%% =====================================================================
%% %CopyrightBegin%
%%
%% Copyright Ericsson AB 2004-2014. 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%
%%
%% Message analysis of Core Erlang programs.
%%
%% Copyright (C) 2002 Richard Carlsson
%%
%% Author contact: [email protected]
%% =====================================================================
%% TODO: might need a "top" (`any') element for any-length value lists.
-module(cerl_messagean).
-export([annotate/1]).
-import(cerl, [alias_pat/1, alias_var/1, ann_c_var/2, ann_c_fun/3,
apply_args/1, apply_op/1, atom_val/1, bitstr_size/1,
bitstr_val/1, binary_segments/1, c_letrec/2,
ann_c_tuple/2, c_nil/0, call_args/1, call_module/1,
call_name/1, case_arg/1, case_clauses/1, catch_body/1,
clause_body/1, clause_guard/1, clause_pats/1, cons_hd/1,
cons_tl/1, fun_body/1, fun_vars/1, get_ann/1, int_val/1,
is_c_atom/1, is_c_int/1, let_arg/1, let_body/1,
let_vars/1, letrec_body/1, letrec_defs/1, module_defs/1,
module_defs/1, module_exports/1, pat_vars/1,
primop_args/1, primop_name/1, receive_action/1,
receive_clauses/1, receive_timeout/1, seq_arg/1,
seq_body/1, set_ann/2, try_arg/1, try_body/1, try_vars/1,
try_evars/1, try_handler/1, tuple_es/1, type/1,
values_es/1]).
-import(cerl_trees, [get_label/1]).
-define(DEF_LIMIT, 4).
%% -export([test/1, test1/1, ttest/1]).
%% ttest(F) ->
%% {T, _} = cerl_trees:label(user_default:read(F)),
%% {Time0, _} = erlang:statistics(runtime),
%% analyze(T),
%% {Time1, _} = erlang:statistics(runtime),
%% Time1 - Time0.
%% test(F) ->
%% {T, _} = cerl_trees:label(user_default:read(F)),
%% {Time0, _} = erlang:statistics(runtime),
%% {Esc, _Vars} = analyze(T),
%% {Time1, _} = erlang:statistics(runtime),
%% io:fwrite("messages: ~p.\n", [Esc]),
%% Set = sets:from_list(Esc),
%% H = fun (Node, Ctxt, Cont) ->
%% Doc = case get_ann(Node) of
%% [{label, L} | _] ->
%% B = sets:is_element(L, Set),
%% bf(Node, Ctxt, Cont, B);
%% _ ->
%% bf(Node, Ctxt, Cont, false)
%% end,
%% case type(Node) of
%% cons -> color(Doc);
%% tuple -> color(Doc);
%% _ -> Doc
%% end
%% end,
%% {ok, FD} = file:open("out.html",[write]),
%% Txt = cerl_prettypr:format(T, [{hook, H},{user,false}]),
%% io:put_chars(FD, "<pre>\n"),
%% io:put_chars(FD, html(Txt)),
%% io:put_chars(FD, "</pre>\n"),
%% file:close(FD),
%% {ok, Time1 - Time0}.
%% test1(F) ->
%% {T, _} = cerl_trees:label(user_default:read(F)),
%% {Time0, _} = erlang:statistics(runtime),
%% {T1, Esc, Vars} = annotate(T),
%% {Time1, _} = erlang:statistics(runtime),
%% io:fwrite("messages: ~p.\n", [Esc]),
%% %%% io:fwrite("vars: ~p.\n", [[X || X <- dict:to_list(Vars)]]),
%% T2 = hhl_transform:transform(T1, Vars),
%% Set = sets:from_list(Esc),
%% H = fun (Node, Ctxt, Cont) ->
%% case get_ann(Node) of
%% [{label, L} | _] ->
%% B = sets:is_element(L, Set),
%% bf(Node, Ctxt, Cont, B);
%% _ ->
%% bf(Node, Ctxt, Cont, false)
%% end
%% end,
%% {ok, FD} = file:open("out.html",[write]),
%% Txt = cerl_prettypr:format(T2, [{hook, H},{user,false}]),
%% io:put_chars(FD, "<pre>\n"),
%% io:put_chars(FD, html(Txt)),
%% io:put_chars(FD, "</pre>\n"),
%% file:close(FD),
%% {ok, Time1 - Time0}.
%% html(Cs) ->
%% html(Cs, []).
%% html([$#, $< | Cs], As) ->
%% html_1(Cs, [$< | As]);
%% html([$< | Cs], As) ->
%% html(Cs, ";tl&" ++ As);
%% html([$> | Cs], As) ->
%% html(Cs, ";tg&" ++ As);
%% html([$& | Cs], As) ->
%% html(Cs, ";pma&" ++ As);
%% html([C | Cs], As) ->
%% html(Cs, [C | As]);
%% html([], As) ->
%% lists:reverse(As).
%% html_1([$> | Cs], As) ->
%% html(Cs, [$> | As]);
%% html_1([C | Cs], As) ->
%% html_1(Cs, [C | As]).
