// Copyright 2010 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package math
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// Coefficients _sin[] and _cos[] are found in pkg/math/sin.go.
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// Sincos returns Sin(x), Cos(x).
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//
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// Special cases are:
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// Sincos(±0) = ±0, 1
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// Sincos(±Inf) = NaN, NaN
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// Sincos(NaN) = NaN, NaN
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func Sincos(x float64) (sin, cos float64) {
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const (
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PI4A = 7.85398125648498535156E-1 // 0x3fe921fb40000000, Pi/4 split into three parts
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PI4B = 3.77489470793079817668E-8 // 0x3e64442d00000000,
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PI4C = 2.69515142907905952645E-15 // 0x3ce8469898cc5170,
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)
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// special cases
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switch {
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case x == 0:
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return x, 1 // return ±0.0, 1.0
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case IsNaN(x) || IsInf(x, 0):
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return NaN(), NaN()
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}
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// make argument positive
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sinSign, cosSign := false, false
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if x < 0 {
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x = -x
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sinSign = true
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}
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var j uint64
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var y, z float64
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if x >= reduceThreshold {
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j, z = trigReduce(x)
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} else {
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j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
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y = float64(j) // integer part of x/(Pi/4), as float
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if j&1 == 1 { // map zeros to origin
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j++
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y++
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}
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j &= 7 // octant modulo 2Pi radians (360 degrees)
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z = ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic
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}
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if j > 3 { // reflect in x axis
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j -= 4
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sinSign, cosSign = !sinSign, !cosSign
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}
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if j > 1 {
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cosSign = !cosSign
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}
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zz := z * z
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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])
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sin = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5])
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if j == 1 || j == 2 {
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sin, cos = cos, sin
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}
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if cosSign {
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cos = -cos
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}
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if sinSign {
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sin = -sin
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}
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return
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}
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