Dynamic arrays.
The Array module provide arrays of fixed length. Dynarray provides arrays whose length can change over time, by adding or removing elements at the end of the array.
This is typically used to accumulate elements whose number is not known in advance or changes during computation, while also providing fast access to elements at arbitrary positions.
let dynarray_of_list li =
let arr = Dynarray.create () in
List.iter (fun v -> Dynarray.add_last arr v) li;
arr
The Buffer module provides similar features, but it is specialized for accumulating characters into a dynamically-resized string.
The Stack module provides a last-in first-out data structure that can be easily implemented on top of dynamic arrays.
Warning. In their current implementation, the memory layout of dynamic arrays differs from the one of Arrays. See the Memory Layout section for more information.
Unsynchronized accesses
Concurrent accesses to dynamic arrays must be synchronized (for instance with a Mutex.t). Unsynchronized accesses to a dynamic array are a programming error that may lead to an invalid dynamic array state, on which some operations would fail with an Invalid_argument exception.
Dynamic arrays
A dynamic array containing values of type 'a.
A dynamic array a provides constant-time get and set operations on indices between 0 and Dynarray.length a - 1 included. Its length may change over time by adding or removing elements to the end of the array.
We say that an index into a dynarray a is valid if it is in 0 .. length a - 1 and invalid otherwise.
val create : unit -> 'a tcreate () is a new, empty array.
val make : int -> 'a -> 'a tmake n x is a new array of length n, filled with x.
val init : int -> (int -> 'a) -> 'a tinit n f is a new array a of length n, such that get a i is f i. In other words, the elements of a are f 0, then f 1, then f 2... and f (n - 1) last, evaluated in that order.
This is similar to Array.init.
val get : 'a t -> int -> 'aget a i is the i-th element of a, starting with index 0.
val set : 'a t -> int -> 'a -> unitset a i x sets the i-th element of a to be x.
i must be a valid index. set does not add new elements to the array -- see add_last to add an element.
length a is the number of elements in the array.
val is_empty : 'a t -> boolis_empty a is true if a is empty, that is, if length a = 0.
val get_last : 'a t -> 'aget_last a is the element of a at index length a - 1.
val find_last : 'a t -> 'a optionfind_last a is None if a is empty and Some (get_last a) otherwise.
copy a is a shallow copy of a, a new array containing the same elements as a.
Adding elements
Note: all operations adding elements raise Invalid_argument if the length needs to grow beyond Sys.max_array_length.
val add_last : 'a t -> 'a -> unitadd_last a x adds the element x at the end of the array a.
val append_array : 'a t -> 'a array -> unitappend_array a b adds all elements of b at the end of a, in the order they appear in b.
For example:
let a = Dynarray.of_list [1;2] in
Dynarray.append_array a [|3; 4|];
assert (Dynarray.to_list a = [1; 2; 3; 4])
val append_list : 'a t -> 'a list -> unitval append : 'a t -> 'a t -> unitappend a b is like append_array a b, but b is itself a dynamic array instead of a fixed-size array.
Warning: append a a is a programming error because it iterates on a and adds elements to it at the same time -- see the Iteration section below. It fails with Invalid_argument. If you really want to append a copy of a to itself, you can use Dynarray.append_array a (Dynarray.to_array a) which copies a into a temporary array.
val append_seq : 'a t -> 'a Seq.t -> unitLike append_array but with a sequence.
Warning: append_seq a (to_seq_reentrant a) simultaneously traverses a and adds element to it; the ordering of those operations is unspecified, and may result in an infinite loop -- the new elements may in turn be produced by to_seq_reentrant a and get added again and again.
val append_iter : 'a t -> (('a -> unit) -> 'x -> unit) -> 'x -> unitappend_iter a iter x adds each element of x to the end of a. This is iter (add_last a) x.
For example, append_iter a List.iter [1;2;3] would add elements 1, 2, and then 3 at the end of a. append_iter a Queue.iter q adds elements from the queue q.
