ref: d4f4b292ca9c8665ef938036340ff32bf5128755
dir: /libmath/fdlibm/e_acosh.c/
/* derived from /netlib/fdlibm */
/* @(#)e_acosh.c 1.3 95/01/18 */
/*
* ====================================================
* 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.
* ====================================================
*
*/
/* __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 "fdlibm.h"
static const double
one = 1.0,
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
double __ieee754_acosh(double x)
{
double t;
int hx;
hx = __HI(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;
} else
return __ieee754_log(x)+ln2; /* acosh(Huge)=log(2x) */
} else if(((hx-0x3ff00000)|__LO(x))==0) {
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
t=x*x;
return __ieee754_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));
}
}