chore: Persist initial header in local store

[spalladino]

The buildInitialHeader method from the merkle tree db just used the current state reference to build the header and return it, so it was only valid when called if the merkle tree db was still empty.

This PR fixes the issue by computing the initial header when init is called, and persisting it to the local store, so it can be retrieved even when loading an empty db.

---

An alternative approach would have been something in the lines of:

if (!fromDb) {
  const initialState = await this.getStateReference(true);
-  await this.#saveInitialStateReference(initialState);
+  this.initialState = initialState;
  await this.#updateArchive(this.getInitialHeader(), true);
+ } else {
+  const emptyTrees = MerkleTrees.new(openTmpStore()).init();
+  this.initialState = emptyTrees.getStateReference(true);
+ }

However, a downside of this approach is that, if the shape of the trees state change at some point during the chain history, then we'd be returning a wrong initial hash. Though, to be fair, a lot more things would probably break.

[AztecBot]

Benchmark results

Metrics with a significant change:

• protocol_circuit_simulation_time_in_ms (private-kernel-tail-to-public): 3,969 (-42%)
• avm_simulation_time_ms (Token:assert_minter_and_mint): 50.6 (-44%)
• protocol_circuit_proving_time_in_ms (base-parity): 1,936 (+38%)

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.

Proof generation

Each column represents the number of threads used in proof generation.

Metric	1 threads	4 threads	16 threads	32 threads	64 threads
proof_construction_time_sha256_ms	5,735	1,541	715 (+1%)	768 (+1%)	768 (-1%)
proof_construction_time_sha256_30_ms	11,758	3,151	1,419	1,453	1,469
proof_construction_time_sha256_100_ms	43,710	12,080	5,473 (-1%)	5,420 (-3%)	5,409 (-3%)
proof_construction_time_poseidon_hash_ms	78.0	35.0 (+3%)	34.0	59.0	88.0 (-2%)
proof_construction_time_poseidon_hash_30_ms	1,521	416	202 (+1%)	223	267 (-1%)
proof_construction_time_poseidon_hash_100_ms	5,618	1,517	680 (-1%)	728	750

L2 block published to L1

Each column represents the number of txs on an L2 block published to L1.

Metric	4 txs	8 txs	16 txs
l1_rollup_calldata_size_in_bytes	708	708	708
l1_rollup_calldata_gas	6,588	6,594	6,588
l1_rollup_execution_gas	583,050	583,207	583,352
l2_block_processing_time_in_ms	756	1,430 (+1%)	2,701
l2_block_building_time_in_ms	13,184	25,741	50,951
l2_block_rollup_simulation_time_in_ms	13,184	25,741	50,950
l2_block_public_tx_process_time_in_ms	11,074	23,406	48,555

L2 chain processing

Each column represents the number of blocks on the L2 chain where each block has 8 txs.

Metric	3 blocks	5 blocks
node_history_sync_time_in_ms	7,180 (+2%)	10,009
node_database_size_in_bytes	12,709,968 (+2%)	16,871,504 (+3%)
pxe_database_size_in_bytes	16,254	26,813

Circuits stats

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

Circuit	simulation_time_in_ms	witness_generation_time_in_ms	input_size_in_bytes	output_size_in_bytes	proving_time_in_ms	proof_size_in_bytes	num_public_inputs	size_in_gates
private-kernel-init	116 (-1%)	418 (+5%)	21,732	54,085	N/A	N/A	N/A	N/A
private-kernel-inner	228	743 (-1%)	81,199	54,264	N/A	N/A	N/A	N/A
private-kernel-tail	1,115	2,509 (+2%)	61,568	62,127	N/A	N/A	N/A	N/A
base-parity	6.60 (+1%)	844 (+2%)	160	96.0	⚠️ 1,936 (+38%)	12,676	3.00	131,072
root-parity	108 (+1%)	110 (-13%)	64,860	96.0	28,067 (-12%)	12,676	3.00	4,194,304
base-rollup	4,207	5,190 (+5%)	181,083	632	41,142 (-7%)	13,476	28.0	4,194,304
root-rollup	155 (+2%)	109 (-11%)	51,261	652	25,425 (-11%)	13,412	26.0	4,194,304
public-kernel-setup	200 (+3%)	2,352 (-5%)	113,048	80,822	15,720 (-12%)	119,428	3,339	2,097,152
public-kernel-app-logic	151	3,346	113,048	80,822	8,864 (-13%)	119,428	3,339	1,048,576
public-kernel-tail	899 (+1%)	24,058 (-12%)	410,181	10,814	61,854 (-7%)	25,860	415	8,388,608
private-kernel-reset-tiny	309 (+3%)	1,041 (+4%)	77,007	53,954	N/A	N/A	N/A	N/A
private-kernel-tail-to-public	⚠️ 3,969 (-42%)	2,918 (+2%)	773,262	1,632	N/A	N/A	N/A	N/A
public-kernel-teardown	141 (+1%)	3,318 (-2%)	113,048	80,822	16,261 (-12%)	119,428	3,339	2,097,152
merge-rollup	57.5	N/A	33,566	632	N/A	N/A	N/A	N/A
undefined	N/A	N/A	N/A	N/A	173,046 (-1%)	N/A	N/A	N/A

