feat: introduce initialize_or_replace

[nventuro]

This fixes the issue described in these comments, which highlighted that PrivateMutable was providing a poor API as it forced users to call unconstrained functions and leave correctness up to them. This is a simple replacement to make #6442 cleaner and help guide future development, but it should only be considered a patch - we'll eventually do a more thoughtful complete pass over the entire API to bring coherency to it.

I tried adding tests for this (I wanted to test that regardless what the return value of the nullifier check oracle was, either an inclusion proof or a new nullifier would be included in the context), but this proved to be very hard because notes are sent to the oracle as raw fields in a custom packed format which oracle::get_notes decodes on the spot. We'd need to have that be a separate library, but that exceeds the scope of this PR.

[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.

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	5,704	1,548 (-1%)	715	777 (+2%)	776

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	1,412	1,412	1,412
l1_rollup_calldata_gas	9,464	9,428 (-1%)	9,464
l1_rollup_execution_gas	616,105	616,069	616,105
l2_block_processing_time_in_ms	1,322 (-5%)	5,114 (-1%)	10,114 (-1%)
l2_block_building_time_in_ms	45,289 (-4%)	179,325 (-4%)	371,918
l2_block_rollup_simulation_time_in_ms	45,120 (-4%)	178,706 (-4%)	370,668
l2_block_public_tx_process_time_in_ms	24,235 (-4%)	100,829 (-4%)	215,413 (+1%)

L2 chain processing

Each column represents the number of blocks on the L2 chain where each block has 16 txs.

Metric	3 blocks	5 blocks
node_history_sync_time_in_ms	10,015 (+1%)	15,303 (+1%)
node_database_size_in_bytes	14,463,056	21,348,432
pxe_database_size_in_bytes	18,071	29,868

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	158 (-1%)	3,648	22,153	19,990	61,798	86,720	2,643	1,048,576
private-kernel-inner	600 (-1%)	4,208	47,671 (-2%)	88,862	61,798	86,720	2,643	2,097,152
private-kernel-tail	526 (-1%)	3,007 (+6%)	35,343	86,653	76,438	10,624	265	2,097,152
base-parity	6.48 (-1%)	1,223	2,898 (-1%)	128	64.0	2,208	2.00	131,072
root-parity	49.2 (-1%)	48.6 (-12%)	44,071 (+1%)	27,084	64.0	2,720	18.0	2,097,152
base-rollup	777	2,293 (-1%)	74,271	119,578	756	3,648	47.0	4,194,304
root-rollup	114	63.5 (-6%)	19,258 (-1%)	25,297	620	3,456	41.0	1,048,576
public-kernel-app-logic	521	2,846	47,322	103,405	84,766	116,832	3,584	2,097,152
public-kernel-tail	1,181 (-1%)	25,509 (+2%)	156,893 (+2%)	393,850	7,490	10,624	265	8,388,608
private-kernel-reset-small	579	2,182 (-4%)	27,027 (+8%)	118,173	61,798	86,720	2,643	1,048,576
merge-rollup	28.6 (-1%)	N/A	N/A	16,534	756	N/A	N/A	N/A
public-kernel-setup	624	N/A	N/A	103,405	84,766	N/A	N/A	N/A
public-kernel-teardown	527 (-1%)	N/A	N/A	103,405	84,766	N/A	N/A	N/A
private-kernel-tail-to-public	N/A	9,584 (+1%)	83,598 (+2%)	N/A	N/A	116,832	3,584	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	16,128	46,102	2,097,152	437
Token:transfer	16,128	46,141 (+7%)	2,097,152	437

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	11.3	18.4 (-1%)	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	0.657	0.566 (-1%)	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	52.9	80.5 (-1%)	256 (-3%)	504	991	1,960	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	0.541	0.496 (-1%)	0.465 (-3%)	0.471	0.470	0.468	N/A
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	62.3 (-1%)	119	367 (-4%)	743	1,498 (+1%)	2,937	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	0.540 (-1%)	0.534	0.498 (-4%)	0.511	0.511	0.511	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	66.7
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	107
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	0.592

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	82,705	664,768

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	11,598 (+4%)	4,193 (-1%)	70,017

Metric	1 public data writes	2 public data writes	3 public data writes	4 public data writes	8 public data writes
tx_sequencer_processing_time_ms	3,190	2,108 (-2%)	6,038	2,294	2,587