e_asinf.c

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/* e_asinf.c -- float version of e_asin.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 */
huge =  1.000e+30,
pio2_hi =  1.5707962513e+00, /* 0x3fc90fda */
pio2_lo =  7.5497894159e-08, /* 0x33a22168 */
pio4_hi =  7.8539818525e-01, /* 0x3f490fdb */
    /* coefficient for R(x^2) */
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
asinf(float x)
{
    float t,w,p,q,c,r,s;
    int32_t hx,ix;
    GET_FLOAT_WORD(hx,x);
    ix = hx&0x7fffffff;
    if(ix==0x3f800000) {
        /* asin(1)=+-pi/2 with inexact */
        return x*pio2_hi+x*pio2_lo; 
    } else if(ix> 0x3f800000) { /* |x|>= 1 */
        return (x-x)/(x-x);     /* asin(|x|>1) is NaN */   
    } else if (ix<0x3f000000) { /* |x|<0.5 */
        if(ix<0x32000000) {     /* if |x| < 2**-27 */
        if(huge+x>one) return x;/* return x with inexact if x!=0*/
        } else 
        t = x*x;
        p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
        q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
        w = p/q;
        return x+x*w;
    }
    /* 1> |x|>= 0.5 */
    w = one-fabsf(x);
    t = w*(float)0.5;
    p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
    q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
    s = sqrtf(t);
    if(ix>=0x3F79999A) {    /* if |x| > 0.975 */
        w = p/q;
        t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
    } else {
        int32_t iw;
        w  = s;
        GET_FLOAT_WORD(iw,w);
        SET_FLOAT_WORD(w,iw&0xfffff000);
        c  = (t-w*w)/(s+w);
        r  = p/q;
        p  = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
        q  = pio4_hi-(float)2.0*w;
        t  = pio4_hi-(p-q);
    }    
    if(hx>0) return t; else return -t;    
}