array.mli

# 2 "array.mli"
(**************************************************************************)
(*                                                                        *)
(*                                 OCaml                                  *)
(*                                                                        *)
(*             Xavier Leroy, projet Cristal, INRIA Rocquencourt           *)
(*                                                                        *)
(*   Copyright 1996 Institut National de Recherche en Informatique et     *)
(*     en Automatique.                                                    *)
(*                                                                        *)
(*   All rights reserved.  This file is distributed under the terms of    *)
(*   the GNU Lesser General Public License version 2.1, with the          *)
(*   special exception on linking described in the file LICENSE.          *)
(*                                                                        *)
(**************************************************************************)

open! Stdlib

(* NOTE:
   If this file is arrayLabels.mli, run tools/sync_stdlib_docs after editing it
   to generate array.mli.

   If this file is array.mli, do not edit it directly -- edit
   arrayLabels.mli instead.
 *)

(** Array operations.

    The labeled version of this module can be used as described in the
    {!StdLabels} module.
*)

type 'a t = 'a array
(** An alias for the type of arrays. *)

external length : 'a array -> int = "%array_length"
(** Return the length (number of elements) of the given array. *)

external get : 'a array -> int -> 'a = "%array_safe_get"
(** [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].

   @raise Invalid_argument
   if [n] is outside the range 0 to [(length a - 1)]. *)

external set : 'a array -> int -> 'a -> unit = "%array_safe_set"
(** [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].

   @raise Invalid_argument
   if [n] is outside the range 0 to [length a - 1]. *)

external make : int -> 'a -> 'a array = "caml_make_vect"
(** [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.

   @raise 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].*)

external create_float: int -> float array = "caml_make_float_vect"
(** [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 in order to the integers [0] to [n-1].

   @raise 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)].

   @raise 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 init_matrix : int -> int -> (int -> int -> 'a) -> 'a array array
(** [init_matrix dimx dimy f] returns a two-dimensional array
   (an array of arrays)
   with first dimension [dimx] and second dimension [dimy],
   where the element at index ([x,y]) is initialized with [f x y].
   The element ([x,y]) of a matrix [m] is accessed
   with the notation [m.(x).(y)].

   @raise Invalid_argument if [dimx] or [dimy] is negative or
   greater than {!Sys.max_array_length}.
   If the return type of [f] is [float],
   then the maximum size is only [Sys.max_array_length / 2].

   @since 5.2 *)

val append : 'a array -> 'a array -> 'a array
(** [append v1 v2] returns a fresh array containing the
   concatenation of the arrays [v1] and [v2].
   @raise Invalid_argument if
   [length v1 + length v2 > Sys.max_array_length]. *)

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].

   @raise 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].

   @raise Invalid_argument if [pos] and [len] do not
   designate a valid subarray of [a]. *)

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.

   @raise 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].

   @raise Invalid_argument if the length of [l] is greater than
   [Sys.max_array_length]. *)

(** {1 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 map_inplace : ('a -> 'a) -> 'a array -> unit
(** [map_inplace f a] applies function [f] to all elements of [a],
    and updates their values in place.
    @since 5.1 *)

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 mapi_inplace : (int -> 'a -> 'a) -> 'a array -> unit
(** Same as {!map_inplace}, but the function is applied to the index of the
    element as first argument, and the element itself as second argument.
    @since 5.1 *)

val fold_left : ('acc -> 'a -> 'acc) -> 'acc -> 'a array -> 'acc
(** [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 :
  ('acc -> 'a -> 'acc * 'b) -> 'acc -> 'a array -> 'acc * 'b array
(** [fold_left_map] is a combination of {!fold_left} and {!map} that threads an
    accumulator through calls to [f].
    @since 4.13 *)

val fold_right : ('a -> 'acc -> 'acc) -> 'a array -> 'acc -> 'acc
(** [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]. *)


(** {1 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].
   @raise Invalid_argument if the arrays are not the same size.
   @since 4.03 (4.05 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)|]].
   @raise Invalid_argument if the arrays are not the same size.
   @since 4.03 (4.05 in ArrayLabels) *)


(** {1 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 *)

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 *)

val for_all2 : ('a -> 'b -> bool) -> 'a array -> 'b array -> bool
(** Same as {!for_all}, but for a two-argument predicate.
   @raise Invalid_argument if the two arrays have different lengths.
   @since 4.11 *)

val exists2 : ('a -> 'b -> bool) -> 'a array -> 'b array -> bool
(** Same as {!exists}, but for a two-argument predicate.
   @raise Invalid_argument if the two arrays have different lengths.
   @since 4.11 *)

val mem : 'a -> 'a array -> bool
(** [mem a set] is true if and only if [a] is structurally equal
    to an element of [set] (i.e. there is an [x] in [set] such that
    [compare a x = 0]).
    @since 4.03 *)

val memq : 'a -> 'a array -> bool
(** Same as {!mem}, but uses physical equality
   instead of structural equality to compare array elements.
   @since 4.03 *)

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 *)

val find_index : ('a -> bool) -> 'a array -> int option
(** [find_index f a] returns [Some i], where [i] is the index of the first
    element of the array [a] that satisfies [f x], if there is such an
    element.

    It returns [None] if there is no such element.

    @since 5.1 *)

val find_map : ('a -> 'b option) -> 'a array -> 'b option
(** [find_map f a] applies [f] to the elements of [a] in order, and returns the
    first result of the form [Some v], or [None] if none exist.

    @since 4.13 *)

val find_mapi : (int -> 'a -> 'b option) -> 'a array -> 'b option
(** Same as [find_map], but the predicate is applied to the index of
   the element as first argument (counting from 0), and the element
   itself as second argument.

   @since 5.1 *)

(** {1 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 *)

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 *)

(** {1:sorting_and_shuffling Sorting and shuffling} *)

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. *)

val shuffle :
  rand: (* thwart tools/sync_stdlib_docs *) (int -> int) -> 'a array -> unit
(** [shuffle rand a] randomly permutes [a]'s element using [rand] for
    randomness. The distribution of permutations is uniform.

    [rand] must be such that a call to [rand n] returns a uniformly
    distributed random number in the range \[[0];[n-1]\].
    {!Random.int} can be used for this (do not forget to
    {{!Random.self_init}initialize} the generator).

    @since 5.2 *)

(** {1 Arrays and Sequences} *)

val to_seq : 'a array -> 'a Seq.t
(** Iterate on the array, in increasing order. Modifications of the
    array during iteration will be reflected in the sequence.
    @since 4.07 *)

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 *)

(** {1:array_concurrency 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.

    {2:array_atomicity 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}).

    {2:array_data_race 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).

    {2:array_data_race_exceptions 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.
*)

(**/**)

(** {1 Undocumented functions} *)

(* The following is for system use only. Do not call directly. *)

external unsafe_get : 'a array -> int -> 'a = "%array_unsafe_get"
external unsafe_set : 'a array -> int -> 'a -> unit = "%array_unsafe_set"

module Floatarray : sig
  external create : int -> floatarray = "caml_floatarray_create"
  external length : floatarray -> int = "%floatarray_length"
  external get : floatarray -> int -> float = "%floatarray_safe_get"
  external set : floatarray -> int -> float -> unit = "%floatarray_safe_set"
  external unsafe_get : floatarray -> int -> float = "%floatarray_unsafe_get"
  external unsafe_set : floatarray -> int -> float -> unit
      = "%floatarray_unsafe_set"
end