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

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