math/s_ctan_template.c

   1 /* Complex tangent function for a complex float type.
   2    Copyright (C) 1997-2022 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, see
  17    <https://www.gnu.org/licenses/>.  */
  18
  19 #include <complex.h>
  20 #include <fenv.h>
  21 #include <math.h>
  22 #include <math_private.h>
  23 #include <math-underflow.h>
  24 #include <float.h>
  25
  26 CFLOAT
  27 M_DECL_FUNC (__ctan) (CFLOAT x)
  28 {
  29   CFLOAT res;
  30
  31   if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
  32     {
  33       if (isinf (__imag__ x))
  34         {
  35           if (isfinite (__real__ x) && M_FABS (__real__ x) > 1)
  36             {
  37               FLOAT sinrx, cosrx;
  38               M_SINCOS (__real__ x, &sinrx, &cosrx);
  39               __real__ res = M_COPYSIGN (0, sinrx * cosrx);
  40             }
  41           else
  42             __real__ res = M_COPYSIGN (0, __real__ x);
  43           __imag__ res = M_COPYSIGN (1, __imag__ x);
  44         }
  45       else if (__real__ x == 0)
  46         {
  47           res = x;
  48         }
  49       else
  50         {
  51           __real__ res = M_NAN;
  52           if (__imag__ x == 0)
  53             __imag__ res = __imag__ x;
  54           else
  55             __imag__ res = M_NAN;
  56
  57           if (isinf (__real__ x))
  58             feraiseexcept (FE_INVALID);
  59         }
  60     }
  61   else
  62     {
  63       FLOAT sinrx, cosrx;
  64       FLOAT den;
  65       const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2);
  66
  67       /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
  68          = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
  69
  70       if (__glibc_likely (M_FABS (__real__ x) > M_MIN))
  71         {
  72           M_SINCOS (__real__ x, &sinrx, &cosrx);
  73         }
  74       else
  75         {
  76           sinrx = __real__ x;
  77           cosrx = 1;
  78         }
  79
  80       if (M_FABS (__imag__ x) > t)
  81         {
  82           /* Avoid intermediate overflow when the real part of the
  83              result may be subnormal.  Ignoring negligible terms, the
  84              imaginary part is +/- 1, the real part is
  85              sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
  86           FLOAT exp_2t = M_EXP (2 * t);
  87
  88           __imag__ res = M_COPYSIGN (1, __imag__ x);
  89           __real__ res = 4 * sinrx * cosrx;
  90           __imag__ x = M_FABS (__imag__ x);
  91           __imag__ x -= t;
  92           __real__ res /= exp_2t;
  93           if (__imag__ x > t)
  94             {
  95               /* Underflow (original imaginary part of x has absolute
  96                  value > 2t).  */
  97               __real__ res /= exp_2t;
  98             }
  99           else
 100             __real__ res /= M_EXP (2 * __imag__ x);
 101         }
 102       else
 103         {
 104           FLOAT sinhix, coshix;
 105           if (M_FABS (__imag__ x) > M_MIN)
 106             {
 107               sinhix = M_SINH (__imag__ x);
 108               coshix = M_COSH (__imag__ x);
 109             }
 110           else
 111             {
 112               sinhix = __imag__ x;
 113               coshix = 1;
 114             }
 115
 116           if (M_FABS (sinhix) > M_FABS (cosrx) * M_EPSILON)
 117             den = cosrx * cosrx + sinhix * sinhix;
 118           else
 119             den = cosrx * cosrx;
 120           __real__ res = sinrx * cosrx / den;
 121           __imag__ res = sinhix * coshix / den;
 122         }
 123       math_check_force_underflow_complex (res);
 124     }
 125
 126   return res;
 127 }
 128
 129 declare_mgen_alias (__ctan, ctan)