// Copyright 2010 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package math
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// The original C code, the long comment, and the constants
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// below are from FreeBSD's /usr/src/lib/msun/src/s_asinh.c
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// and came with this notice. The go code is a simplified
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// version of the original C.
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//
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// ====================================================
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// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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//
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// Developed at SunPro, a Sun Microsystems, Inc. business.
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// Permission to use, copy, modify, and distribute this
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// software is freely granted, provided that this notice
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// is preserved.
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// ====================================================
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//
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//
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// asinh(x)
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// Method :
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// Based on
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// asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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// we have
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// asinh(x) := x if 1+x*x=1,
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// := sign(x)*(log(x)+ln2)) for large |x|, else
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// := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
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// := sign(x)*log1p(|x| + x**2/(1 + sqrt(1+x**2)))
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//
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// Asinh returns the inverse hyperbolic sine of x.
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//
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// Special cases are:
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// Asinh(±0) = ±0
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// Asinh(±Inf) = ±Inf
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// Asinh(NaN) = NaN
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func Asinh(x float64) float64
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func asinh(x float64) float64 {
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const (
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Ln2 = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
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NearZero = 1.0 / (1 << 28) // 2**-28
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Large = 1 << 28 // 2**28
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)
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// special cases
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if IsNaN(x) || IsInf(x, 0) {
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return x
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}
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sign := false
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if x < 0 {
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x = -x
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sign = true
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}
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var temp float64
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switch {
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case x > Large:
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temp = Log(x) + Ln2 // |x| > 2**28
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case x > 2:
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temp = Log(2*x + 1/(Sqrt(x*x+1)+x)) // 2**28 > |x| > 2.0
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case x < NearZero:
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temp = x // |x| < 2**-28
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default:
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temp = Log1p(x + x*x/(1+Sqrt(1+x*x))) // 2.0 > |x| > 2**-28
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}
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if sign {
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temp = -temp
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}
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return temp
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}
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