feat: Add support for uint256 to DSL bigint

[guipublic]

uint256 in dsl big int are implemented by extending the bigfield class into bigfieldyn class, which is the same code, except that:

• it does not use a template for the bigfield modulus
• it allows for any modulus up to 2^{256} (included)

For now this class only works with 2^{256} modulus, but can be very easily extended to support any 256 bits (or less) prime.
Support for non-prime can be added with moderate effort. Only the witness generation part will need to be adapted because Montgomery multiplication does not work with power-of-2 limbs and even modulus.
In this PR, we simply use uint256_t for the witness generation.

I also added U256 in Noir stdlib

[AztecBot]

Benchmark results

Metrics with a significant change:

• circuit_simulation_time_in_ms (base-parity): 3,225 (-21%)
• circuit_simulation_time_in_ms (root-parity): 1,337 (+16%)
• circuit_simulation_time_in_ms (base-rollup): 7,738 (-46%)
• circuit_simulation_time_in_ms (private-kernel-inner): 394 (+75%)
• circuit_simulation_time_in_ms (public-kernel-app-logic): 257 (+112%)
• circuit_input_size_in_bytes (base-rollup): 140,076 (+20%)
• circuit_output_size_in_bytes (private-kernel-ordering): 27,130 (-31%)
• circuit_output_size_in_bytes (public-kernel-tail): 20,464 (+54%)
• tx_pxe_processing_time_ms (0): 2,128 (+25%)
• tx_pxe_processing_time_ms (1): 1,346 (+22%)
• tx_size_in_bytes (0): 31,367 (-23%)
• tx_sequencer_processing_time_ms (1): 859 (+49%)
• note_history_trial_decrypting_time_in_ms (10): 181 (+77%)
• l2_block_building_time_in_ms (8): 14,448 (+22%)
• l2_block_building_time_in_ms (32): 53,440 (+25%)
• l2_block_building_time_in_ms (64): 105,509 (+25%)
• l2_block_public_tx_process_time_in_ms (8): 6,923 (+47%)
• l2_block_public_tx_process_time_in_ms (32): 27,327 (+48%)
• l2_block_public_tx_process_time_in_ms (64): 54,623 (+48%)

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 e0e72008 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	64 txs
l1_rollup_calldata_size_in_bytes	676	676	676
l1_rollup_calldata_gas	6,418	6,400	6,412
l1_rollup_execution_gas	585,751	585,733	585,745
l2_block_processing_time_in_ms	1,294 (+1%)	4,648 (-5%)	8,996 (-3%)
note_successful_decrypting_time_in_ms	208 (-13%)	565 (+5%)	983 (+2%)
note_trial_decrypting_time_in_ms	62.3 (+64%)	80.2 (+62%)	58.9 (-28%)
l2_block_building_time_in_ms	⚠️ 14,448 (+22%)	⚠️ 53,440 (+25%)	⚠️ 105,509 (+25%)
l2_block_rollup_simulation_time_in_ms	7,497 (+6%)	26,024 (+8%)	50,716 (+8%)
l2_block_public_tx_process_time_in_ms	⚠️ 6,923 (+47%)	⚠️ 27,327 (+48%)	⚠️ 54,623 (+48%)

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	14,423 (+4%)	28,068 (+5%)
note_history_successful_decrypting_time_in_ms	1,350 (+4%)	2,481 (+3%)
note_history_trial_decrypting_time_in_ms	89.5 (-3%)	⚠️ 181 (+77%)
node_database_size_in_bytes	18,645,072	34,998,352
pxe_database_size_in_bytes	29,859	59,414

