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4.2 KiB

package kzg
import (
"bytes"
"crypto/rand"
"math/big"
"testing"
"github.com/stretchr/testify/assert"
)
func randBI() *big.Int {
maxbits := 256
b := make([]byte, (maxbits/8)-1)
_, err := rand.Read(b)
if err != nil {
panic(err)
}
r := new(big.Int).SetBytes(b)
return new(big.Int).Mod(r, Q)
}
func neg(a *big.Int) *big.Int {
return new(big.Int).Neg(a)
}
func TestPolynomial(t *testing.T) {
b0 := big.NewInt(int64(0))
b1 := big.NewInt(int64(1))
b2 := big.NewInt(int64(2))
b3 := big.NewInt(int64(3))
b4 := big.NewInt(int64(4))
b5 := big.NewInt(int64(5))
b6 := big.NewInt(int64(6))
b16 := big.NewInt(int64(16))
a := []*big.Int{b1, b0, b5}
b := []*big.Int{b3, b0, b1}
// new Finite Field
r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10) //nolint:lll
assert.True(nil, ok)
// polynomial multiplication
o := polynomialMul(a, b)
assert.Equal(t, o, []*big.Int{b3, b0, b16, b0, b5})
// polynomial division
quo, rem := polynomialDiv(a, b)
assert.Equal(t, quo[0].Int64(), int64(5))
// check the rem result without modulo
assert.Equal(t, new(big.Int).Sub(rem[0], r).Int64(), int64(-14))
c := []*big.Int{neg(b4), b0, neg(b2), b1}
d := []*big.Int{neg(b3), b1}
quo2, rem2 := polynomialDiv(c, d)
assert.Equal(t, quo2, []*big.Int{b3, b1, b1})
assert.Equal(t, rem2[0].Int64(), int64(5))
// polynomial addition
o = polynomialAdd(a, b)
assert.Equal(t, o, []*big.Int{b4, b0, b6})
// polynomial subtraction
o1 := polynomialSub(a, b)
o2 := polynomialSub(b, a)
o = polynomialAdd(o1, o2)
assert.True(t, bytes.Equal(b0.Bytes(), o[0].Bytes()))
assert.True(t, bytes.Equal(b0.Bytes(), o[1].Bytes()))
assert.True(t, bytes.Equal(b0.Bytes(), o[2].Bytes()))
c = []*big.Int{b5, b6, b1}
d = []*big.Int{b1, b3}
o = polynomialSub(c, d)
assert.Equal(t, o, []*big.Int{b4, b3, b1})
// NewPolZeroAt
o = newPolZeroAt(3, 4, b4)
assert.Equal(t, polynomialEval(o, big.NewInt(3)), b4)
o = newPolZeroAt(2, 4, b3)
assert.Equal(t, polynomialEval(o, big.NewInt(2)), b3)
// polynomialEval
// p(x) = x^3 + x + 5
p := []*big.Int{
big.NewInt(5),
big.NewInt(1), // x^1
big.NewInt(0), // x^2
big.NewInt(1), // x^3
}
assert.Equal(t, "x³ + x¹ + 5", PolynomialToString(p))
assert.Equal(t, "35", polynomialEval(p, big.NewInt(3)).String())
assert.Equal(t, "1015", polynomialEval(p, big.NewInt(10)).String())
assert.Equal(t, "16777477", polynomialEval(p, big.NewInt(256)).String())
assert.Equal(t, "125055", polynomialEval(p, big.NewInt(50)).String())
assert.Equal(t, "7", polynomialEval(p, big.NewInt(1)).String())
}
func BenchmarkArithmetic(b *testing.B) {
// generate arrays with bigint
var p, q []*big.Int
for i := 0; i < 1000; i++ {
pi := randBI()
p = append(p, pi)
}
for i := 1000 - 1; i >= 0; i-- {
q = append(q, p[i])
}
b.Run("polynomialSub", func(b *testing.B) {
for i := 0; i < b.N; i++ {
polynomialSub(p, q)
}
})
b.Run("polynomialMul", func(b *testing.B) {
for i := 0; i < b.N; i++ {
polynomialMul(p, q)
}
})
b.Run("polynomialDiv", func(b *testing.B) {
for i := 0; i < b.N; i++ {
polynomialDiv(p, q)
}
})
}
func TestLagrangeInterpolation(t *testing.T) {
x0 := big.NewInt(3)
y0 := big.NewInt(35)
x1 := big.NewInt(10)
y1 := big.NewInt(1015)
x2 := big.NewInt(256)
y2 := big.NewInt(16777477)
x3 := big.NewInt(50)
y3 := big.NewInt(125055)
xs := []*big.Int{x0, x1, x2, x3}
ys := []*big.Int{y0, y1, y2, y3}
p, err := LagrangeInterpolation(xs, ys)
assert.Nil(t, err)
assert.Equal(t, "x³ + x¹ + 5", PolynomialToString(p))
assert.Equal(t, y0, polynomialEval(p, x0))
assert.Equal(t, y1, polynomialEval(p, x1))
assert.Equal(t, y2, polynomialEval(p, x2))
}
func TestZeroPolynomial(t *testing.T) {
x0 := big.NewInt(1)
x1 := big.NewInt(40)
x2 := big.NewInt(512)
xs := []*big.Int{x0, x1, x2}
z := zeroPolynomial(xs)
assert.Equal(t, "x³ "+
"+ 21888242871839275222246405745257275088548364400416034343698204186575808495064x² "+
"+ 21032x¹ + 21888242871839275222246405745257275088548364400416034343698204186575808475137",
PolynomialToString(z))
assert.Equal(t, "0", polynomialEval(z, x0).String())
assert.Equal(t, "0", polynomialEval(z, x1).String())
assert.Equal(t, "0", polynomialEval(z, x2).String())
}