2 (***********************************************************************)
4 (* Copyright (C) Jean-Christophe Filliatre *)
6 (* This software is free software; you can redistribute it and/or *)
7 (* modify it under the terms of the GNU Library General Public *)
8 (* License version 2.1, with the special exception on linking *)
9 (* described in file http://www.lri.fr/~filliatr/ftp/ocaml/ds/LICENSE *)
11 (* This software is distributed in the hope that it will be useful, *)
12 (* but WITHOUT ANY WARRANTY; without even the implied warranty of *)
13 (* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *)
15 (***********************************************************************)
17 (* Modified by Kim Nguyen *)
18 (* The Patricia trees are themselves deeply hash-consed. The module
19 provides a Make (and Weak) functor to build hash-consed patricia
20 trees whose elements are Abstract hash-consed values.
27 module type HConsBuilder =
28 functor (H : Sigs.AUX.HashedType) -> Hcons.S with type data = H.t
30 module Builder (HCB : HConsBuilder) (H : Hcons.Abstract) :
31 S with type elt = H.t =
38 | Branch of int * int * 'a * 'a
40 module rec Node : Hcons.S with type data = Data.t = HCB(Data)
41 and Data : Sigs.AUX.HashedType with type t = Node.t set =
47 | Leaf k1, Leaf k2 -> k1 == k2
48 | Branch(b1,i1,l1,r1), Branch(b2,i2,l2,r2) ->
49 b1 == b2 && i1 == i2 && (Node.equal l1 l2) && (Node.equal r1 r2)
55 | Leaf i -> HASHINT2 (PRIME1, Uid.to_int (H.uid i))
57 HASHINT4(b, i, Uid.to_int l.Node.id, Uid.to_int r.Node.id)
62 let empty = Node.make Empty
64 let is_empty s = (Node.node s) == Empty
66 let branch p m l r = Node.make (Branch(p,m,l,r))
68 let leaf k = Node.make (Leaf k)
70 (* To enforce the invariant that a branch contains two non empty
72 let branch_ne p m t0 t1 =
73 if (is_empty t0) then t1
74 else if is_empty t1 then t0 else branch p m t0 t1
76 (******** from here on, only use the smart constructors ************)
78 let zero_bit k m = (k land m) == 0
80 let singleton k = leaf k
83 match Node.node n with Leaf _ -> true
87 let kid = Uid.to_int (H.uid k) in
88 let rec loop n = match Node.node n with
91 | Branch (p, _, l, r) -> if kid <= p then loop l else loop r
94 let rec min_elt n = match Node.node n with
95 | Empty -> raise Not_found
97 | Branch (_,_,s,_) -> min_elt s
99 let rec max_elt n = match Node.node n with
100 | Empty -> raise Not_found
102 | Branch (_,_,_,t) -> max_elt t
105 let rec elements_aux acc n = match Node.node n with
108 | Branch (_,_,l,r) -> elements_aux (elements_aux acc r) l
112 let mask k m = (k lor (m-1)) land (lnot m)
114 let naive_highest_bit x =
117 if i = 0 then 1 else if x lsr i = 1 then 1 lsl i else loop (i-1)
121 let hbit = Array.init 256 naive_highest_bit
123 external clz : int -> int = "caml_clz" "noalloc"
124 external leading_bit : int -> int = "caml_leading_bit" "noalloc"
128 let n = (x) lsr 24 in
129 if n != 0 then hbit.(n) lsl 24
130 else let n = (x) lsr 16 in if n != 0 then hbit.(n) lsl 16
131 else let n = (x) lsr 8 in if n != 0 then hbit.(n) lsl 8
134 _ -> raise (Invalid_argument ("highest_bit " ^ (string_of_int x)))
136 let highest_bit64 x =
137 let n = x lsr 32 in if n != 0 then highest_bit n lsl 32
140 let branching_bit p0 p1 = highest_bit64 (p0 lxor p1)
142 let join p0 t0 p1 t1 =
143 let m = branching_bit p0 p1 in
144 let msk = mask p0 m in
145 if zero_bit p0 m then
146 branch_ne msk m t0 t1
148 branch_ne msk m t1 t0
150 let match_prefix k p m = (mask k m) == p
153 let kid = Uid.to_int (H.uid k) in
155 let rec ins n = match Node.node n with
157 | Leaf j -> if j == k then n else join kid (leaf k) (Uid.to_int (H.uid j)) n
158 | Branch (p,m,t0,t1) ->
159 if match_prefix kid p m then
160 if zero_bit kid m then
161 branch_ne p m (ins t0) t1
163 branch_ne p m t0 (ins t1)
165 join kid (leaf k) p n
170 let kid = Uid.to_int(H.uid k) in
171 let rec rmv n = match Node.node n with
173 | Leaf j -> if k == j then empty else n
174 | Branch (p,m,t0,t1) ->
175 if match_prefix kid p m then
176 if zero_bit kid m then
177 branch_ne p m (rmv t0) t1
179 branch_ne p m t0 (rmv t1)
185 (* should run in O(1) thanks to Hash consing *)
187 let equal a b = Node.equal a b
189 let compare a b = (Uid.to_int (Node.uid a)) - (Uid.to_int (Node.uid b))