%% bf(Node, Ctxt, Cont, B) ->
%% B0 = cerl_prettypr:get_ctxt_user(Ctxt),
%% if B /= B0 ->
%% Ctxt1 = cerl_prettypr:set_ctxt_user(Ctxt, B),
%% Doc = Cont(Node, Ctxt1),
%% case B of
%% true ->
%% Start = "<b>",
%% End = "</b>";
%% false ->
%% Start = "</b>",
%% End = "<b>"
%% end,
%% markup(Doc, Start, End);
%% true ->
%% Cont(Node, Ctxt)
%% end.
%% color(Doc) ->
%% % Doc.
%% markup(Doc, "<font color=blue>", "</font>").
%% markup(Doc, Start, End) ->
%% prettypr:beside(
%% prettypr:null_text([$# | Start]),
%% prettypr:beside(Doc,
%% prettypr:null_text([$# | End]))).
%% =====================================================================
%% annotate(Tree) -> {Tree1, Escapes, Vars}
%%
%% Tree = cerl:cerl()
%%
%% Analyzes `Tree' (see `analyze') and appends a term 'escapes', to
%% the annotation list of each constructor expression node and of
%% `Tree', corresponding to the escape information derived by the
%% analysis. Any previous such annotations are removed from `Tree'.
%% `Tree1' is the modified tree; for details on `OutList',
%% `Outputs' , `Dependencies', `Escapes' and `Parents', see
%% `analyze'.
%%
%% Note: `Tree' must be annotated with labels in order to use this
%% function; see `analyze' for details.
-type label() :: integer() | 'external' | 'top'.
-type ordset(X) :: [X]. % XXX: TAKE ME OUT
-spec annotate(cerl:cerl()) -> {cerl:cerl(), ordset(label()), dict:dict()}.
annotate(Tree) ->
{Esc0, Vars} = analyze(Tree),
Esc = sets:from_list(Esc0),
F = fun (T) ->
case type(T) of
literal -> T;
%%% var ->
%%% L = get_label(T),
%%% T1 = ann_escape(T, L, Esc),
%%% X = dict:fetch(L, Vars),
%%% set_ann(T1, append_ann({s,X}, get_ann(T1)));
_ ->
L = get_label(T),
ann_escape(T, L, Esc)
end
end,
{cerl_trees:map(F, Tree), Esc0, Vars}.
ann_escape(T, L, Esc) ->
case sets:is_element(L, Esc) of
true ->
set_ann(T, append_ann(escapes, get_ann(T)));
false ->
T
end.
append_ann(Tag, [X | Xs]) ->
if tuple_size(X) >= 1, element(1, X) =:= Tag ->
append_ann(Tag, Xs);
true ->
[X | append_ann(Tag, Xs)]
end;
append_ann(Tag, []) ->
[Tag].
%% =====================================================================
%% analyze(Tree) -> Escapes
%%
%% Tree = cerl:cerl()
%% Escapes = ordset(Label)
%% Label = integer() | external | top
%%
%% Analyzes a module or an expression represented by `Tree'.
%%
%% `Escapes' is the set of labels of constructor expressions in
%% `Tree' such that the created values may be accessed from outside
%% `Tree'.
%%
%% Note: `Tree' must be annotated with labels (as done by the
%% function `cerl_trees:label/1') in order to use this function.
%% The label annotation `{label, L}' (where L should be an integer)
%% must be the first element of the annotation list of each node in
%% the tree. Instances of variables bound in `Tree' which denote
%% the same variable must have the same label; apart from this,
%% labels should be unique. Constant literals do not need to be
%% labeled.
-record(state, {vars, out, dep, work, funs, k}).
%% Note: We assume that all remote calls and primops return a single
%% value.
%% The analysis determines which objects (identified by the
%% corresponding "cons-point" labels in the code) are likely to be
%% passed in a message. (If so, we say that they "escape".) It is always
%% safe to assume either case, because the send operation will assure
%% that things are copied if necessary. This analysis tries to
%% anticipate that copying will be done.
%%
%% Rules:
%% 1) An object passed as message argument (or part of such an
%% argument) to a known send-operation, will probably be a message.
%% 2) A received value is always a message (safe).
%% 3) The external function can return any object (unsafe).
%% 4) A function called from the external function can receive any
%% object (unsafe) as argument.
%% 5) Unknown functions/operations can return any object (unsafe).
%% We wrap the given syntax tree T in a fun-expression labeled `top',
%% which is initially in the set of escaped labels. `top' will be
%% visited at least once.
%%
%% We create a separate function labeled `external', defined as:
%% "'external'/1 = fun () -> Any", which will represent any and all
%% functions outside T, and which returns the 'unsafe' value.
analyze(Tree) ->
analyze(Tree, ?DEF_LIMIT).
analyze(Tree, Limit) ->
{_, _, Esc, Dep, _Par} = cerl_closurean:analyze(Tree),
%%% io:fwrite("dependencies: ~w.\n", [dict:to_list(Dep)]),
analyze(Tree, Limit, Dep, Esc).
analyze(Tree, Limit, Dep0, Esc0) ->
%% Note that we use different name spaces for variable labels and
%% function/call site labels, so we can reuse some names here. We
%% assume that the labeling of Tree only uses integers, not atoms.
