math/s_ctanh_template.c

   1 /* Complex hyperbolic tangent for float types.
   2    Copyright (C) 1997-2017 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 <fenv.h>
  22 #include <math.h>
  23 #include <math_private.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           __real__ res = M_NAN;
  52           __imag__ res = M_NAN;
  53
  54           if (isinf (__imag__ x))
  55             feraiseexcept (FE_INVALID);
  56         }
  57     }
  58   else
  59     {
  60       FLOAT sinix, cosix;
  61       FLOAT den;
  62       const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2);
  63
  64       /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
  65          = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
  66
  67       if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
  68         {
  69           M_SINCOS (__imag__ x, &sinix, &cosix);
  70         }
  71       else
  72         {
  73           sinix = __imag__ x;
  74           cosix = 1;
  75         }
  76
  77       if (M_FABS (__real__ x) > t)
  78         {
  79           /* Avoid intermediate overflow when the imaginary part of
  80              the result may be subnormal.  Ignoring negligible terms,
  81              the real part is +/- 1, the imaginary part is
  82              sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
  83           FLOAT exp_2t = M_EXP (2 * t);
  84
  85           __real__ res = M_COPYSIGN (1, __real__ x);
  86           __imag__ res = 4 * sinix * cosix;
  87           __real__ x = M_FABS (__real__ x);
  88           __real__ x -= t;
  89           __imag__ res /= exp_2t;
  90           if (__real__ x > t)
  91             {
  92               /* Underflow (original real part of x has absolute value
  93                  > 2t).  */
  94               __imag__ res /= exp_2t;
  95             }
  96           else
  97             __imag__ res /= M_EXP (2 * __real__ x);
  98         }
  99       else
 100         {
 101           FLOAT sinhrx, coshrx;
 102           if (M_FABS (__real__ x) > M_MIN)
 103             {
 104               sinhrx = M_SINH (__real__ x);
 105               coshrx = M_COSH (__real__ x);
 106             }
 107           else
 108             {
 109               sinhrx = __real__ x;
 110               coshrx = 1;
 111             }
 112
 113           if (M_FABS (sinhrx) > M_FABS (cosix) * M_EPSILON)
 114             den = sinhrx * sinhrx + cosix * cosix;
 115           else
 116             den = cosix * cosix;
 117           __real__ res = sinhrx * coshrx / den;
 118           __imag__ res = sinix * cosix / den;
 119         }
 120       math_check_force_underflow_complex (res);
 121     }
 122
 123   return res;
 124 }
 125
 126 declare_mgen_alias (__ctanh, ctanh)
 127
 128 #if M_LIBM_NEED_COMPAT (ctanh)
 129 declare_mgen_libm_compat (__ctanh, ctanh)
 130 #endif