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  1.  
  2. /* @(#)e_atanh.c 5.1 93/09/24 */
  3. /*
  4.  * ====================================================
  5.  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  6.  *
  7.  * Developed at SunPro, a Sun Microsystems, Inc. business.
  8.  * Permission to use, copy, modify, and distribute this
  9.  * software is freely granted, provided that this notice
  10.  * is preserved.
  11.  * ====================================================
  12.  *
  13.  */
  14.  
  15. /* __ieee754_atanh(x)
  16.  * Method :
  17.  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
  18.  *    2.For x>=0.5
  19.  *                  1              2x                          x
  20.  *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  21.  *                  2             1 - x                      1 - x
  22.  *     
  23.  *      For x<0.5
  24.  *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
  25.  *
  26.  * Special cases:
  27.  *      atanh(x) is NaN if |x| > 1 with signal;
  28.  *      atanh(NaN) is that NaN with no signal;
  29.  *      atanh(+-1) is +-INF with signal.
  30.  *
  31.  */
  32.  
  33. #include "fdlibm.h"
  34.  
  35. #ifndef _DOUBLE_IS_32BITS
  36.  
  37. #ifdef __STDC__
  38. static const double one = 1.0, huge = 1e300;
  39. #else
  40. static double one = 1.0, huge = 1e300;
  41. #endif
  42.  
  43. #ifdef __STDC__
  44. static const double zero = 0.0;
  45. #else
  46. static double zero = 0.0;
  47. #endif
  48.  
  49. #ifdef __STDC__
  50.         double __ieee754_atanh(double x)
  51. #else
  52.         double __ieee754_atanh(x)
  53.         double x;
  54. #endif
  55. {
  56.         double t;
  57.         __int32_t hx,ix;
  58.         __uint32_t lx;
  59.         EXTRACT_WORDS(hx,lx,x);
  60.         ix = hx&0x7fffffff;
  61.         if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
  62.             return (x-x)/(x-x);
  63.         if(ix==0x3ff00000)
  64.             return x/zero;
  65.         if(ix<0x3e300000&&(huge+x)>zero) return x;      /* x<2**-28 */
  66.         SET_HIGH_WORD(x,ix);
  67.         if(ix<0x3fe00000) {             /* x < 0.5 */
  68.             t = x+x;
  69.             t = 0.5*log1p(t+t*x/(one-x));
  70.         } else
  71.             t = 0.5*log1p((x+x)/(one-x));
  72.         if(hx>=0) return t; else return -t;
  73. }
  74.  
  75. #endif /* defined(_DOUBLE_IS_32BITS) */
  76.