%%
%% %CopyrightBegin%
%%
%% Copyright Ericsson AB 2007-2012. All Rights Reserved.
%%
%% The contents of this file are subject to the Erlang Public License,
%% Version 1.1, (the "License"); you may not use this file except in
%% compliance with the License. You should have received a copy of the
%% Erlang Public License along with this software. If not, it can be
%% retrieved online at http://www.erlang.org/.
%%
%% Software distributed under the License is distributed on an "AS IS"
%% basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See
%% the License for the specific language governing rights and limitations
%% under the License.
%%
%% %CopyrightEnd%
%%
%% Purpose : Common utilities used by several optimization passes.
%%
-module(beam_utils).
-export([is_killed_block/2,is_killed/3,is_killed_at/3,
is_not_used/3,is_not_used_at/3,
empty_label_index/0,index_label/3,index_labels/1,
code_at/2,bif_to_test/3,is_pure_test/1,
live_opt/1,delete_live_annos/1,combine_heap_needs/2]).
-import(lists, [member/2,sort/1,reverse/1,splitwith/2]).
-record(live,
{bl, %Block check fun.
lbl, %Label to code index.
res}). %Result cache for each label.
%% is_killed_block(Register, [Instruction]) -> true|false
%% Determine whether a register is killed by the instruction sequence inside
%% a block.
%%
%% If true is returned, it means that the register will not be
%% referenced in ANY way (not even indirectly by an allocate instruction);
%% i.e. it is OK to enter the instruction sequence with Register
%% containing garbage.
is_killed_block(R, Is) ->
case check_killed_block(R, Is) of
killed -> true;
used -> false;
transparent -> false
end.
%% is_killed(Register, [Instruction], State) -> true|false
%% Determine whether a register is killed by the instruction sequence.
%% If true is returned, it means that the register will not be
%% referenced in ANY way (not even indirectly by an allocate instruction);
%% i.e. it is OK to enter the instruction sequence with Register
%% containing garbage.
%%
%% The state (constructed by index_instructions/1) is used to allow us
%% to determine the kill state across branches.
is_killed(R, Is, D) ->
St = #live{bl=fun check_killed_block/2,lbl=D,res=gb_trees:empty()},
case check_liveness(R, Is, St) of
{killed,_} -> true;
{used,_} -> false;
{unknown,_} -> false
end.
%% is_killed_at(Reg, Lbl, State) -> true|false
%% Determine whether Reg is killed at label Lbl.
is_killed_at(R, Lbl, D) when is_integer(Lbl) ->
St0 = #live{bl=fun check_killed_block/2,lbl=D,res=gb_trees:empty()},
case check_liveness_at(R, Lbl, St0) of
{killed,_} -> true;
{used,_} -> false;
{unknown,_} -> false
end.
%% is_not_used(Register, [Instruction], State) -> true|false
%% Determine whether a register is never used in the instruction sequence
%% (it could still be referenced by an allocate instruction, meaning that
%% it MUST be initialized, but that its value does not matter).
%% The state is used to allow us to determine the usage state
%% across branches.
is_not_used(R, Is, D) ->
St = #live{bl=fun check_used_block/2,lbl=D,res=gb_trees:empty()},
case check_liveness(R, Is, St) of
{killed,_} -> true;
{used,_} -> false;
{unknown,_} -> false
end.
%% is_not_used(Register, [Instruction], State) -> true|false
%% Determine whether a register is never used in the instruction sequence
%% (it could still be referenced by an allocate instruction, meaning that
%% it MUST be initialized, but that its value does not matter).
%% The state is used to allow us to determine the usage state
%% across branches.
is_not_used_at(R, Lbl, D) ->
St = #live{bl=fun check_used_block/2,lbl=D,res=gb_trees:empty()},
case check_liveness_at(R, Lbl, St) of
{killed,_} -> true;
{used,_} -> false;
{unknown,_} -> false
end.
%% index_labels(FunctionIs) -> State
%% Index the instruction sequence so that we can quickly
%% look up the instruction following a specific label.
index_labels(Is) ->
index_labels_1(Is, []).
%% empty_label_index() -> State
%% Create an empty label index.
empty_label_index() ->
gb_trees:empty().
%% index_label(Label, [Instruction], State) -> State
%% Add an index for a label.
index_label(Lbl, Is0, Acc) ->
Is = lists:dropwhile(fun({label,_}) -> true;
(_) -> false end, Is0),
gb_trees:enter(Lbl, Is, Acc).
%% code_at(Label, State) -> [I].
%% Retrieve the code at the given label.
code_at(L, Ll) ->
case gb_trees:lookup(L, Ll) of
{value,Code} -> Code;
none -> none
end.
