feat: Counters in private functions

[sirasistant]

This PR adds counter usage in private functions. The counters are used in the ordering kernel to ensure correct squashing and to reorder commitment and nullifier arrays.

Checklist:

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• 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_input_size_in_bytes (private-kernel-ordering): 43,753 (+41%)

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 fbaa7264 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	220,980	865,748	3,446,204
l1_rollup_execution_gas	934,124	3,968,222	24,789,740
l2_block_processing_time_in_ms	1,344 (+1%)	5,183 (+2%)	21,216 (+1%)
note_successful_decrypting_time_in_ms	331 (+1%)	1,021 (+1%)	3,688 (-1%)
note_trial_decrypting_time_in_ms	41.9 (+13%)	39.3	141 (-25%)
l2_block_building_time_in_ms	14,956 (+1%)	59,342 (+1%)	238,114 (+1%)
l2_block_rollup_simulation_time_in_ms	10,492	41,956	168,810
l2_block_public_tx_process_time_in_ms	4,395 (+2%)	17,290 (+1%)	69,022 (+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	15,366	29,444
note_history_successful_decrypting_time_in_ms	2,383 (-2%)	4,722 (-1%)
note_history_trial_decrypting_time_in_ms	86.0 (-1%)	180 (-2%)
node_database_size_in_bytes	3,623,944	3,729,557
pxe_database_size_in_bytes	29,923	59,478

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	212	44,681	25,561
private-kernel-ordering	165 (+19%)	⚠️ 43,753 (+41%)	14,809
base-rollup	1,064 (-1%)	128,338	881
root-rollup	80.8 (-1%)	4,088	709
private-kernel-inner	291	71,208	25,561
public-kernel-private-input	205	31,863	25,561
public-kernel-non-first-iteration	203	31,905	25,561
merge-rollup	8.46	2,608	881

Tree insertion stats

The duration to insert a fixed batch of leaves into each tree type.

Metric	1 leaves	2 leaves	8 leaves	16 leaves	32 leaves	64 leaves	128 leaves	512 leaves	1024 leaves	2048 leaves	8192 leaves
batch_insert_into_append_only_tree_ms	11.2	90.3 (+4%)	13.7 (-11%)	17.8 (-1%)	24.2 (+2%)	50.1	89.8 (-3%)	241	472 (-1%)	920 (+1%)	3,577 (+1%)
batch_insert_into_indexed_tree_ms	N/A	N/A	N/A	65.0	N/A	59.7	111	361	736 (-1%)	1,420 (+1%)	5,589 (-2%)

Miscellaneous

Transaction sizes based on how many contracts are deployed in the tx.

Metric	0 deployed contracts	1 deployed contracts
tx_size_in_bytes	15,455	32,231 (+1%)

Transaction processing duration by data writes.

Metric	0 new commitments	1 new commitments
tx_pxe_processing_time_ms	373 (+8%)	1,082 (+11%)

Metric	1 public data writes
tx_sequencer_processing_time_ms	536

[github-actions]

Changes to circuit sizes

Generated at commit: 3acffde928d6ad1d7733820eb684550cc2b0b6e1, compared to commit: fbaa72641c50cc7f05712e266416f12c4edf8fe9

🧾 Summary (100% most significant diffs)

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
private_kernel_ordering	+6,644 ❌	+2.29%	+40,951 ❌	+4.61%
public_kernel_public_previous	+329 ❌	+0.40%	+576 ❌	+0.14%
public_kernel_private_previous	+329 ❌	+0.40%	+576 ❌	+0.14%
private_kernel_inner	+371 ❌	+0.25%	+648 ❌	+0.09%
private_kernel_init	+83 ❌	+0.17%	+145 ❌	+0.04%
rollup_base	+288 ❌	+0.10%	+504 ❌	+0.03%

---

Full diff report 👇

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
private_kernel_ordering	297,172 (+6,644)	+2.29%	929,413 (+40,951)	+4.61%
public_kernel_public_previous	81,752 (+329)	+0.40%	417,509 (+576)	+0.14%
public_kernel_private_previous	81,760 (+329)	+0.40%	417,517 (+576)	+0.14%
private_kernel_inner	151,016 (+371)	+0.25%	753,606 (+648)	+0.09%
private_kernel_init	48,062 (+83)	+0.17%	382,536 (+145)	+0.04%
rollup_base	294,201 (+288)	+0.10%	1,670,919 (+504)	+0.03%

[LeilaWang]

Only a minor thing. Great works!! 🎉