@@ -10,7 +10,7 @@ - [FRI](https://github.com/succinctlabs/gnark-plonky2-verifier/blob/main/plonky2_verifier/fri.go)
 
 ## Requirements
 
-- [Go (1.20.1+)](https://go.dev/doc/install)
+- [Go (1.19+)](https://go.dev/doc/install)
 
 ## Benchmark
 

@@ -15,13 +15,13 @@ type Chip struct {
 	api               frontend.API `gnark:"-"`
 	poseidonChip      *poseidon.GoldilocksChip
 	poseidonBN254Chip *poseidon.BN254Chip
-	spongeState       [poseidon.SPONGE_WIDTH]gl.Variable
+	spongeState       poseidon.GoldilocksState
 	inputBuffer       []gl.Variable
 	outputBuffer      []gl.Variable
 }
 
 func NewChip(api frontend.API) *Chip {
-	var spongeState [poseidon.SPONGE_WIDTH]gl.Variable
+	var spongeState poseidon.GoldilocksState
 	var inputBuffer []gl.Variable
 	var outputBuffer []gl.Variable
 	for i := 0; i < poseidon.SPONGE_WIDTH; i++ {
@@ -40,7 +40,8 @@ }
 }
 
 func (c *Chip) ObserveElement(element gl.Variable) {
-	c.outputBuffer = clearBuffer(c.outputBuffer)
+	// Clear the output buffer
+	c.outputBuffer = make([]gl.Variable, 0)
 	c.inputBuffer = append(c.inputBuffer, element)
 	if len(c.inputBuffer) == poseidon.SPONGE_RATE {
 		c.duplexing()
@@ -110,14 +111,13 @@ return gl.QuadraticExtensionVariable{values[0], values[1]}
 }
 
 func (c *Chip) GetHash() poseidon.GoldilocksHashOut {
-	return [4]gl.Variable{c.GetChallenge(), c.GetChallenge(), c.GetChallenge(), c.GetChallenge()}
+	return [poseidon.POSEIDON_GL_HASH_SIZE]gl.Variable{c.GetChallenge(), c.GetChallenge(), c.GetChallenge(), c.GetChallenge()}
 }
 
 func (c *Chip) GetFriChallenges(
 	commitPhaseMerkleCaps []variables.FriMerkleCap,
 	finalPoly variables.PolynomialCoeffs,
 	powWitness gl.Variable,
-	degreeBits uint64,
 	config types.FriConfig,
 ) variables.FriChallenges {
 	numFriQueries := config.NumQueryRounds
@@ -143,10 +143,6 @@ FriQueryIndices: friQueryIndices,
 	}
 }
 
-func clearBuffer(buffer []gl.Variable) []gl.Variable {
-	return make([]gl.Variable, 0)
-}
-
 func (c *Chip) duplexing() {
 	if len(c.inputBuffer) > poseidon.SPONGE_RATE {
 		fmt.Println(len(c.inputBuffer))
@@ -158,9 +154,12 @@
 	for i := 0; i < len(c.inputBuffer); i++ {
 		c.spongeState[i] = glApi.Reduce(c.inputBuffer[i])
 	}
-	c.inputBuffer = clearBuffer(c.inputBuffer)
+	// Clear the input buffer
+	c.inputBuffer = make([]gl.Variable, 0)
 	c.spongeState = c.poseidonChip.Poseidon(c.spongeState)
-	clearBuffer(c.outputBuffer)
+
+	// Clear the output buffer
+	c.outputBuffer = make([]gl.Variable, 0)
 	for i := 0; i < poseidon.SPONGE_RATE; i++ {
 		c.outputBuffer = append(c.outputBuffer, c.spongeState[i])
 	}

@@ -49,14 +49,14 @@ gl.NewVariable(g.Uint64()).ToQuadraticExtension(),
 		zeta,
 	)
 
-	zetaNextBath := BatchInfo{
+	zetaNextBatch := BatchInfo{
 		Point:       zetaNext,
 		Polynomials: friZSPolys(f.commonData),
 	}
 
 	return InstanceInfo{
 		Oracles: friOracles(f.commonData),
-		Batches: []BatchInfo{zetaBatch, zetaNextBath},
+		Batches: []BatchInfo{zetaBatch, zetaNextBatch},
 	}
 }
 
@@ -73,12 +73,10 @@ return Openings{Batches: []OpeningBatch{zetaBatch, zetaNextBatch}}
 }
 
 func (f *Chip) assertLeadingZeros(powWitness gl.Variable, friConfig types.FriConfig) {
-	// Asserts that powWitness'es big-endian bit representation has at least `leading_zeros` leading zeros.
+	// Asserts that powWitness'es big-endian bit representation has at least friConfig.ProofOfWorkBits leading zeros.
 	// Note that this is assuming that the Goldilocks field is being used.  Specfically that the
-	// field is 64 bits long
-	maxPowWitness := uint64(math.Pow(2, float64(64-friConfig.ProofOfWorkBits))) - 1
-	reducedPowWitness := f.gl.Reduce(powWitness)
-	f.api.AssertIsLessOrEqual(reducedPowWitness.Limb, frontend.Variable(maxPowWitness))
+	// field is 64 bits long.
+	f.gl.RangeCheckWithMaxBits(powWitness, 64-friConfig.ProofOfWorkBits)
 }
 
 func (f *Chip) fromOpeningsAndAlpha(
@@ -128,13 +126,15 @@ panic(errorMsg)
 	}
 
 	const NUM_LEAF_LOOKUPS = 4
+	// Each lookup gadget will connect to 4 merkleCap entries
+	const STRIDE_LENGTH = 4
 	var leafLookups [NUM_LEAF_LOOKUPS]poseidon.BN254HashOut
 	// First create the "leaf" lookup2 circuits
-	// The will use the least significant bits of the capIndexBits array
+	// This will use the least significant bits of the capIndexBits array
 	for i := 0; i < NUM_LEAF_LOOKUPS; i++ {
 		leafLookups[i] = f.api.Lookup2(
 			capIndexBits[0], capIndexBits[1],
-			merkleCap[i*NUM_LEAF_LOOKUPS], merkleCap[i*NUM_LEAF_LOOKUPS+1], merkleCap[i*NUM_LEAF_LOOKUPS+2], merkleCap[i*NUM_LEAF_LOOKUPS+3],
+			merkleCap[i*STRIDE_LENGTH], merkleCap[i*STRIDE_LENGTH+1], merkleCap[i*STRIDE_LENGTH+2], merkleCap[i*STRIDE_LENGTH+3],
 		)
 	}
 
