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-rw-r--r--lib/hipe/opt/Makefile3
-rw-r--r--lib/hipe/opt/hipe_bb_weights.erl449
2 files changed, 451 insertions, 1 deletions
diff --git a/lib/hipe/opt/Makefile b/lib/hipe/opt/Makefile
index 684d6f45b4..5a729d04ae 100644
--- a/lib/hipe/opt/Makefile
+++ b/lib/hipe/opt/Makefile
@@ -43,7 +43,8 @@ RELSYSDIR = $(RELEASE_PATH)/lib/hipe-$(VSN)
# ----------------------------------------------------
# Target Specs
# ----------------------------------------------------
-MODULES = hipe_spillmin hipe_spillmin_color hipe_spillmin_scan
+MODULES = hipe_spillmin hipe_spillmin_color hipe_spillmin_scan \
+ hipe_bb_weights
HRL_FILES=
ERL_FILES= $(MODULES:%=%.erl)
diff --git a/lib/hipe/opt/hipe_bb_weights.erl b/lib/hipe/opt/hipe_bb_weights.erl
new file mode 100644
index 0000000000..8ef113b94c
--- /dev/null
+++ b/lib/hipe/opt/hipe_bb_weights.erl
@@ -0,0 +1,449 @@
+%% -*- erlang-indent-level: 2 -*-
+%%
+%% Licensed under the Apache License, Version 2.0 (the "License");
+%% you may not use this file except in compliance with the License.
+%% You may obtain a copy of the License at
+%%
+%% http://www.apache.org/licenses/LICENSE-2.0
+%%
+%% Unless required by applicable law or agreed to in writing, software
+%% distributed under the License is distributed on an "AS IS" BASIS,
+%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+%% See the License for the specific language governing permissions and
+%% limitations under the License.
+%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%@doc
+%% BASIC BLOCK WEIGHTING
+%%
+%% Computes basic block weights by using branch probabilities as weights in a
+%% linear equation system, that is then solved using Gauss-Jordan Elimination.
+%%
+%% The equation system representation is intentionally sparse, since most blocks
+%% have at most two successors.
+-module(hipe_bb_weights).
+-export([compute/3, compute_fast/3, weight/2, call_exn_pred/0]).
+-export_type([bb_weights/0]).
+
+-compile(inline).
+
+%%-define(DO_ASSERT,1).
+%%-define(DEBUG,1).
+-include("../main/hipe.hrl").
+
+%% If the equation system is large, it might take too long to solve it exactly.
+%% Thus, if there are more than ?HEUR_MAX_SOLVE labels, we use the iterative
+%% approximation.
+-define(HEUR_MAX_SOLVE, 10000).
+
+-opaque bb_weights() :: #{label() => float()}.
+
+-type cfg() :: any().
+-type target_module() :: module().
+-type target_context() :: any().
+-type target() :: {target_module(), target_context()}.
+
+-type label() :: integer().
+-type var() :: label().
+-type assignment() :: {var(), float()}.
+-type eq_assoc() :: [{var(), key()}].
+-type solution() :: [assignment()].
+
+%% Constant. Predicted probability of a call resulting in an exception.
+-spec call_exn_pred() -> float().
+call_exn_pred() -> 0.01.
+
+-spec compute(cfg(), target_module(), target_context()) -> bb_weights().
+compute(CFG, TgtMod, TgtCtx) ->
+ Target = {TgtMod, TgtCtx},
+ Labels = labels(CFG, Target),
+ if length(Labels) > ?HEUR_MAX_SOLVE ->
+ ?debug_msg("~w: Too many labels (~w), approximating.~n",
+ [?MODULE, length(Labels)]),
+ compute_fast(CFG, TgtMod, TgtCtx);
+ true ->
+ {EqSys, EqAssoc} = build_eq_system(CFG, Labels, Target),
+ case solve(EqSys, EqAssoc) of
+ {ok, Solution} ->
+ maps:from_list(Solution)
+ end
+ end.
