src/math/e_acosf.c

/* e_acosf.c -- float version of e_acos.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * 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.
 * ====================================================
 */

#include <math.h>
#include "math_private.h"

static const float
one =  1.0000000000e+00, /* 0x3F800000 */
pi =  3.1415925026e+00, /* 0x40490fda */
pio2_hi =  1.5707962513e+00, /* 0x3fc90fda */
pio2_lo =  7.5497894159e-08, /* 0x33a22168 */
pS0 =  1.6666667163e-01, /* 0x3e2aaaab */
pS1 = -3.2556581497e-01, /* 0xbea6b090 */
pS2 =  2.0121252537e-01, /* 0x3e4e0aa8 */
pS3 = -4.0055535734e-02, /* 0xbd241146 */
pS4 =  7.9153501429e-04, /* 0x3a4f7f04 */
pS5 =  3.4793309169e-05, /* 0x3811ef08 */
qS1 = -2.4033949375e+00, /* 0xc019d139 */
qS2 =  2.0209457874e+00, /* 0x4001572d */
qS3 = -6.8828397989e-01, /* 0xbf303361 */
qS4 =  7.7038154006e-02; /* 0x3d9dc62e */

float
acosf(float x)
{
        float z,p,q,r,w,s,c,df;
        int32_t hx,ix;
        GET_FLOAT_WORD(hx,x);
        ix = hx&0x7fffffff;
        if(ix==0x3f800000) {            /* |x|==1 */
            if(hx>0) return 0.0;        /* acos(1) = 0  */
            else return pi+(float)2.0*pio2_lo;  /* acos(-1)= pi */
        } else if(ix>0x3f800000) {      /* |x| >= 1 */
            return (x-x)/(x-x);         /* acos(|x|>1) is NaN */
        }
        if(ix<0x3f000000) {     /* |x| < 0.5 */
            if(ix<=0x23000000) 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)*(float)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 = sqrtf(z);
            r = p/q;
            w = r*s-pio2_lo;
            return pi - (float)2.0*(s+w);
        } else {                        /* x > 0.5 */
            int32_t idf;
            z = (one-x)*(float)0.5;
            s = sqrtf(z);
            df = s;
            GET_FLOAT_WORD(idf,df);
            SET_FLOAT_WORD(df,idf&0xfffff000);
            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 (float)2.0*(df+w);
        }
}