1
2/* @(#)e_acosh.c 1.3 95/01/18 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 *
13 */
14
15#include <sys/cdefs.h>
16__FBSDID("$FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das $");
17
18/* __ieee754_acosh(x)
19 * Method :
20 * Based on
21 * acosh(x) = log [ x + sqrt(x*x-1) ]
22 * we have
23 * acosh(x) := log(x)+ln2, if x is large; else
24 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
25 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
26 *
27 * Special cases:
28 * acosh(x) is NaN with signal if x<1.
29 * acosh(NaN) is NaN without signal.
30 */
31
32#include "math.h"
33#include "math_private.h"
34
35static const double
36one = 1.0,
37ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
38
39double
40__ieee754_acosh(double x)
41{
42 double t;
43 int32_t hx;
44 u_int32_t lx;
45 EXTRACT_WORDS(hx,lx,x);
46 if(hx<0x3ff00000) { /* x < 1 */
47 return (x-x)/(x-x);
48 } else if(hx >=0x41b00000) { /* x > 2**28 */
49 if(hx >=0x7ff00000) { /* x is inf of NaN */
50 return x+x;
51 } else
52 return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
53 } else if(((hx-0x3ff00000)|lx)==0) {
54 return 0.0; /* acosh(1) = 0 */
55 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
56 t=x*x;
57 return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
58 } else { /* 1<x<2 */
59 t = x-one;
60 return log1p(t+sqrt(2.0*t+t*t));
61 }
62}