mirror of
https://github.com/autc04/Retro68.git
synced 2024-11-28 05:51:04 +00:00
61 lines
1.7 KiB
Go
61 lines
1.7 KiB
Go
// Copyright 2010 The Go Authors. All rights reserved.
|
|
// Use of this source code is governed by a BSD-style
|
|
// license that can be found in the LICENSE file.
|
|
|
|
package math
|
|
|
|
// The original C code, the long comment, and the constants
|
|
// below are from FreeBSD's /usr/src/lib/msun/src/e_acosh.c
|
|
// and came with this notice. The go code is a simplified
|
|
// version of the original C.
|
|
//
|
|
// ====================================================
|
|
// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
//
|
|
// Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
// Permission to use, copy, modify, and distribute this
|
|
// software is freely granted, provided that this notice
|
|
// is preserved.
|
|
// ====================================================
|
|
//
|
|
//
|
|
// __ieee754_acosh(x)
|
|
// Method :
|
|
// Based on
|
|
// acosh(x) = log [ x + sqrt(x*x-1) ]
|
|
// we have
|
|
// acosh(x) := log(x)+ln2, if x is large; else
|
|
// acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
|
|
// acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
|
|
//
|
|
// Special cases:
|
|
// acosh(x) is NaN with signal if x<1.
|
|
// acosh(NaN) is NaN without signal.
|
|
//
|
|
|
|
// Acosh returns the inverse hyperbolic cosine of x.
|
|
//
|
|
// Special cases are:
|
|
// Acosh(+Inf) = +Inf
|
|
// Acosh(x) = NaN if x < 1
|
|
// Acosh(NaN) = NaN
|
|
func Acosh(x float64) float64 {
|
|
const (
|
|
Ln2 = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
|
|
Large = 1 << 28 // 2**28
|
|
)
|
|
// first case is special case
|
|
switch {
|
|
case x < 1 || IsNaN(x):
|
|
return NaN()
|
|
case x == 1:
|
|
return 0
|
|
case x >= Large:
|
|
return Log(x) + Ln2 // x > 2**28
|
|
case x > 2:
|
|
return Log(2*x - 1/(x+Sqrt(x*x-1))) // 2**28 > x > 2
|
|
}
|
|
t := x - 1
|
|
return Log1p(t + Sqrt(2*t+t*t)) // 2 >= x > 1
|
|
}
|