/* @(#)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 <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;
}