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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 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) {
const (
PI4A = 7.85398125648498535156e-1 // 0x3fe921fb40000000, Pi/4 split into three parts
PI4B = 3.77489470793079817668e-8 // 0x3e64442d00000000,
PI4C = 2.69515142907905952645e-15 // 0x3ce8469898cc5170,
)
// 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
}
var j uint64
var y, z float64
if x >= reduceThreshold {
j, z = trigReduce(x)
} else {
j = uint64(x * (4 / Pi)) // 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++
y++
}
j &= 7 // octant modulo 2Pi radians (360 degrees)
z = ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic
}
if j > 3 { // reflect in x axis
j -= 4
sinSign, cosSign = !sinSign, !cosSign
}
if j > 1 {
cosSign = !cosSign
}
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
}