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//
37//	Asinh(±0) = ±0
38//	Asinh(±Inf) = ±Inf
39//	Asinh(NaN) = NaN
40func Asinh(x float64) float64 {
41	if haveArchAsinh {
42		return archAsinh(x)
43	}
44	return asinh(x)
45}
46
47func 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