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Merge pull request #117 from rleonid/add_negate

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change `CCBV` to track size, with some breaking changes (thank to @rleonid)
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Simon Cruanes 2017-04-19 22:25:07 +02:00 • committed by GitHub
commit 02f1d5c4a0
3 changed files with 303 additions and 130 deletions
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1
AUTHORS.adoc
View file

@ -20,3 +20,4 @@
- David Sheets (@dsheets) - David Sheets (@dsheets)
- Glenn Slotte (glennsl) - Glenn Slotte (glennsl)
- @LemonBoy - @LemonBoy
- Leonid Rozenberg (@rleonid)

348
src/data/CCBV.ml
View file

@ -1,79 +1,122 @@
(* This file is free software, part of containers. See file "license" for more details. *)
(** {2 Imperative Bitvectors} *) (** {2 Imperative Bitvectors} *)
let __width = Sys.word_size - 2 let width_ = Sys.word_size - 1
(* int with [n] ones *) (** We use OCamls ints to store the bits. We index them from the
let rec __shift bv n = least significant bit. We create masks to zero out the most significant
if n = 0 bits that aren't used to store values. This is necessary when we are
then bv constructing or negating a bit vector. *)
else __shift ((bv lsl 1) lor 1) (n-1) let lsb_masks_ =
let a = Array.make (width_ + 1) 0 in
for i = 1 to width_ do
a.(i) <- a.(i-1) lor (1 lsl (i - 1))
done;
a
(* only ones *) let all_ones_ = lsb_masks_.(width_)
let __all_ones = __shift 0 __width
(* count the 1 bits in [n]. See https://en.wikipedia.org/wiki/Hamming_weight *)
let count_bits_ n =
let rec recurse count n =
if n = 0 then count else recurse (count+1) (n land (n-1))
in
recurse 0 n
(* Can I access the "private" members in testing? $Q
(Q.int_bound (Sys.word_size - 1)) (fun i -> count_bits_ lsb_masks_.(i) = i)
*)
type t = { type t = {
mutable a : int array; mutable a : int array;
mutable size : int;
} }
let empty () = { a = [| |] } let length t = t.size
let empty () = { a = [| |] ; size = 0 }
let array_length_of_size size =
if size mod width_ = 0 then size / width_ else (size / width_) + 1
let create ~size default = let create ~size default =
if size = 0 then { a = [| |] } if size = 0 then { a = [| |]; size }
else begin else (
let n = if size mod __width = 0 then size / __width else (size / __width) + 1 in let n = array_length_of_size size in
let arr = if default let a = if default
then Array.make n __all_ones then Array.make n all_ones_
else Array.make n 0 else Array.make n 0
in in
(* adjust last bits *) (* adjust last bits *)
if default && (size mod __width) <> 0 let r = size mod width_ in
then arr.(n-1) <- __shift 0 (size - (n-1) * __width); if default && r <> 0 then (
{ a = arr } Array.unsafe_set a (n-1) lsb_masks_.(r);
end );
{ a; size }
)
(*$Q
(Q.pair Q.small_int Q.bool) (fun (size, b) -> create ~size b |> length = size)
*)
(*$T (*$T
create ~size:17 true |> cardinal = 17 create ~size:17 true |> cardinal = 17
create ~size:32 true |> cardinal= 32 create ~size:32 true |> cardinal = 32
create ~size:132 true |> cardinal = 132 create ~size:132 true |> cardinal = 132
create ~size:200 false |> cardinal = 0 create ~size:200 false |> cardinal = 0
