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Source file src/math/sincos.go

Documentation: math

  // 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.
  
  // +build !386
  
  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,
  		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++
  		y++
  	}
  	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
  }
  

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