/* @(#)e_acos.c 1.3 95/01/18 */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunSoft, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice 

 * is preserved.

 * ====================================================

 */

/* __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: sqrt

 */

#include "fdlibm.h"

#ifdef __STDC__

static const double 

#else

static double 

#endif

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 */

#ifdef __STDC__

	double __ieee754_acos(double x)

#else

	double __ieee754_acos(x)

	double x;

#endif

{

	double z,p,q,r,w,s,c,df;

	int hx,ix;

	hx = __HI(x);

	ix = hx&0x7fffffff;

	if(ix>=0x3ff00000) {	/* |x| >= 1 */

	    if(((ix-0x3ff00000)|__LO(x))==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 = 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 = sqrt(z);

	    df = s;

	    __LO(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);

	}

}