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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

        )

        // special cases

        if 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

}