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Finished Karr

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soyouzpanda 2024-06-09 20:30:11 +02:00
parent f34d1b9e52
commit 0c1e540883
1 changed files with 129 additions and 43 deletions
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134
domains/karr.ml
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@ -23,9 +23,11 @@ module Matrix : sig
val add : t -> t -> t val add : t -> t -> t
val sub : t -> t -> t val sub : t -> t -> t
val mul : t -> t -> t val mul : t -> t -> t
val linear_combine : t -> int -> int -> Q.t -> unit
val transpose : t -> t val transpose : t -> t
val gauss : t * t -> t * t val gauss : t * t -> t * t
val extend : t -> t -> t val extend : t -> t -> t
val delete_line : t -> int -> t
val print : Format.formatter -> t -> unit val print : Format.formatter -> t -> unit
end = struct end = struct
type t = { height : int; width : int; data : Q.t array array } type t = { height : int; width : int; data : Q.t array array }
@ -77,6 +79,13 @@ end = struct
Q.zero Q.zero
(List.init mat1.width (fun x -> x))) (List.init mat1.width (fun x -> x)))
let linear_combine mat line from_line coef =
for i = 0 to mat.width - 1 do
mat.data.(line).(i) <-
Q.add mat.data.(line).(i) (Q.mul coef mat.data.(from_line).(i))
done;
()
let transpose mat = init mat.width mat.height (fun i j -> mat.data.(j).(i)) let transpose mat = init mat.width mat.height (fun i j -> mat.data.(j).(i))
let gauss (m, c) = let gauss (m, c) =
@ -88,14 +97,6 @@ end = struct
else if not (Q.equal m'.data.(l).(column) Q.zero) then Some l else if not (Q.equal m'.data.(l).(column) Q.zero) then Some l
else search_pivot (l + 1) else search_pivot (l + 1)
in in
let sub_line l sl coef =
for i = 0 to m'.width - 1 do
m'.data.(l).(i) <- Q.sub m'.data.(l).(i) (Q.mul coef m'.data.(sl).(i))
done;
for i = 0 to c'.width - 1 do
c'.data.(l).(i) <- Q.sub c'.data.(l).(i) (Q.mul coef c'.data.(sl).(i))
done
in
match search_pivot line with match search_pivot line with
| Some pline -> | Some pline ->
swap m'.data line pline; swap m'.data line pline;
@ -109,7 +110,8 @@ end = struct
done; done;
if line <> m'.height - 1 then if line <> m'.height - 1 then
for l = line + 1 to m'.height - 1 do for l = line + 1 to m'.height - 1 do
sub_line l line m'.data.(l).(column) linear_combine m' l line (Q.neg m'.data.(l).(column));
linear_combine c' l line (Q.neg m'.data.(l).(column))
done; done;
line + 1 line + 1
| None -> line | None -> line
@ -134,6 +136,12 @@ end = struct
data = Array.append mat1.data mat2.data; data = Array.append mat1.data mat2.data;
} }
let delete_line mat line =
if line >= mat.height then mat
else
init (mat.height - 1) mat.width (fun i j ->
if i < line then mat.data.(i).(j) else mat.data.(i + 1).(j))
let print fmt mat = let print fmt mat =
Format.pp_print_string fmt "["; Format.pp_print_string fmt "[";
Array.iter Array.iter
@ -148,7 +156,7 @@ end = struct
Format.pp_print_string fmt "\n]" Format.pp_print_string fmt "\n]"
end end
module Kaar : DOMAIN = struct module Karr : DOMAIN = struct
type t = Bot | E of Matrix.t * Matrix.t type t = Bot | E of Matrix.t * Matrix.t
exception Cant_assign exception Cant_assign
@ -156,21 +164,16 @@ module Kaar : DOMAIN = struct
let init n = E (Matrix.zero 0 n, Matrix.zero 0 1) let init n = E (Matrix.zero 0 n, Matrix.zero 0 1)
let bottom = Bot let bottom = Bot
let assign env var expr = let rec explore e n =
match env with
| Bot -> Bot
| E (vars, consts) -> (
let n = Matrix.width vars in
let rec explore e =
match e with match e with
| CFG_int_unary (unop, e') -> ( | CFG_int_unary (unop, e') -> (
let v, c = explore e' in let v, c = explore e' n in
match unop with match unop with
| AST_UNARY_PLUS -> (v, c) | AST_UNARY_PLUS -> (v, c)
| AST_UNARY_MINUS -> (Matrix.neg v, Q.neg c)) | AST_UNARY_MINUS -> (Matrix.neg v, Q.neg c))
| CFG_int_binary (binop, e', e'') -> ( | CFG_int_binary (binop, e', e'') -> (
let v', c' = explore e' in let v', c' = explore e' n in
