/* @(#)s_asinh.c 1.3 95/01/18 */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunSoft, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice 

 * is preserved.

 * ====================================================

 */

/* asinh(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)*(log(x)+ln2)) for large |x|, else

 *		 := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else

 *		 := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))  

 */

#include "fdlibm.h"

#ifdef __STDC__

static const double 

#else

static double 

#endif

one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */

ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */

huge=  1.00000000000000000000e+300; 

#ifdef __STDC__

	double asinh(double x)

#else

	double asinh(x)

	double x;

#endif

{	

	double t,w;

	int hx,ix;

	hx = __HI(x);

	ix = hx&0x7fffffff;

	if(ix>=0x7ff00000) return x+x;	/* x is inf or NaN */

	if(ix< 0x3e300000) {	/* |x|<2**-28 */

	    if(huge+x>one) return x;	/* return x inexact except 0 */

	} 

	if(ix>0x41b00000) {	/* |x| > 2**28 */

	    w = __ieee754_log(fabs(x))+ln2;

	} else if (ix>0x40000000) {	/* 2**28 > |x| > 2.0 */

	    t = fabs(x);

	    w = __ieee754_log(2.0*t+one/(sqrt(x*x+one)+t));

	} else {		/* 2.0 > |x| > 2**-28 */

	    t = x*x;

	    w =log1p(fabs(x)+t/(one+sqrt(one+t)));

	}

	if(hx>0) return w; else return -w;

}