%% bif_to_test(Bif, [Op], Fail) -> {test,Test,Fail,[Op]}
%% Convert a BIF to a test. Fail if not possible.
bif_to_test(is_atom, [_]=Ops, Fail) -> {test,is_atom,Fail,Ops};
bif_to_test(is_boolean, [_]=Ops, Fail) -> {test,is_boolean,Fail,Ops};
bif_to_test(is_binary, [_]=Ops, Fail) -> {test,is_binary,Fail,Ops};
bif_to_test(is_bitstring,[_]=Ops, Fail) -> {test,is_bitstr,Fail,Ops};
bif_to_test(is_float, [_]=Ops, Fail) -> {test,is_float,Fail,Ops};
bif_to_test(is_function, [_]=Ops, Fail) -> {test,is_function,Fail,Ops};
bif_to_test(is_function, [_,_]=Ops, Fail) -> {test,is_function2,Fail,Ops};
bif_to_test(is_integer, [_]=Ops, Fail) -> {test,is_integer,Fail,Ops};
bif_to_test(is_list, [_]=Ops, Fail) -> {test,is_list,Fail,Ops};
bif_to_test(is_number, [_]=Ops, Fail) -> {test,is_number,Fail,Ops};
bif_to_test(is_pid, [_]=Ops, Fail) -> {test,is_pid,Fail,Ops};
bif_to_test(is_port, [_]=Ops, Fail) -> {test,is_port,Fail,Ops};
bif_to_test(is_reference, [_]=Ops, Fail) -> {test,is_reference,Fail,Ops};
bif_to_test(is_tuple, [_]=Ops, Fail) -> {test,is_tuple,Fail,Ops};
bif_to_test('=<', [A,B], Fail) -> {test,is_ge,Fail,[B,A]};
bif_to_test('>', [A,B], Fail) -> {test,is_lt,Fail,[B,A]};
bif_to_test('<', [_,_]=Ops, Fail) -> {test,is_lt,Fail,Ops};
bif_to_test('>=', [_,_]=Ops, Fail) -> {test,is_ge,Fail,Ops};
bif_to_test('==', [A,[]], Fail) -> {test,is_nil,Fail,[A]};
bif_to_test('==', [_,_]=Ops, Fail) -> {test,is_eq,Fail,Ops};
bif_to_test('/=', [_,_]=Ops, Fail) -> {test,is_ne,Fail,Ops};
bif_to_test('=:=', [A,[]], Fail) -> {test,is_nil,Fail,[A]};
bif_to_test('=:=', [_,_]=Ops, Fail) -> {test,is_eq_exact,Fail,Ops};
bif_to_test('=/=', [_,_]=Ops, Fail) -> {test,is_ne_exact,Fail,Ops};
bif_to_test(is_record, [_,_,_]=Ops, Fail) -> {test,is_record,Fail,Ops}.
%% is_pure_test({test,Op,Fail,Ops}) -> true|false.
%% Return 'true' if the test instruction does not modify any
%% registers and/or bit syntax matching state, nor modifies
%% any bit syntax matching state.
%%
is_pure_test({test,is_eq,_,[_,_]}) -> true;
is_pure_test({test,is_ne,_,[_,_]}) -> true;
is_pure_test({test,is_eq_exact,_,[_,_]}) -> true;
is_pure_test({test,is_ne_exact,_,[_,_]}) -> true;
is_pure_test({test,is_ge,_,[_,_]}) -> true;
is_pure_test({test,is_lt,_,[_,_]}) -> true;
is_pure_test({test,is_nil,_,[_]}) -> true;
is_pure_test({test,is_nonempty_list,_,[_]}) -> true;
is_pure_test({test,test_arity,_,[_,_]}) -> true;
is_pure_test({test,Op,_,Ops}) ->
erl_internal:new_type_test(Op, length(Ops)).
%% live_opt([Instruction]) -> [Instruction].
%% Go through the instruction sequence in reverse execution
%% order, keep track of liveness and remove 'move' instructions
%% whose destination is a register that will not be used.
%% Also insert {'%live',Live} annotations at the beginning
%% and end of each block.
%%
live_opt(Is0) ->
{[{label,Fail}|_]=Bef,[Fi|Is]} =
splitwith(fun({func_info,_,_,_}) -> false;
(_) -> true
end, Is0),
{func_info,_,_,Live} = Fi,
D = gb_trees:insert(Fail, live_call(Live), gb_trees:empty()),
Bef ++ [Fi|live_opt(reverse(Is), 0, D, [])].
%% delete_live_annos([Instruction]) -> [Instruction].
%% Delete all live annotations.
