323 lines
10 KiB
OCaml
323 lines
10 KiB
OCaml
open Domain
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open Cfg
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open Abstract_syntax_tree
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let swap arr i j =
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let tmp = arr.(i) in
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arr.(i) <- arr.(j);
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arr.(j) <- tmp
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module Matrix : sig
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type t
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val width : t -> int
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val height : t -> int
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val set : t -> int -> int -> Q.t -> unit
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val get : t -> int -> int -> Q.t
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val init : int -> int -> (int -> int -> Q.t) -> t
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val copy : t -> t
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val zero : int -> int -> t
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val is_all_zero : t -> bool
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val map : t -> (Q.t -> Q.t) -> t
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val neg : t -> t
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val add : t -> t -> t
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val sub : t -> t -> t
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val mul : t -> t -> t
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val linear_combine : t -> int -> int -> Q.t -> unit
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val transpose : t -> t
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val gauss : t * t -> t * t
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val extend : t -> t -> t
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val delete_line : t -> int -> t
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val print : Format.formatter -> t -> unit
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end = struct
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type t = { height : int; width : int; data : Q.t array array }
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exception Incorrect_matrix_size
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let width mat = mat.width
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let height mat = mat.height
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let set mat i j q =
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mat.data.(i).(j) <- q;
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()
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let get mat i j = mat.data.(i).(j)
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let init n m f =
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{
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height = n;
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width = m;
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data = Array.init n (fun i -> Array.init m (fun j -> f i j));
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}
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let copy m = init m.height m.width (fun i j -> m.data.(i).(j))
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let zero n m = init n m (fun _ _ -> Q.zero)
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let is_all_zero mat =
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Array.for_all
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(fun a -> Array.for_all (fun elt -> Q.equal elt Q.zero) a)
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mat.data
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let map mat f = init mat.height mat.width (fun i j -> f mat.data.(i).(j))
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let neg mat = init mat.height mat.width (fun i j -> Q.neg mat.data.(i).(j))
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let add mat1 mat2 =
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if mat1.width <> mat2.width || mat1.height <> mat2.height then
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raise Incorrect_matrix_size
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else
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init mat1.height mat1.width (fun i j ->
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Q.add mat1.data.(i).(j) mat2.data.(i).(j))
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let sub mat1 mat2 = add mat1 (neg mat2)
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let mul mat1 mat2 =
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if mat1.width <> mat2.height then raise Incorrect_matrix_size
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else
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init mat1.height mat2.width (fun i j ->
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List.fold_left
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(fun sum k -> Q.add sum (Q.mul mat1.data.(i).(k) mat2.data.(k).(j)))
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Q.zero
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(List.init mat1.width (fun x -> x)))
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let linear_combine mat line from_line coef =
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for i = 0 to mat.width - 1 do
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mat.data.(line).(i) <-
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Q.add mat.data.(line).(i) (Q.mul coef mat.data.(from_line).(i))
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done;
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()
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let transpose mat = init mat.width mat.height (fun i j -> mat.data.(j).(i))
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let gauss (m, c) =
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let m' = copy m in
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let c' = copy c in
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let pivot line column =
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let rec search_pivot l =
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if l >= m'.height then None
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else if not (Q.equal m'.data.(l).(column) Q.zero) then Some l
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else search_pivot (l + 1)
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in
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match search_pivot line with
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| Some pline ->
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swap m'.data line pline;
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swap c'.data line pline;
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let d = m'.data.(line).(column) in
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for i = 0 to m'.width - 1 do
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m'.data.(line).(i) <- Q.div m'.data.(line).(i) d
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done;
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for i = 0 to c'.width - 1 do
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c'.data.(line).(i) <- Q.div c'.data.(line).(i) d
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done;
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if line <> m'.height - 1 then
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for l = line + 1 to m'.height - 1 do
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linear_combine m' l line (Q.neg m'.data.(l).(column));
