diff options
| author | Ulrich Drepper <drepper@redhat.com> | 2001-03-12 00:04:52 +0000 |
|---|---|---|
| committer | Ulrich Drepper <drepper@redhat.com> | 2001-03-12 00:04:52 +0000 |
| commit | e4d8276142b9c07b23043ef44b0fe8fa7bcc3121 (patch) | |
| tree | f153a80b6ce0fdd3261ff18a16fd80bd965231c3 /sysdeps/ieee754/dbl-64 | |
| parent | d3c8723f6415af59a6ec14fcb918ad0e4d1fb588 (diff) | |
| download | glibc-e4d8276142b9c07b23043ef44b0fe8fa7bcc3121.tar.gz glibc-e4d8276142b9c07b23043ef44b0fe8fa7bcc3121.tar.xz glibc-e4d8276142b9c07b23043ef44b0fe8fa7bcc3121.zip | |
Update.
2001-03-11 Ulrich Drepper <drepper@redhat.com> Last-bit accurate math library implementation by IBM Haifa. Contributed by Abraham Ziv <ziv@il.ibm.com>, Moshe Olshansky <olshansk@il.ibm.com>, Ealan Henis <ealan@il.ibm.com>, and Anna Reitman <reitman@il.ibm.com>. * math/Makefile (dbl-only-routines): New variable. (libm-routines): Add $(dbl-only-routines). * sysdeps/ieee754/dbl-64/e_acos.c: Empty, definition is in e_asin.c. * sysdeps/ieee754/dbl-64/e_asin.c: Replaced with accurate asin implementation. * sysdeps/ieee754/dbl-64/e_atan2.c: Replaced with accurate atan2 implementation. * sysdeps/ieee754/dbl-64/e_exp.c: Replaced with accurate exp implementation. * sysdeps/ieee754/dbl-64/e_lgamma_r.c: Don't use __kernel_sin and __kernel_cos. * sysdeps/ieee754/dbl-64/e_log.c: Replaced with accurate log implementation. * sysdeps/ieee754/dbl-64/e_remainder.c: Replaced with accurate remainder implementation. * sysdeps/ieee754/dbl-64/e_pow.c: Replaced with accurate pow implementation. * sysdeps/ieee754/dbl-64/e_sqrt.c: Replaced with accurate sqrt implementation. * sysdeps/ieee754/dbl-64/k_cos.c: Empty, definition is in s_sin.c. * sysdeps/ieee754/dbl-64/k_sin.c: Empty, definition is in s_sin.c. * sysdeps/ieee754/dbl-64/s_atan.c: Replaced with accurate atan implementation. * sysdeps/ieee754/dbl-64/s_cos.c: Empty, definition is in s_sin.c. * sysdeps/ieee754/dbl-64/s_sin.c: Replaced with accurate sin/cos implementation. * sysdeps/ieee754/dbl-64/s_sincos.c: Rewritten to not use __kernel_sin and __kernel_cos. * sysdeps/ieee754/dbl-64/s_tan.c: Replaced with accurate tan implementation. * sysdeps/ieee754/dbl-64/Dist: Add new non-code files. * sysdeps/ieee754/dbl-64/MathLib.h: New file. * sysdeps/ieee754/dbl-64/asincos.tbl: New file. * sysdeps/ieee754/dbl-64/atnat.h: New file. * sysdeps/ieee754/dbl-64/atnat2.h: New file. * sysdeps/ieee754/dbl-64/branred.c: New file. * sysdeps/ieee754/dbl-64/branred.h: New file. * sysdeps/ieee754/dbl-64/dla.h: New file. * sysdeps/ieee754/dbl-64/doasin.c: New file. * sysdeps/ieee754/dbl-64/doasin.h: New file. * sysdeps/ieee754/dbl-64/dosincos.c: New file. * sysdeps/ieee754/dbl-64/dosincos.h: New file. * sysdeps/ieee754/dbl-64/endian.h: New file. * sysdeps/ieee754/dbl-64/halfulp.c: New file. * sysdeps/ieee754/dbl-64/mpa.c: New file. * sysdeps/ieee754/dbl-64/mpa.h: New file. * sysdeps/ieee754/dbl-64/mpa2.h: New file. * sysdeps/ieee754/dbl-64/mpatan.c: New file. * sysdeps/ieee754/dbl-64/mpatan.h: New file. * sysdeps/ieee754/dbl-64/mpatan2.c: New file. * sysdeps/ieee754/dbl-64/mpexp.c: New file. * sysdeps/ieee754/dbl-64/mpexp.h: New file. * sysdeps/ieee754/dbl-64/mplog.c: New file. * sysdeps/ieee754/dbl-64/mplog.h: New file. * sysdeps/ieee754/dbl-64/mpsqrt.c: New file. * sysdeps/ieee754/dbl-64/mpsqrt.h: New file. * sysdeps/ieee754/dbl-64/mptan.c: New file. * sysdeps/ieee754/dbl-64/mydefs.h: New file. * sysdeps/ieee754/dbl-64/powtwo.tbl: New file. * sysdeps/ieee754/dbl-64/root.tbl: New file. * sysdeps/ieee754/dbl-64/sincos.tbl: New file. * sysdeps/ieee754/dbl-64/sincos32.c: New file. * sysdeps/ieee754/dbl-64/sincos32.h: New file. * sysdeps/ieee754/dbl-64/slowexp.c: New file. * sysdeps/ieee754/dbl-64/slowpow.c: New file. * sysdeps/ieee754/dbl-64/uasncs.h: New file. * sysdeps/ieee754/dbl-64/uatan.tbl: New file. * sysdeps/ieee754/dbl-64/uexp.h: New file. * sysdeps/ieee754/dbl-64/uexp.tbl: New file. * sysdeps/ieee754/dbl-64/ulog.h: New file. * sysdeps/ieee754/dbl-64/ulog.tbl: New file. * sysdeps/ieee754/dbl-64/upow.h: New file. * sysdeps/ieee754/dbl-64/upow.tbl: New file. * sysdeps/ieee754/dbl-64/urem.h: New file. * sysdeps/ieee754/dbl-64/uroot.h: New file. * sysdeps/ieee754/dbl-64/usncs.h: New file. * sysdeps/ieee754/dbl-64/utan.h: New file. * sysdeps/ieee754/dbl-64/utan.tbl: New file. * sysdeps/i386/fpu/branred.c: New file. * sysdeps/i386/fpu/doasin.c: New file. * sysdeps/i386/fpu/dosincos.c: New file. * sysdeps/i386/fpu/halfulp.c: New file. * sysdeps/i386/fpu/mpa.c: New file. * sysdeps/i386/fpu/mpatan.c: New file. * sysdeps/i386/fpu/mpatan2.c: New file. * sysdeps/i386/fpu/mpexp.c: New file. * sysdeps/i386/fpu/mplog.c: New file. * sysdeps/i386/fpu/mpsqrt.c: New file. * sysdeps/i386/fpu/mptan.c: New file. * sysdeps/i386/fpu/sincos32.c: New file. * sysdeps/i386/fpu/slowexp.c: New file. * sysdeps/i386/fpu/slowpow.c: New file. * sysdeps/ia64/fpu/branred.c: New file. * sysdeps/ia64/fpu/doasin.c: New file. * sysdeps/ia64/fpu/dosincos.c: New file. * sysdeps/ia64/fpu/halfulp.c: New file. * sysdeps/ia64/fpu/mpa.c: New file. * sysdeps/ia64/fpu/mpatan.c: New file. * sysdeps/ia64/fpu/mpatan2.c: New file. * sysdeps/ia64/fpu/mpexp.c: New file. * sysdeps/ia64/fpu/mplog.c: New file. * sysdeps/ia64/fpu/mpsqrt.c: New file. * sysdeps/ia64/fpu/mptan.c: New file. * sysdeps/ia64/fpu/sincos32.c: New file. * sysdeps/ia64/fpu/slowexp.c: New file. * sysdeps/ia64/fpu/slowpow.c: New file. * sysdeps/m68k/fpu/branred.c: New file. * sysdeps/m68k/fpu/doasin.c: New file. * sysdeps/m68k/fpu/dosincos.c: New file. * sysdeps/m68k/fpu/halfulp.c: New file. * sysdeps/m68k/fpu/mpa.c: New file. * sysdeps/m68k/fpu/mpatan.c: New file. * sysdeps/m68k/fpu/mpatan2.c: New file. * sysdeps/m68k/fpu/mpexp.c: New file. * sysdeps/m68k/fpu/mplog.c: New file. * sysdeps/m68k/fpu/mpsqrt.c: New file. * sysdeps/m68k/fpu/mptan.c: New file. * sysdeps/m68k/fpu/sincos32.c: New file. * sysdeps/m68k/fpu/slowexp.c: New file. * sysdeps/m68k/fpu/slowpow.c: New file. * iconvdata/gconv-modules: Add a number of alias, mostly for IBM codepages.
Diffstat (limited to 'sysdeps/ieee754/dbl-64')
64 files changed, 42109 insertions, 2186 deletions
diff --git a/sysdeps/ieee754/dbl-64/Dist b/sysdeps/ieee754/dbl-64/Dist index 1bb7be3537..4e1cb25f59 100644 --- a/sysdeps/ieee754/dbl-64/Dist +++ b/sysdeps/ieee754/dbl-64/Dist @@ -1 +1,34 @@ +asincos.tbl +atnat.h +atnat2.h +branred.h +dla.h +doasin.h +dosincos.h +endian.h +MathLib.h +mpa.h +mpa2.h +mpatan.h +mpexp.h +mplog.h +mpsqrt.h +mydefs.h +powtwo.tbl +root.tbl +sincos.tbl +sincos32.h t_exp2.h +uasncs.h +uatan.tbl +uexp.h +uexp.tbl +ulog.h +ulog.tbl +upow.h +upow.tbl +urem.h +uroot.h +usncs.h +utan.h +utan.tbl diff --git a/sysdeps/ieee754/dbl-64/MathLib.h b/sysdeps/ieee754/dbl-64/MathLib.h new file mode 100644 index 0000000000..40a2944fa2 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/MathLib.h @@ -0,0 +1,102 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation; either version 2 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 General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/********************************************************************/ +/* 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(); + +/********************************************************************/ +/* 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/sysdeps/ieee754/dbl-64/asincos.tbl b/sysdeps/ieee754/dbl-64/asincos.tbl new file mode 100644 index 0000000000..ffae0bc288 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/asincos.tbl @@ -0,0 +1,5149 @@ +/***************************************************************************/ +/* Table for arcsin() and arccos() FUNCTIONS */ +/***************************************************************************/ + +#ifdef BIG_ENDI +static const union {int4 i[5136];double x[2568];} asncs = { +/**/ 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, +/**/ 0x3FBBD95A, 0x160F3472, +/**/ 0x3FB26708, 0x39844810, +/**/ 0x3C994228, 0x698BC8EA, +/**/ 0x3FC6DF1B, 0x6D8C14A0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F422819, 0x754477AC, +/**/ 0x3FC74000, 0x00000000, +/**/ 0x3FF0454A, 0x285A8CEB, +/**/ 0x3FB87332, 0xC21B9224, +/**/ 0x3FC8BB10, 0x92A93402, +/**/ 0x3FB40A9F, 0x3ED3F586, +/**/ 0x3FBC499F, 0x643217C8, +/**/ 0x3FB3061A, 0x5D29A16B, +/**/ 0xBCA3B2DF, 0x3DF9F2D7, +/**/ 0x3FC76139, 0x9DE6A160, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F5528A1, 0x6A33AB4B, +/**/ 0x3FC7C000, 0x00000000, +/**/ 0x3FF04861, 0xD9E48D58, +/**/ 0x3FB9080E, 0x81461BF6, +/**/ 0x3FC8E3B4, 0x00E32FFA, +/**/ 0x3FB4992F, 0xAFB1F2A5, +/**/ 0x3FBCBDAB, 0xF33705D5, +/**/ 0x3FB3A97A, 0x7E23EE89, +/**/ 0x3C7AAD12, 0xCCE44C41, +/**/ 0x3FC7E370, 0x4187FAE0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F60C3B3, 0xC91AAF11, +/**/ 0x3FC84000, 0x00000000, +/**/ 0x3FF04B8C, 0x36478509, +/**/ 0x3FB99DE1, 0x70FAC1B4, +/**/ 0x3FC90D76, 0xDAA92166, +/**/ 0x3FB52A0E, 0x06C416A6, +/**/ 0x3FBD359A, 0x1CDCA344, +/**/ 0x3FB45155, 0x7EFD4CA0, +/**/ 0x3C396CA5, 0x35A8895D, +/**/ 0x3FC865BF, 0xED4C6EF0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F67186C, 0x8F0A11A4, +/**/ 0x3FC8C000, 0x00000000, +/**/ 0x3FF04EC9, 0x5CD5E248, +/**/ 0x3FBA34B2, 0x5BB94403, +/**/ 0x3FC9385D, 0xCF5CA73A, +/**/ 0x3FB5BD4D, 0xF01AFDBE, +/**/ 0x3FBDB185, 0x4D61A7A9, +/**/ 0x3FB4FDDA, 0x00BD47CF, +/**/ 0xBC9D1119, 0x727E8B64, +/**/ 0x3FC8E829, 0x37077E20, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F6D92B9, 0xABC490CB, +/**/ 0x3FC94000, 0x00000000, +/**/ 0x3FF05219, 0x6DBD2A10, +/**/ 0x3FBACC88, 0x2894CAA1, +/**/ 0x3FC9646D, 0xB6427516, +/**/ 0x3FB65303, 0xA3A864D7, +/**/ 0x3FBE318A, 0x0E3CF3D4, +/**/ 0x3FB5AF38, 0x78CDA678, +/**/ 0x3CA3841D, 0xDA9D51DF, +/**/ 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0x3FECD000, 0x00000000, +/**/ 0x40026327, 0x6B3395AA, +/**/ 0x4015DD66, 0x33FB1467, +/**/ 0x403C0610, 0xDCF3437C, +/**/ 0x406607CE, 0xC9D7C47A, +/**/ 0x409360FB, 0xA330DC5C, +/**/ 0x40C240B4, 0x38A3194B, +/**/ 0x40F20437, 0xBAA6A879, +/**/ 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 = { +/**/ 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, +/**/ 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0x5376CB61, 0xBCA34428, +/**/ 0x236FE314, 0x3FF182D4, +/**/ 0x00000000, 0x40018000, +/**/ 0xE15169A9, 0xBF7B5F40, +/**/ 0x00000000, 0x3FEC9000, +/**/ 0x91B4C8D8, 0x4001BE19, +/**/ 0xBE69BAE6, 0x4013795B, +/**/ 0xCD6F8B02, 0x40373151, +/**/ 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/sysdeps/ieee754/dbl-64/atnat.h b/sysdeps/ieee754/dbl-64/atnat.h new file mode 100644 index 0000000000..7ddf235f03 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/atnat.h @@ -0,0 +1,166 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/************************************************************************/ +/* 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 */ +/**/ zero = {0x00000000, 0x00000000, }, /* 0 */ +/**/ one = {0x3ff00000, 0x00000000, }, /* 1 */ +/**/ 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 */ +/**/ two8 = {0x40700000, 0x00000000, }, /* 2**8=256 */ +/**/ two52 = {0x43300000, 0x00000000, }; /* 2**52 */ + +#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 */ +/**/ zero = {0x00000000, 0x00000000, }, /* 0 */ +/**/ one = {0x00000000, 0x3ff00000, }, /* 1 */ +/**/ 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 */ +/**/ two8 = {0x00000000, 0x40700000, }, /* 2**8=256 */ +/**/ two52 = {0x00000000, 0x43300000, }; /* 2**52 */ + +#endif +#endif + +#define ZERO zero.d +#define ONE one.d +#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 +#define TWO8 two8.d +#define TWO52 two52.d + +#endif diff --git a/sysdeps/ieee754/dbl-64/atnat2.h b/sysdeps/ieee754/dbl-64/atnat2.h new file mode 100644 index 0000000000..967bbc30b9 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/atnat2.h @@ -0,0 +1,183 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/************************************************************************/ +/* 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 */ +/**/ zero = {0x00000000, 0x00000000, }, /* 0 */ +/**/ mzero = {0x80000000, 0x00000000, }, /* -0 */ +/**/ one = {0x3ff00000, 0x00000000, }, /* 1 */ +/**/ 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 */ +/**/ qpi1 = {0x3c81a626, 0x33145c07, }, /* pi/4-qpi */ +/**/ mqpi = {0xbfe921fb, 0x54442d18, }, /* -pi/4 */ +/**/ tqpi = {0x4002d97c, 0x7f3321d2, }, /* 3pi/4 */ +/**/ tqpi1 = {0x3c9a7939, 0x4c9e8a0a, }, /* 3pi/4-tqpi */ +/**/ 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 */ +/**/ two8 = {0x40700000, 0x00000000, }, /* 2**8=256 */ +/**/ two52 = {0x43300000, 0x00000000, }, /* 2**52 */ +/**/ two500 = {0x5f300000, 0x00000000, }, /* 2**500 */ +/**/ twom500 = {0x20b00000, 0x00000000, }, /* 2**(-500) */ +/**/ twom1022 = {0x00100000, 0x00000000, }; /* 2**(-1022) */ + +#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 */ +/**/ zero = {0x00000000, 0x00000000, }, /* 0 */ +/**/ mzero = {0x00000000, 0x80000000, }, /* -0 */ +/**/ one = {0x00000000, 0x3ff00000, }, /* 1 */ +/**/ 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 */ +/**/ qpi1 = {0x33145c07, 0x3c81a626, }, /* pi/4-qpi */ +/**/ mqpi = {0x54442d18, 0xbfe921fb, }, /* -pi/4 */ +/**/ tqpi = {0x7f3321d2, 0x4002d97c, }, /* 3pi/4 */ +/**/ tqpi1 = {0x4c9e8a0a, 0x3c9a7939, }, /* 3pi/4-tqpi */ +/**/ 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 */ +/**/ two8 = {0x00000000, 0x40700000, }, /* 2**8=256 */ +/**/ two52 = {0x00000000, 0x43300000, }, /* 2**52 */ +/**/ two500 = {0x00000000, 0x5f300000, }, /* 2**500 */ +/**/ twom500 = {0x00000000, 0x20b00000, }, /* 2**(-500) */ +/**/ twom1022 = {0x00000000, 0x00100000, }; /* 2**(-1022) */ + +#endif +#endif + +#define ZERO zero.d +#define MZERO mzero.d +#define ONE one.d +#define TWO8 two8.d +#define TWO52 two52.d +#define TWOM1022 twom1022.d + +#endif diff --git a/sysdeps/ieee754/dbl-64/branred.c b/sysdeps/ieee754/dbl-64/branred.c new file mode 100644 index 0000000000..09b55602bf --- /dev/null +++ b/sysdeps/ieee754/dbl-64/branred.c @@ -0,0 +1,139 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/*******************************************************************/ +/* */ +/* 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" + + + +/*******************************************************************/ +/* 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 branred(double x, double *a, double *aa) +{ + int i,k,n; + mynumber u,v,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 = (ABS(b1)>ABS(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/sysdeps/ieee754/dbl-64/branred.h b/sysdeps/ieee754/dbl-64/branred.h new file mode 100644 index 0000000000..2258e58eb1 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/branred.h @@ -0,0 +1,80 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/************************************************************************/ +/* MODULE_NAME: branred.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + +#ifndef BRANRED_H +#define BRANRED_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 = 134217729.0; + +#endif diff --git a/sysdeps/ieee754/dbl-64/dla.h b/sysdeps/ieee754/dbl-64/dla.h new file mode 100644 index 0000000000..693d1a1f79 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/dla.h @@ -0,0 +1,173 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/***********************************************************************/ +/*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 */ +#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=(ABS(x)>ABS(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=(ABS(x)>ABS(y)) ? (((x)-(z))-(y)) : ((x)-((y)+(z))); + + +/* 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. */ + +#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; + + +/* 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. */ + +#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; + + +/* 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=(ABS(x)>ABS(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=(ABS(x)>ABS(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 (ABS(x)>ABS(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=(ABS(xx)>ABS(yy)) ? (((xx)-s)+(yy)) : (((yy)-s)+(xx)); \ + u=r+s; \ + uu=(ABS(r)>ABS(s)) ? ((r-u)+s) : ((s-u)+r) ; \ + w=uu+ss; z=u+w; \ + zz=(ABS(u)>ABS(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 (ABS(x)>ABS(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=(ABS(xx)>ABS(yy)) ? (((xx)-s)-(yy)) : ((xx)-((yy)+s)); \ + u=r+s; \ + uu=(ABS(r)>ABS(s)) ? ((r-u)+s) : ((s-u)+r) ; \ + w=uu+ss; z=u+w; \ + zz=(ABS(u)>ABS(w)) ? ((u-z)+w) : ((w-z)+u) ; } + + + + + + + diff --git a/sysdeps/ieee754/dbl-64/doasin.c b/sysdeps/ieee754/dbl-64/doasin.c new file mode 100644 index 0000000000..4ea108b9d7 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/doasin.c @@ -0,0 +1,81 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/**********************************************************************/ +/* 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" + +/********************************************************************/ +/* 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 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 hx,tx,hy,ty,tp,tq,tc,tcc; + + +/* 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/sysdeps/ieee754/dbl-64/doasin.h b/sysdeps/ieee754/dbl-64/doasin.h new file mode 100644 index 0000000000..01f44e0adb --- /dev/null +++ b/sysdeps/ieee754/dbl-64/doasin.h @@ -0,0 +1,62 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/************************************************************************/ +/* 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/sysdeps/ieee754/dbl-64/dosincos.c b/sysdeps/ieee754/dbl-64/dosincos.c new file mode 100644 index 0000000000..2a5f8fcc34 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/dosincos.c @@ -0,0 +1,181 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/********************************************************************/ +/* */ +/* 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 "sincos.tbl" +#include "dla.h" +#include "dosincos.h" +/***********************************************************************/ +/* 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 dubsin(double x, double dx, double v[]) { + double xx,y,yy,z,zz,r,s,p,hx,tx,hy,ty,q,c,cc,d,dd,d2,dd2,e,ee, + sn,ssn,cs,ccs,ds,dss,dc,dcc; + 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=sincos.x[k]; /* */ + ssn=sincos.x[k+1]; /* sin(Xi) and cos(Xi) */ + cs=sincos.x[k+2]; /* */ + ccs=sincos.x[k+3]; /* */ + MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc); /* Taylor */ + 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); /* series */ + 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); /* for sin */ + MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); + ADD2(ds,dss,d,dd,ds,dss,r,s); /* ds=sin(t) */ + + MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc); ;/* Taylor */ + 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); /* series */ + 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); /* for cos */ + 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); /* dc=cos(t) */ + + 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 dubcos(double x, double dx, double v[]) { + double xx,y,yy,z,zz,r,s,p,hx,tx,hy,ty,q,c,cc,d,dd,d2,dd2,e,ee, + sn,ssn,cs,ccs,ds,dss,dc,dcc; + 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=sincos.x[k]; /* */ + ssn=sincos.x[k+1]; /* sin(Xi) and cos(Xi) */ + cs=sincos.x[k+2]; /* */ + ccs=sincos.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 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/sysdeps/ieee754/dbl-64/dosincos.h b/sysdeps/ieee754/dbl-64/dosincos.h new file mode 100644 index 0000000000..20f4ede78c --- /dev/null +++ b/sysdeps/ieee754/dbl-64/dosincos.h @@ -0,0 +1,79 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/************************************************************************/ +/* 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/sysdeps/ieee754/dbl-64/e_acos.c b/sysdeps/ieee754/dbl-64/e_acos.c index eb4080a8b8..8f7cd89249 100644 --- a/sysdeps/ieee754/dbl-64/e_acos.c +++ b/sysdeps/ieee754/dbl-64/e_acos.c @@ -1,144 +1 @@ -/* @(#)e_acos.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: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $"; -#endif - -/* __ieee754_acos(x) - * Method : - * acos(x) = pi/2 - asin(x) - * acos(-x) = pi/2 + asin(x) - * For |x|<=0.5 - * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) - * For x>0.5 - * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) - * = 2asin(sqrt((1-x)/2)) - * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) - * = 2f + (2c + 2s*z*R(z)) - * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term - * for f so that f+c ~ sqrt(z). - * For x<-0.5 - * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) - * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) - * - * Special cases: - * if x is NaN, return x itself; - * if |x|>1, return NaN with invalid signal. - * - * Function needed: __ieee754_sqrt - */ - -#include "math.h" -#include "math_private.h" -#define one qS[0] - -#ifdef __STDC__ -static const double -#else -static double -#endif -pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ -pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ -pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ -pS[] = {1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ - -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ - 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ - -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ - 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ - 3.47933107596021167570e-05}, /* 0x3F023DE1, 0x0DFDF709 */ -qS[] ={1.0, -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ - 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ - -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ - 7.70381505559019352791e-02}; /* 0x3FB3B8C5, 0xB12E9282 */ - -#ifdef __STDC__ - double __ieee754_acos(double x) -#else - double __ieee754_acos(x) - double x; -#endif -{ - double z,p,q,r,w,s,c,df,p1,p2,p3,q1,q2,z2,z4,z6; - int32_t hx,ix; - GET_HIGH_WORD(hx,x); - ix = hx&0x7fffffff; - if(ix>=0x3ff00000) { /* |x| >= 1 */ - u_int32_t lx; - GET_LOW_WORD(lx,x); - if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ - if(hx>0) return 0.0; /* acos(1) = 0 */ - else return pi+2.0*pio2_lo; /* acos(-1)= pi */ - } - return (x-x)/(x-x); /* acos(|x|>1) is NaN */ - } - if(ix<0x3fe00000) { /* |x| < 0.5 */ - if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ - z = x*x; -#ifdef DO_NOT_USE_THIS - p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); - q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); -#else - p1 = z*pS[0]; z2=z*z; - p2 = pS[1]+z*pS[2]; z4=z2*z2; - p3 = pS[3]+z*pS[4]; z6=z4*z2; - q1 = one+z*qS[1]; - q2 = qS[2]+z*qS[3]; - p = p1 + z2*p2 + z4*p3 + z6*pS[5]; - q = q1 + z2*q2 + z4*qS[4]; -#endif - r = p/q; - return pio2_hi - (x - (pio2_lo-x*r)); - } else if (hx<0) { /* x < -0.5 */ - z = (one+x)*0.5; -#ifdef DO_NOT_USE_THIS - p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); - q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); -#else - p1 = z*pS[0]; z2=z*z; - p2 = pS[1]+z*pS[2]; z4=z2*z2; - p3 = pS[3]+z*pS[4]; z6=z4*z2; - q1 = one+z*qS[1]; - q2 = qS[2]+z*qS[3]; - p = p1 + z2*p2 + z4*p3 + z6*pS[5]; - q = q1 + z2*q2 + z4*qS[4]; -#endif - s = __ieee754_sqrt(z); - r = p/q; - w = r*s-pio2_lo; - return pi - 2.0*(s+w); - } else { /* x > 0.5 */ - z = (one-x)*0.5; - s = __ieee754_sqrt(z); - df = s; - SET_LOW_WORD(df,0); - c = (z-df*df)/(s+df); -#ifdef DO_NOT_USE_THIS - p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); - q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); -#else - p1 = z*pS[0]; z2=z*z; - p2 = pS[1]+z*pS[2]; z4=z2*z2; - p3 = pS[3]+z*pS[4]; z6=z4*z2; - q1 = one+z*qS[1]; - q2 = qS[2]+z*qS[3]; - p = p1 + z2*p2 + z4*p3 + z6*pS[5]; - q = q1 + z2*q2 + z4*qS[4]; -#endif - r = p/q; - w = r*s+c; - return 2.0*(df+w); - } -} +/* In e_asin.c */ diff --git a/sysdeps/ieee754/dbl-64/e_asin.c b/sysdeps/ieee754/dbl-64/e_asin.c index aa19598848..2096de2297 100644 --- a/sysdeps/ieee754/dbl-64/e_asin.c +++ b/sysdeps/ieee754/dbl-64/e_asin.c @@ -1,143 +1,623 @@ -/* @(#)e_asin.c 5.1 93/09/24 */ /* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 * - * 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: e_asin.c,v 1.9 1995/05/12 04:57:22 jtc Exp $"; -#endif - -/* __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) - * where - * R(x^2) is a rational approximation of (asin(x)-x)/x^3 - * and its remez error is bounded by - * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) + * 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 of the License, or + * (at your option) any later version. * - * 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. + * 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ +/******************************************************************/ +/* 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" + +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 __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,nn; + u.x = x; + m = u.i[HIGH_HALF]; + k = 0x7fffffff&m; /* no sign */ -#include "math.h" -#include "math_private.h" -#define one qS[0] -#ifdef __STDC__ -static const double -#else -static double -#endif -huge = 1.000e+300, -pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ -pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ -pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ - /* coefficient for R(x^2) */ -pS[] = {1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ - -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ - 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ - -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ - 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ - 3.47933107596021167570e-05}, /* 0x3F023DE1, 0x0DFDF709 */ -qS[] = {1.0, -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ - 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ - -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ - 7.70381505559019352791e-02}; /* 0x3FB3B8C5, 0xB12E9282 */ + if (k < 0x3e500000) 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=ABS(x); + res=ABS(w[0]); + res1=ABS(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]-ABS(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=ABS(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]-ABS(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=ABS(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]-ABS(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=ABS(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]-ABS(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=ABS(x); + return (m>0)?sin32(y,res,res1):-sin32(y,res,res1); + } + } + } + } /* else if (k < 0x3fee8000) */ -#ifdef __STDC__ - double __ieee754_asin(double x) -#else - double __ieee754_asin(x) - double x; -#endif + /*--------------------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]-ABS(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=ABS(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=ABS(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 { + 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 */ + } +} + +/*******************************************************************/ +/* */ +/* End of arcsine, below is arccosine */ +/* */ +/*******************************************************************/ + +double __ieee754_acos(double x) { - double t,w,p,q,c,r,s,p1,p2,p3,q1,q2,z2,z4,z6; - int32_t hx,ix; - GET_HIGH_WORD(hx,x); - ix = hx&0x7fffffff; - if(ix>= 0x3ff00000) { /* |x|>= 1 */ - u_int32_t lx; - GET_LOW_WORD(lx,x); - if(((ix-0x3ff00000)|lx)==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<0x3fe00000) { /* |x|<0.5 */ - if(ix<0x3e400000) { /* if |x| < 2**-27 */ - if(huge+x>one) return x;/* return x with inexact if x!