chore: included subrelation witness degrees in the relations relevant…

… to zk-sumcheck (#7479)

The subrelation witness degrees are used in zk-sumcheck and affect the
sizes of the univariates in the SumcheckTupleOfTuplesOfUnivariates as
well as the sizes of the sumcheck round univariates.

In several relations, I used upper bounds on the witness degrees which
are simply given by the corresponding subrelation's length - 1.
Indicated explicitly that those are upper bounds. Computed the precise
constants for the relations relevant to Mega.

The auxiliary and logderiv_lookup_relation contain a trick allowing to
re-use the values accumulated by an accumulator of a different size
using ShortView.

barretenberg/cpp/src/barretenberg/relations/auxiliary_relation.hpp

@@ -39,6 +39,21 @@ template <typename FF_> class AuxiliaryRelationImpl {
         6, // RAM consistency sub-relation 2
         6  // RAM consistency sub-relation 3
     };
+    /**
+     * @brief For ZK-Flavors: The degrees of subrelations considered as polynomials only in witness polynomials,
+     * i.e. all selectors and public polynomials are treated as constants.
+     *
+     */
+    static constexpr std::array<size_t, 6> SUBRELATION_WITNESS_DEGREES{
+        2, // auxiliary sub-relation;
+        2, // ROM consistency sub-relation 1: adjacent values match if adjacent indices match and next access is a read
+           // operation
+        2, // ROM consistency sub-relation 2: index is monotonously increasing
+        3, // RAM consistency sub-relation 1: adjacent values match if adjacent indices match and next access is a read
+           // operation
+        2, // RAM consistency sub-relation 2: index is monotonously increasing
+        2  // RAM consistency sub-relation 3: next gate access type is boolean
+    };
 
     static constexpr std::array<size_t, 6> TOTAL_LENGTH_ADJUSTMENTS{
         1, // auxiliary sub-relation
@@ -96,9 +111,13 @@ template <typename FF_> class AuxiliaryRelationImpl {
                                   const FF& scaling_factor)
     {
         BB_OP_COUNT_TIME_NAME("Auxiliary::accumulate");
-        // All subrelations have the same length so we use the same length view for all calculations
-        using Accumulator = typename std::tuple_element_t<0, ContainerOverSubrelations>;
+        // declare the accumulator of the maximum length, in non-ZK Flavors, they are of the same length,
+        // whereas in ZK Flavors, the accumulator corresponding to RAM consistency sub-relation 1 is the longest
+        using Accumulator = typename std::tuple_element_t<3, ContainerOverSubrelations>;
         using View = typename Accumulator::View;
+        // allows to re-use the values accumulated by accumulators of the sizes smaller or equal to
+        // the size of Accumulator declared above
+        using ShortView = typename std::tuple_element_t<0, ContainerOverSubrelations>::View;
         using ParameterView = GetParameterView<Parameters, View>;
 
         const auto& eta = ParameterView(params.eta);
@@ -260,9 +279,10 @@ template <typename FF_> class AuxiliaryRelationImpl {
         auto q_one_by_two_by_aux_by_scaling = q_one_by_two * q_aux_by_scaling;
 
         std::get<1>(accumulators) +=
-            adjacent_values_match_if_adjacent_indices_match * q_one_by_two_by_aux_by_scaling;            // deg 5
-        std::get<2>(accumulators) += index_is_monotonically_increasing * q_one_by_two_by_aux_by_scaling; // deg 5
-        auto ROM_consistency_check_identity = memory_record_check * q_one_by_two;                        // deg 3 or 4
+            ShortView(adjacent_values_match_if_adjacent_indices_match * q_one_by_two_by_aux_by_scaling); // deg 5
+        std::get<2>(accumulators) +=
+            ShortView(index_is_monotonically_increasing * q_one_by_two_by_aux_by_scaling); // deg 5
+        auto ROM_consistency_check_identity = memory_record_check * q_one_by_two;          // deg 3 or 4
 
