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  1. /* ef_asin.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 "fdlibm.h"
  17.  
  18. #ifdef __STDC__
  19. static const float
  20. #else
  21. static float
  22. #endif
  23. one =  1.0000000000e+00, /* 0x3F800000 */
  24. huge =  1.000e+30,
  25. pio2_hi = 1.57079637050628662109375f,
  26. pio2_lo = -4.37113900018624283e-8f,
  27. pio4_hi = 0.785398185253143310546875f,
  28.         /* coefficient for R(x^2) */
  29. pS0 =  1.6666667163e-01, /* 0x3e2aaaab */
  30. pS1 = -3.2556581497e-01, /* 0xbea6b090 */
  31. pS2 =  2.0121252537e-01, /* 0x3e4e0aa8 */
  32. pS3 = -4.0055535734e-02, /* 0xbd241146 */
  33. pS4 =  7.9153501429e-04, /* 0x3a4f7f04 */
  34. pS5 =  3.4793309169e-05, /* 0x3811ef08 */
  35. qS1 = -2.4033949375e+00, /* 0xc019d139 */
  36. qS2 =  2.0209457874e+00, /* 0x4001572d */
  37. qS3 = -6.8828397989e-01, /* 0xbf303361 */
  38. qS4 =  7.7038154006e-02; /* 0x3d9dc62e */
  39.  
  40. #ifdef __STDC__
  41.         float __ieee754_asinf(float x)
  42. #else
  43.         float __ieee754_asinf(x)
  44.         float x;
  45. #endif
  46. {
  47.         float t,w,p,q,c,r,s;
  48.         __int32_t hx,ix;
  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.         }
  67.         /* 1> |x|>= 0.5 */
  68.         w = one-fabsf(x);
  69.         t = w*(float)0.5;
  70.         p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
  71.         q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
  72.         s = __ieee754_sqrtf(t);
  73.         if(ix>=0x3F79999A) {    /* if |x| > 0.975 */
  74.             w = p/q;
  75.             t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
  76.         } else {
  77.             __int32_t iw;
  78.             w  = s;
  79.             GET_FLOAT_WORD(iw,w);
  80.             SET_FLOAT_WORD(w,iw&0xfffff000);
  81.             c  = (t-w*w)/(s+w);
  82.             r  = p/q;
  83.             p  = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
  84.             q  = pio4_hi-(float)2.0*w;
  85.             t  = pio4_hi-(p-q);
  86.         }    
  87.         if(hx>0) return t; else return -t;    
  88. }
  89.