math/s_ctanh_template.c

   1 /* Complex hyperbolic tangent for float types.
   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 <fenv.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 (__ctanh) (CFLOAT x)
  28 {
  29   CFLOAT res;
  30
  31   if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
  32     {
  33       if (isinf (__real__ x))
  34         {
  35           __real__ res = M_COPYSIGN (1, __real__ x);
  36           if (isfinite (__imag__ x) && M_FABS (__imag__ x) > 1)
  37             {
  38               FLOAT sinix, cosix;
  39               M_SINCOS (__imag__ x, &sinix, &cosix);
  40               __imag__ res = M_COPYSIGN (0, sinix * cosix);
  41             }
  42           else
  43             __imag__ res = M_COPYSIGN (0, __imag__ x);
  44         }
  45       else if (__imag__ x == 0)
  46         {
  47           res = x;
  48         }
  49       else
  50         {
  51           if (__real__ x == 0)
  52             __real__ res = __real__ x;
  53           else
  54             __real__ res = M_NAN;
  55           __imag__ res = M_NAN;
  56
  57           if (isinf (__imag__ x))
  58             feraiseexcept (FE_INVALID);
  59         }
  60     }
  61   else
  62     {
  63       FLOAT sinix, cosix;
  64       FLOAT den;
  65       const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2);
  66
  67       /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
  68          = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
  69
  70       if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
  71         {
  72           M_SINCOS (__imag__ x, &sinix, &cosix);
  73         }
  74       else
  75         {
  76           sinix = __imag__ x;
  77           cosix = 1;
  78         }
  79
  80       if (M_FABS (__real__ x) > t)
  81         {
  82           /* Avoid intermediate overflow when the imaginary part of
  83              the result may be subnormal.  Ignoring negligible terms,
  84              the real part is +/- 1, the imaginary part is
  85              sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
  86           FLOAT exp_2t = M_EXP (2 * t);
  87
  88           __real__ res = M_COPYSIGN (1, __real__ x);
  89           __imag__ res = 4 * sinix * cosix;
  90           __real__ x = M_FABS (__real__ x);
  91           __real__ x -= t;
  92           __imag__ res /= exp_2t;
  93           if (__real__ x > t)
  94             {
  95               /* Underflow (original real part of x has absolute value
  96                  > 2t).  */
  97               __imag__ res /= exp_2t;
  98             }
  99           else
 100             __imag__ res /= M_EXP (2 * __real__ x);
 101         }
 102       else
 103         {
 104           FLOAT sinhrx, coshrx;
 105           if (M_FABS (__real__ x) > M_MIN)
 106             {
 107               sinhrx = M_SINH (__real__ x);
 108               coshrx = M_COSH (__real__ x);
 109             }
 110           else
 111             {
 112               sinhrx = __real__ x;
 113               coshrx = 1;
 114             }
 115
 116           if (M_FABS (sinhrx) > M_FABS (cosix) * M_EPSILON)
 117             den = sinhrx * sinhrx + cosix * cosix;
 118           else
 119             den = cosix * cosix;
 120           __real__ res = sinhrx * coshrx / den;
 121           __imag__ res = sinix * cosix / den;
 122         }
 123       math_check_force_underflow_complex (res);
 124     }
 125
 126   return res;
 127 }
 128
 129 declare_mgen_alias (__ctanh, ctanh)