math/s_catan.c

   1 /* Return arc tangent of complex 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, 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 __catan (__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 (rcls == FP_INFINITE)
  35         {
  36           __real__ res = __copysign (M_PI_2, __real__ x);
  37           __imag__ res = __copysign (0.0, __imag__ x);
  38         }
  39       else if (icls == FP_INFINITE)
  40         {
  41           if (rcls >= FP_ZERO)
  42             __real__ res = __copysign (M_PI_2, __real__ x);
  43           else
  44             __real__ res = __nan ("");
  45           __imag__ res = __copysign (0.0, __imag__ x);
  46         }
  47       else if (icls == FP_ZERO || icls == FP_INFINITE)
  48         {
  49           __real__ res = __nan ("");
  50           __imag__ res = __copysign (0.0, __imag__ x);
  51         }
  52       else
  53         {
  54           __real__ res = __nan ("");
  55           __imag__ res = __nan ("");
  56         }
  57     }
  58   else if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
  59     {
  60       res = x;
  61     }
  62   else
  63     {
  64       double r2, num, den;
  65
  66       r2 = __real__ x * __real__ x;
  67
  68       den = 1 - r2 - __imag__ x * __imag__ x;
  69
  70       __real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den);
  71
  72       num = __imag__ x + 1.0;
  73       num = r2 + num * num;
  74
  75       den = __imag__ x - 1.0;
  76       den = r2 + den * den;
  77
  78       __imag__ res = 0.25 * __ieee754_log (num / den);
  79     }
  80
  81   return res;
  82 }
  83 weak_alias (__catan, catan)
  84 #ifdef NO_LONG_DOUBLE
  85 strong_alias (__catan, __catanl)
  86 weak_alias (__catan, catanl)
  87 #endif