# Source file src/math/asinh.go

```     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  // ====================================================
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
```

View as plain text