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linear_combine c' l line (Q.neg m'.data.(l).(column))
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done;
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line + 1
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| None -> line
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in
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if m'.height <> c'.height then raise Incorrect_matrix_size
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else
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let line = ref 0 in
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for i = 0 to m'.width - 1 do
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line := pivot !line i
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done;
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let m'' = init !line m'.width (fun i j -> m'.data.(i).(j)) in
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let c'' = init !line c'.width (fun i j -> c'.data.(i).(j)) in
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(m'', c'')
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let extend mat1 mat2 =
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if mat1.width <> mat2.width then raise Incorrect_matrix_size
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else
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{
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height = mat1.height + mat2.height;
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width = mat1.width;
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data = Array.append mat1.data mat2.data;
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}
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let delete_line mat line =
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if line >= mat.height then mat
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else
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init (mat.height - 1) mat.width (fun i j ->
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if i < line then mat.data.(i).(j) else mat.data.(i + 1).(j))
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let print fmt mat =
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Format.pp_print_string fmt "[";
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Array.iter
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(fun arr ->
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Format.pp_print_string fmt "\n";
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Array.iter
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(fun elt ->
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Format.pp_print_string fmt " ";
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Q.pp_print fmt elt)
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arr)
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mat.data;
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Format.pp_print_string fmt "\n]"
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end
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module Karr : DOMAIN = struct
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type t = Bot | E of Matrix.t * Matrix.t
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exception Cant_assign
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let init n =
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E (Matrix.zero 0 n, Matrix.zero 0 1)
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let bottom = Bot
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let rec explore e n =
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match e with
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| CFG_int_unary (unop, e') -> (
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let v, c = explore e' n in
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match unop with
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| AST_UNARY_PLUS -> (v, c)
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| AST_UNARY_MINUS -> (Matrix.neg v, Q.neg c))
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| CFG_int_binary (binop, e', e'') -> (
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let v', c' = explore e' n in
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let v'', c'' = explore e'' n in
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match binop with
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| AST_PLUS -> (Matrix.add v' v'', Q.add c' c'')
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| AST_MINUS -> (Matrix.sub v' v'', Q.sub c' c'')
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| AST_MULTIPLY ->
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if Matrix.is_all_zero v' then
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(Matrix.map v'' (fun q -> Q.mul q c'), Q.mul c' c'')
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else if Matrix.is_all_zero v'' then
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(Matrix.map v' (fun q -> Q.mul q c''), Q.mul c' c'')
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else raise Cant_assign
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| AST_DIVIDE ->
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if Matrix.is_all_zero v'' then
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(Matrix.map v' (fun q -> Q.div q c''), Q.div c' c'')
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else raise Cant_assign
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| AST_MODULO -> raise Cant_assign)
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| CFG_int_var var ->
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( Matrix.init 1 n (fun i j -> if j = var.var_id - 1 then Q.one else Q.zero),
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Q.zero )
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| CFG_int_const const -> (Matrix.zero 1 n, Q.make const Z.one)
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| CFG_int_rand (_, _) -> raise Cant_assign
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let assign env var expr =
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match env with
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| Bot -> Bot
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| E (vars, consts) -> (
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let n = Matrix.width vars in
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try
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let new_line, new_const = explore expr n in
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Matrix.set new_line 0 (var.var_id - 1)
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(Q.add (Matrix.get new_line 0 (var.var_id - 1)) Q.one);
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let new_vars = Matrix.extend vars new_line in
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let new_consts =
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Matrix.extend consts (Matrix.init 1 1 (fun _ _ -> new_const))
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in
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let v, c = Matrix.gauss (new_vars, new_consts) in
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E (v, c)
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with Cant_assign -> env)
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let rec guard env expr =
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match env with
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| Bot -> Bot
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| E (vars, consts) -> (
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let n = Matrix.width vars in
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let expr = rm_negations expr in
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match expr with
