diff options
Diffstat (limited to 'sysdeps/libm-ieee754')
| -rw-r--r-- | sysdeps/libm-ieee754/s_cbrt.c | 128 | ||||
| -rw-r--r-- | sysdeps/libm-ieee754/s_cbrtf.c | 118 | ||||
| -rw-r--r-- | sysdeps/libm-ieee754/s_cbrtl.c | 176 | ||||
| -rw-r--r-- | sysdeps/libm-ieee754/s_nan.c | 1 | ||||
| -rw-r--r-- | sysdeps/libm-ieee754/s_nanf.c | 1 | ||||
| -rw-r--r-- | sysdeps/libm-ieee754/s_nanl.c | 1 |
6 files changed, 168 insertions, 257 deletions
diff --git a/sysdeps/libm-ieee754/s_cbrt.c b/sysdeps/libm-ieee754/s_cbrt.c index 24a9c9adbd..a5033ff468 100644 --- a/sysdeps/libm-ieee754/s_cbrt.c +++ b/sysdeps/libm-ieee754/s_cbrt.c @@ -1,95 +1,71 @@ -/* @(#)s_cbrt.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. - * ==================================================== - */ +/* Compute cubic root of double value. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Dirk Alboth <dirka@uni-paderborn.de> and + Ulrich Drepper <drepper@cygnus.com>, 1997. -#if defined(LIBM_SCCS) && !defined(lint) -static char rcsid[] = "$NetBSD: s_cbrt.c,v 1.8 1995/05/10 20:46:49 jtc Exp $"; -#endif + 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. */ #include "math.h" #include "math_private.h" -/* cbrt(x) - * Return cube root of x - */ -#ifdef __STDC__ -static const u_int32_t -#else -static u_int32_t -#endif - B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ - B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ -#ifdef __STDC__ -static const double -#else -static double -#endif -C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ -D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ -E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ -F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ -G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ +#define CBRT2 1.2599210498948731648 /* 2^(1/3) */ +#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */ -#ifdef __STDC__ - double __cbrt(double x) -#else - double __cbrt(x) - double x; -#endif +static const double factor[5] = { - int32_t hx; - double r,s,t=0.0,w; - u_int32_t sign; - u_int32_t high,low; + 1.0 / SQR_CBRT2, + 1.0 / CBRT2, + 1.0, + CBRT2, + SQR_CBRT2 +}; - GET_HIGH_WORD(hx,x); - sign=hx&0x80000000; /* sign= sign(x) */ - hx ^=sign; - if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ - GET_LOW_WORD(low,x); - if((hx|low)==0) - return(x); /* cbrt(0) is itself */ - SET_HIGH_WORD(x,hx); /* x <- |x| */ - /* rough cbrt to 5 bits */ - if(hx<0x00100000) /* subnormal number */ - {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ - t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2); - } - else - SET_HIGH_WORD(t,hx/3+B1); +double +__cbrt (double x) +{ + double xm, ym, u, t2; + int xe; + /* Reduce X. XM now is an range 1.0 to 0.5. */ + xm = __frexp (fabs (x), &xe); - /* new cbrt to 23 bits, may be implemented in single precision */ - r=t*t/x; - s=C+r*t; - t*=G+F/(s+E+D/s); + /* If X is not finite or is null return it (with raising exceptions + if necessary. */ + if (xe == 0) + return x + x; - /* chopped to 20 bits and make it larger than cbrt(x) */ - GET_HIGH_WORD(high,t); - INSERT_WORDS(t,high+0x00000001,0); + u = (0.354895765043919860 + + ((1.50819193781584896 + + ((-2.11499494167371287 + + ((2.44693122563534430 + + ((-1.83469277483613086 + + (0.784932344976639262 - 0.145263899385486377 * xm) * xm) + * xm)) + * xm)) + * xm)) + * xm)); + t2 = u * u * u; - /* one step newton iteration to 53 bits with error less than 0.667 ulps */ - s=t*t; /* t*t is exact */ - r=x/s; - w=t+t; - r=(r-t)/(w+r); /* r-s is exact */ - t=t+t*r; + ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3]; - /* retore the sign bit */ - GET_HIGH_WORD(high,t); - SET_HIGH_WORD(t,high|sign); - return(t); + return __ldexp (x > 0.0 ? ym : -ym, xe / 3); } weak_alias (__cbrt, cbrt) #ifdef NO_LONG_DOUBLE diff --git a/sysdeps/libm-ieee754/s_cbrtf.c b/sysdeps/libm-ieee754/s_cbrtf.c index a2b3c8106c..f9f687c011 100644 --- a/sysdeps/libm-ieee754/s_cbrtf.c +++ b/sysdeps/libm-ieee754/s_cbrtf.c @@ -1,84 +1,62 @@ -/* s_cbrtf.c -- float version of s_cbrt.c. - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ - -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static char rcsid[] = "$NetBSD: s_cbrtf.c,v 1.4 1995/05/10 20:46:51 jtc Exp $"; -#endif +/* Compute cubic root of float value. