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  1. /* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */
  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. #if defined(LIBM_SCCS) && !defined(lint)
  15. static char rcsid[] = "$Id: e_atanh.c,v 1.6 1994/08/18 23:05:12 jtc Exp $";
  16. #endif
  17.  
  18. /* __ieee754_atanh(x)
  19.  * Method :
  20.  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
  21.  *    2.For x>=0.5
  22.  *                  1              2x                          x
  23.  *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  24.  *                  2             1 - x                      1 - x
  25.  *     
  26.  *      For x<0.5
  27.  *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
  28.  *
  29.  * Special cases:
  30.  *      atanh(x) is NaN if |x| > 1 with signal;
  31.  *      atanh(NaN) is that NaN with no signal;
  32.  *      atanh(+-1) is +-INF with signal.
  33.  *
  34.  */
  35.  
  36. #include "math.h"
  37. #include "math_private.h"
  38.  
  39. #ifdef __STDC__
  40. static const double one = 1.0, huge = 1e300;
  41. #else
  42. static double one = 1.0, huge = 1e300;
  43. #endif
  44.  
  45. #ifdef __STDC__
  46. static const double zero = 0.0;
  47. #else
  48. static double zero = 0.0;
  49. #endif
  50.  
  51. #ifdef __STDC__
  52.         double __ieee754_atanh(double x)
  53. #else
  54.         double __ieee754_atanh(x)
  55.         double x;
  56. #endif
  57. {
  58.         double t;
  59.         int32_t hx,ix;
  60.         u_int32_t lx;
  61.         EXTRACT_WORDS(hx,lx,x);
  62.         ix = hx&0x7fffffff;
  63.         if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
  64.             return (x-x)/(x-x);
  65.         if(ix==0x3ff00000)
  66.             return x/zero;
  67.         if(ix<0x3e300000&&(huge+x)>zero) return x;      /* x<2**-28 */
  68.         SET_HIGH_WORD(x,ix);
  69.         if(ix<0x3fe00000) {             /* x < 0.5 */
  70.             t = x+x;
  71.             t = 0.5*log1p(t+t*x/(one-x));
  72.         } else
  73.             t = 0.5*log1p((x+x)/(one-x));
  74.         if(hx>=0) return t; else return -t;
  75. }
  76.