OpenLibm/ld80/s_asinhl.c

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/* @(#)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;
}