Source file dba.ml
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(** Definition of DBA type *)
let invalid_boolean = Invalid_argument "not a boolean expression"
let bad_bound = Invalid_argument "index out of bound"
let mismatched_operands = Invalid_argument "mismatched operands size"
let invalid_assignment = Invalid_argument "mismatched assign"
type size = int
type endianness = Basic_types.endianness = LittleEndian | BigEndian
type id = int
(** An [id] is a local identifier which characterizes an atomic instruction
inside a Dba.block *)
type address = { base : Virtual_address.t; id : id }
(** A DBA [address] is the association of a DBA block address represented by
[base] and a unique [id].
The first element of a block has [id] [0]. *)
type addresses = address list
type 'a jump_target =
| JInner of 'a (** Jump inside the same block, to a label *)
| JOuter of address (** Jump outside the block to its first element *)
type tag =
| Default
| Call of address
| Return (** For call address of return site *)
type state =
| OK
| KO
| Undecoded of string (** Stop because of unanticipated string of bytes **)
| Unsupported of string (** Stop because instr is not supported by Binsec **)
module Unary_op = struct
type t =
| UMinus
| Not
| Sext of size
| Uext of size
| Restrict of int Interval.t
end
module Binary_op = struct
type t =
| Plus
| Minus
| Mult
| DivU
| DivS
| RemU
| RemS
| Or
| And
| Xor
| Concat
| LShift
| RShiftU
| RShiftS
| LeftRotate
| RightRotate
| Eq
| Diff
| LeqU
| LtU
| GeqU
| GtU
| LeqS
| LtS
| GeqS
| GtS
let invert = function
| Eq -> Diff
| Diff -> Eq
| LeqU -> GtU
| LtU -> GeqU
| GeqU -> LtU
| GtU -> LeqU
| LeqS -> GtS
| LtS -> GeqS
| GeqS -> LtS
| GtS -> LeqS
| _ -> failwith "BinaryOperator.invert"
let has_inverse = function
| Eq | Diff | LeqU | LtU | GeqU | GtU | LeqS | LtS | GeqS | GtS -> true
| _ -> false
end
module Var : sig
module Tag : sig
type attribute = Value | Size | Last | Plt
module Attribute : sig
type t = attribute
val compare : t -> t -> int
val pp : Format.formatter -> t -> unit
module Map : Map.S with type key = t
end
type t =
| Flag
| Temp
| Register
| Symbol of attribute * Bitvector.t lazy_t
| Empty
include Sigs.HASHABLE with type t := t
end
type t = private { id : int; name : string; size : size; info : Tag.t }
val create : string -> bitsize:Size.Bit.t -> tag:Tag.t -> t
val flag : ?bitsize:Size.Bit.t -> string -> t
(** [flag ~size fname] creates a flag variable.
- [size] defaults to 1
*)
val temporary : string -> Size.Bit.t -> t
val temp : Size.Bit.t -> t
(** [temp n] creates a lvalue representing a temporary of size [n] with name
[Format.sprintf "temp%d" n]. *)
val compare : t -> t -> int
include Hashtbl.HashedType with type t := t
val from_id : int -> t
(** [from_id id] returns the variable identified by [id].
@raise Not_found if [id] is not a valid identifier.
*)
end = struct
module Tag = struct
type attribute = Value | Size | Last | Plt
module Attribute = struct
type t = attribute
let to_int : t -> int = function
| Value -> 0
| Size -> 1
| Last -> 2
| Plt -> 3
let compare : t -> t -> int = fun x y -> to_int x - to_int y
let pp ppf = function
| Value -> ()
| Size -> Format.pp_print_string ppf ":size"
| Last -> Format.pp_print_string ppf ":last"
| Plt -> Format.pp_print_string ppf "@plt"
module Map = Map.Make (struct
type nonrec t = t
let compare = compare
end)
end
type t =
| Flag
| Temp
| Register
| Symbol of attribute * Bitvector.t lazy_t
| Empty
let compare a b =
match (a, b) with
| Flag, Flag -> 0
| Flag, (Temp | Register | Symbol _ | Empty) -> -1
| Temp, Flag -> 1
| Temp, Temp -> 0
| Temp, (Register | Symbol _ | Empty) -> -1
| Register, (Flag | Temp) -> 1
| Register, Register -> 0
| Register, (Symbol _ | Empty) -> -1
| Symbol _, (Flag | Temp | Register) -> 1
| Symbol (attr, _), Symbol (attr', _) -> compare attr attr'
