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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

// Coefficients _sin[] and _cos[] are found in pkg/math/sin.go.

// Sincos(x) returns Sin(x), Cos(x).

//

// Special cases are:

//      Sincos(±0) = ±0, 1

//      Sincos(±Inf) = NaN, NaN

//      Sincos(NaN) = NaN, NaN

func Sincos(x float64) (sin, cos float64) {

        return sincos(x)

}

func sincos(x float64) (sin, cos float64) {

        const (

                PI4A = 7.85398125648498535156E-1                             // 0x3fe921fb40000000, Pi/4 split into three parts

                PI4B = 3.77489470793079817668E-8                             // 0x3e64442d00000000,

                PI4C = 2.69515142907905952645E-15                            // 0x3ce8469898cc5170,

                M4PI = 1.273239544735162542821171882678754627704620361328125 // 4/pi

        )

        // special cases

        switch {

        case x == 0:

                return x, 1 // return ±0.0, 1.0

        case IsNaN(x) || IsInf(x, 0):

                return NaN(), NaN()

        }

        // make argument positive

        sinSign, cosSign := false, false

        if x < 0 {

                x = -x

                sinSign = true

        }

        j := int64(x * M4PI) // integer part of x/(Pi/4), as integer for tests on the phase angle

        y := float64(j)      // integer part of x/(Pi/4), as float

        if j&1 == 1 { // map zeros to origin

                j += 1

                y += 1

        }

        j &= 7     // octant modulo 2Pi radians (360 degrees)

        if j > 3 { // reflect in x axis

                j -= 4

                sinSign, cosSign = !sinSign, !cosSign

        }

        if j > 1 {

                cosSign = !cosSign

        }

        z := ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic

        zz := z * z

        cos = 1.0 - 0.5*zz + zz*zz*((((((_cos[0]*zz)+_cos[1])*zz+_cos[2])*zz+_cos[3])*zz+_cos[4])*zz+_cos[5])

        sin = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5])

        if j == 1 || j == 2 {

                sin, cos = cos, sin

        }

        if cosSign {

                cos = -cos

        }

        if sinSign {

                sin = -sin

        }

        return

}