[BACK]Return to s_cbrt.c CVS log [TXT][DIR] Up to [cvs.NetBSD.org] / src / lib / libm / src

File: [cvs.NetBSD.org] / src / lib / libm / src / s_cbrt.c (download)

Revision 1.11, Sun May 26 22:01:54 2002 UTC (11 years, 11 months ago) by wiz
Branch: MAIN
CVS Tags: yamt-pf42-baseX, yamt-pf42-base4, yamt-pf42-base3, yamt-pf42-base2, yamt-pf42-base, yamt-pf42, yamt-pagecache-base8, yamt-pagecache-base7, yamt-pagecache-base6, yamt-pagecache-base5, yamt-pagecache-base4, yamt-pagecache-base3, yamt-pagecache-base2, yamt-pagecache-base, yamt-pagecache, wrstuden-revivesa-base-3, wrstuden-revivesa-base-2, wrstuden-revivesa-base-1, wrstuden-revivesa-base, wrstuden-revivesa, wrstuden-fixsa-newbase, wrstuden-fixsa-base-1, wrstuden-fixsa-base, wrstuden-fixsa, tls-maxphys-base, tls-maxphys, riastradh-drm2-base2, riastradh-drm2-base1, riastradh-drm2-base, riastradh-drm2, netbsd-6-base, netbsd-6-1-RELEASE, netbsd-6-1-RC4, netbsd-6-1-RC3, netbsd-6-1-RC2, netbsd-6-1-RC1, netbsd-6-1-4-RELEASE, netbsd-6-1-3-RELEASE, netbsd-6-1-2-RELEASE, netbsd-6-1-1-RELEASE, netbsd-6-1, netbsd-6-0-RELEASE, netbsd-6-0-RC2, netbsd-6-0-RC1, netbsd-6-0-5-RELEASE, netbsd-6-0-4-RELEASE, netbsd-6-0-3-RELEASE, netbsd-6-0-2-RELEASE, netbsd-6-0-1-RELEASE, netbsd-6-0, netbsd-6, netbsd-5-base, netbsd-5-2-RELEASE, netbsd-5-2-RC1, netbsd-5-2-2-RELEASE, netbsd-5-2-1-RELEASE, netbsd-5-2, netbsd-5-1-RELEASE, netbsd-5-1-RC4, netbsd-5-1-RC3, netbsd-5-1-RC2, netbsd-5-1-RC1, netbsd-5-1-4-RELEASE, netbsd-5-1-3-RELEASE, netbsd-5-1-2-RELEASE, netbsd-5-1-1-RELEASE, netbsd-5-1, netbsd-5-0-RELEASE, netbsd-5-0-RC4, netbsd-5-0-RC3, netbsd-5-0-RC2, netbsd-5-0-RC1, netbsd-5-0-2-RELEASE, netbsd-5-0-1-RELEASE, netbsd-5-0, netbsd-5, netbsd-4-base, netbsd-4-0-RELEASE, netbsd-4-0-RC5, netbsd-4-0-RC4, netbsd-4-0-RC3, netbsd-4-0-RC2, netbsd-4-0-RC1, netbsd-4-0-1-RELEASE, netbsd-4-0, netbsd-4, netbsd-3-base, netbsd-3-1-RELEASE, netbsd-3-1-RC4, netbsd-3-1-RC3, netbsd-3-1-RC2, netbsd-3-1-RC1, netbsd-3-1-1-RELEASE, netbsd-3-1, netbsd-3-0-RELEASE, netbsd-3-0-RC6, netbsd-3-0-RC5, netbsd-3-0-RC4, netbsd-3-0-RC3, netbsd-3-0-RC2, netbsd-3-0-RC1, netbsd-3-0-3-RELEASE, netbsd-3-0-2-RELEASE, netbsd-3-0-1-RELEASE, netbsd-3-0, netbsd-3, netbsd-2-base, netbsd-2-1-RELEASE, netbsd-2-1-RC6, netbsd-2-1-RC5, netbsd-2-1-RC4, netbsd-2-1-RC3, netbsd-2-1-RC2, netbsd-2-1-RC1, netbsd-2-1, netbsd-2-0-base, netbsd-2-0-RELEASE, netbsd-2-0-RC5, netbsd-2-0-RC4, netbsd-2-0-RC3, netbsd-2-0-RC2, netbsd-2-0-RC1, netbsd-2-0-3-RELEASE, netbsd-2-0-2-RELEASE, netbsd-2-0-1-RELEASE, netbsd-2-0, netbsd-2, mjf-devfs2-base, mjf-devfs2, matt-premerge-20091211, matt-nb6-plus-nbase, matt-nb6-plus-base, matt-nb6-plus, matt-nb5-pq3-base, matt-nb5-pq3, matt-nb5-mips64-u2-k2-k4-k7-k8-k9, matt-nb5-mips64-u1-k1-k5, matt-nb5-mips64-premerge-20101231, matt-nb5-mips64-premerge-20091211, matt-nb5-mips64-k15, matt-nb5-mips64, matt-nb4-mips64-k7-u2a-k9b, matt-mips64-premerge-20101231, matt-mips64-base2, matt-mips64-base, matt-mips64, matt-armv6-prevmlocking, matt-armv6-nbase, matt-armv6-base, matt-armv6, keiichi-mipv6-base, keiichi-mipv6, jym-xensuspend-nbase, jym-xensuspend-base, jym-xensuspend, hpcarm-cleanup-nbase, hpcarm-cleanup-base, hpcarm-cleanup, fvdl_fs64_base, cube-autoconf-base, cube-autoconf, cherry-xenmp-base, cherry-xenmp, bouyer-quota2-nbase, bouyer-quota2-base, bouyer-quota2, agc-symver-base, agc-symver, abandoned-netbsd-4-base, abandoned-netbsd-4
Changes since 1.10: +3 -15 lines

__STDC__ is always defined on NetBSD.

/* @(#)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.
 * ====================================================
 */

#include <sys/cdefs.h>
#if defined(LIBM_SCCS) && !defined(lint)
__RCSID("$NetBSD: s_cbrt.c,v 1.11 2002/05/26 22:01:54 wiz Exp $");
#endif

#include "math.h"
#include "math_private.h"

/* cbrt(x)
 * Return cube root of x
 */
static const u_int32_t
	B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
	B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */

static const double
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 */

double
cbrt(double x)
{
	int32_t	hx;
	double r,s,t=0.0,w;
	u_int32_t sign;
	u_int32_t high,low;

	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);


    /* 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 20 bits and make it larger than cbrt(x) */
	GET_HIGH_WORD(high,t);
	INSERT_WORDS(t,high+0x00000001,0);


    /* 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_HIGH_WORD(high,t);
	SET_HIGH_WORD(t,high|sign);
	return(t);
}