libquadmath/math/ctanhq.c

   1 /* Complex hyperbolic tangent for float types.
   2    Copyright (C) 1997-2018 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 "quadmath-imp.h"
  21
  22 __complex128
  23 ctanhq (__complex128 x)
  24 {
  25   __complex128 res;
  26
  27   if (__glibc_unlikely (!finiteq (__real__ x) || !finiteq (__imag__ x)))
  28     {
  29       if (isinfq (__real__ x))
  30         {
  31           __real__ res = copysignq (1, __real__ x);
  32           if (finiteq (__imag__ x) && fabsq (__imag__ x) > 1)
  33             {
  34               __float128 sinix, cosix;
  35               sincosq (__imag__ x, &sinix, &cosix);
  36               __imag__ res = copysignq (0, sinix * cosix);
  37             }
  38           else
  39             __imag__ res = copysignq (0, __imag__ x);
  40         }
  41       else if (__imag__ x == 0)
  42         {
  43           res = x;
  44         }
  45       else
  46         {
  47           if (__real__ x == 0)
  48             __real__ res = __real__ x;
  49           else
  50             __real__ res = nanq ("");
  51           __imag__ res = nanq ("");
  52
  53           if (isinfq (__imag__ x))
  54             feraiseexcept (FE_INVALID);
  55         }
  56     }
  57   else
  58     {
  59       __float128 sinix, cosix;
  60       __float128 den;
  61       const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2);
  62
  63       /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
  64          = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
  65
  66       if (__glibc_likely (fabsq (__imag__ x) > FLT128_MIN))
  67         {
  68           sincosq (__imag__ x, &sinix, &cosix);
  69         }
  70       else
  71         {
  72           sinix = __imag__ x;
  73           cosix = 1;
  74         }
  75
  76       if (fabsq (__real__ x) > t)
  77         {
  78           /* Avoid intermediate overflow when the imaginary part of
  79              the result may be subnormal.  Ignoring negligible terms,
  80              the real part is +/- 1, the imaginary part is
  81              sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
  82           __float128 exp_2t = expq (2 * t);
  83
  84           __real__ res = copysignq (1, __real__ x);
  85           __imag__ res = 4 * sinix * cosix;
  86           __real__ x = fabsq (__real__ x);
  87           __real__ x -= t;
  88           __imag__ res /= exp_2t;
  89           if (__real__ x > t)
  90             {
  91               /* Underflow (original real part of x has absolute value
  92                  > 2t).  */
  93               __imag__ res /= exp_2t;
  94             }
  95           else
  96             __imag__ res /= expq (2 * __real__ x);
  97         }
  98       else
  99         {
 100           __float128 sinhrx, coshrx;
 101           if (fabsq (__real__ x) > FLT128_MIN)
 102             {
 103               sinhrx = sinhq (__real__ x);
 104               coshrx = coshq (__real__ x);
 105             }
 106           else
 107             {
 108               sinhrx = __real__ x;
 109               coshrx = 1;
 110             }
 111
 112           if (fabsq (sinhrx) > fabsq (cosix) * FLT128_EPSILON)
 113             den = sinhrx * sinhrx + cosix * cosix;
 114           else
 115             den = cosix * cosix;
 116           __real__ res = sinhrx * coshrx / den;
 117           __imag__ res = sinix * cosix / den;
 118         }
 119       math_check_force_underflow_complex (res);
 120     }
 121
 122   return res;
 123 }