bigarray.mli

(**************************************************************************)
(*                                                                        *)
(*                                 OCaml                                  *)
(*                                                                        *)
(*          Manuel Serrano and Xavier Leroy, INRIA Rocquencourt           *)
(*                                                                        *)
(*   Copyright 2000 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.          *)
(*                                                                        *)
(**************************************************************************)

(** Large, multi-dimensional, numerical arrays.

   This module implements multi-dimensional arrays of integers and
   floating-point numbers, thereafter referred to as 'Bigarrays',
   to distinguish them from the standard OCaml arrays described in
   {!module:Array}.

   The implementation allows efficient sharing of large numerical
   arrays between OCaml code and C or Fortran numerical libraries.

   The main differences between 'Bigarrays' and standard OCaml
   arrays are as follows:
   - Bigarrays are not limited in size, unlike OCaml arrays.
     (Normal float arrays are limited to 2,097,151 elements on a 32-bit
     platform, and normal arrays of other types to 4,194,303 elements.)
   - Bigarrays are multi-dimensional.  Any number of dimensions
     between 0 and 16 is supported.  In contrast, OCaml arrays
     are mono-dimensional and require encoding multi-dimensional
     arrays as arrays of arrays.
   - Bigarrays can only contain integers and floating-point numbers,
     while OCaml arrays can contain arbitrary OCaml data types.
   - Bigarrays provide more space-efficient storage of
     integer and floating-point elements than normal OCaml arrays, in
     particular because they support 'small' types such as
     single-precision floats and 8 and 16-bit integers, in addition to
     the standard OCaml types of double-precision floats and 32 and
     64-bit integers.
   - The memory layout of Bigarrays is entirely compatible with that
     of arrays in C and Fortran, allowing large arrays to be passed
     back and forth between OCaml code and C / Fortran code with no
     data copying at all.
   - Bigarrays support interesting high-level operations that normal
     arrays do not provide efficiently, such as extracting sub-arrays
     and 'slicing' a multi-dimensional array along certain dimensions,
     all without any copying.

   Users of this module are encouraged to do [open Bigarray] in their
   source, then refer to array types and operations via short dot
   notation, e.g. [Array1.t] or [Array2.sub].

   Bigarrays support all the OCaml ad-hoc polymorphic operations:
   - comparisons ([=], [<>], [<=], etc, as well as {!Stdlib.compare});
   - hashing (module [Hash]);
   - and structured input-output (the functions from the
     {!Marshal} module, as well as {!Stdlib.output_value}
     and {!Stdlib.input_value}).
*)

(** {1:elementkinds Element kinds} *)

(** Bigarrays can contain elements of the following kinds:
- IEEE half precision (16 bits) floating-point numbers
   ({!Bigarray.float16_elt}),
- IEEE single precision (32 bits) floating-point numbers
   ({!Bigarray.float32_elt}),
- IEEE double precision (64 bits) floating-point numbers
   ({!Bigarray.float64_elt}),
- IEEE single precision (2 * 32 bits) floating-point complex numbers
   ({!Bigarray.complex32_elt}),
- IEEE double precision (2 * 64 bits) floating-point complex numbers
   ({!Bigarray.complex64_elt}),
- 8-bit integers (signed or unsigned)
   ({!Bigarray.int8_signed_elt} or {!Bigarray.int8_unsigned_elt}),
- 16-bit integers (signed or unsigned)
   ({!Bigarray.int16_signed_elt} or {!Bigarray.int16_unsigned_elt}),
- OCaml integers (signed, 31 bits on 32-bit architectures,
   63 bits on 64-bit architectures) ({!Bigarray.int_elt}),
- 32-bit signed integers ({!Bigarray.int32_elt}),
- 64-bit signed integers ({!Bigarray.int64_elt}),
- platform-native signed integers (32 bits on 32-bit architectures,
   64 bits on 64-bit architectures) ({!Bigarray.nativeint_elt}).

   Each element kind is represented at the type level by one of the
   [*_elt] types defined below (defined with a single constructor instead
   of abstract types for technical injectivity reasons).