+
+-spec build_eq_system(cfg(), [label()], target()) -> {eq_system(), eq_assoc()}.
+build_eq_system(CFG, Labels, Target) ->
+ StartLb = hipe_gen_cfg:start_label(CFG),
+ EQS0 = eqs_new(),
+ {EQS1, Assoc} = build_eq_system(Labels, CFG, Target, [], EQS0),
+ {StartLb, StartKey} = lists:keyfind(StartLb, 1, Assoc),
+ StartRow0 = eqs_get(StartKey, EQS1),
+ StartRow = row_set_const(-1.0, StartRow0), % -1.0 since StartLb coef is -1.0
+ EQS = eqs_put(StartKey, StartRow, EQS1),
+ {EQS, Assoc}.
+
+build_eq_system([], _CFG, _Target, Map, EQS) -> {EQS, lists:reverse(Map)};
+build_eq_system([L|Ls], CFG, Target, Map, EQS0) ->
+ PredProb = pred_prob(L, CFG, Target),
+ {Key, EQS} = eqs_insert(row_new([{L, -1.0}|PredProb], 0.0), EQS0),
+ build_eq_system(Ls, CFG, Target, [{L, Key}|Map], EQS).
+
+pred_prob(L, CFG, Target) ->
+ [begin
+ BB = bb(CFG, Pred, Target),
+ Ps = branch_preds(hipe_bb:last(BB), Target),
+ ?ASSERT(length(lists:ukeysort(1, Ps))
+ =:= length(hipe_gen_cfg:succ(CFG, Pred))),
+ case lists:keyfind(L, 1, Ps) of
+ {L, Prob} when is_float(Prob) -> {Pred, Prob}
+ end
+ end || Pred <- hipe_gen_cfg:pred(CFG, L)].
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+-spec triangelise(eq_system(), eq_assoc()) -> {eq_system(), eq_assoc()}.
+triangelise(EQS, VKs) ->
+ triangelise_1(mk_triix(EQS, VKs), []).
+
+triangelise_1(TIX0, Acc) ->
+ case triix_is_empty(TIX0) of
+ true -> {triix_eqs(TIX0), lists:reverse(Acc)};
+ false ->
+ {V,Key,TIX1} = triix_pop_smallest(TIX0),
+ Row0 = triix_get(Key, TIX1),
+ case row_get(V, Row0) of
+ Coef when Coef > -0.0001, Coef < 0.0001 ->
+ throw(error);
+ _ ->
+ Row = row_normalise(V, Row0),
+ TIX2 = triix_put(Key, Row, TIX1),
+ TIX = eliminate_triix(V, Key, Row, TIX2),
+ triangelise_1(TIX, [{V,Key}|Acc])
+ end
+ end.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Triangelisation maintains its own index, outside of eqs. This index is
+%% essentially a BST (used as a heap) of all equations by size, with {Key,Var}
+%% as the values and only containing a subset of all the keys in the whole
+%% equation system. The key operation is triix_pop_smallest/1, which pops a
+%% {Key,Var} from the heap corresponding to one of the smallest equations. This
+%% is critical in order to prevent the equations from growing during
+%% triangelisation, which would make the algorithm O(n^2) in the common case.
+-type tri_eq_system() :: {eq_system(),
+ gb_trees:tree(non_neg_integer(),
+ gb_trees:tree(key(), var()))}.
+
+triix_eqs({EQS, _}) -> EQS.
+triix_get(Key, {EQS, _}) -> eqs_get(Key, EQS).
+triix_is_empty({_, Tree}) -> gb_trees:is_empty(Tree).
+triix_lookup(V, {EQS, _}) -> eqs_lookup(V, EQS).
+
+mk_triix(EQS, VKs) ->
+ {EQS,
+ lists:foldl(fun({V,Key}, Tree) ->
+ Size = row_size(eqs_get(Key, EQS)),
+ sitree_insert(Size, Key, V, Tree)
+ end, gb_trees:empty(), VKs)}.
