libquadmath/math/ctanq.c

   1 /* Complex tangent function for complex __float128.
   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 "quadmath-imp.h"
  21
  22 #ifdef HAVE_FENV_H
  23 # include <fenv.h>
  24 #endif
  25
  26
  27 __complex128
  28 ctanq (__complex128 x)
  29 {
  30   __complex128 res;
  31
  32   if (__builtin_expect (!finiteq (__real__ x) || !finiteq (__imag__ x), 0))
  33     {
  34       if (__quadmath_isinf_nsq (__imag__ x))
  35         {
  36           __real__ res = copysignq (0.0Q, __real__ x);
  37           __imag__ res = copysignq (1.0Q, __imag__ x);
  38         }
  39       else if (__real__ x == 0.0Q)
  40         {
  41           res = x;
  42         }
  43       else
  44         {
  45           __real__ res = nanq ("");
  46           __imag__ res = nanq ("");
  47
  48 #ifdef HAVE_FENV_H
  49           if (__quadmath_isinf_nsq (__real__ x))
  50             feraiseexcept (FE_INVALID);
  51 #endif
  52         }
  53     }
  54   else
  55     {
  56       __float128 sinrx, cosrx;
  57       __float128 den;
  58       const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2.0Q);
  59       int rcls = fpclassifyq (__real__ x);
  60
  61       /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
  62          = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
  63
  64       if (__builtin_expect (rcls != QUADFP_SUBNORMAL, 1))
  65         {
  66           sincosq (__real__ x, &sinrx, &cosrx);
  67         }
  68       else
  69         {
  70           sinrx = __real__ x;
  71           cosrx = 1.0Q;
  72         }
  73
  74       if (fabsq (__imag__ x) > t)
  75         {
  76           /* Avoid intermediate overflow when the real part of the
  77              result may be subnormal.  Ignoring negligible terms, the
  78              imaginary part is +/- 1, the real part is
  79              sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
  80           __float128 exp_2t = expq (2 * t);
  81
  82           __imag__ res = copysignq (1.0Q, __imag__ x);
  83           __real__ res = 4 * sinrx * cosrx;
  84           __imag__ x = fabsq (__imag__ x);
  85           __imag__ x -= t;
  86           __real__ res /= exp_2t;
  87           if (__imag__ x > t)
  88             {
  89               /* Underflow (original imaginary part of x has absolute
  90                  value > 2t).  */
  91               __real__ res /= exp_2t;
  92             }
  93           else
  94             __real__ res /= expq (2 * __imag__ x);
  95         }
  96       else
  97         {
  98           __float128 sinhix, coshix;
  99           if (fabsq (__imag__ x) > FLT128_MIN)
 100             {
 101               sinhix = sinhq (__imag__ x);
 102               coshix = coshq (__imag__ x);
 103             }
 104           else
 105             {
 106               sinhix = __imag__ x;
 107               coshix = 1.0Q;
 108             }
 109
 110           if (fabsq (sinhix) > fabsq (cosrx) * FLT128_EPSILON)
 111             den = cosrx * cosrx + sinhix * sinhix;
 112           else
 113             den = cosrx * cosrx;
 114           __real__ res = sinrx * cosrx / den;
 115           __imag__ res = sinhix * coshix / den;
 116         }
 117     }
 118
 119   return res;
 120 }