sysdeps/ieee754/dbl-64/e_atanh.c

   1 /* Copyright (C) 2011-2015 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 <float.h>
  39 #include <inttypes.h>
  40 #include <math.h>
  41 #include <math_private.h>
  42
  43 static const double huge = 1e300;
  44
  45 double
  46 __ieee754_atanh (double x)
  47 {
  48   double xa = fabs (x);
  49   double t;
  50   if (isless (xa, 0.5))
  51     {
  52       if (__glibc_unlikely (xa < 0x1.0p-28))
  53         {
  54           math_force_eval (huge + x);
  55           if (fabs (x) < DBL_MIN)
  56             {
  57               double force_underflow = x * x;
  58               math_force_eval (force_underflow);
  59             }
  60           return x;
  61         }
  62
  63       t = xa + xa;
  64       t = 0.5 * __log1p (t + t * xa / (1.0 - xa));
  65     }
  66   else if (__glibc_likely (isless (xa, 1.0)))
  67     t = 0.5 * __log1p ((xa + xa) / (1.0 - xa));
  68   else
  69     {
  70       if (isgreater (xa, 1.0))
  71         return (x - x) / (x - x);
  72
  73       return x / 0.0;
  74     }
  75
  76   return __copysign (t, x);
  77 }
  78 strong_alias (__ieee754_atanh, __atanh_finite)