1  /* e_asinf.c -- float version of e_asin.c.
       2   */
       3  
       4  /*
       5   * ====================================================
       6   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       7   *
       8   * Developed at SunPro, a Sun Microsystems, Inc. business.
       9   * Permission to use, copy, modify, and distribute this
      10   * software is freely granted, provided that this notice
      11   * is preserved.
      12   * ====================================================
      13   */
      14  
      15  /*
      16    Modifications for single precision expansion are
      17    Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
      18    and are incorporated herein by permission of the author.  The author
      19    reserves the right to distribute this material elsewhere under different
      20    copying permissions.  These modifications are distributed here under
      21    the following terms:
      22  
      23      This library is free software; you can redistribute it and/or
      24      modify it under the terms of the GNU Lesser General Public
      25      License as published by the Free Software Foundation; either
      26      version 2.1 of the License, or (at your option) any later version.
      27  
      28      This library is distributed in the hope that it will be useful,
      29      but WITHOUT ANY WARRANTY; without even the implied warranty of
      30      MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      31      Lesser General Public License for more details.
      32  
      33      You should have received a copy of the GNU Lesser General Public
      34      License along with this library; if not, see
      35      <https://www.gnu.org/licenses/>.  */
      36  
      37  #if defined(LIBM_SCCS) && !defined(lint)
      38  static char rcsid[] = "$NetBSD: e_asinf.c,v 1.5 1995/05/12 04:57:25 jtc Exp $";
      39  #endif
      40  
      41  #include <float.h>
      42  #include <math.h>
      43  #include <math_private.h>
      44  #include <math-underflow.h>
      45  #include <libm-alias-finite.h>
      46  
      47  static const float
      48  one =  1.0000000000e+00, /* 0x3F800000 */
      49  huge =  1.000e+30,
      50  
      51  pio2_hi = 1.57079637050628662109375f,
      52  pio2_lo = -4.37113900018624283e-8f,
      53  pio4_hi = 0.785398185253143310546875f,
      54  
      55  /* asin x = x + x^3 p(x^2)
      56     -0.5 <= x <= 0.5;
      57     Peak relative error 4.8e-9 */
      58  p0 = 1.666675248e-1f,
      59  p1 = 7.495297643e-2f,
      60  p2 = 4.547037598e-2f,
      61  p3 = 2.417951451e-2f,
      62  p4 = 4.216630880e-2f;
      63  
      64  float __ieee754_asinf(float x)
      65  {
      66  	float t,w,p,q,c,r,s;
      67  	int32_t hx,ix;
      68  	GET_FLOAT_WORD(hx,x);
      69  	ix = hx&0x7fffffff;
      70  	if(ix==0x3f800000) {
      71  		/* asin(1)=+-pi/2 with inexact */
      72  	    return x*pio2_hi+x*pio2_lo;
      73  	} else if(ix> 0x3f800000) {	/* |x|>= 1 */
      74  	    return (x-x)/(x-x);		/* asin(|x|>1) is NaN */
      75  	} else if (ix<0x3f000000) {	/* |x|<0.5 */
      76  	    if(ix<0x32000000) {		/* if |x| < 2**-27 */
      77  		math_check_force_underflow (x);
      78  		if(huge+x>one) return x;/* return x with inexact if x!=0*/
      79  	    } else {
      80  		t = x*x;
      81  		w = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4))));
      82  		return x+x*w;
      83  	    }
      84  	}
      85  	/* 1> |x|>= 0.5 */
      86  	w = one-fabsf(x);
      87  	t = w*0.5f;
      88  	p = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4))));
      89  	s = sqrtf(t);
      90  	if(ix>=0x3F79999A) {	/* if |x| > 0.975 */
      91  	    t = pio2_hi-(2.0f*(s+s*p)-pio2_lo);
      92  	} else {
      93  	    int32_t iw;
      94  	    w  = s;
      95  	    GET_FLOAT_WORD(iw,w);
      96  	    SET_FLOAT_WORD(w,iw&0xfffff000);
      97  	    c  = (t-w*w)/(s+w);
      98  	    r  = p;
      99  	    p  = 2.0f*s*r-(pio2_lo-2.0f*c);
     100  	    q  = pio4_hi-2.0f*w;
     101  	    t  = pio4_hi-(p-q);
     102  	}
     103  	if(hx>0) return t; else return -t;
     104  }
     105  libm_alias_finite (__ieee754_asinf, __asinf)