   @since 4.07 Moved from otherlibs to stdlib.
   @since 5.2 Added float16_elt element kind.
*)

type float16_elt = Float16_elt
type float32_elt = Float32_elt
type float64_elt = Float64_elt
type int8_signed_elt = Int8_signed_elt
type int8_unsigned_elt = Int8_unsigned_elt
type int16_signed_elt = Int16_signed_elt
type int16_unsigned_elt = Int16_unsigned_elt
type int32_elt = Int32_elt
type int64_elt = Int64_elt
type int_elt = Int_elt
type nativeint_elt = Nativeint_elt
type complex32_elt = Complex32_elt
type complex64_elt = Complex64_elt

type ('a, 'b) kind =
  | Float32 : (float, float32_elt) kind
  | Float64 : (float, float64_elt) kind
  | Int8_signed : (int, int8_signed_elt) kind
  | Int8_unsigned : (int, int8_unsigned_elt) kind
  | Int16_signed : (int, int16_signed_elt) kind
  | Int16_unsigned : (int, int16_unsigned_elt) kind
  | Int32 : (int32, int32_elt) kind
  | Int64 : (int64, int64_elt) kind
  | Int : (int, int_elt) kind
  | Nativeint : (nativeint, nativeint_elt) kind
  | Complex32 : (Complex.t, complex32_elt) kind
  | Complex64 : (Complex.t, complex64_elt) kind
  | Char : (char, int8_unsigned_elt) kind
  | Float16 : (float, float16_elt) kind  (**)
(** To each element kind is associated an OCaml type, which is
   the type of OCaml values that can be stored in the Bigarray
   or read back from it.  This type is not necessarily the same
   as the type of the array elements proper: for instance,
   a Bigarray whose elements are of kind [float32_elt] contains
   32-bit single precision floats, but reading or writing one of
   its elements from OCaml uses the OCaml type [float], which is
   64-bit double precision floats.

   The GADT type [('a, 'b) kind] captures this association
   of an OCaml type ['a] for values read or written in the Bigarray,
   and of an element kind ['b] which represents the actual contents
   of the Bigarray. Its constructors list all possible associations
   of OCaml types with element kinds, and are re-exported below for
   backward-compatibility reasons.

   Using a generalized algebraic datatype (GADT) here allows writing
   well-typed polymorphic functions whose return type depend on the
   argument type, such as:

{[
  let zero : type a b. (a, b) kind -> a = function
    | Float32 -> 0.0 | Complex32 -> Complex.zero
    | Float64 -> 0.0 | Complex64 -> Complex.zero
    | Float16 -> 0.0
    | Int8_signed -> 0 | Int8_unsigned -> 0
    | Int16_signed -> 0 | Int16_unsigned -> 0
    | Int32 -> 0l | Int64 -> 0L
    | Int -> 0 | Nativeint -> 0n
    | Char -> '\000'
]}

   @since 5.2 Constructor Float16 for the GADT.
*)

val float16 : (float, float16_elt) kind
(** See {!Bigarray.char}.
   @since 5.2 *)

val float32 : (float, float32_elt) kind
(** See {!Bigarray.char}. *)

val float64 : (float, float64_elt) kind
(** See {!Bigarray.char}. *)

val complex32 : (Complex.t, complex32_elt) kind
(** See {!Bigarray.char}. *)

val complex64 : (Complex.t, complex64_elt) kind
(** See {!Bigarray.char}. *)

val int8_signed : (int, int8_signed_elt) kind
(** See {!Bigarray.char}. *)

val int8_unsigned : (int, int8_unsigned_elt) kind
(** See {!Bigarray.char}. *)

val int16_signed : (int, int16_signed_elt) kind
(** See {!Bigarray.char}. *)

val int16_unsigned : (int, int16_unsigned_elt) kind
(** See {!Bigarray.char}. *)

val int : (int, int_elt) kind
(** See {!Bigarray.char} and {!section:elementkinds}.

   Beware that this is a bigarray containing OCaml integers
   (signed, 31 bits on 32-bit architectures, 63 bits on 64-bit architectures),
   which does not match the [C] int type.
 *)

val int32 : (int32, int32_elt) kind
(** See {!Bigarray.char}. *)

val int64 : (int64, int64_elt) kind
(** See {!Bigarray.char}. *)

val nativeint : (nativeint, nativeint_elt) kind
(** See {!Bigarray.char}. *)

val char : (char, int8_unsigned_elt) kind
(** As shown by the types of the values above,
   Bigarrays of kind [float16_elt], [float32_elt] and [float64_elt] are
   accessed using the OCaml type [float].  Bigarrays of complex kinds
   [complex32_elt], [complex64_elt] are accessed with the OCaml type
   {!Complex.t}. Bigarrays of
   integer kinds are accessed using the smallest OCaml integer
   type large enough to represent the array elements:
   [int] for 8- and 16-bit integer Bigarrays, as well as OCaml-integer
   Bigarrays; [int32] for 32-bit integer Bigarrays; [int64]
   for 64-bit integer Bigarrays; and [nativeint] for
   platform-native integer Bigarrays.  Finally, Bigarrays of
   kind [int8_unsigned_elt] can also be accessed as arrays of
   characters instead of arrays of small integers, by using
   the kind value [char] instead of [int8_unsigned]. *)

val kind_size_in_bytes : ('a, 'b) kind -> int
(** [kind_size_in_bytes k] is the number of bytes used to store
   an element of type [k].

