sincos.mx raw

   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  //
  13  //	Sincos(±0) = ±0, 1
  14  //	Sincos(±Inf) = NaN, NaN
  15  //	Sincos(NaN) = NaN, NaN
  16  func Sincos(x float64) (sin, cos float64) {
  17  	const (
  18  		PI4A = 7.85398125648498535156e-1  // 0x3fe921fb40000000, Pi/4 split into three parts
  19  		PI4B = 3.77489470793079817668e-8  // 0x3e64442d00000000,
  20  		PI4C = 2.69515142907905952645e-15 // 0x3ce8469898cc5170,
  21  	)
  22  	// special cases
  23  	switch {
  24  	case x == 0:
  25  		return x, 1 // return ±0.0, 1.0
  26  	case IsNaN(x) || IsInf(x, 0):
  27  		return NaN(), NaN()
  28  	}
  29  
  30  	// make argument positive
  31  	sinSign, cosSign := false, false
  32  	if x < 0 {
  33  		x = -x
  34  		sinSign = true
  35  	}
  36  
  37  	var j uint64
  38  	var y, z float64
  39  	if x >= reduceThreshold {
  40  		j, z = trigReduce(x)
  41  	} else {
  42  		j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
  43  		y = float64(j)           // integer part of x/(Pi/4), as float
  44  
  45  		if j&1 == 1 { // map zeros to origin
  46  			j++
  47  			y++
  48  		}
  49  		j &= 7                               // octant modulo 2Pi radians (360 degrees)
  50  		z = ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic
  51  	}
  52  	if j > 3 { // reflect in x axis
  53  		j -= 4
  54  		sinSign, cosSign = !sinSign, !cosSign
  55  	}
  56  	if j > 1 {
  57  		cosSign = !cosSign
  58  	}
  59  
  60  	zz := z * z
  61  	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])
  62  	sin = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5])
  63  	if j == 1 || j == 2 {
  64  		sin, cos = cos, sin
  65  	}
  66  	if cosSign {
  67  		cos = -cos
  68  	}
  69  	if sinSign {
  70  		sin = -sin
  71  	}
  72  	return
  73  }
  74