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  // +build !386
     6  
     7  package math
     8  
     9  // Coefficients _sin[] and _cos[] are found in pkg/math/sin.go.
    10  
    11  // Sincos returns Sin(x), Cos(x).
    12  //
    13  // Special cases are:
    14  //	Sincos(±0) = ±0, 1
    15  //	Sincos(±Inf) = NaN, NaN
    16  //	Sincos(NaN) = NaN, NaN
    17  func Sincos(x float64) (sin, cos float64) {
    18  	const (
    19  		PI4A = 7.85398125648498535156E-1                             // 0x3fe921fb40000000, Pi/4 split into three parts
    20  		PI4B = 3.77489470793079817668E-8                             // 0x3e64442d00000000,
    21  		PI4C = 2.69515142907905952645E-15                            // 0x3ce8469898cc5170,
    22  		M4PI = 1.273239544735162542821171882678754627704620361328125 // 4/pi
    23  	)
    24  	// special cases
    25  	switch {
    26  	case x == 0:
    27  		return x, 1 // return ±0.0, 1.0
    28  	case IsNaN(x) || IsInf(x, 0):
    29  		return NaN(), NaN()
    30  	}
    31  
    32  	// make argument positive
    33  	sinSign, cosSign := false, false
    34  	if x < 0 {
    35  		x = -x
    36  		sinSign = true
    37  	}
    38  
    39  	j := int64(x * M4PI) // integer part of x/(Pi/4), as integer for tests on the phase angle
    40  	y := float64(j)      // integer part of x/(Pi/4), as float
    41  
    42  	if j&1 == 1 { // map zeros to origin
    43  		j++
    44  		y++
    45  	}
    46  	j &= 7     // octant modulo 2Pi radians (360 degrees)
    47  	if j > 3 { // reflect in x axis
    48  		j -= 4
    49  		sinSign, cosSign = !sinSign, !cosSign
    50  	}
    51  	if j > 1 {
    52  		cosSign = !cosSign
    53  	}
    54  
    55  	z := ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic
    56  	zz := z * z
    57  	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])
    58  	sin = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5])
    59  	if j == 1 || j == 2 {
    60  		sin, cos = cos, sin
    61  	}
    62  	if cosSign {
    63  		cos = -cos
    64  	}
    65  	if sinSign {
    66  		sin = -sin
    67  	}
    68  	return
    69  }
    70
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