feat: protogalaxy perturbator! (#2624)

This PR implements the power perturbator polynomial (F(X) in the paper),
following the tree technique in the paper, allowing computation of the
polynomial in coefficient form in O(N) time where N is the size of the
instance. Resolves
[#693](#693) and
[#687](#687)

The relation-related functionality from sumcheck that is now used in
both sumcheck and PG has been moved in a shared `RelationUtils` file

cpp/src/barretenberg/honk/flavor/ecc_vm.hpp

@@ -656,7 +656,8 @@ template <typename CycleGroup_T, typename Curve_T, typename PCS_T> class ECCVMBa
     using FoldedPolynomials = AllEntities<std::vector<FF>, PolynomialHandle>;
 
     /**
-     * @brief A field element for each entity of the flavor.
+     * @brief A field element for each entity of the flavor.  These entities represent the prover polynomials evaluated
+     * at one point.
      */
     class AllValues : public AllEntities<FF, FF> {
       public:
@@ -678,7 +679,7 @@ template <typename CycleGroup_T, typename Curve_T, typename PCS_T> class ECCVMBa
      */
     class AllPolynomials : public AllEntities<Polynomial, PolynomialHandle> {
       public:
-        AllValues get_row(const size_t row_idx)
+        AllValues get_row(const size_t row_idx) const
         {
             AllValues result;
             size_t column_idx = 0; // // TODO(https://github.com/AztecProtocol/barretenberg/issues/391) zip
@@ -720,10 +721,14 @@ template <typename CycleGroup_T, typename Curve_T, typename PCS_T> class ECCVMBa
                                       barretenberg::Univariate<FF, MAX_RELATION_LENGTH>>;
 
     /**
-     * @brief A container for polynomials handles; only stores spans.
+     * @brief A container for the prover polynomials handles; only stores spans.
      */
     class ProverPolynomials : public AllEntities<PolynomialHandle, PolynomialHandle> {
       public:
+        /**
+         * @brief Returns the evaluations of all prover polynomials at one point on the boolean hypercube, which
+         * represents one row in the execution trace.
+         */
         AllValues get_row(const size_t row_idx)
         {
             AllValues result;

cpp/src/barretenberg/honk/flavor/goblin_ultra.hpp

@@ -302,11 +302,6 @@ class GoblinUltra {
      */
     using VerificationKey = VerificationKey_<PrecomputedEntities<Commitment, CommitmentHandle>>;
 
-    /**
-     * @brief A container for polynomials handles; only stores spans.
-     */
-    using ProverPolynomials = AllEntities<PolynomialHandle, PolynomialHandle>;
-
     /**
      * @brief A container for storing the partially evaluated multivariates produced by sumcheck.
      */
@@ -332,7 +327,8 @@ class GoblinUltra {
                                       barretenberg::Univariate<FF, MAX_RELATION_LENGTH>>;
 
     /**
-     * @brief A field element for each entity of the flavor.
+     * @brief A field element for each entity of the flavor. These entities represent the prover polynomials evaluated
+     * at one point.
      */
     class AllValues : public AllEntities<FF, FF> {
       public:
@@ -341,6 +337,23 @@ class GoblinUltra {
         AllValues(std::array<FF, NUM_ALL_ENTITIES> _data_in) { this->_data = _data_in; }
     };
 
+    /**
+     * @brief A container for the prover polynomials handles; only stores spans.
+     */
+    class ProverPolynomials : public AllEntities<PolynomialHandle, PolynomialHandle> {
+      public:
+        AllValues get_row(const size_t row_idx) const
+        {
+            AllValues result;
+            size_t column_idx = 0; // TODO(https://github.com/AztecProtocol/barretenberg/issues/391) zip
+            for (auto& column : this->_data) {
+                result[column_idx] = column[row_idx];
+                column_idx++;
+            }
+            return result;
+        }
+    };
+
     /**
      * @brief A container for commitment labels.
      * @note It's debatable whether this should inherit from AllEntities. since most entries are not strictly needed. It
@@ -429,7 +442,7 @@ class GoblinUltra {
 
     class FoldingParameters {
       public:
-        FF gate_separation_challenge;
+        std::vector<FF> gate_separation_challenges;
         FF target_sum;
     };
 };

cpp/src/barretenberg/honk/flavor/goblin_ultra_recursive.hpp

@@ -343,7 +343,8 @@ template <typename BuilderType> class GoblinUltraRecursive_ {
     };
 
     /**
-     * @brief A field element for each entity of the flavor.
+     * @brief A field element for each entity of the flavor. These entities represent the prover polynomials evaluated
+     * at one point.
      */
     class AllValues : public AllEntities<FF, FF> {
       public:

cpp/src/barretenberg/honk/flavor/ultra.hpp

@@ -272,7 +272,8 @@ class Ultra {
     using VerificationKey = VerificationKey_<PrecomputedEntities<Commitment, CommitmentHandle>>;
 
