/* Complex hyperbolic tangent for float types.

   Copyright (C) 1997-2018 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 <math-underflow.h>

#include <float.h>

CFLOAT

M_DECL_FUNC (__ctanh) (CFLOAT x)

{

  CFLOAT res;

  if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))

    {

      if (isinf (__real__ x))

	{

	  __real__ res = M_COPYSIGN (1, __real__ x);

	  if (isfinite (__imag__ x) && M_FABS (__imag__ x) > 1)

	    {

	      FLOAT sinix, cosix;

	      M_SINCOS (__imag__ x, &sinix, &cosix);

	      __imag__ res = M_COPYSIGN (0, sinix * cosix);

	    }

	  else

	    __imag__ res = M_COPYSIGN (0, __imag__ x);

	}

      else if (__imag__ x == 0)

	{

	  res = x;

	}

      else

	{

	  if (__real__ x == 0)

	    __real__ res = __real__ x;

	  else

	    __real__ res = M_NAN;

	  __imag__ res = M_NAN;

	  if (isinf (__imag__ x))

	    feraiseexcept (FE_INVALID);

	}

    }

  else

    {

      FLOAT sinix, cosix;

      FLOAT den;

      const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2);

      /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))

	 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */

      if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))

	{

	  M_SINCOS (__imag__ x, &sinix, &cosix);

	}

      else

	{

	  sinix = __imag__ x;

	  cosix = 1;

	}

      if (M_FABS (__real__ x) > t)

	{

	  /* Avoid intermediate overflow when the imaginary part of

	     the result may be subnormal.  Ignoring negligible terms,

	     the real part is +/- 1, the imaginary part is

	     sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */

	  FLOAT exp_2t = M_EXP (2 * t);

	  __real__ res = M_COPYSIGN (1, __real__ x);

	  __imag__ res = 4 * sinix * cosix;

	  __real__ x = M_FABS (__real__ x);

	  __real__ x -= t;

	  __imag__ res /= exp_2t;

	  if (__real__ x > t)

	    {

	      /* Underflow (original real part of x has absolute value

		 > 2t).  */

	      __imag__ res /= exp_2t;

	    }

	  else

	    __imag__ res /= M_EXP (2 * __real__ x);

	}

      else

	{

	  FLOAT sinhrx, coshrx;

	  if (M_FABS (__real__ x) > M_MIN)

	    {

	      sinhrx = M_SINH (__real__ x);

	      coshrx = M_COSH (__real__ x);

	    }

	  else

	    {

	      sinhrx = __real__ x;

	      coshrx = 1;

	    }

	  if (M_FABS (sinhrx) > M_FABS (cosix) * M_EPSILON)

	    den = sinhrx * sinhrx + cosix * cosix;

	  else

	    den = cosix * cosix;

	  __real__ res = sinhrx * coshrx / den;

	  __imag__ res = sinix * cosix / den;

	}

      math_check_force_underflow_complex (res);

    }

  return res;

}

declare_mgen_alias (__ctanh, ctanh)