { true, 0x7ffe, false, 1, false }, + { false, 0x7ffe, false, 0x100000000ULL, false }, + { true, 0x7ffe, false, 0x100000000ULL, false }, + { false, 0x7fff, true, 0, true }, + { true, 0x7fff, true, 0, true }, + { false, 0x7fff, true, 1, true }, + { true, 0x7fff, true, 1, true }, + { false, 0x7fff, true, 0x100000000ULL, true }, + { true, 0x7fff, true, 0x100000000ULL, true }, + { false, 0x7fff, false, 0, M68K_VARIANT }, + { true, 0x7fff, false, 0, M68K_VARIANT }, + { false, 0x7fff, false, 1, M68K_VARIANT }, + { true, 0x7fff, false, 1, M68K_VARIANT }, + { false, 0x7fff, false, 0x100000000ULL, M68K_VARIANT }, + { true, 0x7fff, false, 0x100000000ULL, M68K_VARIANT }, + }; + +static int +do_test (void) +{ + int result = 0; + + for (size_t i = 0; i < sizeof (tests) / sizeof (tests[0]); i++) + { + long double ld; + SET_LDOUBLE_WORDS (ld, tests[i].exponent | (tests[i].sign << 15), + (tests[i].mantissa >> 32) | (tests[i].high << 31), + tests[i].mantissa & 0xffffffffULL); + bool canonical = iscanonical (ld); + if (canonical == tests[i].canonical) + { + printf ("PASS: iscanonical test %zu\n", i); + long double ldc = 12345.0L; + bool canonicalize_ret = canonicalizel (&ldc, &ld); + if (canonicalize_ret == !canonical) + { + printf ("PASS: canonicalizel test %zu\n", i); + bool canon_ok; + if (!canonical) + canon_ok = ldc == 12345.0L; + else if (isnan (ld)) + canon_ok = isnan (ldc) && !issignaling (ldc); + else + canon_ok = ldc == ld; + if (canon_ok) + printf ("PASS: canonicalized value test %zu\n", i); + else + { + printf ("FAIL: canonicalized value test %zu\n", i); + result = 1; + } + } + else + { + printf ("FAIL: canonicalizel test %zu\n", i); + result = 1; + } + } + else + { + printf ("FAIL: iscanonical test %zu\n", i); + result = 1; + } + } + + return result; +} + +#define TEST_FUNCTION do_test () +#include "../test-skeleton.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/test-totalorderl-ldbl-96.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/test-totalorderl-ldbl-96.c new file mode 100644 index 0000000000..4e01f15aa9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/test-totalorderl-ldbl-96.c @@ -0,0 +1,82 @@ +/* Test totalorderl and totalordermagl for ldbl-96. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_ldbl.h> +#include <stdbool.h> +#include <stdint.h> +#include <stdio.h> + +static const uint64_t tests[] = + { + 0, 1, 0x4000000000000000ULL, 0x4000000000000001ULL, + 0x7fffffffffffffffULL + }; + +static int +do_test (void) +{ + int result = 0; + + if (LDBL_MIN_EXP == -16382) + for (size_t i = 0; i < sizeof (tests) / sizeof (tests[0]); i++) + { + long double ldx, ldy, ldnx, ldny; + /* Verify that the high bit of the mantissa is ignored for + infinities and NaNs for the M68K variant of this + format. */ + SET_LDOUBLE_WORDS (ldx, 0x7fff, + tests[i] >> 32, tests[i] & 0xffffffffULL); + SET_LDOUBLE_WORDS (ldy, 0x7fff, + (tests[i] >> 32) | 0x80000000, + tests[i] & 0xffffffffULL); + SET_LDOUBLE_WORDS (ldnx, 0xffff, + tests[i] >> 32, tests[i] & 0xffffffffULL); + SET_LDOUBLE_WORDS (ldny, 0xffff, + (tests[i] >> 32) | 0x80000000, + tests[i] & 0xffffffffULL); + bool to1 = totalorderl (ldx, ldy); + bool to2 = totalorderl (ldy, ldx); + bool to3 = totalorderl (ldnx, ldny); + bool to4 = totalorderl (ldny, ldnx); + if (to1 && to2 && to3 && to4) + printf ("PASS: test %zu\n", i); + else + { + printf ("FAIL: test %zu\n", i); + result = 1; + } + to1 = totalordermagl (ldx, ldy); + to2 = totalordermagl (ldy, ldx); + to3 = totalordermagl (ldnx, ldny); + to4 = totalordermagl (ldny, ldnx); + if (to1 && to2 && to3 && to4) + printf ("PASS: test %zu (totalordermagl)\n", i); + else + { + printf ("FAIL: test %zu (totalordermagl)\n", i); + result = 1; + } + } + + return result; +} + +#define TEST_FUNCTION do_test () +#include "../test-skeleton.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/w_expl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/w_expl_compat.c new file mode 100644 index 0000000000..a0b852a3e2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/w_expl_compat.c @@ -0,0 +1,34 @@ +/* Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@gmail.com>, 2011. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* wrapper expl */ +long double +__expl (long double x) +{ + long double z = __ieee754_expl (x); + if (__builtin_expect (!isfinite (z) || z == 0, 0) + && isfinite (x) && _LIB_VERSION != _IEEE_) + return __kernel_standard_l (x, x, 206 + !!signbit (x)); + + return z; +} +hidden_def (__expl) +weak_alias (__expl, expl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/x2y2m1.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/x2y2m1.c new file mode 100644 index 0000000000..a20e89309e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/x2y2m1.c @@ -0,0 +1,39 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +#if FLT_EVAL_METHOD == 0 + +# include <sysdeps/ieee754/dbl-64/x2y2m1.c> + +#else + +/* Return X^2 + Y^2 - 1, computed without large cancellation error. + It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >= + 0.5. */ + +double +__x2y2m1 (double x, double y) +{ + return (double) __x2y2m1l (x, y); +} + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/x2y2m1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/x2y2m1l.c new file mode 100644 index 0000000000..a301fb3589 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/x2y2m1l.c @@ -0,0 +1,75 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_splitl.h> +#include <stdlib.h> + +/* Calculate X + Y exactly and store the result in *HI + *LO. It is + given that |X| >= |Y| and the values are small enough that no + overflow occurs. */ + +static inline void +add_split (long double *hi, long double *lo, long double x, long double y) +{ + /* Apply Dekker's algorithm. */ + *hi = x + y; + *lo = (x - *hi) + y; +} + +/* Compare absolute values of floating-point values pointed to by P + and Q for qsort. */ + +static int +compare (const void *p, const void *q) +{ + long double pld = fabsl (*(const long double *) p); + long double qld = fabsl (*(const long double *) q); + if (pld < qld) + return -1; + else if (pld == qld) + return 0; + else + return 1; +} + +/* Return X^2 + Y^2 - 1, computed without large cancellation error. + It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >= + 0.5. */ + +long double +__x2y2m1l (long double x, long double y) +{ + long double vals[5]; + SET_RESTORE_ROUNDL (FE_TONEAREST); + mul_splitl (&vals[1], &vals[0], x, x); + mul_splitl (&vals[3], &vals[2], y, y); + vals[4] = -1.0L; + qsort (vals, 5, sizeof (long double), compare); + /* Add up the values so that each element of VALS has absolute value + at most equal to the last set bit of the next nonzero + element. */ + for (size_t i = 0; i <= 3; i++) + { + add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); + qsort (vals + i + 1, 4 - i, sizeof (long double), compare); + } + /* Now any error from this addition will be small. */ + return vals[4] + vals[3] + vals[2] + vals[1] + vals[0]; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/Makefile b/REORG.TODO/sysdeps/ieee754/ldbl-opt/Makefile new file mode 100644 index 0000000000..81429d0ddd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/Makefile @@ -0,0 +1,167 @@ +# The`long double' type is a distinct type we support if +# -mlong-double-128 option is used (or when it becomes a default +# when -mlong-double-64 is not used). +long-double-fcts = yes +ifeq (,$(filter -mlong-double-128,$(sysdep-CFLAGS))) +sysdep-CFLAGS += -mlong-double-128 +endif + +ifeq ($(subdir),math) +libm-routines += s_nexttowardfd +routines += math_ldbl_opt nldbl-compat + +extra-libs += libnldbl +libnldbl-calls = asprintf dprintf fprintf fscanf fwprintf fwscanf iovfscanf \ + obstack_printf obstack_vprintf printf scanf snprintf \ + sprintf sscanf swprintf swscanf vasprintf vdprintf vfprintf \ + vfscanf vfwprintf vfwscanf vprintf vscanf vsnprintf \ + vsprintf vsscanf vswprintf vswscanf vwprintf vwscanf \ + wprintf wscanf printf_fp printf_size \ + fprintf_chk fwprintf_chk printf_chk snprintf_chk sprintf_chk \ + swprintf_chk vfprintf_chk vfwprintf_chk vprintf_chk \ + vsnprintf_chk vsprintf_chk vswprintf_chk vwprintf_chk \ + wprintf_chk asprintf_chk vasprintf_chk dprintf_chk \ + vdprintf_chk obstack_printf_chk obstack_vprintf_chk \ + syslog syslog_chk vsyslog vsyslog_chk \ + strfmon strfmon_l \ + strfroml \ + strtold strtold_l strtoldint wcstold wcstold_l wcstoldint \ + qecvt qfcvt qgcvt qecvt_r qfcvt_r \ + isinf isnan finite signbit scalb log2 lgamma_r ceil \ + significand acos asin atan atan2 cos sin tan cosh sinh \ + tanh acosh asinh atanh exp log log10 exp10 pow10 expm1 \ + log1p logb exp2 sqrt cbrt fabs floor j0 j1 y0 y1 erf erfc \ + lgamma tgamma gamma rint nearbyint round trunc \ + copysign fdim fmax fmin nextafter pow hypot fmod \ + remainder ldexp scalbn frexp modf scalbln fma nan sincos \ + jn yn ilogb remquo lrint lround llrint llround nexttowardf \ + nexttoward conj cacos cacosh casin catan catanh ccos ccosh \ + casinh cexp clog cproj csin csinh csqrt ctan ctanh cpow \ + cabs carg cimag creal clog10 \ + isoc99_scanf isoc99_fscanf isoc99_sscanf \ + isoc99_vscanf isoc99_vfscanf isoc99_vsscanf \ + isoc99_wscanf isoc99_fwscanf isoc99_swscanf \ + isoc99_vwscanf isoc99_vfwscanf isoc99_vswscanf \ + nextup nextdown totalorder totalordermag getpayload \ + canonicalize setpayload setpayloadsig llogb fmaxmag fminmag \ + roundeven fromfp ufromfp fromfpx ufromfpx +libnldbl-routines = $(libnldbl-calls:%=nldbl-%) +libnldbl-inhibit-o = $(object-suffixes) +libnldbl-static-only-routines = $(libnldbl-routines) +extra-objs += $(addsuffix .oS, $(libnldbl-routines)) + +CFLAGS-nldbl-acos.c = -fno-builtin-acosl +CFLAGS-nldbl-acosh.c = -fno-builtin-acoshl +CFLAGS-nldbl-asin.c = -fno-builtin-asinl +CFLAGS-nldbl-asinh.c = -fno-builtin-asinhl +CFLAGS-nldbl-atan.c = -fno-builtin-atanl +CFLAGS-nldbl-atan2.c = -fno-builtin-atan2l +CFLAGS-nldbl-atanh.c = -fno-builtin-atanhl +CFLAGS-nldbl-cabs.c = -fno-builtin-cabsl +CFLAGS-nldbl-cacos.c = -fno-builtin-cacosl +CFLAGS-nldbl-cacosh.c = -fno-builtin-cacoshl +CFLAGS-nldbl-canonicalize.c = -fno-builtin-canonicalizel +CFLAGS-nldbl-carg.c = -fno-builtin-cargl +CFLAGS-nldbl-casin.c = -fno-builtin-casinl +CFLAGS-nldbl-casinh.c = -fno-builtin-casinhl +CFLAGS-nldbl-catan.c = -fno-builtin-catanl +CFLAGS-nldbl-catanh.c = -fno-builtin-catanhl +CFLAGS-nldbl-cbrt.c = -fno-builtin-cbrtl +CFLAGS-nldbl-ccos.c = -fno-builtin-ccosl +CFLAGS-nldbl-ccosh.c = -fno-builtin-ccoshl +CFLAGS-nldbl-ceil.c = -fno-builtin-ceill +CFLAGS-nldbl-cexp.c = -fno-builtin-cexpl +CFLAGS-nldbl-cimag.c = -fno-builtin-cimagl +CFLAGS-nldbl-clog.c = -fno-builtin-clogl +CFLAGS-nldbl-clog10.c = -fno-builtin-clog10l +CFLAGS-nldbl-conj.c = -fno-builtin-conjl +CFLAGS-nldbl-copysign.c = -fno-builtin-copysignl +CFLAGS-nldbl-cos.c = -fno-builtin-cosl +CFLAGS-nldbl-cosh.c = -fno-builtin-coshl +CFLAGS-nldbl-cpow.c = -fno-builtin-cpowl +CFLAGS-nldbl-cproj.c = -fno-builtin-cprojl +CFLAGS-nldbl-creal.c = -fno-builtin-creall +CFLAGS-nldbl-csin.c = -fno-builtin-csinl +CFLAGS-nldbl-csinh.c = -fno-builtin-csinhl +CFLAGS-nldbl-csqrt.c = -fno-builtin-csqrtl +CFLAGS-nldbl-ctan.c = -fno-builtin-ctanl +CFLAGS-nldbl-ctanh.c = -fno-builtin-ctanhl +CFLAGS-nldbl-erf.c = -fno-builtin-erfl +CFLAGS-nldbl-erfc.c = -fno-builtin-erfcl +CFLAGS-nldbl-exp.c = -fno-builtin-expl +CFLAGS-nldbl-exp10.c = -fno-builtin-exp10l +CFLAGS-nldbl-exp2.c = -fno-builtin-exp2l +CFLAGS-nldbl-expm1.c = -fno-builtin-expm1l +CFLAGS-nldbl-fabs.c = -fno-builtin-fabsl +CFLAGS-nldbl-fdim.c = -fno-builtin-fdiml +CFLAGS-nldbl-finite.c = -fno-builtin-finitel +CFLAGS-nldbl-floor.c = -fno-builtin-floorl +CFLAGS-nldbl-fma.c = -fno-builtin-fmal +CFLAGS-nldbl-fmax.c = -fno-builtin-fmaxl +CFLAGS-nldbl-fmaxmag.c = -fno-builtin-fmaxmagl +CFLAGS-nldbl-fmin.c = -fno-builtin-fminl +CFLAGS-nldbl-fminmag.c = -fno-builtin-fminmagl +CFLAGS-nldbl-fmod.c = -fno-builtin-fmodl +CFLAGS-nldbl-frexp.c = -fno-builtin-frexpl +CFLAGS-nldbl-fromfp.c = -fno-builtin-fromfpl +CFLAGS-nldbl-fromfpx.c = -fno-builtin-fromfpxl +CFLAGS-nldbl-gamma.c = -fno-builtin-gammal +CFLAGS-nldbl-getpayload.c = -fno-builtin-getpayloadl +CFLAGS-nldbl-hypot.c = -fno-builtin-hypotl +CFLAGS-nldbl-ilogb.c = -fno-builtin-ilogbl +CFLAGS-nldbl-isinf.c = -fno-builtin-isinfl +CFLAGS-nldbl-isnan.c = -fno-builtin-isnanl +CFLAGS-nldbl-j0.c = -fno-builtin-j0l +CFLAGS-nldbl-j1.c = -fno-builtin-j1l +CFLAGS-nldbl-jn.c = -fno-builtin-jnl +CFLAGS-nldbl-ldexp.c = -fno-builtin-ldexpl +CFLAGS-nldbl-lgamma.c = -fno-builtin-lgammal +CFLAGS-nldbl-lgamma_r.c = -fno-builtin-lgammal_r +CFLAGS-nldbl-llogb.c = -fno-builtin-llogbl +CFLAGS-nldbl-llrint.c = -fno-builtin-llrintl +CFLAGS-nldbl-llround.c = -fno-builtin-llroundl +CFLAGS-nldbl-log.c = -fno-builtin-logl +CFLAGS-nldbl-log10.c = -fno-builtin-log10l +CFLAGS-nldbl-log1p.c = -fno-builtin-log1pl +CFLAGS-nldbl-log2.c = -fno-builtin-log2l +CFLAGS-nldbl-logb.c = -fno-builtin-logbl +CFLAGS-nldbl-lrint.c = -fno-builtin-lrintl +CFLAGS-nldbl-lround.c = -fno-builtin-lroundl +CFLAGS-nldbl-modf.c = -fno-builtin-modfl +CFLAGS-nldbl-nan.c = -fno-builtin-nanl +CFLAGS-nldbl-nearbyint.c = -fno-builtin-nearbyintl +CFLAGS-nldbl-nextafter.c = -fno-builtin-nextafterl +CFLAGS-nldbl-nextdown.c = -fno-builtin-nextdownl +CFLAGS-nldbl-nexttoward.c = -fno-builtin-nexttoward -fno-builtin-nexttowardl +CFLAGS-nldbl-nexttowardf.c = -fno-builtin-nexttowardf +CFLAGS-nldbl-nextup.c = -fno-builtin-nextupl +CFLAGS-nldbl-pow.c = -fno-builtin-powl +CFLAGS-nldbl-pow10.c = -fno-builtin-pow10l +CFLAGS-nldbl-remainder.c = -fno-builtin-remainderl -fno-builtin-dreml +CFLAGS-nldbl-remquo.c = -fno-builtin-remquol +CFLAGS-nldbl-rint.c = -fno-builtin-rintl +CFLAGS-nldbl-round.c = -fno-builtin-roundl +CFLAGS-nldbl-roundeven.c = -fno-builtin-roundevenl +CFLAGS-nldbl-scalb.c = -fno-builtin-scalbl +CFLAGS-nldbl-scalbln.c = -fno-builtin-scalblnl +CFLAGS-nldbl-scalbn.c = -fno-builtin-scalbnl +CFLAGS-nldbl-setpayload.c = -fno-builtin-setpayloadl +CFLAGS-nldbl-setpayloadsig.c = -fno-builtin-setpayloadsigl +CFLAGS-nldbl-significand.c = -fno-builtin-significandl +CFLAGS-nldbl-sin.c = -fno-builtin-sinl +CFLAGS-nldbl-sincos.c = -fno-builtin-sincosl +CFLAGS-nldbl-sinh.c = -fno-builtin-sinhl +CFLAGS-nldbl-sqrt.c = -fno-builtin-sqrtl +CFLAGS-nldbl-tan.c = -fno-builtin-tanl +CFLAGS-nldbl-tanh.c = -fno-builtin-tanhl +CFLAGS-nldbl-tgamma.c = -fno-builtin-tgammal +CFLAGS-nldbl-totalorder.c = -fno-builtin-totalorderl +CFLAGS-nldbl-totalordermag.c = -fno-builtin-totalordermagl +CFLAGS-nldbl-trunc.c = -fno-builtin-truncl +CFLAGS-nldbl-ufromfp.c = -fno-builtin-ufromfpl +CFLAGS-nldbl-ufromfpx.c = -fno-builtin-ufromfpxl +CFLAGS-nldbl-y0.c = -fno-builtin-y0l +CFLAGS-nldbl-y1.c = -fno-builtin-y1l +CFLAGS-nldbl-yn.c = -fno-builtin-ynl + +endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/Versions b/REORG.TODO/sysdeps/ieee754/ldbl-opt/Versions new file mode 100644 index 0000000000..d3f0beaef2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/Versions @@ -0,0 +1,100 @@ +%include <nldbl-abi.h> +%ifndef NLDBL_VERSION +% error "nldbl-abi.h must define NLDBL_VERSION" +%endif + +libc { + NLDBL_VERSION { + # IEEE quad long double functions (older symver is for + # IEEE double long double). + ldexpl; copysignl; finitel; frexpl; isinfl; isnanl; modfl; + __isinfl; __isnanl; __finitel; __signbitl; + scalbnl; + qecvt; qfcvt; qgcvt; qecvt_r; qfcvt_r; + + strtold; __strtold_internal; wcstold; __wcstold_internal; + __strtold_l; strtold_l; __wcstold_l; wcstold_l; + + strfmon; __strfmon_l; strfmon_l; + __nldbl_strfmon; __nldbl___strfmon_l; __nldbl_strfmon_l; + __nldbl___vstrfmon; __nldbl___vstrfmon_l; + + syslog; vsyslog; + __nldbl_syslog; __nldbl_vsyslog; + __nldbl___syslog_chk; __nldbl___vsyslog_chk; + + # *printf* family, using IEEE quad long double + __asprintf; asprintf; dprintf; fprintf; fwprintf; _IO_fprintf; + _IO_printf; _IO_sprintf; _IO_vfprintf; _IO_vsprintf; obstack_printf; + obstack_vprintf; printf; __printf_fp; printf_size; snprintf; sprintf; + swprintf; vasprintf; vdprintf; vfprintf; vfwprintf; vprintf; vsnprintf; + __vsnprintf; vsprintf; vswprintf; vwprintf; wprintf; + + # *printf* family, using IEEE double as long double + # The standard functions are __REDIRECTed to these if -mlong-double-64 + __nldbl___asprintf; __nldbl_asprintf; __nldbl_dprintf; __nldbl_fprintf; + __nldbl_fwprintf; __nldbl__IO_fprintf; __nldbl__IO_printf; + __nldbl__IO_sprintf; __nldbl__IO_vfprintf; __nldbl__IO_vsprintf; + __nldbl_obstack_printf; __nldbl_obstack_vprintf; __nldbl_printf; + __nldbl___printf_fp; __nldbl_printf_size; __nldbl_snprintf; + __nldbl_sprintf; __nldbl_swprintf; __nldbl_vasprintf; __nldbl_vdprintf; + __nldbl_vfprintf; __nldbl_vfwprintf; __nldbl_vprintf; __nldbl_vsnprintf; + __nldbl___vsnprintf; __nldbl_vsprintf; __nldbl_vswprintf; + __nldbl_vwprintf; __nldbl_wprintf; + + # *scanf family, using IEEE quad long double + _IO_sscanf; _IO_vfscanf; __vfscanf; __vsscanf; fscanf; fwscanf; scanf; + sscanf; swscanf; vfscanf; vfwscanf; vscanf; vsscanf; vswscanf; vwscanf; + wscanf; + + # *scanf family, using IEEE double as long double + __nldbl__IO_sscanf; __nldbl__IO_vfscanf; __nldbl___vfscanf; + __nldbl___vsscanf; __nldbl_fscanf; __nldbl_fwscanf; __nldbl_scanf; + __nldbl_sscanf; __nldbl_swscanf; __nldbl_vfscanf; __nldbl_vfwscanf; + __nldbl_vscanf; __nldbl_vsscanf; __nldbl_vswscanf; __nldbl_vwscanf; + __nldbl_wscanf; + + # checking versions, using IEEE quad long double + __sprintf_chk; __vsprintf_chk; __snprintf_chk; __vsnprintf_chk; + __printf_chk; __fprintf_chk; __vprintf_chk; __vfprintf_chk; + + # checking versions, using IEEE double as long double + __nldbl___sprintf_chk; __nldbl___vsprintf_chk; __nldbl___snprintf_chk; + __nldbl___vsnprintf_chk; __nldbl___printf_chk; __nldbl___fprintf_chk; + __nldbl___vprintf_chk; __nldbl___vfprintf_chk; + __nldbl___swprintf_chk; __nldbl___vswprintf_chk; __nldbl___fwprintf_chk; + __nldbl___wprintf_chk; __nldbl___vfwprintf_chk; __nldbl___vwprintf_chk; + } + GLIBC_2.7 { + __nldbl___isoc99_scanf; __nldbl___isoc99_fscanf; + __nldbl___isoc99_sscanf; __nldbl___isoc99_vscanf; + __nldbl___isoc99_vfscanf; __nldbl___isoc99_vsscanf; + __nldbl___isoc99_wscanf; __nldbl___isoc99_fwscanf; + __nldbl___isoc99_swscanf; __nldbl___isoc99_vwscanf; + __nldbl___isoc99_vfwscanf; __nldbl___isoc99_vswscanf; + } + GLIBC_2.8 { + __nldbl___asprintf_chk; __nldbl___vasprintf_chk; + __nldbl___dprintf_chk; __nldbl___vdprintf_chk; + __nldbl___obstack_printf_chk; __nldbl___obstack_vprintf_chk; + } +} +libm { + NLDBL_VERSION { + # IEEE quad long double functions (older symver is for + # IEEE double as long double). + cabsl; cargl; cimagl; conjl; creall; cacosl; cacoshl; casinl; + catanl; catanhl; ccosl; ccoshl; casinhl; cexpl; clogl; __clog10l; + clog10l; cpowl; cprojl; csinl; csinhl; csqrtl; ctanl; ctanhl; + fdiml; fmal; fmaxl; fminl; ldexpl; nanl; nextafterl; nexttowardl; + significandl; acosl; acoshl; asinl; atan2l; atanhl; coshl; dreml; + exp10l; pow10l; exp2l; fmodl; hypotl; j0l; y0l; j1l; y1l; jnl; ynl; + lgammal; gammal; lgammal_r; logl; log10l; log2l; powl; remainderl; + scalbl; sinhl; sqrtl; tgammal; asinhl; atanl; cbrtl; ceill; copysignl; + erfl; erfcl; expm1l; fabsl; finitel; floorl; frexpl; ilogbl; + llrintl; llroundl; log1pl; logbl; lrintl; lroundl; modfl; + nearbyintl; remquol; rintl; roundl; scalblnl; scalbnl; sinl; cosl; + sincosl; tanl; tanhl; truncl; expl; __finitel; __signbitl; + __fpclassifyl; nexttowardf; nexttoward; __nldbl_nexttowardf; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/bits/long-double.h b/REORG.TODO/sysdeps/ieee754/ldbl-opt/bits/long-double.h new file mode 100644 index 0000000000..67db5b9d0c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/bits/long-double.h @@ -0,0 +1,24 @@ +/* Properties of long double type. ldbl-opt version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef __NO_LONG_DOUBLE_MATH +# define __LONG_DOUBLE_MATH_OPTIONAL 1 +# ifndef __LONG_DOUBLE_128__ +# define __NO_LONG_DOUBLE_MATH 1 +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/configure b/REORG.TODO/sysdeps/ieee754/ldbl-opt/configure new file mode 100644 index 0000000000..ad9d77b88c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/configure @@ -0,0 +1,39 @@ +# This file is generated from configure.ac by Autoconf. DO NOT EDIT! + # Local configure fragment for sysdeps/ieee754/ldbl-opt/. + + +{ $as_echo "$as_me:${as_lineno-$LINENO}: checking whether $CC $CFLAGS supports -mlong-double-128" >&5 +$as_echo_n "checking whether $CC $CFLAGS supports -mlong-double-128... " >&6; } +if ${libc_cv_mlong_double_128+:} false; then : + $as_echo_n "(cached) " >&6 +else + save_CFLAGS="$CFLAGS" +CFLAGS="$CFLAGS -mlong-double-128" +cat confdefs.h - <<_ACEOF >conftest.$ac_ext +/* end confdefs.h. */ + +int +main () +{ + +#ifndef __LONG_DOUBLE_128__ +# error "compiler did not predefine __LONG_DOUBLE_128__ as expected" +#endif +long double foobar (long double x) { return x; } + ; + return 0; +} +_ACEOF +if ac_fn_c_try_compile "$LINENO"; then : + libc_cv_mlong_double_128=yes +else + libc_cv_mlong_double_128=no +fi +rm -f core conftest.err conftest.$ac_objext conftest.