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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
}