let v'', c'' = explore e'' in let v'', c'' = explore e'' n in
match binop with match binop with
| AST_PLUS -> (Matrix.add v' v'', Q.add c' c'') | AST_PLUS -> (Matrix.add v' v'', Q.add c' c'')
| AST_MINUS -> (Matrix.sub v' v'', Q.sub c' c'') | AST_MINUS -> (Matrix.sub v' v'', Q.sub c' c'')
@ -186,14 +189,18 @@ module Kaar : DOMAIN = struct
else raise Cant_assign else raise Cant_assign
| AST_MODULO -> raise Cant_assign) | AST_MODULO -> raise Cant_assign)
| CFG_int_var var -> | CFG_int_var var ->
( Matrix.init 1 n (fun i j -> ( Matrix.init 1 n (fun i j -> if j = var.var_id then Q.one else Q.zero),
if j = var.var_id then Q.one else Q.zero),
Q.zero ) Q.zero )
| CFG_int_const const -> (Matrix.zero 1 n, Q.make const Z.one) | CFG_int_const const -> (Matrix.zero 1 n, Q.make const Z.one)
| CFG_int_rand (_, _) -> raise Cant_assign | CFG_int_rand (_, _) -> raise Cant_assign
in
let assign env var expr =
match env with
| Bot -> Bot
| E (vars, consts) -> (
let n = Matrix.width vars in
try try
let new_line, new_const = explore expr in let new_line, new_const = explore expr n in
Matrix.set new_line 0 var.var_id Matrix.set new_line 0 var.var_id
(Q.add (Matrix.get new_line 0 var.var_id) Q.one); (Q.add (Matrix.get new_line 0 var.var_id) Q.one);
let new_vars = Matrix.extend vars new_line in let new_vars = Matrix.extend vars new_line in
@ -204,6 +211,86 @@ module Kaar : DOMAIN = struct
E (v, c) E (v, c)
with Cant_assign -> env) with Cant_assign -> env)
let rec guard env expr =
match env with
| Bot -> Bot
| E (vars, consts) -> (
let n = Matrix.width vars in
let expr = rm_negations expr in
match expr with
| CFG_bool_unary (_, _) -> failwith "impossible"
| CFG_bool_binary (_, e, e') -> guard (guard env e) e'
| CFG_compare (AST_EQUAL, e, e') -> (
try
let v, c = explore (CFG_int_binary (AST_MINUS, e, e')) n in
E
( Matrix.extend vars v,
Matrix.extend consts (Matrix.init 1 1 (fun _ _ -> Q.neg c)) )
with Cant_assign -> env)
| _ -> env)
let join a b =
match (a, b) with
| Bot, x | x, Bot -> x
| E (vars, consts), E (vars', consts') ->
let av = ref (Matrix.copy vars) in
let ac = ref (Matrix.copy consts) in
let bv = ref (Matrix.copy vars') in
let bc = ref (Matrix.copy consts') in
if Matrix.width !av <> Matrix.width !bv then failwith "invalid size";
let n = Matrix.width !av in
let rec effective_join r s =
if s >= n then ()
else if
Q.equal (Matrix.get !av r s) Q.one
&& Q.equal (Matrix.get !bv r s) Q.one
then effective_join (r + 1) (s + 1)
else if Q.equal (Matrix.get !av r s) Q.one then (
for i = 0 to r - 1 do
Matrix.linear_combine !av i r (Matrix.get !bv i s);
Matrix.linear_combine !ac i r (Matrix.get !bv i s)
done;
av := Matrix.delete_line !av r;
effective_join r (s + 1))
else if Q.equal (Matrix.get !bv r s) Q.one then (
for i = 0 to r - 1 do
Matrix.linear_combine !bv i r (Matrix.get !av i s);
Matrix.linear_combine !bc i r (Matrix.get !av i s)
done;
bv := Matrix.delete_line !bv r;
effective_join r (s + 1))
else if
r <> 0
&& not
(List.for_all
(fun i -> Q.equal (Matrix.get !av i s) (Matrix.get !bv i s))
(List.init r (fun x -> x)))
then (
let t = ref (-1) in
for i = r - 1 downto 0 do
if
!t = -1
&& not (Q.equal (Matrix.get !av i s) (Matrix.get !bv i s))
then t := i
done;
let divid = Q.sub (Matrix.get !av !t s) (Matrix.get !bv !t s) in
for i = 0 to r - 1 do
let coef =
Q.div (Q.sub (Matrix.get !av i s) (Matrix.get !bv i s)) divid
in
Matrix.linear_combine !av i !t coef;
Matrix.linear_combine !ac i !t coef;
Matrix.linear_combine !bv i !t coef;
Matrix.linear_combine !bc i !t coef
done;
av := Matrix.delete_line !av !t;
bv := Matrix.delete_line !bv !t;
effective_join (r - 1) (s + 1))
else effective_join r (s + 1)
in
effective_join 0 0;
E (!av, !ac)
let meet a b = let meet a b =
match (a, b) with match (a, b) with
| Bot, _ | _, Bot -> Bot | Bot, _ | _, Bot -> Bot
@ -214,7 +301,6 @@ module Kaar : DOMAIN = struct
E (v, c) E (v, c)
let widen = join let widen = join
let narrow = meet let narrow = meet
let subset a b = let subset a b =