diff options
Diffstat (limited to 'sysdeps/libm-ieee754/s_cbrtl.c')
| -rw-r--r-- | sysdeps/libm-ieee754/s_cbrtl.c | 176 |
1 files changed, 65 insertions, 111 deletions
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) |