+
+sitree_insert(Size, Key, V, SiTree) ->
+ SubTree1 =
+ case gb_trees:lookup(Size, SiTree) of
+ none -> gb_trees:empty();
+ {value, SubTree0} -> SubTree0
+ end,
+ SubTree = gb_trees:insert(Key, V, SubTree1),
+ gb_trees:enter(Size, SubTree, SiTree).
+
+sitree_update_subtree(Size, SubTree, SiTree) ->
+ case gb_trees:is_empty(SubTree) of
+ true -> gb_trees:delete(Size, SiTree);
+ false -> gb_trees:update(Size, SubTree, SiTree)
+ end.
+
+triix_put(Key, Row, {EQS, Tree0}) ->
+ OldSize = row_size(eqs_get(Key, EQS)),
+ case row_size(Row) of
+ OldSize -> {eqs_put(Key, Row, EQS), Tree0};
+ Size ->
+ Tree =
+ case gb_trees:lookup(OldSize, Tree0) of
+ none -> Tree0;
+ {value, SubTree0} ->
+ case gb_trees:lookup(Key, SubTree0) of
+ none -> Tree0;
+ {value, V} ->
+ SubTree = gb_trees:delete(Key, SubTree0),
+ Tree1 = sitree_update_subtree(OldSize, SubTree, Tree0),
+ sitree_insert(Size, Key, V, Tree1)
+ end
+ end,
+ {eqs_put(Key, Row, EQS), Tree}
+ end.
+
+triix_pop_smallest({EQS, Tree}) ->
+ {Size, SubTree0} = gb_trees:smallest(Tree),
+ {Key, V, SubTree} = gb_trees:take_smallest(SubTree0),
+ {V, Key, {EQS, sitree_update_subtree(Size, SubTree, Tree)}}.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+row_normalise(Var, Row) ->
+ %% Normalise v's coef to 1.0
+ %% row_set_coef ensures the coef is exactly 1.0 (no rounding errors)
+ row_set_coef(Var, 1.0, row_scale(Row, 1.0/row_get(Var, Row))).
+
+%% Precondition: Row must be normalised; i.e. Vars coef must be 1.0 (mod
+%% rounding errors)
+-spec eliminate(var(), key(), row(), eq_system()) -> eq_system().
+eliminate(Var, Key, Row, TIX0) ->
+ eliminate_abstr(Var, Key, Row, TIX0,
+ fun eqs_get/2, fun eqs_lookup/2, fun eqs_put/3).
+
+-spec eliminate_triix(var(), key(), row(), tri_eq_system()) -> tri_eq_system().
+eliminate_triix(Var, Key, Row, TIX0) ->
+ eliminate_abstr(Var, Key, Row, TIX0,
+ fun triix_get/2, fun triix_lookup/2, fun triix_put/3).
+
+%% The same function implemented for two data types, eqs and triix.
+-compile({inline, eliminate_abstr/7}).
+-spec eliminate_abstr(var(), key(), row(), ADT, fun((key(), ADT) -> row()),
+ fun((var(), ADT) -> [key()]),
+ fun((key(), row(), ADT) -> ADT)) -> ADT.
+eliminate_abstr(Var, Key, Row, ADT0, GetFun, LookupFun, PutFun) ->
+ ?ASSERT(1.0 =:= row_get(Var, Row)),
+ ADT =
+ lists:foldl(fun(RK, ADT1) when RK =:= Key -> ADT1;
+ (RK, ADT1) ->
+ R = GetFun(RK, ADT1),
+ PutFun(RK, row_addmul(R, Row, -row_get(Var, R)), ADT1)
+ end, ADT0, LookupFun(Var, ADT0)),
+ [Key] = LookupFun(Var, ADT),
+ ADT.
+
+-spec solve(eq_system(), eq_assoc()) -> error | {ok, solution()}.
