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286 lines
10 KiB
286 lines
10 KiB
(*
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* Copyright (c) Facebook, Inc. and its affiliates.
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*
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* This source code is licensed under the MIT license found in the
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* LICENSE file in the root directory of this source tree.
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*)
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(** Interval abstract domain *)
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open Apron
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let equal_apron_typ =
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(* Apron.Texpr1.typ is a sum of nullary constructors *)
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Poly.equal
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(** Apron-managed map from variables to intervals *)
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type t = Box.t Abstract1.t
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let equal : t -> t -> bool = Poly.equal
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let compare : t -> t -> int = Poly.compare
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let man = lazy (Box.manager_alloc ())
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let join l r = Some (Abstract1.join (Lazy.force man) l r)
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let is_false x = Abstract1.is_bottom (Lazy.force man) x
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let bindings (itv : t) =
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let itv = Abstract1.minimize_environment (Lazy.force man) itv in
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let box = Abstract1.to_box (Lazy.force man) itv in
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let vars =
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Environment.vars box.box1_env |> fun (i, r) -> Array.append i r
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in
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Array.combine_exn vars box.interval_array
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let sexp_of_t (itv : t) =
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let sexps =
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Array.fold_right (bindings itv) [] ~f:(fun (v, i) acc ->
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Sexp.List
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[ Sexp.Atom (Var.to_string v)
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; Sexp.Atom (Scalar.to_string i.inf)
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; Sexp.Atom (Scalar.to_string i.sup) ]
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:: acc )
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in
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Sexp.List sexps
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let pp fs =
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let pp_pair a_pp b_pp fs (a, b) =
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Format.fprintf fs "@[(%a@,%a)@]" a_pp a b_pp b
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in
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bindings >> Array.pp "@," (pp_pair Var.print Interval.print) fs
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let report_fmt_thunk = Fun.flip pp
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let init _gs = Abstract1.top (Lazy.force man) (Environment.make [||] [||])
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let apron_var_of_name = (fun nm -> "%" ^ nm) >> Apron.Var.of_string
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let apron_var_of_reg = Llair.Reg.name >> apron_var_of_name
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let rec apron_typ_of_llair_typ : Llair.Typ.t -> Texpr1.typ option = function
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| Pointer {elt= _} -> apron_typ_of_llair_typ Llair.Typ.siz
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| Integer {bits= _} -> Some Texpr1.Int
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| Float {bits= 32; enc= `IEEE} -> Some Texpr1.Single
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| Float {bits= 64; enc= `IEEE} -> Some Texpr1.Double
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| Float {bits= 80; enc= `Extended} -> Some Texpr1.Extended
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| Float {bits= 128; enc= `IEEE} -> Some Texpr1.Quad
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| t ->
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warn "No corresponding apron type for llair type %a " Llair.Typ.pp t
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() ;
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None
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let rec apron_texpr_of_llair_exp exp q =
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match (exp : Llair.Exp.t) with
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| Reg {name} | Global {name} | Function {name} ->
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Some (Texpr1.Var (apron_var_of_name name))
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| Integer {data} -> Some (Texpr1.Cst (Coeff.s_of_int (Z.to_int data)))
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| Float {data} -> (
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match Float.of_string_exn data with
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| f -> Some (Texpr1.Cst (Coeff.s_of_float f))
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| exception Invalid_argument _ -> None )
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| Ap1 (Signed {bits}, _, _) ->
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let n = Int.shift_left 1 (bits - 1) in
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Some (Texpr1.Cst (Coeff.i_of_int (-n) (n - 1)))
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| Ap1 (Unsigned {bits}, _, _) ->
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let n = Int.shift_left 1 (bits - 1) in
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Some (Texpr1.Cst (Coeff.i_of_int 0 n))
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| Ap1 (Convert {src}, dst, x) ->
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let* src' = apron_typ_of_llair_typ src in
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let* dst' = apron_typ_of_llair_typ dst in
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let subtm = apron_texpr_of_llair_exp x q in
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if equal_apron_typ src' dst' then subtm
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else
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let+ t = subtm in
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Texpr1.Unop (Texpr1.Cast, t, dst', Texpr0.Rnd)
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| Ap2 (op, typ, x, y) -> (
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let* typ' = apron_typ_of_llair_typ typ in
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let* x' = apron_texpr_of_llair_exp x q in
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let* y' = apron_texpr_of_llair_exp y q in
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(* abstract evaluation of boolean binary operation [te1 op te2] at [q]
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by translation to [te1 - te2 op 0] and intersection with [q] *)
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let bool_binop q op x' y' =
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let env = Abstract1.env q in
