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