Avoid backfill when we already have messages to return (#15737)

We now only block the client to backfill when we see a large gap in the events (more than 2 events missing in a row according to `depth`), more than 3 single-event holes, or not enough messages to fill the response. Otherwise, we return the messages directly to the client and backfill in the background for eventual consistency sake. 

Fix https://github.com/matrix-org/synapse/issues/15696

changelog.d/15737.feature

@@ -0,0 +1 @@
+Improve `/messages` response time by avoiding backfill when we already have messages to return.

synapse/handlers/pagination.py

@@ -40,6 +40,11 @@ if TYPE_CHECKING:
 
 logger = logging.getLogger(__name__)
 
+# How many single event gaps we tolerate returning in a `/messages` response before we
+# backfill and try to fill in the history. This is an arbitrarily picked number so feel
+# free to tune it in the future.
+BACKFILL_BECAUSE_TOO_MANY_GAPS_THRESHOLD = 3
+
 
 @attr.s(slots=True, auto_attribs=True)
 class PurgeStatus:
@@ -486,13 +491,17 @@ class PaginationHandler:
                         room_id, room_token.stream
                     )
 
-                if not use_admin_priviledge and membership == Membership.LEAVE:
             # If they have left the room then clamp the token to be before
             # they left the room, to save the effort of loading from the
             # database.
-
+            if (
-                    # This is only None if the room is world_readable, in which
+                pagin_config.direction == Direction.BACKWARDS
-                    # case "JOIN" would have been returned.
+                and not use_admin_priviledge
+                and membership == Membership.LEAVE
+            ):
+                # This is only None if the room is world_readable, in which case
+                # "Membership.JOIN" would have been returned and we should never hit
+                # this branch.
                 assert member_event_id
 
                 leave_token = await self.store.get_topological_token_for_event(
@@ -505,16 +514,12 @@ class PaginationHandler:
                         StreamKeyType.ROOM, leave_token
                     )
 
-                await self.hs.get_federation_handler().maybe_backfill(
-                    room_id,
-                    curr_topo,
-                    limit=pagin_config.limit,
-                )
-
             to_room_key = None
             if pagin_config.to_token:
                 to_room_key = pagin_config.to_token.room_key
 
+            # Initially fetch the events from the database. With any luck, we can return
+            # these without blocking on backfill (handled below).
             events, next_key = await self.store.paginate_room_events(
                 room_id=room_id,
                 from_key=from_token.room_key,
@@ -524,6 +529,94 @@ class PaginationHandler:
                 event_filter=event_filter,
             )
 
+            if pagin_config.direction == Direction.BACKWARDS:
+                # We use a `Set` because there can be multiple events at a given depth
+                # and we only care about looking at the unique continum of depths to
+                # find gaps.
+                event_depths: Set[int] = {event.depth for event in events}
+                sorted_event_depths = sorted(event_depths)
+
+                # Inspect the depths of the returned events to see if there are any gaps
+                found_big_gap = False
+                number_of_gaps = 0
+                previous_event_depth = (
+                    sorted_event_depths[0] if len(sorted_event_depths) > 0 else 0
+                )
+                for event_depth in sorted_event_depths:
+                    # We don't expect a negative depth but we'll just deal with it in
+                    # any case by taking the absolute value to get the true gap between
+                    # any two integers.
+                    depth_gap = abs(event_depth - previous_event_depth)
+                    # A `depth_gap` of 1 is a normal continuous chain to the next event
+                    # (1 <-- 2 <-- 3) so anything larger indicates a missing event (it's
+                    # also possible there is no event at a given depth but we can't ever
+                    # know that for sure)
+                    if depth_gap > 1:
+                        number_of_gaps += 1
+
+                    # We only tolerate a small number single-event long gaps in the
+                    # returned events because those are most likely just events we've
+                    # failed to pull in the past. Anything longer than that is probably
+                    # a sign that we're missing a decent chunk of history and we should
+                    # try to backfill it.
+                    #
+                    # XXX: It's possible we could tolerate longer gaps if we checked
+                    # that a given events `prev_events` is one that has failed pull
+                    # attempts and we could just treat it like a dead branch of history
+                    # for now or at least something that we don't need the block the
+                    # client on to try pulling.
+                    #
+                    # XXX: If we had something like MSC3871 to indicate gaps in the
+                    # timeline to the client, we could also get away with any sized gap
+                    # and just have the client refetch the holes as they see fit.
+                    if depth_gap > 2:
+                        found_big_gap = True
+                        break
+                    previous_event_depth = event_depth
+
+                # Backfill in the foreground if we found a big gap, have too many holes,
+                # or we don't have enough events to fill the limit that the client asked
+                # for.
+                missing_too_many_events = (
+                    number_of_gaps > BACKFILL_BECAUSE_TOO_MANY_GAPS_THRESHOLD
+                )
+                not_enough_events_to_fill_response = len(events) < pagin_config.limit
+                if (
+                    found_big_gap
+                    or missing_too_many_events
+                    or not_enough_events_to_fill_response
+                ):
+                    did_backfill = (
+                        await self.hs.get_federation_handler().maybe_backfill(
+                            room_id,
+                            curr_topo,
+                            limit=pagin_config.limit,
+                        )
+                    )
+
+                    # If we did backfill something, refetch the events from the database to
+                    # catch anything new that might have been added since we last fetched.
+                    if did_backfill:
+                        events, next_key = await self.store.paginate_room_events(
+                            room_id=room_id,
+                            from_key=from_token.room_key,
+                            to_key=to_room_key,
+                            direction=pagin_config.direction,
+                            limit=pagin_config.limit,
+                            event_filter=event_filter,
+                        )
+                else:
+                    # Otherwise, we can backfill in the background for eventual
+                    # consistency's sake but we don't need to block the client waiting
+                    # for a costly federation call and processing.
+                    run_as_background_process(
+                        "maybe_backfill_in_the_background",
+                        self.hs.get_federation_handler().maybe_backfill,
+                        room_id,
+                        curr_topo,
+                        limit=pagin_config.limit,
+                    )
+
             next_token = from_token.copy_and_replace(StreamKeyType.ROOM, next_key)
 
         # if no events are returned from pagination, that implies