package containers

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Array utils

type 'a iter = ('a -> unit) -> unit

Fast internal iterator.

  • since 2.8
type 'a gen = unit -> 'a option
type 'a equal = 'a -> 'a -> bool
type 'a ord = 'a -> 'a -> int
type 'a random_gen = Random.State.t -> 'a
type 'a printer = Format.formatter -> 'a -> unit

Arrays

Documentation for the standard Array module

type 'a t = 'a array

An alias for the type of arrays.

val length : 'a array -> int

Return the length (number of elements) of the given array.

val get : 'a array -> int -> 'a

get a n returns the element number n of array a. The first element has number 0. The last element has number length a - 1. You can also write a.(n) instead of get a n.

val set : 'a array -> int -> 'a -> unit

set a n x modifies array a in place, replacing element number n with x. You can also write a.(n) <- x instead of set a n x.

val make : int -> 'a -> 'a array

make n x returns a fresh array of length n, initialized with x. All the elements of this new array are initially physically equal to x (in the sense of the == predicate). Consequently, if x is mutable, it is shared among all elements of the array, and modifying x through one of the array entries will modify all other entries at the same time.

  • raises Invalid_argument

    if n < 0 or n > Sys.max_array_length. If the value of x is a floating-point number, then the maximum size is only Sys.max_array_length / 2.

val create_float : int -> float array

create_float n returns a fresh float array of length n, with uninitialized data.

  • since 4.03
val init : int -> (int -> 'a) -> 'a array

init n f returns a fresh array of length n, with element number i initialized to the result of f i. In other terms, init n f tabulates the results of f applied to the integers 0 to n-1.

  • raises Invalid_argument

    if n < 0 or n > Sys.max_array_length. If the return type of f is float, then the maximum size is only Sys.max_array_length / 2.

val make_matrix : int -> int -> 'a -> 'a array array

make_matrix dimx dimy e returns a two-dimensional array (an array of arrays) with first dimension dimx and second dimension dimy. All the elements of this new matrix are initially physically equal to e. The element (x,y) of a matrix m is accessed with the notation m.(x).(y).

  • raises Invalid_argument

    if dimx or dimy is negative or greater than Sys.max_array_length. If the value of e is a floating-point number, then the maximum size is only Sys.max_array_length / 2.

val append : 'a array -> 'a array -> 'a array

append v1 v2 returns a fresh array containing the concatenation of the arrays v1 and v2.

val concat : 'a array list -> 'a array

Same as append, but concatenates a list of arrays.

val sub : 'a array -> int -> int -> 'a array

sub a pos len returns a fresh array of length len, containing the elements number pos to pos + len - 1 of array a.

  • raises Invalid_argument

    if pos and len do not designate a valid subarray of a; that is, if pos < 0, or len < 0, or pos + len > length a.

val copy : 'a array -> 'a array

copy a returns a copy of a, that is, a fresh array containing the same elements as a.

val fill : 'a array -> int -> int -> 'a -> unit

fill a pos len x modifies the array a in place, storing x in elements number pos to pos + len - 1.

val blit : 'a array -> int -> 'a array -> int -> int -> unit

blit src src_pos dst dst_pos len copies len elements from array src, starting at element number src_pos, to array dst, starting at element number dst_pos. It works correctly even if src and dst are the same array, and the source and destination chunks overlap.

  • raises Invalid_argument

    if src_pos and len do not designate a valid subarray of src, or if dst_pos and len do not designate a valid subarray of dst.

val to_list : 'a array -> 'a list

to_list a returns the list of all the elements of a.

val of_list : 'a list -> 'a array

of_list l returns a fresh array containing the elements of l.

  • raises Invalid_argument

    if the length of l is greater than Sys.max_array_length.

Iterators

val iter : ('a -> unit) -> 'a array -> unit

iter f a applies function f in turn to all the elements of a. It is equivalent to f a.(0); f a.(1); ...; f a.(length a - 1); ().

val iteri : (int -> 'a -> unit) -> 'a array -> unit

Same as iter, but the function is applied to the index of the element as first argument, and the element itself as second argument.

val map : ('a -> 'b) -> 'a array -> 'b array

map f a applies function f to all the elements of a, and builds an array with the results returned by f: [| f a.(0); f a.(1); ...; f a.(length a - 1) |].

val mapi : (int -> 'a -> 'b) -> 'a array -> 'b array

Same as map, but the function is applied to the index of the element as first argument, and the element itself as second argument.

val fold_left : ('a -> 'b -> 'a) -> 'a -> 'b array -> 'a

fold_left f init a computes f (... (f (f init a.(0)) a.(1)) ...) a.(n-1), where n is the length of the array a.

val fold_left_map : ('a -> 'b -> 'a * 'c) -> 'a -> 'b array -> 'a * 'c array

fold_left_map is a combination of fold_left and map that threads an accumulator through calls to f.

