feat: laying out a new recursion constraint for honk

[lucasxia01]

Create new recursion constraint for honk, which is the same as the plonk recursion constraint, but with a default aggregation object added in. This PR is mostly for setup.

Set up for AztecProtocol/barretenberg#933.
Resolves AztecProtocol/barretenberg#988.

Please read contributing guidelines and remove this line.

[AztecBot]

Benchmark results

Metrics with a significant change:

• protocol_circuit_witness_generation_time_in_ms (base-parity): 339 (-56%)
• protocol_circuit_proving_time_in_ms (public-kernel-app-logic): 854 (-16%)

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.

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	740	740	740
l1_rollup_calldata_gas	6,680	6,668	6,680
l1_rollup_execution_gas	586,865	586,853	586,865
l2_block_processing_time_in_ms	1,608 (-1%)	6,063 (-1%)	12,003 (-1%)
l2_block_building_time_in_ms	35,154 (-1%)	138,810	276,267 (-1%)
l2_block_rollup_simulation_time_in_ms	34,939 (-1%)	138,036	274,729 (-1%)
l2_block_public_tx_process_time_in_ms	16,470 (-1%)	70,583	142,307 (-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	17,992	33,562
node_database_size_in_bytes	21,377,104	37,937,232
pxe_database_size_in_bytes	29,868	59,425

Circuits stats

Stats on running time and I/O sizes collected for every kernel circuit run across all benchmarks.

Circuit	protocol_circuit_simulation_time_in_ms	protocol_circuit_witness_generation_time_in_ms	protocol_circuit_proving_time_in_ms	protocol_circuit_input_size_in_bytes	protocol_circuit_output_size_in_bytes	protocol_circuit_proof_size_in_bytes	protocol_circuit_num_public_inputs	protocol_circuit_size_in_gates
private-kernel-init	162 (-1%)	3,591	22,465	20,412	62,374	85,376	2,601	1,048,576
private-kernel-inner	534 (-1%)	4,622 (+1%)	45,380 (+1%)	89,855	62,374	85,376	2,601	2,097,152
private-kernel-reset	995 (-1%)	6,261 (-10%)	87,657	330,808	62,374	85,376	2,601	4,194,304
private-kernel-tail	533 (-1%)	5,004 (+1%)	38,271	87,224	79,333	10,656	266	2,097,152
base-parity	8.22	⚠️ 339 (-56%)	4,177 (+15%)	128	64.0	2,208	2.00	131,072
root-parity	52.0 (+1%)	127 (+1%)	39,952 (+1%)	27,064	64.0	2,720	18.0	2,097,152
base-rollup	913 (-1%)	4,904 (+2%)	43,646	111,126	925	3,104	30.0	2,097,152
root-rollup	72.8	168	8,399 (+1%)	11,454	789	3,424	40.0	524,288
public-kernel-app-logic	192 (-1%)	298 (-9%)	⚠️ 854 (-16%)	96,791	84,967	113,344	3,475	4,096
public-kernel-tail	885	841 (-9%)	1,093 (+1%)	388,047	7,723	10,144	250	512
public-kernel-setup	164 (+2%)	376 (-9%)	915 (-2%)	137,024	84,967	113,344	3,475	4,096
public-kernel-teardown	168 (-2%)	517 (+11%)	1,089 (+4%)	141,902	84,967	113,344	3,475	4,096
merge-rollup	6.76 (-1%)	89.2 (+2%)	1,590 (-2%)	2,696	925	3,104	30.0	65,536
private-kernel-tail-to-public	N/A	10,235 (-1%)	68,805	N/A	N/A	113,856	3,491	4,194,304

Stats on running time collected for app circuits

Function	app_circuit_proof_size_in_bytes	app_circuit_proving_time_in_ms	app_circuit_size_in_gates	app_circuit_num_public_inputs
SchnorrAccount:entrypoint	15,456	48,244 (-1%)	2,097,152	416
Test:emit_nullifier	15,456	2,386 (-3%)	65,536	416
FPC:fee_entrypoint_public	15,456	8,644 (+1%)	524,288	416
Token:transfer	15,456	39,355 (-1%)	2,097,152	416
FPC:fee_entrypoint_private	15,456	9,169 (+2%)	524,288	416
Token:unshield	15,456	37,340 (+1%)	2,097,152	416
SchnorrAccount:spend_private_authwit	15,456	2,674 (+2%)	131,072	416

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	13.1	21.9 (+2%)	N/A	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_count	16.7	31.8	N/A	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_ms	0.769	0.673 (+2%)	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	61.6	97.1	314 (-1%)	611	1,188 (-2%)	2,361 (-1%)	N/A
batch_insert_into_append_only_tree_32_depth_hash_count	N/A	N/A	95.9	159	543	1,055	2,079	4,127	N/A
batch_insert_into_append_only_tree_32_depth_hash_ms	N/A	N/A	0.632	0.601	0.571 (-1%)	0.571	0.565 (-1%)	0.564 (-1%)	N/A
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	73.7	143 (-1%)	453 (-1%)	893	1,774 (-1%)	3,530 (-2%)	N/A
batch_insert_into_indexed_tree_20_depth_hash_count	N/A	N/A	106	208	692	1,363	2,707	5,395	N/A
batch_insert_into_indexed_tree_20_depth_hash_ms	N/A	N/A	0.645	0.643 (-1%)	0.617 (-1%)	0.616	0.616 (-1%)	0.615 (-1%)	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	80.5
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	108
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	0.709

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	84,315	673,143

Transaction size based on fee payment method

| Metric | |
| - | |

Transaction processing duration by data writes.

Metric	0 new note hashes	1 new note hashes	2 new note hashes
tx_pxe_processing_time_ms	37,087 (+1%)	3,656 (-1%)	114,064 (+1%)

Metric	0 public data writes	1 public data writes	2 public data writes	4 public data writes	8 public data writes
tx_sequencer_processing_time_ms	1,310 (+1%)	2,284 (+1%)	1,900	2,839	1,813

[vezenovm]

Suggested change

	// These are set and modified whenever we encounter a recursion opcode
	//
	// These should not be set by the caller
	// TODO(maxim): Check if this is always the case. ie I won't receive a proof that will set the first
	// TODO(maxim): input_aggregation_object to be non-zero.
	// TODO(maxim): if not, we can add input_aggregation_object to the proof too for all recursive proofs
	// TODO(maxim): This might be the case for proof trees where the proofs are created on different machines
	// This is set and modified whenever we encounter a recursion opcode

[lucasxia01]

we'll just throw this in the cleanup PR