math/s_catan.c

   1 /* Return arc tangent of complex double value.
   2    Copyright (C) 1997-2015 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 #include <float.h>
  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 (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
  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 (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
  59     {
  60       res = x;
  61     }
  62   else
  63     {
  64       if (fabs (__real__ x) >= 16.0 / DBL_EPSILON
  65           || fabs (__imag__ x) >= 16.0 / DBL_EPSILON)
  66         {
  67           __real__ res = __copysign (M_PI_2, __real__ x);
  68           if (fabs (__real__ x) <= 1.0)
  69             __imag__ res = 1.0 / __imag__ x;
  70           else if (fabs (__imag__ x) <= 1.0)
  71             __imag__ res = __imag__ x / __real__ x / __real__ x;
  72           else
  73             {
  74               double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0);
  75               __imag__ res = __imag__ x / h / h / 4.0;
  76             }
  77         }
  78       else
  79         {
  80           double den, absx, absy;
  81
  82           absx = fabs (__real__ x);
  83           absy = fabs (__imag__ x);
  84           if (absx < absy)
  85             {
  86               double t = absx;
  87               absx = absy;
  88               absy = t;
  89             }
  90
  91           if (absy < DBL_EPSILON / 2.0)
  92             {
  93               den = (1.0 - absx) * (1.0 + absx);
  94               if (den == -0.0)
  95                 den = 0.0;
  96             }
  97           else if (absx >= 1.0)
  98             den = (1.0 - absx) * (1.0 + absx) - absy * absy;
  99           else if (absx >= 0.75 || absy >= 0.5)
 100             den = -__x2y2m1 (absx, absy);
 101           else
 102             den = (1.0 - absx) * (1.0 + absx) - absy * absy;
 103
 104           __real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den);
 105
 106           if (fabs (__imag__ x) == 1.0
 107               && fabs (__real__ x) < DBL_EPSILON * DBL_EPSILON)
 108             __imag__ res = (__copysign (0.5, __imag__ x)
 109                             * (M_LN2 - __ieee754_log (fabs (__real__ x))));
 110           else
 111             {
 112               double r2 = 0.0, num, f;
 113
 114               if (fabs (__real__ x) >= DBL_EPSILON * DBL_EPSILON)
 115                 r2 = __real__ x * __real__ x;
 116
 117               num = __imag__ x + 1.0;
 118               num = r2 + num * num;
 119
 120               den = __imag__ x - 1.0;
 121               den = r2 + den * den;
 122
 123               f = num / den;
 124               if (f < 0.5)
 125                 __imag__ res = 0.25 * __ieee754_log (f);
 126               else
 127                 {
 128                   num = 4.0 * __imag__ x;
 129                   __imag__ res = 0.25 * __log1p (num / den);
 130                 }
 131             }
 132         }
 133
 134       if (fabs (__real__ res) < DBL_MIN)
 135         {
 136           volatile double force_underflow = __real__ res * __real__ res;
 137           (void) force_underflow;
 138         }
 139       if (fabs (__imag__ res) < DBL_MIN)
 140         {
 141           volatile double force_underflow = __imag__ res * __imag__ res;
 142           (void) force_underflow;
 143         }
 144     }
 145
 146   return res;
 147 }
 148 weak_alias (__catan, catan)
 149 #ifdef NO_LONG_DOUBLE
 150 strong_alias (__catan, __catanl)
 151 weak_alias (__catan, catanl)
 152 #endif