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
5package 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
16func 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