math/s_ctanhf.c

   1 /* Complex hyperbole tangent for float.
   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 <complex.h>
  21 #include <fenv.h>
  22 #include <math.h>
  23 #include <math_private.h>
  24 #include <float.h>
  25
  26 __complex__ float
  27 __ctanhf (__complex__ float x)
  28 {
  29   __complex__ float res;
  30
  31   if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0))
  32     {
  33       if (__isinf_nsf (__real__ x))
  34         {
  35           __real__ res = __copysignf (1.0, __real__ x);
  36           __imag__ res = __copysignf (0.0, __imag__ x);
  37         }
  38       else if (__imag__ x == 0.0)
  39         {
  40           res = x;
  41         }
  42       else
  43         {
  44           __real__ res = __nanf ("");
  45           __imag__ res = __nanf ("");
  46
  47           if (__isinf_nsf (__imag__ x))
  48             feraiseexcept (FE_INVALID);
  49         }
  50     }
  51   else
  52     {
  53       float sinix, cosix;
  54       float den;
  55       const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2);
  56
  57       /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
  58          = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
  59
  60       __sincosf (__imag__ x, &sinix, &cosix);
  61
  62       if (fabsf (__real__ x) > t)
  63         {
  64           /* Avoid intermediate overflow when the imaginary part of
  65              the result may be subnormal.  Ignoring negligible terms,
  66              the real part is +/- 1, the imaginary part is
  67              sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
  68           float exp_2t = __ieee754_expf (2 * t);
  69
  70           __real__ res = __copysignf (1.0, __real__ x);
  71           __imag__ res = 4 * sinix * cosix;
  72           __real__ x = fabsf (__real__ x);
  73           __real__ x -= t;
  74           __imag__ res /= exp_2t;
  75           if (__real__ x > t)
  76             {
  77               /* Underflow (original real part of x has absolute value
  78                  > 2t).  */
  79               __imag__ res /= exp_2t;
  80             }
  81           else
  82             __imag__ res /= __ieee754_expf (2 * __real__ x);
  83         }
  84       else
  85         {
  86           float sinhrx, coshrx;
  87           if (fabsf (__real__ x) > FLT_MIN)
  88             {
  89               sinhrx = __ieee754_sinhf (__real__ x);
  90               coshrx = __ieee754_coshf (__real__ x);
  91             }
  92           else
  93             {
  94               sinhrx = __real__ x;
  95               coshrx = 1.0f;
  96             }
  97
  98           if (fabsf (sinhrx) > fabsf (cosix) * FLT_EPSILON)
  99             den = sinhrx * sinhrx + cosix * cosix;
 100           else
 101             den = cosix * cosix;
 102           __real__ res = sinhrx * coshrx / den;
 103           __imag__ res = sinix * cosix / den;
 104         }
 105     }
 106
 107   return res;
 108 }
 109 #ifndef __ctanhf
 110 weak_alias (__ctanhf, ctanhf)
 111 #endif