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/s_asinh.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 // asinh(x)
23 // Method :
24 // Based on
25 // asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
26 // we have
27 // asinh(x) := x if 1+x*x=1,
28 // := sign(x)*(log(x)+ln2) for large |x|, else
29 // := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
30 // := sign(x)*log1p(|x| + x**2/(1 + sqrt(1+x**2)))
31 //
32 33 // Asinh returns the inverse hyperbolic sine of x.
34 //
35 // Special cases are:
36 //
37 // Asinh(±0) = ±0
38 // Asinh(±Inf) = ±Inf
39 // Asinh(NaN) = NaN
40 func Asinh(x float64) float64 {
41 if haveArchAsinh {
42 return archAsinh(x)
43 }
44 return asinh(x)
45 }
46 47 func asinh(x float64) float64 {
48 const (
49 Ln2 = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
50 NearZero = 1.0 / (1 << 28) // 2**-28
51 Large = 1 << 28 // 2**28
52 )
53 // special cases
54 if IsNaN(x) || IsInf(x, 0) {
55 return x
56 }
57 sign := false
58 if x < 0 {
59 x = -x
60 sign = true
61 }
62 var temp float64
63 switch {
64 case x > Large:
65 temp = Log(x) + Ln2 // |x| > 2**28
66 case x > 2:
67 temp = Log(2*x + 1/(Sqrt(x*x+1)+x)) // 2**28 > |x| > 2.0
68 case x < NearZero:
69 temp = x // |x| < 2**-28
70 default:
71 temp = Log1p(x + x*x/(1+Sqrt(1+x*x))) // 2.0 > |x| > 2**-28
72 }
73 if sign {
74 temp = -temp
75 }
76 return temp
77 }
78