compiler: Limit depth of sharing state tree

With OTP 27.0 the xmerl tests showed a markedly increased run-time.
Profiling pointed to beam_ssa_ss:prune/2 as the culprit. It turns out
that if there are long value derivation chains which are extended one
element at a time (such as in the ss_depth_limit.erl test-case in this
patch), the effective time complexity of prune will be O(n^2) where n
is the number of elements in the chain.

By limiting the depth of the sharing state tree, we can avoid the
drastically increased run-times for the alias analysis. This is a
stop-gap fix until the alias analysis can be improved to avoid this
pit-fall.

lib/compiler/src/beam_ssa_alias.erl

@@ -90,12 +90,20 @@
 opt(StMap0, FuncDb0) ->
     %% Ignore functions which are not in the function db (never
     %% called).
-    Funs = [ F || F <- maps:keys(StMap0), is_map_key(F, FuncDb0)],
-    StMap1 = #{ F=>expand_record_update(OptSt) || F:=OptSt <- StMap0},
-    KillsMap = killsets(Funs, StMap1),
-    {StMap2, FuncDb} = aa(Funs, KillsMap, StMap1, FuncDb0),
-    StMap = #{ F=>restore_update_record(OptSt) || F:=OptSt <- StMap2},
-    {StMap, FuncDb}.
+    try
+        Funs = [ F || F <- maps:keys(StMap0), is_map_key(F, FuncDb0)],
+        StMap1 = #{ F=>expand_record_update(OptSt) || F:=OptSt <- StMap0},
+        KillsMap = killsets(Funs, StMap1),
+        {StMap2, FuncDb} = aa(Funs, KillsMap, StMap1, FuncDb0),
+        StMap = #{ F=>restore_update_record(OptSt) || F:=OptSt <- StMap2},
+        {StMap, FuncDb}
+    catch
+        throw:too_deep ->
+            %% Give up and leave the module unmodified. Thrown by
+            %% beam_ssa_ss:prune/2 when the depth of sharing state
+            %% value chains exceeds a fixed limit.
+            {StMap0,FuncDb0}
+    end.
 
 %%%
 %%% Calculate the set of variables killed at each instruction. The

lib/compiler/src/beam_ssa_ss.erl

@@ -54,6 +54,7 @@
 -import(lists, [foldl/3]).
 
 -define(ARGS_DEPTH_LIMIT, 4).
+-define(SS_DEPTH_LIMIT, 250).
 
 %% -define(DEBUG, true).
 
@@ -412,28 +413,36 @@ accumulate_edges(V, State, Edges0) ->
 new() ->
     beam_digraph:new().
 
+%%%
+%%% Throws `too_deep` if the depth of sharing state value chains
+%%% exceeds SS_DEPTH_LIMIT.
+%%%
 -spec prune(sets:set(beam_ssa:b_var()), sharing_state()) -> sharing_state().
 prune(LiveVars, State) ->
     ?assert_state(State),
     ?DP("Pruning to ~p~n", [sets:to_list(LiveVars)]),
     ?DBG(dump(State)),
-    R = prune(sets:to_list(LiveVars), [], new(), State),
+    R = prune([{0,V} || V <- sets:to_list(LiveVars)], [], new(), State),
     ?DP("Pruned result~n"),
     ?DBG(dump(R)),
     ?assert_state(R).
 
-prune([V|Wanted], Edges, New0, Old) ->
+prune([{Depth0,V}|Wanted], Edges, New0, Old) ->
     case beam_digraph:has_vertex(New0, V) of
         true ->
-            %% This variable is alread added.
+            %% This variable is already added.
             prune(Wanted, Edges, New0, Old);
-        false ->
+        false when Depth0 < ?SS_DEPTH_LIMIT ->
             %% This variable has to be kept. Add it to the new graph.
             New = add_vertex(New0, V, beam_digraph:vertex(Old, V)),
             %% Add all incoming edges to this node.
             InEdges = beam_digraph:in_edges(Old, V),
-            InNodes = [From || {From,_,_} <- InEdges],
-            prune(InNodes ++ Wanted, InEdges ++ Edges, New, Old)
+            Depth = Depth0 + 1,
+            InNodes = [{Depth, From} || {From,_,_} <- InEdges],
+            prune(InNodes ++ Wanted, InEdges ++ Edges, New, Old);
+        false ->
+            %% We're in too deep, give up.
+            throw(too_deep)
     end;
 prune([], Edges, New0, _Old) ->
     foldl(fun({Src,Dst,Lbl}, New) ->

lib/compiler/test/beam_ssa_check_SUITE.erl

@@ -87,7 +87,8 @@ end_per_group(_GroupName, Config) ->
 alias_checks(Config) when is_list(Config) ->
     run_post_ssa_opt(alias, Config),
     run_post_ssa_opt(alias_non_convergence, Config),
-    run_post_ssa_opt(alias_chain, Config).
+    run_post_ssa_opt(alias_chain, Config),
+    run_post_ssa_opt(ss_depth_limit, Config).
 
 annotation_checks(Config) when is_list(Config) ->
     run_post_ssa_opt(annotations, Config).

lib/compiler/test/beam_ssa_check_SUITE_data/ss_depth_limit.erl

@@ -0,0 +1,283 @@
+%%%
+%%% Check that the limit imposed on the depth of sharing state value
+%%% chains is imposed.
+%%%
+
+-module(ss_depth_limit).
+
+-export([f/0]).
+
+-if(false).
+%% f/0 is generated by the following program. N should be
+%% SS_DEPTH_LIMIT + 1 (from beam_ssa_ss.erl).
+do(N) ->
+    Data = [
+	    "-module(ss_depth_limit).\n\n",
+	    "-export([f/0]).\n\n",
+	    "f() ->\n",
+	    "%ssa% fail () when post_ssa_opt ->\n"
+	    "%ssa% ret(X) { unique => [X] }.\n"
+	    "  X0 = e:f(),\n",
+	    [io_lib:format("  X~p = {X~p,e:f()},~n", [X, X-1])
+	     || X<- lists:seq(1, N)],
+	    io_lib:format("  X~p.~n", [N])
+	   ],
+    file:write_file("ss_depth_limit.erl", Data).
+-endif.
+
+f() ->
+%ssa% fail () when post_ssa_opt ->
+%ssa% ret(X) { unique => [X] }.
+  X0 = e:f(),
+  X1 = {X0,e:f()},
+  X2 = {X1,e:f()},
+  X3 = {X2,e:f()},
+  X4 = {X3,e:f()},
+  X5 = {X4,e:f()},
+  X6 = {X5,e:f()},
+  X7 = {X6,e:f()},
+  X8 = {X7,e:f()},
+  X9 = {X8,e:f()},
+  X10 = {X9,e:f()},
+  X11 = {X10,e:f()},
+  X12 = {X11,e:f()},
+  X13 = {X12,e:f()},
+  X14 = {X13,e:f()},
+  X15 = {X14,e:f()},
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+  X251.