aboutsummaryrefslogtreecommitdiffstats
path: root/lib/compiler/src/beam_ssa_opt.erl
diff options
context:
space:
mode:
Diffstat (limited to 'lib/compiler/src/beam_ssa_opt.erl')
-rw-r--r--lib/compiler/src/beam_ssa_opt.erl1765
1 files changed, 1765 insertions, 0 deletions
diff --git a/lib/compiler/src/beam_ssa_opt.erl b/lib/compiler/src/beam_ssa_opt.erl
new file mode 100644
index 0000000000..ac2d943fef
--- /dev/null
+++ b/lib/compiler/src/beam_ssa_opt.erl
@@ -0,0 +1,1765 @@
+%%
+%% %CopyrightBegin%
+%%
+%% Copyright Ericsson AB 2018. All Rights Reserved.
+%%
+%% 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.
+%%
+%% %CopyrightEnd%
+%%
+
+-module(beam_ssa_opt).
+-export([module/2]).
+
+-include("beam_ssa.hrl").
+-import(lists, [all/2,append/1,foldl/3,keyfind/3,member/2,reverse/1,reverse/2,
+ splitwith/2,takewhile/2,unzip/1]).
+
+-spec module(beam_ssa:b_module(), [compile:option()]) ->
+ {'ok',beam_ssa:b_module()}.
+
+module(#b_module{body=Fs0}=Module, Opts) ->
+ Ps = passes(Opts),
+ Fs = functions(Fs0, Ps),
+ {ok,Module#b_module{body=Fs}}.
+
+functions([F|Fs], Ps) ->
+ [function(F, Ps)|functions(Fs, Ps)];
+functions([], _Ps) -> [].
+
+-type b_blk() :: beam_ssa:b_blk().
+-type b_var() :: beam_ssa:b_var().
+-type label() :: beam_ssa:label().
+
+-record(st, {ssa :: beam_ssa:block_map() | [{label(),b_blk()}],
+ args :: [b_var()],
+ cnt :: label()}).
+-define(PASS(N), {N,fun N/1}).
+
+passes(Opts0) ->
+ Ps = [?PASS(ssa_opt_split_blocks),
+ ?PASS(ssa_opt_coalesce_phis),
+ ?PASS(ssa_opt_element),
+ ?PASS(ssa_opt_linearize),
+ ?PASS(ssa_opt_record),
+
+ %% Run ssa_opt_cse twice, because it will help ssa_opt_dead,
+ %% and ssa_opt_dead will help ssa_opt_cse. Run ssa_opt_live
+ %% twice, because it will help ssa_opt_dead and ssa_opt_dead
+ %% will help ssa_opt_live.
+ ?PASS(ssa_opt_cse),
+ ?PASS(ssa_opt_type),
+ ?PASS(ssa_opt_live),
+ ?PASS(ssa_opt_dead),
+ ?PASS(ssa_opt_cse), %Second time.
+ ?PASS(ssa_opt_float),
+ ?PASS(ssa_opt_live), %Second time.
+
+ ?PASS(ssa_opt_bsm),
+ ?PASS(ssa_opt_bsm_units),
+ ?PASS(ssa_opt_bsm_shortcut),
+ ?PASS(ssa_opt_misc),
+ ?PASS(ssa_opt_tuple_size),
+ ?PASS(ssa_opt_sw),
+ ?PASS(ssa_opt_blockify),
+ ?PASS(ssa_opt_sink),
+ ?PASS(ssa_opt_merge_blocks),
+ ?PASS(ssa_opt_trim_unreachable)],
+ Negations = [{list_to_atom("no_"++atom_to_list(N)),N} ||
+ {N,_} <- Ps],
+ Opts = proplists:substitute_negations(Negations, Opts0),
+ [case proplists:get_value(Name, Opts, true) of
+ true ->
+ P;
+ false ->
+ {NoName,Name} = keyfind(Name, 2, Negations),
+ {NoName,fun(S) -> S end}
+ end || {Name,_}=P <- Ps].
+
+function(#b_function{anno=Anno,bs=Blocks0,args=Args,cnt=Count0}=F, Ps) ->
+ try
+ St = #st{ssa=Blocks0,args=Args,cnt=Count0},
+ #st{ssa=Blocks,cnt=Count} = compile:run_sub_passes(Ps, St),
+ F#b_function{bs=Blocks,cnt=Count}
+ catch
+ Class:Error:Stack ->
+ #{func_info:={_,Name,Arity}} = Anno,
+ io:fwrite("Function: ~w/~w\n", [Name,Arity]),
+ erlang:raise(Class, Error, Stack)
+ end.
+
+%%%
+%%% Trivial sub passes.
+%%%
+
+ssa_opt_dead(#st{ssa=Linear}=St) ->
+ St#st{ssa=beam_ssa_dead:opt(Linear)}.
+
+ssa_opt_linearize(#st{ssa=Blocks}=St) ->
+ St#st{ssa=beam_ssa:linearize(Blocks)}.
+
+ssa_opt_type(#st{ssa=Linear,args=Args}=St) ->
+ St#st{ssa=beam_ssa_type:opt(Linear, Args)}.
+
+ssa_opt_blockify(#st{ssa=Linear}=St) ->
+ St#st{ssa=maps:from_list(Linear)}.
+
+ssa_opt_trim_unreachable(#st{ssa=Blocks}=St) ->
+ St#st{ssa=beam_ssa:trim_unreachable(Blocks)}.
+
+%%%
+%%% Split blocks before certain instructions to enable more optimizations.
+%%%
+%%% Splitting before element/2 enables the optimization that swaps
+%%% element/2 instructions.
+%%%
+%%% Splitting before call and make_fun instructions gives more opportunities
+%%% for sinking get_tuple_element instructions.
+%%%
+
+ssa_opt_split_blocks(#st{ssa=Blocks0,cnt=Count0}=St) ->
+ P = fun(#b_set{op={bif,element}}) -> true;
+ (#b_set{op=call}) -> true;
+ (#b_set{op=make_fun}) -> true;
+ (_) -> false
+ end,
+ {Blocks,Count} = beam_ssa:split_blocks(P, Blocks0, Count0),
+ St#st{ssa=Blocks,cnt=Count}.
+
+%%%
+%%% Coalesce phi nodes.
+%%%
+%%% Nested cases can led to code such as this:
+%%%
+%%% 10:
+%%% _1 = phi {literal value1, label 8}, {Var, label 9}
+%%% br 11
+%%%
+%%% 11:
+%%% _2 = phi {_1, label 10}, {literal false, label 3}
+%%%
+%%% The phi nodes can be coalesced like this:
+%%%
+%%% 11:
+%%% _2 = phi {literal value1, label 8}, {Var, label 9}, {literal false, label 3}
+%%%
+%%% Coalescing can help other optimizations, and can in some cases reduce register
+%%% shuffling (if the phi variables for two phi nodes happens to be allocated to
+%%% different registers).
+%%%
+
+ssa_opt_coalesce_phis(#st{ssa=Blocks0}=St) ->
+ Ls = beam_ssa:rpo(Blocks0),
+ Blocks = c_phis_1(Ls, Blocks0),
+ St#st{ssa=Blocks}.
+
+c_phis_1([L|Ls], Blocks0) ->
+ case maps:get(L, Blocks0) of
+ #b_blk{is=[#b_set{op=phi}|_]}=Blk ->
+ Blocks = c_phis_2(L, Blk, Blocks0),
+ c_phis_1(Ls, Blocks);
+ #b_blk{} ->
+ c_phis_1(Ls, Blocks0)
+ end;
+c_phis_1([], Blocks) -> Blocks.
+
+c_phis_2(L, #b_blk{is=Is0}=Blk0, Blocks0) ->
+ case c_phis_args(Is0, Blocks0) of
+ none ->
+ Blocks0;
+ {_,_,Preds}=Info ->
+ Is = c_rewrite_phis(Is0, Info),
+ Blk = Blk0#b_blk{is=Is},
+ Blocks = Blocks0#{L:=Blk},
+ c_fix_branches(Preds, L, Blocks)
+ end.
+
+c_phis_args([#b_set{op=phi,args=Args0}|Is], Blocks) ->
+ case c_phis_args_1(Args0, Blocks) of
+ none ->
+ c_phis_args(Is, Blocks);
+ Res ->
+ Res
+ end;
+c_phis_args(_, _Blocks) -> none.
+
+c_phis_args_1([{Var,Pred}|As], Blocks) ->
+ case c_get_pred_vars(Var, Pred, Blocks) of
+ none ->
+ c_phis_args_1(As, Blocks);
+ Result ->
+ Result
+ end;
+c_phis_args_1([], _Blocks) -> none.
+
+c_get_pred_vars(Var, Pred, Blocks) ->
+ case maps:get(Pred, Blocks) of
+ #b_blk{is=[#b_set{op=phi,dst=Var,args=Args}]} ->
+ {Var,Pred,Args};
+ #b_blk{} ->
+ none
+ end.
+
+c_rewrite_phis([#b_set{op=phi,args=Args0}=I|Is], Info) ->
+ Args = c_rewrite_phi(Args0, Info),
+ [I#b_set{args=Args}|c_rewrite_phis(Is, Info)];
+c_rewrite_phis(Is, _Info) -> Is.
+
+c_rewrite_phi([{Var,Pred}|As], {Var,Pred,Values}) ->
+ Values ++ As;
+c_rewrite_phi([{Value,Pred}|As], {_,Pred,Values}) ->
+ [{Value,P} || {_,P} <- Values] ++ As;
+c_rewrite_phi([A|As], Info) ->
+ [A|c_rewrite_phi(As, Info)];
+c_rewrite_phi([], _Info) -> [].
+
+c_fix_branches([{_,Pred}|As], L, Blocks0) ->
+ #b_blk{last=Last0} = Blk0 = maps:get(Pred, Blocks0),
+ #b_br{bool=#b_literal{val=true}} = Last0, %Assertion.