@@ -162,7 +162,7 @@ exponentBits []frontend.Variable,
 ) gl.Variable {
 	product := gl.One()
 	for i, bit := range exponentBits {
-		// If the bit is on, we multiply product by base^pow.
+		// If the bit is 1, we multiply product by base^pow.
 		// We can arithmetize this as:
 		//     product *= 1 + bit (base^pow - 1)
 		//     product = (base^pow - 1) product bit + product
@@ -238,9 +238,11 @@ reducedEvals := f.gl.ReduceWithPowers(evals, friAlpha)
 		numerator := f.gl.SubExtensionNoReduce(reducedEvals, reducedOpenings)
 		denominator := f.gl.SubExtension(subgroupX_QE, point)
 		sum = f.gl.MulExtension(f.gl.ExpExtension(friAlpha, uint64(len(evals))), sum)
+		inv, hasInv := f.gl.InverseExtension(denominator)
+		f.api.AssertIsEqual(hasInv, frontend.Variable(1))
 		sum = f.gl.MulAddExtension(
 			numerator,
-			f.gl.InverseExtension(denominator),
+			inv,
 			sum,
 		)
 	}
@@ -272,17 +274,23 @@ lX = f.gl.SubMulExtension(x, xPoints[i], lX)
 	}
 
 	sum := gl.ZeroExtension()
+
+	lookupFromPoints := frontend.Variable(1)
 	for i := 0; i < len(xPoints); i++ {
+		quotient, hasQuotient := f.gl.DivExtension(
+			barycentricWeights[i],
+			f.gl.SubExtension(
+				x,
+				xPoints[i],
+			),
+		)
+
+		lookupFromPoints = f.api.Mul(hasQuotient, lookupFromPoints)
+
 		sum = f.gl.AddExtension(
 			f.gl.MulExtension(
-				f.gl.DivExtension(
-					barycentricWeights[i],
-					f.gl.SubExtension(
-						x,
-						xPoints[i],
-					),
-				),
 				yPoints[i],
+				quotient,
 			),
 			sum,
 		)
@@ -290,17 +298,17 @@ }
 
 	interpolation := f.gl.MulExtension(lX, sum)
 
-	returnField := interpolation
+	lookupVal := gl.ZeroExtension()
 	// Now check if x is already within the xPoints
 	for i := 0; i < len(xPoints); i++ {
-		returnField = f.gl.Lookup(
+		lookupVal = f.gl.Lookup(
 			f.gl.IsZero(f.gl.SubExtension(x, xPoints[i])),
-			returnField,
+			lookupVal,
 			yPoints[i],
 		)
 	}
 
-	return returnField
+	return f.gl.Lookup(lookupFromPoints, lookupVal, interpolation)
 }
 
 func (f *Chip) computeEvaluation(
@@ -312,7 +320,7 @@ beta gl.QuadraticExtensionVariable,
 ) gl.QuadraticExtensionVariable {
 	arity := 1 << arityBits
 	if (len(evals)) != arity {
-		panic("len(evals) ! arity")
+		panic("len(evals) != arity")
 	}
 	if arityBits > 8 {
 		panic("currently assuming that arityBits is <= 8")
@@ -327,8 +335,8 @@ // element's new index is the bit reverse of it's original index.
 	// OPTIMIZE - Since the size of the evals array should be constant (e.g. 2^arityBits),
 	//        we can just hard code the permutation.
 	permutedEvals := make([]gl.QuadraticExtensionVariable, len(evals))
-	for i := uint8(0); i < uint8(len(evals)); i++ {
-		newIndex := bits.Reverse8(i) >> arityBits
+	for i := uint8(0); i <= uint8(len(evals)-1); i++ {
+		newIndex := bits.Reverse8(i) >> (8 - arityBits)
 		permutedEvals[newIndex] = evals[i]
 	}
 
@@ -367,7 +375,9 @@ }
 		}
 		// Take the inverse of the barycentric weights
 		// OPTIMIZE: Can provide a witness to this value
-		barycentricWeights[i] = f.gl.InverseExtension(barycentricWeights[i])
+		inv, hasInv := f.gl.InverseExtension(barycentricWeights[i])
+		f.api.AssertIsEqual(hasInv, frontend.Variable(1))
+		barycentricWeights[i] = inv
 	}
 
 	return f.interpolate(beta, xPoints, yPoints, barycentricWeights)

@@ -52,7 +52,6 @@ friChallenges := challengerChip.GetFriChallenges(
 		proofWithPis.Proof.OpeningProof.CommitPhaseMerkleCaps,
 		proofWithPis.Proof.OpeningProof.FinalPoly,
 		proofWithPis.Proof.OpeningProof.PowWitness,
-		commonCircuitData.DegreeBits,
 		commonCircuitData.Config.FriConfig,
 	)
 

@@ -38,9 +38,6 @@
 // The modulus of the field.
 var MODULUS *big.Int = emulated.Goldilocks{}.Modulus()
 