=0*/ - } else { - t = x*x; -#ifdef DO_NOT_USE_THIS - p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); - q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); -#else - p1 = t*pS[0]; z2=t*t; - p2 = pS[1]+t*pS[2]; z4=z2*z2; - p3 = pS[3]+t*pS[4]; z6=z4*z2; - q1 = one+t*qS[1]; - q2 = qS[2]+t*qS[3]; - p = p1 + z2*p2 + z4*p3 + z6*pS[5]; - q = q1 + z2*q2 + z4*qS[4]; -#endif - w = p/q; - return x+x*w; - } + double x1,x2,xx,s1,s2,res1,p,t,res,r,cor,cc,y,c,z,w[2],eps; + double fc; + mynumber u,v; + int4 k,m,n,nn; + 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); } - /* 1> |x|>= 0.5 */ - w = one-fabs(x); - t = w*0.5; -#ifdef DO_NOT_USE_THIS - p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); - q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); -#else - p1 = t*pS[0]; z2=t*t; - p2 = pS[1]+t*pS[2]; z4=z2*z2; - p3 = pS[3]+t*pS[4]; z6=z4*z2; - q1 = one+t*qS[1]; - q2 = qS[2]+t*qS[3]; - p = p1 + z2*p2 + z4*p3 + z6*pS[5]; - q = q1 + z2*q2 + z4*qS[4]; -#endif - s = __ieee754_sqrt(t); - if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ - w = p/q; - t = pio2_hi-(2.0*(s+s*w)-pio2_lo); - } else { - w = s; - SET_LOW_WORD(w,0); - 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); + } + } + } /* 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); } - if(hx>0) return t; else return -t; + } + } + 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 { + 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; + } } diff --git a/sysdeps/ieee754/dbl-64/e_atan2.c b/sysdeps/ieee754/dbl-64/e_atan2.c index ae7d759a9f..11342d87d3 100644 --- a/sysdeps/ieee754/dbl-64/e_atan2.c +++ b/sysdeps/ieee754/dbl-64/e_atan2.c @@ -1,130 +1,395 @@ -/* @(#)e_atan2.c 5.1 93/09/24 */ /* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 * - * 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_atan2.c,v 1.8 1995/05/10 20:44:51 jtc Exp $"; -#endif - -/* __ieee754_atan2(y,x) - * Method : - * 1. Reduce y to positive by atan2(y,x)=-atan2(-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: + * 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 of the License, or + * (at your option) any later version. * - * 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; + * 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 General Public License for more details. * - * 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. + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ +/************************************************************************/ +/* 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" +/************************************************************************/ +/* 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[]); +static double signArctan2(double ,double); +static double normalized(double ,double,double ,double); +void __mpatan2(mp_no *,mp_no *,mp_no *,int); + +double __ieee754_atan2(double y,double x) { + + int i,de,ux,dx,uy,dy,p; + static const int pr[MM]={6,8,10,20,32}; + double ax,ay,u,du,u9,ua,v,vv,dv,t1,t2,t3,t4,t5,t6,t7,t8, + z,zz,z1,z2,cor,s1,ss1,s2,ss2; + number num; + mp_no mperr,mpt1,mpx,mpy,mpz,mpz1,mpz2; + + 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+x; } + 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 ZERO; + else return opi.d; } } + else if (uy==0x80000000) { + if (dy==0x00000000) { + if ((ux&0x80000000)==0x00000000) return MZERO; + else return mopi.d;} } + + /* x=+-0 */ + if (x==ZERO) { + 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 ZERO; + else return MZERO; } + } + } + 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; } + + /* either x/y or y/x is very close to zero */ + ax = (x<ZERO) ? -x : x; ay = (y<ZERO) ? -y : y; + de = (uy & 0x7ff00000) - (ux & 0x7ff00000); + if (de>=ep) { return ((y>ZERO) ? hpi.d : mhpi.d); } + else if (de<=em) { + if (x>ZERO) { + if ((z=ay/ax)<TWOM1022) return normalized(ax,ay,y,z); + else return signArctan2(y,z); } + else { return ((y>ZERO) ? 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; } + + /* 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; } -#include "math.h" -#include "math_private.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -tiny = 1.0e-300, -zero = 0.0, -pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ -pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ -pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ -pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ - -#ifdef __STDC__ - double __ieee754_atan2(double y, double x) -#else - double __ieee754_atan2(y,x) - double y,x; -#endif -{ - double z; - int32_t k,m,hx,hy,ix,iy; - u_int32_t lx,ly; - - EXTRACT_WORDS(hx,lx,x); - ix = hx&0x7fffffff; - EXTRACT_WORDS(hy,ly,y); - iy = hy&0x7fffffff; - if(((ix|((lx|-lx)>>31))>0x7ff00000)|| - ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ - return x+y; - if(((hx-0x3ff00000)|lx)==0) return __atan(y); /* x=1.0 */ - m = ((hy>>31)&1)|((hx>>30)&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==0x7ff00000) { - if(iy==0x7ff00000) { - 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 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ - case 3: return -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==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; - - /* compute y/x */ - k = (iy-ix)>>20; - if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ - else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ - else z=__atan(fabs(y/x)); /* safe to do y/x */ - switch (m) { - case 0: return z ; /* atan(+,+) */ - case 1: { - u_int32_t zh; - GET_HIGH_WORD(zh,z); - SET_HIGH_WORD(z,zh ^ 0x80000000); - } - return z ; /* atan(-,+) */ - case 2: return pi-(z-pi_lo);/* atan(+,-) */ - default: /* case 3 */ - return (z-pi_lo)-pi;/* atan(-,-) */ - } + if (x>ZERO) { + + /* (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,ZERO,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); + } + else { + 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,ZERO,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) */ + else { + 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,ZERO,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); + } + else { + 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,ZERO,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); + } + } + } + else { + + /* (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,ZERO,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); + } + else { + 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,ZERO,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) */ + else { + 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,ZERO,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); + } + else { + 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,ZERO,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); + } + } + } +} + /* Treat the Denormalized case */ +static double 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); +} + /* Fix the sign and return after stage 1 or stage 2 */ +static double signArctan2(double y,double z) +{ + return ((y<ZERO) ? -z : z); +} + /* Stage 3: Perform a multi-Precision computation */ +static double 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) return z1; + } + return z1; /*if unpossible to do exact computing */ } diff --git a/sysdeps/ieee754/dbl-64/e_exp.c b/sysdeps/ieee754/dbl-64/e_exp.c index 6486cc3cfe..30d3941887 100644 --- a/sysdeps/ieee754/dbl-64/e_exp.c +++ b/sysdeps/ieee754/dbl-64/e_exp.c @@ -1,163 +1,243 @@ -/* Double-precision floating point e^x. - Copyright (C) 1997, 1998, 2000 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 Library General Public License as - published by the Free Software Foundation; either version 2 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 - Library General Public License for more details. - - You should have received a copy of the GNU Library General Public - License along with the GNU C Library; see the file COPYING.LIB. If not, - write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, - Boston, MA 02111-1307, USA. */ - -/* How this works: - 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. - - The input value, x, is written as - - x = n * ln(2)_0 + t/512 + delta[t] + x + n * ln(2)_1 - - where: - - n is an integer, 1024 >= n >= -1075; - - ln(2)_0 is the first 43 bits of ln(2), and ln(2)_1 is the remainder, so - that |ln(2)_1| < 2^-32; - - 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_1 ( 2^n_0 e^(t/512 + delta[t]) - + ( 2^n_0 e^(t/512 + delta[t]) - * ( p(x + n * ln(2)_1) - - n*ln(2)_1 - - n*ln(2)_1 * p(x + n * ln(2)_1) ) ) ) - - where - - p(x) is a polynomial approximating e(x)-1; - - e^(t/512 + delta[t]) is obtained from a table; - - n_1 + n_0 = n, so that |n_0| < DBL_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 <stdlib.h> -#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 volatile double TWO1023 = 8.988465674311579539e+307; -static const volatile double TWOM1000 = 9.3326361850321887899e-302; - -double -__ieee754_exp (double x) -{ - static const double himark = 709.7827128933840868; - static const double lomark = -745.1332191019412221; - /* Check for usual case. */ - if (isless (x, himark) && isgreater (x, lomark)) - { - static const double THREEp42 = 13194139533312.0; - static const double THREEp51 = 6755399441055744.0; - /* 1/ln(2). */ - static const double M_1_LN2 = 1.442695040888963387; - /* ln(2), part 1 */ - static const double M_LN2_0 = .6931471805598903302; - /* ln(2), part 2 */ - static const double M_LN2_1 = 5.497923018708371155e-14; - - int tval, unsafe, n_i; - double x22, n, t, dely, result; - union ieee754_double ex2_u, scale_u; - fenv_t oldenv; - - feholdexcept (&oldenv); -#ifdef FE_TONEAREST - fesetround (FE_TONEAREST); -#endif - - /* Calculate n. */ - n = x * M_1_LN2 + THREEp51; - n -= THREEp51; - x = x - n*M_LN2_0; - - /* Calculate t/512. */ - t = x + THREEp42; - t -= THREEp42; - x -= t; - - /* Compute tval = t. */ - tval = (int) (t * 512.0); - - if (t >= 0) - x -= __exp_deltatable[tval]; - else - x += __exp_deltatable[-tval]; - - /* Now, the variable x contains x + n*ln(2)_1. */ - dely = n*M_LN2_1; - - /* Compute ex2 = 2^n_0 e^(t/512+delta[t]). */ - ex2_u.d = __exp_atable[tval+177]; - n_i = (int)n; - /* 'unsafe' is 1 iff n_1 != 0. */ - unsafe = abs(n_i) >= -DBL_MIN_EXP - 1; - ex2_u.ieee.exponent += n_i >> unsafe; - - /* Compute scale = 2^n_1. */ - scale_u.d = 1.0; - scale_u.ieee.exponent += n_i - (n_i >> unsafe); - - /* Approximate e^x2 - 1, using a fourth-degree polynomial, - with maximum error in [-2^-10-2^-28,2^-10+2^-28] - less than 4.9e-19. */ - x22 = (((0.04166666898464281565 - * x + 0.1666666766008501610) - * x + 0.499999999999990008) - * x + 0.9999999999999976685) * x; - /* Allow for impact of dely. */ - x22 -= dely + dely*x22; - - /* Return result. */ - fesetenv (&oldenv); - - result = x22 * ex2_u.d + ex2_u.d; - if (!unsafe) - return result; - else - return result * scale_u.d; +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/***************************************************************************/ +/* 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 "endian.h" +#include "uexp.h" +#include "mydefs.h" +#include "MathLib.h" +#include "uexp.tbl" +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 __ieee754_exp(double x) { + double bexp, t, eps, del, base, y, al, bet, res, rem, cor; + mynumber junk1, junk2, binexp = {0,0}; + int4 k,i,j,m,n,ex; + + 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)) return res*binexp.x; + else return __slowexp(x); /*if error is over bound */ + } + + if (n <= smallint) return 1.0; + + 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) - 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)) return res*binexp.x; + else return __slowexp(x); /*if error is over bound */ } - /* Exceptional cases: */ - else if (isless (x, himark)) - { - if (__isinf (x)) - /* e^-inf == 0, with no error. */ - return 0; - else - /* Underflow */ - return TWOM1000 * TWOM1000; + 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; + return (res-1.0)*binexp.x; } - else - /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ - return TWO1023*x; + else return __slowexp(x); /* if error is over bound */ + } + else { + binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+767)<<20; + if (res == (res+cor*err_0)) return res*binexp.x*t256.x; + else return __slowexp(x); + } +} + +/************************************************************************/ +/* Compute e^(x+xx)(Double-Length number) .The routine also receive */ +/* bound of error of previous calculation .If after computing exp */ +/* error bigger than allows routine return non positive number */ +/*else return e^(x + xx) (always positive ) */ +/************************************************************************/ + +double __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 k,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/sysdeps/ieee754/dbl-64/e_lgamma_r.c b/sysdeps/ieee754/dbl-64/e_lgamma_r.c index ad775c616a..e5b402a023 100644 --- a/sysdeps/ieee754/dbl-64/e_lgamma_r.c +++ b/sysdeps/ieee754/dbl-64/e_lgamma_r.c @@ -199,14 +199,14 @@ static double zero= 0.00000000000000000000e+00; } } switch (n) { - case 0: y = __kernel_sin(pi*y,zero,0); break; + case 0: y = sin(pi*y); break; case 1: - case 2: y = __kernel_cos(pi*(0.5-y),zero); break; + case 2: y = cos(pi*(0.5-y)); break; case 3: - case 4: y = __kernel_sin(pi*(one-y),zero,0); break; + case 4: y = sin(pi*(one-y)); break; case 5: - case 6: y = -__kernel_cos(pi*(y-1.5),zero); break; - default: y = __kernel_sin(pi*(y-2.0),zero,0); break; + case 6: y = -cos(pi*(y-1.5)); break; + default: y = sin(pi*(y-2.0)); break; } return -y; } diff --git a/sysdeps/ieee754/dbl-64/e_log.c b/sysdeps/ieee754/dbl-64/e_log.c index 851bd30198..e55d74e561 100644 --- a/sysdeps/ieee754/dbl-64/e_log.c +++ b/sysdeps/ieee754/dbl-64/e_log.c @@ -1,165 +1,197 @@ -/* @(#)e_log.c 5.1 93/09/24 */ /* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 * - * 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: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $"; -#endif - -/* __ieee754_log(x) - * Return the logarithm 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) + * 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 of the License, or + * (at your option) any later version. * - * 3. Finally, log(x) = k*ln2 + log(1+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. + * 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 General Public License for more details. * - * Special cases: - * log(x) is NaN with signal if x < 0 (including -INF) ; - * log(+INF) is +INF; log(0) is -INF with signal; - * log(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. + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ +/*********************************************************************/ +/* */ +/* MODULE_NAME:ulog.h */ +/* */ +/* 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" +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 __ieee754_log(double x) { +#define M 4 + static const int pr[M]={8,10,18,32}; + int i,j,k,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,t3,t4,t5,t6,t7,t8,t,ra,rb,ww, + a0,aa0,s1,s2,ss2,s3,ss3,a1,aa1,a,aa,b,bb,c; + 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 (ux < 0x00100000) { + if (((ux & 0x7fffffff) | dx) == 0) return MHALF/ZERO; /* return -INF */ + if (ux < 0) return (x-x)/ZERO; /* return NaN */ + n -= 54; x *= two54.d; /* scale x */ + num.d = x; + } + if (ux >= 0x7ff00000) return x+x; /* INF or NaN */ + + /* Regular values of x */ + + w = x-ONE; + if (ABS(w) > U03) { goto case_03; } + + + /*--- 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 = (b0.d+w*(b1.d+w*(b2.d+w*(b3.d+w*(b4.d+ + w*(b5.d+w*(b6.d+w*(b7.d+w*b8.d))))))))*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 = d11.d+w*(d12.d+w*(d13.d+w*(d14.d+w*(d15.d+w*(d16.d+ + w*(d17.d+w*(d18.d+w*(d19.d+w*d20.d)))))))); + EMULV(w,a,s2,ss2,t1,t2,t3,t4,t5) + ADD2(d10.d,dd10.d,s2,ss2,s3,ss3,t1,t2) + MUL2(w,ZERO,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,ZERO,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,ZERO,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,ZERO,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,ZERO,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,ZERO,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,ZERO,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,ZERO,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,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) + MUL2(w,ZERO,s2,ss2,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8) + ADD2(w,ZERO, 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=(ONE+(i-75)*DEL_U)*(ONE+(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*((ONE-sa)-sb); + EADD(r0,t,ra,rb) + + /* Compute w */ + MUL2(q,ZERO,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: -#include "math.h" -#include "math_private.h" -#define half Lg[8] -#define two Lg[9] -#ifdef __STDC__ -static const double -#else -static double -#endif -ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ -ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ -two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ - Lg[] = {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 */ - 0.5, - 2.0}; -#ifdef __STDC__ -static const double zero = 0.0; -#else -static double zero = 0.0; -#endif - -#ifdef __STDC__ - double __ieee754_log(double x) -#else - double __ieee754_log(x) - double x; -#endif -{ - double hfsq,f,s,z,R,w,dk,t11,t12,t21,t22,w2,zw2; -#ifdef DO_NOT_USE_THIS - double t1,t2; -#endif - int32_t k,hx,i,j; - u_int32_t lx; - - EXTRACT_WORDS(hx,lx,x); - - k=0; - if (hx < 0x00100000) { /* x < 2**-1022 */ - if (((hx&0x7fffffff)|lx)==0) - return -two54/(x-x); /* log(+-0)=-inf */ - if (hx<0) return (x-x)/(x-x); /* log(-#) = NaN */ - k -= 54; x *= two54; /* subnormal number, scale up x */ - GET_HIGH_WORD(hx,x); - } - if (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); - f = x-1.0; - if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ - if(f==zero) { - if(k==0) return zero; else {dk=(double)k; - return dk*ln2_hi+dk*ln2_lo;} - } - R = f*f*(half-0.33333333333333333*f); - if(k==0) return f-R; else {dk=(double)k; - return dk*ln2_hi-((R-dk*ln2_lo)-f);} - } - s = f/(two+f); - dk = (double)k; - z = s*s; - i = hx-0x6147a; - w = z*z; - j = 0x6b851-hx; -#ifdef DO_NOT_USE_THIS - t1= w*(Lg2+w*(Lg4+w*Lg6)); - t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); - R = t2+t1; -#else - t21 = Lg[5]+w*Lg[7]; w2=w*w; - t22 = Lg[1]+w*Lg[3]; zw2=z*w2; - t11 = Lg[4]+w*Lg[6]; - t12 = w*Lg[2]; - R = t12 + w2*t11 + z*t22 + zw2*t21; -#endif - i |= j; - if(i>0) { - hfsq=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); - } + 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) return y1; + } + return y1; } diff --git a/sysdeps/ieee754/dbl-64/e_pow.c b/sysdeps/ieee754/dbl-64/e_pow.c index 73e8f471f6..5c5bbb58d7 100644 --- a/sysdeps/ieee754/dbl-64/e_pow.c +++ b/sysdeps/ieee754/dbl-64/e_pow.c @@ -1,356 +1,328 @@ -/* @(#)e_pow.c 5.1 93/09/24 */ /* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 * - * 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: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; -#endif - -/* __ieee754_pow(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 53-24 = 29 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) + * 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 of the License, or + * (at your option) any later version. * - * 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 + * 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 General Public License for more details. * - * Accuracy: - * pow(x,y) returns x**y nearly rounded. In particular - * pow(integer,integer) - * always returns the correct integer provided it is - * representable. - * - * 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. + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ +/***************************************************************************/ +/* MODULE_NAME: upow.c */ +/* */ +/* FUNCTIONS: upow */ +/* power1 */ +/* 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 "endian.h" +#include "upow.h" +#include "dla.h" +#include "mydefs.h" +#include "MathLib.h" +#include "upow.tbl" -#include "math.h" -#include "math_private.h" -#define zero C[0] -#define one C[1] -#define two C[2] -#define two53 C[3] -#define huge C[4] -#define tiny C[5] -#define L1 C[6] -#define L2 C[7] -#define L3 C[8] -#define L4 C[9] -#define L5 C[10] -#define L6 C[11] -#define P1 C[12] -#define P2 C[13] -#define P3 C[14] -#define P4 C[15] -#define P5 C[16] -#define lg2 C[17] -#define lg2_h C[18] -#define lg2_l C[19] -#define ovt C[20] -#define cp C[21] -#define cp_h C[22] -#define cp_l C[23] -#define ivln2 C[24] -#define ivln2_h C[25] -#define ivln2_l C[26] -#ifdef __STDC__ -static const double -#else -static double -#endif -bp[] = {1.0, 1.5,}, -dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ -dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ -C[] = { -0.0, -1.0, -2.0, -9007199254740992.0 , -1.0e300, -1.0e-300, -5.99999999999994648725e-01 , -4.28571428578550184252e-01 , -3.33333329818377432918e-01 , -2.72728123808534006489e-01 , -2.30660745775561754067e-01 , -2.06975017800338417784e-01 , -1.66666666666666019037e-01 , --2.77777777770155933842e-03 , -6.61375632143793436117e-05 , --1.65339022054652515390e-06 , -4.13813679705723846039e-08 , -6.93147180559945286227e-01 , -6.93147182464599609375e-01 , --1.90465429995776804525e-09 , -8.0085662595372944372e-0017 , -9.61796693925975554329e-01 , -9.61796700954437255859e-01 , --7.02846165095275826516e-09 , -1.44269504088896338700e+00 , -1.44269502162933349609e+00 , -1.92596299112661746887e-08 }; +double __exp1(double x, double xx, double error); +static double log1(double x, double *delta, double *error); +static double 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); -#ifdef __STDC__ - double __ieee754_pow(double x, double y) -#else - double __ieee754_pow(x,y) - double x, y; -#endif -{ - double z,ax,z_h,z_l,p_h,p_l; - double y1,t1,t2,r,s,t,u,v,w, t12,t14,r_1,r_2,r_3; - int32_t i,j,k,yisint,n; - int32_t hx,hy,ix,iy; - u_int32_t lx,ly; +/***************************************************************************/ +/* An ultimate power routine. Given two IEEE double machine numbers y,x */ +/* it computes the correctly rounded (to nearest) value of X^y. */ +/***************************************************************************/ +double __ieee754_upow(double x, double y) { + double z,a,aa,error, t,a1,a2,y1,y2,gor=1.0; + 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; + /* Checking if x is not too small to compute */ + if (((qx==0x7ff00000)&&(u.i[LOW_HALF]!=0))||(qx>0x7ff00000)) return NaNQ.x; + if (y == 1.0) return x; + if (y == 2.0) return x*x; + if (y == -1.0) return (x!=0)?1.0/x:NaNQ.x; + if (y == 0) return ((x>0)&&(qx<0x7ff00000))?1.0:NaNQ.x; + } + /* 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 */ + z = log1(x,&aa,&error); /* x^y =e^(y log (X)) */ + t = y*134217729.0; + y1 = t - (t-y); + y2 = y - y1; + t = z*134217729.0; + 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*ABS(y); + t = __exp1(a1,a2,1.9e16*error); /* return -10 or 0 if wasn't computed exactly */ + return (t>0)?t:power1(x,y); + } - EXTRACT_WORDS(hx,lx,x); - EXTRACT_WORDS(hy,ly,y); - ix = hx&0x7fffffff; iy = hy&0x7fffffff; + if (x == 0) { + if (ABS(y) > 1.0e20) return (y>0)?0:NaNQ.x; + k = checkint(y); + if (k == 0 || y < 0) return NaNQ.x; + else return (k==1)?0:x; /* return 0 */ + } + /* if x<0 */ + if (u.i[HIGH_HALF] < 0) { + k = checkint(y); + if (k==0) return NaNQ.x; /* y not integer and x<0 */ + return (k==1)?upow(-x,y):-upow(-x,y); /* if y even or odd */ + } + /* x>0 */ + qx = u.i[HIGH_HALF]&0x7fffffff; /* no sign */ + qy = v.i[HIGH_HALF]&0x7fffffff; /* no sign */ - /* y==zero: x**0 = 1 */ - if((iy|ly)==0) return C[1]; + if (qx > 0x7ff00000 || (qx == 0x7ff00000 && u.i[LOW_HALF] != 0)) return NaNQ.x; + /* if 0<x<2^-0x7fe */ + if (qy > 0x7ff00000 || (qy == 0x7ff00000 && v.i[LOW_HALF] != 0)) return NaNQ.x; + /* if y<2^-0x7fe */ - /* x==+-1 */ - if(x == 1.0) return C[1]; - if(x == -1.0 && isinf(y)) return C[1]; + if (qx == 0x7ff00000) /* x= 2^-0x3ff */ + {if (y == 0) return NaNQ.x; + return (y>0)?x:0; } - /* +-NaN return x+y */ - if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || - iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) - return x+y; + if (qy > 0x45f00000 && qy < 0x7ff00000) { + 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; + } - /* 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>=0x43400000) yisint = 2; /* even integer y */ - else if(iy>=0x3ff00000) { - k = (iy>>20)-0x3ff; /* exponent */ - if(k>20) { - j = ly>>(52-k); - if((u_int32_t)(j<<(52-k))==ly) yisint = 2-(j&1); - } else if(ly==0) { - j = iy>>(20-k); - if((int32_t)(j<<(20-k))==iy) yisint = 2-(j&1); - } - } - } + if (x == 1.0) return NaNQ.x; + 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 */ +} - /* special value of y */ - if(ly==0) { - if (iy==0x7ff00000) { /* y is +-inf */ - if(((ix-0x3ff00000)|lx)==0) - return y - y; /* inf**+-1 is NaN */ - else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ - return (hy>=0)? y: C[0]; - else /* (|x|<1)**-,+inf = inf,0 */ - return (hy<0)?-y: C[0]; - } - if(iy==0x3ff00000) { /* y is +-1 */ - if(hy<0) return C[1]/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_sqrt(x); - } - } +/**************************************************************************/ +/* Computing x^y using more accurate but more slow log routine */ +/**************************************************************************/ +static double power1(double x, double y) { + double z,a,aa,error, t,a1,a2,y1,y2; + z = log2(x,&aa,&error); + t = y*134217729.0; + y1 = t - (t-y); + y2 = y - y1; + t = z*134217729.0; + 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*ABS(y); + t = __exp1(a1,a2,1.9e16*error); + return (t >= 0)?t:slowpow(x,y,z); +} - ax = fabs(x); - /* special value of x */ - if(lx==0) { - if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ - z = ax; /*x is +-0,+-inf,+-1*/ - if(hy<0) z = C[1]/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; - } - } +/****************************************************************************/ +/* Computing log(x) (x is left argument). The result is the returned double */ +/* + the parameter delta. */ +/* The result is bounded by error (rightmost argument) */ +/****************************************************************************/ +static double log1(double x, double *delta, double *error) { + int i,j,m,n; + double uu,vv,eps,nx,e,e1,e2,t,t1,t2,res,cor,add=0; + mynumber u,v; - /* (x<0)**(non-int) is NaN */ - if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); + 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];} - /* |y| is huge */ - if(iy>0x41e00000) { /* if |y| > 2**31 */ - if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ - if(ix<=0x3fefffff) return (hy<0)? C[4]*C[4]:C[5]*C[5]; - if(ix>=0x3ff00000) return (hy>0)? C[4]*C[4]:C[5]*C[5]; - } - /* over/underflow if x is not close to one */ - if(ix<0x3fefffff) return (hy<0)? C[4]*C[4]:C[5]*C[5]; - if(ix>0x3ff00000) return (hy>0)? C[4]*C[4]:C[5]*C[5]; - /* now |1-x| is tiny <= 2**-20, suffice to compute - log(x) by x-x^2/2+x^3/3-x^4/4 */ - t = x-1; /* t has 20 trailing zeros */ - w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); - u = C[25]*t; /* ivln2_h has 21 sig. bits */ - v = t*C[26]-w*C[24]; - t1 = u+v; - SET_LOW_WORD(t1,0); - t2 = v-(t1-u); - } else { - double s2,s_h,s_l,t_h,t_l,s22,s24,s26,r1,r2,r3; - n = 0; - /* take care subnormal number */ - if(ix<0x00100000) - {ax *= C[3]; n -= 53; GET_HIGH_WORD(ix,ax); } - n += ((ix)>>20)-0x3ff; - j = ix&0x000fffff; - /* determine interval */ - ix = j|0x3ff00000; /* normalize ix */ - if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ - else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ - else {k=0;n+=1;ix -= 0x00100000;} - SET_HIGH_WORD(ax,ix); + 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; } - /* 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 = C[1]/(ax+bp[k]); - s = u*v; - s_h = s; - SET_LOW_WORD(s_h,0); - /* t_h=ax+bp[k] High */ - t_h = C[0]; - SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18)); - 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; -#ifdef DO_NOT_USE_THIS - r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); -#else - r1 = C[10]+s2*C[11]; s22=s2*s2; - r2 = C[8]+s2*C[9]; s24=s22*s22; - r3 = C[6]+s2*C[7]; s26=s24*s22; - r = r3*s22 + r2*s24 + r1*s26; -#endif - r += s_l*(s_h+s); - s2 = s_h*s_h; - t_h = 3.0+s2+r; - SET_LOW_WORD(t_h,0); - 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; - SET_LOW_WORD(p_h,0); - p_l = v-(p_h-u); - z_h = C[22]*p_h; /* cp_h+cp_l = 2/(3*log2) */ - z_l = C[23]*p_h+p_l*C[21]+dp_l[k]; - /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ - t = (double)n; - t1 = (((z_h+z_l)+dp_h[k])+t); - SET_LOW_WORD(t1,0); - t2 = z_l-(((t1-t)-dp_h[k])-z_h); - } + 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*ABS(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 */ +} + +/****************************************************************************/ +/* More slow but more accurate routine of log */ +/* Computing log(x)(x is left argument).The result is return double + delta.