golang acosh 代码
文件路径：/src/math/acosh.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 {
if haveArchAcosh {
return archAcosh(x)
}
return acosh(x)
}
func acosh(x float64) float64 {
const 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
}