+solve(EQS0, EqAssoc0) ->
+ try triangelise(EQS0, EqAssoc0)
+ of {EQS1, EqAssoc} ->
+ {ok, solve_1(EqAssoc, maps:from_list(EqAssoc), EQS1, [])}
+ catch error -> error
+ end.
+
+solve_1([], _VarEqs, _EQS, Acc) -> Acc;
+solve_1([{V,K}|Ps], VarEqs, EQS0, Acc0) ->
+ Row0 = eqs_get(K, EQS0),
+ VarsToKill = [Var || {Var, _} <- row_coefs(Row0), Var =/= V],
+ Row1 = kill_vars(VarsToKill, VarEqs, EQS0, Row0),
+ [{V,_}] = row_coefs(Row1), % assertion
+ Row = row_normalise(V, Row1),
+ [{V,1.0}] = row_coefs(Row), % assertion
+ EQS = eliminate(V, K, Row, EQS0),
+ [K] = eqs_lookup(V, EQS),
+ solve_1(Ps, VarEqs, eqs_remove(K, EQS), [{V, row_const(Row)}|Acc0]).
+
+kill_vars([], _VarEqs, _EQS, Row) -> Row;
+kill_vars([V|Vs], VarEqs, EQS, Row0) ->
+ VRow0 = eqs_get(maps:get(V, VarEqs), EQS),
+ VRow = row_normalise(V, VRow0),
+ ?ASSERT(1.0 =:= row_get(V, VRow)),
+ Row = row_addmul(Row0, VRow, -row_get(V, Row0)),
+ ?ASSERT(0.0 =:= row_get(V, Row)), % V has been killed
+ kill_vars(Vs, VarEqs, EQS, Row).
+
+-spec weight(label(), bb_weights()) -> float().
+weight(Lbl, Weights) ->
+ maps:get(Lbl, Weights).
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Row datatype
+%% Invariant: No 0.0 coefficiets!
+-spec row_empty() -> row().
+row_empty() -> {orddict:new(), 0.0}.
+
+-spec row_new([{var(), float()}], float()) -> row().
+row_new(Coefs, Const) when is_float(Const) ->
+ row_ensure_invar({row_squash_multiples(lists:keysort(1, Coefs)), Const}).
+
+row_squash_multiples([{K, C1},{K, C2}|Ps]) ->
+ row_squash_multiples([{K,C1+C2}|Ps]);
+row_squash_multiples([P|Ps]) -> [P|row_squash_multiples(Ps)];
+row_squash_multiples([]) -> [].
+
+row_ensure_invar({Coef, Const}) ->
+ {orddict:filter(fun(_, 0.0) -> false; (_, F) when is_float(F) -> true end,
+ Coef), Const}.
+
+row_const({_, Const}) -> Const.
+row_coefs({Coefs, _}) -> orddict:to_list(Coefs).
+row_size({Coefs, _}) -> orddict:size(Coefs).
+
+row_get(Var, {Coefs, _}) ->
+ case lists:keyfind(Var, 1, Coefs) of
+ false -> 0.0;
+ {_, Coef} -> Coef
+ end.
+
+row_set_coef(Var, 0.0, {Coefs, Const}) ->
+ {orddict:erase(Var, Coefs), Const};
+row_set_coef(Var, Coef, {Coefs, Const}) ->
+ {orddict:store(Var, Coef, Coefs), Const}.
+
+row_set_const(Const, {Coefs, _}) -> {Coefs, Const}.
+
+%% Lhs + Rhs*Factor
+-spec row_addmul(row(), row(), float()) -> row().
+row_addmul({LhsCoefs, LhsConst}, {RhsCoefs, RhsConst}, Factor)
+ when is_float(Factor) ->
+ Coefs = row_addmul_coefs(LhsCoefs, RhsCoefs, Factor),
+ Const = LhsConst + RhsConst * Factor,
+ {Coefs, Const}.
