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package r1csqap
import (
"bytes"
"math/big"
"testing"
"github.com/arnaucube/go-snark/fields"
"github.com/stretchr/testify/assert"
)
func TestTranspose(t *testing.T) {
b0 := big.NewInt(int64(0))
b1 := big.NewInt(int64(1))
bFive := big.NewInt(int64(5))
a := [][]*big.Int{
[]*big.Int{b0, b1, b0, b0, b0, b0},
[]*big.Int{b0, b0, b0, b1, b0, b0},
[]*big.Int{b0, b1, b0, b0, b1, b0},
[]*big.Int{bFive, b0, b0, b0, b0, b1},
}
aT := Transpose(a)
assert.Equal(t, aT, [][]*big.Int{
[]*big.Int{b0, b0, b0, bFive},
[]*big.Int{b1, b0, b1, b0},
[]*big.Int{b0, b0, b0, b0},
[]*big.Int{b0, b1, b0, b0},
[]*big.Int{b0, b0, b1, b0},
[]*big.Int{b0, b0, b0, b1},
})
}
func neg(a *big.Int) *big.Int {
return new(big.Int).Neg(a)
}
func TestPol(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)
assert.True(nil, ok)
f := fields.NewFq(r)
// new Polynomial Field
pf := NewPolynomialField(f)
// polynomial multiplication
o := pf.Mul(a, b)
assert.Equal(t, o, []*big.Int{b3, b0, b16, b0, b5})
// polynomial division
quo, rem := pf.Div(a, b)
assert.Equal(t, quo[0].Int64(), int64(5))
assert.Equal(t, new(big.Int).Sub(rem[0], r).Int64(), int64(-14)) // check the rem result without modulo
c := []*big.Int{neg(b4), b0, neg(b2), b1}
d := []*big.Int{neg(b3), b1}
quo2, rem2 := pf.Div(c, d)
assert.Equal(t, quo2, []*big.Int{b3, b1, b1})
assert.Equal(t, rem2[0].Int64(), int64(5))
// polynomial addition
o = pf.Add(a, b)
assert.Equal(t, o, []*big.Int{b4, b0, b6})
// polynomial subtraction
o1 := pf.Sub(a, b)
o2 := pf.Sub(b, a)
o = pf.Add(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 = pf.Sub(c, d)
assert.Equal(t, o, []*big.Int{b4, b3, b1})
// NewPolZeroAt
o = pf.NewPolZeroAt(3, 4, b4)
assert.Equal(t, pf.Eval(o, big.NewInt(3)), b4)
o = pf.NewPolZeroAt(2, 4, b3)
assert.Equal(t, pf.Eval(o, big.NewInt(2)), b3)
}
func TestLagrangeInterpolation(t *testing.T) {
// new Finite Field
r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
assert.True(nil, ok)
f := fields.NewFq(r)
// new Polynomial Field
pf := NewPolynomialField(f)
b0 := big.NewInt(int64(0))
b5 := big.NewInt(int64(5))
a := []*big.Int{b0, b0, b0, b5}
alpha := pf.LagrangeInterpolation(a)
assert.Equal(t, pf.Eval(alpha, big.NewInt(int64(4))), b5)
aux := pf.Eval(alpha, big.NewInt(int64(3))).Int64()
assert.Equal(t, aux, int64(0))
}
func TestR1CSToQAP(t *testing.T) {
// new Finite Field
r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
assert.True(nil, ok)
f := fields.NewFq(r)
// new Polynomial Field
pf := NewPolynomialField(f)
b0 := big.NewInt(int64(0))
b1 := big.NewInt(int64(1))
b3 := big.NewInt(int64(3))
b5 := big.NewInt(int64(5))
b9 := big.NewInt(int64(9))
b27 := big.NewInt(int64(27))
b30 := big.NewInt(int64(30))
b35 := big.NewInt(int64(35))
a := [][]*big.Int{
[]*big.Int{b0, b1, b0, b0, b0, b0},
[]*big.Int{b0, b0, b0, b1, b0, b0},
[]*big.Int{b0, b1, b0, b0, b1, b0},
[]*big.Int{b5, b0, b0, b0, b0, b1},
}
b := [][]*big.Int{
[]*big.Int{b0, b1, b0, b0, b0, b0},
[]*big.Int{b0, b1, b0, b0, b0, b0},
[]*big.Int{b1, b0, b0, b0, b0, b0},
[]*big.Int{b1, b0, b0, b0, b0, b0},
}
c := [][]*big.Int{
[]*big.Int{b0, b0, b0, b1, b0, b0},
[]*big.Int{b0, b0, b0, b0, b1, b0},
[]*big.Int{b0, b0, b0, b0, b0, b1},
[]*big.Int{b0, b0, b1, b0, b0, b0},
}
alphas, betas, gammas, zx := pf.R1CSToQAP(a, b, c)
// fmt.Println(alphas)
// fmt.Println(betas)
// fmt.Println(gammas)
// fmt.Print("Z(x): ")
// fmt.Println(zx)
w := []*big.Int{b1, b3, b35, b9, b27, b30}
ax, bx, cx, px := pf.CombinePolynomials(w, alphas, betas, gammas)
// fmt.Println(ax)
// fmt.Println(bx)
// fmt.Println(cx)
// fmt.Println(px)
hx := pf.DivisorPolynomial(px, zx)
// fmt.Println(hx)
// hx==px/zx so px==hx*zx
assert.Equal(t, px, pf.Mul(hx, zx))
// p(x) = a(x) * b(x) - c(x) == h(x) * z(x)
abc := pf.Sub(pf.Mul(ax, bx), cx)
assert.Equal(t, abc, px)
hz := pf.Mul(hx, zx)
assert.Equal(t, abc, hz)
}