ocaml-containers/misc/fHashtbl.ml

(*
Copyright (c) 2013, Simon Cruanes
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(** {1 Functional (persistent) hashtable} *)

(** {2 Signatures} *)

module type HASH = sig
  type t
  val equal : t -> t -> bool
  val hash : t -> int
end

(** The signature for such a functional hashtable *)
module type S = sig
  type 'a t
  type key

  val empty : int -> 'a t
    (** The empty hashtable (with sub-hashtables of given size) *)

  val is_empty : _ t -> bool

  val find : 'a t -> key -> 'a
    (** Find the binding for this key, or raise Not_found *)

  val mem : 'a t -> key -> bool
    (** Check whether the key is bound in this hashtable *)

  val replace : 'a t -> key -> 'a -> 'a t
    (** [replace t key val] returns a copy of [t] where [key] binds to [val] *)

  val remove : 'a t -> key -> 'a t
    (** Remove the bindings for the given key *)

  val fold : ('b -> key -> 'a -> 'b) -> 'b -> 'a t -> 'b
    (** Fold on bindings *)

  val iter : (key -> 'a -> unit) -> 'a t -> unit
    (** Iterate on bindings *)

  val size : 'a t -> int
    (** Number of bindings *)

  val to_seq : 'a t -> (key * 'a) CCSequence.t

  val of_seq : ?size:int -> (key * 'a) CCSequence.t -> 'a t
end

(** {2 Persistent array} *)

module PArray = struct
  type 'a t = 'a zipper ref
  and 'a zipper =
    | Array of 'a array
    | Diff of int * 'a * 'a zipper ref

  (* XXX maybe having a snapshot of the array from point to point may help? *)

  let make size elt =
    let a = Array.create size elt in
    ref (Array a)

  (** Recover the given version of the shared array. Returns the array
      itself. *)
  let rec reroot t =
    match !t with
    | Array a -> a
    | Diff (i, v, t') ->
      begin
        let a = reroot t' in
        let v' = a.(i) in
        t' := Diff (i, v', t);
        a.(i) <- v;
        t := Array a;
        a
      end

  let get t i =
    match !t with
    | Array a -> a.(i)
    | Diff _ -> 
      let a = reroot t in
      a.(i)

  let set t i v =
    let a =
      match !t with
      | Array a -> a
      | Diff _ -> reroot t in
    let v' = a.(i) in
    if v == v'
      then t (* no change *)
      else begin
        let t' = ref (Array a) in
        a.(i) <- v;
        t := Diff (i, v', t');
        t' (* create new array *)
      end

  let fold_left f acc t =
    let a = reroot t in
    Array.fold_left f acc a

  let rec length t =
    match !t with
    | Array a -> Array.length a
    | Diff (_, _, t') -> length t'
end

(** {2 Tree-like hashtable} *)

module Tree(X : HASH) = struct
  (** The hashtable is a binary tree, with persistent arrays as leaves.
      Nodes at depth n of the tree are split on the n-th digit of the hash
      (starting with the least significant bit as 0).
      
      The left child is for bit=0, the right one for bit=1. *)

  type key = X.t

  type 'a t =
    | Split of 'a t * 'a t    (** Split on the last digit of the hash *)
    | Table of 'a buckets     (** Hashtable as a persistent array *)
    (** The hashtable, as a tree of persistent open addressing hashtables *)
  and 'a buckets = 'a bucket PArray.t
    (** A persistent array of buckets *)
  and 'a bucket =
    | Empty
    | Deleted
    | Used of key * 'a
    (** One buckets stores one key->value binding *)

  let empty_buckets size =
    PArray.make size Empty

  (** Empty hashtable *)
  let empty size =
    let size = max size 4 in  (* size >= 4 *)
    Table (empty_buckets size)

  let rec is_empty_array a i =
    if i = Array.length a then true
    else (a.(i) = Empty || a.(i) = Deleted) && is_empty_array a (i+1)

  let rec is_empty t =
    match t with
    | Split (l, r) -> is_empty l && is_empty r
    | Table a -> is_empty_array (PArray.reroot a) 0

  (** The address in a bucket array, after probing [i] times *)
  let addr n h i = ((h land max_int) + i) mod n

  (** Find the bucket that contains the given [key]. [h] is
      not necessarily the hash of the key, because it can have been
      shifted to right several times. *)
  let rec probe_find buckets n h key i =
    if i = n then raise Not_found else begin
      let j = addr n h i in
      match PArray.get buckets j with
      | Empty -> raise Not_found
      | Used (key', value) when X.equal key key' ->
        value (* found *)
      | Used _ | Deleted ->
        probe_find buckets n h key (i+1)  (* go further *)
    end
    
  (** Find the value bound to the given [key] *)
  let find t key =
    let h = X.hash key in
    (* find the appropriate leaf *)
    let rec find h t =
      match t with
      | Split (l, r) ->
        if h land 0x1 = 0
          then find (h lsr 1) l   (* bit=0, goto left *)
          else find (h lsr 1) r   (* bit=1, goto right *)
      | Table buckets ->
        probe_find buckets (PArray.length buckets) h key 0
    in
    find h t