%%
delete_live_annos([{block,Bl0}|Is]) ->
case delete_live_annos(Bl0) of
[] -> delete_live_annos(Is);
[_|_]=Bl -> [{block,Bl}|delete_live_annos(Is)]
end;
delete_live_annos([{'%live',_}|Is]) ->
delete_live_annos(Is);
delete_live_annos([I|Is]) ->
[I|delete_live_annos(Is)];
delete_live_annos([]) -> [].
%% combine_heap_needs(HeapNeed1, HeapNeed2) -> HeapNeed
%% Combine the heap need for two allocation instructions.
combine_heap_needs({alloc,Alloc1}, {alloc,Alloc2}) ->
{alloc,combine_alloc_lists(Alloc1, Alloc2)};
combine_heap_needs({alloc,Alloc}, Words) when is_integer(Words) ->
{alloc,combine_alloc_lists(Alloc, [{words,Words}])};
combine_heap_needs(Words, {alloc,Alloc}) when is_integer(Words) ->
{alloc,combine_alloc_lists(Alloc, [{words,Words}])};
combine_heap_needs(H1, H2) when is_integer(H1), is_integer(H2) ->
H1+H2.
%%%
%%% Local functions.
%%%
%% check_liveness(Reg, [Instruction], {State,BlockCheckFun}) ->
%% {killed | used | unknown,UpdateState}
%% Finds out how Reg is used in the instruction sequence. Returns one of:
%% killed - Reg is assigned a new value or killed by an allocation instruction
%% used - Reg is used (or possibly referenced by an allocation instruction)
%% unknown - not possible to determine (perhaps because of an instruction
%% that we don't recognize)
check_liveness(R, [{set,_,_,_}=I|_], St) ->
erlang:error(only_allowed_in_blocks, [R,I,St]);
check_liveness(R, [{block,Blk}|Is], #live{bl=BlockCheck}=St) ->
case BlockCheck(R, Blk) of
transparent -> check_liveness(R, Is, St);
Other when is_atom(Other) -> {Other,St}
end;
check_liveness(R, [{label,_}|Is], St) ->
check_liveness(R, Is, St);
check_liveness(R, [{test,_,{f,Fail},As}|Is], St0) ->
case member(R, As) of
true ->
{used,St0};
false ->
case check_liveness_at(R, Fail, St0) of
{killed,St} -> check_liveness(R, Is, St);
{_,_}=Other -> Other
end
end;
check_liveness(R, [{test,_,{f,Fail},Live,Ss,_}|Is], St0) ->
case R of
{x,X} ->
case X < Live orelse member(R, Ss) of
true -> {used,St0};
false -> check_liveness_at(R, Fail, St0)
end;
{y,_} ->
case check_liveness_at(R, Fail, St0) of
{killed,St} -> check_liveness(R, Is, St);
{_,_}=Other -> Other
end
end;
check_liveness(R, [{select_val,R,_,_}|_], St) ->
{used,St};
check_liveness(R, [{select_val,_,Fail,{list,Branches}}|_], St) ->
check_liveness_everywhere(R, [Fail|Branches], St);
check_liveness(R, [{select_tuple_arity,R,_,_}|_], St) ->
{used,St};
check_liveness(R, [{select_tuple_arity,_,Fail,{list,Branches}}|_], St) ->
check_liveness_everywhere(R, [Fail|Branches], St);
check_liveness(R, [{jump,{f,F}}|_], St) ->
check_liveness_at(R, F, St);
check_liveness(R, [{case_end,Used}|_], St) ->
check_liveness_ret(R, Used, St);
check_liveness(R, [{badmatch,Used}|_], St) ->
check_liveness_ret(R, Used, St);
check_liveness(_, [if_end|_], St) ->
{killed,St};
check_liveness(R, [{func_info,_,_,Ar}|_], St) ->
case R of
{x,X} when X < Ar -> {used,St};
_ -> {killed,St}
end;
check_liveness(R, [{kill,R}|_], St) ->
{killed,St};
check_liveness(R, [{kill,_}|Is], St) ->
check_liveness(R, Is, St);
check_liveness(R, [bs_init_writable|Is], St) ->
if
R =:= {x,0} -> {used,St};
true -> check_liveness(R, Is, St)
end;
check_liveness(R, [{bs_private_append,_,Bits,_,Bin,_,Dst}|Is], St) ->
case R of
Bits -> {used,St};
Bin -> {used,St};
Dst -> {killed,St};
_ -> check_liveness(R, Is, St)
end;
check_liveness(R, [{bs_append,_,Bits,_,_,_,Bin,_,Dst}|Is], St) ->
case R of
Bits -> {used,St};
Bin -> {used,St};
Dst -> {killed,St};
_ -> check_liveness(R, Is, St)
end;
check_liveness(R, [{bs_init2,_,_,_,_,_,Dst}|Is], St) ->
if
R =:= Dst -> {killed,St};
true -> check_liveness(R, Is, St)
end;
check_liveness(R, [{bs_init_bits,_,_,_,_,_,Dst}|Is], St) ->
if
R =:= Dst -> {killed,St};
true -> check_liveness(R, Is, St)
end;
