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Revision 1.12, Sun May 26 22:01:47 2002 UTC (12 years, 5 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-tag8, yamt-pagecache-base9, 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, tls-earlyentropy-base, tls-earlyentropy, riastradh-xf86-video-intel-2-7-1-pre-2-21-15, riastradh-drm2-base3, riastradh-drm2-base2, riastradh-drm2-base1, riastradh-drm2-base, riastradh-drm2, netbsd-7-base, netbsd-7, netbsd-6-base, netbsd-6-1-RELEASE, netbsd-6-1-RC4, netbsd-6-1-RC3, netbsd-6-1-RC2, netbsd-6-1-RC1, netbsd-6-1-5-RELEASE, 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-6-0-6-RELEASE, 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, HEAD
Changes since 1.11: +3 -11 lines

__STDC__ is always defined on NetBSD.

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

#include <sys/cdefs.h>
#if defined(LIBM_SCCS) && !defined(lint)
__RCSID("$NetBSD: e_acos.c,v 1.12 2002/05/26 22:01:47 wiz 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"

static const double
one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */

double
__ieee754_acos(double x)
{
	double z,p,q,r,w,s,c,df;
	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;
	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
	    r = p/q;
	    return pio2_hi - (x - (pio2_lo-x*r));
	} else  if (hx<0) {		/* x < -0.5 */
	    z = (one+x)*0.5;
	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
	    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);
	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
	    r = p/q;
	    w = r*s+c;
	    return 2.0*(df+w);
	}
}