%%
%% %CopyrightBegin%
%%
%% Copyright Ericsson AB 2004-2017. All Rights Reserved.
%%
%% Licensed under the Apache License, Version 2.0 (the "License");
%% you may not use this file except in compliance with the License.
%% You may obtain a copy of the License at
%%
%% http://www.apache.org/licenses/LICENSE-2.0
%%
%% Unless required by applicable law or agreed to in writing, software
%% distributed under the License is distributed on an "AS IS" BASIS,
%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
%% See the License for the specific language governing permissions and
%% limitations under the License.
%%
%% %CopyrightEnd%
-module(beam_validator).
-compile({no_auto_import,[min/2]}).
%% Avoid warning for local function error/1 clashing with autoimported BIF.
-compile({no_auto_import,[error/1]}).
%% Interface for compiler.
-export([module/2, format_error/1]).
-include("beam_disasm.hrl").
-import(lists, [any/2,dropwhile/2,foldl/3,foreach/2,reverse/1]).
%% To be called by the compiler.
-spec module(beam_utils:module_code(), [compile:option()]) ->
{'ok',beam_utils:module_code()}.
module({Mod,Exp,Attr,Fs,Lc}=Code, _Opts)
when is_atom(Mod), is_list(Exp), is_list(Attr), is_integer(Lc) ->
case validate(Mod, Fs) of
[] ->
{ok,Code};
Es0 ->
Es = [{?MODULE,E} || E <- Es0],
{error,[{atom_to_list(Mod),Es}]}
end.
-spec format_error(term()) -> iolist().
format_error({{_M,F,A},{I,Off,limit}}) ->
io_lib:format(
"function ~p/~p+~p:~n"
" An implementation limit was reached.~n"
" Try reducing the complexity of this function.~n~n"
" Instruction: ~p~n", [F,A,Off,I]);
format_error({{_M,F,A},{undef_labels,Lbls}}) ->
io_lib:format(
"function ~p/~p:~n"
" Internal consistency check failed - please report this bug.~n"
" The following label(s) were referenced but not defined:~n", [F,A]) ++
" " ++ [[integer_to_list(L)," "] || L <- Lbls] ++ "\n";
format_error({{_M,F,A},{I,Off,Desc}}) ->
io_lib:format(
"function ~p/~p+~p:~n"
" Internal consistency check failed - please report this bug.~n"
" Instruction: ~p~n"
" Error: ~p:~n", [F,A,Off,I,Desc]);
format_error(Error) ->
io_lib:format("~p~n", [Error]).
%%%
%%% Local functions follow.
%%%
%%%
%%% The validator follows.
%%%
%%% The purpose of the validator is to find errors in the generated
%%% code that may cause the emulator to crash or behave strangely.
%%% We don't care about type errors in the user's code that will
%%% cause a proper exception at run-time.
%%%
%%% Things currently not checked. XXX
%%%
%%% - Heap allocation for binaries.
%%%
%% validate(Module, [Function]) -> [] | [Error]
%% A list of functions with their code. The code is in the same
%% format as used in the compiler and in .S files.
validate(Module, Fs) ->
Ft = index_bs_start_match(Fs, []),
validate_0(Module, Fs, Ft).
index_bs_start_match([{function,_,_,Entry,Code0}|Fs], Acc0) ->
Code = dropwhile(fun({label,L}) when L =:= Entry -> false;
(_) -> true
end, Code0),
case Code of
[{label,Entry}|Is] ->
Acc = index_bs_start_match_1(Is, Entry, Acc0),
index_bs_start_match(Fs, Acc);
_ ->
%% Something serious is wrong. Ignore it for now.
%% It will be detected and diagnosed later.
index_bs_start_match(Fs, Acc0)
end;
index_bs_start_match([], Acc) ->
gb_trees:from_orddict(lists:sort(Acc)).
index_bs_start_match_1([{test,bs_start_match2,_,_,_,_}=I|_], Entry, Acc) ->
[{Entry,[I]}|Acc];
index_bs_start_match_1([{test,_,{f,F},_},{bs_context_to_binary,_}|Is0], Entry, Acc) ->
[{label,F}|Is] = dropwhile(fun({label,L}) when L =:= F -> false;
(_) -> true
end, Is0),
index_bs_start_match_1(Is, Entry, Acc);
index_bs_start_match_1(_, _, Acc) -> Acc.
validate_0(_Module, [], _) -> [];
validate_0(Module, [{function,Name,Ar,Entry,Code}|Fs], Ft) ->
try validate_1(Code, Name, Ar, Entry, Ft) of
_ -> validate_0(Module, Fs, Ft)
catch
throw:Error ->
%% Controlled error.
[Error|validate_0(Module, Fs, Ft)];
Class:Error:Stack ->
%% Crash.
io:fwrite("Function: ~w/~w\n", [Name,Ar]),
erlang:raise(Class, Error, Stack)
end.
-type index() :: non_neg_integer().
-type reg_tab() :: gb_trees:tree(index(), 'none' | {'value', _}).
-record(st, %Emulation state
{x=init_regs(0, term) :: reg_tab(),%x register info.
y=init_regs(0, initialized) :: reg_tab(),%y register info.
f=init_fregs(), %
numy=none, %Number of y registers.
h=0, %Available heap size.
hf=0, %Available heap size for floats.
fls=undefined, %Floating point state.
ct=[], %List of hot catch/try labels
setelem=false, %Previous instruction was setelement/3.
puts_left=none %put/1 instructions left.
}).
-type label() :: integer().
-type label_set() :: gb_sets:set(label()).
-type branched_tab() :: gb_trees:tree(label(), #st{}).
-type ft_tab() :: gb_trees:tree().
-record(vst, %Validator state
{current=none :: #st{} | 'none', %Current state
branched=gb_trees:empty() :: branched_tab(), %States at jumps
labels=gb_sets:empty() :: label_set(), %All defined labels
ft=gb_trees:empty() :: ft_tab() %Some other functions
% in the module (those that start with bs_start_match2).
}).
%% Match context type.
-record(ms,
{id=make_ref() :: reference(), %Unique ID.
valid=0 :: non_neg_integer(), %Valid slots
slots=0 :: non_neg_integer() %Number of slots
}).
validate_1(Is, Name, Arity, Entry, Ft) ->
validate_2(labels(Is), Name, Arity, Entry, Ft).
validate_2({Ls1,[{func_info,{atom,Mod},{atom,Name},Arity}=_F|Is]},
Name, Arity, Entry, Ft) ->
validate_3(labels(Is), Name, Arity, Entry, Mod, Ls1, Ft);
validate_2({Ls1,Is}, Name, Arity, _Entry, _Ft) ->
error({{'_',Name,Arity},{first(Is),length(Ls1),illegal_instruction}}).
validate_3({Ls2,Is}, Name, Arity, Entry, Mod, Ls1, Ft) ->
Offset = 1 + length(Ls1) + 1 + length(Ls2),
EntryOK = lists:member(Entry, Ls2),
if
EntryOK ->
St = init_state(Arity),
Vst0 = #vst{current=St,
branched=gb_trees_from_list([{L,St} || L <- Ls1]),
labels=gb_sets:from_list(Ls1++Ls2),
ft=Ft},
MFA = {Mod,Name,Arity},
Vst = valfun(Is, MFA, Offset, Vst0),
validate_fun_info_branches(Ls1, MFA, Vst);
true ->
error({{Mod,Name,Arity},{first(Is),Offset,no_entry_label}})
end.
validate_fun_info_branches([L|Ls], MFA, #vst{branched=Branches}=Vst0) ->
Vst = Vst0#vst{current=gb_trees:get(L, Branches)},
validate_fun_info_branches_1(0, MFA, Vst),
validate_fun_info_branches(Ls, MFA, Vst);
validate_fun_info_branches([], _, _) -> ok.
validate_fun_info_branches_1(Arity, {_,_,Arity}, _) -> ok;
validate_fun_info_branches_1(X, {Mod,Name,Arity}=MFA, Vst) ->
try
get_term_type({x,X}, Vst)
catch Error ->
I = {func_info,{atom,Mod},{atom,Name},Arity},
Offset = 2,
error({MFA,{I,Offset,Error}})
end,
validate_fun_info_branches_1(X+1, MFA, Vst).
first([X|_]) -> X;
first([]) -> [].
labels(Is) ->
labels_1(Is, []).
labels_1([{label,L}|Is], R) ->
labels_1(Is, [L|R]);
labels_1([{line,_}|Is], R) ->
labels_1(Is, R);
labels_1(Is, R) ->
{reverse(R),Is}.
init_state(Arity) ->
Xs = init_regs(Arity, term),
Ys = init_regs(0, initialized),
kill_heap_allocation(#st{x=Xs,y=Ys,numy=none,ct=[]}).
kill_heap_allocation(St) ->
St#st{h=0,hf=0}.
init_regs(0, _) ->
gb_trees:empty();
init_regs(N, Type) ->
gb_trees_from_list([{R,Type} || R <- lists:seq(0, N-1)]).
valfun([], MFA, _Offset, #vst{branched=Targets0,labels=Labels0}=Vst) ->
Targets = gb_trees:keys(Targets0),
Labels = gb_sets:to_list(Labels0),
case Targets -- Labels of
[] -> Vst;
Undef ->
Error = {undef_labels,Undef},
error({MFA,Error})
end;
valfun([I|Is], MFA, Offset, Vst0) ->
valfun(Is, MFA, Offset+1,
try
Vst = val_dsetel(I, Vst0),
valfun_1(I, Vst)
catch Error ->
error({MFA,{I,Offset,Error}})
end).
