beam_ssa_pre_codegen.erl

%%
%% %CopyrightBegin%
%%
%% Copyright Ericsson AB 2018-2020. 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%
%%
%% Purpose: Prepare for code generation, including register allocation.
%%
%% The output of this compiler pass is still in the SSA format, but
%% it has been annotated and transformed to help the code generator.
%%
%% * Some instructions are translated to other instructions closer to
%% the BEAM instructions. For example, the binary matching
%% instructions are transformed from the optimization-friendly
%% internal format to instruction more similar to the actual BEAM
%% instructions.
%%
%% * Blocks that will need an instruction for allocating a stack frame
%% are annotated with a {frame_size,Size} annotation.
%%
%% * 'copy' instructions are added for all variables that need
%% to be saved to the stack frame. Additional 'copy' instructions
%% can be added as an optimization to reuse y registers (see
%% the copy_retval sub pass).
%%
%% * Each function is annotated with a {register,RegisterMap}
%% annotation that maps each variable to a BEAM register. The linear
%% scan algorithm is used to allocate registers.
%%
%% There are four kind of registers. x, y, fr (floating point register),
%% and z. A variable will be allocated to a z register if it is only
%% used by the instruction following the instruction that defines the
%% the variable. The code generator will typically combine those
%% instructions to a test instruction. z registers are also used for
%% some instructions that don't have a return value.
%%
%% References:
%%
%% [1] H. Mössenböck and M. Pfeiffer. Linear scan register allocation
%% in the context of SSA form and register constraints. In Proceedings
%% of the International Conference on Compiler Construction, pages
%% 229–246. LNCS 2304, Springer-Verlag, 2002.
%%
%% [2] C. Wimmer and H. Mössenböck. Optimized interval splitting in a
%% linear scan register allocator. In Proceedings of the ACM/USENIX
%% International Conference on Virtual Execution Environments, pages
%% 132–141. ACM Press, 2005.
%%
%% [3] C. Wimmer and M. Franz. Linear Scan Register Allocation on SSA
%% Form. In Proceedings of the International Symposium on Code
%% Generation and Optimization, pages 170-179. ACM Press, 2010.
%%

-module(beam_ssa_pre_codegen).

-export([module/2]).

-include("beam_ssa.hrl").

-import(lists, [all/2,any/2,append/1,duplicate/2,
                foldl/3,last/1,member/2,partition/2,
                reverse/1,reverse/2,sort/1,splitwith/2,zip/2]).

-spec module(beam_ssa:b_module(), [compile:option()]) ->
                    {'ok',beam_ssa:b_module()}.

module(#b_module{body=Fs0}=Module, Opts) ->
    UseBSM3 = not proplists:get_bool(no_bsm3, Opts),
    Ps = passes(Opts),
    Fs = functions(Fs0, Ps, UseBSM3),
    {ok,Module#b_module{body=Fs}}.

functions([F|Fs], Ps, UseBSM3) ->
    [function(F, Ps, UseBSM3)|functions(Fs, Ps, UseBSM3)];
functions([], _Ps, _UseBSM3) -> [].

-type b_var() :: beam_ssa:b_var().
-type var_name() :: beam_ssa:var_name().
-type instr_number() :: pos_integer().
-type range() :: {instr_number(),instr_number()}.
-type reg_num() :: beam_asm:reg_num().
-type xreg() :: {'x',reg_num()}.
-type yreg() :: {'y',reg_num()}.
-type ypool() :: {'y',beam_ssa:label()}.
-type reservation() :: 'fr' | {'prefer',xreg()} | 'x' | {'x',xreg()} |
                       ypool() | {yreg(),ypool()} | 'z'.
-type ssa_register() :: beam_ssa_codegen:ssa_register().

-define(TC(Body), tc(fun() -> Body end, ?FILE, ?LINE)).
-record(st, {ssa :: beam_ssa:block_map(),
             args :: [b_var()],
             cnt :: beam_ssa:label(),
             use_bsm3 :: boolean(),
             frames=[] :: [beam_ssa:label()],
             intervals=[] :: [{b_var(),[range()]}],
             res=[] :: [{b_var(),reservation()}] | #{b_var():=reservation()},
             regs=#{} :: #{b_var():=ssa_register()},
             extra_annos=[] :: [{atom(),term()}],
             location :: term()
            }).
-define(PASS(N), {N,fun N/1}).

passes(Opts) ->
    AddPrecgAnnos = proplists:get_bool(dprecg, Opts),
    FixTuples = proplists:get_bool(no_put_tuple2, Opts),
    Ps = [?PASS(assert_no_critical_edges),

          %% Preliminaries.
          ?PASS(fix_bs),
          ?PASS(sanitize),
          ?PASS(match_fail_instructions),
          case FixTuples of
              false -> ignore;
              true -> ?PASS(fix_tuples)
          end,
          ?PASS(use_set_tuple_element),
          ?PASS(place_frames),
          ?PASS(fix_receives),

          %% Find and reserve Y registers.
          ?PASS(find_yregs),
          ?PASS(reserve_yregs),

          %% Handle legacy binary match instruction that don't
          %% accept a Y register as destination.
          ?PASS(legacy_bs),

          %% Improve reuse of Y registers to potentially
          %% reduce the size of the stack frame.
          ?PASS(copy_retval),
          ?PASS(opt_get_list),

          %% Calculate live intervals.
          ?PASS(number_instructions),
          ?PASS(live_intervals),
          ?PASS(reserve_regs),

          %% If needed for a .precg file, save the live intervals
          %% so they can be included in an annotation.
          case AddPrecgAnnos of
              false -> ignore;
              true -> ?PASS(save_live_intervals)
          end,

          %% Allocate registers.
          ?PASS(linear_scan),
          ?PASS(frame_size),
          ?PASS(turn_yregs),

          ?PASS(assert_no_critical_edges)],
    [P || P <- Ps, P =/= ignore].

function(#b_function{anno=Anno,args=Args,bs=Blocks0,cnt=Count0}=F0,
         Ps, UseBSM3) ->
    try
        Location = maps:get(location, Anno, none),
        St0 = #st{ssa=Blocks0,args=Args,use_bsm3=UseBSM3,
                  cnt=Count0,location=Location},
        St = compile:run_sub_passes(Ps, St0),
        #st{ssa=Blocks,cnt=Count,regs=Regs,extra_annos=ExtraAnnos} = St,
        F1 = add_extra_annos(F0, ExtraAnnos),
        F = beam_ssa:add_anno(registers, Regs, F1),
        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.

save_live_intervals(#st{intervals=Intervals}=St) ->
    St#st{extra_annos=[{live_intervals,Intervals}]}.

%% Add extra annotations when a .precg listing file is being produced.
add_extra_annos(F, Annos) ->
    foldl(fun({Name,Value}, Acc) ->
                  beam_ssa:add_anno(Name, Value, Acc)
          end, F, Annos).

%% assert_no_critical_edges(St0) -> St.
%%  The code generator will not work if there are critial edges.
%%  Abort if any critical edges are found.

assert_no_critical_edges(#st{ssa=Blocks}=St) ->
    F = fun assert_no_ces/3,
    RPO = beam_ssa:rpo(Blocks),
    beam_ssa:fold_blocks(F, RPO, Blocks, Blocks),
    St.

assert_no_ces(_, #b_blk{is=[#b_set{op=phi,args=[_,_]=Phis}|_]}, Blocks) ->
    %% This block has multiple predecessors. Make sure that none
    %% of the precessors have more than one successor.
    true = all(fun({_,P}) ->
                       length(beam_ssa:successors(P, Blocks)) =:= 1
               end, Phis),                      %Assertion.
    Blocks;
assert_no_ces(_, _, Blocks) -> Blocks.

%% fix_bs(St0) -> St.
%%  Fix up the binary matching instructions:
%%
%%    * Insert bs_save and bs_restore instructions where needed.
%%
%%    * Combine bs_match and bs_extract instructions to bs_get
%%      instructions.

fix_bs(#st{ssa=Blocks,cnt=Count0,use_bsm3=UseBSM3}=St) ->
    F = fun(#b_set{op=bs_start_match,dst=Dst}, A) ->
                %% Mark the root of the match context list.
                [{Dst,{context,Dst}}|A];
           (#b_set{op=bs_match,dst=Dst,args=[_,ParentCtx|_]}, A) ->
                %% Link this match context the previous match context.
                [{Dst,ParentCtx}|A];
           (_, A) ->
                A
        end,
    RPO = beam_ssa:rpo(Blocks),
    case beam_ssa:fold_instrs(F, RPO, [], Blocks) of
        [] ->
            %% No binary matching in this function.
            St;
        [_|_]=M ->
            CtxChain = maps:from_list(M),
            Linear0 = beam_ssa:linearize(Blocks),

            %% Insert position instructions where needed.
            {Linear1,Count} = case UseBSM3 of
                                  true ->
                                      bs_pos_bsm3(Linear0, CtxChain, Count0);
                                  false ->
                                      bs_pos_bsm2(Linear0, CtxChain, Count0)
                              end,

            %% Rename instructions.
            Linear = bs_instrs(Linear1, CtxChain, []),

            St#st{ssa=maps:from_list(Linear),cnt=Count}
    end.

%% Insert bs_get_position and bs_set_position instructions as needed.
bs_pos_bsm3(Linear0, CtxChain, Count0) ->
    Rs0 = bs_restores(Linear0, CtxChain, #{}, #{}),
    Rs = maps:values(Rs0),
    S0 = sofs:relation(Rs, [{context,save_point}]),
    S1 = sofs:relation_to_family(S0),
    S = sofs:to_external(S1),

    {SavePoints,Count1} = make_bs_pos_dict(S, Count0, []),

    {Gets,Count2} = make_bs_getpos_map(Rs, SavePoints, Count1, []),
    {Sets,Count} = make_bs_setpos_map(maps:to_list(Rs0), SavePoints, Count2, []),

    %% Now insert all saves and restores.
    {bs_insert_bsm3(Linear0, Gets, Sets), Count}.

make_bs_getpos_map([{Ctx,Save}=Ps|T], SavePoints, Count, Acc) ->
    SavePoint = get_savepoint(Ps, SavePoints),
    I = #b_set{op=bs_get_position,dst=SavePoint,args=[Ctx]},
    make_bs_getpos_map(T, SavePoints, Count+1, [{Save,I}|Acc]);
make_bs_getpos_map([], _, Count, Acc) ->
    {maps:from_list(Acc),Count}.

make_bs_setpos_map([{Bef,{Ctx,_}=Ps}|T], SavePoints, Count, Acc) ->
    Ignored = #b_var{name={'@ssa_ignored',Count}},
    Args = [Ctx, get_savepoint(Ps, SavePoints)],
    I = #b_set{op=bs_set_position,dst=Ignored,args=Args},
    make_bs_setpos_map(T, SavePoints, Count+1, [{Bef,I}|Acc]);
make_bs_setpos_map([], _, Count, Acc) ->
    {maps:from_list(Acc),Count}.

get_savepoint({_,_}=Ps, SavePoints) ->
    Name = {'@ssa_bs_position', map_get(Ps, SavePoints)},
    #b_var{name=Name}.

make_bs_pos_dict([{Ctx,Pts}|T], Count0, Acc0) ->
    {Acc, Count} = make_bs_pos_dict_1(Pts, Ctx, Count0, Acc0),
    make_bs_pos_dict(T, Count, Acc);
make_bs_pos_dict([], Count, Acc) ->
    {maps:from_list(Acc), Count}.

make_bs_pos_dict_1([H|T], Ctx, I, Acc) ->
    make_bs_pos_dict_1(T, Ctx, I+1, [{{Ctx,H},I}|Acc]);
make_bs_pos_dict_1([], Ctx, I, Acc) ->
    {[{Ctx,I}|Acc], I}.

%% As bs_position but without OTP-22 instructions. This is only used when
%% cross-compiling to older versions.
bs_pos_bsm2(Linear0, CtxChain, Count0) ->
    Rs0 = bs_restores(Linear0, CtxChain, #{}, #{}),
    Rs = maps:values(Rs0),
    S0 = sofs:relation(Rs, [{context,save_point}]),
    S1 = sofs:relation_to_family(S0),
    S = sofs:to_external(S1),
    Slots = make_save_point_dict(S, []),
    {Saves,Count1} = make_save_map(Rs, Slots, Count0, []),
    {Restores,Count} = make_restore_map(maps:to_list(Rs0), Slots, Count1, []),

    %% Now insert all saves and restores.
    {bs_insert_bsm2(Linear0, Saves, Restores, Slots),Count}.

make_save_map([{Ctx,Save}=Ps|T], Slots, Count, Acc) ->
    Ignored = #b_var{name={'@ssa_ignored',Count}},
    case make_slot(Ps, Slots) of
        #b_literal{val=start} ->
            make_save_map(T, Slots, Count, Acc);
        Slot ->
            I = #b_set{op=bs_save,dst=Ignored,args=[Ctx,Slot]},
            make_save_map(T, Slots, Count+1, [{Save,I}|Acc])
    end;
make_save_map([], _, Count, Acc) ->
    {maps:from_list(Acc),Count}.

make_restore_map([{Bef,{Ctx,_}=Ps}|T], Slots, Count, Acc) ->
    Ignored = #b_var{name={'@ssa_ignored',Count}},
    I = #b_set{op=bs_restore,dst=Ignored,args=[Ctx,make_slot(Ps, Slots)]},
    make_restore_map(T, Slots, Count+1, [{Bef,I}|Acc]);
make_restore_map([], _, Count, Acc) ->
    {maps:from_list(Acc),Count}.

make_slot({Same,Same}, _Slots) ->
    #b_literal{val=start};
make_slot({_,_}=Ps, Slots) ->
    #b_literal{val=map_get(Ps, Slots)}.

make_save_point_dict([{Ctx,Pts}|T], Acc0) ->
    Acc = make_save_point_dict_1(Pts, Ctx, 0, Acc0),
    make_save_point_dict(T, Acc);
make_save_point_dict([], Acc) ->
    maps:from_list(Acc).

make_save_point_dict_1([Ctx|T], Ctx, I, Acc) ->
    %% Special {atom,start} save point. Does not need a
    %% bs_save instruction.
    make_save_point_dict_1(T, Ctx, I, Acc);
make_save_point_dict_1([H|T], Ctx, I, Acc) ->
    make_save_point_dict_1(T, Ctx, I+1, [{{Ctx,H},I}|Acc]);
make_save_point_dict_1([], Ctx, I, Acc) ->
    [{Ctx,I}|Acc].

bs_restores([{L,#b_blk{is=Is,last=Last}}|Bs], CtxChain, D0, Rs0) ->
    InPos = maps:get(L, D0, #{}),
    {SuccPos, FailPos, Rs} = bs_restores_is(Is, CtxChain, InPos, InPos, Rs0),

    D = bs_update_successors(Last, SuccPos, FailPos, D0),
    bs_restores(Bs, CtxChain, D, Rs);
bs_restores([], _, _, Rs) -> Rs.

bs_update_successors(#b_br{succ=Succ,fail=Fail}, SPos, FPos, D) ->
    join_positions([{Succ,SPos},{Fail,FPos}], D);
bs_update_successors(#b_switch{fail=Fail,list=List}, SPos, FPos, D) ->
    SPos = FPos,                                %Assertion.
    Update = [{L,SPos} || {_,L} <- List] ++ [{Fail,SPos}],
    join_positions(Update, D);
bs_update_successors(#b_ret{}, SPos, FPos, D) ->
    SPos = FPos,                                %Assertion.
    D.

join_positions([{L,MapPos0}|T], D) ->
    case D of
        #{L:=MapPos0} ->
            %% Same map.
            join_positions(T, D);
        #{L:=MapPos1} ->
            %% Different maps.
            MapPos = join_positions_1(MapPos0, MapPos1),
            join_positions(T, D#{L:=MapPos});
        #{} ->
            join_positions(T, D#{L=>MapPos0})
    end;
join_positions([], D) -> D.

join_positions_1(LHS, RHS) ->
    if
        map_size(LHS) < map_size(RHS) ->
            join_positions_2(maps:keys(LHS), RHS, LHS);
        true ->
            join_positions_2(maps:keys(RHS), LHS, RHS)
    end.

join_positions_2([V | Vs], Bigger, Smaller) ->
    case {Bigger, Smaller} of
        {#{ V := Same }, #{ V := Same }} ->
            join_positions_2(Vs, Bigger, Smaller);
        {#{ V := _ }, #{ V := _ }} ->
            join_positions_2(Vs, Bigger, Smaller#{ V := unknown });
        {#{}, #{ V := _ }} ->
            join_positions_2(Vs, Bigger, maps:remove(V, Smaller))
    end;
join_positions_2([], _Bigger, Smaller) ->
    Smaller.