$ac_ext +CFLAGS="$save_CFLAGS" +fi +{ $as_echo "$as_me:${as_lineno-$LINENO}: result: $libc_cv_mlong_double_128" >&5 +$as_echo "$libc_cv_mlong_double_128" >&6; } +if test "$libc_cv_mlong_double_128" = no; then + as_fn_error $? "this configuration requires -mlong-double-128 support" "$LINENO" 5 +fi diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/configure.ac b/REORG.TODO/sysdeps/ieee754/ldbl-opt/configure.ac new file mode 100644 index 0000000000..a77fadd1c4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/configure.ac @@ -0,0 +1,19 @@ +sinclude(./aclocal.m4)dnl Autoconf lossage +GLIBC_PROVIDES dnl See aclocal.m4 in the top level source directory. +# Local configure fragment for sysdeps/ieee754/ldbl-opt/. + +AC_CACHE_CHECK(whether $CC $CFLAGS supports -mlong-double-128, + libc_cv_mlong_double_128, [dnl +save_CFLAGS="$CFLAGS" +CFLAGS="$CFLAGS -mlong-double-128" +AC_TRY_COMPILE(, [ +#ifndef __LONG_DOUBLE_128__ +# error "compiler did not predefine __LONG_DOUBLE_128__ as expected" +#endif +long double foobar (long double x) { return x; }], + libc_cv_mlong_double_128=yes, + libc_cv_mlong_double_128=no) +CFLAGS="$save_CFLAGS"]) +if test "$libc_cv_mlong_double_128" = no; then + AC_MSG_ERROR([this configuration requires -mlong-double-128 support]) +fi diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/math-type-macros-double.h b/REORG.TODO/sysdeps/ieee754/ldbl-opt/math-type-macros-double.h new file mode 100644 index 0000000000..67b5268dc4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/math-type-macros-double.h @@ -0,0 +1,38 @@ +/* Overrides for ldbl-opt versioning for double types. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_TYPE_MACROS_DOUBLE + +#include <math_ldbl_opt.h> +#include <first-versions.h> + +/* Define compat symbols for long double on platforms + where it was not always a distinct type. */ +#if !defined M_LIBM_NEED_COMPAT +# define M_LIBM_NEED_COMPAT(f) \ + LONG_DOUBLE_COMPAT (libm, FIRST_VERSION_libm_ ## f ## l) +#endif + +#if !defined declare_mgen_libm_compat +# define declare_mgen_libm_compat(from, to) \ + compat_symbol (libm, from, to ## l, \ + FIRST_VERSION_libm_ ## to ## l); +#endif + +#include_next <math-type-macros-double.h> +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/math-type-macros-ldouble.h b/REORG.TODO/sysdeps/ieee754/ldbl-opt/math-type-macros-ldouble.h new file mode 100644 index 0000000000..20873ae6b5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/math-type-macros-ldouble.h @@ -0,0 +1,38 @@ +/* Overrides for ldbl-opt versioning for long double types. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_TYPE_MACROS_LDOUBLE + +#include <math_ldbl_opt.h> +#include <ldbl-compat-choose.h> + +#define maybe_long_double_symbol(lib, from, to) \ + LONG_DOUBLE_COMPAT_CHOOSE_ ## lib ## _ ## to (long_double_symbol (lib, \ + from, \ + to), \ + weak_alias (from, to)) + +/* Use properly versioned symbols for long double on platforms where + it was not always a distinct type. */ +#if !defined declare_mgen_alias +# define declare_mgen_alias(from, to) \ + maybe_long_double_symbol (libm, from ## l, to ## l); +#endif + +#include_next <math-type-macros-ldouble.h> +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/math_ldbl_opt.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/math_ldbl_opt.c new file mode 100644 index 0000000000..49c5c1249b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/math_ldbl_opt.c @@ -0,0 +1,3 @@ +/* Set temporarily to non-zero if long double should be considered + the same as double. */ +__thread int __no_long_double attribute_tls_model_ie attribute_hidden; diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/math_ldbl_opt.h b/REORG.TODO/sysdeps/ieee754/ldbl-opt/math_ldbl_opt.h new file mode 100644 index 0000000000..af861c11ea --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/math_ldbl_opt.h @@ -0,0 +1,46 @@ +/* -mlong-double-64 compatibility mode macros. */ + +#include <nldbl-abi.h> +#ifndef LONG_DOUBLE_COMPAT_VERSION +# error "nldbl-abi.h must define LONG_DOUBLE_COMPAT_VERSION" +#endif + +#include <shlib-compat.h> +#define LONG_DOUBLE_COMPAT(lib, introduced) \ + SHLIB_COMPAT(lib, introduced, LONG_DOUBLE_COMPAT_VERSION) +#define long_double_symbol(lib, local, symbol) \ + long_double_symbol_1 (lib, local, symbol, LONG_DOUBLE_COMPAT_VERSION) +#ifdef SHARED +# define ldbl_hidden_def(local, name) libc_hidden_ver (local, name) +# define ldbl_strong_alias(name, aliasname) \ + strong_alias (name, __GL_##name##_##aliasname) \ + long_double_symbol (libc, __GL_##name##_##aliasname, aliasname); +# define ldbl_weak_alias(name, aliasname) \ + weak_alias (name, __GL_##name##_##aliasname) \ + long_double_symbol (libc, __GL_##name##_##aliasname, aliasname); +# define long_double_symbol_1(lib, local, symbol, version) \ + versioned_symbol (lib, local, symbol, version) +#else +# define ldbl_hidden_def(local, name) libc_hidden_def (name) +# define ldbl_strong_alias(name, aliasname) strong_alias (name, aliasname) +# define ldbl_weak_alias(name, aliasname) weak_alias (name, aliasname) +# ifndef __ASSEMBLER__ +/* Note that weak_alias cannot be used - it is defined to nothing + in most of the C files. */ +# define long_double_symbol_1(lib, local, symbol, version) \ + _weak_alias (local, symbol) +# else +# define long_double_symbol_1(lib, local, symbol, version) \ + weak_alias (local, symbol) +# endif +#endif + +#ifndef __ASSEMBLER__ +# include <math.h> +# include <math_private.h> + +/* Set temporarily to non-zero if long double should be considered + the same as double. */ +extern __thread int __no_long_double attribute_tls_model_ie attribute_hidden; +# define __ldbl_is_dbl __builtin_expect (__no_long_double, 0) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-acos.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-acos.c new file mode 100644 index 0000000000..813a17e9d6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-acos.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +acosl (double x) +{ + return acos (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-acosh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-acosh.c new file mode 100644 index 0000000000..75508e30d7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-acosh.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +acoshl (double x) +{ + return acosh (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-asin.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-asin.c new file mode 100644 index 0000000000..5bbe6cd992 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-asin.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +asinl (double x) +{ + return asin (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-asinh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-asinh.c new file mode 100644 index 0000000000..512f68519b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-asinh.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +asinhl (double x) +{ + return asinh (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-asprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-asprintf.c new file mode 100644 index 0000000000..4be216d610 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-asprintf.c @@ -0,0 +1,17 @@ +#include "nldbl-compat.h" + +attribute_hidden +int +__asprintf (char **string_ptr, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vasprintf (string_ptr, fmt, arg); + va_end (arg); + + return done; +} +extern __typeof (__asprintf) asprintf attribute_hidden; +weak_alias (__asprintf, asprintf) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-asprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-asprintf_chk.c new file mode 100644 index 0000000000..b520181db7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-asprintf_chk.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +attribute_hidden +int +__asprintf_chk (char **string_ptr, int flag, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vasprintf_chk (string_ptr, flag, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-atan.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-atan.c new file mode 100644 index 0000000000..2849e48d03 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-atan.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +atanl (double x) +{ + return atan (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-atan2.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-atan2.c new file mode 100644 index 0000000000..d4e5a91702 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-atan2.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +atan2l (double x, double y) +{ + return atan2 (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-atanh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-atanh.c new file mode 100644 index 0000000000..82b54ca6d4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-atanh.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +atanhl (double x) +{ + return atanh (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cabs.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cabs.c new file mode 100644 index 0000000000..837822d2d6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cabs.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double +attribute_hidden +cabsl (double _Complex x) +{ + return cabs (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cacos.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cacos.c new file mode 100644 index 0000000000..d935b511b4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cacos.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +cacosl (double _Complex x) +{ + return cacos (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cacosh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cacosh.c new file mode 100644 index 0000000000..67f994b849 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cacosh.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +cacoshl (double _Complex x) +{ + return cacosh (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-canonicalize.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-canonicalize.c new file mode 100644 index 0000000000..9d46163208 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-canonicalize.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for canonicalize. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +int +attribute_hidden +canonicalizel (double *cx, double *x) +{ + return canonicalize (cx, x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-carg.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-carg.c new file mode 100644 index 0000000000..bfff141c11 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-carg.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double +attribute_hidden +cargl (double _Complex x) +{ + return carg (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-casin.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-casin.c new file mode 100644 index 0000000000..310aa0ac21 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-casin.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +casinl (double _Complex x) +{ + return casin (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-casinh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-casinh.c new file mode 100644 index 0000000000..71b466ea22 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-casinh.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +casinhl (double _Complex x) +{ + return casinh (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-catan.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-catan.c new file mode 100644 index 0000000000..ea5f528ee5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-catan.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +catanl (double _Complex x) +{ + return catan (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-catanh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-catanh.c new file mode 100644 index 0000000000..e6f58aa048 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-catanh.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +catanhl (double _Complex x) +{ + return catanh (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cbrt.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cbrt.c new file mode 100644 index 0000000000..1c353a6e6b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cbrt.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +cbrtl (double x) +{ + return cbrt (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ccos.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ccos.c new file mode 100644 index 0000000000..0e1c2e70f3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ccos.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +ccosl (double _Complex x) +{ + return ccos (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ccosh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ccosh.c new file mode 100644 index 0000000000..da2bf580af --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ccosh.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +ccoshl (double _Complex x) +{ + return ccosh (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ceil.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ceil.c new file mode 100644 index 0000000000..a8fc3d548a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ceil.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +ceill (double x) +{ + return ceil (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cexp.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cexp.c new file mode 100644 index 0000000000..f1837afc28 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cexp.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +cexpl (double _Complex x) +{ + return cexp (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cimag.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cimag.c new file mode 100644 index 0000000000..fffbdd58ec --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cimag.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double +attribute_hidden +cimagl (double _Complex x) +{ + return cimag (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-clog.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-clog.c new file mode 100644 index 0000000000..ecbae7ba91 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-clog.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +clogl (double _Complex x) +{ + return clog (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-clog10.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-clog10.c new file mode 100644 index 0000000000..193f40104a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-clog10.c @@ -0,0 +1,11 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +clog10l (double _Complex x) +{ + return clog10 (x); +} +extern __typeof (clog10l) __clog10l attribute_hidden; +weak_alias (clog10l, __clog10l) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-compat.c new file mode 100644 index 0000000000..84c4aeeed9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-compat.c @@ -0,0 +1,1085 @@ +/* *printf* family compatibility routines for IEEE double as long double + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jakub@cygnus.com>, 2006. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <stdarg.h> +#include <stdio.h> +#include <libioP.h> +#include <wchar.h> +#include <printf.h> +#include <monetary.h> +#include <locale/localeinfo.h> +#include <sys/syslog.h> +#include <libc-lock.h> + +#include "nldbl-compat.h" + +libc_hidden_proto (__nldbl_vfprintf) +libc_hidden_proto (__nldbl_vsscanf) +libc_hidden_proto (__nldbl_vsprintf) +libc_hidden_proto (__nldbl_vfscanf) +libc_hidden_proto (__nldbl_vfwscanf) +libc_hidden_proto (__nldbl_vdprintf) +libc_hidden_proto (__nldbl_vswscanf) +libc_hidden_proto (__nldbl_vfwprintf) +libc_hidden_proto (__nldbl_vswprintf) +libc_hidden_proto (__nldbl_vsnprintf) +libc_hidden_proto (__nldbl_vasprintf) +libc_hidden_proto (__nldbl_obstack_vprintf) +libc_hidden_proto (__nldbl___vfwprintf_chk) +libc_hidden_proto (__nldbl___vsnprintf_chk) +libc_hidden_proto (__nldbl___vfprintf_chk) +libc_hidden_proto (__nldbl___vsyslog_chk) +libc_hidden_proto (__nldbl___vsprintf_chk) +libc_hidden_proto (__nldbl___vswprintf_chk) +libc_hidden_proto (__nldbl___vasprintf_chk) +libc_hidden_proto (__nldbl___vdprintf_chk) +libc_hidden_proto (__nldbl___obstack_vprintf_chk) +libc_hidden_proto (__nldbl___vstrfmon) +libc_hidden_proto (__nldbl___vstrfmon_l) +libc_hidden_proto (__nldbl___isoc99_vsscanf) +libc_hidden_proto (__nldbl___isoc99_vfscanf) +libc_hidden_proto (__nldbl___isoc99_vswscanf) +libc_hidden_proto (__nldbl___isoc99_vfwscanf) + +static void +__nldbl_cleanup (void *arg) +{ + __no_long_double = 0; +} + +#define set_no_long_double() \ + __libc_cleanup_push (__nldbl_cleanup, NULL); __no_long_double = 1 +#define clear_no_long_double() \ + __no_long_double = 0; __libc_cleanup_pop (0) + +/* Compatibility with IEEE double as long double. + IEEE quad long double is used by default for most programs, so + we don't need to split this into one file per function for the + sake of statically linked programs. */ + +int +attribute_compat_text_section +__nldbl___asprintf (char **string_ptr, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vasprintf (string_ptr, fmt, arg); + va_end (arg); + + return done; +} +weak_alias (__nldbl___asprintf, __nldbl_asprintf) + +int +attribute_compat_text_section +__nldbl_dprintf (int d, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vdprintf (d, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl_fprintf (FILE *stream, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfprintf (stream, fmt, arg); + va_end (arg); + + return done; +} +weak_alias (__nldbl_fprintf, __nldbl__IO_fprintf) + +int +attribute_compat_text_section weak_function +__nldbl_fwprintf (FILE *stream, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfwprintf (stream, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl_printf (const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfprintf (stdout, fmt, arg); + va_end (arg); + + return done; +} +strong_alias (__nldbl_printf, __nldbl__IO_printf) + +int +attribute_compat_text_section +__nldbl_sprintf (char *s, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vsprintf (s, fmt, arg); + va_end (arg); + + return done; +} +strong_alias (__nldbl_sprintf, __nldbl__IO_sprintf) + +int +attribute_compat_text_section +__nldbl_vfprintf (FILE *s, const char *fmt, va_list ap) +{ + int done; + set_no_long_double (); + done = _IO_vfprintf (s, fmt, ap); + clear_no_long_double (); + return done; +} +libc_hidden_def (__nldbl_vfprintf) +strong_alias (__nldbl_vfprintf, __nldbl__IO_vfprintf) + +int +attribute_compat_text_section +__nldbl__IO_vsprintf (char *string, const char *fmt, va_list ap) +{ + int done; + __no_long_double = 1; + done = _IO_vsprintf (string, fmt, ap); + __no_long_double = 0; + return done; +} +weak_alias (__nldbl__IO_vsprintf, __nldbl_vsprintf) +libc_hidden_def (__nldbl_vsprintf) + +int +attribute_compat_text_section +__nldbl_obstack_vprintf (struct obstack *obstack, const char *fmt, + va_list ap) +{ + int done; + __no_long_double = 1; + done = _IO_obstack_vprintf (obstack, fmt, ap); + __no_long_double = 0; + return done; +} +libc_hidden_def (__nldbl_obstack_vprintf) + +int +attribute_compat_text_section +__nldbl_obstack_printf (struct obstack *obstack, const char *fmt, ...) +{ + int result; + va_list ap; + va_start (ap, fmt); + result = __nldbl_obstack_vprintf (obstack, fmt, ap); + va_end (ap); + return result; +} + +int +attribute_compat_text_section weak_function +__nldbl_snprintf (char *s, size_t maxlen, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vsnprintf (s, maxlen, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl_swprintf (wchar_t *s, size_t n, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vswprintf (s, n, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section weak_function +__nldbl_vasprintf (char **result_ptr, const char *fmt, va_list ap) +{ + int res; + __no_long_double = 1; + res = _IO_vasprintf (result_ptr, fmt, ap); + __no_long_double = 0; + return res; +} +libc_hidden_def (__nldbl_vasprintf) + +int +attribute_compat_text_section +__nldbl_vdprintf (int d, const char *fmt, va_list arg) +{ + int res; + set_no_long_double (); + res = _IO_vdprintf (d, fmt, arg); + clear_no_long_double (); + return res; +} +libc_hidden_def (__nldbl_vdprintf) + +int +attribute_compat_text_section weak_function +__nldbl_vfwprintf (FILE *s, const wchar_t *fmt, va_list ap) +{ + int res; + set_no_long_double (); + res = _IO_vfwprintf (s, fmt, ap); + clear_no_long_double (); + return res; +} +libc_hidden_def (__nldbl_vfwprintf) + +int +attribute_compat_text_section +__nldbl_vprintf (const char *fmt, va_list ap) +{ + return __nldbl_vfprintf (stdout, fmt, ap); +} + +int +attribute_compat_text_section +__nldbl_vsnprintf (char *string, size_t maxlen, const char *fmt, + va_list ap) +{ + int res; + __no_long_double = 1; + res = _IO_vsnprintf (string, maxlen, fmt, ap); + __no_long_double = 0; + return res; +} +libc_hidden_def (__nldbl_vsnprintf) +weak_alias (__nldbl_vsnprintf, __nldbl___vsnprintf) + +int +attribute_compat_text_section weak_function +__nldbl_vswprintf (wchar_t *string, size_t maxlen, const wchar_t *fmt, + va_list ap) +{ + int res; + __no_long_double = 1; + res = _IO_vswprintf (string, maxlen, fmt, ap); + __no_long_double = 0; + return res; +} +libc_hidden_def (__nldbl_vswprintf) + +int +attribute_compat_text_section +__nldbl_vwprintf (const wchar_t *fmt, va_list ap) +{ + return __nldbl_vfwprintf (stdout, fmt, ap); +} + +int +attribute_compat_text_section +__nldbl_wprintf (const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfwprintf (stdout, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl__IO_vfscanf (FILE *s, const char *fmt, _IO_va_list ap, + int *errp) +{ + int res; + set_no_long_double (); + res = _IO_vfscanf (s, fmt, ap, errp); + clear_no_long_double (); + return res; +} + +int +attribute_compat_text_section +__nldbl___vfscanf (FILE *s, const char *fmt, va_list ap) +{ + int res; + set_no_long_double (); + res = _IO_vfscanf (s, fmt, ap, NULL); + clear_no_long_double (); + return res; +} +weak_alias (__nldbl___vfscanf, __nldbl_vfscanf) +libc_hidden_def (__nldbl_vfscanf) + +int +attribute_compat_text_section +__nldbl_sscanf (const char *s, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vsscanf (s, fmt, arg); + va_end (arg); + + return done; +} +strong_alias (__nldbl_sscanf, __nldbl__IO_sscanf) + +int +attribute_compat_text_section +__nldbl___vsscanf (const char *string, const char *fmt, va_list ap) +{ + int res; + __no_long_double = 1; + res = _IO_vsscanf (string, fmt, ap); + __no_long_double = 0; + return res; +} +weak_alias (__nldbl___vsscanf, __nldbl_vsscanf) +libc_hidden_def (__nldbl_vsscanf) + +int +attribute_compat_text_section weak_function +__nldbl_vscanf (const char *fmt, va_list ap) +{ + return __nldbl_vfscanf (stdin, fmt, ap); +} + +int +attribute_compat_text_section +__nldbl_fscanf (FILE *stream, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfscanf (stream, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl_scanf (const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfscanf (stdin, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl_vfwscanf (FILE *s, const wchar_t *fmt, va_list ap) +{ + int res; + set_no_long_double (); + res = _IO_vfwscanf (s, fmt, ap, NULL); + clear_no_long_double (); + return res; +} +libc_hidden_def (__nldbl_vfwscanf) + +int +attribute_compat_text_section +__nldbl_swscanf (const wchar_t *s, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vswscanf (s, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl_vswscanf (const wchar_t *string, const wchar_t *fmt, va_list ap) +{ + int res; + __no_long_double = 1; + res = vswscanf (string, fmt, ap); + __no_long_double = 0; + return res; +} +libc_hidden_def (__nldbl_vswscanf) + +int +attribute_compat_text_section weak_function +__nldbl_vwscanf (const wchar_t *fmt, va_list ap) +{ + return __nldbl_vfwscanf (stdin, fmt, ap); +} + +int +attribute_compat_text_section +__nldbl_fwscanf (FILE *stream, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfwscanf (stream, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl_wscanf (const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfwscanf (stdin, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___fprintf_chk (FILE *stream, int flag, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vfprintf_chk (stream, flag, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___fwprintf_chk (FILE *stream, int flag, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vfwprintf_chk (stream, flag, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___printf_chk (int flag, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vfprintf_chk (stdout, flag, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___snprintf_chk (char *s, size_t maxlen, int flag, size_t slen, + const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vsnprintf_chk (s, maxlen, flag, slen, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___sprintf_chk (char *s, int flag, size_t slen, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vsprintf_chk (s, flag, slen, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___swprintf_chk (wchar_t *s, size_t n, int flag, size_t slen, + const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vswprintf_chk (s, n, flag, slen, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___vfprintf_chk (FILE *s, int flag, const char *fmt, va_list ap) +{ + int res; + set_no_long_double (); + res = __vfprintf_chk (s, flag, fmt, ap); + clear_no_long_double (); + return res; +} +libc_hidden_def (__nldbl___vfprintf_chk) + +int +attribute_compat_text_section +__nldbl___vfwprintf_chk (FILE *s, int flag, const wchar_t *fmt, va_list ap) +{ + int res; + set_no_long_double (); + res = __vfwprintf_chk (s, flag, fmt, ap); + clear_no_long_double (); + return res; +} +libc_hidden_def (__nldbl___vfwprintf_chk) + +int +attribute_compat_text_section +__nldbl___vprintf_chk (int flag, const char *fmt, va_list ap) +{ + return __nldbl___vfprintf_chk (stdout, flag, fmt, ap); +} + +int +attribute_compat_text_section +__nldbl___vsnprintf_chk (char *string, size_t maxlen, int flag, size_t slen, + const char *fmt, va_list ap) +{ + int res; + __no_long_double = 1; + res = __vsnprintf_chk (string, maxlen, flag, slen, fmt, ap); + __no_long_double = 0; + return res; +} +libc_hidden_def (__nldbl___vsnprintf_chk) + +int +attribute_compat_text_section +__nldbl___vsprintf_chk (char *string, int flag, size_t slen, const char *fmt, + va_list ap) +{ + int res; + __no_long_double = 1; + res = __vsprintf_chk (string, flag, slen, fmt, ap); + __no_long_double = 0; + return res; +} +libc_hidden_def (__nldbl___vsprintf_chk) + +int +attribute_compat_text_section +__nldbl___vswprintf_chk (wchar_t *string, size_t maxlen, int flag, size_t slen, + const wchar_t *fmt, va_list ap) +{ + int res; + __no_long_double = 1; + res = __vswprintf_chk (string, maxlen, flag, slen, fmt, ap); + __no_long_double = 0; + return res; +} +libc_hidden_def (__nldbl___vswprintf_chk) + +int +attribute_compat_text_section +__nldbl___vwprintf_chk (int flag, const wchar_t *fmt, va_list ap) +{ + return __nldbl___vfwprintf_chk (stdout, flag, fmt, ap); +} + +int +attribute_compat_text_section +__nldbl___wprintf_chk (int flag, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vfwprintf_chk (stdout, flag, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___vasprintf_chk (char **ptr, int flag, const char *fmt, va_list arg) +{ + int res; + __no_long_double = 1; + res = __vasprintf_chk (ptr, flag, fmt, arg); + __no_long_double = 0; + return res; +} +libc_hidden_def (__nldbl___vasprintf_chk) + +int +attribute_compat_text_section +__nldbl___asprintf_chk (char **ptr, int flag, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vasprintf_chk (ptr, flag, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___vdprintf_chk (int d, int flag, const char *fmt, va_list arg) +{ + int res; + set_no_long_double (); + res = __vdprintf_chk (d, flag, fmt, arg); + clear_no_long_double (); + return res; +} +libc_hidden_def (__nldbl___vdprintf_chk) + +int +attribute_compat_text_section +__nldbl___dprintf_chk (int d, int flag, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vdprintf_chk (d, flag, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___obstack_vprintf_chk (struct obstack *obstack, int flag, + const char *fmt, va_list arg) +{ + int res; + __no_long_double = 1; + res = __obstack_vprintf_chk (obstack, flag, fmt, arg); + __no_long_double = 0; + return res; +} +libc_hidden_def (__nldbl___obstack_vprintf_chk) + +int +attribute_compat_text_section +__nldbl___obstack_printf_chk (struct obstack *obstack, int flag, + const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___obstack_vprintf_chk (obstack, flag, fmt, arg); + va_end (arg); + + return done; +} + +extern __typeof (printf_size) __printf_size; + +int +attribute_compat_text_section +__nldbl_printf_size (FILE *fp, const struct printf_info *info, + const void *const *args) +{ + struct printf_info info_no_ldbl = *info; + + info_no_ldbl.is_long_double = 0; + return __printf_size (fp, &info_no_ldbl, args); +} + +extern __typeof (__printf_fp) ___printf_fp; + +int +attribute_compat_text_section +__nldbl___printf_fp (FILE *fp, const struct printf_info *info, + const void *const *args) +{ + struct printf_info info_no_ldbl = *info; + + info_no_ldbl.is_long_double = 0; + return ___printf_fp (fp, &info_no_ldbl, args); +} + +ssize_t +attribute_compat_text_section +__nldbl_strfmon (char *s, size_t maxsize, const char *format, ...) +{ + va_list ap; + ssize_t res; + + va_start (ap, format); + res = __nldbl___vstrfmon (s, maxsize, format, ap); + va_end (ap); + return res; +} + +ssize_t +attribute_compat_text_section +__nldbl___strfmon_l (char *s, size_t maxsize, __locale_t loc, + const char *format, ...) +{ + va_list ap; + ssize_t res; + + va_start (ap, format); + res = __nldbl___vstrfmon_l (s, maxsize, loc, format, ap); + va_end (ap); + return res; +} +weak_alias (__nldbl___strfmon_l, __nldbl_strfmon_l) + +ssize_t +attribute_compat_text_section +__nldbl___vstrfmon (char *s, size_t maxsize, const char *format, va_list ap) +{ + ssize_t res; + __no_long_double = 1; + res = __vstrfmon_l (s, maxsize, _NL_CURRENT_LOCALE, format, ap); + __no_long_double = 0; + va_end (ap); + return res; +} +libc_hidden_def (__nldbl___vstrfmon) + +ssize_t +attribute_compat_text_section +__nldbl___vstrfmon_l (char *s, size_t maxsize, __locale_t loc, + const char *format, va_list ap) +{ + ssize_t res; + __no_long_double = 1; + res = __vstrfmon_l (s, maxsize, loc, format, ap); + __no_long_double = 0; + va_end (ap); + return res; +} +libc_hidden_def (__nldbl___vstrfmon_l) + +void +attribute_compat_text_section +__nldbl_syslog (int pri, const char *fmt, ...) +{ + va_list ap; + va_start (ap, fmt); + __nldbl___vsyslog_chk (pri, -1, fmt, ap); + va_end (ap); +} + +void +attribute_compat_text_section +__nldbl___syslog_chk (int pri, int flag, const char *fmt, ...) +{ + va_list ap; + + va_start (ap, fmt); + __nldbl___vsyslog_chk (pri, flag, fmt, ap); + va_end(ap); +} + +void +attribute_compat_text_section +__nldbl___vsyslog_chk (int pri, int flag, const char *fmt, va_list ap) +{ + set_no_long_double (); + __vsyslog_chk (pri, flag, fmt, ap); + clear_no_long_double (); +} +libc_hidden_def (__nldbl___vsyslog_chk) + +void +attribute_compat_text_section +__nldbl_vsyslog (int pri, const char *fmt, va_list ap) +{ + __nldbl___vsyslog_chk (pri, -1, fmt, ap); +} + +int +attribute_compat_text_section +__nldbl___isoc99_vfscanf (FILE *s, const char *fmt, va_list ap) +{ + int res; + set_no_long_double (); + res = __isoc99_vfscanf (s, fmt, ap); + clear_no_long_double (); + return res; +} +libc_hidden_def (__nldbl___isoc99_vfscanf) + +int +attribute_compat_text_section +__nldbl___isoc99_sscanf (const char *s, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___isoc99_vsscanf (s, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___isoc99_vsscanf (const char *string, const char *fmt, va_list ap) +{ + int res; + __no_long_double = 1; + res = __isoc99_vsscanf (string, fmt, ap); + __no_long_double = 0; + return res; +} +libc_hidden_def (__nldbl___isoc99_vsscanf) + +int +attribute_compat_text_section +__nldbl___isoc99_vscanf (const char *fmt, va_list ap) +{ + return __nldbl___isoc99_vfscanf (stdin, fmt, ap); +} + +int +attribute_compat_text_section +__nldbl___isoc99_fscanf (FILE *stream, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___isoc99_vfscanf (stream, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___isoc99_scanf (const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___isoc99_vfscanf (stdin, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___isoc99_vfwscanf (FILE *s, const wchar_t *fmt, va_list ap) +{ + int res; + set_no_long_double (); + res = __isoc99_vfwscanf (s, fmt, ap); + clear_no_long_double (); + return res; +} +libc_hidden_def (__nldbl___isoc99_vfwscanf) + +int +attribute_compat_text_section +__nldbl___isoc99_swscanf (const wchar_t *s, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___isoc99_vswscanf (s, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___isoc99_vswscanf (const wchar_t *string, const wchar_t *fmt, + va_list ap) +{ + int res; + __no_long_double = 1; + res = __isoc99_vswscanf (string, fmt, ap); + __no_long_double = 0; + return res; +} +libc_hidden_def (__nldbl___isoc99_vswscanf) + +int +attribute_compat_text_section +__nldbl___isoc99_vwscanf (const wchar_t *fmt, va_list ap) +{ + return __nldbl___isoc99_vfwscanf (stdin, fmt, ap); +} + +int +attribute_compat_text_section +__nldbl___isoc99_fwscanf (FILE *stream, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___isoc99_vfwscanf (stream, fmt, arg); + va_end (arg); + + return done; +} + +int +attribute_compat_text_section +__nldbl___isoc99_wscanf (const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___isoc99_vfwscanf (stdin, fmt, arg); + va_end (arg); + + return done; +} + +#if LONG_DOUBLE_COMPAT(libc, GLIBC_2_0) +compat_symbol (libc, __nldbl__IO_printf, _IO_printf, GLIBC_2_0); +compat_symbol (libc, __nldbl__IO_sprintf, _IO_sprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl__IO_vfprintf, _IO_vfprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl__IO_vsprintf, _IO_vsprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl_dprintf, dprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl_fprintf, fprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl_printf, printf, GLIBC_2_0); +compat_symbol (libc, __nldbl_sprintf, sprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl_vfprintf, vfprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl_vprintf, vprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl__IO_fprintf, _IO_fprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl___vsnprintf, __vsnprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl_asprintf, asprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl_obstack_printf, obstack_printf, GLIBC_2_0); +compat_symbol (libc, __nldbl_obstack_vprintf, obstack_vprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl_snprintf, snprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl_vasprintf, vasprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl_vdprintf, vdprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl_vsnprintf, vsnprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl_vsprintf, vsprintf, GLIBC_2_0); +compat_symbol (libc, __nldbl__IO_sscanf, _IO_sscanf, GLIBC_2_0); +compat_symbol (libc, __nldbl__IO_vfscanf, _IO_vfscanf, GLIBC_2_0); +compat_symbol (libc, __nldbl___vfscanf, __vfscanf, GLIBC_2_0); +compat_symbol (libc, __nldbl___vsscanf, __vsscanf, GLIBC_2_0); +compat_symbol (libc, __nldbl_fscanf, fscanf, GLIBC_2_0); +compat_symbol (libc, __nldbl_scanf, scanf, GLIBC_2_0); +compat_symbol (libc, __nldbl_sscanf, sscanf, GLIBC_2_0); +compat_symbol (libc, __nldbl_vfscanf, vfscanf, GLIBC_2_0); +compat_symbol (libc, __nldbl_vscanf, vscanf, GLIBC_2_0); +compat_symbol (libc, __nldbl_vsscanf, vsscanf, GLIBC_2_0); +compat_symbol (libc, __nldbl___printf_fp, __printf_fp, GLIBC_2_0); +compat_symbol (libc, __nldbl_strfmon, strfmon, GLIBC_2_0); +compat_symbol (libc, __nldbl_syslog, syslog, GLIBC_2_0); +compat_symbol (libc, __nldbl_vsyslog, vsyslog, GLIBC_2_0); +#endif +#if LONG_DOUBLE_COMPAT(libc, GLIBC_2_1) +compat_symbol (libc, __nldbl___asprintf, __asprintf, GLIBC_2_1); +compat_symbol (libc, __nldbl_printf_size, printf_size, GLIBC_2_1); +compat_symbol (libc, __nldbl___strfmon_l, __strfmon_l, GLIBC_2_1); +#endif +#if LONG_DOUBLE_COMPAT(libc, GLIBC_2_2) +compat_symbol (libc, __nldbl_swprintf, swprintf, GLIBC_2_2); +compat_symbol (libc, __nldbl_vwprintf, vwprintf, GLIBC_2_2); +compat_symbol (libc, __nldbl_wprintf, wprintf, GLIBC_2_2); +compat_symbol (libc, __nldbl_fwprintf, fwprintf, GLIBC_2_2); +compat_symbol (libc, __nldbl_vfwprintf, vfwprintf, GLIBC_2_2); +compat_symbol (libc, __nldbl_vswprintf, vswprintf, GLIBC_2_2); +compat_symbol (libc, __nldbl_fwscanf, fwscanf, GLIBC_2_2); +compat_symbol (libc, __nldbl_swscanf, swscanf, GLIBC_2_2); +compat_symbol (libc, __nldbl_vfwscanf, vfwscanf, GLIBC_2_2); +compat_symbol (libc, __nldbl_vswscanf, vswscanf, GLIBC_2_2); +compat_symbol (libc, __nldbl_vwscanf, vwscanf, GLIBC_2_2); +compat_symbol (libc, __nldbl_wscanf, wscanf, GLIBC_2_2); +#endif +#if LONG_DOUBLE_COMPAT(libc, GLIBC_2_3) +compat_symbol (libc, __nldbl_strfmon_l, strfmon_l, GLIBC_2_3); +#endif +#if LONG_DOUBLE_COMPAT(libc, GLIBC_2_3_4) +compat_symbol (libc, __nldbl___sprintf_chk, __sprintf_chk, GLIBC_2_3_4); +compat_symbol (libc, __nldbl___vsprintf_chk, __vsprintf_chk, GLIBC_2_3_4); +compat_symbol (libc, __nldbl___snprintf_chk, __snprintf_chk, GLIBC_2_3_4); +compat_symbol (libc, __nldbl___vsnprintf_chk, __vsnprintf_chk, GLIBC_2_3_4); +compat_symbol (libc, __nldbl___printf_chk, __printf_chk, GLIBC_2_3_4); +compat_symbol (libc, __nldbl___fprintf_chk, __fprintf_chk, GLIBC_2_3_4); +compat_symbol (libc, __nldbl___vprintf_chk, __vprintf_chk, GLIBC_2_3_4); +compat_symbol (libc, __nldbl___vfprintf_chk, __vfprintf_chk, GLIBC_2_3_4); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-compat.h b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-compat.h new file mode 100644 index 0000000000..72ec0db390 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-compat.h @@ -0,0 +1,104 @@ +/* Prototypes for compatibility double == long double entry points. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jakub@cygnus.com>, 2006. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef __NLDBL_COMPAT_H +#define __NLDBL_COMPAT_H 1 + +/* Avoid long double prototypes. */ +#define __NO_LONG_DOUBLE_MATH 1 +#include <stdarg.h> +#include <stdlib.h> +#include <stdint.h> +#include <stdio.h> +#include <printf.h> +#include <wchar.h> +#include <math.h> +#include <monetary.h> +#include <sys/syslog.h> + + +/* Declare the __nldbl_NAME function the wrappers call that's in libc.so. */ +#define NLDBL_DECL(name) extern __typeof (name) __nldbl_##name + +NLDBL_DECL (_IO_vfscanf); +NLDBL_DECL (vfscanf); +NLDBL_DECL (vfwscanf); +NLDBL_DECL (obstack_vprintf); +NLDBL_DECL (vasprintf); +NLDBL_DECL (dprintf); +NLDBL_DECL (vdprintf); +NLDBL_DECL (fprintf); +NLDBL_DECL (vfprintf); +NLDBL_DECL (vfwprintf); +NLDBL_DECL (vsnprintf); +NLDBL_DECL (vsprintf); +NLDBL_DECL (vsscanf); +NLDBL_DECL (vswprintf); +NLDBL_DECL (vswscanf); +NLDBL_DECL (__asprintf); +NLDBL_DECL (asprintf); +NLDBL_DECL (__printf_fp); +NLDBL_DECL (printf_size); +NLDBL_DECL (syslog); +NLDBL_DECL (vsyslog); +NLDBL_DECL (qecvt); +NLDBL_DECL (qfcvt); +NLDBL_DECL (qgcvt); +NLDBL_DECL (__vstrfmon_l); +NLDBL_DECL (__isoc99_scanf); +NLDBL_DECL (__isoc99_fscanf); +NLDBL_DECL (__isoc99_sscanf); +NLDBL_DECL (__isoc99_vscanf); +NLDBL_DECL (__isoc99_vfscanf); +NLDBL_DECL (__isoc99_vsscanf); +NLDBL_DECL (__isoc99_wscanf); +NLDBL_DECL (__isoc99_fwscanf); +NLDBL_DECL (__isoc99_swscanf); +NLDBL_DECL (__isoc99_vwscanf); +NLDBL_DECL (__isoc99_vfwscanf); +NLDBL_DECL (__isoc99_vswscanf); + +/* This one does not exist in the normal interface, only + __nldbl___vstrfmon really exists. */ +extern ssize_t __nldbl___vstrfmon (char *, size_t, const char *, va_list) + __THROW; + +/* These don't use __typeof because they were not declared by the headers, + since we don't compile with _FORTIFY_SOURCE. */ +extern int __nldbl___vfprintf_chk (FILE *__restrict, int, + const char *__restrict, _G_va_list); +extern int __nldbl___vfwprintf_chk (FILE *__restrict, int, + const wchar_t *__restrict, __gnuc_va_list); +extern int __nldbl___vsprintf_chk (char *__restrict, int, size_t, + const char *__restrict, _G_va_list) __THROW; +extern int __nldbl___vsnprintf_chk (char *__restrict, size_t, int, size_t, + const char *__restrict, _G_va_list) + __THROW; +extern int __nldbl___vswprintf_chk (wchar_t *__restrict, size_t, int, size_t, + const wchar_t *__restrict, __gnuc_va_list) + __THROW; +extern int __nldbl___vasprintf_chk (char **, int, const char *, _G_va_list) + __THROW; +extern int __nldbl___vdprintf_chk (int, int, const char *, _G_va_list); +extern int __nldbl___obstack_vprintf_chk (struct obstack *, int, const char *, + _G_va_list) __THROW; +extern void __nldbl___vsyslog_chk (int, int, const char *, va_list); + + +#endif /* __NLDBL_COMPAT_H */ diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-conj.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-conj.c new file mode 100644 index 0000000000..8927ea9968 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-conj.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +conjl (double _Complex x) +{ + return conj (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-copysign.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-copysign.c new file mode 100644 index 0000000000..045f00dda8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-copysign.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +copysignl (double x, double y) +{ + return __copysign (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cos.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cos.c new file mode 100644 index 0000000000..08738af048 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cos.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +cosl (double x) +{ + return cos (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cosh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cosh.c new file mode 100644 index 0000000000..0ab834ffd9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cosh.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +coshl (double x) +{ + return cosh (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cpow.