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2/* @(#)e_acosh.c 1.3 95/01/18 */
3/* \$FreeBSD: head/lib/msun/src/e_acosh.c 251599 2013-06-10 06:04:58Z das \$ */
4/*
5 * ====================================================
7 *
8 * Developed at SunSoft, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 *
14 */
15
16/* __ieee754_acosh(x)
17 * Method :
18 * Based on
19 * acosh(x) = log [ x + sqrt(x*x-1) ]
20 * we have
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.
24 *
25 * Special cases:
26 * acosh(x) is NaN with signal if x<1.
27 * acosh(NaN) is NaN without signal.
28 */
29
30#include <float.h>
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}
63
64#if LDBL_MANT_DIG == 53
65__weak_reference(acosh, acoshl);
66#endif