libquadmath/math/ctanhq.c

   1 /* Complex hyperbole tangent for __float128.
   2    Copyright (C) 1997-2012 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 #ifdef HAVE_FENV_H
  23 # include <fenv.h>
  24 #endif
  25
  26
  27 __complex128
  28 ctanhq (__complex128 x)
  29 {
  30   __complex128 res;
  31
  32   if (__builtin_expect (!finiteq (__real__ x) || !finiteq (__imag__ x), 0))
  33     {
  34       if (__quadmath_isinf_nsq (__real__ x))
  35         {
  36           __real__ res = copysignq (1.0Q, __real__ x);
  37           __imag__ res = copysignq (0.0Q, __imag__ x);
  38         }
  39       else if (__imag__ x == 0.0Q)
  40         {
  41           res = x;
  42         }
  43       else
  44         {
  45           __real__ res = nanq ("");
  46           __imag__ res = nanq ("");
  47
  48 #ifdef HAVE_FENV_H
  49           if (__quadmath_isinf_nsq (__imag__ x))
  50             feraiseexcept (FE_INVALID);
  51 #endif
  52         }
  53     }
  54   else
  55     {
  56       __float128 sinix, cosix;
  57       __float128 den;
  58       const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2);
  59       int icls = fpclassifyq (__imag__ x);
  60
  61       /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
  62          = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
  63
  64       if (__builtin_expect (icls != QUADFP_SUBNORMAL, 1))
  65         {
  66           sincosq (__imag__ x, &sinix, &cosix);
  67         }
  68       else
  69         {
  70           sinix = __imag__ x;
  71           cosix = 1.0Q;
  72         }
  73
  74       if (fabsq (__real__ x) > t)
  75         {
  76           /* Avoid intermediate overflow when the imaginary part of
  77              the result may be subnormal.  Ignoring negligible terms,
  78              the real part is +/- 1, the imaginary part is
  79              sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
  80           __float128 exp_2t = expq (2 * t);
  81
  82           __real__ res = copysignq (1.0, __real__ x);
  83           __imag__ res = 4 * sinix * cosix;
  84           __real__ x = fabsq (__real__ x);
  85           __real__ x -= t;
  86           __imag__ res /= exp_2t;
  87           if (__real__ x > t)
  88             {
  89               /* Underflow (original real part of x has absolute value
  90                  > 2t).  */
  91               __imag__ res /= exp_2t;
  92             }
  93           else
  94             __imag__ res /= expq (2 * __real__ x);
  95         }
  96       else
  97         {
  98           __float128 sinhrx, coshrx;
  99           if (fabsq (__real__ x) > FLT128_MIN)
 100             {
 101               sinhrx = sinhq (__real__ x);
 102               coshrx = coshq (__real__ x);
 103             }
 104           else
 105             {
 106               sinhrx = __real__ x;
 107               coshrx = 1.0Q;
 108             }
 109
 110           if (fabsq (sinhrx) > fabsq (cosix) * FLT128_EPSILON)
 111             den = sinhrx * sinhrx + cosix * cosix;
 112           else
 113             den = cosix * cosix;
 114           __real__ res = sinhrx * coshrx / den;
 115           __imag__ res = sinix * cosix / den;
 116         }
 117     }
 118
 119   return res;
 120 }