  • since 4.13.0
val fold_right : ('b -> 'a -> 'a) -> 'b array -> 'a -> 'a

fold_right f a init computes f a.(0) (f a.(1) ( ... (f a.(n-1) init) ...)), where n is the length of the array a.

Iterators on two arrays

val iter2 : ('a -> 'b -> unit) -> 'a array -> 'b array -> unit

iter2 f a b applies function f to all the elements of a and b.

  • since 4.03.0 (4.05.0 in ArrayLabels)
val map2 : ('a -> 'b -> 'c) -> 'a array -> 'b array -> 'c array

map2 f a b applies function f to all the elements of a and b, and builds an array with the results returned by f: [| f a.(0) b.(0); ...; f a.(length a - 1) b.(length b - 1)|].

  • since 4.03.0 (4.05.0 in ArrayLabels)

Array scanning

val for_all : ('a -> bool) -> 'a array -> bool

for_all f [|a1; ...; an|] checks if all elements of the array satisfy the predicate f. That is, it returns (f a1) && (f a2) && ... && (f an).

  • since 4.03.0
val exists : ('a -> bool) -> 'a array -> bool

exists f [|a1; ...; an|] checks if at least one element of the array satisfies the predicate f. That is, it returns (f a1) || (f a2) || ... || (f an).

  • since 4.03.0
val memq : 'a -> 'a array -> bool

Same as mem, but uses physical equality instead of structural equality to compare list elements.

  • since 4.03.0
val find_opt : ('a -> bool) -> 'a array -> 'a option

find_opt f a returns the first element of the array a that satisfies the predicate f, or None if there is no value that satisfies f in the array a.

  • since 4.13.0

Arrays of pairs

val split : ('a * 'b) array -> 'a array * 'b array

split [|(a1,b1); ...; (an,bn)|] is ([|a1; ...; an|], [|b1; ...; bn|]).

  • since 4.13.0
val combine : 'a array -> 'b array -> ('a * 'b) array

combine [|a1; ...; an|] [|b1; ...; bn|] is [|(a1,b1); ...; (an,bn)|]. Raise Invalid_argument if the two arrays have different lengths.

  • since 4.13.0

Sorting

val sort : ('a -> 'a -> int) -> 'a array -> unit

Sort an array in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see below for a complete specification). For example, Stdlib.compare is a suitable comparison function. After calling sort, the array is sorted in place in increasing order. sort is guaranteed to run in constant heap space and (at most) logarithmic stack space.

The current implementation uses Heap Sort. It runs in constant stack space.

Specification of the comparison function: Let a be the array and cmp the comparison function. The following must be true for all x, y, z in a :

  • cmp x y > 0 if and only if cmp y x < 0
  • if cmp x y >= 0 and cmp y z >= 0 then cmp x z >= 0

When sort returns, a contains the same elements as before, reordered in such a way that for all i and j valid indices of a :

  • cmp a.(i) a.(j) >= 0 if and only if i >= j
val stable_sort : ('a -> 'a -> int) -> 'a array -> unit

Same as sort, but the sorting algorithm is stable (i.e. elements that compare equal are kept in their original order) and not guaranteed to run in constant heap space.

The current implementation uses Merge Sort. It uses a temporary array of length n/2, where n is the length of the array. It is usually faster than the current implementation of sort.

val fast_sort : ('a -> 'a -> int) -> 'a array -> unit

Same as sort or stable_sort, whichever is faster on typical input.

Arrays and Sequences

val to_seqi : 'a array -> (int * 'a) Seq.t

Iterate on the array, in increasing order, yielding indices along elements. Modifications of the array during iteration will be reflected in the sequence.

