feat: define Aztec prelude

[TomAFrench]

This PR breaks the definition of the prelude out from #4496 as the contents of the prelude is uncontroversial and changes to the imports are very prone to merge conflicts. I'd then like to merge this change to the imports separately as we can do this quickly (allowing aztec to iterate on what goes into the prelude) and we can improve how this is imported with a proper prelude syntax in a followup PR.

I've also removed the explicit imports of Option as this is part of the Noir prelude.

[vezenovm]

Just noting that the followup PR should also update any naming that is done in aztec_macros to use the full import path from aztec-nr rather than reserving the name with the assumption that the import has been provided.

[TomAFrench]

Agreed, it seems like aztec_macros was relying on NoteHeader being imported which meant that we got mystery compile failures if we didn't import it despite appearing to not use it at all.

[AztecBot]

Benchmark results

Metrics with a significant change:

• note_successful_decrypting_time_in_ms (32): 547 (-37%)
• note_trial_decrypting_time_in_ms (8): 114 (+933%)

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 ecfcb787 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	5,700	18,884	36,452
l1_rollup_calldata_gas	66,012	239,120	469,832
l1_rollup_execution_gas	193,960	500,426	909,090
l2_block_processing_time_in_ms	1,202	4,515 (+1%)	9,004 (+2%)
note_successful_decrypting_time_in_ms	198 (-3%)	⚠️ 547 (-37%)	999 (+1%)
note_trial_decrypting_time_in_ms	⚠️ 114 (+933%)	71.0 (-28%)	133 (+4%)
l2_block_building_time_in_ms	15,901 (-1%)	63,045	126,549
l2_block_rollup_simulation_time_in_ms	12,098 (-1%)	48,000	96,497
l2_block_public_tx_process_time_in_ms	3,773 (-1%)	14,973	29,924

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	14,955 (+4%)	27,461 (+2%)
note_history_successful_decrypting_time_in_ms	1,384 (+5%)	2,447 (+1%)
note_history_trial_decrypting_time_in_ms	114 (+38%)	139 (-4%)
node_database_size_in_bytes	18,800,720	35,536,976
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	247	44,736	28,001
private-kernel-ordering	177	52,625	14,627
base-rollup	1,282	177,932	933
root-rollup	70.0 (-1%)	4,192	825
private-kernel-inner	311 (-1%)	73,715	28,001
public-kernel-app-logic	191 (+1%)	32,254	25,379
merge-rollup	5.78 (+1%)	2,712	933

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	4096 leaves
batch_insert_into_append_only_tree_16_depth_ms	9.91 (-2%)	10.2	13.7 (-22%)	16.7 (+3%)	22.0 (+1%)	35.5 (+1%)	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_count	16.9	17.5	23.0	31.6	47.0	79.0	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_ms	0.574 (-2%)	0.569	0.580 (-23%)	0.516 (+3%)	0.460	0.441	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_32_depth_ms	N/A	N/A	N/A	N/A	N/A	46.0 (-2%)	72.6 (+1%)	230	451 (+2%)	866 (+2%)	1,729 (+2%)
batch_insert_into_append_only_tree_32_depth_hash_count	N/A	N/A	N/A	N/A	N/A	96.0	159	543	1,055	2,079	4,127
batch_insert_into_append_only_tree_32_depth_hash_ms	N/A	N/A	N/A	N/A	N/A	0.471 (-2%)	0.448 (+1%)	0.420	0.422 (+2%)	0.412 (+2%)	0.414 (+2%)
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	N/A	N/A	N/A	54.0 (-2%)	108 (+1%)	338	674 (+2%)	1,309 (+1%)	2,627 (+2%)
batch_insert_into_indexed_tree_20_depth_hash_count	N/A	N/A	N/A	N/A	N/A	104	207	691	1,363	2,707	5,395
batch_insert_into_indexed_tree_20_depth_hash_ms	N/A	N/A	N/A	N/A	N/A	0.480 (-2%)	0.485 (+1%)	0.457	0.463 (+1%)	0.454 (+1%)	0.452 (+2%)
batch_insert_into_indexed_tree_40_depth_ms	N/A	N/A	N/A	N/A	62.4 (+2%)	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_indexed_tree_40_depth_hash_count	N/A	N/A	N/A	N/A	109	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_indexed_tree_40_depth_hash_ms	N/A	N/A	N/A	N/A	0.545 (+1%)	N/A	N/A	N/A	N/A	N/A	N/A

Miscellaneous

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

Metric	0 deployed contracts
tx_size_in_bytes	19,179

Transaction processing duration by data writes.

Metric	0 new note hashes	1 new note hashes
tx_pxe_processing_time_ms	2,543	1,353

Metric	0 public data writes	1 public data writes
tx_sequencer_processing_time_ms	0.0312 (+10%)	467