create ~size:29 true |> to_sorted_list = CCList.range 0 28 create ~size:29 true |> to_sorted_list = CCList.range 0 28
*) *)
let copy bv = { a=Array.copy bv.a; } let copy bv = { bv with a = Array.copy bv.a }
(*$Q (*$Q
(Q.list Q.small_int) (fun l -> \ (Q.list Q.small_int) (fun l -> \
let bv = of_list l in to_list bv = to_list (copy bv)) let bv = of_list l in to_list bv = to_list (copy bv))
*) *)
let length bv = Array.length bv.a let capacity bv = width_ * Array.length bv.a
let resize bv len =
if len > Array.length bv.a
then begin
let a' = Array.make len 0 in
Array.blit bv.a 0 a' 0 (Array.length bv.a);
bv.a <- a'
end
(* count the 1 bits in [n]. See https://en.wikipedia.org/wiki/Hamming_weight *)
let __count_bits n =
let rec recurse count n =
if n = 0 then count else recurse (count+1) (n land (n-1))
in
if n < 0
then recurse 1 (n lsr 1) (* only on unsigned *)
else recurse 0 n
let cardinal bv = let cardinal bv =
if bv.size = 0 then 0
else (
let n = ref 0 in let n = ref 0 in
for i = 0 to length bv - 1 do for i = 0 to Array.length bv.a - 1 do
n := !n + __count_bits bv.a.(i) n := !n + count_bits_ bv.a.(i) (* MSB of last element are all 0 *)
done; done;
!n !n
)
(*$Q
Q.small_int (fun size -> create ~size true |> cardinal = size)
*)
let really_resize_ bv ~desired ~current size =
let a' = Array.make desired 0 in
Array.blit bv.a 0 a' 0 current;
bv.a <- a';
bv.size <- size
let grow_ bv size =
if size <= capacity bv (* within capacity *)
then bv.size <- size
else ( (* beyond capacity *)
let desired = array_length_of_size size in
let current = Array.length bv.a in
really_resize_ bv ~desired ~current size
)
let shrink_ bv size =
let desired = array_length_of_size size in
let current = Array.length bv.a in
really_resize_ bv ~desired ~current size
let resize bv size =
if size < 0 then invalid_arg "resize: negative size" else
if size < bv.size (* shrink *)
then shrink_ bv size
else if size = bv.size
then ()
else grow_ bv size
(*$R (*$R
let bv1 = CCBV.create ~size:87 true in let bv1 = CCBV.create ~size:87 true in
@ -87,18 +130,18 @@ let cardinal bv =
let is_empty bv = let is_empty bv =
try try
for i = 0 to Array.length bv.a - 1 do for i = 0 to Array.length bv.a - 1 do
if bv.a.(i) <> 0 then raise Exit if bv.a.(i) <> 0 then raise Exit (* MSB of last element are all 0 *)
done; done;
true true
with Exit -> with Exit ->
false false
let get bv i = let get bv i =
let n = i / __width in if i < 0 then invalid_arg "get: negative index";
let n = i / width_ in
let i = i mod width_ in
if n < Array.length bv.a if n < Array.length bv.a
then then (Array.unsafe_get bv.a n) land (1 lsl i) <> 0
let i = i - n * __width in
bv.a.(n) land (1 lsl i) <> 0
else false else false
(*$R (*$R
@ -118,11 +161,13 @@ let get bv i =
*) *)
let set bv i = let set bv i =
let n = i / __width in if i < 0 then invalid_arg "set: negative index"
if n >= Array.length bv.a else (
then resize bv (n+1); let n = i / width_ in
let i = i - n * __width in let j = i mod width_ in
bv.a.(n) <- bv.a.(n) lor (1 lsl i) if i >= bv.size then grow_ bv (i+1);
Array.unsafe_set bv.a n ((Array.unsafe_get bv.a n) lor (1 lsl j))
)
(*$T (*$T
let bv = create ~size:3 false in set bv 0; get bv 0 let bv = create ~size:3 false in set bv 0; get bv 0
@ -130,40 +175,44 @@ let set bv i =
*) *)