%%
%% Updates the restore and position maps according to the given instructions.
%%
%% Note that positions may be updated even when a match fails; if a match
%% requires a restore, the position at the fail block will be the position
%% we've *restored to* and not the one we entered the current block with.
%%

bs_restores_is([#b_set{op=bs_start_match,dst=Start}|Is],
               CtxChain, SPos0, _FPos, Rs) ->
    %% Match instructions leave the position unchanged on failure, so
    %% FPos must be the SPos we entered the *instruction* with, and not the
    %% *block*.
    %%
    %% This is important when we have multiple matches in a single block where
    %% all but the last are guaranteed to succeed; the upcoming fail block must
    %% restore to the position of the next-to-last match, not the position we
    %% entered the current block with.
    FPos = SPos0,
    SPos = SPos0#{Start=>Start},
    bs_restores_is(Is, CtxChain, SPos, FPos, Rs);
bs_restores_is([#b_set{op=bs_match,dst=NewPos,args=Args}=I|Is],
               CtxChain, SPos0, _FPos, Rs0) ->
    Start = bs_subst_ctx(NewPos, CtxChain),
    [_,FromPos|_] = Args,
    case SPos0 of
        #{Start:=FromPos} ->
            %% Same position, no restore needed.
            SPos = case bs_match_type(I) of
                       plain ->
                            %% Update position to new position.
                            SPos0#{Start:=NewPos};
                        _ ->
                            %% Position will not change (test_unit
                            %% instruction or no instruction at
                            %% all).
                            SPos0
                   end,
            FPos = SPos0,
            bs_restores_is(Is, CtxChain, SPos, FPos, Rs0);
        #{Start:=_} ->
            %% Different positions, might need a restore instruction.
            case bs_match_type(I) of
                none ->
                    %% This is a tail test that will be optimized away.
                    %% There's no need to do a restore, and all
                    %% positions are unchanged.
                    FPos = SPos0,
                    bs_restores_is(Is, CtxChain, SPos0, FPos, Rs0);
                test_unit ->
                    %% This match instruction will be replaced by
                    %% a test_unit instruction. We will need a
                    %% restore. The new position will be the position
                    %% restored to (NOT NewPos).
                    SPos = SPos0#{Start:=FromPos},
                    FPos = SPos,
                    Rs = Rs0#{NewPos=>{Start,FromPos}},
                    bs_restores_is(Is, CtxChain, SPos, FPos, Rs);
                plain ->
                    %% Match or skip. Position will be changed.
                    SPos = SPos0#{Start:=NewPos},
                    FPos = SPos0#{Start:=FromPos},
                    Rs = Rs0#{NewPos=>{Start,FromPos}},
                    bs_restores_is(Is, CtxChain, SPos, FPos, Rs)
            end
    end;
bs_restores_is([#b_set{op=bs_extract,args=[FromPos|_]}|Is],
               CtxChain, SPos, _FPos, Rs) ->
    Start = bs_subst_ctx(FromPos, CtxChain),

    #{Start:=FromPos} = SPos,                   %Assertion.
    FPos = SPos,

    bs_restores_is(Is, CtxChain, SPos, FPos, Rs);
bs_restores_is([#b_set{op=call,dst=Dst,args=Args}|Is],
               CtxChain, SPos0, _FPos, Rs0) ->
    {SPos1, Rs} = bs_restore_args(Args, SPos0, CtxChain, Dst, Rs0),

    SPos = bs_invalidate_pos(Args, SPos1, CtxChain),
    FPos = SPos,

    bs_restores_is(Is, CtxChain, SPos, FPos, Rs);
bs_restores_is([#b_set{op=Op,dst=Dst,args=Args}|Is],
               CtxChain, SPos0, _FPos, Rs0)
  when Op =:= bs_test_tail;
       Op =:= bs_get_tail ->
    {SPos, Rs} = bs_restore_args(Args, SPos0, CtxChain, Dst, Rs0),
    FPos = SPos,

    bs_restores_is(Is, CtxChain, SPos, FPos, Rs);
bs_restores_is([#b_set{op={succeeded,guard},args=[Arg]}],
               CtxChain, SPos, FPos0, Rs) ->
    %% If we're branching on a match operation, the positions will be different
    %% depending on whether it succeeds.
    Ctx = bs_subst_ctx(Arg, CtxChain),
    FPos = case SPos of
               #{ Ctx := _ } -> FPos0;
               #{} -> SPos
           end,
    {SPos, FPos, Rs};
bs_restores_is([_ | Is], CtxChain, SPos, _FPos, Rs) ->
    FPos = SPos,
    bs_restores_is(Is, CtxChain, SPos, FPos, Rs);
bs_restores_is([], _CtxChain, SPos, _FPos, Rs) ->
    FPos = SPos,
    {SPos, FPos, Rs}.

bs_match_type(#b_set{args=[#b_literal{val=skip},_Ctx,
                             #b_literal{val=binary},_Flags,
                             #b_literal{val=all},#b_literal{val=U}]}) ->
    case U of
        1 -> none;
        _ -> test_unit
    end;
bs_match_type(_) ->
    plain.

%% Call instructions leave the match position in an undefined state,
%% requiring us to invalidate each affected argument.
bs_invalidate_pos([#b_var{}=Arg|Args], Pos0, CtxChain) ->
    Start = bs_subst_ctx(Arg, CtxChain),
    case Pos0 of
        #{Start:=_} ->
            Pos = Pos0#{Start:=unknown},
            bs_invalidate_pos(Args, Pos, CtxChain);
        #{} ->
            %% Not a match context.
            bs_invalidate_pos(Args, Pos0, CtxChain)
    end;
bs_invalidate_pos([_|Args], Pos, CtxChain) ->
    bs_invalidate_pos(Args, Pos, CtxChain);
bs_invalidate_pos([], Pos, _CtxChain) ->
    Pos.

bs_restore_args([#b_var{}=Arg|Args], Pos0, CtxChain, Dst, Rs0) ->
    Start = bs_subst_ctx(Arg, CtxChain),
    case Pos0 of
        #{Start:=Arg} ->
            %% Same position, no restore needed.
            bs_restore_args(Args, Pos0, CtxChain, Dst, Rs0);
        #{Start:=_} ->
            %% Different positions, need a restore instruction.
            Pos = Pos0#{Start:=Arg},
            Rs = Rs0#{Dst=>{Start,Arg}},
            bs_restore_args(Args, Pos, CtxChain, Dst, Rs);
        #{} ->
            %% Not a match context.
            bs_restore_args(Args, Pos0, CtxChain, Dst, Rs0)
    end;
bs_restore_args([_|Args], Pos, CtxChain, Dst, Rs) ->
    bs_restore_args(Args, Pos, CtxChain, Dst, Rs);
bs_restore_args([], Pos, _CtxChain, _Dst, Rs) ->
    {Pos, Rs}.

%% Insert all bs_save and bs_restore instructions.

bs_insert_bsm3(Blocks, Saves, Restores) ->
    bs_insert_1(Blocks, [], Saves, Restores, fun(I) -> I end).

bs_insert_bsm2(Blocks, Saves, Restores, Slots) ->
    %% The old instructions require bs_start_match to be annotated with the
    %% number of position slots it needs.
    bs_insert_1(Blocks, [], Saves, Restores,
                fun(#b_set{op=bs_start_match,dst=Dst}=I0) ->
                        NumSlots = case Slots of
                                       #{Dst:=NumSlots0} -> NumSlots0;
                                       #{} -> 0
                                   end,
                        beam_ssa:add_anno(num_slots, NumSlots, I0);
                   (I) ->
                        I
                end).

bs_insert_1([{L,#b_blk{is=Is0}=Blk} | Bs], Deferred0, Saves, Restores, XFrm) ->
    Is1 = bs_insert_deferred(Is0, Deferred0),
    {Is, Deferred} = bs_insert_is(Is1, Saves, Restores, XFrm, []),
    [{L,Blk#b_blk{is=Is}} | bs_insert_1(Bs, Deferred, Saves, Restores, XFrm)];
bs_insert_1([], [], _, _, _) ->
    [].

bs_insert_deferred([#b_set{op=bs_extract}=I | Is], Deferred) ->
    [I | bs_insert_deferred(Is, Deferred)];
bs_insert_deferred(Is, Deferred) ->
    Deferred ++ Is.

bs_insert_is([#b_set{dst=Dst}=I0|Is], Saves, Restores, XFrm, Acc0) ->
    I = XFrm(I0),
    Pre = case Restores of
              #{Dst:=R} -> [R];
              #{} -> []
          end,
    Post = case Saves of
               #{Dst:=S} -> [S];
               #{} -> []
           end,
    Acc = [I | Pre] ++ Acc0,
    case Is of
        [#b_set{op={succeeded,_},args=[Dst]}] ->
            %% Defer the save sequence to the success block.
            {reverse(Acc, Is), Post};
        _ ->
            bs_insert_is(Is, Saves, Restores, XFrm, Post ++ Acc)
    end;
bs_insert_is([], _, _, _, Acc) ->
    {reverse(Acc), []}.

%% Translate bs_match instructions to bs_get, bs_match_string,
%% or bs_skip. Also rename match context variables to use the
%% variable assigned to by the start_match instruction.

bs_instrs([{L,#b_blk{is=Is0}=Blk}|Bs], CtxChain, Acc0) ->
    case bs_instrs_is(Is0, CtxChain, []) of
        [#b_set{op=bs_extract,dst=Dst,args=[Ctx]}|Is] ->
            %% Drop this instruction. Rewrite the corresponding
            %% bs_match instruction in the previous block to
            %% a bs_get instruction.
            Acc = bs_combine(Dst, Ctx, Acc0),
            bs_instrs(Bs, CtxChain, [{L,Blk#b_blk{is=Is}}|Acc]);
        Is ->
            bs_instrs(Bs, CtxChain, [{L,Blk#b_blk{is=Is}}|Acc0])
    end;
bs_instrs([], _, Acc) ->
    reverse(Acc).

bs_instrs_is([#b_set{op={succeeded,_}}=I|Is], CtxChain, Acc) ->
    %% This instruction refers to a specific operation, so we must not
    %% substitute the context argument.
    bs_instrs_is(Is, CtxChain, [I | Acc]);
bs_instrs_is([#b_set{op=Op,args=Args0}=I0|Is], CtxChain, Acc) ->
    Args = [bs_subst_ctx(A, CtxChain) || A <- Args0],
    I1 = I0#b_set{args=Args},
    I = case {Op,Args} of
            {bs_match,[#b_literal{val=skip},Ctx,Type|As]} ->
                I1#b_set{op=bs_skip,args=[Type,Ctx|As]};
            {bs_match,[#b_literal{val=string},Ctx|As]} ->
                I1#b_set{op=bs_match_string,args=[Ctx|As]};
            {_,_} ->
                I1
        end,
    bs_instrs_is(Is, CtxChain, [I|Acc]);
bs_instrs_is([], _, Acc) ->
    reverse(Acc).

%% Combine a bs_match instruction with the destination register
%% taken from a bs_extract instruction.

bs_combine(Dst, Ctx, [{L,#b_blk{is=Is0}=Blk}|Acc]) ->
    [#b_set{}=Succeeded,
     #b_set{op=bs_match,args=[Type,_|As]}=BsMatch|Is1] = reverse(Is0),
    Is = reverse(Is1, [BsMatch#b_set{op=bs_get,dst=Dst,args=[Type,Ctx|As]},
                       Succeeded#b_set{args=[Dst]}]),
    [{L,Blk#b_blk{is=Is}}|Acc].

bs_subst_ctx(#b_var{}=Var, CtxChain) ->
    case CtxChain of
        #{Var:={context,Ctx}} ->
            Ctx;
        #{Var:=ParentCtx} ->
            bs_subst_ctx(ParentCtx, CtxChain);
        #{} ->
            %% Not a match context variable.
            Var
    end;
bs_subst_ctx(Other, _CtxChain) ->
    Other.

%% legacy_bs(St0) -> St.
%%  Binary matching instructions in OTP 21 and earlier don't support
%%  a Y register as destination. If St#st.use_bsm3 is false,
%%  we will need to rewrite those instructions so that the result
%%  is first put in an X register and then moved to a Y register
%%  if the operation succeeded.

legacy_bs(#st{use_bsm3=false,ssa=Blocks0,cnt=Count0,res=Res}=St) ->
    IsYreg = maps:from_list([{V,true} || {V,{y,_}} <- Res]),
    Linear0 = beam_ssa:linearize(Blocks0),
    {Linear,Count} = legacy_bs(Linear0, IsYreg, Count0, #{}, []),
    Blocks = maps:from_list(Linear),
    St#st{ssa=Blocks,cnt=Count};
legacy_bs(#st{use_bsm3=true}=St) -> St.

legacy_bs([{L,Blk}|Bs], IsYreg, Count0, Copies0, Acc) ->
    #b_blk{is=Is0,last=Last} = Blk,
    Is1 = case Copies0 of
              #{L:=Copy} -> [Copy|Is0];
              #{} -> Is0
          end,
    {Is,Count,Copies} = legacy_bs_is(Is1, Last, IsYreg, Count0, Copies0, []),
    legacy_bs(Bs, IsYreg, Count, Copies, [{L,Blk#b_blk{is=Is}}|Acc]);
legacy_bs([], _IsYreg, Count, _Copies, Acc) ->
    {Acc,Count}.

legacy_bs_is([#b_set{op=Op,dst=Dst}=I0,
              #b_set{op=succeeded,dst=SuccDst,args=[Dst]}=SuccI0],
             Last, IsYreg, Count0, Copies0, Acc) ->
    NeedsFix = is_map_key(Dst, IsYreg) andalso
        case Op of
            bs_get -> true;
            bs_init -> true;
            _ -> false
        end,
    case NeedsFix of
        true ->
            TempDst = #b_var{name={'@bs_temp_dst',Count0}},
            Count = Count0 + 1,
            I = I0#b_set{dst=TempDst},
            SuccI = SuccI0#b_set{args=[TempDst]},
            Copy = #b_set{op=copy,dst=Dst,args=[TempDst]},
            #b_br{bool=SuccDst,succ=SuccL} = Last,
            Copies = Copies0#{SuccL=>Copy},
            legacy_bs_is([], Last, IsYreg, Count, Copies, [SuccI,I|Acc]);
        false ->
            legacy_bs_is([], Last, IsYreg, Count0, Copies0, [SuccI0,I0|Acc])
    end;
legacy_bs_is([I|Is], Last, IsYreg, Count, Copies, Acc) ->
    legacy_bs_is(Is, Last, IsYreg, Count, Copies, [I|Acc]);
legacy_bs_is([], _Last, _IsYreg, Count, Copies, Acc) ->
    {reverse(Acc),Count,Copies}.

%% sanitize(St0) -> St.
%%  Remove constructs that can cause problems later:
%%
%%  * Unreachable blocks may cause problems for determination of
%%  dominators.
%%
%%  * Some instructions (such as get_hd) don't accept literal
%%  arguments. Evaluate the instructions and remove them.

sanitize(#st{ssa=Blocks0,cnt=Count0}=St) ->
    Ls = beam_ssa:rpo(Blocks0),
    {Blocks,Count} = sanitize(Ls, Count0, Blocks0, #{}),
    St#st{ssa=Blocks,cnt=Count}.

sanitize([L|Ls], Count0, Blocks0, Values0) ->
    #b_blk{is=Is0,last=Last0} = Blk0 = map_get(L, Blocks0),
    case sanitize_is(Is0, Last0, Count0, Values0, false, []) of
        no_change ->
            sanitize(Ls, Count0, Blocks0, Values0);
        {Is,Last,Count,Values} ->
            Blk = Blk0#b_blk{is=Is,last=Last},
            Blocks = Blocks0#{L:=Blk},
            sanitize(Ls, Count, Blocks, Values)
    end;
sanitize([], Count, Blocks0, Values) ->
    Blocks = if
                 map_size(Values) =:= 0 ->
                     Blocks0;
                 true ->
                     RPO = beam_ssa:rpo(Blocks0),
                     beam_ssa:rename_vars(Values, RPO, Blocks0)
             end,

    %% Unreachable blocks can cause problems for the dominator calculations.
    Ls = beam_ssa:rpo(Blocks),
    Reachable = gb_sets:from_list(Ls),
    {case map_size(Blocks) =:= gb_sets:size(Reachable) of
         true -> Blocks;
         false -> remove_unreachable(Ls, Blocks, Reachable, [])
     end,Count}.

