/****************************************************************************
 *
 * $Source: /usr/local/cvsroot/gccsdk/unixlib/source/math/acosh.c,v $
 * $Date: 2002/12/22 18:22:28 $
 * $Revision: 1.3 $
 * $State: Exp $
 * $Author: admin $
 *
 ***************************************************************************/

/* @(#)e_acosh.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_acosh.c,v 1.9 1995/05/12 04:57:18 jtc Exp $";
#endif

/* __ieee754_acosh(x)
 * Method :
 *      Based on
 *              acosh(x) = log [ x + sqrt(x*x-1) ]
 *      we have
 *              acosh(x) := log(x)+ln2, if x is large; else
 *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
 *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
 *
 * Special cases:
 *      acosh(x) is NaN with signal if x<1.
 *      acosh(NaN) is NaN without signal.
 */

#include <math.h>
#include <unixlib/math.h>
#include <unixlib/types.h>

static const double
  one = 1.0, ln2 = 6.93147180559945286227e-01;	/* 0x3FE62E42, 0xFEFA39EF */

double
acosh (double x)
{
  double t;
  __int32_t hx;
  __uint32_t lx;

  EXTRACT_WORDS (hx, lx, x);
  if (hx < 0x3ff00000)
    {				/* x < 1 */
      return (x - x) / (x - x);
    }
  else if (hx >= 0x41b00000)
    {				/* x > 2**28 */
      if (hx >= 0x7ff00000)
	{			/* x is inf of NaN */
	  return x + x;
	}
      else
	return log (x) + ln2;	/* acosh(huge)=log(2x) */
    }
  else if (((hx - 0x3ff00000) | lx) == 0)
    {
      return 0.0;		/* acosh(1) = 0 */
    }
  else if (hx > 0x40000000)
    {				/* 2**28 > x > 2 */
      t = x * x;
      return log (2.0 * x - one / (x + sqrt (t - one)));
    }
  else
    {				/* 1<x<2 */
      t = x - one;
      return log1p (t + sqrt (2.0 * t + t * t));
    }
}
