-(* Original file : *)
-
+(* Original file: *)
(***********************************************************************)
(* *)
(* Copyright (C) Jean-Christophe Filliatre *)
(***********************************************************************)
(* Modified by Kim Nguyen *)
-(* The Patricia trees are themselves deeply hashconsed. The module
- provides a Make (and Weak) functor to build hashconsed patricia
- trees whose elements are Abstract hashconsed values. This allows
- to build sets of integers without boxing them in an hacons structure
+(* The Patricia trees are themselves deeply hash-consed. The module
+ provides a Make (and Weak) functor to build hash-consed patricia
+ trees whose elements are Abstract hash-consed values.
*)
+
INCLUDE "utils.ml"
include Sigs.PTSET
| Branch of int * int * 'a * 'a
module rec Node : Hcons.S with type data = Data.t = HCB(Data)
- and Data : Sigs.AUX.HashedType with type t = Node.t set =
+ and Data : Sigs.AUX.HashedType with type t = Node.t set =
struct
type t = Node.t set
let equal x y =
match x,y with
- Empty,Empty -> true
+ | Empty,Empty -> true
| Leaf k1, Leaf k2 -> k1 == k2
- | Branch(b1,i1,l1,r1),Branch(b2,i2,l2,r2) ->
- b1 == b2 && i1 == i2 && (Node.equal l1 l2) && (Node.equal r1 r2)
+ | Branch(b1,i1,l1,r1), Branch(b2,i2,l2,r2) ->
+ b1 == b2 && i1 == i2 && (Node.equal l1 l2) && (Node.equal r1 r2)
| _ -> false
let hash = function
- | Empty -> 0
- | Leaf i -> HASHINT2 (PRIME1, Uid.to_int (H.uid i))
- | Branch (b,i,l,r) ->
+ | Empty -> 0
+ | Leaf i -> HASHINT2 (PRIME1, Uid.to_int (H.uid i))
+ | Branch (b,i,l,r) ->
HASHINT4(b, i, Uid.to_int l.Node.id, Uid.to_int r.Node.id)
end
let leaf k = Node.make (Leaf k)
- (* To enforce the invariant that a branch contains two non empty
- sub-trees *)
+ (* To enforce the invariant that a branch contains two non empty
+ sub-trees *)
let branch_ne p m t0 t1 =
if (is_empty t0) then t1
else if is_empty t1 then t0 else branch p m t0 t1
- (******** from here on, only use the smart constructors ************)
+ (******** from here on, only use the smart constructors ************)
let zero_bit k m = (k land m) == 0
let is_singleton n =
match Node.node n with Leaf _ -> true
- | _ -> false
+ | _ -> false
let mem (k:elt) n =
let kid = Uid.to_int (H.uid k) in
let rec loop n = match Node.node n with
- | Empty -> false
- | Leaf j -> k == j
- | Branch (p, _, l, r) -> if kid <= p then loop l else loop r
+ | Empty -> false
+ | Leaf j -> k == j
+ | Branch (p, _, l, r) -> if kid <= p then loop l else loop r
in loop n
let rec min_elt n = match Node.node n with
- | Empty -> raise Not_found
- | Leaf k -> k
- | Branch (_,_,s,_) -> min_elt s
+ | Empty -> raise Not_found
+ | Leaf k -> k
+ | Branch (_,_,s,_) -> min_elt s
let rec max_elt n = match Node.node n with
- | Empty -> raise Not_found
- | Leaf k -> k
- | Branch (_,_,_,t) -> max_elt t
+ | Empty -> raise Not_found
+ | Leaf k -> k
+ | Branch (_,_,_,t) -> max_elt t
let elements s =
let rec elements_aux acc n = match Node.node n with
- | Empty -> acc
- | Leaf k -> k :: acc
- | Branch (_,_,l,r) -> elements_aux (elements_aux acc r) l
+ | Empty -> acc
+ | Leaf k -> k :: acc
+ | Branch (_,_,l,r) -> elements_aux (elements_aux acc r) l
in
- elements_aux [] s
+ elements_aux [] s
let mask k m = (k lor (m-1)) land (lnot m)