%% Instructions that are allowed in dead code or when failing,
%% that is while the state is undecided in some way.
valfun_1({label,Lbl}, #vst{current=St0,branched=B,labels=Lbls}=Vst) ->
St = merge_states(Lbl, St0, B),
Vst#vst{current=St,branched=gb_trees:enter(Lbl, St, B),
labels=gb_sets:add(Lbl, Lbls)};
valfun_1(_I, #vst{current=none}=Vst) ->
%% Ignore instructions after erlang:error/1,2, which
%% the original R10B compiler thought would return.
Vst;
valfun_1({badmatch,Src}, Vst) ->
assert_term(Src, Vst),
kill_state(Vst);
valfun_1({case_end,Src}, Vst) ->
assert_term(Src, Vst),
kill_state(Vst);
valfun_1(if_end, Vst) ->
kill_state(Vst);
valfun_1({try_case_end,Src}, Vst) ->
assert_term(Src, Vst),
kill_state(Vst);
%% Instructions that can not cause exceptions
valfun_1({bs_context_to_binary,Ctx}, #vst{current=#st{x=Xs}}=Vst) ->
case Ctx of
{Tag,X} when Tag =:= x; Tag =:= y ->
Type = case gb_trees:lookup(X, Xs) of
{value,#ms{}} -> term;
_ -> get_term_type(Ctx, Vst)
end,
set_type_reg(Type, Ctx, Vst);
_ ->
error({bad_source,Ctx})
end;
valfun_1(bs_init_writable=I, Vst) ->
call(I, 1, Vst);
valfun_1(build_stacktrace=I, Vst) ->
call(I, 1, Vst);
valfun_1({move,{y,_}=Src,{y,_}=Dst}, Vst) ->
%% The stack trimming optimization may generate a move from an initialized
%% but unassigned Y register to another Y register.
case get_term_type_1(Src, Vst) of
{catchtag,_} -> error({catchtag,Src});
{trytag,_} -> error({trytag,Src});
Type -> set_type_reg(Type, Dst, Vst)
end;
valfun_1({move,Src,Dst}, Vst) ->
Type = get_move_term_type(Src, Vst),
set_type_reg(Type, Dst, Vst);
valfun_1({fmove,Src,{fr,_}=Dst}, Vst) ->
assert_type(float, Src, Vst),
set_freg(Dst, Vst);
valfun_1({fmove,{fr,_}=Src,Dst}, Vst0) ->
assert_freg_set(Src, Vst0),
assert_fls(checked, Vst0),
Vst = eat_heap_float(Vst0),
set_type_reg({float,[]}, Dst, Vst);
valfun_1({kill,{y,_}=Reg}, Vst) ->
set_type_y(initialized, Reg, Vst);
valfun_1({init,{y,_}=Reg}, Vst) ->
set_type_y(initialized, Reg, Vst);
valfun_1({test_heap,Heap,Live}, Vst) ->
test_heap(Heap, Live, Vst);
valfun_1({bif,Op,{f,_},Src,Dst}=I, Vst) ->
case is_bif_safe(Op, length(Src)) of
false ->
%% Since the BIF can fail, make sure that any catch state
%% is updated.
valfun_2(I, Vst);
true ->
%% It can't fail, so we finish handling it here (not updating
%% catch state).
validate_src(Src, Vst),
Type = bif_type(Op, Src, Vst),
set_type_reg(Type, Dst, Vst)
end;
%% Put instructions.
valfun_1({put_list,A,B,Dst}, Vst0) ->
assert_term(A, Vst0),
assert_term(B, Vst0),
Vst = eat_heap(2, Vst0),
set_type_reg(cons, Dst, Vst);
valfun_1({put_tuple,Sz,Dst}, Vst0) when is_integer(Sz) ->
Vst1 = eat_heap(1, Vst0),
Vst = set_type_reg(tuple_in_progress, Dst, Vst1),
#vst{current=St0} = Vst,
St = St0#st{puts_left={Sz,{Dst,{tuple,Sz}}}},
Vst#vst{current=St};
valfun_1({put,Src}, Vst0) ->
assert_term(Src, Vst0),
Vst = eat_heap(1, Vst0),
#vst{current=St0} = Vst,
case St0 of
#st{puts_left=none} ->
error(not_building_a_tuple);
#st{puts_left={1,{Dst,Type}}} ->
St = St0#st{puts_left=none},
set_type_reg(Type, Dst, Vst#vst{current=St});
#st{puts_left={PutsLeft,Info}} when is_integer(PutsLeft) ->
St = St0#st{puts_left={PutsLeft-1,Info}},
Vst#vst{current=St}
end;
%% Instructions for optimization of selective receives.
valfun_1({recv_mark,{f,Fail}}, Vst) when is_integer(Fail) ->
Vst;
valfun_1({recv_set,{f,Fail}}, Vst) when is_integer(Fail) ->
Vst;
%% Misc.
valfun_1(remove_message, Vst) ->
%% The message term is no longer fragile. It can be used
%% without restrictions.
remove_fragility(Vst);
valfun_1({'%',_}, Vst) ->
Vst;
valfun_1({line,_}, Vst) ->
Vst;
%% Exception generating calls
valfun_1({call_ext,Live,Func}=I, Vst) ->
case return_type(Func, Vst) of
exception ->
verify_live(Live, Vst),
kill_state(Vst);
_ ->
valfun_2(I, Vst)
end;
valfun_1(_I, #vst{current=#st{ct=undecided}}) ->
error(unknown_catch_try_state);
%%
%% Allocate and deallocate, et.al
valfun_1({allocate,Stk,Live}, Vst) ->
allocate(false, Stk, 0, Live, Vst);
valfun_1({allocate_heap,Stk,Heap,Live}, Vst) ->
allocate(false, Stk, Heap, Live, Vst);
valfun_1({allocate_zero,Stk,Live}, Vst) ->
allocate(true, Stk, 0, Live, Vst);
valfun_1({allocate_heap_zero,Stk,Heap,Live}, Vst) ->
allocate(true, Stk, Heap, Live, Vst);
valfun_1({deallocate,StkSize}, #vst{current=#st{numy=StkSize}}=Vst) ->
verify_no_ct(Vst),
deallocate(Vst);
valfun_1({deallocate,_}, #vst{current=#st{numy=NumY}}) ->
error({allocated,NumY});
valfun_1({trim,N,Remaining}, #vst{current=#st{y=Yregs0,numy=NumY}=St}=Vst) ->
if
N =< NumY, N+Remaining =:= NumY ->
Yregs1 = [{Y-N,Type} || {Y,Type} <- gb_trees:to_list(Yregs0), Y >= N],
Yregs = gb_trees_from_list(Yregs1),
Vst#vst{current=St#st{y=Yregs,numy=NumY-N}};
true ->
error({trim,N,Remaining,allocated,NumY})
end;
%% Catch & try.
valfun_1({'catch',Dst,{f,Fail}}, Vst0) when Fail /= none ->
Vst = #vst{current=#st{ct=Fails}=St} =
set_type_y({catchtag,[Fail]}, Dst, Vst0),
Vst#vst{current=St#st{ct=[[Fail]|Fails]}};
valfun_1({'try',Dst,{f,Fail}}, Vst0) ->
Vst = #vst{current=#st{ct=Fails}=St} =
set_type_y({trytag,[Fail]}, Dst, Vst0),
Vst#vst{current=St#st{ct=[[Fail]|Fails]}};
valfun_1({catch_end,Reg}, #vst{current=#st{ct=[Fail|Fails]}}=Vst0) ->
case get_special_y_type(Reg, Vst0) of
{catchtag,Fail} ->
Vst = #vst{current=St} = set_catch_end(Reg, Vst0),
Xs = gb_trees_from_list([{0,term}]),
Vst#vst{current=St#st{x=Xs,ct=Fails,fls=undefined}};
Type ->
error({bad_type,Type})
end;
valfun_1({try_end,Reg}, #vst{current=#st{ct=[Fail|Fails]}=St0}=Vst0) ->
case get_special_y_type(Reg, Vst0) of
{trytag,Fail} ->
Vst = case Fail of
[FailLabel] -> branch_state(FailLabel, Vst0);
_ -> Vst0
end,
St = St0#st{ct=Fails,fls=undefined},
set_catch_end(Reg, Vst#vst{current=St});
Type ->
error({bad_type,Type})
end;
valfun_1({try_case,Reg}, #vst{current=#st{ct=[Fail|Fails]}}=Vst0) ->
case get_special_y_type(Reg, Vst0) of
{trytag,Fail} ->
Vst = #vst{current=St} = set_catch_end(Reg, Vst0),
Xs = gb_trees_from_list([{0,{atom,[]}},{1,term},{2,term}]),
Vst#vst{current=St#st{x=Xs,ct=Fails,fls=undefined}};
Type ->
error({bad_type,Type})
end;
valfun_1(I, Vst) ->
valfun_2(I, Vst).
%% Update branched state if necessary and try next set of instructions.
valfun_2(I, #vst{current=#st{ct=[]}}=Vst) ->
valfun_3(I, Vst);
valfun_2(I, #vst{current=#st{ct=[[Fail]|_]}}=Vst) when is_integer(Fail) ->
%% Update branched state
valfun_3(I, branch_state(Fail, Vst));
valfun_2(_, _) ->
error(ambiguous_catch_try_state).
%% Handle the remaining floating point instructions here.
