-(* Original file: *)
-(***********************************************************************)
-(* *)
-(* Copyright (C) Jean-Christophe Filliatre *)
-(* *)
-(* This software is free software; you can redistribute it and/or *)
-(* modify it under the terms of the GNU Library General Public *)
-(* License version 2.1, with the special exception on linking *)
-(* described in file http://www.lri.fr/~filliatr/ftp/ocaml/ds/LICENSE *)
-(* *)
-(* This software is distributed in the hope that it will be useful, *)
-(* but WITHOUT ANY WARRANTY; without even the implied warranty of *)
-(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *)
-(* *)
-(***********************************************************************)
-
-(*
- Time-stamp: <Last modified on 2013-01-30 19:07:53 CET by Kim Nguyen>
-*)
-
-(* Modified by Kim Nguyen *)
-(* 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
-
-module type HConsBuilder =
- functor (H : Sigs.AUX.HashedType) -> Hcons.S with type data = H.t
-
-module Builder (HCB : HConsBuilder) (H : Hcons.Abstract) :
- S with type elt = H.t =
-struct
- type elt = H.t
-
- type 'a set =
- | Empty
- | Leaf of elt
- | 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 =
- struct
- type t = Node.t set
- let equal x y =
- match x,y with
- | 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)
-
- | _ -> false
-
- let hash = function
- | 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
-
- include Node
-
- let empty = Node.make Empty
-
- let is_empty s = (Node.node s) == Empty
-
- let branch p m l r = Node.make (Branch(p,m,l,r))
-
- let leaf k = Node.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 Node.node n with Leaf _ -> true
- | _ -> 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
- 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
-
- let rec max_elt n = match Node.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 Node.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
- (*
- 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)
- with
- _ -> raise (Invalid_argument ("highest_bit " ^ (string_of_int x)))
-
- let highest_bit64 x =
- let n = x lsr 32 in if n != 0 then highest_bit n lsl 32
- else highest_bit x
-
- let branching_bit p0 p1 = highest_bit64 (p0 lxor p1)
-
- 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
-
- 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);
- 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) ->
- 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)
- 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) ->
- 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 = Node.equal a b
-
- let compare a b = (Uid.to_int (Node.uid a)) - (Uid.to_int (Node.uid b))
-
- let rec merge s t =
- if equal s t (* This is cheap thanks to hash-consing *)
- 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) ->
- 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_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)
- else
- (* 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) ->
- 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 *)
-
- 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) ->
- 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 (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)
- 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 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
- | 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
- | 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
- | 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
- | 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
- | 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
- | 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 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
- 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 from_list l = List.fold_left (fun acc e -> add e acc) empty l
-
-
-end
-
-module Make = Builder(Hcons.Make)
-module Weak = Builder(Hcons.Weak)
-
-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
projects / tatoo.git / commitdiff