libquadmath/math/cacoshq.c

/* Return arc hyperbole cosine for __float128 value.
   Copyright (C) 1997, 1998, 2006 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, write to the Free
   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
   02111-1307 USA.  */

#include "quadmath-imp.h"


__complex128
cacoshq (__complex128 x)
{
  __complex128 res;
  int rcls = fpclassifyq (__real__ x);
  int icls = fpclassifyq (__imag__ x);

  if (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE)
    {
      if (icls == QUADFP_INFINITE)
	{
	  __real__ res = HUGE_VALQ;

	  if (rcls == QUADFP_NAN)
	    __imag__ res = nanq ("");
	  else
	    __imag__ res = copysignq ((rcls == QUADFP_INFINITE
				       ? (__real__ x < 0.0
					  ? M_PIq - M_PI_4q : M_PI_4q)
				       : M_PI_2q), __imag__ x);
	}
      else if (rcls == QUADFP_INFINITE)
	{
	  __real__ res = HUGE_VALQ;

	  if (icls >= QUADFP_ZERO)
	    __imag__ res = copysignq (signbitq (__real__ x) ? M_PIq : 0.0,
				      __imag__ x);
	  else
	    __imag__ res = nanq ("");
	}
      else
	{
	  __real__ res = nanq ("");
	  __imag__ res = nanq ("");
	}
    }
  else if (rcls == QUADFP_ZERO && icls == QUADFP_ZERO)
    {
      __real__ res = 0.0;
      __imag__ res = copysignq (M_PI_2q, __imag__ x);
    }
  /* The factor 16 is just a guess.  */
  else if (16.0Q * fabsq (__imag__ x) < fabsq (__real__ x))
    {
      /* Kahan's formula which avoid cancellation through subtraction in
	 some cases.  */
      res = 2.0Q * clogq (csqrtq ((x + 1.0Q) / 2.0Q)
			    + csqrtq ((x - 1.0Q) / 2.0Q));
      if (signbitq (__real__ res))
	__real__ res = 0.0Q;
    }
  else
    {
      __complex128 y;

      __real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0;
      __imag__ y = 2.0 * __real__ x * __imag__ x;

      y = csqrtq (y);

      if (signbitq (x))
	y = -y;

      __real__ y += __real__ x;
      __imag__ y += __imag__ x;

      res = clogq (y);
    }

  return res;
}