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/e_acosh.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 // __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 //
40 // Acosh(+Inf) = +Inf
41 // Acosh(x) = NaN if x < 1
42 // Acosh(NaN) = NaN
43 func Acosh(x float64) float64 {
44 if haveArchAcosh {
45 return archAcosh(x)
46 }
47 return acosh(x)
48 }
49 50 func acosh(x float64) float64 {
51 const Large = 1 << 28 // 2**28
52 // first case is special case
53 switch {
54 case x < 1 || IsNaN(x):
55 return NaN()
56 case x == 1:
57 return 0
58 case x >= Large:
59 return Log(x) + Ln2 // x > 2**28
60 case x > 2:
61 return Log(2*x - 1/(x+Sqrt(x*x-1))) // 2**28 > x > 2
62 }
63 t := x - 1
64 return Log1p(t + Sqrt(2*t+t*t)) // 2 >= x > 1
65 }
66