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 (+14%)	44,340	27,145 (+4%)
private-kernel-ordering	185 (+11%)	51,791 (+2%)	⚠️ 27,130 (-31%)
base-parity	⚠️ 3,225 (-21%)	128	311
root-parity	⚠️ 1,337 (+16%)	1,244	311
base-rollup	⚠️ 7,738 (-46%)	⚠️ 140,076 (+20%)	861
root-rollup	49.5 (-3%)	4,359	725
private-kernel-inner	⚠️ 394 (+75%)	72,661 (+1%)	27,138 (+4%)
public-kernel-app-logic	⚠️ 257 (+112%)	41,499 (-13%)	34,476 (-15%)
public-kernel-tail	168 (+2%)	47,323 (-11%)	⚠️ 20,464 (+54%)
merge-rollup	8.48 (-13%)	2,568	861
public-kernel-teardown	117 (+1%)	47,695	40,661
public-kernel-setup	116 (+1%)	47,695	40,661

Tree insertion stats

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

Metric	1 leaves	16 leaves	64 leaves	128 leaves	512 leaves	1024 leaves	2048 leaves	4096 leaves	32 leaves
batch_insert_into_append_only_tree_16_depth_ms	10.2 (+2%)	16.1	N/A	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_count	16.8	31.6	N/A	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_ms	0.593 (+2%)	0.499	N/A	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_32_depth_ms	N/A	N/A	45.5 (-1%)	78.1 (+8%)	228	443 (-1%)	859	1,694 (-1%)	N/A
batch_insert_into_append_only_tree_32_depth_hash_count	N/A	N/A	96.0	159	543	1,055	2,079	4,127	N/A
batch_insert_into_append_only_tree_32_depth_hash_ms	N/A	N/A	0.467 (-1%)	0.482 (+8%)	0.415	0.414 (-1%)	0.408	0.405 (-1%)	N/A
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	53.5 (-1%)	114 (+7%)	332 (-3%)	656 (-1%)	1,292	2,580	N/A
batch_insert_into_indexed_tree_20_depth_hash_count	N/A	N/A	104 (-1%)	207	691	1,363	2,707	5,395	N/A
batch_insert_into_indexed_tree_20_depth_hash_ms	N/A	N/A	0.474 (-1%)	0.513 (+6%)	0.451 (-3%)	0.452 (-1%)	0.448	0.448	N/A
batch_insert_into_indexed_tree_40_depth_ms	N/A	N/A	N/A	N/A	N/A	N/A	N/A	N/A	61.0
batch_insert_into_indexed_tree_40_depth_hash_count	N/A	N/A	N/A	N/A	N/A	N/A	N/A	N/A	109
batch_insert_into_indexed_tree_40_depth_hash_ms	N/A	N/A	N/A	N/A	N/A	N/A	N/A	N/A	0.533

Miscellaneous

Transaction sizes based on how many contract classes are registered in the tx.

Metric	0 registered classes	1 registered classes
tx_size_in_bytes	⚠️ 31,367 (-23%)	501,142

Transaction size based on fee payment method

Metric	native fee payment method	fpc_public fee payment method	fpc_private fee payment method
tx_with_fee_size_in_bytes	905	1,161	1,377

Transaction processing duration by data writes.

Metric	0 new note hashes	1 new note hashes	2 new note hashes
tx_pxe_processing_time_ms	⚠️ 2,128 (+25%)	⚠️ 1,346 (+22%)	5,382

Metric	0 public data writes	1 public data writes	2 public data writes	3 public data writes	4 public data writes	5 public data writes	8 public data writes
tx_sequencer_processing_time_ms	11.0	⚠️ 859 (+49%)	435	1,069	491 (-6%)	1,747	581 (-1%)

[TomAFrench]

We can put these test functions inside of the stdlib.

This is also not being run currently.

[guipublic]

The function is now called by the test.
I have not added it to stdlib test because I do not see any other test in the stdlib

[TomAFrench]

https://github.com/noir-lang/noir/blob/d202a086790f6dae33f9df385ab39b64ec8b54db/noir_stdlib/src/field/bn254.nr#L105-L181

[TomAFrench]

Closing this as we've been told that crypto team isn't comfortable with the changes.