glibc/sysdeps/libm-ieee754/e_acos.c

/* @(#)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.
 * ====================================================
 */
/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25,
   for performance improvement on pipelined processors.
 */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc 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"
#define one qS[0]

#ifdef __STDC__
static const double
#else
static double
#endif
pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pS[] =  {1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
 -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
 -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
  3.47933107596021167570e-05}, /* 0x3F023DE1, 0x0DFDF709 */
qS[] ={1.0, -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
 -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
  7.70381505559019352791e-02}; /* 0x3FB3B8C5, 0xB12E9282 */

#ifdef __STDC__
	double __ieee754_acos(double x)
#else
	double __ieee754_acos(x)
	double x;
#endif
{
	double z,p,q,r,w,s,c,df,p1,p2,p3,q1,q2,z2,z4,z6;
	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;
#ifdef DO_NOT_USE_THIS
	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
#else
 	    p1 = z*pS[0]; z2=z*z;
 	    p2 = pS[1]+z*pS[2]; z4=z2*z2;
 	    p3 = pS[3]+z*pS[4]; z6=z4*z2;
 	    q1 = one+z*qS[1];
 	    q2 = qS[2]+z*qS[3];
 	    p = p1 + z2*p2 + z4*p3 + z6*pS[5];
 	    q = q1 + z2*q2 + z4*qS[4];
#endif
	    r = p/q;
	    return pio2_hi - (x - (pio2_lo-x*r));
	} else  if (hx<0) {		/* x < -0.5 */
	    z = (one+x)*0.5;
#ifdef DO_NOT_USE_THIS
	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
#else
	    p1 = z*pS[0]; z2=z*z;
	    p2 = pS[1]+z*pS[2]; z4=z2*z2;
	    p3 = pS[3]+z*pS[4]; z6=z4*z2;
	    q1 = one+z*qS[1];
	    q2 = qS[2]+z*qS[3];
	    p = p1 + z2*p2 + z4*p3 + z6*pS[5];
	    q = q1 + z2*q2 + z4*qS[4];
#endif
	    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);
#ifdef DO_NOT_USE_THIS
	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
#else
	    p1 = z*pS[0]; z2=z*z;
	    p2 = pS[1]+z*pS[2]; z4=z2*z2;
	    p3 = pS[3]+z*pS[4]; z6=z4*z2;
	    q1 = one+z*qS[1];
	    q2 = qS[2]+z*qS[3];
	    p = p1 + z2*p2 + z4*p3 + z6*pS[5];
	    q = q1 + z2*q2 + z4*qS[4];
#endif
	    r = p/q;
	    w = r*s+c;
	    return 2.0*(df+w);
	}
}