check_liveness(R, [{bs_put_string,_,_}|Is], St) ->
check_liveness(R, Is, St);
check_liveness(R, [{deallocate,_}|Is], St) ->
case R of
{y,_} -> {killed,St};
_ -> check_liveness(R, Is, St)
end;
check_liveness(R, [return|_], St) ->
check_liveness_live_ret(R, 1, St);
check_liveness(R, [{call_last,Live,_,_}|_], St) ->
check_liveness_live_ret(R, Live, St);
check_liveness(R, [{call_only,Live,_}|_], St) ->
check_liveness_live_ret(R, Live, St);
check_liveness(R, [{call_ext_last,Live,_,_}|_], St) ->
check_liveness_live_ret(R, Live, St);
check_liveness(R, [{call_ext_only,Live,_}|_], St) ->
check_liveness_live_ret(R, Live, St);
check_liveness(R, [{call,Live,_}|Is], St) ->
case R of
{x,X} when X < Live -> {used,St};
{x,_} -> {killed,St};
{y,_} -> check_liveness(R, Is, St)
end;
check_liveness(R, [{call_ext,Live,Func}|Is], St) ->
case R of
{x,X} when X < Live ->
{used,St};
{x,_} ->
{killed,St};
{y,_} ->
{extfunc,Mod,Name,Arity} = Func,
case erl_bifs:is_exit_bif(Mod, Name, Arity) of
false ->
check_liveness(R, Is, St);
true ->
%% We must make sure we don't check beyond this instruction
%% or we will fall through into random unrelated code and
%% get stuck in a loop.
%%
%% We don't want to overwrite a 'catch', so consider this
%% register in use.
%%
{used,St}
end
end;
check_liveness(R, [{call_fun,Live}|Is], St) ->
case R of
{x,X} when X =< Live -> {used,St};
{x,_} -> {killed,St};
{y,_} -> check_liveness(R, Is, St)
end;
check_liveness(R, [{apply,Args}|Is], St) ->
case R of
{x,X} when X < Args+2 -> {used,St};
{x,_} -> {killed,St};
{y,_} -> check_liveness(R, Is, St)
end;
check_liveness(R, [{apply_last,Args,_}|_], St) ->
check_liveness_live_ret(R, Args+2, St);
check_liveness(R, [send|Is], St) ->
case R of
{x,X} when X < 2 -> {used,St};
{x,_} -> {killed,St};
{y,_} -> check_liveness(R, Is, St)
end;
check_liveness({x,R}, [{'%live',Live}|Is], St) ->
if
R < Live -> check_liveness(R, Is, St);
true -> {killed,St}
end;
check_liveness(R, [{bif,Op,{f,Fail},Ss,D}|Is], St0) ->
case check_liveness_fail(R, Op, Ss, Fail, St0) of
{killed,St} = Killed ->
case member(R, Ss) of
true -> {used,St};
false when R =:= D -> Killed;
false -> check_liveness(R, Is, St)
end;
Other ->
Other
end;
check_liveness(R, [{gc_bif,Op,{f,Fail},Live,Ss,D}|Is], St0) ->
case R of
{x,X} when X >= Live ->
{killed,St0};
{x,_} ->
{used,St0};
_ ->
case check_liveness_fail(R, Op, Ss, Fail, St0) of
{killed,St}=Killed ->
case member(R, Ss) of
true -> {used,St};
false when R =:= D -> Killed;
false -> check_liveness(R, Is, St)
end;
Other ->
Other
end
end;
check_liveness(R, [{bs_add,{f,0},Ss,D}|Is], St) ->
case member(R, Ss) of
true -> {used,St};
false when R =:= D -> {killed,St};
false -> check_liveness(R, Is, St)
end;
check_liveness(R, [{bs_put_binary,{f,0},Sz,_,_,Src}|Is], St) ->
case member(R, [Sz,Src]) of
true -> {used,St};
false -> check_liveness(R, Is, St)
end;
check_liveness(R, [{bs_put_integer,{f,0},Sz,_,_,Src}|Is], St) ->
case member(R, [Sz,Src]) of
true -> {used,St};
false -> check_liveness(R, Is, St)
end;
check_liveness(R, [{bs_put_float,{f,0},Sz,_,_,Src}|Is], St) ->
case member(R, [Sz,Src]) of
true -> {used,St};
false -> check_liveness(R, Is, St)
end;
check_liveness(R, [{bs_restore2,S,_}|Is], St) ->
case R of
S -> {used,St};
_ -> check_liveness(R, Is, St)
end;
check_liveness(R, [{bs_save2,S,_}|Is], St) ->
case R of
S -> {used,St};
_ -> check_liveness(R, Is, St)
end;
check_liveness(R, [{move,S,D}|Is], St) ->
case R of
S -> {used,St};
D -> {killed,St};
_ -> check_liveness(R, Is, St)
end;
check_liveness(R, [{make_fun2,_,_,_,NumFree}|Is], St) ->
case R of
{x,X} when X < NumFree -> {used,St};
{x,_} -> {killed,St};
_ -> check_liveness(R, Is, St)
end;
check_liveness({x,_}=R, [{'catch',_,_}|Is], St) ->
%% All x registers will be killed if an exception occurs.
