diff options
Diffstat (limited to 'sysdeps/libm-ieee754/s_cbrt.c')
| -rw-r--r-- | sysdeps/libm-ieee754/s_cbrt.c | 128 |
1 files changed, 52 insertions, 76 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 |