Source file cse.ml
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module rec Expr : (Term.S with type a := Dba.Var.t and type b := Layer.t) =
Term.Make (Dba.Var) (Layer)
and Store : sig
type t
val empty : t
val store : Bitvector.t -> Expr.t -> t -> t
val select : (Z.t -> int -> Expr.t) -> Bitvector.t -> int -> t -> Expr.t
val iter : (Z.t -> Expr.t -> unit) -> t -> unit
val rev_iter : (Z.t -> Expr.t -> unit) -> t -> unit
end = struct
module Chunk = struct
type t = Expr.t
let equal = Expr.is_equal
let len t = Expr.sizeof t lsr 3
let crop ~lo ~hi t = Expr.restrict ~lo:(lo lsl 3) ~hi:((hi lsl 3) + 7) t
let concat = Expr.append
end
include Lmap.Make (Chunk)
let store addr value t =
let z = Bitvector.value_of addr and s = Chunk.len value in
let u = Z.add z (Z.of_int s) in
let n = Bitvector.size_of addr in
if Z.numbits u > n && Z.popcount u > 1 then
let o = Z.to_int (Z.extract u 0 n) in
store z
(Chunk.crop ~hi:(s - o - 1) ~lo:0 value)
(store Z.zero (Chunk.crop ~hi:(s - 1) ~lo:(s - o) value) t)
else store z value t
let select f addr s t =
let z = Bitvector.value_of addr in
let u = Z.add z (Z.of_int s) in
let n = Bitvector.size_of addr in
if Z.numbits u > n && Z.popcount u > 1 then
let o = Z.to_int (Z.extract u 0 n) in
Chunk.concat (select f Z.zero o t) (select f z (s - o) t)
else select f z s t
end
and Layer : sig
type t =
| Base of string option
| Layer of {
id : int;
over : t;
base : string option;
addr : Expr.t;
store : Store.t;
}
val base : t -> string option
val write : read:bool -> addr:Expr.t -> Expr.t -> Expr.endianness -> t -> t
val read : addr:Expr.t -> int -> Expr.endianness -> t -> Expr.t * bool
include Sigs.HASHABLE with type t := t
end = struct
type t =
| Base of string option
| Layer of {
id : int;
over : t;
base : string option;
addr : Expr.t;
store : Store.t;
}
let id = ref 0
let hash = function Base b -> Hashtbl.hash b | Layer { id; _ } -> id
let compare t t' =
match (t, t') with
| Base b, Base b' -> compare b b'
| Layer { id; _ }, Layer { id = id'; _ } -> id - id'
| Base _, Layer _ -> -1
| Layer _, Base _ -> 1
let equal t t' = compare t t' = 0
let bswap =
let rec iter e i r =
if i = 0 then r
else
iter e (i - 8) (Expr.append (Expr.restrict ~hi:(i - 1) ~lo:(i - 8) e) r)
in
fun e ->
let size = Expr.sizeof e in
assert (size land 0x7 = 0);
iter e (size - 8) (Expr.restrict ~hi:(size - 1) ~lo:(size - 8) e)
let rebase (addr : Expr.t) =
match addr with
| Cst bv -> (Expr.zeros (Bitvector.size_of bv), bv)
| Binary { f = Plus; x; y = Cst bv; _ } -> (x, bv)
| Binary { f = Minus; x; y = Cst bv; _ } -> (x, Bitvector.neg bv)
| _ -> (addr, Bitvector.zeros (Expr.sizeof addr))
let base = function Base base | Layer { base; _ } -> base
let write addr value over =
let addr, offset = rebase addr in
incr id;
Layer
{
id = !id;
over;
base = base over;
addr;
store = Store.store offset value Store.empty;
}
let write ~read ~addr value (dir : Expr.endianness) over =
let value =
match dir with LittleEndian -> value | BigEndian -> bswap value
in
match over with
| Base _ -> write addr value over
| Layer _ when read -> write addr value over
| Layer { base = base'; addr = addr'; store = store'; over = over'; _ } -> (