%% Therefore we only need to check the liveness for the
%% instructions following the catch instruction.
check_liveness(R, Is, St);
check_liveness({x,_}=R, [{'try',_,_}|Is], St) ->
%% All x registers will be killed if an exception occurs.
%% Therefore we only need to check the liveness for the
%% instructions inside the 'try' block.
check_liveness(R, Is, St);
check_liveness(R, [{try_end,Y}|Is], St) ->
case R of
Y ->
{killed,St};
{y,_} ->
%% y registers will be used if an exception occurs and
%% control transfers to the label given in the previous
%% try/2 instruction.
{used,St};
_ ->
check_liveness(R, Is, St)
end;
check_liveness(R, [{catch_end,Y}|Is], St) ->
case R of
Y -> {killed,St};
_ -> check_liveness(R, Is, St)
end;
check_liveness(R, [{get_tuple_element,S,_,D}|Is], St) ->
case R of
S -> {used,St};
D -> {killed,St};
_ -> check_liveness(R, Is, St)
end;
check_liveness(R, [{bs_context_to_binary,S}|Is], St) ->
case R of
S -> {used,St};
_ -> check_liveness(R, Is, St)
end;
check_liveness(R, [{loop_rec,{f,_},{x,0}}|_], St) ->
case R of
{x,_} ->
{killed,St};
_ ->
%% y register. Rarely happens. Be very conversative.
{unknown,St}
end;
check_liveness(R, [{loop_rec_end,{f,Fail}}|_], St) ->
check_liveness_at(R, Fail, St);
check_liveness(R, [{line,_}|Is], St) ->
check_liveness(R, Is, St);
check_liveness(_R, Is, St) when is_list(Is) ->
%% case Is of
%% [I|_] ->
%% io:format("~p ~p\n", [_R,I]);
%% _ -> ok
%% end,
{unknown,St}.
check_liveness_everywhere(R, [{f,Lbl}|T], St0) ->
case check_liveness_at(R, Lbl, St0) of
{killed,St} -> check_liveness_everywhere(R, T, St);
{_,_}=Other -> Other
end;
check_liveness_everywhere(R, [_|T], St) ->
check_liveness_everywhere(R, T, St);
check_liveness_everywhere(_, [], St) ->
{killed,St}.
check_liveness_at(R, Lbl, #live{lbl=Ll,res=ResMemorized}=St0) ->
case gb_trees:lookup(Lbl, ResMemorized) of
{value,Res} ->
{Res,St0};
none ->
{Res,St} = case gb_trees:lookup(Lbl, Ll) of
{value,Is} -> check_liveness(R, Is, St0);
none -> {unknown,St0}
end,
{Res,St#live{res=gb_trees:insert(Lbl, Res, St#live.res)}}
end.
check_liveness_ret(R, R, St) -> {used,St};
check_liveness_ret(_, _, St) -> {killed,St}.
check_liveness_live_ret({x,R}, Live, St) ->
if
R < Live -> {used,St};
true -> {killed,St}
end;
check_liveness_live_ret({y,_}, _, St) ->
{killed,St}.
check_liveness_fail(_, _, _, 0, St) ->
{killed,St};
check_liveness_fail(R, Op, Args, Fail, St) ->
Arity = length(Args),
case erl_internal:comp_op(Op, Arity) orelse
erl_internal:new_type_test(Op, Arity) of
true -> {killed,St};
false -> check_liveness_at(R, Fail, St)
end.
%% check_killed_block(Reg, [Instruction], State) -> killed | transparent | used
%% Finds out how Reg is used in the instruction sequence inside a block.
%% Returns one of:
%% killed - Reg is assigned a new value or killed by an allocation instruction
%% transparent - Reg is neither used nor killed
%% used - Reg is used or referenced by an allocation instruction.