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cpow.c new file mode 100644 index 0000000000..709e7d73b1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cpow.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +cpowl (double _Complex x, double _Complex y) +{ + return cpow (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cproj.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cproj.c new file mode 100644 index 0000000000..6f88b88bf2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-cproj.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +cprojl (double _Complex x) +{ + return cproj (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-creal.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-creal.c new file mode 100644 index 0000000000..b02ce6e5e4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-creal.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double +attribute_hidden +creall (double _Complex x) +{ + return creal (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-csin.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-csin.c new file mode 100644 index 0000000000..b2e2c9c8ef --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-csin.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +csinl (double _Complex x) +{ + return csin (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-csinh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-csinh.c new file mode 100644 index 0000000000..2bcba920e3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-csinh.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +csinhl (double _Complex x) +{ + return csinh (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-csqrt.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-csqrt.c new file mode 100644 index 0000000000..ae00a29885 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-csqrt.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +csqrtl (double _Complex x) +{ + return csqrt (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ctan.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ctan.c new file mode 100644 index 0000000000..422c5cce94 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ctan.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +ctanl (double _Complex x) +{ + return ctan (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ctanh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ctanh.c new file mode 100644 index 0000000000..f3842ed26f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ctanh.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" +#include <complex.h> + +double _Complex +attribute_hidden +ctanhl (double _Complex x) +{ + return ctanh (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-dprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-dprintf.c new file mode 100644 index 0000000000..6e26db2a24 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-dprintf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +attribute_hidden +int +dprintf (int d, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vdprintf (d, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-dprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-dprintf_chk.c new file mode 100644 index 0000000000..b3e2359128 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-dprintf_chk.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +attribute_hidden +int +__dprintf_chk (int d, int flag, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vdprintf_chk (d, flag, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-erf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-erf.c new file mode 100644 index 0000000000..0032c1febc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-erf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +erfl (double x) +{ + return erf (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-erfc.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-erfc.c new file mode 100644 index 0000000000..21d09680aa --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-erfc.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +erfcl (double x) +{ + return erfc (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-exp.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-exp.c new file mode 100644 index 0000000000..ad2c89b6d5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-exp.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +expl (double x) +{ + return exp (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-exp10.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-exp10.c new file mode 100644 index 0000000000..2d0ead686b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-exp10.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +exp10l (double x) +{ + return exp10 (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-exp2.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-exp2.c new file mode 100644 index 0000000000..d5fce3970d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-exp2.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +exp2l (double x) +{ + return exp2 (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-expm1.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-expm1.c new file mode 100644 index 0000000000..be5c6e51c4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-expm1.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +expm1l (double x) +{ + return expm1 (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fabs.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fabs.c new file mode 100644 index 0000000000..10729a6ec0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fabs.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +fabsl (double x) +{ + return fabs (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fdim.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fdim.c new file mode 100644 index 0000000000..72896b63ed --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fdim.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +fdiml (double x, double y) +{ + return fdim (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-finite.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-finite.c new file mode 100644 index 0000000000..fc51508f16 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-finite.c @@ -0,0 +1,10 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__finitel (double x) +{ + return isfinite (x); +} +extern __typeof (__finitel) finitel attribute_hidden; +weak_alias (__finitel, finitel) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-floor.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-floor.c new file mode 100644 index 0000000000..c7e9f834b6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-floor.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +floorl (double x) +{ + return floor (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fma.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fma.c new file mode 100644 index 0000000000..9474483673 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fma.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +fmal (double x, double y, double z) +{ + return fma (x, y, z); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fmax.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fmax.c new file mode 100644 index 0000000000..f5a84776ed --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fmax.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +fmaxl (double x, double y) +{ + return fmax (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fmaxmag.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fmaxmag.c new file mode 100644 index 0000000000..28aab5791a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fmaxmag.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for fmaxmag. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +double +attribute_hidden +fmaxmagl (double x, double y) +{ + return fmaxmag (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fmin.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fmin.c new file mode 100644 index 0000000000..a353cf9484 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fmin.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +fminl (double x, double y) +{ + return fmin (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fminmag.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fminmag.c new file mode 100644 index 0000000000..f1743acd4d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fminmag.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for fminmag. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +double +attribute_hidden +fminmagl (double x, double y) +{ + return fminmag (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fmod.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fmod.c new file mode 100644 index 0000000000..aa692b9f36 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fmod.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +fmodl (double x, double y) +{ + return fmod (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fprintf.c new file mode 100644 index 0000000000..9df4c4bc34 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fprintf.c @@ -0,0 +1,17 @@ +#include "nldbl-compat.h" + +attribute_hidden +int +fprintf (FILE *stream, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfprintf (stream, fmt, arg); + va_end (arg); + + return done; +} +extern __typeof (fprintf) _IO_fprintf attribute_hidden; +weak_alias (fprintf, _IO_fprintf) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fprintf_chk.c new file mode 100644 index 0000000000..43a7618183 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fprintf_chk.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__fprintf_chk (FILE *stream, int flag, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vfprintf_chk (stream, flag, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-frexp.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-frexp.c new file mode 100644 index 0000000000..0ec97e10e3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-frexp.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +frexpl (double x, int *exponent) +{ + return frexp (x, exponent); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fromfp.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fromfp.c new file mode 100644 index 0000000000..6ef95f4ab4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fromfp.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for fromfp. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +intmax_t +attribute_hidden +fromfpl (double x, int round, unsigned int width) +{ + return fromfp (x, round, width); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fromfpx.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fromfpx.c new file mode 100644 index 0000000000..193d9b6ce1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fromfpx.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for fromfpx. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +intmax_t +attribute_hidden +fromfpxl (double x, int round, unsigned int width) +{ + return fromfpx (x, round, width); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fscanf.c new file mode 100644 index 0000000000..1b768e306f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fscanf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +fscanf (FILE *stream, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl__IO_vfscanf (stream, fmt, arg, NULL); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fwprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fwprintf.c new file mode 100644 index 0000000000..18362af013 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fwprintf.c @@ -0,0 +1,16 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +weak_function +fwprintf (FILE *stream, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfwprintf (stream, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fwprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fwprintf_chk.c new file mode 100644 index 0000000000..09731cf29d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fwprintf_chk.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__fwprintf_chk (FILE *stream, int flag, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vfwprintf_chk (stream, flag, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fwscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fwscanf.c new file mode 100644 index 0000000000..27fc1a7271 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-fwscanf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +fwscanf (FILE *stream, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfwscanf (stream, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-gamma.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-gamma.c new file mode 100644 index 0000000000..10dc640b92 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-gamma.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +gammal (double x) +{ + return gamma (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-getpayload.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-getpayload.c new file mode 100644 index 0000000000..f15f9231ec --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-getpayload.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for getpayload. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +double +attribute_hidden +getpayloadl (const double *x) +{ + return getpayload (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-hypot.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-hypot.c new file mode 100644 index 0000000000..2105f3eba8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-hypot.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +hypotl (double x, double y) +{ + return hypot (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ilogb.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ilogb.c new file mode 100644 index 0000000000..e840b2a447 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ilogb.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +ilogbl (double x) +{ + return ilogb (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-iovfscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-iovfscanf.c new file mode 100644 index 0000000000..05581c0354 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-iovfscanf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +_IO_vfscanf (FILE *s, const char *fmt, _IO_va_list ap, int *errp) +{ + return __nldbl__IO_vfscanf (s, fmt, ap, errp); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isinf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isinf.c new file mode 100644 index 0000000000..577ab2db28 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isinf.c @@ -0,0 +1,10 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isinfl (double x) +{ + return isinf (x); +} +extern __typeof (__isinfl) isinfl attribute_hidden; +weak_alias (__isinfl, isinfl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isnan.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isnan.c new file mode 100644 index 0000000000..2d87bf85fb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isnan.c @@ -0,0 +1,10 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isnanl (double x) +{ + return isnan (x); +} +extern __typeof (__isnanl) isnanl attribute_hidden; +weak_alias (__isnanl, isnanl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_fscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_fscanf.c new file mode 100644 index 0000000000..1d736668a4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_fscanf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isoc99_fscanf (FILE *stream, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___isoc99_vfscanf (stream, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_fwscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_fwscanf.c new file mode 100644 index 0000000000..dbea1512cf --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_fwscanf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isoc99_fwscanf (FILE *stream, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___isoc99_vfwscanf (stream, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_scanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_scanf.c new file mode 100644 index 0000000000..ec2ec53291 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_scanf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isoc99_scanf (const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___isoc99_vfscanf (stdin, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_sscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_sscanf.c new file mode 100644 index 0000000000..52e1bd5d2a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_sscanf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isoc99_sscanf (const char *s, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___isoc99_vsscanf (s, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_swscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_swscanf.c new file mode 100644 index 0000000000..927d024923 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_swscanf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isoc99_swscanf (const wchar_t *s, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___isoc99_vswscanf (s, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vfscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vfscanf.c new file mode 100644 index 0000000000..55556c375c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vfscanf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isoc99_vfscanf (FILE *s, const char *fmt, va_list ap) +{ + return __nldbl___isoc99_vfscanf (s, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vfwscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vfwscanf.c new file mode 100644 index 0000000000..4fd54cb176 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vfwscanf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isoc99_vfwscanf (FILE *s, const wchar_t *fmt, va_list ap) +{ + return __nldbl___isoc99_vfwscanf (s, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vscanf.c new file mode 100644 index 0000000000..6284c9339b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vscanf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isoc99_vscanf (const char *fmt, va_list ap) +{ + return __nldbl___isoc99_vfscanf (stdin, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vsscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vsscanf.c new file mode 100644 index 0000000000..0c19032b15 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vsscanf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isoc99_vsscanf (const char *string, const char *fmt, va_list ap) +{ + return __nldbl___isoc99_vsscanf (string, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vswscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vswscanf.c new file mode 100644 index 0000000000..5f34221b62 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vswscanf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isoc99_vswscanf (const wchar_t *string, const wchar_t *fmt, va_list ap) +{ + return __nldbl___isoc99_vswscanf (string, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vwscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vwscanf.c new file mode 100644 index 0000000000..a8a76ff54b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_vwscanf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isoc99_vwscanf (const wchar_t *fmt, va_list ap) +{ + return __nldbl___isoc99_vfwscanf (stdin, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_wscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_wscanf.c new file mode 100644 index 0000000000..fc2f6f8598 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-isoc99_wscanf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__isoc99_wscanf (const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___isoc99_vfwscanf (stdin, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-j0.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-j0.c new file mode 100644 index 0000000000..9d59f0a015 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-j0.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +j0l (double x) +{ + return j0 (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-j1.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-j1.c new file mode 100644 index 0000000000..dba7366861 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-j1.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +j1l (double x) +{ + return j1 (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-jn.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-jn.c new file mode 100644 index 0000000000..3f19bbb1a8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-jn.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +jnl (int n, double x) +{ + return jn (n, x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ldexp.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ldexp.c new file mode 100644 index 0000000000..360f8f0f6b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ldexp.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +ldexpl (double x, int exponent) +{ + return ldexp (x, exponent); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-lgamma.