math/s_catan_template.c

   1 /* Return arc tangent of complex float type.
   2    Copyright (C) 1997-2019 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    <https://www.gnu.org/licenses/>.  */
  19
  20 #include <complex.h>
  21 #include <math.h>
  22 #include <math_private.h>
  23 #include <math-underflow.h>
  24 #include <float.h>
  25
  26 CFLOAT
  27 M_DECL_FUNC (__catan) (CFLOAT x)
  28 {
  29   CFLOAT res;
  30   int rcls = fpclassify (__real__ x);
  31   int icls = fpclassify (__imag__ x);
  32
  33   if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
  34     {
  35       if (rcls == FP_INFINITE)
  36         {
  37           __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
  38           __imag__ res = M_COPYSIGN (0, __imag__ x);
  39         }
  40       else if (icls == FP_INFINITE)
  41         {
  42           if (rcls >= FP_ZERO)
  43             __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
  44           else
  45             __real__ res = M_NAN;
  46           __imag__ res = M_COPYSIGN (0, __imag__ x);
  47         }
  48       else if (icls == FP_ZERO || icls == FP_INFINITE)
  49         {
  50           __real__ res = M_NAN;
  51           __imag__ res = M_COPYSIGN (0, __imag__ x);
  52         }
  53       else
  54         {
  55           __real__ res = M_NAN;
  56           __imag__ res = M_NAN;
  57         }
  58     }
  59   else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
  60     {
  61       res = x;
  62     }
  63   else
  64     {
  65       if (M_FABS (__real__ x) >= 16 / M_EPSILON
  66           || M_FABS (__imag__ x) >= 16 / M_EPSILON)
  67         {
  68           __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
  69           if (M_FABS (__real__ x) <= 1)
  70             __imag__ res = 1 / __imag__ x;
  71           else if (M_FABS (__imag__ x) <= 1)
  72             __imag__ res = __imag__ x / __real__ x / __real__ x;
  73           else
  74             {
  75               FLOAT h = M_HYPOT (__real__ x / 2, __imag__ x / 2);
  76               __imag__ res = __imag__ x / h / h / 4;
  77             }
  78         }
  79       else
  80         {
  81           FLOAT den, absx, absy;
  82
  83           absx = M_FABS (__real__ x);
  84           absy = M_FABS (__imag__ x);
  85           if (absx < absy)
  86             {
  87               FLOAT t = absx;
  88               absx = absy;
  89               absy = t;
  90             }
  91
  92           if (absy < M_EPSILON / 2)
  93             {
  94               den = (1 - absx) * (1 + absx);
  95               if (den == 0)
  96                 den = 0;
  97             }
  98           else if (absx >= 1)
  99             den = (1 - absx) * (1 + absx) - absy * absy;
 100           else if (absx >= M_LIT (0.75) || absy >= M_LIT (0.5))
 101             den = -M_SUF (__x2y2m1) (absx, absy);
 102           else
 103             den = (1 - absx) * (1 + absx) - absy * absy;
 104
 105           __real__ res = M_LIT (0.5) * M_ATAN2 (2 * __real__ x, den);
 106
 107           if (M_FABS (__imag__ x) == 1
 108               && M_FABS (__real__ x) < M_EPSILON * M_EPSILON)
 109             __imag__ res = (M_COPYSIGN (M_LIT (0.5), __imag__ x)
 110                             * ((FLOAT) M_MLIT (M_LN2)
 111                                - M_LOG (M_FABS (__real__ x))));
 112           else
 113             {
 114               FLOAT r2 = 0, num, f;
 115
 116               if (M_FABS (__real__ x) >= M_EPSILON * M_EPSILON)
 117                 r2 = __real__ x * __real__ x;
 118
 119               num = __imag__ x + 1;
 120               num = r2 + num * num;
 121
 122               den = __imag__ x - 1;
 123               den = r2 + den * den;
 124
 125               f = num / den;
 126               if (f < M_LIT (0.5))
 127                 __imag__ res = M_LIT (0.25) * M_LOG (f);
 128               else
 129                 {
 130                   num = 4 * __imag__ x;
 131                   __imag__ res = M_LIT (0.25) * M_LOG1P (num / den);
 132                 }
 133             }
 134         }
 135
 136       math_check_force_underflow_complex (res);
 137     }
 138
 139   return res;
 140 }
 141
 142 declare_mgen_alias (__catan, catan)