%%
%% (Unknown instructions will cause an exception.)
check_killed_block({x,X}, [{set,_,_,{alloc,Live,_}}|_]) ->
if
X >= Live -> killed;
true -> used
end;
check_killed_block(R, [{set,Ds,Ss,_Op}|Is]) ->
case member(R, Ss) of
true -> used;
false ->
case member(R, Ds) of
true -> killed;
false -> check_killed_block(R, Is)
end
end;
check_killed_block(R, [{'%live',Live}|Is]) ->
case R of
{x,X} when X >= Live -> killed;
_ -> check_killed_block(R, Is)
end;
check_killed_block(_, []) -> transparent.
%% check_used_block(Reg, [Instruction], State) -> killed | transparent | used
%% Finds out how Reg is used in the instruction sequence inside a block.
%% Returns one of:
%% killed - Reg is assigned a new value or killed by an allocation instruction
%% transparent - Reg is neither used nor killed
%% used - Reg is explicitly used by an instruction
%%
%% (Unknown instructions will cause an exception.)
check_used_block({x,X}=R, [{set,_,_,{alloc,Live,_}}|Is]) ->
if
X >= Live -> killed;
true -> check_used_block(R, Is)
end;
check_used_block(R, [{set,Ds,Ss,_Op}|Is]) ->
case member(R, Ss) of
true -> used;
false ->
case member(R, Ds) of
true -> killed;
false -> check_used_block(R, Is)
end
end;
check_used_block(R, [{'%live',Live}|Is]) ->
case R of
{x,X} when X >= Live -> killed;
_ -> check_used_block(R, Is)
end;
check_used_block(_, []) -> transparent.
index_labels_1([{label,Lbl}|Is0], Acc) ->
Is = lists:dropwhile(fun({label,_}) -> true;
(_) -> false end, Is0),
index_labels_1(Is0, [{Lbl,Is}|Acc]);
index_labels_1([_|Is], Acc) ->
index_labels_1(Is, Acc);
index_labels_1([], Acc) -> gb_trees:from_orddict(sort(Acc)).
%% Help functions for combine_heap_needs.
combine_alloc_lists(Al1, Al2) ->
combine_alloc_lists_1(sort(Al1++Al2)).
combine_alloc_lists_1([{words,W1},{words,W2}|T])
when is_integer(W1), is_integer(W2) ->
[{words,W1+W2}|combine_alloc_lists_1(T)];
combine_alloc_lists_1([{floats,F1},{floats,F2}|T])
when is_integer(F1), is_integer(F2) ->
[{floats,F1+F2}|combine_alloc_lists_1(T)];
combine_alloc_lists_1([{words,_}=W|T]) ->
[W|combine_alloc_lists_1(T)];
combine_alloc_lists_1([{floats,_}=F|T]) ->
[F|combine_alloc_lists_1(T)];
combine_alloc_lists_1([]) -> [].
%% live_opt/4.
%% Bit syntax instructions.
live_opt([{bs_context_to_binary,Src}=I|Is], Regs0, D, Acc) ->
Regs = x_live([Src], Regs0),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_add,Fail,[Src1,Src2,_],Dst}=I|Is], Regs0, D, Acc) ->
Regs1 = x_live([Src1,Src2], x_dead([Dst], Regs0)),
Regs = live_join_label(Fail, D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_init2,Fail,Sz,Extra,Live0,Fl,Dst}|Is], Regs0, D, Acc) ->
Regs1 = x_dead([Dst], Regs0),
Live = live_regs(Regs1),
true = Live =< Live0, %Assertion.
Regs2 = live_call(Live),
Regs = live_join_label(Fail, D, Regs2),
I = {bs_init2,Fail,Sz,Extra,Live,Fl,Dst},
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_init_bits,Fail,Sz,Extra,Live0,Fl,Dst}|Is], Regs0, D, Acc) ->
Regs1 = x_dead([Dst], Regs0),
Live = live_regs(Regs1),
true = Live =< Live0, %Assertion.
Regs2 = live_call(Live),
Regs = live_join_label(Fail, D, Regs2),
I = {bs_init_bits,Fail,Sz,Extra,Live,Fl,Dst},
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_append,Fail,Bits,Extra,Live0,Unit,Src,Fl,Dst}|Is],
Regs0, D, Acc) ->
Regs1 = x_live([Src], x_dead([Dst], Regs0)),
Live = live_regs(Regs1),
true = Live =< Live0, %Assertion.