         /**
          * RAM Consistency Check
@@ -308,10 +328,12 @@ template <typename FF_> class AuxiliaryRelationImpl {
         // Putting it all together...
         std::get<3>(accumulators) +=
             adjacent_values_match_if_adjacent_indices_match_and_next_access_is_a_read_operation *
-            q_arith_by_aux_and_scaling;                                                              // deg 5 or 6
-        std::get<4>(accumulators) += index_is_monotonically_increasing * q_arith_by_aux_and_scaling; // deg 4
-        std::get<5>(accumulators) += next_gate_access_type_is_boolean * q_arith_by_aux_and_scaling;  // deg 4 or 6
-        auto RAM_consistency_check_identity = access_check * (q_arith);                              // deg 3 or 5
+            q_arith_by_aux_and_scaling; // deg 5 or 6
+        std::get<4>(accumulators) += ShortView(index_is_monotonically_increasing * q_arith_by_aux_and_scaling); // deg 4
+        std::get<5>(accumulators) +=
+            ShortView(next_gate_access_type_is_boolean * q_arith_by_aux_and_scaling); // deg 4 or 6
+
+        auto RAM_consistency_check_identity = access_check * (q_arith); // deg 3 or 5
 
         /**
          * RAM Timestamp Consistency Check
@@ -339,7 +361,7 @@ template <typename FF_> class AuxiliaryRelationImpl {
         // (deg 3 or 5) + (deg 4) + (deg 3)
         auto auxiliary_identity = memory_identity + non_native_field_identity + limb_accumulator_identity;
         auxiliary_identity *= q_aux_by_scaling; // deg 5 or 6
-        std::get<0>(accumulators) += auxiliary_identity;
+        std::get<0>(accumulators) += ShortView(auxiliary_identity);
     };
 };
 

barretenberg/cpp/src/barretenberg/relations/databus_lookup_relation.hpp

@@ -57,6 +57,19 @@ template <typename FF_> class DatabusLookupRelationImpl {
         LENGTH  // log-derivative lookup argument subrelation
     };
 
+    /**
+     * @brief For ZK-Flavors: Upper bound on the degrees of subrelations considered as polynomials only in witness
+polynomials,
+     * i.e. all selectors and public polynomials are treated as constants. The subrelation witness degree does not
+     * exceed the subrelation partial degree, which is given by LENGTH - 1 in this case.
+     */
+    static constexpr std::array<size_t, NUM_BUS_COLUMNS * 2> SUBRELATION_WITNESS_DEGREES{
+        LENGTH - 1, // inverse polynomial correctness subrelation
+        LENGTH - 1, // log-derivative lookup argument subrelation
+        LENGTH - 1, // inverse polynomial correctness subrelation
+        LENGTH - 1  // log-derivative lookup argument subrelation
+    };
+
     // The lookup subrelations are "linearly dependent" in the sense that they establish the value of a sum across the
     // entire execution trace rather than a per-row identity.
     static constexpr std::array<bool, NUM_BUS_COLUMNS* 2> SUBRELATION_LINEARLY_INDEPENDENT = {
@@ -290,4 +303,4 @@ template <typename FF_> class DatabusLookupRelationImpl {
 
 template <typename FF> using DatabusLookupRelation = Relation<DatabusLookupRelationImpl<FF>>;
 
-} // namespace bb
+} // namespace bb

barretenberg/cpp/src/barretenberg/relations/delta_range_constraint_relation.hpp

@@ -13,6 +13,17 @@ template <typename FF_> class DeltaRangeConstraintRelationImpl {
         6, // range constrain sub-relation 3
         6  // range constrain sub-relation 4
     };
+    /**
+     * @brief For ZK-Flavors: The degrees of subrelations considered as polynomials only in witness polynomials,
+     * i.e. all selectors and public polynomials are treated as constants.
+     *
+     */
+    static constexpr std::array<size_t, 4> SUBRELATION_WITNESS_DEGREES{
+        3, // range constrain sub-relation 1
+        3, // range constrain sub-relation 2
+        3, // range constrain sub-relation 3
+        3  // range constrain sub-relation 4
+    };
 