let reset bv i = let reset bv i =
let n = i / __width in if i < 0 then invalid_arg "reset: negative index"
if n >= Array.length bv.a else (
then resize bv (n+1); let n = i / width_ in
let i = i - n * __width in let j = i mod width_ in
bv.a.(n) <- bv.a.(n) land (lnot (1 lsl i)) if i >= bv.size then grow_ bv (i+1);
Array.unsafe_set bv.a n ((Array.unsafe_get bv.a n) land (lnot (1 lsl j)))
)
(*$T (*$T
let bv = create ~size:3 false in set bv 0; reset bv 0; not (get bv 0) let bv = create ~size:3 false in set bv 0; reset bv 0; not (get bv 0)
*) *)
let flip bv i = let flip bv i =
let n = i / __width in if i < 0 then invalid_arg "reset: negative index"
if n >= Array.length bv.a else (
then resize bv (n+1); let n = i / width_ in
let i = i - n * __width in let j = i mod width_ in
bv.a.(n) <- bv.a.(n) lxor (1 lsl i) if i >= bv.size then grow_ bv (i+1);
Array.unsafe_set bv.a n ((Array.unsafe_get bv.a n) lxor (1 lsl j))
)
(*$R (*$R
let bv = of_list [1;10; 11; 30] in let bv = of_list [1;10; 11; 30] in
flip bv 10; flip bv 10;
assert_equal [1;11;30] (to_sorted_list bv); assert_equal ~printer:Q.Print.(list int) [1;11;30] (to_sorted_list bv);
assert_equal false (get bv 10); assert_equal ~printer:Q.Print.bool false (get bv 10);
flip bv 10; flip bv 10;
assert_equal true (get bv 10); assert_equal ~printer:Q.Print.bool true (get bv 10);
flip bv 5; flip bv 5;
assert_equal [1;5;10;11;30] (to_sorted_list bv); assert_equal ~printer:Q.Print.(list int) [1;5;10;11;30] (to_sorted_list bv);
assert_equal true (get bv 5); assert_equal ~printer:Q.Print.bool true (get bv 5);
flip bv 100; flip bv 100;
assert_equal [1;5;10;11;30;100] (to_sorted_list bv); assert_equal ~printer:Q.Print.(list int) [1;5;10;11;30;100] (to_sorted_list bv);
assert_equal true (get bv 100); assert_equal ~printer:Q.Print.bool true (get bv 100);
*) *)
let clear bv = let clear bv =
Array.iteri (fun i _ -> bv.a.(i) <- 0) bv.a Array.fill bv.a 0 (Array.length bv.a) 0
(*$T (*$T
let bv = create ~size:37 true in cardinal bv = 37 && (clear bv; cardinal bv= 0) let bv = create ~size:37 true in cardinal bv = 37 && (clear bv; cardinal bv= 0)
@ -179,11 +228,17 @@ let clear bv =
let iter bv f = let iter bv f =
let len = Array.length bv.a in let len = Array.length bv.a in
for n = 0 to len - 1 do for n = 0 to len - 2 do
let j = __width * n in let j = width_ * n in
for i = 0 to __width - 1 do for i = 0 to width_ - 1 do
f (j+i) (bv.a.(n) land (1 lsl i) <> 0) f (j+i) (bv.a.(n) land (1 lsl i) <> 0)
done done
done;
let j = width_ * (len - 1) in
let r = bv.size mod width_ in
let final_length = if r = 0 then width_ else r in
for i = 0 to final_length - 1 do
f (j + i) (bv.a.(len - 1) land (1 lsl i) <> 0)
done done
(*$R (*$R
@ -195,14 +250,7 @@ let iter bv f =
*) *)
let iter_true bv f = let iter_true bv f =
let len = Array.length bv.a in iter bv (fun i b -> if b then f i else ())
for n = 0 to len - 1 do
let j = __width * n in
for i = 0 to __width - 1 do
if bv.a.(n) land (1 lsl i) <> 0
then f (j+i)
done
done
(*$T (*$T
of_list [1;5;7] |> iter_true |> Sequence.to_list |> List.sort CCOrd.compare = [1;5;7] of_list [1;5;7] |> iter_true |> Sequence.to_list |> List.sort CCOrd.compare = [1;5;7]
@ -242,8 +290,9 @@ let to_list bv =
let to_sorted_list bv = let to_sorted_list bv =
