sysdeps/ieee754/ldbl-128ibm/s_ctanl.c

   1 /* Complex tangent function for long double.  IBM extended format version.
   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_ldbl_opt.h>
  24 #include <float.h>
  25
  26 #include <math_private.h>
  27
  28 /* IBM long double GCC builtin sets LDBL_EPSILON == LDBL_DENORM_MIN  */
  29 static const long double ldbl_eps = 0x1p-106L;
  30
  31 __complex__ long double
  32 __ctanl (__complex__ long double x)
  33 {
  34   __complex__ long double res;
  35
  36   if (!isfinite (__real__ x) || !isfinite (__imag__ x))
  37     {
  38       if (__isinfl (__imag__ x))
  39         {
  40           __real__ res = __copysignl (0.0, __real__ x);
  41           __imag__ res = __copysignl (1.0, __imag__ x);
  42         }
  43       else if (__real__ x == 0.0)
  44         {
  45           res = x;
  46         }
  47       else
  48         {
  49           __real__ res = __nanl ("");
  50           __imag__ res = __nanl ("");
  51
  52           if (__isinf_nsl (__real__ x))
  53             feraiseexcept (FE_INVALID);
  54         }
  55     }
  56   else
  57     {
  58       long double sinrx, cosrx;
  59       long double den;
  60       const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2.0L);
  61
  62       /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
  63         = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
  64
  65       __sincosl (__real__ x, &sinrx, &cosrx);
  66
  67       if (fabsl (__imag__ x) > t)
  68         {
  69           /* Avoid intermediate overflow when the real part of the
  70             result may be subnormal.  Ignoring negligible terms, the
  71             imaginary part is +/- 1, the real part is
  72             sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
  73           long double exp_2t = __ieee754_expl (2 * t);
  74
  75           __imag__ res = __copysignl (1.0L, __imag__ x);
  76           __real__ res = 4 * sinrx * cosrx;
  77           __imag__ x = fabsl (__imag__ x);
  78           __imag__ x -= t;
  79           __real__ res /= exp_2t;
  80           if (__imag__ x > t)
  81             {
  82               /* Underflow (original imaginary part of x has absolute
  83                  value > 2t).  */
  84               __real__ res /= exp_2t;
  85             }
  86           else
  87             __real__ res /= __ieee754_expl (2.0L * __imag__ x);
  88         }
  89       else
  90         {
  91           long double sinhix, coshix;
  92           if (fabsl (__imag__ x) > LDBL_MIN)
  93             {
  94               sinhix = __ieee754_sinhl (__imag__ x);
  95               coshix = __ieee754_coshl (__imag__ x);
  96             }
  97           else
  98             {
  99               sinhix = __imag__ x;
 100               coshix = 1.0L;
 101             }
 102
 103           if (fabsl (sinhix) > fabsl (cosrx) * ldbl_eps)
 104             den = cosrx * cosrx + sinhix * sinhix;
 105           else
 106             den = cosrx * cosrx;
 107           __real__ res = sinrx * (cosrx / den);
 108           __imag__ res = sinhix * (coshix / den);
 109         }
 110
 111       /* __gcc_qmul does not respect -0.0 so we need the following fixup.  */
 112       if ((__real__ res == 0.0L) && (__real__ x == 0.0L))
 113         __real__ res = __real__ x;
 114
 115       if ((__real__ res == 0.0L) && (__imag__ x == 0.0L))
 116         __imag__ res = __imag__ x;
 117     }
 118
 119   return res;
 120 }
 121 long_double_symbol (libm, __ctanl, ctanl);