%% Floating point.
valfun_3({fconv,Src,{fr,_}=Dst}, Vst) ->
assert_term(Src, Vst),
set_freg(Dst, Vst);
valfun_3({bif,fadd,_,[_,_]=Src,Dst}, Vst) ->
float_op(Src, Dst, Vst);
valfun_3({bif,fdiv,_,[_,_]=Src,Dst}, Vst) ->
float_op(Src, Dst, Vst);
valfun_3({bif,fmul,_,[_,_]=Src,Dst}, Vst) ->
float_op(Src, Dst, Vst);
valfun_3({bif,fnegate,_,[_]=Src,Dst}, Vst) ->
float_op(Src, Dst, Vst);
valfun_3({bif,fsub,_,[_,_]=Src,Dst}, Vst) ->
float_op(Src, Dst, Vst);
valfun_3(fclearerror, Vst) ->
case get_fls(Vst) of
undefined -> ok;
checked -> ok;
Fls -> error({bad_floating_point_state,Fls})
end,
set_fls(cleared, Vst);
valfun_3({fcheckerror,_}, Vst) ->
assert_fls(cleared, Vst),
set_fls(checked, Vst);
valfun_3(I, Vst) ->
%% The instruction is not a float instruction.
case get_fls(Vst) of
undefined ->
valfun_4(I, Vst);
checked ->
valfun_4(I, Vst);
Fls ->
error({unsafe_instruction,{float_error_state,Fls}})
end.
%% Instructions that can cause exceptions.
valfun_4({apply,Live}, Vst) ->
call(apply, Live+2, Vst);
valfun_4({apply_last,Live,_}, Vst) ->
tail_call(apply, Live+2, Vst);
valfun_4({call_fun,Live}, Vst) ->
validate_src([{x,Live}], Vst),
call('fun', Live+1, Vst);
valfun_4({call,Live,Func}, Vst) ->
call(Func, Live, Vst);
valfun_4({call_ext,Live,Func}, Vst) ->
%% Exception BIFs has already been taken care of above.
call(Func, Live, Vst);
valfun_4({call_only,Live,Func}, Vst) ->
tail_call(Func, Live, Vst);
valfun_4({call_ext_only,Live,Func}, Vst) ->
tail_call(Func, Live, Vst);
valfun_4({call_last,Live,Func,StkSize}, #vst{current=#st{numy=StkSize}}=Vst) ->
tail_call(Func, Live, Vst);
valfun_4({call_last,_,_,_}, #vst{current=#st{numy=NumY}}) ->
error({allocated,NumY});
valfun_4({call_ext_last,Live,Func,StkSize},
#vst{current=#st{numy=StkSize}}=Vst) ->
tail_call(Func, Live, Vst);
valfun_4({call_ext_last,_,_,_}, #vst{current=#st{numy=NumY}}) ->
error({allocated,NumY});
valfun_4({make_fun2,_,_,_,Live}, Vst) ->
call(make_fun, Live, Vst);
%% Other BIFs
valfun_4({bif,tuple_size,{f,Fail},[Tuple],Dst}, Vst0) ->
TupleType0 = get_term_type(Tuple, Vst0),
Vst1 = branch_state(Fail, Vst0),
TupleType = upgrade_tuple_type({tuple,[0]}, TupleType0),
Vst = set_type(TupleType, Tuple, Vst1),
set_type_reg({integer,[]}, Dst, Vst);
valfun_4({bif,element,{f,Fail},[Pos,Tuple],Dst}, Vst0) ->
TupleType0 = get_term_type(Tuple, Vst0),
PosType = get_term_type(Pos, Vst0),
Vst1 = branch_state(Fail, Vst0),
TupleType = upgrade_tuple_type({tuple,[get_tuple_size(PosType)]}, TupleType0),
Vst = set_type(TupleType, Tuple, Vst1),
set_type_reg(term, Tuple, Dst, Vst);
valfun_4({bif,raise,{f,0},Src,_Dst}, Vst) ->
validate_src(Src, Vst),
kill_state(Vst);
valfun_4(raw_raise=I, Vst) ->
call(I, 3, Vst);
valfun_4({bif,Op,{f,Fail},Src,Dst}, Vst0) ->
validate_src(Src, Vst0),
Vst = branch_state(Fail, Vst0),
Type0 = bif_type(Op, Src, Vst),
Type = propagate_fragility(Type0, Src, Vst),
set_type_reg(Type, Dst, Vst);
valfun_4({gc_bif,Op,{f,Fail},Live,Src,Dst}, #vst{current=St0}=Vst0) ->
verify_live(Live, Vst0),
verify_y_init(Vst0),
St = kill_heap_allocation(St0),
Vst1 = Vst0#vst{current=St},
Vst2 = branch_state(Fail, Vst1),
Vst = prune_x_regs(Live, Vst2),
validate_src(Src, Vst),
Type0 = bif_type(Op, Src, Vst),
Type = propagate_fragility(Type0, Src, Vst),
set_type_reg(Type, Dst, Vst);
valfun_4(return, #vst{current=#st{numy=none}}=Vst) ->
assert_term({x,0}, Vst),
kill_state(Vst);
valfun_4(return, #vst{current=#st{numy=NumY}}) ->
error({stack_frame,NumY});
valfun_4({jump,{f,Lbl}}, Vst) ->
kill_state(branch_state(Lbl, Vst));
valfun_4({loop_rec,{f,Fail},Dst}, Vst0) ->
Vst = branch_state(Fail, Vst0),
%% This term may not be part of the root set until
%% remove_message/0 is executed. If control transfers
%% to the loop_rec_end/1 instruction, no part of this
%% this term must be stored in a Y register.
set_type_reg({fragile,term}, Dst, Vst);
valfun_4({wait,_}, Vst) ->
verify_y_init(Vst),
kill_state(Vst);
valfun_4({wait_timeout,_,Src}, Vst) ->
assert_term(Src, Vst),
verify_y_init(Vst),
Vst;
valfun_4({loop_rec_end,_}, Vst) ->
verify_y_init(Vst),
kill_state(Vst);
valfun_4(timeout, #vst{current=St}=Vst) ->
Vst#vst{current=St#st{x=init_regs(0, term)}};
valfun_4(send, Vst) ->
call(send, 2, Vst);
valfun_4({set_tuple_element,Src,Tuple,I}, Vst) ->
assert_term(Src, Vst),
assert_type({tuple_element,I+1}, Tuple, Vst),
Vst;
%% Match instructions.
valfun_4({select_val,Src,{f,Fail},{list,Choices}}, Vst) ->
assert_term(Src, Vst),
Lbls = [L || {f,L} <- Choices]++[Fail],
kill_state(foldl(fun(L, S) -> branch_state(L, S) end, Vst, Lbls));
valfun_4({select_tuple_arity,Tuple,{f,Fail},{list,Choices}}, Vst) ->
assert_type(tuple, Tuple, Vst),
kill_state(branch_arities(Choices, Tuple, branch_state(Fail, Vst)));
valfun_4({get_list,Src,D1,D2}, Vst0) ->
assert_type(cons, Src, Vst0),
Vst = set_type_reg(term, Src, D1, Vst0),
set_type_reg(term, Src, D2, Vst);
valfun_4({get_hd,Src,Dst}, Vst) ->
assert_type(cons, Src, Vst),
set_type_reg(term, Src, Dst, Vst);
valfun_4({get_tl,Src,Dst}, Vst) ->
assert_type(cons, Src, Vst),
set_type_reg(term, Src, Dst, Vst);
valfun_4({get_tuple_element,Src,I,Dst}, Vst) ->
assert_type({tuple_element,I+1}, Src, Vst),
set_type_reg(term, Src, Dst, Vst);
%% New bit syntax matching instructions.
valfun_4({test,bs_start_match2,{f,Fail},Live,[Ctx,NeedSlots],Ctx}, Vst0) ->
%% If source and destination registers are the same, match state
%% is OK as input.
CtxType = get_move_term_type(Ctx, Vst0),
verify_live(Live, Vst0),
Vst1 = prune_x_regs(Live, Vst0),
BranchVst = case CtxType of
#ms{} ->
%% The failure branch will never be taken when Ctx
%% is a match context. Therefore, the type for Ctx
%% at the failure label must not be match_context
%% (or we could reject legal code).
set_type_reg(term, Ctx, Vst1);
_ ->
Vst1
end,
Vst = branch_state(Fail, BranchVst),
set_type_reg(bsm_match_state(NeedSlots), Ctx, Vst);
valfun_4({test,bs_start_match2,{f,Fail},Live,[Src,Slots],Dst}, Vst0) ->
assert_term(Src, Vst0),
verify_live(Live, Vst0),
Vst1 = prune_x_regs(Live, Vst0),
Vst = branch_state(Fail, Vst1),
set_type_reg(bsm_match_state(Slots), Src, Dst, Vst);
valfun_4({test,bs_match_string,{f,Fail},[Ctx,_,_]}, Vst) ->
bsm_validate_context(Ctx, Vst),
branch_state(Fail, Vst);
valfun_4({test,bs_skip_bits2,{f,Fail},[Ctx,Src,_,_]}, Vst) ->
bsm_validate_context(Ctx, Vst),
assert_term(Src, Vst),
branch_state(Fail, Vst);
valfun_4({test,bs_test_tail2,{f,Fail},[Ctx,_]}, Vst) ->
bsm_validate_context(Ctx, Vst),
branch_state(Fail, Vst);
valfun_4({test,bs_test_unit,{f,Fail},[Ctx,_]}, Vst) ->
bsm_validate_context(Ctx, Vst),
branch_state(Fail, Vst);
valfun_4({test,bs_skip_utf8,{f,Fail},[Ctx,Live,_]}, Vst) ->
validate_bs_skip_utf(Fail, Ctx, Live, Vst);
valfun_4({test,bs_skip_utf16,{f,Fail},[Ctx,Live,_]}, Vst) ->
validate_bs_skip_utf(Fail, Ctx, Live, Vst);
valfun_4({test,bs_skip_utf32,{f,Fail},[Ctx,Live,_]}, Vst) ->
validate_bs_skip_utf(Fail, Ctx, Live, Vst);
valfun_4({test,bs_get_integer2,{f,Fail},Live,[Ctx,_,_,_],Dst}, Vst) ->
validate_bs_get(Fail, Ctx, Live, {integer, []}, Dst, Vst);
valfun_4({test,bs_get_float2,{f,Fail},Live,[Ctx,_,_,_],Dst}, Vst) ->
validate_bs_get(Fail, Ctx, Live, {float, []}, Dst, Vst);
valfun_4({test,bs_get_binary2,{f,Fail},Live,[Ctx,_,_,_],Dst}, Vst) ->
Type = propagate_fragility(term, [Ctx], Vst),
validate_bs_get(Fail, Ctx, Live, Type, Dst, Vst);
valfun_4({test,bs_get_utf8,{f,Fail},Live,[Ctx,_],Dst}, Vst) ->
validate_bs_get(Fail, Ctx, Live, {integer, []}, Dst, Vst);
valfun_4({test,bs_get_utf16,{f,Fail},Live,[Ctx,_],Dst}, Vst) ->
validate_bs_get(Fail, Ctx, Live, {integer, []}, Dst, Vst);
valfun_4({test,bs_get_utf32,{f,Fail},Live,[Ctx,_],Dst}, Vst) ->
validate_bs_get(Fail, Ctx, Live, {integer, []}, Dst, Vst);
valfun_4({bs_save2,Ctx,SavePoint}, Vst) ->
bsm_save(Ctx, SavePoint, Vst);
valfun_4({bs_restore2,Ctx,SavePoint}, Vst) ->
bsm_restore(Ctx, SavePoint, Vst);
%% Other test instructions.