let rec loop i =
if i = 0 then 1 else if x lsr i = 1 then 1 lsl i else loop (i-1)
in
- loop 7
+ loop 7
let hbit = Array.init 256 naive_highest_bit
-(*
- external clz : int -> int = "caml_clz" "noalloc"
- external leading_bit : int -> int = "caml_leading_bit" "noalloc"
-*)
+ (*
+ external clz : int -> int = "caml_clz" "noalloc"
+ external leading_bit : int -> int = "caml_leading_bit" "noalloc"
+ *)
let highest_bit x =
try
let n = (x) lsr 24 in
if n != 0 then hbit.(n) lsl 24
else let n = (x) lsr 16 in if n != 0 then hbit.(n) lsl 16
- else let n = (x) lsr 8 in if n != 0 then hbit.(n) lsl 8
- else hbit.(x)
+ else let n = (x) lsr 8 in if n != 0 then hbit.(n) lsl 8
+ else hbit.(x)
with
_ -> raise (Invalid_argument ("highest_bit " ^ (string_of_int x)))
let join p0 t0 p1 t1 =
let m = branching_bit p0 p1 in
let msk = mask p0 m in
- if zero_bit p0 m then
- branch_ne msk m t0 t1
- else
- branch_ne msk m t1 t0
+ if zero_bit p0 m then
+ branch_ne msk m t0 t1
+ else
+ branch_ne msk m t1 t0
let match_prefix k p m = (mask k m) == p
let add k t =
let kid = Uid.to_int (H.uid k) in
- assert (kid >=0);
+ assert (kid >=0);
let rec ins n = match Node.node n with
- | Empty -> leaf k
- | Leaf j -> if j == k then n else join kid (leaf k) (Uid.to_int (H.uid j)) n
- | Branch (p,m,t0,t1) ->
+ | Empty -> leaf k
+ | Leaf j -> if j == k then n else join kid (leaf k) (Uid.to_int (H.uid j)) n
+ | Branch (p,m,t0,t1) ->
if match_prefix kid p m then
- if zero_bit kid m then
- branch_ne p m (ins t0) t1
- else
- branch_ne p m t0 (ins t1)
+ if zero_bit kid m then
+ branch_ne p m (ins t0) t1
else
- join kid (leaf k) p n
+ branch_ne p m t0 (ins t1)
+ else
+ join kid (leaf k) p n
in
ins t
let remove k t =
let kid = Uid.to_int(H.uid k) in
let rec rmv n = match Node.node n with
- | Empty -> empty
- | Leaf j -> if k == j then empty else n
- | Branch (p,m,t0,t1) ->
+ | Empty -> empty
+ | Leaf j -> if k == j then empty else n
+ | Branch (p,m,t0,t1) ->
if match_prefix kid p m then
- if zero_bit kid m then
- branch_ne p m (rmv t0) t1
- else
- branch_ne p m t0 (rmv t1)
+ if zero_bit kid m then
+ branch_ne p m (rmv t0) t1
+ else
+ branch_ne p m t0 (rmv t1)
else
- n
+ n
in
rmv t
- (* should run in O(1) thanks to Hash consing *)
+ (* should run in O(1) thanks to Hash consing *)
let equal a b = Node.equal a b
then s
else
match Node.node s, Node.node t with
- | Empty, _ -> t
- | _, Empty -> s
- | Leaf k, _ -> add k t
- | _, Leaf k -> add k s
- | Branch (p,m,s0,s1), Branch (q,n,t0,t1) ->
+ | Empty, _ -> t
+ | _, Empty -> s
+ | Leaf k, _ -> add k t
+ | _, Leaf k -> add k s
+ | Branch (p,m,s0,s1), Branch (q,n,t0,t1) ->
if m == n && match_prefix q p m then
- branch p m (merge s0 t0) (merge s1 t1)
+ branch p m (merge s0 t0) (merge s1 t1)
else if m > n && match_prefix q p m then
- if zero_bit q m then
- branch_ne p m (merge s0 t) s1
- else
- branch_ne p m s0 (merge s1 t)
+ if zero_bit q m then
+ branch_ne p m (merge s0 t) s1
+ else
+ branch_ne p m s0 (merge s1 t)
else if m < n && match_prefix p q n then
- if zero_bit p n then
- branch_ne q n (merge s t0) t1
- else
- branch_ne q n t0 (merge s t1)
+ if zero_bit p n then
+ branch_ne q n (merge s t0) t1
+ else
+ branch_ne q n t0 (merge s t1)
else
- (* The prefixes disagree. *)
- join p s q t
+ (* The prefixes disagree. *)
