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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
}