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/* @(#)e_acos.c 5.1 93/09/24 */
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/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
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#ifndef lint
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static char rcsid[] = "$\Id: e_acos.c,v 1.2.6.1 1997/02/23 11:02:58 joerg Exp $";
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#endif
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/* __ieee754_acos(x)
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 * Method :
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 *      acos(x)  = pi/2 - asin(x)
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 *      acos(-x) = pi/2 + asin(x)
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 * For |x|<=0.5
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 *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
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 * For x>0.5
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 *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
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 *              = 2asin(sqrt((1-x)/2))
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 *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
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 *              = 2f + (2c + 2s*z*R(z))
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 *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
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 *     for f so that f+c ~ sqrt(z).
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 * For x<-0.5
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 *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
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 *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
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 *
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 * Special cases:
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 *      if x is NaN, return x itself;
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 *      if |x|>1, return NaN with invalid signal.
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 *
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 * Function needed: sqrt
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 */
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#include "math.h"
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#include "math_private.h"
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
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pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
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pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
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pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
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pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
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pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
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pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
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pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
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pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
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qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
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qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
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qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
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qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
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#ifdef __STDC__
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        double __generic___ieee754_acos(double x)
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#else
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        double __generic___ieee754_acos(x)
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        double x;
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#endif
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{
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        double z,p,q,r,w,s,c,df;
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        int32_t hx,ix;
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        GET_HIGH_WORD(hx,x);
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        ix = hx&0x7fffffff;
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        if(ix>=0x3ff00000) {    /* |x| >= 1 */
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            u_int32_t lx;
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            GET_LOW_WORD(lx,x);
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            if(((ix-0x3ff00000)|lx)==0) {       /* |x|==1 */
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                if(hx>0) return 0.0;            /* acos(1) = 0  */
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                else return pi+2.0*pio2_lo;     /* acos(-1)= pi */
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            }
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            return (x-x)/(x-x);         /* acos(|x|>1) is NaN */
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        }
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        if(ix<0x3fe00000) {     /* |x| < 0.5 */
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            if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
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            z = x*x;
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            p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
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            q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
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            r = p/q;
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            return pio2_hi - (x - (pio2_lo-x*r));
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        } else  if (hx<0) {             /* x < -0.5 */
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            z = (one+x)*0.5;
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            p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
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            q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
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            s = sqrt(z);
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            r = p/q;
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            w = r*s-pio2_lo;
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            return pi - 2.0*(s+w);
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        } else {                        /* x > 0.5 */
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            z = (one-x)*0.5;
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            s = sqrt(z);
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            df = s;
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            SET_LOW_WORD(df,0);
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            c  = (z-df*df)/(s+df);
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            p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
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            q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
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            r = p/q;
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            w = r*s+c;
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            return 2.0*(df+w);
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        }
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}