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#include <libm-alias-finite.h>
30
31static const double
32one = 1.0,
33ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
34
35double
36__ieee754_acosh (double x)
37{
38 int64_t hx;
39 EXTRACT_WORDS64 (hx, x);
40
41 if (hx > INT64_C (0x4000000000000000))
42 {
43 if (__glibc_unlikely (hx >= INT64_C (0x41b0000000000000)))
44 {
45 /* x > 2**28 */
46 if (hx >= INT64_C (0x7ff0000000000000))
47 /* x is inf of NaN */
48 return x + x;
49 else
50 return __ieee754_log (x) + ln2;/* acosh(huge)=log(2x) */
51 }
52
53 /* 2**28 > x > 2 */
54 double t = x * x;
55 return __ieee754_log (2.0 * x - one / (x + sqrt (t - one)));
56 }
57 else if (__glibc_likely (hx > INT64_C (0x3ff0000000000000)))
58 {
59 /* 1<x<2 */
60 double t = x - one;
61 return __log1p (t + sqrt (2.0 * t + t * t));
62 }
63 else if (__glibc_likely (hx == INT64_C (0x3ff0000000000000)))
64 return 0.0; /* acosh(1) = 0 */
65 else /* x < 1 */
66 return (x - x) / (x - x);
67}
68libm_alias_finite (__ieee754_acosh, __acosh)
69