refactor(topicidx): simplify seek instructions

Which also avoids comparing filter tail repeatedly when evaluating
it.

apps/emqx/src/emqx_trie_search.erl

@@ -137,7 +137,7 @@ get_topic({Filter, _ID}) when is_list(Filter) ->
 get_topic({Topic, _ID}) ->
     Topic.
 
--compile({inline, [base/1, move_up/2, match_add/2, compare/3]}).
+-compile({inline, [base/1, move_up/2, match_add/2, compare/4]}).
 
 %% Make the base-key which can be used to locate the desired search target.
 base(Prefix) ->
@@ -210,31 +210,29 @@ search_new(Words0, NewBase, NextF, Acc) ->
 
 %% Search to the bigger end of ordered collection of topics and topic-filters.
 search_up(Words, {Filter, _} = Cursor, NextF, Acc) ->
-    case compare(Filter, Words, false) of
+    case compare(Filter, Words, 0, false) of
         match_full ->
             search_new(Words, Cursor, NextF, match_add(Cursor, Acc));
         match_prefix ->
             search_new(Words, Cursor, NextF, Acc);
         lower ->
             {Cursor, Acc};
-        [SeekWord | FilterTail] ->
+        {Pos, SeekWord} ->
             % NOTE
-            % This is a seek instruction.
-            % If we visualize the `Filter` as `FilterHead ++ [_] ++ FilterTail`, we need to
-            % seek to `FilterHead ++ [SeekWord]`. It carries the `FilterTail` because it's
-            % much cheaper to return it from `compare/3` than anything more usable.
-            NewBase = base(seek(SeekWord, Filter, FilterTail)),
+            % This is a seek instruction. It means we need to take `Pos` words
+            % from the current topic filter and attach `SeekWord` to the end of it.
+            NewBase = base(seek(Pos, SeekWord, Filter)),
             search_new(Words, NewBase, NextF, Acc)
     end.
 
-seek(SeekWord, [_ | FilterTail], FilterTail) ->
+seek(_Pos = 0, SeekWord, _FilterTail) ->
     [SeekWord];
-seek(SeekWord, [FilterWord | Rest], FilterTail) ->
-    [FilterWord | seek(SeekWord, Rest, FilterTail)].
+seek(Pos, SeekWord, [FilterWord | Rest]) ->
+    [FilterWord | seek(Pos - 1, SeekWord, Rest)].
 
-compare(NotFilter, _, _) when is_binary(NotFilter) ->
+compare(NotFilter, _, _, _) when is_binary(NotFilter) ->
     lower;
-compare([], [], _) ->
+compare([], [], _, _) ->
     % NOTE
     %  Topic: a/b/c/d
     % Filter: a/+/+/d
@@ -244,7 +242,7 @@ compare([], [], _) ->
     % * a/+/+/d (same topic but a different ID)
     % * a/+/+/d/# (also a match)
     match_full;
-compare([], _Words, _) ->
+compare([], _Words, _, _) ->
     % NOTE
     %  Topic: a/b/c/d
     % Filter: a/+/c
@@ -257,7 +255,7 @@ compare([], _Words, _) ->
     % TODO
     % We might probably instead seek to a/+/c/# right away.
     match_prefix;
-compare(['#'], _Words, _) ->
+compare(['#'], _Words, _, _) ->
     % NOTE
     %  Topic: a/b/c/d
     % Filter: a/+/+/d/#
@@ -266,57 +264,57 @@ compare(['#'], _Words, _) ->
     % Closest possible next entries that we must not miss:
     % * a/+/+/d/# (same topic but a different ID)
     match_full;
-compare(['+' | TF], [HW | TW], _PrevBacktrack) ->
+compare(['+' | TF], [HW | TW], Pos, _PrevBacktrack) ->
     % NOTE
     % We need to keep backtrack point each time we encounter a plus. To safely skip over
     % parts of the search space, we may need last backtrack point when recursion terminates.
     % See next clauses for examples.
-    compare(TF, TW, [HW | TF]);
-compare([HW | TF], [HW | TW], Backtrack) ->
+    compare(TF, TW, Pos + 1, {Pos, HW});
+compare([HW | TF], [HW | TW], Pos, Backtrack) ->
     % NOTE
     % Skip over the same word in both topic and filter, keeping the last backtrack point.
-    compare(TF, TW, Backtrack);
-compare([HF | _], [HW | _], false) when HF > HW ->
+    compare(TF, TW, Pos + 1, Backtrack);
+compare([HF | _], [HW | _], _, false) when HF > HW ->
     % NOTE
     %  Topic: a/b/c/d
     % Filter: a/b/c/e/1
     % The topic is lower than a topic filter. There's nowhere to backtrackto, we're out of
     % the search space. We should stop the search.
     lower;
-compare([HF | _], [HW | _], Backtrack) when HF > HW ->
+compare([HF | _], [HW | _], _, Backtrack) when HF > HW ->
     % NOTE
     %  Topic: a/b/c/d
     % Filter: a/+/+/e/1
     % The topic is lower than a topic filter. There was a plus, last time at the 3rd level,
     % we have a backtrack point to seek to:
-    % Seek: [c | e/1]
+    % Seek: {2, c}
     % We need to skip over part of search space, and seek to the next possible match:
     % Next: a/+/c
     Backtrack;
-compare([_ | _], [], false) ->
+compare([_ | _], [], _, false) ->
     % NOTE
     %  Topic: a/b/c/d
     % Filter: a/b/c/d/1
-    % The topic is lower than a topic filter. (since it's shorter). There's nowhere to
+    % The topic is lower than a topic filter (since it's shorter). There's nowhere to
     % backtrack to, we're out of the search space. We should stop the search.
     lower;
-compare([_ | _], [], Backtrack) ->
+compare([_ | _], [], _, Backtrack) ->
     % NOTE
     %  Topic: a/b/c/d
     % Filter: a/+/c/d/1
     % The topic is lower than a topic filter. There was a plus, last and only time at the
     % 3rd level, we have a backtrack point:
-    % Seek: [b | c/d/1]
+    % Seek: {1, b}
     % Next: a/b
     Backtrack;
-compare([_HF | TF], [HW | _], _) ->
+compare([_ | _], [HW | _], Pos, _) ->
     % NOTE
     %  Topic: a/b/c/d
     % Filter: a/+/+/0/1/2
     % Topic is higher than the filter, we need to skip over to the next possible filter.
-    % Seek: [d | 0/1/2]
+    % Seek: {3, d}
     % Next: a/+/+/d
-    [HW | TF].
+    {Pos, HW}.
 
 match_add(K = {_Filter, ID}, Acc = #{}) ->
     % NOTE: ensuring uniqueness by record ID