-// The threshold maximum number of bits at which we must reduce the element.
-var REDUCE_NB_BITS_THRESHOLD uint8 = 254 - 64
-
 // The number of bits to use for range checks on inner products of field elements.
 var RANGE_CHECK_NB_BITS int = 140
 
@@ -90,38 +87,41 @@ rangeChecker := rangecheck.New(api)
 	return &Chip{api: api, rangeChecker: rangeChecker}
 }
 
-// Adds two field elements such that x + y = z within the Golidlocks field.
+// Adds two goldilocks field elements and returns a value within the goldilocks field.
 func (p *Chip) Add(a Variable, b Variable) Variable {
 	return p.MulAdd(a, NewVariable(1), b)
 }
 
-// Adds two field elements such that x + y = z within the Golidlocks field without reducing.
+// Adds two goldilocks field elements and returns a value that may not be within the goldilocks field
+// (e.g. the sum is not reduced).
 func (p *Chip) AddNoReduce(a Variable, b Variable) Variable {
 	return NewVariable(p.api.Add(a.Limb, b.Limb))
 }
 
-// Subtracts two field elements such that x + y = z within the Golidlocks field.
+// Subracts two goldilocks field elements and returns a value within the goldilocks field.
 func (p *Chip) Sub(a Variable, b Variable) Variable {
-	return p.MulAdd(b, NewVariable(MODULUS.Uint64()-1), a)
+	return p.MulAdd(b, NegOne(), a)
 }
 
-// Subtracts two field elements such that x + y = z within the Golidlocks field without reducing.
+// Subracts two goldilocks field elements and returns a value that may not be within the goldilocks field
+// (e.g. the difference is not reduced).
 func (p *Chip) SubNoReduce(a Variable, b Variable) Variable {
-	return NewVariable(p.api.Add(a.Limb, p.api.Mul(b.Limb, MODULUS.Uint64()-1)))
+	return NewVariable(p.api.Add(a.Limb, p.api.Mul(b.Limb, NegOne().Limb)))
 }
 
-// Multiplies two field elements such that x * y = z within the Golidlocks field.
+// Multiplies two goldilocks field elements and returns a value within the goldilocks field.
 func (p *Chip) Mul(a Variable, b Variable) Variable {
 	return p.MulAdd(a, b, Zero())
 }
 
-// Multiplies two field elements such that x * y = z within the Golidlocks field without reducing.
+// Multiplies two goldilocks field elements and returns a value that may not be within the goldilocks field
+// (e.g. the product is not reduced).
 func (p *Chip) MulNoReduce(a Variable, b Variable) Variable {
 	return NewVariable(p.api.Mul(a.Limb, b.Limb))
 }
 
-// Multiplies two field elements and adds a field element such that x * y + z = c within the
-// Golidlocks field.
+// Multiplies two field elements and adds a field element (e.g. computes a * b + c).  The returned value
+// will be within the goldilocks field.
 func (p *Chip) MulAdd(a Variable, b Variable, c Variable) Variable {
 	result, err := p.api.Compiler().NewHint(MulAddHint, 2, a.Limb, b.Limb, c.Limb)
 	if err != nil {
@@ -131,7 +131,8 @@
 	quotient := NewVariable(result[0])
 	remainder := NewVariable(result[1])
 
-	lhs := p.api.MulAcc(c.Limb, a.Limb, b.Limb)
+	cLimbCopy := p.api.Mul(c.Limb, 1)
+	lhs := p.api.MulAcc(cLimbCopy, a.Limb, b.Limb)
 	rhs := p.api.MulAcc(remainder.Limb, MODULUS, quotient.Limb)
 	p.api.AssertIsEqual(lhs, rhs)
 
@@ -140,10 +141,11 @@ p.RangeCheck(remainder)
 	return remainder
 }
 
-// Multiplies two field elements and adds a field element such that x * y + z = c within the
-// Golidlocks field without reducing.
+// Multiplies two field elements and adds a field element (e.g. computes a * b + c).  The returned value
+// may no be within the goldilocks field (e.g. the result is not reduced).
 func (p *Chip) MulAddNoReduce(a Variable, b Variable, c Variable) Variable {
-	return NewVariable(p.api.MulAcc(c.Limb, a.Limb, b.Limb))
+	cLimbCopy := p.api.Mul(c.Limb, 1)
+	return NewVariable(p.api.MulAcc(cLimbCopy, a.Limb, b.Limb))
 }
 
 // The hint used to compute MulAdd.
@@ -179,18 +181,7 @@ // Must check that offset \in [0, MODULUS) and carry \in [0, 2^RANGE_CHECK_NB_BITS) to ensure
 	// that this computation does not overflow. We use 2^RANGE_CHECK_NB_BITS to reduce the cost of the range check
 	//
 	// In other words, we assume that we at most compute a a dot product with dimension at most RANGE_CHECK_NB_BITS - 128.
-
-	result, err := p.api.Compiler().NewHint(ReduceHint, 2, x.Limb)
-	if err != nil {
-		panic(err)
-	}
-
-	quotient := result[0]
-	p.rangeChecker.Check(quotient, RANGE_CHECK_NB_BITS)
-
-	remainder := NewVariable(result[1])
-	p.RangeCheck(remainder)
-	return remainder
+	return p.ReduceWithMaxBits(x, uint64(RANGE_CHECK_NB_BITS))
 }
 
 // Reduces a field element x such that x % MODULUS = y.
@@ -212,6 +203,9 @@ p.rangeChecker.Check(quotient, int(maxNbBits))
 
 	remainder := NewVariable(result[1])
 	p.RangeCheck(remainder)
+
+	p.api.AssertIsEqual(x.Limb, p.api.Add(p.api.Mul(quotient, MODULUS), remainder.Limb))
+
 	return remainder
 }
 
