sysdeps/ieee754/dbl-64/e_atanh.c

   1 /* Copyright (C) 2011-2024 Free Software Foundation, Inc.
   2    This file is part of the GNU C Library.
   3
   4    The GNU C Library is free software; you can redistribute it and/or
   5    modify it under the terms of the GNU Lesser General Public
   6    License as published by the Free Software Foundation; either
   7    version 2.1 of the License, or (at your option) any later version.
   8
   9    The GNU C Library is distributed in the hope that it will be useful,
  10    but WITHOUT ANY WARRANTY; without even the implied warranty of
  11    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  12    Lesser General Public License for more details.
  13
  14    You should have received a copy of the GNU Lesser General Public
  15    License along with the GNU C Library; if not, see
  16    <https://www.gnu.org/licenses/>.  */
  17
  18
  19 /* __ieee754_atanh(x)
  20    Method :
  21       1.Reduced x to positive by atanh(-x) = -atanh(x)
  22       2.For x>=0.5
  23                     1              2x                          x
  24         atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  25                     2             1 - x                      1 - x
  26
  27         For x<0.5
  28         atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
  29
  30    Special cases:
  31         atanh(x) is NaN if |x| > 1 with signal;
  32         atanh(NaN) is that NaN with no signal;
  33         atanh(+-1) is +-INF with signal.
  34
  35  */
  36
  37 #include <float.h>
  38 #include <inttypes.h>
  39 #include <math.h>
  40 #include <math-barriers.h>
  41 #include <math_private.h>
  42 #include <math-underflow.h>
  43 #include <libm-alias-finite.h>
  44
  45 static const double huge = 1e300;
  46
  47 double
  48 __ieee754_atanh (double x)
  49 {
  50   double xa = fabs (x);
  51   double t;
  52   if (isless (xa, 0.5))
  53     {
  54       if (__glibc_unlikely (xa < 0x1.0p-28))
  55         {
  56           math_force_eval (huge + x);
  57           math_check_force_underflow (x);
  58           return x;
  59         }
  60
  61       t = xa + xa;
  62       t = 0.5 * __log1p (t + t * xa / (1.0 - xa));
  63     }
  64   else if (__glibc_likely (isless (xa, 1.0)))
  65     t = 0.5 * __log1p ((xa + xa) / (1.0 - xa));
  66   else
  67     {
  68       if (isgreater (xa, 1.0))
  69         return (x - x) / (x - x);
  70
  71       return x / 0.0;
  72     }
  73
  74   return copysign (t, x);
  75 }
  76 libm_alias_finite (__ieee754_atanh, __atanh)