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