text: /* Complex tangent function for double.
     Copyright (C) 1997-2012 Free Software Foundation, Inc.
     This file is part of the GNU C Library.
     Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
  
     The GNU C Library is free software; you can redistribute it and/or
     modify it under the terms of the GNU Lesser General Public
     License as published by the Free Software Foundation; either
     version 2.1 of the License, or (at your option) any later version.
  
     The GNU C Library is distributed in the hope that it will be useful,
     but WITHOUT ANY WARRANTY; without even the implied warranty of
     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
     Lesser General Public License for more details.
  
     You should have received a copy of the GNU Lesser General Public
     License along with the GNU C Library; if not, see
     <http://www.gnu.org/licenses/>.  */
  
  #include <complex.h>
  #include <fenv.h>
  #include <math.h>
  #include <math_private.h>
  #include <float.h>
  
  __complex__ double
  __ctan (__complex__ double x)
  {
    __complex__ double res;
  
    if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0))
      {
        if (__isinf_ns (__imag__ x))
  	{
  	  __real__ res = __copysign (0.0, __real__ x);
  	  __imag__ res = __copysign (1.0, __imag__ x);
  	}
        else if (__real__ x == 0.0)
  	{
  	  res = x;
  	}
        else
  	{
  	  __real__ res = __nan ("");
  	  __imag__ res = __nan ("");
  
  	  if (__isinf_ns (__real__ x))
  	    feraiseexcept (FE_INVALID);
  	}
      }
    else
      {
        double sinrx, cosrx;
        double den;
        const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
  
        /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
  	 = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
  
        __sincos (__real__ x, &sinrx, &cosrx);
  
        if (fabs (__imag__ x) > t)
  	{
  	  /* Avoid intermediate overflow when the real part of the
  	     result may be subnormal.  Ignoring negligible terms, the
  	     imaginary part is +/- 1, the real part is
  	     sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
  	  double exp_2t = __ieee754_exp (2 * t);
  
  	  __imag__ res = __copysign (1.0, __imag__ x);
  	  __real__ res = 4 * sinrx * cosrx;
  	  __imag__ x = fabs (__imag__ x);
  	  __imag__ x -= t;
  	  __real__ res /= exp_2t;
  	  if (__imag__ x > t)
  	    {
  	      /* Underflow (original imaginary part of x has absolute
  		 value > 2t).  */
  	      __real__ res /= exp_2t;
  	    }
  	  else
  	    __real__ res /= __ieee754_exp (2 * __imag__ x);
  	}
        else
  	{
  	  double sinhix = __ieee754_sinh (__imag__ x);
  	  double coshix = __ieee754_cosh (__imag__ x);
  
  	  den = cosrx * cosrx + sinhix * sinhix;
  	  __real__ res = sinrx * cosrx / den;
  	  __imag__ res = sinhix * coshix / den;
  	}
      }
  
    return res;
  }
  weak_alias (__ctan, ctan)
  #ifdef NO_LONG_DOUBLE
  strong_alias (__ctan, __ctanl)
  weak_alias (__ctan, ctanl)
  #endif
  