math/s_catanh_template.c

   1 /* Return arc hyperbolic tangent for a complex float type.
   2    Copyright (C) 1997-2022 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 (__catanh) (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 (icls == FP_INFINITE)
  35         {
  36           __real__ res = M_COPYSIGN (0, __real__ x);
  37           __imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x);
  38         }
  39       else if (rcls == FP_INFINITE || rcls == FP_ZERO)
  40         {
  41           __real__ res = M_COPYSIGN (0, __real__ x);
  42           if (icls >= FP_ZERO)
  43             __imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x);
  44           else
  45             __imag__ res = M_NAN;
  46         }
  47       else
  48         {
  49           __real__ res = M_NAN;
  50           __imag__ res = M_NAN;
  51         }
  52     }
  53   else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
  54     {
  55       res = x;
  56     }
  57   else
  58     {
  59       if (M_FABS (__real__ x) >= 16 / M_EPSILON
  60           || M_FABS (__imag__ x) >= 16 / M_EPSILON)
  61         {
  62           __imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x);
  63           if (M_FABS (__imag__ x) <= 1)
  64             __real__ res = 1 / __real__ x;
  65           else if (M_FABS (__real__ x) <= 1)
  66             __real__ res = __real__ x / __imag__ x / __imag__ x;
  67           else
  68             {
  69               FLOAT h = M_HYPOT (__real__ x / 2, __imag__ x / 2);
  70               __real__ res = __real__ x / h / h / 4;
  71             }
  72         }
  73       else
  74         {
  75           if (M_FABS (__real__ x) == 1
  76               && M_FABS (__imag__ x) < M_EPSILON * M_EPSILON)
  77             __real__ res = (M_COPYSIGN (M_LIT (0.5), __real__ x)
  78                             * (M_MLIT (M_LN2)
  79                                - M_LOG (M_FABS (__imag__ x))));
  80           else
  81             {
  82               FLOAT i2 = 0;
  83               if (M_FABS (__imag__ x) >= M_EPSILON * M_EPSILON)
  84                 i2 = __imag__ x * __imag__ x;
  85
  86               FLOAT num = 1 + __real__ x;
  87               num = i2 + num * num;
  88
  89               FLOAT den = 1 - __real__ x;
  90               den = i2 + den * den;
  91
  92               FLOAT f = num / den;
  93               if (f < M_LIT (0.5))
  94                 __real__ res = M_LIT (0.25) * M_LOG (f);
  95               else
  96                 {
  97                   num = 4 * __real__ x;
  98                   __real__ res = M_LIT (0.25) * M_LOG1P (num / den);
  99                 }
 100             }
 101
 102           FLOAT absx, absy, den;
 103
 104           absx = M_FABS (__real__ x);
 105           absy = M_FABS (__imag__ x);
 106           if (absx < absy)
 107             {
 108               FLOAT t = absx;
 109               absx = absy;
 110               absy = t;
 111             }
 112
 113           if (absy < M_EPSILON / 2)
 114             {
 115               den = (1 - absx) * (1 + absx);
 116               if (den == 0)
 117                 den = 0;
 118             }
 119           else if (absx >= 1)
 120             den = (1 - absx) * (1 + absx) - absy * absy;
 121           else if (absx >= M_LIT (0.75) || absy >= M_LIT (0.5))
 122             den = -M_SUF (__x2y2m1) (absx, absy);
 123           else
 124             den = (1 - absx) * (1 + absx) - absy * absy;
 125
 126           __imag__ res = M_LIT (0.5) * M_ATAN2 (2 * __imag__ x, den);
 127         }
 128
 129       math_check_force_underflow_complex (res);
 130     }
 131
 132   return res;
 133 }
 134
 135 declare_mgen_alias (__catanh, catanh)