sanitize_is([#b_set{op=get_map_element,args=Args0}=I0|Is],
            Last, Count0, Values, Changed, Acc) ->
    case sanitize_args(Args0, Values) of
        [#b_literal{}=Map,Key] ->
            %% Bind the literal map to a variable.
            {MapVar,Count} = new_var('@ssa_map', Count0),
            I = I0#b_set{args=[MapVar,Key]},
            Copy = #b_set{op=copy,dst=MapVar,args=[Map]},
            sanitize_is(Is, Last, Count, Values, true, [I,Copy|Acc]);
        [_,_]=Args0 ->
            sanitize_is(Is, Last, Count0, Values, Changed, [I0|Acc]);
        [_,_]=Args ->
            I = I0#b_set{args=Args},
            sanitize_is(Is, Last, Count0, Values, true, [I|Acc])
    end;
sanitize_is([#b_set{op={succeeded,guard},dst=Dst,args=[Arg0]}=I0],
            #b_br{bool=Dst}=Last, Count, Values, _Changed, Acc0) ->
    %% We no longer need to distinguish between guard and body checks, so we'll
    %% rewrite this as a plain 'succeeded'.
    case sanitize_arg(Arg0, Values) of
        #b_var{}=Arg ->
            case Acc0 of
                [#b_set{op=call,
                        args=[#b_remote{mod=#b_literal{val=erlang},
                                        name=#b_literal{val=error},
                                        arity=1},_],
                        dst=Arg0}|Acc] ->
                    %% This erlang:error/1 is the result from a
                    %% sanitized bs_add or bs_init instruction. Calls
                    %% to erlang:error/1 in receive is not allowed, so
                    %% we will have to rewrite this instruction
                    %% sequence to an unconditional branch to the
                    %% failure label.
                    Fail = Last#b_br.fail,
                    Br = #b_br{bool=#b_literal{val=true},succ=Fail,fail=Fail},
                    {reverse(Acc), Br, Count, Values};
                _ ->
                    I = I0#b_set{op=succeeded,args=[Arg]},
                    {reverse(Acc0, [I]), Last, Count, Values}
            end;
        #b_literal{} ->
            Value = #b_literal{val=true},
            {reverse(Acc0), Last, Count, Values#{ Dst => Value }}
    end;
sanitize_is([#b_set{op={succeeded,body},dst=Dst,args=[Arg0]}=I0],
            #b_br{bool=Dst}=Last, Count, Values, _Changed, Acc) ->
    %% We no longer need to distinguish between guard and body checks, so we'll
    %% rewrite this as a plain 'succeeded'.
    case sanitize_arg(Arg0, Values) of
        #b_var{}=Arg ->
            I = I0#b_set{op=succeeded,args=[Arg]},
            {reverse(Acc, [I]), Last, Count, Values};
        #b_literal{} ->
            Value = #b_literal{val=true},
            {reverse(Acc), Last, Count, Values#{ Dst => Value }}
    end;
sanitize_is([#b_set{op={succeeded,Kind},args=[Arg0]} | Is],
            Last, Count, Values, _Changed, Acc) ->
    %% We're no longer branching on this instruction and can safely remove it.
    [] = Is, #b_br{succ=Same,fail=Same} = Last, %Assertion.
    if
        Same =:= ?EXCEPTION_BLOCK ->
            %% The checked instruction always fails at runtime and we're not
            %% in a try/catch; rewrite the terminator to a return.
            body = Kind,                        %Assertion.
            Arg = sanitize_arg(Arg0, Values),
            sanitize_is(Is, #b_ret{arg=Arg}, Count, Values, true, Acc);
        Same =/= ?EXCEPTION_BLOCK ->
            %% We either always succeed, or always fail to somewhere other than
            %% the exception block.
            true = Kind =:= guard orelse Kind =:= body, %Assertion.
            sanitize_is(Is, Last, Count, Values, true, Acc)
    end;
sanitize_is([#b_set{op=Op}=I|Is], Last, Count, Values, Changed, Acc) ->
    case Last of
        #b_br{succ=Same,fail=Same} ->
            case is_test_op(Op) of
                true ->
                    sanitize_is(Is, Last, Count, Values, true, Acc);
                false ->
                    do_sanitize_is(I, Is,  Last, Count, Values, Changed, Acc)
            end;
        _ ->
            do_sanitize_is(I, Is,  Last, Count, Values, Changed, Acc)
    end;
sanitize_is([], Last, Count, Values, Changed, Acc) ->
    case Changed of
        true ->
            {reverse(Acc), Last, Count, Values};
        false ->
            no_change
    end.

is_test_op(bs_put) -> true;
is_test_op(bs_test_tail) -> true;
is_test_op(_) -> false.
    
do_sanitize_is(#b_set{op=Op,dst=Dst,args=Args0}=I0,
               Is, Last, Count, Values, Changed0, Acc) ->
    Args = sanitize_args(Args0, Values),
    case sanitize_instr(Op, Args, I0) of
        {value,Value0} ->
            Value = #b_literal{val=Value0},
            sanitize_is(Is, Last, Count, Values#{Dst=>Value}, true, Acc);
        {ok,I} ->
            sanitize_is(Is, Last, Count, Values, true, [I|Acc]);
        ok ->
            I = I0#b_set{args=Args},
            Changed = Changed0 orelse Args =/= Args0,
            sanitize_is(Is, Last, Count, Values, Changed, [I|Acc])
    end.

sanitize_args(Args, Values) ->
    [sanitize_arg(Arg, Values) || Arg <- Args].

sanitize_arg(#b_var{}=Var, Values) ->
    case Values of
        #{Var:=New} -> New;
        #{} -> Var
    end;
sanitize_arg(Arg, _Values) ->
    Arg.


sanitize_instr(phi, PhiArgs, _I) ->
    case phi_all_same_literal(PhiArgs) of
        true ->
            %% (Can only happen when some optimizations have been
            %% turned off.)
            %%
            %% This phi node always produces the same literal value.
            %% We must do constant progation of the value to ensure
            %% that we can sanitize any instructions that don't accept
            %% literals (such as `get_hd`). This is necessary for
            %% correctness, because beam_ssa_codegen:prefer_xregs/2
            %% does constant propagation and could propagate a literal
            %% into an instruction that don't accept literals.
            [{#b_literal{val=Val},_}|_] = PhiArgs,
            {value,Val};
        false ->
            ok
    end;
sanitize_instr({bif,Bif}, [#b_literal{val=Lit}], _I) ->
    case erl_bifs:is_pure(erlang, Bif, 1) of
        false ->
            ok;
        true ->
            try
                {value,erlang:Bif(Lit)}
            catch
                error:_ ->
                    ok
            end
    end;
sanitize_instr({bif,Bif}, [#b_literal{val=Lit1},#b_literal{val=Lit2}], _I) ->
    true = erl_bifs:is_pure(erlang, Bif, 2),    %Assertion.
    try
        {value,erlang:Bif(Lit1, Lit2)}
    catch
        error:_ ->
            ok
    end;
sanitize_instr(bs_match, Args, I) ->
    %% Matching of floats are never changed to a bs_skip even when the
    %% value is never used, because the match can always fail (for example,
    %% if it is a NaN).
    [#b_literal{val=float}|_] = Args,           %Assertion.
    {ok,I#b_set{op=bs_get}};
sanitize_instr(get_hd, [#b_literal{val=[Hd|_]}], _I) ->
    {value,Hd};
sanitize_instr(get_tl, [#b_literal{val=[_|Tl]}], _I) ->
    {value,Tl};
sanitize_instr(get_tuple_element, [#b_literal{val=T},
                                   #b_literal{val=I}], _I)
  when I < tuple_size(T) ->
    {value,element(I+1, T)};
sanitize_instr(is_nonempty_list, [#b_literal{val=Lit}], _I) ->
    {value,case Lit of
               [_|_] -> true;
               _ -> false
           end};
sanitize_instr(is_tagged_tuple, [#b_literal{val=Tuple},
                                 #b_literal{val=Arity},
                                 #b_literal{val=Tag}], _I)
  when is_integer(Arity), is_atom(Tag) ->
    if
        tuple_size(Tuple) =:= Arity, element(1, Tuple) =:= Tag ->
            {value,true};
        true ->
            {value,false}
    end;
sanitize_instr(bs_add, [Arg1,Arg2,_|_], I0) ->
    case all(fun(#b_literal{val=Size}) -> is_integer(Size) andalso Size >= 0;
                (#b_var{}) -> true
             end, [Arg1,Arg2]) of
        true -> ok;
        false -> {ok,sanitize_badarg(I0)}
    end;
sanitize_instr(bs_init, [#b_literal{val=new},#b_literal{val=Sz}|_], I0) ->
    if
        is_integer(Sz), Sz >= 0 -> ok;
        true -> {ok,sanitize_badarg(I0)}
    end;
sanitize_instr(bs_init, [#b_literal{},_,#b_literal{val=Sz}|_], I0) ->
    if
        is_integer(Sz), Sz >= 0 -> ok;
        true -> {ok,sanitize_badarg(I0)}
    end;
sanitize_instr(_, _, _) ->
    ok.

sanitize_badarg(I) ->
    Func = #b_remote{mod=#b_literal{val=erlang},
                     name=#b_literal{val=error},arity=1},
    I#b_set{op=call,args=[Func,#b_literal{val=badarg}]}.

remove_unreachable([L|Ls], Blocks, Reachable, Acc) ->
    #b_blk{is=Is0} = Blk0 = map_get(L, Blocks),
    case split_phis(Is0) of
        {[_|_]=Phis,Rest} ->
            Is = [prune_phi(Phi, Reachable) || Phi <- Phis] ++ Rest,
            Blk = Blk0#b_blk{is=Is},
            remove_unreachable(Ls, Blocks, Reachable, [{L,Blk}|Acc]);
        {[],_} ->
            remove_unreachable(Ls, Blocks, Reachable, [{L,Blk0}|Acc])
    end;
remove_unreachable([], _Blocks, _, Acc) ->
    maps:from_list(Acc).

prune_phi(#b_set{args=Args0}=Phi, Reachable) ->
    Args = [A || {_,Pred}=A <- Args0,
                 gb_sets:is_element(Pred, Reachable)],
    Phi#b_set{args=Args}.

phi_all_same_literal([{#b_literal{}=Arg, _From} | Phis]) ->
    phi_all_same_literal_1(Phis, Arg);
phi_all_same_literal([_|_]) ->
    false.

phi_all_same_literal_1([{Arg, _From} | Phis], Arg) ->
    phi_all_same_literal_1(Phis, Arg);
phi_all_same_literal_1([], _Arg) ->
    true;
phi_all_same_literal_1(_Phis, _Arg) ->
    false.

%%% Rewrite certain calls to erlang:error/{1,2} to specialized
%%% instructions:
%%%
%%% erlang:error({badmatch,Value})       => badmatch Value
%%% erlang:error({case_clause,Value})    => case_end Value
%%% erlang:error({try_clause,Value})     => try_case_end Value
%%% erlang:error(if_clause)              => if_end
%%% erlang:error(function_clause, Args)  => jump FuncInfoLabel
%%%
%%% In SSA code, we represent those instructions as a 'match_fail'
%%% instruction with the name of the BEAM instruction as the first
%%% argument.

match_fail_instructions(#st{ssa=Blocks0,args=Args,location=Location}=St) ->
    Ls = maps:to_list(Blocks0),
    Info = {length(Args),Location},
    Blocks = match_fail_instrs_1(Ls, Info, Blocks0),
    St#st{ssa=Blocks}.

match_fail_instrs_1([{L,#b_blk{is=Is0}=Blk}|Bs], Arity, Blocks0) ->
    case match_fail_instrs_blk(Is0, Arity, []) of
        none ->
            match_fail_instrs_1(Bs, Arity, Blocks0);
        Is ->
            Blocks = Blocks0#{L:=Blk#b_blk{is=Is}},
            match_fail_instrs_1(Bs, Arity, Blocks)
    end;
match_fail_instrs_1([], _Arity, Blocks) -> Blocks.

match_fail_instrs_blk([#b_set{op=put_tuple,dst=Dst,
                              args=[#b_literal{val=Tag},Val]},
                       #b_set{op=call,
                              args=[#b_remote{mod=#b_literal{val=erlang},
                                              name=#b_literal{val=error}},
                                    Dst]}=Call|Is],
                      _Arity, Acc) ->
    match_fail_instr(Call, Tag, Val, Is, Acc);
match_fail_instrs_blk([#b_set{op=call,
                              args=[#b_remote{mod=#b_literal{val=erlang},
                                              name=#b_literal{val=error}},
                                    #b_literal{val={Tag,Val}}]}=Call|Is],
                      _Arity, Acc) ->
    match_fail_instr(Call, Tag, #b_literal{val=Val}, Is, Acc);
match_fail_instrs_blk([#b_set{op=call,
                              args=[#b_remote{mod=#b_literal{val=erlang},
                                              name=#b_literal{val=error}},
                                    #b_literal{val=if_clause}]}=Call|Is],
                      _Arity, Acc) ->
    I = Call#b_set{op=match_fail,args=[#b_literal{val=if_end}]},
    reverse(Acc, [I|Is]);
match_fail_instrs_blk([#b_set{op=call,anno=Anno,
                              args=[#b_remote{mod=#b_literal{val=erlang},
                                              name=#b_literal{val=error}},
                                    #b_literal{val=function_clause},
                                    Stk]}=Call],
                      {Arity,Location}, Acc) ->
    case match_fail_stk(Stk, Acc, [], []) of
        {[_|_]=Vars,Is} when length(Vars) =:= Arity ->
            case maps:get(location, Anno, none) of
                Location ->
                    I = Call#b_set{op=match_fail,
                                   args=[#b_literal{val=function_clause}|Vars]},
                    Is ++ [I];
                _ ->
                    %% erlang:error/2 has a different location than the
                    %% func_info instruction at the beginning of the function
                    %% (probably because of inlining). Keep the original call.
                    reverse(Acc, [Call])
            end;
        _ ->
            %% Either the stacktrace could not be picked apart (for example,
            %% if the call to erlang:error/2 was handwritten) or the number
            %% of arguments in the stacktrace was different from the arity
            %% of the host function (because it is the implementation of a
            %% fun). Keep the original call.
            reverse(Acc, [Call])
    end;
match_fail_instrs_blk([I|Is], Arity, Acc) ->
    match_fail_instrs_blk(Is, Arity, [I|Acc]);
match_fail_instrs_blk(_, _, _) ->
    none.

match_fail_instr(Call, Tag, Val, Is, Acc) ->
    Op = case Tag of
             badmatch -> Tag;
             case_clause -> case_end;
             try_clause -> try_case_end;
             _ -> none
         end,
    case Op of
        none ->
            none;
        _ ->
            I = Call#b_set{op=match_fail,args=[#b_literal{val=Op},Val]},
            reverse(Acc, [I|Is])
    end.

match_fail_stk(#b_var{}=V, [#b_set{op=put_list,dst=V,args=[H,T]}|Is], IAcc, VAcc) ->
    match_fail_stk(T, Is, IAcc, [H|VAcc]);
match_fail_stk(#b_literal{val=[H|T]}, Is, IAcc, VAcc) ->
    match_fail_stk(#b_literal{val=T}, Is, IAcc, [#b_literal{val=H}|VAcc]);
match_fail_stk(#b_literal{val=[]}, [], IAcc, VAcc) ->
    {reverse(VAcc),IAcc};
match_fail_stk(T, [#b_set{op=Op}=I|Is], IAcc, VAcc)
  when Op =:= bs_get_tail; Op =:= bs_set_position ->
    match_fail_stk(T, Is, [I|IAcc], VAcc);
match_fail_stk(_, _, _, _) -> none.

%%%
%%% Fix tuples.
%%%

%% fix_tuples(St0) -> St.
%%  If compatibility with a previous version of Erlang has been
%%  requested, tuple creation must be split into two instruction to
%%  mirror the the way tuples are created in BEAM prior to OTP 22.
%%  Each put_tuple instruction is split into put_tuple_arity followed
%%  by put_tuple_elements.

fix_tuples(#st{ssa=Blocks0,cnt=Count0}=St) ->
    F = fun (#b_set{op=put_tuple,args=Args}=Put, C0) ->
                Arity = #b_literal{val=length(Args)},
                {Ignore,C} = new_var('@ssa_ignore', C0),
                {[Put#b_set{op=put_tuple_arity,args=[Arity]},
                  #b_set{dst=Ignore,op=put_tuple_elements,args=Args}],C};
           (I, C) -> {[I],C}
        end,
    RPO = beam_ssa:rpo(Blocks0),
    {Blocks,Count} = beam_ssa:flatmapfold_instrs(F, RPO, Count0, Blocks0),
    St#st{ssa=Blocks,cnt=Count}.

%%%
%%% Introduce the set_tuple_element instructions to make
%%% multiple-field record updates faster.
%%%
%%% The expansion of record field updates, when more than one field is
%%% updated, but not a majority of the fields, will create a sequence of
%%% calls to `erlang:setelement(Index, Value, Tuple)` where Tuple in the
%%% first call is the original record tuple, and in the subsequent calls
%%% Tuple is the result of the previous call. Furthermore, all Index
%%% values are constant positive integers, and the first call to
%%% `setelement` will have the greatest index. Thus all the following
%%% calls do not actually need to test at run-time whether Tuple has type
%%% tuple, nor that the index is within the tuple bounds.
%%%
%%% Since this optimization introduces destructive updates, it used to
%%% be done as the very last Core Erlang pass before going to
%%% lower-level code. However, it turns out that this kind of destructive
%%% updates are awkward also in SSA code and can prevent or complicate
%%% type analysis and aggressive optimizations.
%%%
%%% NOTE: Because there no write barriers in the system, this kind of
%%% optimization can only be done when we are sure that garbage
%%% collection will not be triggered between the creation of the tuple
%%% and the destructive updates - otherwise we might insert pointers
%%% from an older generation to a newer.
%%%

use_set_tuple_element(#st{ssa=Blocks0}=St) ->
    Uses = count_uses(Blocks0),
    RPO = reverse(beam_ssa:rpo(Blocks0)),
    Blocks = use_ste_1(RPO, Uses, Blocks0),
    St#st{ssa=Blocks}.

use_ste_1([L|Ls], Uses, Blocks) ->
    #b_blk{is=Is0} = Blk0 = map_get(L, Blocks),
    case use_ste_is(Is0, Uses) of
        Is0 ->
            use_ste_1(Ls, Uses, Blocks);
        Is ->
            Blk = Blk0#b_blk{is=Is},
            use_ste_1(Ls, Uses, Blocks#{L:=Blk})
    end;
use_ste_1([], _, Blocks) -> Blocks.