   @since 4.03 *)

(** {1 Array layouts} *)

type c_layout = C_layout_typ (**)
(** See {!type:Bigarray.fortran_layout}.*)

type fortran_layout = Fortran_layout_typ (**)
(** To facilitate interoperability with existing C and Fortran code,
   this library supports two different memory layouts for Bigarrays,
   one compatible with the C conventions,
   the other compatible with the Fortran conventions.

   In the C-style layout, array indices start at 0, and
   multi-dimensional arrays are laid out in row-major format.
   That is, for a two-dimensional array, all elements of
   row 0 are contiguous in memory, followed by all elements of
   row 1, etc.  In other terms, the array elements at [(x,y)]
   and [(x, y+1)] are adjacent in memory.

   In the Fortran-style layout, array indices start at 1, and
   multi-dimensional arrays are laid out in column-major format.
   That is, for a two-dimensional array, all elements of
   column 0 are contiguous in memory, followed by all elements of
   column 1, etc.  In other terms, the array elements at [(x,y)]
   and [(x+1, y)] are adjacent in memory.

   Each layout style is identified at the type level by the
   phantom types {!type:Bigarray.c_layout} and {!type:Bigarray.fortran_layout}
   respectively. *)

(** {2 Supported layouts}

   The GADT type ['a layout] represents one of the two supported
   memory layouts: C-style or Fortran-style. Its constructors are
   re-exported as values below for backward-compatibility reasons.
*)

type 'a layout =
    C_layout: c_layout layout
  | Fortran_layout: fortran_layout layout

val c_layout : c_layout layout
val fortran_layout : fortran_layout layout


(** {1 Generic arrays (of arbitrarily many dimensions)} *)

module Genarray :
  sig
  type (!'a, !'b, !'c) t
  (** The type [Genarray.t] is the type of Bigarrays with variable
     numbers of dimensions.  Any number of dimensions between 0 and 16
     is supported.

     The three type parameters to [Genarray.t] identify the array element
     kind and layout, as follows:
     - the first parameter, ['a], is the OCaml type for accessing array
       elements ([float], [int], [int32], [int64], [nativeint]);
     - the second parameter, ['b], is the actual kind of array elements
       ([float32_elt], [float64_elt], [int8_signed_elt], [int8_unsigned_elt],
       etc);
     - the third parameter, ['c], identifies the array layout
       ([c_layout] or [fortran_layout]).

     For instance, [(float, float32_elt, fortran_layout) Genarray.t]
     is the type of generic Bigarrays containing 32-bit floats
     in Fortran layout; reads and writes in this array use the
     OCaml type [float]. *)

  external create: ('a, 'b) kind -> 'c layout -> int array -> ('a, 'b, 'c) t
    = "caml_ba_create"
  (** [Genarray.create kind layout dimensions] returns a new Bigarray
     whose element kind is determined by the parameter [kind] (one of
     [float32], [float64], [int8_signed], etc) and whose layout is
     determined by the parameter [layout] (one of [c_layout] or
     [fortran_layout]).  The [dimensions] parameter is an array of
     integers that indicate the size of the Bigarray in each dimension.
     The length of [dimensions] determines the number of dimensions
     of the Bigarray.

     For instance, [Genarray.create int32 c_layout [|4;6;8|]]
     returns a fresh Bigarray of 32-bit integers, in C layout,
     having three dimensions, the three dimensions being 4, 6 and 8
     respectively.

     Bigarrays returned by [Genarray.create] are not initialized:
     the initial values of array elements is unspecified.

     [Genarray.create] raises [Invalid_argument] if the number of dimensions
     is not in the range 0 to 16 inclusive, or if one of the dimensions
     is negative. *)

  val init: ('a, 'b) kind -> 'c layout -> int array -> (int array -> 'a) ->
            ('a, 'b, 'c) t
  (** [Genarray.init kind layout dimensions f] returns a new Bigarray [b]
      whose element kind is determined by the parameter [kind] (one of
      [float32], [float64], [int8_signed], etc) and whose layout is
      determined by the parameter [layout] (one of [c_layout] or
      [fortran_layout]).  The [dimensions] parameter is an array of
      integers that indicate the size of the Bigarray in each dimension.
      The length of [dimensions] determines the number of dimensions
      of the Bigarray.

      Each element [Genarray.get b i] is initialized to the result of [f i].
      In other words, [Genarray.init kind layout dimensions f] tabulates
      the results of [f] applied to the indices of a new Bigarray whose
      layout is described by [kind], [layout] and [dimensions].  The index
      array [i] may be shared and mutated between calls to f.