+ Last = Last0#b_br{bool=#b_literal{val=true},succ=L,fail=L},
+ Blk = Blk0#b_blk{last=Last},
+ Blocks = Blocks0#{Pred:=Blk},
+ c_fix_branches(As, L, Blocks);
+c_fix_branches([], _, Blocks) -> Blocks.
+
+%%%
+%%% Order element/2 calls.
+%%%
+%%% Order an unbroken chain of element/2 calls for the same tuple
+%%% with the same failure label so that the highest element is
+%%% retrieved first. That will allow the other element/2 calls to
+%%% be replaced with get_tuple_element/3 instructions.
+%%%
+
+ssa_opt_element(#st{ssa=Blocks}=St) ->
+ %% Collect the information about element instructions in this
+ %% function.
+ GetEls = collect_element_calls(beam_ssa:linearize(Blocks)),
+
+ %% Collect the element instructions into chains. The
+ %% element calls in each chain are ordered in reverse
+ %% execution order.
+ Chains = collect_chains(GetEls, []),
+
+ %% For each chain, swap the first element call with the
+ %% element call with the highest index.
+ St#st{ssa=swap_element_calls(Chains, Blocks)}.
+
+collect_element_calls([{L,#b_blk{is=Is0,last=Last}}|Bs]) ->
+ case {Is0,Last} of
+ {[#b_set{op={bif,element},dst=Element,
+ args=[#b_literal{val=N},#b_var{}=Tuple]},
+ #b_set{op=succeeded,dst=Bool,args=[Element]}],
+ #b_br{bool=Bool,succ=Succ,fail=Fail}} ->
+ Info = {L,Succ,{Tuple,Fail},N},
+ [Info|collect_element_calls(Bs)];
+ {_,_} ->
+ collect_element_calls(Bs)
+ end;
+collect_element_calls([]) -> [].
+
+collect_chains([{This,_,V,_}=El|Els], [{_,This,V,_}|_]=Chain) ->
+ %% Add to the previous chain.
+ collect_chains(Els, [El|Chain]);
+collect_chains([El|Els], [_,_|_]=Chain) ->
+ %% Save the previous chain and start a new chain.
+ [Chain|collect_chains(Els, [El])];
+collect_chains([El|Els], _Chain) ->
+ %% The previous chain is too short; discard it and start a new.
+ collect_chains(Els, [El]);
+collect_chains([], [_,_|_]=Chain) ->
+ %% Save the last chain.
+ [Chain];
+collect_chains([], _) -> [].
+
+swap_element_calls([[{L,_,_,N}|_]=Chain|Chains], Blocks0) ->
+ Blocks = swap_element_calls_1(Chain, {N,L}, Blocks0),
+ swap_element_calls(Chains, Blocks);
+swap_element_calls([], Blocks) -> Blocks.
+
+swap_element_calls_1([{L1,_,_,N1}], {N2,L2}, Blocks) when N2 > N1 ->
+ %% We have reached the end of the chain, and the first
+ %% element instrution to be executed. Its index is lower
+ %% than the maximum index found while traversing the chain,
+ %% so we will need to swap the instructions.
+ #{L1:=Blk1,L2:=Blk2} = Blocks,
+ [#b_set{dst=Dst1}=GetEl1,Succ1] = Blk1#b_blk.is,
+ [#b_set{dst=Dst2}=GetEl2,Succ2] = Blk2#b_blk.is,
+ Is1 = [GetEl2,Succ1#b_set{args=[Dst2]}],
+ Is2 = [GetEl1,Succ2#b_set{args=[Dst1]}],
+ Blocks#{L1:=Blk1#b_blk{is=Is1},L2:=Blk2#b_blk{is=Is2}};
+swap_element_calls_1([{L,_,_,N1}|Els], {N2,_}, Blocks) when N1 > N2 ->
+ swap_element_calls_1(Els, {N2,L}, Blocks);
+swap_element_calls_1([_|Els], Highest, Blocks) ->
+ swap_element_calls_1(Els, Highest, Blocks);
+swap_element_calls_1([], _, Blocks) ->
+ %% Nothing to do. The element call with highest index
+ %% is already the first one to be executed.
+ Blocks.
+
+%%%
+%%% Record optimization.
+%%%
+%%% Replace tuple matching with an is_tagged_tuple instruction
+%%% when applicable.
+%%%
+
+ssa_opt_record(#st{ssa=Linear}=St) ->
+ Blocks = maps:from_list(Linear),
+ St#st{ssa=record_opt(Linear, Blocks)}.
+
+record_opt([{L,#b_blk{is=Is0,last=Last}=Blk0}|Bs], Blocks) ->
+ Is = record_opt_is(Is0, Last, Blocks),
+ Blk = Blk0#b_blk{is=Is},
+ [{L,Blk}|record_opt(Bs, Blocks)];
+record_opt([], _Blocks) -> [].
+
+record_opt_is([#b_set{op={bif,is_tuple},dst=Bool,args=[Tuple]}=Set],
+ Last, Blocks) ->
+ case is_tagged_tuple(Tuple, Bool, Last, Blocks) of
+ {yes,Size,Tag} ->
+ Args = [Tuple,Size,Tag],
+ [Set#b_set{op=is_tagged_tuple,args=Args}];
+ no ->
+ [Set]
+ end;
+record_opt_is([I|Is], Last, Blocks) ->
+ [I|record_opt_is(Is, Last, Blocks)];
+record_opt_is([], _Last, _Blocks) -> [].
+
+is_tagged_tuple(#b_var{}=Tuple, Bool,
+ #b_br{bool=Bool,succ=Succ,fail=Fail},
+ Blocks) ->
+ SuccBlk = maps:get(Succ, Blocks),
+ is_tagged_tuple_1(SuccBlk, Tuple, Fail, Blocks);
+is_tagged_tuple(_, _, _, _) -> no.
+
+is_tagged_tuple_1(#b_blk{is=Is,last=Last}, Tuple, Fail, Blocks) ->
+ case Is of
+ [#b_set{op={bif,tuple_size},dst=ArityVar,
+ args=[#b_var{}=Tuple]},
+ #b_set{op={bif,'=:='},
+ dst=Bool,
+ args=[ArityVar, #b_literal{val=ArityVal}=Arity]}]
+ when is_integer(ArityVal) ->
+ case Last of
+ #b_br{bool=Bool,succ=Succ,fail=Fail} ->
+ SuccBlk = maps:get(Succ, Blocks),
+ case is_tagged_tuple_2(SuccBlk, Tuple, Fail) of
+ no ->
+ no;
+ {yes,Tag} ->
+ {yes,Arity,Tag}
+ end;
+ _ ->
+ no
+ end;
+ _ ->
+ no
+ end.
+
+is_tagged_tuple_2(#b_blk{is=Is,
+ last=#b_br{bool=#b_var{}=Bool,fail=Fail}},
+ Tuple, Fail) ->
+ is_tagged_tuple_3(Is, Bool, Tuple);
+is_tagged_tuple_2(#b_blk{}, _, _) -> no.
+
+is_tagged_tuple_3([#b_set{op=get_tuple_element,
+ dst=TagVar,
+ args=[#b_var{}=Tuple,#b_literal{val=0}]}|Is],
+ Bool, Tuple) ->
+ is_tagged_tuple_4(Is, Bool, TagVar);
+is_tagged_tuple_3([_|Is], Bool, Tuple) ->
+ is_tagged_tuple_3(Is, Bool, Tuple);
+is_tagged_tuple_3([], _, _) -> no.
+
+is_tagged_tuple_4([#b_set{op={bif,'=:='},dst=Bool,
+ args=[#b_var{}=TagVar,
+ #b_literal{val=TagVal}=Tag]}],
+ Bool, TagVar) when is_atom(TagVal) ->
+ {yes,Tag};
+is_tagged_tuple_4([_|Is], Bool, TagVar) ->
+ is_tagged_tuple_4(Is, Bool, TagVar);
+is_tagged_tuple_4([], _, _) -> no.
+
+%%%
+%%% Common subexpression elimination (CSE).
+%%%
+%%% Eliminate repeated evaluation of identical expressions. To avoid
+%%% increasing the size of the stack frame, we don't eliminate
+%%% subexpressions across instructions that clobber the X registers.
+%%%
+
+ssa_opt_cse(#st{ssa=Linear}=St) ->
+ M = #{0=>#{}},
+ St#st{ssa=cse(Linear, #{}, M)}.
+
+cse([{L,#b_blk{is=Is0,last=Last0}=Blk}|Bs], Sub0, M0) ->
+ Es0 = maps:get(L, M0),
+ {Is1,Es,Sub} = cse_is(Is0, Es0, Sub0, []),
+ Last = sub(Last0, Sub),
+ M = cse_successors(Is1, Blk, Es, M0),
+ Is = reverse(Is1),
+ [{L,Blk#b_blk{is=Is,last=Last}}|cse(Bs, Sub, M)];
+cse([], _, _) -> [].
+
+cse_successors([#b_set{op=succeeded,args=[Src]},Bif|_], Blk, EsSucc, M0) ->
+ case cse_suitable(Bif) of
+ true ->
+ %% The previous instruction only has a valid value at the success branch.
+ %% We must remove the substitution for Src from the failure branch.
+ #b_blk{last=#b_br{succ=Succ,fail=Fail}} = Blk,
+ M = cse_successors_1([Succ], EsSucc, M0),
+ EsFail = maps:filter(fun(_, Val) -> Val =/= Src end, EsSucc),
+ cse_successors_1([Fail], EsFail, M);
+ false ->
+ %% There can't be any replacement for Src in EsSucc. No need for
+ %% any special handling.
+ cse_successors_1(beam_ssa:successors(Blk), EsSucc, M0)
+ end;
+cse_successors(_Is, Blk, Es, M) ->
+ cse_successors_1(beam_ssa:successors(Blk), Es, M).
+
+cse_successors_1([L|Ls], Es0, M) ->
+ case M of
+ #{L:=Es1} when map_size(Es1) =:= 0 ->
+ %% The map is already empty. No need to do anything
+ %% since the intersection will be empty.
+ cse_successors_1(Ls, Es0, M);
+ #{L:=Es1} ->
+ %% Calculate the intersection of the two maps.