Any = ann_c_var([{label, any}], 'Any'),
External = ann_c_var([{label, external}], {external, 1}),
ExtFun = ann_c_fun([{label, external}], [], Any),
%%% io:fwrite("external fun:\n~s.\n",
%%% [cerl_prettypr:format(ExtFun, [noann, {paper, 80}])]),
Top = ann_c_var([{label, top}], {top, 0}),
TopFun = ann_c_fun([{label, top}], [], Tree),
%% The "start fun" just makes the initialisation easier. It is not
%% itself in the call graph.
StartFun = ann_c_fun([{label, start}], [],
c_letrec([{External, ExtFun}, {Top, TopFun}],
c_nil())),
%%% io:fwrite("start fun:\n~s.\n",
%%% [cerl_prettypr:format(StartFun, [{paper, 80}])]),
%% Initialise the Any and Escape variables. Gather a database of all
%% fun-expressions in Tree and initialise their outputs and parameter
%% variables. All escaping functions can receive any values as
%% inputs. Bind all module- and letrec-defined variables to their
%% corresponding labels.
Esc = sets:from_list(Esc0),
Unsafe = unsafe(),
Empty = empty(),
Funs0 = dict:new(),
Vars0 = dict:store(escape, empty(),
dict:store(any, Unsafe, dict:new())),
Out0 = dict:new(),
F = fun (T, S = {Fs, Vs, Os}) ->
case type(T) of
'fun' ->
L = get_label(T),
As = fun_vars(T),
X = case sets:is_element(L, Esc) of
true -> Unsafe;
false -> Empty
end,
{dict:store(L, T, Fs),
bind_vars_single(As, X, Vs),
dict:store(L, none, Os)};
letrec ->
{Fs, bind_defs(letrec_defs(T), Vs), Os};
module ->
{Fs, bind_defs(module_defs(T), Vs), Os};
_ ->
S
end
end,
{Funs, Vars, Out} = cerl_trees:fold(F, {Funs0, Vars0, Out0}, StartFun),
%% Add the dependency for the loop in 'external':
Dep = add_dep(loop, external, Dep0),
%% Enter the fixpoint iteration at the StartFun.
St = loop(StartFun, start, #state{vars = Vars,
out = Out,
dep = Dep,
work = init_work(),
funs = Funs,
k = Limit}),
Ms = labels(dict:fetch(escape, St#state.vars)),
{Ms, St#state.vars}.
loop(T, L, St0) ->
%%% io:fwrite("analyzing: ~w.\n",[L]),
%%% io:fwrite("work: ~w.\n", [St0#state.work]),
Xs0 = dict:fetch(L, St0#state.out),
{Xs1, St1} = visit(fun_body(T), L, St0),
Xs = limit(Xs1, St1#state.k),
{W, M} = case equal(Xs0, Xs) of
true ->
{St1#state.work, St1#state.out};
false ->
%%% io:fwrite("out (~w) changed: ~w <- ~w.\n",
%%% [L, Xs, Xs0]),
M1 = dict:store(L, Xs, St1#state.out),
case dict:find(L, St1#state.dep) of
{ok, S} ->
{add_work(set__to_list(S), St1#state.work),
M1};
error ->
{St1#state.work, M1}
end
end,
St2 = St1#state{out = M},
case take_work(W) of
{ok, L1, W1} ->
T1 = dict:fetch(L1, St2#state.funs),
loop(T1, L1, St2#state{work = W1});
none ->
St2
end.
visit(T, L, St) ->
%%% io:fwrite("visiting: ~w.\n",[type(T)]),
case type(T) of
literal ->
%% This is (or should be) a constant, even if it's compound,
%% so it's bugger all whether it is sent or not.
case cerl:concrete(T) of
[] -> {[empty()], St};
X when is_atom(X) -> {[empty()], St};
X when is_integer(X) -> {[empty()], St};
X when is_float(X) -> {[empty()], St};
_ ->
exit({not_literal, T})
end;
var ->
%% If a variable is not already in the store here, it must
%% be free in the program.
L1 = get_label(T),
Vars = St#state.vars,
case dict:find(L1, Vars) of
{ok, X} ->
{[X], St};
error ->
%%% io:fwrite("free var: ~w.\n",[L1]),
X = unsafe(),
St1 = St#state{vars = dict:store(L1, X, Vars)},
{[X], St1}
end;
'fun' ->
%% Must revisit the fun also, because its environment might
%% have changed. (We don't keep track of such dependencies.)
L1 = get_label(T),
St1 = St#state{work = add_work([L1], St#state.work)},
%% Currently, lambda expressions can only be locally
%% allocated, and therefore we have to force copying by
%% treating them as "unsafe" for now.