Regs2 = live_call(Live),
Regs = live_join_label(Fail, D, Regs2),
I = {bs_append,Fail,Bits,Extra,Live,Unit,Src,Fl,Dst},
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_private_append,Fail,Src1,_,Src2,_,Dst}=I|Is], Regs0, D, Acc) ->
Regs1 = x_live([Src1,Src2], x_dead([Dst], Regs0)),
Regs = live_join_label(Fail, D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_put_binary,Fail,Src1,_,_,Src2}=I|Is], Regs0, D, Acc) ->
Regs1 = x_live([Src1,Src2], Regs0),
Regs = live_join_label(Fail, D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_put_float,Fail,Src1,_,_,Src2}=I|Is], Regs0, D, Acc) ->
Regs1 = x_live([Src1,Src2], Regs0),
Regs = live_join_label(Fail, D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_put_integer,Fail,Src1,_,_,Src2}=I|Is], Regs0, D, Acc) ->
Regs1 = x_live([Src1,Src2], Regs0),
Regs = live_join_label(Fail, D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_put_utf8,Fail,_,Src}=I|Is], Regs0, D, Acc) ->
Regs1 = x_live([Src], Regs0),
Regs = live_join_label(Fail, D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_put_utf16,Fail,_,Src}=I|Is], Regs0, D, Acc) ->
Regs1 = x_live([Src], Regs0),
Regs = live_join_label(Fail, D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_put_utf32,Fail,_,Src}=I|Is], Regs0, D, Acc) ->
Regs1 = x_live([Src], Regs0),
Regs = live_join_label(Fail, D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_restore2,Src,_}=I|Is], Regs0, D, Acc) ->
Regs = x_live([Src], Regs0),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_save2,Src,_}=I|Is], Regs0, D, Acc) ->
Regs = x_live([Src], Regs0),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_utf8_size,Fail,Src,Dst}=I|Is], Regs0, D, Acc) ->
Regs1 = x_live([Src], x_dead([Dst], Regs0)),
Regs = live_join_label(Fail, D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{bs_utf16_size,Fail,Src,Dst}=I|Is], Regs0, D, Acc) ->
Regs1 = x_live([Src], x_dead([Dst], Regs0)),
Regs = live_join_label(Fail, D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{test,bs_start_match2,Fail,Live,[Src,_],_}=I|Is], _, D, Acc) ->
Regs0 = live_call(Live),
Regs1 = x_live([Src], Regs0),
Regs = live_join_label(Fail, D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
%% Other instructions.
live_opt([{block,Bl0}|Is], Regs0, D, Acc) ->
Live0 = {'%live',live_regs(Regs0)},
{Bl,Regs} = live_opt_block(reverse(Bl0), Regs0, D, [Live0]),
Live = {'%live',live_regs(Regs)},
live_opt(Is, Regs, D, [{block,[Live|Bl]}|Acc]);
live_opt([{label,L}=I|Is], Regs, D0, Acc) ->
D = gb_trees:insert(L, Regs, D0),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{jump,{f,L}}=I|Is], _, D, Acc) ->
Regs = gb_trees:get(L, D),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([return=I|Is], _, D, Acc) ->
live_opt(Is, 1, D, [I|Acc]);
live_opt([{catch_end,_}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(1), D, [I|Acc]);
live_opt([{badmatch,Src}=I|Is], _, D, Acc) ->
Regs = x_live([Src], 0),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{case_end,Src}=I|Is], _, D, Acc) ->
Regs = x_live([Src], 0),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{try_case_end,Src}=I|Is], _, D, Acc) ->
Regs = x_live([Src], 0),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([if_end=I|Is], _, D, Acc) ->
Regs = 0,
live_opt(Is, Regs, D, [I|Acc]);
live_opt([bs_init_writable=I|Is], _, D, Acc) ->
live_opt(Is, live_call(1), D, [I|Acc]);
live_opt([{call,Arity,_}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(Arity), D, [I|Acc]);
live_opt([{call_ext,Arity,_}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(Arity), D, [I|Acc]);
live_opt([{call_fun,Arity}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(Arity+1), D, [I|Acc]);
live_opt([{call_last,Arity,_,_}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(Arity), D, [I|Acc]);
live_opt([{call_ext_last,Arity,_,_}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(Arity), D, [I|Acc]);
live_opt([{apply,Arity}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(Arity+2), D, [I|Acc]);
live_opt([{apply_last,Arity,_}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(Arity+2), D, [I|Acc]);
live_opt([{call_only,Arity,_}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(Arity), D, [I|Acc]);
live_opt([{call_ext_only,Arity,_}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(Arity), D, [I|Acc]);
live_opt([{make_fun2,_,_,_,Arity}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(Arity), D, [I|Acc]);
live_opt([send=I|Is], _, D, Acc) ->
live_opt(Is, live_call(2), D, [I|Acc]);
live_opt([{test,_,Fail,Ss}=I|Is], Regs0, D, Acc) ->
Regs1 = x_live(Ss, Regs0),
Regs = live_join_label(Fail, D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{test,_,Fail,Live,Ss,_}=I|Is], _, D, Acc) ->
Regs0 = live_call(Live),
Regs1 = x_live(Ss, Regs0),
Regs = live_join_label(Fail, D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{select_val,Src,Fail,{list,List}}=I|Is], Regs0, D, Acc) ->
Regs1 = x_live([Src], Regs0),
Regs = live_join_labels([Fail|List], D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{select_tuple_arity,Src,Fail,{list,List}}=I|Is], Regs0, D, Acc) ->
Regs1 = x_live([Src], Regs0),
Regs = live_join_labels([Fail|List], D, Regs1),
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{'try',_,_}=I|Is], Regs, D, Acc) ->
%% If an exeption happens, all x registers will be killed.