*/ +/* The result is bounded by error (right argument) */ +/****************************************************************************/ +static double log2(double x, double *delta, double *error) { + int i,j,m,n; + double uu,vv,eps,nx,e,e1,e2,t,t1,t2,res,cor,add=0; + double ou1,ou2,lu1,lu2,ov,lv1,lv2,a,a1,a2; + double y,yy,z,zz,j1,j2,j3,j4,j5,j6,j7,j8; + mynumber u,v; + + 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]; } - s = C[1]; /* s (sign of result -ve**odd) = -1 else = 1 */ - if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) - s = -C[1];/* (-ve)**(odd int) */ + 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*ABS(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; + } +} - /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ - y1 = y; - SET_LOW_WORD(y1,0); - p_l = (y-y1)*t1+y*t2; - p_h = y1*t1; - z = p_l+p_h; - EXTRACT_WORDS(j,i,z); - if (j>=0x40900000) { /* z >= 1024 */ - if(((j-0x40900000)|i)!=0) /* if z > 1024 */ - return s*C[4]*C[4]; /* overflow */ - else { - if(p_l+C[20]>z-p_h) return s*C[4]*C[4]; /* overflow */ - } - } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ - if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ - return s*C[5]*C[5]; /* underflow */ - else { - if(p_l<=z-p_h) return s*C[5]*C[5]; /* 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 = j+(0x00100000>>(k+1)); - k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ - t = C[0]; - SET_HIGH_WORD(t,n&~(0x000fffff>>k)); - n = ((n&0x000fffff)|0x00100000)>>(20-k); - if(j<0) n = -n; - p_h -= t; - } - t = p_l+p_h; - SET_LOW_WORD(t,0); - u = t*C[18]; - v = (p_l-(t-p_h))*C[17]+t*C[19]; - z = u+v; - w = v-(z-u); - t = z*z; -#ifdef DO_NOT_USE_THIS - t1 = z - t*(C[12]+t*(C[13]+t*(C[14]+t*(C[15]+t*C[16])))); -#else - r_1 = C[15]+t*C[16]; t12 = t*t; - r_2 = C[13]+t*C[14]; t14 = t12*t12; - r_3 = t*C[12]; - t1 = z - r_3 - t12*r_2 - t14*r_1; -#endif - r = (z*t1)/(t1-C[2])-(w+z*w); - z = C[1]-(r-z); - GET_HIGH_WORD(j,z); - j += (n<<20); - if((j>>20)<=0) z = __scalbn(z,n); /* subnormal output */ - else SET_HIGH_WORD(z,j); - return s*z; +/**********************************************************************/ +/* Routine 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 checkint(double x) { + union {int4 i[2]; double x;} u; + int k,l,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)) return 0; /* if not integer */ + return (n<<(k-21))?-1:1; + } + if (n) return 0; /*if not integer*/ + if (k == 20) return (m&1)? -1:1; + if (m<<(k+12)) return 0; + return (m<<(k+11))?-1:1; } diff --git a/sysdeps/ieee754/dbl-64/e_remainder.c b/sysdeps/ieee754/dbl-64/e_remainder.c index 6418081182..631c2fcf01 100644 --- a/sysdeps/ieee754/dbl-64/e_remainder.c +++ b/sysdeps/ieee754/dbl-64/e_remainder.c @@ -1,80 +1,111 @@ -/* @(#)e_remainder.c 5.1 93/09/24 */ /* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 * - * 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_remainder.c,v 1.8 1995/05/10 20:46:05 jtc Exp $"; -#endif - -/* __ieee754_remainder(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 fmod() return x-[x/p]chopped*p exactlp. + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ +/**************************************************************************/ +/* 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 "math.h" -#include "math_private.h" +#include "endian.h" +#include "mydefs.h" +#include "urem.h" +#include "MathLib.h" -#ifdef __STDC__ -static const double zero = 0.0; -#else -static double zero = 0.0; -#endif - - -#ifdef __STDC__ - double __ieee754_remainder(double x, double p) -#else - double __ieee754_remainder(x,p) - double x,p; -#endif +/**************************************************************************/ +/* 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) { - int32_t hx,hp; - u_int32_t sx,lx,lp; - double p_half; - - EXTRACT_WORDS(hx,lx,x); - EXTRACT_WORDS(hp,lp,p); - sx = hx&0x80000000; - hp &= 0x7fffffff; - hx &= 0x7fffffff; - - /* purge off exception values */ - if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */ - if((hx>=0x7ff00000)|| /* x not finite */ - ((hp>=0x7ff00000)&& /* p is NaN */ - (((hp-0x7ff00000)|lp)!=0))) - return (x*p)/(x*p); - + double z,d,xx,yy; + int4 kx,ky,m,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| < 2^1024 and 2^-970 < |y| < 2^1024 ------------------*/ + if (kx<0x7ff00000 && ky<0x7ff00000 && ky>=0x03500000) { + 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 (ABS(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 (ABS(u.x)<0.5*t.x) return (u.x!=0)?u.x:((x>0)?ZERO.x:nZERO.x); + else + if (ABS(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);} + } - if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */ - if (((hx-hp)|(lx-lp))==0) return zero*x; - x = fabs(x); - p = fabs(p); - if (hp<0x00200000) { - if(x+x>p) { - x-=p; - if(x+x>=p) x -= p; - } - } else { - p_half = 0.5*p; - if(x>p_half) { - x-=p; - if(x>=p_half) x -= p; - } - } - GET_HIGH_WORD(hx,x); - SET_HIGH_WORD(x,hx^sx); - return x; + } /* (kx<0x7ff00000&&ky<0x7ff00000&&ky>=0x03500000) */ + else { + if (kx<0x7ff00000&&ky<0x7ff00000&&(ky>0||t.i[LOW_HALF]!=0)) { + y=ABS(y)*t128.x; + z=uremainder(x,y)*t128.x; + z=uremainder(z,y)*tm128.x; + return z; + } + else { /* if x is too big */ + if (kx>=0x7ff00000||(ky==0&&t.i[LOW_HALF]==0)||ky>0x7ff00000|| + (ky==0x7ff00000&&t.i[LOW_HALF]!=0)) + return (u.i[HIGH_HALF]&0x80000000)?nNAN.x:NAN.x; + else return x; + } + } } diff --git a/sysdeps/ieee754/dbl-64/e_sqrt.c b/sysdeps/ieee754/dbl-64/e_sqrt.c index 67da5455f9..5ec6b5e7cf 100644 --- a/sysdeps/ieee754/dbl-64/e_sqrt.c +++ b/sysdeps/ieee754/dbl-64/e_sqrt.c @@ -1,452 +1,89 @@ -/* @(#)e_sqrt.c 5.1 93/09/24 */ /* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 * - * 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_sqrt.c,v 1.8 1995/05/10 20:46:17 jtc Exp $"; -#endif - -/* __ieee754_sqrt(x) - * Return correctly rounded sqrt. - * ------------------------------------------ - * | Use the hardware sqrt if you have one | - * ------------------------------------------ - * Method: - * Bit by bit method using integer arithmetic. (Slow, but portable) - * 1. Normalization - * Scale x to y in [1,4) with even powers of 2: - * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then - * sqrt(x) = 2^k * sqrt(y) - * 2. Bit by bit computation - * Let q = sqrt(y) truncated to i bit after binary point (q = 1), - * i 0 - * i+1 2 - * s = 2*q , and y = 2 * ( y - q ). (1) - * i i i i - * - * To compute q from q , one checks whether - * i+1 i - * - * -(i+1) 2 - * (q + 2 ) <= y. (2) - * i - * -(i+1) - * If (2) is false, then q = q ; otherwise q = q + 2 . - * i+1 i i+1 i - * - * With some algebraic manipulation, it is not difficult to see - * that (2) is equivalent to - * -(i+1) - * s + 2 <= y (3) - * i i - * - * The advantage of (3) is that s and y can be computed by - * i i - * the following recurrence formula: - * if (3) is false - * - * s = s , y = y ; (4) - * i+1 i i+1 i - * - * otherwise, - * -i -(i+1) - * s = s + 2 , y = y - s - 2 (5) - * i+1 i i+1 i i + * 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 of the License, or + * (at your option) any later version. * - * One may easily use induction to prove (4) and (5). - * Note. Since the left hand side of (3) contain only i+2 bits, - * it does not necessary to do a full (53-bit) comparison - * in (3). - * 3. Final rounding - * After generating the 53 bits result, we compute one more bit. - * Together with the remainder, we can decide whether the - * result is exact, bigger than 1/2ulp, or less than 1/2ulp - * (it will never equal to 1/2ulp). - * The rounding mode can be detected by checking whether - * huge + tiny is equal to huge, and whether huge - tiny is - * equal to huge for some floating point number "huge" and "tiny". + * 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 General Public License for more details. * - * Special cases: - * sqrt(+-0) = +-0 ... exact - * sqrt(inf) = inf - * sqrt(-ve) = NaN ... with invalid signal - * sqrt(NaN) = NaN ... with invalid signal for signaling NaN - * - * Other methods : see the appended file at the end of the program below. - *--------------- + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ - -#include "math.h" -#include "math_private.h" - -#ifdef __STDC__ -static const double one = 1.0, tiny=1.0e-300; -#else -static double one = 1.0, tiny=1.0e-300; -#endif - -#ifdef __STDC__ - double __ieee754_sqrt(double x) -#else - double __ieee754_sqrt(x) - double x; -#endif -{ - double z; - int32_t sign = (int)0x80000000; - int32_t ix0,s0,q,m,t,i; - u_int32_t r,t1,s1,ix1,q1; - - EXTRACT_WORDS(ix0,ix1,x); - - /* take care of Inf and NaN */ - if((ix0&0x7ff00000)==0x7ff00000) { - return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf - sqrt(-inf)=sNaN */ - } - /* take care of zero */ - if(ix0<=0) { - if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */ - else if(ix0<0) - return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ - } - /* normalize x */ - m = (ix0>>20); - if(m==0) { /* subnormal x */ - while(ix0==0) { - m -= 21; - ix0 |= (ix1>>11); ix1 <<= 21; - } - for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1; - m -= i-1; - ix0 |= (ix1>>(32-i)); - ix1 <<= i; - } - m -= 1023; /* unbias exponent */ - ix0 = (ix0&0x000fffff)|0x00100000; - if(m&1){ /* odd m, double x to make it even */ - ix0 += ix0 + ((ix1&sign)>>31); - ix1 += ix1; - } - m >>= 1; /* m = [m/2] */ - - /* generate sqrt(x) bit by bit */ - ix0 += ix0 + ((ix1&sign)>>31); - ix1 += ix1; - q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */ - r = 0x00200000; /* r = moving bit from right to left */ - - while(r!=0) { - t = s0+r; - if(t<=ix0) { - s0 = t+r; - ix0 -= t; - q += r; - } - ix0 += ix0 + ((ix1&sign)>>31); - ix1 += ix1; - r>>=1; - } - - r = sign; - while(r!=0) { - t1 = s1+r; - t = s0; - if((t<ix0)||((t==ix0)&&(t1<=ix1))) { - s1 = t1+r; - if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1; - ix0 -= t; - if (ix1 < t1) ix0 -= 1; - ix1 -= t1; - q1 += r; - } - ix0 += ix0 + ((ix1&sign)>>31); - ix1 += ix1; - r>>=1; - } - - /* use floating add to find out rounding direction */ - if((ix0|ix1)!=0) { - z = one-tiny; /* trigger inexact flag */ - if (z>=one) { - z = one+tiny; - if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;} - else if (z>one) { - if (q1==(u_int32_t)0xfffffffe) q+=1; - q1+=2; - } else - q1 += (q1&1); - } - } - ix0 = (q>>1)+0x3fe00000; - ix1 = q1>>1; - if ((q&1)==1) ix1 |= sign; - ix0 += (m <<20); - INSERT_WORDS(z,ix0,ix1); - return z; +/*********************************************************************/ +/* 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 "endian.h" +#include "mydefs.h" +#include "dla.h" +#include "MathLib.h" +#include "root.tbl" + +/*********************************************************************/ +/* An ultimate aqrt 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) { +#include "uroot.h" + 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, big1 = 134217729.0; + double y,t,del,res,res1,hy,z,zz,p,hx,tx,ty,s; + mynumber a,b,c={0,0}; + int4 n,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) { + 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))) return 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 */ + return ((((z-s)+zz)<0)?max(res,res1):min(res,res1))*c.x; + } + } + else { + if (k>0x7ff00000) /* x -> infinity */ + return (big1-big1)/(big-big); + if (k<0x00100000) { /* x -> -infinity */ + if (x==0) return x; + if (k<0) return (big1-big1)/(big-big); + else return tm256.x*usqrt(x*t512.x); + } + else return (a.i[LOW_HALF]==0)?x:(big1-big1)/(big-big); + } } - -/* -Other methods (use floating-point arithmetic) -------------- -(This is a copy of a drafted paper by Prof W. Kahan -and K.C. Ng, written in May, 1986) - - Two algorithms are given here to implement sqrt(x) - (IEEE double precision arithmetic) in software. - Both supply sqrt(x) correctly rounded. The first algorithm (in - Section A) uses newton iterations and involves four divisions. - The second one uses reciproot iterations to avoid division, but - requires more multiplications. Both algorithms need the ability - to chop results of arithmetic operations instead of round them, - and the INEXACT flag to indicate when an arithmetic operation - is executed exactly with no roundoff error, all part of the - standard (IEEE 754-1985). The ability to perform shift, add, - subtract and logical AND operations upon 32-bit words is needed - too, though not part of the standard. - -A. sqrt(x) by Newton Iteration - - (1) Initial approximation - - Let x0 and x1 be the leading and the trailing 32-bit words of - a floating point number x (in IEEE double format) respectively - - 1 11 52 ...widths - ------------------------------------------------------ - x: |s| e | f | - ------------------------------------------------------ - msb lsb msb lsb ...order - - - ------------------------ ------------------------ - x0: |s| e | f1 | x1: | f2 | - ------------------------ ------------------------ - - By performing shifts and subtracts on x0 and x1 (both regarded - as integers), we obtain an 8-bit approximation of sqrt(x) as - follows. - - k := (x0>>1) + 0x1ff80000; - y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits - Here k is a 32-bit integer and T1[] is an integer array containing - correction terms. Now magically the floating value of y (y's - leading 32-bit word is y0, the value of its trailing word is 0) - approximates sqrt(x) to almost 8-bit. - - Value of T1: - static int T1[32]= { - 0, 1024, 3062, 5746, 9193, 13348, 18162, 23592, - 29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215, - 83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581, - 16499, 12183, 8588, 5674, 3403, 1742, 661, 130,}; - - (2) Iterative refinement - - Apply Heron's rule three times to y, we have y approximates - sqrt(x) to within 1 ulp (Unit in the Last Place): - - y := (y+x/y)/2 ... almost 17 sig. bits - y := (y+x/y)/2 ... almost 35 sig. bits - y := y-(y-x/y)/2 ... within 1 ulp - - - Remark 1. - Another way to improve y to within 1 ulp is: - - y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x) - y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x) - - 2 - (x-y )*y - y := y + 2* ---------- ...within 1 ulp - 2 - 3y + x - - - This formula has one division fewer than the one above; however, - it requires more multiplications and additions. Also x must be - scaled in advance to avoid spurious overflow in evaluating the - expression 3y*y+x. Hence it is not recommended uless division - is slow. If division is very slow, then one should use the - reciproot algorithm given in section B. - - (3) Final adjustment - - By twiddling y's last bit it is possible to force y to be - correctly rounded according to the prevailing rounding mode - as follows. Let r and i be copies of the rounding mode and - inexact flag before entering the square root program. Also we - use the expression y+-ulp for the next representable floating - numbers (up and down) of y. Note that y+-ulp = either fixed - point y+-1, or multiply y by nextafter(1,+-inf) in chopped - mode. - - I := FALSE; ... reset INEXACT flag I - R := RZ; ... set rounding mode to round-toward-zero - z := x/y; ... chopped quotient, possibly inexact - If(not I) then { ... if the quotient is exact - if(z=y) { - I := i; ... restore inexact flag - R := r; ... restore rounded mode - return sqrt(x):=y. - } else { - z := z - ulp; ... special rounding - } - } - i := TRUE; ... sqrt(x) is inexact - If (r=RN) then z=z+ulp ... rounded-to-nearest - If (r=RP) then { ... round-toward-+inf - y = y+ulp; z=z+ulp; - } - y := y+z; ... chopped sum - y0:=y0-0x00100000; ... y := y/2 is correctly rounded. - I := i; ... restore inexact flag - R := r; ... restore rounded mode - return sqrt(x):=y. - - (4) Special cases - - Square root of +inf, +-0, or NaN is itself; - Square root of a negative number is NaN with invalid signal. - - -B. sqrt(x) by Reciproot Iteration - - (1) Initial approximation - - Let x0 and x1 be the leading and the trailing 32-bit words of - a floating point number x (in IEEE double format) respectively - (see section A). By performing shifs and subtracts on x0 and y0, - we obtain a 7.8-bit approximation of 1/sqrt(x) as follows. - - k := 0x5fe80000 - (x0>>1); - y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits - - Here k is a 32-bit integer and T2[] is an integer array - containing correction terms. Now magically the floating - value of y (y's leading 32-bit word is y0, the value of - its trailing word y1 is set to zero) approximates 1/sqrt(x) - to almost 7.8-bit. - - Value of T2: - static int T2[64]= { - 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866, - 0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f, - 0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d, - 0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0, - 0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989, - 0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd, - 0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e, - 0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,}; - - (2) Iterative refinement - - Apply Reciproot iteration three times to y and multiply the - result by x to get an approximation z that matches sqrt(x) - to about 1 ulp. To be exact, we will have - -1ulp < sqrt(x)-z<1.0625ulp. - - ... set rounding mode to Round-to-nearest - y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x) - y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x) - ... special arrangement for better accuracy - z := x*y ... 29 bits to sqrt(x), with z*y<1 - z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x) - - Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that - (a) the term z*y in the final iteration is always less than 1; - (b) the error in the final result is biased upward so that - -1 ulp < sqrt(x) - z < 1.0625 ulp - instead of |sqrt(x)-z|<1.03125ulp. - - (3) Final adjustment - - By twiddling y's last bit it is possible to force y to be - correctly rounded according to the prevailing rounding mode - as follows. Let r and i be copies of the rounding mode and - inexact flag before entering the square root program. Also we - use the expression y+-ulp for the next representable floating - numbers (up and down) of y. Note that y+-ulp = either fixed - point y+-1, or multiply y by nextafter(1,+-inf) in chopped - mode. - - R := RZ; ... set rounding mode to round-toward-zero - switch(r) { - case RN: ... round-to-nearest - if(x<= z*(z-ulp)...chopped) z = z - ulp; else - if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp; - break; - case RZ:case RM: ... round-to-zero or round-to--inf - R:=RP; ... reset rounding mod to round-to-+inf - if(x<z*z ... rounded up) z = z - ulp; else - if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp; - break; - case RP: ... round-to-+inf - if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else - if(x>z*z ...chopped) z = z+ulp; - break; - } - - Remark 3. The above comparisons can be done in fixed point. For - example, to compare x and w=z*z chopped, it suffices to compare - x1 and w1 (the trailing parts of x and w), regarding them as - two's complement integers. - - ...Is z an exact square root? - To determine whether z is an exact square root of x, let z1 be the - trailing part of z, and also let x0 and x1 be the leading and - trailing parts of x. - - If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0 - I := 1; ... Raise Inexact flag: z is not exact - else { - j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2 - k := z1 >> 26; ... get z's 25-th and 26-th - fraction bits - I := i or (k&j) or ((k&(j+j+1))!=(x1&3)); - } - R:= r ... restore rounded mode - return sqrt(x):=z. - - If multiplication is cheaper then the foregoing red tape, the - Inexact flag can be evaluated by - - I := i; - I := (z*z!=x) or I. - - Note that z*z can overwrite I; this value must be sensed if it is - True. - - Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be - zero. - - -------------------- - z1: | f2 | - -------------------- - bit 31 bit 0 - - Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd - or even of logb(x) have the following relations: - - ------------------------------------------------- - bit 27,26 of z1 bit 1,0 of x1 logb(x) - ------------------------------------------------- - 00 00 odd and even - 01 01 even - 10 10 odd - 10 00 even - 11 01 even - ------------------------------------------------- - - (4) Special cases (see (4) of Section A). - - */ diff --git a/sysdeps/ieee754/dbl-64/endian.h b/sysdeps/ieee754/dbl-64/endian.h new file mode 100644 index 0000000000..76f0d7c084 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/endian.h @@ -0,0 +1,11 @@ +#include <endian.h> + +#if __FLOAT_WORD_ORDER == __BIG_ENDIAN +#define HIGH_HALF 0 +#define LOW_HALF 1 +#else +#if __FLOAT_WORD_ORDER == __LITTLE_ENDIAN +#define HIGH_HALF 1 +#define LOW_HALF 0 +#endif +#endif diff --git a/sysdeps/ieee754/dbl-64/halfulp.c b/sysdeps/ieee754/dbl-64/halfulp.c new file mode 100644 index 0000000000..7901ec4e36 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/halfulp.c @@ -0,0 +1,124 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/************************************************************************/ +/* */ +/* 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" + +double usqrt(double x); + +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 halfulp(double x, double y) +{ + mynumber v; + double z,u,uu,j1,j2,j3,j4,j5; + 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 = usqrt(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/sysdeps/ieee754/dbl-64/k_cos.c b/sysdeps/ieee754/dbl-64/k_cos.c index 7e38ef7915..cc5c205a5f 100644 --- a/sysdeps/ieee754/dbl-64/k_cos.c +++ b/sysdeps/ieee754/dbl-64/k_cos.c @@ -1,107 +1 @@ -/* @(#)k_cos.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: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $"; -#endif - -/* - * __kernel_cos( x, y ) - * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 - * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. - * - * Algorithm - * 1. Since cos(-x) = cos(x), we need only to consider positive x. - * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. - * 3. cos(x) is approximated by a polynomial of degree 14 on - * [0,pi/4] - * 4 14 - * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x - * where the remez error is - * - * | 2 4 6 8 10 12 14 | -58 - * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 - * | | - * - * 4 6 8 10 12 14 - * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then - * cos(x) = 1 - x*x/2 + r - * since cos(x+y) ~ cos(x) - sin(x)*y - * ~ cos(x) - x*y, - * a correction term is necessary in cos(x) and hence - * cos(x+y) = 1 - (x*x/2 - (r - x*y)) - * For better accuracy when x > 0.3, let qx = |x|/4 with - * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. - * Then - * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). - * Note that 1-qx and (x*x/2-qx) is EXACT here, and the - * magnitude of the latter is at least a quarter of x*x/2, - * thus, reducing the rounding error in the subtraction. - */ - -#include "math.h" -#include "math_private.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -C[] = { - 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ - 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ - -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ - 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ - -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ - 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ - -1.13596475577881948265e-11}; /* 0xBDA8FAE9, 0xBE8838D4 */ - -#ifdef __STDC__ - double __kernel_cos(double x, double y) -#else - double __kernel_cos(x, y) - double x,y; -#endif -{ - double a,hz,z,r,qx,r1,r2,r3,z1,z2,z3; - int32_t ix; - z = x*x; - GET_HIGH_WORD(ix,x); - ix &= 0x7fffffff; /* ix = |x|'s high word*/ - if(ix<0x3e400000) { /* if x < 2**27 */ - if(((int)x)==0) return C[0]; /* generate inexact */ - } -#ifdef DO_NOT_USE_THIS - r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); -#else - r1=z*C[6];r1=r1+C[5];z1=z*z; - r2=z*C[4];r2=r2+C[3];z2=z1*z; - r3=z*C[2];r3=r3+C[1];z3=z2*z1; - r=z3*r1+z2*r2+z*r3; -#endif - if(ix < 0x3FD33333) /* if |x| < 0.3 */ - return C[0] - (0.5*z - (z*r - x*y)); - else { - if(ix > 0x3fe90000) { /* x > 0.78125 */ - qx = 0.28125; - } else { - INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */ - } - hz = 0.5*z-qx; - a = C[0]-qx; - return a - (hz - (z*r-x*y)); - } -} +/* Not needed anymore. */ diff --git a/sysdeps/ieee754/dbl-64/k_sin.c b/sysdeps/ieee754/dbl-64/k_sin.c index 49c59228e0..cc5c205a5f 100644 --- a/sysdeps/ieee754/dbl-64/k_sin.c +++ b/sysdeps/ieee754/dbl-64/k_sin.c @@ -1,91 +1 @@ -/* @(#)k_sin.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: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $"; -#endif - -/* __kernel_sin( x, y, iy) - * kernel sin 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 iy indicates whether y is 0. (if iy=0, y assume to be 0). - * - * Algorithm - * 1. Since sin(-x) = -sin(x), we need only to consider positive x. - * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. - * 3. sin(x) is approximated by a polynomial of degree 13 on - * [0,pi/4] - * 3 13 - * sin(x) ~ x + S1*x + ... + S6*x - * where - * - * |sin(x) 2 4 6 8 10 12 | -58 - * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 - * | x | - * - * 4. sin(x+y) = sin(x) + sin'(x')*y - * ~ sin(x) + (1-x*x/2)*y - * For better accuracy, let - * 3 2 2 2 2 - * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) - * then 3 2 - * sin(x) = x + (S1*x + (x *(r-y/2)+y)) - */ - -#include "math.h" -#include "math_private.