1 /* @(#)e_acosh.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
12 * $NetBSD: e_acosh.c,v 1.12 2002/05/26 22:01:48 wiz Exp $
13 * $DragonFly: src/lib/libm/src/e_acosh.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
20 * acosh(x) = log [ x + sqrt(x*x-1) ]
22 * acosh(x) := log(x)+ln2, if x is large; else
23 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
24 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
27 * acosh(x) is NaN with signal if x<1.
28 * acosh(NaN) is NaN without signal.
32 #include "math_private.h"
36 ln2
= 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
44 EXTRACT_WORDS(hx
,lx
,x
);
45 if(hx
<0x3ff00000) { /* x < 1 */
47 } else if(hx
>=0x41b00000) { /* x > 2**28 */
48 if(hx
>=0x7ff00000) { /* x is inf of NaN */
51 return log(x
)+ln2
; /* acosh(huge)=log(2x) */
52 } else if(((hx
-0x3ff00000)|lx
)==0) {
53 return 0.0; /* acosh(1) = 0 */
54 } else if (hx
> 0x40000000) { /* 2**28 > x > 2 */
56 return log(2.0*x
-one
/(x
+sqrt(t
-one
)));
59 return log1p(t
+sqrt(2.0*t
+t
*t
));