{[unsafe()], St1};
%% {[singleton(L1)], St1};
values ->
visit_list(values_es(T), L, St);
cons ->
{[X1, X2], St1} = visit_list([cons_hd(T), cons_tl(T)], L, St),
L1 = get_label(T),
X = make_cons(L1, X1, X2),
%% Also store the values of the elements.
Hd = get_hd(X),
Tl = get_tl(X),
St2 = St1#state{vars = dict:store(L1, [Hd, Tl], St1#state.vars)},
{[X], St2};
tuple ->
{Xs, St1} = visit_list(tuple_es(T), L, St),
L1 = get_label(T),
%% Also store the values of the elements.
St2 = St1#state{vars = dict:store(L1, Xs, St1#state.vars)},
{[struct(L1, Xs)], St2};
'let' ->
{Xs, St1} = visit(let_arg(T), L, St),
Vars = bind_vars(let_vars(T), Xs, St1#state.vars),
visit(let_body(T), L, St1#state{vars = Vars});
seq ->
{_, St1} = visit(seq_arg(T), L, St),
visit(seq_body(T), L, St1);
apply ->
{_F, St1} = visit(apply_op(T), L, St),
{As, St2} = visit_list(apply_args(T), L, St1),
L1 = get_label(T),
Ls = get_deps(L1, St#state.dep),
Out = St2#state.out,
Xs1 = join_list([dict:fetch(X, Out) || X <- Ls]),
{Xs1, call_site(Ls, As, St2)};
call ->
M = call_module(T),
F = call_name(T),
As = call_args(T),
{_, St1} = visit(M, L, St),
{_, St2} = visit(F, L, St1),
{Xs, St3} = visit_list(As, L, St2),
L1 = get_label(T),
remote_call(M, F, Xs, As, L1, St3);
primop ->
As = primop_args(T),
{Xs, St1} = visit_list(As, L, St),
F = atom_val(primop_name(T)),
primop_call(F, length(Xs), Xs, As, St1);
'case' ->
{Xs, St1} = visit(case_arg(T), L, St),
visit_clauses(Xs, case_clauses(T), L, St1);
'receive' ->
%% The received value is of course a message, so it
%% is 'empty()', not 'unsafe()'.
X = empty(),
{Xs1, St1} = visit_clauses([X], receive_clauses(T), L, St),
{_, St2} = visit(receive_timeout(T), L, St1),
{Xs2, St3} = visit(receive_action(T), L, St2),
{join(Xs1, Xs2), St3};
'try' ->
{Xs1, St1} = visit(try_arg(T), L, St),
X = unsafe(),
Vars = bind_vars(try_vars(T), Xs1, St1#state.vars),
{Xs2, St2} = visit(try_body(T), L, St1#state{vars = Vars}),
EVars = bind_vars(try_evars(T), [X, X, X], St2#state.vars),
{Xs3, St3} = visit(try_handler(T), L, St2#state{vars = EVars}),
{join(Xs2, Xs3), St3};
'catch' ->
%% If we catch an exception, we can get unsafe data.
{Xs, St1} = visit(catch_body(T), L, St),
{join([unsafe()], Xs), St1};
binary ->
%% Binaries are heap objects, but we don't have special
%% shared-heap allocation operators for them at the moment.
%% They must therefore be treated as unsafe.
{_, St1} = visit_list(binary_segments(T), L, St),
{[unsafe()], St1};
bitstr ->
%% The other fields are constant literals.
{_, St1} = visit(bitstr_val(T), L, St),
{_, St2} = visit(bitstr_size(T), L, St1),
{none, St2};
letrec ->
%% All the bound funs should be revisited, because the
%% environment might have changed.
Ls = [get_label(F) || {_, F} <- letrec_defs(T)],
St1 = St#state{work = add_work(Ls, St#state.work)},
visit(letrec_body(T), L, St1);
module ->
%% We regard a module as a tuple of function variables in
%% the body of a `letrec'.
visit(c_letrec(module_defs(T),
ann_c_tuple([{label, get_label(T)}],
module_exports(T))),
L, St)
end.
visit_clause(T, Xs, L, St) ->
Vars = bind_pats(clause_pats(T), Xs, St#state.vars),
{_, St1} = visit(clause_guard(T), L, St#state{vars = Vars}),
visit(clause_body(T), L, St1).
%% We assume correct value-list typing.
visit_list([T | Ts], L, St) ->
{Xs, St1} = visit(T, L, St),
{Xs1, St2} = visit_list(Ts, L, St1),
X = case Xs of
[X1] -> X1;
_ -> empty()
end,
{[X | Xs1], St2};
visit_list([], _L, St) ->
{[], St}.
visit_clauses(Xs, [T | Ts], L, St) ->
{Xs1, St1} = visit_clause(T, Xs, L, St),
{Xs2, St2} = visit_clauses(Xs, Ts, L, St1),
{join(Xs1, Xs2), St2};
visit_clauses(_, [], _L, St) ->
{none, St}.
bind_defs([{V, F} | Ds], Vars) ->
bind_defs(Ds, dict:store(get_label(V), singleton(get_label(F)), Vars));
bind_defs([], Vars) ->
Vars.
bind_pats(Ps, none, Vars) ->
bind_pats_single(Ps, empty(), Vars);
bind_pats(Ps, Xs, Vars) ->
if length(Xs) =:= length(Ps) ->
bind_pats_list(Ps, Xs, Vars);
true ->
bind_pats_single(Ps, empty(), Vars)
end.