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -S[] = { - 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ - -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ - 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ - -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ - 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ - -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ - 1.58969099521155010221e-10}; /* 0x3DE5D93A, 0x5ACFD57C */ - -#ifdef __STDC__ - double __kernel_sin(double x, double y, int iy) -#else - double __kernel_sin(x, y, iy) - double x,y; int iy; /* iy=0 if y is zero */ -#endif -{ - double z,r,v,z1,r1,r2; - int32_t ix; - GET_HIGH_WORD(ix,x); - ix &= 0x7fffffff; /* high word of x */ - if(ix<0x3e400000) /* |x| < 2**-27 */ - {if((int)x==0) return x;} /* generate inexact */ - z = x*x; - v = z*x; -#ifdef DO_NOT_USE_THIS - 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); -#else - r1 = S[5]+z*S[6]; z1 = z*z*z; - r2 = S[3]+z*S[4]; - r = S[2] + z*r2 + z1*r1; - if(iy==0) return x+v*(S[1]+z*r); - else return x-((z*(S[0]*y-v*r)-y)-v*S[1]); -#endif -} +/* Not needed anymore. */ diff --git a/sysdeps/ieee754/dbl-64/mpa.c b/sysdeps/ieee754/dbl-64/mpa.c new file mode 100644 index 0000000000..cdd15a1602 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mpa.c @@ -0,0 +1,497 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/************************************************************************/ +/* MODULE_NAME: mpa.c */ +/* */ +/* FUNCTIONS: */ +/* mcr */ +/* acr */ +/* cr */ +/* cpy */ +/* cpymn */ +/* 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 "mpa2.h" +/* mcr() compares the sizes of the mantissas of two multiple precision */ +/* numbers. Mantissas are compared regardless of the signs of the */ +/* numbers, even if x->d[0] or y->d[0] are zero. Exponents are also */ +/* disregarded. */ +static int mcr(const mp_no *x, const mp_no *y, int p) { + int i; + for (i=1; i<=p; i++) { + if (X[i] == Y[i]) continue; + else if (X[i] > Y[i]) return 1; + else return -1; } + return 0; +} + + + +/* acr() compares the absolute values of two multiple precision numbers */ +int acr(const mp_no *x, const mp_no *y, int p) { + int i; + + if (X[0] == ZERO) { + if (Y[0] == ZERO) i= 0; + else i=-1; + } + else if (Y[0] == ZERO) i= 1; + else { + if (EX > EY) i= 1; + else if (EX < EY) i=-1; + else i= mcr(x,y,p); + } + + return i; +} + + +/* cr90 compares the values of two multiple precision numbers */ +int cr(const mp_no *x, const mp_no *y, int p) { + int i; + + if (X[0] > Y[0]) i= 1; + else if (X[0] < Y[0]) i=-1; + else if (X[0] < ZERO ) i= acr(y,x,p); + else i= acr(x,y,p); + + return i; +} + + +/* Copy a multiple precision number. Set *y=*x. x=y is permissible. */ +void cpy(const mp_no *x, mp_no *y, int p) { + int i; + + EY = EX; + for (i=0; i <= p; i++) Y[i] = X[i]; + + return; +} + + +/* Copy a multiple precision number x of precision m into a */ +/* multiple precision number y of precision n. In case n>m, */ +/* the digits of y beyond the m'th are set to zero. In case */ +/* n<m, the digits of x beyond the n'th are ignored. */ +/* x=y is permissible. */ + +void cpymn(const mp_no *x, int m, mp_no *y, int n) { + + int i,k; + + EY = EX; k=MIN(m,n); + for (i=0; i <= k; i++) Y[i] = X[i]; + for ( ; i <= n; i++) Y[i] = ZERO; + + return; +} + +/* Convert a multiple precision number *x into a double precision */ +/* number *y, normalized case (|x| >= 2**(-1022))) */ +static void norm(const mp_no *x, double *y, int p) +{ + #define R radixi.d + int i,k; + double a,c,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 if (p==4) c =(X[1] + R* X[2]) + R*R*(X[3] + R*X[4]); + } + else { + for (a=ONE, z[1]=X[1]; z[1] < TWO23; ) + {a *= TWO; z[1] *= TWO; } + + for (i=2; i<5; i++) { + z[i] = X[i]*a; + u = (z[i] + CUTTER)-CUTTER; + if (u > z[i]) u -= RADIX; + z[i] -= u; + z[i-1] += u*RADIXI; + } + + u = (z[3] + TWO71) - TWO71; + if (u > z[3]) u -= TWO19; + v = z[3]-u; + + if (v == TWO18) { + if (z[4] == ZERO) { + for (i=5; i <= p; i++) { + if (X[i] == ZERO) continue; + else {z[3] += ONE; break; } + } + } + else z[3] += ONE; + } + + 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; + return; +#undef R +} + +/* Convert a multiple precision number *x into a double precision */ +/* number *y, denormalized case (|x| < 2**(-1022))) */ +static void denorm(const mp_no *x, double *y, int p) +{ + int i,k; + double a,c,u,v,z[5]; + +#define R radixi.d + if (EX<-44 || (EX==-44 && X[1]<TWO5)) + { *y=ZERO; return; } + + if (p==1) { + if (EX==-42) {z[1]=X[1]+TWO10; z[2]=ZERO; z[3]=ZERO; k=3;} + else if (EX==-43) {z[1]= TWO10; z[2]=X[1]; z[3]=ZERO; k=2;} + else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;} + } + else if (p==2) { + if (EX==-42) {z[1]=X[1]+TWO10; z[2]=X[2]; z[3]=ZERO; 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]=ZERO; 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]=ZERO; k=1;} + z[3] = X[k]; + } + + u = (z[3] + TWO57) - TWO57; + if (u > z[3]) u -= TWO5; + + if (u==z[3]) { + for (i=k+1; i <= p; i++) { + if (X[i] == ZERO) continue; + else {z[3] += ONE; break; } + } + } + + c = X[0]*((z[1] + R*(z[2] + R*z[3])) - TWO10); + + *y = c*TWOM1032; + return; + +#undef R +} + +/* Convert a multiple precision number *x into a double precision number *y. */ +/* The result is correctly rounded to the nearest/even. *x is left unchanged */ + +void mp_dbl(const mp_no *x, double *y, int p) { + + int i,k; + double a,c,u,v,z[5]; + + if (X[0] == ZERO) {*y = ZERO; return; } + + if (EX> -42) norm(x,y,p); + else if (EX==-42 && X[1]>=TWO10) norm(x,y,p); + else denorm(x,y,p); +} + + +/* dbl_mp() converts a double precision number x into a multiple precision */ +/* number *y. If the precision p is too small the result is truncated. x is */ +/* left unchanged. */ + +void dbl_mp(double x, mp_no *y, int p) { + + int i,n; + double u; + + /* Sign */ + if (x == ZERO) {Y[0] = ZERO; return; } + else if (x > ZERO) Y[0] = ONE; + else {Y[0] = MONE; x=-x; } + + /* Exponent */ + for (EY=ONE; x >= RADIX; EY += ONE) x *= RADIXI; + for ( ; x < ONE; EY -= ONE) x *= RADIX; + + /* Digits */ + n=MIN(p,4); + for (i=1; i<=n; i++) { + u = (x + TWO52) - TWO52; + if (u>x) u -= ONE; + Y[i] = u; x -= u; x *= RADIX; } + for ( ; i<=p; i++) Y[i] = ZERO; + return; +} + + +/* add_magnitudes() adds the magnitudes of *x & *y assuming that */ +/* abs(*x) >= abs(*y) > 0. */ +/* The sign of the sum *z is undefined. x&y may overlap but not x&z or y&z. */ +/* No guard digit is used. The result equals the exact sum, truncated. */ +/* *x & *y are left unchanged. */ + +static void add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) { + + int i,j,k; + + EZ = EX; + + i=p; j=p+ EY - EX; k=p+1; + + if (j<1) + {cpy(x,z,p); return; } + else Z[k] = ZERO; + + for (; j>0; i--,j--) { + Z[k] += X[i] + Y[j]; + if (Z[k] >= RADIX) { + Z[k] -= RADIX; + Z[--k] = ONE; } + else + Z[--k] = ZERO; + } + + for (; i>0; i--) { + Z[k] += X[i]; + if (Z[k] >= RADIX) { + Z[k] -= RADIX; + Z[--k] = ONE; } + else + Z[--k] = ZERO; + } + + if (Z[1] == ZERO) { + for (i=1; i<=p; i++) Z[i] = Z[i+1]; } + else EZ += ONE; +} + + +/* sub_magnitudes() subtracts the magnitudes of *x & *y assuming that */ +/* abs(*x) > abs(*y) > 0. */ +/* The sign of the difference *z is undefined. x&y may overlap but not x&z */ +/* or y&z. One guard digit is used. The error is less than one ulp. */ +/* *x & *y are left unchanged. */ + +static void sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) { + + int i,j,k; + + EZ = EX; + + if (EX == EY) { + i=j=k=p; + Z[k] = Z[k+1] = ZERO; } + else { + j= EX - EY; + if (j > p) {cpy(x,z,p); return; } + else { + i=p; j=p+1-j; k=p; + if (Y[j] > ZERO) { + Z[k+1] = RADIX - Y[j--]; + Z[k] = MONE; } + else { + Z[k+1] = ZERO; + Z[k] = ZERO; j--;} + } + } + + for (; j>0; i--,j--) { + Z[k] += (X[i] - Y[j]); + if (Z[k] < ZERO) { + Z[k] += RADIX; + Z[--k] = MONE; } + else + Z[--k] = ZERO; + } + + for (; i>0; i--) { + Z[k] += X[i]; + if (Z[k] < ZERO) { + Z[k] += RADIX; + Z[--k] = MONE; } + else + Z[--k] = ZERO; + } + + for (i=1; Z[i] == ZERO; i++) ; + EZ = EZ - i + 1; + for (k=1; i <= p+1; ) + Z[k++] = Z[i++]; + for (; k <= p; ) + Z[k++] = ZERO; + + return; +} + + +/* Add two multiple precision numbers. Set *z = *x + *y. x&y may overlap */ +/* but not x&z or y&z. One guard digit is used. The error is less than */ +/* one ulp. *x & *y are left unchanged. */ + +void add(const mp_no *x, const mp_no *y, mp_no *z, int p) { + + int n; + + if (X[0] == ZERO) {cpy(y,z,p); return; } + else if (Y[0] == ZERO) {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] = ZERO; + } + return; +} + + +/* Subtract two multiple precision numbers. *z is set to *x - *y. x&y may */ +/* overlap but not x&z or y&z. One guard digit is used. The error is */ +/* less than one ulp. *x & *y are left unchanged. */ + +void sub(const mp_no *x, const mp_no *y, mp_no *z, int p) { + + int n; + + if (X[0] == ZERO) {cpy(y,z,p); Z[0] = -Z[0]; return; } + else if (Y[0] == ZERO) {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] = ZERO; + } + return; +} + + +/* Multiply two multiple precision numbers. *z is set to *x * *y. x&y */ +/* may overlap but not x&z or y&z. In case p=1,2,3 the exact result is */ +/* truncated to p digits. In case p>3 the error is bounded by 1.001 ulp. */ +/* *x & *y are left unchanged. */ + +void mul(const mp_no *x, const mp_no *y, mp_no *z, int p) { + + int i, i1, i2, j, k, k2; + double u; + + /* Is z=0? */ + if (X[0]*Y[0]==ZERO) + { Z[0]=ZERO; return; } + + /* Multiply, add and carry */ + k2 = (p<3) ? p+p : p+3; + Z[k2]=ZERO; + for (k=k2; k>1; ) { + if (k > p) {i1=k-p; i2=p+1; } + else {i1=1; i2=k; } + for (i=i1,j=i2-1; i<i2; i++,j--) Z[k] += X[i]*Y[j]; + + u = (Z[k] + CUTTER)-CUTTER; + if (u > Z[k]) u -= RADIX; + Z[k] -= u; + Z[--k] = u*RADIXI; + } + + /* Is there a carry beyond the most significant digit? */ + if (Z[1] == ZERO) { + for (i=1; i<=p; i++) Z[i]=Z[i+1]; + EZ = EX + EY - 1; } + else + EZ = EX + EY; + + Z[0] = X[0] * Y[0]; + return; +} + + +/* Invert a multiple precision number. Set *y = 1 / *x. */ +/* Relative error bound = 1.001*r**(1-p) for p=2, 1.063*r**(1-p) for p=3, */ +/* 2.001*r**(1-p) for p>3. */ +/* *x=0 is not permissible. *x is left unchanged. */ + +void inv(const mp_no *x, mp_no *y, int p) { + int i,l; + 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}; + const mp_no mptwo = {1,1.0,2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, + 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,}; + + cpy(x,&z,p); z.e=0; mp_dbl(&z,&t,p); + t=ONE/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); + } + return; +} + + +/* Divide one multiple precision number by another.Set *z = *x / *y. *x & *y */ +/* are left unchanged. x&y may overlap but not x&z or y&z. */ +/* Relative error bound = 2.001*r**(1-p) for p=2, 2.063*r**(1-p) for p=3 */ +/* and 3.001*r**(1-p) for p>3. *y=0 is not permissible. */ + +void dvd(const mp_no *x, const mp_no *y, mp_no *z, int p) { + + mp_no w; + + if (X[0] == ZERO) Z[0] = ZERO; + else {inv(y,&w,p); mul(x,&w,z,p);} + return; +} + diff --git a/sysdeps/ieee754/dbl-64/mpa.h b/sysdeps/ieee754/dbl-64/mpa.h new file mode 100644 index 0000000000..59c58efadf --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mpa.h @@ -0,0 +1,79 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/************************************************************************/ +/* MODULE_NAME: mpa.h */ +/* */ +/* FUNCTIONS: */ +/* mcr */ +/* acr */ +/* cr */ +/* cpy */ +/* cpymn */ +/* mp_dbl */ +/* dbl_mp */ +/* add */ +/* sub */ +/* mul */ +/* inv */ +/* dvd */ +/* */ +/* Arithmetic functions for multiple precision numbers. */ +/* Common types and definition */ +/************************************************************************/ + + +typedef struct {/* This structure holds the details of a multi-precision */ + int e; /* floating point number, x: d[0] holds its sign (-1,0 or 1) */ + double d[40]; /* e holds its exponent (...,-2,-1,0,1,2,...) and */ +} mp_no; /* d[1]...d[p] hold its mantissa digits. The value of x is, */ + /* x = d[1]*r**(e-1) + d[2]*r**(e-2) + ... + d[p]*r**(e-p). */ + /* Here r = 2**24, 0 <= d[i] < r and 1 <= p <= 32. */ + /* p is a global variable. A multi-precision number is */ + /* always normalized. Namely, d[1] > 0. An exception is */ + /* a zero which is characterized by d[0] = 0. The terms */ + /* d[p+1], d[p+2], ... of a none zero number have no */ + /* significance and so are the terms e, d[1],d[2],... */ + /* of a zero. */ + +typedef union { int i[2]; double d; } number; + +#define X x->d +#define Y y->d +#define Z z->d +#define EX x->e +#define EY y->e +#define EZ z->e + +#define MAX(x,y) ((x) < (y) ? (y) : (x)) +#define MIN(x,y) ((x) < (y) ? (x) : (y)) +#define ABS(x) ((x) < 0 ? -(x) : (x)) + +int acr(const mp_no *, const mp_no *, int); +int cr(const mp_no *, const mp_no *, int); +void cpy(const mp_no *, mp_no *, int); +void cpymn(const mp_no *, int, 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 inv(const mp_no *, mp_no *, int); +void dvd(const mp_no *, const mp_no *, mp_no *, int); + diff --git a/sysdeps/ieee754/dbl-64/mpa2.h b/sysdeps/ieee754/dbl-64/mpa2.h new file mode 100644 index 0000000000..2b677fd750 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mpa2.h @@ -0,0 +1,93 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/**************************************************************************/ +/* */ +/* MODULE_NAME:mpa2.h */ +/* */ +/* */ +/* variables prototype and definition according to type of processor */ +/* types definition */ +/**************************************************************************/ + +#ifndef MPA2_H +#define MPA2_H + + +#ifdef BIG_ENDI +static const number +/**/ radix = {0x41700000, 0x00000000, }, /* 2**24 */ +/**/ radixi = {0x3e700000, 0x00000000, }, /* 2**-24 */ +/**/ cutter = {0x44b00000, 0x00000000, }, /* 2**76 */ +/**/ zero = {0x00000000, 0x00000000, }, /* 0 */ +/**/ one = {0x3ff00000, 0x00000000, }, /* 1 */ +/**/ mone = {0xbff00000, 0x00000000, }, /* -1 */ +/**/ two = {0x40000000, 0x00000000, }, /* 2 */ +/**/ two5 = {0x40400000, 0x00000000, }, /* 2**5 */ +/**/ two10 = {0x40900000, 0x00000000, }, /* 2**10 */ +/**/ two18 = {0x41100000, 0x00000000, }, /* 2**18 */ +/**/ two19 = {0x41200000, 0x00000000, }, /* 2**19 */ +/**/ two23 = {0x41600000, 0x00000000, }, /* 2**23 */ +/**/ two52 = {0x43300000, 0x00000000, }, /* 2**52 */ +/**/ two57 = {0x43800000, 0x00000000, }, /* 2**57 */ +/**/ two71 = {0x44600000, 0x00000000, }, /* 2**71 */ +/**/ twom1032 = {0x00000400, 0x00000000, }; /* 2**-1032 */ + +#else +#ifdef LITTLE_ENDI +static const number +/**/ radix = {0x00000000, 0x41700000, }, /* 2**24 */ +/**/ radixi = {0x00000000, 0x3e700000, }, /* 2**-24 */ +/**/ cutter = {0x00000000, 0x44b00000, }, /* 2**76 */ +/**/ zero = {0x00000000, 0x00000000, }, /* 0 */ +/**/ one = {0x00000000, 0x3ff00000, }, /* 1 */ +/**/ mone = {0x00000000, 0xbff00000, }, /* -1 */ +/**/ two = {0x00000000, 0x40000000, }, /* 2 */ +/**/ two5 = {0x00000000, 0x40400000, }, /* 2**5 */ +/**/ two10 = {0x00000000, 0x40900000, }, /* 2**10 */ +/**/ two18 = {0x00000000, 0x41100000, }, /* 2**18 */ +/**/ two19 = {0x00000000, 0x41200000, }, /* 2**19 */ +/**/ two23 = {0x00000000, 0x41600000, }, /* 2**23 */ +/**/ two52 = {0x00000000, 0x43300000, }, /* 2**52 */ +/**/ two57 = {0x00000000, 0x43800000, }, /* 2**57 */ +/**/ two71 = {0x00000000, 0x44600000, }, /* 2**71 */ +/**/ twom1032 = {0x00000000, 0x00000400, }; /* 2**-1032 */ + +#endif +#endif + +#define RADIX radix.d +#define RADIXI radixi.d +#define CUTTER cutter.d +#define ZERO zero.d +#define ONE one.d +#define MONE mone.d +#define TWO two.d +#define TWO5 two5.d +#define TWO10 two10.d +#define TWO18 two18.d +#define TWO19 two19.d +#define TWO23 two23.d +#define TWO52 two52.d +#define TWO57 two57.d +#define TWO71 two71.d +#define TWOM1032 twom1032.d + + +#endif diff --git a/sysdeps/ieee754/dbl-64/mpatan.c b/sysdeps/ieee754/dbl-64/mpatan.c new file mode 100644 index 0000000000..b10775def6 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mpatan.c @@ -0,0 +1,101 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* */ +/* 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" +void mpsqrt(mp_no *, mp_no *, int); + +void mpatan(mp_no *x, mp_no *y, int p) { +#include "mpatan.h" + + int i,m,n; + double dx; + mp_no + mpone = {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,}, + mptwo = {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,}, + 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 mpone, mptwo & mptwoim1 */ + if (EX>0) m=7; + else if (EX<0) m=0; + else { + mp_dbl(x,&dx,p); dx=ABS(dx); + for (m=6; m>0; m--) + {if (dx>xm[m].d) break;} + } + mpone.e = mptwo.e = mptwoim1.e = 1; + mpone.d[0] = mpone.d[1] = mptwo.d[0] = mptwoim1.d[0] = ONE; + mptwo.d[1] = TWO; + + /* Reduce x m times */ + mul(x,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=np[p]; mptwoim1.d[1] = twonm1[p].d; + dvd(&mpsm,&mptwoim1,&mpt,p); + for (i=n-1; i>1; i--) { + mptwoim1.d[1] -= TWO; + 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] = twom[m].d; + mul(&mptwoim1,&mpt,y,p); + + return; +} diff --git a/sysdeps/ieee754/dbl-64/mpatan.h b/sysdeps/ieee754/dbl-64/mpatan.h new file mode 100644 index 0000000000..7c77001c38 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mpatan.h @@ -0,0 +1,172 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* */ +/* MODULE_NAME:mpatan.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef MPATAN_H +#define MPATAN_H + +#ifdef BIG_ENDI + static const number + 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 */ + }; + static const number + 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 */ + }; + + static const number + twom[8] = { /* 2**m */ +/**/ {0x3ff00000, 0x00000000, }, /* 1.0 */ +/**/ {0x40000000, 0x00000000, }, /* 2.0 */ +/**/ {0x40100000, 0x00000000, }, /* 4.0 */ +/**/ {0x40200000, 0x00000000, }, /* 8.0 */ +/**/ {0x40300000, 0x00000000, }, /* 16.0 */ +/**/ {0x40400000, 0x00000000, }, /* 32.0 */ +/**/ {0x40500000, 0x00000000, }, /* 64.0 */ +/**/ {0x40600000, 0x00000000, }, /* 128.0 */ + }; + + static const number +/**/ one = {0x3ff00000, 0x00000000, }, /* 1 */ +/**/ two = {0x40000000, 0x00000000, }; /* 2 */ + +#else +#ifdef LITTLE_ENDI + + static const number + 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 */ + }; + static const number + 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 */ + }; + + static const number + twom[8] = { /* 2**m */ +/**/ {0x00000000, 0x3ff00000, }, /* 1.0 */ +/**/ {0x00000000, 0x40000000, }, /* 2.0 */ +/**/ {0x00000000, 0x40100000, }, /* 4.0 */ +/**/ {0x00000000, 0x40200000, }, /* 8.0 */ +/**/ {0x00000000, 0x40300000, }, /* 16.0 */ +/**/ {0x00000000, 0x40400000, }, /* 32.0 */ +/**/ {0x00000000, 0x40500000, }, /* 64.0 */ +/**/ {0x00000000, 0x40600000, }, /* 128.0 */ + }; + + static const number +/**/ one = {0x00000000, 0x3ff00000, }, /* 1 */ +/**/ two = {0x00000000, 0x40000000, }; /* 2 */ + +#endif +#endif + +#define ONE one.d +#define TWO two.d + + static const int + 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 diff --git a/sysdeps/ieee754/dbl-64/mpatan2.c b/sysdeps/ieee754/dbl-64/mpatan2.c new file mode 100644 index 0000000000..6e0c587685 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mpatan2.c @@ -0,0 +1,69 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* 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" + +void mpsqrt(mp_no *, mp_no *, int); +void mpatan(mp_no *, mp_no *, int); + +/* Multi-Precision Atan2(y,x) function subroutine, for p >= 4. */ +/* y=0 is not permitted if x<=0. No error messages are given. */ +void mpatan2(mp_no *y, mp_no *x, mp_no *z, int p) { + + static const double ZERO = 0.0, ONE = 1.0; + + mp_no mpone = {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 mpt1,mpt2,mpt3; + + + if (X[0] <= ZERO) { + mpone.e = 1; mpone.d[0] = mpone.d[1] = ONE; + dvd(x,y,&mpt1,p); mul(&mpt1,&mpt1,&mpt2,p); + if (mpt1.d[0] != ZERO) mpt1.d[0] = ONE; + 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); + } + + return; +} diff --git a/sysdeps/ieee754/dbl-64/mpexp.c b/sysdeps/ieee754/dbl-64/mpexp.c new file mode 100644 index 0000000000..2d1167550d --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mpexp.c @@ -0,0 +1,105 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/*************************************************************************/ +/* 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 "mpexp.h" + +/* Multi-Precision exponential function subroutine (for p >= 4, */ +/* 2**(-55) <= abs(x) <= 1024). */ +void mpexp(mp_no *x, mp_no *y, int p) { + + int i,j,k,m,m1,m2,n; + double a,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 mpone = {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 mpk = {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,mpak,mpt1,mpt2; + + /* Choose m,n and compute a=2**(-m) */ + n = np[p]; m1 = m1p[p]; a = twomm1[p].d; + for (i=0; i<EX; i++) a *= RADIXI; + for ( ; i>EX; i--) a *= RADIX; + b = X[1]*RADIXI; m2 = 24*EX; + for (; b<HALF; m2--) { a *= TWO; b *= TWO; } + if (b == HALF) { + for (i=2; i<=p; i++) { if (X[i]!=ZERO) break; } + if (i==p+1) { m2--; a *= TWO; } + } + if ((m=m1+m2) <= 0) { + m=0; a=ONE; + for (i=n-1; i>0; i--,n--) { if (m1np[i][p]+m2>0) break; } + } + + /* Compute s=x*2**(-m). Put result in mps */ + dbl_mp(a,&mpt1,p); + mul(x,&mpt1,&mps,p); + + /* Evaluate the polynomial. Put result in mpt2 */ + mpone.e=1; mpone.d[0]=ONE; mpone.d[1]=ONE; + mpk.e = 1; mpk.d[0] = ONE; mpk.d[1]=nn[n].d; + dvd(&mps,&mpk,&mpt1,p); + add(&mpone,&mpt1,&mpak,p); + for (k=n-1; k>1; k--) { + mul(&mps,&mpak,&mpt1,p); + mpk.d[1]=nn[k].d; + dvd(&mpt1,&mpk,&mpt2,p); + add(&mpone,&mpt2,&mpak,p); + } + mul(&mps,&mpak,&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; ) { + mul(&mpt2,&mpt2,&mpt1,p); k++; + if (k==m) { j=1; break; } + mul(&mpt1,&mpt1,&mpt2,p); k++; + } + if (j) cpy(&mpt1,y,p); + else cpy(&mpt2,y,p); + return; +} + diff --git a/sysdeps/ieee754/dbl-64/mpexp.h b/sysdeps/ieee754/dbl-64/mpexp.h new file mode 100644 index 0000000000..16f957e2b0 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mpexp.h @@ -0,0 +1,157 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* */ +/* MODULE_NAME:mpexp.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef MPEXP_H +#define MPEXP_H + +#ifdef BIG_ENDI + static const number + twomm1[33] = { /* 2**-m1 */ +/**/ {0x00000000, 0x00000000, }, /* 0 */ +/**/ {0x00000000, 0x00000000, }, /* 0 */ +/**/ {0x00000000, 0x00000000, }, /* 0 */ +/**/ {0x00000000, 0x00000000, }, /* 0 */ +/**/ {0x3ee00000, 0x00000000, }, /* 2**-17 */ +/**/ {0x3e800000, 0x00000000, }, /* 2**-23 */ +/**/ {0x3e800000, 0x00000000, }, /* 2**-23 */ +/**/ {0x3e300000, 0x00000000, }, /* 2**-28 */ +/**/ {0x3e400000, 0x00000000, }, /* 2**-27 */ +/**/ {0x3d900000, 0x00000000, }, /* 2**-38 */ +/**/ {0x3d500000, 0x00000000, }, /* 2**-42 */ +/**/ {0x3d800000, 0x00000000, }, /* 2**-39 */ +/**/ {0x3d400000, 0x00000000, }, /* 2**-43 */ +/**/ {0x3d000000, 0x00000000, }, /* 2**-47 */ +/**/ {0x3d400000, 0x00000000, }, /* 2**-43 */ +/**/ {0x3d000000, 0x00000000, }, /* 2**-47 */ +/**/ {0x3cd00000, 0x00000000, }, /* 2**-50 */ +/**/ {0x3c900000, 0x00000000, }, /* 2**-54 */ +/**/ {0x3c600000, 0x00000000, }, /* 2**-57 */ +/**/ {0x3c300000, 0x00000000, }, /* 2**-60 */ +/**/ {0x3bf00000, 0x00000000, }, /* 2**-64 */ +/**/ {0x3bc00000, 0x00000000, }, /* 2**-67 */ +/**/ {0x3b800000, 0x00000000, }, /* 2**-71 */ +/**/ {0x3b500000, 0x00000000, }, /* 2**-74 */ +/**/ {0x3bb00000, 0x00000000, }, /* 2**-68 */ +/**/ {0x3b800000, 0x00000000, }, /* 2**-71 */ +/**/ {0x3b500000, 0x00000000, }, /* 2**-74 */ +/**/ {0x3b200000, 0x00000000, }, /* 2**-77 */ +/**/ {0x3b900000, 0x00000000, }, /* 2**-70 */ +/**/ {0x3b600000, 0x00000000, }, /* 2**-73 */ +/**/ {0x3b300000, 0x00000000, }, /* 2**-76 */ +/**/ {0x3b100000, 0x00000000, }, /* 2**-78 */ +/**/ {0x3ae00000, 0x00000000, }, /* 2**-81 */ + }; + static const number + nn[9]={ /* n */ +/**/ {0x00000000, 0x00000000, }, /* 0 */ +/**/ {0x3ff00000, 0x00000000, }, /* 1 */ +/**/ {0x40000000, 0x00000000, }, /* 2 */ +/**/ {0x40080000, 0x00000000, }, /* 3 */ +/**/ {0x40100000, 0x00000000, }, /* 4 */ +/**/ {0x40140000, 0x00000000, }, /* 5 */ +/**/ {0x40180000, 0x00000000, }, /* 6 */ +/**/ {0x401c0000, 0x00000000, }, /* 7 */ +/**/ {0x40200000, 0x00000000, }, /* 8 */ + }; + + static const number +/**/ radix = {0x41700000, 0x00000000, }, /* 2**24 */ +/**/ radixi = {0x3e700000, 0x00000000, }, /* 2**-24 */ +/**/ zero = {0x00000000, 0x00000000, }, /* 0 */ +/**/ one = {0x3ff00000, 0x00000000, }, /* 1 */ +/**/ two = {0x40000000, 0x00000000, }, /* 2 */ +/**/ half = {0x3fe00000, 0x00000000, }; /* 1/2 */ + +#else +#ifdef LITTLE_ENDI + static const number + twomm1[33] = { /* 2**-m1 */ +/**/ {0x00000000, 0x00000000, }, /* 0 */ +/**/ {0x00000000, 0x00000000, }, /* 0 */ +/**/ {0x00000000, 0x00000000, }, /* 0 */ +/**/ {0x00000000, 0x00000000, }, /* 0 */ +/**/ {0x00000000, 0x3ee00000, }, /* 2**-17 */ +/**/ {0x00000000, 0x3e800000, }, /* 2**-23 */ +/**/ {0x00000000, 0x3e800000, }, /* 2**-23 */ +/**/ {0x00000000, 0x3e300000, }, /* 2**-28 */ +/**/ {0x00000000, 0x3e400000, }, /* 2**-27 */ +/**/ {0x00000000, 0x3d900000, }, /* 2**-38 */ +/**/ {0x00000000, 0x3d500000, }, /* 2**-42 */ +/**/ {0x00000000, 0x3d800000, }, /* 2**-39 */ +/**/ {0x00000000, 0x3d400000, }, /* 2**-43 */ +/**/ {0x00000000, 0x3d000000, }, /* 2**-47 */ +/**/ {0x00000000, 0x3d400000, }, /* 2**-43 */ +/**/ {0x00000000, 0x3d000000, }, /* 2**-47 */ +/**/ {0x00000000, 0x3cd00000, }, /* 2**-50 */ +/**/ {0x00000000, 0x3c900000, }, /* 2**-54 */ +/**/ {0x00000000, 0x3c600000, }, /* 2**-57 */ +/**/ {0x00000000, 0x3c300000, }, /* 2**-60 */ +/**/ {0x00000000, 0x3bf00000, }, /* 2**-64 */ +/**/ {0x00000000, 0x3bc00000, }, /* 2**-67 */ +/**/ {0x00000000, 0x3b800000, }, /* 2**-71 */ +/**/ {0x00000000, 0x3b500000, }, /* 2**-74 */ +/**/ {0x00000000, 0x3bb00000, }, /* 2**-68 */ +/**/ {0x00000000, 0x3b800000, }, /* 2**-71 */ +/**/ {0x00000000, 0x3b500000, }, /* 2**-74 */ +/**/ {0x00000000, 0x3b200000, }, /* 2**-77 */ +/**/ {0x00000000, 0x3b900000, }, /* 2**-70 */ +/**/ {0x00000000, 0x3b600000, }, /* 2**-73 */ +/**/ {0x00000000, 0x3b300000, }, /* 2**-76 */ +/**/ {0x00000000, 0x3b100000, }, /* 2**-78 */ +/**/ {0x00000000, 0x3ae00000, }, /* 2**-81 */ + }; + static const number + nn[9]={ /* n */ +/**/ {0x00000000, 0x00000000, }, /* 0 */ +/**/ {0x00000000, 0x3ff00000, }, /* 1 */ +/**/ {0x00000000, 0x40000000, }, /* 2 */ +/**/ {0x00000000, 0x40080000, }, /* 3 */ +/**/ {0x00000000, 0x40100000, }, /* 4 */ +/**/ {0x00000000, 0x40140000, }, /* 5 */ +/**/ {0x00000000, 0x40180000, }, /* 6 */ +/**/ {0x00000000, 0x401c0000, }, /* 7 */ +/**/ {0x00000000, 0x40200000, }, /* 8 */ + }; + + static const number +/**/ radix = {0x00000000, 0x41700000, }, /* 2**24 */ +/**/ radixi = {0x00000000, 0x3e700000, }, /* 2**-24 */ +/**/ zero = {0x00000000, 0x00000000, }, /* 0 */ +/**/ one = {0x00000000, 0x3ff00000, }, /* 1 */ +/**/ two = {0x00000000, 0x40000000, }, /* 2 */ +/**/ half = {0x00000000, 0x3fe00000, }; /* 1/2 */ + +#endif +#endif + +#define RADIX radix.d +#define RADIXI radixi.d +#define ZERO zero.d +#define ONE one.d +#define TWO two.d +#define HALF half.d + +#endif diff --git a/sysdeps/ieee754/dbl-64/mplog.c b/sysdeps/ieee754/dbl-64/mplog.c new file mode 100644 index 0000000000..78aec799f2 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mplog.c @@ -0,0 +1,68 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/************************************************************************/ +/* */ +/* 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 mpexp(mp_no *, mp_no *, int); + +void mplog(mp_no *x, mp_no *y, int p) { +#include "mplog.h" + int i,j,k,m,m1,m2,n; + double a,b; + 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 mpone = {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 mpt1,mpt2; + + /* Choose m and initiate mpone */ + m = mp[p]; mpone.e = 1; mpone.d[0]=mpone.d[1]=ONE; + + /* 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); + } + return; +} diff --git a/sysdeps/ieee754/dbl-64/mplog.h b/sysdeps/ieee754/dbl-64/mplog.h new file mode 100644 index 0000000000..e21f898f52 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mplog.h @@ -0,0 +1,44 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* */ +/* MODULE_NAME:mplog.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef MPLOG_H +#define MPLOG_H + +#ifdef BIG_ENDI + static const number +/**/ one = {0x3ff00000, 0x00000000, }; /* 1 */ + +#else +#ifdef LITTLE_ENDI + static const number +/**/ one = {0x00000000, 0x3ff00000, }; /* 1 */ + +#endif +#endif + +#define ONE one.d + +#endif diff --git a/sysdeps/ieee754/dbl-64/mpsqrt.c b/sysdeps/ieee754/dbl-64/mpsqrt.c new file mode 100644 index 0000000000..6f73fae137 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mpsqrt.c @@ -0,0 +1,102 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/****************************************************************************/ +/* 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" + +/****************************************************************************/ +/* 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 */ +/****************************************************************************/ + +double fastiroot(double); + +void mpsqrt(mp_no *x, mp_no *y, int p) { +#include "mpsqrt.h" + + int i,m,ex,ey; + double dx,dy; + mp_no + mphalf = {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,}, + mp3halfs = {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 mpxn,mpz,mpu,mpt1,mpt2; + + /* Prepare multi-precision 1/2 and 3/2 */ + mphalf.e =0; mphalf.d[0] =ONE; mphalf.d[1] =HALFRAD; + mp3halfs.e=1; mp3halfs.d[0]=ONE; mp3halfs.d[1]=ONE; mp3halfs.d[2]=HALFRAD; + + ex=EX; 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=mp[p]; + for (i=0; i<m; i++) { + mul(&mpu,&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; + + return; +} + +/***********************************************************/ +/* Compute a double precision approximation for 1/sqrt(x) */ +/* with the relative error bounded by 2**-51. */ +/***********************************************************/ +double fastiroot(double x) { + union {long i[2]; double d;} p,q; + double y,z, t; + long n; + static const double c0 = 0.99674, c1 = -0.53380, 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/sysdeps/ieee754/dbl-64/mpsqrt.h b/sysdeps/ieee754/dbl-64/mpsqrt.h new file mode 100644 index 0000000000..830b8aa132 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mpsqrt.h @@ -0,0 +1,50 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* */ +/* MODULE_NAME:mpatan.