     /**
      * @brief Returns true if the contribution from all subrelations for the provided inputs is identically zero
@@ -95,4 +106,4 @@ template <typename FF_> class DeltaRangeConstraintRelationImpl {
 
 template <typename FF> using DeltaRangeConstraintRelation = Relation<DeltaRangeConstraintRelationImpl<FF>>;
 
-} // namespace bb
+} // namespace bb

barretenberg/cpp/src/barretenberg/relations/ecc_op_queue_relation.hpp

@@ -17,6 +17,21 @@ template <typename FF_> class EccOpQueueRelationImpl {
         3, // op-queue-wire vanishes sub-relation 3
         3  // op-queue-wire vanishes sub-relation 4
     };
+    /**
+     * @brief For ZK-Flavors: The degrees of subrelations considered as polynomials only in witness polynomials,
+     * i.e. all selectors and public polynomials are treated as constants.
+     *
+     */
+    static constexpr std::array<size_t, 8> SUBRELATION_WITNESS_DEGREES{
+        1, // wire - op-queue-wire consistency sub-relation 1
+        1, // wire - op-queue-wire consistency sub-relation 2
+        1, // wire - op-queue-wire consistency sub-relation 3
+        1, // wire - op-queue-wire consistency sub-relation 4
+        1, // op-queue-wire vanishes sub-relation 1
+        1, // op-queue-wire vanishes sub-relation 2
+        1, // op-queue-wire vanishes sub-relation 3
+        1  // op-queue-wire vanishes sub-relation 4
+    };
 
     template <typename AllEntities> inline static bool skip([[maybe_unused]] const AllEntities& in)
     {
@@ -108,4 +123,4 @@ template <typename FF_> class EccOpQueueRelationImpl {
 
 template <typename FF> using EccOpQueueRelation = Relation<EccOpQueueRelationImpl<FF>>;
 
-} // namespace bb
+} // namespace bb

barretenberg/cpp/src/barretenberg/relations/ecc_vm/ecc_bools_relation.hpp

@@ -20,6 +20,15 @@ template <typename FF_> class ECCVMBoolsRelationImpl {
     static constexpr std::array<size_t, 19> SUBRELATION_PARTIAL_LENGTHS{
         3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
     };
+    /**
+     * @brief For ZK-Flavors: Upper bound on the degrees of subrelations considered as polynomials only in witness
+polynomials,
+     * i.e. all selectors and public polynomials are treated as constants. The subrelation witness degree does not
+     * exceed the subrelation partial degree given by SUBRELATION_PARTIAL_LENGTH - 1.
+     */
+    static constexpr std::array<size_t, 19> SUBRELATION_WITNESS_DEGREES{
+        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
+    };
 
     template <typename ContainerOverSubrelations, typename AllEntities, typename Parameters>
     static void accumulate(ContainerOverSubrelations& accumulator,
@@ -30,4 +39,4 @@ template <typename FF_> class ECCVMBoolsRelationImpl {
 
 template <typename FF> using ECCVMBoolsRelation = Relation<ECCVMBoolsRelationImpl<FF>>;
 
-} // namespace bb
+} // namespace bb

barretenberg/cpp/src/barretenberg/relations/ecc_vm/ecc_lookup_relation.hpp

@@ -21,6 +21,16 @@ template <typename FF_> class ECCVMLookupRelationImpl {
         LENGTH, // grand product construction sub-relation
         LENGTH  // left-shiftable polynomial sub-relation
     };
+    /**
+     * @brief For ZK-Flavors: Upper bound on the degrees of subrelations considered as polynomials only in witness
+polynomials,
+     * i.e. all selectors and public polynomials are treated as constants. The subrelation witness degree does not
+     * exceed the subrelation partial degree given by LENGTH - 1.
+     */
+    static constexpr std::array<size_t, 2> SUBRELATION_WITNESS_DEGREES{
+        LENGTH - 1, // grand product construction sub-relation
+        LENGTH - 1  // left-shiftable polynomial sub-relation
+    };
 
     static constexpr std::array<bool, 2> SUBRELATION_LINEARLY_INDEPENDENT = { true, false };
 