%% The lists might not be of the same length.
bind_pats_list([P | Ps], [X | Xs], Vars) ->
bind_pats_list(Ps, Xs, bind_pat_vars(P, X, Vars));
bind_pats_list(Ps, [], Vars) ->
bind_pats_single(Ps, empty(), Vars);
bind_pats_list([], _, Vars) ->
Vars.
bind_pats_single([P | Ps], X, Vars) ->
bind_pats_single(Ps, X, bind_pat_vars(P, X, Vars));
bind_pats_single([], _X, Vars) ->
Vars.
bind_pat_vars(P, X, Vars) ->
case type(P) of
var ->
dict:store(get_label(P), X, Vars);
literal ->
Vars;
cons ->
bind_pats_list([cons_hd(P), cons_tl(P)],
[get_hd(X), get_tl(X)], Vars);
tuple ->
case elements(X) of
none ->
bind_vars_single(pat_vars(P), X, Vars);
Xs ->
bind_pats_list(tuple_es(P), Xs, Vars)
end;
binary ->
%% See the handling of binary-expressions.
bind_pats_single(binary_segments(P), unsafe(), Vars);
bitstr ->
%% See the handling of binary-expressions.
bind_pats_single([bitstr_val(P), bitstr_size(P)],
unsafe(), Vars);
alias ->
P1 = alias_pat(P),
Vars1 = bind_pat_vars(P1, X, Vars),
dict:store(get_label(alias_var(P)), X, Vars1)
end.
%%% %% This is the "exact" version of list representation, which simply
%%% %% mimics the actual cons, head and tail operations.
%%% make_cons(L, X1, X2) ->
%%% struct(L1, [X1, X2]).
%%% get_hd(X) ->
%%% case elements(X) of
%%% none -> X;
%%% [X1 | _] -> X1;
%%% _ -> empty()
%%% end.
%%% get_tl(X) ->
%%% case elements(X) of
%%% none -> X;
%%% [_, X2 | _] -> X2;
%%% _ -> empty()
%%% end.
%% This version does not unnecessarily confuse spine labels with element
%% labels, and is safe. However, it loses precision if cons cells are
%% used for other things than proper lists.
make_cons(L, X1, X2) ->
%% join subtypes and cons locations
join_single(struct(L, [X1]), X2).
get_hd(X) ->
case elements(X) of
none -> X;
[X1 | _] -> X1; % First element represents list subtype.
_ -> empty()
end.
get_tl(X) -> X. % Tail of X has same type as X.
bind_vars(Vs, none, Vars) ->
bind_vars_single(Vs, empty(), Vars);
bind_vars(Vs, Xs, Vars) ->
if length(Vs) =:= length(Xs) ->
bind_vars_list(Vs, Xs, Vars);
true ->
bind_vars_single(Vs, empty(), Vars)
end.
bind_vars_list([V | Vs], [X | Xs], Vars) ->
bind_vars_list(Vs, Xs, dict:store(get_label(V), X, Vars));
bind_vars_list([], [], Vars) ->
Vars.
bind_vars_single([V | Vs], X, Vars) ->
bind_vars_single(Vs, X, dict:store(get_label(V), X, Vars));
bind_vars_single([], _X, Vars) ->
Vars.
%% This handles a call site, updating parameter variables with respect
%% to the actual parameters. The 'external' function is handled
%% specially, since it can get an arbitrary number of arguments. For our
%% purposes here, calls to the external function can be ignored.
call_site(Ls, Xs, St) ->
%%% io:fwrite("call site: ~w -> ~w (~w).\n", [L, Ls, Xs]),
{W, V} = call_site(Ls, Xs, St#state.work, St#state.vars,
St#state.funs, St#state.k),
St#state{work = W, vars = V}.
call_site([external | Ls], Xs, W, V, Fs, Limit) ->
call_site(Ls, Xs, W, V, Fs, Limit);
call_site([L | Ls], Xs, W, V, Fs, Limit) ->
Vs = fun_vars(dict:fetch(L, Fs)),
case bind_args(Vs, Xs, V, Limit) of
{V1, true} ->
call_site(Ls, Xs, add_work([L], W), V1, Fs, Limit);
{V1, false} ->
call_site(Ls, Xs, W, V1, Fs, Limit)
end;
call_site([], _, W, V, _, _) ->
{W, V}.
add_dep(Source, Target, Deps) ->
case dict:find(Source, Deps) of
{ok, X} ->
case set__is_member(Target, X) of
true ->
Deps;
false ->
%%% io:fwrite("new dep: ~w <- ~w.\n", [Target, Source]),
dict:store(Source, set__add(Target, X), Deps)
end;
error ->
%%% io:fwrite("new dep: ~w <- ~w.\n", [Target, Source]),
dict:store(Source, set__singleton(Target), Deps)
end.