List.rev (to_list bv) List.rev (to_list bv)
(* Interpret these as indices. *)
let of_list l = let of_list l =
let size = List.fold_left max 0 l in let size = (List.fold_left max 0 l) + 1 in
let bv = create ~size false in let bv = create ~size false in
List.iter (fun i -> set bv i) l; List.iter (fun i -> set bv i) l;
bv bv
@ -256,15 +305,19 @@ let of_list l =
exception FoundFirst of int exception FoundFirst of int
let first bv = let first_exn bv =
try try
iter_true bv (fun i -> raise (FoundFirst i)); iter_true bv (fun i -> raise (FoundFirst i));
raise Not_found raise Not_found
with FoundFirst i -> with FoundFirst i ->
i i
let first bv =
try Some (first_exn bv)
with Not_found -> None
(*$T (*$T
of_list [50; 10; 17; 22; 3; 12] |> first = 3 of_list [50; 10; 17; 22; 3; 12] |> first = Some 3
*) *)
let filter bv p = let filter bv p =
@ -276,18 +329,61 @@ let filter bv p =
to_sorted_list bv = [2;4;6] to_sorted_list bv = [2;4;6]
*) *)
let negate_self b =
let len = Array.length b.a in
for n = 0 to len - 1 do
Array.unsafe_set b.a n (lnot (Array.unsafe_get b.a n))
done;
let r = b.size mod width_ in
if r <> 0 then
let l = Array.length b.a - 1 in
Array.unsafe_set b.a l (lsb_masks_.(r) land (Array.unsafe_get b.a l))
(*$T
let v = of_list [1;2;5;7;] in negate_self v; \
cardinal v = (List.length [0;3;4;6])
*)
let negate b =
let a = Array.map (lnot) b.a in
let r = b.size mod width_ in
if r <> 0 then begin
let l = Array.length b.a - 1 in
Array.unsafe_set a l (lsb_masks_.(r) land (Array.unsafe_get a l))
end;
{ a ; size = b.size }
(*$Q
Q.small_int (fun size -> create ~size false |> negate |> cardinal = size)
*)
(* Underlying size grows for union. *)
let union_into ~into bv = let union_into ~into bv =
if length into < length bv if into.size < bv.size
then resize into (length bv); then grow_ into bv.size;
let len = Array.length bv.a in for i = 0 to (Array.length into.a) - 1 do
for i = 0 to len - 1 do Array.unsafe_set into.a i
into.a.(i) <- into.a.(i) lor bv.a.(i) ((Array.unsafe_get into.a i) lor (Array.unsafe_get bv.a i))
done done
let union bv1 bv2 = (* To avoid potentially 2 passes, figure out what we need to copy. *)
let bv = copy bv1 in let union b1 b2 =
union_into ~into:bv bv2; if b1.size <= b2.size
bv then (
let into = copy b2 in
for i = 0 to (Array.length b1.a) - 1 do
Array.unsafe_set into.a i
((Array.unsafe_get into.a i) lor (Array.unsafe_get b1.a i))
done;
into
) else (
let into = copy b1 in
for i = 0 to (Array.length b1.a) - 1 do
Array.unsafe_set into.a i
((Array.unsafe_get into.a i) lor (Array.unsafe_get b2.a i))
done;
into
)
(*$R (*$R
let bv1 = CCBV.of_list [1;2;3;4] in let bv1 = CCBV.of_list [1;2;3;4] in
@ -302,22 +398,32 @@ let union bv1 bv2 =
union (of_list [1;2;3;4;5]) (of_list [7;3;5;6]) |> to_sorted_list = CCList.range 1 7 union (of_list [1;2;3;4;5]) (of_list [7;3;5;6]) |> to_sorted_list = CCList.range 1 7
*) *)
(* Underlying size shrinks for inter. *)
let inter_into ~into bv = let inter_into ~into bv =
let n = min (length into) (length bv) in if into.size > bv.size
for i = 0 to n - 1 do then shrink_ into bv.size;
into.a.(i) <- into.a.(i) land bv.a.(i) for i = 0 to (Array.length into.a) - 1 do
Array.unsafe_set into.a i
((Array.unsafe_get into.a i) land (Array.unsafe_get bv.a i))
