perf(labrinth/random_projects_get): speed up through spatial queries according to profiling results

apps/labrinth/migrations/20250609134334_spatial-random-project-index.sql

@@ -0,0 +1,12 @@
+-- The spatial query for retrieving random searchable projects is greatly sped
+-- up by this index on a fixture of 1M mods, bringing down the total cost of
+-- the query plan and runtime to be comparable to primary key lookups. See the
+-- `labrinth::routes::v3::projects::random_projects_get` function and the
+-- previous 20250608183828_random-project-index.sql migration for more details.
+--
+-- That previous migration created a non-spatial index for the status column which
+-- does not get used in the new spatial query, but may still be useful for other
+-- queries that filter mods by status.
+
+CREATE INDEX mods_searchable_ids_gist ON mods USING gist (POINT(id, 0))
+    WHERE status = ANY(ARRAY['approved', 'archived']);

apps/labrinth/src/models/v3/projects.rs

@@ -519,6 +519,9 @@ impl ProjectStatus {
     }
 
     // Project can be displayed in search
+    // IMPORTANT: if this is changed, make sure to update the `mods_searchable_ids_gist`
+    // index in the DB to keep random project queries fast (see the
+    // `20250609134334_spatial-random-project-index.sql` migration)
     pub fn is_searchable(&self) -> bool {
         matches!(self, ProjectStatus::Approved | ProjectStatus::Archived)
     }

apps/labrinth/src/routes/v3/projects.rs

@@ -94,12 +94,16 @@ pub async fn random_projects_get(
     })?;
 
     let project_ids = sqlx::query!(
-        // IDs are randomly generated (see the `generate_ids` macro), so ID order is
-        // equivalent to a random order
-        "SELECT id FROM mods WHERE status = ANY($1)
-        ORDER BY id
-        LIMIT $2
-        OFFSET GREATEST(ROUND(RANDOM() * (SELECT COUNT(*) FROM mods WHERE status = ANY($1)))::int8 - $2, 0)",
+        // IDs are randomly generated (see the `generate_ids` macro), so fetching a
+        // number of mods nearest to a random point in the ID space is equivalent to
+        // random sampling
+        "WITH random_id_point AS (
+            SELECT POINT(RANDOM() * ((SELECT MAX(id) FROM mods) - (SELECT MIN(id) FROM mods) + 1) + (SELECT MIN(id) FROM mods), 0) AS point
+        )
+        SELECT id FROM mods
+        WHERE status = ANY($1)
+        ORDER BY POINT(id, 0) <-> (SELECT point FROM random_id_point)
+        LIMIT $2",
         &*crate::models::projects::ProjectStatus::iterator()
             .filter(|x| x.is_searchable())
             .map(|x| x.to_string())