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/* @(#)e_acosh.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.
* ====================================================
*/
/* __ieee754_acosh(x)
* Method :
* Based on
* acosh(x) = log [ x + sqrt(x*x-1) ]
* we have
* acosh(x) := log(x)+ln2, if x is large; else
* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
*
* Special cases:
* acosh(x) is NaN with signal if x<1.
* acosh(NaN) is NaN without signal.
*/
#include <math.h>
#include <math_private.h>
#include <libm-alias-finite.h>
static const long double
one = 1.0L,
ln2 = M_LN2l;
long double
__ieee754_acoshl(long double x)
{
long double t;
int64_t hx;
uint64_t lx;
double xhi, xlo;
ldbl_unpack (x, &xhi, &xlo);
EXTRACT_WORDS64 (hx, xhi);
EXTRACT_WORDS64 (lx, xlo);
if(hx<0x3ff0000000000000LL) { /* x < 1 */
return (x-x)/(x-x);
} else if(hx >=0x4370000000000000LL) { /* x >= 2**56 */
if(hx >=0x7ff0000000000000LL) { /* x is inf of NaN */
return x+x;
} else
return __ieee754_logl(x)+ln2; /* acosh(huge)=log(2x) */
} else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) {
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x4000000000000000LL) { /* 2**56 > x > 2 */
t=x*x;
return __ieee754_logl(2.0*x-one/(x+sqrtl(t-one)));
} else { /* 1<x<2 */
t = x-one;
return __log1pl(t+sqrtl(2.0*t+t*t));
}
}
libm_alias_finite (__ieee754_acoshl, __acoshl)
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