1141296Sdas
2141296Sdas/* @(#)e_acos.c 1.3 95/01/18 */
32116Sjkh/*
42116Sjkh * ====================================================
52116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
62116Sjkh *
7141296Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business.
82116Sjkh * Permission to use, copy, modify, and distribute this
9141296Sdas * software is freely granted, provided that this notice
102116Sjkh * is preserved.
112116Sjkh * ====================================================
122116Sjkh */
132116Sjkh
14176451Sdas#include <sys/cdefs.h>
15176451Sdas__FBSDID("$FreeBSD$");
162116Sjkh
172116Sjkh/* __ieee754_acos(x)
18141296Sdas * Method :
192116Sjkh *	acos(x)  = pi/2 - asin(x)
202116Sjkh *	acos(-x) = pi/2 + asin(x)
212116Sjkh * For |x|<=0.5
222116Sjkh *	acos(x) = pi/2 - (x + x*x^2*R(x^2))	(see asin.c)
232116Sjkh * For x>0.5
242116Sjkh * 	acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
25141296Sdas *		= 2asin(sqrt((1-x)/2))
262116Sjkh *		= 2s + 2s*z*R(z) 	...z=(1-x)/2, s=sqrt(z)
272116Sjkh *		= 2f + (2c + 2s*z*R(z))
282116Sjkh *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
292116Sjkh *     for f so that f+c ~ sqrt(z).
302116Sjkh * For x<-0.5
312116Sjkh *	acos(x) = pi - 2asin(sqrt((1-|x|)/2))
322116Sjkh *		= pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
332116Sjkh *
342116Sjkh * Special cases:
352116Sjkh *	if x is NaN, return x itself;
362116Sjkh *	if |x|>1, return NaN with invalid signal.
372116Sjkh *
38141296Sdas * Function needed: sqrt
392116Sjkh */
402116Sjkh
41181074Sdas#include <float.h>
42181074Sdas
432116Sjkh#include "math.h"
442116Sjkh#include "math_private.h"
452116Sjkh
468870Srgrimesstatic const double
472116Sjkhone=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
482116Sjkhpi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
49181062Sdaspio2_hi =  1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
50181062Sdasstatic volatile double
51181062Sdaspio2_lo =  6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
52181062Sdasstatic const double
532116SjkhpS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
542116SjkhpS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
552116SjkhpS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
562116SjkhpS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
572116SjkhpS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
582116SjkhpS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
592116SjkhqS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
602116SjkhqS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
612116SjkhqS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
622116SjkhqS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
632116Sjkh
6497407Salfreddouble
65117912Speter__ieee754_acos(double x)
662116Sjkh{
672116Sjkh	double z,p,q,r,w,s,c,df;
682116Sjkh	int32_t hx,ix;
692116Sjkh	GET_HIGH_WORD(hx,x);
702116Sjkh	ix = hx&0x7fffffff;
712116Sjkh	if(ix>=0x3ff00000) {	/* |x| >= 1 */
722116Sjkh	    u_int32_t lx;
732116Sjkh	    GET_LOW_WORD(lx,x);
742116Sjkh	    if(((ix-0x3ff00000)|lx)==0) {	/* |x|==1 */
752116Sjkh		if(hx>0) return 0.0;		/* acos(1) = 0  */
762116Sjkh		else return pi+2.0*pio2_lo;	/* acos(-1)= pi */
772116Sjkh	    }
782116Sjkh	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
792116Sjkh	}
802116Sjkh	if(ix<0x3fe00000) {	/* |x| < 0.5 */
812116Sjkh	    if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
822116Sjkh	    z = x*x;
832116Sjkh	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
842116Sjkh	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
852116Sjkh	    r = p/q;
862116Sjkh	    return pio2_hi - (x - (pio2_lo-x*r));
872116Sjkh	} else  if (hx<0) {		/* x < -0.5 */
882116Sjkh	    z = (one+x)*0.5;
892116Sjkh	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
902116Sjkh	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
91141296Sdas	    s = sqrt(z);
922116Sjkh	    r = p/q;
932116Sjkh	    w = r*s-pio2_lo;
942116Sjkh	    return pi - 2.0*(s+w);
952116Sjkh	} else {			/* x > 0.5 */
962116Sjkh	    z = (one-x)*0.5;
97141296Sdas	    s = sqrt(z);
982116Sjkh	    df = s;
992116Sjkh	    SET_LOW_WORD(df,0);
1002116Sjkh	    c  = (z-df*df)/(s+df);
1012116Sjkh	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
1022116Sjkh	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
1032116Sjkh	    r = p/q;
1042116Sjkh	    w = r*s+c;
1052116Sjkh	    return 2.0*(df+w);
1062116Sjkh	}
1072116Sjkh}
108181074Sdas
109181074Sdas#if LDBL_MANT_DIG == 53
110181074Sdas__weak_reference(acos, acosl);
111181074Sdas#endif
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