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Diffstat (limited to 'lib/hipe/opt/hipe_bb_weights.erl')
| -rw-r--r-- | lib/hipe/opt/hipe_bb_weights.erl | 449 |
1 files changed, 449 insertions, 0 deletions
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). |