math/s_ctanf.c

   1 /* Complex tangent function for float.
   2    Copyright (C) 1997-2012 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 __complex__ float
  27 __ctanf (__complex__ float x)
  28 {
  29   __complex__ float res;
  30
  31   if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0))
  32     {
  33       if (__isinf_nsf (__imag__ x))
  34         {
  35           __real__ res = __copysignf (0.0, __real__ x);
  36           __imag__ res = __copysignf (1.0, __imag__ x);
  37         }
  38       else if (__real__ x == 0.0)
  39         {
  40           res = x;
  41         }
  42       else
  43         {
  44           __real__ res = __nanf ("");
  45           __imag__ res = __nanf ("");
  46
  47           if (__isinf_nsf (__real__ x))
  48             feraiseexcept (FE_INVALID);
  49         }
  50     }
  51   else
  52     {
  53       float sinrx, cosrx;
  54       float den;
  55       const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2);
  56
  57       /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
  58          = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
  59
  60       __sincosf (__real__ x, &sinrx, &cosrx);
  61
  62       if (fabsf (__imag__ x) > t)
  63         {
  64           /* Avoid intermediate overflow when the real part of the
  65              result may be subnormal.  Ignoring negligible terms, the
  66              imaginary part is +/- 1, the real part is
  67              sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
  68           float exp_2t = __ieee754_expf (2 * t);
  69
  70           __imag__ res = __copysignf (1.0, __imag__ x);
  71           __real__ res = 4 * sinrx * cosrx;
  72           __imag__ x = fabsf (__imag__ x);
  73           __imag__ x -= t;
  74           __real__ res /= exp_2t;
  75           if (__imag__ x > t)
  76             {
  77               /* Underflow (original imaginary part of x has absolute
  78                  value > 2t).  */
  79               __real__ res /= exp_2t;
  80             }
  81           else
  82             __real__ res /= __ieee754_expf (2 * __imag__ x);
  83         }
  84       else
  85         {
  86           float sinhix, coshix;
  87           if (fabsf (__imag__ x) > FLT_MIN)
  88             {
  89               sinhix = __ieee754_sinhf (__imag__ x);
  90               coshix = __ieee754_coshf (__imag__ x);
  91             }
  92           else
  93             {
  94               sinhix = __imag__ x;
  95               coshix = 1.0f;
  96             }
  97
  98           if (fabsf (sinhix) > fabsf (cosrx) * FLT_EPSILON)
  99             den = cosrx * cosrx + sinhix * sinhix;
 100           else
 101             den = cosrx * cosrx;
 102           __real__ res = sinrx * cosrx / den;
 103           __imag__ res = sinhix * coshix / den;
 104         }
 105     }
 106
 107   return res;
 108 }
 109 #ifndef __ctanf
 110 weak_alias (__ctanf, ctanf)
 111 #endif