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/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//	Asinh(±0) = ±0
37//	Asinh(±Inf) = ±Inf
38//	Asinh(NaN) = NaN
39func Asinh(x float64) float64 {
40	const (
41		Ln2      = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
42		NearZero = 1.0 / (1 << 28)            // 2**-28
43		Large    = 1 << 28                    // 2**28
44	)
45	// special cases
46	if IsNaN(x) || IsInf(x, 0) {
47		return x
48	}
49	sign := false
50	if x < 0 {
51		x = -x
52		sign = true
53	}
54	var temp float64
55	switch {
56	case x > Large:
57		temp = Log(x) + Ln2 // |x| > 2**28
58	case x > 2:
59		temp = Log(2*x + 1/(Sqrt(x*x+1)+x)) // 2**28 > |x| > 2.0
60	case x < NearZero:
61		temp = x // |x| < 2**-28
62	default:
63		temp = Log1p(x + x*x/(1+Sqrt(1+x*x))) // 2.0 > |x| > 2**-28
64	}
65	if sign {
66		temp = -temp
67	}
68	return temp
69}
70