math/s_ctanh.c

   1 /* Complex hyperbole tangent for double.
   2    Copyright (C) 1997-2015 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 __complex__ double
  27 __ctanh (__complex__ double x)
  28 {
  29   __complex__ double res;
  30
  31   if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
  32     {
  33       if (__isinf_ns (__real__ x))
  34         {
  35           __real__ res = __copysign (1.0, __real__ x);
  36           __imag__ res = __copysign (0.0, __imag__ x);
  37         }
  38       else if (__imag__ x == 0.0)
  39         {
  40           res = x;
  41         }
  42       else
  43         {
  44           __real__ res = __nan ("");
  45           __imag__ res = __nan ("");
  46
  47           if (__isinf_ns (__imag__ x))
  48             feraiseexcept (FE_INVALID);
  49         }
  50     }
  51   else
  52     {
  53       double sinix, cosix;
  54       double den;
  55       const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
  56
  57       /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
  58          = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
  59
  60       if (__glibc_likely (fabs (__imag__ x) > DBL_MIN))
  61         {
  62           __sincos (__imag__ x, &sinix, &cosix);
  63         }
  64       else
  65         {
  66           sinix = __imag__ x;
  67           cosix = 1.0;
  68         }
  69
  70       if (fabs (__real__ x) > t)
  71         {
  72           /* Avoid intermediate overflow when the imaginary part of
  73              the result may be subnormal.  Ignoring negligible terms,
  74              the real part is +/- 1, the imaginary part is
  75              sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
  76           double exp_2t = __ieee754_exp (2 * t);
  77
  78           __real__ res = __copysign (1.0, __real__ x);
  79           __imag__ res = 4 * sinix * cosix;
  80           __real__ x = fabs (__real__ x);
  81           __real__ x -= t;
  82           __imag__ res /= exp_2t;
  83           if (__real__ x > t)
  84             {
  85               /* Underflow (original real part of x has absolute value
  86                  > 2t).  */
  87               __imag__ res /= exp_2t;
  88             }
  89           else
  90             __imag__ res /= __ieee754_exp (2 * __real__ x);
  91         }
  92       else
  93         {
  94           double sinhrx, coshrx;
  95           if (fabs (__real__ x) > DBL_MIN)
  96             {
  97               sinhrx = __ieee754_sinh (__real__ x);
  98               coshrx = __ieee754_cosh (__real__ x);
  99             }
 100           else
 101             {
 102               sinhrx = __real__ x;
 103               coshrx = 1.0;
 104             }
 105
 106           if (fabs (sinhrx) > fabs (cosix) * DBL_EPSILON)
 107             den = sinhrx * sinhrx + cosix * cosix;
 108           else
 109             den = cosix * cosix;
 110           __real__ res = sinhrx * coshrx / den;
 111           __imag__ res = sinix * cosix / den;
 112         }
 113     }
 114
 115   return res;
 116 }
 117 weak_alias (__ctanh, ctanh)
 118 #ifdef NO_LONG_DOUBLE
 119 strong_alias (__ctanh, __ctanhl)
 120 weak_alias (__ctanh, ctanhl)
 121 #endif