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%% ``The contents of this file are subject to the Erlang Public License,
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%% Version 1.1, (the "License"); you may not use this file except in
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%% compliance with the License. You should have received a copy of the
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%% Erlang Public License along with this software. If not, it can be
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%% retrieved via the world wide web at http://www.erlang.org/.
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%% Software distributed under the License is distributed on an "AS IS"
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%% basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See
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%% the License for the specific language governing rights and limitations
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%% The Initial Developer of the Original Code is Ericsson Utvecklings AB.
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%% Portions created by Ericsson are Copyright 1999, Ericsson Utvecklings
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%% AB. All Rights Reserved.''
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%% $Id: beam_type.erl,v 1.1 2008/12/17 09:53:41 mikpe Exp $
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%% Purpose : Type-based optimisations.
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-import(lists, [map/2,foldl/3,reverse/1,reverse/2,filter/2,member/2]).
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module({Mod,Exp,Attr,Fs0,Lc}, Opt) ->
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AllowFloatOpts = not member(no_float_opt, Opt),
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Fs = map(fun(F) -> function(F, AllowFloatOpts) end, Fs0),
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{ok,{Mod,Exp,Attr,Fs,Lc}}.
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function({function,Name,Arity,CLabel,Asm0}, AllowFloatOpts) ->
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Asm = opt(Asm0, AllowFloatOpts, [], tdb_new()),
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{function,Name,Arity,CLabel,Asm}.
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%% opt([Instruction], AllowFloatOpts, Accumulator, TypeDb) -> {[Instruction'],TypeDb'}
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%% Keep track of type information; try to simplify.
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opt([{block,Body1}|Is], AllowFloatOpts, [{block,Body0}|Acc], Ts0) ->
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{Body2,Ts} = simplify(Body1, Ts0, AllowFloatOpts),
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Body = beam_block:merge_blocks(Body0, Body2),
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opt(Is, AllowFloatOpts, [{block,Body}|Acc], Ts);
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opt([{block,Body0}|Is], AllowFloatOpts, Acc, Ts0) ->
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{Body,Ts} = simplify(Body0, Ts0, AllowFloatOpts),
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opt(Is, AllowFloatOpts, [{block,Body}|Acc], Ts);
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opt([I0|Is], AllowFloatOpts, Acc, Ts0) ->
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case simplify([I0], Ts0, AllowFloatOpts) of
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{[],Ts} -> opt(Is, AllowFloatOpts, Acc, Ts);
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{[I],Ts} -> opt(Is, AllowFloatOpts, [I|Acc], Ts)
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opt([], _, Acc, _) -> reverse(Acc).
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%% simplify(Instruction, TypeDb, AllowFloatOpts) -> NewInstruction
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%% Simplify an instruction using type information (this is
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%% technically a "strength reduction").
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simplify(Is, TypeDb, false) ->
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simplify(Is, TypeDb, no_float_opt, []);
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simplify(Is, TypeDb, true) ->
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case are_live_regs_determinable(Is) of
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false -> simplify(Is, TypeDb, no_float_opt, []);
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true -> simplify(Is, TypeDb, [], [])
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simplify([{set,[D],[{integer,Index},Reg],{bif,element,_}}=I0|Is]=Is0, Ts0, Rs0, Acc0) ->
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I = case max_tuple_size(Reg, Ts0) of
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Sz when 0 < Index, Index =< Sz ->
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{set,[D],[Reg],{get_tuple_element,Index-1}};
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{Rs,Acc} = flush(Rs0, Is0, Acc0),
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simplify(Is, Ts, Rs, [I|checkerror(Acc)]);
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simplify([{set,[D0],[A],{bif,'-',{f,0}}}=I|Is]=Is0, Ts0, Rs0, Acc0)
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when Rs0 =/= no_float_opt ->
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case tdb_find(A, Ts0) of
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{Rs1,Acc1} = load_reg(A, Ts0, Rs0, Acc0),
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{D,Rs} = find_dest(D0, Rs1),
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Areg = fetch_reg(A, Rs),
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Acc = [{set,[D],[Areg],{bif,fnegate,{f,0}}}|clearerror(Acc1)],
