feat: Base rollup in noir

[sirasistant]

This PR ports the logic for the base rollup from CPP to noir. There are multiple optimizations for this circuit in the pipeline:

• Change the indexed tree insertion algorithm to eliminate the second branch. Experimental branch here feat: circuit optimized indexed tree batch insertion #3367
• Brillig array optimisation. Experimental branch here Arv/experiment cow opt #3377
• Switch the public data tree to indexed

Checklist:

Remove the checklist to signal you've completed it. Enable auto-merge if the PR is ready to merge.

• If the pull request requires a cryptography review (e.g. cryptographic algorithm implementations) I have added the 'crypto' tag.
• I have reviewed my diff in github, line by line and removed unexpected formatting changes, testing logs, or commented-out code.
• Every change is related to the PR description.
• I have linked this pull request to relevant issues (if any exist).

[AztecBot]

Benchmark results

Metrics with a significant change:

• circuit_simulation_time_in_ms (base-rollup): 4,076 (+132%)
• l2_block_building_time_in_ms (8): 30,111 (+46%)
• l2_block_building_time_in_ms (32): 119,352 (+46%)
• l2_block_building_time_in_ms (128): 473,598 (+44%)
• l2_block_rollup_simulation_time_in_ms (8): 21,476 (+80%)
• l2_block_rollup_simulation_time_in_ms (32): 84,951 (+79%)
• l2_block_rollup_simulation_time_in_ms (128): 338,574 (+79%)
• note_trial_decrypting_time_in_ms (8): 100 (+1635%)

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 2001d474 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	222,948	868,112	3,447,872
l1_rollup_execution_gas	842,035	3,595,220	22,203,241
l2_block_processing_time_in_ms	2,057 (+1%)	7,666 (-1%)	29,890 (-1%)
note_successful_decrypting_time_in_ms	297 (-1%)	877	3,194 (-1%)
note_trial_decrypting_time_in_ms	⚠️ 100 (+1635%)	87.7 (-4%)	140
l2_block_building_time_in_ms	⚠️ 30,111 (+46%)	⚠️ 119,352 (+46%)	⚠️ 473,598 (+44%)
l2_block_rollup_simulation_time_in_ms	⚠️ 21,476 (+80%)	⚠️ 84,951 (+79%)	⚠️ 338,574 (+79%)
l2_block_public_tx_process_time_in_ms	8,592	34,256	134,510 (-3%)

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	21,763	42,293
note_history_successful_decrypting_time_in_ms	2,028 (-1%)	3,956 (-1%)
note_history_trial_decrypting_time_in_ms	126	154 (-1%)
node_database_size_in_bytes	1,631,174	1,097,877
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	766	61,697	18,905
private-kernel-ordering	126 (-1%)	24,297	8,153
base-rollup	⚠️ 4,076 (+132%)	656,428	873
root-rollup	141 (-16%)	4,072	1,097
private-kernel-inner	790	81,568	18,905
public-kernel-private-input	562 (-2%)	41,519	18,905
public-kernel-non-first-iteration	406 (-1%)	41,561	18,905
merge-rollup	15.4	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	8,787	27,547

[LeilaWang]

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