+ join p s q t
let rec subset s1 s2 = (equal s1 s2) ||
match (Node.node s1,Node.node s2) with
- | Empty, _ -> true
- | _, Empty -> false
- | Leaf k1, _ -> mem k1 s2
- | Branch _, Leaf _ -> false
- | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
+ | Empty, _ -> true
+ | _, Empty -> false
+ | Leaf k1, _ -> mem k1 s2
+ | Branch _, Leaf _ -> false
+ | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
if m1 == m2 && p1 == p2 then
- subset l1 l2 && subset r1 r2
+ subset l1 l2 && subset r1 r2
else if m1 < m2 && match_prefix p1 p2 m2 then
- if zero_bit p1 m2 then
- subset l1 l2 && subset r1 l2
- else
- subset l1 r2 && subset r1 r2
+ if zero_bit p1 m2 then
+ subset l1 l2 && subset r1 l2
+ else
+ subset l1 r2 && subset r1 r2
else
- false
+ false
let union s1 s2 = merge s1 s2
- (* Todo replace with e Memo Module *)
+ (* Todo replace with e Memo Module *)
let rec inter s1 s2 =
if equal s1 s2
then s1
else
- match (Node.node s1,Node.node s2) with
- | Empty, _ -> empty
- | _, Empty -> empty
- | Leaf k1, _ -> if mem k1 s2 then s1 else empty
- | _, Leaf k2 -> if mem k2 s1 then s2 else empty
- | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
+ match (Node.node s1,Node.node s2) with
+ | Empty, _ -> empty
+ | _, Empty -> empty
+ | Leaf k1, _ -> if mem k1 s2 then s1 else empty
+ | _, Leaf k2 -> if mem k2 s1 then s2 else empty
+ | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
if m1 == m2 && p1 == p2 then
- merge (inter l1 l2) (inter r1 r2)
+ merge (inter l1 l2) (inter r1 r2)
else if m1 > m2 && match_prefix p2 p1 m1 then
- inter (if zero_bit p2 m1 then l1 else r1) s2
+ inter (if zero_bit p2 m1 then l1 else r1) s2
else if m1 < m2 && match_prefix p1 p2 m2 then
- inter s1 (if zero_bit p1 m2 then l2 else r2)
+ inter s1 (if zero_bit p1 m2 then l2 else r2)
else
- empty
+ empty
let rec diff s1 s2 =
if equal s1 s2
then empty
else
- match (Node.node s1,Node.node s2) with
- | Empty, _ -> empty
- | _, Empty -> s1
- | Leaf k1, _ -> if mem k1 s2 then empty else s1
- | _, Leaf k2 -> remove k2 s1
- | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
+ match (Node.node s1,Node.node s2) with
+ | Empty, _ -> empty
+ | _, Empty -> s1
+ | Leaf k1, _ -> if mem k1 s2 then empty else s1
+ | _, Leaf k2 -> remove k2 s1
+ | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
if m1 == m2 && p1 == p2 then
- merge (diff l1 l2) (diff r1 r2)
+ merge (diff l1 l2) (diff r1 r2)
else if m1 > m2 && match_prefix p2 p1 m1 then
- if zero_bit p2 m1 then
- merge (diff l1 s2) r1
- else
- merge l1 (diff r1 s2)
+ if zero_bit p2 m1 then
+ merge (diff l1 s2) r1
+ else
+ merge l1 (diff r1 s2)
else if m1 < m2 && match_prefix p1 p2 m2 then
- if zero_bit p1 m2 then diff s1 l2 else diff s1 r2
+ if zero_bit p1 m2 then diff s1 l2 else diff s1 r2
else
- s1
+ s1
-(*s All the following operations ([cardinal], [iter], [fold], [for_all],
+ (*s All the following operations ([cardinal], [iter], [fold], [for_all],
[exists], [filter], [partition], [choose], [elements]) are
implemented as for any other kind of binary trees. *)
-let rec cardinal n = match Node.node n with
+ let rec cardinal n = match Node.node n with
| Empty -> 0
| Leaf _ -> 1
| Branch (_,_,t0,t1) -> cardinal t0 + cardinal t1
-let rec iter f n = match Node.node n with
+ let rec iter f n = match Node.node n with