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Ts = tdb_update([{D0,float}], Ts0),
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simplify(Is, Ts, Rs, Acc);
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{Rs,Acc} = flush(Rs0, Is0, Acc0),
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simplify(Is, Ts, Rs, [I|checkerror(Acc)])
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simplify([{set,[_],[_],{bif,_,{f,0}}}=I|Is]=Is0, Ts0, Rs0, Acc0) ->
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{Rs,Acc} = flush(Rs0, Is0, Acc0),
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simplify(Is, Ts, Rs, [I|checkerror(Acc)]);
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simplify([{set,[D0],[A,B],{bif,Op0,{f,0}}}=I|Is]=Is0, Ts0, Rs0, Acc0)
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when Rs0 =/= no_float_opt ->
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case float_op(Op0, A, B, Ts0) of
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{Rs,Acc} = flush(Rs0, Is0, Acc0),
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simplify(Is, Ts, Rs, [I|checkerror(Acc)]);
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{Rs1,Acc1} = load_reg(A, Ts0, Rs0, Acc0),
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{Rs2,Acc2} = load_reg(B, Ts0, Rs1, Acc1),
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{D,Rs} = find_dest(D0, Rs2),
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Areg = fetch_reg(A, Rs),
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Breg = fetch_reg(B, Rs),
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Acc = [{set,[D],[Areg,Breg],{bif,Op,{f,0}}}|clearerror(Acc2)],
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Ts = tdb_update([{D0,float}], Ts0),
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simplify(Is, Ts, Rs, Acc)
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simplify([{set,[D],[TupleReg],{get_tuple_element,0}}=I|Is0], Ts0, Rs0, Acc0) ->
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case tdb_find(TupleReg, Ts0) of
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{tuple,_,[Contents]} ->
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Ts = tdb_update([{D,Contents}], Ts0),
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{Rs,Acc} = flush(Rs0, Is0, Acc0),
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simplify(Is0, Ts, Rs, [{set,[D],[Contents],move}|Acc]);
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{Rs,Acc} = flush(Rs0, Is0, Acc0),
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simplify(Is0, Ts, Rs, [I|checkerror(Acc)])
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simplify([{set,_,_,{'catch',_}}=I|Is]=Is0, _Ts, Rs0, Acc0) ->
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Acc = flush_all(Rs0, Is0, Acc0),
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simplify(Is, tdb_new(), Rs0, [I|Acc]);
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simplify([{test,is_tuple,_,[R]}=I|Is], Ts, Rs, Acc) ->
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case tdb_find(R, Ts) of
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{tuple,_,_} -> simplify(Is, Ts, Rs, Acc);
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simplify(Is, Ts, Rs, [I|Acc])
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simplify([{test,test_arity,_,[R,Arity]}=I|Is], Ts0, Rs, Acc) ->
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case tdb_find(R, Ts0) of
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simplify(Is, Ts0, Rs, Acc);
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simplify(Is, Ts, Rs, [I|Acc])
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simplify([{test,is_eq_exact,Fail,[R,{atom,_}=Atom]}=I|Is0], Ts0, Rs0, Acc0) ->
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Acc1 = case tdb_find(R, Ts0) of
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{atom,_}=Atom -> Acc0;
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{atom,_} -> [{jump,Fail}|Acc0];
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{Rs,Acc} = flush(Rs0, Is0, Acc1),
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simplify(Is0, Ts, Rs, Acc);
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simplify([I|Is]=Is0, Ts0, Rs0, Acc0) ->
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{Rs,Acc} = flush(Rs0, Is0, Acc0),
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simplify(Is, Ts, Rs, [I|Acc]);
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simplify([], Ts, Rs, Acc) ->
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Is0 = reverse(flush_all(Rs, [], Acc)),
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Is1 = opt_fmoves(Is0, []),
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Is = add_ftest_heap(Is1),
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opt_fmoves([{set,[{x,_}=R],[{fr,_}]=Src,fmove}=I1,
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{set,[{y,_}]=Dst,[{x,_}=R],move}=I2|Is], Acc) ->
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case beam_block:is_killed(R, Is) of
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false -> opt_fmoves(Is, [I2,I1|Acc]);
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true -> opt_fmoves(Is, [{set,Dst,Src,fmove}|Acc])
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opt_fmoves([I|Is], Acc) ->
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opt_fmoves(Is, [I|Acc]);
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opt_fmoves([], Acc) -> reverse(Acc).
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clearerror([{set,[],[],fclearerror}|_], OrigIs) -> OrigIs;
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clearerror([{set,[],[],fcheckerror}|_], OrigIs) -> [{set,[],[],fclearerror}|OrigIs];
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clearerror([_|Is], OrigIs) -> clearerror(Is, OrigIs);
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clearerror([], OrigIs) -> [{set,[],[],fclearerror}|OrigIs].
