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 // Copyright 2010 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package math // Coefficients _sin[] and _cos[] are found in pkg/math/sin.go. // Sincos returns Sin(x), Cos(x). // // Special cases are: // // Sincos(±0) = ±0, 1 // Sincos(±Inf) = NaN, NaN // Sincos(NaN) = NaN, NaN func Sincos(x float64) (sin, cos float64) { const ( PI4A = 7.85398125648498535156e-1 // 0x3fe921fb40000000, Pi/4 split into three parts PI4B = 3.77489470793079817668e-8 // 0x3e64442d00000000, PI4C = 2.69515142907905952645e-15 // 0x3ce8469898cc5170, ) // special cases switch { case x == 0: return x, 1 // return ±0.0, 1.0 case IsNaN(x) || IsInf(x, 0): return NaN(), NaN() } // make argument positive sinSign, cosSign := false, false if x < 0 { x = -x sinSign = true } var j uint64 var y, z float64 if x >= reduceThreshold { j, z = trigReduce(x) } else { j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle y = float64(j) // integer part of x/(Pi/4), as float if j&1 == 1 { // map zeros to origin j++ y++ } j &= 7 // octant modulo 2Pi radians (360 degrees) z = ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic } if j > 3 { // reflect in x axis j -= 4 sinSign, cosSign = !sinSign, !cosSign } if j > 1 { cosSign = !cosSign } zz := z * z 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]) sin = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5]) if j == 1 || j == 2 { sin, cos = cos, sin } if cosSign { cos = -cos } if sinSign { sin = -sin } return }