`type 'a t = 'a array`

The type of arrays.

`include BatEnum.Enumerable with type 'a enumerable = 'a t`
`type 'a enumerable = 'a t`

The data structure, e.g. `'a List.t`

`include BatInterfaces.Mappable with type 'a mappable = 'a t`
`type 'a mappable = 'a t`

The data structure, e.g. `'a List.t`

`val length : 'a array -> int`

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

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

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

- raises `Invalid_argument`

  if `n` is outside the range 0 to `(Array.length a - 1)`.

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

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

- raises `Invalid_argument`

  if `n` is outside the range 0 to `Array.length a - 1`.

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

`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`
`val make_float : int -> float array`

`Array.make_float n` returns a fresh float array of length `n`, with uninitialized data.

- since 2.3.0

`val init_matrix : int -> int -> (int -> int -> 'a) -> 'a array array`
`val of_seq : 'a Stdlib.Seq.t -> 'a array`
`val to_seq : 'a array -> 'a Stdlib.Seq.t`
`val to_seqi : 'a array -> (int * 'a) Stdlib.Seq.t`
`val init : int -> (int -> 'a) -> 'a array`

`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, `Array.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`

`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`

`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 `Array.append`, but concatenates a list of arrays.

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

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

- raises `Invalid_argument`

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

`val copy : 'a array -> 'a array`

`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`

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

- raises `Invalid_argument`

  if `ofs` and `len` do not designate a valid subarray of `a`.

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

`Array.blit v1 o1 v2 o2 len` copies `len` elements from array `v1`, starting at element number `o1`, to array `v2`, starting at element number `o2`. It works correctly even if `v1` and `v2` are the same array, and the source and destination chunks overlap.

- raises `Invalid_argument`

  if `o1` and `len` do not designate a valid subarray of `v1`, or if `o2` and `len` do not designate a valid subarray of `v2`.

`val to_list : 'a array -> 'a list`

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

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

`Array.split a` converts the array of pairs `a` into a pair of arrays.

`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 3.4.0

`val of_list : 'a list -> 'a array`

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

`val max : 'a array -> 'a`

`max a` returns the largest value in `a` as judged by `Pervasives.compare`

- raises `Invalid_argument`

  on empty input

`val min : 'a array -> 'a`

`min a` returns the smallest value in `a` as judged by `Pervasives.compare`

- raises `Invalid_argument`

  on empty input

`val min_max : 'a array -> 'a * 'a`

`min_max a` returns the (smallest, largest) pair of values from `a` as judged by `Pervasives.compare`

- raises `Invalid_argument`

  on empty input

`val sum : int array -> int`

`sum l` returns the sum of the integers of `l`

`val fsum : float array -> float`

`fsum l` returns the sum of the floats of `l`

`val kahan_sum : float array -> float`

`kahan_sum l` returns a numerically-accurate sum of the floats of `l`.

You should consider using Kahan summation when you really care about very small differences in the result, while the result or one of the intermediate sums can be very large (which usually results in loss of precision of floating-point addition).

The worst-case rounding error is constant, instead of growing with (the square root of) the length of the input array as with `fsum`. On the other hand, processing each element requires four floating-point operations instead of one. See the wikipedia article on Kahan summation for more details.

- since 2.2.0

`val avg : int array -> float`

`avg l` returns the average of `l`

- since 2.1

`val favg : float array -> float`

`favg l` returns the average of `l`

- since 2.1

`val left : 'a array -> int -> 'a array`

`left r len` returns the array containing the `len` first elements of `r`. If `r` contains less than `len` elements, it returns `r`.

Examples: `Array.left [|0;1;2;3;4;5;6|] 4 = [|0;1;2;3|]` `Array.left [|1;2;3|] 0 = [||]` `Array.left [|1;2;3|] 10 = [|1;2;3|]`

`val right : 'a array -> int -> 'a array`

`left r len` returns the array containing the `len` last characters of `r`. If `r` contains less than `len` characters, it returns `r`.

