.

go.mod

@@ -1,6 +1,6 @@
 module github.com/lorenzotinfena/goji
 
-go 1.20
+go 1.21
 
 require (
 	github.com/stretchr/testify v1.8.4

math/fft.go

@@ -0,0 +1,71 @@
+package math
+
+import (
+	"math"
+)
+
+func FastFourierTransform(p []complex128, inverse bool) []complex128 {
+	n := len(p)
+	if n == 1 {
+		return p
+	}
+	p0 := make([]complex128, n/2)
+	p1 := make([]complex128, n/2)
+
+	for i := 0; i < n/2; i++ {
+		p0[i] = p[2*i]
+		p1[i] = p[2*i+1]
+	}
+
+	y0 := FastFourierTransform(p0, inverse)
+	y1 := FastFourierTransform(p1, inverse)
+
+	y := make([]complex128, n)
+
+	w := complex(1, 0)
+	var angle float64
+	if inverse {
+		angle = -(2 * math.Pi) / float64(n)
+	} else {
+		angle = (2 * math.Pi) / float64(n)
+	}
+	w1 := complex(math.Cos(angle), math.Sin(angle))
+	for i := 0; i < n/2; i++ {
+		y[i] = y0[i] + w*y1[i]
+		y[i+n/2] = y0[i] - w*y1[i]
+
+		if inverse {
+			y[i] /= 2
+			y[i+n/2] /= 2
+		}
+		w *= w1
+	}
+	return y
+}
+
+func MultiplyPolynomials(p1, p2 []int) []int {
+	n := 1
+	for n < len(p1)+len(p2) {
+		n *= 2
+	}
+	p1c := make([]complex128, n)
+	p2c := make([]complex128, n)
+	for i := 0; i < len(p1); i++ {
+		p1c[i] = complex(float64(p1[i]), 0)
+	}
+	for i := 0; i < len(p2); i++ {
+		p2c[i] = complex(float64(p2[i]), 0)
+	}
+	y1 := FastFourierTransform(p1c, false)
+	y2 := FastFourierTransform(p2c, false)
+	y := make([]complex128, n)
+	for i := 0; i < n; i++ {
+		y[i] = y1[i] * y2[i]
+	}
+	pc := FastFourierTransform(y, true)
+	p := make([]int, n)
+	for i := 0; i < n; i++ {
+		p[i] = int(math.Round(real(pc[i])))
+	}
+	return p
+}

math/fft_test.go

@@ -0,0 +1,42 @@
+package math_test
+
+import (
+	"testing"
+
+	"github.com/lorenzotinfena/goji/math"
+	"github.com/stretchr/testify/assert"
+)
+
+func Test1MultiplyPolynomials(t *testing.T) {
+	p1 := []int{1, 2}
+	p2 := []int{1, 2}
+	n := 1
+	for n < len(p1)+len(p2) {
+		n *= 2
+	}
+	res := make([]int, n)
+
+	for i := 0; i < len(p1); i++ {
+		for j := 0; j < len(p2); j++ {
+			res[i+j] += p1[i] * p2[j]
+		}
+	}
+	assert.Equal(t, math.MultiplyPolynomials(p1, p2), res)
+}
+
+func Test2MultiplyPolynomials(t *testing.T) {
+	p1 := []int{1, 2, -3, 2, 5, -2}
+	p2 := []int{8, 2, 2, 5, -2, 1, 3, -3, 7}
+	n := 1
+	for n < len(p1)+len(p2) {
+		n *= 2
+	}
+	res := make([]int, n)
+
+	for i := 0; i < len(p1); i++ {
+		for j := 0; j < len(p2); j++ {
+			res[i+j] += p1[i] * p2[j]
+		}
+	}
+	assert.Equal(t, math.MultiplyPolynomials(p1, p2), res)
+}