%%% Optimize within a single block.

use_ste_is([#b_set{}=I|Is0], Uses) ->
    Is = use_ste_is(Is0, Uses),
    case extract_ste(I) of
        none ->
            [I|Is];
        Extracted ->
            use_ste_call(Extracted, I, Is, Uses)
    end;
use_ste_is([], _Uses) -> [].

use_ste_call({Dst0,Pos0,_Var0,_Val0}, Call1, Is0, Uses) ->
    case get_ste_call(Is0, []) of
        {Prefix,{Dst1,Pos1,Dst0,Val1},Call2,Is}
          when Pos1 > 0, Pos0 > Pos1 ->
            case is_single_use(Dst0, Uses) of
                true ->
                    Call = Call1#b_set{dst=Dst1},
                    Args = [Val1,Dst1,#b_literal{val=Pos1-1}],
                    Dsetel = Call2#b_set{op=set_tuple_element,
                                         dst=Dst0,
                                         args=Args},
                    [Call|Prefix] ++ [Dsetel|Is];
                false ->
                    [Call1|Is0]
            end;
        _ ->
            [Call1|Is0]
    end.

get_ste_call([#b_set{op=get_tuple_element}=I|Is], Acc) ->
    get_ste_call(Is, [I|Acc]);
get_ste_call([#b_set{op=call}=I|Is], Acc) ->
    case extract_ste(I) of
        none ->
            none;
        Extracted ->
            {reverse(Acc),Extracted,I,Is}
    end;
get_ste_call(_, _) -> none.

extract_ste(#b_set{op=call,dst=Dst,
                   args=[#b_remote{mod=#b_literal{val=M},
                                  name=#b_literal{val=F}}|Args]}) ->
    case {M,F,Args} of
        {erlang,setelement,[#b_literal{val=Pos},Tuple,Val]} ->
            {Dst,Pos,Tuple,Val};
        {_,_,_} ->
            none
    end;
extract_ste(#b_set{}) -> none.

%% Count how many times each variable is used.

count_uses(Blocks) ->
    count_uses_blk(maps:values(Blocks), #{}).

count_uses_blk([#b_blk{is=Is,last=Last}|Bs], CountMap0) ->
    F = fun(I, CountMap) ->
                foldl(fun(Var, Acc) ->
                              case Acc of
                                  #{Var:=2} -> Acc;
                                  #{Var:=C} -> Acc#{Var:=C+1};
                                  #{} ->       Acc#{Var=>1}
                              end
                      end, CountMap, beam_ssa:used(I))
        end,
    CountMap = F(Last, foldl(F, CountMap0, Is)),
    count_uses_blk(Bs, CountMap);
count_uses_blk([], CountMap) -> CountMap.

is_single_use(V, Uses) ->
    case Uses of
        #{V:=1} -> true;
        #{} -> false
    end.

%%%
%%% Find out where frames should be placed.
%%%

%% place_frames(St0) -> St.
%%   Return a list of the labels for the blocks that need stack frame
%%   allocation instructions.
%%
%%   This function attempts to place stack frames as tight as possible
%%   around the code, to avoid building stack frames for code paths
%%   that don't need one.
%%
%%   Stack frames are placed in blocks that dominate all of their
%%   descendants. That guarantees that the deallocation instructions
%%   cannot be reached from other execution paths that didn't set up
%%   a stack frame or set up a stack frame with a different size.

place_frames(#st{ssa=Blocks}=St) ->
    Ls = beam_ssa:rpo(Blocks),
    {Doms,_} = beam_ssa:dominators(Ls, Blocks),
    Tried = gb_sets:empty(),
    Frames0 = [],
    {Frames,_} = place_frames_1(Ls, Blocks, Doms, Tried, Frames0),
    St#st{frames=Frames}.

place_frames_1([L|Ls], Blocks, Doms, Tried0, Frames0) ->
    Blk = map_get(L, Blocks),
    case need_frame(Blk) of
        true ->
            %% This block needs a frame. Try to place it here.
            {Frames,Tried} = do_place_frame(L, Blocks, Doms, Tried0, Frames0),

            %% Successfully placed. Try to place more frames in descendants
            %% that are not dominated by this block.
            place_frames_1(Ls, Blocks, Doms, Tried, Frames);
        false ->
            try
                place_frames_1(Ls, Blocks, Doms, Tried0, Frames0)
            catch
                throw:{need_frame,For,Tried1}=Reason ->
                    %% An descendant block needs a stack frame. Try to
                    %% place it here.
                    case is_dominated_by(For, L, Doms) of
                        true ->
                            %% Try to place a frame here.
                            {Frames,Tried} = do_place_frame(L, Blocks, Doms,
                                                            Tried1, Frames0),
                            place_frames_1(Ls, Blocks, Doms, Tried, Frames);
                        false ->
                            %% Wrong place. This block does not dominate
                            %% the block that needs the frame. Pass it on
                            %% to our ancestors.
                            throw(Reason)
                    end
            end
    end;
place_frames_1([], _, _, Tried, Frames) ->
    {Frames,Tried}.

%% do_place_frame(Label, Blocks, Dominators, Tried0, Frames0) -> {Frames,Tried}.
%%  Try to place a frame in this block. This function returns
%%  successfully if it either succeds at placing a frame in this
%%  block, if an ancestor that dominates this block has already placed
%%  a frame, or if we have already tried to put a frame in this block.
%%
%%  An {need_frame,Label,Tried} exception will be thrown if this block
%%  block is not suitable for having a stack frame (i.e. it does not dominate
%%  all of its descendants). The exception means that an ancestor will have to
%%  place the frame needed by this block.

do_place_frame(L, Blocks, Doms, Tried0, Frames) ->
    case gb_sets:is_element(L, Tried0) of
        true ->
            %% We have already tried to put a frame in this block.
            {Frames,Tried0};
        false ->
            %% Try to place a frame in this block.
            Tried = gb_sets:insert(L, Tried0),
            case place_frame_here(L, Blocks, Doms, Frames) of
                yes ->
                    %% We need a frame and it is safe to place it here.
                    {[L|Frames],Tried};
                no ->
                    %% An ancestor has a frame. Not needed.
                    {Frames,Tried};
                ancestor ->
                    %% This block does not dominate all of its
                    %% descendants. We must place the frame in
                    %% an ancestor.
                    throw({need_frame,L,Tried})
            end
    end.

%% place_frame_here(Label, Blocks, Doms, Frames) -> no|yes|ancestor.
%%  Determine whether a frame should be placed in block Label.

place_frame_here(L, Blocks, Doms, Frames) ->
    B0 = any(fun(DomBy) ->
                     is_dominated_by(L, DomBy, Doms)
             end, Frames),
    case B0 of
        true ->
            %% This block is dominated by an ancestor block that
            %% defines a frame. Not needed/allowed to put a frame
            %% here.
            no;
        false ->
            %% No frame in any ancestor. We need a frame.
            %% Now check whether the frame can be placed here.
            %% If this block dominates all of its descendants
            %% and the predecessors of any phi nodes it can be
            %% placed here.
            Descendants = beam_ssa:rpo([L], Blocks),
            PhiPredecessors = phi_predecessors(L, Blocks),
            MustDominate = ordsets:from_list(PhiPredecessors ++ Descendants),
            Dominates = all(fun(?EXCEPTION_BLOCK) ->
                                    %% This block defines no variables and calls
                                    %% erlang:error(badarg). It does not matter
                                    %% whether L dominates ?EXCEPTION_BLOCK or not;
                                    %% it is still safe to put the frame in L.
                                    true;
                               (Bl) ->
                                    is_dominated_by(Bl, L, Doms)
                            end, MustDominate),

            %% Also, this block must not be a loop header.
            IsLoopHeader = is_loop_header(L, Blocks),
            case Dominates andalso not IsLoopHeader of
                true -> yes;
                false -> ancestor
            end
    end.

%% phi_predecessors(Label, Blocks) ->
%%  Return all predecessors referenced in phi nodes.

phi_predecessors(L, Blocks) ->
    #b_blk{is=Is} = map_get(L, Blocks),
    [P || #b_set{op=phi,args=Args} <- Is, {_,P} <- Args].

%% is_dominated_by(Label, DominatedBy, Dominators) -> true|false.
%%  Test whether block Label is dominated by block DominatedBy.

is_dominated_by(L, DomBy, Doms) ->
    DominatedBy = map_get(L, Doms),
    member(DomBy, DominatedBy).

%% need_frame(#b_blk{}) -> true|false.
%%  Test whether any of the instructions in the block requires a stack frame.

need_frame(#b_blk{is=Is,last=#b_ret{arg=Ret}}) ->
    need_frame_1(Is, {return,Ret});
need_frame(#b_blk{is=Is}) ->
    need_frame_1(Is, body).

need_frame_1([#b_set{op=old_make_fun,dst=Fun}|Is], {return,Ret}=Context) ->
    case need_frame_1(Is, Context) of
        true ->
            true;
        false ->
            %% Since old_make_fun clobbers X registers, a stack frame is
            %% needed if any of the following instructions use any
            %% other variable than the one holding the reference to
            %% the created fun.
            Defs = ordsets:from_list([Dst || #b_set{dst=Dst} <- Is]),
            Blk = #b_blk{is=Is,last=#b_ret{arg=Ret}},
            Used = ordsets:subtract(beam_ssa:used(Blk), Defs),
            case Used of
                [] -> false;
                [Fun] -> false;
                [_|_] -> true
            end
        end;
need_frame_1([#b_set{op=new_try_tag}|_], _) ->
    true;
need_frame_1([#b_set{op=call,dst=Val}]=Is, {return,Ret}) ->
    if
        Val =:= Ret -> need_frame_1(Is, tail);
        true -> need_frame_1(Is, body)
    end;
need_frame_1([#b_set{op=call,args=[Func|_]}|Is], Context) ->
    case Func of
        #b_remote{mod=#b_literal{val=Mod},
                  name=#b_literal{val=Name},
                  arity=Arity} when is_atom(Mod), is_atom(Name) ->
            Context =:= body orelse
                Is =/= [] orelse
                is_trap_bif(Mod, Name, Arity);
        #b_remote{} ->
            %% This is an apply(), which always needs a frame.
            true;
        #b_local{} ->
            Context =:= body orelse Is =/= [];
        _ ->
             %% A fun call always needs a frame.
            true
    end;
need_frame_1([I|Is], Context) ->
    beam_ssa:clobbers_xregs(I) orelse need_frame_1(Is, Context);
need_frame_1([], _) -> false.

%% is_trap_bif(Mod, Name, Arity) -> true|false.
%%   Test whether we need a stack frame for this BIF.

is_trap_bif(erlang, '!', 2) -> true;
is_trap_bif(erlang, link, 1) -> true;
is_trap_bif(erlang, unlink, 1) -> true;
is_trap_bif(erlang, monitor_node, 2) -> true;
is_trap_bif(erlang, group_leader, 2) -> true;
is_trap_bif(erlang, exit, 2) -> true;
is_trap_bif(_, _, _) -> false.

%%%
%%% Fix variables used in matching in receive.
%%%
%%% The loop_rec/2 instruction may return a reference to a
%%% message outside of any heap or heap fragment. If the message
%%% does not match, it is not allowed to store any reference to
%%% the message (or part of the message) on the stack. If we do,
%%% the message will be corrupted if there happens to be a GC.
%%%
%%% Here we make sure to introduce copies of variables that are
%%% matched out and subsequently used after the remove_message/0
%%% instructions. That will make sure that only X registers are
%%% used during matching.
%%%
%%% Depending on where variables are defined and used, they must
%%% be handled in two different ways.
%%%
%%% Variables that are always defined in the receive (before branching
%%% out into the different clauses of the receive) and used after the
%%% receive must be handled in the following way: Before each
%%% remove_message instruction, each such variable must be copied, and
%%% all variables must be consolidated using a phi node in the
%%% common exit block for the receive.
%%%
%%% Variables that are matched out and used in the same clause
%%% need copy instructions before the remove_message instruction
%%% in that clause.
%%%

fix_receives(#st{ssa=Blocks0,cnt=Count0}=St) ->
    {Blocks,Count} = fix_receives_1(maps:to_list(Blocks0),
                                    Blocks0, Count0),
    St#st{ssa=Blocks,cnt=Count}.

fix_receives_1([{L,Blk}|Ls], Blocks0, Count0) ->
    case Blk of
        #b_blk{is=[#b_set{op=peek_message}|_]} ->
            Rm = find_rm_blocks(L, Blocks0),
            LoopExit = find_loop_exit(Rm, Blocks0),
            RPO = beam_ssa:rpo([L], Blocks0),
            Defs0 = beam_ssa:def(RPO, Blocks0),
            CommonUsed = recv_common(Defs0, LoopExit, Blocks0),
            {Blocks1,Count1} = recv_crit_edges(Rm, LoopExit, Blocks0, Count0),
            {Blocks2,Count2} = recv_fix_common(CommonUsed, LoopExit, Rm,
                                               Blocks1, Count1),
            Defs = ordsets:subtract(Defs0, CommonUsed),
            {Blocks,Count} = fix_receive(Rm, Defs, Blocks2, Count2),
            fix_receives_1(Ls, Blocks, Count);
        #b_blk{} ->
            fix_receives_1(Ls, Blocks0, Count0)
    end;
fix_receives_1([], Blocks, Count) ->
    {Blocks,Count}.

recv_common(_Defs, none, _Blocks) ->
    %% There is no common exit block because receive is used
    %% in the tail position of a function.
    [];
recv_common(Defs, Exit, Blocks) ->
    RPO = beam_ssa:rpo([Exit], Blocks),
    {ExitDefs,ExitUnused} = beam_ssa:def_unused(RPO, Defs, Blocks),
    Def = ordsets:subtract(Defs, ExitDefs),
    ordsets:subtract(Def, ExitUnused).

%% recv_crit_edges([RemoveMessageLabel], LoopExit,
%%                 Blocks0, Count0) -> {Blocks,Count}.
%%
%%  Adds dummy blocks on all conditional jumps to the exit block so that
%%  recv_fix_common/5 can insert phi nodes without having to worry about
%%  critical edges.

recv_crit_edges(_Rms, none, Blocks0, Count0) ->
    {Blocks0, Count0};
recv_crit_edges(Rms, Exit, Blocks0, Count0) ->
    Ls = beam_ssa:rpo(Rms, Blocks0),
    rce_insert_edges(Ls, Exit, Count0, Blocks0).

rce_insert_edges([L | Ls], Exit, Count0, Blocks0) ->
    Successors = beam_ssa:successors(map_get(L, Blocks0)),
    case member(Exit, Successors) of
        true when Successors =/= [Exit] ->
            {Blocks, Count} = rce_insert_edge(L, Exit, Count0, Blocks0),
            rce_insert_edges(Ls, Exit, Count, Blocks);
        _ ->
            rce_insert_edges(Ls, Exit, Count0, Blocks0)
    end;
rce_insert_edges([], _Exit, Count, Blocks) ->
    {Blocks, Count}.

rce_insert_edge(L, Exit, Count, Blocks0) ->
    #b_blk{last=Last0} = FromBlk0 = map_get(L, Blocks0),

    ToExit = #b_br{bool=#b_literal{val=true},succ=Exit,fail=Exit},

    FromBlk = FromBlk0#b_blk{last=rce_reroute_terminator(Last0, Exit, Count)},
    EdgeBlk = #b_blk{anno=#{},is=[],last=ToExit},

    Blocks = Blocks0#{ Count => EdgeBlk, L => FromBlk },
    {Blocks, Count + 1}.

rce_reroute_terminator(#b_br{succ=Exit}=Last, Exit, New) ->
    rce_reroute_terminator(Last#b_br{succ=New}, Exit, New);
rce_reroute_terminator(#b_br{fail=Exit}=Last, Exit, New) ->
    rce_reroute_terminator(Last#b_br{fail=New}, Exit, New);
rce_reroute_terminator(#b_br{}=Last, _Exit, _New) ->
    Last;
rce_reroute_terminator(#b_switch{fail=Exit}=Last, Exit, New) ->
    rce_reroute_terminator(Last#b_switch{fail=New}, Exit, New);
rce_reroute_terminator(#b_switch{list=List0}=Last, Exit, New) ->
    List = [if
                Lbl =:= Exit -> {Arg, New};
                Lbl =/= Exit -> {Arg, Lbl}
            end || {Arg, Lbl} <- List0],
    Last#b_switch{list=List}.

%% recv_fix_common([CommonVar], LoopExit, [RemoveMessageLabel],
%%                 Blocks0, Count0) -> {Blocks,Count}.
%%  Handle variables alwys defined in a receive and used
%%  in the exit block following the receive.

recv_fix_common([Msg0|T], Exit, Rm, Blocks0, Count0) ->
    {Msg,Count1} = new_var('@recv', Count0),
    RPO = beam_ssa:rpo([Exit], Blocks0),
    Blocks1 = beam_ssa:rename_vars(#{Msg0=>Msg}, RPO, Blocks0),
    N = length(Rm),
    {MsgVars,Count} = new_vars(duplicate(N, '@recv'), Count1),
    PhiArgs = fix_exit_phi_args(MsgVars, Rm, Exit, Blocks1),
    Phi = #b_set{op=phi,dst=Msg,args=PhiArgs},
    ExitBlk0 = map_get(Exit, Blocks1),
    ExitBlk = ExitBlk0#b_blk{is=[Phi|ExitBlk0#b_blk.is]},
    Blocks2 = Blocks1#{Exit:=ExitBlk},
    Blocks = recv_fix_common_1(MsgVars, Rm, Msg0, Blocks2),
    recv_fix_common(T, Exit, Rm, Blocks, Count);
recv_fix_common([], _, _, Blocks, Count) ->
    {Blocks,Count}.

recv_fix_common_1([V|Vs], [Rm|Rms], Msg, Blocks0) ->
    Ren = #{Msg=>V},
    RPO = beam_ssa:rpo([Rm], Blocks0),
    Blocks1 = beam_ssa:rename_vars(Ren, RPO, Blocks0),
    #b_blk{is=Is0} = Blk0 = map_get(Rm, Blocks1),
    Copy = #b_set{op=copy,dst=V,args=[Msg]},
    Is = insert_after_phis(Is0, [Copy]),
    Blk = Blk0#b_blk{is=Is},
    Blocks = Blocks1#{Rm:=Blk},
    recv_fix_common_1(Vs, Rms, Msg, Blocks);
recv_fix_common_1([], [], _Msg, Blocks) -> Blocks.

fix_exit_phi_args([V|Vs], [Rm|Rms], Exit, Blocks) ->
    Path = beam_ssa:rpo([Rm], Blocks),
    Preds = exit_predecessors(Path, Exit, Blocks),
    [{V,Pred} || Pred <- Preds] ++ fix_exit_phi_args(Vs, Rms, Exit, Blocks);
fix_exit_phi_args([], [], _, _) -> [].

exit_predecessors([L|Ls], Exit, Blocks) ->
    Blk = map_get(L, Blocks),
    case member(Exit, beam_ssa:successors(Blk)) of
        true ->
            [L|exit_predecessors(Ls, Exit, Blocks)];
        false ->
            exit_predecessors(Ls, Exit, Blocks)
    end;
exit_predecessors([], _Exit, _Blocks) -> [].

