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_atanh.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_atanh(x)
23// Method :
24//	1. Reduce x to positive by atanh(-x) = -atanh(x)
25//	2. For x>=0.5
26//	            1              2x                          x
27//	atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
28//	            2             1 - x                      1 - x
29//
30//	For x<0.5
31//	atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
32//
33// Special cases:
34//	atanh(x) is NaN if |x| > 1 with signal;
35//	atanh(NaN) is that NaN with no signal;
36//	atanh(+-1) is +-INF with signal.
37//
38
39// Atanh returns the inverse hyperbolic tangent of x.
40//
41// Special cases are:
42//	Atanh(1) = +Inf
43//	Atanh(±0) = ±0
44//	Atanh(-1) = -Inf
45//	Atanh(x) = NaN if x < -1 or x > 1
46//	Atanh(NaN) = NaN
47func Atanh(x float64) float64 {
48	const NearZero = 1.0 / (1 << 28) // 2**-28
49	// special cases
50	switch {
51	case x < -1 || x > 1 || IsNaN(x):
52		return NaN()
53	case x == 1:
54		return Inf(1)
55	case x == -1:
56		return Inf(-1)
57	}
58	sign := false
59	if x < 0 {
60		x = -x
61		sign = true
62	}
63	var temp float64
64	switch {
65	case x < NearZero:
66		temp = x
67	case x < 0.5:
68		temp = x + x
69		temp = 0.5 * Log1p(temp+temp*x/(1-x))
70	default:
71		temp = 0.5 * Log1p((x+x)/(1-x))
72	}
73	if sign {
74		temp = -temp
75	}
76	return temp
77}
78