Example: `Array.right [|1;2;3;4;5;6|] 4 = [|3;4;5;6|]`

`val head : 'a array -> int -> 'a array`

as `left`

`val tail : 'a array -> int -> 'a array`

`tail r pos` returns the array containing all but the `pos` first characters of `r`

Example: `Array.tail [|1;2;3;4;5;6|] 4 = [|5;6|]`

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

`Array.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.(Array.length a - 1); ()`.

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

`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.(Array.length a - 1) |]`.

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

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

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

Same as `Array.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`

`Array.fold_left f x a` computes `f (... (f (f x 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 3.4.0

`val fold_while : ('acc -> 'a -> bool) -> ('acc -> 'a -> 'acc) -> 'acc -> 'a array -> 'acc * int`

`fold_while p f init a`, accumulates elements `x` of array `a` using function `f`, as long as the predicate `p acc x` holds. At the end, the accumulated value along with the first index i where `p acc a.(i)` does not hold is returned. If the returned index is equal to `length a`, the whole array was folded.

`val fold : ('a -> 'b -> 'a) -> 'a -> 'b array -> 'a`

Alias for `fold_left`.

`val fold_right : ('b -> 'a -> 'a) -> 'b array -> 'a -> 'a`

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

`val modify : ('a -> 'a) -> 'a array -> unit`

`modify f a` replaces every element `x` of `a` with `f x`.

`val modifyi : (int -> 'a -> 'a) -> 'a array -> unit`

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

`val fold_lefti : ('a -> int -> 'b -> 'a) -> 'a -> 'b array -> 'a`

As `fold_left`, but with the index of the element as additional argument

`val fold_righti : (int -> 'b -> 'a -> 'a) -> 'b array -> 'a -> 'a`

As `fold_right`, but with the index of the element as additional argument

`val reduce : ('a -> 'a -> 'a) -> 'a array -> 'a`

`Array.reduce f a` is `fold_left f a.(0) [|a.(1); ..; a.(n-1)|]`. This is useful for merging a group of things that have no reasonable default value to return if the group is empty.

- raises `Invalid_argument`

  on empty arrays.

`val singleton : 'a -> 'a array`

Create an array consisting of exactly one element.

- since 2.1

## 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, `Pervasives.compare` is a suitable comparison function, provided there are no floating-point NaN values in the data. After calling `Array.sort`, the array is sorted in place in increasing order. `Array.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 `Array.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 `Array.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 `n/2` words of heap space, where `n` is the length of the array. It is usually faster than the current implementation of `Array.sort`.

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

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

`val decorate_stable_sort : ('a -> 'b) -> 'a array -> 'a array`

`decorate_stable_sort f a` returns a sorted copy of `a` such that if `f x < f y` then `x` is earlier in the result than `y`. This function is useful when `f` is expensive, as it only computes `f x` once for each element in the array. See Schwartzian Transform.

It is unnecessary to have an additional comparison function as argument, as the builtin `Pervasives.compare` is used to compare the `'b` values. This is deemed sufficient.

`val decorate_fast_sort : ('a -> 'b) -> 'a array -> 'a array`

As `Array.decorate_stable_sort`, but uses fast_sort internally.

`val bsearch : 'a BatOrd.ord -> 'a array -> 'a -> [ `All_lower | `All_bigger | `Just_after of int | `Empty | `At of int ]`

`bsearch cmp arr x` finds the index of the object `x` in the array `arr`, provided `arr` 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 (dichotomic search).

