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b34b60bc
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1/* @(#)e_acosh.c 5.1 93/09/24 */
2/*
3 * ====================================================
5 *
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
9 * is preserved.
10 * ====================================================
11 *
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 \$
14 */
15
16
17/* acosh(x)
18 * Method :
19 * Based on
20 * acosh(x) = log [ x + sqrt(x*x-1) ]
21 * we have
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.
25 *
26 * Special cases:
27 * acosh(x) is NaN with signal if x<1.
28 * acosh(NaN) is NaN without signal.
29 */
30
31#include <math.h>
32#include "math_private.h"
33
34static const double
35one = 1.0,
36ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
37
38double
39acosh(double x)
40{
41 double t;
42 int32_t hx;
43 u_int32_t lx;
44 EXTRACT_WORDS(hx,lx,x);
45 if(hx<0x3ff00000) { /* x < 1 */
46 return (x-x)/(x-x);
47 } else if(hx >=0x41b00000) { /* x > 2**28 */
48 if(hx >=0x7ff00000) { /* x is inf of NaN */
49 return x+x;
50 } else
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 */
55 t=x*x;
56 return log(2.0*x-one/(x+sqrt(t-one)));
57 } else { /* 1<x<2 */
58 t = x-one;
59 return log1p(t+sqrt(2.0*t+t*t));
60 }
61}