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# Source file src/math/acosh.go

## Documentation: math

2  // Use of this source code is governed by a BSD-style
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_acosh.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  // __ieee754_acosh(x)
23  // Method :
24  //	Based on
25  //	        acosh(x) = log [ x + sqrt(x*x-1) ]
26  //	we have
27  //	        acosh(x) := log(x)+ln2,	if x is large; else
28  //	        acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
29  //	        acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
30  //
31  // Special cases:
32  //	acosh(x) is NaN with signal if x<1.
33  //	acosh(NaN) is NaN without signal.
34  //
35
36  // Acosh returns the inverse hyperbolic cosine of x.
37  //
38  // Special cases are:
39  //	Acosh(+Inf) = +Inf
40  //	Acosh(x) = NaN if x < 1
41  //	Acosh(NaN) = NaN
42  func Acosh(x float64) float64
43
44  func acosh(x float64) float64 {
45  	const (
46  		Ln2   = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
47  		Large = 1 << 28                    // 2**28
48  	)
49  	// first case is special case
50  	switch {
51  	case x < 1 || IsNaN(x):
52  		return NaN()
53  	case x == 1:
54  		return 0
55  	case x >= Large:
56  		return Log(x) + Ln2 // x > 2**28
57  	case x > 2:
58  		return Log(2*x - 1/(x+Sqrt(x*x-1))) // 2**28 > x > 2
59  	}
60  	t := x - 1
61  	return Log1p(t + Sqrt(2*t+t*t)) // 2 >= x > 1
62  }
63

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