github.com/consensys/gnark-crypto@v0.14.0/internal/generator/tower/template/fq12over6over2/tests/fq2.go.tmpl

{{$Name := .Curve.Name}}

import (
	"testing"
	"crypto/rand"

	"github.com/consensys/gnark-crypto/ecc/{{toLower $Name}}/fp"
	"github.com/leanovate/gopter"
	"github.com/leanovate/gopter/prop"
)

// ------------------------------------------------------------
// tests

const (
	nbFuzzShort = 10
	nbFuzz = 50
)

func TestE2ReceiverIsOperand(t *testing.T) {

	t.Parallel()
	parameters := gopter.DefaultTestParameters()
	if testing.Short() {
		parameters.MinSuccessfulTests = nbFuzzShort
	} else {
		parameters.MinSuccessfulTests = nbFuzz
	}

	properties := gopter.NewProperties(parameters)

	genA := GenE2()
	genB := GenE2()
	genfp := GenFp()

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (addition) should output the same result", prop.ForAll(
		func(a, b *E2) bool {
			var c, d E2
			d.Set(a)
			c.Add(a, b)
			a.Add(a, b)
			b.Add(&d, b)
			return a.Equal(b) && a.Equal(&c) && b.Equal(&c)
		},
		genA,
		genB,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (sub) should output the same result", prop.ForAll(
		func(a, b *E2) bool {
			var c, d E2
			d.Set(a)
			c.Sub(a, b)
			a.Sub(a, b)
			b.Sub(&d, b)
			return a.Equal(b) && a.Equal(&c) && b.Equal(&c)
		},
		genA,
		genB,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (mul) should output the same result", prop.ForAll(
		func(a, b *E2) bool {
			var c, d E2
			d.Set(a)
			c.Mul(a, b)
			a.Mul(a, b)
			b.Mul(&d, b)
			return a.Equal(b) && a.Equal(&c) && b.Equal(&c)
		},
		genA,
		genB,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (square) should output the same result", prop.ForAll(
		func(a *E2) bool {
			var b E2
			b.Square(a)
			a.Square(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (neg) should output the same result", prop.ForAll(
		func(a *E2) bool {
			var b E2
			b.Neg(a)
			a.Neg(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (double) should output the same result", prop.ForAll(
		func(a *E2) bool {
			var b E2
			b.Double(a)
			a.Double(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (mul by non residue) should output the same result", prop.ForAll(
		func(a *E2) bool {
			var b E2
			b.MulByNonResidue(a)
			a.MulByNonResidue(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (mul by non residue inverse) should output the same result", prop.ForAll(
		func(a *E2) bool {
			var b E2
			b.MulByNonResidueInv(a)
			a.MulByNonResidueInv(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (Inverse) should output the same result", prop.ForAll(
		func(a *E2) bool {
			var b E2
			b.Inverse(a)
			a.Inverse(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (Conjugate) should output the same result", prop.ForAll(
		func(a *E2) bool {
			var b E2
			b.Conjugate(a)
			a.Conjugate(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (mul by element) should output the same result", prop.ForAll(
		func(a *E2, b fp.Element) bool {
			var c E2
			c.MulByElement(a, &b)
			a.MulByElement(a, &b)
			return a.Equal(&c)
		},
		genA,
		genfp,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (Sqrt) should output the same result", prop.ForAll(
		func(a *E2) bool {
			var b, c, d, s E2

			s.Square(a)
			a.Set(&s)
			b.Set(&s)

			a.Sqrt(a)
			b.Sqrt(&b)

			c.Square(a)
			d.Square(&b)
			return c.Equal(&d)
		},
		genA,
	))

	properties.TestingRun(t, gopter.ConsoleReporter(false))


}

func TestE2MulMaxed(t *testing.T) {
	// let's pick a and b, with maxed A0 and A1
	var a,b E2
	fpMaxValue := fp.Element{
		{{- range $i := .Curve.Fp.NbWordsIndexesFull}}
		{{index $.Curve.Fp.Q $i}},{{end}}
	}
	fpMaxValue[0]--

	a.A0 = fpMaxValue
	a.A1 = fpMaxValue
	b.A0 = fpMaxValue
	b.A1 = fpMaxValue



	var c, d E2
	d.Inverse(&b)
	c.Set(&a)
	c.Mul(&c, &b).Mul(&c, &d)
	if !c.Equal(&a) {
		t.Fatal("mul with max fp failed")
	}
}

func TestE2Ops(t *testing.T) {

	t.Parallel()
	parameters := gopter.DefaultTestParameters()
	if testing.Short() {
		parameters.MinSuccessfulTests = nbFuzzShort
	} else {
		parameters.MinSuccessfulTests = nbFuzz
	}

	properties := gopter.NewProperties(parameters)

	genA := GenE2()
	genB := GenE2()
	genfp := GenFp()

	properties.Property("[{{ toUpper $Name }}] sub & add should leave an element invariant", prop.ForAll(
		func(a, b *E2) bool {
			var c E2
			c.Set(a)
			c.Add(&c, b).Sub(&c, b)
			return c.Equal(a)
		},
		genA,
		genB,
	))

	properties.Property("[{{ toUpper $Name }}] mul & inverse should leave an element invariant", prop.ForAll(
		func(a, b *E2) bool {
			var c, d E2
			d.Inverse(b)
			c.Set(a)
			c.Mul(&c, b).Mul(&c, &d)
			return c.Equal(a)
		},
		genA,
		genB,
	))

	properties.Property("[{{ toUpper $Name }}] BatchInvertE2 should output the same result as Inverse", prop.ForAll(
		func(a, b, c *E2) bool {

			batch := BatchInvertE2([]E2{*a, *b, *c})
			a.Inverse(a)
			b.Inverse(b)
			c.Inverse(c)
			return a.Equal(&batch[0]) && b.Equal(&batch[1]) && c.Equal(&batch[2])
		},
		genA,
		genA,
		genA,
	))

