Blame |
Last modification |
View Log
| RSS feed
/* @(#)e_acosh.c 5.1 93/09/24 */
/*
* ====================================================
* 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.
* ====================================================
*/
#ifndef lint
static char rcsid
[] = "$\Id: e_acosh.c,v 1.2 1995/05/30 05:47:53 rgrimes Exp $";
#endif
/* __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"
#ifdef __STDC__
static const double
#else
static double
#endif
one
= 1.0,
ln2
= 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
#ifdef __STDC__
double __ieee754_acosh
(double x
)
#else
double __ieee754_acosh
(x
)
double x
;
#endif
{
double t
;
int32_t hx
;
u_int32_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
;
} else
return __ieee754_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 __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
));
}
}