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/* e_acoshl.c -- long double version of e_acosh.c.
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* 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_acoshl(x)
* Method :
* Based on
* acoshl(x) = logl [ x + sqrtl(x*x-1) ]
* we have
* acoshl(x) := logl(x)+ln2, if x is large; else
* acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
* acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
*
* Special cases:
* acoshl(x) is NaN with signal if x<1.
* acoshl(NaN) is NaN without signal.
*/
#include <math.h>
#include <math_private.h>
#include <libm-alias-finite.h>
static const _Float128
one = 1.0,
ln2 = L(0.6931471805599453094172321214581766);
_Float128
__ieee754_acoshl(_Float128 x)
{
_Float128 t;
uint64_t lx;
int64_t hx;
GET_LDOUBLE_WORDS64(hx,lx,x);
if(hx<0x3fff000000000000LL) { /* x < 1 */
return (x-x)/(x-x);
} else if(hx >=0x4035000000000000LL) { /* x > 2**54 */
if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */
return x+x;
} else
return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */
} else if(((hx-0x3fff000000000000LL)|lx)==0) {
return 0; /* acosh(1) = 0 */
} else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
t=x*x;
return __ieee754_logl(2*x-one/(x+sqrtl(t-one)));
} else { /* 1<x<2 */
t = x-one;
return __log1pl(t+sqrtl(2*t+t*t));
}
}
libm_alias_finite (__ieee754_acoshl, __acoshl)
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