Coset Interpolation Gate (#15)

* helper functions for coset_interpolation_gate

* coset interpolation gate working

* hard coded the coset gate (for now)

field/field.go

@@ -35,6 +35,7 @@ func NewFieldAPI(api frontend.API) frontend.API {
 
 var ONE_F = NewFieldElement(1)
 var ZERO_F = NewFieldElement(0)
+var NEG_ONE_F = NewFieldElement(EmulatedField{}.Modulus().Uint64() - 1)
 
 var GOLDILOCKS_MULTIPLICATIVE_GROUP_GENERATOR = goldilocks.NewElement(7)
 var GOLDILOCKS_TWO_ADICITY = uint64(32)
@@ -52,3 +53,20 @@ func GoldilocksPrimitiveRootOfUnity(nLog uint64) goldilocks.Element {
 
 	return res
 }
+
+func TwoAdicSubgroup(nLog uint64) []goldilocks.Element {
+	if nLog > GOLDILOCKS_TWO_ADICITY {
+		panic("nLog is greater than GOLDILOCKS_TWO_ADICITY")
+	}
+
+	var res []goldilocks.Element
+	rootOfUnity := GoldilocksPrimitiveRootOfUnity(nLog)
+	res = append(res, goldilocks.NewElement(1))
+
+	for i := 0; i < (1 << nLog); i++ {
+		lastElement := res[len(res)-1]
+		res = append(res, *lastElement.Mul(&lastElement, &rootOfUnity))
+	}
+
+	return res
+}

field/quadratic_extension.go

@@ -4,6 +4,7 @@ import (
 	"fmt"
 	"math/bits"
 
+	"github.com/consensys/gnark-crypto/field/goldilocks"
 	"github.com/consensys/gnark/frontend"
 )
 
@@ -237,3 +238,42 @@ func (c *QuadraticExtensionAPI) SubExtensionAlgebra(a, b QEAlgebra) QEAlgebra {
 
 	return diff
 }
+
+func (c *QuadraticExtensionAPI) PartialInterpolateExtAlgebra(
+	domain []goldilocks.Element,
+	values []QEAlgebra,
+	barycentricWeights []goldilocks.Element,
+	point QEAlgebra,
+	initialEval QEAlgebra,
+	initialPartialProd QEAlgebra,
+) (QEAlgebra, QEAlgebra) {
+	n := len(values)
+	if n == 0 {
+		panic("Cannot interpolate with no values")
+	}
+	if n != len(domain) {
+		panic("Domain and values must have the same length")
+	}
+	if n != len(barycentricWeights) {
+		panic("Domain and barycentric weights must have the same length")
+	}
+
+	newEval := initialEval
+	newPartialProd := initialPartialProd
+	for i := 0; i < n; i++ {
+		val := values[i]
+		x := domain[i]
+		xField := NewFieldElement(x.Uint64())
+		xQE := QuadraticExtension{xField, ZERO_F}
+		xQEAlgebra := QEAlgebra{xQE, c.ZERO_QE}
+		weight := QuadraticExtension{NewFieldElement(barycentricWeights[i].Uint64()), ZERO_F}
+		term := c.SubExtensionAlgebra(point, xQEAlgebra)
+		weightedVal := c.ScalarMulExtensionAlgebra(weight, val)
+		newEval = c.MulExtensionAlgebra(newEval, term)
+		tmp := c.MulExtensionAlgebra(weightedVal, newPartialProd)
+		newEval = c.AddExtensionAlgebra(newEval, tmp)
+		newPartialProd = c.MulExtensionAlgebra(newPartialProd, term)
+	}
+
+	return newEval, newPartialProd
+}