  • since 4.07
val of_seq : 'a Seq.t -> 'a array

Create an array from the generator

  • since 4.07

Arrays and concurrency safety

Care must be taken when concurrently accessing arrays from multiple domains: accessing an array will never crash a program, but unsynchronized accesses might yield surprising (non-sequentially-consistent) results.

Atomicity

Every array operation that accesses more than one array element is not atomic. This includes iteration, scanning, sorting, splitting and combining arrays.

For example, consider the following program:

let size = 100_000_000
let a = Array.make size 1
let d1 = Domain.spawn (fun () ->
   Array.iteri (fun i x -> a.(i) <- x + 1) a
)
let d2 = Domain.spawn (fun () ->
  Array.iteri (fun i x -> a.(i) <- 2 * x + 1) a
)
let () = Domain.join d1; Domain.join d2

After executing this code, each field of the array a is either 2, 3, 4 or 5. If atomicity is required, then the user must implement their own synchronization (for example, using Mutex.t).

Data races

If two domains only access disjoint parts of the array, then the observed behaviour is the equivalent to some sequential interleaving of the operations from the two domains.

A data race is said to occur when two domains access the same array element without synchronization and at least one of the accesses is a write. In the absence of data races, the observed behaviour is equivalent to some sequential interleaving of the operations from different domains.

Whenever possible, data races should be avoided by using synchronization to mediate the accesses to the array elements.

Indeed, in the presence of data races, programs will not crash but the observed behaviour may not be equivalent to any sequential interleaving of operations from different domains. Nevertheless, even in the presence of data races, a read operation will return the value of some prior write to that location (with a few exceptions for float arrays).

Float arrays

Float arrays have two supplementary caveats in the presence of data races.

First, the blit operation might copy an array byte-by-byte. Data races between such a blit operation and another operation might produce surprising values due to tearing: partial writes interleaved with other operations can create float values that would not exist with a sequential execution.

For instance, at the end of

let zeros = Array.make size 0.
let max_floats = Array.make size Float.max_float
let res = Array.copy zeros
let d1 = Domain.spawn (fun () -> Array.blit zeros 0 res 0 size)
let d2 = Domain.spawn (fun () -> Array.blit max_floats 0 res 0 size)
let () = Domain.join d1; Domain.join d2

the res array might contain values that are neither 0. nor max_float.

Second, on 32-bit architectures, getting or setting a field involves two separate memory accesses. In the presence of data races, the user may observe tearing on any operation.

val empty : 'a t

empty is the empty array, physically equal to [||].

val equal : 'a equal -> 'a t equal

equal eq a1 a2 is true if the lengths of a1 and a2 are the same and if their corresponding elements test equal, using eq.

val compare : 'a ord -> 'a t ord

compare cmp a1 a2 compares arrays a1 and a2 using the function comparison cmp.

val swap : 'a t -> int -> int -> unit

swap a i j swaps elements at indices i and j.

  • since 1.4
val get_safe : 'a t -> int -> 'a option

get_safe a i returns Some a.(i) if i is a valid index.

  • since 0.18
val map_inplace : ('a -> 'a) -> 'a t -> unit

map_inplace f a replace all elements of a by its image by f.

  • since 3.8
val fold : ('a -> 'b -> 'a) -> 'a -> 'b t -> 'a

fold f init a computes f (… (f (f init a.(0)) a.(1)) …) a.(n-1), where n is the length of the array a. Same as Array.fold_left

val foldi : ('a -> int -> 'b -> 'a) -> 'a -> 'b t -> 'a

foldi f init a is just like fold, but it also passes in the index of each element as the second argument to the folded function f.

val fold_while : ('a -> 'b -> 'a * [ `Stop | `Continue ]) -> 'a -> 'b t -> 'a

fold_while f init a folds left on array a until a stop condition via ('a, `Stop) is indicated by the accumulator.

  • since 0.8
val fold_map : ('acc -> 'a -> 'acc * 'b) -> 'acc -> 'a t -> 'acc * 'b t

fold_map f init a is a fold_left-like function, but it also maps the array to another array.

  • since 1.2, but only
  • since 2.1 with labels
val scan_left : ('acc -> 'a -> 'acc) -> 'acc -> 'a t -> 'acc t

scan_left f init a returns the array [|init; f init x0; f (f init a.(0)) a.(1); …|] .

