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/* Optimized for 64-bit by Ulrich Drepper <drepper@gmail.com>, 2012 */
/*
* ====================================================
* 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 double
one = 1.0,
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
double
__ieee754_acosh (double x)
{
int64_t hx;
EXTRACT_WORDS64 (hx, x);
if (hx > INT64_C (0x4000000000000000))
{
if (__glibc_unlikely (hx >= INT64_C (0x41b0000000000000)))
{
/* x > 2**28 */
if (hx >= INT64_C (0x7ff0000000000000))
/* x is inf of NaN */
return x + x;
else
return __ieee754_log (x) + ln2;/* acosh(huge)=log(2x) */
}
/* 2**28 > x > 2 */
double t = x * x;
return __ieee754_log (2.0 * x - one / (x + sqrt (t - one)));
}
else if (__glibc_likely (hx > INT64_C (0x3ff0000000000000)))
{
/* 1<x<2 */
double t = x - one;
return __log1p (t + sqrt (2.0 * t + t * t));
}
else if (__glibc_likely (hx == INT64_C (0x3ff0000000000000)))
return 0.0; /* acosh(1) = 0 */
else /* x < 1 */
return (x - x) / (x - x);
}
libm_alias_finite (__ieee754_acosh, __acosh)
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