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef MPSQRT_H +#define MPSQRT_H + +#ifdef BIG_ENDI + static const number +/**/ one = {0x3ff00000, 0x00000000, }, /* 1 */ +/**/ halfrad = {0x41600000, 0x00000000, }; /* 2**23 */ + +#else +#ifdef LITTLE_ENDI + static const number +/**/ one = {0x00000000, 0x3ff00000, }, /* 1 */ +/**/ halfrad = {0x00000000, 0x41600000, }; /* 2**23 */ + +#endif +#endif + +#define ONE one.d +#define HALFRAD halfrad.d + + static const int 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 diff --git a/sysdeps/ieee754/dbl-64/mptan.c b/sysdeps/ieee754/dbl-64/mptan.c new file mode 100644 index 0000000000..6a9c85e958 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mptan.c @@ -0,0 +1,59 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/**********************************************************************/ +/* 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" + +int mpranred(double, mp_no *, int); +void c32(mp_no *, mp_no *, mp_no *, int); + +void mptan(double x, mp_no *mpy, int p) { + + static const double MONE = -1.0; + + int n; + mp_no mpw, mpc, mps; + + n = mpranred(x, &mpw, p) & 0x00000001; /* negative or positive result */ + c32(&mpw, &mpc, &mps, p); /* computing sin(x) and cos(x) */ + if (n) /* second or fourth quarter of unit circle */ + { dvd(&mpc,&mps,mpy,p); + mpy->d[0] *= MONE; + } /* tan is negative in this area */ + else dvd(&mps,&mpc,mpy,p); + + return; +} diff --git a/sysdeps/ieee754/dbl-64/mydefs.h b/sysdeps/ieee754/dbl-64/mydefs.h new file mode 100644 index 0000000000..70ac5cc08a --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mydefs.h @@ -0,0 +1,37 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* */ +/* 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 ABS(x) (((x)>0)?(x):-(x)) +#define max(x,y) (((y)>(x))?(y):(x)) +#define min(x,y) (((y)<(x))?(y):(x)) + +#endif diff --git a/sysdeps/ieee754/dbl-64/powtwo.tbl b/sysdeps/ieee754/dbl-64/powtwo.tbl new file mode 100644 index 0000000000..6cb6ca8afd --- /dev/null +++ b/sysdeps/ieee754/dbl-64/powtwo.tbl @@ -0,0 +1,12 @@ +/****************************************************************/ +/* 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/sysdeps/ieee754/dbl-64/root.tbl b/sysdeps/ieee754/dbl-64/root.tbl new file mode 100644 index 0000000000..8d3526a623 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/root.tbl @@ -0,0 +1,38 @@ +/****************************************************************/ +/* 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/sysdeps/ieee754/dbl-64/s_atan.c b/sysdeps/ieee754/dbl-64/s_atan.c index cad3ba12a8..997e29b5e4 100644 --- a/sysdeps/ieee754/dbl-64/s_atan.c +++ b/sysdeps/ieee754/dbl-64/s_atan.c @@ -1,163 +1,221 @@ -/* @(#)s_atan.c 5.1 93/09/24 */ /* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 * - * 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_atan.c,v 1.8 1995/05/10 20:46:45 jtc Exp $"; -#endif - -/* atan(x) - * Method - * 1. Reduce x to positive by atan(x) = -atan(-x). - * 2. According to the integer k=4t+0.25 chopped, t=x, the argument - * is further reduced to one of the following intervals and the - * arctangent of t is evaluated by the corresponding formula: + * 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 of the License, or + * (at your option) any later version. * - * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) - * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) - * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) - * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) - * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) + * 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 General Public License for more details. * - * 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. + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ +/************************************************************************/ +/* 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 "math.h" -#include "math_private.h" +#include "dla.h" +#include "mpa.h" +#include "MathLib.h" +#include "uatan.tbl" +#include "atnat.h" + +void __mpatan(mp_no *,mp_no *,int); /* see definition in mpatan.c */ +static double atanMp(double,const int[]); +double __signArctan(double,double); +/* 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,t4,t5,t6,t7,t8,t9,t10,u,u2,u3, + v,vv,w,ww,y,yy,y1,y2,z,zz; + int i,ux,dx,p; + static const int pr[M]={6,8,10,32}; + number num; + + mp_no mpt1,mpx,mpy,mpy1,mpy2,mperr; + + 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 */ + u = (x<ZERO) ? -x : x; + if (u<C) { + if (u<B) { + if (u<A) { /* u < A */ + return x; } + else { /* A <= u < B */ + v=x*x; yy=x*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d))))); + 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=v*(f11.d+v*(f13.d+v*(f15.d+v*(f17.d+v*f19.d)))); + ADD2(f9.d,ff9.d,s1,ZERO,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,ZERO,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) + ADD2(x,ZERO,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=z*(cij[i][2].d+z*(cij[i][3].d+z*(cij[i][4].d+ + z*(cij[i][5].d+z* cij[i][6].d)))); + 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=z*(hij[i][11].d+z*(hij[i][12].d+z*(hij[i][13].d+ + z*(hij[i][14].d+z* hij[i][15].d)))); + ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2) + MUL2(z,ZERO,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,ZERO,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,ZERO,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,ZERO,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=ONE/u; + EMULV(w,u,t1,t2,t3,t4,t5,t6,t7) + ww=w*((ONE-t1)-t2); + i=(TWO52+TWO8*w)-TWO52; i-=16; + z=(w-cij[i][0].d)+ww; + yy=HPI1-z*(cij[i][2].d+z*(cij[i][3].d+z*(cij[i][4].d+ + z*(cij[i][5].d+z* cij[i][6].d)))); + 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(ONE,ZERO,u,ZERO,w,ww,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) + t1=w-hij[i][0].d; + EADD(t1,ww,z,zz) + s1=z*(hij[i][11].d+z*(hij[i][12].d+z*(hij[i][13].d+ + z*(hij[i][14].d+z* hij[i][15].d)))); + ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,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=ONE/u; v=w*w; + EMULV(w,u,t1,t2,t3,t4,t5,t6,t7) + yy=w*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d))))); + ww=w*((ONE-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(ONE,ZERO,u,ZERO,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=v*(f11.d+v*(f13.d+v*(f15.d+v*(f17.d+v*f19.d)))); + ADD2(f9.d,ff9.d,s1,ZERO,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; } + } + } -#ifdef __STDC__ -static const double atanhi[] = { -#else -static double atanhi[] = { -#endif - 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ - 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ - 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ - 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ -}; - -#ifdef __STDC__ -static const double atanlo[] = { -#else -static double atanlo[] = { -#endif - 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ - 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ - 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ - 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ -}; - -#ifdef __STDC__ -static const double aT[] = { -#else -static double aT[] = { -#endif - 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ - -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ - 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ - -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ - 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ - -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ - 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ - -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ - 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ - -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ - 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ -}; - -#ifdef __STDC__ - static const double -#else - static double -#endif -one = 1.0, -huge = 1.0e300; - -#ifdef __STDC__ - double __atan(double x) -#else - double __atan(x) - double x; -#endif -{ - double w,s1,z,s,w2,w4,s11,s12,s13,s21,s22,s23; - int32_t ix,hx,id; - - GET_HIGH_WORD(hx,x); - ix = hx&0x7fffffff; - if(ix>=0x44100000) { /* if |x| >= 2^66 */ - u_int32_t low; - GET_LOW_WORD(low,x); - if(ix>0x7ff00000|| - (ix==0x7ff00000&&(low!=0))) - return x+x; /* NaN */ - if(hx>0) return atanhi[3]+atanlo[3]; - else return -atanhi[3]-atanlo[3]; - } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ - if (ix < 0x3e200000) { /* |x| < 2^-29 */ - if(huge+x>one) return x; /* raise inexact */ - } - id = -1; - } else { - x = fabs(x); - if (ix < 0x3ff30000) { /* |x| < 1.1875 */ - if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ - id = 0; x = (2.0*x-one)/(2.0+x); - } else { /* 11/16<=|x|< 19/16 */ - id = 1; x = (x-one)/(x+one); - } - } else { - if (ix < 0x40038000) { /* |x| < 2.4375 */ - id = 2; x = (x-1.5)/(one+1.5*x); - } else { /* 2.4375 <= |x| < 2^66 */ - id = 3; x = -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 */ -#ifdef DO_NOT_USE_THIS - 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; - } -#else - s11 = aT[8]+w*aT[10]; w2=w*w; - s12 = aT[4]+w*aT[6]; w4=w2*w2; - s13 = aT[0]+w*aT[2]; - s21 = aT[7]+w*aT[9]; - s22 = aT[3]+w*aT[5]; - s23 = w*aT[1]; - s1 = s13 + w2*s12 + w4*s11; - s = s23 + w2*s22 + w4*s21 + z*s1; - if (id<0) return x - x*(s); - else { - z = atanhi[id] - ((x*(s) - atanlo[id]) - x); - return (hx<0)? -z:z; - } -#endif } -weak_alias (__atan, atan) + + + /* Fix the sign of y and return */ +double __signArctan(double x,double y){ + + if (x<ZERO) return -y; + else return y; +} + + /* 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) return y1; + } + return y1; /*if unpossible to do exact computing */ +} + #ifdef NO_LONG_DOUBLE -strong_alias (__atan, __atanl) -weak_alias (__atan, atanl) +weak_alias (atan, atanl) #endif diff --git a/sysdeps/ieee754/dbl-64/s_cos.c b/sysdeps/ieee754/dbl-64/s_cos.c index 7edb5deafe..4be1276ccb 100644 --- a/sysdeps/ieee754/dbl-64/s_cos.c +++ b/sysdeps/ieee754/dbl-64/s_cos.c @@ -1,87 +1 @@ -/* @(#)s_cos.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_cos.c,v 1.7 1995/05/10 20:47:02 jtc Exp $"; -#endif - -/* cos(x) - * Return cosine function of x. - * - * kernel function: - * __kernel_sin ... sine function on [-pi/4,pi/4] - * __kernel_cos ... cosine function on [-pi/4,pi/4] - * __ieee754_rem_pio2 ... 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 "math.h" -#include "math_private.h" - -#ifdef __STDC__ - double __cos(double x) -#else - double __cos(x) - double x; -#endif -{ - double y[2],z=0.0; - int32_t n, ix; - - /* High word of x. */ - GET_HIGH_WORD(ix,x); - - /* |x| ~< pi/4 */ - ix &= 0x7fffffff; - if(ix <= 0x3fe921fb) return __kernel_cos(x,z); - - /* cos(Inf or NaN) is NaN */ - else if (ix>=0x7ff00000) return x-x; - - /* argument reduction needed */ - else { - n = __ieee754_rem_pio2(x,y); - switch(n&3) { - case 0: return __kernel_cos(y[0],y[1]); - case 1: return -__kernel_sin(y[0],y[1],1); - case 2: return -__kernel_cos(y[0],y[1]); - default: - return __kernel_sin(y[0],y[1],1); - } - } -} -weak_alias (__cos, cos) -#ifdef NO_LONG_DOUBLE -strong_alias (__cos, __cosl) -weak_alias (__cos, cosl) -#endif +/* In s_sin.c. */ diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c index 376c69ed00..b40c47f389 100644 --- a/sysdeps/ieee754/dbl-64/s_sin.c +++ b/sysdeps/ieee754/dbl-64/s_sin.c @@ -1,87 +1,1113 @@ -/* @(#)s_sin.c 5.1 93/09/24 */ /* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 * - * 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_sin.c,v 1.7 1995/05/10 20:48:15 jtc Exp $"; -#endif - -/* sin(x) - * Return sine function of x. - * - * kernel function: - * __kernel_sin ... sine function on [-pi/4,pi/4] - * __kernel_cos ... cose function on [-pi/4,pi/4] - * __ieee754_rem_pio2 ... 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 - * ---------------------------------------------------------- + * 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 of the License, or + * (at your option) any later version. * - * Special cases: - * Let trig be any of sin, cos, or tan. - * trig(+-INF) is NaN, with signals; - * trig(NaN) is that NaN; + * 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 General Public License for more details. * - * Accuracy: - * TRIG(x) returns trig(x) nearly rounded + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ +/****************************************************************************/ +/* */ +/* MODULE_NAME:usncs.c */ +/* */ +/* FUNCTIONS: usin */ +/* ucos */ +/* slow */ +/* slow1 */ +/* slow2 */ +/* sloww */ +/* sloww1 */ +/* sloww2 */ +/* bsloww */ +/* bsloww1 */ +/* bsloww2 */ +/* cslow2 */ +/* csloww */ +/* csloww1 */ +/* csloww2 */ +/* 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 "math.h" -#include "math_private.h" -#ifdef __STDC__ - double __sin(double x) -#else - double __sin(x) - double x; -#endif -{ - double y[2],z=0.0; - int32_t n, ix; - - /* High word of x. */ - GET_HIGH_WORD(ix,x); - - /* |x| ~< pi/4 */ - ix &= 0x7fffffff; - if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); - - /* sin(Inf or NaN) is NaN */ - else if (ix>=0x7ff00000) return x-x; - - /* argument reduction needed */ - else { - n = __ieee754_rem_pio2(x,y); - switch(n&3) { - case 0: return __kernel_sin(y[0],y[1],1); - case 1: return __kernel_cos(y[0],y[1]); - case 2: return -__kernel_sin(y[0],y[1],1); - default: - return -__kernel_cos(y[0],y[1]); +#include "endian.h" +#include "mydefs.h" +#include "usncs.h" +#include "MathLib.h" +#include "sincos.tbl" + +static const double + sn3 = -1.66666666666664880952546298448555E-01, + sn5 = 8.33333214285722277379541354343671E-03, + cs2 = 4.99999999999999999999950396842453E-01, + cs4 = -4.16666666666664434524222570944589E-02, + cs6 = 1.38888874007937613028114285595617E-03; + +void dubsin(double x, double dx, double w[]); +void docos(double x, double dx, double w[]); +double mpsin(double x, double dx); +double mpcos(double x, double dx); +double mpsin1(double x); +double mpcos1(double x); +static double slow(double x); +static double slow1(double x); +static double slow2(double x); +static double sloww(double x, double dx, double orig); +static double sloww1(double x, double dx, double orig); +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); +static double csloww(double x, double dx, double orig); +static double csloww1(double x, double dx, double orig); +static double csloww2(double x, double dx, double orig, int n); +/*******************************************************************/ +/* An ultimate sin routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of sin(x) */ +/*******************************************************************/ +double sin(double x){ + double xx,res,t,cor,y,w[2],s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2; + mynumber u,v; + int4 k,m,n,nn; + + u.x = x; + m = u.i[HIGH_HALF]; + k = 0x7fffffff&m; /* no sign */ + if (k < 0x3e500000) /* if x->0 =>sin(x)=x */ + return x; + /*---------------------------- 2^-26 < |x|< 0.25 ----------------------*/ + else if (k < 0x3fd00000){ + xx = x*x; + /*Taylor series */ + t = ((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*(xx*x); + res = x+t; + cor = (x-res)+t; + return (res == res + 1.07*cor)? res : slow(x); + } /* else if (k < 0x3fd00000) */ +/*---------------------------- 0.25<|x|< 0.855469---------------------- */ + else if (k < 0x3feb6000) { + u.x=(m>0)?big.x+x:big.x-x; + y=(m>0)?x-(u.x-big.x):x+(u.x-big.x); + xx=y*y; + s = y + y*xx*(sn3 +xx*sn5); + c = xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=(m>0)?sincos.x[k]:-sincos.x[k]; + ssn=(m>0)?sincos.x[k+1]:-sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + cor=(ssn+s*ccs-sn*c)+cs*s; + res=sn+cor; + cor=(sn-res)+cor; + return (res==res+1.025*cor)? res : slow1(x); + } /* else if (k < 0x3feb6000) */ + +/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/ + else if (k < 0x400368fd ) { + + y = (m>0)? hp0.x-x:hp0.x+x; + if (y>=0) { + u.x = big.x+y; + y = (y-(u.x-big.x))+hp1.x; + } + else { + u.x = big.x-y; + y = (-hp1.x) - (y+(u.x-big.x)); + } + xx=y*y; + s = y + y*xx*(sn3 +xx*sn5); + c = xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + cor=(ccs-s*ssn-cs*c)-sn*s; + res=cs+cor; + cor=(cs-res)+cor; + return (res==res+1.020*cor)? ((m>0)?res:-res) : slow2(x); + } /* else if (k < 0x400368fd) */ + +/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/ + else if (k < 0x419921FB ) { + t = (x*hpinv.x + toint.x); + xn = t - toint.x; + v.x = t; + y = (x - xn*mp1.x) - xn*mp2.x; + n =v.i[LOW_HALF]&3; + da = xn*mp3.x; + a=y-da; + da = (y-a)-da; + eps = ABS(x)*1.2e-30; + + switch (n) { /* quarter of unit circle */ + case 0: + case 2: + xx = a*a; + if (n) {a=-a;da=-da;} + if (xx < 0.01588) { + /*Taylor series */ + t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da; + res = a+t; + cor = (a-res)+t; + cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps; + return (res == res + cor)? res : sloww(a,da,x); } - } + else { + if (a>0) + {m=1;t=a;db=da;} + else + {m=0;t=-a;db=-da;} + u.x=big.x+t; + y=t-(u.x-big.x); + xx=y*y; + s = y + (db+y*xx*(sn3 +xx*sn5)); + c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + cor=(ssn+s*ccs-sn*c)+cs*s; + res=sn+cor; + cor=(sn-res)+cor; + cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps; + return (res==res+cor)? ((m)?res:-res) : sloww1(a,da,x); + } + break; + + case 1: + case 3: + if (a<0) + {a=-a;da=-da;} + u.x=big.x+a; + y=a-(u.x-big.x)+da; + xx=y*y; + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + s = y + y*xx*(sn3 +xx*sn5); + c = xx*(cs2 +xx*(cs4 + xx*cs6)); + cor=(ccs-s*ssn-cs*c)-sn*s; + res=cs+cor; + cor=(cs-res)+cor; + cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps; + return (res==res+cor)? ((n&2)?-res:res) : sloww2(a,da,x,n); + + break; + + } + + } /* else if (k < 0x419921FB ) */ + +/*---------------------105414350 <|x|< 281474976710656 --------------------*/ + else if (k < 0x42F00000 ) { + t = (x*hpinv.x + toint.x); + xn = t - toint.x; + v.x = t; + xn1 = (xn+8.0e22)-8.0e22; + xn2 = xn - xn1; + y = ((((x - xn1*mp1.x) - xn1*mp2.x)-xn2*mp1.x)-xn2*mp2.x); + n =v.i[LOW_HALF]&3; + da = xn1*pp3.x; + t=y-da; + da = (y-t)-da; + da = (da - xn2*pp3.x) -xn*pp4.x; + a = t+da; + da = (t-a)+da; + eps = 1.0e-24; + + switch (n) { + case 0: + case 2: + xx = a*a; + if (n) {a=-a;da=-da;} + if (xx < 0.01588) { + /* Taylor series */ + t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da; + res = a+t; + cor = (a-res)+t; + cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps; + return (res == res + cor)? res : bsloww(a,da,x,n); + } + else { + if (a>0) {m=1;t=a;db=da;} + else {m=0;t=-a;db=-da;} + u.x=big.x+t; + y=t-(u.x-big.x); + xx=y*y; + s = y + (db+y*xx*(sn3 +xx*sn5)); + c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + cor=(ssn+s*ccs-sn*c)+cs*s; + res=sn+cor; + cor=(sn-res)+cor; + cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps; + return (res==res+cor)? ((m)?res:-res) : bsloww1(a,da,x,n); + } + break; + + case 1: + case 3: + if (a<0) + {a=-a;da=-da;} + u.x=big.x+a; + y=a-(u.x-big.x)+da; + xx=y*y; + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + s = y + y*xx*(sn3 +xx*sn5); + c = xx*(cs2 +xx*(cs4 + xx*cs6)); + cor=(ccs-s*ssn-cs*c)-sn*s; + res=cs+cor; + cor=(cs-res)+cor; + cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps; + return (res==res+cor)? ((n&2)?-res:res) : bsloww2(a,da,x,n); + + break; + + } + + } /* else if (k < 0x42F00000 ) */ + +/* -----------------281474976710656 <|x| <2^1024----------------------------*/ + else if (k < 0x7ff00000) { + + n = branred(x,&a,&da); + switch (n) { + case 0: + if (a*a < 0.01588) return bsloww(a,da,x,n); + else return bsloww1(a,da,x,n); + break; + case 2: + if (a*a < 0.01588) return bsloww(-a,-da,x,n); + else return bsloww1(-a,-da,x,n); + break; + + case 1: + case 3: + return bsloww2(a,da,x,n); + break; + } + + } /* else if (k < 0x7ff00000 ) */ + +/*--------------------- |x| > 2^1024 ----------------------------------*/ + else return NAN.x; + return 0; /* unreachable */ +} + + +/*******************************************************************/ +/* An ultimate cos routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of cos(x) */ +/*******************************************************************/ + +double cos(double x) +{ + double y,xx,res,t,cor,s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2; + mynumber u,v; + int4 k,m,n; + + u.x = x; + m = u.i[HIGH_HALF]; + k = 0x7fffffff&m; + + if (k < 0x3e400000 ) return 1.0; /* |x|<2^-27 => cos(x)=1 */ + + else if (k < 0x3feb6000 ) {/* 2^-27 < |x| < 0.855469 */ + y=ABS(x); + u.x = big.x+y; + y = y-(u.x-big.x); + xx=y*y; + s = y + y*xx*(sn3 +xx*sn5); + c = xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + cor=(ccs-s*ssn-cs*c)-sn*s; + res=cs+cor; + cor=(cs-res)+cor; + return (res==res+1.020*cor)? res : cslow2(x); + +} /* else if (k < 0x3feb6000) */ + + else if (k < 0x400368fd ) {/* 0.855469 <|x|<2.426265 */; + y=hp0.x-ABS(x); + a=y+hp1.x; + da=(y-a)+hp1.x; + xx=a*a; + if (xx < 0.01588) { + t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da; + res = a+t; + cor = (a-res)+t; + cor = (cor>0)? 1.02*cor+1.0e-31 : 1.02*cor -1.0e-31; + return (res == res + cor)? res : csloww(a,da,x); + } + else { + if (a>0) {m=1;t=a;db=da;} + else {m=0;t=-a;db=-da;} + u.x=big.x+t; + y=t-(u.x-big.x); + xx=y*y; + s = y + (db+y*xx*(sn3 +xx*sn5)); + c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + cor=(ssn+s*ccs-sn*c)+cs*s; + res=sn+cor; + cor=(sn-res)+cor; + cor = (cor>0)? 1.035*cor+1.0e-31 : 1.035*cor-1.0e-31; + return (res==res+cor)? ((m)?res:-res) : csloww1(a,da,x); } -weak_alias (__sin, sin) + +} /* else if (k < 0x400368fd) */ + + + else if (k < 0x419921FB ) {/* 2.426265<|x|< 105414350 */ + t = (x*hpinv.x + toint.x); + xn = t - toint.x; + v.x = t; + y = (x - xn*mp1.x) - xn*mp2.x; + n =v.i[LOW_HALF]&3; + da = xn*mp3.x; + a=y-da; + da = (y-a)-da; + eps = ABS(x)*1.2e-30; + + switch (n) { + case 1: + case 3: + xx = a*a; + if (n == 1) {a=-a;da=-da;} + if (xx < 0.01588) { + t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da; + res = a+t; + cor = (a-res)+t; + cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps; + return (res == res + cor)? res : csloww(a,da,x); + } + else { + if (a>0) {m=1;t=a;db=da;} + else {m=0;t=-a;db=-da;} + u.x=big.x+t; + y=t-(u.x-big.x); + xx=y*y; + s = y + (db+y*xx*(sn3 +xx*sn5)); + c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + cor=(ssn+s*ccs-sn*c)+cs*s; + res=sn+cor; + cor=(sn-res)+cor; + cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps; + return (res==res+cor)? ((m)?res:-res) : csloww1(a,da,x); + } + break; + + case 0: + case 2: + if (a<0) {a=-a;da=-da;} + u.x=big.x+a; + y=a-(u.x-big.x)+da; + xx=y*y; + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + s = y + y*xx*(sn3 +xx*sn5); + c = xx*(cs2 +xx*(cs4 + xx*cs6)); + cor=(ccs-s*ssn-cs*c)-sn*s; + res=cs+cor; + cor=(cs-res)+cor; + cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps; + return (res==res+cor)? ((n)?-res:res) : csloww2(a,da,x,n); + + break; + + } + + } /* else if (k < 0x419921FB ) */ + + + else if (k < 0x42F00000 ) { + t = (x*hpinv.x + toint.x); + xn = t - toint.x; + v.x = t; + xn1 = (xn+8.0e22)-8.0e22; + xn2 = xn - xn1; + y = ((((x - xn1*mp1.x) - xn1*mp2.x)-xn2*mp1.x)-xn2*mp2.x); + n =v.i[LOW_HALF]&3; + da = xn1*pp3.x; + t=y-da; + da = (y-t)-da; + da = (da - xn2*pp3.x) -xn*pp4.x; + a = t+da; + da = (t-a)+da; + eps = 1.0e-24; + + switch (n) { + case 1: + case 3: + xx = a*a; + if (n==1) {a=-a;da=-da;} + if (xx < 0.01588) { + t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da; + res = a+t; + cor = (a-res)+t; + cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps; + return (res == res + cor)? res : bsloww(a,da,x,n); + } + else { + if (a>0) {m=1;t=a;db=da;} + else {m=0;t=-a;db=-da;} + u.x=big.x+t; + y=t-(u.x-big.x); + xx=y*y; + s = y + (db+y*xx*(sn3 +xx*sn5)); + c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + cor=(ssn+s*ccs-sn*c)+cs*s; + res=sn+cor; + cor=(sn-res)+cor; + cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps; + return (res==res+cor)? ((m)?res:-res) : bsloww1(a,da,x,n); + } + break; + + case 0: + case 2: + if (a<0) {a=-a;da=-da;} + u.x=big.x+a; + y=a-(u.x-big.x)+da; + xx=y*y; + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + s = y + y*xx*(sn3 +xx*sn5); + c = xx*(cs2 +xx*(cs4 + xx*cs6)); + cor=(ccs-s*ssn-cs*c)-sn*s; + res=cs+cor; + cor=(cs-res)+cor; + cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps; + return (res==res+cor)? ((n)?-res:res) : bsloww2(a,da,x,n); + break; + + } + + } /* else if (k < 0x42F00000 ) */ + + else if (k < 0x7ff00000) {/* 281474976710656 <|x| <2^1024 */ + + n = branred(x,&a,&da); + switch (n) { + case 1: + if (a*a < 0.01588) return bsloww(-a,-da,x,n); + else return bsloww1(-a,-da,x,n); + break; + case 3: + if (a*a < 0.01588) return bsloww(a,da,x,n); + else return bsloww1(a,da,x,n); + break; + + case 0: + case 2: + return bsloww2(a,da,x,n); + break; + } + + } /* else if (k < 0x7ff00000 ) */ + + + + + else return NAN.x; /* |x| > 2^1024 */ + return 0; + +} + +/************************************************************************/ +/* 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 double slow(double x) { +static const double th2_36 = 206158430208.0; /* 1.5*2**37 */ + double y,x1,x2,xx,r,t,res,cor,w[2]; + x1=(x+th2_36)-th2_36; + y = aa.x*x1*x1*x1; + r=x+y; + x2=x-x1; + xx=x*x; + t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2; + t=((x-r)+y)+t; + res=r+t; + cor = (r-res)+t; + if (res == res + 1.0007*cor) return res; + else { + dubsin(ABS(x),0,w); + if (w[0] == w[0]+1.000000001*w[1]) return (x>0)?w[0]:-w[0]; + else return (x>0)?mpsin(x,0):-mpsin(-x,0); + } +} +/*******************************************************************************/ +/* Routine compute sin(x) for 0.25<|x|< 0.855469 by sincos.tbl and Taylor */ +/* and if result still doesn't accurate enough by mpsin or dubsin */ +/*******************************************************************************/ + +static double slow1(double x) { + mynumber u; + double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res; + static const double t22 = 6291456.0; + int4 k; + y=ABS(x); + u.x=big.x+y; + y=y-(u.x-big.x); + xx=y*y; + s = y*xx*(sn3 +xx*sn5); + c = xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; /* Data */ + ssn=sincos.x[k+1]; /* from */ + cs=sincos.x[k+2]; /* tables */ + ccs=sincos.x[k+3]; /* sincos.tbl */ + y1 = (y+t22)-t22; + y2 = y - y1; + c1 = (cs+t22)-t22; + c2=(cs-c1)+ccs; + cor=(ssn+s*ccs+cs*s+c2*y+c1*y2)-sn*c; + y=sn+c1*y1; + cor = cor+((sn-y)+c1*y1); + res=y+cor; + cor=(y-res)+cor; + if (res == res+1.0005*cor) return (x>0)?res:-res; + else { + dubsin(ABS(x),0,w); + if (w[0] == w[0]+1.000000005*w[1]) return (x>0)?w[0]:-w[0]; + else return (x>0)?mpsin(x,0):-mpsin(-x,0); + } +} +/**************************************************************************/ +/* Routine compute sin(x) for 0.855469 <|x|<2.426265 by sincos.tbl */ +/* and if result still doesn't accurate enough by mpsin or dubsin */ +/**************************************************************************/ +static double slow2(double x) { + mynumber u; + double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res,del; + static const double t22 = 6291456.0; + int4 k; + y=ABS(x); + y = hp0.x-y; + if (y>=0) { + u.x = big.x+y; + y = y-(u.x-big.x); + del = hp1.x; + } + else { + u.x = big.x-y; + y = -(y+(u.x-big.x)); + del = -hp1.x; + } + xx=y*y; + s = y*xx*(sn3 +xx*sn5); + c = y*del+xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + y1 = (y+t22)-t22; + y2 = (y - y1)+del; + e1 = (sn+t22)-t22; + e2=(sn-e1)+ssn; + cor=(ccs-cs*c-e1*y2-e2*y)-sn*s; + y=cs-e1*y1; + cor = cor+((cs-y)-e1*y1); + res=y+cor; + cor=(y-res)+cor; + if (res == res+1.0005*cor) return (x>0)?res:-res; + else { + y=ABS(x)-hp0.x; + y1=y-hp1.x; + y2=(y-y1)-hp1.x; + docos(y1,y2,w); + if (w[0] == w[0]+1.000000005*w[1]) return (x>0)?w[0]:-w[0]; + else return (x>0)?mpsin(x,0):-mpsin(-x,0); + } +} +/***************************************************************************/ +/* Routine compute sin(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 mpsin1 or dubsin */ +/***************************************************************************/ + +static double sloww(double x,double dx, double orig) { + static const double th2_36 = 206158430208.0; /* 1.5*2**37 */ + double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn; + union {int4 i[2]; double x;} v; + int4 n; + x1=(x+th2_36)-th2_36; + y = aa.x*x1*x1*x1; + r=x+y; + x2=(x-x1)+dx; + xx=x*x; + t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx; + t=((x-r)+y)+t; + res=r+t; + cor = (r-res)+t; + cor = (cor>0)? 