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-lgamma.c new file mode 100644 index 0000000000..0055212628 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-lgamma.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +lgammal (double x) +{ + return lgamma (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-lgamma_r.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-lgamma_r.c new file mode 100644 index 0000000000..e1ab9a1d0a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-lgamma_r.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +lgammal_r (double x, int *signgamp) +{ + return lgamma_r (x, signgamp); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-llogb.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-llogb.c new file mode 100644 index 0000000000..76042b2f48 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-llogb.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for llogb. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +long int +attribute_hidden +llogbl (double x) +{ + return llogb (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-llrint.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-llrint.c new file mode 100644 index 0000000000..6dfce89d0d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-llrint.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +long long int +attribute_hidden +llrintl (double x) +{ + return llrint (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-llround.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-llround.c new file mode 100644 index 0000000000..0157a079f4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-llround.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +long long int +attribute_hidden +llroundl (double x) +{ + return llround (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-log.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-log.c new file mode 100644 index 0000000000..a5a1ae7cd7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-log.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +logl (double x) +{ + return log (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-log10.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-log10.c new file mode 100644 index 0000000000..1477866dc6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-log10.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +log10l (double x) +{ + return log10 (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-log1p.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-log1p.c new file mode 100644 index 0000000000..455b25a9f4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-log1p.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +log1pl (double x) +{ + return log1p (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-log2.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-log2.c new file mode 100644 index 0000000000..8c1ae344e5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-log2.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +log2l (double x) +{ + return log2 (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-logb.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-logb.c new file mode 100644 index 0000000000..d9ce8de075 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-logb.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +logbl (double x) +{ + return logb (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-lrint.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-lrint.c new file mode 100644 index 0000000000..0acd3d4ae6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-lrint.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +long int +attribute_hidden +lrintl (double x) +{ + return lrint (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-lround.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-lround.c new file mode 100644 index 0000000000..aadb111f88 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-lround.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +long int +attribute_hidden +lroundl (double x) +{ + return lround (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-modf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-modf.c new file mode 100644 index 0000000000..bcbe6bb435 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-modf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +modfl (double x, double *iptr) +{ + return modf (x, iptr); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nan.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nan.c new file mode 100644 index 0000000000..8db157a0ea --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nan.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +nanl (const char *tag) +{ + return nan (tag); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nearbyint.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nearbyint.c new file mode 100644 index 0000000000..fd4a24684d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nearbyint.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +nearbyintl (double x) +{ + return nearbyint (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nextafter.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nextafter.c new file mode 100644 index 0000000000..b0bae43f49 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nextafter.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +nextafterl (double x, double y) +{ + return nextafter (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nextdown.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nextdown.c new file mode 100644 index 0000000000..b20c788401 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nextdown.c @@ -0,0 +1,27 @@ +/* Compatibility routine for IEEE double as long double for nextdown. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +/* Return the greatest floating-point number less than X. */ +double +attribute_hidden +nextdownl (double x) +{ + return nextdown (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nexttoward.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nexttoward.c new file mode 100644 index 0000000000..acbd01a0cf --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nexttoward.c @@ -0,0 +1,14 @@ +#define nexttoward nexttoward_XXX +#define nexttowardl nexttowardl_XXX +#include "nldbl-compat.h" +#undef nexttoward +#undef nexttowardl + +double +attribute_hidden +nexttoward (double x, double y) +{ + return nextafter (x, y); +} +extern __typeof (nexttoward) nexttowardl attribute_hidden; +strong_alias (nexttoward, nexttowardl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nexttowardf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nexttowardf.c new file mode 100644 index 0000000000..350b08d39e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nexttowardf.c @@ -0,0 +1,12 @@ +#define nexttowardf nexttowardf_XXX +#include "nldbl-compat.h" +#undef nexttowardf + +extern float __nldbl_nexttowardf (float x, double y); + +float +attribute_hidden +nexttowardf (float x, double y) +{ + return __nldbl_nexttowardf (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nextup.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nextup.c new file mode 100644 index 0000000000..71dc8d4816 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-nextup.c @@ -0,0 +1,27 @@ +/* Compatibility routine for IEEE double as long double for nextup. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +/* Return the least floating-point number greater than X. */ +double +attribute_hidden +nextupl (double x) +{ + return nextup (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-obstack_printf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-obstack_printf.c new file mode 100644 index 0000000000..4abff2dc0d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-obstack_printf.c @@ -0,0 +1,13 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +obstack_printf (struct obstack *obstack, const char *fmt, ...) +{ + int result; + va_list ap; + va_start (ap, fmt); + result = __nldbl_obstack_vprintf (obstack, fmt, ap); + va_end (ap); + return result; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-obstack_printf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-obstack_printf_chk.c new file mode 100644 index 0000000000..8e7d8eb4ad --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-obstack_printf_chk.c @@ -0,0 +1,13 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__obstack_printf_chk (struct obstack *obstack, int flag, const char *fmt, ...) +{ + int result; + va_list ap; + va_start (ap, fmt); + result = __nldbl___obstack_vprintf_chk (obstack, flag, fmt, ap); + va_end (ap); + return result; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-obstack_vprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-obstack_vprintf.c new file mode 100644 index 0000000000..228a50726b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-obstack_vprintf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +obstack_vprintf (struct obstack *obstack, const char *fmt, va_list ap) +{ + return __nldbl_obstack_vprintf (obstack, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-obstack_vprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-obstack_vprintf_chk.c new file mode 100644 index 0000000000..a06f6bf9b4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-obstack_vprintf_chk.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__obstack_vprintf_chk (struct obstack *obstack, int flag, const char *fmt, + va_list ap) +{ + return __nldbl___obstack_vprintf_chk (obstack, flag, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-pow.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-pow.c new file mode 100644 index 0000000000..a5cc446555 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-pow.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +powl (double x, double y) +{ + return pow (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-pow10.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-pow10.c new file mode 100644 index 0000000000..20ebf8d1bb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-pow10.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +pow10l (double x) +{ + return pow10 (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-printf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-printf.c new file mode 100644 index 0000000000..e4b0fbae0c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-printf.c @@ -0,0 +1,17 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +printf (const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfprintf (stdout, fmt, arg); + va_end (arg); + + return done; +} +extern __typeof (printf) _IO_printf attribute_hidden; +strong_alias (printf, _IO_printf) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-printf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-printf_chk.c new file mode 100644 index 0000000000..926db412f9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-printf_chk.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__printf_chk (int flag, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vfprintf_chk (stdout, flag, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-printf_fp.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-printf_fp.c new file mode 100644 index 0000000000..057dfe0b8a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-printf_fp.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__printf_fp (FILE *fp, const struct printf_info *info, + const void *const *args) +{ + return __nldbl___printf_fp (fp, info, args); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-printf_size.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-printf_size.c new file mode 100644 index 0000000000..d8b1fc9995 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-printf_size.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +printf_size (FILE *__restrict fp, const struct printf_info *info, + const void *const *__restrict args) +{ + return __nldbl_printf_size (fp, info, args); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qecvt.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qecvt.c new file mode 100644 index 0000000000..9f0b0a66a9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qecvt.c @@ -0,0 +1,10 @@ +#define qecvt qecvt_XXX +#include "nldbl-compat.h" +#undef qecvt + +attribute_hidden +char * +qecvt (double val, int ndigit, int *__restrict decpt, int *__restrict sign) +{ + return ecvt (val, ndigit, decpt, sign); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qecvt_r.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qecvt_r.c new file mode 100644 index 0000000000..06f99146cc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qecvt_r.c @@ -0,0 +1,11 @@ +#define qecvt_r qecvt_r_XXX +#include "nldbl-compat.h" +#undef qecvt_r + +int +attribute_hidden +qecvt_r (double val, int ndigit, int *__restrict decpt, int *__restrict sign, + char *__restrict buf, size_t len) +{ + return ecvt_r (val, ndigit, decpt, sign, buf, len); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qfcvt.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qfcvt.c new file mode 100644 index 0000000000..37fa7f0467 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qfcvt.c @@ -0,0 +1,10 @@ +#define qfcvt qfcvt_XXX +#include "nldbl-compat.h" +#undef qfcvt + +attribute_hidden +char * +qfcvt (double val, int ndigit, int *__restrict decpt, int *__restrict sign) +{ + return fcvt (val, ndigit, decpt, sign); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qfcvt_r.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qfcvt_r.c new file mode 100644 index 0000000000..03224fefa9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qfcvt_r.c @@ -0,0 +1,11 @@ +#define qfcvt_r qfcvt_r_XXX +#include "nldbl-compat.h" +#undef qfcvt_r + +int +attribute_hidden +qfcvt_r (double val, int ndigit, int *__restrict decpt, int *__restrict sign, + char *__restrict buf, size_t len) +{ + return fcvt_r (val, ndigit, decpt, sign, buf, len); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qgcvt.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qgcvt.c new file mode 100644 index 0000000000..b935d0962e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-qgcvt.c @@ -0,0 +1,10 @@ +#define qgcvt qgcvt_XXX +#include "nldbl-compat.h" +#undef qgcvt + +attribute_hidden +char * +qgcvt (double val, int ndigit, char *buf) +{ + return gcvt (val, ndigit, buf); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-remainder.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-remainder.c new file mode 100644 index 0000000000..581dc78a4d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-remainder.c @@ -0,0 +1,10 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +remainderl (double x, double y) +{ + return remainder (x, y); +} +extern __typeof (remainderl) dreml attribute_hidden; +weak_alias (remainderl, dreml) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-remquo.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-remquo.c new file mode 100644 index 0000000000..592dadae8d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-remquo.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +remquol (double x, double y, int *quo) +{ + return remquo (x, y, quo); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-rint.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-rint.c new file mode 100644 index 0000000000..00f942f1a7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-rint.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +rintl (double x) +{ + return rint (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-round.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-round.c new file mode 100644 index 0000000000..be9bd5112e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-round.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +roundl (double x) +{ + return round (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-roundeven.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-roundeven.c new file mode 100644 index 0000000000..1a46fa50d2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-roundeven.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for roundeven. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +double +attribute_hidden +roundevenl (double x) +{ + return roundeven (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-scalb.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-scalb.c new file mode 100644 index 0000000000..00d3e2e714 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-scalb.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +scalbl (double x, double n) +{ + return scalb (x, n); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-scalbln.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-scalbln.c new file mode 100644 index 0000000000..b5bd501250 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-scalbln.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +scalblnl (double x, long int n) +{ + return scalbln (x, n); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-scalbn.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-scalbn.c new file mode 100644 index 0000000000..b1914ebf49 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-scalbn.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +scalbnl (double x, int n) +{ + return scalbn (x, n); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-scanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-scanf.c new file mode 100644 index 0000000000..bbab371cbe --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-scanf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +scanf (const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl__IO_vfscanf (stdin, fmt, arg, NULL); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-setpayload.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-setpayload.c new file mode 100644 index 0000000000..df902cad99 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-setpayload.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for setpayload. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +int +attribute_hidden +setpayloadl (double *x, double payload) +{ + return setpayload (x, payload); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-setpayloadsig.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-setpayloadsig.c new file mode 100644 index 0000000000..1ca497502c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-setpayloadsig.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for setpayloadsig. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +int +attribute_hidden +setpayloadsigl (double *x, double payload) +{ + return setpayloadsig (x, payload); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-signbit.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-signbit.c new file mode 100644 index 0000000000..2e98c07396 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-signbit.c @@ -0,0 +1,10 @@ +#define __signbitl __signbitl_XXX +#include "nldbl-compat.h" +#undef __signbitl + +int +attribute_hidden +__signbitl (double x) +{ + return signbit (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-significand.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-significand.c new file mode 100644 index 0000000000..624381dde7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-significand.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +significandl (double x) +{ + return significand (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sin.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sin.c new file mode 100644 index 0000000000..0e76e05e6b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sin.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +sinl (double x) +{ + return sin (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sincos.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sincos.c new file mode 100644 index 0000000000..9f2ab2b9fc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sincos.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +void +attribute_hidden +sincosl (double x, double *sinx, double *cosx) +{ + sincos (x, sinx, cosx); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sinh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sinh.c new file mode 100644 index 0000000000..99ea62e8dc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sinh.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +sinhl (double x) +{ + return sinh (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-snprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-snprintf.c new file mode 100644 index 0000000000..ef6fb96a2c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-snprintf.c @@ -0,0 +1,16 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +weak_function +snprintf (char *s, size_t maxlen, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vsnprintf (s, maxlen, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-snprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-snprintf_chk.c new file mode 100644 index 0000000000..944d3de9db --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-snprintf_chk.c @@ -0,0 +1,16 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__snprintf_chk (char *s, size_t maxlen, int flag, size_t slen, + const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vsnprintf_chk (s, maxlen, flag, slen, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sprintf.c new file mode 100644 index 0000000000..5d37a7e7f0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sprintf.c @@ -0,0 +1,17 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +sprintf (char *s, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vsprintf (s, fmt, arg); + va_end (arg); + + return done; +} +extern __typeof (sprintf) _IO_sprintf attribute_hidden; +strong_alias (sprintf, _IO_sprintf) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sprintf_chk.c new file mode 100644 index 0000000000..349b7c5c22 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sprintf_chk.