+
+row_addmul_coefs(Ls, [], Factor) when is_float(Factor) -> Ls;
+row_addmul_coefs([], Rs, Factor) when is_float(Factor) ->
+ row_scale_coefs(Rs, Factor);
+row_addmul_coefs([L={LV, _}|Ls], Rs=[{RV,_}|_], Factor)
+ when LV < RV, is_float(Factor) ->
+ [L|row_addmul_coefs(Ls, Rs, Factor)];
+row_addmul_coefs(Ls=[{LV, _}|_], [{RV, RC}|Rs], Factor)
+ when LV > RV, is_float(RC), is_float(Factor) ->
+ [{RV, RC*Factor}|row_addmul_coefs(Ls, Rs, Factor)];
+row_addmul_coefs([{V, LC}|Ls], [{V, RC}|Rs], Factor)
+ when is_float(LC), is_float(RC), is_float(Factor) ->
+ case LC + RC * Factor of
+ 0.0 -> row_addmul_coefs(Ls, Rs, Factor);
+ C -> [{V,C}|row_addmul_coefs(Ls, Rs, Factor)]
+ end.
+
+row_scale(_, 0.0) -> row_empty();
+row_scale({RowCoefs, RowConst}, Factor) when is_float(Factor) ->
+ {row_scale_coefs(RowCoefs, Factor), RowConst * Factor}.
+
+row_scale_coefs([{V,C}|Cs], Factor) when is_float(Factor), is_float(C) ->
+ [{V,C*Factor}|row_scale_coefs(Cs, Factor)];
+row_scale_coefs([], Factor) when is_float(Factor) ->
+ [].
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Equation system ADT
+%%
+%% Stores a linear equation system, allowing for efficient updates and efficient
+%% queries for all equations mentioning a variable.
+%%
+%% It is sort of like a "database" table of {Primary, Terms, Const} indexed both
+%% on Primary as well as the vars (map keys) in Terms.
+-type row() :: {Terms :: orddict:orddict(var(), float()),
+ Const :: float()}.
+-type key() :: non_neg_integer().
+-type rev_index() :: #{var() => ordsets:ordset(key())}.
+-record(eq_system, {
+ rows = #{} :: #{key() => row()},
+ revidx = revidx_empty() :: rev_index(),
+ next_key = 0 :: key()
+ }).
+-type eq_system() :: #eq_system{}.
+
+eqs_new() -> #eq_system{}.
+
+-spec eqs_insert(row(), eq_system()) -> {key(), eq_system()}.
+eqs_insert(Row, EQS=#eq_system{next_key=NextKey0}) ->
+ Key = NextKey0,
+ NextKey = NextKey0 + 1,
+ {Key, eqs_insert(Key, Row, EQS#eq_system{next_key=NextKey})}.
+
+eqs_insert(Key, Row, EQS=#eq_system{rows=Rows, revidx=RevIdx0}) ->
+ RevIdx = revidx_add(Key, Row, RevIdx0),
+ EQS#eq_system{rows=Rows#{Key => Row}, revidx=RevIdx}.
+
+eqs_put(Key, Row, EQS0) ->
+ eqs_insert(Key, Row, eqs_remove(Key, EQS0)).
+
+eqs_remove(Key, EQS=#eq_system{rows=Rows, revidx=RevIdx0}) ->
+ OldRow = maps:get(Key, Rows),
+ RevIdx = revidx_remove(Key, OldRow, RevIdx0),
+ EQS#eq_system{rows = maps:remove(Key, Rows), revidx=RevIdx}.
+
+-spec eqs_get(key(), eq_system()) -> row().
+eqs_get(Key, #eq_system{rows=Rows}) -> maps:get(Key, Rows).
+
+%% Keys of all equations containing a nonzero coefficient for Var
+-spec eqs_lookup(var(), eq_system()) -> ordsets:ordset(key()).
+eqs_lookup(Var, #eq_system{revidx=RevIdx}) -> maps:get(Var, RevIdx).
+
+%% eqs_rows(#eq_system{rows=Rows}) -> maps:to_list(Rows).