1.0005*cor+ABS(orig)*3.1e-30 : 1.0005*cor-ABS(orig)*3.1e-30; + if (res == res + cor) return res; + else { + (x>0)? dubsin(x,dx,w) : dubsin(-x,-dx,w); + cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-30 : 1.000000001*w[1] - ABS(orig)*1.1e-30; + if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0]; + else { + t = (orig*hpinv.x + toint.x); + xn = t - toint.x; + v.x = t; + y = (orig - xn*mp1.x) - xn*mp2.x; + n =v.i[LOW_HALF]&3; + da = xn*pp3.x; + t=y-da; + da = (y-t)-da; + y = xn*pp4.x; + a = t - y; + da = ((t-a)-y)+da; + if (n&2) {a=-a; da=-da;} + (a>0)? dubsin(a,da,w) : dubsin(-a,-da,w); + cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-40 : 1.000000001*w[1] - ABS(orig)*1.1e-40; + if (w[0] == w[0]+cor) return (a>0)?w[0]:-w[0]; + else return mpsin1(orig); + } + } +} +/***************************************************************************/ +/* Routine compute sin(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 mpsin1 or dubsin */ +/***************************************************************************/ + +static double sloww1(double x, double dx, double orig) { + mynumber u; + double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res; + static const double t22 = 6291456.0; + int4 k; + y=ABS(x); + u.x=big.x+y; + y=y-(u.x-big.x); + dx=(x>0)?dx:-dx; + xx=y*y; + s = y*xx*(sn3 +xx*sn5); + c = xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + y1 = (y+t22)-t22; + y2 = (y - y1)+dx; + c1 = (cs+t22)-t22; + c2=(cs-c1)+ccs; + cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c; + y=sn+c1*y1; + cor = cor+((sn-y)+c1*y1); + res=y+cor; + cor=(y-res)+cor; + cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig); + if (res == res + cor) return (x>0)?res:-res; + else { + dubsin(ABS(x),dx,w); + cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig); + if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0]; + else return mpsin1(orig); + } +} +/***************************************************************************/ +/* 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 double sloww2(double x, double dx, double orig, int n) { + mynumber u; + double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res; + static const double t22 = 6291456.0; + int4 k; + y=ABS(x); + u.x=big.x+y; + y=y-(u.x-big.x); + dx=(x>0)?dx:-dx; + xx=y*y; + s = y*xx*(sn3 +xx*sn5); + c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + + y1 = (y+t22)-t22; + y2 = (y - y1)+dx; + e1 = (sn+t22)-t22; + e2=(sn-e1)+ssn; + cor=(ccs-cs*c-e1*y2-e2*y)-sn*s; + y=cs-e1*y1; + cor = cor+((cs-y)-e1*y1); + res=y+cor; + cor=(y-res)+cor; + cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig); + if (res == res + cor) return (n&2)?-res:res; + else { + docos(ABS(x),dx,w); + cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig); + if (w[0] == w[0]+cor) return (n&2)?-w[0]:w[0]; + else return mpsin1(orig); + } +} +/***************************************************************************/ +/* 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 double bsloww(double x,double dx, double orig,int n) { + static const double th2_36 = 206158430208.0; /* 1.5*2**37 */ + double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn; + union {int4 i[2]; double x;} v; + x1=(x+th2_36)-th2_36; + y = aa.x*x1*x1*x1; + r=x+y; + x2=(x-x1)+dx; + xx=x*x; + t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx; + t=((x-r)+y)+t; + res=r+t; + cor = (r-res)+t; + cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24; + if (res == res + cor) return res; + else { + (x>0)? dubsin(x,dx,w) : dubsin(-x,-dx,w); + cor = (w[1]>0)? 1.000000001*w[1] + 1.1e-24 : 1.000000001*w[1] - 1.1e-24; + if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0]; + else return (n&1)?mpcos1(orig):mpsin1(orig); + } +} + +/***************************************************************************/ +/* 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 double bsloww1(double x, double dx, double orig,int n) { +mynumber u; + double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res; + static const double t22 = 6291456.0; + int4 k; + y=ABS(x); + u.x=big.x+y; + y=y-(u.x-big.x); + dx=(x>0)?dx:-dx; + xx=y*y; + s = y*xx*(sn3 +xx*sn5); + c = xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + y1 = (y+t22)-t22; + y2 = (y - y1)+dx; + c1 = (cs+t22)-t22; + c2=(cs-c1)+ccs; + cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c; + y=sn+c1*y1; + cor = cor+((sn-y)+c1*y1); + res=y+cor; + cor=(y-res)+cor; + cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24; + if (res == res + cor) return (x>0)?res:-res; + else { + dubsin(ABS(x),dx,w); + cor = (w[1]>0)? 1.000000005*w[1]+1.1e-24: 1.000000005*w[1]-1.1e-24; + if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0]; + else return (n&1)?mpcos1(orig):mpsin1(orig); + } +} + +/***************************************************************************/ +/* 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 double bsloww2(double x, double dx, double orig, int n) { +mynumber u; + double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res; + static const double t22 = 6291456.0; + int4 k; + y=ABS(x); + u.x=big.x+y; + y=y-(u.x-big.x); + dx=(x>0)?dx:-dx; + xx=y*y; + s = y*xx*(sn3 +xx*sn5); + c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + + y1 = (y+t22)-t22; + y2 = (y - y1)+dx; + e1 = (sn+t22)-t22; + e2=(sn-e1)+ssn; + cor=(ccs-cs*c-e1*y2-e2*y)-sn*s; + y=cs-e1*y1; + cor = cor+((cs-y)-e1*y1); + res=y+cor; + cor=(y-res)+cor; + cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24; + if (res == res + cor) return (n&2)?-res:res; + else { + docos(ABS(x),dx,w); + cor = (w[1]>0)? 1.000000005*w[1]+1.1e-24 : 1.000000005*w[1]-1.1e-24; + if (w[0] == w[0]+cor) return (n&2)?-w[0]:w[0]; + else return (n&1)?mpsin1(orig):mpcos1(orig); + } +} + +/************************************************************************/ +/* 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 double cslow2(double x) { + mynumber u; + double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res; + static const double t22 = 6291456.0; + int4 k; + y=ABS(x); + u.x = big.x+y; + y = y-(u.x-big.x); + xx=y*y; + s = y*xx*(sn3 +xx*sn5); + c = xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + y1 = (y+t22)-t22; + y2 = y - y1; + e1 = (sn+t22)-t22; + e2=(sn-e1)+ssn; + cor=(ccs-cs*c-e1*y2-e2*y)-sn*s; + y=cs-e1*y1; + cor = cor+((cs-y)-e1*y1); + res=y+cor; + cor=(y-res)+cor; + if (res == res+1.0005*cor) + return res; + else { + y=ABS(x); + docos(y,0,w); + if (w[0] == w[0]+1.000000005*w[1]) return w[0]; + else return mpcos(x,0); + } +} + +/***************************************************************************/ +/* Routine compute cos(x+dx) (Double-Length number) where x is small enough*/ +/* to use Taylor series around zero and (x+dx) .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 double csloww(double x,double dx, double orig) { + static const double th2_36 = 206158430208.0; /* 1.5*2**37 */ + double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn; + union {int4 i[2]; double x;} v; + int4 n; + x1=(x+th2_36)-th2_36; + y = aa.x*x1*x1*x1; + r=x+y; + x2=(x-x1)+dx; + xx=x*x; + /* Taylor series */ + t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx; + t=((x-r)+y)+t; + res=r+t; + cor = (r-res)+t; + cor = (cor>0)? 1.0005*cor+ABS(orig)*3.1e-30 : 1.0005*cor-ABS(orig)*3.1e-30; + if (res == res + cor) return res; + else { + (x>0)? dubsin(x,dx,w) : dubsin(-x,-dx,w); + cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-30 : 1.000000001*w[1] - ABS(orig)*1.1e-30; + if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0]; + else { + t = (orig*hpinv.x + toint.x); + xn = t - toint.x; + v.x = t; + y = (orig - xn*mp1.x) - xn*mp2.x; + n =v.i[LOW_HALF]&3; + da = xn*pp3.x; + t=y-da; + da = (y-t)-da; + y = xn*pp4.x; + a = t - y; + da = ((t-a)-y)+da; + if (n==1) {a=-a; da=-da;} + (a>0)? dubsin(a,da,w) : dubsin(-a,-da,w); + cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-40 : 1.000000001*w[1] - ABS(orig)*1.1e-40; + if (w[0] == w[0]+cor) return (a>0)?w[0]:-w[0]; + else return mpcos1(orig); + } + } +} + +/***************************************************************************/ +/* Routine compute sin(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 double csloww1(double x, double dx, double orig) { + mynumber u; + double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res; + static const double t22 = 6291456.0; + int4 k; + y=ABS(x); + u.x=big.x+y; + y=y-(u.x-big.x); + dx=(x>0)?dx:-dx; + xx=y*y; + s = y*xx*(sn3 +xx*sn5); + c = xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + y1 = (y+t22)-t22; + y2 = (y - y1)+dx; + c1 = (cs+t22)-t22; + c2=(cs-c1)+ccs; + cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c; + y=sn+c1*y1; + cor = cor+((sn-y)+c1*y1); + res=y+cor; + cor=(y-res)+cor; + cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig); + if (res == res + cor) return (x>0)?res:-res; + else { + dubsin(ABS(x),dx,w); + cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig); + if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0]; + else return mpcos1(orig); + } +} + + +/***************************************************************************/ +/* 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 other routines */ +/***************************************************************************/ + +static double csloww2(double x, double dx, double orig, int n) { + mynumber u; + double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res; + static const double t22 = 6291456.0; + int4 k; + y=ABS(x); + u.x=big.x+y; + y=y-(u.x-big.x); + dx=(x>0)?dx:-dx; + xx=y*y; + s = y*xx*(sn3 +xx*sn5); + c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6)); + k=u.i[LOW_HALF]<<2; + sn=sincos.x[k]; + ssn=sincos.x[k+1]; + cs=sincos.x[k+2]; + ccs=sincos.x[k+3]; + + y1 = (y+t22)-t22; + y2 = (y - y1)+dx; + e1 = (sn+t22)-t22; + e2=(sn-e1)+ssn; + cor=(ccs-cs*c-e1*y2-e2*y)-sn*s; + y=cs-e1*y1; + cor = cor+((cs-y)-e1*y1); + res=y+cor; + cor=(y-res)+cor; + cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig); + if (res == res + cor) return (n)?-res:res; + else { + docos(ABS(x),dx,w); + cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig); + if (w[0] == w[0]+cor) return (n)?-w[0]:w[0]; + else return mpcos1(orig); + } +} + #ifdef NO_LONG_DOUBLE -strong_alias (__sin, __sinl) -weak_alias (__sin, sinl) +weak_alias (sin, sinl) +weak_alias (cos, cosl) #endif diff --git a/sysdeps/ieee754/dbl-64/s_sincos.c b/sysdeps/ieee754/dbl-64/s_sincos.c index 5bc564ba5b..7c1f572a3f 100644 --- a/sysdeps/ieee754/dbl-64/s_sincos.c +++ b/sysdeps/ieee754/dbl-64/s_sincos.c @@ -1,5 +1,5 @@ /* Compute sine and cosine of argument. - Copyright (C) 1997 Free Software Foundation, Inc. + Copyright (C) 1997, 2001 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. @@ -33,42 +33,15 @@ __sincos (double x, double *sinx, double *cosx) /* |x| ~< pi/4 */ ix &= 0x7fffffff; - if (ix <= 0x3fe921fb) - { - *sinx = __kernel_sin (x, 0.0, 0); - *cosx = __kernel_cos (x, 0.0); - } - else if (ix>=0x7ff00000) + if (ix>=0x7ff00000) { /* sin(Inf or NaN) is NaN */ *sinx = *cosx = x - x; } else { - /* Argument reduction needed. */ - double y[2]; - int n; - - n = __ieee754_rem_pio2 (x, y); - switch (n & 3) - { - case 0: - *sinx = __kernel_sin (y[0], y[1], 1); - *cosx = __kernel_cos (y[0], y[1]); - break; - case 1: - *sinx = __kernel_cos (y[0], y[1]); - *cosx = -__kernel_sin (y[0], y[1], 1); - break; - case 2: - *sinx = -__kernel_sin (y[0], y[1], 1); - *cosx = -__kernel_cos (y[0], y[1]); - break; - default: - *sinx = -__kernel_cos (y[0], y[1]); - *cosx = __kernel_sin (y[0], y[1], 1); - break; - } + *sinx = sin (x); + *cosx = cos (x); } } weak_alias (__sincos, sincos) diff --git a/sysdeps/ieee754/dbl-64/s_tan.c b/sysdeps/ieee754/dbl-64/s_tan.c index 714cf27dd2..2db8673389 100644 --- a/sysdeps/ieee754/dbl-64/s_tan.c +++ b/sysdeps/ieee754/dbl-64/s_tan.c @@ -1,81 +1,480 @@ -/* @(#)s_tan.c 5.1 93/09/24 */ /* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 * - * 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_tan.c,v 1.7 1995/05/10 20:48:18 jtc Exp $"; -#endif - -/* tan(x) - * Return tangent function of x. - * - * kernel function: - * __kernel_tan ... tangent function on [-pi/4,pi/4] - * __ieee754_rem_pio2 ... 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 - * ---------------------------------------------------------- + * 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 of the License, or + * (at your option) any later version. * - * Special cases: - * Let trig be any of sin, cos, or tan. - * trig(+-INF) is NaN, with signals; - * trig(NaN) is that NaN; + * 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 General Public License for more details. * - * Accuracy: - * TRIG(x) returns trig(x) nearly rounded + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ +/*********************************************************************/ +/* 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 "endian.h" +#include "dla.h" +#include "mpa.h" +#include "MathLib.h" +static double tanMp(double); +void __mptan(double, mp_no *, int); -#include "math.h" -#include "math_private.h" +double tan(double x) { +#include "utan.h" +#include "utan.tbl" -#ifdef __STDC__ - double __tan(double x) -#else - double __tan(x) - double x; -#endif -{ - double y[2],z=0.0; - int32_t n, ix; + 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,t5,t6,t7,t8,t9,t10,w,x2,xn,xx2,y,ya,yya,z0,z,zz,z2,zz2; + int p; + number num,v; + mp_no mpa,mpy,mpt1,mpt2; + + int branred(double, double *, double *); + int mpranred(double, mp_no *, int); + + /* x=+-INF, x=NaN */ + num.d = x; ux = num.i[HIGH_HALF]; + if ((ux&0x7ff00000)==0x7ff00000) return x-x; + + w=(x<ZERO) ? -x : x; + + /* (I) The case abs(x) <= 1.259e-8 */ + if (w<=g1.d) return x; + + /* (II) The case 1.259e-8 < abs(x) <= 0.0608 */ + if (w<=g2.d) { + + /* First stage */ + x2 = x*x; + t2 = x*x2*(d3.d+x2*(d5.d+x2*(d7.d+x2*(d9.d+x2*d11.d)))); + if ((y=x+(t2-u1.d*t2)) == x+(t2+u1.d*t2)) return y; + + /* Second stage */ + c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+ + x2*a27.d)))))); + EMULV(x,x,x2,xx2,t1,t2,t3,t4,t5) + ADD2(a13.d,aa13.d,c1,zero.d,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 ,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8) + ADD2(x ,zero.d,c2,cc2,c1,cc1,t1,t2) + if ((y=c1+(cc1-u2.d*c1)) == c1+(cc1+u2.d*c1)) return y; + return tanMp(x); + } + + /* (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<ZERO) ? MONE : ONE; + 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)) return (s*y); + t3 = (t2<ZERO) ? -t2 : t2; + if ((y=fi+(t2-(t4=fi*ua3.d+t3*ub3.d)))==fi+(t2+t4)) return (s*y); + + /* 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,zero.d,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 ,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8) + ADD2(z ,zero.d,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(one.d,zero.d,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)) return (s*y); + return tanMp(x); + } + + /* (---) 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<ZERO) {ya=-a; yya=-da; sy=MONE;} + else {ya= a; yya= da; sy= ONE;} + + /* (IV),(V) The case 0.787 < abs(x) <= 25, abs(y) <= 1e-7 */ + if (ya<=gy1.d) return tanMp(x); + + /* (VI) The case 0.787 < abs(x) <= 25, 1e-7 < abs(y) <= 0.0608 */ + if (ya<=gy2.d) { + a2 = a*a; + t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d)))); + if (n) { + /* First stage -cot */ + EADD(a,t2,b,db) + DIV2(one.d,zero.d,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)) return (-y); } + else { + /* First stage tan */ + if ((y=a+(t2-u5.d*a))==a+(t2+u5.d*a)) return y; } + /* 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 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+ + x2*a27.d)))))); + ADD2(a13.d,aa13.d,c1,zero.d,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(one.d,zero.d,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)) return (-y); } + else { + /* Second stage tan */ + if ((y=c1+(cc1-u7.d*c1)) == c1+(cc1+u7.d*c1)) return y; } + return tanMp(x); + } + + /* (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; - /* High word of x. */ - GET_HIGH_WORD(ix,x); + if (n) { + /* -cot */ + t2 = pz*(fi+gi)/(fi+pz); + if ((y=gi-(t2-gi*u10.d))==gi-(t2+gi*u10.d)) return (-sy*y); + t3 = (t2<ZERO) ? -t2 : t2; + if ((y=gi-(t2-(t4=gi*ua10.d+t3*ub10.d)))==gi-(t2+t4)) return (-sy*y); } + else { + /* tan */ + t2 = pz*(gi+fi)/(gi-pz); + if ((y=fi+(t2-fi*u9.d))==fi+(t2+fi*u9.d)) return (sy*y); + t3 = (t2<ZERO) ? -t2 : t2; + if ((y=fi+(t2-(t4=fi*ua9.d+t3*ub9.d)))==fi+(t2+t4)) return (sy*y); } - /* |x| ~< pi/4 */ - ix &= 0x7fffffff; - if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); + /* 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,zero.d,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) - /* tan(Inf or NaN) is NaN */ - else if (ix>=0x7ff00000) return x-x; /* NaN */ + 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(one.d,zero.d,c3,cc3,c1,cc1,t1,t2) - /* argument reduction needed */ - else { - n = __ieee754_rem_pio2(x,y); - return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even - -1 -- n odd */ - } + 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)) return (-sy*y); } + 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)) return (sy*y); } + + return tanMp(x); + } + + /* (---) 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<ZERO) {ya=-a; yya=-da; sy=MONE;} + else {ya= a; yya= da; sy= ONE;} + + /* (+++) The case 25 < abs(x) <= 1e8, abs(y) <= 1e-7 */ + if (ya<=gy1.d) return tanMp(x); + + /* (VIII) The case 25 < abs(x) <= 1e8, 1e-7 < abs(y) <= 0.0608 */ + if (ya<=gy2.d) { + a2 = a*a; + t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d)))); + if (n) { + /* First stage -cot */ + EADD(a,t2,b,db) + DIV2(one.d,zero.d,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)) return (-y); } + else { + /* First stage tan */ + if ((y=a+(t2-u13.d*a))==a+(t2+u13.d*a)) return y; } + + /* Second stage */ + MUL2(a,da,a,da,x2,xx2,t1,t2,t3,t4,t5,t6,t7,t8) + c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+ + x2*a27.d)))))); + ADD2(a13.d,aa13.d,c1,zero.d,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(one.d,zero.d,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)) return (-y); } + else { + /* Second stage tan */ + if ((y=c1+(cc1-u15.d*c1)) == c1+(cc1+u15.d*c1)) return (y); } + return tanMp(x); + } + + /* (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)) return (-sy*y); + t3 = (t2<ZERO) ? -t2 : t2; + if ((y=gi-(t2-(t4=gi*ua18.d+t3*ub18.d)))==gi-(t2+t4)) return (-sy*y); } + else { + /* tan */ + t2 = pz*(gi+fi)/(gi-pz); + if ((y=fi+(t2-fi*u17.d))==fi+(t2+fi*u17.d)) return (sy*y); + t3 = (t2<ZERO) ? -t2 : t2; + if ((y=fi+(t2-(t4=fi*ua17.d+t3*ub17.d)))==fi+(t2+t4)) return (sy*y); } + + /* 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,zero.d,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(one.d,zero.d,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)) return (-sy*y); } + 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)) return (sy*y); } + return tanMp(x); + } + + /* (---) 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<ZERO) {ya=-a; yya=-da; sy=MONE;} + else {ya= a; yya= da; sy= ONE;} + + /* (+++) The case 1e8 < abs(x) < 2**1024, abs(y) <= 1e-7 */ + if (ya<=gy1.d) return tanMp(x); + + /* (X) The case 1e8 < abs(x) < 2**1024, 1e-7 < abs(y) <= 0.0608 */ + if (ya<=gy2.d) { + a2 = a*a; + t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d)))); + if (n) { + /* First stage -cot */ + EADD(a,t2,b,db) + DIV2(one.d,zero.d,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)) return (-y); } + else { + /* First stage tan */ + if ((y=a+(t2-u21.d*a))==a+(t2+u21.d*a)) return y; } + + /* 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 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+ + x2*a27.d)))))); + ADD2(a13.d,aa13.d,c1,zero.d,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(one.d,zero.d,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)) return (-y); } + else { + /* Second stage tan */ + if ((y=c1+(cc1-u23.d*c1)) == c1+(cc1+u23.d*c1)) return y; } + return tanMp(x); + } + + /* (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)) return (-sy*y); + t3 = (t2<ZERO) ? -t2 : t2; + if ((y=gi-(t2-(t4=gi*ua26.d+t3*ub26.d)))==gi-(t2+t4)) return (-sy*y); } + else { + /* tan */ + t2 = pz*(gi+fi)/(gi-pz); + if ((y=fi+(t2-fi*u25.d))==fi+(t2+fi*u25.d)) return (sy*y); + t3 = (t2<ZERO) ? -t2 : t2; + if ((y=fi+(t2-(t4=fi*ua25.d+t3*ub25.d)))==fi+(t2+t4)) return (sy*y); } + + /* 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,zero.d,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(one.d,zero.d,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)) return (-sy*y); } + 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)) return (sy*y); } + return tanMp(x); +} + + +/* multiple precision stage */ +/* Convert x to multi precision number,compute tan(x) by mptan() routine */ +/* and converts result back to double */ +static double tanMp(double x) +{ + int p; + double y; + mp_no mpy; + p=32; + __mptan(x, &mpy, p); + __mp_dbl(&mpy,&y,p); + return y; } -weak_alias (__tan, tan) + #ifdef NO_LONG_DOUBLE -strong_alias (__tan, __tanl) -weak_alias (__tan, tanl) +weak_alias (tan, tanl) #endif diff --git a/sysdeps/ieee754/dbl-64/sincos.tbl b/sysdeps/ieee754/dbl-64/sincos.tbl new file mode 100644 index 0000000000..2cfb957f27 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/sincos.tbl @@ -0,0 +1,892 @@ +/****************************************************************/ +/* TABLES FOR THE usin() and ucos() FUNCTION */ +/****************************************************************/ + + +#ifdef BIG_ENDI +static const union {int4 i[880]; double x[40];}sincos = { +/**/ 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 +static const union {int4 i[880]; double x[440];} sincos = { +/**/ 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, +/**/ 0x2EFAA944, 0x3FC8D763, +/**/ 0x62CBB953, 0xBC620FA2, +/**/ 0xFEB82ACD, 0x3FEF643E, +/**/ 0xC1FE28AC, 0x3C76B00A, +/**/ 0xD0CEC312, 0x3FC9D252, +/**/ 0x80B1137D, 0x3C59C43D, +/**/ 0x8CFF6797, 0x3FEF5794, +/**/ 0x3E03B1D5, 0x3C6E3A0D, +/**/ 0x297A0765, 0x3FCACCDB, +/**/ 0x57D6CDEB, 0xBC59883B, +/**/ 0xBD1E3A79, 0x3FEF4A6C, +/**/ 0xEDAEBB57, 0x3C813DF0, +/**/ 0x4EDC6199, 0x3FCBC6F8, +/**/ 0x6A7B0CAB, 0x3C69C1A5, +/**/ 0xC3B3D16E, 0x3FEF3CC7, +/**/ 0xD28A3494, 0xBC621A3A, +/**/ 0x588289A3, 0x3FCCC0A6, +/**/ 0x9BC87C6B, 0xBC6868D0, +/**/ 0xD753FFED, 0x3FEF2EA5, +/**/ 0x5F56D583, 0x3C8CC421, +/**/ 0x5FB5A5D0, 0x3FCDB9E1, +/**/ 0xD6CC6FC2, 0xBC632E20, +/**/ 0x3086649F, 0x3FEF2007, +/**/ 0x16C1984B, 0x3C7B9404, +/**/ 0x7F8AE5A3, 0x3FCEB2A5, +/**/ 0xAF572CEB, 0xBC60BE06, +/**/ 0x09C5873B, 0x3FEF10EC, +/**/ 0x762C1283, 0x3C8D9072, +/**/ 0xD4F31577, 0x3FCFAAEE, +/**/ 0x508E32B8, 0xBC615D88, +/**/ 0x9F7DEEA1, 0x3FEF0154, +/**/ 0x99E5CAFD, 0x3C8D3C1E, +/**/ 0xBF65155C, 0x3FD0515C, +/**/ 0x9DFD8EC8, 0xBC79B8C2, +/**/ 0x300D2F26, 0x3FEEF141, +/**/ 0x08DED372, 0xBC82AA1B, +/**/ 0xCEF36436, 0x3FD0CD00, +/**/ 0x0C93E2B5, 0xBC79FB0A, +/**/ 0xFBC0F11C, 0x3FEEE0B1, +/**/ 0x80BBC3B1, 0xBC4BFD23, +/**/ 0xAA94DDEB, 0x3FD14861, +/**/ 0xB5B615A4, 0xBC6BE881, +/**/ 0x44D5EFA1, 0x3FEECFA7, +/**/ 0x4AF541D0, 0xBC556D0A, +/**/ 0x64C6B876, 0x3FD1C37D, +/**/ 0xFE0DCFF5, 0x3C746076, +/**/ 0x4F76EFA8, 0x3FEEBE21, +/**/ 0x12BA543E, 0xBC802F9F, +/**/ 0x111AAF36, 0x3FD23E52, +/**/ 0x334EFF18, 0xBC74F080, +/**/ 0x61BBAF4F, 0x3FEEAC20, +/**/ 0x3E94658D, 0x3C62C1D5, +/**/ 0xC43EB49F, 0x3FD2B8DD, +/**/ 0x99F2D807, 0x3C615538, +/**/ 0xC3A7CD83, 0x3FEE99A4, +/**/ 0x1BC53CE8, 0xBC82264B, +/**/ 0x94049F87, 0x3FD3331E, +/**/ 0xB40C302C, 0x3C7E0CB6, +/**/ 0xBF29A9ED, 0x3FEE86AE, +/**/ 0xFDBB58A7, 0x3C89397A, +/**/ 0x9769D3D8, 0x3FD3AD12, +/**/ 0x04878398, 0x3C003D55, +/**/ 0xA0193D40, 0x3FEE733E, +/**/ 0x3546CE13, 0xBC86428B, +/**/ 0xE69EE697, 0x3FD426B7, +/**/ 0x5705C59F, 0xBC7F09C7, +/**/ 0xB436E9D0, 0x3FEE5F54, +/**/ 0xD02FC8BC, 0x3C87EB0F, +/**/ 0x9B0F3D20, 0x3FD4A00C, +/**/ 0x6BB08EAD, 0x3C7823BA, +/**/ 0x4B2A449C, 0x3FEE4AF1, +/**/ 0x2E8A6833, 0xBC868CA0, +/**/ 0xCF68A77A, 0x3FD5190E, +/**/ 0x55EEF0F3, 0x3C7B3571, +/**/ 0xB680D6A5, 0x3FEE3614, +/**/ 0xAA015237, 0xBC727793, +/**/ 0x9FA2F597, 0x3FD591BC, +/**/ 0xAC3FE0CB, 0x3C67C74B, +/**/ 0x49ACD6C1, 0x3FEE20BF, +/**/ 0xC7EF636C, 0xBC5660AE, +/**/ 0x29078775, 0x3FD60A14, +/**/ 0x0BA89133, 0x3C5B1FD8, +/**/ 0x5A03DBCE, 0x3FEE0AF1, +/**/ 0x02771AE6, 0x3C5FE8E7, +/**/ 0x8A38D7F7, 0x3FD68213, +/**/ 0x02444AAD, 0xBC7D8892, +/**/ 0x3EBD875E, 0x3FEDF4AB, +/**/ 0x7E6736C4, 0xBC8E2D8A, +/**/ 0xE33A0255, 0x3FD6F9B8, +/**/ 0x4EE9DA0D, 0x3C742BC1, +/**/ 0x50F228D6, 0x3FEDDDED, +/**/ 0xD42BA2BF, 0xBC6E80C8, +/**/ 0x55764214, 0x3FD77102, +/**/ 0x314BB6CE, 0xBC66EAD7, +/**/ 0xEB995912, 0x3FEDC6B7, +/**/ 0x776DCD35, 0x3C54B364, +/**/ 0x03C86D4E, 0x3FD7E7EE, +/**/ 0xDABF5AF2, 0xBC7B63BC, +/**/ 0x6B888E83, 0x3FEDAF0B, +/**/ 0x2B5E5CEA, 0x3C8A249E, +/**/ 0x12826949, 0x3FD85E7A, +/**/ 0x9B5FACE0, 0x3C78A40E, +/**/ 0x2F71A9DC, 0x3FED96E8, +/**/ 0xD5D2039D, 0x3C8FF61B, +/**/ 0xA774992F, 0x3FD8D4A4, +/**/ 0xEA766326, 0x3C744A02, +/**/ 0x97E17B4A, 0x3FED7E4E, +/**/ 0x352BED94, 0xBC63B770, +/**/ 0xE9F546C5, 0x3FD94A6B, +/**/ 0x3E683F58, 0xBC769CE1, +/**/ 0x073E4040, 0x3FED653F, +/**/ 0x434BEC37, 0xBC876236, +/**/ 0x02E80510, 0x3FD9BFCE, +/**/ 0xA320B0A4, 0x3C709E39, +/**/ 0xE1C619E0, 0x3FED4BB9, +/**/ 0x77858F61, 0x3C8F34BB, +/**/ 0x1CC50CCA, 0x3FDA34C9, +/**/ 0x3B50CECD, 0xBC5A310E, +/**/ 0x8D8D7C06, 0x3FED31BF, +/**/ 0x3089CBDD, 0x3C7E60DD, +/**/ 0x63A09277, 0x3FDAA95B, +/**/ 0xB13C0381, 0xBC66293E, +/**/ 0x727D94F0, 0x3FED1750, +/**/ 0x1EC1A48E, 0x3C80D52B, +/**/ 0x05321617, 0x3FDB1D83, +/**/ 0xCB99F519, 0xBC7AE242, +/**/ 0xFA52AD9F, 0x3FECFC6C, +/**/ 0x508F2A0D, 0x3C88B5B5, +/**/ 0x30DBAC43, 0x3FDB913E, +/**/ 0x2F6C3FF1, 0xBC7E38AD, +/**/ 0x909A82E5, 0x3FECE115, +/**/ 0xBB31109A, 0x3C81F139, +/**/ 0x17B140A3, 0x3FDC048B, +/**/ 0x757E9FA7, 0x3C619FE6, +/**/ 0xA2B2972E, 0x3FECC54A, +/**/ 0x2BA83A98, 0x3C64EE16, +/**/ 0xEC7FD19E, 0x3FDC7767, +/**/ 0x1A3D5826, 0xBC5EB14D, +/**/ 0x9FC67D0B, 0x3FECA90C, +/**/ 0x485E3462, 0xBC646A81, +/**/ 0xE3D4A51F, 0x3FDCE9D2, +/**/ 0x12DAE298, 0xBC62FC8A, +/**/ 0xF8CE1A84, 0x3FEC8C5B, +/**/ 0xA1590123, 0x3C7AB3D1, +/**/ 0x34047661, 0x3FDD5BCA, +/**/ 0xA75FC29C, 0x3C728A44, +/**/ 0x208BE53B, 0x3FEC6F39, +/**/ 0xFBAADB42, 0xBC8741DB, +/**/ 0x15329C9A, 0x3FDDCD4C, +/**/ 0xE171FD9A, 0x3C70D4C6, +/**/ 0x8B8B175E, 0x3FEC51A4, +/**/ 0x3B9AA880, 0xBC61BBB4, +/**/ 0xC1582A69, 0x3FDE3E56, +/**/ 0x1099F88F, 0xBC50A482, +/**/ 0xB01DDD81, 0x3FEC339E, +/**/ 0xEE82C5C0, 0xBC8CAAF5, +/**/ 0x744B05F0, 0x3FDEAEE8, +/**/ 0x3C9B027D, 0xBC5789B4, +/**/ 0x065B7D50, 0x3FEC1528, +/**/ 0x1312E828, 0xBC889211, +/**/ 0x6BC4F97B, 0x3FDF1EFF, +/**/ 0xF8A7525C, 0x3C717212, +/**/ 0x081E7536, 0x3FEBF641, +/**/ 0x1628A9A1, 0x3C8B7BD7, +/**/ 0xE76ABC97, 0x3FDF8E99, +/**/ 0xAF2D00A3, 0x3C59D950, +/**/ 0x310294F5, 0x3FEBD6EA, +/**/ 0xC88C109D, 0x3C731BBC, +/**/ 0x28D2F57A, 0x3FDFFDB6, +/**/ 0x2E905B6A, 0x3C6F4A99, +/**/ 0xFE630F32, 0x3FEBB723, +/**/ 0x452D0A39, 0x3C772BD2, +/**/ 0x39C69955, 0x3FE03629, +/**/ 0x78397B01, 0xBC82D8CD, +/**/ 0xEF58840E, 0x3FEB96EE, +/**/ 0xC78FADE0, 0x3C545A3C, +/**/ 0x86946E5B, 0x3FE06D36, +/**/ 0x4538FF1B, 0x3C83F5AE, +/**/ 0x84B704C2, 0x3FEB764B, +/**/ 0xC21B389B, 0xBC8F5848, +/**/ 0x1E9E1001, 0x3FE0A402, +/**/ 0xA13914F6, 0xBC86F643, +/**/ 0x410C104E, 0x3FEB553A, +/**/ 0x47027A16, 0x3C58FF79, +/**/ 0x26B5672E, 0x3FE0DA8B, +/**/ 0xF0BEE909, 0xBC8A58DE, +/**/ 0xA89C8948, 0x3FEB33BB, +/**/ 0x1D1F6CA9, 0x3C8EA6A5, +/**/ 0xC4B69C3B, 0x3FE110D0, +/**/ 0x98809981, 0x3C8D9189, +/**/ 0x4162A4C6, 0x3FEB11D0, +/**/ 0x1EFBC0C2, 0x3C71DD56, +/**/ 0x1F8B7F82, 0x3FE146D2, +/**/ 0x5E2739A8, 0x3C7BF953, +/**/ 0x930BD275, 0x3FEAEF78, +/**/ 0x79746F94, 0xBC7F8362, +/**/ 0x5F2EEDB0, 0x3FE17C8E, +/**/ 0x102E2488, 0x3C635E57, +/**/ 0x26F69DE5, 0x3FEACCB5, +/**/ 0x8DD6B6CC, 0x3C88FB6A, +/**/ 0xACB02FDD, 0x3FE1B204, +/**/ 0x70CBB5FF, 0xBC5F190C, +/**/ 0x88308913, 0x3FEAA986, +/**/ 0x07CD5070, 0xBC0B83D6, +/**/ 0x3236574C, 0x3FE1E734, +/**/ 0xA4F41D5A, 0x3C722A3F, +/**/ 0x4373E02D, 0x3FEA85ED, +/**/ 0x385EC792, 0x3C69BE06, +/**/ 0x1B0394CF, 0x3FE21C1C, +/**/ 0x4B23AA31, 0x3C5E5B32, +/**/ 0xE72586AF, 0x3FEA61E9, +/**/ 0xE2FD453F, 0x3C858330, +/**/ 0x93788BBB, 0x3FE250BB, +/**/ 0x2457BCCE, 0x3C7EA3D0, +/**/ 0x0352BDCF, 0x3FEA3D7D, +/**/ 0xECA19669, 0xBC868DBA, +/**/ 0xC917A067, 0x3FE28511, +/**/ 0xD9A16B70, 0xBC801DF1, +/**/ 0x29AEE445, 0x3FEA18A7, +/**/ 0x736C0358, 0x3C395E25, +/**/ 0xEA88421E, 0x3FE2B91D, +/**/ 0xDB216AB0, 0xBC8FA371, +/**/ 0xED912F85, 0x3FE9F368, +/**/ 0xC5791606, 0xBC81D200, +/**/ 0x279A3082, 0x3FE2ECDF, +/**/ 0xE0E7E37E, 0x3C8D3557, +/**/ 0xE3F25E5C, 0x3FE9CDC2, +/**/ 0x12993F62, 0x3C83F991, +/**/ 0xB148BC4F, 0x3FE32054, +/**/ 0x095A135B, 0x3C8F6B42, +/**/ 0xA36A6514, 0x3FE9A7B5, +/**/ 0xCC9FA7A9, 0x3C8722CF, +/**/ 0xB9BE0367, 0x3FE3537D, +/**/ 0x7AF040F0, 0x3C6B327E, +/**/ 0xC42E1310, 0x3FE98141, +/**/ 0x0488F08D, 0x3C8D1FF8, +/**/ 0x7456282B, 0x3FE38659, +/**/ 0xA93B07A8, 0xBC710FAD, +/**/ 0xE00CB1FD, 