| Symbol _, Empty -> -1
| Empty, (Flag | Temp | Register | Symbol _) -> 1
| Empty, Empty -> 0
let equal a b =
match (a, b) with
| Flag, Flag | Temp, Temp | Register, Register | Empty, Empty -> true
| Symbol (attr, _), Symbol (attr', _) -> attr = attr'
| ( (Flag | Temp | Register | Symbol _ | Empty),
(Flag | Temp | Register | Symbol _ | Empty) ) ->
false
let weak_equal a b =
match (a, b) with
| (Flag | Temp | Register | Empty), (Flag | Temp | Register | Empty) ->
true
| ( (Flag | Temp | Register | Symbol _ | Empty),
(Flag | Temp | Register | Symbol _ | Empty) ) ->
false
let hash = function
| Flag -> 129913994
| Temp -> 883721435
| Register -> 648017920
| Symbol (Value, _) -> 543159235
| Symbol (Size, _) -> 72223805
| Symbol (Last, _) -> 828390822
| Symbol (Plt, _) -> 985696643
| Empty -> 152507349
let weak_hash = function
| Flag -> 152507349
| Temp -> 152507349
| Register -> 152507349
| Symbol (Value, _) -> 543159235
| Symbol (Size, _) -> 72223805
| Symbol (Last, _) -> 828390822
| Symbol (Plt, _) -> 985696643
| Empty -> 152507349
end
type t = { id : int; name : string; size : size; info : Tag.t }
module C = Weak.Make (struct
type nonrec t = t
let equal t t' =
t.size = t'.size
&& Tag.weak_equal t.info t'.info
&& String.equal t.name t'.name
let hash { name; size; info; _ } =
Hash.(
return
(fold_string
(fold_int (fold_int (seed 0) size) (Tag.weak_hash info))
name))
end)
module R = Weak.Make (struct
type nonrec t = t
let equal t t' = t.id = t'.id
let hash { id; _ } = id
end)
let cons = C.create 128
let id = ref 0
let rev = R.create 128
let create name ~bitsize ~tag =
let t = { id = !id; name; size = Size.Bit.to_int bitsize; info = tag } in
let t' = C.merge cons t in
if t == t' then (
incr id;
R.add rev t');
t'
let flag ?(bitsize = Size.Bit.bits1) flagname =
create flagname ~bitsize ~tag:Tag.Flag
let temporary tempname bitsize = create tempname ~bitsize ~tag:Tag.Temp
let temp nbits =
let name = Format.asprintf "temp%a" Size.Bit.pp nbits in
temporary name nbits
let hash { id; _ } = id
let equal = ( == )
let compare t t' = t.id - t'.id
let from_id id =
let t = { id; name = ""; size = 0; info = Tag.Empty } in
R.find rev t
end
module Expr : sig
type t = private
| Var of Var.t
| Load of size * endianness * t * string option
| Cst of Bitvector.t
| Unary of Unary_op.t * t
| Binary of Binary_op.t * t * t
| Ite of t * t * t
val v : Var.t -> t
val var : ?tag:Var.Tag.t -> string -> int -> t
val is_equal : t -> t -> bool
val size_of : t -> int
val is_constant : t -> bool
val constant : Bitvector.t -> t
val temporary : size:int -> string -> t
val zeros : int -> t
val ones : int -> t
val one : t
val _true : t
val zero : t
val _false : t
val binary : Binary_op.t -> t -> t -> t
val add : t -> t -> t
val addi : t -> int -> t
val addz : t -> Z.t -> t
val sub : t -> t -> t
val subi : t -> int -> t
val subz : t -> Z.t -> t
val mul : t -> t -> t
val srem : t -> t -> t
val urem : t -> t -> t
val udiv : t -> t -> t
val sdiv : t -> t -> t
val append : t -> t -> t
include Sigs.COMPARISON with type t := t and type boolean = t
val unary : Unary_op.t -> t -> t
val uminus : t -> t
include Sigs.LOGICAL with type t := t
val logxor : t -> t -> t
val shift_left : t -> t -> t
val shift_right : t -> t -> t
val shift_right_signed : t -> t -> t
val rotate_left : t -> t -> t
val rotate_right : t -> t -> t
val sext : int -> t -> t
val uext : int -> t -> t
val ite : t -> t -> t -> t
val restrict : int -> int -> t -> t
val bit_restrict : int -> t -> t
val load : ?array:string -> Size.Byte.t -> endianness -> t -> t
val is_max : t -> bool
end = struct
open Binary_op
type t =
| Var of Var.t
| Load of size * endianness * t * string option
| Cst of Bitvector.t
| Unary of Unary_op.t * t
| Binary of Binary_op.t * t * t
| Ite of t * t * t
type boolean = t
let rec size_of = function
