math/s_ctan_template.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 <complex.h>
  21 #include <fenv.h>
  22 #include <math.h>
  23 #include <math_private.h>
  24 #include <math-underflow.h>
  25 #include <float.h>
  26
  27 CFLOAT
  28 M_DECL_FUNC (__ctan) (CFLOAT x)
  29 {
  30   CFLOAT res;
  31
  32   if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
  33     {
  34       if (isinf (__imag__ x))
  35         {
  36           if (isfinite (__real__ x) && M_FABS (__real__ x) > 1)
  37             {
  38               FLOAT sinrx, cosrx;
  39               M_SINCOS (__real__ x, &sinrx, &cosrx);
  40               __real__ res = M_COPYSIGN (0, sinrx * cosrx);
  41             }
  42           else
  43             __real__ res = M_COPYSIGN (0, __real__ x);
  44           __imag__ res = M_COPYSIGN (1, __imag__ x);
  45         }
  46       else if (__real__ x == 0)
  47         {
  48           res = x;
  49         }
  50       else
  51         {
  52           __real__ res = M_NAN;
  53           if (__imag__ x == 0)
  54             __imag__ res = __imag__ x;
  55           else
  56             __imag__ res = M_NAN;
  57
  58           if (isinf (__real__ x))
  59             feraiseexcept (FE_INVALID);
  60         }
  61     }
  62   else
  63     {
  64       FLOAT sinrx, cosrx;
  65       FLOAT den;
  66       const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2);
  67
  68       /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
  69          = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
  70
  71       if (__glibc_likely (M_FABS (__real__ x) > M_MIN))
  72         {
  73           M_SINCOS (__real__ x, &sinrx, &cosrx);
  74         }
  75       else
  76         {
  77           sinrx = __real__ x;
  78           cosrx = 1;
  79         }
  80
  81       if (M_FABS (__imag__ x) > t)
  82         {
  83           /* Avoid intermediate overflow when the real part of the
  84              result may be subnormal.  Ignoring negligible terms, the
  85              imaginary part is +/- 1, the real part is
  86              sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
  87           FLOAT exp_2t = M_EXP (2 * t);
  88
  89           __imag__ res = M_COPYSIGN (1, __imag__ x);
  90           __real__ res = 4 * sinrx * cosrx;
  91           __imag__ x = M_FABS (__imag__ x);
  92           __imag__ x -= t;
  93           __real__ res /= exp_2t;
  94           if (__imag__ x > t)
  95             {
  96               /* Underflow (original imaginary part of x has absolute
  97                  value > 2t).  */
  98               __real__ res /= exp_2t;
  99             }
 100           else
 101             __real__ res /= M_EXP (2 * __imag__ x);
 102         }
 103       else
 104         {
 105           FLOAT sinhix, coshix;
 106           if (M_FABS (__imag__ x) > M_MIN)
 107             {
 108               sinhix = M_SINH (__imag__ x);
 109               coshix = M_COSH (__imag__ x);
 110             }
 111           else
 112             {
 113               sinhix = __imag__ x;
 114               coshix = 1;
 115             }
 116
 117           if (M_FABS (sinhix) > M_FABS (cosrx) * M_EPSILON)
 118             den = cosrx * cosrx + sinhix * sinhix;
 119           else
 120             den = cosrx * cosrx;
 121           __real__ res = sinrx * cosrx / den;
 122           __imag__ res = sinhix * coshix / den;
 123         }
 124       math_check_force_underflow_complex (res);
 125     }
 126
 127   return res;
 128 }
 129
 130 declare_mgen_alias (__ctan, ctan)