0x3FE95A67, +/**/ 0xA21F862D, 0xBC80BEFD, +/**/ 0x15A2840A, 0x3FE3B8E7, +/**/ 0xA7D2F07B, 0xBC797653, +/**/ 0x926D9E92, 0x3FE93328, +/**/ 0x03600CDA, 0xBC8BB770, +/**/ 0xD36CD53A, 0x3FE3EB25, +/**/ 0xE1570FC0, 0xBC5BE570, +/**/ 0x784DDAF7, 0x3FE90B84, +/**/ 0x0AB93B87, 0xBC70FEB1, +/**/ 0xE4BA6790, 0x3FE41D14, +/**/ 0xD287ECF5, 0x3C84608F, +/**/ 0x303D9AD1, 0x3FE8E37C, +/**/ 0xB53D4BF8, 0xBC6463A4, +/**/ 0x81CF386B, 0x3FE44EB3, +/**/ 0x1E6A5505, 0xBC83ED6C, +/**/ 0x5A5DC900, 0x3FE8BB10, +/**/ 0x3E9474C1, 0x3C8863E0, +/**/ 0xE431159F, 0x3FE48000, +/**/ 0x7463ED10, 0xBC8B194A, +/**/ 0x985D871F, 0x3FE89241, +/**/ 0xC413ED84, 0x3C8C48D9, +/**/ 0x46AAB761, 0x3FE4B0FC, +/**/ 0x738CC59A, 0x3C20DA05, +/**/ 0x8D77A6C6, 0x3FE86910, +/**/ 0xE2BFE9DD, 0x3C7338FF, +/**/ 0xE54ED51B, 0x3FE4E1A4, +/**/ 0x89B7C76A, 0xBC8A492F, +/**/ 0xDE701CA0, 0x3FE83F7D, +/**/ 0x609BC6E8, 0xBC4152CF, +/**/ 0xFD7B351C, 0x3FE511F9, +/**/ 0x61C48831, 0xBC85C0E8, +/**/ 0x31916D5D, 0x3FE8158A, +/**/ 0x0B8228DE, 0xBC6DE8B9, +/**/ 0xCDDBB724, 0x3FE541FA, +/**/ 0x8520D391, 0x3C7232C2, +/**/ 0x2EAA1488, 0x3FE7EB36, +/**/ 0xA4A5959F, 0x3C5A1D65, +/**/ 0x966D59B3, 0x3FE571A6, +/**/ 0x4D0FB198, 0x3C5C843B, +/**/ 0x7F09E54F, 0x3FE7C082, +/**/ 0xD72AEE68, 0xBC6C73D6, +/**/ 0x98813A12, 0x3FE5A0FC, +/**/ 0xB7D4227B, 0xBC8D82E2, +/**/ 0xCD7F6543, 0x3FE7956F, +/**/ 0xE9D45AE4, 0xBC8AB276, +/**/ 0x16BF8F0D, 0x3FE5CFFC, +/**/ 0x70EB578A, 0x3C896CB3, +/**/ 0xC655211F, 0x3FE769FE, +/**/ 0xCF8C68C5, 0xBC6827D5, +/**/ 0x552A9E57, 0x3FE5FEA4, +/**/ 0xF7EE20B7, 0x3C80B6CE, +/**/ 0x174EFBA1, 0x3FE73E30, +/**/ 0x3D94AD5F, 0xBC65D3AE, +/**/ 0x9921AC79, 0x3FE62CF4, +/**/ 0x55B6241A, 0xBC8EDD98, +/**/ 0x6FA77678, 0x3FE71204, +/**/ 0xA5029C81, 0x3C8425B0, +/**/ 0x2963E755, 0x3FE65AEC, +/**/ 0x6B71053C, 0x3C8126F9, +/**/ 0x800CF55E, 0x3FE6E57C, +/**/ 0xDEDBD0A6, 0x3C860286, +/**/ 0x4E134B2F, 0x3FE6888A, +/**/ 0x7644D5E6, 0xBC86B7D3, +/**/ 0xFA9EFB5D, 0x3FE6B898, +/**/ 0x86CCF4B2, 0x3C715AC7, +/**/ 0x50B7821A, 0x3FE6B5CE, +/**/ 0x8F702E0F, 0xBC65D515, +/**/ 0x92EB6253, 0x3FE68B5A, +/**/ 0xD985F89C, 0xBC89A91A, +/**/ 0x7C40BDE1, 0x3FE6E2B7, +/**/ 0x857FAD53, 0xBC70E729, +/**/ 0xFDEB8CBA, 0x3FE65DC1, +/**/ 0x47337C77, 0xBC597C1B, +/**/ 0x1D0A8C40, 0x3FE70F45, +/**/ 0x3885770D, 0x3C697EDE, +/**/ 0xF20191C7, 0x3FE62FCF, +/**/ 0x895756EF, 0x3C6D9143, +/**/ 0x80DEA578, 0x3FE73B76, +/**/ 0x06DC12A2, 0xBC722483, +/**/ 0x26F563DF, 0x3FE60185, +/**/ 0xE0E432D0, 0x3C846CA5, +/**/ 0xF6F7B524, 0x3FE7674A, +/**/ 0x94AC84A8, 0x3C7E9D3F, +/**/ 0x55F1F17A, 0x3FE5D2E2, +/**/ 0x04C8892B, 0x3C803141, +/**/ 0xD0041D52, 0x3FE792C1, +/**/ 0xEEB354EB, 0xBC8ABF05, +/**/ 0x39824077, 0x3FE5A3E8, +/**/ 0x2759BE62, 0x3C8428AA, +/**/ 0x5E28B3C2, 0x3FE7BDDA, +/**/ 0x7CCD0393, 0x3C4AD119, +/**/ 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/sysdeps/ieee754/dbl-64/sincos32.c b/sysdeps/ieee754/dbl-64/sincos32.c new file mode 100644 index 0000000000..41fe2f281a --- /dev/null +++ b/sysdeps/ieee754/dbl-64/sincos32.c @@ -0,0 +1,339 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/****************************************************************/ +/* 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" + +/****************************************************************/ +/* Compute Multi-Precision sin() function for given p. Receive */ +/* Multi Precision number x and result stored at y */ +/****************************************************************/ +void ss32(mp_no *x, mp_no *y, int p) { + int i; + double a,b; + static const mp_no mpone = {1,1.0,1.0}; + mp_no mpt1,mpt2,x2,gor,sum ,mpk={1,1.0}; + for (i=1;i<=p;i++) mpk.d[i]=0; + + mul(x,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 */ +/**********************************************************************/ +void cc32(mp_no *x, mp_no *y, int p) { + int i; + double a,b; + static const mp_no mpone = {1,1.0,1.0}; + mp_no mpt1,mpt2,x2,gor,sum ,mpk={1,1.0}; + for (i=1;i<=p;i++) mpk.d[i]=0; + + mul(x,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); +} + +/***************************************************************************/ +/* c32() computes both sin(x), cos(x) as Multi precision numbers */ +/***************************************************************************/ +void c32(mp_no *x, mp_no *y, mp_no *z, int p) { + static const mp_no mpt={1,1.0,2.0}, one={1,1.0,1.0}; + 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(&mpt,&c,&t1,p); + mul(&t1,&c,&t2,p); + add(&t2,&t2,&c,p); + } + sub(&one,&c,y,p); + cpy(&s,z,p); +} + +/************************************************************************/ +/*Routine 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 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) return (res<res1)?res:res1; + else return (res>res1)?res:res1; +} + +/************************************************************************/ +/*Routine 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 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) return (res>res1)?res:res1; + else return (res<res1)?res:res1; +} + +/*******************************************************************/ +/*Compute sin(x+dx) as Multi Precision number and return result as */ +/* double */ +/*******************************************************************/ +double mpsin(double x, double dx) { + int p; + double y; + mp_no a,b,c; + p=32; + dbl_mp(x,&a,p); + dbl_mp(dx,&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(x+dx) */ + mp_dbl(&b,&y,p); + return y; +} + +/*******************************************************************/ +/* Compute cos()of double-length number (x+dx) as Multi Precision */ +/* number and return result as double */ +/*******************************************************************/ +double mpcos(double x, double dx) { + int p; + double y; + mp_no a,b,c; + p=32; + dbl_mp(x,&a,p); + dbl_mp(dx,&b,p); + add(&a,&b,&c,p); + if (x>0.8) + { sub(&hp,&c,&b,p); + c32(&b,&a,&c,p); + } + else c32(&c,&a,&b,p); /* a = cos(x+dx) */ + mp_dbl(&a,&y,p); + return y; +} + +/******************************************************************/ +/* mpranred() 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,.... */ +/* Return int which indicates in which quarter of circle x is */ +/******************************************************************/ +int mpranred(double x, mp_no *y, int p) +{ + number v; + double t,xn; + int i,k,n; + static const mp_no one = {1,1.0,1.0}; + mp_no a,b,c; + + if (ABS(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] >= 8388608.0) + { t +=1.0; + sub(&c,&one,&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); + } +} + +/*******************************************************************/ +/* Multi-Precision sin() function subroutine, for p=32. It is */ +/* based on the routines mpranred() and c32(). */ +/*******************************************************************/ +double mpsin1(double x) +{ + int p; + int n; + mp_no u,s,c; + double y; + p=32; + n=mpranred(x,&u,p); /* n is 0, 1, 2 or 3 */ + c32(&u,&c,&s,p); + switch (n) { /* in which quarter of unit circle y is*/ + case 0: + mp_dbl(&s,&y,p); + return y; + break; + + case 2: + mp_dbl(&s,&y,p); + return -y; + break; + + case 1: + mp_dbl(&c,&y,p); + return y; + break; + + case 3: + mp_dbl(&c,&y,p); + return -y; + break; + + } + return 0; /* unreachable, to make the compiler happy */ +} + +/*****************************************************************/ +/* Multi-Precision cos() function subroutine, for p=32. It is */ +/* based on the routines mpranred() and c32(). */ +/*****************************************************************/ + +double mpcos1(double x) +{ + int p; + int n; + mp_no u,s,c; + double y; + + p=32; + n=mpranred(x,&u,p); /* n is 0, 1, 2 or 3 */ + c32(&u,&c,&s,p); + switch (n) { /* in what quarter of unit circle y is*/ + + case 0: + mp_dbl(&c,&y,p); + return y; + break; + + case 2: + mp_dbl(&c,&y,p); + return -y; + break; + + case 1: + mp_dbl(&s,&y,p); + return -y; + break; + + case 3: + mp_dbl(&s,&y,p); + return y; + break; + + } + return 0; /* unreachable, to make the compiler happy */ +} +/******************************************************************/ diff --git a/sysdeps/ieee754/dbl-64/sincos32.h b/sysdeps/ieee754/dbl-64/sincos32.h new file mode 100644 index 0000000000..fa510e84be --- /dev/null +++ b/sysdeps/ieee754/dbl-64/sincos32.h @@ -0,0 +1,81 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* */ +/* 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/sysdeps/ieee754/dbl-64/slowexp.c b/sysdeps/ieee754/dbl-64/slowexp.c new file mode 100644 index 0000000000..d394dc3438 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/slowexp.c @@ -0,0 +1,60 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/**************************************************************************/ +/* 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 "mpa.h" + +void mpexp(mp_no *x, mp_no *y, int p); + +/*Converting from double precision to Multi-precision and calculating e^x */ +double slowexp(double x) { + double y,w,z,res,eps=3.0e-26; + int orig,i,p; + mp_no mpx, mpy, mpz,mpw,mpeps,mpcor; + + p=6; + dbl_mp(x,&mpx,p); /* Convert a double precision number x */ + /* into a multiple precision number mpx with prec. p. */ + mpexp(&mpx, &mpy, p); /* Multi-Precision exponential function */ + 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) return w; + else { /* if calculating is not exactly */ + p = 32; + dbl_mp(x,&mpx,p); + mpexp(&mpx, &mpy, p); + mp_dbl(&mpy, &res, p); + return res; + } +} + diff --git a/sysdeps/ieee754/dbl-64/slowpow.c b/sysdeps/ieee754/dbl-64/slowpow.c new file mode 100644 index 0000000000..efb607255a --- /dev/null +++ b/sysdeps/ieee754/dbl-64/slowpow.c @@ -0,0 +1,73 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/*************************************************************************/ +/* 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" + +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 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; + + res = halfulp(x,y); /* halfulp() returns -10 or x^y */ + if (res >= 0) return res; /* if result was really computed by halfulp */ + /* else, if result was not really computed by halfulp */ + p = 10; /* p=precision */ + dbl_mp(x,&mpx,p); + dbl_mp(y,&mpy,p); + dbl_mp(z,&mpz,p); + mplog(&mpx, &mpz, p); /* log(x) = z */ + mul(&mpy,&mpz,&mpw,p); /* y * z =w */ + mpexp(&mpw, &mpp, p); /* e^w =pp */ + add(&mpp,&eps,&mpr,p); /* pp+eps =r */ + mp_dbl(&mpr, &res, p); + sub(&mpp,&eps,&mpr1,p); /* pp -eps =r1 */ + mp_dbl(&mpr1, &res1, p); /* converting into double precision */ + if (res == res1) return res; + + p = 32; /* if we get here result wasn't calculated exactly, continue */ + dbl_mp(x,&mpx,p); /* for more exact calculation */ + dbl_mp(y,&mpy,p); + dbl_mp(z,&mpz,p); + mplog(&mpx, &mpz, p); /* log(c)=z */ + mul(&mpy,&mpz,&mpw,p); /* y*z =w */ + mpexp(&mpw, &mpp, p); /* e^w=pp */ + mp_dbl(&mpp, &res, p); /* converting into double precision */ + return res; +} diff --git a/sysdeps/ieee754/dbl-64/uasncs.h b/sysdeps/ieee754/dbl-64/uasncs.h new file mode 100644 index 0000000000..aade0b694a --- /dev/null +++ b/sysdeps/ieee754/dbl-64/uasncs.h @@ -0,0 +1,69 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* */ +/* 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/sysdeps/ieee754/dbl-64/uatan.tbl b/sysdeps/ieee754/dbl-64/uatan.tbl new file mode 100644 index 0000000000..d6abfce08f --- /dev/null +++ b/sysdeps/ieee754/dbl-64/uatan.tbl @@ -0,0 +1,11116 @@ +/****************************************************************/ +/* 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, },}, +/**/ {{0X3FC10003, 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0XDD6453A0, }, +/**/ {0X3FE2FB6F, 0XCFFFCC1E, }, +/**/ {0XBFD2A648, 0X6F8D8291, }, +/**/ {0X3FB2D56F, 0X03654CC3, }, +/**/ {0X3FA07EE3, 0X4BB6E7A6, }, +/**/ {0XBFAA5F2A, 0X87992F03, },}, +/**/ {{0X3FEAA000, 0XDD839D49, }, +/**/ {0X3FE634FF, 0XB412C9A0, }, +/**/ {0X3FE2E8D0, 0XE2D59E01, }, +/**/ {0XBFD2981C, 0X5467CFDD, }, +/**/ {0X3FB2F5E8, 0XFF1FADB5, }, +/**/ {0X3F9FF7D6, 0XA3BA803C, }, +/**/ {0XBFAA04E3, 0X46AF8DB7, },}, +/**/ {{0X3FEAC000, 0X770DF220, }, +/**/ {0X3FE647DE, 0XFEF70020, }, +/**/ {0X3FE2D640, 0X220AFF7F, }, +/**/ {0XBFD289D8, 0X36F9E74F, }, +/**/ {0X3FB3155E, 0XE509140A, }, +/**/ {0X3F9EF56B, 0X61AB0B7F, }, +/**/ {0XBFA9AAE2, 0X98CE391F, },}, +/**/ {{0X3FEAE001, 0X125BBE48, }, +/**/ {0X3FE65AAC, 0X57A24D20, }, +/**/ {0X3FE2C3BD, 0X1BFB3559, }, +/**/ {0XBFD27B7C, 0X6DDE55DD, }, +/**/ {0X3FB333D5, 0X15C4C270, }, +/**/ {0X3F9DF67A, 0X9BAC4ECF, }, +/**/ {0XBFA9512F, 0X363A972B, },}, +/**/ {{0X3FEAFFFE, 0X7C321839, }, +/**/ {0X3FE66D65, 0X569B83C0, }, +/**/ {0X3FE2B14A, 0X53FBF8D9, }, +/**/ {0XBFD26D0B, 0X9CFA03CE, }, +/**/ {0X3FB3514B, 0X2CAA2E0C, }, +/**/ {0X3F9CFB22, 0X4597BE9A, }, +/**/ {0XBFA8F7CF, 0X99110022, },}, +/**/ {{0X3FEB1FFE, 0X75486924, }, +/**/ {0X3FE6800D, 0X68CEFB40, }, +/**/ {0X3FE29EE4, 0X8E6AA814, }, +/**/ {0XBFD25E83, 0XE8AFA7EB, }, +/**/ {0X3FB36DC9, 0XFB0E8AC8, }, +/**/ {0X3F9C0331, 0XAD5D66CA, }, +/**/ {0XBFA89EC9, 0XFEDB1E8B, },}, +/**/ {{0X3FEB4001, 0X5FB8DEB8, }, +/**/ {0X3FE692A4, 0XD137C500, }, +/**/ {0X3FE28C8B, 0XABFF668E, }, +/**/ {0XBFD24FE5, 0XD8E71E0A, }, +/**/ {0X3FB38955, 0X1297317A, }, +/**/ {0X3F9B0EA3, 0X1D844655, }, +/**/ {0XBFA84624, 0X6914067D, },}, +/**/ {{0X3FEB6000, 0X386C27B9, }, +/**/ {0X3FE6A527, 0X8CDF6FC0, }, +/**/ {0X3FE27A43, 0XC5758DB8, }, +/**/ {0XBFD24135, 0X59CADCE0, }, +/**/ {0X3FB3A3E9, 0XEE34AE91, }, +/**/ {0X3F9A1DA8, 0X1C5FFF05, }, +/**/ {0XBFA7EDE4, 0X9EC8AAC6, },}, +/**/ {{0X3FEB8000, 0XD1EFDDB3, }, +/**/ {0X3FE6B799, 0X0ACCB660, }, +/**/ {0X3FE26809, 0X9983AAB2, }, +/**/ {0XBFD23270, 0X76047E08, }, +/**/ {0X3FB3BD90, 0XF132139B, }, +/**/ {0X3F993010, 0X58DEB3E1, }, +/**/ {0XBFA79610, 0X2D194CE9, },}, +/**/ {{0X3FEB9FFE, 0X42CC4047, }, +/**/ {0X3FE6C9F6, 0X86445E60, }, +/**/ {0X3FE255E0, 0X069F871F, }, +/**/ {0XBFD2239A, 0X25461639, }, +/**/ {0X3FB3D649, 0XA926C127, }, +/**/ {0X3F9845FB, 0XC5A21F70, }, +/**/ {0XBFA73EAC, 0X68E20BE6, },}, +/**/ {{0X3FEBC001, 0X951AEAAD, }, +/**/ {0X3FE6DC45, 0X3C4E45A0, }, +/**/ {0X3FE243C1, 0XFF6573B0, }, +/**/ {0XBFD214AE, 0XE38FA7E7, }, +/**/ {0X3FB3EE1E, 0X5EA1330F, }, +/**/ {0X3F975F24, 0X2BCCE6DF, }, +/**/ {0XBFA6E7BE, 0X6F3902C5, },}, +/**/ {{0X3FEBDFFE, 0X6616FE11, }, +/**/ {0X3FE6EE7E, 0X27106FE0, }, +/**/ {0X3FE231B6, 0X97B587F0, }, +/**/ {0XBFD205B5, 0X240FEF32, }, +/**/ {0X3FB40509, 0X44EB818C, }, +/**/ {0X3F967BDE, 0X108160F9, }, +/**/ {0XBFA6914B, 0X271D18AD, },}, +/**/ {{0X3FEBFFFF, 0X54511C72, }, +/**/ {0X3FE700A7, 0X643BBB40, }, +/**/ {0X3FE21FB7, 0XE1823C8B, }, +/**/ {0XBFD1F6A8, 0X9A854F7A, }, +/**/ {0X3FB41B15, 0X71F04837, }, +/**/ {0X3F959BD8, 0XBBD10F7C, }, +/**/ {0XBFA63B57, 0X41F03711, },}, +/**/ {{0X3FEC2000, 0XC537593E, }, +/**/ {0X3FE712BE, 0XF36D6400, }, +/**/ {0X3FE20DC7, 0XF754B2D5, }, +/**/ {0XBFD1E78B, 0X9D24DBED, }, +/**/ {0X3FB43043, 0X94F485E0, }, +/**/ {0X3F94BF29, 0X122A6884, }, +/**/ {0XBFA5E5E7, 0X3D2AA4E9, },}, +/**/ {{0X3FEC4000, 0XDDD35719, }, +/**/ {0X3FE724C3, 0XD7FA3000, }, +/**/ {0X3FE1FBE7, 0XF2A8B1BF, }, +/**/ {0XBFD1D85F, 0XB25DDDF6, }, +/**/ {0X3FB44495, 0XD2E3B20F, }, +/**/ {0X3F93E5D6, 0X7FCC1B30, }, +/**/ {0XBFA590FF, 0X62D0D00F, },}, +/**/ {{0X3FEC6000, 0X402375B6, }, +/**/ {0X3FE736B6, 0X7DFF3720, }, +/**/ {0X3FE1EA17, 0X86C92387, }, +/**/ {0XBFD1C925, 0X31DDFC58, }, +/**/ {0X3FB4580F, 0XF8B6CBC2, }, +/**/ {0X3F930FD7, 0X00CE998E, }, +/**/ {0XBFA53CA3, 0XCB299E5F, },}, +/**/ {{0X3FEC7FFF, 0X19904FE4, }, +/**/ {0X3FE74897, 0X0F395860, }, +/**/ {0X3FE1D856, 0XA825BA33, }, +/**/ {0XBFD1B9DC, 0XA75E0FC5, }, +/**/ {0X3FB46AB5, 0X79F8FD7D, }, +/**/ {0X3F923D23, 0XA5A90AFE, }, +/**/ {0XBFA4E8D8, 0X5D2F574B, },}, +/**/ {{0X3FEC9FFE, 0XF9E2409D, }, +/**/ {0X3FE75A66, 0X79E7F1C0, }, +/**/ {0X3FE1C6A4, 0X8740D2E9, }, +/**/ {0XBFD1AA85, 0XF198392C, }, +/**/ {0X3FB47C8A, 0X808C583A, }, +/**/ {0X3F916DAC, 0X857F2526, }, +/**/ {0XBFA495A0, 0XD0477576, },}, +/**/ {{0X3FECC001, 0XE038EF72, }, +/**/ {0X3FE76C25, 0XE6815140, }, +/**/ {0X3FE1B500, 0X19BDADF8, }, +/**/ {0XBFD19B20, 0XB4A469AE, }, +/**/ {0X3FB48D93, 0X42387EA2, }, +/**/ {0X3F90A15F, 0X7305BAF5, }, +/**/ {0XBFA44300, 0XACAE4E17, },}, +/**/ {{0X3FECDFFE, 0XEB72037F, }, +/**/ {0X3FE77DD0, 0X7A7A4AA0, }, +/**/ {0X3FE1A36E, 0X4F1F6702, }, +/**/ {0XBFD18BB1, 0XD0992CF8, }, +/**/ {0X3FB49DCE, 0X5AA4990D, }, +/**/ {0X3F8FB0DD, 0X63759665, }, +/**/ {0XBFA3F0FB, 0X4D2F0C0F, },}, +/**/ {{0X3FECFFFF, 0XEA4839ED, }, +/**/ {0X3FE78F6B, 0XB17088C0, }, +/**/ {0X3FE191E9, 0XCF32122F, }, +/**/ {0XBFD17C35, 0X220400AC, }, +/**/ {0X3FB4AD44, 0X0A159641, }, +/**/ {0X3F8E252C, 0X80894CA9, }, +/**/ {0XBFA39F93, 0XDF89C265, },}, +/**/ {{0X3FED1FFD, 0XEC3EC8B2, }, +/**/ {0X3FE7A0F3, 0XC8C6C880, }, +/**/ {0X3FE18076, 0X729F01D6, }, +/**/ {0XBFD16CAE, 0X98515540, }, +/**/ {0X3FB4BBF4, 0X1B0933FF, }, +/**/ {0X3F8C9FF5, 0XE09A60CD, }, +/**/ {0XBFA34ECD, 0X662A5704, },}, +/**/ {{0X3FED3FFF, 0X7084EDD4, }, +/**/ {0X3FE7B26C, 0X5F02F220, }, +/**/ {0X3FE16F10, 0XB9973206, }, +/**/ {0XBFD15D1B, 0X9E1E0A54, }, +/**/ {0X3FB4C9E4, 0XAC2C9A30, }, +/**/ {0X3F8B20DD, 0XEFCE76CC, }, +/**/ {0XBFA2FEAA, 0XB888BC37, },}, +/**/ {{0X3FED5FFE, 0X8D728E7C, }, +/**/ {0X3FE7C3D2, 0X488D7E80, }, +/**/ {0X3FE15DBB, 0XE622A5A7, }, +/**/ {0XBFD14D7F, 0XA305CEB2, }, +/**/ {0X3FB4D716, 0X417BF1C7, }, +/**/ {0X3F89A81E, 0XE19FE239, }, +/**/ {0XBFA2AF2E, 0X84DDAD07, },}, +/**/ {{0X3FED7FFF, 0X70AA3B03, }, +/**/ {0X3FE7D527, 0XDB239580, }, +/**/ {0X3FE14C75, 0XBE4FEA01, }, +/**/ {0XBFD13DD9, 0X2AD706AA, }, +/**/ {0X3FB4E38D, 0XB49D32AA, }, +/**/ {0X3F88357A, 0X37DF2B6D, }, +/**/ {0XBFA2605B, 0X507CD77B, },}, +/**/ {{0X3FED9FFF, 0X1434FBA3, }, +/**/ {0X3FE7E66B, 0X82C8A720, }, +/**/ {0X3FE13B3F, 0XED9B7FED, }, +/**/ {0XBFD12E2A, 0X3AC9D646, }, +/**/ {0X3FB4EF4C, 0XE7B01CF5, }, +/**/ {0X3F86C905, 0XD25FD52D, }, +/**/ {0XBFA21233, 0X798666EF, },}, +/**/ {{0X3FEDBFFE, 0XA8C8DE8C, }, +/**/ {0X3FE7F79D, 0XF4A0A520, }, +/**/ {0X3FE12A19, 0XD7FC2119, }, +/**/ {0XBFD11E72, 0XC6BE19DF, }, +/**/ {0X3FB4FA57, 0X634E1B91, }, +/**/ {0X3F8562A6, 0X47F96DF5, }, +/**/ {0XBFA1C4B9, 0X373AF599, },}, +/**/ {{0X3FEDE000, 0X26573DF5, }, +/**/ {0X3FE808C0, 0X4DBCB960, }, +/**/ {0X3FE11902, 0X7903E4B9, }, +/**/ {0XBFD10EB2, 0X5CDFED06, }, +/**/ {0X3FB504B0, 0XCCA681FA, }, +/**/ {0X3F840238, 0X6F3CDE09, }, +/**/ {0XBFA177EE, 0X9BA8FA6A, },}, +/**/ {{0X3FEDFFFE, 0X35009B66, }, +/**/ {0X3FE819CF, 0XC2CB5340, }, +/**/ {0X3FE107FC, 0XB1C942B5, }, +/**/ {0XBFD0FEEC, 0X230D7D92, }, +/**/ {0X3FB50E5A, 0X75C5B4F1, }, +/**/ {0X3F82A7E8, 0XE3C139D8, }, +/**/ {0XBFA12BD5, 0X93FA642B, },}, +/**/ {{0X3FEE2000, 0X492D4C68, }, +/**/ {0X3FE82AD0, 0X5CCB8680, }, +/**/ {0X3FE0F704, 0X928E55DF, }, +/**/ {0XBFD0EF1C, 0XEE0B0721, }, +/**/ {0X3FB51759, 0X937BFB74, }, +/**/ {0X3F815359, 0X2BC9FDDB, }, +/**/ {0XBFA0E06F, 0XEA1D1824, },}, +/**/ {{0X3FEE4000, 0X9412BB65, }, +/**/ {0X3FE83BBF, 0X14001A60, }, +/**/ {0X3FE0E61D, 0X37F485DA, }, +/**/ {0XBFD0DF48, 0X1B2BD37D, }, +/**/ {0X3FB51FAF, 0X64024D14, }, +/**/ {0X3F8004B9, 0X9B849698, }, +/**/ {0XBFA095BF, 0X450A2434, },}, +/**/ {{0X3FEE5FFF, 0X4758EF2F, }, +/**/ {0X3FE84C9C, 0X1531C180, }, +/**/ {0X3FE0D546, 0X8B7FECE7, }, +/**/ {0XBFD0CF6E, 0X105BFE1E, }, +/**/ {0X3FB5275E, 0XF9C5E03A, }, +/**/ {0X3F7D77F2, 0X17AA1137, }, +/**/ {0XBFA04BC5, 0X2A6891E1, },}, +/**/ {{0X3FEE8000, 0X380F819F, }, +/**/ {0X3FE85D69, 0X74CCC060, }, +/**/ {0X3FE0C47E, 0X8F1DA5B5, }, +/**/ {0XBFD0BF8D, 0X62AD700F, }, +/**/ {0X3FB52E6C, 0X1F3FBC2B, }, +/**/ {0X3F7AF1C3, 0XEE24AD7D, }, +/**/ {0XBFA00282, 0XFECE26C9, },}, +/**/ {{0X3FEEA000, 0XA6D8CB7B, }, +/**/ {0X3FE86E25, 0XD00E3A60, }, +/**/ {0X3FE0B3C6, 0XBA314D62, }, +/**/ {0XBFD0AFA7, 0XE7CB2D84, }, +/**/ {0X3FB534D9, 0X08E9071F, }, +/**/ {0X3F787704, 0X4CE5E5C9, }, +/**/ {0XBF9F73F4, 0X0EB7C9D5, },}, +/**/ {{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, 0x00000000, }, +/**/ {0x3fc0e6ad, 0xccf40882, }, +/**/ {0xbc6d71a3, 0x1bb98d0d, }, +/**/ {0x3fef7201, 0x32978bad, }, +/**/ {0x3c816476, 0x599381e9, }, +/**/ {0xbfc06a70, 0x011b81fd, }, +/**/ {0xbc422f5d, 0x9ba697ca, }, +/**/ {0xbfd32c01, 0x802fc0a5, }, +/**/ {0x3c7d8e47, 0x08a20868, }, +/**/ {0x3fbf24de, 0xb59597fe, }, +/**/ {0xbc43288f, 0x410d31eb, }, +/**/ {0x3fc35b16, 0x070feb24, }, +/**/ {0xbfbcd2bf, 0xe4565b78, }, +/**/ {0xbfb4b922, 0x128768c6, }, +/**/ {0x3fb9f9cb, 0x5c42a097, }, +/**/ {0x3fa39fa2, 0xc7f97f2e, },}, +/**/ {{0x3fc18000, 0x00000000, }, +/**/ {0x3fc16465, 0x41060850, }, +/**/ {0x3c66bcee, 0x8ae7ea92, }, +/**/ {0x3fef69af, 0x483f492b, }, +/**/ {0xbc6e3280, 0x57db963e, }, +/**/ {0xbfc0dd19, 0xdacaa844, }, +/**/ {0xbc6133c7, 0xad7fc21e, }, +/**/ {0xbfd30c7c, 0x6addaea8, }, +/**/ {0xbc71443d, 0x89161c76, }, +/**/ {0x3fbfe4ba, 0x6a6d3cd2, }, +/**/ {0x3c50d4b8, 0x423ee67a, }, +/**/ {0x3fc303c7, 0x092e569a, }, +/**/ {0xbfbd60f5, 0x5b11d3b6, }, +/**/ {0xbfb3e7fd, 0x283b5c55, }, +/**/ {0x3fba4e19, 0x9d9a6ab7, }, +/**/ {0x3fa1d82f, 0x3487cc29, },}, +/**/ {{0x3fc20000, 0x00000000, }, +/**/ {0x3fc1e1fa, 0xfb043727, }, +/**/ {0xbc4b4859, 0x14dacf8c, }, +/**/ {0x3fef6124, 0x38a14f5e, }, +/**/ {0x3c798e9e, 0x001f6124, }, +/**/ {0xbfc14f04, 0x59d3fb7c, }, +/**/ {0x3c531efa, 0x4cc99cb2, }, +/**/ {0xbfd2ec39, 0x31219b34, }, +/**/ {0xbc618697, 0x6e004611, }, +/**/ {0x3fc05092, 0x68736312, }, +/**/ {0x3c67aad4, 0x8a06e4b5, }, +/**/ {0x3fc2aad6, 0x07eca5ec, }, +/**/ {0xbfbde969, 0xe19fe31c, }, +/**/ {0xbfb31455, 0xdb6b9127, }, +/**/ {0x3fba9a62, 0xf53dd9ee, }, +/**/ {0x3fa00f5b, 0xa8e4ede0, },}, +/**/ {{0x3fc28000, 0x00000000, }, +/**/ {0x3fc25f6e, 0x171a535c, }, +/**/ {0x3c67c6d7, 0xbde1a310, }, +/**/ {0x3fef5860, 0x64866d22, }, +/**/ {0x3c88c6ff, 0xd1f6326c, }, +/**/ {0xbfc1c02b, 0x13c11396, }, +/**/ {0xbc51b469, 0xffeb1a0f, }, +/**/ {0xbfd2cb3b, 0x4c571b0f, }, +/**/ {0x3c6e4f76, 0x2fb0b163, }, +/**/ {0x3fc0ad06, 0xf5c213ab, }, +/**/ {0x3c625bf2, 0xabea9e66, }, +/**/ {0x3fc25054, 0x5f93bbb2, }, +/**/ {0xbfbe6c0c, 0xc80a32c8, }, +/**/ {0xbfb23e6c, 0x678d0d1e, }, +/**/ {0x3fbadea2, 0xebf8ae4b, }, +/**/ 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{0xbfa34eca, 0x2caf50ea, }, +/**/ {0x3f9ad1af, 0x03888c77, }, +/**/ {0xbf7f33c4, 0x71ac3a86, }, +/**/ {0xbf70d2b9, 0x6296fd58, }, +/**/ {0x3f7c2938, 0x886d16b8, },}, +/**/ {{0x3fed4000, 0x00000000, }, +/**/ {0x3fe7b26c, 0xad2e50fe, }, +/**/ {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, 0xc964501a, }, +/**/ {0x3f7ac6f9, 0xeb913697, },}, +/**/ {{0x3fed8000, 0x00000000, }, +/**/ {0x3fe7d528, 0x289fa093, }, +/**/ {0x3c856082, 0x1e2f3aa9, }, +/**/ {0x3fe14c75, 0x711551bb, }, +/**/ {0xbc80c88e, 0x71970f2c, }, +/**/ {0xbfd13dd8, 0xe4aa5095, }, +/**/ {0x3c66dd31, 0xb4b7ae12, }, +/**/ {0x3fb4e38d, 0xead4c211, }, +/**/ {0x3c513fb0, 0xe392a31e, }, +/**/ {0x3f88355f, 0xf6b74576, }, +/**/ {0x3ba8cb44, 0xf3561ab7, }, +/**/ {0xbfa26058, 0x0de0faaa, }, +/**/ {0x3f9a29f8, 0x989371f0, }, +/**/ {0xbf805261, 0x2b085d9a, }, +/**/ {0xbf6beccb, 0x2511c555, }, +/**/ {0x3f7a1863, 0x87b9d333, },}, +/**/ {{0x3feda000, 0x00000000, }, +/**/ {0x3fe7e66c, 0x01c114fe, }, +/**/ {0xbc8c82b8, 0x8b760b8d, }, +/**/ {0x3fe13b3f, 0x6f037c44, }, +/**/ {0xbc635393, 0x8562c8c0, }, +/**/ {0xbfd12e29, 0xc7182435, }, +/**/ {0xbc73da80, 0x0d0fda95, }, +/**/ {0x3fb4ef4d, 0x3ba21a8b, }, +/**/ {0xbc17c450, 0x9aa41146, }, +/**/ {0x3f86c8e7, 0xc39dff46, }, +/**/ {0x3c1ddd70, 0x800ba9ae, }, +/**/ {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, }, +/**/ {0x3fb504b0, 0xc0a99255, }, +/**/ {0x3c55c054, 0x142e134f, }, +/**/ {0x3f840226, 0xc2f371cf, }, +/**/ {0xbbfc85b0, 0xfc7d6225, }, +/**/ {0xbfa177eb, 0x53d58f53, }, +/**/ {0x3f997b60, 0xa6a1627d, }, +/**/ {0xbf80e9d7, 0x89757c78, }, +/**/ {0xbf66a205, 0x0d433cd6, }, +/**/ {0x3f7817bf, 0x9c5dbd9f, },}, +/**/ {{0x3fee0000, 0x00000000, }, +/**/ {0x3fe819d0, 0xb7158a4d, }, +/**/ {0xbc7bf762, 0x29d3b917, }, +/**/ {0x3fe107fb, 0xbe011080, }, +/**/ {0xbc8107fb, 0xbe011080, }, +/**/ {0xbfd0feeb, 0x40894fcd, }, +/**/ {0x3c76fbb9, 0xc155af9a, }, +/**/ {0x3fb50e5a, 0xfb9125f7, }, +/**/ {0x3c357762, 0x2f3313b0, }, +/**/ {0x3f82a7c2, 0x843ba55a, }, +/**/ {0x3c1f4994, 0x3fc197b7, }, +/**/ {0xbfa12bd2, 0x4b4ae875, }, +/**/ {0x3f993fe0, 0xf3b1b1ee, }, +/**/ {0xbf81156d, 0xd4c2083b, }, +/**/ {0xbf64f63b, 0x0c35aa9c, }, +/**/ {0x3f7770d0, 0xe5d0462f, },}, +/**/ {{0x3fee2000, 0x00000000, }, +/**/ {0x3fe82ad0, 0x36000005, }, +/**/ {0x3c74592f, 0xce924d24, }, +/**/ {0x3fe0f704, 0xb947c8b7, }, +/**/ {0x3c436cd7, 0x48a651b3, }, +/**/ {0xbfd0ef1d, 0x1237505b, }, +/**/ {0x3c69239b, 0x1b86b9d1, }, +/**/ {0x3fb51759, 0x7fac4e21, }, +/**/ {0xbc42a8cc, 0xbfce0e36, }, +/**/ {0x3f815349, 0x3b5f3edd, }, +/**/ {0xbc25e1f1, 0x88c702d9, }, +/**/ {0xbfa0e06c, 0xa0df17a9, }, +/**/ {0x3f9903ce, 0x7e56b8b1, }, +/**/ {0xbf813db8, 0x3c701e30, }, +/**/ {0xbf63561b, 0x30c99e47, }, +/**/ {0x3f76cbf6, 0xd5bffce0, },}, +/**/ {{0x3fee4000, 0x00000000, }, +/**/ {0x3fe83bbe, 0xc5cdee22, }, +/**/ {0x3c631071, 0x04ffc6c3, }, +/**/ {0x3fe0e61d, 0x86071468, }, +/**/ {0xbc70ccc4, 0x59be09c9, }, +/**/ {0xbfd0df48, 0x647af38b, }, +/**/ {0x3c7dd47c, 0x427c295b, }, +/**/ {0x3fb51faf, 0x3ef25277, }, +/**/ {0x3bdf056a, 0xa81026a7, }, +/**/ {0x3f8004ac, 0xd443a18b, }, +/**/ {0x3c027610, 0x8178f329, }, +/**/ {0xbfa095bb, 0xfbb3a658, }, +/**/ {0x3f98c734, 0xa7859d46, }, +/**/ {0xbf8162cd, 0xeefe9a81, }, +/**/ {0xbf61c17f, 0x8330eac0, }, +/**/ {0x3f76293f, 0xe421c20a, },}, +/**/ {{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, }, +/**/ {0x3f984c96, 0xc756b7d7, }, +/**/ {0xbf81a3b6, 0x6c3ca3ae, }, +/**/ {0xbf5d7470, 0x13459246, }, +/**/ {0x3f74ea6f, 0x1e70d9a4, },}, +/**/ {{0x3feea000, 0x00000000, }, +/**/ {0x3fe86e25, 0x78f87ae5, }, +/**/ {0x3c8022b1, 0x375cfe34, }, +/**/ {0x3fe0b3c7, 0x11319104, }, +/**/ {0x3c8ac394, 0x25152519, }, +/**/ {0xbfd0afa8, 0x3ab87c8a, }, +/**/ {0x3c724f26, 0x27b31384, }, +/**/ {0x3fb534d8, 0xe904e078, }, +/**/ {0xbc55bfde, 0xf8948323, }, +/**/ {0x3f7876ec, 0xa7bb2dfb, }, +/**/ {0xbc197116, 0x8a87be50, }, +/**/ {0xbf9f73ed, 0x7f5f95b4, }, +/**/ {0x3f980ea7, 0xf11c3266, }, +/**/ {0xbf81bfb6, 0x0c032389, }, +/**/ {0xbf5a8e77, 0x8bf305a1, }, +/**/ {0x3f744e6c, 0x3ec72e6d, },}, +/**/ {{0x3feec000, 0x00000000, }, +/**/ {0x3fe87ed0, 0xeadc5a2a, }, +/**/ {0x3c70af5a, 0xd957f4bc, }, +/**/ {0x3fe0a31f, 0x5d8701b3, }, +/**/ {0xbc869b25, 0x263ce937, }, +/**/ {0xbfd09fbe, 0x60757b83, }, +/**/ {0x3c767aff, 0xa96db9ef, }, +/**/ {0x3fb53aa8, 0x7a589afb, }, +/**/ {0xbc4b7e8e, 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, },}, +/**/ {{0X2B193F81, 0X3FC5FFFF, }, +/**/ {0X4F73E000, 0X3FC5C980, }, +/**/ {0XAE110E29, 0X3FEF14F1, }, +/**/ {0X9098B3D2, 0XBFC4C16E, }, +/**/ {0X8F058241, 0XBFD1D10F, }, +/**/ {0XA14FA897, 0X3FC300C6, }, +/**/ {0XD56607C0, 0X3FBF61A6, },}, +/**/ {{0X4460E6E1, 0X3FC68008, }, +/**/ {0X04A55E20, 0X3FC645C8, }, +/**/ {0X8FA36EC5, 0X3FEF0A75, }, +/**/ {0XD62FA883, 0XBFC52BE9, }, +/**/ {0X69A74048, 0XBFD1AABD, }, +/**/ {0X1679EB02, 0X3FC34E45, }, +/**/ {0XF7C14C3D, 0X3FBE989E, },}, +/**/ {{0X9E99A846, 0X3FC6FFFB, }, +/**/ {0X4B35FD40, 0X3FC6C1D0, }, +/**/ {0X3EF8EF95, 0X3FEEFFC6, }, +/**/ {0X76A2FE63, 0XBFC5956B, }, +/**/ {0XDDC78DDF, 0XBFD183D8, }, +/**/ {0XAC606D66, 0X3FC399BD, }, +/**/ {0X070D286A, 0X3FBDCDBA, },}, +/**/ {{0X0FFCD490, 0X3FC78008, }, +/**/ {0XB55758E0, 0X3FC73DC5, }, +/**/ {0X457E2065, 0X3FEEF4E0, }, +/**/ {0X7D6FF9BC, 0XBFC5FE16, }, +/**/ {0X9FADD384, 0XBFD15C57, }, +/**/ {0X73E52D32, 0X3FC3E347, }, +/**/ {0X9A65AE4B, 0X3FBD011C, },}, +/**/ {{0X148E79C1, 0X3FC80006, }, +/**/ {0X2B7F8CA0, 0X3FC7B981, }, +/**/ {0X701687ED, 0X3FEEE9C7, }, +/**/ {0X0E1EF36D, 0XBFC665C7, }, +/**/ {0XCCBCBDAB, 0XBFD13449, }, +/**/ {0X5C71B3E8, 0X3FC42AC7, }, +/**/ {0X3E81980E, 0X3FBC32EB, },}, +/**/ {{0X0F487C17, 0X3FC88006, }, +/**/ {0XBC0E3640, 0X3FC83511, }, +/**/ {0XD2D55329, 0X3FEEDE7A, }, +/**/ {0X37E644BA, 0XBFC6CC87, }, +/**/ {0X60597557, 0XBFD10BAE, }, +/**/ {0X13E26FBE, 0X3FC47043, }, +/**/ {0X6FB18BF4, 0X3FBB634A, },}, +/**/ {{0XD3518D76, 0X3FC90004, }, +/**/ {0X8874C100, 0X3FC8B073, }, +/**/ {0X2ED6673B, 0X3FEED2FB, }, +/**/ {0X2A6EBAC3, 0XBFC73251, }, +/**/ {0X6924232F, 0XBFD0E28A, }, +/**/ {0X73BCC03F, 0X3FC4B3B5, }, +/**/ {0X8C72507F, 0X3FBA925E, },}, +/**/ {{0XD2F20D5C, 0X3FC97FFF, }, +/**/ {0X51AF5920, 0X3FC92BA3, }, +/**/ {0X3D32449F, 0X3FEEC749, }, +/**/ {0XC308255F, 0XBFC7971F, }, +/**/ {0XD572D28F, 0XBFD0B8E2, }, +/**/ {0X337448FE, 0X3FC4F51A, }, +/**/ {0XCFCBC620, 0X3FB9C04B, },}, +/**/ {{0XBF80F060, 0X3FCA0005, }, +/**/ {0X6E9E8960, 0X3FC9A6AE, }, +/**/ {0X1EF200E7, 0X3FEEBB64, }, +/**/ {0X6E96E5C1, 0XBFC7FAFB, }, +/**/ {0XEC6AD647, 0XBFD08EB6, }, +/**/ {0XF53D0BA6, 0X3FC53475, }, +/**/ {0X4433C20E, 0X3FB8ED36, },}, +/**/ {{0XDEECA8E4, 0X3FCA7FF7, }, +/**/ {0X948578E0, 0X3FCA2176, }, +/**/ {0X328FF98B, 0X3FEEAF4F, }, +/**/ {0X58149B1C, 0XBFC85DC9, }, +/**/ {0XF933A1AB, 0XBFD06414, }, +/**/ {0X60C45A8F, 0X3FC571B7, }, +/**/ {0XBE58C308, 0X3FB81941, },}, +/**/ {{0X7DEFD553, 0X3FCAFFFF, }, +/**/ {0X9EBA6B80, 0X3FCA9C22, }, +/**/ {0X10A85E10, 0X3FEEA307, }, +/**/ {0X7F9DEA61, 0XBFC8BFA6, }, +/**/ {0X5A474E8F, 0XBFD038F3, }, +/**/ {0X30C225D2, 0X3FC5ACF0, }, +/**/ {0XD062812F, 0X3FB74491, },}, +/**/ {{0X669932A5, 0X3FCB7FFE, }, +/**/ {0XCFF6DFE0, 0X3FCB1694, }, +/**/ {0X1921D387, 0X3FEE968F, }, +/**/ {0XE075D95A, 0XBFC92078, }, +/**/ {0X526793C4, 0XBFD00D60, }, +/**/ {0X73842A52, 0X3FC5E610, }, +/**/ {0XC5331D5A, 0X3FB66F49, },}, +/**/ {{0XB44759F3, 0X3FCBFFF9, }, +/**/ {0X5073A2A0, 0X3FCB90D1, }, +/**/ {0X56598313, 0X3FEE89E7, }, +/**/ {0XCFB9203D, 0XBFC98041, }, +/**/ {0XBED91B37, 0XBFCFC2BC, }, +/**/ {0X6D4FC2FC, 0X3FC61D19, }, +/**/ {0X9411537E, 0X3FB5998C, },}, +/**/ {{0X5568F3EC, 0X3FCC8007, }, +/**/ {0X4A31DBE0, 0X3FCC0AEC, }, +/**/ {0X18F270A8, 0X3FEE7D0E, }, +/**/ {0XF522B132, 0XBFC9DF0E, }, +/**/ {0X2179C242, 0XBFCF69D4, }, +/**/ {0X36646FCD, 0X3FC65213, }, +/**/ {0XDC699095, 0X3FB4C37C, },}, +/**/ {{0X601A799F, 0X3FCCFFF8, }, +/**/ {0X49DB66A0, 0X3FCC84B8, }, +/**/ {0XA0EE780E, 0X3FEE7008, }, +/**/ {0X3A403934, 0XBFCA3CBB, }, +/**/ {0XD490BE32, 0XBFCF102F, }, +/**/ {0X037D4137, 0X3FC684EA, }, +/**/ {0XD9EC855A, 0X3FB3ED3C, },}, +/**/ {{0X7BBF1497, 0X3FCD7FF9, }, +/**/ {0X1E008CE0, 0X3FCCFE5F, }, +/**/ {0XF04615C7, 0X3FEE62D2, }, +/**/ {0X15AADE2C, 0XBFCA9965, }, +/**/ {0X0B44B682, 0XBFCEB5B9, }, +/**/ {0X92EC8D57, 0X3FC6B5AF, }, +/**/ {0X60D831AE, 0X3FB316EE, },}, +/**/ {{0X40209B20, 0X3FCE0008, }, +/**/ {0XB145A760, 0X3FCD77DD, }, +/**/ {0XBE1DFDF1, 0X3FEE556D, }, +/**/ {0X2186AF0F, 0XBFCAF508, }, +/**/ {0X9420489D, 0XBFCE5A79, }, +/**/ {0X454FEB2C, 0X3FC6E462, }, +/**/ {0XD2945A8C, 0X3FB240B2, },}, +/**/ {{0XC0AE943C, 0X3FCE8000, }, +/**/ {0X3CA10100, 0X3FCDF111, }, +/**/ {0X59E7308B, 0X3FEE47DD, }, +/**/ {0X9439F69F, 0XBFCB4F88, }, +/**/ {0X798DE600, 0XBFCDFE93, }, +/**/ 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{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, }, +/**/ 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{0x0c032389, 0xbf81bfb6, }, +/**/ {0x8bf305a1, 0xbf5a8e77, }, +/**/ {0x3ec72e6d, 0x3f744e6c, },}, +/**/ {{0x00000000, 0x3feec000, }, +/**/ {0xeadc5a2a, 0x3fe87ed0, }, +/**/ {0xd957f4bc, 0x3c70af5a, }, +/**/ {0x5d8701b3, 0x3fe0a31f, }, +/**/ {0x263ce937, 0xbc869b25, }, +/**/ {0x60757b83, 0xbfd09fbe, }, +/**/ {0xa96db9ef, 0x3c767aff, }, +/**/ {0x7a589afb, 0x3fb53aa8, }, +/**/ {0x0844ff86, 0xbc4b7e8e, }, +/**/ {0xacf1a65c, 0x3f76077c, }, +/**/ {0xb13331a9, 0xbc19a3b2, }, +/**/ {0x472733eb, 0xbf9ee450, }, +/**/ {0x21e541d7, 0x3f97d05c, }, +/**/ {0x9d9d4dfc, 0xbf81d8da, }, +/**/ {0xd3ce1b4a, 0xbf57be45, }, +/**/ {0x7cb60047, 0x3f73b4ba, },}, +/**/ {{0x00000000, 0x3feee000, }, +/**/ {0xbd023119, 0x3fe88f6b, }, +/**/ {0x25aba660, 0xbc532d1d, }, +/**/ {0x95d126c6, 0x3fe09287, }, +/**/ {0xeccc37a6, 0x3c85aad3, }, +/**/ {0x649e7367, 0xbfd08fd0, }, +/**/ {0xed21a127, 0x3c71e96c, }, +/**/ {0x957ec910, 0x3fb53fdd, }, +/**/ {0xaf97a601, 0xbc339c23, }, +/**/ {0x5a18e5a2, 0x3f73a336, }, +/**/ {0x477571de, 0xbc1f7225, }, +/**/ {0xd4044135, 0xbf9e5629, }, +/**/ {0x32786dc4, 0x3f9791bd, }, +/**/ {0xbdf030c4, 0xbf81ef39, }, +/**/ {0xe21b8bcb, 0xbf550386, }, +/**/ {0x97aa7fb2, 0x3f731d62, },}, +/**/ {{0x00000000, 0x3fef0000, }, +/**/ {0xff57f1f8, 0x3fe89ff5, }, +/**/ {0x5e177a1b, 0xbc855b9a, }, +/**/ {0xbdf80108, 0x3fe081ff, }, +/**/ {0x80108200, 0x3c6ffbdf, }, +/**/ {0xba010928, 0xbfd07fde, }, +/**/ {0x7bae0295, 0x3c38d37f, }, +/**/ {0x0136e69f, 0x3fb5447b, }, +/**/ {0x0dda278d, 0x3c50316a, }, +/**/ {0x55103947, 0x3f7149fc, }, +/**/ {0x849e505f, 0x3c176e96, }, +/**/ {0xfbe9a2ee, 0xbf9dc97b, }, +/**/ {0xb08adda9, 0x3f9752d4, }, +/**/ {0xb540d106, 0xbf8202e8, }, +/**/ {0x859de3e9, 0xbf525de5, }, +/**/ {0x4afd9f21, 0x3f72886c, },}, +/**/ {{0x00000000, 0x3fef2000, }, +/**/ {0xc1cf3dff, 0x3fe8b06f, }, +/**/ {0x2656db6d, 0xbc80fb31, }, +/**/ {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/sysdeps/ieee754/dbl-64/uexp.h b/sysdeps/ieee754/dbl-64/uexp.h new file mode 100644 index 0000000000..973aae7535 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/uexp.h @@ -0,0 +1,69 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* */ +/* MODULE_NAME:uexp.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef UEXP_H +#define UEXP_H + +#include "mydefs.h" + +const static double one = 1.0, 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/sysdeps/ieee754/dbl-64/uexp.tbl b/sysdeps/ieee754/dbl-64/uexp.tbl new file mode 100644 index 0000000000..d096aeedf1 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/uexp.tbl @@ -0,0 +1,1767 @@ +/****************************************************************/ +/* TABLES FOR THE ulog() FUNCTION */ +/****************************************************************/ + +#ifdef BIG_ENDI + +static const union { + int i[1424]; + double x[712]; +} coar = { + 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 = { + 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 = { + 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 = { + 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/sysdeps/ieee754/dbl-64/ulog.h b/sysdeps/ieee754/dbl-64/ulog.h new file mode 100644 index 0000000000..8710c1f8f2 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/ulog.h @@ -0,0 +1,195 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* */ +/* 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 */ +/**/ c1 = {0x3ff00000, 0x00000000, }, /* 1 */ +/**/ 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 */ +/**/ zero = {0x00000000, 0x00000000, }, /* 0 */ +/**/ one = {0x3ff00000, 0x00000000, }, /* 1 */ +/**/ half = {0x3fe00000, 0x00000000, }, /* 1/2 */ +/**/ mhalf = {0xbfe00000, 0x00000000, }, /* -1/2 */ +/**/ 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 */ +/**/ c1 = {0x00000000, 0x3ff00000, }, /* 1 */ +/**/ 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 */ +/**/ zero = {0x00000000, 0x00000000, }, /* 0 */ +/**/ one = {0x00000000, 0x3ff00000, }, /* 1 */ +/**/ half = {0x00000000, 0x3fe00000, }, /* 1/2 */ +/**/ mhalf = {0x00000000, 0xbfe00000, }, /* -1/2 */ +/**/ 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 ZERO zero.d +#define ONE one.d +#define HALF half.d +#define MHALF mhalf.d +#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/sysdeps/ieee754/dbl-64/ulog.tbl b/sysdeps/ieee754/dbl-64/ulog.tbl new file mode 100644 index 0000000000..84c30de9aa --- /dev/null +++ b/sysdeps/ieee754/dbl-64/ulog.tbl @@ -0,0 +1,3307 @@ +/****************************************************************/ +/* 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, }, +/**/ 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{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, }, +/**/ 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{0xa23f359c, 0xbbfc53d3, },}, +/**/ {{0x43496198, 0x3f59bad3, }, +/**/ {0xaed6b50f, 0x3bf0c270, },}, +/**/ {{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/sysdeps/ieee754/dbl-64/upow.h b/sysdeps/ieee754/dbl-64/upow.h new file mode 100644 index 0000000000..633190b671 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/upow.h @@ -0,0 +1,82 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* */ +/* 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 +/**/ INF = {0x7ff00000, 0x00000000 }, /* INF */ +/**/ NaNQ = {0x7ff80000, 0x00000000 }, /* NaNQ */ +/**/ sqrt_2 = {0x3ff6a09e, 0x667f3bcc }, /* sqrt(2) */ +/**/ 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' */ + + mynumber +/**/ two52 = {0x43300000, 0x00000000 }; /* 2**52 */ + +#else +#ifdef LITTLE_ENDI + const static mynumber +/**/ INF = {0x00000000, 0x7ff00000 }, /* INF */ +/**/ NaNQ = {0x00000000, 0x7ff80000 }, /* NaNQ */ +/**/ sqrt_2 = {0x667f3bcc, 0x3ff6a09e }, /* sqrt(2) */ +/**/ 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' */ + + mynumber +/**/ two52 = {0x00000000, 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/sysdeps/ieee754/dbl-64/upow.tbl b/sysdeps/ieee754/dbl-64/upow.tbl new file mode 100644 index 0000000000..71e9f27d98 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/upow.tbl @@ -0,0 +1,10169 @@ +/****************************************************************/ +/* TABLES FOR THE upow() FUNCTION */ +/****************************************************************/ + + + +#ifdef BIG_ENDI +static const union {int4 i[5800]; double x[2900];} ui = { +/**/ 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, +/**/ 0xBD0C1D74, 0x0C53C72E, +/**/ 0x3FF16000, 0x00000000, +/**/ 0xBF05B7C9, 0xB487BCAD, +/**/ 0xBFB51887, 0x42260000, +/**/ 0xBD330A1D, 0x96258B3E, +/**/ 0x3FF15C00, 0x00000000, +/**/ 0xBF2C3411, 0x5B1E5F75, +/**/ 0xBFB4D311, 0x5D208000, +/**/ 0x3CF53A25, 0x82F4E1EF, +/**/ 0x3FF15800, 0x00000000, +/**/ 0xBF39543F, 0xEEA99544, +/**/ 0xBFB48DAE, 0x4BC30000, +/**/ 0xBD30185B, 0x208C200C, +/**/ 0x3FF15000, 0x00000000, +/**/ 0x3F3B9A3F, 0xDD5C8CB8, +/**/ 0xBFB4485E, 0x03DBC000, +/**/ 0xBD3FAD46, 0xE8D26AB7, +/**/ 0x3FF14C00, 0x00000000, +/**/ 0x3F30B155, 0xB19AE5C7, +/**/ 0xBFB40320, 0x7B414000, +/**/ 0xBD26FD84, 0xAA8157C0, +/**/ 0x3FF14800, 0x00000000, +/**/ 0x3F17C382, 0xB34EDA32, +/**/ 0xBFB3BDF5, 0xA7D20000, +/**/ 0x3D319BD0, 0xAD125895, +/**/ 0x3FF14400, 0x00000000, +/**/ 0xBF129CFF, 0xBAF129D0, +/**/ 0xBFB378DD, 0x7F748000, +/**/ 0xBD371411, 0x28F1FACA, +/**/ 0x3FF14000, 0x00000000, +/**/ 0xBF2E2E59, 0x771B7C7F, +/**/ 0xBFB333D7, 0xF8184000, +/**/ 0x3CE692B6, 0xA81B8848, +/**/ 0x3FF13C00, 0x00000000, +/**/ 0xBF395F06, 0x30FE1D9C, +/**/ 0xBFB2EEE5, 0x07B40000, +/**/ 0xBD08081E, 0xDD77C860, +/**/ 0x3FF13400, 0x00000000, +/**/ 0x3F3C8113, 0x5C81135D, +/**/ 0xBFB2AA04, 0xA4470000, +/**/ 0xBD37A48B, 0xA8B1CB41, +/**/ 0x3FF13000, 0x00000000, +/**/ 0x3F3288FF, 0xBB3B5DC0, +/**/ 0xBFB26536, 0xC3D8C000, +/**/ 0xBD0B4BAC, 0x097C5BA3, +/**/ 0x3FF12C00, 0x00000000, +/**/ 0x3F21713D, 0xB81577AE, +/**/ 0xBFB2207B, 0x5C784000, +/**/ 0xBD349D8C, 0xFC10C7BF, +/**/ 0x3FF12800, 0x00000000, +/**/ 0xBEEE05E5, 0xBAD6FC84, +/**/ 0xBFB1DBD2, 0x643D0000, +/**/ 0xBD390B24, 0xD977C494, +/**/ 0x3FF12400, 0x00000000, +/**/ 0xBF24E314, 0x59F992BF, +/**/ 0xBFB1973B, 0xD1464000, +/**/ 0xBD3566D1, 0x54F930B3, +/**/ 0x3FF12000, 0x00000000, +/**/ 0xBF33CB91, 0xC9F6E7A8, +/**/ 0xBFB152B7, 0x99BB4000, +/**/ 0x3D09BB29, 0x07030829, +/**/ 0x3FF11C00, 0x00000000, +/**/ 0xBF3CFE65, 0x8B7D9851, +/**/ 0xBFB10E45, 0xB3CB0000, +/**/ 0x3D37CF69, 0x284A3465, +/**/ 0x3FF11400, 0x00000000, +/**/ 0x3F39F5DB, 0x29605DF7, +/**/ 0xBFB0C9E6, 0x15AC4000, +/**/ 0xBD2C2DA8, 0x0974D976, +/**/ 0x3FF11000, 0x00000000, +/**/ 0x3F311111, 0x11111111, +/**/ 0xBFB08598, 0xB59E4000, +/**/ 0x3D17E5DD, 0x7009902C, +/**/ 0x3FF10C00, 0x00000000, +/**/ 0x3F20A63A, 0x12A5B1AE, +/**/ 0xBFB0415D, 0x89E74000, +/**/ 0xBD1111C0, 0x5CF1D753, +/**/ 0x3FF10800, 0x00000000, +/**/ 0xBED107FB, 0xBE011080, +/**/ 0xBFAFFA69, 0x11AB8000, +/**/ 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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 = { +/**/ 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, +/**/ 0xBF3D61AF, 0x93000000, +/**/ 0xBD0FD473, 0xFAD0B844, +/**/ 0x3F3D4357, 0xF1CC609A, +/**/ 0xBF3D41AB, 0xE8800000, +/**/ 0xBD388716, 0x298657C2, +/**/ 0x3F3D2350, 0xA48CB882, +/**/ 0xBF3D21A8, 0x42400000, +/**/ 0x3D32023A, 0x0B68711A, +/**/ 0x3F3D0349, 0x5F4FCC0A, +/**/ 0xBF3D01A4, 0x9FC00000, +/**/ 0xBD117676, 0x23A704B0, +/**/ 0x3F3CE342, 0x22159830, +/**/ 0xBF3CE1A1, 0x01400000, +/**/ 0xBD3BA59C, 0x8F391F09, +/**/ 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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, +/**/ 0x3F315F69, 0x14C00000, +/**/ 0x3D341A2F, 0x02C11605, +/**/ 0xBF317ECD, 0xD4EDF1BC, +/**/ 0x3F317F66, 0xE7000000, +/**/ 0xBD1798F3, 0xB2B7E8C5, +/**/ 0xBF319EC9, 0x716191A8, +/**/ 0x3F319F64, 0xB5400000, +/**/ 0xBD3F5AB7, 0x35D62ED5, +/**/ 0xBF31BEC5, 0x05D6D85A, +/**/ 0x3F31BF62, 0x7F400000, +/**/ 0x3D1EF6FF, 0xCA7EC7CD, +/**/ 0xBF31DEC0, 0x924DC8D2, +/**/ 0x3F31DF60, 0x45800000, +/**/ 0xBD309BD7, 0xA8550396, +/**/ 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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 = { +/**/ 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, +/**/ 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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, +/**/ 0x769FC000, 0xBFBBF968, +/**/ 0x8D824283, 0xBD24218C, +/**/ 0x00000000, 0x3FF1D400, +/**/ 0xFC60F0AE, 0xBECABDFA, +/**/ 0x936D8000, 0xBFBBB20E, +/**/ 0x35459B8E, 0x3D368BA8, +/**/ 0x00000000, 0x3FF1D000, +/**/ 0xAFDC61F3, 0xBF2F2A4B, +/**/ 0x8DAD4000, 0xBFBB6AC8, +/**/ 0xF50225C7, 0xBD3B1BDF, +/**/ 0x00000000, 0x3FF1CC00, +/**/ 0xAB802394, 0xBF3EC8AF, +/**/ 0x5A530000, 0xBFBB2396, +/**/ 0xEA137079, 0x3CEFF64E, +/**/ 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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 = { +/**/ 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, +/**/ 0x3AA58554, 0x3F40B22D, +/**/ 0x91400000, 0xBF40B116, +/**/ 0x7DD9EED3, 0x3D333B55, +/**/ 0x0FD54E74, 0x3F40A229, +/**/ 0x7C000000, 0xBF40A114, +/**/ 0x7AA78478, 0x3D3E048F, +/**/ 0xE906A6FC, 0x3F409224, +/**/ 0x68A00000, 0xBF409112, +/**/ 0x644DDE88, 0xBD383C6A, +/**/ 0xC6398D6B, 0x3F408220, +/**/ 0x57600000, 0xBF408110, +/**/ 0x76B8C83A, 0xBD2F0D2F, +/**/ 0xA76E0040, 0x3F40721C, +/**/ 0x48200000, 0xBF40710E, +/**/ 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0x2B2027B4, 0xBD3DD29F, +/**/ 0xCE702F5C, 0x3F22C0AF, +/**/ 0xE6000000, 0xBF22C057, +/**/ 0x6959A7D0, 0xBD32B00B, +/**/ 0x262F2134, 0x3F2280AB, +/**/ 0x92000000, 0xBF228055, +/**/ 0x19FAAC2D, 0xBD1F61EF, +/**/ 0x8DEFCF2C, 0x3F2240A6, +/**/ 0x46000000, 0xBF224053, +/**/ 0xCB16B8A8, 0x3D05A87E, +/**/ 0x05B23344, 0x3F2200A2, +/**/ 0x02000000, 0xBF220051, +/**/ 0x23B9B257, 0x3D29F32F, +/**/ 0x8D76477A, 0x3F21C09D, +/**/ 0xC6000000, 0xBF21C04E, +/**/ 0x7E214821, 0x3D36F61B, +/**/ 0x253C05CD, 0x3F218099, +/**/ 0x91800000, 0xBF21804C, +/**/ 0x46FDFCA2, 0xBD3F5464, +/**/ 0xCD03683D, 0x3F214094, +/**/ 0x65800000, 0xBF21404A, +/**/ 0xA30F2308, 0xBD35E4E7, +/**/ 0x84CC68C9, 0x3F210090, +/**/ 0x41800000, 0xBF210048, +/**/ 0xF800CC34, 0xBD2974DC, +/**/ 0x4C970171, 0x3F20C08C, +/**/ 0x25800000, 0xBF20C046, +/**/ 0xC1006E9D, 0xBD0E9FC5, +/**/ 0x24632C32, 0x3F208088, +/**/ 0x11800000, 0xBF208044, +/**/ 0x078E4438, 0x3D133DE7, +/**/ 0x0C30E30D, 0x3F204084, +/**/ 0x05800000, 0xBF204042, +/**/ 0x15F82A7B, 0x3D2A61D2, +/**/ 0x04002001, 0x3F200080, +/**/ 0x01800000, 0xBF200040, +/**/ 0x3BBB110C, 0x3D355155, +/**/ 0x17A1BA1A, 0x3F1F80F8, +/**/ 0x0B000000, 0xBF1F807C, +/**/ 0x6C520A9B, 0x3D3D31BE, +/**/ 0x47462860, 0x3F1F00F0, +/**/ 0x22000000, 0xBF1F0078, +/**/ 0x4B6D83F6, 0xBD3B2CDB, +/**/ 0x96ED7ED3, 0x3F1E80E8, +/**/ 0x4A000000, 0xBF1E8074, +/**/ 0xD4122C5A, 0xBD33C977, +/**/ 0x0697B172, 0x3F1E00E1, +/**/ 0x82000000, 0xBF1E0070, +/**/ 0x2D1517C4, 0xBD29462E, +/**/ 0x9644B43B, 0x3F1D80D9, +/**/ 0xCA000000, 0xBF1D806C, +/**/ 0xF0952D45, 0xBD16E2E3, +/**/ 0x45F47B2C, 0x3F1D00D2, +/**/ 0x22000000, 0xBF1D0069, +/**/ 0x2DDC2A8D, 0x3CEED452, +/**/ 0x15A6FA46, 0x3F1C80CB, +/**/ 0x8A000000, 0xBF1C8065, +/**/ 0xA08CEBE8, 0x3D1DAFEE, +/**/ 0x055C2585, 0x3F1C00C4, +/**/ 0x02000000, 0xBF1C0062, +/**/ 0xBB11EF55, 0x3D2B50A4, +/**/ 0x1513F0E9, 0x3F1B80BD, +/**/ 0x8A000000, 0xBF1B805E, +/**/ 0xC6D142BF, 0x3D33ACA6, +/**/ 0x44CE5071, 0x3F1B00B6, +/**/ 0x22000000, 0xBF1B005B, +/**/ 0xF8CD3D11, 0x3D3979F8, +/**/ 0x948B381A, 0x3F1A80AF, +/**/ 0xCA000000, 0xBF1A8057, +/**/ 0x07EDFD29, 0x3D3F1149, +/**/ 0x044A9BE5, 0x3F1A00A9, +/**/ 0x81000000, 0xBF1A0054, +/**/ 0xF7BB7092, 0xBD3B8C68, +/**/ 0x940C6FCF, 0x3F1980A2, +/**/ 0x49000000, 0xBF198051, +/**/ 0xF27E09A9, 0xBD365E1C, +/**/ 0x43D0A7D8, 0x3F19009C, +/**/ 0x21000000, 0xBF19004E, +/**/ 0xD508D564, 0xBD3162D2, +/**/ 0x139737FE, 0x3F188096, +/**/ 0x09000000, 0xBF18804B, +/**/ 0x18D5C93E, 0xBD293315, +/**/ 0x03601440, 0x3F180090, +/**/ 0x01000000, 0xBF180048, +/**/ 0x0C26A328, 0xBD200288, +/**/ 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, +/**/ 0x4AB05909, 0xBF2ABE9A, +/**/ 0x22000000, 0x3F2ABF4D, +/**/ 0x2CE7BDAC, 0x3D3D6E96, +/**/ 0x9337BC90, 0xBF2AFE93, +/**/ 0xC6800000, 0x3F2AFF49, +/**/ 0xCB7D724C, 0xBD2800DC, +/**/ 0xCBC1A7D1, 0xBF2B3E8C, +/**/ 0x62800000, 0x3F2B3F46, +/**/ 0xFA591B29, 0x3D25F908, +/**/ 0xF44E20CE, 0xBF2B7E85, +/**/ 0xF7000000, 0x3F2B7F42, +/**/ 0x53021ED8, 0xBD3D9991, +/**/ 0x0CDD2D83, 0xBF2BBE7F, +/**/ 0x83000000, 0x3F2BBF3F, +/**/ 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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/sysdeps/ieee754/dbl-64/urem.h b/sysdeps/ieee754/dbl-64/urem.h new file mode 100644 index 0000000000..84f9a5cf08 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/urem.h @@ -0,0 +1,50 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/************************************************************************/ +/* 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 */ + NAN = {0x7ff80000, 0}, /* NaN */ + nNAN = {0xfff80000, 0}; /* -NaN */ +#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 */ + NAN = {0, 0x7ff80000}, /* NaN */ + nNAN = {0, 0xfff80000}; /* -NaN */ +#endif +#endif + +#endif diff --git a/sysdeps/ieee754/dbl-64/uroot.h b/sysdeps/ieee754/dbl-64/uroot.h new file mode 100644 index 0000000000..8d22b9e242 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/uroot.h @@ -0,0 +1,43 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* */ +/* MODULE_NAME:uroot.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef UROOT_H +#define UROOT_H + +#ifdef BIG_ENDI + static const mynumber +/**/ t512 = {0x5ff00000, 0x00000000 }, /* 2^512 */ +/**/ tm256 = {0x2ff00000, 0x00000000 }; /* 2^-256 */ + +#else +#ifdef LITTLE_ENDI + static const mynumber +/**/ t512 = {0x00000000, 0x5ff00000 }, /* 2^512 */ +/**/ tm256 = {0x00000000, 0x2ff00000 }; /* 2^-256 */ +#endif +#endif + +#endif diff --git a/sysdeps/ieee754/dbl-64/usncs.h b/sysdeps/ieee754/dbl-64/usncs.h new file mode 100644 index 0000000000..01a954d140 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/usncs.h @@ -0,0 +1,79 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/************************************************************************/ +/* MODULE_NAME: dosincos.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + +#ifndef USNCS_H +#define USNCS_H + +#ifdef BIG_ENDI +static const mynumber + +/**/ NAN = {0x7ff80000, 0x00000000 }, /* NaN */ +/**/ s1 = {0xBFC55555, 0x55555555 }, /* -0.16666666666666666 */ +/**/ s2 = {0x3F811111, 0x11110ECE }, /* 0.0083333333333323288 */ +/**/ s3 = {0xBF2A01A0, 0x19DB08B8 }, /* -0.00019841269834414642 */ +/**/ s4 = {0x3EC71DE2, 0x7B9A7ED9 }, /* 2.755729806860771e-06 */ +/**/ s5 = {0xBE5ADDFF, 0xC2FCDF59 }, /* -2.5022014848318398e-08 */ +/**/ aa = {0xBFC55580, 0x00000000 }, /* -0.1666717529296875 */ +/**/ bb = {0x3ED55555, 0x55556E24 }, /* 5.0862630208387126e-06 */ +/**/ big = {0x42c80000, 0x00000000 }, /* 52776558133248 */ +/**/ hp0 = {0x3FF921FB, 0x54442D18 }, /* 1.5707963267948966 */ +/**/ hp1 = {0x3C91A626, 0x33145C07 }, /* 6.123233995736766e-17 */ +/**/ mp1 = {0x3FF921FB, 0x58000000 }, /* 1.5707963407039642 */ +/**/ mp2 = {0xBE4DDE97, 0x3C000000 }, /* -1.3909067564377153e-08 */ +/**/ mp3 = {0xBC8CB3B3, 0x99D747F2 }, /* -4.9789962505147994e-17 */ +/**/ pp3 = {0xBC8CB3B3, 0x98000000 }, /* -4.9789962314799099e-17 */ +/**/ pp4 = {0xbacd747f, 0x23e32ed7 }, /* -1.9034889620193266e-25 */ +/**/ hpinv = {0x3FE45F30, 0x6DC9C883 }, /* 0.63661977236758138 */ +/**/ toint = {0x43380000, 0x00000000 }; /* 6755399441055744 */ + +#else +#ifdef LITTLE_ENDI +static const mynumber + +/**/ NAN = {0x00000000, 0x7ff80000 },/* NaN */ +/**/ s1 = {0x55555555, 0xBFC55555 },/* -0.16666666666666666 */ +/**/ s2 = {0x11110ECE, 0x3F811111 },/* 0.0083333333333323288 */ +/**/ s3 = {0x19DB08B8, 0xBF2A01A0 },/* -0.00019841269834414642 */ +/**/ s4 = {0x7B9A7ED9, 0x3EC71DE2 },/* 2.755729806860771e-06 */ +/**/ s5 = {0xC2FCDF59, 0xBE5ADDFF },/* -2.5022014848318398e-08 */ +/**/ aa = {0x00000000, 0xBFC55580 },/* -0.1666717529296875 */ +/**/ bb = {0x55556E24, 0x3ED55555 },/* 5.0862630208387126e-06 */ +/**/ big = {0x00000000, 0x42c80000 },/* 52776558133248 */ +/**/ hp0 = {0x54442D18, 0x3FF921FB },/* 1.5707963267948966 */ +/**/ hp1 = {0x33145C07, 0x3C91A626 },/* 6.123233995736766e-17 */ +/**/ mp1 = {0x58000000, 0x3FF921FB },/* 1.5707963407039642 */ +/**/ mp2 = {0x3C000000, 0xBE4DDE97 },/* -1.3909067564377153e-08 */ +/**/ mp3 = {0x99D747F2, 0xBC8CB3B3 },/* -4.9789962505147994e-17 */ +/**/ pp3 = {0x98000000, 0xBC8CB3B3 },/* -4.9789962314799099e-17 */ +/**/ pp4 = {0x23e32ed7, 0xbacd747f },/* -1.9034889620193266e-25 */ +/**/ hpinv = {0x6DC9C883, 0x3FE45F30 },/* 0.63661977236758138 */ +/**/ toint = {0x00000000, 0x43380000 };/* 6755399441055744 */ + + +#endif +#endif + +#endif diff --git a/sysdeps/ieee754/dbl-64/utan.h b/sysdeps/ieee754/dbl-64/utan.h new file mode 100644 index 0000000000..f1045c0c66 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/utan.h @@ -0,0 +1,251 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * 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 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 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, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/******************************************************************/ +/* */ +/* 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, }, /* . */ +/**/ aa15 = {0xbbf25789, 0xb285d2ed, }, /* . */ +/**/ a17 = {0x3f435582, 0x48036744, }, /* . */ +/**/ aa17 = {0x3be488d9, 0x563f1f23, }, /* . */ +/**/ a19 = {0x3f2f57d7, 0x734d1664, }, /* . */ +/**/ aa19 = {0x3bb0d55a, 0x913ccb50, }, /* . */ +/**/ a21 = {0x3f1967e1, 0x8afcafad, }, /* . */ +/**/ aa21 = {0xbbbd7614, 0xa42d44e6, }, /* . */ +/**/ a23 = {0x3f0497d8, 0xeea25259, }, /* . */ +/**/ aa23 = {0x3b99f2d0, 0x2e4d2863, }, /* . */ +/**/ a25 = {0x3ef0b132, 0xd39a6050, }, /* . */ +/**/ aa25 = {0x3b93b274, 0xc2c19614, }, /* . */ +/**/ a27 = {0x3edb0f72, 0xd3ee24e9, }, /* . */ +/**/ aa27 = {0x3b61688d, 0xdd595609, }, /* . */ + /* polynomial III */ +/**/ e0 = {0x3FD55555, 0x55554DBD, }, /* . */ +/**/ e1 = {0x3FC11112, 0xE0A6B45F, }, /* . */ + + /* constants */ +/**/ zero = {0x00000000, 0x00000000, }, /* 0 */ +/**/ one = {0x3ff00000, 0x00000000, }, /* 1 */ +/**/ mone = {0xbff00000, 0x00000000, }, /*-1 */ +/**/ mfftnhf = {0xc02f0000, 0x00000000, }, /*-15.5 */ +/**/ two8 = {0x40700000, 0x00000000, }, /* 256 */ + +/**/ 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, }, /* . */ +/**/ aa15 = {0xb285d2ed, 0xbbf25789, }, /* . */ +/**/ a17 = {0x48036744, 0x3f435582, }, /* . */ +/**/ aa17 = {0x563f1f23, 0x3be488d9, }, /* . */ +/**/ a19 = {0x734d1664, 0x3f2f57d7, }, /* . */ +/**/ aa19 = {0x913ccb50, 0x3bb0d55a, }, /* . */ +/**/ a21 = {0x8afcafad, 0x3f1967e1, }, /* . */ +/**/ aa21 = {0xa42d44e6, 0xbbbd7614, }, /* . */ +/**/ a23 = {0xeea25259, 0x3f0497d8, }, /* . */ +/**/ aa23 = {0x2e4d2863, 0x3b99f2d0, }, /* . */ +/**/ a25 = {0xd39a6050, 0x3ef0b132, }, /* . */ +/**/ aa25 = {0xc2c19614, 0x3b93b274, }, /* . */ +/**/ a27 = {0xd3ee24e9, 0x3edb0f72, }, /* . */ +/**/ aa27 = {0xdd595609, 0x3b61688d, }, /* . */ + /* polynomial III */ +/**/ e0 = {0x55554DBD, 0x3FD55555, }, /* . */ +/**/ e1 = {0xE0A6B45F, 0x3FC11112, }, /* . */ + + /* constants */ +/**/ zero = {0x00000000, 0x00000000, }, /* 0 */ +/**/ one = {0x00000000, 0x3ff00000, }, /* 1 */ +/**/ mone = {0x00000000, 0xbff00000, }, /*-1 */ +/**/ mfftnhf = {0x00000000, 0xc02f0000, }, /*-15.5 */ +/**/ two8 = {0x00000000, 0x40700000, }, /* 256 */ + +/**/ 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 + + +#define ZERO zero.d +#define ONE one.d +#define MONE mone.d +#define TWO8 two8.d + +#endif diff --git a/sysdeps/ieee754/dbl-64/utan.tbl b/sysdeps/ieee754/dbl-64/utan.tbl new file mode 100644 index 0000000000..7ec6df2e13 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/utan.tbl @@ -0,0 +1,1507 @@ +/****************************************************************/ +/* 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, 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+/**/ {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, 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{{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, }, +/**/ {0x1ad7a9c2, 0x3bebc31b, },}, +/**/ {{0x042d9639, 0x3fe28000, }, +/**/ {0xb64540d1, 0x3fe4e136, }, +/**/ {0xf4374938, 0x3ff88578, }, +/**/ {0x1b85e901, 0x3be36de9, },}, +/**/ {{0x03be29a0, 0x3fe2a000, }, +/**/ {0x52bffd96, 0x3fe50ef4, }, +/**/ {0xc0042c06, 0x3ff85035, }, +/**/ {0x76f5efbd, 0x3be15d01, },}, +/**/ {{0xfaa91f12, 0x3fe2bfff, }, +/**/ {0x3e2f4e0d, 0x3fe53cee, }, +/**/ {0x8542df07, 0x3ff81b93, }, +/**/ {0x17662a2b, 0x3be555cd, },}, +/**/ {{0xfe884891, 0x3fe2dfff, }, +/**/ {0x6c1a2470, 0x3fe56b25, }, +/**/ {0xe422ea70, 0x3ff7e78e, }, +/**/ {0xbd030c11, 0x3bf03504, },}, +/**/ {{0xfe87152b, 0x3fe2ffff, }, +/**/ {0x9beaaaa1, 0x3fe5999a, }, +/**/ {0xd18fe9b3, 0x3ff7b424, }, +/**/ {0x773e0e64, 0xbb649a5f, },}, +/**/ {{0xffc1a721, 0x3fe31fff, }, +/**/ {0xafe0e564, 0x3fe5c84e, }, +/**/ {0x338db8d4, 0x3ff78152, }, +/**/ {0x5da8e935, 0x3beaf428, },}, +/**/ {{0xff70a372, 0x3fe33fff, }, +/**/ {0x82191d64, 0x3fe5f742, }, +/**/ {0x1122bcae, 0x3ff74f14, }, +/**/ {0xdee4bfaf, 0x3bdb1c4b, },}, +/**/ {{0x0436e836, 0x3fe36000, }, +/**/ {0xfde6ccff, 0x3fe62676, }, +/**/ {0x7644252c, 0x3ff71d67, }, +/**/ {0xe08c3afb, 0xbbec3d10, },}, +/**/ {{0xfcbe9641, 0x3fe37fff, }, +/**/ {0xee9ffdaf, 0x3fe655ec, }, +/**/ {0xa6fc0515, 0x3ff6ec49, }, +/**/ {0x2ed29567, 0x3bdda453, },}, +/**/ {{0xffb6d6ca, 0x3fe39fff, }, +/**/ {0x5e67a1e1, 0x3fe685a5, }, +/**/ {0xbc2ae969, 0x3ff6bbb7, }, +/**/ {0x2ef43882, 0x3becbf7b, },}, +/**/ {{0x04934fec, 0x3fe3c000, }, +/**/ {0x2cc07d75, 0x3fe6b5a1, }, +/**/ {0x10b02ef8, 0x3ff68baf, }, +/**/ {0xfeb7cabd, 0xbbe7c8fb, },}, +/**/ {{0x03f5cf7f, 0x3fe3e000, }, +/**/ {0x3e59def6, 0x3fe6e5e1, }, +/**/ {0x0e61500f, 0x3ff65c2d, }, +/**/ {0x035f7845, 0xbbe30ba4, },}, +/**/ {{0x05280ad9, 0x3fe40000, }, +/**/ {0x91ab4c3e, 0x3fe71666, }, +/**/ {0x19f01c90, 0x3ff62d2f, }, +/**/ {0xffe95f6a, 0xbbf1e9f5, },}, +/**/ {{0x049efb65, 0x3fe42000, }, +/**/ {0x18af3b9d, 0x3fe74732, }, +/**/ {0xb86465e4, 0x3ff5feb2, }, +/**/ {0x280d591e, 0x3bc4cad7, },}, +/**/ {{0x0035ccb6, 0x3fe44000, }, +/**/ {0xcb4ff1e5, 0x3fe77844, }, +/**/ {0x7c455428, 0x3ff5d0b5, }, +/**/ {0x7ba5617c, 0x3bed8c18, },}, +/**/ {{0x03346717, 0x3fe46000, }, +/**/ {0xba258778, 0x3fe7a99f, }, +/**/ {0xf4392254, 0x3ff5a334, }, +/**/ {0xfc84a570, 0xbbefd14a, },}, +/**/ {{0x03002575, 0x3fe48000, }, +/**/ {0xd836768f, 0x3fe7db43, }, +/**/ {0xdcf97e0c, 0x3ff5762e, }, 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0x3bf1b8b2, },}, +/**/ {{0x0331b46a, 0x3fe58000, }, +/**/ {0x38e83134, 0x3fe9732f, }, +/**/ {0x68d8b41b, 0x3ff41e30, }, +/**/ {0xb90bc28b, 0xbbee24d8, },}, +/**/ {{0xfc14848e, 0x3fe59fff, }, +/**/ {0x8471b489, 0x3fe9a796, }, +/**/ {0x5de3aa73, 0x3ff3f518, }, +/**/ {0xe0761536, 0xbbecacd9, },}, +/**/ {{0xfb7cd395, 0x3fe5bfff, }, +/**/ {0x24a8b955, 0x3fe9dc52, }, +/**/ {0x4f8fff15, 0x3ff3cc66, }, +/**/ {0x82045611, 0xbbf67c97, },}, +/**/ {{0x000dcc40, 0x3fe5e000, }, +/**/ {0x4df5b93e, 0x3fea1163, }, +/**/ {0x75853228, 0x3ff3a418, }, +/**/ {0xd481f350, 0xbbf585da, },}, +/**/ {{0x02efd2fc, 0x3fe60000, }, +/**/ {0x30d16323, 0x3fea46cb, }, +/**/ {0x187962ae, 0x3ff37c2d, }, +/**/ {0xa5f77bb0, 0x3bf004c3, },}, +/**/ {{0xfeb8088a, 0x3fe61fff, }, +/**/ {0x053920c0, 0x3fea7c8b, }, +/**/ {0x891769a9, 0x3ff354a2, }, +/**/ {0x3fee3029, 0x3bbc6b30, },}, +/**/ {{0x00f3ca06, 0x3fe64000, }, +/**/ {0x28a1911a, 0x3feab2a4, }, +/**/ {0x0a6f0a4a, 0x3ff32d77, }, +/**/ {0xfac5081a, 0x3bf2a6f8, },}, +/**/ {{0xfe9ec2f4, 0x3fe65fff, }, +/**/ {0xd4ce7239, 0x3feae917, }, +/**/ {0x0751a948, 0x3ff306a9, }, +/**/ {0x51ab9dbd, 0xbbe950b5, },}, +/**/ {{0x03d43966, 0x3fe68000, }, +/**/ {0x708b998a, 0x3feb1fe7, }, +/**/ {0xd7a153c7, 0x3ff2e036, }, +/**/ {0xa1e4a14e, 0x3bdd36e2, },}, +/**/ {{0xfab67783, 0x3fe69fff, }, +/**/ {0x2e575464, 0x3feb5714, }, +/**/ {0x05006cb6, 0x3ff2ba1f, }, +/**/ {0x473c2e31, 0x3bea9a4a, },}, +/**/ {{0xfcb65f89, 0x3fe6bfff, }, +/**/ {0x981efd2f, 0x3feb8e9f, }, +/**/ {0xe948d9f7, 0x3ff2945f, }, +/**/ {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 + |