valfun_4({test,is_float,{f,Lbl},[Float]}, Vst) ->
assert_term(Float, Vst),
set_type({float,[]}, Float, branch_state(Lbl, Vst));
valfun_4({test,is_tuple,{f,Lbl},[Tuple]}, Vst) ->
Type0 = get_term_type(Tuple, Vst),
Type = upgrade_tuple_type({tuple,[0]}, Type0),
set_type(Type, Tuple, branch_state(Lbl, Vst));
valfun_4({test,is_nonempty_list,{f,Lbl},[Cons]}, Vst) ->
assert_term(Cons, Vst),
set_type(cons, Cons, branch_state(Lbl, Vst));
valfun_4({test,test_arity,{f,Lbl},[Tuple,Sz]}, Vst) when is_integer(Sz) ->
assert_type(tuple, Tuple, Vst),
set_type_reg({tuple,Sz}, Tuple, branch_state(Lbl, Vst));
valfun_4({test,is_tagged_tuple,{f,Lbl},[Src,Sz,_Atom]}, Vst) ->
validate_src([Src], Vst),
set_type_reg({tuple, Sz}, Src, branch_state(Lbl, Vst));
valfun_4({test,has_map_fields,{f,Lbl},Src,{list,List}}, Vst) ->
assert_type(map, Src, Vst),
assert_unique_map_keys(List),
branch_state(Lbl, Vst);
valfun_4({test,is_map,{f,Lbl},[Src]}, Vst0) ->
Vst = branch_state(Lbl, Vst0),
case Src of
{Tag,_} when Tag =:= x; Tag =:= y ->
set_type_reg(map, Src, Vst);
{literal,Map} when is_map(Map) ->
Vst;
_ ->
kill_state(Vst)
end;
valfun_4({test,_Op,{f,Lbl},Src}, Vst) ->
validate_src(Src, Vst),
branch_state(Lbl, Vst);
valfun_4({bs_add,{f,Fail},[A,B,_],Dst}, Vst) ->
assert_term(A, Vst),
assert_term(B, Vst),
set_type_reg({integer,[]}, Dst, branch_state(Fail, Vst));
valfun_4({bs_utf8_size,{f,Fail},A,Dst}, Vst) ->
assert_term(A, Vst),
set_type_reg({integer,[]}, Dst, branch_state(Fail, Vst));
valfun_4({bs_utf16_size,{f,Fail},A,Dst}, Vst) ->
assert_term(A, Vst),
set_type_reg({integer,[]}, Dst, branch_state(Fail, Vst));
valfun_4({bs_init2,{f,Fail},Sz,Heap,Live,_,Dst}, Vst0) ->
verify_live(Live, Vst0),
verify_y_init(Vst0),
if
is_integer(Sz) ->
ok;
true ->
assert_term(Sz, Vst0)
end,
Vst1 = heap_alloc(Heap, Vst0),
Vst2 = branch_state(Fail, Vst1),
Vst = prune_x_regs(Live, Vst2),
set_type_reg(binary, Dst, Vst);
valfun_4({bs_init_bits,{f,Fail},Sz,Heap,Live,_,Dst}, Vst0) ->
verify_live(Live, Vst0),
verify_y_init(Vst0),
if
is_integer(Sz) ->
ok;
true ->
assert_term(Sz, Vst0)
end,
Vst1 = heap_alloc(Heap, Vst0),
Vst2 = branch_state(Fail, Vst1),
Vst = prune_x_regs(Live, Vst2),
set_type_reg(binary, Dst, Vst);
valfun_4({bs_append,{f,Fail},Bits,Heap,Live,_Unit,Bin,_Flags,Dst}, Vst0) ->
verify_live(Live, Vst0),
verify_y_init(Vst0),
assert_term(Bits, Vst0),
assert_term(Bin, Vst0),
Vst1 = heap_alloc(Heap, Vst0),
Vst2 = branch_state(Fail, Vst1),
Vst = prune_x_regs(Live, Vst2),
set_type_reg(binary, Dst, Vst);
valfun_4({bs_private_append,{f,Fail},Bits,_Unit,Bin,_Flags,Dst}, Vst0) ->
assert_term(Bits, Vst0),
assert_term(Bin, Vst0),
Vst = branch_state(Fail, Vst0),
set_type_reg(binary, Dst, Vst);
valfun_4({bs_put_string,Sz,_}, Vst) when is_integer(Sz) ->
Vst;
valfun_4({bs_put_binary,{f,Fail},Sz,_,_,Src}, Vst) ->
assert_term(Sz, Vst),
assert_term(Src, Vst),
branch_state(Fail, Vst);
valfun_4({bs_put_float,{f,Fail},Sz,_,_,Src}, Vst) ->
assert_term(Sz, Vst),
assert_term(Src, Vst),
branch_state(Fail, Vst);
valfun_4({bs_put_integer,{f,Fail},Sz,_,_,Src}, Vst) ->
assert_term(Sz, Vst),
assert_term(Src, Vst),
branch_state(Fail, Vst);
valfun_4({bs_put_utf8,{f,Fail},_,Src}, Vst) ->
assert_term(Src, Vst),
branch_state(Fail, Vst);
valfun_4({bs_put_utf16,{f,Fail},_,Src}, Vst) ->
assert_term(Src, Vst),
branch_state(Fail, Vst);
valfun_4({bs_put_utf32,{f,Fail},_,Src}, Vst) ->
assert_term(Src, Vst),
branch_state(Fail, Vst);
%% Map instructions.
valfun_4({put_map_assoc,{f,Fail},Src,Dst,Live,{list,List}}, Vst) ->
verify_put_map(Fail, Src, Dst, Live, List, Vst);
valfun_4({put_map_exact,{f,Fail},Src,Dst,Live,{list,List}}, Vst) ->
verify_put_map(Fail, Src, Dst, Live, List, Vst);
valfun_4({get_map_elements,{f,Fail},Src,{list,List}}, Vst) ->
verify_get_map(Fail, Src, List, Vst);
valfun_4(_, _) ->
error(unknown_instruction).
verify_get_map(Fail, Src, List, Vst0) ->
assert_type(map, Src, Vst0),
Vst1 = foldl(fun(D, Vsti) ->
case is_reg_defined(D,Vsti) of
true -> set_type_reg(term,D,Vsti);
false -> Vsti
end
end, Vst0, extract_map_vals(List)),
Vst2 = branch_state(Fail, Vst1),
Keys = extract_map_keys(List),
assert_unique_map_keys(Keys),
verify_get_map_pair(List, Src, Vst0, Vst2).
extract_map_vals([_Key,Val|T]) ->
[Val|extract_map_vals(T)];
extract_map_vals([]) -> [].
extract_map_keys([Key,_Val|T]) ->
[Key|extract_map_keys(T)];
extract_map_keys([]) -> [].
verify_get_map_pair([Src,Dst|Vs], Map, Vst0, Vsti0) ->
assert_term(Src, Vst0),
Vsti = set_type_reg(term, Map, Dst, Vsti0),
verify_get_map_pair(Vs, Map, Vst0, Vsti);
verify_get_map_pair([], _Map, _Vst0, Vst) -> Vst.
verify_put_map(Fail, Src, Dst, Live, List, Vst0) ->
assert_type(map, Src, Vst0),
verify_live(Live, Vst0),
verify_y_init(Vst0),
foreach(fun (Term) -> assert_term(Term, Vst0) end, List),
Vst1 = heap_alloc(0, Vst0),
Vst2 = branch_state(Fail, Vst1),
Vst = prune_x_regs(Live, Vst2),
Keys = extract_map_keys(List),
assert_unique_map_keys(Keys),
set_type_reg(map, Dst, Vst).
%%
%% Common code for validating bs_get* instructions.
%%
validate_bs_get(Fail, Ctx, Live, Type, Dst, Vst0) ->
bsm_validate_context(Ctx, Vst0),
verify_live(Live, Vst0),
Vst1 = prune_x_regs(Live, Vst0),
Vst = branch_state(Fail, Vst1),
set_type_reg(Type, Dst, Vst).
%%
%% Common code for validating bs_skip_utf* instructions.
%%
validate_bs_skip_utf(Fail, Ctx, Live, Vst0) ->
bsm_validate_context(Ctx, Vst0),
verify_live(Live, Vst0),
Vst = prune_x_regs(Live, Vst0),
branch_state(Fail, Vst).