      For instance, [Genarray.init int c_layout [|2; 1; 3|]
      (Array.fold_left (+) 0)] returns a fresh Bigarray of integers, in C
      layout, having three dimensions (2, 1, 3, respectively), with the
      element values 0, 1, 2, 1, 2, 3.

      [Genarray.init] raises [Invalid_argument] if the number of dimensions
      is not in the range 0 to 16 inclusive, or if one of the dimensions
      is negative.

      @since 4.12 *)

  external num_dims: ('a, 'b, 'c) t -> int = "caml_ba_num_dims"
  (** Return the number of dimensions of the given Bigarray. *)

  val dims : ('a, 'b, 'c) t -> int array
  (** [Genarray.dims a] returns all dimensions of the Bigarray [a],
     as an array of integers of length [Genarray.num_dims a]. *)

  external nth_dim: ('a, 'b, 'c) t -> int -> int = "caml_ba_dim"
  (** [Genarray.nth_dim a n] returns the [n]-th dimension of the
     Bigarray [a].  The first dimension corresponds to [n = 0];
     the second dimension corresponds to [n = 1]; the last dimension,
     to [n = Genarray.num_dims a - 1].
     @raise Invalid_argument if [n] is less than 0 or greater or equal than
     [Genarray.num_dims a]. *)

  external kind: ('a, 'b, 'c) t -> ('a, 'b) kind = "caml_ba_kind"
  (** Return the kind of the given Bigarray. *)

  external layout: ('a, 'b, 'c) t -> 'c layout = "caml_ba_layout"
  (** Return the layout of the given Bigarray. *)

  external change_layout: ('a, 'b, 'c) t -> 'd layout -> ('a, 'b, 'd) t
      = "caml_ba_change_layout"
  (** [Genarray.change_layout a layout] returns a Bigarray with the
      specified [layout], sharing the data with [a] (and hence having
      the same dimensions as [a]). No copying of elements is involved: the
      new array and the original array share the same storage space.
      The dimensions are reversed, such that [get v [| a; b |]] in
      C layout becomes [get v [| b+1; a+1 |]] in Fortran layout.

      @since 4.04
  *)

  val size_in_bytes : ('a, 'b, 'c) t -> int
  (** [size_in_bytes a] is the number of elements in [a] multiplied
    by [a]'s {!kind_size_in_bytes}.

    @since 4.03 *)

  external get: ('a, 'b, 'c) t -> int array -> 'a = "caml_ba_get_generic"
  (** Read an element of a generic Bigarray.
     [Genarray.get a [|i1; ...; iN|]] returns the element of [a]
     whose coordinates are [i1] in the first dimension, [i2] in
     the second dimension, ..., [iN] in the [N]-th dimension.

     If [a] has C layout, the coordinates must be greater or equal than 0
     and strictly less than the corresponding dimensions of [a].
     If [a] has Fortran layout, the coordinates must be greater or equal
     than 1 and less or equal than the corresponding dimensions of [a].

     If [N > 3], alternate syntax is provided: you can write
     [a.{i1, i2, ..., iN}] instead of [Genarray.get a [|i1; ...; iN|]].
     (The syntax [a.{...}] with one, two or three coordinates is
     reserved for accessing one-, two- and three-dimensional arrays
     as described below.)

     @raise Invalid_argument if the array [a] does not have exactly [N]
     dimensions, or if the coordinates are outside the array bounds.
  *)

  external set: ('a, 'b, 'c) t -> int array -> 'a -> unit
    = "caml_ba_set_generic"
  (** Assign an element of a generic Bigarray.
     [Genarray.set a [|i1; ...; iN|] v] stores the value [v] in the
     element of [a] whose coordinates are [i1] in the first dimension,
     [i2] in the second dimension, ..., [iN] in the [N]-th dimension.

     The array [a] must have exactly [N] dimensions, and all coordinates
     must lie inside the array bounds, as described for [Genarray.get];
     otherwise, [Invalid_argument] is raised.

     If [N > 3], alternate syntax is provided: you can write
     [a.{i1, i2, ..., iN} <- v] instead of
     [Genarray.set a [|i1; ...; iN|] v].
     (The syntax [a.{...} <- v] with one, two or three coordinates is
     reserved for updating one-, two- and three-dimensional arrays
     as described below.) *)

  external sub_left: ('a, 'b, c_layout) t -> int -> int -> ('a, 'b, c_layout) t
    = "caml_ba_sub"
  (** Extract a sub-array of the given Bigarray by restricting the
     first (left-most) dimension.  [Genarray.sub_left a ofs len]
     returns a Bigarray with the same number of dimensions as [a],
     and the same dimensions as [a], except the first dimension,
     which corresponds to the interval [[ofs ... ofs + len - 1]]
     of the first dimension of [a].  No copying of elements is
     involved: the sub-array and the original array share the same
     storage space.  In other terms, the element at coordinates
     [[|i1; ...; iN|]] of the sub-array is identical to the
     element at coordinates [[|i1+ofs; ...; iN|]] of the original
     array [a].

