sysdeps/ieee754/dbl-64/e_atanh.c

   1 /* Copyright (C) 2011-2014 Free Software Foundation, Inc.
   2    This file is part of the GNU C Library.
   3    Contributed by Ulrich Drepper <drepper@gmail.com>, 2011.
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, see
  17    <http://www.gnu.org/licenses/>.  */
  18
  19
  20 /* __ieee754_atanh(x)
  21    Method :
  22       1.Reduced x to positive by atanh(-x) = -atanh(x)
  23       2.For x>=0.5
  24                     1              2x                          x
  25         atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  26                     2             1 - x                      1 - x
  27
  28         For x<0.5
  29         atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
  30
  31    Special cases:
  32         atanh(x) is NaN if |x| > 1 with signal;
  33         atanh(NaN) is that NaN with no signal;
  34         atanh(+-1) is +-INF with signal.
  35
  36  */
  37
  38 #include <inttypes.h>
  39 #include <math.h>
  40 #include <math_private.h>
  41
  42 static const double huge = 1e300;
  43
  44 double
  45 __ieee754_atanh (double x)
  46 {
  47   double xa = fabs (x);
  48   double t;
  49   if (isless (xa, 0.5))
  50     {
  51       if (__builtin_expect (xa < 0x1.0p-28, 0))
  52         {
  53           math_force_eval (huge + x);
  54           return x;
  55         }
  56
  57       t = xa + xa;
  58       t = 0.5 * __log1p (t + t * xa / (1.0 - xa));
  59     }
  60   else if (__builtin_expect (isless (xa, 1.0), 1))
  61     t = 0.5 * __log1p ((xa + xa) / (1.0 - xa));
  62   else
  63     {
  64       if (isgreater (xa, 1.0))
  65         return (x - x) / (x - x);
  66
  67       return x / 0.0;
  68     }
  69
  70   return __copysign (t, x);
  71 }
  72 strong_alias (__ieee754_atanh, __atanh_finite)