Source file src/pkg/math/sincos.go

     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(x) 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	
    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 += 1
    44			y += 1
    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	}