     [Genarray.sub_left] applies only to Bigarrays in C layout.
     @raise Invalid_argument if [ofs] and [len] do not designate
     a valid sub-array of [a], that is, if [ofs < 0], or [len < 0],
     or [ofs + len > Genarray.nth_dim a 0]. *)

  external sub_right:
    ('a, 'b, fortran_layout) t -> int -> int -> ('a, 'b, fortran_layout) t
    = "caml_ba_sub"
  (** Extract a sub-array of the given Bigarray by restricting the
     last (right-most) dimension.  [Genarray.sub_right a ofs len]
     returns a Bigarray with the same number of dimensions as [a],
     and the same dimensions as [a], except the last dimension,
     which corresponds to the interval [[ofs ... ofs + len - 1]]
     of the last dimension of [a].  No copying of elements is
     involved: the sub-array and the original array share the same
     storage space.  In other terms, the element at coordinates
     [[|i1; ...; iN|]] of the sub-array is identical to the
     element at coordinates [[|i1; ...; iN+ofs|]] of the original
     array [a].

     [Genarray.sub_right] applies only to Bigarrays in Fortran layout.
     @raise Invalid_argument if [ofs] and [len] do not designate
     a valid sub-array of [a], that is, if [ofs < 1], or [len < 0],
     or [ofs + len > Genarray.nth_dim a (Genarray.num_dims a - 1)]. *)

  external slice_left:
    ('a, 'b, c_layout) t -> int array -> ('a, 'b, c_layout) t
    = "caml_ba_slice"
  (** Extract a sub-array of lower dimension from the given Bigarray
     by fixing one or several of the first (left-most) coordinates.
     [Genarray.slice_left a [|i1; ... ; iM|]] returns the 'slice'
     of [a] obtained by setting the first [M] coordinates to
     [i1], ..., [iM].  If [a] has [N] dimensions, the slice has
     dimension [N - M], and the element at coordinates
     [[|j1; ...; j(N-M)|]] in the slice is identical to the element
     at coordinates [[|i1; ...; iM; j1; ...; j(N-M)|]] in the original
     array [a].  No copying of elements is involved: the slice and
     the original array share the same storage space.

     [Genarray.slice_left] applies only to Bigarrays in C layout.
     @raise Invalid_argument if [M >= N], or if [[|i1; ... ; iM|]]
     is outside the bounds of [a]. *)

  external slice_right:
    ('a, 'b, fortran_layout) t -> int array -> ('a, 'b, fortran_layout) t
    = "caml_ba_slice"
  (** Extract a sub-array of lower dimension from the given Bigarray
     by fixing one or several of the last (right-most) coordinates.
     [Genarray.slice_right a [|i1; ... ; iM|]] returns the 'slice'
     of [a] obtained by setting the last [M] coordinates to
     [i1], ..., [iM].  If [a] has [N] dimensions, the slice has
     dimension [N - M], and the element at coordinates
     [[|j1; ...; j(N-M)|]] in the slice is identical to the element
     at coordinates [[|j1; ...; j(N-M); i1; ...; iM|]] in the original
     array [a].  No copying of elements is involved: the slice and
     the original array share the same storage space.

     [Genarray.slice_right] applies only to Bigarrays in Fortran layout.
     @raise Invalid_argument if [M >= N], or if [[|i1; ... ; iM|]]
     is outside the bounds of [a]. *)

  external blit: ('a, 'b, 'c) t -> ('a, 'b, 'c) t -> unit
      = "caml_ba_blit"
  (** Copy all elements of a Bigarray in another Bigarray.
     [Genarray.blit src dst] copies all elements of [src] into
     [dst].  Both arrays [src] and [dst] must have the same number of
     dimensions and equal dimensions.  Copying a sub-array of [src]
     to a sub-array of [dst] can be achieved by applying [Genarray.blit]
     to sub-array or slices of [src] and [dst]. *)

  external fill: ('a, 'b, 'c) t -> 'a -> unit = "caml_ba_fill"
  (** Set all elements of a Bigarray to a given value.
     [Genarray.fill a v] stores the value [v] in all elements of
     the Bigarray [a].  Setting only some elements of [a] to [v]
     can be achieved by applying [Genarray.fill] to a sub-array
     or a slice of [a]. *)
  end

