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/* e_acoshl.c -- long double version of e_acosh.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, drepper@cygnus.com.
*/
/*
* ====================================================
* 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 long double
one = 1.0,
ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
long double
__ieee754_acoshl(long double x)
{
long double t;
uint32_t se,i0,i1;
GET_LDOUBLE_WORDS(se,i0,i1,x);
if(se<0x3fff || se & 0x8000) { /* x < 1 */
return (x-x)/(x-x);
} else if(se >=0x401d) { /* x > 2**30 */
if(se >=0x7fff) { /* x is inf of NaN */
return x+x;
} else
return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */
} else if(((se-0x3fff)|(i0^0x80000000)|i1)==0) {
return 0.0; /* acosh(1) = 0 */
} else if (se > 0x4000) { /* 2**28 > 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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