feat: Prototype native merkle trees

[PhilWindle]

This PR contains work around understanding the performance of our hash functions and merkle trees.

1. Parameterise our existing MerkleTree and NulliferTree to accept any compatible hash function
2. Creates a new native AppendOnlyTree only allowing addition of leaves at the end
3. Creates a new multi-threaded native IndexedMerkleTree.
4. Add tests to validate new trees against previous ones
5. Adds benchmarks for hash functions and new trees.
6. Exposes poseidon hash functions over the WASM and benchmarks it.

Benchmarks

Hash Functions

Pedersen - Native

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Benchmark                                                Time             CPU   Iterations
------------------------------------------------------------------------------------------
native_pedersen_hash_pair_bench/min_time:3.000       0.178 ms        0.178 ms        23450

Pedersen - Single hash over WASM 1000 times

Executed 1000 hashes at an average 593.7273874282837us / hash

Pedersen - 1024 hashes over WASM 10 times

Executed 10240 hashes at an average 581.7138370126486us / hash

Poseidon - Native

----------------------------------------------------------------------------------
Benchmark                                        Time             CPU   Iterations
----------------------------------------------------------------------------------
poseiden_hash_bench                          0.012 ms        0.012 ms        57022

Poseidon - Single hash over WASM 1000 times

Executed 1000 hashes at an average 48.4412202835083us / hash

Poseidon - 1024 hashes over WASM 10 times

Executed 10240 hashes at an average 37.44762847200036us / hash

Merkle Trees

The following benchmarks follow the format of {benchmark-type}/{batch-insertion-size}/{iteration-count}.

Append Only Tree

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Benchmark                                                      Time             CPU   Iterations
------------------------------------------------------------------------------------------------
append_only_tree_bench<Pedersen>/2/iterations:100           5.75 ms         5.75 ms          100
append_only_tree_bench<Pedersen>/4/iterations:100           6.02 ms         6.02 ms          100
append_only_tree_bench<Pedersen>/8/iterations:100           6.65 ms         6.65 ms          100
append_only_tree_bench<Pedersen>/16/iterations:100          7.89 ms         7.89 ms          100
append_only_tree_bench<Pedersen>/32/iterations:100          10.7 ms         10.7 ms          100
append_only_tree_bench<Pedersen>/64/iterations:100          16.3 ms         16.3 ms          100
append_only_tree_bench<Pedersen>/128/iterations:100         27.8 ms         27.8 ms          100

append_only_tree_bench<Poseidon2>/2/iterations:1000        0.395 ms        0.395 ms         1000
append_only_tree_bench<Poseidon2>/4/iterations:1000        0.407 ms        0.408 ms         1000
append_only_tree_bench<Poseidon2>/8/iterations:1000        0.454 ms        0.454 ms         1000
append_only_tree_bench<Poseidon2>/16/iterations:1000       0.531 ms        0.531 ms         1000
append_only_tree_bench<Poseidon2>/32/iterations:1000       0.726 ms        0.726 ms         1000
append_only_tree_bench<Poseidon2>/64/iterations:1000        1.11 ms         1.11 ms         1000
append_only_tree_bench<Poseidon2>/128/iterations:1000       1.89 ms         1.89 ms         1000

Indexed Tree

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Benchmark                                                                Time             CPU   Iterations
----------------------------------------------------------------------------------------------------------
single_thread_indexed_tree_bench<Pedersen>/2/iterations:100           18.2 ms         18.2 ms          100
single_thread_indexed_tree_bench<Pedersen>/4/iterations:100           31.3 ms         31.3 ms          100
single_thread_indexed_tree_bench<Pedersen>/8/iterations:100           57.2 ms         57.2 ms          100
single_thread_indexed_tree_bench<Pedersen>/16/iterations:100           108 ms          108 ms          100
single_thread_indexed_tree_bench<Pedersen>/32/iterations:100           210 ms          210 ms          100
single_thread_indexed_tree_bench<Pedersen>/64/iterations:100           415 ms          415 ms          100
single_thread_indexed_tree_bench<Pedersen>/128/iterations:100          824 ms          824 ms          100

multi_thread_indexed_tree_bench<Pedersen>/2/iterations:100            12.8 ms         6.65 ms          100
multi_thread_indexed_tree_bench<Pedersen>/4/iterations:100            14.8 ms         7.31 ms          100
multi_thread_indexed_tree_bench<Pedersen>/8/iterations:100            18.5 ms         8.80 ms          100
multi_thread_indexed_tree_bench<Pedersen>/16/iterations:100           23.9 ms         12.0 ms          100
multi_thread_indexed_tree_bench<Pedersen>/32/iterations:100           35.1 ms         18.5 ms          100
multi_thread_indexed_tree_bench<Pedersen>/64/iterations:100           59.3 ms         31.6 ms          100
multi_thread_indexed_tree_bench<Pedersen>/128/iterations:100           109 ms         66.5 ms          100

single_thread_indexed_tree_bench<Poseidon2>/2/iterations:1000         1.26 ms         1.26 ms         1000
single_thread_indexed_tree_bench<Poseidon2>/4/iterations:1000         2.15 ms         2.15 ms         1000
single_thread_indexed_tree_bench<Poseidon2>/8/iterations:1000         3.88 ms         3.88 ms         1000
single_thread_indexed_tree_bench<Poseidon2>/16/iterations:1000        7.41 ms         7.41 ms         1000
single_thread_indexed_tree_bench<Poseidon2>/32/iterations:1000        14.6 ms         14.6 ms         1000
single_thread_indexed_tree_bench<Poseidon2>/64/iterations:1000        28.7 ms         28.7 ms         1000
single_thread_indexed_tree_bench<Poseidon2>/128/iterations:1000       56.8 ms         56.8 ms         1000

