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 * $FreeBSD: src/lib/msun/src/e_acosh.c,v 1.6 1999/08/28 00:06:28 peter Exp $
13 * $DragonFly: src/lib/msun/src/Attic/e_acosh.c,v 1.2 2003/06/17 04:26:52 dillon Exp $
19 * acosh(x) = log [ x + sqrt(x*x-1) ]
21 * acosh(x) := log(x)+ln2, if x is large; else
22 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
23 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
26 * acosh(x) is NaN with signal if x<1.
27 * acosh(NaN) is NaN without signal.
31 #include "math_private.h"
39 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
42 double __ieee754_acosh(double x)
44 double __ieee754_acosh(x)
51 EXTRACT_WORDS(hx,lx,x);
52 if(hx<0x3ff00000) { /* x < 1 */
54 } else if(hx >=0x41b00000) { /* x > 2**28 */
55 if(hx >=0x7ff00000) { /* x is inf of NaN */
58 return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
59 } else if(((hx-0x3ff00000)|lx)==0) {
60 return 0.0; /* acosh(1) = 0 */
61 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
63 return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
66 return log1p(t+__ieee754_sqrt(2.0*t+t*t));