- returns
  - ``At i` if `cmp arr.(i) x = 0` (for some i)
  - ``All_lower` if all elements of `arr` are lower than `x`
  - ``All_bigger` if all elements of `arr` are bigger than `x`
  - ``Just_after i` if `arr.(i) < x < arr.(i+1)`
  - ``Empty` if the array is empty

- raises `Invalid_argument`

  if the array is found to be unsorted w.r.t `cmp`

- since 2.2.0

`val pivot_split : 'a BatOrd.ord -> 'a array -> 'a -> int * int`

`pivot_split cmp arr x` assumes that `arr` is sorted w.r.t `cmp`. It splits an array `arr` of length `len` into three parts, by returning a couple (i,j) such as:

- all elements with indices 0..i-1 (`sub arr 0 i`) are lower than `x`
- all elements with indices i..j-1 (`sub arr i (j-i)`) are equal to `x`
- all elements with indices j..len-1 (`sub arr j (len-j)`) are bigger than `x`

In particular, it returns:

- (0, 0) if all elements of `arr` are bigger than `x`
- (len, len) if all elements are lower than `x`
- (0, len) if all elements are equal to `x`

Complexity: logarithmic in the size of the array

- raises `Invalid_argument`

  if the array is found not to be sorted

## Operations on two arrays

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

`Array.iter2 f [|a0; a1; ...; an|] [|b0; b1; ...; bn|]` performs calls `f a0 b0; f a1 b1; ...; f an bn` in that order.

- raises `Invalid_argument`

  if the two arrays have different lengths.

`val iter2i : (int -> 'a -> 'b -> unit) -> 'a array -> 'b array -> unit`

`Array.iter2i f [|a0; a1; ...; an|] [|b0; b1; ...; bn|]` performs calls `f 0 a0 b0; f 1 a1 b1; ...; f n an bn` in that order.

- raises `Invalid_argument`

  if the two arrays have different lengths.

`val for_all2 : ('a -> 'b -> bool) -> 'a array -> 'b array -> bool`

As `Array.for_all` but on two arrays.

- raises `Invalid_argument`

  if the two arrays have different lengths.

`val exists2 : ('a -> 'b -> bool) -> 'a array -> 'b array -> bool`

As `Array.exists` but on two arrays.

- raises `Invalid_argument`

  if the two arrays have different lengths.

`val map2 : ('a -> 'b -> 'c) -> 'a array -> 'b array -> 'c array`

As `Array.map` but on two arrays.

- raises `Invalid_argument`

  if the two arrays have different lengths.

`val cartesian_product : 'a array -> 'b array -> ('a * 'b) array`

Cartesian product of the two arrays.

- since 2.2.0

## Predicates

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

`for_all p [|a0; a1; ...; an|]` checks if all elements of the array satisfy the predicate `p`. That is, it returns `(p a0) && (p a1) && ... && (p an)`.

`val exists : ('a -> bool) -> 'a array -> bool`

`exists p [|a0; a1; ...; an|]` checks if at least one element of the array satisfies the predicate `p`. That is, it returns `(p a0) || (p a1) || ... || (p an)`.

`val find : ('a -> bool) -> 'a array -> 'a`

`find p a` returns the first element of array `a` that satisfies the predicate `p`.

- raises `Not_found`

  if there is no value that satisfies `p` in the array `a`.

`val find_opt : ('a -> bool) -> 'a array -> 'a option`

`find_opt p a` returns the first element of the array `a` that satisfies the predicate `p`, or `None` if there is no such element.

- since 3.4.0

`val mem : 'a -> 'a array -> bool`

`mem m a` is true if and only if `m` is equal to an element of `a`.

`val memq : 'a -> 'a array -> bool`

Same as `Array.mem` but uses physical equality instead of structural equality to compare array elements.

`val findi : ('a -> bool) -> 'a array -> int`

`findi p a` returns the index of the first element of array `a` that satisfies the predicate `p`.

- raises `Not_found`

  if there is no value that satisfies `p` in the array `a`.

`val filter : ('a -> bool) -> 'a array -> 'a array`

`filter p a` returns all the elements of the array `a` that satisfy the predicate `p`. The order of the elements in the input array is preserved.

`val filteri : (int -> 'a -> bool) -> 'a array -> 'a array`

As `filter` but with the index passed to the predicate.

`val filter_map : ('a -> 'b option) -> 'a array -> 'b array`

`filter_map f e` returns an array consisting of all elements `x` such that `f y` returns `Some x` , where `y` is an element of `e`.