%% fix_receive([Label], Defs, Blocks0, Count0) -> {Blocks,Count}.
%%  Add a copy instruction for all variables that are matched out and
%%  later used within a clause of the receive.

fix_receive([L|Ls], Defs, Blocks0, Count0) ->
    RPO = beam_ssa:rpo([L], Blocks0),
    {RmDefs,Unused} = beam_ssa:def_unused(RPO, Defs, Blocks0),
    Def = ordsets:subtract(Defs, RmDefs),
    Used = ordsets:subtract(Def, Unused),
    {NewVars,Count} = new_vars([Base || #b_var{name=Base} <- Used], Count0),
    Ren = zip(Used, NewVars),
    Blocks1 = beam_ssa:rename_vars(Ren, RPO, Blocks0),
    #b_blk{is=Is0} = Blk1 = map_get(L, Blocks1),
    CopyIs = [#b_set{op=copy,dst=New,args=[Old]} || {Old,New} <- Ren],
    Is = insert_after_phis(Is0, CopyIs),
    Blk = Blk1#b_blk{is=Is},
    Blocks = Blocks1#{L:=Blk},
    fix_receive(Ls, Defs, Blocks, Count);
fix_receive([], _Defs, Blocks, Count) ->
    {Blocks,Count}.

%% find_loop_exit([Label], Blocks) -> Label | none.
%%  Given the list of all blocks with the remove_message instructions
%%  for this receive, find the block to which control is transferred
%%  when the receive loop is exited (if any).

find_loop_exit([_,_|_]=RmBlocks, Blocks) ->
    %% We used to only analyze the path from two of the remove_message
    %% blocks. That would fail to find a common block if one or both
    %% of the blocks happened to raise an exception. To be sure that
    %% we always find a common block if there is one (shared by at
    %% least two clauses), we must analyze the path from all
    %% remove_message blocks.
    RPO = beam_ssa:rpo(Blocks),
    {Dominators,_} = beam_ssa:dominators(RPO, Blocks),
    RmSet = cerl_sets:from_list(RmBlocks),
    RmRPO = beam_ssa:rpo(RmBlocks, Blocks),
    find_loop_exit_1(RmRPO, RmSet, Dominators, Blocks);
find_loop_exit(_, _) ->
    %% There is (at most) a single clause. There is no common
    %% loop exit block.
    none.

find_loop_exit_1([?EXCEPTION_BLOCK|Ls], RmSet, Dominators, Blocks) ->
    %% ?EXCEPTION_BLOCK is a marker and not an actual block, so it is not
    %% the block we are looking for.
    find_loop_exit_1(Ls, RmSet, Dominators, Blocks);
find_loop_exit_1([L|Ls0], RmSet, Dominators, Blocks) ->
    DomBy = map_get(L, Dominators),
    case any(fun(E) -> cerl_sets:is_element(E, RmSet) end, DomBy) of
        true ->
            %% This block is dominated by one of the remove_message blocks,
            %% which means that the block is part of only one clause.
            %% It is not the block we are looking for.
            find_loop_exit_1(Ls0, RmSet, Dominators, Blocks);
        false ->
            %% This block is the first block that is not dominated by
            %% any of the blocks with remove_message instructions.
            case map_get(L, Blocks) of
                #b_blk{is=[#b_set{op=landingpad}|_]} ->
                    %% This is the landing pad reached when an
                    %% exception is caught. It is not the block
                    %% we are looking for. Furthermore, none of the
                    %% blocks reachable from this block can be
                    %% the exit block we are looking for.
                    Ls = Ls0 -- beam_ssa:rpo([L], Blocks),
                    find_loop_exit_1(Ls, RmSet, Dominators, Blocks);
                #b_blk{} ->
                    %% This block is not dominated by any of the receive
                    %% clauses and is not the landing pad for an exception.
                    %% It is the common exit block we are looking for.
                    L
            end
    end;
find_loop_exit_1([], _, _, _) ->
    %% None of clauses transfers control to a common block after the receive
    %% statement. That means that the receive statement is a the end of a
    %% function (or that all clauses raise exceptions).
    none.

%% find_rm_blocks(StartLabel, Blocks) -> [Label].
%%  Find all blocks that start with remove_message within the receive
%%  loop whose peek_message label is StartLabel.

find_rm_blocks(L, Blocks) ->
    Seen = gb_sets:singleton(L),
    Blk = map_get(L, Blocks),
    Succ = beam_ssa:successors(Blk),
    find_rm_blocks_1(Succ, Seen, Blocks).

find_rm_blocks_1([L|Ls], Seen0, Blocks) ->
    case gb_sets:is_member(L, Seen0) of
        true ->
            find_rm_blocks_1(Ls, Seen0, Blocks);
        false ->
            Seen = gb_sets:insert(L, Seen0),
            Blk = map_get(L, Blocks),
            case find_rm_act(Blk#b_blk.is) of
                prune ->
                    %% Looping back. Don't look at any successors.
                    find_rm_blocks_1(Ls, Seen, Blocks);
                continue ->
                    %% Neutral block. Do nothing here, but look at
                    %% all successors.
                    Succ = beam_ssa:successors(Blk),
                    find_rm_blocks_1(Succ++Ls, Seen, Blocks);
                found ->
                    %% Found remove_message instruction.
                    [L|find_rm_blocks_1(Ls, Seen, Blocks)]
            end
    end;
find_rm_blocks_1([], _, _) -> [].

find_rm_act([#b_set{op=Op}|Is]) ->
    case Op of
        remove_message -> found;
        peek_message -> prune;
        recv_next -> prune;
        wait_timeout -> prune;
        wait -> prune;
        _ -> find_rm_act(Is)
    end;
find_rm_act([]) ->
    continue.

%%%
%%% Find out which variables need to be stored in Y registers.
%%%

-record(dk, {d :: ordsets:ordset(var_name()),
             k :: cerl_sets:set(var_name())
            }).

%% find_yregs(St0) -> St.
%%  Find all variables that must be stored in Y registers. Annotate
%%  the blocks that allocate frames with the set of Y registers
%%  used within that stack frame.
%%
%%  Basically, we following all execution paths starting from a block
%%  that allocates a frame, keeping track of of all defined registers
%%  and all registers killed by an instruction that clobbers X
%%  registers. For every use of a variable, we check if if it is in
%%  the set of killed variables; if it is, it must be stored in an Y
%%  register.

find_yregs(#st{frames=[]}=St) ->
    St;
find_yregs(#st{frames=[_|_]=Frames,args=Args,ssa=Blocks0}=St) ->
    FrameDefs = find_defs(Frames, Blocks0, [V || #b_var{}=V <- Args]),
    Blocks = find_yregs_1(FrameDefs, Blocks0),
    St#st{ssa=Blocks}.

find_yregs_1([{F,Defs}|Fs], Blocks0) ->
    DK = #dk{d=Defs,k=cerl_sets:new()},
    D0 = #{F=>DK},
    Ls = beam_ssa:rpo([F], Blocks0),
    Yregs0 = cerl_sets:new(),
    Yregs = find_yregs_2(Ls, Blocks0, D0, Yregs0),
    Blk0 = map_get(F, Blocks0),
    Blk = beam_ssa:add_anno(yregs, Yregs, Blk0),
    Blocks = Blocks0#{F:=Blk},
    find_yregs_1(Fs, Blocks);
find_yregs_1([], Blocks) -> Blocks.

find_yregs_2([L|Ls], Blocks0, D0, Yregs0) ->
    Blk0 = map_get(L, Blocks0),
    #b_blk{is=Is,last=Last} = Blk0,
    Ys0 = map_get(L, D0),
    {Yregs1,Ys} = find_yregs_is(Is, Ys0, Yregs0),
    Yregs = find_yregs_terminator(Last, Ys, Yregs1),
    Successors = beam_ssa:successors(Blk0),
    D = find_update_succ(Successors, Ys, D0),
    find_yregs_2(Ls, Blocks0, D, Yregs);
find_yregs_2([], _Blocks, _D, Yregs) -> Yregs.

find_defs(Frames, Blocks, Defs) ->
    Seen = gb_sets:empty(),
    FramesSet = gb_sets:from_list(Frames),
    {FrameDefs,_} = find_defs_1([0], Blocks, FramesSet, Seen, Defs, []),
    FrameDefs.

find_defs_1([L|Ls], Blocks, Frames, Seen0, Defs0, Acc0) ->
    case gb_sets:is_member(L, Frames) of
        true ->
            OrderedDefs = ordsets:from_list(Defs0),
            find_defs_1(Ls, Blocks, Frames, Seen0, Defs0,
                        [{L,OrderedDefs}|Acc0]);
        false ->
            case gb_sets:is_member(L, Seen0) of
                true ->
                    find_defs_1(Ls, Blocks, Frames, Seen0, Defs0, Acc0);
                false ->
                    Seen1 = gb_sets:insert(L, Seen0),
                    {Acc,Seen} = find_defs_1(Ls, Blocks, Frames, Seen1, Defs0, Acc0),
                    #b_blk{is=Is} = Blk = map_get(L, Blocks),
                    Defs = find_defs_is(Is, Defs0),
                    Successors = beam_ssa:successors(Blk),
                    find_defs_1(Successors, Blocks, Frames, Seen, Defs, Acc)
            end
    end;
find_defs_1([], _, _, Seen, _, Acc) ->
    {Acc,Seen}.

find_defs_is([#b_set{dst=Dst}|Is], Acc) ->
    find_defs_is(Is, [Dst|Acc]);
find_defs_is([], Acc) -> Acc.

find_update_succ([S|Ss], #dk{d=Defs0,k=Killed0}=DK0, D0) ->
    case D0 of
        #{S:=#dk{d=Defs1,k=Killed1}} ->
            Defs = ordsets:intersection(Defs0, Defs1),
            Killed = cerl_sets:union(Killed0, Killed1),
            DK = #dk{d=Defs,k=Killed},
            D = D0#{S:=DK},
            find_update_succ(Ss, DK0, D);
        #{} ->
            D = D0#{S=>DK0},
            find_update_succ(Ss, DK0, D)
    end;
find_update_succ([], _, D) -> D.

find_yregs_is([#b_set{dst=Dst}=I|Is], #dk{d=Defs0,k=Killed0}=Ys, Yregs0) ->
    Yregs1 = intersect_used(I, Killed0),
    Yregs = cerl_sets:union(Yregs0, Yregs1),
    case beam_ssa:clobbers_xregs(I) of
        false ->
            Defs = ordsets:add_element(Dst, Defs0),
            find_yregs_is(Is, Ys#dk{d=Defs}, Yregs);
        true ->
            Killed = cerl_sets:union(cerl_sets:from_list(Defs0), Killed0),
            Defs = [Dst],
            find_yregs_is(Is, Ys#dk{d=Defs,k=Killed}, Yregs)
    end;
find_yregs_is([], Ys, Yregs) -> {Yregs,Ys}.

find_yregs_terminator(Terminator, #dk{k=Killed}, Yregs0) ->
    Yregs = intersect_used(Terminator, Killed),
    cerl_sets:union(Yregs0, Yregs).

intersect_used(#b_br{bool=#b_var{}=V}, Set) ->
    intersect_used_keep_singleton(V, Set);
intersect_used(#b_ret{arg=#b_var{}=V}, Set) ->
    intersect_used_keep_singleton(V, Set);
intersect_used(#b_set{op=phi,args=Args}, Set) ->
    cerl_sets:from_list([V || {#b_var{}=V,_} <- Args, cerl_sets:is_element(V, Set)]);
intersect_used(#b_set{args=Args}, Set) ->
    cerl_sets:from_list(intersect_used_keep(used_args(Args), Set));
intersect_used(#b_switch{arg=#b_var{}=V}, Set) ->
    intersect_used_keep_singleton(V, Set);
intersect_used(_, _) -> cerl_sets:new().

intersect_used_keep_singleton(V, Set) ->
    case cerl_sets:is_element(V, Set) of
        true -> cerl_sets:from_list([V]);
        false -> cerl_sets:new()
    end.

intersect_used_keep(Vs, Set) ->
    [V || V <- Vs, cerl_sets:is_element(V, Set)].

used_args([#b_var{}=V|As]) ->
    [V|used_args(As)];
used_args([#b_remote{mod=Mod,name=Name}|As]) ->
    used_args([Mod,Name|As]);
used_args([_|As]) ->
    used_args(As);
used_args([]) -> [].

%%%
%%% Try to reduce the size of the stack frame, by adding an explicit
%%% 'copy' instructions for return values from 'call' and 'old_make_fun' that
%%% need to be saved in Y registers. Here is an example to show
%%% how that's useful. First, here is the Erlang code:
%%%
%%% f(Pid) ->
%%%    Res = foo(42),
%%%    _ = node(Pid),
%%%    bar(),
%%%    Res.
%%%
%%% Compiled to SSA format, the main part of the code looks like this:
%%%
%%% 0:
%%%   Res = call local literal foo/1, literal 42
%%%   @ssa_bool:1 = succeeded:body Res
%%%   br @ssa_bool:1, label 2, label 1
%%% 2:
%%%   _1 = bif:node Pid
%%%   @ssa_bool:2 = succeeded:body _1
%%%   br @ssa_bool:2, label 3, label 1
%%% 3:
%%%   _2 = call local literal bar/0
%%%   @ssa_bool:3 = succeeded:body _2
%%%   br @ssa_bool:3, label 4, label 1
%%% 4:
%%%   ret Res
%%%
%%% It can be seen that the variables Pid and Res must be saved in Y
%%% registers in order to survive the function calls. A previous sub
%%% pass has inserted a 'copy' instruction to save the value of the
%%% variable Pid:
%%%
%%% 0:
%%%   Pid:4 = copy Pid
%%%   Res = call local literal foo/1, literal 42
%%%   @ssa_bool:1 = succeeded:body Res
%%%   br @ssa_bool:1, label 2, label 1
%%% 2:
%%%   _1 = bif:node Pid:4
%%%   @ssa_bool:2 = succeeded:body _1
%%%   br @ssa_bool:2, label 3, label 1
%%% 3:
%%%   _2 = call local literal bar/0
%%%   @ssa_bool:3 = succeeded:body _2
%%%   br @ssa_bool:3, label 4, label 1
%%% 4:
%%%   ret Res
%%%
%%% The Res and Pid:4 variables must be assigned to different Y registers
%%% because they are live at the same time. copy_retval() inserts a
%%% 'copy' instruction to copy Res to a new variable:
%%%
%%% 0:
%%%   Pid:4 = copy Pid
%%%   Res:6 = call local literal foo/1, literal 42
%%%   @ssa_bool:1 = succeeded:body Res:6
%%%   br @ssa_bool:1, label 2, label 1
%%% 2:
%%%   _1 = bif:node Pid:4
%%%   @ssa_bool:2 = succeeded:body _1
%%%   br @ssa_bool:2, label 3, label 1
%%% 3:
%%%   Res = copy Res:6
%%%   _2 = call local literal bar/0
%%%   @ssa_bool:3 = succeeded:body _2
%%%   br @ssa_bool:3, label 4, label 1
%%% 4:
%%%   ret Res
%%%
%%% The new variable Res:6 is used to capture the return value from the call.
%%% The variables Pid:4 and Res are no longer live at the same time, so they
%%% can be assigned to the same Y register.
%%%

copy_retval(#st{frames=Frames,ssa=Blocks0,cnt=Count0}=St) ->
    {Blocks,Count} = copy_retval_1(Frames, Blocks0, Count0),
    St#st{ssa=Blocks,cnt=Count}.

copy_retval_1([F|Fs], Blocks0, Count0) ->
    #b_blk{anno=#{yregs:=Yregs0},is=Is} = map_get(F, Blocks0),
    Yregs = collect_yregs(Is, Yregs0),
    Ls = beam_ssa:rpo([F], Blocks0),
    {Blocks,Count} = copy_retval_2(Ls, Yregs, none, Blocks0, Count0),
    copy_retval_1(Fs, Blocks, Count);
copy_retval_1([], Blocks, Count) ->
    {Blocks,Count}.

collect_yregs([#b_set{op=copy,dst=Y,args=[#b_var{}=X]}|Is],
              Yregs0) ->
    true = cerl_sets:is_element(X, Yregs0),        %Assertion.
    Yregs = cerl_sets:add_element(Y, cerl_sets:del_element(X, Yregs0)),
    collect_yregs(Is, Yregs);
collect_yregs([#b_set{}|Is], Yregs) ->
    collect_yregs(Is, Yregs);
collect_yregs([], Yregs) -> Yregs.