@@ -229,16 +223,22 @@ return nil
 }
 
 // Computes the inverse of a field element x such that x * x^-1 = 1.
-func (p *Chip) Inverse(x Variable) Variable {
+func (p *Chip) Inverse(x Variable) (Variable, frontend.Variable) {
 	result, err := p.api.Compiler().NewHint(InverseHint, 1, x.Limb)
 	if err != nil {
 		panic(err)
 	}
 
 	inverse := NewVariable(result[0])
+	isZero := p.api.IsZero(x.Limb)
+	hasInv := p.api.Sub(1, isZero)
+	p.RangeCheck(inverse)
+
 	product := p.Mul(inverse, x)
-	p.api.AssertIsEqual(product.Limb, frontend.Variable(1))
-	return inverse
+	productToCheck := p.api.Select(hasInv, product.Limb, frontend.Variable(1))
+	p.api.AssertIsEqual(productToCheck, frontend.Variable(1))
+
+	return inverse, hasInv
 }
 
 // The hint used to compute Inverse.
@@ -254,6 +254,8 @@ }
 
 	inputGl := goldilocks.NewElement(input.Uint64())
 	resultGl := goldilocks.NewElement(0)
+
+	// Will set resultGL if inputGL == 0
 	resultGl.Inverse(&inputGl)
 
 	result := big.NewInt(0)
@@ -262,28 +264,6 @@
 	return nil
 }
 
-// Computes a field element raised to some power.
-func (p *Chip) Exp(x Variable, k *big.Int) Variable {
-	if k.IsUint64() && k.Uint64() == 0 {
-		return One()
-	}
-
-	e := k
-	if k.Sign() == -1 {
-		panic("Unsupported negative exponent. Need to implement inversion.")
-	}
-
-	z := x
-	for i := e.BitLen() - 2; i >= 0; i-- {
-		z = p.Mul(z, z)
-		if e.Bit(i) == 1 {
-			z = p.Mul(z, x)
-		}
-	}
-
-	return z
-}
-
 // The hint used to split a GoldilocksVariable into 2 32 bit limbs.
 func SplitLimbsHint(_ *big.Int, inputs []*big.Int, results []*big.Int) error {
 	if len(inputs) != 1 {
@@ -348,6 +328,11 @@ frontend.Variable(0),
 	)
 }
 
+// This function will assert that the field element x is less than 2^maxNbBits.
+func (p *Chip) RangeCheckWithMaxBits(x Variable, maxNbBits uint64) {
+	p.rangeChecker.Check(x.Limb, int(maxNbBits))
+}
+
 func (p *Chip) AssertIsEqual(x, y Variable) {
 	p.api.AssertIsEqual(x.Limb, y.Limb)
 }
@@ -373,7 +358,7 @@ var res []goldilocks.Element
 	rootOfUnity := PrimitiveRootOfUnity(nLog)
 	res = append(res, goldilocks.NewElement(1))
 
-	for i := 0; i < (1 << nLog); i++ {
+	for i := 0; i < (1<<nLog)-1; i++ {
 		lastElement := res[len(res)-1]
 		res = append(res, *lastElement.Mul(&lastElement, &rootOfUnity))
 	}

@@ -58,15 +58,13 @@
 // Multiplies quadratic extension variable in the Goldilocks field.
 func (p *Chip) MulExtension(a, b QuadraticExtensionVariable) QuadraticExtensionVariable {
 	product := p.MulExtensionNoReduce(a, b)
-	product[0] = p.Reduce(product[0])
-	product[1] = p.Reduce(product[1])
-	return product
+	return p.ReduceExtension(product)
 }
 
 // Multiplies quadratic extension variable in the Goldilocks field without reducing.
 func (p *Chip) MulExtensionNoReduce(a, b QuadraticExtensionVariable) QuadraticExtensionVariable {
 	c0o0 := p.MulNoReduce(a[0], b[0])
-	c0o1 := p.MulNoReduce(p.MulNoReduce(NewVariable(7), a[1]), b[1])
+	c0o1 := p.MulNoReduce(p.MulNoReduce(NewVariable(W), a[1]), b[1])
 	c0 := p.AddNoReduce(c0o0, c0o1)
 	c1 := p.AddNoReduce(p.MulNoReduce(a[0], b[1]), p.MulNoReduce(a[1], b[0]))
 	return NewQuadraticExtensionVariable(c0, c1)
@@ -77,9 +75,7 @@ // be less than RANGE_CHECK_NB_BITS bits.
 func (p *Chip) MulAddExtension(a, b, c QuadraticExtensionVariable) QuadraticExtensionVariable {
 	product := p.MulExtensionNoReduce(a, b)
 	sum := p.AddExtensionNoReduce(product, c)
-	sum[0] = p.Reduce(sum[0])
-	sum[1] = p.Reduce(sum[1])
-	return sum
+	return p.ReduceExtension(sum)
 }
 
 func (p *Chip) MulAddExtensionNoReduce(a, b, c QuadraticExtensionVariable) QuadraticExtensionVariable {
@@ -88,14 +84,12 @@ sum := p.AddExtensionNoReduce(product, c)
 	return sum
 }
 
-// Multiplies two operands a and b and subtracts to c in the Goldilocks extension field. a * b - c must
+// Subtracts two operands a and b and multiplies the diff by c in the Goldilocks extension field. (a - b) * c must
 // be less than RANGE_CHECK_NB_BITS bits.
 func (p *Chip) SubMulExtension(a, b, c QuadraticExtensionVariable) QuadraticExtensionVariable {
 	difference := p.SubExtensionNoReduce(a, b)
 	product := p.MulExtensionNoReduce(difference, c)
-	product[0] = p.Reduce(product[0])
-	product[1] = p.Reduce(product[1])
-	return product
+	return p.ReduceExtension(product)
 }
 