+ %% Both keys and values must match.
+ Es = maps:filter(fun(Key, Value) ->
+ case Es1 of
+ #{Key:=Value} -> true;
+ #{} -> false
+ end
+ end, Es0),
+ cse_successors_1(Ls, Es0, M#{L:=Es});
+ #{} ->
+ cse_successors_1(Ls, Es0, M#{L=>Es0})
+ end;
+cse_successors_1([], _, M) -> M.
+
+cse_is([#b_set{op=succeeded,dst=Bool,args=[Src]}=I0|Is], Es, Sub0, Acc) ->
+ I = sub(I0, Sub0),
+ case I of
+ #b_set{args=[Src]} ->
+ cse_is(Is, Es, Sub0, [I|Acc]);
+ #b_set{} ->
+ %% The previous instruction has been eliminated. Eliminate the
+ %% 'succeeded' instruction too.
+ Sub = Sub0#{Bool=>#b_literal{val=true}},
+ cse_is(Is, Es, Sub, Acc)
+ end;
+cse_is([#b_set{dst=Dst}=I0|Is], Es0, Sub0, Acc) ->
+ I = sub(I0, Sub0),
+ case beam_ssa:clobbers_xregs(I) of
+ true ->
+ %% Retaining the expressions map across calls and other
+ %% clobbering instructions would work, but it would cause
+ %% the common subexpressions to be saved to Y registers,
+ %% which would probably increase the size of the stack
+ %% frame.
+ cse_is(Is, #{}, Sub0, [I|Acc]);
+ false ->
+ case cse_expr(I) of
+ none ->
+ %% Not suitable for CSE.
+ cse_is(Is, Es0, Sub0, [I|Acc]);
+ {ok,ExprKey} ->
+ case Es0 of
+ #{ExprKey:=Src} ->
+ Sub = Sub0#{Dst=>Src},
+ cse_is(Is, Es0, Sub, Acc);
+ #{} ->
+ Es = Es0#{ExprKey=>Dst},
+ cse_is(Is, Es, Sub0, [I|Acc])
+ end
+ end
+ end;
+cse_is([], Es, Sub, Acc) ->
+ {Acc,Es,Sub}.
+
+cse_expr(#b_set{op=Op,args=Args}=I) ->
+ case cse_suitable(I) of
+ true -> {ok,{Op,Args}};
+ false -> none
+ end.
+
+cse_suitable(#b_set{op=get_hd}) -> true;
+cse_suitable(#b_set{op=get_tl}) -> true;
+cse_suitable(#b_set{op=put_list}) -> true;
+cse_suitable(#b_set{op=put_tuple}) -> true;
+cse_suitable(#b_set{op={bif,tuple_size}}) ->
+ %% Doing CSE for tuple_size/1 can prevent the
+ %% creation of test_arity and select_tuple_arity
+ %% instructions. That could decrease performance
+ %% and beam_validator could fail to understand
+ %% that tuple operations that follow are safe.
+ false;
+cse_suitable(#b_set{anno=Anno,op={bif,Name},args=Args}) ->
+ %% Doing CSE for floating point operators is unsafe.
+ %% Doing CSE for comparison operators would prevent
+ %% creation of 'test' instructions.
+ Arity = length(Args),
+ not (is_map_key(float_op, Anno) orelse
+ erl_internal:new_type_test(Name, Arity) orelse
+ erl_internal:comp_op(Name, Arity) orelse
+ erl_internal:bool_op(Name, Arity));
+cse_suitable(#b_set{}) -> false.
+
+%%%
+%%% Using floating point instructions.
+%%%
+%%% Use the special floating points version of arithmetic
+%%% instructions, if the operands are known to be floats or the result
+%%% of the operation will be a float.
+%%%
+%%% The float instructions were never used in guards before, so we
+%%% will take special care to keep not using them in guards. Using
+%%% them in guards would require a new version of the 'fconv'
+%%% instruction that would take a failure label. Since it is unlikely
+%%% that using float instructions in guards would be benefical, why
+%%% bother implementing a new instruction? Also, implementing float
+%%% instructions in guards in HiPE could turn out to be a lot of work.
+%%%
+
+-record(fs,
+ {s=undefined :: 'undefined' | 'cleared',
+ regs=#{} :: #{beam_ssa:b_var():=beam_ssa:b_var()},
+ fail=none :: 'none' | beam_ssa:label(),
+ non_guards :: gb_sets:set(beam_ssa:label()),
+ bs :: beam_ssa:block_map()
+ }).
+
+ssa_opt_float(#st{ssa=Linear0,cnt=Count0}=St) ->
+ NonGuards0 = float_non_guards(Linear0),
+ NonGuards = gb_sets:from_list(NonGuards0),
+ Blocks = maps:from_list(Linear0),
+ Fs = #fs{non_guards=NonGuards,bs=Blocks},
+ {Linear,Count} = float_opt(Linear0, Count0, Fs),
+ St#st{ssa=Linear,cnt=Count}.
+
+float_non_guards([{L,#b_blk{is=Is}}|Bs]) ->
+ case Is of
+ [#b_set{op=landingpad}|_] ->
+ [L|float_non_guards(Bs)];
+ _ ->
+ float_non_guards(Bs)
+ end;
+float_non_guards([]) -> [?BADARG_BLOCK].
+
+float_opt([{L,#b_blk{last=#b_br{fail=F}}=Blk}|Bs0],
+ Count0, #fs{non_guards=NonGuards}=Fs) ->
+ case gb_sets:is_member(F, NonGuards) of
+ true ->
+ %% This block is not inside a guard.
+ %% We can do the optimization.
+ float_opt_1(L, Blk, Bs0, Count0, Fs);
+ false ->
+ %% This block is inside a guard. Don't do
+ %% any floating point optimizations.
+ {Bs,Count} = float_opt(Bs0, Count0, Fs),
+ {[{L,Blk}|Bs],Count}
+ end;
+float_opt([{L,Blk}|Bs], Count, Fs) ->
+ float_opt_1(L, Blk, Bs, Count, Fs);
+float_opt([], Count, _Fs) ->
+ {[],Count}.
+
+float_opt_1(L, #b_blk{is=Is0}=Blk0, Bs0, Count0, Fs0) ->
+ case float_opt_is(Is0, Fs0, Count0, []) of
+ {Is1,Fs1,Count1} ->
+ Fs2 = float_fail_label(Blk0, Fs1),
+ Fail = Fs2#fs.fail,
+ {Flush,Blk,Fs,Count2} = float_maybe_flush(Blk0, Fs2, Count1),
+ Split = float_split_conv(Is1, Blk),
+ {Blks0,Count3} = float_number(Split, L, Count2),
+ {Blks,Count4} = float_conv(Blks0, Fail, Count3),
+ {Bs,Count} = float_opt(Bs0, Count4, Fs),
+ {Blks++Flush++Bs,Count};
+ none ->
+ {Bs,Count} = float_opt(Bs0, Count0, Fs0),
+ {[{L,Blk0}|Bs],Count}
+ end.
+
+%% Split {float,convert} instructions into individual blocks.
+float_split_conv(Is0, Blk) ->
+ Br = #b_br{bool=#b_literal{val=true},succ=0,fail=0},
+ case splitwith(fun(#b_set{op=Op}) ->
+ Op =/= {float,convert}
+ end, Is0) of
+ {Is,[]} ->
+ [Blk#b_blk{is=Is}];
+ {[_|_]=Is1,[#b_set{op={float,convert}}=Conv|Is2]} ->
+ [#b_blk{is=Is1,last=Br},
+ #b_blk{is=[Conv],last=Br}|float_split_conv(Is2, Blk)];
+ {[],[#b_set{op={float,convert}}=Conv|Is1]} ->
+ [#b_blk{is=[Conv],last=Br}|float_split_conv(Is1, Blk)]
+ end.
+
+%% Number the blocks that were split.
+float_number([B|Bs0], FirstL, Count0) ->
+ {Bs,Count} = float_number(Bs0, Count0),
+ {[{FirstL,B}|Bs],Count}.
+
+float_number([B|Bs0], Count0) ->
+ {Bs,Count} = float_number(Bs0, Count0+1),
+ {[{Count0,B}|Bs],Count};
+float_number([], Count) ->
+ {[],Count}.
+
+%% Insert 'succeeded' instructions after each {float,convert}
+%% instruction.
+float_conv([{L,#b_blk{is=Is0}=Blk0}|Bs0], Fail, Count0) ->
+ case Is0 of
+ [#b_set{op={float,convert}}=Conv] ->
+ {Bool0,Count1} = new_reg('@ssa_bool', Count0),
+ Bool = #b_var{name=Bool0},
+ Succeeded = #b_set{op=succeeded,dst=Bool,
+ args=[Conv#b_set.dst]},
+ Is = [Conv,Succeeded],
+ [{NextL,_}|_] = Bs0,
+ Br = #b_br{bool=Bool,succ=NextL,fail=Fail},
+ Blk = Blk0#b_blk{is=Is,last=Br},
+ {Bs,Count} = float_conv(Bs0, Fail, Count1),
+ {[{L,Blk}|Bs],Count};
+ [_|_] ->
+ case Bs0 of
+ [{NextL,_}|_] ->
+ Br = #b_br{bool=#b_literal{val=true},
+ succ=NextL,fail=NextL},
+ Blk = Blk0#b_blk{last=Br},
+ {Bs,Count} = float_conv(Bs0, Fail, Count0),
+ {[{L,Blk}|Bs],Count};
+ [] ->
+ {[{L,Blk0}],Count0}
+ end
+ end.
+
+float_maybe_flush(Blk0, #fs{s=cleared,fail=Fail,bs=Blocks}=Fs0, Count0) ->
+ #b_blk{last=#b_br{bool=#b_var{},succ=Succ}=Br} = Blk0,
+ #b_blk{is=Is} = maps:get(Succ, Blocks),
+ case Is of
+ [#b_set{anno=#{float_op:=_}}|_] ->
+ %% The next operation is also a floating point operation.
+ %% No flush needed.
+ {[],Blk0,Fs0,Count0};
+ _ ->
+ %% Flush needed.