     /**
-     * @brief A field element for each entity of the flavor.
+     * @brief A field element for each entity of the flavor. These entities represent the prover polynomials evaluated
+     * at one point.
      */
     class AllValues : public AllEntities<FF, FF> {
       public:
@@ -286,7 +287,7 @@ class Ultra {
      */
     class ProverPolynomials : public AllEntities<PolynomialHandle, PolynomialHandle> {
       public:
-        AllValues get_row(const size_t row_idx)
+        AllValues get_row(const size_t row_idx) const
         {
             AllValues result;
             size_t column_idx = 0; // TODO(https://github.com/AztecProtocol/barretenberg/issues/391) zip
@@ -404,7 +405,7 @@ class Ultra {
 
     class FoldingParameters {
       public:
-        FF gate_separation_challenge;
+        std::vector<FF> gate_separation_challenges;
         FF target_sum;
     };
 };

cpp/src/barretenberg/honk/flavor/ultra_recursive.hpp

@@ -308,7 +308,8 @@ template <typename BuilderType> class UltraRecursive_ {
     };
 
     /**
-     * @brief A field element for each entity of the flavor.
+     * @brief A field element for each entity of the flavor. These entities represent the prover polynomials evaluated
+     * at one point.
      */
     class AllValues : public AllEntities<FF, FF> {
       public:

cpp/src/barretenberg/honk/instance/instances.hpp

@@ -11,7 +11,7 @@ template <typename Flavor_, size_t NUM_> struct ProverInstances_ {
   public:
     static constexpr size_t NUM = NUM_;
     ArrayType _data;
-    Instance const& operator[](size_t idx) const { return _data[idx]; }
+    std::shared_ptr<Instance> const& operator[](size_t idx) const { return _data[idx]; }
     typename ArrayType::iterator begin() { return _data.begin(); };
     typename ArrayType::iterator end() { return _data.end(); };
     ProverInstances_(std::vector<std::shared_ptr<Instance>> data)
@@ -27,12 +27,12 @@ template <typename Flavor_, size_t NUM_> struct VerifierInstances_ {
     using Flavor = Flavor_;
     using VerificationKey = typename Flavor::VerificationKey;
     using Instance = VerifierInstance_<Flavor>;
-    using ArrayType = std::array<Instance, NUM_>;
+    using ArrayType = std::array<std::shared_ptr<Instance>, NUM_>;
 
   public:
     static constexpr size_t NUM = NUM_;
     ArrayType _data;
-    Instance const& operator[](size_t idx) const { return _data[idx]; }
+    std::shared_ptr<Instance> const& operator[](size_t idx) const { return _data[idx]; }
     typename ArrayType::iterator begin() { return _data.begin(); };
     typename ArrayType::iterator end() { return _data.end(); };
     VerifierInstances_(std::vector<std::shared_ptr<VerificationKey>> vks)
@@ -41,7 +41,7 @@ template <typename Flavor_, size_t NUM_> struct VerifierInstances_ {
         for (size_t idx = 0; idx < vks.size(); idx++) {
             Instance inst;
             inst.verification_key = std::move(vks[idx]);
-            _data[idx] = inst;
+            _data[idx] = std::make_unique<Instance>(inst);
         }
     };
 };

cpp/src/barretenberg/honk/instance/prover_instance.hpp

@@ -28,8 +28,6 @@ template <class Flavor> class ProverInstance_ {
     using Polynomial = typename Flavor::Polynomial;
 
   public:
-    // offset due to placing zero wires at the start of execution trace
-
     std::shared_ptr<ProvingKey> proving_key;
     std::shared_ptr<VerificationKey> verification_key;
     std::shared_ptr<CommitmentKey> commitment_key;
@@ -39,10 +37,14 @@ template <class Flavor> class ProverInstance_ {
     // The number of public inputs has to be the same for all instances because they are
     // folded element by element.
     std::vector<FF> public_inputs;
+    // offset due to placing zero wires at the start of execution trace
+    // non-zero  for Instances constructed from circuits, this concept doesn't exist for accumulated
+    // instances
     size_t pub_inputs_offset = 0;
     proof_system::RelationParameters<FF> relation_parameters;
     std::vector<uint32_t> recursive_proof_public_input_indices;
-    FoldingParameters folding_params;
+    // non-empty for the accumulated instances
+    FoldingParameters folding_parameters;
 
     ProverInstance_(Circuit& circuit)
     {
@@ -55,7 +57,7 @@ template <class Flavor> class ProverInstance_ {
         : verification_key(std::move(result.verification_key))
         , prover_polynomials(result.folded_prover_polynomials)
         , public_inputs(result.folded_public_inputs)
-        , folding_params(result.params){};
+        , folding_parameters(result.folding_parameters){};
 
     ~ProverInstance_() = default;
 

cpp/src/barretenberg/honk/instance/verifier_instance.hpp

@@ -12,7 +12,7 @@ template <class Flavor> class VerifierInstance_ {
     std::vector<FF> public_inputs;
     size_t pub_inputs_offset;
     size_t public_input_size;
-    size_t circuit_size;
+    size_t instance_size;
     RelationParameters<FF> relation_parameters;
     FoldingParameters folding_params;
 };

cpp/src/barretenberg/honk/proof_system/folding_result.hpp

@@ -1,5 +1,6 @@
 #pragma once
 #include "barretenberg/proof_system/flavor/flavor.hpp"
+#include "barretenberg/proof_system/relations/relation_parameters.hpp"
 namespace proof_system::honk {
 template <class Flavor> struct ProverFoldingResult {
   public:
@@ -33,6 +34,6 @@ template <class Flavor> struct FoldingResult {
     ProverPolynomials folded_prover_polynomials;
     std::vector<FF> folded_public_inputs;
     std::shared_ptr<VerificationKey> verification_key;
-    FoldingParameters params;
+    FoldingParameters folding_parameters;
 };
 } // namespace proof_system::honk