done done
let inter bv1 bv2 = let inter b1 b2 =
if length bv1 < length bv2 if b1.size <= b2.size
then then (
let bv = copy bv1 in let into = copy b1 in
let () = inter_into ~into:bv bv2 in for i = 0 to (Array.length b1.a) - 1 do
bv Array.unsafe_set into.a i
else ((Array.unsafe_get into.a i) land (Array.unsafe_get b2.a i))
let bv = copy bv2 in done;
let () = inter_into ~into:bv bv1 in into
bv ) else (
let into = copy b2 in
for i = 0 to (Array.length b2.a) - 1 do
Array.unsafe_set into.a i
((Array.unsafe_get into.a i) land (Array.unsafe_get b1.a i))
done;
into
)
(*$T (*$T
inter (of_list [1;2;3;4]) (of_list [2;4;6;1]) |> to_sorted_list = [1;2;4] inter (of_list [1;2;3;4]) (of_list [2;4;6;1]) |> to_sorted_list = [1;2;4]
@ -331,6 +437,28 @@ let inter bv1 bv2 =
assert_equal [3;4] l; assert_equal [3;4] l;
*) *)
(* Underlying size depends on the 'in_' set for diff, so we don't change
it's size! *)
let diff_into ~into bv =
let n = min (Array.length into.a) (Array.length bv.a) in
for i = 0 to n - 1 do
Array.unsafe_set into.a i
((Array.unsafe_get into.a i) land (lnot (Array.unsafe_get bv.a i)))
done
let diff in_ not_in =
let into = copy in_ in
diff_into ~into not_in;
into
(*$T
diff (of_list [1;2;3]) (of_list [1;2;3]) |> to_list = [];
diff (of_list [1;2;3]) (of_list [1;2;3;4]) |> to_list = [];
diff (of_list [1;2;3;4]) (of_list [1;2;3]) |> to_list = [4];
diff (of_list [1;2;3]) (of_list [1;2;3;400]) |> to_list = [];
diff (of_list [1;2;3;400]) (of_list [1;2;3]) |> to_list = [400];
*)
let select bv arr = let select bv arr =
let l = ref [] in let l = ref [] in
begin try begin try
@ -369,10 +497,10 @@ let selecti bv arr =
assert_equal [("b",1); ("c",2); ("f",5)] l; assert_equal [("b",1); ("c",2); ("f",5)] l;
*) *)
(*$T (*$= & ~printer:Q.Print.(list (pair int int))
selecti (of_list [1;4;3]) [| 0;1;2;3;4;5;6;7;8 |] \ [1,1; 3,3; 4,4] (selecti (of_list [1;4;3]) [| 0;1;2;3;4;5;6;7;8 |] \
|> List.sort CCOrd.compare = [1, 1; 3,3; 4,4] |> List.sort CCOrd.compare)
*) *)
type 'a sequence = ('a -> unit) -> unit type 'a sequence = ('a -> unit) -> unit

78
src/data/CCBV.mli
View file

@ -3,9 +3,13 @@
(** {2 Imperative Bitvectors} (** {2 Imperative Bitvectors}
The size of the bitvector is rounded up to the multiple of 30 or 62. {b BREAKING CHANGES} since NEXT_RELEASE:
In other words some functions such as {!iter} might iterate on more size is now stored along with the bitvector. Some functions have
bits than what was originally asked for. a new signature.
The size of the bitvector used to be rounded up to the multiple of 30 or 62.
In other words some functions such as {!iter} would iterate on more
bits than what was originally asked for. This is not the case anymore.
*) *)
type t type t
@ -21,29 +25,39 @@ val copy : t -> t
(** Copy of bitvector *) (** Copy of bitvector *)
val cardinal : t -> int val cardinal : t -> int
(** Number of bits set *) (** Number of bits set to one, seen as a set of bits. *)
val length : t -> int val length : t -> int
(** Length of underlying array *) (** Size of underlying bitvector.
This is not related to the underlying implementation.
Changed at NEXT_RELEASE
*)
val capacity : t -> int
(** The number of bits this bitvector can store without resizing.
