chore: add bigint solver in ACVM and add a unit test for bigints in Noir

[guipublic]

The PR enable bigints in ACVM, i.e you can now compile and execute Noir programs using bigint opcodes.
This is demonstrated in the added unit test.

[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 d953090c 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	45,636	180,516	720,036
l1_rollup_calldata_gas	222,552	871,044	3,462,492
l1_rollup_execution_gas	315,039	988,784	3,682,149
l2_block_processing_time_in_ms	1,157	4,349 (-1%)	17,212 (-1%)
note_successful_decrypting_time_in_ms	304	978 (-1%)	3,642 (-1%)
note_trial_decrypting_time_in_ms	16.2 (+11%)	107 (-12%)	141 (-7%)
l2_block_building_time_in_ms	17,840	70,211	282,251
l2_block_rollup_simulation_time_in_ms	13,050	51,578	207,901
l2_block_public_tx_process_time_in_ms	4,729 (-1%)	18,549	74,111 (-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	13,890 (-1%)	26,481 (-1%)
note_history_successful_decrypting_time_in_ms	2,353 (-4%)	4,585 (-5%)
note_history_trial_decrypting_time_in_ms	86.1 (-22%)	151 (-34%)
node_database_size_in_bytes	17,322,064	33,046,608
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	308 (-1%)	44,481	26,193
private-kernel-ordering	194 (-1%)	44,513	14,929
base-rollup	1,402	128,970	881
root-rollup	82.3 (-1%)	4,088	677
private-kernel-inner	415	71,640	26,193
public-kernel-private-input	239 (-1%)	32,615	26,193
public-kernel-non-first-iteration	238 (-1%)	32,657	26,193
merge-rollup	7.60 (-2%)	2,608	881

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	11.3 (+1%)	12.8 (+2%)	16.9 (-3%)	22.7 (-1%)	63.5 (-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	0.594	0.630 (+1%)	0.544 (+1%)	0.524 (-3%)	0.477 (-1%)	0.439 (-1%)	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	74.5 (-1%)	47.4	240	462 (-1%)	899 (-1%)	3,541 (-1%)
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	0.461	0.487	0.438	0.433	0.428 (-1%)	0.426 (-1%)
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	N/A	N/A	N/A	104 (-1%)	56.6 (-1%)	349	690 (-1%)	1,369 (+1%)	5,407
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	0.495	0.495	0.476	0.475	0.475 (+1%)	0.471
batch_insert_into_indexed_tree_40_depth_ms	N/A	N/A	N/A	56.5 (-1%)	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	15,575	38,323

Transaction processing duration by data writes.

Metric	0 new commitments	1 new commitments
tx_pxe_processing_time_ms	552	1,224 (-1%)

Metric	0 public data writes	1 public data writes
tx_sequencer_processing_time_ms	0.502 (-25%)	574 (-1%)

[kevaundray]

This is okay to merge, but I think we should likely just have different BigInt structures so that we get type safety. Can you open up an issue for this?

[guipublic]

noir-lang/noir#4257

[kevaundray]

Generally okay, I think we can clean up nits on this once merged