Multi-constraint Relations (AztecProtocol/barretenberg#444)

Allow for correct and efficient batching over identities in the Sumcheck relation

circuits/cpp/barretenberg/cpp/src/barretenberg/honk/composer/standard_honk_composer.test.cpp

@@ -1,13 +1,12 @@
 #include "standard_honk_composer.hpp"
-#include "barretenberg/honk/sumcheck/relations/relation.hpp"
+#include "barretenberg/honk/sumcheck/relations/relation_parameters.hpp"
 #include "barretenberg/numeric/uint256/uint256.hpp"
 #include <cstddef>
 #include <cstdint>
 #include <vector>
 #include "barretenberg/honk/proof_system/prover.hpp"
 #include "barretenberg/honk/sumcheck/sumcheck_round.hpp"
-#include "barretenberg/honk/sumcheck/relations/grand_product_computation_relation.hpp"
-#include "barretenberg/honk/sumcheck/relations/grand_product_initialization_relation.hpp"
+#include "barretenberg/honk/sumcheck/relations/permutation_relation.hpp"
 #include "barretenberg/polynomials/polynomial.hpp"
 
 #pragma GCC diagnostic ignored "-Wunused-variable"

circuits/cpp/barretenberg/cpp/src/barretenberg/honk/composer/ultra_honk_composer.test.cpp

@@ -1,14 +1,13 @@
 #include "ultra_honk_composer.hpp"
 #include "barretenberg/common/log.hpp"
 #include "barretenberg/honk/proof_system/ultra_prover.hpp"
-#include "barretenberg/honk/sumcheck/relations/relation.hpp"
+#include "barretenberg/honk/sumcheck/relations/relation_parameters.hpp"
 #include "barretenberg/numeric/uint256/uint256.hpp"
 #include <cstddef>
 #include <cstdint>
 #include "barretenberg/honk/proof_system/prover.hpp"
 #include "barretenberg/honk/sumcheck/sumcheck_round.hpp"
-#include "barretenberg/honk/sumcheck/relations/grand_product_computation_relation.hpp"
-#include "barretenberg/honk/sumcheck/relations/grand_product_initialization_relation.hpp"
+#include "barretenberg/honk/sumcheck/relations/permutation_relation.hpp"
 #include "barretenberg/honk/utils/grand_product_delta.hpp"
 #include "barretenberg/proof_system/plookup_tables/types.hpp"
 
@@ -649,7 +648,6 @@ TEST(UltraHonkComposer, non_native_field_multiplication)
 
     fq a = fq::random_element();
     fq b = fq::random_element();
-
     uint256_t modulus = fq::modulus;
 
     uint1024_t a_big = uint512_t(uint256_t(a));

circuits/cpp/barretenberg/cpp/src/barretenberg/honk/flavor/standard.hpp

@@ -10,8 +10,7 @@
 #include "barretenberg/honk/sumcheck/polynomials/univariate.hpp"
 #include "barretenberg/ecc/curves/bn254/g1.hpp"
 #include "barretenberg/honk/sumcheck/relations/arithmetic_relation.hpp"
-#include "barretenberg/honk/sumcheck/relations/grand_product_computation_relation.hpp"
-#include "barretenberg/honk/sumcheck/relations/grand_product_initialization_relation.hpp"
+#include "barretenberg/honk/sumcheck/relations/permutation_relation.hpp"
 #include "barretenberg/honk/transcript/transcript.hpp"
 #include "barretenberg/plonk/proof_system/proving_key/proving_key.hpp"
 #include "barretenberg/polynomials/evaluation_domain.hpp"
@@ -53,17 +52,20 @@ class Standard {
     static constexpr size_t NUM_WITNESS_ENTITIES = 4;
 
     // define the tuple of Relations that comprise the Sumcheck relation
-    using Relations = std::tuple<sumcheck::ArithmeticRelation<FF>,
-                                 sumcheck::GrandProductComputationRelation<FF>,
-                                 sumcheck::GrandProductInitializationRelation<FF>>;
+    using Relations = std::tuple<sumcheck::ArithmeticRelation<FF>, sumcheck::PermutationRelation<FF>>;
 
     static constexpr size_t MAX_RELATION_LENGTH = get_max_relation_length<Relations>();
     static constexpr size_t NUM_RELATIONS = std::tuple_size<Relations>::value;
 