(** {1 Zero-dimensional arrays} *)

(** Zero-dimensional arrays. The [Array0] structure provides operations
   similar to those of {!Bigarray.Genarray}, but specialized to the case
   of zero-dimensional arrays that only contain a single scalar value.
   Statically knowing the number of dimensions of the array allows
   faster operations, and more precise static type-checking.
   @since 4.05 *)
module Array0 : sig
  type (!'a, !'b, !'c) t
  (** The type of zero-dimensional Bigarrays whose elements have
     OCaml type ['a], representation kind ['b], and memory layout ['c]. *)

  val create: ('a, 'b) kind -> 'c layout -> ('a, 'b, 'c) t
  (** [Array0.create kind layout] returns a new Bigarray of zero dimension.
     [kind] and [layout] determine the array element kind and the array
     layout as described for {!Genarray.create}. *)

  val init: ('a, 'b) kind -> 'c layout -> 'a -> ('a, 'b, 'c) t
  (** [Array0.init kind layout v] behaves like [Array0.create kind layout]
     except that the element is additionally initialized to the value [v].

     @since 4.12 *)

  external kind: ('a, 'b, 'c) t -> ('a, 'b) kind = "caml_ba_kind"
  (** Return the kind of the given Bigarray. *)

  external layout: ('a, 'b, 'c) t -> 'c layout = "caml_ba_layout"
  (** Return the layout of the given Bigarray. *)

  val change_layout: ('a, 'b, 'c) t -> 'd layout -> ('a, 'b, 'd) t
  (** [Array0.change_layout a layout] returns a Bigarray with the
      specified [layout], sharing the data with [a]. No copying of elements
      is involved: the new array and the original array share the same
      storage space.

      @since 4.06
  *)

  val size_in_bytes : ('a, 'b, 'c) t -> int
  (** [size_in_bytes a] is [a]'s {!kind_size_in_bytes}. *)

  val get: ('a, 'b, 'c) t -> 'a
  (** [Array0.get a] returns the only element in [a]. *)

  val set: ('a, 'b, 'c) t -> 'a -> unit
  (** [Array0.set a x v] stores the value [v] in [a]. *)

  external blit: ('a, 'b, 'c) t -> ('a, 'b, 'c) t -> unit = "caml_ba_blit"
  (** Copy the first Bigarray to the second Bigarray.
     See {!Genarray.blit} for more details. *)

  external fill: ('a, 'b, 'c) t -> 'a -> unit = "caml_ba_fill"
  (** Fill the given Bigarray with the given value.
     See {!Genarray.fill} for more details. *)

  val of_value: ('a, 'b) kind -> 'c layout -> 'a -> ('a, 'b, 'c) t
  (** Build a zero-dimensional Bigarray initialized from the
     given value.  *)

end


(** {1 One-dimensional arrays} *)

(** One-dimensional arrays. The [Array1] structure provides operations
   similar to those of
   {!Bigarray.Genarray}, but specialized to the case of one-dimensional arrays.
   (The {!Array2} and {!Array3} structures below provide operations
   specialized for two- and three-dimensional arrays.)
   Statically knowing the number of dimensions of the array allows
   faster operations, and more precise static type-checking. *)
module Array1 : sig
  type (!'a, !'b, !'c) t
  (** The type of one-dimensional Bigarrays whose elements have
     OCaml type ['a], representation kind ['b], and memory layout ['c]. *)

  val create: ('a, 'b) kind -> 'c layout -> int -> ('a, 'b, 'c) t
  (** [Array1.create kind layout dim] returns a new Bigarray of
     one dimension, whose size is [dim].  [kind] and [layout]
     determine the array element kind and the array layout
     as described for {!Genarray.create}. *)

  val init: ('a, 'b) kind -> 'c layout -> int -> (int -> 'a) ->
            ('a, 'b, 'c) t
  (** [Array1.init kind layout dim f] returns a new Bigarray [b]
     of one dimension, whose size is [dim].  [kind] and [layout]
     determine the array element kind and the array layout
     as described for {!Genarray.create}.

     Each element [Array1.get b i] of the array is initialized to the
     result of [f i].

     In other words, [Array1.init kind layout dimensions f] tabulates
     the results of [f] applied to the indices of a new Bigarray whose
     layout is described by [kind], [layout] and [dim].

