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/* origin: FreeBSD /usr/src/lib/msun/src/e_acosh.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/* 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 "libm.h"
static const double
one = 1.0,
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
double acosh(double x)
{
double t;
int32_t hx;
uint32_t lx;
EXTRACT_WORDS(hx, lx, x);
if (hx < 0x3ff00000) { /* x < 1 */
return (x-x)/(x-x);
} else if (hx >= 0x41b00000) { /* x > 2**28 */
if (hx >= 0x7ff00000) /* x is inf of NaN */
return x+x;
return log(x) + ln2; /* acosh(huge) = log(2x) */
} else if ((hx-0x3ff00000 | lx) == 0) {
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
t = x*x;
return log(2.0*x - one/(x+sqrt(t-one)));
} else { /* 1 < x < 2 */
t = x-one;
return log1p(t + sqrt(2.0*t+t*t));
}
}
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