feat: Multithreaded prover folding (#5147)

We only get an 80% reduction on 16 threads, but it's still a nice
improvement of overall time.

## Before
```
Benchmarking lock created at ~/BENCHMARK_IN_PROGRESS.
client_ivc_bench                                                              100%   15MB  48.4MB/s   00:00    
2024-03-12T03:38:23+00:00
Running ./client_ivc_bench
Run on (16 X 3000 MHz CPU s)
CPU Caches:
  L1 Data 32 KiB (x8)
  L1 Instruction 32 KiB (x8)
  L2 Unified 1024 KiB (x8)
  L3 Unified 36608 KiB (x1)
Load Average: 0.00, 0.00, 0.11
--------------------------------------------------------------------------------
Benchmark                      Time             CPU   Iterations UserCounters...
--------------------------------------------------------------------------------
ClientIVCBench/Full/6      29446 ms        24872 ms            1 Decider::construct_proof=1 Decider::construct_proof(t)=753.082M ECCVMComposer::compute_commitment_key=1 ECCVMComposer::compute_commitment_key(t)=3.78026M ECCVMComposer::compute_witness=1 ECCVMComposer::compute_witness(t)=1.73739G ECCVMComposer::create_prover=1 ECCVMComposer::create_prover(t)=3.40893G ECCVMComposer::create_proving_key=1 ECCVMComposer::create_proving_key(t)=1.66752G ECCVMProver::construct_proof=1 ECCVMProver::construct_proof(t)=1.76066G Goblin::merge=11 Goblin::merge(t)=128.627M GoblinTranslatorCircuitBuilder::constructor=1 GoblinTranslatorCircuitBuilder::constructor(t)=56.5845M GoblinTranslatorComposer::create_prover=1 GoblinTranslatorComposer::create_prover(t)=123.279M GoblinTranslatorProver::construct_proof=1 GoblinTranslatorProver::construct_proof(t)=927.524M ProtoGalaxyProver_::accumulator_update_round=10 ProtoGalaxyProver_::accumulator_update_round(t)=3.46156G ProtoGalaxyProver_::combiner_quotient_round=10 ProtoGalaxyProver_::combiner_quotient_round(t)=7.17713G ProtoGalaxyProver_::perturbator_round=10 ProtoGalaxyProver_::perturbator_round(t)=1.38221G ProtoGalaxyProver_::preparation_round=10 ProtoGalaxyProver_::preparation_round(t)=4.1G ProtogalaxyProver::fold_instances=10 ProtogalaxyProver::fold_instances(t)=16.1209G ProverInstance(Circuit&)=11 ProverInstance(Circuit&)(t)=1.945G batch_mul_with_endomorphism=30 batch_mul_with_endomorphism(t)=562.528M commit=425 commit(t)=3.96966G compute_combiner=10 compute_combiner(t)=7.175G compute_perturbator=9 compute_perturbator(t)=1.38188G compute_univariate=48 compute_univariate(t)=1.41821G construct_circuits=6 construct_circuits(t)=4.20217G
Benchmarking lock deleted.
client_ivc_bench.json                                                         100% 4015   130.4KB/s   00:00    
function                                        ms     % sum
construct_circuits(t)                         4202    14.31%
ProverInstance(Circuit&)(t)                   1945     6.62%
ProtogalaxyProver::fold_instances(t)         16121    54.89%
Decider::construct_proof(t)                    753     2.56%
ECCVMComposer::create_prover(t)               3409    11.61%
GoblinTranslatorComposer::create_prover(t)     123     0.42%
ECCVMProver::construct_proof(t)               1761     5.99%
GoblinTranslatorProver::construct_proof(t)     928     3.16%
Goblin::merge(t)                               129     0.44%

Total time accounted for: 29370ms/29446ms = 99.74%

Major contributors:
function                                        ms    % sum
commit(t)                                     3970   13.52%
compute_combiner(t)                           7175   24.43%
compute_perturbator(t)                        1382    4.71%
compute_univariate(t)                         1418    4.83%

Breakdown of ECCVMProver::create_prover:
ECCVMComposer::compute_witness(t)             1737    50.97%
ECCVMComposer::create_proving_key(t)          1668    48.92%

Breakdown of ProtogalaxyProver::fold_instances:
ProtoGalaxyProver_::preparation_round(t)           4100    25.43%
ProtoGalaxyProver_::perturbator_round(t)           1382     8.57%
ProtoGalaxyProver_::combiner_quotient_round(t)     7177    44.52%
ProtoGalaxyProver_::accumulator_update_round(t)    3462    21.47%
```

