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.
8 // The original C code, the long comment, and the constants
9 // below are from FreeBSD's /usr/src/lib/msun/src/e_acosh.c
10 // and came with this notice. The go code is a simplified
11 // version of the original C.
13 // ====================================================
14 // Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
16 // Developed at SunPro, a Sun Microsystems, Inc. business.
17 // Permission to use, copy, modify, and distribute this
18 // software is freely granted, provided that this notice
20 // ====================================================
26 // acosh(x) = log [ x + sqrt(x*x-1) ]
28 // acosh(x) := log(x)+ln2, if x is large; else
29 // acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
30 // acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
33 // acosh(x) is NaN with signal if x<1.
34 // acosh(NaN) is NaN without signal.
37 // Acosh(x) calculates the inverse hyperbolic cosine of x.
40 // Acosh(x) = NaN if x < 1
42 func Acosh(x
float64) float64 {
44 Ln2
= 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
45 Large
= 1 << 28 // 2**28
47 // TODO(rsc): Remove manual inlining of IsNaN
48 // when compiler does it for us
49 // first case is special case
51 case x
< 1 || x
!= x
: // x < 1 || IsNaN(x):
56 return Log(x
) + Ln2
// x > 2**28
58 return Log(2*x
- 1/(x
+Sqrt(x
*x
-1))) // 2**28 > x > 2
61 return Log1p(t
+ Sqrt(2*t
+t
*t
)) // 2 >= x > 1