	{{if or (eq $Name "bn254") (eq $Name "bls12-381")}}

	properties.Property("[{{ toUpper $Name }}] mulGeneric & mul should be equal", prop.ForAll(
		func(a, b *E2) bool {
			var c, d E2
			mulGenericE2(&c, a, b)
			d.Mul(a, b)
			return d.Equal(&c)
		},
		genA,
		genB,
	))

	{{ end }}

	properties.Property("[{{ toUpper $Name }}] inverse twice should leave an element invariant", prop.ForAll(
		func(a *E2) bool {
			var b E2
			b.Inverse(a).Inverse(&b)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] neg twice should leave an element invariant", prop.ForAll(
		func(a *E2) bool {
			var b E2
			b.Neg(a).Neg(&b)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] square and mul should output the same result", prop.ForAll(
		func(a *E2) bool {
			var b, c E2
			b.Mul(a, a)
			c.Square(a)
			return b.Equal(&c)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] MulByElement MulByElement inverse should leave an element invariant", prop.ForAll(
		func(a *E2, b fp.Element) bool {
			var c E2
			var d fp.Element
			d.Inverse(&b)
			c.MulByElement(a, &b).MulByElement(&c, &d)
			return c.Equal(a)
		},
		genA,
		genfp,
	))

	properties.Property("[{{ toUpper $Name }}] Double and mul by 2 should output the same result", prop.ForAll(
		func(a *E2) bool {
			var b E2
			var c fp.Element
			c.SetUint64(2)
			b.Double(a)
			a.MulByElement(a, &c)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] Mulbynonres mulbynonresinv should leave the element invariant", prop.ForAll(
		func(a *E2) bool {
			var b E2
			b.MulByNonResidue(a).MulByNonResidueInv(&b)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] a + pi(a), a-pi(a) should be real", prop.ForAll(
		func(a *E2) bool {
			var b, c, d E2
			var e, f fp.Element
			b.Conjugate(a)
			c.Add(a, &b)
			d.Sub(a, &b)
			e.Double(&a.A0)
			f.Double(&a.A1)
			return c.A1.IsZero() && d.A0.IsZero() && e.Equal(&c.A0) && f.Equal(&d.A1)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] Legendre on square should output 1", prop.ForAll(
		func(a *E2) bool {
			var b E2
			b.Square(a)
			c := b.Legendre()
			return c == 1
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] square(sqrt) should leave an element invariant", prop.ForAll(
		func(a *E2) bool {
			var b, c, d, e E2
			b.Square(a)
			c.Sqrt(&b)
			d.Square(&c)
			e.Neg(a)
			return (c.Equal(a) || c.Equal(&e)) && d.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] neg(E2) == neg(E2.A0, E2.A1)", prop.ForAll(
		func(a *E2) bool {
			var b, c E2
			b.Neg(a)
			c.A0.Neg(&a.A0)
			c.A1.Neg(&a.A1)
			return c.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] Cmp and LexicographicallyLargest should be consistent", prop.ForAll(
		func(a *E2) bool {
			var negA E2
			negA.Neg(a)
			cmpResult := a.Cmp(&negA)
			lResult := a.LexicographicallyLargest()
			if lResult && cmpResult == 1 {
				return true
			}
			if !lResult && cmpResult !=1 {
				return true
			}
			return false
		},
		genA,
	))

	properties.TestingRun(t, gopter.ConsoleReporter(false))

}

// ------------------------------------------------------------
// benches

func BenchmarkE2Add(b *testing.B) {
	var a, c E2
_,_=	a.SetRandom()
_,_=	c.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Add(&a, &c)
	}
}

func BenchmarkE2Sub(b *testing.B) {
	var a, c E2
_,_=	a.SetRandom()
_,_=	c.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Sub(&a, &c)
	}
}

func BenchmarkE2Mul(b *testing.B) {
	var a, c E2
_,_=	a.SetRandom()
_,_=	c.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Mul(&a, &c)
	}
}

func BenchmarkE2MulByElement(b *testing.B) {
	var a E2
	var c fp.Element
_,_=	c.SetRandom()
_,_=	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.MulByElement(&a, &c)
	}
}

func BenchmarkE2Square(b *testing.B) {
	var a E2
_,_=	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Square(&a)
	}
}

func BenchmarkE2Sqrt(b *testing.B) {
	var a E2
_,_=	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Sqrt(&a)
	}
}

func BenchmarkE2Exp(b *testing.B) {
	var x E2
_,_=	x.SetRandom()
	b1, _ := rand.Int(rand.Reader, fp.Modulus())
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		x.Exp(x, b1)
	}
}



func BenchmarkE2Inverse(b *testing.B) {
	var a E2
_,_=	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Inverse(&a)
	}
}

func BenchmarkE2MulNonRes(b *testing.B) {
	var a E2
_,_=	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.MulByNonResidue(&a)
	}
}

func BenchmarkE2MulNonResInv(b *testing.B) {
	var a E2
_,_=	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.MulByNonResidueInv(&a)
	}
}

func BenchmarkE2Conjugate(b *testing.B) {
	var a E2
_,_=	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Conjugate(&a)
	}
}
{{ template "base" .}}