192 if (equal s t) (* This is cheap thanks to hash-consing *)
195 match Node.node s, Node.node t with
198 | Leaf k, _ -> add k t
199 | _, Leaf k -> add k s
200 | Branch (p,m,s0,s1), Branch (q,n,t0,t1) ->
201 if m == n && match_prefix q p m then
202 branch p m (merge s0 t0) (merge s1 t1)
203 else if m > n && match_prefix q p m then
205 branch_ne p m (merge s0 t) s1
207 branch_ne p m s0 (merge s1 t)
208 else if m < n && match_prefix p q n then
210 branch_ne q n (merge s t0) t1
212 branch_ne q n t0 (merge s t1)
214 (* The prefixes disagree. *)
220 let rec subset s1 s2 = (equal s1 s2) ||
221 match (Node.node s1,Node.node s2) with
224 | Leaf k1, _ -> mem k1 s2
225 | Branch _, Leaf _ -> false
226 | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
227 if m1 == m2 && p1 == p2 then
228 subset l1 l2 && subset r1 r2
229 else if m1 < m2 && match_prefix p1 p2 m2 then
230 if zero_bit p1 m2 then
231 subset l1 l2 && subset r1 l2
233 subset l1 r2 && subset r1 r2
238 let union s1 s2 = merge s1 s2
239 (* Todo replace with e Memo Module *)
241 let rec inter s1 s2 =
245 match (Node.node s1,Node.node s2) with
248 | Leaf k1, _ -> if mem k1 s2 then s1 else empty
249 | _, Leaf k2 -> if mem k2 s1 then s2 else empty
250 | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
251 if m1 == m2 && p1 == p2 then
252 merge (inter l1 l2) (inter r1 r2)
253 else if m1 > m2 && match_prefix p2 p1 m1 then
254 inter (if zero_bit p2 m1 then l1 else r1) s2
255 else if m1 < m2 && match_prefix p1 p2 m2 then
256 inter s1 (if zero_bit p1 m2 then l2 else r2)
264 match (Node.node s1,Node.node s2) with
267 | Leaf k1, _ -> if mem k1 s2 then empty else s1
268 | _, Leaf k2 -> remove k2 s1
269 | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
270 if m1 == m2 && p1 == p2 then
271 merge (diff l1 l2) (diff r1 r2)
272 else if m1 > m2 && match_prefix p2 p1 m1 then
273 if zero_bit p2 m1 then
274 merge (diff l1 s2) r1
276 merge l1 (diff r1 s2)
277 else if m1 < m2 && match_prefix p1 p2 m2 then
278 if zero_bit p1 m2 then diff s1 l2 else diff s1 r2
283 (*s All the following operations ([cardinal], [iter], [fold], [for_all],
284 [exists], [filter], [partition], [choose], [elements]) are
285 implemented as for any other kind of binary trees. *)
287 let rec cardinal n = match Node.node n with
290 | Branch (_,_,t0,t1) -> cardinal t0 + cardinal t1
292 let rec iter f n = match Node.node n with
295 | Branch (_,_,t0,t1) -> iter f t0; iter f t1
297 let rec fold f s accu = match Node.node s with
300 | Branch (_,_,t0,t1) -> fold f t0 (fold f t1 accu)
303 let rec for_all p n = match Node.node n with
306 | Branch (_,_,t0,t1) -> for_all p t0 && for_all p t1
308 let rec exists p n = match Node.node n with
311 | Branch (_,_,t0,t1) -> exists p t0 || exists p t1
313 let rec filter pr n = match Node.node n with
315 | Leaf k -> if pr k then n else empty
316 | Branch (p,m,t0,t1) -> branch_ne p m (filter pr t0) (filter pr t1)
319 let rec part (t,f as acc) n = match Node.node n with
321 | Leaf k -> if p k then (add k t, f) else (t, add k f)
322 | Branch (_,_,t0,t1) -> part (part acc t0) t1
324 part (empty, empty) s
326 let rec choose n = match Node.node n with
327 | Empty -> raise Not_found
329 | Branch (_, _,t0,_) -> choose t0 (* we know that [t0] is non-empty *)
333 let coll k (l, b, r) =
334 if k < x then add k l, b, r
335 else if k > x then l, b, add k r
338 fold coll s (empty, false, empty)
340 (*s Additional functions w.r.t to [Set.S]. *)
342 let rec intersect s1 s2 = (equal s1 s2) ||
343 match (Node.node s1,Node.node s2) with
346 | Leaf k1, _ -> mem k1 s2
347 | _, Leaf k2 -> mem k2 s1
348 | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
349 if m1 == m2 && p1 == p2 then
350 intersect l1 l2 || intersect r1 r2
351 else if m1 < m2 && match_prefix p2 p1 m1 then
352 intersect (if zero_bit p2 m1 then l1 else r1) s2
353 else if m1 > m2 && match_prefix p1 p2 m2 then
354 intersect s1 (if zero_bit p1 m2 then l2 else r2)
359 let from_list l = List.fold_left (fun acc e -> add e acc) empty l
364 module Make = Builder(Hcons.Make)
365 module Weak = Builder(Hcons.Weak)
370 include Make(Hcons.PosInt)
372 Format.pp_print_string ppf "{ ";
373 iter (fun i -> Format.fprintf ppf "%i " i) s;
374 Format.pp_print_string ppf "}";
375 Format.pp_print_flush ppf ()