%% If the arity does not match the call, nothing is done here.
bind_args(Vs, Xs, Vars, Limit) ->
if length(Vs) =:= length(Xs) ->
bind_args(Vs, Xs, Vars, Limit, false);
true ->
{Vars, false}
end.
bind_args([V | Vs], [X | Xs], Vars, Limit, Ch) ->
L = get_label(V),
{Vars1, Ch1} = bind_arg(L, X, Vars, Limit, Ch),
bind_args(Vs, Xs, Vars1, Limit, Ch1);
bind_args([], [], Vars, _Limit, Ch) ->
{Vars, Ch}.
%% bind_arg(L, X, Vars, Limit) ->
%% bind_arg(L, X, Vars, Limit, false).
bind_arg(L, X, Vars, Limit, Ch) ->
X0 = dict:fetch(L, Vars),
X1 = limit_single(join_single(X, X0), Limit),
case equal_single(X0, X1) of
true ->
{Vars, Ch};
false ->
%%% io:fwrite("arg (~w) changed: ~w <- ~w + ~w.\n",
%%% [L, X1, X0, X]),
{dict:store(L, X1, Vars), true}
end.
%% This handles escapes from things like primops and remote calls.
escape(Xs, Ns, St) ->
escape(Xs, Ns, 1, St).
escape([_ | Xs], Ns=[N1 | _], N, St) when is_integer(N1), N1 > N ->
escape(Xs, Ns, N + 1, St);
escape([X | Xs], [N | Ns], N, St) ->
Vars = St#state.vars,
X0 = dict:fetch(escape, Vars),
X1 = join_single(X, X0),
case equal_single(X0, X1) of
true ->
escape(Xs, Ns, N + 1, St);
false ->
%%% io:fwrite("escape changed: ~w <- ~w + ~w.\n", [X1, X0, X]),
Vars1 = dict:store(escape, X1, Vars),
escape(Xs, Ns, N + 1, St#state{vars = Vars1})
end;
escape(Xs, [_ | Ns], N, St) ->
escape(Xs, Ns, N + 1, St);
escape(_, _, _, St) ->
St.
%% Handle primop calls: (At present, we assume that all unknown calls
%% yield exactly one value. This might have to be changed.)
primop_call(F, A, Xs, _As, St0) ->
%% St1 = case is_escape_op(F, A) of
%% [] -> St0;
%% Ns -> escape(Xs, Ns, St0)
%% end,
St1 = St0,
case is_imm_op(F, A) of
true ->
{[empty()], St1};
false ->
call_unknown(Xs, St1)
end.
%% Handle remote-calls: (At present, we assume that all unknown calls
%% yield exactly one value. This might have to be changed.)
remote_call(M, F, Xs, As, L, St) ->
case is_c_atom(M) andalso is_c_atom(F) of
true ->
remote_call_1(atom_val(M), atom_val(F), length(Xs),
Xs, As, L, St);
false ->
%% Unknown function
call_unknown(Xs, St)
end.
%% When calling an unknown function, we assume that the result does
%% *not* contain any of the constructors in its arguments (but it could
%% return locally allocated data that we don't know about). Note that
%% even a "pure" function can still cons up new data.
call_unknown(_Xs, St) ->
{[unsafe()], St}.
%% We need to handle some important standard functions in order to get
%% decent precision.
%% TODO: foldl, map, mapfoldl
remote_call_1(erlang, hd, 1, [X], _As, _L, St) ->
{[get_hd(X)], St};
remote_call_1(erlang, tl, 1, [X], _As, _L, St) ->
{[get_tl(X)], St};
remote_call_1(erlang, element, 2, [_,X], [N|_], _L, St) ->
case elements(X) of
none -> {[X], St};
Xs ->
case is_c_int(N) of
true ->
N1 = int_val(N),
if is_integer(N1), 1 =< N1, N1 =< length(Xs) ->
{[nth(N1, Xs)], St};
true ->
{none, St}
end;
false ->
%% Even if we don't know which element is selected,
%% we know that the top level is never part of the
%% returned value.
{[join_single_list(Xs)], St}
end
end;
remote_call_1(erlang, setelement, 3, [_,X, Y], [N|_], L, St) ->
%% The constructor gets the label of the call operation.
case elements(X) of
none -> {[join_single(singleton(L), join_single(X, Y))], St};
Xs ->
case is_c_int(N) of
true ->
N1 = int_val(N),
if is_integer(N1), 1 =< N1, N1 =< length(Xs) ->
Xs1 = set_nth(N1, Y, Xs),
{[struct(L, Xs1)], St};
true ->
{none, St}
end;
false ->
%% Even if we don't know which element is selected,
%% we know that the top level is never part of the
%% returned value (a new tuple is always created).
