math/s_catanh.c

   1 /* Return arc hyperbole tangent for double value.
   2    Copyright (C) 1997, 2011 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, write to the Free
  18    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  19    02111-1307 USA.  */
  20
  21 #include <complex.h>
  22 #include <math.h>
  23 #include <math_private.h>
  24
  25
  26 __complex__ double
  27 __catanh (__complex__ double x)
  28 {
  29   __complex__ double res;
  30   int rcls = fpclassify (__real__ x);
  31   int icls = fpclassify (__imag__ x);
  32
  33   if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
  34     {
  35       if (icls == FP_INFINITE)
  36         {
  37           __real__ res = __copysign (0.0, __real__ x);
  38           __imag__ res = __copysign (M_PI_2, __imag__ x);
  39         }
  40       else if (rcls == FP_INFINITE || rcls == FP_ZERO)
  41         {
  42           __real__ res = __copysign (0.0, __real__ x);
  43           if (icls >= FP_ZERO)
  44             __imag__ res = __copysign (M_PI_2, __imag__ x);
  45           else
  46             __imag__ res = __nan ("");
  47         }
  48       else
  49         {
  50           __real__ res = __nan ("");
  51           __imag__ res = __nan ("");
  52         }
  53     }
  54   else if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
  55     {
  56       res = x;
  57     }
  58   else
  59     {
  60       double i2 = __imag__ x * __imag__ x;
  61
  62       double num = 1.0 + __real__ x;
  63       num = i2 + num * num;
  64
  65       double den = 1.0 - __real__ x;
  66       den = i2 + den * den;
  67
  68       __real__ res = 0.25 * (__ieee754_log (num) - __ieee754_log (den));
  69
  70       den = 1 - __real__ x * __real__ x - i2;
  71
  72       __imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den);
  73     }
  74
  75   return res;
  76 }
  77 weak_alias (__catanh, catanh)
  78 #ifdef NO_LONG_DOUBLE
  79 strong_alias (__catanh, __catanhl)
  80 weak_alias (__catanh, catanhl)
  81 #endif