  • since 1.2, but only
  • since 2.1 with labels
val reverse_in_place : 'a t -> unit

reverse_in_place a reverses the array a in place.

val sorted : ('a -> 'a -> int) -> 'a t -> 'a array

sorted f a makes a copy of a and sorts it with f.

  • since 1.0
val sort_indices : ('a -> 'a -> int) -> 'a t -> int array

sort_indices f a returns a new array b, with the same length as a, such that b.(i) is the index at which the i-th element of sorted f a appears in a. a is not modified.

In other words, map (fun i -> a.(i)) (sort_indices f a) = sorted f a. sort_indices yields the inverse permutation of sort_ranking.

  • since 1.0
val sort_ranking : ('a -> 'a -> int) -> 'a t -> int array

sort_ranking f a returns a new array b, with the same length as a, such that b.(i) is the index at which the i-th element of a appears in sorted f a. a is not modified.

In other words, map (fun i -> (sorted f a).(i)) (sort_ranking f a) = a. sort_ranking yields the inverse permutation of sort_indices.

In the absence of duplicate elements in a, we also have lookup_exn a.(i) (sorted a) = (sorted_ranking a).(i).

  • since 1.0
val mem : ?eq:('a -> 'a -> bool) -> 'a -> 'a t -> bool

mem ~eq x a return true if x is present in a. Linear time.

  • since 3.0
val find_map : ('a -> 'b option) -> 'a t -> 'b option

find_map f a returns Some y if there is an element x such that f x = Some y. Otherwise returns None.

  • since 1.3, but only
  • since 2.1 with labels
val find_map_i : (int -> 'a -> 'b option) -> 'a t -> 'b option

find_map_i f a is like find_map, but the index of the element is also passed to the predicate function f.

  • since 1.3, but only
  • since 2.1 with labels
val find_idx : ('a -> bool) -> 'a t -> (int * 'a) option

find_idx f a returns Some (i,x) where x is the i-th element of a, and f x holds. Otherwise returns None.

  • since 0.3.4
val lookup : cmp:'a ord -> 'a -> 'a t -> int option

lookup ~cmp key a lookups the index of some key key in a sorted array a. Undefined behavior if the array a is not sorted wrt ~cmp. Complexity: O(log (n)) (dichotomic search).

  • returns

    None if the key key is not present, or Some i (i the index of the key) otherwise.

val lookup_exn : cmp:'a ord -> 'a -> 'a t -> int

lookup_exn ~cmp key a is like lookup, but

  • raises Not_found

    if the key key is not present.

val bsearch : cmp:('a -> 'a -> int) -> 'a -> 'a t -> [ `All_lower | `All_bigger | `Just_after of int | `Empty | `At of int ]

bsearch ~cmp key a finds the index of the object key in the array a, provided a is sorted using cmp. If the array is not sorted, the result is not specified (may raise Invalid_argument).

Complexity: O(log n) where n is the length of the array a (dichotomic search).

  • returns
    • `At i if cmp a.(i) key = 0 (for some i).
    • `All_lower if all elements of a are lower than key.
    • `All_bigger if all elements of a are bigger than key.
    • `Just_after i if a.(i) < key < a.(i+1).
    • `Empty if the array a is empty.
  • since 0.13
val for_all2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool

for_all2 f [|a1; …; an|] [|b1; …; bn|] is true if each pair of elements ai bi satisfies the predicate f. That is, it returns (f a1 b1) && (f a2 b2) && … && (f an bn).

  • since 0.20
val exists2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool

exists2 f [|a1; …; an|] [|b1; …; bn|] is true if any pair of elements ai bi satisfies the predicate f. That is, it returns (f a1 b1) || (f a2 b2) || … || (f an bn).

  • since 0.20
val fold2 : ('acc -> 'a -> 'b -> 'acc) -> 'acc -> 'a t -> 'b t -> 'acc

fold2 f init a b fold on two arrays a and b stepwise. It computes f (… (f init a1 b1) …) an bn.

  • since 0.20
val shuffle : 'a t -> unit

shuffle a randomly shuffles the array a, in place.

val shuffle_with : Random.State.t -> 'a t -> unit

shuffle_with rs a randomly shuffles the array a (like shuffle) but a specialized random state rs is used to control the random numbers being produced during shuffling (for reproducibility).

val random_choose : 'a t -> 'a random_gen

random_choose a rs randomly chooses an element of a.

