math/s_ctanl.c

   1 /* Complex tangent function for long 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 /* To avoid spurious underflows, use this definition to treat IBM long
  27    double as approximating an IEEE-style format.  */
  28 #if LDBL_MANT_DIG == 106
  29 # undef LDBL_EPSILON
  30 # define LDBL_EPSILON 0x1p-106L
  31 #endif
  32
  33 __complex__ long double
  34 __ctanl (__complex__ long double x)
  35 {
  36   __complex__ long double res;
  37
  38   if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
  39     {
  40       if (__isinf_nsl (__imag__ x))
  41         {
  42           __real__ res = __copysignl (0.0, __real__ x);
  43           __imag__ res = __copysignl (1.0, __imag__ x);
  44         }
  45       else if (__real__ x == 0.0)
  46         {
  47           res = x;
  48         }
  49       else
  50         {
  51           __real__ res = __nanl ("");
  52           __imag__ res = __nanl ("");
  53
  54           if (__isinf_nsl (__real__ x))
  55             feraiseexcept (FE_INVALID);
  56         }
  57     }
  58   else
  59     {
  60       long double sinrx, cosrx;
  61       long double den;
  62       const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
  63
  64       /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
  65          = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
  66
  67       if (__glibc_likely (fabsl (__real__ x) > LDBL_MIN))
  68         {
  69           __sincosl (__real__ x, &sinrx, &cosrx);
  70         }
  71       else
  72         {
  73           sinrx = __real__ x;
  74           cosrx = 1.0;
  75         }
  76
  77       if (fabsl (__imag__ x) > t)
  78         {
  79           /* Avoid intermediate overflow when the real part of the
  80              result may be subnormal.  Ignoring negligible terms, the
  81              imaginary part is +/- 1, the real part is
  82              sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
  83           long double exp_2t = __ieee754_expl (2 * t);
  84
  85           __imag__ res = __copysignl (1.0, __imag__ x);
  86           __real__ res = 4 * sinrx * cosrx;
  87           __imag__ x = fabsl (__imag__ x);
  88           __imag__ x -= t;
  89           __real__ res /= exp_2t;
  90           if (__imag__ x > t)
  91             {
  92               /* Underflow (original imaginary part of x has absolute
  93                  value > 2t).  */
  94               __real__ res /= exp_2t;
  95             }
  96           else
  97             __real__ res /= __ieee754_expl (2 * __imag__ x);
  98         }
  99       else
 100         {
 101           long double sinhix, coshix;
 102           if (fabsl (__imag__ x) > LDBL_MIN)
 103             {
 104               sinhix = __ieee754_sinhl (__imag__ x);
 105               coshix = __ieee754_coshl (__imag__ x);
 106             }
 107           else
 108             {
 109               sinhix = __imag__ x;
 110               coshix = 1.0L;
 111             }
 112
 113           if (fabsl (sinhix) > fabsl (cosrx) * LDBL_EPSILON)
 114             den = cosrx * cosrx + sinhix * sinhix;
 115           else
 116             den = cosrx * cosrx;
 117           __real__ res = sinrx * cosrx / den;
 118           __imag__ res = sinhix * coshix / den;
 119         }
 120     }
 121
 122   return res;
 123 }
 124 weak_alias (__ctanl, ctanl)