# code: 9ferno

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/* derived from /netlib/fdlibm */

/* @(#)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"

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;
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);
}
}