| Cst b -> Bitvector.size_of b
| Var v -> v.size
| Load (bytesize, _, _, _) -> 8 * bytesize
| Ite (_, e, _) | Unary ((Unary_op.UMinus | Unary_op.Not), e) -> size_of e
| Unary ((Unary_op.Sext bits | Unary_op.Uext bits), _) -> bits
| Unary (Unary_op.Restrict { Interval.lo; Interval.hi }, _) -> hi - lo + 1
| Binary (bop, e1, e2) -> (
match bop with
| Concat -> size_of e1 + size_of e2
| Eq | Diff | LeqU | LtU | GeqU | GtU | LeqS | LtS | GeqS | GtS -> 1
| Plus | Minus | Mult | DivU | DivS | RemU | RemS | Or | And | Xor
| LShift | RShiftU | RShiftS | LeftRotate | RightRotate ->
size_of e1)
let rec is_equal e1 e2 =
match (e1, e2) with
| Var v1, Var v2 -> v1 = v2
| Load (sz1, en1, e1, arr1), Load (sz2, en2, e2, arr2) ->
sz1 = sz2 && en1 = en2 && is_equal e1 e2 && arr1 = arr2
| Cst bv1, Cst bv2 -> Bitvector.equal bv1 bv2
| Unary (unop1, e1), Unary (unop2, e2) -> unop1 = unop2 && is_equal e1 e2
| Binary (binop1, lexpr1, rexpr1), Binary (binop2, lexpr2, rexpr2) ->
binop1 = binop2 && is_equal lexpr1 lexpr2 && is_equal rexpr1 rexpr2
| Ite (c1, e11, e12), Ite (c2, e21, e22) ->
is_equal c1 c2 && is_equal e11 e21 && is_equal e12 e22
| _, _ -> false
let is_constant = function Cst _ -> true | _ -> false
let _is_zero = function Cst bv -> Bitvector.is_zeros bv | _ -> false
let _is_one = function Cst bv -> Bitvector.is_ones bv | _ -> false
let is_max = function Cst bv -> Bitvector.is_max_ubv bv | _ -> false
let v va = Var va
let var ?(tag = Var.Tag.Empty) name size =
Var (Var.create ~tag name ~bitsize:(Size.Bit.create size))
let temporary ~size name = var name size ~tag:Var.Tag.Temp
let constant bv = Cst bv
let zeros length = constant (Bitvector.zeros length)
let ones length = constant (Bitvector.ones length)
let zero = constant Bitvector.zero
let _false = zero
let one = constant Bitvector.one
let _true = one
let ite condition then_expr else_expr =
if size_of condition <> 1 then raise invalid_boolean;
if size_of then_expr <> size_of else_expr then raise mismatched_operands;
match condition with
| Cst b when Bitvector.is_zero b -> else_expr
| Cst b when Bitvector.is_one b -> then_expr
| _ -> Ite (condition, then_expr, else_expr)
let load ?array nbytes endianness e =
let nbytes = Size.Byte.to_int nbytes in
Load (nbytes, endianness, e, array)
module Straight = struct
let unary op e = Unary (op, e)
let lognot = unary Unary_op.Not
let uminus = unary Unary_op.UMinus
let sext bits = unary (Unary_op.Sext bits)
let uext bits = unary (Unary_op.Uext bits)
let restrict lo hi e =
if hi >= size_of e || hi < lo || lo < 0 then raise bad_bound;
unary (Unary_op.Restrict { Interval.lo; Interval.hi }) e
let binary op e1 e2 = Binary (op, e1, e2)
let append = binary Concat
let shift_binary op e1 e2 =
let s1 = size_of e1 and s2 = size_of e2 in
if s1 < s2 then raise mismatched_operands
else if s2 < s1 then
binary op e1
(match e2 with
| Cst bv -> constant (Bitvector.extend bv s1)
| _ -> uext s1 e2)
else binary op e1 e2
let shift_left = shift_binary LShift
let shift_right = shift_binary RShiftU
let shift_right_signed = shift_binary RShiftS
let rotate_left = shift_binary LeftRotate
let rotate_right = shift_binary RightRotate
let symmetric_binary op e1 e2 =
if size_of e1 <> size_of e2 then raise mismatched_operands;
binary op e1 e2
let add = symmetric_binary Plus
let sub = symmetric_binary Minus
let mul = symmetric_binary Mult
let srem = symmetric_binary RemS
let urem = symmetric_binary RemU
let udiv = symmetric_binary DivU
let sdiv = symmetric_binary DivS
let logor = symmetric_binary Or
let logxor = symmetric_binary Xor
let logand = symmetric_binary And
let equal = symmetric_binary Eq
let diff = symmetric_binary Diff
let ule = symmetric_binary LeqU
let sle = symmetric_binary LeqS
let ult = symmetric_binary LtU
let slt = symmetric_binary LtS
let uge = symmetric_binary GeqU
let sge = symmetric_binary GeqS