 // Multiplies quadratic extension variable in the Goldilocks field by a scalar.
@@ -126,21 +120,23 @@ return p.ReduceExtension(acc)
 }
 
 // Computes the inverse of a quadratic extension variable in the Goldilocks field.
-func (p *Chip) InverseExtension(a QuadraticExtensionVariable) QuadraticExtensionVariable {
-	a0IsZero := p.api.IsZero(a[0].Limb)
-	a1IsZero := p.api.IsZero(a[1].Limb)
-	p.api.AssertIsEqual(p.api.Mul(a0IsZero, a1IsZero), frontend.Variable(0))
+func (p *Chip) InverseExtension(a QuadraticExtensionVariable) (QuadraticExtensionVariable, frontend.Variable) {
+	aIsZero := p.IsZero(a)
+	p.api.AssertIsEqual(aIsZero, frontend.Variable(0))
 	aPowRMinus1 := QuadraticExtensionVariable{
 		a[0],
 		p.Mul(a[1], NewVariable(DTH_ROOT)),
 	}
 	aPowR := p.MulExtension(aPowRMinus1, a)
-	return p.ScalarMulExtension(aPowRMinus1, p.Inverse(aPowR[0]))
+
+	aPowRInv, hasInv := p.Inverse(aPowR[0])
+	return p.ScalarMulExtension(aPowRMinus1, aPowRInv), hasInv
 }
 
 // Divides two quadratic extension variables in the Goldilocks field.
-func (p *Chip) DivExtension(a, b QuadraticExtensionVariable) QuadraticExtensionVariable {
-	return p.MulExtension(a, p.InverseExtension(b))
+func (p *Chip) DivExtension(a, b QuadraticExtensionVariable) (QuadraticExtensionVariable, frontend.Variable) {
+	bInv, hasInv := p.InverseExtension(b)
+	return p.MulExtension(a, bInv), hasInv
 }
 
 // Exponentiates a quadratic extension variable to some exponent in the Golidlocks field.
@@ -213,7 +209,7 @@ c1 := p.api.Select(b, y[1].Limb, x[1].Limb)
 	return NewQuadraticExtensionVariable(NewVariable(c0), NewVariable(c1))
 }
 
-// Lookup2 is similar to select2, but returns the first variable if the bit is zero and vice-versa.
+// Lookup2 is similar to Lookup2.  It returns the ith qe value (0 indexed) where i is bit decomposed to b0,b1 (little endian).
 func (p *Chip) Lookup2(
 	b0 frontend.Variable,
 	b1 frontend.Variable,

@@ -14,7 +14,7 @@ return QuadraticExtensionAlgebraVariable{a, b}
 }
 
 func (p QuadraticExtensionVariable) ToQuadraticExtensionAlgebra() QuadraticExtensionAlgebraVariable {
-	return [2]QuadraticExtensionVariable{p, ZeroExtension()}
+	return [D]QuadraticExtensionVariable{p, ZeroExtension()}
 }
 
 func ZeroExtensionAlgebra() QuadraticExtensionAlgebraVariable {

@@ -59,7 +59,7 @@ }
 
 func (c *TestQuadraticExtensionDivCircuit) Define(api frontend.API) error {
 	glAPI := New(api)
-	actualRes := glAPI.DivExtension(c.Operand1, c.Operand2)
+	actualRes, _ := glAPI.DivExtension(c.Operand1, c.Operand2)
 	glAPI.AssertIsEqual(actualRes[0], c.ExpectedResult[0])
 	glAPI.AssertIsEqual(actualRes[1], c.ExpectedResult[1])
 	return nil

@@ -9,7 +9,7 @@ "github.com/consensys/gnark/frontend"
 	gl "github.com/succinctlabs/gnark-plonky2-verifier/goldilocks"
 )
 
-var aritheticExtensionGateRegex = regexp.MustCompile("ArithmeticExtensionGate { num_ops: (?P<numOps>[0-9]+) }")
+var arithmeticExtensionGateRegex = regexp.MustCompile("ArithmeticExtensionGate { num_ops: (?P<numOps>[0-9]+) }")
 
 func deserializeExtensionArithmeticGate(parameters map[string]string) Gate {
 	// Has the format "ArithmeticExtensionGate { num_ops: 10 }"

@@ -9,7 +9,7 @@ "github.com/consensys/gnark/frontend"
 	gl "github.com/succinctlabs/gnark-plonky2-verifier/goldilocks"
 )
 
-var aritheticGateRegex = regexp.MustCompile("ArithmeticGate { num_ops: (?P<numOps>[0-9]+) }")
+var arithmeticGateRegex = regexp.MustCompile("ArithmeticGate { num_ops: (?P<numOps>[0-9]+) }")
 
 func deserializeArithmeticGate(parameters map[string]string) Gate {
 	// Has the format "ArithmeticGate { num_ops: 10 }"

@@ -51,7 +51,7 @@ }
 }
 
 func (g *BaseSumGate) Id() string {
-	return fmt.Sprintf("BaseSumGate { num_ops: %d } + Base: %d", g.numLimbs, g.base)
+	return fmt.Sprintf("BaseSumGate { num_limbs: %d } + Base: %d", g.numLimbs, g.base)
 }
 
 func (g *BaseSumGate) limbs() []uint64 {

@@ -41,14 +41,14 @@ return fmt.Sprintf("ConstantGate { num_consts: %d }", g.numConsts)
 }
 
 func (g *ConstantGate) ConstInput(i uint64) uint64 {
-	if i > g.numConsts {
+	if i >= g.numConsts {
 		panic("Invalid constant index")
 	}
 	return i
 }
 
 func (g *ConstantGate) WireOutput(i uint64) uint64 {
-	if i > g.numConsts {
+	if i >= g.numConsts {
 		panic("Invalid wire index")
 	}
 	return i