+
+%% eqs_print(EQS) ->
+%% lists:foreach(fun({_, Row}) ->
+%% row_print(Row)
+%% end, lists:sort(eqs_rows(EQS))).
+
+%% row_print(Row) ->
+%% CoefStrs = [io_lib:format("~wl~w", [Coef, Var])
+%% || {Var, Coef} <- row_coefs(Row)],
+%% CoefStr = lists:join(" + ", CoefStrs),
+%% io:format("~w = ~s~n", [row_const(Row), CoefStr]).
+
+revidx_empty() -> #{}.
+
+-spec revidx_add(key(), row(), rev_index()) -> rev_index().
+revidx_add(Key, Row, RevIdx0) ->
+ orddict:fold(fun(Var, _Coef, RevIdx1) ->
+ ?ASSERT(_Coef /= 0.0),
+ RevIdx1#{Var => ordsets:add_element(
+ Key, maps:get(Var, RevIdx1, ordsets:new()))}
+ end, RevIdx0, row_coefs(Row)).
+
+-spec revidx_remove(key(), row(), rev_index()) -> rev_index().
+revidx_remove(Key, {Coefs, _}, RevIdx0) ->
+ orddict:fold(fun(Var, _Coef, RevIdx1) ->
+ case RevIdx1 of
+ #{Var := Keys0} ->
+ case ordsets:del_element(Key, Keys0) of
+ [] -> maps:remove(Var, RevIdx1);
+ Keys -> RevIdx1#{Var := Keys}
+ end
+ end
+ end, RevIdx0, Coefs).
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+-define(FAST_ITERATIONS, 5).
+
+%% @doc Computes a rough approximation of BB weights. The approximation is
+%% particularly poor (converges slowly) for recursive functions and loops.
+-spec compute_fast(cfg(), target_module(), target_context()) -> bb_weights().
+compute_fast(CFG, TgtMod, TgtCtx) ->
+ Target = {TgtMod, TgtCtx},
+ StartLb = hipe_gen_cfg:start_label(CFG),
+ RPO = reverse_postorder(CFG, Target),
+ PredProbs = [{L, pred_prob(L, CFG, Target)} || L <- RPO, L =/= StartLb],
+ Probs0 = (maps:from_list([{L, 0.0} || L <- RPO]))#{StartLb := 1.0},
+ fast_iterate(?FAST_ITERATIONS, PredProbs, Probs0).
+
+fast_iterate(0, _Pred, Probs) -> Probs;
+fast_iterate(Iters, Pred, Probs0) ->
+ fast_iterate(Iters-1, Pred,
+ fast_one(Pred, Probs0)).
+
+fast_one([{L, Pred}|Ls], Probs0) ->
+ Weight = fast_sum(Pred, Probs0, 0.0),
+ Probs = Probs0#{L => Weight},
+ fast_one(Ls, Probs);
+fast_one([], Probs) ->
+ Probs.
+
+fast_sum([{P,EWt}|Pred], Probs, Acc) when is_float(EWt), is_float(Acc) ->
+ case Probs of
+ #{P := PWt} when is_float(PWt) ->
+ fast_sum(Pred, Probs, Acc + PWt * EWt)
+ end;
+fast_sum([], _Probs, Acc) when is_float(Acc) ->
+ Acc.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Target module interface functions
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+-define(TGT_IFACE_0(N), N( {M,C}) -> M:N( C)).
+-define(TGT_IFACE_1(N), N(A1, {M,C}) -> M:N(A1, C)).
+-define(TGT_IFACE_2(N), N(A1,A2, {M,C}) -> M:N(A1,A2, C)).
+-define(TGT_IFACE_3(N), N(A1,A2,A3,{M,C}) -> M:N(A1,A2,A3,C)).
+
+?TGT_IFACE_2(bb).
+?TGT_IFACE_1(branch_preds).
+?TGT_IFACE_1(labels).
+?TGT_IFACE_1(reverse_postorder).