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/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_acoshl.c */
/*
* ====================================================
* 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.
* ====================================================
*/
/* 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 "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double acoshl(long double x)
{
return acosh(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
static const long double
one = 1.0,
ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
long double 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 or NaN */
return x+x;
return logl(x) + ln2; /* acoshl(huge) = logl(2x) */
} else if (((se-0x3fff)|i0|i1) == 0) {
return 0.0; /* acosh(1) = 0 */
} else if (se > 0x4000) { /* x > 2 */
t = x*x;
return logl(2.0*x - one/(x + sqrtl(t - one)));
}
/* 1 < x <= 2 */
t = x - one;
return log1pl(t + sqrtl(2.0*t + t*t));
}
#endif
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