let ugt = symmetric_binary GtU
let sgt = symmetric_binary GtS
end
let rec split_apply f g e1 e2 e3 =
let s1 = size_of e1 and s3 = size_of e3 in
let e1_2 = restrict s3 (s1 - 1) e1 and e1_3 = restrict 0 (s3 - 1) e1 in
g (f e1_2 e2) (f e1_3 e3)
and uminus = function
| Cst bv -> constant (Bitvector.neg bv)
| Unary (Unary_op.UMinus, e) -> e
| e -> Straight.uminus e
and lognot = function
| Cst bv -> constant (Bitvector.lognot bv)
| Unary (Unary_op.Not, e) -> e
| Unary (Unary_op.Sext n, e) when size_of e = 1 -> sext n (lognot e)
| Binary (op, e1, e2) when Binary_op.has_inverse op ->
binary (Binary_op.invert op) e1 e2
| e -> Straight.lognot e
and uext size = function
| e when size = size_of e -> e
| Cst bv -> constant Bitvector.(extend bv size)
| Unary (Unary_op.Uext _, e) | e -> Straight.uext size e
and sext size = function
| e when size = size_of e -> e
| Cst bv -> constant Bitvector.(extend_signed bv size)
| Unary (Unary_op.Uext _, e) -> Straight.uext size e
| Unary (Unary_op.Sext _, e) | e -> Straight.sext size e
and restrict lo hi = function
| e when lo = 0 && hi = size_of e - 1 -> e
| Cst bv -> constant (Bitvector.extract ~hi ~lo bv)
| Load (sz, LittleEndian, addr, array) when (8 * sz) - hi > 8 ->
let sz' = Size.Byte.create (sz - (((8 * sz) - hi - 1) / 8)) in
restrict lo hi (load sz' LittleEndian addr ?array)
| Load (sz, LittleEndian, addr, array) when lo >= 8 ->
let bz' = lo / 8 in
let lo' = lo - (8 * bz') and hi' = hi - (8 * bz') in
let sz' = Size.Byte.create (sz - bz') in
let size = size_of addr in
let addr' = add addr (constant (Bitvector.of_int ~size bz')) in
restrict lo' hi' (load sz' LittleEndian addr' ?array)
| Unary (Unary_op.Restrict { Interval.lo = lo'; _ }, e) ->
Straight.restrict (lo' + lo) (lo' + hi) e
| Unary (Unary_op.Uext _, e) when size_of e <= lo -> zeros (hi - lo + 1)
| Unary ((Unary_op.Uext _ | Unary_op.Sext _), e) when size_of e > hi ->
restrict lo hi e
| Unary (Unary_op.Uext _, e) ->
uext (hi - lo + 1) (restrict lo (size_of e - 1) e)
| Unary (Unary_op.Sext _, e) when lo < size_of e ->
sext (hi - lo + 1) (restrict (min lo (size_of e - 1)) (size_of e - 1) e)
| Binary (((Binary_op.And | Binary_op.Or | Binary_op.Xor) as op), e1, e2) ->
binary op (restrict lo hi e1) (restrict lo hi e2)
| Binary (Binary_op.LShift, _, Cst b2) when Bitvector.to_uint b2 > hi ->
zeros (hi - lo + 1)
| Binary (Binary_op.LShift, e1, Cst b2) when Bitvector.to_uint b2 <= lo ->
restrict (lo - Bitvector.to_uint b2) (hi - Bitvector.to_uint b2) e1
| Binary ((Binary_op.RShiftU | Binary_op.RShiftS), e1, Cst b2)
when size_of e1 > hi + Bitvector.to_uint b2 ->
restrict (lo + Bitvector.to_uint b2) (hi + Bitvector.to_uint b2) e1
| Binary (Binary_op.Concat, _, e2) when hi < size_of e2 -> restrict lo hi e2
| Binary (Binary_op.Concat, e1, e2) when lo >= size_of e2 ->
restrict (lo - size_of e2) (hi - size_of e2) e1
| Binary (Binary_op.Concat, e1, e2) ->
append
(restrict 0 (hi - size_of e2) e1)
(restrict lo (size_of e2 - 1) e2)
| e -> Straight.restrict lo hi e
and bit_restrict off = restrict off off
and unary op e =
match op with
| Unary_op.Not -> lognot e
| Unary_op.UMinus -> uminus e
| Unary_op.Sext s -> sext s e
| Unary_op.Uext s -> uext s e
| Unary_op.Restrict { Interval.lo; Interval.hi } -> restrict lo hi e
and add e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.add b1 b2)
| Cst _, _ -> add e2 e1
| Binary (Binary_op.Plus, e3, Cst b1), Cst b2 ->
add e3 (constant (Bitvector.add b1 b2))
| Binary (Binary_op.Plus, e3, (Cst _ as c4)), _ -> add (add e3 e2) c4
| Binary (Binary_op.Minus, e3, Cst b1), Cst b2 when Bitvector.sge b2 b1 ->
add e3 (constant (Bitvector.sub b2 b1))
| Binary (Binary_op.Minus, e3, Cst b1), Cst b2 ->
sub e3 (constant (Bitvector.sub b1 b2))
| Binary (Binary_op.Minus, Cst b1, e3), Cst b2 ->
sub (constant (Bitvector.add b1 b2)) e3