match Expr.sub addr addr' with
| Expr.Cst bv ->
let store = Store.store bv value store' in
incr id;
Layer { id = !id; over = over'; base = base'; addr = addr'; store }
| _ -> write addr value over)
let rec read ~addr bytes (dir : Expr.endianness) t =
match t with
| Base _ -> (Expr.load bytes dir addr t, true)
| Layer { addr = addr'; store; over; _ } -> (
match Expr.sub addr addr' with
| Expr.Cst bv ->
let miss i s =
fst (read ~addr:(Expr.addz addr' i) s Expr.LittleEndian over)
in
let bytes = Store.select miss bv bytes store in
let bytes =
match dir with LittleEndian -> bytes | BigEndian -> bswap bytes
in
(bytes, false)
| _ -> (Expr.load bytes dir addr t, true))
end
module StrMap = Basic_types.String.Map
module VarMap = Map.Make (struct
type t = Dba.Var.t
let compare (x : t) (y : t) = x.id - y.id
end)
let uop (e : Dba.Expr.t) (op : Dba.Unary_op.t) : Term.unary Term.operator =
match op with
| Not -> Not
| UMinus -> Minus
| Sext n -> Sext (n - Dba.Expr.size_of e)
| Uext n -> Uext (n - Dba.Expr.size_of e)
| Restrict interval -> Restrict interval
let bop (op : Dba.Binary_op.t) : Term.binary Term.operator =
match op with
| Plus -> Plus
| Minus -> Minus
| Mult -> Mul
| DivU -> Udiv
| DivS -> Sdiv
| ModU -> Umod
| ModS -> Smod
| Eq -> Eq
| Diff -> Diff
| LeqU -> Ule
| LtU -> Ult
| GeqU -> Uge
| GtU -> Ugt
| LeqS -> Sle
| LtS -> Slt
| GeqS -> Sge
| GtS -> Sgt
| Xor -> Xor
| And -> And
| Or -> Or
| Concat -> Concat
| LShift -> Lsl
| RShiftU -> Lsr
| RShiftS -> Asr
| LeftRotate -> Rol
| RightRotate -> Ror
module Env = struct
type t = {
vars : Expr.t VarMap.t;
layers : (Layer.t * bool) StrMap.t;
rev_reads : Expr.t list;
input_vars : Expr.t VarMap.t;
}
let is_empty { vars; layers; rev_reads; _ } =
VarMap.is_empty vars && StrMap.is_empty layers && rev_reads = []
let rec eval (e : Types.Expr.t) t =
match e with
| Cst bv | Var { info = Symbol (_, (lazy bv)); _ } -> (Expr.constant bv, t)
| Var var -> lookup var t
| Load (len, dir, addr, base) -> load len dir addr base t
| Unary (f, x) ->
let x', t' = eval x t in
(Expr.unary (uop x f) x', t')
| Binary (f, x, y) ->
let x', t' = eval x t in
let y', t' = eval y t' in
(Expr.binary (bop f) x' y', t')
| Ite (c, r, e) ->
let c', t' = eval c t in
let r', t' = eval r t' in
let e', t' = eval e t' in
(Expr.ite c' r' e', t')
and lookup var t =
try (VarMap.find var t.vars, t)
with Not_found ->
let input = Expr.var "" var.size var in
( input,
{
t with
vars = VarMap.add var input t.vars;
input_vars = VarMap.add var input t.input_vars;
} )
and load len dir addr base t =
let name = Option.value ~default:"" base in
let layer, read =
try StrMap.find name t.layers with Not_found -> (Layer.Base base, true)
in
let addr, t' = eval addr t in
let bytes, read' = Layer.read ~addr len dir layer in
( bytes,
{
t' with
layers = StrMap.add name (layer, read || read') t'.layers;
rev_reads = (if read' then bytes :: t'.rev_reads else t'.rev_reads);
} )
let empty =
{
vars = VarMap.empty;
layers = StrMap.empty;
rev_reads = [];
input_vars = VarMap.empty;
}
let assign var value t =
let value', t' = eval value t in
{ t' with vars = VarMap.add var value' t'.vars }
let clobber var t =