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Dirk Alboth <dirka@uni-paderborn.de> and + Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU 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. */ #include "math.h" #include "math_private.h" -/* cbrtf(x) - * Return cube root of x - */ -#ifdef __STDC__ -static const unsigned -#else -static unsigned -#endif - B1 = 709958130, /* B1 = (84+2/3-0.03306235651)*2**23 */ - B2 = 642849266; /* B2 = (76+2/3-0.03306235651)*2**23 */ -#ifdef __STDC__ -static const float -#else -static float -#endif -C = 5.4285717010e-01, /* 19/35 = 0x3f0af8b0 */ -D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */ -E = 1.4142856598e+00, /* 99/70 = 0x3fb50750 */ -F = 1.6071428061e+00, /* 45/28 = 0x3fcdb6db */ -G = 3.5714286566e-01; /* 5/14 = 0x3eb6db6e */ +#define CBRT2 1.2599210498948731648 /* 2^(1/3) */ +#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */ + +static const double factor[5] = +{ + 1.0 / SQR_CBRT2, + 1.0 / CBRT2, + 1.0, + CBRT2, + SQR_CBRT2 +}; + -#ifdef __STDC__ - float __cbrtf(float x) -#else - float __cbrtf(x) - float x; -#endif +float +__cbrtf (float x) { - float r,s,t; - int32_t hx; - u_int32_t sign; - u_int32_t high; + float xm, ym, u, t2; + int xe; + + /* Reduce X. XM now is an range 1.0 to 0.5. */ + xm = __frexpf (fabsf (x), &xe); - GET_FLOAT_WORD(hx,x); - sign=hx&0x80000000; /* sign= sign(x) */ - hx ^=sign; - if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */ - if(hx==0) - return(x); /* cbrt(0) is itself */ + /* If X is not finite or is null return it (with raising exceptions + if necessary. */ + if (xe == 0) + return x + x; - SET_FLOAT_WORD(x,hx); /* x <- |x| */ - /* rough cbrt to 5 bits */ - if(hx<0x00800000) /* subnormal number */ - {SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */ - t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2); - } - else - SET_FLOAT_WORD(t,hx/3+B1); + u = (0.492659620528969547 + (0.697570460207922770 + - 0.191502161678719066 * xm) * xm); + t2 = u * u * u; - /* new cbrt to 23 bits */ - r=t*t/x; - s=C+r*t; - t*=G+F/(s+E+D/s); + ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3]; - /* retore the sign bit */ - GET_FLOAT_WORD(high,t); - SET_FLOAT_WORD(t,high|sign); - return(t); + return __ldexpf (x > 0.0 ? ym : -ym, xe / 3); } weak_alias (__cbrtf, cbrtf) diff --git a/sysdeps/libm-ieee754/s_cbrtl.c b/sysdeps/libm-ieee754/s_cbrtl.c index 21e7727728..b3a53a39e1 100644 --- a/sysdeps/libm-ieee754/s_cbrtl.c +++ b/sysdeps/libm-ieee754/s_cbrtl.c @@ -1,122 +1,76 @@ -/* s_cbrtl.c -- long double version of s_cbrt.c. - * Conversion to long double by Ulrich Drepper, - * Cygnus Support, drepper@cygnus.com. - */ - -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static char rcsid[] = "$NetBSD: $"; -#endif +/* Compute cubic root of double value. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Dirk Alboth <dirka@uni-paderborn.de> and + Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU 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. */ #include "math.h" #include "math_private.h" -/* cbrtl(x) - * Return cube root of x - */ -#ifdef __STDC__ -static const u_int32_t -#else -static u_int32_t -#endif - B1_EXP = 10921, /* = Int(B1) */ - B1_MANT = 0x7bc4b064, /* = Int(1.0-0.03306235651)*2**31 */ - - B2_EXP = 10900, - B2_MANT = 0x7bc4b064; /* = Int(1.0-0.03306235651)*2**31 */ -#ifdef __STDC__ -static const long double -#else -static long double -#endif -C = 5.42857142857142815906e-01L, /* 19/35 */ -D = -7.05306122448979611050e-01L, /* -864/1225 */ -E = 1.41428571428571436819e+00L, /* 99/70 */ -F = 1.60714285714285720630e+00L, /* 45/28 */ -G = 3.57142857142857150787e-01L; /* 5/14 */ +#define CBRT2 1.2599210498948731648 /* 2^(1/3) */ +#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */ -#ifdef __STDC__ - long double __cbrtl(long double x) -#else - long double __cbrtl(x) - long double x; -#endif +/* We don't use long double values here since U need not be computed + with full precision. */ +static const double factor[5] = { - long double r,s,t=0.0,w; - u_int32_t sign, se, x0, x1; - - GET_LDOUBLE_WORDS(se,x0,x1,x); - sign=se&0x8000; /* sign= sign(x) */ - se ^= sign; - if(se==0x7fff) return(x+x); /* cbrt(NaN,INF) is itself */ - if((se|x0|x1)==0) - return(x); /* cbrt(0) is itself */ - - SET_LDOUBLE_EXP(x,se); /* x <- |x| */ - -/* XXX I don't know whether the numbers for correct are correct. The - precalculation is extended from 20 bits to 32 bits. This hopefully - gives us the needed bits to get us still along with one iteration - step. */ + 1.0 / SQR_CBRT2, + 1.0 / CBRT2, + 1.0, + CBRT2, + SQR_CBRT2 +}; - /* rough cbrt to 5 bits */ - if(se==0) /* subnormal number */ - { - u_int64_t xxl; - u_int32_t set,t0,t1; - SET_LDOUBLE_EXP(t,0x4035); /* set t= 2**54 */ - SET_LDOUBLE_MSW(t,0x80000000); - t*=x; - GET_LDOUBLE_WORDS(set,t0,t1,t); - xxl = ((u_int64_t) set) << 32 | t0; - xxl /= 3; - xxl += B2_EXP << 16 | B2_MANT; - t0 = xxl & 0xffffffffu; - set = xxl >> 32; - SET_LDOUBLE_WORDS(t,set,t0,t1); - } - else - { - u_int64_t xxl = ((u_int64_t) se) << 32 | x0; - xxl /= 3; - xxl += ((u_int64_t) B1_EXP) << 32 | B1_MANT; - SET_LDOUBLE_MSW(t,xxl&0xffffffffu); - xxl >>= 32; - SET_LDOUBLE_EXP(t,xxl); - } - - /* new cbrt to 23 bits, may be implemented in single precision */ - r=t*t/x; - s=C+r*t; - t*=G+F/(s+E+D/s); - - /* chopped to 32 bits and make it larger than cbrt(x) */ - GET_LDOUBLE_WORDS(se,x0,x1,t); - SET_LDOUBLE_WORDS(t,se,x0+1,0); - - - /* one step newton iteration to 53 bits with error less than 0.667 ulps */ - s=t*t; /* t*t is exact */ - r=x/s; - w=t+t; - r=(r-t)/(w+r); /* r-s is exact */ - t=t+t*r; - - /* retore the sign bit */ - GET_LDOUBLE_EXP(se,t); - SET_LDOUBLE_EXP(t,se|sign); - return(t); +long double +__cbrtl (long double x) +{ + long double xm, ym, u, t2; + int xe; + + /* Reduce X. XM now is an range 1.0 to 0.5. */ + xm = __frexpl (fabs (x), &xe); + + /* If X is not finite or is null return it (with raising exceptions + if necessary. */ + if (xe == 0) + return x + x; + + u = (0.338058687610520237 + + (1.67595307700780102 + + (-2.82414939754975962 + + (4.09559907378707839 + + (-4.11151425200350531 + + (2.65298938441952296 + + (-0.988553671195413709 + + 0.161617097923756032 * xm) + * xm) + * xm) + * xm) + * xm) + * xm) + *xm); + + t2 = u * u * u; + + ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3]; + + return __ldexpl (x > 0.0 ? ym : -ym, xe / 3); } weak_alias (__cbrtl, cbrtl) diff --git a/sysdeps/libm-ieee754/s_nan.c b/sysdeps/libm-ieee754/s_nan.c index 35d92646c0..1d2319cbd8 100644 --- a/sysdeps/libm-ieee754/s_nan.c +++ b/sysdeps/libm-ieee754/s_nan.c @@ -19,6 +19,7 @@ Boston, MA 02111-1307, USA. */ #include <math.h> +#include <stdio.h> #include <stdlib.h> #include <string.h> #include <ieee754.h> diff --git a/sysdeps/libm-ieee754/s_nanf.c b/sysdeps/libm-ieee754/s_nanf.c index 8e6e3fc1fd..56fb9e7e3d 100644 --- a/sysdeps/libm-ieee754/s_nanf.c +++ b/sysdeps/libm-ieee754/s_nanf.c @@ -19,6 +19,7 @@ Boston, MA 02111-1307, USA. */ #include <math.h> +#include <stdio.h> #include <stdlib.h> #include <string.h> #include <ieee754.h> diff --git a/sysdeps/libm-ieee754/s_nanl.c b/sysdeps/libm-ieee754/s_nanl.c index 1cd026e00c..279e070492 100644 --- a/sysdeps/libm-ieee754/s_nanl.c +++ b/sysdeps/libm-ieee754/s_nanl.c @@ -19,6 +19,7 @@ Boston, MA 02111-1307, USA. */ #include <math.h> +#include <stdio.h> #include <stdlib.h> #include <string.h> #include <ieee754.h> |