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         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 }