Xs1 = [join_single(Y, X1) || X1 <- Xs],
{[struct(L, Xs1)], St}
end
end;
remote_call_1(erlang, '++', 2, [X1,X2], _As, _L, St) ->
%% Note: this is unsafe for non-proper lists! (See make_cons/3).
%% No safe version is implemented.
{[join_single(X1, X2)], St};
remote_call_1(erlang, '--', 2, [X1,_X2], _As, _L, St) ->
{[X1], St};
remote_call_1(lists, append, 2, Xs, As, L, St) ->
remote_call_1(erlang, '++', 2, Xs, As, L, St);
remote_call_1(lists, subtract, 2, Xs, As, L, St) ->
remote_call_1(erlang, '--', 2, Xs, As, L, St);
remote_call_1(M, F, A, Xs, _As, _L, St0) ->
St1 = case is_escape_op(M, F, A) of
[] -> St0;
Ns -> escape(Xs, Ns, St0)
end,
case is_imm_op(M, F, A) of
true ->
{[empty()], St1};
false ->
call_unknown(Xs, St1)
end.
%% 1-based n:th-element list selector and update function.
nth(1, [X | _Xs]) -> X;
nth(N, [_X | Xs]) when N > 1 -> nth(N - 1, Xs).
set_nth(1, Y, [_X | Xs]) -> [Y | Xs];
set_nth(N, Y, [X | Xs]) when N > 1 -> [X | set_nth(N - 1, Y, Xs)].
%% Domain: none | [V], where V = {S, none} | {S, [V]}, S = set(integer()).
join(none, Xs2) -> Xs2;
join(Xs1, none) -> Xs1;
join(Xs1, Xs2) ->
if length(Xs1) =:= length(Xs2) ->
join_1(Xs1, Xs2);
true ->
none
end.
join_1([X1 | Xs1], [X2 | Xs2]) ->
[join_single(X1, X2) | join_1(Xs1, Xs2)];
join_1([], []) ->
[].
join_list([Xs | Xss]) ->
join(Xs, join_list(Xss));
join_list([]) ->
none.
empty() -> {set__new(), []}.
singleton(X) -> {set__singleton(X), []}.
struct(X, Xs) -> {set__singleton(X), Xs}.
elements({_, Xs}) -> Xs.
unsafe() -> {set__singleton(unsafe), none}.
equal(none, none) -> true;
equal(none, _) -> false;
equal(_, none) -> false;
equal(X1, X2) -> equal_1(X1, X2).
equal_1([X1 | Xs1], [X2 | Xs2]) ->
equal_single(X1, X2) andalso equal_1(Xs1, Xs2);
equal_1([], []) -> true;
equal_1(_, _) -> false.
equal_single({S1, none}, {S2, none}) ->
set__equal(S1, S2);
equal_single({_, none}, _) ->
false;
equal_single(_, {_, none}) ->
false;
equal_single({S1, Vs1}, {S2, Vs2}) ->
set__equal(S1, S2) andalso equal_single_lists(Vs1, Vs2).
equal_single_lists([X1 | Xs1], [X2 | Xs2]) ->
equal_single(X1, X2) andalso equal_single_lists(Xs1, Xs2);
equal_single_lists([], []) ->
true;
equal_single_lists(_, _) ->
false.
join_single({S, none}, V) ->
{set__union(S, labels(V)), none};
join_single(V, {S, none}) ->
{set__union(S, labels(V)), none};
join_single({S1, Vs1}, {S2, Vs2}) ->
{set__union(S1, S2), join_single_lists(Vs1, Vs2)}.
join_single_list([V | Vs]) ->
join_single(V, join_single_list(Vs));
join_single_list([]) ->
empty().
%% If one list has more elements that the other, and N is the length of
%% the longer list, then the result has N elements.
join_single_lists([V1], [V2]) ->
[join_single(V1, V2)];
join_single_lists([V1 | Vs1], [V2 | Vs2]) ->
[join_single(V1, V2) | join_single_lists(Vs1, Vs2)];
join_single_lists([], Vs) -> Vs;
join_single_lists(Vs, []) -> Vs.
collapse(V) ->
{labels(V), none}.
%% collapse_list([]) ->
%% empty();
%% collapse_list(Vs) ->
%% {labels_list(Vs), none}.
labels({S, none}) -> S;
labels({S, []}) -> S;
labels({S, Vs}) -> set__union(S, labels_list(Vs)).
labels_list([V]) ->
labels(V);
labels_list([V | Vs]) ->
set__union(labels(V), labels_list(Vs)).
limit(none, _K) -> none;
limit(X, K) -> limit_list(X, K).
limit_list([X | Xs], K) ->
[limit_single(X, K) | limit_list(Xs, K)];
limit_list([], _) ->
[].
limit_single({_, none} = V, _K) ->
V;
limit_single({_, []} = V, _K) ->
V;
limit_single({S, Vs}, K) when K > 0 ->
{S, limit_list(Vs, K - 1)};
limit_single(V, _K) ->
collapse(V).
%% Set abstraction for label sets in the domain.