+ {Bool0,Count1} = new_reg('@ssa_bool', Count0),
+ Bool = #b_var{name=Bool0},
+
+ %% Allocate block numbers.
+ CheckL = Count1, %For checkerror.
+ FlushL = Count1 + 1, %For flushing of float regs.
+ Count = Count1 + 2,
+ Blk = Blk0#b_blk{last=Br#b_br{succ=CheckL}},
+
+ %% Build the block with the checkerror instruction.
+ CheckIs = [#b_set{op={float,checkerror},dst=Bool}],
+ CheckBr = #b_br{bool=Bool,succ=FlushL,fail=Fail},
+ CheckBlk = #b_blk{is=CheckIs,last=CheckBr},
+
+ %% Build the block that flushes all registers.
+ FlushIs = float_flush_regs(Fs0),
+ FlushBr = #b_br{bool=#b_literal{val=true},succ=Succ,fail=Succ},
+ FlushBlk = #b_blk{is=FlushIs,last=FlushBr},
+
+ %% Update state and blocks.
+ Fs = Fs0#fs{s=undefined,regs=#{},fail=none},
+ FlushBs = [{CheckL,CheckBlk},{FlushL,FlushBlk}],
+ {FlushBs,Blk,Fs,Count}
+ end;
+float_maybe_flush(Blk, Fs, Count) ->
+ {[],Blk,Fs,Count}.
+
+float_opt_is([#b_set{op=succeeded,args=[Src]}=I0],
+ #fs{regs=Rs}=Fs, Count, Acc) ->
+ case Rs of
+ #{Src:=Fr} ->
+ I = I0#b_set{args=[Fr]},
+ {reverse(Acc, [I]),Fs,Count};
+ #{} ->
+ {reverse(Acc, [I0]),Fs,Count}
+ end;
+float_opt_is([#b_set{anno=Anno0}=I0|Is0], Fs0, Count0, Acc) ->
+ case Anno0 of
+ #{float_op:=FTypes} ->
+ Anno = maps:remove(float_op, Anno0),
+ I1 = I0#b_set{anno=Anno},
+ {Is,Fs,Count} = float_make_op(I1, FTypes, Fs0, Count0),
+ float_opt_is(Is0, Fs, Count, reverse(Is, Acc));
+ #{} ->
+ float_opt_is(Is0, Fs0#fs{regs=#{}}, Count0, [I0|Acc])
+ end;
+float_opt_is([], Fs, _Count, _Acc) ->
+ #fs{s=undefined} = Fs, %Assertion.
+ none.
+
+float_make_op(#b_set{op={bif,Op},dst=Dst,args=As0}=I0,
+ Ts, #fs{s=S,regs=Rs0}=Fs, Count0) ->
+ {As1,Rs1,Count1} = float_load(As0, Ts, Rs0, Count0, []),
+ {As,Is0} = unzip(As1),
+ {Fr,Count2} = new_reg('@fr', Count1),
+ FrDst = #b_var{name=Fr},
+ I = I0#b_set{op={float,Op},dst=FrDst,args=As},
+ Rs = Rs1#{Dst=>FrDst},
+ Is = append(Is0) ++ [I],
+ case S of
+ undefined ->
+ {Ignore,Count} = new_reg('@ssa_ignore', Count2),
+ C = #b_set{op={float,clearerror},dst=#b_var{name=Ignore}},
+ {[C|Is],Fs#fs{s=cleared,regs=Rs},Count};
+ cleared ->
+ {Is,Fs#fs{regs=Rs},Count2}
+ end.
+
+float_load([A|As], [T|Ts], Rs0, Count0, Acc) ->
+ {Load,Rs,Count} = float_reg_arg(A, T, Rs0, Count0),
+ float_load(As, Ts, Rs, Count, [Load|Acc]);
+float_load([], [], Rs, Count, Acc) ->
+ {reverse(Acc),Rs,Count}.
+
+float_reg_arg(A, T, Rs, Count0) ->
+ case Rs of
+ #{A:=Fr} ->
+ {{Fr,[]},Rs,Count0};
+ #{} ->
+ {Fr,Count} = new_float_copy_reg(Count0),
+ Dst = #b_var{name=Fr},
+ I = float_load_reg(T, A, Dst),
+ {{Dst,[I]},Rs#{A=>Dst},Count}
+ end.
+
+float_load_reg(convert, #b_var{}=Src, Dst) ->
+ #b_set{op={float,convert},dst=Dst,args=[Src]};
+float_load_reg(convert, #b_literal{val=Val}=Src, Dst) ->
+ try float(Val) of
+ F ->
+ #b_set{op={float,put},dst=Dst,args=[#b_literal{val=F}]}
+ catch
+ error:_ ->
+ %% Let the exception happen at runtime.
+ #b_set{op={float,convert},dst=Dst,args=[Src]}
+ end;
+float_load_reg(float, Src, Dst) ->
+ #b_set{op={float,put},dst=Dst,args=[Src]}.
+
+new_float_copy_reg(Count) ->
+ new_reg('@fr_copy', Count).
+
+new_reg(Base, Count) ->
+ Fr = {Base,Count},
+ {Fr,Count+1}.
+
+float_fail_label(#b_blk{last=Last}, Fs) ->
+ case Last of
+ #b_br{bool=#b_var{},fail=Fail} ->
+ Fs#fs{fail=Fail};
+ _ ->
+ Fs
+ end.
+
+float_flush_regs(#fs{regs=Rs}) ->
+ maps:fold(fun(_, #b_var{name={'@fr_copy',_}}, Acc) ->
+ Acc;
+ (Dst, Fr, Acc) ->
+ [#b_set{op={float,get},dst=Dst,args=[Fr]}|Acc]
+ end, [], Rs).
+
+%%%
+%%% Live optimization.
+%%%
+%%% Optimize instructions whose values are not used. They could be
+%%% removed if they have no side effects, or in a few cases replaced
+%%% with a cheaper instructions
+%%%
+
+ssa_opt_live(#st{ssa=Linear}=St) ->
+ St#st{ssa=live_opt(reverse(Linear), #{}, [])}.
+
+live_opt([{L,Blk0}|Bs], LiveMap0, Acc) ->
+ Successors = beam_ssa:successors(Blk0),
+ Live0 = live_opt_succ(Successors, L, LiveMap0),
+ {Blk,Live} = live_opt_blk(Blk0, Live0),
+ LiveMap = live_opt_phis(Blk#b_blk.is, L, Live, LiveMap0),
+ live_opt(Bs, LiveMap, [{L,Blk}|Acc]);
+live_opt([], _, Acc) -> Acc.
+
+live_opt_succ([S|Ss], L, LiveMap) ->
+ Live0 = live_opt_succ(Ss, L, LiveMap),
+ Key = {S,L},
+ case LiveMap of
+ #{Key:=Live} ->
+ gb_sets:union(Live, Live0);
+ #{S:=Live} ->
+ gb_sets:union(Live, Live0);
+ #{} ->
+ Live0
+ end;
+live_opt_succ([], _, _) ->
+ gb_sets:empty().
+
+live_opt_phis(Is, L, Live0, LiveMap0) ->
+ LiveMap = LiveMap0#{L=>Live0},
+ Phis = takewhile(fun(#b_set{op=Op}) -> Op =:= phi end, Is),
+ case Phis of
+ [] ->
+ LiveMap;
+ [_|_] ->
+ PhiArgs = append([Args || #b_set{args=Args} <- Phis]),
+ case [{P,V} || {#b_var{}=V,P} <- PhiArgs] of
+ [_|_]=PhiVars ->
+ PhiLive0 = rel2fam(PhiVars),
+ PhiLive = [{{L,P},gb_sets:union(gb_sets:from_list(Vs), Live0)} ||
+ {P,Vs} <- PhiLive0],
+ maps:merge(LiveMap, maps:from_list(PhiLive));
+ [] ->
+ %% There were only literals in the phi node(s).
+ LiveMap
+ end
+ end.
+
+live_opt_blk(#b_blk{is=Is0,last=Last}=Blk, Live0) ->
+ Live1 = gb_sets:union(Live0, gb_sets:from_ordset(beam_ssa:used(Last))),
+ {Is,Live} = live_opt_is(reverse(Is0), Live1, []),
+ {Blk#b_blk{is=Is},Live}.
+
+live_opt_is([#b_set{op=phi,dst=Dst}=I|Is], Live, Acc) ->
+ case gb_sets:is_member(Dst, Live) of
+ true ->
+ live_opt_is(Is, Live, [I|Acc]);
+ false ->
+ live_opt_is(Is, Live, Acc)
+ end;
+live_opt_is([#b_set{op=succeeded,dst=SuccDst=SuccDstVar,
+ args=[Dst]}=SuccI,
+ #b_set{dst=Dst}=I|Is], Live0, Acc) ->
+ case gb_sets:is_member(Dst, Live0) of
+ true ->
+ case gb_sets:is_member(SuccDst, Live0) of
+ true ->
+ Live1 = gb_sets:add(Dst, Live0),
+ Live = gb_sets:delete_any(SuccDst, Live1),
+ live_opt_is([I|Is], Live, [SuccI|Acc]);
+ false ->
+ live_opt_is([I|Is], Live0, Acc)
+ end;
+ false ->
+ case live_opt_unused(I) of
+ {replace,NewI0} ->
+ NewI = NewI0#b_set{dst=SuccDstVar},
+ live_opt_is([NewI|Is], Live0, Acc);
+ keep ->
+ case gb_sets:is_member(SuccDst, Live0) of
+ true ->
+ Live1 = gb_sets:add(Dst, Live0),
+ Live = gb_sets:delete_any(SuccDst, Live1),
+ live_opt_is([I|Is], Live, [SuccI|Acc]);
+ false ->
+ live_opt_is([I|Is], Live0, Acc)
+ end
+ end
+ end;
+live_opt_is([#b_set{dst=Dst}=I|Is], Live0, Acc) ->
+ case gb_sets:is_member(Dst, Live0) of
+ true ->
+ Live1 = gb_sets:union(Live0, gb_sets:from_ordset(beam_ssa:used(I))),
+ Live = gb_sets:delete_any(Dst, Live1),
+ live_opt_is(Is, Live, [I|Acc]);
+ false ->
+ case beam_ssa:no_side_effect(I) of
+ true ->
+ live_opt_is(Is, Live0, Acc);
+ false ->
+ Live = gb_sets:union(Live0, gb_sets:from_ordset(beam_ssa:used(I))),
+ live_opt_is(Is, Live, [I|Acc])
+ end
+ end;
+live_opt_is([], Live, Acc) ->
+ {Acc,Live}.
