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// Copyright 2009 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

/*

        Floating-point hyperbolic sine and cosine.

        The exponential func is called for arguments

        greater in magnitude than 0.5.

        A series is used for arguments smaller in magnitude than 0.5.

        Cosh(x) is computed from the exponential func for

        all arguments.

*/

// Sinh returns the hyperbolic sine of x.

//

// Special cases are:

//      Sinh(±0) = ±0

//      Sinh(±Inf) = ±Inf

//      Sinh(NaN) = NaN

func Sinh(x float64) float64 {

        // The coefficients are #2029 from Hart & Cheney. (20.36D)

        const (

                P0 = -0.6307673640497716991184787251e+6

                P1 = -0.8991272022039509355398013511e+5

                P2 = -0.2894211355989563807284660366e+4

                P3 = -0.2630563213397497062819489e+2

                Q0 = -0.6307673640497716991212077277e+6

                Q1 = 0.1521517378790019070696485176e+5

                Q2 = -0.173678953558233699533450911e+3

        )

        sign := false

        if x < 0 {

                x = -x

                sign = true

        }

        var temp float64

        switch true {

        case x > 21:

                temp = Exp(x) / 2

        case x > 0.5:

                temp = (Exp(x) - Exp(-x)) / 2

        default:

                sq := x * x

                temp = (((P3*sq+P2)*sq+P1)*sq + P0) * x

                temp = temp / (((sq+Q2)*sq+Q1)*sq + Q0)

        }

        if sign {

                temp = -temp

        }

        return temp

}

// Cosh returns the hyperbolic cosine of x.

//

// Special cases are:

//      Cosh(±0) = 1

//      Cosh(±Inf) = +Inf

//      Cosh(NaN) = NaN

func Cosh(x float64) float64 {

        if x < 0 {

                x = -x

        }

        if x > 21 {

                return Exp(x) / 2

        }

        return (Exp(x) + Exp(-x)) / 2

}