Removing elements
val pop_last_opt : 'a t -> 'a optionpop_last_opt a removes and returns the last element of a, or None if the array is empty.
val pop_last : 'a t -> 'apop_last a removes and returns the last element of a.
val remove_last : 'a t -> unitremove_last a removes the last element of a, if any. It does nothing if a is empty.
val truncate : 'a t -> int -> unittruncate a n truncates a to have at most n elements.
It removes elements whose index is greater or equal to n. It does nothing if n >= length a.
truncate a n is equivalent to:
if n < 0 then invalid_argument "...";
while length a > n do
remove_last a
done
clear a is truncate a 0, it removes all the elements of a.
Iteration
The iteration functions traverse the elements of a dynamic array. Traversals of a are computed in increasing index order: from the element of index 0 to the element of index length a - 1.
It is a programming error to change the length of an array (by adding or removing elements) during an iteration on the array. Any iteration function will fail with Invalid_argument if it detects such a length change.
val iter : ('a -> unit) -> 'a t -> unititer f a calls f on each element of a.
val iteri : (int -> 'a -> unit) -> 'a t -> unititeri f a calls f i x for each x at index i in a.
val map : ('a -> 'b) -> 'a t -> 'b tmap f a is a new array of elements of the form f x for each element x of a.
For example, if the elements of a are x0, x1, x2, then the elements of b are f x0, f x1, f x2.
val mapi : (int -> 'a -> 'b) -> 'a t -> 'b tmapi f a is a new array of elements of the form f i x for each element x of a at index i.
For example, if the elements of a are x0, x1, x2, then the elements of b are f 0 x0, f 1 x1, f 2 x2.
val fold_left : ('acc -> 'a -> 'acc) -> 'acc -> 'a t -> 'accfold_left f acc a folds f over a in order, starting with accumulator acc.
For example, if the elements of a are x0, x1, then fold f acc a is
let acc = f acc x0 in
let acc = f acc x1 in
acc
val fold_right : ('a -> 'acc -> 'acc) -> 'a t -> 'acc -> 'accfold_right f a acc computes f x0 (f x1 (... (f xn acc) ...)) where x0, x1, ..., xn are the elements of a.
val exists : ('a -> bool) -> 'a t -> boolexists f a is true if some element of a satisfies f.
For example, if the elements of a are x0, x1, x2, then exists f a is f x0 || f x1 || f x2.
val for_all : ('a -> bool) -> 'a t -> boolfor_all f a is true if all elements of a satisfy f. This includes the case where a is empty.
For example, if the elements of a are x0, x1, then exists f a is f x0 && f x1 && f x2.
val filter : ('a -> bool) -> 'a t -> 'a tfilter f a is a new array of all the elements of a that satisfy f. In other words, it is an array b such that, for each element x in a in order, x is added to b if f x is true.
For example, filter (fun x -> x >= 0) a is a new array of all non-negative elements of a, in order.
val filter_map : ('a -> 'b option) -> 'a t -> 'b tfilter_map f a is a new array of elements y such that f x is Some y for an element x of a. In others words, it is an array b such that, for each element x of a in order:
- if
f x = Some y, then y is added to b, - if
f x = None, then no element is added to b.
For example, filter_map int_of_string_opt inputs returns a new array of integers read from the strings in inputs, ignoring strings that cannot be converted to integers.
Conversions to other data structures
Note: the of_* functions raise Invalid_argument if the length needs to grow beyond Sys.max_array_length.
The to_* functions, except those specifically marked "reentrant", iterate on their dynarray argument. In particular it is a programming error if the length of the dynarray changes during their execution, and the conversion functions raise Invalid_argument if they observe such a change.
val of_array : 'a array -> 'a tof_array arr returns a dynamic array corresponding to the fixed-sized array a. Operates in O(n) time by making a copy.
val to_array : 'a t -> 'a arrayto_array a returns a fixed-sized array corresponding to the dynamic array a. This always allocate a new array and copies elements into it.
val of_list : 'a list -> 'a tof_list l is the array containing the elements of l in the same order.
val to_list : 'a t -> 'a listto_list a is a list with the elements contained in the array a.
of_seq seq is an array containing the same elements as seq.
