val from_list : elt list -> t
end
-module Int : S with type elt = int =
-struct
- type elt = int
- external hash_elt : elt -> int = "%identity"
- external uid_elt : elt -> int = "%identity"
- let equal_elt : elt -> elt -> bool = (==);;
-
-DEFINE USE_PTSET_INCLUDE
-INCLUDE "ptset_include.ml"
-
-end
module Make ( H : Hcons.S ) : S with type elt = H.t =
struct
type elt = H.t
- let hash_elt = H.hash
- let uid_elt = H.uid
- let equal_elt = H.equal
-INCLUDE "ptset_include.ml"
+
+ type 'a node =
+ | Empty
+ | Leaf of elt
+ | Branch of int * int * 'a * 'a
+
+ module rec HNode : Hcons.S with type data = Node.t = Hcons.Make (Node)
+ and Node : Hashtbl.HashedType with type t = HNode.t node =
+ struct
+ type t = HNode.t node
+ let equal x y =
+ match x,y with
+ | Empty,Empty -> true
+ | Leaf k1, Leaf k2 -> H.equal k1 k2
+ | Branch(b1,i1,l1,r1),Branch(b2,i2,l2,r2) ->
+ b1 == b2 && i1 == i2 &&
+ (HNode.equal l1 l2) &&
+ (HNode.equal r1 r2)
+ | _ -> false
+ let hash = function
+ | Empty -> 0
+ | Leaf i -> HASHINT2(HALF_MAX_INT,H.hash i)
+ | Branch (b,i,l,r) -> HASHINT4(b,i,HNode.hash l, HNode.hash r)
+ end
+ ;;
+
+ type t = HNode.t
+ let hash = HNode.hash
+ let uid = HNode.uid
+
+ let empty = HNode.make Empty
+
+ let is_empty s = (HNode.node s) == Empty
+
+ let branch p m l r = HNode.make (Branch(p,m,l,r))
+
+ let leaf k = HNode.make (Leaf k)
+
+ (* 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 *************)
+
+ let zero_bit k m = (k land m) == 0
+
+ let singleton k = leaf k
+
+ let is_singleton n =
+ match HNode.node n with Leaf _ -> true
+ | _ -> false
+
+ let mem (k:elt) n =
+ let kid = H.uid k in
+ let rec loop n = match HNode.node n with
+ | Empty -> false
+ | Leaf j -> H.equal k j
+ | Branch (p, _, l, r) -> if kid <= p then loop l else loop r
+ in loop n
+
+ let rec min_elt n = match HNode.node n with
+ | Empty -> raise Not_found
+ | Leaf k -> k
+ | Branch (_,_,s,_) -> min_elt s
+
+ let rec max_elt n = match HNode.node n with
+ | Empty -> raise Not_found
+ | Leaf k -> k
+ | Branch (_,_,_,t) -> max_elt t
+
+ let elements s =
+ let rec elements_aux acc n = match HNode.node n with
+ | Empty -> acc
+ | Leaf k -> k :: acc
+ | Branch (_,_,l,r) -> elements_aux (elements_aux acc r) l
+ in
+ elements_aux [] s
+
+ let mask k m = (k lor (m-1)) land (lnot m)
+
+ let naive_highest_bit x =
+ assert (x < 256);
+ 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
+
+ let hbit = Array.init 256 naive_highest_bit
+
+
+ let highest_bit x = let n = (x) lsr 24 in
+ if n != 0 then Array.unsafe_get hbit n lsl 24
+ else let n = (x) lsr 16 in if n != 0 then Array.unsafe_get hbit n lsl 16
+ else let n = (x) lsr 8 in if n != 0 then Array.unsafe_get hbit n lsl 8
+ else Array.unsafe_get hbit (x)
+
+IFDEF WORDIZE64
+THEN
+ let highest_bit64 x =
+ let n = x lsr 32 in if n != 0 then highest_bit n lsl 32
+ else highest_bit x
+END
+
+
+ let branching_bit p0 p1 = highest_bit (p0 lxor p1)
+
+ let join p0 t0 p1 t1 =
+ let m = branching_bit p0 p1 in
+ if zero_bit p0 m then
+ branch (mask p0 m) m t0 t1
+ else
+ branch (mask p0 m) m t1 t0
+
+ let match_prefix k p m = (mask k m) == p
+
+ let add k t =
+ let kid = H.uid k in
+ let rec ins n = match HNode.node n with
+ | Empty -> leaf k
+ | Leaf j -> if H.equal j k then n else join kid (leaf k) (H.uid j) n
+ | Branch (p,m,t0,t1) ->
+ if match_prefix kid p m then
+ if zero_bit kid m then
+ branch p m (ins t0) t1
+ else
+ branch p m t0 (ins t1)
+ else
+ join kid (leaf k) p n
+ in
+ ins t
+
+ let remove k t =
+ let kid = H.uid k in
+ let rec rmv n = match HNode.node n with
+ | Empty -> empty
+ | Leaf j -> if H.equal 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)
+ else
+ n
+ in
+ rmv t
+
+ (* should run in O(1) thanks to Hash consing *)
+
+ let equal a b = HNode.equal a b