@@ -247,4 +257,4 @@ template <typename FF_> class ECCVMLookupRelationImpl {
 
 template <typename FF> using ECCVMLookupRelation = Relation<ECCVMLookupRelationImpl<FF>>;
 
-} // namespace bb
+} // namespace bb

barretenberg/cpp/src/barretenberg/relations/ecc_vm/ecc_msm_relation.hpp

@@ -41,6 +41,15 @@ template <typename FF_> class ECCVMMSMRelationImpl {
     static constexpr std::array<size_t, 36> SUBRELATION_PARTIAL_LENGTHS{ 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
                                                                          8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
                                                                          8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8 };
+    /**
+     * @brief For ZK-Flavors: Upper bound on the degrees of subrelations considered as polynomials only in witness
+polynomials,
+     * i.e. all selectors and public polynomials are treated as constants. The subrelation witness degree does not
+     * exceed the subrelation partial degree given by SUBRELATION_PARTIAL_LENGTH - 1.
+     */
+    static constexpr std::array<size_t, 36> SUBRELATION_WITNESS_DEGREES{ 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+                                                                         7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+                                                                         7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 };
 
     template <typename ContainerOverSubrelations, typename AllEntities, typename Parameters>
     static void accumulate(ContainerOverSubrelations& accumulator,
@@ -51,4 +60,4 @@ template <typename FF_> class ECCVMMSMRelationImpl {
 
 template <typename FF> using ECCVMMSMRelation = Relation<ECCVMMSMRelationImpl<FF>>;
 
-} // namespace bb
+} // namespace bb

barretenberg/cpp/src/barretenberg/relations/ecc_vm/ecc_point_table_relation.hpp

@@ -1,3 +1,4 @@
+
 #pragma once
 #include "barretenberg/relations/relation_types.hpp"
 
@@ -20,6 +21,13 @@ template <typename FF_> class ECCVMPointTableRelationImpl {
     using FF = FF_;
 
     static constexpr std::array<size_t, 6> SUBRELATION_PARTIAL_LENGTHS{ 6, 6, 6, 6, 6, 6 };
+    /**
+     * @brief For ZK-Flavors: Upper bound on the degrees of subrelations considered as polynomials only in witness
+polynomials,
+     * i.e. all selectors and public polynomials are treated as constants. The subrelation witness degree does not
+     * exceed the subrelation partial degree given by SUBRELATION_PARTIAL_LENGTH - 1.
+     */
+    static constexpr std::array<size_t, 6> SUBRELATION_WITNESS_DEGREES{ 5, 5, 5, 5, 5, 5 };
 
     template <typename ContainerOverSubrelations, typename AllEntities, typename Parameters>
     static void accumulate(ContainerOverSubrelations& accumulator,

barretenberg/cpp/src/barretenberg/relations/ecc_vm/ecc_set_relation.hpp

@@ -17,6 +17,16 @@ template <typename FF_> class ECCVMSetRelationImpl {
         21, // grand product construction sub-relation
         21  // left-shiftable polynomial sub-relation
     };
+    /**
+     * @brief For ZK-Flavors: Upper bound on the degrees of subrelations considered as polynomials only in witness
+polynomials,
+     * i.e. all selectors and public polynomials are treated as constants. The subrelation witness degree does not
+     * exceed the subrelation partial degree given by SUBRELATION_PARTIAL_LENGTH - 1.
+     */
+    static constexpr std::array<size_t, 2> SUBRELATION_WITNESS_DEGREES{
+        20, // grand product construction sub-relation
+        20  // left-shiftable polynomial sub-relation
+    };
 
     template <typename Accumulator> static Accumulator convert_to_wnaf(const auto& s0, const auto& s1)
     {
@@ -46,4 +56,4 @@ template <typename FF_> class ECCVMSetRelationImpl {
 
 template <typename FF> using ECCVMSetRelation = Relation<ECCVMSetRelationImpl<FF>>;
 
