/*      $NetBSD: n_asinh.c,v 1.7 2008/04/29 15:10:02 uwe Exp $  */
/*
* Copyright (c) 1985, 1993
*      The Regents of the University of California.  All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
*    notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
*    notice, this list of conditions and the following disclaimer in the
*    documentation and/or other materials provided with the distribution.
* 3. Neither the name of the University nor the names of its contributors
*    may be used to endorse or promote products derived from this software
*    without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/

#ifndef lint
#if 0
static char sccsid[] = "@(#)asinh.c     8.1 (Berkeley) 6/4/93";
#endif
#endif /* not lint */

/* ASINH(X)
* RETURN THE INVERSE HYPERBOLIC SINE OF X
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
* CODED IN C BY K.C. NG, 2/16/85;
* REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85.
*
* Required system supported functions :
*      copysign(x,y)
*      sqrt(x)
*
* Required kernel function:
*      log1p(x)                ...return log(1+x)
*
* Method :
*      Based on
*              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
*      we have
*      asinh(x) := x  if  1+x*x=1,
*               := sign(x)*(log1p(x)+ln2))      if sqrt(1+x*x)=x, else
*               := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )
*
* Accuracy:
*      asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
*      In a test run with 52,000 random arguments on a VAX, the maximum
*      observed error was 1.58 ulps (units in the last place).
*
* Constants:
* The hexadecimal values are the intended ones for the following constants.
* The decimal values may be used, provided that the compiler will convert
* from decimal to binary accurately enough to produce the hexadecimal values
* shown.
*/
#define _LIBM_STATIC
#include "mathimpl.h"

vc(ln2hi, 6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)

ic(ln2hi, 6.9314718036912381649E-1,   -1, 1.62E42FEE00000)
ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)

#ifdef vccast
#define    ln2hi    vccast(ln2hi)
#define    ln2lo    vccast(ln2lo)
#endif

double
asinh(double x)
{
       double t,s;
       static const double     small=1.0E-10,  /* fl(1+small*small) == 1 */
                               big  =1.0E20,   /* fl(1+big) == big */
                               one  =1.0   ;

#if !defined(__vax__)&&!defined(tahoe)
       if(x!=x) return(x);     /* x is NaN */
#endif  /* !defined(__vax__)&&!defined(tahoe) */
       if((t=copysign(x,one))>small)
           if(t<big) {
               s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
           else        /* if |x| > big */
               {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));}
       else    /* if |x| < small */
           return(x);
}