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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_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(x) calculates 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 {

        const (

                Ln2   = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF

                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

}