glibc/math/k_casinh.c

/* Return arc hyperbole sine for double value, with the imaginary part
   of the result possibly adjusted for use in computing other
   functions.
   Copyright (C) 1997-2013 Free Software Foundation, Inc.
   This file is part of the GNU C Library.

   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 <math.h>
#include <math_private.h>
#include <float.h>

/* Return the complex inverse hyperbolic sine of finite nonzero Z,
   with the imaginary part of the result subtracted from pi/2 if ADJ
   is nonzero.  */

__complex__ double
__kernel_casinh (__complex__ double x, int adj)
{
  __complex__ double res;
  double rx, ix;
  __complex__ double y;

  /* Avoid cancellation by reducing to the first quadrant.  */
  rx = fabs (__real__ x);
  ix = fabs (__imag__ x);

  if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_EPSILON)
    {
      /* For large x in the first quadrant, x + csqrt (1 + x * x)
	 is sufficiently close to 2 * x to make no significant
	 difference to the result; avoid possible overflow from
	 the squaring and addition.  */
      __real__ y = rx;
      __imag__ y = ix;

      if (adj)
	{
	  double t = __real__ y;
	  __real__ y = __copysign (__imag__ y, __imag__ x);
	  __imag__ y = t;
	}

      res = __clog (y);
      __real__ res += M_LN2;
    }
  else if (rx >= 0.5 && ix < DBL_EPSILON / 8.0)
    {
      double s = __ieee754_hypot (1.0, rx);

      __real__ res = __ieee754_log (rx + s);
      if (adj)
	__imag__ res = __ieee754_atan2 (s, __imag__ x);
      else
	__imag__ res = __ieee754_atan2 (ix, s);
    }
  else if (rx < DBL_EPSILON / 8.0 && ix >= 1.5)
    {
      double s = __ieee754_sqrt ((ix + 1.0) * (ix - 1.0));

      __real__ res = __ieee754_log (ix + s);
      if (adj)
	__imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
      else
	__imag__ res = __ieee754_atan2 (s, rx);
    }
  else
    {
      __real__ y = (rx - ix) * (rx + ix) + 1.0;
      __imag__ y = 2.0 * rx * ix;

      y = __csqrt (y);

      __real__ y += rx;
      __imag__ y += ix;

      if (adj)
	{
	  double t = __real__ y;
	  __real__ y = copysign (__imag__ y, __imag__ x);
	  __imag__ y = t;
	}

      res = __clog (y);
    }

  /* Give results the correct sign for the original argument.  */
  __real__ res = __copysign (__real__ res, __real__ x);
  __imag__ res = __copysign (__imag__ res, (adj ? 1.0 : __imag__ x));

  return res;
}