     @since 4.12 *)

  external dim: ('a, 'b, 'c) t -> int = "%caml_ba_dim_1"
  (** Return the size (dimension) of the given one-dimensional
     Bigarray. *)

  external kind: ('a, 'b, 'c) t -> ('a, 'b) kind = "caml_ba_kind"
  (** Return the kind of the given Bigarray. *)

  external layout: ('a, 'b, 'c) t -> 'c layout = "caml_ba_layout"
  (** Return the layout of the given Bigarray. *)

  val change_layout: ('a, 'b, 'c) t -> 'd layout -> ('a, 'b, 'd) t
  (** [Array1.change_layout a layout] returns a Bigarray with the
      specified [layout], sharing the data with [a] (and hence having
      the same dimension as [a]). No copying of elements is involved: the
      new array and the original array share the same storage space.

      @since 4.06
  *)


  val size_in_bytes : ('a, 'b, 'c) t -> int
  (** [size_in_bytes a] is the number of elements in [a]
    multiplied by [a]'s {!kind_size_in_bytes}.

    @since 4.03 *)

  external get: ('a, 'b, 'c) t -> int -> 'a = "%caml_ba_ref_1"
  (** [Array1.get a x], or alternatively [a.{x}],
     returns the element of [a] at index [x].
     [x] must be greater or equal than [0] and strictly less than
     [Array1.dim a] if [a] has C layout.  If [a] has Fortran layout,
     [x] must be greater or equal than [1] and less or equal than
     [Array1.dim a].  Otherwise, [Invalid_argument] is raised. *)

  external set: ('a, 'b, 'c) t -> int -> 'a -> unit = "%caml_ba_set_1"
  (** [Array1.set a x v], also written [a.{x} <- v],
     stores the value [v] at index [x] in [a].
     [x] must be inside the bounds of [a] as described in
     {!Bigarray.Array1.get};
     otherwise, [Invalid_argument] is raised. *)

  external sub: ('a, 'b, 'c) t -> int -> int -> ('a, 'b, 'c) t
      = "caml_ba_sub"
  (** Extract a sub-array of the given one-dimensional Bigarray.
     See {!Genarray.sub_left} for more details. *)

  val slice: ('a, 'b, 'c) t -> int -> ('a, 'b, 'c) Array0.t
  (** Extract a scalar (zero-dimensional slice) of the given one-dimensional
     Bigarray.  The integer parameter is the index of the scalar to
     extract.  See {!Bigarray.Genarray.slice_left} and
     {!Bigarray.Genarray.slice_right} for more details.
     @since 4.05 *)

  external blit: ('a, 'b, 'c) t -> ('a, 'b, 'c) t -> unit
      = "caml_ba_blit"
  (** Copy the first Bigarray to the second Bigarray.
     See {!Genarray.blit} for more details. *)

  external fill: ('a, 'b, 'c) t -> 'a -> unit = "caml_ba_fill"
  (** Fill the given Bigarray with the given value.
     See {!Genarray.fill} for more details. *)

  val of_array: ('a, 'b) kind -> 'c layout -> 'a array -> ('a, 'b, 'c) t
  (** Build a one-dimensional Bigarray initialized from the
     given array.  *)

  external unsafe_get: ('a, 'b, 'c) t -> int -> 'a = "%caml_ba_unsafe_ref_1"
  (** Like {!Bigarray.Array1.get}, but bounds checking is not always performed.
      Use with caution and only when the program logic guarantees that
      the access is within bounds. *)

  external unsafe_set: ('a, 'b, 'c) t -> int -> 'a -> unit
                     = "%caml_ba_unsafe_set_1"
  (** Like {!Bigarray.Array1.set}, but bounds checking is not always performed.
      Use with caution and only when the program logic guarantees that
      the access is within bounds. *)

end


(** {1 Two-dimensional arrays} *)

(** Two-dimensional arrays. The [Array2] structure provides operations
   similar to those of {!Bigarray.Genarray}, but specialized to the
   case of two-dimensional arrays. *)
module Array2 :
  sig
  type (!'a, !'b, !'c) t
  (** The type of two-dimensional Bigarrays whose elements have
     OCaml type ['a], representation kind ['b], and memory layout ['c]. *)

  val create: ('a, 'b) kind ->  'c layout -> int -> int -> ('a, 'b, 'c) t
  (** [Array2.create kind layout dim1 dim2] returns a new Bigarray of
     two dimensions, whose size is [dim1] in the first dimension
     and [dim2] in the second dimension.  [kind] and [layout]
     determine the array element kind and the array layout
     as described for {!Bigarray.Genarray.create}. *)

  val init: ('a, 'b) kind ->  'c layout -> int -> int ->
            (int -> int -> 'a) -> ('a, 'b, 'c) t
  (** [Array2.init kind layout dim1 dim2 f] returns a new Bigarray [b]
     of two dimensions, whose size is [dim2] in the first dimension
     and [dim2] in the second dimension.  [kind] and [layout]
     determine the array element kind and the array layout
     as described for {!Bigarray.Genarray.create}.