+
+live_opt_unused(#b_set{op=get_map_element}=Set) ->
+ {replace,Set#b_set{op=has_map_field}};
+live_opt_unused(_) -> keep.
+
+%%%
+%%% Optimize binary matching instructions.
+%%%
+
+ssa_opt_bsm(#st{ssa=Linear}=St) ->
+ Extracted0 = bsm_extracted(Linear),
+ Extracted = cerl_sets:from_list(Extracted0),
+ St#st{ssa=bsm_skip(Linear, Extracted)}.
+
+bsm_skip([{L,#b_blk{is=Is0}=Blk}|Bs], Extracted) ->
+ Is = bsm_skip_is(Is0, Extracted),
+ [{L,Blk#b_blk{is=Is}}|bsm_skip(Bs, Extracted)];
+bsm_skip([], _) -> [].
+
+bsm_skip_is([I0|Is], Extracted) ->
+ case I0 of
+ #b_set{op=bs_match,args=[#b_literal{val=string}|_]} ->
+ [I0|bsm_skip_is(Is, Extracted)];
+ #b_set{op=bs_match,dst=Ctx,args=[Type,PrevCtx|Args0]} ->
+ I = case cerl_sets:is_element(Ctx, Extracted) of
+ true ->
+ I0;
+ false ->
+ %% The value is never extracted.
+ Args = [#b_literal{val=skip},PrevCtx,Type|Args0],
+ I0#b_set{args=Args}
+ end,
+ [I|Is];
+ #b_set{} ->
+ [I0|bsm_skip_is(Is, Extracted)]
+ end;
+bsm_skip_is([], _) -> [].
+
+bsm_extracted([{_,#b_blk{is=Is}}|Bs]) ->
+ case Is of
+ [#b_set{op=bs_extract,args=[Ctx]}|_] ->
+ [Ctx|bsm_extracted(Bs)];
+ _ ->
+ bsm_extracted(Bs)
+ end;
+bsm_extracted([]) -> [].
+
+%%%
+%%% Short-cutting binary matching instructions.
+%%%
+
+ssa_opt_bsm_shortcut(#st{ssa=Linear}=St) ->
+ Positions = bsm_positions(Linear, #{}),
+ case map_size(Positions) of
+ 0 ->
+ %% No binary matching instructions.
+ St;
+ _ ->
+ St#st{ssa=bsm_shortcut(Linear, Positions)}
+ end.
+
+bsm_positions([{L,#b_blk{is=Is,last=Last}}|Bs], PosMap0) ->
+ PosMap = bsm_positions_is(Is, PosMap0),
+ case {Is,Last} of
+ {[#b_set{op=bs_test_tail,dst=Bool,args=[Ctx,#b_literal{val=Bits0}]}],
+ #b_br{bool=Bool,fail=Fail}} ->
+ Bits = Bits0 + maps:get(Ctx, PosMap0),
+ bsm_positions(Bs, PosMap#{L=>{Bits,Fail}});
+ {_,_} ->
+ bsm_positions(Bs, PosMap)
+ end;
+bsm_positions([], PosMap) -> PosMap.
+
+bsm_positions_is([#b_set{op=bs_start_match,dst=New}|Is], PosMap0) ->
+ PosMap = PosMap0#{New=>0},
+ bsm_positions_is(Is, PosMap);
+bsm_positions_is([#b_set{op=bs_match,dst=New,args=Args}|Is], PosMap0) ->
+ [_,Old|_] = Args,
+ #{Old:=Bits0} = PosMap0,
+ Bits = bsm_update_bits(Args, Bits0),
+ PosMap = PosMap0#{New=>Bits},
+ bsm_positions_is(Is, PosMap);
+bsm_positions_is([_|Is], PosMap) ->
+ bsm_positions_is(Is, PosMap);
+bsm_positions_is([], PosMap) -> PosMap.
+
+bsm_update_bits([#b_literal{val=string},_,#b_literal{val=String}], Bits) ->
+ Bits + bit_size(String);
+bsm_update_bits([#b_literal{val=utf8}|_], Bits) ->
+ Bits + 8;
+bsm_update_bits([#b_literal{val=utf16}|_], Bits) ->
+ Bits + 16;
+bsm_update_bits([#b_literal{val=utf32}|_], Bits) ->
+ Bits + 32;
+bsm_update_bits([_,_,_,#b_literal{val=Sz},#b_literal{val=U}], Bits)
+ when is_integer(Sz) ->
+ Bits + Sz*U;
+bsm_update_bits(_, Bits) -> Bits.
+
+bsm_shortcut([{L,#b_blk{is=Is,last=Last0}=Blk}|Bs], PosMap) ->
+ case {Is,Last0} of
+ {[#b_set{op=bs_match,dst=New,args=[_,Old|_]},
+ #b_set{op=succeeded,dst=Bool,args=[New]}],
+ #b_br{bool=Bool,fail=Fail}} ->
+ case PosMap of
+ #{Old:=Bits,Fail:={TailBits,NextFail}} when Bits > TailBits ->
+ Last = Last0#b_br{fail=NextFail},
+ [{L,Blk#b_blk{last=Last}}|bsm_shortcut(Bs, PosMap)];
+ #{} ->
+ [{L,Blk}|bsm_shortcut(Bs, PosMap)]
+ end;
+ {_,_} ->
+ [{L,Blk}|bsm_shortcut(Bs, PosMap)]
+ end;
+bsm_shortcut([], _PosMap) -> [].
+
+%%%
+%%% Eliminate redundant bs_test_unit2 instructions.
+%%%
+
+ssa_opt_bsm_units(#st{ssa=Linear}=St) ->
+ St#st{ssa=bsm_units(Linear, #{})}.
+
+bsm_units([{L,#b_blk{last=#b_br{succ=Succ,fail=Fail}}=Block0} | Bs], UnitMaps0) ->
+ UnitsIn = maps:get(L, UnitMaps0, #{}),
+ {Block, UnitsOut} = bsm_units_skip(Block0, UnitsIn),
+ UnitMaps1 = bsm_units_join(Succ, UnitsOut, UnitMaps0),
+ UnitMaps = bsm_units_join(Fail, UnitsIn, UnitMaps1),
+ [{L, Block} | bsm_units(Bs, UnitMaps)];
+bsm_units([{L,#b_blk{last=#b_switch{fail=Fail,list=Switch}}=Block} | Bs], UnitMaps0) ->
+ UnitsIn = maps:get(L, UnitMaps0, #{}),
+ Labels = [Fail | [Lbl || {_Arg, Lbl} <- Switch]],
+ UnitMaps = foldl(fun(Lbl, UnitMaps) ->
+ bsm_units_join(Lbl, UnitsIn, UnitMaps)
+ end, UnitMaps0, Labels),
+ [{L, Block} | bsm_units(Bs, UnitMaps)];
+bsm_units([{L, Block} | Bs], UnitMaps) ->
+ [{L, Block} | bsm_units(Bs, UnitMaps)];
+bsm_units([], _UnitMaps) ->
+ [].
+
+bsm_units_skip(Block, Units) ->
+ bsm_units_skip_1(Block#b_blk.is, Block, Units).
+
+bsm_units_skip_1([#b_set{op=bs_start_match,dst=New}|_], Block, Units) ->
+ %% We bail early since there can't be more than one match per block.
+ {Block, Units#{ New => 1 }};
+bsm_units_skip_1([#b_set{op=bs_match,
+ dst=New,
+ args=[#b_literal{val=skip},
+ Ctx,
+ #b_literal{val=binary},
+ _Flags,
+ #b_literal{val=all},
+ #b_literal{val=OpUnit}]}=Skip | Test],
+ Block0, Units) ->
+ [#b_set{op=succeeded,dst=Bool,args=[New]}] = Test, %Assertion.
+ #b_br{bool=Bool} = Last0 = Block0#b_blk.last, %Assertion.
+ CtxUnit = maps:get(Ctx, Units),
+ if
+ CtxUnit rem OpUnit =:= 0 ->
+ Is = takewhile(fun(I) -> I =/= Skip end, Block0#b_blk.is),
+ Last = Last0#b_br{bool=#b_literal{val=true}},
+ Block = Block0#b_blk{is=Is,last=Last},
+ {Block, Units#{ New => CtxUnit }};
+ CtxUnit rem OpUnit =/= 0 ->
+ {Block0, Units#{ New => OpUnit, Ctx => OpUnit }}
+ end;
+bsm_units_skip_1([#b_set{op=bs_match,dst=New,args=Args}|_], Block, Units) ->
+ [_,Ctx|_] = Args,
+ CtxUnit = maps:get(Ctx, Units),
+ OpUnit = bsm_op_unit(Args),
+ {Block, Units#{ New => gcd(OpUnit, CtxUnit) }};
+bsm_units_skip_1([_I | Is], Block, Units) ->
+ bsm_units_skip_1(Is, Block, Units);
+bsm_units_skip_1([], Block, Units) ->
+ {Block, Units}.
+
+bsm_op_unit([_,_,_,Size,#b_literal{val=U}]) ->
+ case Size of
+ #b_literal{val=Sz} when is_integer(Sz) -> Sz*U;
+ _ -> U
+ end;
+bsm_op_unit([#b_literal{val=string},_,#b_literal{val=String}]) ->
+ bit_size(String);
+bsm_op_unit([#b_literal{val=utf8}|_]) ->
+ 8;
+bsm_op_unit([#b_literal{val=utf16}|_]) ->
+ 16;
+bsm_op_unit([#b_literal{val=utf32}|_]) ->
+ 32;
+bsm_op_unit(_) ->
+ 1.
