Improve get auth chain difference algorithm. (#7095)

It was originally implemented by pulling the full auth chain of all
state sets out of the database and doing set comparison. However, that
can take a lot work if the state and auth chains are large.

Instead, lets try and fetch the auth chains at the same time and
calculate the difference on the fly, allowing us to bail early if all
the auth chains converge. Assuming that the auth chains do converge more
often than not, this should improve performance. Hopefully.

synapse/state/v2.py

@@ -227,36 +227,12 @@ def _get_auth_chain_difference(state_sets, event_map, state_res_store):
     Returns:
         Deferred[set[str]]: Set of event IDs
     """
-    common = set(itervalues(state_sets[0])).intersection(
-        *(itervalues(s) for s in state_sets[1:])
+
+    difference = yield state_res_store.get_auth_chain_difference(
+        [set(state_set.values()) for state_set in state_sets]
     )
 
-    auth_sets = []
-    for state_set in state_sets:
-        auth_ids = {
-            eid
-            for key, eid in iteritems(state_set)
-            if (
-                key[0] in (EventTypes.Member, EventTypes.ThirdPartyInvite)
-                or key
-                in (
-                    (EventTypes.PowerLevels, ""),
-                    (EventTypes.Create, ""),
-                    (EventTypes.JoinRules, ""),
-                )
-            )
-            and eid not in common
-        }
-
-        auth_chain = yield state_res_store.get_auth_chain(auth_ids, common)
-        auth_ids.update(auth_chain)
-
-        auth_sets.append(auth_ids)
-
-    intersection = set(auth_sets[0]).intersection(*auth_sets[1:])
-    union = set().union(*auth_sets)
-
-    return union - intersection
+    return difference
 
 
 def _seperate(state_sets):