mirror of
https://git.planet-casio.com/Lephenixnoir/OpenLibm.git
synced 2024-12-28 20:43:41 +01:00
54 lines
1.5 KiB
C
54 lines
1.5 KiB
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.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;
|
|
}
|