chore: add struct for each bigint modulus

[guipublic]

Resolves Noir issue noir-lang/noir#4257

The PR simply adds one struct per modulus, so that the user cannot mix them.

[kevaundray]

Do we want this to also have Bounds for Add, Sub, Mul and Div?

[guipublic]

Could you clarify what do you mean with 'Bounds'?

[kevaundray]

Can create an issue to have BigField inheriting from the Add, Sub, Mul trait Bounds

[AztecBot]

Benchmark results

Metrics with a significant change:

• note_successful_decrypting_time_in_ms (8): 312 (-28%)

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 e63f0226 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	45,956	181,604	724,196
l1_rollup_calldata_gas	227,096	888,812	3,536,072
l1_rollup_execution_gas	320,287	1,007,260	3,756,450
l2_block_processing_time_in_ms	1,196	4,533 (+1%)	17,747
note_successful_decrypting_time_in_ms	⚠️ 312 (-28%)	1,014 (+4%)	3,612
note_trial_decrypting_time_in_ms	26.0 (-38%)	51.1 (-51%)	168 (-5%)
l2_block_building_time_in_ms	18,200	72,297	290,007
l2_block_rollup_simulation_time_in_ms	13,451 (-1%)	53,428	214,618
l2_block_public_tx_process_time_in_ms	4,723 (+1%)	18,788 (+1%)	75,120 (+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	14,934 (-6%)	28,424 (-7%)
note_history_successful_decrypting_time_in_ms	2,329 (+2%)	4,605
note_history_trial_decrypting_time_in_ms	91.8 (+5%)	233 (-6%)
node_database_size_in_bytes	17,256,528	33,181,776
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	328	44,568	25,313
private-kernel-ordering	196	43,633	16,193
base-rollup	1,456	129,774	933
root-rollup	82.6	4,192	729
private-kernel-inner	430 (-1%)	70,859	25,313
public-kernel-private-input	243 (+1%)	33,703	26,945
public-kernel-non-first-iteration	242 (+2%)	33,745	26,945
merge-rollup	7.80	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	10.3 (-1%)	10.8 (-2%)	12.7 (-1%)	17.1 (-1%)	26.5 (+16%)	63.9	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	0.594 (-1%)	0.598 (-3%)	0.538 (-1%)	0.528 (-1%)	0.549 (+15%)	0.441	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	75.3 (-1%)	47.6 (-2%)	238	459 (-2%)	921 (+3%)	3,553
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	0.464 (-1%)	0.488 (-1%)	0.435	0.431 (-2%)	0.436 (+2%)	0.428
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	N/A	N/A	N/A	105 (+1%)	56.7	353	687 (-1%)	1,378 (+1%)	5,404 (-1%)
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	0.498 (+1%)	0.496	0.475 (-1%)	0.472 (-1%)	0.474	0.470
batch_insert_into_indexed_tree_40_depth_ms	N/A	N/A	N/A	56.9	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	35,536

Transaction processing duration by data writes.

Metric	0 new commitments	1 new commitments
tx_pxe_processing_time_ms	553	1,446

Metric	0 public data writes	1 public data writes
tx_sequencer_processing_time_ms	0.529 (+4%)	582 (+1%)