lib/libm/src/e_asinf.c

   1 /* e_asinf.c -- float version of e_asin.c.
   2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 #include <sys/cdefs.h>
  17 #if defined(LIBM_SCCS) && !defined(lint)
  18 __RCSID("$NetBSD: e_asinf.c,v 1.8 2002/05/26 22:01:48 wiz Exp $");
  19 #endif
  20
  21 #include "math.h"
  22 #include "math_private.h"
  23
  24 static const float
  25 one =  1.0000000000e+00, /* 0x3F800000 */
  26 huge =  1.000e+30,
  27 pio2_hi =  1.5707962513e+00, /* 0x3fc90fda */
  28 pio2_lo =  7.5497894159e-08, /* 0x33a22168 */
  29 pio4_hi =  7.8539818525e-01, /* 0x3f490fdb */
  30         /* coefficient for R(x^2) */
  31 pS0 =  1.6666667163e-01, /* 0x3e2aaaab */
  32 pS1 = -3.2556581497e-01, /* 0xbea6b090 */
  33 pS2 =  2.0121252537e-01, /* 0x3e4e0aa8 */
  34 pS3 = -4.0055535734e-02, /* 0xbd241146 */
  35 pS4 =  7.9153501429e-04, /* 0x3a4f7f04 */
  36 pS5 =  3.4793309169e-05, /* 0x3811ef08 */
  37 qS1 = -2.4033949375e+00, /* 0xc019d139 */
  38 qS2 =  2.0209457874e+00, /* 0x4001572d */
  39 qS3 = -6.8828397989e-01, /* 0xbf303361 */
  40 qS4 =  7.7038154006e-02; /* 0x3d9dc62e */
  41
  42 float
  43 __ieee754_asinf(float x)
  44 {
  45         float t,w,p,q,c,r,s;
  46         int32_t hx,ix;
  47
  48         t = 0;
  49         GET_FLOAT_WORD(hx,x);
  50         ix = hx&0x7fffffff;
  51         if(ix==0x3f800000) {
  52                 /* asin(1)=+-pi/2 with inexact */
  53             return x*pio2_hi+x*pio2_lo;
  54         } else if(ix> 0x3f800000) {     /* |x|>= 1 */
  55             return (x-x)/(x-x);         /* asin(|x|>1) is NaN */
  56         } else if (ix<0x3f000000) {     /* |x|<0.5 */
  57             if(ix<0x32000000) {         /* if |x| < 2**-27 */
  58                 if(huge+x>one) return x;/* return x with inexact if x!=0*/
  59             } else
  60                 t = x*x;
  61                 p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
  62                 q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
  63                 w = p/q;
  64                 return x+x*w;
  65         }
  66         /* 1> |x|>= 0.5 */
  67         w = one-fabsf(x);
  68         t = w*(float)0.5;
  69         p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
  70         q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
  71         s = __ieee754_sqrtf(t);
  72         if(ix>=0x3F79999A) {    /* if |x| > 0.975 */
  73             w = p/q;
  74             t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
  75         } else {
  76             int32_t iw;
  77             w  = s;
  78             GET_FLOAT_WORD(iw,w);
  79             SET_FLOAT_WORD(w,iw&0xfffff000);
  80             c  = (t-w*w)/(s+w);
  81             r  = p/q;
  82             p  = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
  83             q  = pio4_hi-(float)2.0*w;
  84             t  = pio4_hi-(p-q);
  85         }
  86         if(hx>0) return t; else return -t;
  87 }