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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/e_atanh.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_atanh(x)

// Method :

//      1. Reduce x to positive by atanh(-x) = -atanh(x)

//      2. For x>=0.5

//                  1              2x                          x

//      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)

//                  2             1 - x                      1 - x

//

//      For x<0.5

//      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))

//

// Special cases:

//      atanh(x) is NaN if |x| > 1 with signal;

//      atanh(NaN) is that NaN with no signal;

//      atanh(+-1) is +-INF with signal.

//

// Atanh(x) calculates the inverse hyperbolic tangent of x.

//

// Special cases are:

//      Atanh(1) = +Inf

//      Atanh(±0) = ±0

//      Atanh(-1) = -Inf

//      Atanh(x) = NaN if x < -1 or x > 1

//      Atanh(NaN) = NaN

func Atanh(x float64) float64 {

        const NearZero = 1.0 / (1 << 28) // 2**-28

        // special cases

        switch {

        case x < -1 || x > 1 || IsNaN(x):

                return NaN()

        case x == 1:

                return Inf(1)

        case x == -1:

                return Inf(-1)

        }

        sign := false

        if x < 0 {

                x = -x

                sign = true

        }

        var temp float64

        switch {

        case x < NearZero:

                temp = x

        case x < 0.5:

                temp = x + x

                temp = 0.5 * Log1p(temp+temp*x/(1-x))

        default:

                temp = 0.5 * Log1p((x+x)/(1-x))

        }

        if sign {

                temp = -temp

        }

        return temp

}