feat: merge recursive verifier

[ledwards2225]

This PR includes

• Recursive merge verifier implementation and independent test
• Incorporation of recursive merge verification into Goblin::accumulate (and therefore into the full goblin recursion tests).
• Verification of the final ultra and merge proofs in goblin recursion tests
• Addition of direct constructors of Ultra and Merge verifiers from minimal inputs - no composer required

Closes AztecProtocol/barretenberg#797

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:

• note_trial_decrypting_time_in_ms (8): 16.6 (-56%)

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 379b5adc 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	222,924	868,112	3,449,408
l1_rollup_execution_gas	842,011	3,595,220	22,204,777
l2_block_processing_time_in_ms	2,231 (-4%)	8,437 (-1%)	34,956 (-2%)
note_successful_decrypting_time_in_ms	306 (-6%)	912 (-1%)	3,330 (-4%)
note_trial_decrypting_time_in_ms	⚠️ 16.6 (-56%)	37.6 (-23%)	201
l2_block_building_time_in_ms	20,027 (-1%)	80,114	320,896 (-1%)
l2_block_rollup_simulation_time_in_ms	16,526 (-1%)	66,304	265,473
l2_block_public_tx_process_time_in_ms	3,471 (-1%)	13,737 (-1%)	55,175 (-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	24,738 (-1%)	47,559
note_history_successful_decrypting_time_in_ms	2,161	4,168 (-1%)
note_history_trial_decrypting_time_in_ms	161 (-1%)	228 (-2%)
node_database_size_in_bytes	3,632,314	3,922,435
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	199	43,109	20,441
private-kernel-ordering	114 (-1%)	25,833	9,689
base-rollup	2,953	667,692	873
root-rollup	89.4 (+5%)	4,072	881
private-kernel-inner	259	64,516	20,441
public-kernel-private-input	170 (-1%)	25,203	20,441
public-kernel-non-first-iteration	168 (-1%)	25,245	20,441
merge-rollup	10.8 (-1%)	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	10,323	25,938

[ledwards2225]

Since recursion is now baked into Goblin, this simpler version of the test doesn't really make sense anymore. It wasn't adding much anyway

[codygunton]

We ran through this together ✅