+
+%% Several paths can lead to the same match instruction and the inferred units
+%% may differ between them, so we can only keep the information that is common
+%% to all paths.
+bsm_units_join(Lbl, MapA, UnitMaps0) when is_map_key(Lbl, UnitMaps0) ->
+ MapB = maps:get(Lbl, UnitMaps0),
+ Merged = if
+ map_size(MapB) =< map_size(MapA) ->
+ bsm_units_join_1(maps:keys(MapB), MapA, MapB);
+ map_size(MapB) > map_size(MapA) ->
+ bsm_units_join_1(maps:keys(MapA), MapB, MapA)
+ end,
+ maps:put(Lbl, Merged, UnitMaps0);
+bsm_units_join(Lbl, MapA, UnitMaps0) when MapA =/= #{} ->
+ maps:put(Lbl, MapA, UnitMaps0);
+bsm_units_join(_Lbl, _MapA, UnitMaps0) ->
+ UnitMaps0.
+
+bsm_units_join_1([Key | Keys], Left, Right) when is_map_key(Key, Left) ->
+ UnitA = maps:get(Key, Left),
+ UnitB = maps:get(Key, Right),
+ bsm_units_join_1(Keys, Left, maps:put(Key, gcd(UnitA, UnitB), Right));
+bsm_units_join_1([Key | Keys], Left, Right) ->
+ bsm_units_join_1(Keys, Left, maps:remove(Key, Right));
+bsm_units_join_1([], _MapA, Right) ->
+ Right.
+
+%%%
+%%% Miscellanous optimizations in execution order.
+%%%
+
+ssa_opt_misc(#st{ssa=Linear}=St) ->
+ St#st{ssa=misc_opt(Linear, #{})}.
+
+misc_opt([{L,#b_blk{is=Is0,last=Last0}=Blk0}|Bs], Sub0) ->
+ {Is,Sub} = misc_opt_is(Is0, Sub0, []),
+ Last = sub(Last0, Sub),
+ Blk = Blk0#b_blk{is=Is,last=Last},
+ [{L,Blk}|misc_opt(Bs, Sub)];
+misc_opt([], _) -> [].
+
+misc_opt_is([#b_set{op=phi}=I0|Is], Sub0, Acc) ->
+ #b_set{dst=Dst,args=Args} = I = sub(I0, Sub0),
+ case all_same(Args) of
+ true ->
+ %% Eliminate the phi node if there is just one source
+ %% value or if the values are identical.
+ [{Val,_}|_] = Args,
+ Sub = Sub0#{Dst=>Val},
+ misc_opt_is(Is, Sub, Acc);
+ false ->
+ misc_opt_is(Is, Sub0, [I|Acc])
+ end;
+misc_opt_is([#b_set{op={bif,'and'}}=I0], Sub, Acc) ->
+ #b_set{dst=Dst,args=Args} = I = sub(I0, Sub),
+ case eval_and(Args) of
+ error ->
+ misc_opt_is([], Sub, [I|Acc]);
+ Val ->
+ misc_opt_is([], Sub#{Dst=>Val}, Acc)
+ end;
+misc_opt_is([#b_set{op={bif,'or'}}=I0], Sub, Acc) ->
+ #b_set{dst=Dst,args=Args} = I = sub(I0, Sub),
+ case eval_or(Args) of
+ error ->
+ misc_opt_is([], Sub, [I|Acc]);
+ Val ->
+ misc_opt_is([], Sub#{Dst=>Val}, Acc)
+ end;
+misc_opt_is([#b_set{}=I0|Is], Sub, Acc) ->
+ #b_set{op=Op,dst=Dst,args=Args} = I = sub(I0, Sub),
+ case make_literal(Op, Args) of
+ #b_literal{}=Literal ->
+ misc_opt_is(Is, Sub#{Dst=>Literal}, Acc);
+ error ->
+ misc_opt_is(Is, Sub, [I|Acc])
+ end;
+misc_opt_is([], Sub, Acc) ->
+ {reverse(Acc),Sub}.
+
+all_same([{H,_}|T]) ->
+ all(fun({E,_}) -> E =:= H end, T).
+
+make_literal(put_tuple, Args) ->
+ case make_literal_list(Args, []) of
+ error ->
+ error;
+ List ->
+ #b_literal{val=list_to_tuple(List)}
+ end;
+make_literal(put_list, [#b_literal{val=H},#b_literal{val=T}]) ->
+ #b_literal{val=[H|T]};
+make_literal(_, _) -> error.
+
+make_literal_list([#b_literal{val=H}|T], Acc) ->
+ make_literal_list(T, [H|Acc]);
+make_literal_list([_|_], _) ->
+ error;
+make_literal_list([], Acc) ->
+ reverse(Acc).
+
+eval_and(Args) ->
+ case Args of
+ [_,#b_literal{val=false}=Res] -> Res;
+ [Res,#b_literal{val=true}] -> Res;
+ [_,_] -> error
+ end.
+
+eval_or(Args) ->
+ case Args of
+ [Res,#b_literal{val=false}] -> Res;
+ [_,#b_literal{val=true}=Res] -> Res;
+ [_,_] -> error
+ end.
+
+%%%
+%%% Optimize expressions such as "tuple_size(Var) =:= 2".
+%%%
+%%% Consider this code:
+%%%
+%%% 0:
+%%% .
+%%% .
+%%% .
+%%% Size = bif:tuple_size Var
+%%% BoolVar1 = succeeded Size
+%%% br BoolVar1, label 4, label 3
+%%%
+%%% 4:
+%%% BoolVar2 = bif:'=:=' Size, literal 2
+%%% br BoolVar2, label 6, label 3
+%%%
+%%% 6: ... %% OK
+%%%
+%%% 3: ... %% Not a tuple of size 2
+%%%
+%%% The BEAM code will look this:
+%%%
+%%% {bif,tuple_size,{f,3},[{x,0}],{x,0}}.
+%%% {test,is_eq_exact,{f,3},[{x,0},{integer,2}]}.
+%%%
+%%% Better BEAM code will be produced if we transform the
+%%% code like this:
+%%%
+%%% 0:
+%%% .
+%%% .
+%%% .
+%%% br label 10
+%%%
+%%% 10:
+%%% NewBoolVar = bif:is_tuple Var
+%%% br NewBoolVar, label 11, label 3
+%%%
+%%% 11:
+%%% Size = bif:tuple_size Var
+%%% br label 4
+%%%
+%%% 4:
+%%% BoolVar2 = bif:'=:=' Size, literal 2
+%%% br BoolVar2, label 6, label 3
+%%%
+%%% (The key part of the transformation is the removal of
+%%% the 'succeeded' instruction to signal to the code generator
+%%% that the call to tuple_size/1 can't fail.)
+%%%
+%%% The BEAM code will look like:
+%%%
+%%% {test,is_tuple,{f,3},[{x,0}]}.
+%%% {test_arity,{f,3},[{x,0},2]}.
+%%%
+%%% Those two instructions will be combined into a single
+%%% is_tuple_of_arity instruction by the loader.
+%%%
+
+ssa_opt_tuple_size(#st{ssa=Linear0,cnt=Count0}=St) ->
+ {Linear,Count} = opt_tup_size(Linear0, Count0, []),
+ St#st{ssa=Linear,cnt=Count}.
+
+opt_tup_size([{L,#b_blk{is=Is,last=Last}=Blk}|Bs], Count0, Acc0) ->
+ case {Is,Last} of
+ {[#b_set{op={bif,'=:='},dst=Bool,args=[#b_var{}=Tup,#b_literal{val=Arity}]}],
+ #b_br{bool=Bool}} when is_integer(Arity), Arity >= 0 ->
+ {Acc,Count} = opt_tup_size_1(Tup, L, Count0, Acc0),
+ opt_tup_size(Bs, Count, [{L,Blk}|Acc]);
+ {_,_} ->
+ opt_tup_size(Bs, Count0, [{L,Blk}|Acc0])
+ end;
+opt_tup_size([], Count, Acc) ->
+ {reverse(Acc),Count}.
+
+opt_tup_size_1(Size, EqL, Count0, [{L,Blk0}|Acc]) ->
+ case Blk0 of
+ #b_blk{is=Is0,last=#b_br{bool=Bool,succ=EqL,fail=Fail}} ->
+ case opt_tup_size_is(Is0, Bool, Size, []) of
+ none ->
+ {[{L,Blk0}|Acc],Count0};
+ {PreIs,TupleSizeIs,Tuple} ->
+ opt_tup_size_2(PreIs, TupleSizeIs, L, EqL,
+ Tuple, Fail, Count0, Acc)
+ end;
+ #b_blk{} ->
+ {[{L,Blk0}|Acc],Count0}
+ end;
+opt_tup_size_1(_, _, Count, Acc) ->
+ {Acc,Count}.
+
+opt_tup_size_2(PreIs, TupleSizeIs, PreL, EqL, Tuple, Fail, Count0, Acc) ->
+ IsTupleL = Count0,
+ TupleSizeL = Count0 + 1,
+ Bool = #b_var{name={'@ssa_bool',Count0+2}},
+ Count = Count0 + 3,
+
+ True = #b_literal{val=true},
+ PreBr = #b_br{bool=True,succ=IsTupleL,fail=IsTupleL},
+ PreBlk = #b_blk{is=PreIs,last=PreBr},
+
+ IsTupleIs = [#b_set{op={bif,is_tuple},dst=Bool,args=[Tuple]}],
+ IsTupleBr = #b_br{bool=Bool,succ=TupleSizeL,fail=Fail},
+ IsTupleBlk = #b_blk{is=IsTupleIs,last=IsTupleBr},
+
+ TupleSizeBr = #b_br{bool=True,succ=EqL,fail=EqL},
+ TupleSizeBlk = #b_blk{is=TupleSizeIs,last=TupleSizeBr},
+ {[{TupleSizeL,TupleSizeBlk},
+ {IsTupleL,IsTupleBlk},
+ {PreL,PreBlk}|Acc],Count}.