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| CFG_bool_unary (_, _) -> failwith "impossible"
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| CFG_bool_binary (_, e, e') -> guard (guard env e) e'
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| CFG_compare (AST_EQUAL, e, e') -> (
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try
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let v, c = explore (CFG_int_binary (AST_MINUS, e, e')) n in
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E
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( Matrix.extend vars v,
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Matrix.extend consts (Matrix.init 1 1 (fun _ _ -> Q.neg c)) )
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with Cant_assign -> env)
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| _ -> env)
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let join a b =
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match (a, b) with
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| Bot, x | x, Bot -> x
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| E (vars, consts), E (vars', consts') ->
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let av = ref (Matrix.copy vars) in
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let ac = ref (Matrix.copy consts) in
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let bv = ref (Matrix.copy vars') in
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let bc = ref (Matrix.copy consts') in
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if Matrix.width !av <> Matrix.width !bv then failwith "invalid size";
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let n = Matrix.width !av in
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let rec effective_join r s =
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if s >= n then ()
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else if
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Q.equal (Matrix.get !av r s) Q.one
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&& Q.equal (Matrix.get !bv r s) Q.one
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then effective_join (r + 1) (s + 1)
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else if Q.equal (Matrix.get !av r s) Q.one then (
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for i = 0 to r - 1 do
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Matrix.linear_combine !av i r (Matrix.get !bv i s);
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Matrix.linear_combine !ac i r (Matrix.get !bv i s)
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done;
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av := Matrix.delete_line !av r;
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effective_join r (s + 1))
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else if Q.equal (Matrix.get !bv r s) Q.one then (
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for i = 0 to r - 1 do
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Matrix.linear_combine !bv i r (Matrix.get !av i s);
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Matrix.linear_combine !bc i r (Matrix.get !av i s)
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done;
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bv := Matrix.delete_line !bv r;
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effective_join r (s + 1))
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else if
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r <> 0
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&& not
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(List.for_all
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(fun i -> Q.equal (Matrix.get !av i s) (Matrix.get !bv i s))
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(List.init r (fun x -> x)))
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then (
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let t = ref (-1) in
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for i = r - 1 downto 0 do
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if
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!t = -1
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&& not (Q.equal (Matrix.get !av i s) (Matrix.get !bv i s))
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then t := i
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done;
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let divid = Q.sub (Matrix.get !av !t s) (Matrix.get !bv !t s) in
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for i = 0 to r - 1 do
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let coef =
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Q.div (Q.sub (Matrix.get !av i s) (Matrix.get !bv i s)) divid
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in
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Matrix.linear_combine !av i !t coef;
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Matrix.linear_combine !ac i !t coef;
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Matrix.linear_combine !bv i !t coef;
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Matrix.linear_combine !bc i !t coef
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done;
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av := Matrix.delete_line !av !t;
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bv := Matrix.delete_line !bv !t;
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effective_join (r - 1) (s + 1))
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else effective_join r (s + 1)
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in
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effective_join 0 0;
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E (!av, !ac)
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let meet a b =
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match (a, b) with
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| Bot, _ | _, Bot -> Bot
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| E (vars, consts), E (vars', consts') ->
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let v, c =
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Matrix.gauss (Matrix.extend vars vars', Matrix.extend consts consts')
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in
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E (v, c)
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let widen = join
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let narrow = meet
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let subset a b =
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match (a, b) with
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| Bot, _ -> true
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| _, Bot -> false
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| E (vars, consts), E (vars', consts') ->
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let v = Matrix.extend vars vars' in
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let c = Matrix.extend consts consts' in
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let v', c' = Matrix.gauss (v, c) in
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Matrix.is_all_zero (Matrix.sub v' vars)
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&& Matrix.is_all_zero (Matrix.sub c' consts)
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let is_bottom = function Bot -> true | _ -> false
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let print fmt = function
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| Bot -> Format.pp_print_string fmt "Bot\n"
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| E (vars, consts) -> Matrix.print fmt vars
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end
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