assign var (Dba.Expr.constant (Bitvector.zeros var.size)) t
let forget var t = { t with vars = VarMap.remove var t.vars }
let load (var : Dba.Var.t) base dir addr t =
let bytes, t' =
eval
(Dba.Expr.load ?array:base (Size.Byte.create (var.size lsr 3)) dir addr)
t
in
{ t' with vars = VarMap.add var bytes t'.vars }
let store base dir ~addr value t =
let name = Option.value ~default:"" base in
let layer, read =
try StrMap.find name t.layers with Not_found -> (Layer.Base base, false)
in
let addr', t' = eval addr t in
let value', t' = eval value t' in
let layer' = Layer.write ~read ~addr:addr' value' dir layer in
{ t' with layers = StrMap.add name (layer', false) t'.layers }
end
type value = Bv of Expr.t | Ax of string option * Expr.t * Expr.t
module VarTbl = Dba_types.Var.Htbl
module VarSet = Dba_types.Var.Set
module BvTbl = Hashtbl.Make (struct
type t = Expr.t
let hash = Expr.hash
let equal = Expr.is_equal
end)
module AxTbl = Hashtbl.Make (Layer)
type t = {
mutable id : int;
mutable rev : value list;
locals : Dba.Var.t BvTbl.t;
layers : unit AxTbl.t;
}
let init () =
{ id = 0; rev = []; locals = BvTbl.create 32; layers = AxTbl.create 4 }
let bv_once = Dba.Var.create ~tag:Dba.Var.Tag.Empty "" ~bitsize:Size.Bit.bits1
let rec visit_bv t bv =
try
if BvTbl.find t.locals bv == bv_once then (
let name = Format.sprintf "$$$%d" t.id in
t.id <- t.id + 1;
BvTbl.replace t.locals bv
(Dba.Var.create ~tag:Dba.Var.Tag.Temp name
~bitsize:(Size.Bit.create (Expr.sizeof bv))))
with Not_found -> (
match bv with
| Var _ -> ()
| Load { addr; label; _ } ->
let name = Format.sprintf "$$$%d" t.id in
t.id <- t.id + 1;
BvTbl.add t.locals bv
(Dba.Var.create ~tag:Dba.Var.Tag.Temp name
~bitsize:(Size.Bit.create (Expr.sizeof bv)));
visit_ax t label;
visit_bv t addr;
t.rev <- Bv bv :: t.rev
| Cst _ -> ()
| Unary { x; _ } ->
BvTbl.add t.locals bv bv_once;
visit_bv t x;
t.rev <- Bv bv :: t.rev
| Binary { x; y; _ } ->
BvTbl.add t.locals bv bv_once;
visit_bv t x;
visit_bv t y;
t.rev <- Bv bv :: t.rev
| Ite { c; t = r; e; _ } ->
BvTbl.add t.locals bv bv_once;
visit_bv t c;
visit_bv t r;
visit_bv t e;
t.rev <- Bv bv :: t.rev)
and visit_ax t ax =
if not (AxTbl.mem t.layers ax) then (
AxTbl.add t.layers ax ();
match ax with
| Base _ -> ()
| Layer { base; addr; store; over; _ } ->
visit_ax t over;
Store.rev_iter
(fun offset value ->
let addr = Expr.addz addr offset in
visit_bv t addr;
visit_bv t value;
t.rev <- Ax (base, addr, value) :: t.rev)
store)
let mk_unop (op : Term.unary Term.operator) x : Dba.Unary_op.t =
match op with
| Not -> Not
| Minus -> UMinus
| Uext n -> Uext (Expr.sizeof x + n)
| Sext n -> Sext (Expr.sizeof x + n)
| Restrict i -> Restrict i
let mk_binop (op : Term.binary Term.operator) : Dba.Binary_op.t =
match op with
| Plus -> Plus
| Minus -> Minus
| Mul -> Mult
| Udiv -> DivU
| Sdiv -> DivS
| Umod -> ModU
| Smod -> ModS
| Eq -> Eq
| Diff -> Diff
| Ule -> LeqU
| Ult -> LtU
| Uge -> GeqU
| Ugt -> GtU
| Sle -> LeqS
| Slt -> LtS
| Sge -> GeqS
| Sgt -> GtS
| Xor -> Xor
| And -> And
| Or -> Or
| Concat -> Concat
| Lsl -> LShift
| Lsr -> RShiftU
| Asr -> RShiftS
| Rol -> LeftRotate
| Ror -> RightRotate
