package gaul

import "math"

const (

LUTSize = 1 << 16

LUTMask = LUTSize - 1

LUTFactor = LUTSize / Tau

)

// TrigLUT is a lookup table for sine and cosine.

// In my tests, it is about 9x faster than math.Sin and math.Cos.

// The margin of error is < 0.005%.

// This LUT is not suitable for tangents, however.

type TrigLUT struct {

sinTable []float64

}

func NewTrigLUT() *TrigLUT {

lut := TrigLUT{}

lut.sinTable = make([]float64, LUTSize)

for i, a := range Linspace(0, Tau, LUTSize, false) {

lut.sinTable[i] = math.Sin(a)

}

return &lut

}

func (lut *TrigLUT) Sin(x float64) float64 {

// pos is the (fractional) table index for x. Flooring rather than

// truncating keeps the index and the interpolation fraction consistent

// for negative x, and masking wraps the index into the table.

pos := x * LUTFactor

base := math.Floor(pos)

i := int(int64(base) & LUTMask)

j := (i + 1) & LUTMask

return Lerp(lut.sinTable[i], lut.sinTable[j], pos-base)

}

func (lut *TrigLUT) Cos(x float64) float64 {

return lut.Sin(x + Tau/4)

}