%%
%% Special state handling for setelement/3 and set_tuple_element/3 instructions.
%% A possibility for garbage collection must not occur between setelement/3 and
%% set_tuple_element/3.
%%
%% Note that #vst.current will be 'none' if the instruction is unreachable.
%%
val_dsetel({move,_,_}, Vst) ->
Vst;
val_dsetel({call_ext,3,{extfunc,erlang,setelement,3}}, #vst{current=#st{}=St}=Vst) ->
Vst#vst{current=St#st{setelem=true}};
val_dsetel({set_tuple_element,_,_,_}, #vst{current=#st{setelem=false}}) ->
error(illegal_context_for_set_tuple_element);
val_dsetel({set_tuple_element,_,_,_}, #vst{current=#st{setelem=true}}=Vst) ->
Vst;
val_dsetel({line,_}, Vst) ->
Vst;
val_dsetel(_, #vst{current=#st{setelem=true}=St}=Vst) ->
Vst#vst{current=St#st{setelem=false}};
val_dsetel(_, Vst) -> Vst.
kill_state(#vst{current=#st{ct=[[Fail]|_]}}=Vst) when is_integer(Fail) ->
%% There is an active catch. Make sure that we merge the state into
%% the catch label before clearing it, so that that we can be sure
%% that the label gets a state.
kill_state_1(branch_state(Fail, Vst));
kill_state(Vst) ->
kill_state_1(Vst).
kill_state_1(Vst) ->
Vst#vst{current=none}.
%% A "plain" call.
%% The stackframe must be initialized.
%% The instruction will return to the instruction following the call.
call(Name, Live, #vst{current=St}=Vst) ->
verify_call_args(Name, Live, Vst),
verify_y_init(Vst),
case return_type(Name, Vst) of
Type when Type =/= exception ->
%% Type is never 'exception' because it has been handled earlier.
Xs = gb_trees_from_list([{0,Type}]),
Vst#vst{current=St#st{x=Xs,f=init_fregs()}}
end.
%% Tail call.
%% The stackframe must have a known size and be initialized.
%% Does not return to the instruction following the call.
tail_call(Name, Live, Vst0) ->
verify_y_init(Vst0),
Vst = deallocate(Vst0),
verify_call_args(Name, Live, Vst),
verify_no_ct(Vst),
kill_state(Vst).
verify_call_args(_, 0, #vst{}) ->
ok;
verify_call_args({f,Lbl}, Live, Vst) when is_integer(Live)->
verify_local_call(Lbl, Live, Vst);
verify_call_args(_, Live, Vst) when is_integer(Live)->
verify_call_args_1(Live, Vst);
verify_call_args(_, Live, _) ->
error({bad_number_of_live_regs,Live}).
verify_call_args_1(0, _) -> ok;
verify_call_args_1(N, Vst) ->
X = N - 1,
get_term_type({x,X}, Vst),
verify_call_args_1(X, Vst).
verify_local_call(Lbl, Live, Vst) ->
case all_ms_in_x_regs(Live, Vst) of
[{R,Ctx}] ->
%% Verify that there is a suitable bs_start_match2 instruction.
verify_call_match_context(Lbl, R, Vst),
%% Since the callee has consumed the match context,
%% there must be no additional copies in Y registers.
#ms{id=Id} = Ctx,
case ms_in_y_regs(Id, Vst) of
[] ->
ok;
[_|_]=Ys ->
error({multiple_match_contexts,[R|Ys]})
end;
[_,_|_]=Xs0 ->
Xs = [R || {R,_} <- Xs0],
error({multiple_match_contexts,Xs});
[] ->
ok
end.
all_ms_in_x_regs(0, _Vst) ->
[];
all_ms_in_x_regs(Live0, Vst) ->
Live = Live0 - 1,
R = {x,Live},
case get_move_term_type(R, Vst) of
#ms{}=M ->
[{R,M}|all_ms_in_x_regs(Live, Vst)];
_ ->
all_ms_in_x_regs(Live, Vst)
end.
ms_in_y_regs(Id, #vst{current=#st{y=Ys0}}) ->
Ys = gb_trees:to_list(Ys0),
[{y,Y} || {Y,#ms{id=OtherId}} <- Ys, OtherId =:= Id].
verify_call_match_context(Lbl, Ctx, #vst{ft=Ft}) ->
case gb_trees:lookup(Lbl, Ft) of
none ->
error(no_bs_start_match2);
{value,[{test,bs_start_match2,_,_,[Ctx,_],Ctx}|_]} ->
ok;
{value,[{test,bs_start_match2,_,_,_,_}=I|_]} ->
error({unsuitable_bs_start_match2,I})
end.
allocate(Zero, Stk, Heap, Live, #vst{current=#st{numy=none}}=Vst0) ->
verify_live(Live, Vst0),
Vst = #vst{current=St} = prune_x_regs(Live, Vst0),
Ys = init_regs(Stk, case Zero of
true -> initialized;
false -> uninitialized
end),
heap_alloc(Heap, Vst#vst{current=St#st{y=Ys,numy=Stk}});
allocate(_, _, _, _, #vst{current=#st{numy=Numy}}) ->
error({existing_stack_frame,{size,Numy}}).
deallocate(#vst{current=St}=Vst) ->
Vst#vst{current=St#st{y=init_regs(0, initialized),numy=none}}.
test_heap(Heap, Live, Vst0) ->
verify_live(Live, Vst0),
verify_y_init(Vst0),
Vst = prune_x_regs(Live, Vst0),
heap_alloc(Heap, Vst).
heap_alloc(Heap, #vst{current=St0}=Vst) ->
St1 = kill_heap_allocation(St0),
St = heap_alloc_1(Heap, St1),
Vst#vst{current=St}.
heap_alloc_1({alloc,Alloc}, St) ->
heap_alloc_2(Alloc, St);
heap_alloc_1(HeapWords, St) when is_integer(HeapWords) ->
St#st{h=HeapWords}.
heap_alloc_2([{words,HeapWords}|T], St0) ->
St = St0#st{h=HeapWords},
heap_alloc_2(T, St);
heap_alloc_2([{floats,Floats}|T], St0) ->
St = St0#st{hf=Floats},
heap_alloc_2(T, St);
heap_alloc_2([], St) -> St.
prune_x_regs(Live, #vst{current=#st{x=Xs0}=St0}=Vst) when is_integer(Live) ->
Xs1 = gb_trees:to_list(Xs0),
Xs = [P || {R,_}=P <- Xs1, R < Live],
St = St0#st{x=gb_trees:from_orddict(Xs)},
Vst#vst{current=St}.
%%%
%%% Floating point checking.
%%%
%%% Possible values for the fls field (=floating point error state).
%%%
%%% undefined - Undefined (initial state). No float operations allowed.
%%%
%%% cleared - fclearerror/0 has been executed. Float operations
%%% are allowed (such as fadd).
%%%
%%% checked - fcheckerror/1 has been executed. It is allowed to
%%% move values out of floating point registers.
%%%
%%% The following instructions may be executed in any state:
%%%
%%% fconv Src {fr,_}
%%% fmove Src {fr,_} %% Move INTO floating point register.
%%%
float_op(Src, Dst, Vst0) ->
foreach (fun(S) -> assert_freg_set(S, Vst0) end, Src),
assert_fls(cleared, Vst0),
Vst = set_fls(cleared, Vst0),
set_freg(Dst, Vst).
assert_fls(Fls, Vst) ->
case get_fls(Vst) of
Fls -> ok;
OtherFls -> error({bad_floating_point_state,OtherFls})
end.
set_fls(Fls, #vst{current=#st{}=St}=Vst) when is_atom(Fls) ->
Vst#vst{current=St#st{fls=Fls}}.
get_fls(#vst{current=#st{fls=Fls}}) when is_atom(Fls) -> Fls.
init_fregs() -> 0.
set_freg({fr,Fr}=Freg, #vst{current=#st{f=Fregs0}=St}=Vst)
when is_integer(Fr), 0 =< Fr ->
check_limit(Freg),
Bit = 1 bsl Fr,
if
Fregs0 band Bit =:= 0 ->
Fregs = Fregs0 bor Bit,
Vst#vst{current=St#st{f=Fregs}};
true -> Vst
end;
set_freg(Fr, _) -> error({bad_target,Fr}).
assert_freg_set({fr,Fr}=Freg, #vst{current=#st{f=Fregs}})
when is_integer(Fr), 0 =< Fr ->
if
(Fregs bsr Fr) band 1 =:= 0 ->
error({uninitialized_reg,Freg});
true ->
ok
end;
assert_freg_set(Fr, _) -> error({bad_source,Fr}).
%%% Maps
%% A single item list may be either a list or a register.
%%
%% A list with more than item must contain unique literals.
%%
%% An empty list is not allowed.
assert_unique_map_keys([]) ->
%% There is no reason to use the get_map_elements and
%% has_map_fields instructions with empty lists.
error(empty_field_list);
assert_unique_map_keys([_]) ->
ok;
assert_unique_map_keys([_,_|_]=Ls) ->
Vs = [get_literal(L) || L <- Ls],
case length(Vs) =:= sets:size(sets:from_list(Vs)) of
true -> ok;
false -> error(keys_not_unique)
end.
%%%
%%% New binary matching instructions.
%%%
bsm_match_state(Slots) ->
#ms{slots=Slots}.
bsm_validate_context(Reg, Vst) ->
_ = bsm_get_context(Reg, Vst),
ok.
bsm_get_context({x,X}=Reg, #vst{current=#st{x=Xs}}=_Vst) when is_integer(X) ->
case gb_trees:lookup(X, Xs) of
{value,#ms{}=Ctx} -> Ctx;
{value,{fragile,#ms{}=Ctx}} -> Ctx;
_ -> error({no_bsm_context,Reg})
end;
bsm_get_context(Reg, _) -> error({bad_source,Reg}).
bsm_save(Reg, {atom,start}, Vst) ->
%% Save point refering to where the match started.