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let lhs = Texpr1.Binop (Texpr1.Sub, x', y', typ', Texpr0.Rnd) in
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let tcons = Tcons1.make (Texpr1.of_expr env lhs) op in
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let ea =
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Tcons1.array_make env 1 $> fun ea -> Tcons1.array_set ea 0 tcons
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in
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(* if meet of q with tree constraint encoding of binop is: (bottom
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-> binop definitely false); (unchanged from q -> binop definitely
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true); (else -> binop may be true or false) *)
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let meet = Abstract1.meet_tcons_array (Lazy.force man) q ea in
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if is_false meet then Some (Texpr1.Cst (Coeff.s_of_int 0))
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else if equal meet q then Some (Texpr1.Cst (Coeff.s_of_int (-1)))
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else Some (Texpr1.Cst (Coeff.i_of_int (-1) 0))
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in
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let arith_bop op x' y' =
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Some (Texpr1.Binop (op, x', y', typ', Texpr0.Rnd))
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in
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match op with
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| Eq -> bool_binop q Tcons0.EQ x' y'
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| Dq -> bool_binop q Tcons0.DISEQ x' y'
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| Gt -> bool_binop q Tcons0.SUP x' y'
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| Ge -> bool_binop q Tcons0.SUPEQ x' y'
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| Lt -> bool_binop q Tcons0.SUP y' x'
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| Le -> bool_binop q Tcons0.SUPEQ y' x'
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| Ugt | Uge | Ult | Ule | Ord | Uno -> None
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| Add -> arith_bop Texpr1.Add x' y'
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| Sub -> arith_bop Texpr1.Sub x' y'
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| Mul -> arith_bop Texpr1.Mul x' y'
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| Div -> arith_bop Texpr1.Div x' y'
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| Rem -> arith_bop Texpr1.Mod x' y'
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| Udiv | Urem -> None
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| And | Or | Xor | Shl | Lshr | Ashr | Update _ -> None )
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| Label _
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|Ap1 ((Splat | Select _), _, _)
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|Ap3 (Conditional, _, _, _, _)
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|ApN (Record, _, _) ->
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None
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let assign reg exp q =
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[%Trace.call fun {pf} ->
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pf "@ {%a}@\n%a := %a" pp q Llair.Reg.pp reg Llair.Exp.pp exp]
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;
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let lval = apron_var_of_reg reg in
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( match apron_texpr_of_llair_exp exp q with
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| Some e ->
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let env = Abstract1.env q in
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let new_env =
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match
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( Environment.mem_var env lval
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, apron_typ_of_llair_typ (Llair.Reg.typ reg) )
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with
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| true, _ -> env
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| false, Some Texpr1.Int -> Environment.add env [|lval|] [||]
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| false, _ -> Environment.add env [||] [|lval|]
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in
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let man = Lazy.force man in
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let q = Abstract1.change_environment man q new_env true in
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Abstract1.assign_texpr man q lval (Texpr1.of_expr new_env e) None
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| _ -> q )
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|>
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[%Trace.retn fun {pf} r -> pf "{%a}" pp r]
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(** block if [e] is known to be false; skip otherwise *)
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let exec_assume q e =
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match apron_texpr_of_llair_exp e q with
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| Some e ->
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let cond =
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Abstract1.bound_texpr (Lazy.force man) q (Texpr1.of_expr q.env e)
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in
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if Interval.is_zero cond then None else Some q
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| _ -> Some q
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(** existentially quantify killed register [r] out of state [q] *)
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let exec_kill r q =
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let apron_v = apron_var_of_reg r in
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if Environment.mem_var (Abstract1.env q) apron_v then
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Abstract1.forget_array (Lazy.force man) q [|apron_v|] false
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else q
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(** perform a series [move_vec] of reg:=exp moves at state [q] *)
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let exec_move move_vec q =
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let defs, uses =
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IArray.fold move_vec (Llair.Reg.Set.empty, Llair.Reg.Set.empty)
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~f:(fun (r, e) (defs, uses) ->
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( Llair.Reg.Set.add r defs
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, Llair.Exp.fold_regs ~f:Llair.Reg.Set.add e uses ) )
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in
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if not (Llair.Reg.Set.disjoint defs uses) then
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todo "overwritten variables in Domain_itv" () ;
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IArray.fold ~f:(fun (r, e) q -> assign r e q) move_vec q
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let exec_inst i q =
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match (i : Llair.inst) with
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| Move {reg_exps; loc= _} -> Some (exec_move reg_exps q)
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| Store {ptr; exp; len= _; loc= _} -> (