plonky2_verifier/coset_interpolation_gate.go

@@ -0,0 +1,175 @@
+package plonky2_verifier
+
+import (
+	"fmt"
+	. "gnark-plonky2-verifier/field"
+
+	"github.com/consensys/gnark-crypto/field/goldilocks"
+)
+
+type CosetInterpolationGate struct {
+	subgroupBits       uint64
+	degree             uint64
+	barycentricWeights []goldilocks.Element
+}
+
+func NewCosetInterpolationGate(subgroupBits uint64, degree uint64, barycentricWeights []goldilocks.Element) *CosetInterpolationGate {
+	return &CosetInterpolationGate{
+		subgroupBits:       subgroupBits,
+		degree:             degree,
+		barycentricWeights: barycentricWeights,
+	}
+}
+
+func (g *CosetInterpolationGate) Id() string {
+
+	return fmt.Sprintf(
+		"CosetInterpolationGate { subgroup_bits: %d, degree: %d, barycentric_weights: %s }",
+		g.subgroupBits,
+		g.degree,
+		fmt.Sprint(g.barycentricWeights),
+	)
+}
+
+func (g *CosetInterpolationGate) numPoints() uint64 {
+	return 1 << g.subgroupBits
+}
+
+// Wire index of the coset shift.
+func (g *CosetInterpolationGate) wireShift() uint64 {
+	return 0
+}
+
+func (g *CosetInterpolationGate) startValues() uint64 {
+	return 1
+}
+
+// Wire indices of the `i`th interpolant value.
+func (g *CosetInterpolationGate) wiresValue(i uint64) Range {
+	if i >= g.numPoints() {
+		panic("Invalid point index")
+	}
+	start := g.startValues() + i*D
+	return Range{start, start + D}
+}
+
+func (g *CosetInterpolationGate) startEvaluationPoint() uint64 {
+	return g.startValues() + g.numPoints()*D
+}
+
+// Wire indices of the point to evaluate the interpolant at.
+func (g *CosetInterpolationGate) wiresEvaluationPoint() Range {
+	start := g.startEvaluationPoint()
+	return Range{start, start + D}
+}
+
+func (g *CosetInterpolationGate) startEvaluationValue() uint64 {
+	return g.startEvaluationPoint() + D
+}
+
+// Wire indices of the interpolated value.
+func (g *CosetInterpolationGate) wiresEvaluationValue() Range {
+	start := g.startEvaluationValue()
+	return Range{start, start + D}
+}
+
+func (g *CosetInterpolationGate) startIntermediates() uint64 {
+	return g.startEvaluationValue() + D
+}
+
+func (g *CosetInterpolationGate) numIntermediates() uint64 {
+	return (g.numPoints() - 2) / (g.degree - 1)
+}
+
+// The wires corresponding to the i'th intermediate evaluation.
+func (g *CosetInterpolationGate) wiresIntermediateEval(i uint64) Range {
+	if i >= g.numIntermediates() {
+		panic("Invalid intermediate index")
+	}
+	start := g.startIntermediates() + D*i
+	return Range{start, start + D}
+}
+
+// The wires corresponding to the i'th intermediate product.
+func (g *CosetInterpolationGate) wiresIntermediateProd(i uint64) Range {
+	if i >= g.numIntermediates() {
+		panic("Invalid intermediate index")
+	}
+	start := g.startIntermediates() + D*(g.numIntermediates()+i)
+	return Range{start, start + D}
+}
+
+// Wire indices of the shifted point to evaluate the interpolant at.
+func (g *CosetInterpolationGate) wiresShiftedEvaluationPoint() Range {
+	start := g.startIntermediates() + D*2*g.numIntermediates()
+	return Range{start, start + D}
+}
+
+func (g *CosetInterpolationGate) EvalUnfiltered(p *PlonkChip, vars EvaluationVars) []QuadraticExtension {
+	constraints := []QuadraticExtension{}
+
+	shift := vars.localWires[g.wireShift()]
+	evaluationPoint := vars.GetLocalExtAlgebra(g.wiresEvaluationPoint())
+	shiftedEvaluationPoint := vars.GetLocalExtAlgebra(g.wiresShiftedEvaluationPoint())
+
+	negShift := p.qeAPI.ScalarMulExtension(shift, NEG_ONE_F)
+
+	tmp := p.qeAPI.ScalarMulExtensionAlgebra(negShift, shiftedEvaluationPoint)
+	tmp = p.qeAPI.AddExtensionAlgebra(tmp, evaluationPoint)
+
+	for i := 0; i < D; i++ {
+		constraints = append(constraints, tmp[i])
+	}
+
+	domain := TwoAdicSubgroup(g.subgroupBits)
+	values := []QEAlgebra{}
+	for i := uint64(0); i < g.numPoints(); i++ {
+		values = append(values, vars.GetLocalExtAlgebra(g.wiresValue(i)))
+	}
+	weights := g.barycentricWeights
+
+	initialEval := p.qeAPI.ZERO_QE_ALGEBRA
+	initialProd := QEAlgebra{p.qeAPI.ONE_QE, p.qeAPI.ZERO_QE}
+	computedEval, computedProd := p.qeAPI.PartialInterpolateExtAlgebra(
+		domain[:g.degree],
+		values[:g.degree],
+		weights[:g.degree],
+		shiftedEvaluationPoint,
+		initialEval,
+		initialProd,
+	)
+
+	for i := uint64(0); i < g.numIntermediates(); i++ {
+		intermediateEval := vars.GetLocalExtAlgebra(g.wiresIntermediateEval(i))
+		intermediateProd := vars.GetLocalExtAlgebra(g.wiresIntermediateProd(i))
+
+		evalDiff := p.qeAPI.SubExtensionAlgebra(intermediateEval, computedEval)
+		for j := 0; j < D; j++ {
+			constraints = append(constraints, evalDiff[j])
+		}
+
+		prodDiff := p.qeAPI.SubExtensionAlgebra(intermediateProd, computedProd)
+		for j := 0; j < D; j++ {
+			constraints = append(constraints, prodDiff[j])
+		}
+
+		startIndex := 1 + (g.degree-1)*(i+1)
+		endIndex := startIndex + g.degree - 1
+		computedEval, computedProd = p.qeAPI.PartialInterpolateExtAlgebra(
+			domain[startIndex:endIndex],
+			values[startIndex:endIndex],
+			weights[startIndex:endIndex],
+			shiftedEvaluationPoint,
+			intermediateEval,
+			intermediateProd,
+		)
+	}
+
+	evaluationValue := vars.GetLocalExtAlgebra(g.wiresEvaluationValue())
+	evalDiff := p.qeAPI.SubExtensionAlgebra(evaluationValue, computedEval)
+	for j := 0; j < D; j++ {
+		constraints = append(constraints, evalDiff[j])
+	}
+
+	return constraints
+}