@@ -32,6 +32,9 @@ degreeInt, err := strconv.ParseUint(degree, 10, 64)
 	if err != nil {
 		panic("invalid degree in CosetInterpolationGate")
 	}
+	if degreeInt < 2 {
+		panic("degree must be at least 2 in CosetInterpolationGate")
+	}
 
 	barycentricWeightsStr := strings.Split(barycentricWeights, ",")
 	barycentricWeightsInt := make([]goldilocks.Element, len(barycentricWeightsStr))
@@ -199,6 +202,10 @@ }
 
 		startIndex := 1 + (g.degree-1)*(i+1)
 		endIndex := startIndex + g.degree - 1
+		if endIndex > g.numPoints() {
+			endIndex = g.numPoints()
+		}
+
 		computedEval, computedProd = glApi.PartialInterpolateExtAlgebra(
 			domain[startIndex:endIndex],
 			values[startIndex:endIndex],

@@ -23,6 +23,20 @@ if err != nil {
 		panic("Invalid num_power_bits field in ExponentiationGate")
 	}
 
+	base, hasBase := parameters["base"]
+	if !hasBase {
+		panic("Missing field base in ExponentiationGate")
+	}
+
+	baseInt, err := strconv.Atoi(base)
+	if err != nil {
+		panic("Invalid base field in ExponentiationGate")
+	}
+
+	if baseInt != gl.D {
+		panic("Expected base field in ExponentiationGate to equal gl.D")
+	}
+
 	return NewExponentiationGate(uint64(numPowerBitsInt))
 }
 

@@ -18,20 +18,20 @@ ) []gl.QuadraticExtensionVariable
 }
 
 var gateRegexHandlers = map[*regexp.Regexp]func(parameters map[string]string) Gate{
-	aritheticGateRegex:          deserializeArithmeticGate,
-	aritheticExtensionGateRegex: deserializeExtensionArithmeticGate,
-	baseSumGateRegex:            deserializeBaseSumGate,
-	constantGateRegex:           deserializeConstantGate,
-	cosetInterpolationGateRegex: deserializeCosetInterpolationGate,
-	exponentiationGateRegex:     deserializeExponentiationGate,
-	mulExtensionGateRegex:       deserializeMulExtensionGate,
-	noopGateRegex:               deserializeNoopGate,
-	poseidonGateRegex:           deserializePoseidonGate,
-	poseidonMdsGateRegex:        deserializePoseidonMdsGate,
-	publicInputGateRegex:        deserializePublicInputGate,
-	randomAccessGateRegex:       deserializeRandomAccessGate,
-	reducingExtensionGateRegex:  deserializeReducingExtensionGate,
-	reducingGateRegex:           deserializeReducingGate,
+	arithmeticGateRegex:          deserializeArithmeticGate,
+	arithmeticExtensionGateRegex: deserializeExtensionArithmeticGate,
+	baseSumGateRegex:             deserializeBaseSumGate,
+	constantGateRegex:            deserializeConstantGate,
+	cosetInterpolationGateRegex:  deserializeCosetInterpolationGate,
+	exponentiationGateRegex:      deserializeExponentiationGate,
+	mulExtensionGateRegex:        deserializeMulExtensionGate,
+	noopGateRegex:                deserializeNoopGate,
+	poseidonGateRegex:            deserializePoseidonGate,
+	poseidonMdsGateRegex:         deserializePoseidonMdsGate,
+	publicInputGateRegex:         deserializePublicInputGate,
+	randomAccessGateRegex:        deserializeRandomAccessGate,
+	reducingExtensionGateRegex:   deserializeReducingExtensionGate,
+	reducingGateRegex:            deserializeReducingGate,
 }
 
 func GateInstanceFromId(gateId string) Gate {

@@ -37,7 +37,7 @@ }
 }
 
 func (g *MultiplicationExtensionGate) Id() string {
-	return fmt.Sprintf("ArithmeticExtensionGate { num_ops: %d }", g.numOps)
+	return fmt.Sprintf("MulExtensionGate { num_ops: %d }", g.numOps)
 }
 
 func (g *MultiplicationExtensionGate) wiresIthMultiplicand0(i uint64) Range {

@@ -90,7 +90,9 @@
 	for i := uint64(0); i < poseidon.SPONGE_WIDTH; i++ {
 		output := vars.GetLocalExtAlgebra(g.WireOutput(i))
 		diff := glApi.SubExtensionAlgebra(output, computed_outputs[i])
-		constraints = append(constraints, diff[0], diff[1])
+		for i := 0; i < gl.D; i++ {
+			constraints = append(constraints, diff[i])
+		}
 	}
 
 	return constraints

@@ -38,7 +38,7 @@ constraints := []gl.QuadraticExtensionVariable{}
 
 	wires := g.WiresPublicInputsHash()
 	hash_parts := vars.publicInputsHash
-	for i := 0; i < 4; i++ {
+	for i := 0; i < len(wires); i++ {
 		wire := wires[i]
 		hash_part := hash_parts[i]
 

@@ -36,6 +36,20 @@ if err != nil {
 		panic("invalid numExtraConstants in RandomAccessGate")
 	}
 
+	base, hasBase := parameters["base"]
+	if !hasBase {
+		panic("Missing field base in RandomAccessGate")
+	}
+
+	baseInt, err := strconv.Atoi(base)
+	if err != nil {
+		panic("Invalid base field in RandomAccessGate")
+	}
+
+	if baseInt != gl.D {
+		panic("Expected base field in RandomAccessGate to equal gl.D")
+	}
+
 	return NewRandomAccessGate(bitsInt, numCopiesInt, numExtraConstantsInt)
 }
 
@@ -151,14 +165,12 @@ x := listItems[i]
 				y := listItems[i+1]
 
