chore: minor pcs fixes

barretenberg/cpp/src/barretenberg/commitment_schemes/gemini/gemini.hpp

@@ -75,9 +75,12 @@ namespace gemini {
  */
 template <class Fr> inline std::vector<Fr> powers_of_rho(const Fr& rho, const size_t num_powers)
 {
-    std::vector<Fr> rhos = { Fr(1), rho };
+    std::vector<Fr> rhos;
     rhos.reserve(num_powers);
-    for (size_t j = 2; j < num_powers; j++) {
+    if (num_powers >= 1) {
+        rhos.emplace_back(Fr(1));
+    }
+    for (size_t j = 1; j < num_powers; j++) {
         rhos.emplace_back(rhos[j - 1] * rho);
     }
     return rhos;
@@ -250,14 +253,12 @@ template <typename Curve> class GeminiProver_ {
 
             Fr r_inv = r_challenge.invert();
             if (has_to_be_shifted_by_one()) {
-                batched_to_be_shifted_by_one *= r_inv;
-                A_0_pos += batched_to_be_shifted_by_one;
-                A_0_neg -= batched_to_be_shifted_by_one;
+                A_0_pos.add_scaled(batched_to_be_shifted_by_one, r_inv);
+                A_0_neg.add_scaled(batched_to_be_shifted_by_one, -r_inv);
             }
             if (!batched_shifted_tail_.is_empty()) {
-                batched_shifted_tail_ *= r_inv;
-                A_0_pos += batched_shifted_tail_;
-                A_0_neg -= batched_shifted_tail_;
+                A_0_pos.add_scaled(batched_shifted_tail_, r_inv);
+                A_0_neg.add_scaled(batched_shifted_tail_, -r_inv);
             }
 
             return { A_0_pos, A_0_neg };

barretenberg/cpp/src/barretenberg/commitment_schemes/gemini/gemini_impl.hpp

@@ -111,6 +111,7 @@ std::vector<typename GeminiProver_<Curve>::Polynomial> GeminiProver_<Curve>::com
     const size_t log_n, std::span<const Fr> multilinear_challenge, const Polynomial& A_0, const bool& has_zk)
 {
     BB_BENCH_NAME("Gemini::compute_fold_polynomials");
+    BB_ASSERT_GTE(log_n, size_t(2), "Gemini folding requires at least 4-element polynomials");
     const size_t virtual_log_n = multilinear_challenge.size();
 
     // Cost per iteration: 1 subtraction + 1 multiplication + 1 addition

barretenberg/cpp/src/barretenberg/commitment_schemes/ipa/ipa.hpp

@@ -575,14 +575,14 @@ template <typename Curve_, size_t log_poly_length = CONST_ECCVM_LOG_N> class IPA
 
         // Step 6.
         // Receive a_zero from the prover
-        const auto a_zero = transcript->template receive_from_prover<Fr>("IPA:a_0");
+        auto a_zero = transcript->template receive_from_prover<Fr>("IPA:a_0");
 
         // OriginTag false positive: G_zero and a_zero are fully determined once all round challenges are fixed - the
         // prover must send the correct values or the final relation check fails.
         if constexpr (Curve::is_stdlib_type) {
             const auto last_round_tag = round_challenges.back().get_origin_tag();
             G_zero.set_origin_tag(last_round_tag);
-            const_cast<Fr&>(a_zero).set_origin_tag(last_round_tag);
+            a_zero.set_origin_tag(last_round_tag);
         }
 
         // Step 7.

barretenberg/cpp/src/barretenberg/commitment_schemes/shplonk/shplemini.hpp

@@ -242,8 +242,7 @@ template <typename Curve, bool HasZK = false> class ShpleminiVerifier_ {
         const Fr gemini_evaluation_challenge = transcript->template get_challenge<Fr>("Gemini:r");
 
         // - Get negative fold evaluations (A₀(−r), A₁(−r²), ... , Aₙ₋₁(−r²⁽ⁿ⁻¹⁾))
-        const std::vector<Fr> gemini_fold_neg_evaluations =
-            GeminiVerifier::get_gemini_evaluations(virtual_log_n, transcript);
+        std::vector<Fr> gemini_fold_neg_evaluations = GeminiVerifier::get_gemini_evaluations(virtual_log_n, transcript);
 
         // - Compute vector (r, r², ... , r^{2^{d-1}}), where d = log_n
         const std::vector<Fr> gemini_eval_challenge_powers =
@@ -290,7 +289,7 @@ template <typename Curve, bool HasZK = false> class ShpleminiVerifier_ {
         if constexpr (Curve::is_stdlib_type) {
             const auto challenge_tag = shplonk_evaluation_challenge.get_origin_tag();
             // Tag the Gemini fold evaluations
-            for (auto& eval : const_cast<std::vector<Fr>&>(gemini_fold_neg_evaluations)) {
+            for (auto& eval : gemini_fold_neg_evaluations) {
                 eval.set_origin_tag(challenge_tag);
             }
         }

barretenberg/cpp/src/barretenberg/polynomials/gate_separator.hpp

@@ -168,7 +168,7 @@ template <typename FF> struct GateSeparatorPolynomial {
         }
 
         BB_BENCH_NAME("GateSeparatorPolynomial::compute_beta_products");
-        size_t pow_size = 1 << log_num_monomials;
+        size_t pow_size = static_cast<size_t>(1) << log_num_monomials;
         Polynomial<FF> beta_products(pow_size, Polynomial<FF>::DontZeroMemory::FLAG);
 
         // Explanations of the algorithm:

barretenberg/cpp/src/barretenberg/sumcheck/sumcheck.hpp

@@ -499,9 +499,9 @@ template <typename Flavor> class SumcheckProver {
         transcript->send_to_verifier("Sumcheck:evaluations", multivariate_evaluations.get_all());
         // For ZK Flavors: the evaluations of Libra univariates are included in the Sumcheck Output
 
+        vinfo("finished sumcheck");
         return SumcheckOutput<Flavor>{ .challenge = multivariate_challenge,
                                        .claimed_evaluations = multivariate_evaluations };
-        vinfo("finished sumcheck");
     };
 
     /**
@@ -671,12 +671,12 @@ template <typename Flavor> class SumcheckProver {
 
         // The sum of the Libra constant term and the evaluations of Libra univariates at corresponding sumcheck
         // challenges is included in the Sumcheck Output
+        vinfo("finished sumcheck");
         return SumcheckOutput<Flavor>{ .challenge = multivariate_challenge,
                                        .claimed_evaluations = multivariate_evaluations,
                                        .claimed_libra_evaluation = libra_evaluation,
                                        .round_univariates = handler.get_univariates(),
                                        .round_univariate_evaluations = handler.get_evaluations() };
-        vinfo("finished sumcheck");
     };
 
     /**

barretenberg/cpp/src/barretenberg/sumcheck/zk_sumcheck_data.hpp

@@ -295,9 +295,6 @@ template <typename Flavor> struct ZKSumcheckData {
                 this->libra_univariates[round_idx].evaluate(round_challenge) / this->libra_scaling_factor;
             // place the evalution into the vector of Libra evaluations
             this->libra_evaluations.emplace_back(libra_evaluation);
-            for (auto univariate : this->libra_univariates) {
-                univariate *= FF(1) / this->libra_challenge;
-            }
         };
     }
 };