Stats on running time collected for app circuits

Function	input_size_in_bytes	output_size_in_bytes	witness_generation_time_in_ms	proof_size_in_bytes	proving_time_in_ms
ContractClassRegisterer:register	1,312	9,344	399 (+1%)	N/A	N/A
ContractInstanceDeployer:deploy	1,376	9,344	25.6 (+2%)	N/A	N/A
MultiCallEntrypoint:entrypoint	1,888	9,344	644 (+1%)	N/A	N/A
GasToken:deploy	1,344	9,344	576 (+2%)	N/A	N/A
SchnorrAccount:constructor	1,280	9,344	470 (+2%)	N/A	N/A
SchnorrAccount:entrypoint	2,272	9,344	803 (+1%)	N/A	N/A
Token:privately_mint_private_note	1,248	9,344	561 (+4%)	N/A	N/A
FPC:fee_entrypoint_public	1,312	9,344	106 (+6%)	N/A	N/A
Token:transfer	1,280	9,344	1,552 (+3%)	N/A	N/A
AuthRegistry:set_authorized (avm)	19,222	N/A	N/A	95,392	2,209 (+8%)
FPC:prepare_fee (avm)	22,670	N/A	N/A	95,456	2,400 (+14%)
Token:transfer_public (avm)	42,914	N/A	N/A	95,456	3,089 (+5%)
AuthRegistry:consume (avm)	33,100	N/A	N/A	95,424	2,726 (+5%)
FPC:pay_refund (avm)	32,835	N/A	N/A	95,424	8,006 (-11%)
Benchmarking:create_note	1,312	9,344	446	N/A	N/A
SchnorrAccount:verify_private_authwit	1,248	9,344	43.4 (+4%)	N/A	N/A
Token:unshield	1,344	9,344	1,256 (+3%)	N/A	N/A
FPC:fee_entrypoint_private	1,344	9,344	1,630 (+1%)	N/A	N/A

AVM Simulation

Time to simulate various public functions in the AVM.

Function	time_ms	bytecode_size_in_bytes
GasToken:_increase_public_balance	100	13,790
GasToken:set_portal	10.8 (+2%)	3,339
Token:constructor	129 (+2%)	23,692
FPC:constructor	91.6 (-2%)	13,592
GasToken:mint_public	82.3 (+1%)	10,158
Token:mint_public	339 (+2%)	19,034
Token:assert_minter_and_mint	⚠️ 50.6 (-44%)	12,925
AuthRegistry:set_authorized	47.5 (+2%)	7,812
FPC:prepare_fee	107 (+10%)	11,068
Token:transfer_public	45.5 (+18%)	31,218
FPC:pay_refund	126 (-7%)	21,266
Benchmarking:increment_balance	1,304	11,281
Token:_increase_public_balance	84.2	15,006
FPC:pay_refund_with_shielded_rebate	107 (-3%)	22,361

Public DB Access

Time to access various public DBs.

Function	time_ms
get-nullifier-index	0.152 (-5%)

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	256 leaves	512 leaves	1024 leaves
batch_insert_into_append_only_tree_16_depth_ms	10.4 (+1%)	16.8 (+1%)	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_count	16.8	31.7	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_ms	0.605 (+1%)	0.517 (+1%)	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_32_depth_ms	N/A	N/A	48.5	76.1 (+1%)	131	248 (+1%)	470
batch_insert_into_append_only_tree_32_depth_hash_count	N/A	N/A	95.9	159	287	543	1,055
batch_insert_into_append_only_tree_32_depth_hash_ms	N/A	N/A	0.496	0.467 (+1%)	0.450	0.448 (+1%)	0.439
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	60.2 (+1%)	112 (+1%)	183 (+1%)	355 (+1%)	693
batch_insert_into_indexed_tree_20_depth_hash_count	N/A	N/A	109	207	355	691	1,363
batch_insert_into_indexed_tree_20_depth_hash_ms	N/A	N/A	0.509 (+1%)	0.503 (+1%)	0.480 (-1%)	0.481 (+1%)	0.477
batch_insert_into_indexed_tree_40_depth_ms	N/A	N/A	73.3 (+1%)	N/A	N/A	N/A	N/A
batch_insert_into_indexed_tree_40_depth_hash_count	N/A	N/A	133	N/A	N/A	N/A	N/A
batch_insert_into_indexed_tree_40_depth_hash_ms	N/A	N/A	0.521 (+1%)	N/A	N/A	N/A	N/A

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	77,362	668,542

Transaction size based on fee payment method

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