math/s_ctanhl.c

   1 /* Complex hyperbole tangent for long 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__ long double
  27 __ctanhl (__complex__ long double x)
  28 {
  29   __complex__ long double res;
  30
  31   if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
  32     {
  33       if (__isinf_nsl (__real__ x))
  34         {
  35           __real__ res = __copysignl (1.0, __real__ x);
  36           __imag__ res = __copysignl (0.0, __imag__ x);
  37         }
  38       else if (__imag__ x == 0.0)
  39         {
  40           res = x;
  41         }
  42       else
  43         {
  44           __real__ res = __nanl ("");
  45           __imag__ res = __nanl ("");
  46
  47           if (__isinf_nsl (__imag__ x))
  48             feraiseexcept (FE_INVALID);
  49         }
  50     }
  51   else
  52     {
  53       long double sinix, cosix;
  54       long double den;
  55       const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
  56       int icls = fpclassify (__imag__ x);
  57
  58       /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
  59          = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
  60
  61       if (__glibc_likely (icls != FP_SUBNORMAL))
  62         {
  63           __sincosl (__imag__ x, &sinix, &cosix);
  64         }
  65       else
  66         {
  67           sinix = __imag__ x;
  68           cosix = 1.0;
  69         }
  70
  71       if (fabsl (__real__ x) > t)
  72         {
  73           /* Avoid intermediate overflow when the imaginary part of
  74              the result may be subnormal.  Ignoring negligible terms,
  75              the real part is +/- 1, the imaginary part is
  76              sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
  77           long double exp_2t = __ieee754_expl (2 * t);
  78
  79           __real__ res = __copysignl (1.0, __real__ x);
  80           __imag__ res = 4 * sinix * cosix;
  81           __real__ x = fabsl (__real__ x);
  82           __real__ x -= t;
  83           __imag__ res /= exp_2t;
  84           if (__real__ x > t)
  85             {
  86               /* Underflow (original real part of x has absolute value
  87                  > 2t).  */
  88               __imag__ res /= exp_2t;
  89             }
  90           else
  91             __imag__ res /= __ieee754_expl (2 * __real__ x);
  92         }
  93       else
  94         {
  95           long double sinhrx, coshrx;
  96           if (fabsl (__real__ x) > LDBL_MIN)
  97             {
  98               sinhrx = __ieee754_sinhl (__real__ x);
  99               coshrx = __ieee754_coshl (__real__ x);
 100             }
 101           else
 102             {
 103               sinhrx = __real__ x;
 104               coshrx = 1.0L;
 105             }
 106
 107           if (fabsl (sinhrx) > fabsl (cosix) * LDBL_EPSILON)
 108             den = sinhrx * sinhrx + cosix * cosix;
 109           else
 110             den = cosix * cosix;
 111           __real__ res = sinhrx * coshrx / den;
 112           __imag__ res = sinix * cosix / den;
 113         }
 114     }
 115
 116   return res;
 117 }
 118 weak_alias (__ctanhl, ctanhl)