sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c

   1 /* Complex hyperbole tangent for long double.  IBM extended format version.
   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 <float.h>
  23 #include <math.h>
  24 #include <math_ldbl_opt.h>
  25
  26 #include <math_private.h>
  27
  28 /* IBM long double GCC builtin sets LDBL_EPSILON == LDBL_DENORM_MIN  */
  29 static const long double ldbl_eps =  0x1p-106L;
  30
  31 __complex__ long double
  32 __ctanhl (__complex__ long double x)
  33 {
  34   __complex__ long double res;
  35
  36   if (!isfinite (__real__ x) || !isfinite (__imag__ x))
  37     {
  38       if (__isinfl (__real__ x))
  39         {
  40           __real__ res = __copysignl (1.0L, __real__ x);
  41           __imag__ res = __copysignl (0.0L, __imag__ x);
  42         }
  43       else if (__imag__ x == 0.0)
  44         {
  45           res = x;
  46         }
  47       else
  48         {
  49           __real__ res = __nanl ("");
  50           __imag__ res = __nanl ("");
  51
  52 #ifdef FE_INVALID
  53           if (__isinfl (__imag__ x))
  54             feraiseexcept (FE_INVALID);
  55 #endif
  56         }
  57     }
  58   else
  59     {
  60       long double sinix, cosix;
  61       long double den;
  62       const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2.0L);
  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       __sincosl (__imag__ x, &sinix, &cosix);
  68
  69       if (fabsl (__real__ x) > t)
  70         {
  71           /* Avoid intermediate overflow when the imaginary part of
  72              the result may be subnormal.  Ignoring negligible terms,
  73              the real part is +/- 1, the imaginary part is
  74              sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
  75           long double exp_2t = __ieee754_expl (2 * t);
  76           __real__ res = __copysignl (1.0L, __real__ x);
  77           __imag__ res = 4 * sinix * cosix;
  78           __real__ x = fabsl (__real__ x);
  79           __real__ x -= t;
  80           __imag__ res /= exp_2t;
  81           if (__real__ x > t)
  82             {
  83               /* Underflow (original real part of x has absolute value
  84                  > 2t).  */
  85               __imag__ res /= exp_2t;
  86             }
  87           else
  88             __imag__ res /= __ieee754_expl (2.0L * __real__ x);
  89         }
  90       else
  91         {
  92           long double sinhrx, coshrx;
  93           if (fabs (__real__ x) > LDBL_MIN)
  94             {
  95               sinhrx = __ieee754_sinhl (__real__ x);
  96               coshrx = __ieee754_coshl (__real__ x);
  97             }
  98           else
  99             {
 100               sinhrx = __real__ x;
 101               coshrx = 1.0L;
 102             }
 103
 104           if (fabsl (sinhrx) > fabsl (cosix) * ldbl_eps)
 105             den = sinhrx * sinhrx + cosix * cosix;
 106           else
 107             den = cosix * cosix;
 108           __real__ res = sinhrx * (coshrx / den);
 109           __imag__ res = sinix * (cosix / den);
 110         }
 111       /* __gcc_qmul does not respect -0.0 so we need the following fixup.  */
 112       if ((__real__ res == 0.0L) && (__real__ x == 0.0L))
 113         __real__ res = __real__ x;
 114
 115       if ((__real__ res == 0.0L) && (__imag__ x == 0.0L))
 116         __imag__ res = __imag__ x;
 117     }
 118
 119   return res;
 120 }
 121 long_double_symbol (libm, __ctanhl, ctanhl);