@since NEXT_RELEASE *)
val resize : t -> int -> unit val resize : t -> int -> unit
(** Resize the BV so that it has at least the given physical length (** Resize the BV so that it has the specified length. This can grow or shrink
[resize bv n] should make [bv] able to store [(Sys.word_size - 2)* n] bits *) the underlying bitvector.
@raise Invalid_arg on negative sizes. *)
val is_empty : t -> bool val is_empty : t -> bool
(** Any bit set? *) (** Are there any true bits? *)
val set : t -> int -> unit val set : t -> int -> unit
(** Set i-th bit. *) (** Set i-th bit, extending the bitvector if needed. *)
val get : t -> int -> bool val get : t -> int -> bool
(** Is the i-th bit true? Returns false if the index is too high*) (** Is the i-th bit true? Returns false if the index is too high*)
val reset : t -> int -> unit val reset : t -> int -> unit
(** Set i-th bit to 0 *) (** Set i-th bit to 0, extending the bitvector if needed. *)
val flip : t -> int -> unit val flip : t -> int -> unit
(** Flip i-th bit *) (** Flip i-th bit, extending the bitvector if needed. *)
val clear : t -> unit val clear : t -> unit
(** Set every bit to 0 *) (** Set every bit to 0 *)
@ -62,21 +76,41 @@ val to_sorted_list : t -> int list
increasing order *) increasing order *)
val of_list : int list -> t val of_list : int list -> t
(** From a list of true bits *) (** From a list of true bits.
val first : t -> int The bits are interpreted as indices into the returned bitvector, so the final
(** First set bit, or bitvector will have [length t] equal to 1 more than max of list indices. *)
@raise Not_found if all bits are 0 *)
val first : t -> int option
(** First set bit, or return None.
changed type at NEXT_RELEASE *)
val first_exn : t -> int
(** First set bit, or
@raise Not_found if all bits are 0
@since NEXT_RELEASE *)
val filter : t -> (int -> bool) -> unit val filter : t -> (int -> bool) -> unit
(** [filter bv p] only keeps the true bits of [bv] whose [index] (** [filter bv p] only keeps the true bits of [bv] whose [index]
satisfies [p index] *) satisfies [p index] *)
val negate_self : t -> unit
(** [negate_self t] flips all of the bits in [t].
@since NEXT_RELEASE *)
val negate : t -> t
(** [negate t] returns a copy of [t] with all of the bits flipped. *)
val union_into : into:t -> t -> unit val union_into : into:t -> t -> unit
(** [union ~into bv] sets [into] to the union of itself and [bv]. *) (** [union ~into bv] sets [into] to the union of itself and [bv].
Also updates the length of [into] to be at least [length bv]. *)
val inter_into : into:t -> t -> unit val inter_into : into:t -> t -> unit
(** [inter ~into bv] sets [into] to the intersection of itself and [bv] *) (** [inter ~into bv] sets [into] to the intersection of itself and [bv]
Also updates the length of [into] to be at most [length bv]. *)
val union : t -> t -> t val union : t -> t -> t
(** [union bv1 bv2] returns the union of the two sets *) (** [union bv1 bv2] returns the union of the two sets *)
@ -84,6 +118,16 @@ val union : t -> t -> t
val inter : t -> t -> t val inter : t -> t -> t
(** [inter bv1 bv2] returns the intersection of the two sets *) (** [inter bv1 bv2] returns the intersection of the two sets *)
val diff_into : into:t -> t -> unit
(** [diff ~into t] Modify [into] with only the bits set but not in [t].
@since NEXT_RELEASE *)
val diff : t -> t -> t
(** [diff t1 t2] Return those bits found [t1] but not in [t2].
@since NEXT_RELEASE *)
val select : t -> 'a array -> 'a list val select : t -> 'a array -> 'a list
(** [select arr bv] selects the elements of [arr] whose index (** [select arr bv] selects the elements of [arr] whose index
corresponds to a true bit in [bv]. If [bv] is too short, elements of [arr] corresponds to a true bit in [bv]. If [bv] is too short, elements of [arr]