+
+opt_tup_size_is([#b_set{op={bif,tuple_size},dst=Size,args=[Tuple]}=I,
+ #b_set{op=succeeded,dst=Bool,args=[Size]}],
+ Bool, Size, Acc) ->
+ {reverse(Acc),[I],Tuple};
+opt_tup_size_is([I|Is], Bool, Size, Acc) ->
+ opt_tup_size_is(Is, Bool, Size, [I|Acc]);
+opt_tup_size_is([], _, _, _Acc) -> none.
+
+%%%
+%%% Optimize #b_switch{} instructions.
+%%%
+%%% If the argument for a #b_switch{} comes from a phi node with all
+%%% literals, any values in the switch list which are not in the phi
+%%% node can be removed.
+%%%
+%%% If the values in the phi node and switch list are the same,
+%%% the failure label can't be reached and be eliminated.
+%%%
+%%% A #b_switch{} with only one value can be rewritten to
+%%% a #b_br{}. A switch that only verifies that the argument
+%%% is 'true' or 'false' can be rewritten to a is_boolean test.
+%%%
+
+ssa_opt_sw(#st{ssa=Linear0,cnt=Count0}=St) ->
+ {Linear,Count} = opt_sw(Linear0, #{}, Count0, []),
+ St#st{ssa=Linear,cnt=Count}.
+
+opt_sw([{L,#b_blk{is=Is,last=#b_switch{}=Last0}=Blk0}|Bs], Phis0, Count0, Acc) ->
+ Phis = opt_sw_phis(Is, Phis0),
+ case opt_sw_last(Last0, Phis) of
+ #b_switch{arg=Arg,fail=Fail,list=[{Lit,Lbl}]} ->
+ %% Rewrite a single value switch to a br.
+ Bool = #b_var{name={'@ssa_bool',Count0}},
+ Count = Count0 + 1,
+ IsEq = #b_set{op={bif,'=:='},dst=Bool,args=[Arg,Lit]},
+ Br = #b_br{bool=Bool,succ=Lbl,fail=Fail},
+ Blk = Blk0#b_blk{is=Is++[IsEq],last=Br},
+ opt_sw(Bs, Phis, Count, [{L,Blk}|Acc]);
+ #b_switch{arg=Arg,fail=Fail,
+ list=[{#b_literal{val=B1},Lbl},{#b_literal{val=B2},Lbl}]}
+ when B1 =:= not B2 ->
+ %% Replace with is_boolean test.
+ Bool = #b_var{name={'@ssa_bool',Count0}},
+ Count = Count0 + 1,
+ IsBool = #b_set{op={bif,is_boolean},dst=Bool,args=[Arg]},
+ Br = #b_br{bool=Bool,succ=Lbl,fail=Fail},
+ Blk = Blk0#b_blk{is=Is++[IsBool],last=Br},
+ opt_sw(Bs, Phis, Count, [{L,Blk}|Acc]);
+ Last0 ->
+ opt_sw(Bs, Phis, Count0, [{L,Blk0}|Acc]);
+ Last ->
+ Blk = Blk0#b_blk{last=Last},
+ opt_sw(Bs, Phis, Count0, [{L,Blk}|Acc])
+ end;
+opt_sw([{L,#b_blk{is=Is}=Blk}|Bs], Phis0, Count, Acc) ->
+ Phis = opt_sw_phis(Is, Phis0),
+ opt_sw(Bs, Phis, Count, [{L,Blk}|Acc]);
+opt_sw([], _Phis, Count, Acc) ->
+ {reverse(Acc),Count}.
+
+opt_sw_phis([#b_set{op=phi,dst=Dst,args=Args}|Is], Phis) ->
+ case opt_sw_literals(Args, []) of
+ error ->
+ opt_sw_phis(Is, Phis);
+ Literals ->
+ opt_sw_phis(Is, Phis#{Dst=>Literals})
+ end;
+opt_sw_phis(_, Phis) -> Phis.
+
+opt_sw_last(#b_switch{arg=Arg,fail=Fail,list=List0}=Sw0, Phis) ->
+ case Phis of
+ #{Arg:=Values0} ->
+ Values = gb_sets:from_list(Values0),
+
+ %% Prune the switch list to only contain the possible values.
+ List1 = [P || {Lit,_}=P <- List0, gb_sets:is_member(Lit, Values)],
+
+ %% Now test whether the failure label can ever be reached.
+ Sw = case gb_sets:size(Values) =:= length(List1) of
+ true ->
+ %% The switch list has the same number of values as the phi node.
+ %% The values must be the same, because the values that were not
+ %% possible were pruned from the switch list. Therefore, the
+ %% failure label can't possibly be reached, and we can choose a
+ %% a new failure label by picking a value from the list.
+ case List1 of
+ [{#b_literal{},Lbl}|List] ->
+ Sw0#b_switch{fail=Lbl,list=List};
+ [] ->
+ Sw0#b_switch{list=List1}
+ end;
+ false ->
+ %% There are some values in the phi node that are not in the
+ %% switch list; thus, the failure label can still be reached.
+ Sw0
+ end,
+ beam_ssa:normalize(Sw);
+ #{} ->
+ %% Ensure that no label in the switch list is the same
+ %% as the failure label.
+ List = [{Val,Lbl} || {Val,Lbl} <- List0, Lbl =/= Fail],
+ Sw = Sw0#b_switch{list=List},
+ beam_ssa:normalize(Sw)
+ end.
+
+opt_sw_literals([{#b_literal{}=Lit,_}|T], Acc) ->
+ opt_sw_literals(T, [Lit|Acc]);
+opt_sw_literals([_|_], _Acc) ->
+ error;
+opt_sw_literals([], Acc) -> Acc.
+
+
+%%%
+%%% Merge blocks.
+%%%
+
+ssa_opt_merge_blocks(#st{ssa=Blocks}=St) ->
+ Preds = beam_ssa:predecessors(Blocks),
+ St#st{ssa=merge_blocks_1(beam_ssa:rpo(Blocks), Preds, Blocks)}.
+
+merge_blocks_1([L|Ls], Preds0, Blocks0) ->
+ case Preds0 of
+ #{L:=[P]} ->
+ #{P:=Blk0,L:=Blk1} = Blocks0,
+ case is_merge_allowed(L, Blk0, Blk1) of
+ true ->
+ #b_blk{is=Is0} = Blk0,
+ #b_blk{is=Is1} = Blk1,
+ Is = Is0 ++ Is1,
+ Blk = Blk1#b_blk{is=Is},
+ Blocks1 = maps:remove(L, Blocks0),
+ Blocks2 = maps:put(P, Blk, Blocks1),
+ Successors = beam_ssa:successors(Blk),
+ Blocks = beam_ssa:update_phi_labels(Successors, L, P, Blocks2),
+ Preds = merge_update_preds(Successors, L, P, Preds0),
+ merge_blocks_1(Ls, Preds, Blocks);
+ false ->
+ merge_blocks_1(Ls, Preds0, Blocks0)
+ end;
+ #{} ->
+ merge_blocks_1(Ls, Preds0, Blocks0)
+ end;
+merge_blocks_1([], _Preds, Blocks) -> Blocks.
+
+merge_update_preds([L|Ls], From, To, Preds0) ->
+ Ps = [rename_label(P, From, To) || P <- maps:get(L, Preds0)],
+ Preds = maps:put(L, Ps, Preds0),
+ merge_update_preds(Ls, From, To, Preds);
+merge_update_preds([], _, _, Preds) -> Preds.
+
+rename_label(From, From, To) -> To;
+rename_label(Lbl, _, _) -> Lbl.
+
+is_merge_allowed(_, _, #b_blk{is=[#b_set{op=peek_message}|_]}) ->
+ false;
+is_merge_allowed(L, Blk0, #b_blk{}) ->
+ case beam_ssa:successors(Blk0) of
+ [L] -> true;
+ [_|_] -> false
+ end.
+
+%%%
+%%% When a tuple is matched, the pattern matching compiler generates a
+%%% get_tuple_element instruction for every tuple element that will
+%%% ever be used in the rest of the function. That often forces the
+%%% extracted tuple elements to be stored in Y registers until it's
+%%% time to use them. It could also mean that there could be execution
+%%% paths that will never use the extracted elements.
+%%%
+%%% This optimization will sink get_tuple_element instructions, that
+%%% is, move them forward in the execution stream to the last possible
+%%% block there they will still dominate all uses. That may reduce the
+%%% size of stack frames, reduce register shuffling, and avoid
+%%% extracting tuple elements on execution paths that never use the
+%%% extracted values.
+%%%
+
+ssa_opt_sink(#st{ssa=Blocks0}=St) ->
+ Linear = beam_ssa:linearize(Blocks0),
+
+ %% Create a map with all variables that define get_tuple_element
+ %% instructions. The variable name map to the block it is defined in.
+ Defs = maps:from_list(def_blocks(Linear)),
+
+ %% Now find all the blocks that use variables defined by get_tuple_element
+ %% instructions.
+ Used = used_blocks(Linear, Defs, []),
+
+ %% Calculate dominators.
+ Dom0 = beam_ssa:dominators(Blocks0),
+
+ %% It is not safe to move get_tuple_element instructions to blocks
+ %% that begin with certain instructions. It is also unsafe to move
+ %% the instructions into any part of a receive. To avoid such
+ %% unsafe moves, pretend that the unsuitable blocks are not
+ %% dominators.
+ Unsuitable = unsuitable(Linear, Blocks0),
+ Dom = case gb_sets:is_empty(Unsuitable) of
+ true ->
+ Dom0;
+ false ->
+ F = fun(_, DomBy) ->
+ [L || L <- DomBy,
+ not gb_sets:is_element(L, Unsuitable)]
+ end,
+ maps:map(F, Dom0)
+ end,
+
+ %% Calculate new positions for get_tuple_element instructions. The new
+ %% position is a block that dominates all uses of the variable.
+ DefLoc = new_def_locations(Used, Defs, Dom),
+
+ %% Now move all suitable get_tuple_element instructions to their
+ %% new blocks.