| Binary (Binary_op.Plus, _, _), Binary (Binary_op.Plus, e3, e4) ->
add (add e1 e3) e4
| _, Binary (Binary_op.Minus, e3, e4) when is_equal e1 e4 -> e3
| Binary (Binary_op.Minus, e3, e4), _ when is_equal e4 e2 -> e3
| _, Cst b2 when Bitvector.is_zeros b2 -> e1
| _, _ -> Straight.add e1 e2
and sub e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.sub b1 b2)
| Cst b1, Binary (Binary_op.Plus, e3, Cst b2) ->
sub (constant (Bitvector.sub b1 b2)) e3
| Cst b1, Binary (Binary_op.Minus, e3, Cst b2) ->
sub (constant (Bitvector.add b1 b2)) e3
| Cst b1, Binary (Binary_op.Minus, Cst b2, e3) when Bitvector.sge b1 b2 ->
add e3 (constant (Bitvector.sub b1 b2))
| Cst b1, Binary (Binary_op.Minus, Cst b2, e3) ->
sub e3 (constant (Bitvector.sub b2 b1))
| Binary (Binary_op.Plus, e3, Cst b1), Cst b2 when Bitvector.sge b1 b2 ->
add e3 (constant (Bitvector.sub b1 b2))
| Binary (Binary_op.Plus, e3, Cst b1), Cst b2 ->
sub e3 (constant (Bitvector.sub b2 b1))
| Binary (Binary_op.Minus, Cst b1, e3), Cst b2 ->
sub (constant (Bitvector.sub b1 b2)) e3
| Binary (Binary_op.Minus, e3, Cst b1), Cst b2 ->
sub e3 (constant (Bitvector.add b1 b2))
| Binary (Binary_op.Minus, e3, (Cst _ as c4)), _ -> sub (sub e3 e2) c4
| Cst b1, _ when Bitvector.is_zeros b1 -> uminus e2
| _, Cst b2 when Bitvector.is_zeros b2 -> e1
| _, _ when is_equal e1 e2 -> zeros (size_of e1)
| _, Binary (Binary_op.Plus, e3, e4) when is_equal e1 e3 -> uminus e4
| _, Binary (Binary_op.Plus, e3, e4) when is_equal e1 e4 -> uminus e3
| Binary (Binary_op.Plus, e3, e4), _ when is_equal e2 e3 -> e4
| Binary (Binary_op.Plus, e3, e4), _ when is_equal e2 e4 -> e3
| _, Binary (Binary_op.Minus, e3, e4) when is_equal e1 e3 -> e4
| Binary (Binary_op.Minus, e3, e4), _ when is_equal e2 e3 -> uminus e4
| Unary (Unary_op.Uext n, e3), Cst b1
when Bitvector.is_ones b1 && size_of e3 = 1 ->
sext n (lognot e3)
| _, _ -> Straight.sub e1 e2
and mul e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.mul b1 b2)
| Cst b1, _ when Bitvector.is_ones b1 -> e2
| Cst b1, _ when Bitvector.is_zeros b1 -> e1
| _, Cst _ -> mul e2 e1
| _, _ -> Straight.mul e1 e2
and udiv e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.udiv b1 b2)
| _, Cst b2 when Bitvector.is_ones b2 -> e1
| _, _ -> Straight.udiv e1 e2
and urem e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.urem b1 b2)
| _, _ -> Straight.urem e1 e2
and sdiv e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.sdiv b1 b2)
| _, Cst b2 when Bitvector.is_ones b2 -> e1
| _, _ -> Straight.sdiv e1 e2
and srem e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.srem b1 b2)
| _, _ -> Straight.srem e1 e2
and logxor e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.logxor b1 b2)
| Cst b1, _ when Bitvector.is_zeros b1 -> e2
| Cst b1, _ when Bitvector.is_fill b1 -> lognot e2
| Cst b1, Binary (Binary_op.Concat, e3, e4) ->
let s2 = size_of e2 and s4 = size_of e4 in
let b3 = Bitvector.extract ~hi:(s2 - 1) ~lo:s4 b1 in
let b4 = Bitvector.extract ~hi:(s4 - 1) ~lo:0 b1 in
let x3 = logxor (constant b3) e3 in
let x4 = logxor (constant b4) e4 in
append x3 x4
| _, Cst _ -> logxor e2 e1
| _, _ when is_equal e1 e2 -> zeros (size_of e1)
| _, _ -> Straight.logxor e1 e2
and logor e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.logor b1 b2)
| Cst b1, _ when Bitvector.is_zeros b1 -> e2
| Cst b1, _ when Bitvector.is_fill b1 -> e1
| Cst b1, Binary (Binary_op.Concat, e3, e4) ->
let s2 = size_of e2 and s4 = size_of e4 in
let b3 = Bitvector.extract ~hi:(s2 - 1) ~lo:s4 b1 in
let b4 = Bitvector.extract ~hi:(s4 - 1) ~lo:0 b1 in
let x3 = logor (constant b3) e3 in
let x4 = logor (constant b4) e4 in
append x3 x4
| _, Cst _ -> logor e2 e1
| _, Unary (Unary_op.Uext _, e3) ->
try_merge ~k:(fun _ -> Straight.logor e1 e2) e3 ~at:0 e1
| _, Binary (Binary_op.LShift, Unary (Unary_op.Uext _, e3), Cst b1) ->
let at = Bitvector.to_uint b1 in
