docs: sumcheck documentation

[iakovenkos]

Re-organized docs for pow, sumcheck, and sumcheck_round

• SumcheckProver/Verifier, SumcheckProver/VerifierRound got detailed descriptions, where steps in the implementations match mathematical descriptions. Detailed descriptions of main methods.
• PowPolynomial struct: cleaned up and moved confusing parts explaining the computation of round univariates to the detailed description of SumcheckProver.
• General: made notation in docs consistent with the objects in the code, got rid of several inconsistencies, mostly in SumcheckVerifier and SumcheckVerifierRound.

Remark1. Made docs easy to find via search in doxygen. E.g. one could type PowPolynomial and go to the page where it's documented.
Remark2. In the case of pow, since it is a struct, the docs have to be placed after the the code to be rendered correctly by doxygen

[AztecBot]

Benchmark results

Metrics with a significant change:

• note_history_trial_decrypting_time_in_ms (5): 82.6 (+141%)
• note_successful_decrypting_time_in_ms (8): 195 (+81%)
• note_successful_decrypting_time_in_ms (32): 387 (+16%)
• note_trial_decrypting_time_in_ms (32): 25.5 (-77%)

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	772	772	772
l1_rollup_calldata_gas	6,844	6,820	6,844
l1_rollup_execution_gas	587,325	587,301	587,325
l2_block_processing_time_in_ms	1,424 (-1%)	5,293 (+3%)	10,295 (+1%)
note_successful_decrypting_time_in_ms	⚠️ 195 (+81%)	⚠️ 387 (+16%)	641 (-12%)
note_trial_decrypting_time_in_ms	84.8 (+17%)	⚠️ 25.5 (-77%)	47.2 (+34%)
l2_block_building_time_in_ms	18,626 (-1%)	73,033 (-1%)	144,841 (-1%)
l2_block_rollup_simulation_time_in_ms	18,413 (-1%)	72,286 (-1%)	143,385 (-1%)
l2_block_public_tx_process_time_in_ms	8,412 (-1%)	33,014 (-1%)	65,969 (-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	15,984 (+2%)	29,845 (-2%)
note_history_successful_decrypting_time_in_ms	864 (-6%)	1,714 (-1%)
note_history_trial_decrypting_time_in_ms	⚠️ 82.6 (+141%)	116 (-27%)
node_database_size_in_bytes	19,161,168	35,868,752
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	155	47,763	31,978
private-kernel-inner	176 (-1%)	80,794	31,978
private-kernel-ordering	136 (-1%)	57,732	50,043
base-parity	72.3 (-5%)	128	265
root-parity	126 (+2%)	1,244	265
base-rollup	12,162 (-1%)	110,926	957
root-rollup	50.0 (+1%)	4,551	821
public-kernel-app-logic	1,646 (-1%)	62,017	52,067
public-kernel-tail	4,238	168,566	7,491
merge-rollup	3,090 (-2%)	2,760	957
public-kernel-teardown	110 (-1%)	62,017	52,067
public-kernel-setup	118 (+1%)	62,017	52,067

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	11.0	17.6	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	0.638	0.545	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	51.6	80.1	259 (+1%)	504	978	1,936	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	0.529	0.495	0.474 (+1%)	0.470	0.465	0.464	N/A
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	60.4	118 (+1%)	371 (-1%)	742	1,450	2,893	N/A
batch_insert_into_indexed_tree_20_depth_hash_count	N/A	N/A	105	207	691	1,363	2,707	5,395	N/A
batch_insert_into_indexed_tree_20_depth_hash_ms	N/A	N/A	0.534	0.533 (+1%)	0.508	0.511 (+1%)	0.504	0.504	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	67.5
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	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	0.588

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	51,411	543,524

Transaction size based on fee payment method

Metric	native fee payment method	fpc_public fee payment method	fpc_private fee payment method
tx_with_fee_size_in_bytes	897	1,145	1,345

Transaction processing duration by data writes.

Metric	0 new note hashes	1 new note hashes	2 new note hashes
tx_pxe_processing_time_ms	1,251 (+1%)	859	3,498 (+1%)

Metric	1 public data writes	2 public data writes	3 public data writes	4 public data writes	5 public data writes	8 public data writes
tx_sequencer_processing_time_ms	834	758	1,349	904	2,074	1,088

[maramihali]

preliminary review

[maramihali]

First pass in case you want to start working on it

[maramihali]

Thanks so much, this is such great work 💜