libquadmath/math/ctanq.c

   1 /* Complex tangent function for a complex float type.
   2    Copyright (C) 1997-2018 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 __complex128
  23 ctanq (__complex128 x)
  24 {
  25   __complex128 res;
  26
  27   if (__glibc_unlikely (!finiteq (__real__ x) || !finiteq (__imag__ x)))
  28     {
  29       if (isinfq (__imag__ x))
  30         {
  31           if (finiteq (__real__ x) && fabsq (__real__ x) > 1)
  32             {
  33               __float128 sinrx, cosrx;
  34               sincosq (__real__ x, &sinrx, &cosrx);
  35               __real__ res = copysignq (0, sinrx * cosrx);
  36             }
  37           else
  38             __real__ res = copysignq (0, __real__ x);
  39           __imag__ res = copysignq (1, __imag__ x);
  40         }
  41       else if (__real__ x == 0)
  42         {
  43           res = x;
  44         }
  45       else
  46         {
  47           __real__ res = nanq ("");
  48           if (__imag__ x == 0)
  49             __imag__ res = __imag__ x;
  50           else
  51             __imag__ res = nanq ("");
  52
  53           if (isinfq (__real__ x))
  54             feraiseexcept (FE_INVALID);
  55         }
  56     }
  57   else
  58     {
  59       __float128 sinrx, cosrx;
  60       __float128 den;
  61       const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2);
  62
  63       /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
  64          = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
  65
  66       if (__glibc_likely (fabsq (__real__ x) > FLT128_MIN))
  67         {
  68           sincosq (__real__ x, &sinrx, &cosrx);
  69         }
  70       else
  71         {
  72           sinrx = __real__ x;
  73           cosrx = 1;
  74         }
  75
  76       if (fabsq (__imag__ x) > t)
  77         {
  78           /* Avoid intermediate overflow when the real part of the
  79              result may be subnormal.  Ignoring negligible terms, the
  80              imaginary part is +/- 1, the real part is
  81              sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
  82           __float128 exp_2t = expq (2 * t);
  83
  84           __imag__ res = copysignq (1, __imag__ x);
  85           __real__ res = 4 * sinrx * cosrx;
  86           __imag__ x = fabsq (__imag__ x);
  87           __imag__ x -= t;
  88           __real__ res /= exp_2t;
  89           if (__imag__ x > t)
  90             {
  91               /* Underflow (original imaginary part of x has absolute
  92                  value > 2t).  */
  93               __real__ res /= exp_2t;
  94             }
  95           else
  96             __real__ res /= expq (2 * __imag__ x);
  97         }
  98       else
  99         {
 100           __float128 sinhix, coshix;
 101           if (fabsq (__imag__ x) > FLT128_MIN)
 102             {
 103               sinhix = sinhq (__imag__ x);
 104               coshix = coshq (__imag__ x);
 105             }
 106           else
 107             {
 108               sinhix = __imag__ x;
 109               coshix = 1;
 110             }
 111
 112           if (fabsq (sinhix) > fabsq (cosrx) * FLT128_EPSILON)
 113             den = cosrx * cosrx + sinhix * sinhix;
 114           else
 115             den = cosrx * cosrx;
 116           __real__ res = sinrx * cosrx / den;
 117           __imag__ res = sinhix * coshix / den;
 118         }
 119       math_check_force_underflow_complex (res);
 120     }
 121
 122   return res;
 123 }