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%% update(Instruction, TypeDb) -> NewTypeDb
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%% Update the type database to account for executing an instruction.
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%% First the cases for instructions inside basic blocks.
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update({set,[D],[S],move}, Ts0) ->
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Ops = case tdb_find(S, Ts0) of
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tdb_update(Ops, Ts0);
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update({set,[D],[{integer,I},Reg],{bif,element,_}}, Ts0) ->
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tdb_update([{Reg,{tuple,I,[]}},{D,kill}], Ts0);
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update({set,[D],[_Index,Reg],{bif,element,_}}, Ts0) ->
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tdb_update([{Reg,{tuple,0,[]}},{D,kill}], Ts0);
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update({set,[D],[S],{get_tuple_element,0}}, Ts) ->
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tdb_update([{D,{tuple_element,S,0}}], Ts);
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update({set,[D],[S],{bif,float,{f,0}}}, Ts0) ->
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%% Make sure we reject non-numeric literal argument.
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case possibly_numeric(S) of
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true -> tdb_update([{D,float}], Ts0);
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update({set,[D],[S1,S2],{bif,'/',{f,0}}}, Ts0) ->
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%% Make sure we reject non-numeric literals.
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case possibly_numeric(S1) andalso possibly_numeric(S2) of
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true -> tdb_update([{D,float}], Ts0);
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update({set,[D],[S1,S2],{bif,Op,{f,0}}}, Ts0) ->
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tdb_update([{D,kill}], Ts0);
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case {tdb_find(S1, Ts0),tdb_find(S2, Ts0)} of
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{float,_} -> tdb_update([{D,float}], Ts0);
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{_,float} -> tdb_update([{D,float}], Ts0);
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{_,_} -> tdb_update([{D,kill}], Ts0)
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update({set,[],_Src,_Op}, Ts0) -> Ts0;
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update({set,[D],_Src,_Op}, Ts0) ->
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tdb_update([{D,kill}], Ts0);
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update({set,[D1,D2],_Src,_Op}, Ts0) ->
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tdb_update([{D1,kill},{D2,kill}], Ts0);
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update({allocate,_,_}, Ts) -> Ts;
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update({init,D}, Ts) ->
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tdb_update([{D,kill}], Ts);
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update({kill,D}, Ts) ->
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tdb_update([{D,kill}], Ts);
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update({'%live',_}, Ts) -> Ts;
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%% Instructions outside of blocks.
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update({test,is_float,_Fail,[Src]}, Ts0) ->
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tdb_update([{Src,float}], Ts0);
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update({test,test_arity,_Fail,[Src,Arity]}, Ts0) ->
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tdb_update([{Src,{tuple,Arity,[]}}], Ts0);
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update({test,is_eq_exact,_,[Reg,{atom,_}=Atom]}, Ts) ->
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case tdb_find(Reg, Ts) of
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{tuple_element,TupleReg,0} ->
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tdb_update([{TupleReg,{tuple,1,[Atom]}}], Ts);
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update({test,_Test,_Fail,_Other}, Ts) -> Ts;
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update({call_ext,1,{extfunc,math,Math,1}}, Ts) ->
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case is_math_bif(Math, 1) of
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true -> tdb_update([{{x,0},float}], Ts);
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false -> tdb_kill_xregs(Ts)
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update({call_ext,2,{extfunc,math,Math,2}}, Ts) ->
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case is_math_bif(Math, 2) of
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true -> tdb_update([{{x,0},float}], Ts);
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false -> tdb_kill_xregs(Ts)
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update({call_ext,3,{extfunc,erlang,setelement,3}}, Ts0) ->
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Op = case tdb_find({x,1}, Ts0) of
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Ts1 = tdb_kill_xregs(Ts0),
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tdb_update([{{x,0},Op}], Ts1);
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update({call,_Arity,_Func}, Ts) -> tdb_kill_xregs(Ts);
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update({call_ext,_Arity,_Func}, Ts) -> tdb_kill_xregs(Ts);
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update({make_fun2,_,_,_,_}, Ts) -> tdb_kill_xregs(Ts);
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%% The instruction is unknown. Kill all information.
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update(_I, _Ts) -> tdb_new().
