Prover/feat/Adding field extension support to Smartvectors (#569)

* field extension support for the maths package

prover/maths/common/polyext/gnarkpoly.go

@@ -0,0 +1,48 @@
+package polyext
+
+import (
+	"github.com/consensys/gnark/frontend"
+	"github.com/consensys/linea-monorepo/prover/maths/field"
+	"github.com/consensys/linea-monorepo/prover/maths/field/fext/gnarkfext"
+)
+
+// EvaluateLagrangeAnyDomainGnark mirrors [EvaluateLagrangesAnyDomain] but in
+// a gnark circuit. The same usage precautions applies for it.
+func EvaluateLagrangeAnyDomainGnark(api frontend.API, domain []gnarkfext.Variable, x gnarkfext.Variable) []gnarkfext.Variable {
+
+	outerAPI := gnarkfext.API{Inner: api}
+	lagrange := make([]gnarkfext.Variable, len(domain))
+
+	for i, hi := range domain {
+		lhix := gnarkfext.Variable{field.One(), field.Zero()}
+		for j, hj := range domain {
+			if i == j {
+				// Skip it
+				continue
+			}
+			// more convenient to store -h instead of h
+			factor := outerAPI.Sub(x, hj)
+			den := outerAPI.Sub(hi, hj) // so x - h
+			den = outerAPI.Inverse(den)
+
+			// accumulate the product
+			lhix = outerAPI.Mul(lhix, factor, den)
+		}
+		lagrange[i] = lhix
+	}
+
+	return lagrange
+
+}
+
+// EvaluateUnivariateGnark evaluate a univariate polynomial in a gnark circuit.
+// It mirrors [EvalUnivariate].
+func EvaluateUnivariateGnark(api frontend.API, pol []gnarkfext.Variable, x gnarkfext.Variable) gnarkfext.Variable {
+	res := gnarkfext.Variable{frontend.Variable(0), frontend.Variable(0)}
+	outerAPI := gnarkfext.API{Inner: api}
+	for i := len(pol) - 1; i >= 0; i-- {
+		res = outerAPI.Mul(res, x)
+		res = outerAPI.Add(res, pol[i])
+	}
+	return res
+}

prover/maths/common/polyext/gnarkpoly_test.go

@@ -0,0 +1,99 @@
+package polyext
+
+import (
+	"github.com/consensys/linea-monorepo/prover/maths/common/vectorext"
+	"github.com/consensys/linea-monorepo/prover/maths/field/fext"
+	"github.com/consensys/linea-monorepo/prover/maths/field/fext/gnarkfext"
+	"testing"
+
+	"github.com/consensys/gnark/frontend"
+	"github.com/consensys/linea-monorepo/prover/utils/gnarkutil"
+	"github.com/stretchr/testify/require"
+)
+
+func TestGnarkEval(t *testing.T) {
+
+	t.Run("normal-poly", func(t *testing.T) {
+
+		def := func(api frontend.API) error {
+			outerAPI := gnarkfext.API{Inner: api}
+			var (
+				pol      = vectorext.IntoGnarkAssignment(vectorext.ForTestFromPairs(1, 2, 3, 4, -1, -2))
+				x        = gnarkfext.Variable{2, 1}
+				expected = gnarkfext.Variable{
+					-5*fext.RootPowers[1] + 3,
+					-2*fext.RootPowers[1] + 1,
+				}
+				res = EvaluateUnivariateGnark(api, pol, x)
+			)
+			outerAPI.AssertIsEqual(expected, res)
+			return nil
+		}
+
+		gnarkutil.AssertCircuitSolved(t, def)
+	})
+
+	t.Run("empty-poly", func(t *testing.T) {
+		def := func(api frontend.API) error {
+			outerAPI := gnarkfext.API{Inner: api}
+			var (
+				pol      = vectorext.IntoGnarkAssignment([]fext.Element{})
+				x        = gnarkfext.Variable{2, 3}
+				expected = gnarkfext.NewZero()
+				res      = EvaluateUnivariateGnark(api, pol, x)
+			)
+			outerAPI.AssertIsEqual(expected, res)
+			return nil
+		}
+		gnarkutil.AssertCircuitSolved(t, def)
+	})
+
+}
+
+func TestGnarkEvalAnyDomain(t *testing.T) {
+
+	t.Run("single-variable", func(t *testing.T) {
+
+		def := func(api frontend.API) error {
+			outerAPI := gnarkfext.API{Inner: api}
+			var (
+				domain   = vectorext.IntoGnarkAssignment(vectorext.ForTestFromPairs(0, 0))
+				x        = gnarkfext.Variable{42, 0}
+				expected = vectorext.IntoGnarkAssignment(vectorext.ForTestFromPairs(1, 0))
+				res      = EvaluateLagrangeAnyDomainGnark(api, domain, x)
+			)
+
+			require.Len(t, res, len(expected))
+			for i := range expected {
+				outerAPI.AssertIsEqual(expected[i], res[i])
+			}
+
+			return nil
+		}
+
+		gnarkutil.AssertCircuitSolved(t, def)
+	})
+
+	t.Run("multiple-variable", func(t *testing.T) {
+
+		def := func(api frontend.API) error {
+			outerAPI := gnarkfext.API{Inner: api}
+			var (
+				domain   = vectorext.IntoGnarkAssignment(vectorext.ForTestFromPairs(0, 0, 1, 0))
+				x        = gnarkfext.Variable{42, 0}
+				expected = vectorext.IntoGnarkAssignment(vectorext.ForTestFromPairs(-41, 0, 42, 0))
+				res      = EvaluateLagrangeAnyDomainGnark(api, domain, x)
+			)
+
+			require.Len(t, res, len(expected))
+			for i := range expected {
+				outerAPI.AssertIsEqual(expected[i], res[i])
+			}
+
+			return nil
+		}
+
+		gnarkutil.AssertCircuitSolved(t, def)
+	})
+
+}

prover/maths/common/polyext/poly.go

@@ -1,7 +1,8 @@
 package polyext
 
 import (
-	"github.com/consensys/linea-monorepo/prover/maths/common/smartvectors/vectorext"
+	"github.com/consensys/linea-monorepo/prover/maths/common/vectorext"
+	"github.com/consensys/linea-monorepo/prover/maths/field"
 	"github.com/consensys/linea-monorepo/prover/maths/field/fext"
 	"github.com/consensys/linea-monorepo/prover/utils"
 )
@@ -22,6 +23,11 @@ func EvalUnivariate(pol []fext.Element, x fext.Element) fext.Element {
 	return res
 }
 
+func EvalUnivariateBase(pol []fext.Element, x field.Element) fext.Element {
+	wrappedX := fext.Element{x, field.Zero()}
+	return EvalUnivariate(pol, wrappedX)
+}
+
 // Mul multiplies two polynomials expressed by their coefficients using the
 // naive method and writes the result in res. `a` and `b` may have distinct
 // degrees and the result is returned in a slice of size len(a) + len(b) - 1.