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__sprintf_chk (char *s, int flag, size_t slen, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vsprintf_chk (s, flag, slen, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sqrt.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sqrt.c new file mode 100644 index 0000000000..4ae65665de --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sqrt.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +sqrtl (double x) +{ + return sqrt (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sscanf.c new file mode 100644 index 0000000000..a771d49996 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-sscanf.c @@ -0,0 +1,17 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +sscanf (const char *s, const char *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vsscanf (s, fmt, arg); + va_end (arg); + + return done; +} +extern __typeof (sscanf) _IO_sscanf attribute_hidden; +strong_alias (sscanf, _IO_sscanf) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strfmon.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strfmon.c new file mode 100644 index 0000000000..38f4071278 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strfmon.c @@ -0,0 +1,14 @@ +#include "nldbl-compat.h" + +ssize_t +attribute_hidden +strfmon (char *s, size_t maxsize, const char *format, ...) +{ + va_list ap; + ssize_t res; + + va_start (ap, format); + res = __nldbl___vstrfmon (s, maxsize, format, ap); + va_end (ap); + return res; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strfmon_l.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strfmon_l.c new file mode 100644 index 0000000000..0db0e8c42f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strfmon_l.c @@ -0,0 +1,16 @@ +#include "nldbl-compat.h" + +ssize_t +attribute_hidden +__strfmon_l (char *s, size_t maxsize, __locale_t loc, const char *format, ...) +{ + va_list ap; + ssize_t res; + + va_start (ap, format); + res = __nldbl___vstrfmon_l (s, maxsize, loc, format, ap); + va_end (ap); + return res; +} +extern __typeof (__strfmon_l) strfmon_l attribute_hidden; +weak_alias (__strfmon_l, strfmon_l) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strfroml.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strfroml.c new file mode 100644 index 0000000000..d6df69e418 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strfroml.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +strfroml (char *dest, size_t size, const char *format, long double f) +{ + return strfromd (dest, size, format, f); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strtold.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strtold.c new file mode 100644 index 0000000000..99b907947b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strtold.c @@ -0,0 +1,10 @@ +#define strtold strtold_XXX +#include "nldbl-compat.h" +#undef strtold + +double +attribute_hidden +strtold (const char *nptr, char **endptr) +{ + return strtod (nptr, endptr); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strtold_l.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strtold_l.c new file mode 100644 index 0000000000..33ff1ca5b5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strtold_l.c @@ -0,0 +1,20 @@ +#define strtold_l strtold_l_XXX +#define __strtold_l __strtold_l_XXX +#define __strtod_l __strtod_l_XXX +#include "nldbl-compat.h" +#undef strtold_l +#undef __strtold_l +#undef __strtod_l + +extern double +__strtod_l (const char *__restrict __nptr, char **__restrict __endptr, + __locale_t __loc); + +double +attribute_hidden +__strtold_l (const char *nptr, char **endptr, __locale_t loc) +{ + return __strtod_l (nptr, endptr, loc); +} +extern __typeof (__strtold_l) strtold_l attribute_hidden; +weak_alias (__strtold_l, strtold_l) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strtoldint.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strtoldint.c new file mode 100644 index 0000000000..0bafabc6e4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-strtoldint.c @@ -0,0 +1,10 @@ +#define __strtold_internal __strtold_internal_XXX +#include "nldbl-compat.h" +#undef __strtold_internal + +double +attribute_hidden +__strtold_internal (const char *nptr, char **endptr, int group) +{ + return __strtod_internal (nptr, endptr, group); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-swprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-swprintf.c new file mode 100644 index 0000000000..7f4f7b04d3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-swprintf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +swprintf (wchar_t *s, size_t n, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vswprintf (s, n, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-swprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-swprintf_chk.c new file mode 100644 index 0000000000..0373f6ebc2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-swprintf_chk.c @@ -0,0 +1,16 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__swprintf_chk (wchar_t *s, size_t n, int flag, size_t slen, + const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vswprintf_chk (s, n, flag, slen, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-swscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-swscanf.c new file mode 100644 index 0000000000..dd058f47ab --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-swscanf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +swscanf (const wchar_t *s, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vswscanf (s, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-syslog.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-syslog.c new file mode 100644 index 0000000000..8687e9f540 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-syslog.c @@ -0,0 +1,11 @@ +#include "nldbl-compat.h" + +void +attribute_hidden +syslog (int pri, const char *fmt, ...) +{ + va_list ap; + va_start (ap, fmt); + __nldbl_vsyslog (pri, fmt, ap); + va_end (ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-syslog_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-syslog_chk.c new file mode 100644 index 0000000000..31ea6a8b9d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-syslog_chk.c @@ -0,0 +1,12 @@ +#include "nldbl-compat.h" + +void +attribute_hidden +__syslog_chk (int pri, int flag, const char *fmt, ...) +{ + va_list ap; + + va_start (ap, fmt); + __nldbl___vsyslog_chk (pri, flag, fmt, ap); + va_end(ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-tan.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-tan.c new file mode 100644 index 0000000000..1a27b6fbdd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-tan.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +tanl (double x) +{ + return tan (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-tanh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-tanh.c new file mode 100644 index 0000000000..fc2fd32eb8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-tanh.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +tanhl (double x) +{ + return tanh (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-tgamma.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-tgamma.c new file mode 100644 index 0000000000..bbf613abe1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-tgamma.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +tgammal (double x) +{ + return tgamma (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-totalorder.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-totalorder.c new file mode 100644 index 0000000000..c528d53555 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-totalorder.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for totalorder. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +double +attribute_hidden +totalorderl (double x, double y) +{ + return totalorder (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-totalordermag.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-totalordermag.c new file mode 100644 index 0000000000..4bc78588ea --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-totalordermag.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for totalordermag. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +double +attribute_hidden +totalordermagl (double x, double y) +{ + return totalordermag (x, y); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-trunc.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-trunc.c new file mode 100644 index 0000000000..d0131e80a3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-trunc.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +truncl (double x) +{ + return trunc (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ufromfp.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ufromfp.c new file mode 100644 index 0000000000..127225734c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ufromfp.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for ufromfp. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +uintmax_t +attribute_hidden +ufromfpl (double x, int round, unsigned int width) +{ + return ufromfp (x, round, width); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ufromfpx.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ufromfpx.c new file mode 100644 index 0000000000..3294f00609 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-ufromfpx.c @@ -0,0 +1,26 @@ +/* Compatibility routine for IEEE double as long double for ufromfpx. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "nldbl-compat.h" + +uintmax_t +attribute_hidden +ufromfpxl (double x, int round, unsigned int width) +{ + return ufromfpx (x, round, width); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vasprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vasprintf.c new file mode 100644 index 0000000000..52fa18ccee --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vasprintf.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +weak_function +vasprintf (char **result_ptr, const char *fmt, va_list ap) +{ + return __nldbl_vasprintf (result_ptr, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vasprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vasprintf_chk.c new file mode 100644 index 0000000000..4f5391a9d7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vasprintf_chk.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__vasprintf_chk (char **result_ptr, int flag, const char *fmt, va_list ap) +{ + return __nldbl___vasprintf_chk (result_ptr, flag, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vdprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vdprintf.c new file mode 100644 index 0000000000..1acbd40625 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vdprintf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +vdprintf (int d, const char *fmt, va_list arg) +{ + return __nldbl_vdprintf (d, fmt, arg); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vdprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vdprintf_chk.c new file mode 100644 index 0000000000..ca1ce01878 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vdprintf_chk.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__vdprintf_chk (int d, int flag, const char *fmt, va_list arg) +{ + return __nldbl___vdprintf_chk (d, flag, fmt, arg); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfprintf.c new file mode 100644 index 0000000000..6ca8437b28 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfprintf.c @@ -0,0 +1,10 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +vfprintf (FILE *s, const char *fmt, va_list ap) +{ + return __nldbl_vfprintf (s, fmt, ap); +} +extern __typeof (vfprintf) _IO_vfprintf attribute_hidden; +strong_alias (vfprintf, _IO_vfprintf) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfprintf_chk.c new file mode 100644 index 0000000000..0f6820af63 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfprintf_chk.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__vfprintf_chk (FILE *s, int flag, const char *fmt, va_list ap) +{ + return __nldbl___vfprintf_chk (s, flag, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfscanf.c new file mode 100644 index 0000000000..f23465ee95 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfscanf.c @@ -0,0 +1,10 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__vfscanf (FILE *s, const char *fmt, va_list ap) +{ + return __nldbl__IO_vfscanf (s, fmt, ap, NULL); +} +extern __typeof (__vfscanf) vfscanf attribute_hidden; +weak_alias (__vfscanf, vfscanf) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfwprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfwprintf.c new file mode 100644 index 0000000000..c3fe76a971 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfwprintf.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +weak_function +vfwprintf (FILE *s, const wchar_t *fmt, va_list ap) +{ + return __nldbl_vfwprintf (s, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfwprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfwprintf_chk.c new file mode 100644 index 0000000000..b3b69f0571 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfwprintf_chk.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__vfwprintf_chk (FILE *s, int flag, const wchar_t *fmt, va_list ap) +{ + return __nldbl___vfwprintf_chk (s, flag, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfwscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfwscanf.c new file mode 100644 index 0000000000..be9febc9a0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vfwscanf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +vfwscanf (FILE *s, const wchar_t *fmt, va_list ap) +{ + return __nldbl_vfwscanf (s, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vprintf.c new file mode 100644 index 0000000000..ed0d27d9a0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vprintf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +vprintf (const char *fmt, va_list ap) +{ + return __nldbl_vfprintf (stdout, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vprintf_chk.c new file mode 100644 index 0000000000..63b3e8f965 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vprintf_chk.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__vprintf_chk (int flag, const char *fmt, va_list ap) +{ + return __nldbl___vfprintf_chk (stdout, flag, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vscanf.c new file mode 100644 index 0000000000..e75907b905 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vscanf.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +weak_function +vscanf (const char *fmt, va_list ap) +{ + return __nldbl__IO_vfscanf (stdin, fmt, ap, NULL); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsnprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsnprintf.c new file mode 100644 index 0000000000..5a9bcbcaee --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsnprintf.c @@ -0,0 +1,10 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +vsnprintf (char *string, size_t maxlen, const char *fmt, va_list ap) +{ + return __nldbl_vsnprintf (string, maxlen, fmt, ap); +} +extern __typeof (vsnprintf) __vsnprintf attribute_hidden; +weak_alias (vsnprintf, __vsnprintf) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsnprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsnprintf_chk.c new file mode 100644 index 0000000000..19380291a3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsnprintf_chk.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__vsnprintf_chk (char *string, size_t maxlen, int flag, size_t slen, + const char *fmt, va_list ap) +{ + return __nldbl___vsnprintf_chk (string, maxlen, flag, slen, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsprintf.c new file mode 100644 index 0000000000..04406d0f6e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsprintf.c @@ -0,0 +1,10 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +_IO_vsprintf (char *string, const char *fmt, va_list ap) +{ + return __nldbl_vsprintf (string, fmt, ap); +} +extern __typeof (_IO_vsprintf) vsprintf attribute_hidden; +weak_alias (_IO_vsprintf, vsprintf) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsprintf_chk.c new file mode 100644 index 0000000000..9df143fcef --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsprintf_chk.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__vsprintf_chk (char *string, int flag, size_t slen, const char *fmt, + va_list ap) +{ + return __nldbl___vsprintf_chk (string, flag, slen, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsscanf.c new file mode 100644 index 0000000000..f5594c122c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsscanf.c @@ -0,0 +1,10 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__vsscanf (const char *string, const char *fmt, va_list ap) +{ + return __nldbl_vsscanf (string, fmt, ap); +} +extern __typeof (__vsscanf) vsscanf attribute_hidden; +weak_alias (__vsscanf, vsscanf) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vswprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vswprintf.c new file mode 100644 index 0000000000..ff3415a072 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vswprintf.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +weak_function +vswprintf (wchar_t *string, size_t maxlen, const wchar_t *fmt, va_list ap) +{ + return __nldbl_vswprintf (string, maxlen, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vswprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vswprintf_chk.c new file mode 100644 index 0000000000..0cd1f96bfe --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vswprintf_chk.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__vswprintf_chk (wchar_t *string, size_t maxlen, int flag, size_t slen, + const wchar_t *fmt, va_list ap) +{ + return __nldbl___vswprintf_chk (string, maxlen, flag, slen, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vswscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vswscanf.c new file mode 100644 index 0000000000..bd4bb5131b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vswscanf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +vswscanf (const wchar_t *string, const wchar_t *fmt, va_list ap) +{ + return __nldbl_vswscanf (string, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsyslog.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsyslog.c new file mode 100644 index 0000000000..eed1010eea --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsyslog.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +attribute_hidden +void +vsyslog (int pri, const char *fmt, va_list ap) +{ + __nldbl_vsyslog (pri, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsyslog_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsyslog_chk.c new file mode 100644 index 0000000000..2221474f97 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vsyslog_chk.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +void +attribute_hidden +__vsyslog_chk (int pri, int flag, const char *fmt, va_list ap) +{ + __nldbl___vsyslog_chk (pri, flag, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vwprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vwprintf.c new file mode 100644 index 0000000000..f46bdb3137 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vwprintf.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +vwprintf (const wchar_t *fmt, va_list ap) +{ + return __nldbl_vfwprintf (stdout, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vwprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vwprintf_chk.c new file mode 100644 index 0000000000..f7e7185977 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vwprintf_chk.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__vwprintf_chk (int flag, const wchar_t *fmt, va_list ap) +{ + return __nldbl___vfwprintf_chk (stdout, flag, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vwscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vwscanf.c new file mode 100644 index 0000000000..d39578ca4e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-vwscanf.c @@ -0,0 +1,9 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +weak_function +vwscanf (const wchar_t *fmt, va_list ap) +{ + return __nldbl_vfwscanf (stdin, fmt, ap); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wcstold.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wcstold.c new file mode 100644 index 0000000000..dbaffaa486 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wcstold.c @@ -0,0 +1,10 @@ +#define wcstold wcstold_XXX +#include "nldbl-compat.h" +#undef wcstold + +double +attribute_hidden +wcstold (const wchar_t *nptr, wchar_t **endptr) +{ + return wcstod (nptr, endptr); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wcstold_l.