fix: BarycentricData instantiation time and unused code in secp curves

cpp/src/barretenberg/ecc/curves/secp256k1/c_bind.cpp

@@ -14,15 +14,15 @@ WASM_EXPORT void ecc_secp256k1__mul(uint8_t const* point_buf, uint8_t const* sca
 
 WASM_EXPORT void ecc_secp256k1__get_random_scalar_mod_circuit_modulus(uint8_t* result)
 {
-    barretenberg::fr output = barretenberg::fr::random_element();
+    secp256k1::fr output = secp256k1::fr::random_element();
     write(result, output);
 }
 
 WASM_EXPORT void ecc_secp256k1__reduce512_buffer_mod_circuit_modulus(uint8_t* input, uint8_t* result)
 {
     uint512_t bigint_input = from_buffer<uint512_t>(input);
 
-    uint512_t barretenberg_modulus(barretenberg::fr::modulus);
+    uint512_t barretenberg_modulus(secp256k1::fr::modulus);
 
     uint512_t target_output = bigint_input % barretenberg_modulus;
     write(result, target_output.lo);

cpp/src/barretenberg/ecc/curves/secp256k1/secp256k1.hpp

@@ -1,36 +1,11 @@
 #pragma once
 
-#include "barretenberg/numeric/uint256/uint256.hpp"
-#include "barretenberg/numeric/uintx/uintx.hpp"
-
 #include "../../fields/field.hpp"
 #include "../../groups/group.hpp"
-#include "../bn254/fq.hpp"
-#include "../bn254/fr.hpp"
 #include "../types.hpp"
 
 namespace secp256k1 {
 
-constexpr uint256_t get_r_squared(const uint256_t prime_256)
-{
-    uint512_t R(0, 1);
-    uint1024_t R_1024 = uint1024_t(R);
-    uint1024_t R_squared = R_1024 * R_1024;
-    uint1024_t modulus = uint1024_t(uint512_t(prime_256));
-
-    uint1024_t R_squared_mod_p = R_squared % modulus;
-    return R_squared_mod_p.lo.lo;
-}
-
-constexpr uint64_t get_r_inv(const uint256_t prime_256)
-{
-    uint512_t r{ 0, 1 };
-    // -(1/q) mod r
-    uint512_t q{ -prime_256, 0 };
-    uint256_t q_inv = q.invmod(r).lo;
-    return (q_inv).data[0];
-}
-
 struct Secp256k1FqParams {
     static constexpr uint64_t modulus_0 = 0xFFFFFFFEFFFFFC2FULL;
     static constexpr uint64_t modulus_1 = 0xFFFFFFFFFFFFFFFFULL;

cpp/src/barretenberg/ecc/curves/secp256r1/secp256r1.hpp

@@ -1,35 +1,10 @@
 #pragma once
 
-#include "barretenberg/numeric/uint256/uint256.hpp"
-#include "barretenberg/numeric/uintx/uintx.hpp"
-
 #include "../../fields/field.hpp"
 #include "../../groups/group.hpp"
-#include "../bn254/fq.hpp"
-#include "../bn254/fr.hpp"
 
 namespace secp256r1 {
 
-constexpr uint256_t get_r_squared(const uint256_t prime_256)
-{
-    uint512_t R(0, 1);
-    uint1024_t R_1024 = uint1024_t(R);
-    uint1024_t R_squared = R_1024 * R_1024;
-    uint1024_t modulus = uint1024_t(uint512_t(prime_256));
-
-    uint1024_t R_squared_mod_p = R_squared % modulus;
-    return R_squared_mod_p.lo.lo;
-}
-
-constexpr uint64_t get_r_inv(const uint256_t prime_256)
-{
-    uint512_t r{ 0, 1 };
-    // -(1/q) mod r
-    uint512_t q{ -prime_256, 0 };
-    uint256_t q_inv = q.invmod(r).lo;
-    return (q_inv).data[0];
-}
-
 struct Secp256r1FqParams {
     static constexpr uint64_t modulus_0 = 0xFFFFFFFFFFFFFFFFULL;
     static constexpr uint64_t modulus_1 = 0x00000000FFFFFFFFULL;

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

@@ -62,9 +62,6 @@ class Standard {
     static constexpr size_t MAX_RANDOM_RELATION_LENGTH = MAX_RELATION_LENGTH + 1;
     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_RANDOM_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>());

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

@@ -53,9 +53,6 @@ class StandardGrumpkin {
     static constexpr size_t MAX_RANDOM_RELATION_LENGTH = MAX_RELATION_LENGTH + 1;
     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_RANDOM_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>());

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

@@ -67,9 +67,6 @@ class Ultra {
     static constexpr size_t MAX_RANDOM_RELATION_LENGTH = MAX_RELATION_LENGTH + 1;
     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_RANDOM_RELATION_LENGTH>());
-
     // define the container for storing the univariate contribution from each relation in Sumcheck
     using RelationUnivariates = decltype(create_relation_univariates_container<FF, Relations>());
     using RelationValues = decltype(create_relation_values_container<FF, Relations>());

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

@@ -65,9 +65,6 @@ class UltraGrumpkin {
     static constexpr size_t MAX_RANDOM_RELATION_LENGTH = MAX_RELATION_LENGTH + 1;
     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_RANDOM_RELATION_LENGTH>());
-
     // define the container for storing the univariate contribution from each relation in Sumcheck
     using RelationUnivariates = decltype(create_relation_univariates_container<FF, Relations>());
     using RelationValues = decltype(create_relation_values_container<FF, Relations>());

cpp/src/barretenberg/honk/sumcheck/polynomials/barycentric_data.hpp

@@ -51,6 +51,34 @@ template <class Fr, size_t domain_size, size_t num_evals> class BarycentricData
         return result;
     }
 
+    static constexpr std::array<Fr, domain_size * num_evals> batch_invert(
+        const std::array<Fr, domain_size * num_evals>& coeffs)
+    {
+        constexpr size_t n = domain_size * num_evals;
+        std::array<Fr, n> temporaries{};
+        std::array<bool, n> skipped{};
+        Fr accumulator = 1;
+        for (size_t i = 0; i < n; ++i) {
+            temporaries[i] = accumulator;
+            if (coeffs[i] == 0) {
+                skipped[i] = true;
+            } else {
+                skipped[i] = false;
+                accumulator *= coeffs[i];
+            }
+        }
+        accumulator = Fr(1) / accumulator;
+        std::array<Fr, n> result{};
+        Fr T0;
+        for (size_t i = n - 1; i < n; --i) {
+            if (!skipped[i]) {
+                T0 = accumulator * temporaries[i];
+                accumulator *= coeffs[i];
+                result[i] = T0;
+            }
+        }
+        return result;
+    }
     // for each x_k in the big domain, build set of domain size-many denominator inverses
     // 1/(d_i*(x_k - x_j)). will multiply against each of these (rather than to divide by something)
     // for each barycentric evaluation
@@ -62,11 +90,10 @@ template <class Fr, size_t domain_size, size_t num_evals> class BarycentricData
             for (size_t j = 0; j < domain_size; ++j) {
                 Fr inv = lagrange_denominators[j];
                 inv *= (big_domain[k] - big_domain[j]);
-                inv = Fr(1) / inv; // prob have self_inverse method; should be part of Field concept
                 result[k * domain_size + j] = inv;
             }
         }
-        return result;
+        return batch_invert(result);
     }
 
     // get full numerator values