-    // define the container for storing the univariate contribution from each relation in Sumcheck
-    using UnivariateTuple = decltype(create_univariate_tuple<FF, Relations>());
+    // Instantiate the BarycentricData needed to extend each Relation Univariate
+    static_assert(instantiate_barycentric_utils<FF, MAX_RELATION_LENGTH>());
+
+    // define the containers for storing the contributions from each relation in Sumcheck
+    using RelationUnivariates = decltype(create_relation_univariates_container<FF, Relations>());
+    using RelationValues = decltype(create_relation_values_container<FF, Relations>());
+
     // define utilities to extend univarates from RELATION_LENGTH to MAX_RELATION_LENGTH for each Relation
-    using BarycentricUtils = decltype(create_barycentric_utils<FF, Relations, MAX_RELATION_LENGTH>());
+    // using BarycentricUtils = decltype(create_barycentric_utils<FF, Relations, MAX_RELATION_LENGTH>());
 
   private:
     /**

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

@@ -17,10 +17,8 @@
 #include "barretenberg/srs/reference_string/reference_string.hpp"
 #include "barretenberg/proof_system/flavor/flavor.hpp"
 #include "barretenberg/honk/sumcheck/relations/ultra_arithmetic_relation.hpp"
-#include "barretenberg/honk/sumcheck/relations/ultra_arithmetic_relation_secondary.hpp"
-#include "barretenberg/honk/sumcheck/relations/grand_product_computation_relation.hpp"
-#include "barretenberg/honk/sumcheck/relations/grand_product_initialization_relation.hpp"
-#include "barretenberg/honk/sumcheck/relations/lookup_grand_product_relation.hpp"
+#include "barretenberg/honk/sumcheck/relations/permutation_relation.hpp"
+#include "barretenberg/honk/sumcheck/relations/lookup_relation.hpp"
 #include "barretenberg/honk/sumcheck/relations/gen_perm_sort_relation.hpp"
 #include "barretenberg/honk/sumcheck/relations/elliptic_relation.hpp"
 #include "barretenberg/honk/sumcheck/relations/auxiliary_relation.hpp"
@@ -52,22 +50,21 @@ class Ultra {
 
     // define the tuple of Relations that comprise the Sumcheck relation
     using Relations = std::tuple<sumcheck::UltraArithmeticRelation<FF>,
-                                 sumcheck::UltraArithmeticRelationSecondary<FF>,
-                                 sumcheck::UltraGrandProductComputationRelation<FF>,
-                                 sumcheck::UltraGrandProductInitializationRelation<FF>,
-                                 sumcheck::LookupGrandProductComputationRelation<FF>,
-                                 sumcheck::LookupGrandProductInitializationRelation<FF>,
+                                 sumcheck::UltraPermutationRelation<FF>,
+                                 sumcheck::LookupRelation<FF>,
                                  sumcheck::GenPermSortRelation<FF>,
                                  sumcheck::EllipticRelation<FF>,
                                  sumcheck::AuxiliaryRelation<FF>>;
 
     static constexpr size_t MAX_RELATION_LENGTH = get_max_relation_length<Relations>();
     static constexpr size_t NUM_RELATIONS = std::tuple_size<Relations>::value;
 
+    // Instantiate the BarycentricData needed to extend each Relation Univariate
+    static_assert(instantiate_barycentric_utils<FF, MAX_RELATION_LENGTH>());
+
     // define the container for storing the univariate contribution from each relation in Sumcheck
-    using UnivariateTuple = decltype(create_univariate_tuple<FF, Relations>());
-    // define utilities to extend univarates from RELATION_LENGTH to MAX_RELATION_LENGTH for each Relation
-    using BarycentricUtils = decltype(create_barycentric_utils<FF, Relations, MAX_RELATION_LENGTH>());
+    using RelationUnivariates = decltype(create_relation_univariates_container<FF, Relations>());
+    using RelationValues = decltype(create_relation_values_container<FF, Relations>());
 
   private:
     template <typename DataType, typename HandleType>

circuits/cpp/barretenberg/cpp/src/barretenberg/honk/proof_system/ultra_prover.hpp