let rec mk_bv t bv =
match BvTbl.find t.locals bv with
| var -> if var == bv_once then mk_bv_no_cons t bv else Dba.Expr.v var
| exception Not_found -> mk_bv_no_cons t bv
and mk_bv_no_cons t bv =
match bv with
| Var { label = var; _ } -> Dba.Expr.v var
| Load _ -> assert false
| Cst bv -> Dba.Expr.constant bv
| Unary { f; x; _ } -> Dba.Expr.unary (mk_unop f x) (mk_bv t x)
| Binary { f; x; y; _ } ->
Dba.Expr.binary (mk_binop f) (mk_bv t x) (mk_bv t y)
| Ite { c; t = r; e; _ } -> Dba.Expr.ite (mk_bv t c) (mk_bv t r) (mk_bv t e)
exception Skip
let rec visit_bv' bindings rev_bindings t (bv : Expr.t) =
match bv with
| Var { label = var; _ } -> (
try
let bv = VarTbl.find bindings var in
BvTbl.remove rev_bindings bv;
if BvTbl.length rev_bindings = 0 then raise_notrace Skip
with Not_found -> ())
| Unary { x; _ } when BvTbl.find t.locals bv == bv_once ->
visit_bv' bindings rev_bindings t x
| Binary { x; y; _ } when BvTbl.find t.locals bv == bv_once ->
visit_bv' bindings rev_bindings t x;
visit_bv' bindings rev_bindings t y
| Ite { c; t = r; e; _ } when BvTbl.find t.locals bv == bv_once ->
visit_bv' bindings rev_bindings t c;
visit_bv' bindings rev_bindings t r;
visit_bv' bindings rev_bindings t e
| Cst _ | Load _ | Unary _ | Binary _ | Ite _ -> ()
let commit (body : Env.t) =
if Env.is_empty body then []
else
let t = init () in
List.iter (visit_bv t) (List.rev body.rev_reads);
StrMap.iter (fun _ (ax, _) -> visit_ax t ax) body.layers;
let bindings = VarTbl.create 32
and inputs = VarTbl.create 32
and rev_bindings = BvTbl.create 32 in
VarMap.iter
(fun var bv ->
match (bv : Expr.t) with
| Var { label = var'; _ } when Dba.Var.equal var var' -> ()
| _ ->
VarTbl.add bindings var bv;
if VarMap.mem var body.input_vars then (
let bv = Expr.var "" var.size var in
let name = Format.sprintf "$$$%d" t.id in
t.id <- t.id + 1;
let tmp =
Dba.Var.create ~tag:Dba.Var.Tag.Temp name
~bitsize:(Size.Bit.create var.size)
in
BvTbl.add t.locals bv tmp;
VarTbl.add inputs var tmp);
if not (BvTbl.mem rev_bindings bv) then
BvTbl.add rev_bindings bv var;
visit_bv t bv)
body.vars;
(try
List.iter
(function
| Bv bv -> (
try
let var = BvTbl.find rev_bindings bv in
BvTbl.replace t.locals bv var;
VarTbl.remove bindings var;
BvTbl.remove rev_bindings bv;
if BvTbl.length rev_bindings = 0 then raise_notrace Skip
with Not_found -> visit_bv' bindings rev_bindings t bv)
| Ax (_, addr, value) ->
visit_bv' bindings rev_bindings t addr;
visit_bv' bindings rev_bindings t value)
t.rev
with Skip -> ());
VarTbl.fold
(fun var tmp assigns ->
Ir.Assign { var = tmp; rval = Dba.Expr.v var } :: assigns)
inputs
(List.fold_left
(fun assigns -> function
| Bv (Load { dir; addr; label; _ } as bv) ->
Ir.Load
{
var = BvTbl.find t.locals bv;
base = Layer.base label;
dir;
addr = mk_bv t addr;
}
:: assigns
| Bv bv ->
let var = BvTbl.find t.locals bv in
if var == bv_once then assigns
else Ir.Assign { var; rval = mk_bv_no_cons t bv } :: assigns
| Ax (base, addr, value) ->
Ir.Store
{
base;
dir = LittleEndian;
addr = mk_bv t addr;
rval = mk_bv t value;
}
:: assigns)
(VarTbl.fold
(fun var bv assigns ->
Ir.Assign { var; rval = mk_bv t bv } :: assigns)
bindings [])
t.rev)