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//
43//	Atanh(1) = +Inf
44//	Atanh(±0) = ±0
45//	Atanh(-1) = -Inf
46//	Atanh(x) = NaN if x < -1 or x > 1
47//	Atanh(NaN) = NaN
48func Atanh(x float64) float64 {
49	if haveArchAtanh {
50		return archAtanh(x)
51	}
52	return atanh(x)
53}
54
55func atanh(x float64) float64 {
56	const NearZero = 1.0 / (1 << 28) // 2**-28
57	// special cases
58	switch {
59	case x < -1 || x > 1 || IsNaN(x):
60		return NaN()
61	case x == 1:
62		return Inf(1)
63	case x == -1:
64		return Inf(-1)
65	}
66	sign := false
67	if x < 0 {
68		x = -x
69		sign = true
70	}
71	var temp float64
72	switch {
73	case x < NearZero:
74		temp = x
75	case x < 0.5:
76		temp = x + x
77		temp = 0.5 * Log1p(temp+temp*x/(1-x))
78	default:
79		temp = 0.5 * Log1p((x+x)/(1-x))
80	}
81	if sign {
82		temp = -temp
83	}
84	return temp
85}
86