libgo/go/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         return sincos(x)
  17 }
  18
  19 func sincos(x float64) (sin, cos float64) {
  20         const (
  21                 PI4A = 7.85398125648498535156E-1                             // 0x3fe921fb40000000, Pi/4 split into three parts
  22                 PI4B = 3.77489470793079817668E-8                             // 0x3e64442d00000000,
  23                 PI4C = 2.69515142907905952645E-15                            // 0x3ce8469898cc5170,
  24                 M4PI = 1.273239544735162542821171882678754627704620361328125 // 4/pi
  25         )
  26         // special cases
  27         switch {
  28         case x == 0:
  29                 return x, 1 // return ±0.0, 1.0
  30         case IsNaN(x) || IsInf(x, 0):
  31                 return NaN(), NaN()
  32         }
  33
  34         // make argument positive
  35         sinSign, cosSign := false, false
  36         if x < 0 {
  37                 x = -x
  38                 sinSign = true
  39         }
  40
  41         j := int64(x * M4PI) // 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 += 1
  46                 y += 1
  47         }
  48         j &= 7     // octant modulo 2Pi radians (360 degrees)
  49         if j > 3 { // reflect in x axis
  50                 j -= 4
  51                 sinSign, cosSign = !sinSign, !cosSign
  52         }
  53         if j > 1 {
  54                 cosSign = !cosSign
  55         }
  56
  57         z := ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic
  58         zz := z * z
  59         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])
  60         sin = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5])
  61         if j == 1 || j == 2 {
  62                 sin, cos = cos, sin
  63         }
  64         if cosSign {
  65                 cos = -cos
  66         }
  67         if sinSign {
  68                 sin = -sin
  69         }
  70         return
  71 }