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wcstold_l.c new file mode 100644 index 0000000000..e32d13a94b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wcstold_l.c @@ -0,0 +1,14 @@ +#define wcstold_l wcstold_l_XXX +#define __wcstold_l __wcstold_l_XXX +#include "nldbl-compat.h" +#undef wcstold_l +#undef __wcstold_l + +double +attribute_hidden +__wcstold_l (const wchar_t *nptr, wchar_t **endptr, __locale_t loc) +{ + return __wcstod_l (nptr, endptr, loc); +} +extern __typeof (__wcstold_l) wcstold_l attribute_hidden; +weak_alias (__wcstold_l, wcstold_l) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wcstoldint.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wcstoldint.c new file mode 100644 index 0000000000..b638a399ad --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wcstoldint.c @@ -0,0 +1,10 @@ +#define __wcstold_internal __wcstold_internal_XXX +#include "nldbl-compat.h" +#undef __wcstold_internal + +double +attribute_hidden +__wcstold_internal (const wchar_t *nptr, wchar_t **endptr, int group) +{ + return __wcstod_internal (nptr, endptr, group); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wprintf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wprintf.c new file mode 100644 index 0000000000..2aa1a7475a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wprintf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +wprintf (const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfwprintf (stdout, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wprintf_chk.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wprintf_chk.c new file mode 100644 index 0000000000..39191e123b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wprintf_chk.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +__wprintf_chk (int flag, const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl___vfwprintf_chk (stdout, flag, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wscanf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wscanf.c new file mode 100644 index 0000000000..4ee3fdc15f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-wscanf.c @@ -0,0 +1,15 @@ +#include "nldbl-compat.h" + +int +attribute_hidden +wscanf (const wchar_t *fmt, ...) +{ + va_list arg; + int done; + + va_start (arg, fmt); + done = __nldbl_vfwscanf (stdin, fmt, arg); + va_end (arg); + + return done; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-y0.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-y0.c new file mode 100644 index 0000000000..e35621f60f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-y0.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +y0l (double x) +{ + return y0 (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-y1.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-y1.c new file mode 100644 index 0000000000..c47abcd3c5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-y1.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +y1l (double x) +{ + return y1 (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-yn.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-yn.c new file mode 100644 index 0000000000..7623d4513b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/nldbl-yn.c @@ -0,0 +1,8 @@ +#include "nldbl-compat.h" + +double +attribute_hidden +ynl (int n, double x) +{ + return yn (n, x); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_asinh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_asinh.c new file mode 100644 index 0000000000..e9bcfaea62 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_asinh.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_asinh.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __asinh, asinhl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_atan.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_atan.c new file mode 100644 index 0000000000..5fbd5e62d6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_atan.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_atan.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, atan, atanl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_cbrt.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_cbrt.c new file mode 100644 index 0000000000..cdc635771e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_cbrt.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_cbrt.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __cbrt, cbrtl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_ceil.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_ceil.c new file mode 100644 index 0000000000..6e4b70795d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_ceil.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_ceil.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __ceil, ceill, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_clog10l.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_clog10l.c new file mode 100644 index 0000000000..15dc3ed891 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_clog10l.c @@ -0,0 +1,31 @@ +/* clog10l alias overrides for platforms where long double + was previously not unique. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define M_DECL_FUNC(x) __clog10l_internal +#include <math-type-macros-ldouble.h> + +#undef declare_mgen_alias +#define declare_mgen_alias(from, to) + +#include <s_clog10_template.c> + +/* __clog10l is also a public symbol. */ +strong_alias (__clog10l_internal, __clog10l__internal) +long_double_symbol (libm, __clog10l_internal, __clog10l); +long_double_symbol (libm, __clog10l__internal, clog10l); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_copysign.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_copysign.c new file mode 100644 index 0000000000..f4303f5768 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_copysign.c @@ -0,0 +1,9 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_copysign.c> +#if IS_IN (libm) +# if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __copysign, copysignl, GLIBC_2_0); +# endif +#elif LONG_DOUBLE_COMPAT(libc, GLIBC_2_0) +compat_symbol (libc, __copysign, copysignl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_erf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_erf.c new file mode 100644 index 0000000000..76f1baa5ca --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_erf.c @@ -0,0 +1,6 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_erf.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __erf, erfl, GLIBC_2_0); +compat_symbol (libm, __erfc, erfcl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_expm1.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_expm1.c new file mode 100644 index 0000000000..ef9b5956db --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_expm1.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_expm1.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __expm1, expm1l, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_fabs.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_fabs.c new file mode 100644 index 0000000000..e7c92187e9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_fabs.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_fabs.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __fabs, fabsl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_finite.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_finite.c new file mode 100644 index 0000000000..7d3ab0068d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_finite.c @@ -0,0 +1,18 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_finite.c> +weak_alias (__finite, ___finite) +#if IS_IN (libm) +# if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __finite, __finitel, GLIBC_2_1); +# endif +# if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, ___finite, finitel, GLIBC_2_0); +# endif +#else +# if LONG_DOUBLE_COMPAT(libc, GLIBC_2_0) +compat_symbol (libm, __finite, __finitel, GLIBC_2_0); +# endif +# if LONG_DOUBLE_COMPAT(libc, GLIBC_2_0) +compat_symbol (libc, ___finite, finitel, GLIBC_2_0); +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_floor.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_floor.c new file mode 100644 index 0000000000..7797944e9e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_floor.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_floor.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __floor, floorl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_fma.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_fma.c new file mode 100644 index 0000000000..1723c5c306 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_fma.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_fma.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __fma, fmal, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_fmal.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_fmal.c new file mode 100644 index 0000000000..bd12dabcbe --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_fmal.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/s_fmal.c> +long_double_symbol (libm, __fmal, fmal); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_frexp.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_frexp.c new file mode 100644 index 0000000000..0e3a5e0830 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_frexp.c @@ -0,0 +1,9 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_frexp.c> +#if IS_IN (libm) +# if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __frexp, frexpl, GLIBC_2_0); +# endif +#elif LONG_DOUBLE_COMPAT(libc, GLIBC_2_0) +compat_symbol (libc, __frexp, frexpl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_isinf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_isinf.c new file mode 100644 index 0000000000..1f760a0320 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_isinf.c @@ -0,0 +1,8 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_isinf.c> +#if !IS_IN (libm) +# if LONG_DOUBLE_COMPAT(libc, GLIBC_2_0) +compat_symbol (libc, __isinf, __isinfl, GLIBC_2_0); +compat_symbol (libc, isinf, isinfl, GLIBC_2_0); +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_isnan.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_isnan.c new file mode 100644 index 0000000000..33f57f1955 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_isnan.c @@ -0,0 +1,8 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_isnan.c> +#if !IS_IN (libm) +# if LONG_DOUBLE_COMPAT(libc, GLIBC_2_0) +compat_symbol (libc, __isnan, __isnanl, GLIBC_2_0); +compat_symbol (libc, isnan, isnanl, GLIBC_2_0); +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_ldexp.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_ldexp.c new file mode 100644 index 0000000000..809080a149 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_ldexp.c @@ -0,0 +1,30 @@ +/* ldexp alias overrides for platforms where long double + was previously not unique. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define M_LIBM_NEED_COMPAT(f) 0 +#include <math-type-macros-double.h> +#include <s_ldexp_template.c> + +#if IS_IN (libm) +# if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __ldexp, ldexpl, GLIBC_2_0); +# endif +#elif LONG_DOUBLE_COMPAT(libc, GLIBC_2_0) +compat_symbol (libc, __ldexp, ldexpl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_ldexpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_ldexpl.c new file mode 100644 index 0000000000..85f34fa2c4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_ldexpl.c @@ -0,0 +1,31 @@ +/* ldexpl alias overrides for platforms where long double + was previously not unique. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define declare_mgen_alias(f,t) +#include <math-type-macros-ldouble.h> +#include <s_ldexp_template.c> + +strong_alias (__ldexpl, __ldexpl_2) +#if IS_IN (libm) +long_double_symbol (libm, __ldexpl, ldexpl); +long_double_symbol (libm, __ldexpl_2, scalbnl); +#else +long_double_symbol (libc, __ldexpl, ldexpl); +long_double_symbol (libc, __ldexpl_2, scalbnl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_llrint.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_llrint.c new file mode 100644 index 0000000000..e6311972e1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_llrint.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_llrint.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __llrint, llrintl, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_llround.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_llround.c new file mode 100644 index 0000000000..36c7e6edac --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_llround.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_llround.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __llround, llroundl, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_log1p.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_log1p.c new file mode 100644 index 0000000000..495fa32e35 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_log1p.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_log1p.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __log1p, log1pl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_logb.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_logb.c new file mode 100644 index 0000000000..4d7a6db275 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_logb.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_logb.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __logb, logbl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_lrint.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_lrint.c new file mode 100644 index 0000000000..b7af812846 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_lrint.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_lrint.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __lrint, lrintl, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_lround.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_lround.c new file mode 100644 index 0000000000..f3a27fa9c9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_lround.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_lround.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __lround, lroundl, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_modf.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_modf.c new file mode 100644 index 0000000000..93acb43ae6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_modf.c @@ -0,0 +1,9 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_modf.c> +#if IS_IN (libm) +# if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __modf, modfl, GLIBC_2_0); +# endif +#elif LONG_DOUBLE_COMPAT(libc, GLIBC_2_0) +compat_symbol (libc, __modf, modfl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_nearbyint.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_nearbyint.c new file mode 100644 index 0000000000..a8b7973acd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_nearbyint.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_nearbyint.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __nearbyint, nearbyintl, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_nextafter.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_nextafter.c new file mode 100644 index 0000000000..78e2c0ff37 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_nextafter.c @@ -0,0 +1,12 @@ +#include <math_ldbl_opt.h> +#include <math/s_nextafter.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __nextafter, nextafterl, GLIBC_2_0); +#endif +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +strong_alias (__nextafter, __nexttowardd) +strong_alias (__nextafter, __nexttowardld) +#undef nexttoward +compat_symbol (libm, __nexttowardd, nexttoward, GLIBC_2_1); +compat_symbol (libm, __nexttowardld, nexttowardl, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_nexttowardfd.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_nexttowardfd.c new file mode 100644 index 0000000000..07e9375b78 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_nexttowardfd.c @@ -0,0 +1,81 @@ +/* Single precision version of nexttoward.c. + Conversion to IEEE single float by Jakub Jelinek, jj@ultra.linux.cz. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* IEEE functions + * __nexttowardfd(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * This is for machines which use different binary type for double and + * long double conditionally, y is long double equal to double. + * Special cases: + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> +#include <float.h> + +float __nldbl_nexttowardf(float x, double y); + +float __nldbl_nexttowardf(float x, double y) +{ + int32_t hx,hy,ix,iy; + u_int32_t ly; + + GET_FLOAT_WORD(hx,x); + EXTRACT_WORDS(hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffff; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + ((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */ + return x+y; + if((double) x==y) return y; /* x=y, return y */ + if(ix==0) { /* x == 0 */ + float u; + SET_FLOAT_WORD(x,(u_int32_t)(hy&0x80000000)|1);/* return +-minsub*/ + u = math_opt_barrier (x); + u = u * u; + math_force_eval (u); /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if(x > y) /* x -= ulp */ + hx -= 1; + else /* x < y, x += ulp */ + hx += 1; + } else { /* x < 0 */ + if(x < y) /* x -= ulp */ + hx -= 1; + else /* x > y, x += ulp */ + hx += 1; + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) { + float u = x+x; /* overflow */ + math_force_eval (u); + __set_errno (ERANGE); + } + if(hy<0x00800000) { + float u = x*x; /* underflow */ + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + SET_FLOAT_WORD(x,hx); + return x; +} + +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __nldbl_nexttowardf, nexttowardf, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_remquo.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_remquo.c new file mode 100644 index 0000000000..9f3d7ba368 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_remquo.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_remquo.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __remquo, remquol, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_rint.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_rint.c new file mode 100644 index 0000000000..d9b156ea27 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_rint.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_rint.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __rint, rintl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_round.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_round.c new file mode 100644 index 0000000000..edff2f017b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_round.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_round.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __round, roundl, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_scalbln.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_scalbln.c new file mode 100644 index 0000000000..391142b769 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_scalbln.c @@ -0,0 +1,9 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_scalbln.c> +#if IS_IN (libm) +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __scalbln, scalblnl, GLIBC_2_1); +#endif +#elif LONG_DOUBLE_COMPAT(libc, GLIBC_2_1) +compat_symbol (libc, __scalbln, scalblnl, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_scalbn.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_scalbn.c new file mode 100644 index 0000000000..1ad81b199e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_scalbn.c @@ -0,0 +1,9 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_scalbn.c> +#if IS_IN (libm) +# if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __scalbn, scalbnl, GLIBC_2_0); +# endif +#elif LONG_DOUBLE_COMPAT(libc, GLIBC_2_0) +compat_symbol (libc, __scalbn, scalbnl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_significand.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_significand.c new file mode 100644 index 0000000000..5287c09066 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_significand.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/s_significand.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __significand, significandl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_significandl.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_significandl.c new file mode 100644 index 0000000000..9339b4780d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_significandl.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/s_significandl.c> +long_double_symbol (libm, __significandl, significandl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_sin.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_sin.c new file mode 100644 index 0000000000..6932ccc080 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_sin.c @@ -0,0 +1,15 @@ +/* dbl-64/s_sin.c uses NAN and sincos identifiers internally. */ +#define sincos sincos_disable +/* These definitions needed for proper unfolding of __MATHDECL_VEC. */ +#define __DECL_SIMD_sincos_disable +#define __DECL_SIMD_sincos_disablef +#define __DECL_SIMD_sincos_disablel +#define __DECL_SIMD_sincos_disablef128 +#include <math_ldbl_opt.h> +#undef NAN +#undef sincos +#include <sysdeps/ieee754/dbl-64/s_sin.