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is_math_bif(cos, 1) -> true;
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is_math_bif(cosh, 1) -> true;
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is_math_bif(sin, 1) -> true;
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is_math_bif(sinh, 1) -> true;
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is_math_bif(tan, 1) -> true;
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is_math_bif(tanh, 1) -> true;
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is_math_bif(acos, 1) -> true;
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is_math_bif(acosh, 1) -> true;
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is_math_bif(asin, 1) -> true;
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is_math_bif(asinh, 1) -> true;
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is_math_bif(atan, 1) -> true;
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is_math_bif(atanh, 1) -> true;
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is_math_bif(erf, 1) -> true;
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is_math_bif(erfc, 1) -> true;
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is_math_bif(exp, 1) -> true;
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is_math_bif(log, 1) -> true;
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is_math_bif(log10, 1) -> true;
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is_math_bif(sqrt, 1) -> true;
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is_math_bif(atan2, 2) -> true;
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is_math_bif(pow, 2) -> true;
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is_math_bif(pi, 0) -> true;
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is_math_bif(_, _) -> false.
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%% Reject non-numeric literals.
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possibly_numeric({x,_}) -> true;
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possibly_numeric({y,_}) -> true;
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possibly_numeric({integer,_}) -> true;
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possibly_numeric({float,_}) -> true;
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possibly_numeric(_) -> false.
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max_tuple_size(Reg, Ts) ->
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case tdb_find(Reg, Ts) of
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float_op('/', A, B, _) ->
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case possibly_numeric(A) andalso possibly_numeric(B) of
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float_op(Op, {float,_}, B, _) ->
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case possibly_numeric(B) of
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true -> arith_op(Op);
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float_op(Op, A, {float,_}, _) ->
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case possibly_numeric(A) of
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true -> arith_op(Op);
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float_op(Op, A, B, Ts) ->
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case {tdb_find(A, Ts),tdb_find(B, Ts)} of
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{float,_} -> arith_op(Op);
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{_,float} -> arith_op(Op);
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case find_reg(V, Rs0) of
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{FR,mark(V, Rs0, dirty)};
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Rs = put_reg(V, Rs0, dirty),
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{ok,FR} = find_reg(V, Rs),
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load_reg({float,_}=F, _, Rs0, Is0) ->
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Rs = put_reg(F, Rs0, clean),
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{ok,FR} = find_reg(F, Rs),
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Is = [{set,[FR],[F],fmove}|Is0],
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load_reg(V, Ts, Rs0, Is0) ->
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case find_reg(V, Rs0) of
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{ok,_FR} -> {Rs0,Is0};
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Rs = put_reg(V, Rs0, clean),
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{ok,FR} = find_reg(V, Rs),
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Op = case tdb_find(V, Ts) of
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Is = [{set,[FR],[V],Op}|Is0],
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arith_op('+') -> {yes,fadd};
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arith_op('-') -> {yes,fsub};
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arith_op('*') -> {yes,fmul};
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arith_op('/') -> {yes,fdiv};
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flush(no_float_opt, _, Acc) -> {no_float_opt,Acc};
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flush(Rs, [{set,[_],[],{put_tuple,_}}|_]=Is0, Acc0) ->
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Acc = flush_all(Rs, Is0, Acc0),
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flush(Rs0, [{set,Ds,Ss,_Op}|_], Acc0) ->
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Save = gb_sets:from_list(Ss),
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Acc = save_regs(Rs0, Save, Acc0),
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Rs1 = foldl(fun(S, A) -> mark(S, A, clean) end, Rs0, Ss),
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Kill = gb_sets:from_list(Ds),
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Rs = kill_regs(Rs1, Kill),
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flush(Rs0, Is, Acc0) ->
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Acc = flush_all(Rs0, Is, Acc0),
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flush_all(no_float_opt, _, Acc) -> Acc;
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flush_all([{_,{float,_},_}|Rs], Is, Acc) ->
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flush_all(Rs, Is, Acc);
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flush_all([{I,V,dirty}|Rs], Is, Acc0) ->
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Acc = checkerror(Acc0),
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case beam_block:is_killed(V, Is) of
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true -> flush_all(Rs, Is, Acc);
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false -> flush_all(Rs, Is, [{set,[V],[{fr,I}],fmove}|Acc])
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flush_all([{_,_,clean}|Rs], Is, Acc) -> flush_all(Rs, Is, Acc);
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flush_all([free|Rs], Is, Acc) -> flush_all(Rs, Is, Acc);
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flush_all([], _, Acc) -> Acc.
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save_regs(Rs, Save, Acc) ->
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foldl(fun(R, A) -> save_reg(R, Save, A) end, Acc, Rs).
