587: Word prefix pair proximity docids indexation refactor r=Kerollmops a=loiclec
# Pull Request
## What does this PR do?
Refactor the code of `WordPrefixPairProximityDocIds` to make it much faster, fix a bug, and add a unit test.
## Why is it faster?
Because we avoid using a sorter to insert the (`word1`, `prefix`, `proximity`) keys and their associated bitmaps, and thus we don't have to sort a potentially very big set of data. I have also added a couple of other optimisations:
1. reusing allocations
2. using a prefix trie instead of an array of prefixes to get all the prefixes of a word
3. inserting directly into the database instead of putting the data in an intermediary grenad when possible. Also avoid checking for pre-existing values in the database when we know for certain that they do not exist.
## What bug was fixed?
When reindexing, the `new_prefix_fst_words` prefixes may look like:
```
["ant", "axo", "bor"]
```
which we group by first letter:
```
[["ant", "axo"], ["bor"]]
```
Later in the code, if we have the word2 "axolotl", we try to find which subarray of prefixes contains its prefixes. This check is done with `word2.starts_with(subarray_prefixes[0])`, but `"axolotl".starts_with("ant")` is false, and thus we wrongly think that there are no prefixes in `new_prefix_fst_words` that are prefixes of `axolotl`.
## StrStrU8Codec
I had to change the encoding of `StrStrU8Codec` to make the second string null-terminated as well. I don't think this should be a problem, but I may have missed some nuances about the impacts of this change.
## Requests when reviewing this PR
I have explained what the code does in the module documentation of `word_pair_proximity_prefix_docids`. It would be nice if someone could read it and give their opinion on whether it is a clear explanation or not.
I also have a couple questions regarding the code itself:
- Should we clean up and factor out the `PrefixTrieNode` code to try and make broader use of it outside this module? For now, the prefixes undergo a few transformations: from FST, to array, to prefix trie. It seems like it could be simplified.
- I wrote a function called `write_into_lmdb_database_without_merging`. (1) Are we okay with such a function existing? (2) Should it be in `grenad_helpers` instead?
## Benchmark Results
We reduce the time it takes to index about 8% in most cases, but it varies between -3% and -20%.
```
group indexing_main_ce90fc62 indexing_word-prefix-pair-proximity-docids-refactor_cbad2023
----- ---------------------- ------------------------------------------------------------
indexing/-geo-delete-facetedNumber-facetedGeo-searchable- 1.00 1893.0±233.03µs ? ?/sec 1.01 1921.2±260.79µs ? ?/sec
indexing/-movies-delete-facetedString-facetedNumber-searchable- 1.05 9.4±3.51ms ? ?/sec 1.00 9.0±2.14ms ? ?/sec
indexing/-movies-delete-facetedString-facetedNumber-searchable-nested- 1.22 18.3±11.42ms ? ?/sec 1.00 15.0±5.79ms ? ?/sec
indexing/-songs-delete-facetedString-facetedNumber-searchable- 1.00 41.4±4.20ms ? ?/sec 1.28 53.0±13.97ms ? ?/sec
indexing/-wiki-delete-searchable- 1.00 285.6±18.12ms ? ?/sec 1.03 293.1±16.09ms ? ?/sec
indexing/Indexing geo_point 1.03 60.8±0.45s ? ?/sec 1.00 58.8±0.68s ? ?/sec
indexing/Indexing movies in three batches 1.14 16.5±0.30s ? ?/sec 1.00 14.5±0.24s ? ?/sec
indexing/Indexing movies with default settings 1.11 13.7±0.07s ? ?/sec 1.00 12.3±0.28s ? ?/sec
indexing/Indexing nested movies with default settings 1.10 10.6±0.11s ? ?/sec 1.00 9.6±0.15s ? ?/sec
indexing/Indexing nested movies without any facets 1.11 9.4±0.15s ? ?/sec 1.00 8.5±0.10s ? ?/sec
indexing/Indexing songs in three batches with default settings 1.18 66.2±0.39s ? ?/sec 1.00 56.0±0.67s ? ?/sec
indexing/Indexing songs with default settings 1.07 58.7±1.26s ? ?/sec 1.00 54.7±1.71s ? ?/sec
indexing/Indexing songs without any facets 1.08 53.1±0.88s ? ?/sec 1.00 49.3±1.43s ? ?/sec
indexing/Indexing songs without faceted numbers 1.08 57.7±1.33s ? ?/sec 1.00 53.3±0.98s ? ?/sec
indexing/Indexing wiki 1.06 1051.1±21.46s ? ?/sec 1.00 989.6±24.55s ? ?/sec
indexing/Indexing wiki in three batches 1.20 1184.8±8.93s ? ?/sec 1.00 989.7±7.06s ? ?/sec
indexing/Reindexing geo_point 1.04 67.5±0.75s ? ?/sec 1.00 64.9±0.32s ? ?/sec
indexing/Reindexing movies with default settings 1.12 13.9±0.17s ? ?/sec 1.00 12.4±0.13s ? ?/sec
indexing/Reindexing songs with default settings 1.05 60.6±0.84s ? ?/sec 1.00 57.5±0.99s ? ?/sec
indexing/Reindexing wiki 1.07 1725.0±17.92s ? ?/sec 1.00 1611.4±9.90s ? ?/sec
```
Co-authored-by: Loïc Lecrenier <loic@meilisearch.com>