+
+ let compare a b = (HNode.uid a) - (HNode.uid b)
+
+ let rec merge s t =
+ if (equal s t) (* This is cheap thanks to hash-consing *)
+ then s
+ else
+ match HNode.node s, HNode.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) ->
+ if m == n && match_prefix q p m then
+ 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 p m (merge s0 t) s1
+ else
+ branch p m s0 (merge s1 t)
+ else if m < n && match_prefix p q n then
+ if zero_bit p n then
+ branch q n (merge s t0) t1
+ else
+ branch q n t0 (merge s t1)
+ else
+ (* The prefixes disagree. *)
+ join p s q t
+
+
+
+
+ let rec subset s1 s2 = (equal s1 s2) ||
+ match (HNode.node s1,HNode.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) ->
+ if m1 == m2 && p1 == p2 then
+ 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
+ else
+ false
+
+
+ let union s1 s2 = merge s1 s2
+ (* Todo replace with e Memo Module *)
+ module MemUnion = Hashtbl.Make(
+ struct
+ type set = t
+ type t = set*set
+ let equal (x,y) (z,t) = (equal x z)&&(equal y t)
+ let equal a b = equal a b || equal b a
+ let hash (x,y) = (* commutative hash *)
+ let x = HNode.hash x
+ and y = HNode.hash y
+ in
+ if x < y then HASHINT2(x,y) else HASHINT2(y,x)
+ end)
+ let h_mem = MemUnion.create MED_H_SIZE
+
+ let mem_union s1 s2 =
+ try MemUnion.find h_mem (s1,s2)
+ with Not_found ->
+ let r = merge s1 s2 in MemUnion.add h_mem (s1,s2) r;r
+
+
+ let rec inter s1 s2 =
+ if equal s1 s2
+ then s1
+ else
+ match (HNode.node s1,HNode.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)
+ else if m1 > m2 && match_prefix p2 p1 m1 then
+ 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)
+ else
+ empty
+
+ let rec diff s1 s2 =
+ if equal s1 s2
+ then empty
+ else
+ match (HNode.node s1,HNode.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)
+ 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)
+ else if m1 < m2 && match_prefix p1 p2 m2 then
+ if zero_bit p1 m2 then diff s1 l2 else diff s1 r2
+ else
+ s1
+
+
+(*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 HNode.node n with
+ | Empty -> 0
+ | Leaf _ -> 1
+ | Branch (_,_,t0,t1) -> cardinal t0 + cardinal t1
+
+let rec iter f n = match HNode.node n with
+ | Empty -> ()
+ | Leaf k -> f k
+ | Branch (_,_,t0,t1) -> iter f t0; iter f t1
+
+let rec fold f s accu = match HNode.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 HNode.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 HNode.node n with
+ | Empty -> false
+ | Leaf k -> p k
+ | Branch (_,_,t0,t1) -> exists p t0 || exists p t1
+
+let rec filter pr n = match HNode.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 HNode.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
+
+let rec choose n = match HNode.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)
+
+
+let make l = List.fold_left (fun acc e -> add e acc ) empty l
+(*i*)
+
+(*s Additional functions w.r.t to [Set.S]. *)
+
+let rec intersect s1 s2 = (equal s1 s2) ||
+ match (HNode.node s1,HNode.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
+ intersect (if zero_bit p2 m1 then l1 else r1) s2
+ else if m1 > m2 && match_prefix p1 p2 m2 then
+ intersect s1 (if zero_bit p1 m2 then l2 else r2)
+ else
+ false
+
+
+
+let rec uncons n = match HNode.node n with
+ | Empty -> raise Not_found
+ | Leaf k -> (k,empty)
+ | Branch (p,m,s,t) -> let h,ns = uncons s in h,branch_ne p m ns t
+
+let from_list l = List.fold_left (fun acc e -> add e acc) empty l
+
+
end
(* Have to benchmark wheter this whole include stuff is worth it *)
-module I : S with type elt = int = Make ( struct type t = int
+module Int : S with type elt = int = Make ( struct type t = int
type data = t
external hash : t -> int = "%identity"
external uid : t -> int = "%identity"
projects / SXSI / xpathcomp.git / blobdiff