docs(yellow-paper): Update function broadcasting functions

[spalladino]

Updates yellow paper with changes from the two PRs below in this stack.

[spalladino]

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This pull request is not mergeable via GitHub because a downstack PR is open. Once all requirements are satisfied, merge this PR as a stack on Graphite.
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• feat: Capture broadcasted functions in node #5353
• chore: Bytecode is buffer not string #5351
• docs(yellow-paper): Update function broadcasting functions #5350 👈
• feat: Capture broadcasted unconstrained functions in node #5349
• feat: Capture broadcasted private fns in node #5318
• master

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[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.

Values are compared against data from master at commit 5d669b93 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	64 txs
l1_rollup_calldata_size_in_bytes	676	676	676
l1_rollup_calldata_gas	6,424	6,424	6,424
l1_rollup_execution_gas	585,757	585,757	585,757
l2_block_processing_time_in_ms	1,342 (+4%)	4,659 (-2%)	8,901 (-1%)
note_successful_decrypting_time_in_ms	147 (-21%)	532 (+2%)	1,038 (+9%)
note_trial_decrypting_time_in_ms	53.0 (-43%)	47.4 (+29%)	64.5 (-23%)
l2_block_building_time_in_ms	16,637 (-3%)	62,882 (-3%)	126,852 (-3%)
l2_block_rollup_simulation_time_in_ms	7,671 (-4%)	27,299 (-3%)	54,530 (-5%)
l2_block_public_tx_process_time_in_ms	8,947 (-3%)	35,532 (-3%)	72,227 (-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	14,341 (+1%)	26,686 (+1%)
note_history_successful_decrypting_time_in_ms	1,262 (+1%)	2,545 (+5%)
note_history_trial_decrypting_time_in_ms	92.3 (-2%)	103 (-16%)
node_database_size_in_bytes	18,657,360	34,943,056
pxe_database_size_in_bytes	29,859	59,414

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	246 (+3%)	44,344	28,181
private-kernel-ordering	216 (+1%)	52,847	14,263
base-parity	4,452 (+1%)	128	311
root-parity	1,606 (-7%)	1,244	311
base-rollup	17,817 (-4%)	165,727	861
root-rollup	49.8	4,359	725
private-kernel-inner	598 (+1%)	73,728	28,181
public-kernel-app-logic	397 (-1%)	35,185	28,151
public-kernel-tail	170 (-1%)	40,862	28,151
merge-rollup	8.78 (+6%)	2,568	861

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	9.89 (-1%)	15.8 (-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	16.8	31.6	N/A	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_ms	0.577 (-1%)	0.489 (-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	45.2 (-2%)	71.1 (-2%)	223 (-6%)	445	859 (-1%)	1,710	N/A
batch_insert_into_append_only_tree_32_depth_hash_count	N/A	N/A	96.0	159	543	1,055	2,079	4,127	N/A
batch_insert_into_append_only_tree_32_depth_hash_ms	N/A	N/A	0.464 (-2%)	0.439 (-2%)	0.408 (-5%)	0.416	0.408 (-1%)	0.410	N/A
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	52.9 (-2%)	106 (-1%)	324 (-3%)	662	1,298	2,547 (-3%)	N/A
batch_insert_into_indexed_tree_20_depth_hash_count	N/A	N/A	104	207	691	1,363	2,707	5,395	N/A
batch_insert_into_indexed_tree_20_depth_hash_ms	N/A	N/A	0.471 (-2%)	0.476 (-1%)	0.441 (-3%)	0.455	0.452	0.443 (-3%)	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	60.7 (-1%)
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	109
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	0.531 (-1%)

Miscellaneous

Transaction sizes based on how many contract classes are registered in the tx.

Metric	0 registered classes
tx_size_in_bytes	21,991

Transaction processing duration by data writes.

Metric	0 new note hashes	1 new note hashes
tx_pxe_processing_time_ms	3,054 (-1%)	1,651

Metric	0 public data writes	1 public data writes
tx_sequencer_processing_time_ms	10.8	1,136 (-1%)

[spalladino]

Closing in favor of merging everything in one go in #5353