1// Copyright 2010 The Go Authors. All rights reserved.
2// Use of this source code is governed by a BSD-style
3// license that can be found in the LICENSE file.
4
5package math
6
7// The original C code, the long comment, and the constants
8// below are from FreeBSD's /usr/src/lib/msun/src/e_acosh.c
9// and came with this notice. The go code is a simplified
10// version of the original C.
11//
12// ====================================================
13// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
14//
15// Developed at SunPro, a Sun Microsystems, Inc. business.
16// Permission to use, copy, modify, and distribute this
17// software is freely granted, provided that this notice
18// is preserved.
19// ====================================================
20//
21//
22// __ieee754_acosh(x)
23// Method :
24//	Based on
25//	        acosh(x) = log [ x + sqrt(x*x-1) ]
26//	we have
27//	        acosh(x) := log(x)+ln2,	if x is large; else
28//	        acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
29//	        acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
30//
31// Special cases:
32//	acosh(x) is NaN with signal if x<1.
33//	acosh(NaN) is NaN without signal.
34//
35
36// Acosh returns the inverse hyperbolic cosine of x.
37//
38// Special cases are:
39//
40//	Acosh(+Inf) = +Inf
41//	Acosh(x) = NaN if x < 1
42//	Acosh(NaN) = NaN
43func Acosh(x float64) float64 {
44	if haveArchAcosh {
45		return archAcosh(x)
46	}
47	return acosh(x)
48}
49
50func acosh(x float64) float64 {
51	const Large = 1 << 28 // 2**28
52	// first case is special case
53	switch {
54	case x < 1 || IsNaN(x):
55		return NaN()
56	case x == 1:
57		return 0
58	case x >= Large:
59		return Log(x) + Ln2 // x > 2**28
60	case x > 2:
61		return Log(2*x - 1/(x+Sqrt(x*x-1))) // 2**28 > x > 2
62	}
63	t := x - 1
64	return Log1p(t + Sqrt(2*t+t*t)) // 2 >= x > 1
65}
66