try_merge ~k:(fun _ -> Straight.logor e1 e2) e3 ~at e1
| Unary (Unary_op.Uext _, _), _
| Binary (Binary_op.LShift, Unary (Unary_op.Uext _, _), Cst _), _ ->
logor e2 e1
| _, _ when is_equal e1 e2 -> e1
| _, _ -> Straight.logor e1 e2
and logand e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.logand b1 b2)
| Cst b1, _ when Bitvector.is_zeros b1 -> e1
| Cst b1, _ when Bitvector.is_fill b1 -> e2
| _, Cst _ -> logand e2 e1
| Cst b1, Binary (Binary_op.Concat, e3, e4) ->
let rec try_refine ~f ~k b e1 e2 =
let hi = Bitvector.size_of b - 1 in
let lo = hi - size_of e1 + 1 in
let b1 = Bitvector.extract ~hi ~lo b in
if Bitvector.is_fill b1 || Bitvector.is_zeros b1 then
let e1 = if Bitvector.is_fill b1 then e1 else constant b1 in
let b2 = Bitvector.extract ~hi:(lo - 1) ~lo:0 b in
match e2 with
| Binary (Binary_op.Concat, e3, e4) ->
try_refine ~f ~k:(fun r -> k (append e1 r)) b2 e3 e4
| _ -> k (append e1 (logand (constant b2) e2))
else f ()
in
try_refine ~f:(fun _ -> Straight.logand e1 e2) ~k:(fun x -> x) b1 e3 e4
| _, _ when is_equal e1 e2 -> e1
| _, _ -> Straight.logand e1 e2
and append e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.append b1 b2)
| Cst b1, _ when Bitvector.is_zeros b1 -> uext (size_of e1 + size_of e2) e2
| Unary (Unary_op.Uext s1, e3), _ -> uext (s1 + size_of e2) (append e3 e2)
| _, Unary (Unary_op.Uext s, e2) ->
Straight.append e1 (Straight.append (zeros (s - size_of e2)) e2)
| ( Unary (Unary_op.Restrict { Interval.lo; Interval.hi }, e1),
Unary (Unary_op.Restrict { Interval.lo = lo'; Interval.hi = hi' }, e2) )
when hi' + 1 = lo && is_equal e1 e2 ->
restrict lo' hi e1
| ( Binary (((Binary_op.And | Binary_op.Or | Binary_op.Xor) as op), e1, e2),
Binary (op', e1', e2') )
when op = op' ->
binary op (append e1 e1') (append e2 e2')
| Binary (Binary_op.Concat, e3, e4), _ -> append e3 (append e4 e2)
| _, _ -> Straight.append e1 e2
and equal e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.of_bool (Bitvector.equal b1 b2))
| Cst b1, _ when Bitvector.is_zero b1 -> lognot e2
| Cst b1, _ when Bitvector.is_one b1 -> e2
| Cst _, Binary (Binary_op.Concat, e3, e4) ->
split_apply equal logand e1 e3 e4
| Cst _, Unary (Unary_op.Uext n, e3) ->
split_apply equal logand e1
(constant (Bitvector.zeros (n - size_of e3)))
e3
| Binary (Binary_op.Concat, e3, e4), Binary (Binary_op.Concat, e5, e6)
when size_of e3 = size_of e5 ->
logand (equal e3 e4) (equal e4 e6)
| _, Cst _ -> equal e2 e1
| _, _ when is_equal e1 e2 -> one
| _, _ -> Straight.equal e1 e2
and diff e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.of_bool (Bitvector.diff b1 b2))
| Cst b1, _ when Bitvector.is_zero b1 -> e2
| Cst b1, _ when Bitvector.is_one b1 -> lognot e2
| Cst _, Binary (Binary_op.Concat, e3, e4) ->
split_apply diff logor e1 e3 e4
| Cst _, Unary (Unary_op.Uext n, e3) ->
split_apply diff logor e1
(constant (Bitvector.zeros (n - size_of e3)))
e3
| Binary (Binary_op.Concat, e3, e4), Binary (Binary_op.Concat, e5, e6)
when size_of e3 = size_of e5 ->
logor (diff e3 e4) (diff e4 e6)
| _, Cst _ -> diff e2 e1
| _, _ when is_equal e1 e2 -> zero
| _, _ -> Straight.diff e1 e2
and ult e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.of_bool (Bitvector.ult b1 b2))
| _, _ when is_equal e1 e2 -> zero
| _, _ -> Straight.ult e1 e2
and ule e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.of_bool (Bitvector.ule b1 b2))
| _, _ when is_equal e1 e2 -> one
| _, _ -> Straight.ule e1 e2
and ugt e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.of_bool (Bitvector.ugt b1 b2))
| _, _ when is_equal e1 e2 -> zero
| _, _ -> Straight.ugt e1 e2
and uge e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.of_bool (Bitvector.uge b1 b2))
| _, _ when is_equal e1 e2 -> one
| _, _ -> Straight.uge e1 e2
and slt e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.of_bool (Bitvector.slt b1 b2))