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save_reg({I,V,dirty}, Save, Acc) ->
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case gb_sets:is_member(V, Save) of
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true -> [{set,[V],[{fr,I}],fmove}|checkerror(Acc)];
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save_reg(_, _, Acc) -> Acc.
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kill_regs(Rs, Kill) ->
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map(fun(R) -> kill_reg(R, Kill) end, Rs).
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kill_reg({_,V,_}=R, Kill) ->
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case gb_sets:is_member(V, Kill) of
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mark(V, [{I,V,_}|Rs], Mark) -> [{I,V,Mark}|Rs];
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mark(V, [R|Rs], Mark) -> [R|mark(V, Rs, Mark)];
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mark(_, [], _) -> [].
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fetch_reg(V, [{I,V,_}|_]) -> {fr,I};
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fetch_reg(V, [_|SRs]) -> fetch_reg(V, SRs).
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find_reg(V, [{I,V,_}|_]) -> {ok,{fr,I}};
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find_reg(V, [_|SRs]) -> find_reg(V, SRs);
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find_reg(_, []) -> error.
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put_reg(V, Rs, Dirty) -> put_reg_1(V, Rs, Dirty, 0).
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put_reg_1(V, [free|Rs], Dirty, I) -> [{I,V,Dirty}|Rs];
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put_reg_1(V, [R|Rs], Dirty, I) -> [R|put_reg_1(V, Rs, Dirty, I+1)];
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put_reg_1(V, [], Dirty, I) -> [{I,V,Dirty}].
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checkerror_1(Is, Is).
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checkerror_1([{set,[],[],fcheckerror}|_], OrigIs) -> OrigIs;
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checkerror_1([{set,[],[],fclearerror}|_], OrigIs) -> OrigIs;
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checkerror_1([{set,_,_,{bif,fadd,_}}|_], OrigIs) -> checkerror_2(OrigIs);
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checkerror_1([{set,_,_,{bif,fsub,_}}|_], OrigIs) -> checkerror_2(OrigIs);
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checkerror_1([{set,_,_,{bif,fmul,_}}|_], OrigIs) -> checkerror_2(OrigIs);
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checkerror_1([{set,_,_,{bif,fdiv,_}}|_], OrigIs) -> checkerror_2(OrigIs);
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checkerror_1([{set,_,_,{bif,fnegate,_}}|_], OrigIs) -> checkerror_2(OrigIs);
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checkerror_1([_|Is], OrigIs) -> checkerror_1(Is, OrigIs);
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checkerror_1([], OrigIs) -> OrigIs.
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checkerror_2(OrigIs) -> [{set,[],[],fcheckerror}|OrigIs].
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add_ftest_heap(Is) ->
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add_ftest_heap_1(reverse(Is), 0, []).
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add_ftest_heap_1([{set,_,[{fr,_}],fmove}=I|Is], Floats, Acc) ->
441
add_ftest_heap_1(Is, Floats+1, [I|Acc]);
442
add_ftest_heap_1([{allocate,_,_}=I|Is], 0, Acc) ->
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reverse(Is, [I|Acc]);
444
add_ftest_heap_1([{allocate,Regs,{Z,Stk,Heap,Inits}}|Is], Floats, Acc) ->
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reverse(Is, [{allocate,Regs,{Z,Stk,Heap,Floats,Inits}}|Acc]);
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add_ftest_heap_1([I|Is], Floats, Acc) ->
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add_ftest_heap_1(Is, Floats, [I|Acc]);
448
add_ftest_heap_1([], 0, Acc) ->
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add_ftest_heap_1([], Floats, Is) ->
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Regs = beam_block:live_at_entry(Is),
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[{allocate,Regs,{nozero,nostack,0,Floats,[]}}|Is].
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are_live_regs_determinable([{allocate,_,_}|_]) -> true;
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are_live_regs_determinable([{'%live',_}|_]) -> true;
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are_live_regs_determinable([_|Is]) -> are_live_regs_determinable(Is);
457
are_live_regs_determinable([]) -> false.
460
%%% Routines for maintaining a type database. The type database
461
%%% associates type information with registers.
463
%%% {tuple,Size,First} means that the corresponding register contains a
464
%%% tuple with *at least* Size elements. An tuple with unknown
465
%%% size is represented as {tuple,0}. First is either [] (meaning that
466
%%% the tuple's first element is unknown) or [FirstElement] (the contents
467
%%% of the first element).