+ Blocks = foldl(fun({V,To}, A) ->
+ From = maps:get(V, Defs),
+ move_defs(V, From, To, A)
+ end, Blocks0, DefLoc),
+ St#st{ssa=Blocks}.
+
+def_blocks([{L,#b_blk{is=Is}}|Bs]) ->
+ def_blocks_is(Is, L, def_blocks(Bs));
+def_blocks([]) -> [].
+
+def_blocks_is([#b_set{op=get_tuple_element,dst=Dst}|Is], L, Acc) ->
+ def_blocks_is(Is, L, [{Dst,L}|Acc]);
+def_blocks_is([_|Is], L, Acc) ->
+ def_blocks_is(Is, L, Acc);
+def_blocks_is([], _, Acc) -> Acc.
+
+used_blocks([{L,Blk}|Bs], Def, Acc0) ->
+ Used = beam_ssa:used(Blk),
+ Acc = [{V,L} || V <- Used, maps:is_key(V, Def)] ++ Acc0,
+ used_blocks(Bs, Def, Acc);
+used_blocks([], _Def, Acc) ->
+ rel2fam(Acc).
+
+%% unsuitable(Linear, Blocks) -> Unsuitable.
+%% Return an ordset of block labels for the blocks that are not
+%% suitable for sinking of get_tuple_element instructions.
+
+unsuitable(Linear, Blocks) ->
+ Predecessors = beam_ssa:predecessors(Blocks),
+ Unsuitable0 = unsuitable_1(Linear),
+ Unsuitable1 = unsuitable_recv(Linear, Blocks, Predecessors),
+ gb_sets:from_list(Unsuitable0 ++ Unsuitable1).
+
+unsuitable_1([{L,#b_blk{is=[#b_set{op=Op}|_]}}|Bs]) ->
+ Unsuitable = case Op of
+ bs_extract -> true;
+ bs_put -> true;
+ {float,_} -> true;
+ landingpad -> true;
+ peek_message -> true;
+ wait_timeout -> true;
+ _ -> false
+ end,
+ case Unsuitable of
+ true ->
+ [L|unsuitable_1(Bs)];
+ false ->
+ unsuitable_1(Bs)
+ end;
+unsuitable_1([{_,#b_blk{}}|Bs]) ->
+ unsuitable_1(Bs);
+unsuitable_1([]) -> [].
+
+unsuitable_recv([{L,#b_blk{is=[#b_set{op=Op}|_]}}|Bs], Blocks, Predecessors) ->
+ Ls = case Op of
+ remove_message ->
+ unsuitable_loop(L, Blocks, Predecessors);
+ recv_next ->
+ unsuitable_loop(L, Blocks, Predecessors);
+ _ ->
+ []
+ end,
+ Ls ++ unsuitable_recv(Bs, Blocks, Predecessors);
+unsuitable_recv([_|Bs], Blocks, Predecessors) ->
+ unsuitable_recv(Bs, Blocks, Predecessors);
+unsuitable_recv([], _, _) -> [].
+
+unsuitable_loop(L, Blocks, Predecessors) ->
+ unsuitable_loop(L, Blocks, Predecessors, []).
+
+unsuitable_loop(L, Blocks, Predecessors, Acc) ->
+ Ps = maps:get(L, Predecessors),
+ unsuitable_loop_1(Ps, Blocks, Predecessors, Acc).
+
+unsuitable_loop_1([P|Ps], Blocks, Predecessors, Acc0) ->
+ case maps:get(P, Blocks) of
+ #b_blk{is=[#b_set{op=peek_message}|_]} ->
+ unsuitable_loop_1(Ps, Blocks, Predecessors, Acc0);
+ #b_blk{} ->
+ case ordsets:is_element(P, Acc0) of
+ false ->
+ Acc1 = ordsets:add_element(P, Acc0),
+ Acc = unsuitable_loop(P, Blocks, Predecessors, Acc1),
+ unsuitable_loop_1(Ps, Blocks, Predecessors, Acc);
+ true ->
+ unsuitable_loop_1(Ps, Blocks, Predecessors, Acc0)
+ end
+ end;
+unsuitable_loop_1([], _, _, Acc) -> Acc.
+
+%% new_def_locations([{Variable,[UsedInBlock]}|Vs], Defs, Dominators) ->
+%% [{Variable,NewDefinitionBlock}]
+%% Calculate new locations for get_tuple_element instructions. For each
+%% variable, the new location is a block that dominates all uses of
+%% variable and as near to the uses of as possible. If no such block
+%% distinct from the block where the instruction currently is, the
+%% variable will not be included in the result list.
+
+new_def_locations([{V,UsedIn}|Vs], Defs, Dom) ->
+ DefIn = maps:get(V, Defs),
+ case common_dom(UsedIn, DefIn, Dom) of
+ [] ->
+ new_def_locations(Vs, Defs, Dom);
+ [_|_]=BetterDef ->
+ L = most_dominated(BetterDef, Dom),
+ [{V,L}|new_def_locations(Vs, Defs, Dom)]
+ end;
+new_def_locations([], _, _) -> [].
+
+common_dom([L|Ls], DefIn, Dom) ->
+ DomBy0 = maps:get(L, Dom),
+ DomBy = ordsets:subtract(DomBy0, maps:get(DefIn, Dom)),
+ common_dom_1(Ls, Dom, DomBy).
+
+common_dom_1(_, _, []) ->
+ [];
+common_dom_1([L|Ls], Dom, [_|_]=DomBy0) ->
+ DomBy1 = maps:get(L, Dom),
+ DomBy = ordsets:intersection(DomBy0, DomBy1),
+ common_dom_1(Ls, Dom, DomBy);
+common_dom_1([], _, DomBy) -> DomBy.
+
+most_dominated([L|Ls], Dom) ->
+ most_dominated(Ls, L, maps:get(L, Dom), Dom).
+
+most_dominated([L|Ls], L0, DomBy, Dom) ->
+ case member(L, DomBy) of
+ true ->
+ most_dominated(Ls, L0, DomBy, Dom);
+ false ->
+ most_dominated(Ls, L, maps:get(L, Dom), Dom)
+ end;
+most_dominated([], L, _, _) -> L.
+
+
+%% Move get_tuple_element instructions to their new locations.
+
+move_defs(V, From, To, Blocks) ->
+ #{From:=FromBlk0,To:=ToBlk0} = Blocks,
+ {Def,FromBlk} = remove_def(V, FromBlk0),
+ try insert_def(V, Def, ToBlk0) of
+ ToBlk ->
+ %%io:format("~p: ~p => ~p\n", [V,From,To]),
+ Blocks#{From:=FromBlk,To:=ToBlk}
+ catch
+ throw:not_possible ->
+ Blocks
+ end.
+
+remove_def(V, #b_blk{is=Is0}=Blk) ->
+ {Def,Is} = remove_def_is(Is0, V, []),
+ {Def,Blk#b_blk{is=Is}}.
+
+remove_def_is([#b_set{dst=Dst}=Def|Is], Dst, Acc) ->
+ {Def,reverse(Acc, Is)};
+remove_def_is([I|Is], Dst, Acc) ->
+ remove_def_is(Is, Dst, [I|Acc]).
+
+insert_def(V, Def, #b_blk{is=Is0}=Blk) ->
+ Is = insert_def_is(Is0, V, Def),
+ Blk#b_blk{is=Is}.
+
+insert_def_is([#b_set{op=phi}=I|Is], V, Def) ->
+ case member(V, beam_ssa:used(I)) of
+ true ->
+ throw(not_possible);
+ false ->
+ [I|insert_def_is(Is, V, Def)]
+ end;
+insert_def_is([#b_set{op=Op}=I|Is]=Is0, V, Def) ->
+ Action0 = case Op of
+ call -> beyond;
+ 'catch_end' -> beyond;
+ set_tuple_element -> beyond;
+ timeout -> beyond;
+ _ -> here
+ end,
+ Action = case Is of
+ [#b_set{op=succeeded}|_] -> here;
+ _ -> Action0
+ end,
+ case Action of
+ beyond ->
+ case member(V, beam_ssa:used(I)) of
+ true ->
+ %% The variable is used by this instruction. We must
+ %% place the definition before this instruction.
+ [Def|Is0];
+ false ->
+ %% Place it beyond the current instruction.
+ [I|insert_def_is(Is, V, Def)]
+ end;
+ here ->
+ [Def|Is0]
+ end;
+insert_def_is([], _V, Def) ->
+ [Def].
+
+
+%%%
+%%% Common utilities.
+%%%
+
+gcd(A, B) ->
+ case A rem B of
+ 0 -> B;
+ X -> gcd(B, X)
+ end.
+
+rel2fam(S0) ->
+ S1 = sofs:relation(S0),
+ S = sofs:rel2fam(S1),
+ sofs:to_external(S).
+
+sub(I, Sub) ->
+ beam_ssa:normalize(sub_1(I, Sub)).
+
+sub_1(#b_set{op=phi,args=Args}=I, Sub) ->
+ I#b_set{args=[{sub_arg(A, Sub),P} || {A,P} <- Args]};
+sub_1(#b_set{args=Args}=I, Sub) ->
+ I#b_set{args=[sub_arg(A, Sub) || A <- Args]};
+sub_1(#b_br{bool=#b_var{}=Old}=Br, Sub) ->
+ New = sub_arg(Old, Sub),
+ Br#b_br{bool=New};
+sub_1(#b_switch{arg=#b_var{}=Old}=Sw, Sub) ->
+ New = sub_arg(Old, Sub),
+ Sw#b_switch{arg=New};
+sub_1(#b_ret{arg=#b_var{}=Old}=Ret, Sub) ->
+ New = sub_arg(Old, Sub),
+ Ret#b_ret{arg=New};
+sub_1(Last, _) -> Last.
+
+sub_arg(#b_remote{mod=Mod,name=Name}=Rem, Sub) ->
+ Rem#b_remote{mod=sub_arg(Mod, Sub),name=sub_arg(Name, Sub)};
+sub_arg(Old, Sub) ->
+ case Sub of
+ #{Old:=New} -> New;
+ #{} -> Old
+ end.