%% set__is_empty([]) -> true;
%% set__is_empty(_) -> false.
set__new() -> [].
set__singleton(X) -> [X].
set__to_list(S) -> S.
%% set__from_list(S) -> ordsets:from_list(S).
set__union(X, Y) -> ordsets:union(X, Y).
set__add(X, S) -> ordsets:add_element(X, S).
set__is_member(X, S) -> ordsets:is_element(X, S).
%% set__subtract(X, Y) -> ordsets:subtract(X, Y).
set__equal(X, Y) -> X =:= Y.
%% A simple but efficient functional queue.
queue__new() -> {[], []}.
queue__put(X, {In, Out}) -> {[X | In], Out}.
queue__get({In, [X | Out]}) -> {ok, X, {In, Out}};
queue__get({[], _}) -> empty;
queue__get({In, _}) ->
[X | In1] = lists:reverse(In),
{ok, X, {[], In1}}.
%% The work list - a queue without repeated elements.
init_work() ->
{queue__new(), sets:new()}.
add_work(Ls, {Q, Set}) ->
add_work(Ls, Q, Set).
%% Note that the elements are enqueued in order.
add_work([L | Ls], Q, Set) ->
case sets:is_element(L, Set) of
true ->
add_work(Ls, Q, Set);
false ->
add_work(Ls, queue__put(L, Q), sets:add_element(L, Set))
end;
add_work([], Q, Set) ->
{Q, Set}.
take_work({Queue0, Set0}) ->
case queue__get(Queue0) of
{ok, L, Queue1} ->
Set1 = sets:del_element(L, Set0),
{ok, L, {Queue1, Set1}};
empty ->
none
end.
get_deps(L, Dep) ->
case dict:find(L, Dep) of
{ok, Ls} -> Ls;
error -> []
end.
%% Escape operators may let their arguments escape. For this analysis,
%% only send-operations are considered as causing escapement, and only
%% in specific arguments.
%% is_escape_op(_F, _A) -> [].
-spec is_escape_op(atom(), atom(), arity()) -> [arity()].
is_escape_op(erlang, '!', 2) -> [2];
is_escape_op(erlang, send, 2) -> [2];
is_escape_op(erlang, spawn, 1) -> [1];
is_escape_op(erlang, spawn, 3) -> [3];
is_escape_op(erlang, spawn, 4) -> [4];
is_escape_op(erlang, spawn_link, 3) -> [3];
is_escape_op(erlang, spawn_link, 4) -> [4];
is_escape_op(_M, _F, _A) -> [].
%% "Immediate" operators will never return heap allocated data. This is
%% of course true for operators that never return, like 'exit/1'. (Note
%% that floats are always heap allocated objects, and that most integer
%% arithmetic can return a bignum on the heap.)
-spec is_imm_op(atom(), arity()) -> boolean().
is_imm_op(match_fail, 1) -> true;
is_imm_op(_, _) -> false.
-spec is_imm_op(atom(), atom(), arity()) -> boolean().
is_imm_op(erlang, self, 0) -> true;
is_imm_op(erlang, '=:=', 2) -> true;
is_imm_op(erlang, '==', 2) -> true;
is_imm_op(erlang, '=/=', 2) -> true;
is_imm_op(erlang, '/=', 2) -> true;
is_imm_op(erlang, '<', 2) -> true;
is_imm_op(erlang, '=<', 2) -> true;
is_imm_op(erlang, '>', 2) -> true;
is_imm_op(erlang, '>=', 2) -> true;
is_imm_op(erlang, 'and', 2) -> true;
is_imm_op(erlang, 'or', 2) -> true;
is_imm_op(erlang, 'xor', 2) -> true;
is_imm_op(erlang, 'not', 1) -> true;
is_imm_op(erlang, is_alive, 0) -> true;
is_imm_op(erlang, is_atom, 1) -> true;
is_imm_op(erlang, is_binary, 1) -> true;
is_imm_op(erlang, is_builtin, 3) -> true;
is_imm_op(erlang, is_float, 1) -> true;
is_imm_op(erlang, is_function, 1) -> true;
is_imm_op(erlang, is_integer, 1) -> true;
is_imm_op(erlang, is_list, 1) -> true;
is_imm_op(erlang, is_number, 1) -> true;
is_imm_op(erlang, is_pid, 1) -> true;
is_imm_op(erlang, is_port, 1) -> true;
is_imm_op(erlang, is_process_alive, 1) -> true;
is_imm_op(erlang, is_reference, 1) -> true;
is_imm_op(erlang, is_tuple, 1) -> true;
is_imm_op(erlang, length, 1) -> true; % never a bignum
is_imm_op(erlang, list_to_atom, 1) -> true;
is_imm_op(erlang, node, 0) -> true;
is_imm_op(erlang, node, 1) -> true;
is_imm_op(erlang, throw, 1) -> true;
is_imm_op(erlang, exit, 1) -> true;
is_imm_op(erlang, error, 1) -> true;
is_imm_op(erlang, error, 2) -> true;
is_imm_op(_M, _F, _A) -> false.