| _, _ when is_equal e1 e2 -> zero
| _, _ -> Straight.slt e1 e2
and sle e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.of_bool (Bitvector.sle b1 b2))
| _, _ when is_equal e1 e2 -> one
| _, _ -> Straight.sle e1 e2
and sgt e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.of_bool (Bitvector.sgt b1 b2))
| _, _ when is_equal e1 e2 -> zero
| _, _ -> Straight.sgt e1 e2
and sge e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 -> constant (Bitvector.of_bool (Bitvector.sge b1 b2))
| _, _ when is_equal e1 e2 -> one
| _, _ -> Straight.sge e1 e2
and rotate_left e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 ->
constant (Bitvector.rotate_left b1 (Bitvector.to_uint b2))
| _, Cst b2 when Bitvector.is_zeros b2 -> e1
| _, _ -> Straight.rotate_left e1 e2
and rotate_right e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 ->
constant (Bitvector.rotate_right b1 (Bitvector.to_uint b2))
| _, Cst b2 when Bitvector.is_zeros b2 -> e1
| _, _ -> Straight.rotate_right e1 e2
and shift_left e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 ->
constant (Bitvector.shift_left b1 (Bitvector.to_uint b2))
| _, Cst b2 when Bitvector.is_zeros b2 -> e1
| Cst b1, _ when Bitvector.is_zeros b1 -> e1
| Binary (Concat, e3, e4), Cst b5 ->
let t = size_of e3 and s = Bitvector.to_uint b5 in
if t = s then append e4 (zeros t)
else if t < s then
append (restrict 0 (size_of e4 - 1 + t - s) e4) (zeros s)
else Straight.shift_left e1 e2
| _, _ -> Straight.shift_left e1 e2
and shift_right e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 ->
constant (Bitvector.shift_right b1 (Bitvector.to_uint b2))
| _, Cst b2 when Bitvector.is_zeros b2 -> e1
| Cst b1, _ when Bitvector.is_zeros b1 -> e1
| _, _ -> Straight.shift_right e1 e2
and shift_right_signed e1 e2 =
match (e1, e2) with
| Cst b1, Cst b2 ->
constant (Bitvector.shift_right_signed b1 (Bitvector.to_uint b2))
| _, Cst b2 when Bitvector.is_zeros b2 -> e1
| Cst b1, _ when Bitvector.is_zeros b1 -> e1
| _, _ -> Straight.shift_right_signed e1 e2
and try_merge ~k e1 ~at e2 =
let sz1 = size_of e1 and sz2 = size_of e2 in
if at + sz1 <= sz2 && restrict at (at + sz1 - 1) e2 = zeros sz1 then
if at = 0 then append (restrict sz1 (sz2 - 1) e2) e1
else if at + sz1 = sz2 then append e1 (restrict 0 (at - 1) e2)
else
append
(append (restrict (at + sz1) (sz2 - 1) e2) e1)
(restrict 0 (at - 1) e2)
else k ()
and binary op =
match op with
| Plus -> add
| Minus -> sub
| Mult -> mul
| DivU -> udiv
| DivS -> sdiv
| RemU -> urem
| RemS -> srem
| And -> logand
| Or -> logor
| Xor -> logxor
| Concat -> append
| LShift -> shift_left
| RShiftU -> shift_right
| RShiftS -> shift_right_signed
| LeftRotate -> rotate_left
| RightRotate -> rotate_right
| Eq -> equal
| Diff -> diff
| LeqU -> ule
| LtU -> ult
| LeqS -> sle
| LtS -> slt
| GeqU -> uge
| GtU -> ugt
| GeqS -> sge
| GtS -> sgt
let addi e i = add e (constant (Bitvector.of_int i ~size:(size_of e)))
let addz e z = add e (constant (Bitvector.create z (size_of e)))
let subi e i = sub e (constant (Bitvector.of_int i ~size:(size_of e)))
let subz e z = sub e (constant (Bitvector.create z (size_of e)))
end
type exprs = Expr.t list
type printable = Exp of Expr.t | Str of string
module Tag = struct
type t = tag
let equal = ( = )
end
module Jump_target = struct
type 'a t = 'a jump_target
let inner n = JInner n
let outer a = JOuter a
let is_inner = function JInner _ -> true | JOuter _ -> false
let is_outer = function JOuter _ -> true | JInner _ -> false
end
module type INSTR = sig
type t
include Sigs.ARITHMETIC with type t := t
include Sigs.BITWISE with type t := t
end
module LValue = struct
type t =
| Var of Var.t
| Restrict of Var.t * int Interval.t
| Store of size * endianness * Expr.t * string option
let equal lv1 lv2 =
match (lv1, lv2) with
| Var v1, Var v2 -> Var.equal v1 v2
