sincos.go

Documentation: math

		 1  // Copyright 2010 The Go Authors. All rights reserved.
		 2  // Use of this source code is governed by a BSD-style
		 3  // license that can be found in the LICENSE file.
		 4  
		 5  package math
		 6  
		 7  // Coefficients _sin[] and _cos[] are found in pkg/math/sin.go.
		 8  
		 9  // Sincos returns Sin(x), Cos(x).
		10  //
		11  // Special cases are:
		12  //	Sincos(±0) = ±0, 1
		13  //	Sincos(±Inf) = NaN, NaN
		14  //	Sincos(NaN) = NaN, NaN
		15  func Sincos(x float64) (sin, cos float64) {
		16  	const (
		17  		PI4A = 7.85398125648498535156e-1	// 0x3fe921fb40000000, Pi/4 split into three parts
		18  		PI4B = 3.77489470793079817668e-8	// 0x3e64442d00000000,
		19  		PI4C = 2.69515142907905952645e-15 // 0x3ce8469898cc5170,
		20  	)
		21  	// special cases
		22  	switch {
		23  	case x == 0:
		24  		return x, 1 // return ±0.0, 1.0
		25  	case IsNaN(x) || IsInf(x, 0):
		26  		return NaN(), NaN()
		27  	}
		28  
		29  	// make argument positive
		30  	sinSign, cosSign := false, false
		31  	if x < 0 {
		32  		x = -x
		33  		sinSign = true
		34  	}
		35  
		36  	var j uint64
		37  	var y, z float64
		38  	if x >= reduceThreshold {
		39  		j, z = trigReduce(x)
		40  	} else {
		41  		j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
		42  		y = float64(j)					 // integer part of x/(Pi/4), as float
		43  
		44  		if j&1 == 1 { // map zeros to origin
		45  			j++
		46  			y++
		47  		}
		48  		j &= 7															 // octant modulo 2Pi radians (360 degrees)
		49  		z = ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic
		50  	}
		51  	if j > 3 { // reflect in x axis
		52  		j -= 4
		53  		sinSign, cosSign = !sinSign, !cosSign
		54  	}
		55  	if j > 1 {
		56  		cosSign = !cosSign
		57  	}
		58  
		59  	zz := z * z
		60  	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])
		61  	sin = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5])
		62  	if j == 1 || j == 2 {
		63  		sin, cos = cos, sin
		64  	}
		65  	if cosSign {
		66  		cos = -cos
		67  	}
		68  	if sinSign {
		69  		sin = -sin
		70  	}
		71  	return
		72  }
		73
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