1/* Optimized for 64-bit by Ulrich Drepper <drepper@gmail.com>, 2012 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
13/* __ieee754_acosh(x)
14 * Method :
15 * Based on
16 * acosh(x) = log [ x + sqrt(x*x-1) ]
17 * we have
18 * acosh(x) := log(x)+ln2, if x is large; else
19 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
20 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
21 *
22 * Special cases:
23 * acosh(x) is NaN with signal if x<1.
24 * acosh(NaN) is NaN without signal.
25 */
26
27#include <math.h>
28#include <math_private.h>
29
30static const double
31one = 1.0,
32ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
33
34double
35__ieee754_acosh (double x)
36{
37 int64_t hx;
38 EXTRACT_WORDS64 (hx, x);
39
40 if (hx > INT64_C (0x4000000000000000))
41 {
42 if (__glibc_unlikely (hx >= INT64_C (0x41b0000000000000)))
43 {
44 /* x > 2**28 */
45 if (hx >= INT64_C (0x7ff0000000000000))
46 /* x is inf of NaN */
47 return x + x;
48 else
49 return __ieee754_log (x) + ln2;/* acosh(huge)=log(2x) */
50 }
51
52 /* 2**28 > x > 2 */
53 double t = x * x;
54 return __ieee754_log (2.0 * x - one / (x + sqrt (t - one)));
55 }
56 else if (__glibc_likely (hx > INT64_C (0x3ff0000000000000)))
57 {
58 /* 1<x<2 */
59 double t = x - one;
60 return __log1p (t + sqrt (2.0 * t + t * t));
61 }
62 else if (__glibc_likely (hx == INT64_C (0x3ff0000000000000)))
63 return 0.0; /* acosh(1) = 0 */
64 else /* x < 1 */
65 return (x - x) / (x - x);
66}
67strong_alias (__ieee754_acosh, __acosh_finite)
68