It traverses seq once and will terminate only if seq is finite.
to_seq a is the sequence of elements get a 0, get a 1... get a (length a - 1).
val to_seq_reentrant : 'a t -> 'a Seq.tto_seq_reentrant a is a reentrant variant of to_seq, in the sense that one may still access its elements after the length of a has changed.
Demanding the i-th element of the resulting sequence (which can happen zero, one or several times) will access the i-th element of a at the time of the demand. The sequence stops if a has less than i elements at this point.
val to_seq_rev : 'a t -> 'a Seq.tto_seq_rev a is the sequence of elements get a (l - 1), get a (l - 2)... get a 0, where l is length a at the time to_seq_rev is invoked.
val to_seq_rev_reentrant : 'a t -> 'a Seq.tto_seq_rev_reentrant a is a reentrant variant of to_seq_rev, in the sense that one may still access its elements after the length of a has changed.
Elements that have been removed from the array by the time they are demanded in the sequence are skipped.
Advanced topics for performance
Backing array, capacity
Internally, a dynamic array uses a backing array (a fixed-size array as provided by the Array module) whose length is greater or equal to the length of the dynamic array. We define the capacity of a dynamic array as the length of its backing array.
The capacity of a dynamic array is relevant in advanced scenarios, when reasoning about the performance of dynamic array programs:
- The memory usage of a dynamic array is proportional to its capacity, rather than its length.
- When there is no empty space left at the end of the backing array, adding elements requires allocating a new, larger backing array.
The implementation uses a standard exponential reallocation strategy which guarantees amortized constant-time operation; in particular, the total capacity of all backing arrays allocated over the lifetime of a dynamic array is at worst proportional to the total number of elements added.
In other words, users need not care about capacity and reallocations, and they will get reasonable behavior by default. However, in some performance-sensitive scenarios the functions below can help control memory usage or guarantee an optimal number of reallocations.
val capacity : 'a t -> intcapacity a is the length of a's backing array.
val ensure_capacity : 'a t -> int -> unitensure_capacity a n makes sure that the capacity of a is at least n.
ensure_extra_capacity a n is ensure_capacity a (length a + n), it makes sure that a has room for n extra items.
val fit_capacity : 'a t -> unitfit_capacity a reallocates a backing array if necessary, so that the resulting capacity is exactly length a, with no additional empty space at the end. This can be useful to make sure there is no memory wasted on a long-lived array.
Note that calling fit_capacity breaks the amortized complexity guarantees provided by the default reallocation strategy. Calling it repeatedly on an array may have quadratic complexity, both in time and in total number of words allocated.
If you know that a dynamic array has reached its final length, which will remain fixed in the future, it is sufficient to call to_array and only keep the resulting fixed-size array. fit_capacity is useful when you need to keep a dynamic array for eventual future resizes.
val set_capacity : 'a t -> int -> unitset_capacity a n reallocates a backing array if necessary, so that the resulting capacity is exactly n. In particular, all elements of index n or greater are removed.
Like fit_capacity, this function breaks the amortized complexity guarantees provided by the reallocation strategy. Calling it repeatedly on an array may have quadratic complexity, both in time and in total number of words allocated.
This is an advanced function; in particular, ensure_capacity should be preferred to increase the capacity, as it preserves those amortized guarantees.
reset a clears a and replaces its backing array by an empty array.
It is equivalent to set_capacity a 0 or clear a; fit_capacity a.
No leaks: preservation of memory liveness
The user-provided values reachable from a dynamic array a are exactly the elements in the positions 0 to length a - 1. In particular, no user-provided values are "leaked" by being present in the backing array in position length a or later.
Memory layout of dynarrays
In the current implementation, the backing array of an 'a Dynarray.t is not an 'a array, but something with the same representation as an 'a option array or 'a ref array. Each element is in a "box", allocated when the element is first added to the array -- see the implementation for more details.
