relibc_openlibm/ld80/s_asinhl.c

/* @(#)s_asinh.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.
 * ====================================================
 */

/* asinhl(x)
 * Method :
 *	Based on
 *		asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
 *	we have
 *	asinhl(x) := x  if  1+x*x=1,
 *		  := signl(x)*(logl(x)+ln2)) for large |x|, else
 *		  := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
 *		  := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
 */

#include <openlibm_math.h>

#include "math_private.h"

static const long double
one =  1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */
ln2 =  6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
huge=  1.000000000000000000e+4900L;

long double
asinhl(long double x)
{
	long double t,w;
	int32_t hx,ix;
	GET_LDOUBLE_EXP(hx,x);
	ix = hx&0x7fff;
	if(ix==0x7fff) return x+x;	/* x is inf or NaN */
	if(ix< 0x3fde) {	/* |x|<2**-34 */
	    if(huge+x>one) return x;	/* return x inexact except 0 */
	}
	if(ix>0x4020) {		/* |x| > 2**34 */
	    w = logl(fabsl(x))+ln2;
	} else if (ix>0x4000) {	/* 2**34 > |x| > 2.0 */
	    t = fabsl(x);
	    w = logl(2.0*t+one/(sqrtl(x*x+one)+t));
	} else {		/* 2.0 > |x| > 2**-28 */
	    t = x*x;
	    w =log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
	}
	if(hx&0x8000) return -w; else return w;
}