-} // namespace bb
+} // namespace bb

barretenberg/cpp/src/barretenberg/relations/ecc_vm/ecc_transcript_relation.hpp

@@ -33,6 +33,15 @@ template <typename FF_> class ECCVMTranscriptRelationImpl {
     static constexpr std::array<size_t, 25> SUBRELATION_PARTIAL_LENGTHS{
         8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
     };
+    /**
+     * @brief For ZK-Flavors: Upper bound on the degrees of subrelations considered as polynomials only in witness
+polynomials,
+     * i.e. all selectors and public polynomials are treated as constants. The subrelation witness degree does not
+     * exceed the subrelation partial degree given by SUBRELATION_PARTIAL_LENGTH - 1.
+     */
+    static constexpr std::array<size_t, 25> SUBRELATION_WITNESS_DEGREES{
+        7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+    };
 
     template <typename ContainerOverSubrelations, typename AllEntities, typename Parameters>
     static void accumulate(ContainerOverSubrelations& accumulator,
@@ -55,4 +64,4 @@ template <typename FF_> class ECCVMTranscriptRelationImpl {
 
 template <typename FF> using ECCVMTranscriptRelation = Relation<ECCVMTranscriptRelationImpl<FF>>;
 
-} // namespace bb
+} // namespace bb

barretenberg/cpp/src/barretenberg/relations/ecc_vm/ecc_wnaf_relation.hpp

@@ -38,6 +38,15 @@ template <typename FF_> class ECCVMWnafRelationImpl {
     static constexpr std::array<size_t, 21> SUBRELATION_PARTIAL_LENGTHS{
         5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
     };
+    /**
+     * @brief For ZK-Flavors: Upper bound on the degrees of subrelations considered as polynomials only in witness
+polynomials,
+     * i.e. all selectors and public polynomials are treated as constants. The subrelation witness degree does not
+     * exceed the subrelation partial degree given by SUBRELATION_PARTIAL_LENGTH - 1.
+     */
+    static constexpr std::array<size_t, 21> SUBRELATION_WITNESS_DEGREES{
+        4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
+    };
 
     template <typename ContainerOverSubrelations, typename AllEntities, typename Parameters>
     static void accumulate(ContainerOverSubrelations& accumulator,
@@ -48,4 +57,4 @@ template <typename FF_> class ECCVMWnafRelationImpl {
 
 template <typename FF> using ECCVMWnafRelation = Relation<ECCVMWnafRelationImpl<FF>>;
 
-} // namespace bb
+} // namespace bb

barretenberg/cpp/src/barretenberg/relations/elliptic_relation.hpp

@@ -13,6 +13,15 @@ template <typename FF_> class EllipticRelationImpl {
         6, // x-coordinate sub-relation
         6, // y-coordinate sub-relation
     };
+    /**
+     * @brief For ZK-Flavors: The degrees of subrelations considered as polynomials only in witness polynomials,
+     * i.e. all selectors and public polynomials are treated as constants.
+     *
+     */
+    static constexpr std::array<size_t, 2> SUBRELATION_WITNESS_DEGREES{
+        3, // x-coordinate sub-relation
+        3, // y-coordinate sub-relation (because of point doubling)
+    };
 
     /**
      * @brief Returns true if the contribution from all subrelations for the provided inputs is identically zero
@@ -108,4 +117,4 @@ template <typename FF_> class EllipticRelationImpl {
 };
 
 template <typename FF> using EllipticRelation = Relation<EllipticRelationImpl<FF>>;
-} // namespace bb
+} // namespace bb