copy_retval_2([L|Ls], Yregs, Copy0, Blocks0, Count0) ->
    #b_blk{is=Is0,last=Last} = Blk = map_get(L, Blocks0),
    RC = case {Last,Ls} of
             {#b_br{succ=Succ,fail=?EXCEPTION_BLOCK},[Succ|_]} ->
                 true;
             {_,_} ->
                 false
         end,
    case copy_retval_is(Is0, RC, Yregs, Copy0, Count0, []) of
        {Is,Count} ->
            case Copy0 =:= none andalso Count0 =:= Count of
                true ->
                    copy_retval_2(Ls, Yregs, none, Blocks0, Count0);
                false ->
                    Blocks = Blocks0#{L=>Blk#b_blk{is=Is}},
                    copy_retval_2(Ls, Yregs, none, Blocks, Count)
            end;
        {Is,Count,Copy} ->
            Blocks = Blocks0#{L=>Blk#b_blk{is=Is}},
            copy_retval_2(Ls, Yregs, Copy, Blocks, Count)
    end;
copy_retval_2([], _Yregs, none, Blocks, Count) ->
    {Blocks,Count}.

copy_retval_is([#b_set{op=put_tuple_elements,args=Args0}=I0], false, _Yregs,
           Copy, Count, Acc) ->
    I = I0#b_set{args=copy_sub_args(Args0, Copy)},
    {reverse(Acc, [I|acc_copy([], Copy)]),Count};
copy_retval_is([#b_set{op=Op}=I0], false, Yregs, Copy, Count0, Acc0)
  when Op =:= call; Op =:= old_make_fun ->
    {I,Count,Acc} = place_retval_copy(I0, Yregs, Copy, Count0, Acc0),
    {reverse(Acc, [I]),Count};
copy_retval_is([#b_set{}]=Is, false, _Yregs, Copy, Count, Acc) ->
    {reverse(Acc, acc_copy(Is, Copy)),Count};
copy_retval_is([#b_set{},#b_set{op=succeeded}]=Is, false, _Yregs, Copy, Count, Acc) ->
    {reverse(Acc, acc_copy(Is, Copy)),Count};
copy_retval_is([#b_set{op=Op,dst=#b_var{name=RetName}=Dst}=I0|Is], RC, Yregs,
           Copy0, Count0, Acc0) when Op =:= call; Op =:= old_make_fun ->
    {I1,Count1,Acc} = place_retval_copy(I0, Yregs, Copy0, Count0, Acc0),
    case cerl_sets:is_element(Dst, Yregs) of
        true ->
            {NewVar,Count} = new_var(RetName, Count1),
            Copy = #b_set{op=copy,dst=Dst,args=[NewVar]},
            I = I1#b_set{dst=NewVar},
            copy_retval_is(Is, RC, Yregs, Copy, Count, [I|Acc]);
        false ->
            copy_retval_is(Is, RC, Yregs, none, Count1, [I1|Acc])
    end;
copy_retval_is([#b_set{args=Args0}=I0|Is], RC, Yregs, Copy, Count, Acc) ->
    I = I0#b_set{args=copy_sub_args(Args0, Copy)},
    case beam_ssa:clobbers_xregs(I) of
        true ->
            copy_retval_is(Is, RC, Yregs, none, Count, [I|acc_copy(Acc, Copy)]);
        false ->
            copy_retval_is(Is, RC, Yregs, Copy, Count, [I|Acc])
        end;
copy_retval_is([], RC, _, Copy, Count, Acc) ->
    case {Copy,RC} of
        {none,_} ->
            {reverse(Acc),Count};
        {#b_set{},true} ->
            {reverse(Acc),Count,Copy};
        {#b_set{},false} ->
            {reverse(Acc, [Copy]),Count}
    end.

%%
%% Consider this code:
%%
%%   Var = ...
%%   ...
%%   A1 = call foo/0
%%   A = copy A1
%%   B = call bar/1, Var
%%
%% If the Var variable is no longer used after this code, its Y register
%% can't be reused for A. To allow the Y register to be reused
%% we will need to insert 'copy' instructions for arguments that are
%% in Y registers:
%%
%%   Var = ...
%%   ...
%%   A1 = call foo/0
%%   Var1 = copy Var
%%   A = copy A1
%%   B = call bar/1, Var1
%%

place_retval_copy(I, _Yregs, none, Count, Acc) ->
    {I,Count,Acc};
place_retval_copy(#b_set{args=[F|Args0]}=I, Yregs, Copy, Count0, Acc0) ->
    #b_set{dst=Avoid} = Copy,
    {Args,Acc1,Count} = copy_func_args(Args0, Yregs, Avoid, Acc0, [], Count0),
    Acc = [Copy|Acc1],
    {I#b_set{args=[F|Args]},Count,Acc}.

copy_func_args([#b_var{name=AName}=A|As], Yregs, Avoid, CopyAcc, Acc, Count0) ->
    case cerl_sets:is_element(A, Yregs) of
        true when A =/= Avoid ->
            {NewVar,Count} = new_var(AName, Count0),
            Copy = #b_set{op=copy,dst=NewVar,args=[A]},
            copy_func_args(As, Yregs, Avoid, [Copy|CopyAcc], [NewVar|Acc], Count);
        _ ->
            copy_func_args(As, Yregs, Avoid, CopyAcc, [A|Acc], Count0)
    end;
copy_func_args([A|As], Yregs, Avoid, CopyAcc, Acc, Count) ->
    copy_func_args(As, Yregs, Avoid, CopyAcc, [A|Acc], Count);
copy_func_args([], _Yregs, _Avoid, CopyAcc, Acc, Count) ->
    {reverse(Acc),CopyAcc,Count}.

acc_copy(Acc, none) -> Acc;
acc_copy(Acc, #b_set{}=Copy) -> [Copy|Acc].

copy_sub_args(Args, none) ->
    Args;
copy_sub_args(Args, #b_set{dst=Dst,args=[Src]}) ->
    [sub_arg(A, Dst, Src) || A <- Args].

sub_arg(Old, Old, New) -> New;
sub_arg(Old, _, _) -> Old.

%%%
%%% Consider:
%%%
%%%   x1/Hd = get_hd x0/Cons
%%%   y0/Tl = get_tl x0/Cons
%%%
%%% Register x0 can't be reused for Hd. If Hd needs to be in x0,
%%% a 'move' instruction must be inserted.
%%%
%%% If we swap get_hd and get_tl when Tl is in a Y register,
%%% x0 can be used for Hd if Cons is not used again:
%%%
%%%   y0/Tl = get_tl x0/Cons
%%%   x0/Hd = get_hd x0/Cons
%%%

opt_get_list(#st{ssa=Blocks,res=Res}=St) ->
    ResMap = maps:from_list(Res),
    Ls = beam_ssa:rpo(Blocks),
    St#st{ssa=opt_get_list_1(Ls, ResMap, Blocks)}.

opt_get_list_1([L|Ls], Res, Blocks0) ->
    #b_blk{is=Is0} = Blk = map_get(L, Blocks0),
    case opt_get_list_is(Is0, Res, [], false) of
        no ->
            opt_get_list_1(Ls, Res, Blocks0);
        {yes,Is} ->
            Blocks = Blocks0#{L:=Blk#b_blk{is=Is}},
            opt_get_list_1(Ls, Res, Blocks)
    end;
opt_get_list_1([], _, Blocks) -> Blocks.

opt_get_list_is([#b_set{op=get_hd,dst=Hd,
                        args=[Cons]}=GetHd,
                 #b_set{op=get_tl,dst=Tl,
                        args=[Cons]}=GetTl|Is],
                Res, Acc, Changed) ->
    %% Note that when this pass is run, only Y registers have
    %% reservations. The absence of an entry for a variable therefore
    %% means that the variable will be in an X register.
    case Res of
        #{Hd:={y,_}} ->
            %% Hd will be in a Y register. Don't swap.
            opt_get_list_is([GetTl|Is], Res, [GetHd|Acc], Changed);
        #{Tl:={y,_}} ->
            %% Tl will be in a Y register. Swap.
            opt_get_list_is([GetHd|Is], Res, [GetTl|Acc], true);
        #{} ->
            %% Both are in X registers. Nothing to do.
            opt_get_list_is([GetTl|Is], Res, [GetHd|Acc], Changed)
    end;
opt_get_list_is([I|Is], Res, Acc, Changed) ->
    opt_get_list_is(Is, Res, [I|Acc], Changed);
opt_get_list_is([], _Res, Acc, Changed) ->
    case Changed of
        true ->
            {yes,reverse(Acc)};
        false ->
            no
    end.

%%%
%%% Number instructions in the order they are executed.
%%%

%% number_instructions(St0) -> St.
%%  Number instructions in the order they are executed. Use a step
%%  size of 2. Don't number phi instructions. All phi variables in
%%  a block will be live one unit before the first non-phi instruction
%%  in the block.

number_instructions(#st{ssa=Blocks0}=St) ->
    Ls = beam_ssa:rpo(Blocks0),
    St#st{ssa=number_is_1(Ls, 1, Blocks0)}.

number_is_1([L|Ls], N0, Blocks0) ->
    #b_blk{is=Is0,last=Last0} = Bl0 = map_get(L, Blocks0),
    {Is,N1} = number_is_2(Is0, N0, []),
    Last = beam_ssa:add_anno(n, N1, Last0),
    N = N1 + 2,
    Bl = Bl0#b_blk{is=Is,last=Last},
    Blocks = Blocks0#{L:=Bl},
    number_is_1(Ls, N, Blocks);
number_is_1([], _, Blocks) -> Blocks.

number_is_2([#b_set{op=phi}=I|Is], N, Acc) ->
    number_is_2(Is, N, [I|Acc]);
number_is_2([I0|Is], N, Acc) ->
    I = beam_ssa:add_anno(n, N, I0),
    number_is_2(Is, N+2, [I|Acc]);
number_is_2([], N, Acc) ->
    {reverse(Acc),N}.

%%%
%%% Calculate live intervals.
%%%

live_intervals(#st{args=Args,ssa=Blocks}=St) ->
    Vars0 = [{V,{0,1}} || #b_var{}=V <- Args],
    PO = reverse(beam_ssa:rpo(Blocks)),
    Vars = live_interval_blk(PO, Blocks, Vars0, #{}),
    Intervals = merge_ranges(rel2fam(Vars)),
    St#st{intervals=Intervals}.

merge_ranges([{V,Rs}|T]) ->
    [{V,merge_ranges_1(Rs)}|merge_ranges(T)];
merge_ranges([]) -> [].

merge_ranges_1([{A,N},{N,Z}|Rs]) ->
    merge_ranges_1([{A,Z}|Rs]);
merge_ranges_1([R|Rs]) ->
    [R|merge_ranges_1(Rs)];
merge_ranges_1([]) -> [].

live_interval_blk([L|Ls], Blocks, Vars0, LiveMap0) ->
    Live0 = [],
    Blk = map_get(L, Blocks),
    Successors = beam_ssa:successors(Blk),
    Live1 = update_successors(Successors, L, Blocks, LiveMap0, Live0),

    %% Add ranges for all variables that are live in the successors.
    #b_blk{is=Is,last=Last} = Blk,
    End = beam_ssa:get_anno(n, Last),
    EndUse = {use,End+1},
    Use = [{V,EndUse} || V <- Live1],

    %% Determine used and defined variables in this block.
    FirstNumber = first_number(Is, Last),
    UseDef0 = live_interval_last(Last, Use),
    UseDef1 = live_interval_blk_is(Is, FirstNumber, UseDef0),
    UseDef = rel2fam(UseDef1),

    %% Update what is live at the beginning of this block and
    %% store it.
    Live = [V || {V,[{use,_}|_]} <- UseDef],
    LiveMap = LiveMap0#{L=>Live},

    %% Construct the ranges for this block.
    Vars = make_block_ranges(UseDef, FirstNumber, Vars0),
    live_interval_blk(Ls, Blocks, Vars, LiveMap);
live_interval_blk([], _Blocks, Vars, _LiveMap) ->
    Vars.

live_interval_last(I, Acc) ->
    N = beam_ssa:get_anno(n, I),
    Used = beam_ssa:used(I),
    [{V,{use,N}} || V <- Used] ++ Acc.

live_interval_blk_is([#b_set{op=phi,dst=Dst}|Is], FirstNumber, Acc0) ->
    Acc = [{Dst,{def,FirstNumber}}|Acc0],
    live_interval_blk_is(Is, FirstNumber, Acc);
live_interval_blk_is([#b_set{dst=Dst}=I|Is], FirstNumber, Acc0) ->
    N = beam_ssa:get_anno(n, I),
    Acc1 = [{Dst,{def,N}}|Acc0],
    Used = beam_ssa:used(I),
    Acc = [{V,{use,N}} || V <- Used] ++ Acc1,
    live_interval_blk_is(Is, FirstNumber, Acc);
live_interval_blk_is([], _FirstNumber, Acc) ->
    Acc.

make_block_ranges([{V,[{def,Def}]}|Vs], First, Acc) ->
    make_block_ranges(Vs, First, [{V,{Def,Def}}|Acc]);
make_block_ranges([{V,[{def,Def}|Uses]}|Vs], First, Acc) ->
    {use,Last} = last(Uses),
    make_block_ranges(Vs, First, [{V,{Def,Last}}|Acc]);
make_block_ranges([{V,[{use,_}|_]=Uses}|Vs], First, Acc) ->
    {use,Last} = last(Uses),
    make_block_ranges(Vs, First, [{V,{First,Last}}|Acc]);
make_block_ranges([], _, Acc) -> Acc.

%% first_number([#b_set{}]) -> InstructionNumber.
%%  Return the number for the first instruction for the block.
%%  Note that this number is one less than the first
%%  non-phi instruction in the block.

first_number([#b_set{op=phi}|Is], Last) ->
    first_number(Is, Last);
first_number([I|_], _) ->
    beam_ssa:get_anno(n, I) - 1;
first_number([], Last) ->
    beam_ssa:get_anno(n, Last) - 1.

update_successors([L|Ls], Pred, Blocks, LiveMap, Live0) ->
    Live1 = ordsets:union(Live0, get_live(L, LiveMap)),
    #b_blk{is=Is} = map_get(L, Blocks),
    Live = update_live_phis(Is, Pred, Live1),
    update_successors(Ls, Pred, Blocks, LiveMap, Live);
update_successors([], _, _, _, Live) -> Live.

get_live(L, LiveMap) ->
    case LiveMap of
        #{L:=Live} -> Live;
        #{} -> []
    end.

update_live_phis([#b_set{op=phi,dst=Killed,args=Args}|Is],
                 Pred, Live0) ->
    Used = [V || {#b_var{}=V,L} <- Args, L =:= Pred],
    Live1 = ordsets:union(ordsets:from_list(Used), Live0),
    Live = ordsets:del_element(Killed, Live1),
    update_live_phis(Is, Pred, Live);
update_live_phis(_, _, Live) -> Live.

%%%
%%% Reserve Y registers.
%%%

%% reserve_yregs(St0) -> St.
%%  In each block that allocates a stack frame, insert instructions
%%  that copy variables that must be in Y registers (given by
%%  the `yregs` annotation) to new variables.
%%
%%  Also allocate specific Y registers for try and catch tags.
%%  The outermost try/catch tag is placed in y0, any directly
%%  nested tag in y1, and so on. Note that this is the reversed
%%  order as required by BEAM; it will be corrected later by
%%  turn_yregs().

reserve_yregs(#st{frames=Frames}=St0) ->
    foldl(fun reserve_yregs_1/2, St0, Frames).

reserve_yregs_1(L, #st{ssa=Blocks0,cnt=Count0,res=Res0}=St) ->
    Blk = map_get(L, Blocks0),
    Yregs = ordsets:from_list(cerl_sets:to_list(beam_ssa:get_anno(yregs, Blk))),
    RPO = beam_ssa:rpo([L], Blocks0),
    {Def,Unused} = beam_ssa:def_unused(RPO, Yregs, Blocks0),
    UsedYregs = ordsets:subtract(Yregs, Unused),
    DefBefore = ordsets:subtract(UsedYregs, Def),
    {BeforeVars,Blocks,Count} = rename_vars(DefBefore, L, RPO, Blocks0, Count0),
    InsideVars = ordsets:subtract(UsedYregs, DefBefore),
    ResTryTags0 = reserve_try_tags(L, Blocks),
    ResTryTags = [{V,{Reg,Count}} || {V,Reg} <- ResTryTags0],
    Vars = BeforeVars ++ InsideVars,
    Res = [{V,{y,Count}} || V <- Vars] ++ ResTryTags ++ Res0,
    St#st{res=Res,ssa=Blocks,cnt=Count+1}.

reserve_try_tags(L, Blocks) ->
    Seen = gb_sets:empty(),
    {Res0,_} = reserve_try_tags_1([L], Blocks, Seen, #{}),
    Res1 = [maps:to_list(M) || {_,M} <- maps:to_list(Res0)],
    Res = [{V,{y,Y}} || {V,Y} <- append(Res1)],
    ordsets:from_list(Res).

reserve_try_tags_1([L|Ls], Blocks, Seen0, ActMap0) ->
    case gb_sets:is_element(L, Seen0) of
        true ->
            reserve_try_tags_1(Ls, Blocks, Seen0, ActMap0);
        false ->
            Seen1 = gb_sets:insert(L, Seen0),
            #b_blk{is=Is} = Blk = map_get(L, Blocks),
            Active0 = get_active(L, ActMap0),
            Active = reserve_try_tags_is(Is, Active0),
            Successors = beam_ssa:successors(Blk),
            ActMap1 = update_act_map(Successors, Active, ActMap0),
            {ActMap,Seen} = reserve_try_tags_1(Ls, Blocks, Seen1, ActMap1),
            reserve_try_tags_1(Successors, Blocks, Seen,ActMap)
    end;
reserve_try_tags_1([], _Blocks, Seen, ActMap) ->
    {ActMap,Seen}.

get_active(L, ActMap) ->
    case ActMap of
        #{L:=Active} -> Active;
        #{} -> #{}
    end.

reserve_try_tags_is([#b_set{op=new_try_tag,dst=V}|Is], Active) ->
    N = map_size(Active),
    reserve_try_tags_is(Is, Active#{V=>N});
reserve_try_tags_is([#b_set{op=kill_try_tag,args=[Tag]}|Is], Active) ->
    reserve_try_tags_is(Is, maps:remove(Tag, Active));
reserve_try_tags_is([_|Is], Active) ->
    reserve_try_tags_is(Is, Active);
reserve_try_tags_is([], Active) -> Active.

update_act_map([L|Ls], Active0, ActMap0) ->
    case ActMap0 of
        #{L:=Active1} ->
            ActMap = ActMap0#{L=>maps:merge(Active0, Active1)},
            update_act_map(Ls, Active0, ActMap);
        #{} ->
            ActMap = ActMap0#{L=>Active0},
            update_act_map(Ls, Active0, ActMap)
    end;
update_act_map([], _, ActMap) -> ActMap.

rename_vars([], _, _, Blocks, Count) ->
    {[],Blocks,Count};
rename_vars(Vs, L, RPO, Blocks0, Count0) ->
    {NewVars,Count} = new_vars([Base || #b_var{name=Base} <- Vs], Count0),
    Ren = zip(Vs, NewVars),
    Blocks1 = beam_ssa:rename_vars(Ren, RPO, Blocks0),
    #b_blk{is=Is0} = Blk0 = map_get(L, Blocks1),
    CopyIs = [#b_set{op=copy,dst=New,args=[Old]} || {Old,New} <- Ren],
    Is = insert_after_phis(Is0, CopyIs),
    Blk = Blk0#b_blk{is=Is},
    Blocks = Blocks1#{L:=Blk},
    {NewVars,Blocks,Count}.

insert_after_phis([#b_set{op=phi}=I|Is], InsertIs) ->
    [I|insert_after_phis(Is, InsertIs)];
insert_after_phis(Is, InsertIs) ->
    InsertIs ++ Is.