469
%%% 'float' means that the register contains a float.
471
%% tdb_new() -> EmptyDataBase
472
%% Creates a new, empty type database.
476
%% tdb_find(Register, Db) -> Information|error
477
%% Returns type information or the atom error if there are no type
478
%% information available for Register.
480
tdb_find(Key, [{K,_}|_]) when Key < K -> error;
481
tdb_find(Key, [{Key,Info}|_]) -> Info;
482
tdb_find(Key, [_|Db]) -> tdb_find(Key, Db);
483
tdb_find(_, []) -> error.
485
%% tdb_update([UpdateOp], Db) -> NewDb
486
%% UpdateOp = {Register,kill}|{Register,NewInfo}
487
%% Updates a type database. If a 'kill' operation is given, the type
488
%% information for that register will be removed from the database.
489
%% A kill operation takes precende over other operations for the same
490
%% register (i.e. [{{x,0},kill},{{x,0},{tuple,5}}] means that the
491
%% the existing type information, if any, will be discarded, and the
492
%% the '{tuple,5}' information ignored.
494
%% If NewInfo information is given and there exists information about
495
%% the register, the old and new type information will be merged.
496
%% For instance, {tuple,5} and {tuple,10} will be merged to produce
499
tdb_update(Uis0, Ts0) ->
500
Uis1 = filter(fun ({{x,_},_Op}) -> true;
501
({{y,_},_Op}) -> true;
504
tdb_update1(lists:sort(Uis1), Ts0).
506
tdb_update1([{Key,kill}|Ops], [{K,_Old}|_]=Db) when Key < K ->
507
tdb_update1(remove_key(Key, Ops), Db);
508
tdb_update1([{Key,_New}=New|Ops], [{K,_Old}|_]=Db) when Key < K ->
509
[New|tdb_update1(Ops, Db)];
510
tdb_update1([{Key,kill}|Ops], [{Key,_}|Db]) ->
511
tdb_update1(remove_key(Key, Ops), Db);
512
tdb_update1([{Key,NewInfo}|Ops], [{Key,OldInfo}|Db]) ->
513
[{Key,merge_type_info(NewInfo, OldInfo)}|tdb_update1(Ops, Db)];
514
tdb_update1([{_,_}|_]=Ops, [Old|Db]) ->
515
[Old|tdb_update1(Ops, Db)];
516
tdb_update1([{Key,kill}|Ops], []) ->
517
tdb_update1(remove_key(Key, Ops), []);
518
tdb_update1([{_,_}=New|Ops], []) ->
519
[New|tdb_update1(Ops, [])];
520
tdb_update1([], Db) -> Db.
522
%% tdb_kill_xregs(Db) -> NewDb
523
%% Kill all information about x registers. Also kill all tuple_element
524
%% dependencies from y registers to x registers.
526
tdb_kill_xregs([{{x,_},_Type}|Db]) -> tdb_kill_xregs(Db);
527
tdb_kill_xregs([{{y,_},{tuple_element,{x,_},_}}|Db]) -> tdb_kill_xregs(Db);
528
tdb_kill_xregs([Any|Db]) -> [Any|tdb_kill_xregs(Db)];
529
tdb_kill_xregs([]) -> [].
531
remove_key(Key, [{Key,_Op}|Ops]) -> remove_key(Key, Ops);
532
remove_key(_, Ops) -> Ops.
534
merge_type_info(I, I) -> I;
535
merge_type_info({tuple,Sz1,Same}, {tuple,Sz2,Same}=Max) when Sz1 < Sz2 ->
537
merge_type_info({tuple,Sz1,Same}=Max, {tuple,Sz2,Same}) when Sz1 > Sz2 ->
539
merge_type_info({tuple,Sz1,[]}, {tuple,Sz2,First}) ->
540
merge_type_info({tuple,Sz1,First}, {tuple,Sz2,First});
541
merge_type_info({tuple,Sz1,First}, {tuple,Sz2,_}) ->
542
merge_type_info({tuple,Sz1,First}, {tuple,Sz2,First});
543
merge_type_info(NewType, _) ->
544
verify_type(NewType),
547
verify_type({tuple,Sz,[]}) when is_integer(Sz) -> ok;
548
verify_type({tuple,Sz,[_]}) when is_integer(Sz) -> ok;
549
verify_type({tuple_element,_,_}) -> ok;
550
verify_type(float) -> ok;
551
verify_type({atom,_}) -> ok.