docs: Yellow paper section on Gas and Fees

[PhilWindle]

This PR contains the section of the yellow paper for Gas and Fees

Checklist:

Remove the checklist to signal you've completed it. Enable auto-merge if the PR is ready to merge.

• 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:

• note_trial_decrypting_time_in_ms (32): 52.1 (-35%)

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 5a18615f 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	222,972	867,692	3,449,660
l1_rollup_execution_gas	842,059	3,594,800	22,205,029
l2_block_processing_time_in_ms	2,236 (+11%)	8,566 (+13%)	33,536 (+12%)
note_successful_decrypting_time_in_ms	298 (+2%)	943 (+8%)	3,314 (+4%)
note_trial_decrypting_time_in_ms	99.9 (+4%)	⚠️ 52.1 (-35%)	135 (-15%)
l2_block_building_time_in_ms	21,017 (+2%)	84,398 (+3%)	337,503 (+3%)
l2_block_rollup_simulation_time_in_ms	12,348 (+3%)	49,792 (+5%)	198,192 (+5%)
l2_block_public_tx_process_time_in_ms	8,628 (+1%)	34,467 (+1%)	138,782 (+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	22,518 (+2%)	47,201 (+10%)
note_history_successful_decrypting_time_in_ms	2,142 (+2%)	4,414 (+9%)
note_history_trial_decrypting_time_in_ms	122 (+2%)	159 (+10%)
node_database_size_in_bytes	1,628,380	1,094,571
pxe_database_size_in_bytes	29,748	59,307

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	767 (+1%)	61,697	18,905
private-kernel-ordering	127 (+2%)	24,297	8,153
base-rollup	1,796 (+1%)	656,428	873
root-rollup	172	4,072	1,097
private-kernel-inner	792 (+1%)	81,568	18,905
public-kernel-private-input	573 (+1%)	41,519	18,905
public-kernel-non-first-iteration	410 (+1%)	41,561	18,905
merge-rollup	15.8 (+4%)	2,592	873

Miscellaneous

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

Metric	0 deployed contracts	1 deployed contracts
tx_size_in_bytes	8,787	27,547

[alexghr]

This is great! Just a couple of minor typos

[alexghr]

This component consists of a single public function call to a contract function specified by the client.

Would this be the same contract as the one used for fee preparation or a different one?

[PhilWindle]

It could be either.

[alexghr]

Suggested change

Any enqueued public function calls can be simulated by the sequencer to obtain an accurate gas profile of the execution. This simulation will enable the sequencer to compute the number of additional state updates to be made, the number of public function calls and the L2 gas consumption of each of those calls. If either the L1 or L2 gas limits are breached, simulation will identify where in the execution trace this takes place and so the sequencer will only need to perform iterations of the public VM and public kernel circuits for the calls that either partially or completely succeeded. This ensures that the sequencer is not forced to exeucte and prove circuits for which they will not be compensated.

Any enqueued public function calls can be simulated by the sequencer to obtain an accurate gas profile of the execution. This simulation will enable the sequencer to compute the number of additional state updates to be made, the number of public function calls and the L2 gas consumption of each of those calls. If either the L1 or L2 gas limits are breached, simulation will identify where in the execution trace this takes place and so the sequencer will only need to perform iterations of the public VM and public kernel circuits for the calls that either partially or completely succeeded. This ensures that the sequencer is not forced to execute and prove circuits for which they will not be compensated.

[alexghr]

Suggested change

	The total fee taken by the sequencer is calculated from the values of consumed L1 and L2 gas and the `feePerGas` values provided with the transaction. Any balance reamining must be refunded.
	The total fee taken by the sequencer is calculated from the values of consumed L1 and L2 gas and the `feePerGas` values provided with the transaction. Any balance remaining must be refunded.