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match Llair.Reg.of_exp ptr with
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| Some reg -> Some (assign reg exp q)
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| None -> Some q )
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| Load {reg; ptr; len= _; loc= _} -> Some (assign reg ptr q)
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| Nondet {reg= Some reg; msg= _; loc= _} -> Some (exec_kill reg q)
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| Nondet {reg= None; msg= _; loc= _} | Alloc _ | Free _ -> Some q
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| Abort _ -> None
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| Intrinsic {reg= Some reg; _} -> Some (exec_kill reg q)
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| Intrinsic {reg= None; _} -> Some q
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type from_call = {areturn: Llair.Reg.t option; caller_q: t}
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[@@deriving sexp_of]
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let recursion_beyond_bound = `prune
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(** existentially quantify locals *)
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let post locals _ (q : t) =
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let locals =
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Llair.Reg.Set.fold locals [] ~f:(fun r a ->
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let v = apron_var_of_reg r in
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if Environment.mem_var q.env v then v :: a else a )
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|> Array.of_list
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in
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Abstract1.forget_array (Lazy.force man) q locals false
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(** drop caller-local variables, add returned value to caller state *)
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let retn _ freturn {areturn; caller_q} callee_q =
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match (areturn, freturn) with
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| Some aret, Some fret ->
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let env_fret_only =
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match apron_typ_of_llair_typ (Llair.Reg.typ fret) with
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| None -> Environment.make [||] [||]
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| Some Texpr1.Int -> Environment.make [|apron_var_of_reg fret|] [||]
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| _ -> Environment.make [||] [|apron_var_of_reg fret|]
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in
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let env = Environment.lce env_fret_only (Abstract1.env caller_q) in
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let man = Lazy.force man in
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let callee_fret =
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(* drop all callee vars, scope to (caller + freturn) env *)
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Abstract1.change_environment man callee_q env_fret_only false
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|> fun q -> Abstract1.change_environment man q env false
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in
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let caller_q = Abstract1.change_environment man caller_q env false in
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let result = Abstract1.meet man callee_fret caller_q in
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Abstract1.rename_array man result
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[|apron_var_of_reg fret|]
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[|apron_var_of_reg aret|]
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| Some aret, None -> exec_kill aret caller_q
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| None, _ -> caller_q
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(** map actuals to formals (via temporary registers), stash constraints on
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caller-local variables. Note that this exploits the non-relational-ness
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of Box to ignore all variables other than the formal/actual params/
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returns; this will not be possible if extended to a relational domain *)
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let call ~summaries ~globals:_ ~actuals ~areturn ~formals ~freturn:_
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~locals:_ q =
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if summaries then
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todo "Summaries not yet implemented for interval analysis" ()
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else
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let mangle r =
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Llair.Reg.mk (Llair.Reg.typ r) 0 ("__tmp__" ^ Llair.Reg.name r)
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in
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let args = IArray.combine_exn formals actuals in
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let q' =
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IArray.fold ~f:(fun (f, a) q -> assign (mangle f) a q) args q
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in
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let callee_env =
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IArray.fold formals ([], []) ~f:(fun f (is, fs) ->
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match apron_typ_of_llair_typ (Llair.Reg.typ f) with
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| None -> (is, fs)
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| Some Texpr1.Int -> (apron_var_of_reg (mangle f) :: is, fs)
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| _ -> (is, apron_var_of_reg (mangle f) :: fs) )
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|> fun (is, fs) ->
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Environment.make (Array.of_list is) (Array.of_list fs)
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in
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let man = Lazy.force man in
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let q'' = Abstract1.change_environment man q' callee_env false in
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let q''' =
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Abstract1.rename_array man q''
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(Array.map
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~f:(mangle >> apron_var_of_reg)
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(IArray.to_array formals))
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(Array.map ~f:apron_var_of_reg (IArray.to_array formals))
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in
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(q''', {areturn; caller_q= q})
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let dnf q = [q]
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let resolve_callee _ _ _ = []
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type summary = t
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let pp_summary = pp
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let apply_summary _ _ = None
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let create_summary ~locals:_ ~formals:_ q = (q, q)
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