  • raises Not_found

    if the array/slice is empty.

val to_string : ?sep:string -> ('a -> string) -> 'a array -> string

to_string ~sep item_to_string a print a to a string using sep as a separator between elements of a.

  • since 2.7
val to_iter : 'a t -> 'a iter

to_iter a returns an iter of the elements of an array a. The input array a is shared with the sequence and modification of it will result in modification of the iterator.

  • since 2.8
val to_seq : 'a t -> 'a Seq.t

to_seq a returns a Seq.t of the elements of an array a. The input array a is shared with the sequence and modification of it will result in modification of the sequence. Renamed from to_std_seq since 3.0.

  • since 3.0
val to_gen : 'a t -> 'a gen

to_gen a returns a gen of the elements of an array a.

IO

val pp : ?pp_start:unit printer -> ?pp_stop:unit printer -> ?pp_sep:unit printer -> 'a printer -> 'a t printer

pp ~pp_start ~pp_stop ~pp_sep pp_item ppf a formats the array a on ppf. Each element is formatted with pp_item, pp_start is called at the beginning, pp_stop is called at the end, pp_sep is called between each elements. By defaults pp_start and pp_stop does nothing and pp_sep defaults to (fun out -> Format.fprintf out ",@ ").

val pp_i : ?pp_start:unit printer -> ?pp_stop:unit printer -> ?pp_sep:unit printer -> (int -> 'a printer) -> 'a t printer

pp_i ~pp_start ~pp_stop ~pp_sep pp_item ppf a prints the array a on ppf. The printing function pp_item is giving both index and element. pp_start is called at the beginning, pp_stop is called at the end, pp_sep is called between each elements. By defaults pp_start and pp_stop does nothing and pp_sep defaults to (fun out -> Format.fprintf out ",@ ").

val rev : 'a t -> 'a t

rev a copies the array a and reverses it in place.

  • since 0.20
val filter : ('a -> bool) -> 'a t -> 'a t

filter f a filters elements out of the array a. Only the elements satisfying the given predicate f will be kept.

val filter_map : ('a -> 'b option) -> 'a t -> 'b t

filter_map f [|a1; …; an|] calls (f a1) … (f an) and returns an array b consisting of all elements bi such as f ai = Some bi. When f returns None, the corresponding element of a is discarded.

val monoid_product : ('a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t

monoid_product f a b passes all combinaisons of tuples from the two arrays a and b to the function f.

  • since 2.8
val flat_map : ('a -> 'b t) -> 'a t -> 'b array

flat_map f a transforms each element of a into an array, then flattens.

val except_idx : 'a t -> int -> 'a list

except_idx a i removes the element of a at given index i, and returns the list of the other elements.

val random : 'a random_gen -> 'a t random_gen
val random_non_empty : 'a random_gen -> 'a t random_gen
val random_len : int -> 'a random_gen -> 'a t random_gen

Generic Functions

module type MONO_ARRAY = sig ... end
val sort_generic : (module MONO_ARRAY with type elt = 'elt and type t = 'arr) -> cmp:('elt -> 'elt -> int) -> 'arr -> unit

sort_generic (module M) ~cmp a sorts the array a, without allocating (eats stack space though). Performance might be lower than Array.sort.

  • since 0.14

Infix Operators

It is convenient to openCCArray.Infix to access the infix operators without cluttering the scope too much.

  • since 2.7
module Infix : sig ... end
include module type of Infix
val (>>=) : 'a t -> ('a -> 'b t) -> 'b t

a >>= f is the infix version of flat_map.

val (>>|) : 'a t -> ('a -> 'b) -> 'b t

a >>| f is the infix version of map.

  • since 0.8
val (>|=) : 'a t -> ('a -> 'b) -> 'b t

a >|= f is the infix version of map.

  • since 0.8
val (--) : int -> int -> int t

x -- y creates an array containing integers in the range x .. y. Bounds included.

val (--^) : int -> int -> int t

x --^ y creates an array containing integers in the range x .. y. Right bound excluded.

  • since 0.17

Let operators on OCaml >= 4.08.0, nothing otherwise

  • since 2.8
val let+ : 'a array -> ('a -> 'b) -> 'b array
val and+ : 'a array -> 'b array -> ('a * 'b) array
val let* : 'a array -> ('a -> 'b array) -> 'b array
val and* : 'a array -> 'b array -> ('a * 'b) array
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