%% Therefore, we should only base liveness of the code inside
%% the try.
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{try_case,_}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(1), D, [I|Acc]);
live_opt([{loop_rec,_Fail,_Dst}=I|Is], _, D, Acc) ->
live_opt(Is, 0, D, [I|Acc]);
live_opt([timeout=I|Is], _, D, Acc) ->
live_opt(Is, 0, D, [I|Acc]);
%% Transparent instructions - they neither use nor modify x registers.
live_opt([{bs_put_string,_,_}=I|Is], Regs, D, Acc) ->
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{deallocate,_}=I|Is], Regs, D, Acc) ->
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{kill,_}=I|Is], Regs, D, Acc) ->
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{try_end,_}=I|Is], Regs, D, Acc) ->
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{loop_rec_end,_}=I|Is], Regs, D, Acc) ->
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{wait,_}=I|Is], Regs, D, Acc) ->
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{wait_timeout,_,{Tag,_}}=I|Is], Regs, D, Acc) when Tag =/= x ->
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{line,_}=I|Is], Regs, D, Acc) ->
live_opt(Is, Regs, D, [I|Acc]);
%% The following instructions can occur if the "compilation" has been
%% started from a .S file using the 'asm' option.
live_opt([{trim,_,_}=I|Is], Regs, D, Acc) ->
live_opt(Is, Regs, D, [I|Acc]);
live_opt([{allocate,_,Live}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(Live), D, [I|Acc]);
live_opt([{allocate_heap,_,_,Live}=I|Is], _, D, Acc) ->
live_opt(Is, live_call(Live), D, [I|Acc]);
live_opt([], _, _, Acc) -> Acc.
live_opt_block([{set,Ds,Ss,Op}=I0|Is], Regs0, D, Acc) ->
Regs1 = x_live(Ss, x_dead(Ds, Regs0)),
{I,Regs} = case Op of
{alloc,Live0,Alloc} ->
%% The life-time analysis used by the code generator
%% is sometimes too conservative, so it may be
%% possible to lower the number of live registers
%% based on the exact liveness information.
%% The main benefit is that more optimizations that
%% depend on liveness information (such as the
%% beam_bool and beam_dead passes) may be applied.
Live = live_regs(Regs1),
true = Live =< Live0, %Assertion.
I1 = {set,Ds,Ss,{alloc,Live,Alloc}},
{I1,live_call(Live)};
_ ->
{I0,Regs1}
end,
case Ds of
[{x,X}] ->
case (not is_live(X, Regs0)) andalso Op =:= move of
true ->
live_opt_block(Is, Regs0, D, Acc);
false ->
live_opt_block(Is, Regs, D, [I|Acc])
end;
_ ->
live_opt_block(Is, Regs, D, [I|Acc])
end;
live_opt_block([], Regs, _, Acc) -> {Acc,Regs}.
live_join_labels([{f,L}|T], D, Regs0) when L =/= 0 ->
Regs = gb_trees:get(L, D) bor Regs0,
live_join_labels(T, D, Regs);
live_join_labels([_|T], D, Regs) ->
live_join_labels(T, D, Regs);
live_join_labels([], _, Regs) -> Regs.
live_join_label({f,0}, _, Regs) ->
Regs;
live_join_label({f,L}, D, Regs) ->
gb_trees:get(L, D) bor Regs.
live_call(Live) -> (1 bsl Live) - 1.
live_regs(Regs) ->
live_regs_1(0, Regs).
live_regs_1(N, 0) -> N;
live_regs_1(N, Regs) -> live_regs_1(N+1, Regs bsr 1).
x_dead([{x,N}|Rs], Regs) -> x_dead(Rs, Regs band (bnot (1 bsl N)));
x_dead([_|Rs], Regs) -> x_dead(Rs, Regs);
x_dead([], Regs) -> Regs.
x_live([{x,N}|Rs], Regs) -> x_live(Rs, Regs bor (1 bsl N));
x_live([_|Rs], Regs) -> x_live(Rs, Regs);
x_live([], Regs) -> Regs.
is_live(X, Regs) -> ((Regs bsr X) band 1) =:= 1.