## After
```
Benchmarking lock created at ~/BENCHMARK_IN_PROGRESS.
client_ivc_bench                                                                                                                                                                                                                                            100%   15MB  53.8MB/s   00:00    
2024-03-12T13:10:44+00:00
Running ./client_ivc_bench
Run on (16 X 3606.49 MHz CPU s)
CPU Caches:
  L1 Data 32 KiB (x8)
  L1 Instruction 32 KiB (x8)
  L2 Unified 1024 KiB (x8)
  L3 Unified 36608 KiB (x1)
Load Average: 0.00, 0.92, 1.95
--------------------------------------------------------------------------------
Benchmark                      Time             CPU   Iterations UserCounters...
--------------------------------------------------------------------------------
ClientIVCBench/Full/6      26935 ms        22185 ms            1 Decider::construct_proof=1 Decider::construct_proof(t)=760.055M ECCVMComposer::compute_commitment_key=1 ECCVMComposer::compute_commitment_key(t)=3.6897M ECCVMComposer::compute_witness=1 ECCVMComposer::compute_witness(t)=1.74049G ECCVMComposer::create_prover=1 ECCVMComposer::create_prover(t)=3.41363G ECCVMComposer::create_proving_key=1 ECCVMComposer::create_proving_key(t)=1.66922G ECCVMProver::construct_proof=1 ECCVMProver::construct_proof(t)=1.76915G Goblin::merge=11 Goblin::merge(t)=128.378M GoblinTranslatorCircuitBuilder::constructor=1 GoblinTranslatorCircuitBuilder::constructor(t)=57.5506M GoblinTranslatorComposer::create_prover=1 GoblinTranslatorComposer::create_prover(t)=121.602M GoblinTranslatorProver::construct_proof=1 GoblinTranslatorProver::construct_proof(t)=927.714M ProtoGalaxyProver_::accumulator_update_round=10 ProtoGalaxyProver_::accumulator_update_round(t)=722M ProtoGalaxyProver_::combiner_quotient_round=10 ProtoGalaxyProver_::combiner_quotient_round(t)=7.24835G ProtoGalaxyProver_::perturbator_round=10 ProtoGalaxyProver_::perturbator_round(t)=1.39394G ProtoGalaxyProver_::preparation_round=10 ProtoGalaxyProver_::preparation_round(t)=4.11739G ProtogalaxyProver::fold_instances=10 ProtogalaxyProver::fold_instances(t)=13.4817G ProverInstance(Circuit&)=11 ProverInstance(Circuit&)(t)=2.0017G batch_mul_with_endomorphism=30 batch_mul_with_endomorphism(t)=564.354M commit=425 commit(t)=3.98668G compute_combiner=10 compute_combiner(t)=7.24616G compute_perturbator=9 compute_perturbator(t)=1.3936G compute_univariate=48 compute_univariate(t)=1.42762G construct_circuits=6 construct_circuits(t)=4.25115G
Benchmarking lock deleted.
client_ivc_bench.json                                                                                                                                                                                                                                       100% 4021   139.1KB/s   00:00    
function                                        ms     % sum
construct_circuits(t)                         4251    15.83%
ProverInstance(Circuit&)(t)                   2002     7.45%
ProtogalaxyProver::fold_instances(t)         13482    50.20%
Decider::construct_proof(t)                    760     2.83%
ECCVMComposer::create_prover(t)               3414    12.71%
GoblinTranslatorComposer::create_prover(t)     122     0.45%
ECCVMProver::construct_proof(t)               1769     6.59%
GoblinTranslatorProver::construct_proof(t)     928     3.45%
Goblin::merge(t)                               128     0.48%

Total time accounted for: 26855ms/26935ms = 99.70%

Major contributors:
function                                        ms    % sum
commit(t)                                     3987   14.85%
compute_combiner(t)                           7246   26.98%
compute_perturbator(t)                        1394    5.19%
compute_univariate(t)                         1428    5.32%

Breakdown of ECCVMProver::create_prover:
ECCVMComposer::compute_witness(t)             1740    50.99%
ECCVMComposer::create_proving_key(t)          1669    48.90%

Breakdown of ProtogalaxyProver::fold_instances:
ProtoGalaxyProver_::preparation_round(t)           4117    30.54%
ProtoGalaxyProver_::perturbator_round(t)           1394    10.34%
ProtoGalaxyProver_::combiner_quotient_round(t)     7248    53.76%
ProtoGalaxyProver_::accumulator_update_round(t)     722     5.36%
```

---------

Co-authored-by: maramihali <mara@aztecprotocol.com>

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

@@ -85,12 +85,17 @@ std::shared_ptr<typename ProverInstances::Instance> ProtoGalaxyProver_<ProverIns
 
     // Fold the prover polynomials
     for (size_t inst_idx = 0; inst_idx < ProverInstances::NUM; inst_idx++) {
-        for (auto [acc_poly, inst_poly] :
-             zip_view(acc_prover_polynomials.get_all(), instances[inst_idx]->prover_polynomials.get_all())) {
-            for (auto [acc_el, inst_el] : zip_view(acc_poly, inst_poly)) {
-                acc_el += inst_el * lagranges[inst_idx];
+        auto accumulator_polys = acc_prover_polynomials.get_all();
+        auto input_polys = instances[inst_idx]->prover_polynomials.get_all();
+        run_loop_in_parallel(Flavor::NUM_ALL_ENTITIES, [&](size_t start_idx, size_t end_idx) {
+            for (size_t poly_idx = start_idx; poly_idx < end_idx; poly_idx++) {
+                auto& acc_poly = accumulator_polys[poly_idx];
+                auto& inst_poly = input_polys[poly_idx];
+                for (auto [acc_el, inst_el] : zip_view(acc_poly, inst_poly)) {
+                    acc_el += inst_el * lagranges[inst_idx];
+                }
             }
-        }
+        });
     }
     next_accumulator->prover_polynomials = std::move(acc_prover_polynomials);