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __sin, sinl, GLIBC_2_0); +compat_symbol (libm, __cos, cosl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_sincos.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_sincos.c new file mode 100644 index 0000000000..6d2a48f25b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_sincos.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_sincos.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __sincos, sincosl, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_tan.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_tan.c new file mode 100644 index 0000000000..6b0fec0063 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_tan.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_tan.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, tan, tanl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_tanh.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_tanh.c new file mode 100644 index 0000000000..e763bbde77 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_tanh.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_tanh.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __tanh, tanhl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_trunc.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_trunc.c new file mode 100644 index 0000000000..9d90a2bd73 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/s_trunc.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/s_trunc.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __trunc, truncl, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_acos_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_acos_compat.c new file mode 100644 index 0000000000..1e6d1b37ec --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_acos_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_acos_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __acos, acosl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_acosh_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_acosh_compat.c new file mode 100644 index 0000000000..40da339a7a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_acosh_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_acosh_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __acosh, acoshl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_acoshl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_acoshl_compat.c new file mode 100644 index 0000000000..df4338d9fa --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_acoshl_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_acoshl_compat.c> +long_double_symbol (libm, __acoshl, acoshl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_acosl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_acosl_compat.c new file mode 100644 index 0000000000..5efc99024c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_acosl_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_acosl_compat.c> +long_double_symbol (libm, __acosl, acosl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_asin_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_asin_compat.c new file mode 100644 index 0000000000..1c52cc22ad --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_asin_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_asin_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __asin, asinl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_asinl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_asinl_compat.c new file mode 100644 index 0000000000..087fab25bb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_asinl_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_asinl_compat.c> +long_double_symbol (libm, __asinl, asinl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_atan2_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_atan2_compat.c new file mode 100644 index 0000000000..d3f7964d7c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_atan2_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_atan2_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __atan2, atan2l, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_atan2l_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_atan2l_compat.c new file mode 100644 index 0000000000..6b12209625 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_atan2l_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_atan2l_compat.c> +long_double_symbol (libm, __atan2l, atan2l); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_atanh_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_atanh_compat.c new file mode 100644 index 0000000000..e15ef1f93d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_atanh_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_atanh_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __atanh, atanhl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_atanhl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_atanhl_compat.c new file mode 100644 index 0000000000..49bae1ee8f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_atanhl_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_atanhl_compat.c> +long_double_symbol (libm, __atanhl, atanhl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_cosh_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_cosh_compat.c new file mode 100644 index 0000000000..af29735e10 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_cosh_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_cosh_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __cosh, coshl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_coshl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_coshl_compat.c new file mode 100644 index 0000000000..a8808778ba --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_coshl_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_coshl_compat.c> +long_double_symbol (libm, __coshl, coshl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_exp10_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_exp10_compat.c new file mode 100644 index 0000000000..142a70bcd6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_exp10_compat.c @@ -0,0 +1,6 @@ +#include <math_ldbl_opt.h> +#include <math/w_exp10_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __exp10, exp10l, GLIBC_2_1); +compat_symbol (libm, __pow10, pow10l, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_exp10l_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_exp10l_compat.c new file mode 100644 index 0000000000..8f2ccd3441 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_exp10l_compat.c @@ -0,0 +1,6 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_exp10l_compat.c> +long_double_symbol (libm, __exp10l, exp10l); +long_double_symbol (libm, __pow10l, pow10l); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_exp_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_exp_compat.c new file mode 100644 index 0000000000..686c9c26d0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_exp_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <sysdeps/ieee754/dbl-64/w_exp_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __exp, expl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_fmod_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_fmod_compat.c new file mode 100644 index 0000000000..9280d39d70 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_fmod_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_fmod_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __fmod, fmodl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_fmodl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_fmodl_compat.c new file mode 100644 index 0000000000..88fe0ac4d2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_fmodl_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_fmodl_compat.c> +long_double_symbol (libm, __fmodl, fmodl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_hypot_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_hypot_compat.c new file mode 100644 index 0000000000..b3979ff0f4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_hypot_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_hypot_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __hypot, hypotl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_hypotl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_hypotl_compat.c new file mode 100644 index 0000000000..68e3997489 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_hypotl_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_hypotl_compat.c> +long_double_symbol (libm, __hypotl, hypotl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_j0_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_j0_compat.c new file mode 100644 index 0000000000..45b4d14764 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_j0_compat.c @@ -0,0 +1,6 @@ +#include <math_ldbl_opt.h> +#include <math/w_j0_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, j0, j0l, GLIBC_2_0); +compat_symbol (libm, y0, y0l, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_j0l_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_j0l_compat.c new file mode 100644 index 0000000000..9050657e03 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_j0l_compat.c @@ -0,0 +1,6 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_j0l_compat.c> +long_double_symbol (libm, __j0l, j0l); +long_double_symbol (libm, __y0l, y0l); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_j1_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_j1_compat.c new file mode 100644 index 0000000000..1071c8fd6a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_j1_compat.c @@ -0,0 +1,6 @@ +#include <math_ldbl_opt.h> +#include <math/w_j1_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, j1, j1l, GLIBC_2_0); +compat_symbol (libm, y1, y1l, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_j1l_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_j1l_compat.c new file mode 100644 index 0000000000..4ed9e2dd12 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_j1l_compat.c @@ -0,0 +1,6 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_j1l_compat.c> +long_double_symbol (libm, __j1l, j1l); +long_double_symbol (libm, __y1l, y1l); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_jn_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_jn_compat.c new file mode 100644 index 0000000000..be29a36041 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_jn_compat.c @@ -0,0 +1,6 @@ +#include <math_ldbl_opt.h> +#include <math/w_jn_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, jn, jnl, GLIBC_2_0); +compat_symbol (libm, yn, ynl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_jnl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_jnl_compat.c new file mode 100644 index 0000000000..d22ee54997 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_jnl_compat.c @@ -0,0 +1,6 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_jnl_compat.c> +long_double_symbol (libm, __jnl, jnl); +long_double_symbol (libm, __ynl, ynl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_lgamma_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_lgamma_compat.c new file mode 100644 index 0000000000..f268e65a88 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_lgamma_compat.c @@ -0,0 +1,7 @@ +#include <math_ldbl_opt.h> +#include <math/w_lgamma_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +strong_alias (__lgamma_compat, __lgammal_dbl_compat) +compat_symbol (libm, __lgammal_dbl_compat, lgammal, GLIBC_2_0); +compat_symbol (libm, __gamma, gammal, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_lgamma_compatl.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_lgamma_compatl.c new file mode 100644 index 0000000000..f60b3d7bcf --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_lgamma_compatl.c @@ -0,0 +1,11 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#define USE_AS_COMPAT 1 +#include <math/lgamma-compat.h> +#undef LGAMMA_OLD_VER +#define LGAMMA_OLD_VER LONG_DOUBLE_COMPAT_VERSION +#include <math/w_lgamma_compatl.c> +#if GAMMA_ALIAS +long_double_symbol (libm, __gammal, gammal); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_lgamma_r_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_lgamma_r_compat.c new file mode 100644 index 0000000000..673954cd1a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_lgamma_r_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_lgamma_r_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __lgamma_r, lgammal_r, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_lgammal_r_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_lgammal_r_compat.c new file mode 100644 index 0000000000..6fdf2bba87 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_lgammal_r_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_lgammal_r_compat.c> +long_double_symbol (libm, __lgammal_r, lgammal_r); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log10_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log10_compat.c new file mode 100644 index 0000000000..5ec6a2b2b6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log10_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_log10_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __log10, log10l, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log10l_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log10l_compat.c new file mode 100644 index 0000000000..17de3e7856 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log10l_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_log10l_compat.c> +long_double_symbol (libm, __log10l, log10l); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log2_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log2_compat.c new file mode 100644 index 0000000000..dffd2c183e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log2_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_log2_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __log2, log2l, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log2l_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log2l_compat.c new file mode 100644 index 0000000000..3c5e734573 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log2l_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_log2l_compat.c> +long_double_symbol (libm, __log2l, log2l); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log_compat.c new file mode 100644 index 0000000000..d2a2bcadde --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_log_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_log_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __log, logl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_logl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_logl_compat.c new file mode 100644 index 0000000000..2b55842139 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_logl_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_logl_compat.c> +long_double_symbol (libm, __logl, logl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_pow_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_pow_compat.c new file mode 100644 index 0000000000..c2a7942019 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_pow_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_pow_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __pow, powl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_powl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_powl_compat.c new file mode 100644 index 0000000000..1897cf1c63 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_powl_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_powl_compat.c> +long_double_symbol (libm, __powl, powl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_remainder_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_remainder_compat.c new file mode 100644 index 0000000000..c823dcb8e7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_remainder_compat.c @@ -0,0 +1,7 @@ +#include <math_ldbl_opt.h> +#include <math/w_remainder_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __remainder, remainderl, GLIBC_2_0); +strong_alias (__remainder, __drem) +compat_symbol (libm, __drem, dreml, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_remainderl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_remainderl_compat.c new file mode 100644 index 0000000000..b2ce5c9563 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_remainderl_compat.c @@ -0,0 +1,7 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_remainderl_compat.c> +long_double_symbol (libm, __remainderl, remainderl); +strong_alias (__remainderl, __dreml) +long_double_symbol (libm, __dreml, dreml); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_scalb_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_scalb_compat.c new file mode 100644 index 0000000000..f6d53a5ba5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_scalb_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_scalb_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __scalb, scalbl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_scalbl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_scalbl_compat.c new file mode 100644 index 0000000000..c8feb654a2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_scalbl_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_scalbl_compat.c> +long_double_symbol (libm, __scalbl, scalbl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_sinh_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_sinh_compat.c new file mode 100644 index 0000000000..b47182c017 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_sinh_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_sinh_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __sinh, sinhl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_sinhl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_sinhl_compat.c new file mode 100644 index 0000000000..305ed82357 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_sinhl_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_sinhl_compat.c> +long_double_symbol (libm, __sinhl, sinhl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_sqrt_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_sqrt_compat.c new file mode 100644 index 0000000000..355d1c20db --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_sqrt_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_sqrt_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0) +compat_symbol (libm, __sqrt, sqrtl, GLIBC_2_0); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_sqrtl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_sqrtl_compat.c new file mode 100644 index 0000000000..1e4526f2c6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_sqrtl_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_sqrtl_compat.c> +long_double_symbol (libm, __sqrtl, sqrtl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_tgamma_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_tgamma_compat.c new file mode 100644 index 0000000000..082ce8aaff --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_tgamma_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#include <math/w_tgamma_compat.c> +#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1) +compat_symbol (libm, __tgamma, tgammal, GLIBC_2_1); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_tgammal_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_tgammal_compat.c new file mode 100644 index 0000000000..aaf5403522 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-opt/w_tgammal_compat.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <math/w_tgammal_compat.c> +long_double_symbol (libm, __tgammal, tgammal); diff --git a/REORG.TODO/sysdeps/ieee754/s_lib_version.c b/REORG.TODO/sysdeps/ieee754/s_lib_version.c new file mode 100644 index 0000000000..bb59300953 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/s_lib_version.c @@ -0,0 +1,41 @@ +/* @(#)s_lib_ver.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_lib_version.c,v 1.6 1995/05/10 20:47:44 jtc Exp $"; +#endif + +/* + * MACRO for standards + */ + +#include <math.h> +#include <math_private.h> + +/* + * define and initialize _LIB_VERSION + */ +#ifdef _POSIX_MODE +_LIB_VERSION_TYPE _LIB_VERSION_INTERNAL = _POSIX_; +#else +#ifdef _XOPEN_MODE +_LIB_VERSION_TYPE _LIB_VERSION_INTERNAL = _XOPEN_; +#else +#ifdef _SVID3_MODE +_LIB_VERSION_TYPE _LIB_VERSION_INTERNAL = _SVID_; +#else /* default _IEEE_MODE */ +_LIB_VERSION_TYPE _LIB_VERSION_INTERNAL = _IEEE_; +#endif +#endif +#endif + +weak_alias (_LIB_VERSION_INTERNAL, _LIB_VERSION) diff --git a/REORG.TODO/sysdeps/ieee754/s_matherr.c b/REORG.TODO/sysdeps/ieee754/s_matherr.c new file mode 100644 index 0000000000..d5dc6f122d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/s_matherr.c @@ -0,0 +1,28 @@ +/* @(#)s_matherr.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_matherr.c,v 1.6 1995/05/10 20:47:53 jtc Exp $"; +#endif + +#include <math.h> +#include <math_private.h> + +int +weak_function +__matherr(struct exception *x) +{ + int n=0; + if(x->arg1!=x->arg1) return 0; + return n; +} +weak_alias (__matherr, matherr) diff --git a/REORG.TODO/sysdeps/ieee754/s_signgam.c b/REORG.TODO/sysdeps/ieee754/s_signgam.c new file mode 100644 index 0000000000..9af3a75f1e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/s_signgam.c @@ -0,0 +1,4 @@ +#include <math.h> +#include <math_private.h> +int __signgam = 0; +weak_alias (__signgam, signgam) |