  (** Check whether the key is bound in this hashtable *)
  let mem t key =
    try ignore (find t key); true
    with Not_found -> false

  (** Maximal depth of the tree (number of bits of the hash) *)
  let max_depth = Sys.word_size - 1

  (** [i] is the length of the current probe. [n] is the size of
      the buckets array. This decides whether the probe, looking
      for a free bucket to insert a binding in, is too long. *)
  let probe_too_long n i =
    i / 5 > n / 8  (* i/n > 5/8 *)

  (** Insert [key] -> [value] in the buckets. *)
  let rec probe_insert buckets ~depth h key value =
    let n = PArray.length buckets in
    let rec probe i =
      if n = i then (assert (depth = max_depth); failwith "FHashtbl is full")
      else if (depth < max_depth && probe_too_long n i)
        (* We are not too deep, and the table starts being full, we
           split it into two sub-tables *)
        then
          let depth' = depth + 1 in
          (* increase size of sub-arrays by 1.5 *)
          let sub_size = min (n + (n lsr 1)) Sys.max_array_length in
          let l, r = PArray.fold_left
            (fun (l,r) bucket -> match bucket with
              | Empty | Deleted -> (l,r)
              | Used (key',value') ->
                let h' = (X.hash key') lsr depth in
                if h' land 0x1 = 0
                  then 
                    let l' = insert l ~depth:depth' (h' lsr 1) key' value' in
                    l', r
                  else
                    let r' = insert r ~depth:depth' (h' lsr 1) key' value' in
                    l, r')
            (empty sub_size, empty sub_size) buckets in
          (* the split of those two sub-hashtables *)
          let new_table = Split (l, r) in
          (* insert in this new hashtable *)
          insert new_table ~depth h key value
        else (* look for an empty slot to insert the bucket *)
          let j = addr n h i in
          match PArray.get buckets j with
          | Empty | Deleted ->
            (* insert here *)
            let buckets' = PArray.set buckets j (Used (key, value)) in
            Table buckets'
          | Used (key', _) when X.equal key key' ->
            (* replace *)
            let buckets' = PArray.set buckets j (Used (key, value)) in
            Table buckets'
          | Used _ -> probe (i+1)  (* probe failed, go further *)
    in
    probe 0
  (** Insert [key] -> [value] in the sub-hashtable *)
  and insert t ~depth h key value =
    match t with
    | Split (l, r) ->
      if h land 0x1 = 0
        then  (* bit=0, goto left *)
          let l' = insert l ~depth:(depth+1) (h lsr 1) key value in
          Split (l', r)
        else  (* bit=1, goto right *)
          let r' = insert r ~depth:(depth+1) (h lsr 1) key value in
          Split (l, r')
    | Table buckets ->
      (* insert in the flat hashtable *)
      probe_insert buckets ~depth h key value

  (** [replace t key val] returns a copy of [t] where [key] binds to [val] *)
  let replace t key value =
    let h = X.hash key in
    insert t ~depth:0 h key value

  (** Recursive removal function *)
  let rec rec_remove t h key =
    match t with
    | Split (l, r) ->
      if h land 0x1 = 0
        then  (* bit=0, goto left *)
          let l' = rec_remove l (h lsr 1) key in
          if l == l' then t else Split (l', r)
        else  (* bit=1, goto right *)
          let r' = rec_remove r (h lsr 1) key in
          if r == r' then t else Split (l, r')
    | Table buckets ->
      (* remove from the flat hashtable *)
      probe_remove t buckets h key
  (* remove key from the buckets *)
  and probe_remove old_table buckets h key =
    let n = PArray.length buckets in
    let rec probe i =
      if i = n
        then old_table (* not present *)
        else
          let j = addr n h i in
          match PArray.get buckets j with
          | Empty -> old_table (* not present *)
          | Deleted -> probe (i+1)
          | Used (key', _) ->
            if X.equal key key'
              then Table (PArray.set buckets j Deleted)
              else probe (i+1)
    in
    probe 0
    

  (** Remove the bindings for the given key *)
  let remove t key =
    let h = X.hash key in
    rec_remove t h key

  (** Fold on bindings *)
  let rec fold f acc t =
    match t with
    | Split (l, r) ->
      let acc' = fold f acc l in
      fold f acc' r
    | Table buckets ->
      PArray.fold_left
        (fun acc bucket -> match bucket with
          | Empty | Deleted -> acc
          | Used (key, value) -> f acc key value)
        acc buckets

  let iter f t =
    fold (fun () k v -> f k v) () t

  let size t =
    fold (fun n _ _ -> n + 1) 0 t

  let to_seq t =
    CCSequence.from_iter (fun k -> iter (fun key value -> k (key, value)) t)

  let of_seq ?(size=32) seq =
    CCSequence.fold
      (fun t (k,v) -> replace t k v)
      (empty size) seq
end

