math/s_ctan.c

   1 /* Complex tangent function for 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__ double
  27 __ctan (__complex__ double x)
  28 {
  29   __complex__ double res;
  30
  31   if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
  32     {
  33       if (__isinf_ns (__imag__ x))
  34         {
  35           __real__ res = __copysign (0.0, __real__ x);
  36           __imag__ res = __copysign (1.0, __imag__ x);
  37         }
  38       else if (__real__ x == 0.0)
  39         {
  40           res = x;
  41         }
  42       else
  43         {
  44           __real__ res = __nan ("");
  45           __imag__ res = __nan ("");
  46
  47           if (__isinf_ns (__real__ x))
  48             feraiseexcept (FE_INVALID);
  49         }
  50     }
  51   else
  52     {
  53       double sinrx, cosrx;
  54       double den;
  55       const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
  56       int rcls = fpclassify (__real__ x);
  57
  58       /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
  59          = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
  60
  61       if (__glibc_likely (rcls != FP_SUBNORMAL))
  62         {
  63           __sincos (__real__ x, &sinrx, &cosrx);
  64         }
  65       else
  66         {
  67           sinrx = __real__ x;
  68           cosrx = 1.0;
  69         }
  70
  71       if (fabs (__imag__ x) > t)
  72         {
  73           /* Avoid intermediate overflow when the real part of the
  74              result may be subnormal.  Ignoring negligible terms, the
  75              imaginary part is +/- 1, the real part is
  76              sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
  77           double exp_2t = __ieee754_exp (2 * t);
  78
  79           __imag__ res = __copysign (1.0, __imag__ x);
  80           __real__ res = 4 * sinrx * cosrx;
  81           __imag__ x = fabs (__imag__ x);
  82           __imag__ x -= t;
  83           __real__ res /= exp_2t;
  84           if (__imag__ x > t)
  85             {
  86               /* Underflow (original imaginary part of x has absolute
  87                  value > 2t).  */
  88               __real__ res /= exp_2t;
  89             }
  90           else
  91             __real__ res /= __ieee754_exp (2 * __imag__ x);
  92         }
  93       else
  94         {
  95           double sinhix, coshix;
  96           if (fabs (__imag__ x) > DBL_MIN)
  97             {
  98               sinhix = __ieee754_sinh (__imag__ x);
  99               coshix = __ieee754_cosh (__imag__ x);
 100             }
 101           else
 102             {
 103               sinhix = __imag__ x;
 104               coshix = 1.0;
 105             }
 106
 107           if (fabs (sinhix) > fabs (cosrx) * DBL_EPSILON)
 108             den = cosrx * cosrx + sinhix * sinhix;
 109           else
 110             den = cosrx * cosrx;
 111           __real__ res = sinrx * cosrx / den;
 112           __imag__ res = sinhix * coshix / den;
 113         }
 114     }
 115
 116   return res;
 117 }
 118 weak_alias (__ctan, ctan)
 119 #ifdef NO_LONG_DOUBLE
 120 strong_alias (__ctan, __ctanl)
 121 weak_alias (__ctan, ctanl)
 122 #endif