 				// This is computing `if b { x } else { y }`
-				// i.e. `bx - (by-y)`.
-				mul1 := glApi.MulExtension(b, x)
-				sub1 := glApi.SubExtension(mul1, x)
-
-				mul2 := glApi.MulExtension(b, y)
-				sub2 := glApi.SubExtension(mul2, sub1)
+				// i.e. `x + b(y - x)`.
+				diff := glApi.SubExtension(y, x)
+				mul := glApi.MulExtension(b, diff)
+				add := glApi.AddExtension(x, mul)
 
-				listItemsTmp = append(listItemsTmp, sub2)
+				listItemsTmp = append(listItemsTmp, add)
 			}
 			listItems = listItemsTmp
 		}

@@ -12,7 +12,7 @@
 var reducingExtensionGateRegex = regexp.MustCompile("ReducingExtensionGate { num_coeffs: (?P<numCoeffs>[0-9]+) }")
 
 func deserializeReducingExtensionGate(parameters map[string]string) Gate {
-	// Has the format "ReducingGate { num_coeffs: 33 }"
+	// Has the format "ReducingExtensionGate { num_coeffs: 33 }"
 	numCoeffs, hasNumCoeffs := parameters["numCoeffs"]
 	if !hasNumCoeffs {
 		panic("Missing field num_coeffs in ReducingExtensionGate")
@@ -39,7 +39,7 @@ }
 }
 
 func (g *ReducingExtensionGate) Id() string {
-	return fmt.Sprintf("ReducingExtensionGate { num_ops: %d }", g.numCoeffs)
+	return fmt.Sprintf("ReducingExtensionGate { num_coeffs: %d }", g.numCoeffs)
 }
 
 func (g *ReducingExtensionGate) wiresOutput() Range {

@@ -39,7 +39,7 @@ }
 }
 
 func (g *ReducingGate) Id() string {
-	return fmt.Sprintf("ReducingExtensionGate { num_ops: %d }", g.numCoeffs)
+	return fmt.Sprintf("ReducingGate { num_coeffs: %d }", g.numCoeffs)
 }
 
 func (g *ReducingGate) wiresOutput() Range {
@@ -96,11 +96,7 @@
 	constraints := []gl.QuadraticExtensionVariable{}
 	acc := oldAcc
 	for i := uint64(0); i < g.numCoeffs; i++ {
-		var coeff gl.QuadraticExtensionAlgebraVariable
-		for j := 0; j < gl.D; j++ {
-			coeff[j] = gl.ZeroExtension()
-		}
-		coeff[0] = coeffs[i]
+		coeff := coeffs[i].ToQuadraticExtensionAlgebra()
 		tmp := glApi.MulExtensionAlgebra(acc, alpha)
 		tmp = glApi.AddExtensionAlgebra(tmp, coeff)
 		tmp = glApi.SubExtensionAlgebra(tmp, accs[i])

@@ -71,10 +71,15 @@ denominator := glApi.SubExtension(
 		glApi.ScalarMulExtension(x, p.DEGREE),
 		p.DEGREE_QE,
 	)
-	return glApi.DivExtension(
+
+	quotient, hasQuotient := glApi.DivExtension(
 		evalZeroPoly,
 		denominator,
 	)
+
+	p.api.AssertIsEqual(hasQuotient, frontend.Variable(1))
+
+	return quotient
 }
 
 func (p *PlonkChip) checkPartialProducts(

@@ -10,6 +10,7 @@
 import (
 	"math/big"
 
+	"github.com/consensys/gnark-crypto/ecc/bn254"
 	"github.com/consensys/gnark/frontend"
 	gl "github.com/succinctlabs/gnark-plonky2-verifier/goldilocks"
 )
@@ -28,6 +29,10 @@ type BN254State = [BN254_SPONGE_WIDTH]frontend.Variable
 type BN254HashOut = frontend.Variable
 
 func NewBN254Chip(api frontend.API) *BN254Chip {
+	if api.Compiler().Field().Cmp(bn254.ID.ScalarField()) != 0 {
+		panic("Gnark compiler not set to BN254 scalar field")
+	}
+
 	return &BN254Chip{api: api, gl: *gl.New(api)}
 }
 
@@ -76,8 +81,10 @@ if len(input) <= 3 {
 		returnVal := frontend.Variable(0)
 
 		alpha := new(big.Int).SetInt64(1 << 32)
+		alpha = new(big.Int).Mul(alpha, alpha)
 		for i, inputElement := range input {
-			returnVal = c.api.MulAcc(returnVal, inputElement, alpha.Exp(alpha, big.NewInt(int64(i)), nil))
+			mulFactor := new(big.Int).Exp(alpha, big.NewInt(int64(i)), nil)
+			returnVal = c.api.MulAcc(returnVal, inputElement.Limb, mulFactor)
 		}
 
 		return BN254HashOut(returnVal)

@@ -7,13 +7,13 @@ )
 
 const HALF_N_FULL_ROUNDS = 4
 const N_PARTIAL_ROUNDS = 22
-const MAX_WIDTH = 12
 const SPONGE_WIDTH = 12
 const SPONGE_RATE = 8
+const POSEIDON_GL_HASH_SIZE = 4
 
 type GoldilocksState = [SPONGE_WIDTH]gl.Variable
 type GoldilocksStateExtension = [SPONGE_WIDTH]gl.QuadraticExtensionVariable
-type GoldilocksHashOut = [4]gl.Variable
+type GoldilocksHashOut = [POSEIDON_GL_HASH_SIZE]gl.Variable
 
 type GoldilocksChip struct {
 	api frontend.API `gnark:"-"`
@@ -77,8 +77,8 @@ for i := 0; i < len(input); i++ {
 		inputVars = append(inputVars, c.gl.Reduce(input[i]))
 	}
 