multi_thread_indexed_tree_bench<Poseidon2>/2/iterations:1000          1.01 ms        0.812 ms         1000
multi_thread_indexed_tree_bench<Poseidon2>/4/iterations:1000          1.17 ms        0.865 ms         1000
multi_thread_indexed_tree_bench<Poseidon2>/8/iterations:1000          1.46 ms        0.979 ms         1000
multi_thread_indexed_tree_bench<Poseidon2>/16/iterations:1000         2.05 ms         1.23 ms         1000
multi_thread_indexed_tree_bench<Poseidon2>/32/iterations:1000         3.24 ms         1.70 ms         1000
multi_thread_indexed_tree_bench<Poseidon2>/64/iterations:1000         5.84 ms         2.54 ms         1000
multi_thread_indexed_tree_bench<Poseidon2>/128/iterations:1000        13.3 ms         6.36 ms         1000

[AztecBot]

Benchmark results

No metrics with a significant change found.

Detailed results

All benchmarks are run on txs on the Benchmarking contract on the repository. Each tx consists of a batch call to create_note and increment_balance, which guarantees that each tx has a private call, a nested private call, a public call, and a nested public call, as well as an emitted private note, an unencrypted log, and public storage read and write.

This benchmark source data is available in JSON format on S3 here.

Values are compared against data from master at commit e58eda80 and shown if the difference exceeds 1%.

L2 block published to L1

Each column represents the number of txs on an L2 block published to L1.

Metric	8 txs	32 txs	128 txs
l1_rollup_calldata_size_in_bytes	45,700	180,580	720,100
l1_rollup_calldata_gas	222,760	871,324	3,465,820
l1_rollup_execution_gas	315,951	989,772	3,686,198
l2_block_processing_time_in_ms	1,151	4,350	17,262
note_successful_decrypting_time_in_ms	322 (+4%)	985	3,748 (+1%)
note_trial_decrypting_time_in_ms	33.4 (+70%)	116 (+1%)	144 (-3%)
l2_block_building_time_in_ms	18,015	70,847	285,185
l2_block_rollup_simulation_time_in_ms	13,259	52,106	209,985
l2_block_public_tx_process_time_in_ms	4,727	18,663	74,940 (+1%)

L2 chain processing

Each column represents the number of blocks on the L2 chain where each block has 16 txs.

Metric	5 blocks	10 blocks
node_history_sync_time_in_ms	13,786 (-1%)	26,508 (+1%)
note_history_successful_decrypting_time_in_ms	2,549 (+8%)	4,651 (+1%)
note_history_trial_decrypting_time_in_ms	141 (+63%)	225 (-1%)
node_database_size_in_bytes	17,305,680	33,026,128
pxe_database_size_in_bytes	29,923	59,478

Circuits stats

Stats on running time and I/O sizes collected for every circuit run across all benchmarks.

Circuit	circuit_simulation_time_in_ms	circuit_input_size_in_bytes	circuit_output_size_in_bytes
private-kernel-init	307	44,528	25,825
private-kernel-ordering	195	44,145	16,225
base-rollup	1,420	128,654	933
root-rollup	82.3	4,192	729
private-kernel-inner	438	71,331	25,825
public-kernel-private-input	242	32,287	25,825
public-kernel-non-first-iteration	238	32,329	25,825
merge-rollup	7.84	2,712	933

Tree insertion stats

The duration to insert a fixed batch of leaves into each tree type.

Metric	1 leaves	2 leaves	8 leaves	16 leaves	32 leaves	128 leaves	64 leaves	512 leaves	1024 leaves	2048 leaves	8192 leaves
batch_insert_into_append_only_tree_16_depth_ms	10.2	11.0 (-7%)	13.0 (+3%)	16.9 (-3%)	22.9 (+1%)	63.7 (-1%)	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_count	16.9	17.5	23.0	31.6	47.0	143	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_ms	0.592	0.614 (-7%)	0.555 (+4%)	0.523 (-3%)	0.480 (+1%)	0.440	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_32_depth_ms	N/A	N/A	N/A	N/A	N/A	74.3 (-7%)	47.6	239	461	898	3,552
batch_insert_into_append_only_tree_32_depth_hash_count	N/A	N/A	N/A	N/A	N/A	159	96.0	543	1,055	2,079	8,223
batch_insert_into_append_only_tree_32_depth_hash_ms	N/A	N/A	N/A	N/A	N/A	0.459 (-7%)	0.488	0.436	0.431	0.427	0.427
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	N/A	N/A	N/A	103 (-2%)	56.7	350 (+1%)	686	1,363	5,405
batch_insert_into_indexed_tree_20_depth_hash_count	N/A	N/A	N/A	N/A	N/A	197	104	691	1,363	2,707	10,771
batch_insert_into_indexed_tree_20_depth_hash_ms	N/A	N/A	N/A	N/A	N/A	0.491 (-1%)	0.497	0.474	0.473	0.473	0.471
batch_insert_into_indexed_tree_40_depth_ms	N/A	N/A	N/A	56.5	N/A	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_indexed_tree_40_depth_hash_count	N/A	N/A	N/A	94.1	N/A	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_indexed_tree_40_depth_hash_ms	N/A	N/A	N/A	0.578	N/A	N/A	N/A	N/A	N/A	N/A	N/A

Miscellaneous

Transaction sizes based on how many contracts are deployed in the tx.

Metric	0 deployed contracts	1 deployed contracts
tx_size_in_bytes	16,859	40,311

Transaction processing duration by data writes.

Metric	0 new commitments	1 new commitments
tx_pxe_processing_time_ms	556 (+1%)	1,309

Metric	0 public data writes	1 public data writes
tx_sequencer_processing_time_ms	0.511 (+2%)	580