glibc/sysdeps/ieee754/flt-32/e_asinf.c

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

/*
  Modifications for single precision expansion are 
  Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
  These modifications are distributed here under the following terms:

    This library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
    License as published by the Free Software Foundation; either
    version 2.1 of the License, or (at your option) any later version.

    This library is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
    Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public
    License along with this library; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307  USA */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_asinf.c,v 1.5 1995/05/12 04:57:25 jtc Exp $";
#endif

#include "math.h"
#include "math_private.h"

#ifdef __STDC__
static const float
#else
static float
#endif
one =  1.0000000000e+00, /* 0x3F800000 */
huge =  1.000e+30,

pio2_hi = 1.57079637050628662109375f,
pio2_lo = -4.37113900018624283e-8f,
pio4_hi = 0.785398185253143310546875f,

/* asin x = x + x^3 p(x^2)
   -0.5 <= x <= 0.5;
   Peak relative error 4.8e-9 */
p0 = 1.666675248e-1f,
p1 = 7.495297643e-2f,
p2 = 4.547037598e-2f,
p3 = 2.417951451e-2f,
p4 = 4.216630880e-2f;

#ifdef __STDC__
	float __ieee754_asinf(float x)
#else
	float __ieee754_asinf(x)
	float x;
#endif
{
	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;
		w = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4))));
		return x+x*w;
	    }
	}
	/* 1> |x|>= 0.5 */
	w = one-fabsf(x);
	t = w*0.5f;
	p = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4))));
	s = __ieee754_sqrtf(t);
	if(ix>=0x3F79999A) { 	/* if |x| > 0.975 */
	    t = pio2_hi-(2.0f*(s+s*p)-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;
	    p  = 2.0f*s*r-(pio2_lo-2.0f*c);
	    q  = pio4_hi-2.0f*w;
	    t  = pio4_hi-(p-q);
	}
	if(hx>0) return t; else return -t;
}