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 /* To avoid spurious underflows, use this definition to treat IBM long
  27    double as approximating an IEEE-style format.  */
  28 #if LDBL_MANT_DIG == 106
  29 # undef LDBL_EPSILON
  30 # define LDBL_EPSILON 0x1p-106L
  31 #endif
  32
  33 __complex__ long double
  34 __ctanhl (__complex__ long double x)
  35 {
  36   __complex__ long double res;
  37
  38   if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
  39     {
  40       if (isinf (__real__ x))
  41         {
  42           __real__ res = __copysignl (1.0, __real__ x);
  43           if (isfinite (__imag__ x) && fabsl (__imag__ x) > 1.0L)
  44             {
  45               long double sinix, cosix;
  46               __sincosl (__imag__ x, &sinix, &cosix);
  47               __imag__ res = __copysignl (0.0L, sinix * cosix);
  48             }
  49           else
  50             __imag__ res = __copysignl (0.0, __imag__ x);
  51         }
  52       else if (__imag__ x == 0.0)
  53         {
  54           res = x;
  55         }
  56       else
  57         {
  58           __real__ res = __nanl ("");
  59           __imag__ res = __nanl ("");
  60
  61           if (isinf (__imag__ x))
  62             feraiseexcept (FE_INVALID);
  63         }
  64     }
  65   else
  66     {
  67       long double sinix, cosix;
  68       long double den;
  69       const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
  70
  71       /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
  72          = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
  73
  74       if (__glibc_likely (fabsl (__imag__ x) > LDBL_MIN))
  75         {
  76           __sincosl (__imag__ x, &sinix, &cosix);
  77         }
  78       else
  79         {
  80           sinix = __imag__ x;
  81           cosix = 1.0;
  82         }
  83
  84       if (fabsl (__real__ x) > t)
  85         {
  86           /* Avoid intermediate overflow when the imaginary part of
  87              the result may be subnormal.  Ignoring negligible terms,
  88              the real part is +/- 1, the imaginary part is
  89              sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
  90           long double exp_2t = __ieee754_expl (2 * t);
  91
  92           __real__ res = __copysignl (1.0, __real__ x);
  93           __imag__ res = 4 * sinix * cosix;
  94           __real__ x = fabsl (__real__ x);
  95           __real__ x -= t;
  96           __imag__ res /= exp_2t;
  97           if (__real__ x > t)
  98             {
  99               /* Underflow (original real part of x has absolute value
 100                  > 2t).  */
 101               __imag__ res /= exp_2t;
 102             }
 103           else
 104             __imag__ res /= __ieee754_expl (2 * __real__ x);
 105         }
 106       else
 107         {
 108           long double sinhrx, coshrx;
 109           if (fabsl (__real__ x) > LDBL_MIN)
 110             {
 111               sinhrx = __ieee754_sinhl (__real__ x);
 112               coshrx = __ieee754_coshl (__real__ x);
 113             }
 114           else
 115             {
 116               sinhrx = __real__ x;
 117               coshrx = 1.0L;
 118             }
 119
 120           if (fabsl (sinhrx) > fabsl (cosix) * LDBL_EPSILON)
 121             den = sinhrx * sinhrx + cosix * cosix;
 122           else
 123             den = cosix * cosix;
 124           __real__ res = sinhrx * coshrx / den;
 125           __imag__ res = sinix * cosix / den;
 126         }
 127       math_check_force_underflow_complex (res);
 128     }
 129
 130   return res;
 131 }
 132 weak_alias (__ctanhl, ctanhl)