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// 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/s_asinh.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.
// ====================================================
//
//
// asinh(x)
// Method :
// Based on
// asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
// we have
// asinh(x) := x if 1+x*x=1,
// := sign(x)*(log(x)+ln2)) for large |x|, else
// := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
// := sign(x)*log1p(|x| + x**2/(1 + sqrt(1+x**2)))
//
// Asinh(x) calculates the inverse hyperbolic sine of x.
//
// Special cases are:
// Asinh(±0) = ±0
// Asinh(±Inf) = ±Inf
// Asinh(NaN) = NaN
func Asinh(x float64) float64 {
const (
Ln2 = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
NearZero = 1.0 / (1 << 28) // 2**-28
Large = 1 << 28 // 2**28
)
// TODO(rsc): Remove manual inlining of IsNaN, IsInf
// when compiler does it for us
// special cases
if x != x || x > MaxFloat64 || x < -MaxFloat64 { // IsNaN(x) || IsInf(x, 0)
return x
}
sign := false
if x < 0 {
x = -x
sign = true
}
var temp float64
switch {
case x > Large:
temp = Log(x) + Ln2 // |x| > 2**28
case x > 2:
temp = Log(2*x + 1/(Sqrt(x*x+1)+x)) // 2**28 > |x| > 2.0
case x < NearZero:
temp = x // |x| < 2**-28
default:
temp = Log1p(x + x*x/(1+Sqrt(1+x*x))) // 2.0 > |x| > 2**-28
}
if sign {
temp = -temp
}
return temp
}
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