feat: Benchmark protogalaxy prover (#3958)

Benchmark Protogalaxy prover. This just benchmarks the current folding
function. Future PRs will make update and augment with values that will
better reflect performance in production.

Results: uses 16 cores (for the x86 build). `fold_one/N` measures the
time to call the `fold_instances` function to fold a single instance
into an accumulator where the instance sizes are $2^N$. Note this is for
the Ultra arithmetization (so no Goblin, Poseidon2 or DataBus
relations).

```
% taskset -c 0-15 ./bin/protogalaxy_bench                   38s ~/barretenberg-cpp/build cg/pg-bench mainframe
2024-01-11T19:39:49+00:00
Running ./bin/protogalaxy_bench
Run on (128 X 2649.99 MHz CPU s)
CPU Caches:
  L1 Data 32 KiB (x64)
  L1 Instruction 32 KiB (x64)
  L2 Unified 512 KiB (x64)
  L3 Unified 32768 KiB (x8)
Load Average: 3.48, 8.51, 27.24
------------------------------------------------------
Benchmark            Time             CPU   Iterations
------------------------------------------------------
fold_one/14        417 ms          259 ms            3
fold_one/15        668 ms          409 ms            2
fold_one/16       1158 ms          696 ms            1
fold_one/17       2245 ms         1433 ms            1
fold_one/18       4168 ms         2644 ms            1
fold_one/19       7890 ms         5119 ms            1
fold_one/20      15809 ms        10633 ms            1
```

Closes AztecProtocol/barretenberg#692

barretenberg/cpp/src/barretenberg/benchmark/CMakeLists.txt

@@ -5,4 +5,5 @@ add_subdirectory(plonk_bench)
 add_subdirectory(ultra_bench)
 add_subdirectory(goblin_bench)
 add_subdirectory(relations_bench)
-add_subdirectory(widgets_bench)
+add_subdirectory(widgets_bench)
+add_subdirectory(protogalaxy_bench)

barretenberg/cpp/src/barretenberg/benchmark/protogalaxy_bench/CMakeLists.txt

@@ -0,0 +1,20 @@
+# Each source represents a separate benchmark suite 
+set(BENCHMARK_SOURCES
+  protogalaxy.bench.cpp
+)
+
+# Required libraries for benchmark suites
+set(LINKED_LIBRARIES
+  ultra_honk
+  protogalaxy
+  stdlib_primitives
+  benchmark::benchmark
+)
+
+# Add executable and custom target for each suite, e.g. ultra_honk_bench
+foreach(BENCHMARK_SOURCE ${BENCHMARK_SOURCES})
+  get_filename_component(BENCHMARK_NAME ${BENCHMARK_SOURCE} NAME_WE) # extract name without extension
+  add_executable(${BENCHMARK_NAME}_bench main.bench.cpp ${BENCHMARK_SOURCE})
+  target_link_libraries(${BENCHMARK_NAME}_bench ${LINKED_LIBRARIES})
+  add_custom_target(run_${BENCHMARK_NAME} COMMAND ${BENCHMARK_NAME} WORKING_DIRECTORY ${CMAKE_BINARY_DIR})
+endforeach()

barretenberg/cpp/src/barretenberg/benchmark/protogalaxy_bench/main.bench.cpp

@@ -0,0 +1,3 @@
+#include <benchmark/benchmark.h>
+
+BENCHMARK_MAIN();

barretenberg/cpp/src/barretenberg/benchmark/protogalaxy_bench/protogalaxy.bench.cpp

@@ -0,0 +1,41 @@
+#include <benchmark/benchmark.h>
+
+#include "barretenberg/benchmark/ultra_bench/benchmark_utilities.hpp"
+#include "barretenberg/proof_system/circuit_builder/ultra_circuit_builder.hpp"
+#include "barretenberg/ultra_honk/ultra_composer.hpp"
+
+using namespace benchmark;
+
+namespace proof_system::honk {
+using Flavor = flavor::Ultra;
+using Instance = ProverInstance_<Flavor>;
+using Instances = ProverInstances_<Flavor, 2>;
+using ProtoGalaxyProver = ProtoGalaxyProver_<Instances>;
+using Builder = Flavor::CircuitBuilder;
+
+// Fold one instance into an accumulator.
+void fold_one(State& state) noexcept
+{
+    barretenberg::srs::init_crs_factory("../srs_db/ignition");
+
+    auto log2_num_gates = static_cast<size_t>(state.range(0));
+    auto composer = UltraComposer();
+
+    const auto construct_instance = [&]() {
+        Builder builder;
+        bench_utils::generate_basic_arithmetic_circuit(builder, log2_num_gates);
+        return composer.create_instance(builder);
+    };
+
+    std::shared_ptr<Instance> instance_1 = construct_instance();
+    std::shared_ptr<Instance> instance_2 = construct_instance();
+
+    auto folding_prover = composer.create_folding_prover({ instance_1, instance_2 }, composer.commitment_key);
+
+    for (auto _ : state) {
+        auto proof = folding_prover.fold_instances();
+    }
+}
+
+BENCHMARK(fold_one)->/* vary the circuit size */ DenseRange(14, 20)->Unit(kMillisecond);
+} // namespace proof_system::honk

barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover.hpp

@@ -91,7 +91,7 @@ template <class ProverInstances_> class ProtoGalaxyProver_ {
      *
      * TODO(https://github.com/AztecProtocol/barretenberg/issues/753): fold goblin polynomials
      */
-    FoldingResult<Flavor> fold_instances();
+    BBERG_PROFILE FoldingResult<Flavor> fold_instances();
 
     /**
      * @brief For a new round challenge δ at each iteration of the ProtoGalaxy protocol, compute the vector