%% It is always valid. But don't forget to validate the context register.
bsm_validate_context(Reg, Vst),
Vst;
bsm_save(Reg, SavePoint, Vst) ->
case bsm_get_context(Reg, Vst) of
#ms{valid=Bits,slots=Slots}=Ctxt0 when SavePoint < Slots ->
Ctx = Ctxt0#ms{valid=Bits bor (1 bsl SavePoint),slots=Slots},
set_type_reg(Ctx, Reg, Vst);
_ -> error({illegal_save,SavePoint})
end.
bsm_restore(Reg, {atom,start}, Vst) ->
%% (Mostly) automatic save point refering to where the match started.
%% It is always valid. But don't forget to validate the context register.
bsm_validate_context(Reg, Vst),
Vst;
bsm_restore(Reg, SavePoint, Vst) ->
case bsm_get_context(Reg, Vst) of
#ms{valid=Bits,slots=Slots} when SavePoint < Slots ->
case Bits band (1 bsl SavePoint) of
0 -> error({illegal_restore,SavePoint,not_set});
_ -> Vst
end;
_ -> error({illegal_restore,SavePoint,range})
end.
%%%
%%% Keeping track of types.
%%%
set_type(Type, {x,_}=Reg, Vst) -> set_type_reg(Type, Reg, Vst);
set_type(Type, {y,_}=Reg, Vst) -> set_type_y(Type, Reg, Vst);
set_type(_, _, #vst{}=Vst) -> Vst.
set_type_reg(Type, Src, Dst, Vst) ->
case get_term_type_1(Src, Vst) of
{fragile,_} ->
set_type_reg(make_fragile(Type), Dst, Vst);
_ ->
set_type_reg(Type, Dst, Vst)
end.
set_type_reg(Type, {x,_}=Reg, Vst) ->
set_type_x(Type, Reg, Vst);
set_type_reg(Type, Reg, Vst) ->
set_type_y(Type, Reg, Vst).
set_type_x(Type, {x,X}=Reg, #vst{current=#st{x=Xs0}=St}=Vst)
when is_integer(X), 0 =< X ->
check_limit(Reg),
Xs = case gb_trees:lookup(X, Xs0) of
none ->
gb_trees:insert(X, Type, Xs0);
{value,{fragile,_}} ->
gb_trees:update(X, make_fragile(Type), Xs0);
{value,_} ->
gb_trees:update(X, Type, Xs0)
end,
Vst#vst{current=St#st{x=Xs}};
set_type_x(Type, Reg, #vst{}) ->
error({invalid_store,Reg,Type}).
set_type_y(Type, {y,Y}=Reg, #vst{current=#st{y=Ys0}=St}=Vst)
when is_integer(Y), 0 =< Y ->
check_limit(Reg),
Ys = case gb_trees:lookup(Y, Ys0) of
none ->
error({invalid_store,Reg,Type});
{value,{catchtag,_}=Tag} ->
error(Tag);
{value,{trytag,_}=Tag} ->
error(Tag);
{value,_} ->
gb_trees:update(Y, Type, Ys0)
end,
check_try_catch_tags(Type, Y, Ys0),
Vst#vst{current=St#st{y=Ys}};
set_type_y(Type, Reg, #vst{}) -> error({invalid_store,Reg,Type}).
make_fragile({fragile,_}=Type) -> Type;
make_fragile(Type) -> {fragile,Type}.
set_catch_end({y,Y}, #vst{current=#st{y=Ys0}=St}=Vst) ->
Ys = gb_trees:update(Y, initialized, Ys0),
Vst#vst{current=St#st{y=Ys}}.
check_try_catch_tags(Type, LastY, Ys) ->
case is_try_catch_tag(Type) of
false ->
ok;
true ->
%% Every catch or try/catch must use a lower Y register
%% number than any enclosing catch or try/catch. That will
%% ensure that when the stack is scanned when an
%% exception occurs, the innermost try/catch tag is found
%% first.
Bad = [{{y,Y},Tag} || {Y,Tag} <- gb_trees:to_list(Ys),
Y < LastY, is_try_catch_tag(Tag)],
case Bad of
[] ->
ok;
[_|_] ->
error({bad_try_catch_nesting,{y,LastY},Bad})
end
end.
is_try_catch_tag({catchtag,_}) -> true;
is_try_catch_tag({trytag,_}) -> true;
is_try_catch_tag(_) -> false.
is_reg_defined({x,_}=Reg, Vst) -> is_type_defined_x(Reg, Vst);
is_reg_defined({y,_}=Reg, Vst) -> is_type_defined_y(Reg, Vst);
is_reg_defined(V, #vst{}) -> error({not_a_register, V}).
is_type_defined_x({x,X}, #vst{current=#st{x=Xs}}) ->
gb_trees:is_defined(X,Xs).
is_type_defined_y({y,Y}, #vst{current=#st{y=Ys}}) ->
gb_trees:is_defined(Y,Ys).
assert_term(Src, Vst) ->
get_term_type(Src, Vst),
ok.
%% The possible types.
%%
%% First non-term types:
%%
%% initialized Only for Y registers. Means that the Y register
%% has been initialized with some valid term so that
%% it is safe to pass to the garbage collector.
%% NOT safe to use in any other way (will not crash the
%% emulator, but clearly points to a bug in the compiler).
%%
%% {catchtag,[Lbl]} A special term used within a catch. Must only be used
%% by the catch instructions; NOT safe to use in other
%% instructions.
%%
%% {trytag,[Lbl]} A special term used within a try block. Must only be
%% used by the catch instructions; NOT safe to use in other
%% instructions.
%%
%% exception Can only be used as a type returned by return_type/2
%% (which gives the type of the value returned by a BIF).
%% Thus 'exception' is never stored as type descriptor
%% for a register.
%%
%% #ms{} A match context for bit syntax matching. We do allow
%% it to moved/to from stack, but otherwise it must only
%% be accessed by bit syntax matching instructions.
%%
%%
%% Normal terms:
%%
%% term Any valid Erlang (but not of the special types above).
%%
%% bool The atom 'true' or the atom 'false'.
%%
%% cons Cons cell: [_|_]
%%
%% nil Empty list: []
%%
%% {tuple,[Sz]} Tuple. An element has been accessed using
%% element/2 or setelement/3 so that it is known that
%% the type is a tuple of size at least Sz.
%%
%% {tuple,Sz} Tuple. A test_arity instruction has been seen
%% so that it is known that the size is exactly Sz.
%%
%% {atom,[]} Atom.
%% {atom,Atom}
%%
%% {integer,[]} Integer.
%% {integer,Integer}
%%
%% {float,[]} Float.
%% {float,Float}
%%
%% number Integer or Float of unknown value
%%
%% map Map.
%%
%%
%%
%% FRAGILITY
%% ---------
%%
%% The loop_rec/2 instruction may return a reference to a term that is
%% not part of the root set. That term or any part of it must not be
%% included in a garbage collection. Therefore, the term (or any part
%% of it) must not be stored in an Y register.
%%
%% Such terms are wrapped in a {fragile,Type} tuple, where Type is one
%% of the types described above.
assert_type(WantedType, Term, Vst) ->
case get_term_type(Term, Vst) of
{fragile,Type} ->
assert_type(WantedType, Type);
Type ->
assert_type(WantedType, Type)
end.
assert_type(Correct, Correct) -> ok;
assert_type(float, {float,_}) -> ok;
assert_type(tuple, {tuple,_}) -> ok;
assert_type(tuple, {literal,Tuple}) when is_tuple(Tuple) -> ok;
assert_type({tuple_element,I}, {tuple,[Sz]})
when 1 =< I, I =< Sz ->
ok;
assert_type({tuple_element,I}, {tuple,Sz})
when is_integer(Sz), 1 =< I, I =< Sz ->
ok;
assert_type({tuple_element,I}, {literal,Lit}) when I =< tuple_size(Lit) ->
ok;
assert_type(cons, {literal,[_|_]}) ->
ok;
assert_type(Needed, Actual) ->
error({bad_type,{needed,Needed},{actual,Actual}}).
%% upgrade_tuple_type(NewTupleType, OldType) -> TupleType.
%% upgrade_tuple_type/2 is used when linear code finds out more and
%% more information about a tuple type, so that the type gets more
%% specialized. If OldType is not a tuple type, the type information
%% is inconsistent, and we know that some instructions will never
%% be executed at run-time.
upgrade_tuple_type(NewType, {fragile,OldType}) ->
make_fragile(upgrade_tuple_type_1(NewType, OldType));
upgrade_tuple_type(NewType, OldType) ->
upgrade_tuple_type_1(NewType, OldType).
upgrade_tuple_type_1({tuple,[Sz]}, {tuple,[OldSz]}=T) when Sz < OldSz ->
%% The old type has a higher value for the least tuple size.
T;
upgrade_tuple_type_1({tuple,[Sz]}, {tuple,OldSz}=T)
when is_integer(Sz), is_integer(OldSz), Sz =< OldSz ->
%% The old size is exact, and the new size is smaller than the old size.
T;
upgrade_tuple_type_1({tuple,_}=T, _) ->
%% The new type information is exact or has a higher value for
%% the least tuple size.
%% Note that inconsistencies are also handled in this
%% clause, e.g. if the old type was an integer or a tuple accessed
%% outside its size; inconsistences will generally cause an exception
%% at run-time but are safe from our point of view.
T.
get_tuple_size({integer,[]}) -> 0;
get_tuple_size({integer,Sz}) -> Sz;
get_tuple_size(_) -> 0.
validate_src(Ss, Vst) when is_list(Ss) ->
foreach(fun(S) -> get_term_type(S, Vst) end, Ss).