`val count_matching : ('a -> bool) -> 'a array -> int`

`count_matching p a` returns the number of elements of `a` satisfying predicate `p`.

`val find_all : ('a -> bool) -> 'a array -> 'a array`

`find_all` is another name for `Array.filter`.

`val partition : ('a -> bool) -> 'a array -> 'a array * 'a array`

`partition p a` returns a pair of arrays `(a1, a2)`, where `a1` is the array of all the elements of `a` that satisfy the predicate `p`, and `a2` is the array of all the elements of `a` that do not satisfy `p`. The order of the elements in the input array is preserved.

## Array transformations

`val rev : 'a array -> 'a array`

Array reversal.

`val rev_in_place : 'a array -> unit`

In-place array reversal. The array argument is updated.

## Conversions

`val enum : 'a array -> 'a BatEnum.t`

Returns an enumeration of the elements of an array. Behavior of the enumeration is undefined if the contents of the array changes afterwards.

`val of_enum : 'a BatEnum.t -> 'a array`

Build an array from an enumeration.

`val backwards : 'a array -> 'a BatEnum.t`

Returns an enumeration of the elements of an array, from last to first.

`val of_backwards : 'a BatEnum.t -> 'a array`

Build an array from an enumeration, with the first element of the enumeration as the last element of the array and vice versa.

## Utilities

`val range : 'a array -> int BatEnum.t`

`range a` returns an enumeration of all valid indexes into the given array. For example, `range [|2;4;6;8|] = 0--3`.

`val insert : 'a array -> 'a -> int -> 'a array`

`insert xs x i` returns a copy of `xs` except the value `x` is inserted in position `i` (and all later indices are shifted to the right).

- raises `Invalid_argument`

  if `i < 0 || i > Array.length xs`.

`val remove_at : int -> 'a array -> 'a array`

`remove_at i a` returns the array `a` without the element at index `i`.

- raises `Invalid_argument`

  if `i` is outside of `a` bounds.

- since 3.3.0

## Boilerplate code

`val print : ?first:string -> ?last:string -> ?sep:string -> ('a, 'b) BatIO.printer -> ('a t, 'b) BatIO.printer`

Print the contents of an array, with `~first` preceding the first item (default: "[|"), `~last` following the last item (default: "|]") and `~sep` separating items (default: "; "). A printing function must be provided to print the items in the array.

Example: IO.to_string (Array.print Int.print) `|2;4;66|` = "`|2; 4; 66|`"

`val compare : 'a BatOrd.comp -> 'a array BatOrd.comp`

`compare c` generates the lexicographical order on arrays induced by `c`. That is, given a comparison function for the elements of an array, this will return a comparison function for arrays of that type.

`val ord : 'a BatOrd.ord -> 'a array BatOrd.ord`

Hoist an element comparison function to compare arrays of those elements, with shorter arrays less than longer ones, and lexicographically for arrays of the same size. This is a different ordering than `compare`, but is often faster.

`val shuffle : ?state:Stdlib.Random.State.t -> 'a array -> unit`

`shuffle ~state:rs a` randomly shuffles in place the elements of `a`. The optional random state `rs` allows to control the random numbers being used during shuffling (for reproducibility).

Shuffling is implemented using the Fisher-Yates algorithm and works in O(n), where n is the number of elements of `a`.

- since 2.6.0

`val equal : 'a BatOrd.eq -> 'a array BatOrd.eq`

Hoist a equality test for elements to arrays. Arrays are only equal if their lengths are the same and corresponding elements test equal.

## Override modules

The following modules replace functions defined in `Array` with functions behaving slightly differently but having the same name. This is by design: the functions are meant to override the corresponding functions of `Array`.

`module Exceptionless : sig ... end`

Operations on `Array` without exceptions.

`module Labels : sig ... end`

Operations on `Array` with labels.

`module Cap : sig ... end`
`module Incubator : sig ... end`