fix: Intermittent invert 0 in Goblin (#5174)

We systematize the work of
#4751 to avoid
scalar multiplication by 0, an issue that has arisen in various ways. In
our case, the acir test `6_array` was reliably failing (failing the with
`Trying to invert zero in the field`) about 1/256 of the time. The error
was thrown from
https://github.com/AztecProtocol/aztec-packages/blob/394a0e06928946c1c9eea1bdfec39269cb2d601a/barretenberg/cpp/src/barretenberg/ecc/groups/element_impl.hpp#L68
coming from this line in Zerormorph verification
https://github.com/AztecProtocol/aztec-packages/blob/394a0e06928946c1c9eea1bdfec39269cb2d601a/barretenberg/cpp/src/barretenberg/commitment_schemes/zeromorph/zeromorph.hpp#L622
Spawning an issue to handle this situation more systmatically:
AztecProtocol/barretenberg#905

The PR allowed the acir test to be run more than 512 times without any
issue.

barretenberg/cpp/src/barretenberg/proof_system/op_queue/ecc_op_queue.hpp

@@ -46,6 +46,19 @@ class ECCOpQueue {
 
     std::array<Point, 4> ultra_ops_commitments;
 
+    // TODO(https://github.com/AztecProtocol/barretenberg/issues/905): Can remove this with better handling of scalar
+    // mul against 0
+    void append_nonzero_ops()
+    {
+        // Add an element and scalar the accumulation of which leaves no Point-at-Infinity commitments
+        const auto x = uint256_t(0xd3c208c16d87cfd3, 0xd97816a916871ca8, 0x9b85045b68181585, 0x30644e72e131a02);
+        const auto y = uint256_t(0x3ce1cc9c7e645a83, 0x2edac647851e3ac5, 0xd0cbe61fced2bc53, 0x1a76dae6d3272396);
+        auto padding_element = Point(x, y);
+        auto padding_scalar = -Fr::one();
+        mul_accumulate(padding_element, padding_scalar);
+        eq();
+    }
+
     Point get_accumulator() { return accumulator; }
 
     /**

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

@@ -53,6 +53,9 @@ template <class Flavor> class ProverInstance_ {
         BB_OP_COUNT_TIME_NAME("ProverInstance(Circuit&)");
         circuit.add_gates_to_ensure_all_polys_are_non_zero();
         circuit.finalize_circuit();
+        if constexpr (IsGoblinFlavor<Flavor>) {
+            circuit.op_queue->append_nonzero_ops();
+        }
 
         dyadic_circuit_size = compute_dyadic_size(circuit);
 

barretenberg/cpp/src/barretenberg/translator_vm/goblin_translator_composer.test.cpp

@@ -49,24 +49,12 @@ TEST_F(GoblinTranslatorComposerTests, Basic)
     using Fr = fr;
     using Fq = fq;
 
-    // Add an element and scalar the accumulation of which leaves no Point-at-Infinity commitments
-    const auto x = uint256_t(0xd3c208c16d87cfd3, 0xd97816a916871ca8, 0x9b85045b68181585, 0x30644e72e131a02);
-    const auto y = uint256_t(0x3ce1cc9c7e645a83, 0x2edac647851e3ac5, 0xd0cbe61fced2bc53, 0x1a76dae6d3272396);
-    auto padding_element = G1(x, y);
-    auto padding_scalar = -Fr::one();
-
     auto P1 = G1::random_element();
     auto P2 = G1::random_element();
     auto z = Fr::random_element();
 
     // Add the same operations to the ECC op queue; the native computation is performed under the hood.
     auto op_queue = std::make_shared<bb::ECCOpQueue>();
-
-    // Accumulate padding so that we don't produce Point-at-Infinity commitments. Currently our transcript can't handle
-    // them
-    op_queue->mul_accumulate(padding_element, padding_scalar);
-
-    // Push everything else
     for (size_t i = 0; i < 500; i++) {
         op_queue->add_accumulate(P1);
         op_queue->mul_accumulate(P2, z);