math/s_catanh.c

   1 /* Return arc hyperbole tangent for double value.
   2    Copyright (C) 1997-2013 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
   5
   6    The GNU C Library is free software; you can redistribute it and/or
   7    modify it under the terms of the GNU Lesser General Public
   8    License as published by the Free Software Foundation; either
   9    version 2.1 of the License, or (at your option) any later version.
  10
  11    The GNU C Library is distributed in the hope that it will be useful,
  12    but WITHOUT ANY WARRANTY; without even the implied warranty of
  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14    Lesser General Public License for more details.
  15
  16    You should have received a copy of the GNU Lesser General Public
  17    License along with the GNU C Library; if not, see
  18    <http://www.gnu.org/licenses/>.  */
  19
  20 #include <complex.h>
  21 #include <math.h>
  22 #include <math_private.h>
  23
  24
  25 __complex__ double
  26 __catanh (__complex__ double x)
  27 {
  28   __complex__ double res;
  29   int rcls = fpclassify (__real__ x);
  30   int icls = fpclassify (__imag__ x);
  31
  32   if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
  33     {
  34       if (icls == FP_INFINITE)
  35         {
  36           __real__ res = __copysign (0.0, __real__ x);
  37           __imag__ res = __copysign (M_PI_2, __imag__ x);
  38         }
  39       else if (rcls == FP_INFINITE || rcls == FP_ZERO)
  40         {
  41           __real__ res = __copysign (0.0, __real__ x);
  42           if (icls >= FP_ZERO)
  43             __imag__ res = __copysign (M_PI_2, __imag__ x);
  44           else
  45             __imag__ res = __nan ("");
  46         }
  47       else
  48         {
  49           __real__ res = __nan ("");
  50           __imag__ res = __nan ("");
  51         }
  52     }
  53   else if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
  54     {
  55       res = x;
  56     }
  57   else
  58     {
  59       double i2 = __imag__ x * __imag__ x;
  60
  61       double num = 1.0 + __real__ x;
  62       num = i2 + num * num;
  63
  64       double den = 1.0 - __real__ x;
  65       den = i2 + den * den;
  66
  67       __real__ res = 0.25 * (__ieee754_log (num) - __ieee754_log (den));
  68
  69       den = 1 - __real__ x * __real__ x - i2;
  70
  71       __imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den);
  72     }
  73
  74   return res;
  75 }
  76 weak_alias (__catanh, catanh)
  77 #ifdef NO_LONG_DOUBLE
  78 strong_alias (__catanh, __catanhl)
  79 weak_alias (__catanh, catanhl)
  80 #endif