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 }