| Empty -> ()
| Leaf k -> f k
| Branch (_,_,t0,t1) -> iter f t0; iter f t1
-let rec fold f s accu = match Node.node s with
+ let rec fold f s accu = match Node.node s with
| Empty -> accu
| Leaf k -> f k accu
| Branch (_,_,t0,t1) -> fold f t0 (fold f t1 accu)
-let rec for_all p n = match Node.node n with
+ let rec for_all p n = match Node.node n with
| Empty -> true
| Leaf k -> p k
| Branch (_,_,t0,t1) -> for_all p t0 && for_all p t1
-let rec exists p n = match Node.node n with
+ let rec exists p n = match Node.node n with
| Empty -> false
| Leaf k -> p k
| Branch (_,_,t0,t1) -> exists p t0 || exists p t1
-let rec filter pr n = match Node.node n with
+ let rec filter pr n = match Node.node n with
| Empty -> empty
| Leaf k -> if pr k then n else empty
| Branch (p,m,t0,t1) -> branch_ne p m (filter pr t0) (filter pr t1)
-let partition p s =
- let rec part (t,f as acc) n = match Node.node n with
+ let partition p s =
+ let rec part (t,f as acc) n = match Node.node n with
| Empty -> acc
| Leaf k -> if p k then (add k t, f) else (t, add k f)
| Branch (_,_,t0,t1) -> part (part acc t0) t1
- in
- part (empty, empty) s
+ in
+ part (empty, empty) s
-let rec choose n = match Node.node n with
+ let rec choose n = match Node.node n with
| Empty -> raise Not_found
| Leaf k -> k
| Branch (_, _,t0,_) -> choose t0 (* we know that [t0] is non-empty *)
-let split x s =
- let coll k (l, b, r) =
- if k < x then add k l, b, r
- else if k > x then l, b, add k r
- else l, true, r
- in
- fold coll s (empty, false, empty)
-
-(*s Additional functions w.r.t to [Set.S]. *)
-
-let rec intersect s1 s2 = (equal s1 s2) ||
- match (Node.node s1,Node.node s2) with
- | Empty, _ -> false
- | _, Empty -> false
- | Leaf k1, _ -> mem k1 s2
- | _, Leaf k2 -> mem k2 s1
- | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
- if m1 == m2 && p1 == p2 then
+ let split x s =
+ let coll k (l, b, r) =
+ if k < x then add k l, b, r
+ else if k > x then l, b, add k r
+ else l, true, r
+ in
+ fold coll s (empty, false, empty)
+
+ (*s Additional functions w.r.t to [Set.S]. *)
+
+ let rec intersect s1 s2 = (equal s1 s2) ||
+ match (Node.node s1,Node.node s2) with
+ | Empty, _ -> false
+ | _, Empty -> false
+ | Leaf k1, _ -> mem k1 s2
+ | _, Leaf k2 -> mem k2 s1
+ | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
+ if m1 == m2 && p1 == p2 then
intersect l1 l2 || intersect r1 r2
- else if m1 < m2 && match_prefix p2 p1 m1 then
+ else if m1 < m2 && match_prefix p2 p1 m1 then
intersect (if zero_bit p2 m1 then l1 else r1) s2
- else if m1 > m2 && match_prefix p1 p2 m2 then
+ else if m1 > m2 && match_prefix p1 p2 m2 then
intersect s1 (if zero_bit p1 m2 then l2 else r2)
- else
+ else
false
-let from_list l = List.fold_left (fun acc e -> add e acc) empty l
+ let from_list l = List.fold_left (fun acc e -> add e acc) empty l
end
module PosInt
=
- struct
- include Make(Hcons.PosInt)
- let print ppf s =
- Format.pp_print_string ppf "{ ";
- iter (fun i -> Format.fprintf ppf "%i " i) s;
- Format.pp_print_string ppf "}";
- Format.pp_print_flush ppf ()
- end
+struct
+ include Make(Hcons.PosInt)
+ let print ppf s =
+ Format.pp_print_string ppf "{ ";
+ iter (fun i -> Format.fprintf ppf "%i " i) s;
+ Format.pp_print_string ppf "}";
+ Format.pp_print_flush ppf ()
+end