feat: implement bigint in Noir, using bigint opcodes

[guipublic]

This PR enables big integers in Noir using the bigint opcodes.
It does not implement bigints in ACVM which is required to solve the opcodes.
It also does not implement bigints opcodes in Barretenberg, which is required to generate the constraints.

However it provides a BigInt structure in the stdlib so you can write code like this in Noir, which will be compiled into ACIR using the bigint opcodes.

    let a = bigint::BigInt::from_le_bytes([3], [23]);
    let b = bigint::BigInt::from_le_bytes([5], [23]);
    let c = a+b;
    let bytes = c.to_le_bytes();
    std::println(bytes[0]);

I did not add a test yet because ACMV solver is not yet implemented.

[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 301f0e6d 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	45,412	179,524	716,068
l1_rollup_calldata_gas	221,668	866,452	3,448,276
l1_rollup_execution_gas	314,087	984,124	3,667,865
l2_block_processing_time_in_ms	1,631 (+1%)	5,373 (+3%)	21,076 (+2%)
note_successful_decrypting_time_in_ms	289 (+1%)	856 (+2%)	3,236 (+2%)
note_trial_decrypting_time_in_ms	100 (+3%)	83.3 (+33%)	135 (-8%)
l2_block_building_time_in_ms	16,331 (+2%)	64,875 (+2%)	259,748 (+2%)
l2_block_rollup_simulation_time_in_ms	11,890 (+2%)	47,277 (+2%)	189,603 (+2%)
l2_block_public_tx_process_time_in_ms	4,413 (+2%)	17,505 (+2%)	69,858 (+2%)

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	16,096 (+1%)	30,658
note_history_successful_decrypting_time_in_ms	2,007 (+1%)	4,020 (+4%)
note_history_trial_decrypting_time_in_ms	159 (+8%)	237 (+2%)
node_database_size_in_bytes	3,518,736	3,548,772
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	215 (+1%)	44,681	25,561
private-kernel-ordering	167 (+1%)	43,753	14,809
base-rollup	1,209 (+1%)	128,338	881
root-rollup	79.7 (+1%)	4,088	677
private-kernel-inner	293 (+1%)	71,208	25,561
public-kernel-private-input	207 (+1%)	31,863	25,561
public-kernel-non-first-iteration	205 (+1%)	31,905	25,561
merge-rollup	7.70 (+1%)	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	12.1 (+1%)	17.5 (-7%)	13.8 (-9%)	19.4 (+1%)	23.8 (-6%)	67.9 (+2%)	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	0.622	0.634 (-4%)	0.555 (-10%)	0.542	0.484	0.451 (+2%)	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	84.1 (+2%)	52.8 (+2%)	254 (+3%)	480	931 (+2%)	3,635 (+2%)
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	0.477 (+2%)	0.505 (+1%)	0.446 (+2%)	0.436	0.436 (+2%)	0.435 (+2%)
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	N/A	N/A	N/A	116 (-1%)	62.8 (+1%)	375 (+2%)	778 (+1%)	1,465 (+3%)	5,698 (+2%)
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	0.502	0.509 (+1%)	0.486 (+2%)	0.488 (+1%)	0.483 (+2%)	0.481 (+2%)
batch_insert_into_indexed_tree_40_depth_ms	N/A	N/A	N/A	68.3 (+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	0.601 (+1%)	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	15,455	32,222

Transaction processing duration by data writes.

Metric	0 new commitments	1 new commitments
tx_pxe_processing_time_ms	378 (+1%)	1,093 (+1%)

Metric	1 public data writes
tx_sequencer_processing_time_ms	540 (+1%)

[kevaundray]

Left some comments

[kevaundray]

Main blocking comment has been resolved -- once the others are resolved up, we can merge