chore: use traits in noir-protocol-circuits

[Thunkar]

Simple use of traits in noir-protocol-circuits and aztec-nr when possible.

Missing: Serialize/Deserialize due to: noir-lang/noir#3471

Renamed ::default() to ::empty(), since it better conveys meaning for our use cases (open to discussion).

[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 5b1e9f2b 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	45,444	179,588	716,132
l1_rollup_calldata_gas	222,948	868,256	3,447,812
l1_rollup_execution_gas	867,057	3,746,309	23,304,577
l2_block_processing_time_in_ms	1,336	5,097 (-4%)	21,048 (-1%)
note_successful_decrypting_time_in_ms	371 (+1%)	1,112 (-2%)	4,085 (-4%)
note_trial_decrypting_time_in_ms	81.7 (+10%)	36.7 (-11%)	134 (-1%)
l2_block_building_time_in_ms	14,898 (-1%)	59,352	237,294
l2_block_rollup_simulation_time_in_ms	10,576 (-2%)	42,238	169,215
l2_block_public_tx_process_time_in_ms	4,288	17,037	67,805 (-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	15,231	29,501 (+2%)
note_history_successful_decrypting_time_in_ms	3,019 (+13%)	5,770 (+7%)
note_history_trial_decrypting_time_in_ms	121 (+27%)	155 (+8%)
node_database_size_in_bytes	3,620,298	3,729,142
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	210	44,709	25,561
private-kernel-ordering	137 (+1%)	30,953	14,809
base-rollup	1,074	128,374	881
root-rollup	82.8	4,088	889
private-kernel-inner	288	71,236	25,561
public-kernel-private-input	202	31,891	25,561
public-kernel-non-first-iteration	201 (+1%)	31,933	25,561
merge-rollup	9.73	2,608	881

Miscellaneous

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

Metric	0 deployed contracts	1 deployed contracts
tx_size_in_bytes	15,487	31,879

[kevaundray]

LGTM!

[TomAFrench]

@Thunkar Is there a reason why is_empty isn't defined on the Empty trait? It seems like every type which implements Empty also has this method.