| ( Restrict (v1, { Interval.lo = o11; Interval.hi = o12 }),
Restrict (v2, { Interval.lo = o21; Interval.hi = o22 }) ) ->
Var.equal v1 v2 && o11 = o21 && o12 = o22
| Store (sz1, en1, e1, arr1), Store (sz2, en2, e2, arr2) ->
sz1 = sz2 && en1 = en2 && Expr.is_equal e1 e2 && arr1 = arr2
| _, _ -> false
let size_of = function
| Var v -> v.size
| Restrict (_, { Interval.lo; Interval.hi }) ->
let restricted_size = hi - lo + 1 in
restricted_size
| Store (sz, _, _, _) -> 8 * sz
let v va = Var va
let var ?(tag = Var.Tag.Empty) ~bitsize name =
Var (Var.create name ~bitsize ~tag)
let flag ?(bitsize = Size.Bit.bits1) flagname =
var flagname ~bitsize ~tag:Var.Tag.Flag
let temporary tempname bitsize = var tempname ~bitsize ~tag:Var.Tag.Temp
let temp nbits =
let name = Format.asprintf "temp%a" Size.Bit.pp nbits in
temporary name nbits
let restrict (v : Var.t) lo hi =
if hi >= v.size || hi < lo || lo < 0 then raise bad_bound;
if hi - lo + 1 = v.size then Var v
else Restrict (v, { Interval.lo; Interval.hi })
let _restrict name bitsize lo hi =
let v = Var.create name ~bitsize ~tag:Var.Tag.Empty in
restrict v lo hi
let bit_restrict v bit = restrict v bit bit
let _bit_restrict name sz bit = _restrict name sz bit bit
let store ?array nbytes endianness e =
let sz = Size.Byte.to_int nbytes in
Store (sz, endianness, e, array)
let is_expr_translatable = function
| Expr.Var _ | Expr.Load _ | Expr.Unary (Unary_op.Restrict _, Expr.Var _) ->
true
| Expr.Cst _ | Expr.Unary _ | Expr.Binary _ | Expr.Ite _ -> false
let of_expr = function
| Expr.Var v -> Var v
| Expr.Load (size, endian, e, array) ->
store (Size.Byte.create size) endian e ?array
| Expr.Unary (Unary_op.Restrict { Interval.lo; Interval.hi }, Expr.Var v) ->
restrict v lo hi
| Expr.Cst _ | Expr.Unary _ | Expr.Binary _ | Expr.Ite _ ->
failwith "LValue.of_expr : Cannot create lvalue from expression"
let to_expr = function
| Var v -> Expr.v v
| Restrict (v, { Interval.lo; hi }) ->
Expr.restrict lo hi (Expr.var v.name v.size ~tag:v.info)
| Store (size, endianness, address, array) ->
Expr.load (Size.Byte.create size) endianness address ?array
let bitsize = function
| Var { size; _ } -> Size.Bit.create size
| Restrict (_, { Interval.lo; Interval.hi }) ->
let res = hi - lo + 1 in
Size.Bit.create res
| Store (sz, _, _, _) -> Size.Byte.(to_bitsize (create sz))
let resize size = function
| Var { name; info = tag; _ } -> var name ~bitsize:size ~tag
| Restrict (v, { Interval.lo; Interval.hi }) -> restrict v lo hi
| Store (_sz, endianness, e, array) ->
store (Size.Byte.of_bitsize size) endianness e ?array
end
module Instr = struct
type t =
| Assign of LValue.t * Expr.t * id
| SJump of id jump_target * tag
| DJump of Expr.t * tag
| If of Expr.t * id jump_target * id
| Stop of state option
| Assert of Expr.t * id
| Assume of Expr.t * id
| Nondet of LValue.t * id
| Undef of LValue.t * id
let assign lval rval nid =
if Size.Bit.to_int (LValue.bitsize lval) <> Expr.size_of rval then
raise invalid_assignment;
Assign (lval, rval, nid)
let static_jump ?(tag = Default) jt = SJump (jt, tag)
let static_inner_jump ?tag n = static_jump (Jump_target.inner n) ?tag
let static_outer_jump ?tag base =
static_jump (Jump_target.outer { base; id = 0 }) ?tag
let call ~return_address jt =
let tag = Some (Call return_address) in
static_jump ?tag jt
let dynamic_jump ?(tag = Default) e =
match e with
| Expr.Cst v ->
let addr = { id = 0; base = Virtual_address.of_bitvector v } in
static_jump (Jump_target.outer addr)
| _ -> DJump (e, tag)
let stop state = Stop state
let ite c goto nid =
if Expr.(is_equal c zero) then static_inner_jump nid
else if Expr.(is_equal c one) then static_jump goto
else If (c, goto, nid)
let undefined lv nid = Undef (lv, nid)
let non_deterministic lv nid = Nondet (lv, nid)
let _assert c nid = Assert (c, nid)
let assume c nid = Assume (c, nid)
end