-	outputVars := c.HashNToMNoPad(inputVars, 4)
-	for i := 0; i < 4; i++ {
+	outputVars := c.HashNToMNoPad(inputVars, len(hash))
+	for i := 0; i < len(hash); i++ {
 		hash[i] = outputVars[i]
 	}
 
@@ -118,7 +118,7 @@ func (c *GoldilocksChip) constantLayer(state GoldilocksState, roundCounter *int) GoldilocksState {
 	for i := 0; i < 12; i++ {
 		if i < SPONGE_WIDTH {
 			roundConstant := ALL_ROUND_CONSTANTS[i+SPONGE_WIDTH*(*roundCounter)]
-			state[i] = c.gl.MulAdd(state[i], gl.NewVariable(1), gl.NewVariable(roundConstant))
+			state[i] = c.gl.Add(state[i], gl.NewVariable(roundConstant))
 		}
 	}
 	return state
@@ -169,7 +169,7 @@ }
 	return state
 }
 
-func (c *GoldilocksChip) mdsRowShf(r int, v [SPONGE_WIDTH]gl.Variable) gl.Variable {
+func (c *GoldilocksChip) mdsRowShf(r int, v GoldilocksState) gl.Variable {
 	res := gl.Zero()
 
 	for i := 0; i < 12; i++ {
@@ -182,7 +182,7 @@ res = c.gl.MulAddNoReduce(v[r], gl.NewVariable(MDS_MATRIX_DIAG_VARS[r]), res)
 	return c.gl.Reduce(res)
 }
 
-func (c *GoldilocksChip) MdsRowShfExtension(r int, v [SPONGE_WIDTH]gl.QuadraticExtensionVariable) gl.QuadraticExtensionVariable {
+func (c *GoldilocksChip) MdsRowShfExtension(r int, v GoldilocksStateExtension) gl.QuadraticExtensionVariable {
 	res := gl.ZeroExtension()
 
 	for i := 0; i < 12; i++ {
@@ -251,7 +251,7 @@
 func (c *GoldilocksChip) mdsPartialLayerInit(state GoldilocksState) GoldilocksState {
 	var result GoldilocksState
 	for i := 0; i < 12; i++ {
-		result[i] = gl.NewVariable(0)
+		result[i] = gl.Zero()
 	}
 
 	result[0] = state[0]

@@ -118,5 +118,10 @@ commonCircuitData.NumPublicInputs = raw.NumPublicInputs
 	commonCircuitData.KIs = raw.KIs
 	commonCircuitData.NumPartialProducts = raw.NumPartialProducts
 
+	// Don't support circuits that have hiding enabled
+	if raw.FriParams.Hiding {
+		panic("Circuit has hiding enabled, which is not supported")
+	}
+
 	return commonCircuitData
 }

@@ -1,21 +0,0 @@
-package types
-
-func ReductionArityBits(
-	arityBits uint64,
-	finalPolyBits uint64,
-	degreeBits uint64,
-	rateBits uint64,
-	capHeight uint64,
-) []uint64 {
-	returnArr := make([]uint64, 0)
-
-	for degreeBits > finalPolyBits && degreeBits+rateBits-arityBits >= capHeight {
-		returnArr = append(returnArr, arityBits)
-		if degreeBits < arityBits {
-			panic("degreeBits < arityBits")
-		}
-		degreeBits -= arityBits
-	}
-
-	return returnArr
-}

@@ -12,18 +12,6 @@ PartialProducts []gl.QuadraticExtensionVariable // Length = CommonCircuitData.NumChallenges * CommonCircuitData.NumPartialProducts
 	QuotientPolys   []gl.QuadraticExtensionVariable // Length = CommonCircuitData.NumChallenges * CommonCircuitData.QuotientDegreeFactor
 }
 
-func NewOpeningSet(numConstants uint64, numRoutedWires uint64, numWires uint64, numChallenges uint64, numPartialProducts uint64, quotientDegreeFactor uint64) OpeningSet {
-	return OpeningSet{
-		Constants:       make([]gl.QuadraticExtensionVariable, numConstants),
-		PlonkSigmas:     make([]gl.QuadraticExtensionVariable, numRoutedWires),
-		Wires:           make([]gl.QuadraticExtensionVariable, numWires),
-		PlonkZs:         make([]gl.QuadraticExtensionVariable, numChallenges),
-		PlonkZsNext:     make([]gl.QuadraticExtensionVariable, numChallenges),
-		PartialProducts: make([]gl.QuadraticExtensionVariable, numChallenges*numPartialProducts),
-		QuotientPolys:   make([]gl.QuadraticExtensionVariable, numChallenges*quotientDegreeFactor),
-	}
-}
-
 type ProofChallenges struct {
 	PlonkBetas    []gl.Variable
 	PlonkGammas   []gl.Variable

@@ -76,7 +76,6 @@ FriChallenges: challenger.GetFriChallenges(
 			proof.OpeningProof.CommitPhaseMerkleCaps,
 			proof.OpeningProof.FinalPoly,
 			proof.OpeningProof.PowWitness,
-			c.commonData.DegreeBits,
 			config.FriConfig,
 		),
 	}
@@ -119,8 +118,10 @@ }
 
 	// Range check the openings proof.
 	for _, queryRound := range proof.OpeningProof.QueryRoundProofs {
-		for _, initialTreesElement := range queryRound.InitialTreesProof.EvalsProofs[0].Elements {
-			c.glChip.RangeCheck(initialTreesElement)
+		for _, evalsProof := range queryRound.InitialTreesProof.EvalsProofs {
+			for _, evalsProofElement := range evalsProof.Elements {
+				c.glChip.RangeCheck(evalsProofElement)
+			}
 		}
 
 		for _, queryStep := range queryRound.Steps {