chore: Clean up and refactor arithmetization

[ledwards2225]

Simplify and consolidate Arithmetization classes and move Arithmetization templating from CircuitBuilderBase to UltraCircuitBuilder_. This will facilitate reuse of Ultra builder functionality for new arithmetizations (e.g. Ultra + DataBus) via inheritance from UltraCircuitBuilder_<NewArithmetization>

[ludamad]

Any reason to not just call it FF instead of doing this using?

[ledwards2225]

This is to allow access to FF via e.g. Standard::FF from outside of this class. This has always felt a bit hacky but I'm not aware of another way to access the template param.

[ludamad]

Gotcha, might not be anything better then, thanks.

[ludamad]

LGTM

[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 db67aa1e 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	223,020	867,836	3,449,612
l1_rollup_execution_gas	842,107	3,594,944	22,204,981
l2_block_processing_time_in_ms	1,971 (-2%)	7,533 (-1%)	29,711
note_successful_decrypting_time_in_ms	294 (+2%)	866 (+2%)	3,155 (-2%)
note_trial_decrypting_time_in_ms	98.0 (+5%)	76.0 (+25%)	134 (-1%)
l2_block_building_time_in_ms	13,283 (+1%)	52,533	209,702
l2_block_rollup_simulation_time_in_ms	11,947 (+1%)	47,265	188,531
l2_block_public_tx_process_time_in_ms	1,297 (+2%)	5,133 (+1%)	20,685 (+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	21,558 (-1%)	42,063
note_history_successful_decrypting_time_in_ms	1,990 (-3%)	3,905 (-2%)
note_history_trial_decrypting_time_in_ms	121	141 (-24%)
node_database_size_in_bytes	1,629,545	1,096,475
pxe_database_size_in_bytes	29,748	59,307

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	72.7	61,697	18,841
private-kernel-ordering	43.4	24,233	8,089
base-rollup	1,770	656,309	811
root-rollup	77.4	4,072	1,097
private-kernel-inner	53.3	81,504	18,841
public-kernel-private-input	41.6	41,455	18,841
public-kernel-non-first-iteration	26.6	41,497	18,841
merge-rollup	0.964 (+6%)	2,592	873

Miscellaneous

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

Metric	0 deployed contracts	1 deployed contracts
tx_size_in_bytes	8,723	27,240