%% frame_size(St0) -> St.
%%  Calculate the frame size for each block that allocates a frame.
%%  Annotate the block with the frame size. Also annotate all
%%  return instructions with {deallocate,FrameSize} to simplify
%%  code generation.

frame_size(#st{frames=Frames,regs=Regs,ssa=Blocks0}=St) ->
    Blocks = foldl(fun(L, Blks) ->
                           frame_size_1(L, Regs, Blks)
                   end, Blocks0, Frames),
    St#st{ssa=Blocks}.

frame_size_1(L, Regs, Blocks0) ->
    RPO = beam_ssa:rpo([L], Blocks0),
    Def = beam_ssa:def(RPO, Blocks0),
    Yregs0 = [map_get(V, Regs) || V <- Def, is_yreg(map_get(V, Regs))],
    Yregs = ordsets:from_list(Yregs0),
    FrameSize = length(ordsets:from_list(Yregs)),
    if
        FrameSize =/= 0 ->
            [{y,0}|_] = Yregs,                  %Assertion.
            {y,Last} = last(Yregs),
            Last = FrameSize - 1,               %Assertion.
            ok;
        true ->
            ok
    end,
    Blk0 = map_get(L, Blocks0),
    Blk = beam_ssa:add_anno(frame_size, FrameSize, Blk0),

    %% Insert an annotation for frame deallocation on
    %% each #b_ret{}.
    Blocks = Blocks0#{L:=Blk},
    Reachable = beam_ssa:rpo([L], Blocks),
    frame_deallocate(Reachable, FrameSize, Blocks).

frame_deallocate([L|Ls], Size, Blocks0) ->
    Blk0 = map_get(L, Blocks0),
    Blk = case Blk0 of
              #b_blk{last=#b_ret{}=Ret0} ->
                  Ret = beam_ssa:add_anno(deallocate, Size, Ret0),
                  Blk0#b_blk{last=Ret};
              #b_blk{} ->
                  Blk0
          end,
    Blocks = Blocks0#{L:=Blk},
    frame_deallocate(Ls, Size, Blocks);
frame_deallocate([], _, Blocks) -> Blocks.


%% turn_yregs(St0) -> St.
%%  Renumber y registers so that {y,0} becomes {y,FrameSize-1},
%%  {y,FrameSize-1} becomes {y,0} and so on. This is to make nested
%%  catches work. The register allocator (linear_scan()) has given
%%  a lower number to the outermost catch.

turn_yregs(#st{frames=Frames,regs=Regs0,ssa=Blocks}=St) ->
    Regs1 = foldl(fun(L, A) ->
                          Blk = map_get(L, Blocks),
                          FrameSize = beam_ssa:get_anno(frame_size, Blk),
                          RPO = beam_ssa:rpo([L], Blocks),
                          Def = beam_ssa:def(RPO, Blocks),
                          [turn_yregs_1(Def, FrameSize, Regs0)|A]
                  end, [], Frames),
    Regs = maps:merge(Regs0, maps:from_list(append(Regs1))),
    St#st{regs=Regs}.

turn_yregs_1(Def, FrameSize, Regs) ->
    Yregs0 = [{map_get(V, Regs),V} || V <- Def, is_yreg(map_get(V, Regs))],
    Yregs1 = rel2fam(Yregs0),
    FrameSize = length(Yregs1),
    Yregs2 = [{{y,FrameSize-Y-1},Vs} || {{y,Y},Vs} <- Yregs1],
    R0 = sofs:family(Yregs2),
    R1 = sofs:family_to_relation(R0),
    R = sofs:converse(R1),
    sofs:to_external(R).

%%%
%%% Reserving registers before register allocation.
%%%

%% reserve_regs(St0) -> St.
%%  Reserve registers prior to register allocation. Y registers
%%  have already been reserved. This function will reserve z,
%%  fr, and specific x registers.

reserve_regs(#st{args=Args,ssa=Blocks,intervals=Intervals,res=Res0}=St) ->
    %% Reserve x0, x1, and so on for the function arguments.
    Res1 = reserve_arg_regs(Args, 0, Res0),
    RPO = beam_ssa:rpo(Blocks),

    %% Reserve Z registers (dummy registers) for instructions with no
    %% return values (e.g. remove_message) or pseudo-return values
    %% (e.g. landingpad).
    Res2 = reserve_zregs(RPO, Blocks, Intervals, Res1),

    %% Reserve float registers.
    Res3 = reserve_fregs(RPO, Blocks, Res2),

    %% Reserve all remaining unreserved variables as X registers.
    Res = maps:from_list(Res3),
    St#st{res=reserve_xregs(RPO, Blocks, Res)}.

reserve_arg_regs([#b_var{}=Arg|Is], N, Acc) ->
    reserve_arg_regs(Is, N+1, [{Arg,{x,N}}|Acc]);
reserve_arg_regs([], _, Acc) -> Acc.

reserve_zregs(RPO, Blocks, Intervals, Res) ->
    ShortLived0 = [V || {V,[{Start,End}]} <- Intervals, Start+2 =:= End],
    ShortLived = cerl_sets:from_list(ShortLived0),
    F = fun(_, #b_blk{is=Is,last=Last}, A) ->
                reserve_zreg(Is, Last, ShortLived, A)
        end,
    beam_ssa:fold_blocks(F, RPO, Res, Blocks).

reserve_zreg([#b_set{op={bif,tuple_size},dst=Dst},
              #b_set{op={bif,'=:='},args=[Dst,Val],dst=Bool}],
             Last, ShortLived, A) ->
    case {Val,Last} of
        {#b_literal{val=Arity},#b_br{bool=Bool}} when Arity bsr 32 =:= 0 ->
            %% These two instructions can be combined to a test_arity
            %% instruction provided that the arity variable is short-lived.
            reserve_test_zreg(Dst, ShortLived, A);
        {_,_} ->
            %% Either the arity is too big, or the boolean value is not
            %% used in a conditional branch.
            A
    end;
reserve_zreg([#b_set{op={bif,tuple_size},dst=Dst}],
             #b_switch{arg=Dst}, ShortLived, A) ->
    reserve_test_zreg(Dst, ShortLived, A);
reserve_zreg([#b_set{op=Op,dst=Dst}], #b_br{bool=Dst}, ShortLived, A) ->
    case use_zreg(Op) of
        yes -> [{Dst,z} | A];
        no -> A;
        maybe -> reserve_test_zreg(Dst, ShortLived, A)
    end;
reserve_zreg([#b_set{op=Op,dst=Dst} | Is], Last, ShortLived, A) ->
    case use_zreg(Op) of
        yes -> reserve_zreg(Is, Last, ShortLived, [{Dst,z} | A]);
        _Other -> reserve_zreg(Is, Last, ShortLived, A)
    end;
reserve_zreg([], _, _, A) -> A.

use_zreg(bs_match_string) -> yes;
use_zreg(bs_save) -> yes;
use_zreg(bs_restore) -> yes;
use_zreg(bs_set_position) -> yes;
use_zreg({float,clearerror}) -> yes;
use_zreg(kill_try_tag) -> yes;
use_zreg(landingpad) -> yes;
use_zreg(put_tuple_elements) -> yes;
use_zreg(remove_message) -> yes;
use_zreg(set_tuple_element) -> yes;
use_zreg(succeeded) -> yes;
use_zreg(timeout) -> yes;
use_zreg(wait_timeout) -> yes;
%% There's no way we can combine these into a test instruction, so we must
%% avoid using a z register if their result is used directly in a branch.
use_zreg(call) -> no;
use_zreg({bif,is_map_key}) -> no;
use_zreg({bif,is_record}) -> no;
use_zreg({bif,map_get}) -> no;
use_zreg({bif,'xor'}) -> no;
use_zreg(get_hd) -> no;
use_zreg(get_tl) -> no;
use_zreg(get_tuple_element) -> no;
%% Assume the instruction can use a z register, provided it's the last in its
%% block and that the result is only used in the terminator.
use_zreg(_) -> maybe.

%% If V is defined just before a branch, we may be able to combine it into a
%% test instruction.
reserve_test_zreg(#b_var{}=V, ShortLived, A) ->
    case cerl_sets:is_element(V, ShortLived) of
        true -> [{V,z}|A];
        false -> A
    end.

reserve_fregs(RPO, Blocks, Res) ->
    F = fun(_, #b_blk{is=Is}, A) ->
                reserve_freg(Is, A)
        end,
    beam_ssa:fold_blocks(F, RPO, Res, Blocks).

reserve_freg([#b_set{op={float,Op},dst=V}|Is], Res) ->
    case Op of
        get ->
            reserve_freg(Is, Res);
        _ ->
            reserve_freg(Is, [{V,fr}|Res])
    end;
reserve_freg([_|Is], Res) ->
    reserve_freg(Is, Res);
reserve_freg([], Res) -> Res.

%% reserve_xregs(St0) -> St.
%%  Reserve all remaining variables as X registers.
%%
%%  If a variable will need to be in a specific X register for a
%%  'call' or 'old_make_fun' (and there is nothing that will kill it
%%  between the definition and use), reserve the register using a
%%  {prefer,{x,X} annotation. That annotation means that the linear
%%  scan algorithm will place the variable in the preferred register,
%%  unless that register is already occupied.
%%
%%  All remaining variables are reserved as X registers. Linear scan
%%  will allocate the lowest free X register for the variable.

reserve_xregs(RPO, Blocks, Res) ->
    Ls = reverse(RPO),
    reserve_xregs(Ls, Blocks, #{}, Res).

reserve_xregs([L|Ls], Blocks, XsMap0, Res0) ->
    #b_blk{anno=Anno,is=Is0,last=Last} = map_get(L, Blocks),

    %% Calculate mapping from variable name to the preferred
    %% register.
    Xs0 = reserve_terminator(L, Is0, Last, Blocks, XsMap0, Res0),

    %% We need to figure out where the code generator will
    %% place instructions that will do a garbage collection.
    %% Insert 'gc' markers as pseudo-instructions in the
    %% instruction sequence.
    Is1 = reverse(Is0),
    Is2 = res_place_gc_instrs(Is1, []),
    Is = res_place_allocate(Anno, Is2),

    %% Add register hints for variables that are defined
    %% in the (reversed) instruction sequence.
    {Res,Xs} = reserve_xregs_is(Is, Res0, Xs0, []),

    XsMap = XsMap0#{L=>Xs},
    reserve_xregs(Ls, Blocks, XsMap, Res);
reserve_xregs([], _, _, Res) -> Res.

%% Insert explicit 'gc' markers points where there will
%% be a garbage collection. (Note that the instruction
%% sequence passed to this function is reversed.)

res_place_gc_instrs([#b_set{op=phi}=I|Is], Acc) ->
    res_place_gc_instrs(Is, [I|Acc]);
res_place_gc_instrs([#b_set{op=Op}=I|Is], Acc)
  when Op =:= call; Op =:= old_make_fun ->
    case Acc of
        [] ->
            res_place_gc_instrs(Is, [I|Acc]);
        [GC|_] when GC =:= gc; GC =:= test_heap ->
            res_place_gc_instrs(Is, [I,gc|Acc]);
        [_|_] ->
            res_place_gc_instrs(Is, [I,gc|Acc])
    end;
res_place_gc_instrs([#b_set{op=Op,args=Args}=I|Is], Acc0) ->
    case beam_ssa_codegen:classify_heap_need(Op, Args) of
        neutral ->
            case Acc0 of
                [test_heap|Acc] ->
                    res_place_gc_instrs(Is, [test_heap,I|Acc]);
                Acc ->
                    res_place_gc_instrs(Is, [I|Acc])
            end;
        {put,_} ->
            res_place_gc_instrs(Is, res_place_test_heap(I, Acc0));
        {put_fun,_} ->
            res_place_gc_instrs(Is, res_place_test_heap(I, Acc0));
        put_float ->
            res_place_gc_instrs(Is, res_place_test_heap(I, Acc0));
        gc ->
            res_place_gc_instrs(Is, [gc,I|Acc0])
    end;
res_place_gc_instrs([], Acc) ->
    %% Reverse and replace 'test_heap' markers with 'gc'.
    %% (The distinction is no longer useful.)
    res_place_gc_instrs_rev(Acc, []).

res_place_test_heap(I, Acc) ->
    case Acc of
        [test_heap|Acc] ->
            [test_heap,I|Acc];
        _ ->
            [test_heap,I|Acc]
    end.

res_place_gc_instrs_rev([test_heap|Is], [gc|_]=Acc) ->
    res_place_gc_instrs_rev(Is, Acc);
res_place_gc_instrs_rev([test_heap|Is], Acc) ->
    res_place_gc_instrs_rev(Is, [gc|Acc]);
res_place_gc_instrs_rev([gc|Is], [gc|_]=Acc) ->
    res_place_gc_instrs_rev(Is, Acc);
res_place_gc_instrs_rev([I|Is], Acc) ->
    res_place_gc_instrs_rev(Is, [I|Acc]);
res_place_gc_instrs_rev([], Acc) -> Acc.

res_place_allocate(#{yregs:=_}, Is) ->
    %% There will be an 'allocate' instruction inserted here.
    Is ++ [gc];
res_place_allocate(#{}, Is) -> Is.

reserve_xregs_is([gc|Is], Res, Xs0, Used) ->
    %% At this point, the code generator will place an instruction
    %% that does a garbage collection. We must prune the remembered
    %% registers.
    Xs = res_xregs_prune(Xs0, Used, Res),
    reserve_xregs_is(Is, Res, Xs, Used);
reserve_xregs_is([#b_set{op=Op,dst=Dst,args=Args}=I|Is], Res0, Xs0, Used0) ->
    Res = reserve_xreg(Dst, Xs0, Res0),
    Used1 = ordsets:union(Used0, beam_ssa:used(I)),
    Used = ordsets:del_element(Dst, Used1),
    case Op of
        call ->
            Xs = reserve_call_args(tl(Args)),
            reserve_xregs_is(Is, Res, Xs, Used);
        old_make_fun ->
            Xs = reserve_call_args(tl(Args)),
            reserve_xregs_is(Is, Res, Xs, Used);
        _ ->
            reserve_xregs_is(Is, Res, Xs0, Used)
    end;
reserve_xregs_is([], Res, Xs, _Used) ->
    {Res,Xs}.