%% get_move_term_type(Src, ValidatorState) -> Type
%% Get the type of the source Src. The returned type Type will be
%% a standard Erlang type (no catch/try tags). Match contexts are OK.
get_move_term_type(Src, Vst) ->
case get_term_type_1(Src, Vst) of
initialized -> error({unassigned,Src});
{catchtag,_} -> error({catchtag,Src});
{trytag,_} -> error({trytag,Src});
tuple_in_progress -> error({tuple_in_progress,Src});
Type -> Type
end.
%% get_term_type(Src, ValidatorState) -> Type
%% Get the type of the source Src. The returned type Type will be
%% a standard Erlang type (no catch/try tags or match contexts).
get_term_type(Src, Vst) ->
case get_move_term_type(Src, Vst) of
#ms{} -> error({match_context,Src});
Type -> Type
end.
%% get_special_y_type(Src, ValidatorState) -> Type
%% Return the type for the Y register without doing any validity checks.
get_special_y_type({y,_}=Reg, Vst) -> get_term_type_1(Reg, Vst);
get_special_y_type(Src, _) -> error({source_not_y_reg,Src}).
get_term_type_1(nil=T, _) -> T;
get_term_type_1({atom,A}=T, _) when is_atom(A) -> T;
get_term_type_1({float,F}=T, _) when is_float(F) -> T;
get_term_type_1({integer,I}=T, _) when is_integer(I) -> T;
get_term_type_1({literal,Map}, _) when is_map(Map) -> map;
get_term_type_1({literal,_}=T, _) -> T;
get_term_type_1({x,X}=Reg, #vst{current=#st{x=Xs}}) when is_integer(X) ->
case gb_trees:lookup(X, Xs) of
{value,Type} -> Type;
none -> error({uninitialized_reg,Reg})
end;
get_term_type_1({y,Y}=Reg, #vst{current=#st{y=Ys}}) when is_integer(Y) ->
case gb_trees:lookup(Y, Ys) of
none -> error({uninitialized_reg,Reg});
{value,uninitialized} -> error({uninitialized_reg,Reg});
{value,Type} -> Type
end;
get_term_type_1(Src, _) -> error({bad_source,Src}).
%% get_literal(Src) -> literal_value().
get_literal(nil) -> [];
get_literal({atom,A}) when is_atom(A) -> A;
get_literal({float,F}) when is_float(F) -> F;
get_literal({integer,I}) when is_integer(I) -> I;
get_literal({literal,L}) -> L;
get_literal(T) -> error({not_literal,T}).
branch_arities([], _, #vst{}=Vst) -> Vst;
branch_arities([Sz,{f,L}|T], Tuple, #vst{current=St}=Vst0)
when is_integer(Sz) ->
Vst1 = set_type_reg({tuple,Sz}, Tuple, Vst0),
Vst = branch_state(L, Vst1),
branch_arities(T, Tuple, Vst#vst{current=St}).
branch_state(0, #vst{}=Vst) ->
%% If the instruction fails, the stack may be scanned
%% looking for a catch tag. Therefore the Y registers
%% must be initialized at this point.
verify_y_init(Vst),
Vst;
branch_state(L, #vst{current=St,branched=B}=Vst) ->
Vst#vst{
branched=case gb_trees:is_defined(L, B) of
false ->
gb_trees:insert(L, St, B);
true ->
MergedSt = merge_states(L, St, B),
gb_trees:update(L, MergedSt, B)
end}.
%% merge_states/3 is used when there are more than one way to arrive
%% at this point, and the type states for the different paths has
%% to be merged. The type states are downgraded to the least common
%% subset for the subsequent code.
merge_states(L, St, Branched) when L =/= 0 ->
case gb_trees:lookup(L, Branched) of
none -> St;
{value,OtherSt} when St =:= none -> OtherSt;
{value,OtherSt} -> merge_states_1(St, OtherSt)
end.
merge_states_1(#st{x=Xs0,y=Ys0,numy=NumY0,h=H0,ct=Ct0},
#st{x=Xs1,y=Ys1,numy=NumY1,h=H1,ct=Ct1}) ->
NumY = merge_stk(NumY0, NumY1),
Xs = merge_regs(Xs0, Xs1),
Ys = merge_y_regs(Ys0, Ys1),
Ct = merge_ct(Ct0, Ct1),
#st{x=Xs,y=Ys,numy=NumY,h=min(H0, H1),ct=Ct}.
merge_stk(S, S) -> S;
merge_stk(_, _) -> undecided.
merge_ct(S, S) -> S;
merge_ct(Ct0, Ct1) -> merge_ct_1(Ct0, Ct1).
merge_ct_1([C0|Ct0], [C1|Ct1]) ->
[ordsets:from_list(C0++C1)|merge_ct_1(Ct0, Ct1)];
merge_ct_1([], []) -> [];
merge_ct_1(_, _) -> undecided.
merge_regs(Rs0, Rs1) ->
Rs = merge_regs_1(gb_trees:to_list(Rs0), gb_trees:to_list(Rs1)),
gb_trees_from_list(Rs).
merge_regs_1([Same|Rs1], [Same|Rs2]) ->
[Same|merge_regs_1(Rs1, Rs2)];
merge_regs_1([{R1,_}|Rs1], [{R2,_}|_]=Rs2) when R1 < R2 ->
merge_regs_1(Rs1, Rs2);
merge_regs_1([{R1,_}|_]=Rs1, [{R2,_}|Rs2]) when R1 > R2 ->
merge_regs_1(Rs1, Rs2);
merge_regs_1([{R,Type1}|Rs1], [{R,Type2}|Rs2]) ->
[{R,merge_types(Type1, Type2)}|merge_regs_1(Rs1, Rs2)];
merge_regs_1([], []) -> [];
merge_regs_1([], [_|_]) -> [];
merge_regs_1([_|_], []) -> [].
merge_y_regs(Rs0, Rs1) ->
case {gb_trees:size(Rs0),gb_trees:size(Rs1)} of
{Sz0,Sz1} when Sz0 < Sz1 ->
merge_y_regs_1(Sz0-1, Rs1, Rs0);
{_,Sz1} ->
merge_y_regs_1(Sz1-1, Rs0, Rs1)
end.
merge_y_regs_1(Y, S, Regs0) when Y >= 0 ->
Type0 = gb_trees:get(Y, Regs0),
case gb_trees:get(Y, S) of
Type0 ->
merge_y_regs_1(Y-1, S, Regs0);
Type1 ->
Type = merge_types(Type0, Type1),
Regs = gb_trees:update(Y, Type, Regs0),
merge_y_regs_1(Y-1, S, Regs)
end;
merge_y_regs_1(_, _, Regs) -> Regs.
%% merge_types(Type1, Type2) -> Type
%% Return the most specific type possible.
%% Note: Type1 must NOT be the same as Type2.
merge_types({fragile,Same}=Type, Same) ->
Type;
merge_types({fragile,T1}, T2) ->
make_fragile(merge_types(T1, T2));
merge_types(Same, {fragile,Same}=Type) ->
Type;
merge_types(T1, {fragile,T2}) ->
make_fragile(merge_types(T1, T2));
merge_types(uninitialized=I, _) -> I;
merge_types(_, uninitialized=I) -> I;
merge_types(initialized=I, _) -> I;
merge_types(_, initialized=I) -> I;
merge_types({catchtag,T0},{catchtag,T1}) ->
{catchtag,ordsets:from_list(T0++T1)};
merge_types({trytag,T0},{trytag,T1}) ->
{trytag,ordsets:from_list(T0++T1)};
merge_types({tuple,A}, {tuple,B}) ->
{tuple,[min(tuple_sz(A), tuple_sz(B))]};
merge_types({Type,A}, {Type,B})
when Type =:= atom; Type =:= integer; Type =:= float ->
if A =:= B -> {Type,A};
true -> {Type,[]}
end;
merge_types({Type,_}, number)
when Type =:= integer; Type =:= float ->
number;
merge_types(number, {Type,_})
when Type =:= integer; Type =:= float ->
number;
merge_types(bool, {atom,A}) ->
merge_bool(A);
merge_types({atom,A}, bool) ->
merge_bool(A);
merge_types(#ms{id=Id1,valid=B1,slots=Slots1},
#ms{id=Id2,valid=B2,slots=Slots2}) ->
Id = if
Id1 =:= Id2 -> Id1;
true -> make_ref()
end,
#ms{id=Id,valid=B1 band B2,slots=min(Slots1, Slots2)};
merge_types(T1, T2) when T1 =/= T2 ->
%% Too different. All we know is that the type is a 'term'.
term.
tuple_sz([Sz]) -> Sz;
tuple_sz(Sz) -> Sz.
merge_bool([]) -> {atom,[]};
merge_bool(true) -> bool;
merge_bool(false) -> bool;
merge_bool(_) -> {atom,[]}.
verify_y_init(#vst{current=#st{y=Ys}}) ->
verify_y_init_1(gb_trees:to_list(Ys)).
verify_y_init_1([]) -> ok;
verify_y_init_1([{Y,uninitialized}|_]) ->
error({uninitialized_reg,{y,Y}});
verify_y_init_1([{Y,{fragile,_}}|_]) ->
%% Unsafe. This term may be outside any heap belonging
%% to the process and would be corrupted by a GC.
error({fragile_message_reference,{y,Y}});
verify_y_init_1([{_,_}|Ys]) ->
verify_y_init_1(Ys).
verify_live(0, #vst{}) -> ok;
verify_live(N, #vst{current=#st{x=Xs}}) ->
verify_live_1(N, Xs).