(** {2 Flat hashtable} *)

module Flat(X : HASH) = struct
  type key = X.t

  (** A hashtable is a persistent array of (key, value) buckets *)
  type 'a t = {
    buckets : 'a bucket PArray.t;
    size : int;
  }
  and 'a bucket =
  | Deleted
  | Empty
  | Used of key * 'a

  let max_load = 0.8

  (** Empty table. Size will be >= 2 *)
  let empty size =
    let size = max 2 size in
    { buckets = PArray.make size Empty;
      size = 0;
    }

  let rec is_empty_array a i =
    if i = Array.length a then true
    else (a.(i) = Empty || a.(i) = Deleted) && is_empty_array a (i+1)

  let is_empty t = is_empty_array (PArray.reroot t.buckets) 0

  (** Index of slot, for i-th probing starting from hash [h] in
      a table of length [n] *)
  let addr h n i = ((h land max_int) + i) mod n
    
  (** Insert (key -> value) in buckets, starting with the hash. *)
  let insert buckets h key value =
    let n = PArray.length buckets in
    (* lookup an empty slot to insert the key->value in. *)
    let rec lookup h n i =
      let j = addr h n i in
      match PArray.get buckets j with
      | Empty ->
        PArray.set buckets j (Used (key, value))
      | Used (key', _) when X.equal key key' ->
        PArray.set buckets j (Used (key, value))
      | _ -> lookup h n (i+1)
    in
    lookup h n 0

  (** Resize the array, by inserting its content into twice as large an array *)
  let resize buckets =
    let new_size = min (PArray.length buckets * 2) Sys.max_array_length in
    let buckets' = PArray.make new_size Empty in
    (* loop to transfer values from buckets to buckets' *)
    let rec tranfer buckets' i =
      if i = PArray.length buckets then buckets'
        else match PArray.get buckets i with
        | Used (key, value) ->
          (* insert key -> value into new array *)
          let buckets' = insert buckets' (X.hash key) key value in
          tranfer buckets' (i+1)
        | _ ->
          tranfer buckets' (i+1)
    in tranfer buckets' 0

  (** Lookup [key] in the table *)
  let find t key =
    let buckets = t.buckets in
    let n = PArray.length buckets in
    let h = X.hash key in
    let rec probe h n i num =
      if num = n then raise Not_found
      else let j = addr h n i in
      match PArray.get buckets j with
      | Used (key', value) when X.equal key key' ->
        value  (* found value for this key *)
      | Deleted | Used _ ->
        probe h n (i+1) (num + 1) (* try next bucket *)
      | Empty -> raise Not_found
    in
    probe h n 0 0

  (** put [key] -> [value] in the hashtable *)
  let replace t key value =
    let load = float_of_int t.size /. float_of_int (PArray.length t.buckets) in
    let t =
      if load > max_load then { t with buckets = resize t.buckets } else t in
    let n = PArray.length t.buckets in
    let h = X.hash key in
    let buckets = t.buckets in
    let rec probe h n i =
      let j = addr h n i in
      match PArray.get buckets j with
      | Used (key', _) when X.equal key key' ->
        let buckets' = PArray.set buckets j (Used (key, value)) in
        { t with buckets = buckets' } (* replace binding *)
      | Deleted | Empty ->
        let buckets' = PArray.set buckets j (Used (key, value)) in
        { buckets = buckets'; size = t.size + 1; } (* add binding *)
      | Used _ ->
        probe h n (i+1) (* go further *)
    in
    probe h n 0

  (** Remove the key from the table *)
  let remove t key =
    let n = PArray.length t.buckets in
    let h = X.hash key in
    let buckets = t.buckets in
    let rec probe h n i =
      let j = addr h n i in
      match PArray.get buckets j with
      | Used (key', _) when X.equal key key' ->
        (* remove slot *)
        let buckets' = PArray.set buckets j Deleted in
        { buckets = buckets'; size = t.size - 1; }
      | Deleted | Used _ ->
        probe h n (i+1) (* search further *)
      | Empty -> t  (* not present *)
    in
    probe h n 0

  (** size of the table *)
  let size t = t.size

  (** Is the key member of the table? *)
  let mem t key =
    try ignore (find t key); true
    with Not_found -> false

  (** Iterate on key -> value pairs *)
  let iter k t =
    let buckets = t.buckets in
    for i = 0 to PArray.length buckets - 1 do
      match PArray.get buckets i with
      | Used (key, value) -> k key value
      | _ -> ()
    done

  (** Fold on key -> value pairs *)
  let fold f acc t =
    PArray.fold_left
      (fun acc bucket -> match bucket with
        | Used (key, value) -> f acc key value
        | _ -> acc)
      acc t.buckets

  let to_seq t =
    CCSequence.from_iter
      (fun k -> iter (fun key value -> k (key, value)) t)

  let of_seq ?(size=32) seq =
    CCSequence.fold (fun t (k,v) -> replace t k v) (empty size) seq
end