%% Pick up register hints from the successors of this blocks.
reserve_terminator(L, Is, #b_br{bool=#b_var{},succ=Succ,fail=Fail},
                   Blocks, XsMap, Res) when Succ =/= Fail,
                                            Fail =/= ?EXCEPTION_BLOCK ->
    #{Succ:=SuccBlk,Fail:=FailBlk} = Blocks,
    case {SuccBlk,FailBlk} of
        {#b_blk{is=[],last=#b_br{succ=PhiL,fail=PhiL}},
         #b_blk{is=[],last=#b_br{succ=PhiL,fail=PhiL}}} ->
            %% Both branches ultimately transfer to the same
            %% block (via two blocks with no instructions).
            %% Pick up register hints from the phi nodes
            %% in the common block.
            #{PhiL:=#b_blk{is=PhiIs}} = Blocks,
            Xs = res_xregs_from_phi(PhiIs, Succ, Res, #{}),
            res_xregs_from_phi(PhiIs, Fail, Res, Xs);
        {_,_} when Is =/= [] ->
            case last(Is) of
                #b_set{op=succeeded,args=[Arg]} ->
                    %% We know that Arg will not be used at the failure
                    %% label, so we can pick up register hints from the
                    %% success label.
                    Br = #b_br{bool=#b_literal{val=true},succ=Succ,fail=Succ},
                    case reserve_terminator(L, [], Br, Blocks, XsMap, Res) of
                        #{Arg:=Reg} -> #{Arg=>Reg};
                        #{} -> #{}
                    end;
                _ ->
                    %% Register hints from the success block may not
                    %% be safe at the failure block, and vice versa.
                    #{}
            end;
        {_,_} ->
            %% Register hints from the success block may not
            %% be safe at the failure block, and vice versa.
            #{}
    end;
reserve_terminator(L, Is, #b_br{bool=Bool,succ=Succ,fail=Fail},
                   Blocks, XsMap, Res) ->
    case {Bool, Fail} of
        {_, ?EXCEPTION_BLOCK} ->
            %% We know that no variables are used from ?EXCEPTION_BLOCK, so any
            %% register hints from the successor block are safe to use.
            reserve_terminator_1(L, Succ, Is, Blocks, XsMap, Res);
        {#b_literal{val=true}, _} ->
            %% We only have one successor, so its hints are safe to use.
            reserve_terminator_1(L, Succ, Is, Blocks, XsMap, Res);
        {_, _} ->
            %% Register hints from the success block may not
            %% be safe at the failure block, and vice versa.
            #{}
    end;
reserve_terminator(_, _, _, _, _, _) ->
    #{}.

reserve_terminator_1(L, Succ, _Is, Blocks, XsMap, Res) ->
    case {Blocks, XsMap} of
        {#{ Succ := #b_blk{is=[#b_set{op=phi}|_]=PhiIs}}, #{}} ->
            res_xregs_from_phi(PhiIs, L, Res, #{});
        {#{}, #{ Succ := Xs }}->
            Xs;
        {#{}, #{}} ->
            #{}
    end.

%% Pick up a reservation from a phi node.
res_xregs_from_phi([#b_set{op=phi,dst=Dst,args=Args}|Is],
                   Pred, Res, Acc) ->
    case [V || {#b_var{}=V,L} <- Args, L =:= Pred] of
        [] ->
            %% The value of the phi node for this predecessor
            %% is a literal. Nothing to do here.
            res_xregs_from_phi(Is, Pred, Res, Acc);
        [V] ->
            case Res of
                #{Dst:={prefer,Reg}} ->
                    %% Try placing V in the same register as for
                    %% the phi node.
                    res_xregs_from_phi(Is, Pred, Res, Acc#{V=>Reg});
                #{Dst:=_} ->
                    res_xregs_from_phi(Is, Pred, Res, Acc)
            end
    end;
res_xregs_from_phi(_, _, _, Acc) -> Acc.

reserve_call_args(Args) ->
    reserve_call_args(Args, 0, #{}).

reserve_call_args([#b_var{}=Var|As], X, Xs) ->
    reserve_call_args(As, X+1, Xs#{Var=>{x,X}});
reserve_call_args([#b_literal{}|As], X, Xs) ->
    reserve_call_args(As, X+1, Xs);
reserve_call_args([], _, Xs) -> Xs.

reserve_xreg(V, Xs, Res) ->
    case Res of
        #{V:=_} ->
            %% Already reserved (but not as an X register).
            Res;
        #{} ->
            case Xs of
                #{V:=X} ->
                    %% Add a hint that this specific X register is
                    %% preferred, unless it is already in use.
                    Res#{V=>{prefer,X}};
                #{} ->
                    %% Reserve as an X register in general.
                    Res#{V=>x}
            end
    end.

%% res_xregs_prune(PreferredRegs, Used, Res) -> PreferredRegs.
%%  Prune the list of preferred registers, to make sure that
%%  there are no "holes" (uninitialized X registers) when
%%  invoking the garbage collector.

res_xregs_prune(Xs, Used, Res) when map_size(Xs) =/= 0 ->
    %% The number of safe registers is the number of the X registers
    %% used after this point. The actual number of safe registers may
    %% be higher than this number, but this is a conservative safe
    %% estimate.
    NumSafe = foldl(fun(V, N) ->
                            case Res of
                                #{V:={x,_}} -> N + 1;
                                #{V:=_} -> N;
                                #{} -> N + 1
                            end
                    end, 0, Used),

    %% Remove unsafe registers from the list of potential
    %% preferred registers.
    maps:filter(fun(_, {x,X}) -> X < NumSafe end, Xs);
res_xregs_prune(Xs, _Used, _Res) -> Xs.

%%%
%%% Register allocation using linear scan.
%%%

-record(i,
        {sort=1 :: instr_number(),
         reg=none :: i_reg(),
         pool=x :: pool_id(),
         var=#b_var{} :: b_var(),
         rs=[] :: [range()]
        }).

-record(l,
        {cur=#i{} :: interval(),
         unhandled_res=[] :: [interval()],
         unhandled_any=[] :: [interval()],
         active=[] :: [interval()],
         inactive=[] :: [interval()],
         free=#{} :: #{var_name()=>pool(),
                       {'next',pool_id()}:=reg_num()},
         regs=[] :: [{b_var(),ssa_register()}]
        }).

-type interval() :: #i{}.
-type i_reg() :: ssa_register() | {'prefer',xreg()} | 'none'.
-type pool_id() :: 'fr' | 'x' | 'z' | instr_number().
-type pool() :: ordsets:ordset(ssa_register()).

linear_scan(#st{intervals=Intervals0,res=Res}=St0) ->
    St = St0#st{intervals=[],res=[]},
    Free = init_free(maps:to_list(Res)),
    Intervals1 = [init_interval(Int, Res) || Int <- Intervals0],
    Intervals = sort(Intervals1),
    IsReserved = fun(#i{reg=Reg}) ->
                         case Reg of
                             none -> false;
                             {prefer,{_,_}} -> false;
                             {_,_} -> true
                         end
                 end,
    {UnhandledRes,Unhandled} = partition(IsReserved, Intervals),
    L = #l{unhandled_res=UnhandledRes,
           unhandled_any=Unhandled,free=Free},
    #l{regs=Regs} = do_linear(L),
    St#st{regs=maps:from_list(Regs)}.

init_interval({V,[{Start,_}|_]=Rs}, Res) ->
    Info = map_get(V, Res),
    Pool = case Info of
               {prefer,{x,_}} -> x;
               x -> x;
               {x,_} -> x;
               {y,Uniq} -> Uniq;
               {{y,_},Uniq} -> Uniq;
               z -> z;
               fr -> fr
           end,
    Reg = case Info of
              {prefer,{x,_}} -> Info;
              {x,_} -> Info;
              {{y,_}=Y,_} -> Y;
              _ -> none
          end,
    #i{sort=Start,var=V,reg=Reg,pool=Pool,rs=Rs}.

init_free(Res) ->
    Free0 = rel2fam([{x,{x,0}}|init_free_1(Res)]),
    #{x:=Xs0} = Free1 = maps:from_list(Free0),
    Xs = init_xregs(Xs0),
    Free = Free1#{x:=Xs},
    Next = maps:fold(fun(K, V, A) -> [{{next,K},length(V)}|A] end, [], Free),
    maps:merge(Free, maps:from_list(Next)).

init_free_1([{_,{prefer,{x,_}=Reg}}|Res]) ->
    [{x,Reg}|init_free_1(Res)];
init_free_1([{_,{x,_}=Reg}|Res]) ->
    [{x,Reg}|init_free_1(Res)];
init_free_1([{_,{y,Uniq}}|Res]) ->
    [{Uniq,{y,0}}|init_free_1(Res)];
init_free_1([{_,{{y,_}=Reg,Uniq}}|Res]) ->
    [{Uniq,Reg}|init_free_1(Res)];
init_free_1([{_,z}|Res]) ->
    [{z,{z,0}}|init_free_1(Res)];
init_free_1([{_,fr}|Res]) ->
    [{fr,{fr,0}}|init_free_1(Res)];
init_free_1([{_,x}|Res]) ->
    init_free_1(Res);
init_free_1([]) -> [].

%% Make sure that the pool of xregs is contiguous.
init_xregs([{x,N},{x,M}|Is]) when N+1 =:= M ->
    [{x,N}|init_xregs([{x,M}|Is])];
init_xregs([{x,N}|[{x,_}|_]=Is]) ->
    [{x,N}|init_xregs([{x,N+1}|Is])];
init_xregs([{x,_}]=Is) -> Is.

do_linear(L0) ->
    case set_next_current(L0) of
        done ->
            L0;
        L1 ->
            L2 = expire_active(L1),
            L3 = check_inactive(L2),
            Available = collect_available(L3),
            L4 = select_register(Available, L3),
            L = make_cur_active(L4),
            do_linear(L)
    end.

set_next_current(#l{unhandled_res=[Cur1|T1],
                    unhandled_any=[Cur2|T2]}=L) ->
    case {Cur1,Cur2} of
        {#i{sort=N1},#i{sort=N2}} when N1 < N2 ->
            L#l{cur=Cur1,unhandled_res=T1};
        {_,_} ->
            L#l{cur=Cur2,unhandled_any=T2}
    end;
set_next_current(#l{unhandled_res=[],
                    unhandled_any=[Cur|T]}=L) ->
    L#l{cur=Cur,unhandled_any=T};
set_next_current(#l{unhandled_res=[Cur|T],
                    unhandled_any=[]}=L) ->
    L#l{cur=Cur,unhandled_res=T};
set_next_current(#l{unhandled_res=[],unhandled_any=[]}) ->
    done.

expire_active(#l{cur=#i{sort=CurBegin},active=Act0}=L0) ->
    {Act,L} = expire_active(Act0, CurBegin, L0, []),
    L#l{active=Act}.

expire_active([#i{reg=Reg,rs=Rs0}=I|Is], CurBegin, L0, Acc) ->
    {_,_} = Reg,                                %Assertion.
    case overlap_status(Rs0, CurBegin) of
        ends_before_cur ->
            L = free_reg(I, L0),
            expire_active(Is, CurBegin, L, Acc);
        overlapping ->
            expire_active(Is, CurBegin, L0, [I|Acc]);
        not_overlapping ->
            Rs = strip_before_current(Rs0, CurBegin),
            L1 = free_reg(I, L0),
            L = L1#l{inactive=[I#i{rs=Rs}|L1#l.inactive]},
            expire_active(Is, CurBegin, L, Acc)
    end;
expire_active([], _CurBegin, L, Acc) ->
    {Acc,L}.

check_inactive(#l{cur=#i{sort=CurBegin},inactive=InAct0}=L0) ->
    {InAct,L} = check_inactive(InAct0, CurBegin, L0, []),
    L#l{inactive=InAct}.

check_inactive([#i{rs=Rs0}=I|Is], CurBegin, L0, Acc) ->
    case overlap_status(Rs0, CurBegin) of
        ends_before_cur ->
            check_inactive(Is, CurBegin, L0, Acc);
        not_overlapping ->
            check_inactive(Is, CurBegin, L0, [I|Acc]);
        overlapping ->
            Rs = strip_before_current(Rs0, CurBegin),
            L1 = L0#l{active=[I#i{rs=Rs}|L0#l.active]},
            L = reserve_reg(I, L1),
            check_inactive(Is, CurBegin, L, Acc)
    end;
check_inactive([], _CurBegin, L, Acc) ->
    {Acc,L}.

strip_before_current([{_,E}|Rs], CurBegin) when E =< CurBegin ->
    strip_before_current(Rs, CurBegin);
strip_before_current(Rs, _CurBegin) -> Rs.

collect_available(#l{cur=#i{reg={prefer,{_,_}=Prefer}}=I}=L) ->
    %% Use the preferred register if it is available.
    Avail = collect_available(L#l{cur=I#i{reg=none}}),
    case member(Prefer, Avail) of
        true -> [Prefer];
        false -> Avail
    end;
collect_available(#l{cur=#i{reg={_,_}=ReservedReg}}) ->
    %% Return the already reserved register.
    [ReservedReg];
collect_available(#l{unhandled_res=Unhandled,cur=Cur}=L) ->
    Free = get_pool(Cur, L),

    %% Note that since the live intervals are constructed from
    %% SSA form, there cannot be any overlap of the current interval
    %% with any inactive interval. See [3], page 175. Therefore we
    %% only have check the unhandled intervals for overlap with
    %% the current interval. As a further optimization, we only need
    %% to check the intervals that have reserved registers.
    collect_available(Unhandled, Cur, Free).

collect_available([#i{pool=Pool1}|Is], #i{pool=Pool2}=Cur, Free)
  when Pool1 =/= Pool2 ->
    %% Wrong pool. Ignore this interval.
    collect_available(Is, Cur, Free);
collect_available([#i{reg={_,_}=Reg}=I|Is], Cur, Free0) ->
    case overlaps(I, Cur) of
        true ->
            Free = ordsets:del_element(Reg, Free0),
            collect_available(Is, Cur, Free);
        false ->
            collect_available(Is, Cur, Free0)
    end;
collect_available([], _, Free) -> Free.

select_register([{_,_}=Reg|_], #l{cur=Cur0,regs=Regs}=L) ->
    Cur = Cur0#i{reg=Reg},
    reserve_reg(Cur, L#l{cur=Cur,regs=[{Cur#i.var,Reg}|Regs]});
select_register([], #l{cur=Cur0,regs=Regs}=L0) ->
    %% Allocate a new register in the pool.
    {Reg,L1} = get_next_free(Cur0, L0),
    Cur = Cur0#i{reg=Reg},
    L = L1#l{cur=Cur,regs=[{Cur#i.var,Reg}|Regs]},
    reserve_reg(Cur, L).

make_cur_active(#l{cur=Cur,active=Act}=L) ->
    L#l{active=[Cur|Act]}.

overlaps(#i{rs=Rs1}, #i{rs=Rs2}) ->
    are_overlapping(Rs1, Rs2).

overlap_status([{S,E}], CurBegin) ->
    if
        E =< CurBegin -> ends_before_cur;
        CurBegin < S -> not_overlapping;
        true -> overlapping
    end;
overlap_status([{S,E}|Rs], CurBegin) ->
    if
        E =< CurBegin ->
            overlap_status(Rs, CurBegin);
        S =< CurBegin ->
            overlapping;
        true ->
            not_overlapping
    end.

reserve_reg(#i{reg={_,_}=Reg}=I, L) ->
    FreeRegs0 = get_pool(I, L),
    FreeRegs = ordsets:del_element(Reg, FreeRegs0),
    update_pool(I, FreeRegs, L).

free_reg(#i{reg={_,_}=Reg}=I, L) ->
    FreeRegs0 = get_pool(I, L),
    FreeRegs = ordsets:add_element(Reg, FreeRegs0),
    update_pool(I, FreeRegs, L).

get_pool(#i{pool=Pool}, #l{free=Free}) ->
    map_get(Pool, Free).

update_pool(#i{pool=Pool}, New, #l{free=Free0}=L) ->
    Free = Free0#{Pool:=New},
    L#l{free=Free}.

get_next_free(#i{pool=Pool}, #l{free=Free0}=L0) ->
    K = {next,Pool},
    N = map_get(K, Free0),
    Free = Free0#{K:=N+1},
    L = L0#l{free=Free},
    if
        is_integer(Pool) -> {{y,N},L};
        is_atom(Pool)    -> {{Pool,N},L}
    end.

%%%
%%% Interval utilities.
%%%

are_overlapping([R|Rs1], Rs2) ->
    case are_overlapping_1(R, Rs2) of
        true ->
            true;
        false ->
            are_overlapping(Rs1, Rs2)
    end;
are_overlapping([], _) -> false.

are_overlapping_1({_S1,E1}, [{S2,_E2}|_]) when E1 < S2 ->
    false;
are_overlapping_1({S1,E1}=R, [{S2,E2}|Rs]) ->
    (S2 < E1 andalso E2 > S1) orelse are_overlapping_1(R, Rs);
are_overlapping_1({_,_}, []) -> false.

%%%
%%% Utilities.
%%%

%% is_loop_header(L, Blocks) -> false|true.
%%  Check whether the block is a loop header.

is_loop_header(L, Blocks) ->
    case map_get(L, Blocks) of
        #b_blk{is=[I|_]} -> beam_ssa:is_loop_header(I);
        #b_blk{} -> false
    end.

rel2fam(S0) ->
    S1 = sofs:relation(S0),
    S = sofs:rel2fam(S1),
    sofs:to_external(S).

split_phis(Is) ->
    splitwith(fun(#b_set{op=Op}) -> Op =:= phi end, Is).

is_yreg({y,_}) -> true;
is_yreg({x,_}) -> false;
is_yreg({z,_}) -> false;
is_yreg({fr,_}) -> false.

new_vars([Base|Vs0], Count0) ->
    {V,Count1} = new_var(Base, Count0),
    {Vs,Count} = new_vars(Vs0, Count1),
    {[V|Vs],Count};
new_vars([], Count) -> {[],Count}.

new_var({Base,Int}, Count)  ->
    true = is_integer(Int),                     %Assertion.
    {#b_var{name={Base,Count}},Count+1};
new_var(Base, Count) ->
    {#b_var{name={Base,Count}},Count+1}.