plonky2_verifier/gate.go

@@ -1,10 +1,13 @@
 package plonky2_verifier
 
 import (
+	"fmt"
 	. "gnark-plonky2-verifier/field"
 	"regexp"
 	"strconv"
 	"strings"
+
+	"github.com/consensys/gnark-crypto/field/goldilocks"
 )
 
 type gate interface {
@@ -104,19 +107,19 @@ func GateInstanceFromId(gateId string) gate {
 		return NewArithmeticExtensionGate(uint64(numOps))
 	}
 
-	if strings.HasPrefix(gateId, "MultiplicationExtension") {
+	if strings.HasPrefix(gateId, "MulExtensionGate") {
-		// Has the format "ArithmeticExtensionGate { num_ops: 10 }"
+		// Has the format "MulExtensionGate { num_ops: 13 }"
 
-		regEx := "MultiplicationExtension { num_ops: (?P<numOps>[0-9]+) }"
+		regEx := "MulExtensionGate { num_ops: (?P<numOps>[0-9]+) }"
 		r, err := regexp.Compile(regEx)
 		if err != nil {
-			panic("Invalid MultiplicationExtension regular expression")
+			panic("Invalid MulExtensionGate regular expression")
 		}
 
 		matches := getRegExMatches(r, gateId)
 		numOps, hasNumOps := matches["numOps"]
 		if !hasNumOps {
-			panic("Invalid MultiplicationExtension ID")
+			panic("Invalid MulExtensionGate ID")
 		}
 
 		return NewMultiplicationExtensionGate(uint64(numOps))
@@ -176,8 +179,51 @@ func GateInstanceFromId(gateId string) gate {
 		return NewExponentiationGate(uint64(numPowerBits))
 	}
 
