math/s_catanh_template.c

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