Using an 'a array would be delicate, as there is no obvious type-correct way to represent the empty space at the end of the backing array -- using user-provided values would either complicate the API or violate the no leaks guarantee. The constraint of remaining memory-safe under unsynchronized concurrent usage makes it even more difficult. Various unsafe ways to do this have been discussed, with no consensus on a standard implementation so far.
On a realistic automated-theorem-proving program that relies heavily on dynamic arrays, we measured the overhead of this extra "boxing" as at most 25%. We believe that the overhead for most uses of dynarray is much smaller, negligible in many cases, but you may still prefer to use your own specialized implementation for performance. (If you know that you do not need the no leaks guarantee, you can also speed up deleting elements.)
Code examples
Min-heaps for mutable priority queues
We can use dynamic arrays to implement a mutable priority queue. A priority queue provides a function to add elements, and a function to extract the minimum element -- according to some comparison function.
(* We present our priority queues as a functor
parametrized on the comparison function. *)
module Heap (Elem : Map.OrderedType) : sig
type t
val create : unit -> t
val add : t -> Elem.t -> unit
val pop_min : t -> Elem.t option
end = struct
(* Our priority queues are implemented using the standard "min heap"
data structure, a dynamic array representing a binary tree. *)
type t = Elem.t Dynarray.t
let create = Dynarray.create
(* The node of index [i] has as children the nodes of index [2 * i + 1]
and [2 * i + 2] -- if they are valid indices in the dynarray. *)
let left_child i = 2 * i + 1
let right_child i = 2 * i + 2
let parent_node i = (i - 1) / 2
(* We use indexing operators for convenient notations. *)
let ( .!() ) = Dynarray.get
let ( .!()<- ) = Dynarray.set
(* Auxiliary functions to compare and swap two elements
in the dynamic array. *)
let order h i j =
Elem.compare h.!(i) h.!(j)
let swap h i j =
let v = h.!(i) in
h.!(i) <- h.!(j);
h.!(j) <- v
(* We say that a heap respects the "heap ordering" if the value of
each node is smaller than the value of its children. The
algorithm manipulates arrays that respect the heap algorithm,
except for one node whose value may be too small or too large.
The auxiliary functions [heap_up] and [heap_down] take
such a misplaced value, and move it "up" (respectively: "down")
the tree by permuting it with its parent value (respectively:
a child value) until the heap ordering is restored. *)
let rec heap_up h i =
if i = 0 then () else
let parent = parent_node i in
if order h i parent < 0 then
(swap h i parent; heap_up h parent)
and heap_down h ~len i =
let left, right = left_child i, right_child i in
if left >= len then () (* no child, stop *) else
let smallest =
if right >= len then left (* no right child *) else
if order h left right < 0 then left else right
in
if order h i smallest > 0 then
(swap h i smallest; heap_down h ~len smallest)
let add h s =
let i = Dynarray.length h in
Dynarray.add_last h s;
heap_up h i
let pop_min h =
if Dynarray.is_empty h then None
else begin
(* Standard trick: swap the 'best' value at index 0
with the last value of the array. *)
let last = Dynarray.length h - 1 in
swap h 0 last;
(* At this point [pop_last] returns the 'best' value,
and leaves a heap with one misplaced element at position 0. *)
let best = Dynarray.pop_last h in
(* Restore the heap ordering -- does nothing if the heap is empty. *)
heap_down h ~len:last 0;
Some best
end
end
The production code from which this example was inspired includes logic to free the backing array when the heap becomes empty, only in the case where the capacity is above a certain threshold. This can be done by calling the following function from pop:
let shrink h =
if Dynarray.length h = 0 && Dynarray.capacity h > 1 lsl 18 then
Dynarray.reset h
The Heap functor can be used to implement a sorting function, by adding all elements into a priority queue and then extracting them in order.
let heap_sort (type a) cmp li =
let module Heap = Heap(struct type t = a let compare = cmp end) in
let heap = Heap.create () in
List.iter (Heap.add heap) li;
List.map (fun _ -> Heap.pop_min heap |> Option.get) li