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 5 package 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
48 func Atanh(x float64) float64 {
49 if haveArchAtanh {
50 return archAtanh(x)
51 }
52 return atanh(x)
53 }
54 55 func 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