@@ -6,7 +6,7 @@
 #include "barretenberg/honk/pcs/kzg/kzg.hpp"
 #include "barretenberg/honk/transcript/transcript.hpp"
 #include "barretenberg/honk/flavor/ultra.hpp"
-#include "barretenberg/honk/sumcheck/relations/relation.hpp"
+#include "barretenberg/honk/sumcheck/relations/relation_parameters.hpp"
 #include "barretenberg/honk/sumcheck/sumcheck_output.hpp"
 
 namespace proof_system::honk {

circuits/cpp/barretenberg/cpp/src/barretenberg/honk/sumcheck/relations/arithmetic_relation.hpp

@@ -3,7 +3,7 @@
 #include <tuple>
 
 #include "../polynomials/univariate.hpp"
-#include "relation.hpp"
+#include "relation_parameters.hpp"
 
 namespace proof_system::honk::sumcheck {
 
@@ -12,6 +12,12 @@ template <typename FF> class ArithmeticRelation {
     // 1 + polynomial degree of this relation
     static constexpr size_t RELATION_LENGTH = 4;
 
+    static constexpr size_t NUM_CONSTRAINTS = 1;
+    static constexpr std::array<size_t, NUM_CONSTRAINTS> CONSTRAINT_LENGTH = { 4 };
+
+    using RelationUnivariates = std::tuple<Univariate<FF, CONSTRAINT_LENGTH[0]>>;
+    using RelationValues = std::array<FF, NUM_CONSTRAINTS>;
+
     /**
      * @brief Expression for the StandardArithmetic gate.
      * @details The relation is defined as C(extended_edges(X)...) =
@@ -22,7 +28,7 @@ template <typename FF> class ArithmeticRelation {
      * @param parameters contains beta, gamma, and public_input_delta, ....
      * @param scaling_factor optional term to scale the evaluation before adding to evals.
      */
-    void add_edge_contribution(Univariate<FF, RELATION_LENGTH>& evals,
+    void add_edge_contribution(RelationUnivariates& evals,
                                const auto& extended_edges,
                                const RelationParameters<FF>&,
                                const FF& scaling_factor) const
@@ -44,10 +50,17 @@ template <typename FF> class ArithmeticRelation {
         tmp += q_o * w_o;
         tmp += q_c;
         tmp *= scaling_factor;
-        evals += tmp;
+        std::get<0>(evals) += tmp;
     };
 
-    void add_full_relation_value_contribution(FF& full_honk_relation_value,
+    /**
+     * @brief Add the result of each identity in this relation evaluated at the multivariate evaluations produced by the
+     * Sumcheck Prover.
+     *
+     * @param full_honk_relation_value
+     * @param purported_evaluations
+     */
+    void add_full_relation_value_contribution(RelationValues& full_honk_relation_value,
                                               const auto& purported_evaluations,
                                               const RelationParameters<FF>&) const
     {
@@ -60,10 +73,10 @@ template <typename FF> class ArithmeticRelation {
         auto q_o = purported_evaluations.q_o;
         auto q_c = purported_evaluations.q_c;
 
-        full_honk_relation_value += w_l * (q_m * w_r + q_l);
-        full_honk_relation_value += q_r * w_r;
-        full_honk_relation_value += q_o * w_o;
-        full_honk_relation_value += q_c;
+        std::get<0>(full_honk_relation_value) += w_l * (q_m * w_r + q_l);
+        std::get<0>(full_honk_relation_value) += q_r * w_r;
+        std::get<0>(full_honk_relation_value) += q_o * w_o;
+        std::get<0>(full_honk_relation_value) += q_c;
     };
 };
 } // namespace proof_system::honk::sumcheck