math/s_catan_template.c

   1 /* Return arc tangent of complex float type.
   2    Copyright (C) 1997-2023 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, see
  17    <https://www.gnu.org/licenses/>.  */
  18
  19 #include <complex.h>
  20 #include <math.h>
  21 #include <math_private.h>
  22 #include <math-underflow.h>
  23 #include <float.h>
  24
  25 CFLOAT
  26 M_DECL_FUNC (__catan) (CFLOAT x)
  27 {
  28   CFLOAT 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 = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
  37           __imag__ res = M_COPYSIGN (0, __imag__ x);
  38         }
  39       else if (icls == FP_INFINITE)
  40         {
  41           if (rcls >= FP_ZERO)
  42             __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
  43           else
  44             __real__ res = M_NAN;
  45           __imag__ res = M_COPYSIGN (0, __imag__ x);
  46         }
  47       else if (icls == FP_ZERO || icls == FP_INFINITE)
  48         {
  49           __real__ res = M_NAN;
  50           __imag__ res = M_COPYSIGN (0, __imag__ x);
  51         }
  52       else
  53         {
  54           __real__ res = M_NAN;
  55           __imag__ res = M_NAN;
  56         }
  57     }
  58   else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
  59     {
  60       res = x;
  61     }
  62   else
  63     {
  64       if (M_FABS (__real__ x) >= 16 / M_EPSILON
  65           || M_FABS (__imag__ x) >= 16 / M_EPSILON)
  66         {
  67           __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
  68           if (M_FABS (__real__ x) <= 1)
  69             __imag__ res = 1 / __imag__ x;
  70           else if (M_FABS (__imag__ x) <= 1)
  71             __imag__ res = __imag__ x / __real__ x / __real__ x;
  72           else
  73             {
  74               FLOAT h = M_HYPOT (__real__ x / 2, __imag__ x / 2);
  75               __imag__ res = __imag__ x / h / h / 4;
  76             }
  77         }
  78       else
  79         {
  80           FLOAT den, absx, absy;
  81
  82           absx = M_FABS (__real__ x);
  83           absy = M_FABS (__imag__ x);
  84           if (absx < absy)
  85             {
  86               FLOAT t = absx;
  87               absx = absy;
  88               absy = t;
  89             }
  90
  91           if (absy < M_EPSILON / 2)
  92             {
  93               den = (1 - absx) * (1 + absx);
  94               if (den == 0)
  95                 den = 0;
  96             }
  97           else if (absx >= 1)
  98             den = (1 - absx) * (1 + absx) - absy * absy;
  99           else if (absx >= M_LIT (0.75) || absy >= M_LIT (0.5))
 100             den = -M_SUF (__x2y2m1) (absx, absy);
 101           else
 102             den = (1 - absx) * (1 + absx) - absy * absy;
 103
 104           __real__ res = M_LIT (0.5) * M_ATAN2 (2 * __real__ x, den);
 105
 106           if (M_FABS (__imag__ x) == 1
 107               && M_FABS (__real__ x) < M_EPSILON * M_EPSILON)
 108             __imag__ res = (M_COPYSIGN (M_LIT (0.5), __imag__ x)
 109                             * (M_MLIT (M_LN2)
 110                                - M_LOG (M_FABS (__real__ x))));
 111           else
 112             {
 113               FLOAT r2 = 0, num, f;
 114
 115               if (M_FABS (__real__ x) >= M_EPSILON * M_EPSILON)
 116                 r2 = __real__ x * __real__ x;
 117
 118               num = __imag__ x + 1;
 119               num = r2 + num * num;
 120
 121               den = __imag__ x - 1;
 122               den = r2 + den * den;
 123
 124               f = num / den;
 125               if (f < M_LIT (0.5))
 126                 __imag__ res = M_LIT (0.25) * M_LOG (f);
 127               else
 128                 {
 129                   num = 4 * __imag__ x;
 130                   __imag__ res = M_LIT (0.25) * M_LOG1P (num / den);
 131                 }
 132             }
 133         }
 134
 135       math_check_force_underflow_complex (res);
 136     }
 137
 138   return res;
 139 }
 140
 141 declare_mgen_alias (__catan, catan)