verify_live_1(0, _) -> ok;
verify_live_1(N, Xs) when is_integer(N) ->
X = N-1,
case gb_trees:is_defined(X, Xs) of
false -> error({{x,X},not_live});
true -> verify_live_1(X, Xs)
end;
verify_live_1(N, _) -> error({bad_number_of_live_regs,N}).
verify_no_ct(#vst{current=#st{numy=none}}) -> ok;
verify_no_ct(#vst{current=#st{numy=undecided}}) ->
error(unknown_size_of_stackframe);
verify_no_ct(#vst{current=#st{y=Ys}}) ->
case [Y || Y <- gb_trees:to_list(Ys), verify_no_ct_1(Y)] of
[] -> ok;
CT -> error({unfinished_catch_try,CT})
end.
verify_no_ct_1({_, {catchtag, _}}) -> true;
verify_no_ct_1({_, {trytag, _}}) -> true;
verify_no_ct_1({_, _}) -> false.
eat_heap(N, #vst{current=#st{h=Heap0}=St}=Vst) ->
case Heap0-N of
Neg when Neg < 0 ->
error({heap_overflow,{left,Heap0},{wanted,N}});
Heap ->
Vst#vst{current=St#st{h=Heap}}
end.
eat_heap_float(#vst{current=#st{hf=HeapFloats0}=St}=Vst) ->
case HeapFloats0-1 of
Neg when Neg < 0 ->
error({heap_overflow,{left,{HeapFloats0,floats}},{wanted,{1,floats}}});
HeapFloats ->
Vst#vst{current=St#st{hf=HeapFloats}}
end.
remove_fragility(#vst{current=#st{x=Xs0,y=Ys0}=St0}=Vst) ->
F = fun(_, {fragile,Type}) -> Type;
(_, Type) -> Type
end,
Xs = gb_trees:map(F, Xs0),
Ys = gb_trees:map(F, Ys0),
St = St0#st{x=Xs,y=Ys},
Vst#vst{current=St}.
propagate_fragility(Type, Ss, Vst) ->
F = fun(S) ->
case get_term_type_1(S, Vst) of
{fragile,_} -> true;
_ -> false
end
end,
case any(F, Ss) of
true -> make_fragile(Type);
false -> Type
end.
bif_type('-', Src, Vst) ->
arith_type(Src, Vst);
bif_type('+', Src, Vst) ->
arith_type(Src, Vst);
bif_type('*', Src, Vst) ->
arith_type(Src, Vst);
bif_type(abs, [Num], Vst) ->
case get_term_type(Num, Vst) of
{float,_}=T -> T;
{integer,_}=T -> T;
_ -> number
end;
bif_type(float, _, _) -> {float,[]};
bif_type('/', _, _) -> {float,[]};
%% Integer operations.
bif_type(ceil, [_], _) -> {integer,[]};
bif_type('div', [_,_], _) -> {integer,[]};
bif_type(floor, [_], _) -> {integer,[]};
bif_type('rem', [_,_], _) -> {integer,[]};
bif_type(length, [_], _) -> {integer,[]};
bif_type(size, [_], _) -> {integer,[]};
bif_type(trunc, [_], _) -> {integer,[]};
bif_type(round, [_], _) -> {integer,[]};
bif_type('band', [_,_], _) -> {integer,[]};
bif_type('bor', [_,_], _) -> {integer,[]};
bif_type('bxor', [_,_], _) -> {integer,[]};
bif_type('bnot', [_], _) -> {integer,[]};
bif_type('bsl', [_,_], _) -> {integer,[]};
bif_type('bsr', [_,_], _) -> {integer,[]};
%% Booleans.
bif_type('==', [_,_], _) -> bool;
bif_type('/=', [_,_], _) -> bool;
bif_type('=<', [_,_], _) -> bool;
bif_type('<', [_,_], _) -> bool;
bif_type('>=', [_,_], _) -> bool;
bif_type('>', [_,_], _) -> bool;
bif_type('=:=', [_,_], _) -> bool;
bif_type('=/=', [_,_], _) -> bool;
bif_type('not', [_], _) -> bool;
bif_type('and', [_,_], _) -> bool;
bif_type('or', [_,_], _) -> bool;
bif_type('xor', [_,_], _) -> bool;
bif_type(is_atom, [_], _) -> bool;
bif_type(is_boolean, [_], _) -> bool;
bif_type(is_binary, [_], _) -> bool;
bif_type(is_float, [_], _) -> bool;
bif_type(is_function, [_], _) -> bool;
bif_type(is_integer, [_], _) -> bool;
bif_type(is_list, [_], _) -> bool;
bif_type(is_map, [_], _) -> bool;
bif_type(is_number, [_], _) -> bool;
bif_type(is_pid, [_], _) -> bool;
bif_type(is_port, [_], _) -> bool;
bif_type(is_reference, [_], _) -> bool;
bif_type(is_tuple, [_], _) -> bool;
%% Misc.
bif_type(node, [], _) -> {atom,[]};
bif_type(node, [_], _) -> {atom,[]};
bif_type(hd, [_], _) -> term;
bif_type(tl, [_], _) -> term;
bif_type(get, [_], _) -> term;
bif_type(Bif, _, _) when is_atom(Bif) -> term.
is_bif_safe('/=', 2) -> true;
is_bif_safe('<', 2) -> true;
is_bif_safe('=/=', 2) -> true;
is_bif_safe('=:=', 2) -> true;
is_bif_safe('=<', 2) -> true;
is_bif_safe('==', 2) -> true;
is_bif_safe('>', 2) -> true;
is_bif_safe('>=', 2) -> true;
is_bif_safe(is_atom, 1) -> true;
is_bif_safe(is_boolean, 1) -> true;
is_bif_safe(is_binary, 1) -> true;
is_bif_safe(is_bitstring, 1) -> true;
is_bif_safe(is_float, 1) -> true;
is_bif_safe(is_function, 1) -> true;
is_bif_safe(is_integer, 1) -> true;
is_bif_safe(is_list, 1) -> true;
is_bif_safe(is_map, 1) -> true;
is_bif_safe(is_number, 1) -> true;
is_bif_safe(is_pid, 1) -> true;
is_bif_safe(is_port, 1) -> true;
is_bif_safe(is_reference, 1) -> true;
is_bif_safe(is_tuple, 1) -> true;
is_bif_safe(get, 1) -> true;
is_bif_safe(self, 0) -> true;
is_bif_safe(node, 0) -> true;
is_bif_safe(_, _) -> false.
arith_type([A,B], Vst) ->
case {get_term_type(A, Vst),get_term_type(B, Vst)} of
{{float,_},_} -> {float,[]};
{_,{float,_}} -> {float,[]};
{_,_} -> number
end;
arith_type(_, _) -> number.
return_type({extfunc,M,F,A}, Vst) -> return_type_1(M, F, A, Vst);
return_type(_, _) -> term.
return_type_1(erlang, setelement, 3, Vst) ->
Tuple = {x,1},
TupleType =
case get_term_type(Tuple, Vst) of
{tuple,_}=TT ->
TT;
{literal,Lit} when is_tuple(Lit) ->
{tuple,tuple_size(Lit)};
_ ->
{tuple,[0]}
end,
case get_term_type({x,0}, Vst) of
{integer,[]} -> TupleType;
{integer,I} -> upgrade_tuple_type({tuple,[I]}, TupleType);
_ -> TupleType
end;
return_type_1(erlang, F, A, _) ->
return_type_erl(F, A);
return_type_1(math, F, A, _) ->
return_type_math(F, A);
return_type_1(M, F, A, _) when is_atom(M), is_atom(F), is_integer(A), A >= 0 ->
term.
return_type_erl(exit, 1) -> exception;
return_type_erl(throw, 1) -> exception;
return_type_erl(error, 1) -> exception;
return_type_erl(error, 2) -> exception;
return_type_erl(F, A) when is_atom(F), is_integer(A), A >= 0 -> term.
return_type_math(cos, 1) -> {float,[]};
return_type_math(cosh, 1) -> {float,[]};
return_type_math(sin, 1) -> {float,[]};
return_type_math(sinh, 1) -> {float,[]};
return_type_math(tan, 1) -> {float,[]};
return_type_math(tanh, 1) -> {float,[]};
return_type_math(acos, 1) -> {float,[]};
return_type_math(acosh, 1) -> {float,[]};
return_type_math(asin, 1) -> {float,[]};
return_type_math(asinh, 1) -> {float,[]};
return_type_math(atan, 1) -> {float,[]};
return_type_math(atanh, 1) -> {float,[]};
return_type_math(erf, 1) -> {float,[]};
return_type_math(erfc, 1) -> {float,[]};
return_type_math(exp, 1) -> {float,[]};
return_type_math(log, 1) -> {float,[]};
return_type_math(log2, 1) -> {float,[]};
return_type_math(log10, 1) -> {float,[]};
return_type_math(sqrt, 1) -> {float,[]};
return_type_math(atan2, 2) -> {float,[]};
return_type_math(pow, 2) -> {float,[]};
return_type_math(ceil, 1) -> {float,[]};
return_type_math(floor, 1) -> {float,[]};
return_type_math(fmod, 2) -> {float,[]};
return_type_math(pi, 0) -> {float,[]};
return_type_math(F, A) when is_atom(F), is_integer(A), A >= 0 -> term.
check_limit({x,X}) when is_integer(X), X < 1023 ->
%% Note: x(1023) is reserved for use by the BEAM loader.
ok;
check_limit({y,Y}) when is_integer(Y), Y < 1024 ->
ok;
check_limit({fr,Fr}) when is_integer(Fr), Fr < 1024 ->
ok;
check_limit(_) ->
error(limit).
min(A, B) when is_integer(A), is_integer(B), A < B -> A;
min(A, B) when is_integer(A), is_integer(B) -> B.
gb_trees_from_list(L) -> gb_trees:from_orddict(lists:sort(L)).
error(Error) -> throw(Error).