-	return nil
+	// CosetInterpolationGate { subgroup_bits: 4, degree: 6, barycentric_weights: [17293822565076172801, 18374686475376656385, 18446744069413535745, 281474976645120, 17592186044416, 18446744069414584577, 18446744000695107601, 18446744065119617025, 1152921504338411520, 72057594037927936, 18446744069415632897, 18446462594437939201, 18446726477228539905, 18446744069414584065, 68719476720, 4294967296], _phantom: PhantomData<plonky2_field::goldilocks_field::GoldilocksField> }<D=2>
-	//panic(fmt.Sprintf("Unknown gate ID %s", gateId))
+	if strings.HasPrefix(gateId, "CosetInterpolationGate") {
+		// Has the format CosetInterpolationGate { subgroup_bits: 4, degree: 6, barycentric_weights: [17293822565076172801, 18374686475376656385, 18446744069413535745, 281474976645120, 17592186044416, 18446744069414584577, 18446744000695107601, 18446744065119617025, 1152921504338411520, 72057594037927936, 18446744069415632897, 18446462594437939201, 18446726477228539905, 18446744069414584065, 68719476720, 4294967296], _phantom: PhantomData<plonky2_field::goldilocks_field::GoldilocksField> }<D=2>
+
+		/*
+			regEx := "CosetInterpolationGate { subgroup_bits: (?P<subgroupBits>[0-9]+), degree: (?P<degree>[0-9]+), barycentric_weights: \\[(?P<barycentricWeights>[0-9, ]+)\\], _phantom: PhantomData<plonky2_field::goldilocks_field::GoldilocksField> }<D=2>"
+			r, err := regexp.Compile(regEx)
+			if err != nil {
+				panic("Invalid CosetInterpolationGate regular expression")
+			}
+
+			matches := getRegExMatches(r, gateId)
+			subgroupBits, hasSubgroupBits := matches["subgroupBits"]
+			degree, hasDegree := matches["degree"]
+			barycentricWeights, hasBarycentricWeights := matches["barycentricWeights"]
+			if !hasSubgroupBits || !hasDegree || !hasBarycentricWeights {
+				panic("Invalid CosetInterpolationGate ID")
+			}*/
+
+		return NewCosetInterpolationGate(
+			4,
+			6,
+			[]goldilocks.Element{
+				goldilocks.NewElement(17293822565076172801),
+				goldilocks.NewElement(18374686475376656385),
+				goldilocks.NewElement(18446744069413535745),
+				goldilocks.NewElement(281474976645120),
+				goldilocks.NewElement(17592186044416),
+				goldilocks.NewElement(18446744069414584577),
+				goldilocks.NewElement(18446744000695107601),
+				goldilocks.NewElement(18446744065119617025),
+				goldilocks.NewElement(1152921504338411520),
+				goldilocks.NewElement(72057594037927936),
+				goldilocks.NewElement(18446744069415632897),
+				goldilocks.NewElement(18446462594437939201),
+				goldilocks.NewElement(18446726477228539905),
+				goldilocks.NewElement(18446744069414584065),
+				goldilocks.NewElement(68719476720),
+				goldilocks.NewElement(4294967296),
+			},
+		)
+
+	}
+
+	panic(fmt.Sprintf("Unknown gate ID %s", gateId))
 }
 
 func getRegExMatches(r *regexp.Regexp, gateId string) map[string]int {

plonky2_verifier/gate_test.go

@@ -5,6 +5,7 @@ import (
 	. "gnark-plonky2-verifier/field"
 	"testing"
 
+	"github.com/consensys/gnark-crypto/field/goldilocks"
 	"github.com/consensys/gnark/frontend"
 	"github.com/consensys/gnark/test"
 )
@@ -771,6 +772,28 @@ func TestGates(t *testing.T) {
 		{&ReducingExtensionGate{numCoeffs: 33}, reducingExtensionGateExpectedConstraints},
 		{&ReducingGate{numCoeffs: 44}, reducingGateExpectedConstraints},
 		{&ExponentiationGate{numPowerBits: 67}, exponentiationGateExpectedConstraints},
+		{&CosetInterpolationGate{
+			subgroupBits: 4,
+			degree:       6,
+			barycentricWeights: []goldilocks.Element{
+				goldilocks.NewElement(17293822565076172801),
+				goldilocks.NewElement(18374686475376656385),
+				goldilocks.NewElement(18446744069413535745),
+				goldilocks.NewElement(281474976645120),
+				goldilocks.NewElement(17592186044416),
+				goldilocks.NewElement(18446744069414584577),
+				goldilocks.NewElement(18446744000695107601),
+				goldilocks.NewElement(18446744065119617025),
+				goldilocks.NewElement(1152921504338411520),
+				goldilocks.NewElement(72057594037927936),
+				goldilocks.NewElement(18446744069415632897),
+				goldilocks.NewElement(18446462594437939201),
+				goldilocks.NewElement(18446726477228539905),
+				goldilocks.NewElement(18446744069414584065),
+				goldilocks.NewElement(68719476720),
+				goldilocks.NewElement(4294967296),
+			},
+		}, cosetInterpolationGateExpectedConstraints},
 	}
 
 	for _, test := range gateTests {