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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.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $";
#endif
/* 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 <math.h>
#include <math_private.h>
#include <math_ldbl_opt.h>
static const long double
one = 1.00000000000000000000e+00L, /* 0x3ff0000000000000, 0 */
ln2 = 0.6931471805599453094172321214581766L, /* 0x3fe62e42fefa39ef, 0x3c7abc9e3b398040 */
huge= 1.00000000000000000000e+300L;
long double __asinhl(long double x)
{
long double t,w;
int64_t hx,ix;
double xhi;
xhi = ldbl_high (x);
EXTRACT_WORDS64 (hx, xhi);
ix = hx&0x7fffffffffffffffLL;
if(ix>=0x7ff0000000000000LL) return x+x; /* x is inf or NaN */
if(ix< 0x3c70000000000000LL) { /* |x|<2**-56 */
if(huge+x>one) return x; /* return x inexact except 0 */
}
if(ix>0x4370000000000000LL) { /* |x| > 2**56 */
w = __ieee754_logl(fabsl(x))+ln2;
} else if (ix>0x4000000000000000LL) { /* 2**56 >= |x| > 2.0 */
t = fabs(x);
w = __ieee754_logl(2.0*t+one/(__ieee754_sqrtl(x*x+one)+t));
} else { /* 2.0 >= |x| >= 2**-56 */
t = x*x;
w =__log1pl(fabsl(x)+t/(one+__ieee754_sqrtl(one+t)));
}
if(hx>0) return w; else return -w;
}
long_double_symbol (libm, __asinhl, asinhl);
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