     Each element [Array2.get b i j] of the array is initialized to
     the result of [f i j].

     In other words, [Array2.init kind layout dim1 dim2 f] tabulates
     the results of [f] applied to the indices of a new Bigarray whose
     layout is described by [kind], [layout], [dim1] and [dim2].

     @since 4.12 *)

  external dim1: ('a, 'b, 'c) t -> int = "%caml_ba_dim_1"
  (** Return the first dimension of the given two-dimensional Bigarray. *)

  external dim2: ('a, 'b, 'c) t -> int = "%caml_ba_dim_2"
  (** Return the second dimension of the given two-dimensional Bigarray. *)

  external kind: ('a, 'b, 'c) t -> ('a, 'b) kind = "caml_ba_kind"
  (** Return the kind of the given Bigarray. *)

  external layout: ('a, 'b, 'c) t -> 'c layout = "caml_ba_layout"
  (** Return the layout of the given Bigarray. *)

  val change_layout: ('a, 'b, 'c) t -> 'd layout -> ('a, 'b, 'd) t
  (** [Array2.change_layout a layout] returns a Bigarray with the
      specified [layout], sharing the data with [a] (and hence having
      the same dimensions as [a]). No copying of elements is involved: the
      new array and the original array share the same storage space.
      The dimensions are reversed, such that [get v [| a; b |]] in
      C layout becomes [get v [| b+1; a+1 |]] in Fortran layout.

      @since 4.06
  *)


  val size_in_bytes : ('a, 'b, 'c) t -> int
  (** [size_in_bytes a] is the number of elements in [a]
    multiplied by [a]'s {!kind_size_in_bytes}.

    @since 4.03 *)

  external get: ('a, 'b, 'c) t -> int -> int -> 'a = "%caml_ba_ref_2"
  (** [Array2.get a x y], also written [a.{x,y}],
     returns the element of [a] at coordinates ([x], [y]).
     [x] and [y] must be within the bounds
     of [a], as described for {!Bigarray.Genarray.get};
     otherwise, [Invalid_argument] is raised. *)

  external set: ('a, 'b, 'c) t -> int -> int -> 'a -> unit = "%caml_ba_set_2"
  (** [Array2.set a x y v], or alternatively [a.{x,y} <- v],
     stores the value [v] at coordinates ([x], [y]) in [a].
     [x] and [y] must be within the bounds of [a],
     as described for {!Bigarray.Genarray.set};
     otherwise, [Invalid_argument] is raised. *)

  external sub_left: ('a, 'b, c_layout) t -> int -> int -> ('a, 'b, c_layout) t
    = "caml_ba_sub"
  (** Extract a two-dimensional sub-array of the given two-dimensional
     Bigarray by restricting the first dimension.
     See {!Bigarray.Genarray.sub_left} for more details.
     [Array2.sub_left] applies only to arrays with C layout. *)

  external sub_right:
    ('a, 'b, fortran_layout) t -> int -> int -> ('a, 'b, fortran_layout) t
    = "caml_ba_sub"
  (** Extract a two-dimensional sub-array of the given two-dimensional
     Bigarray by restricting the second dimension.
     See {!Bigarray.Genarray.sub_right} for more details.
     [Array2.sub_right] applies only to arrays with Fortran layout. *)

  val slice_left: ('a, 'b, c_layout) t -> int -> ('a, 'b, c_layout) Array1.t
  (** Extract a row (one-dimensional slice) of the given two-dimensional
     Bigarray.  The integer parameter is the index of the row to
     extract.  See {!Bigarray.Genarray.slice_left} for more details.
     [Array2.slice_left] applies only to arrays with C layout. *)

  val slice_right:
    ('a, 'b, fortran_layout) t -> int -> ('a, 'b, fortran_layout) Array1.t
  (** Extract a column (one-dimensional slice) of the given
     two-dimensional Bigarray.  The integer parameter is the
     index of the column to extract.  See {!Bigarray.Genarray.slice_right}
     for more details.  [Array2.slice_right] applies only to arrays
     with Fortran layout. *)

  external blit: ('a, 'b, 'c) t -> ('a, 'b, 'c) t -> unit
    = "caml_ba_blit"
  (** Copy the first Bigarray to the second Bigarray.
     See {!Bigarray.Genarray.blit} for more details. *)

  external fill: ('a, 'b, 'c) t -> 'a -> unit = "caml_ba_fill"
  (** Fill the given Bigarray with the given value.
     See {!Bigarray.Genarray.fill} for more details. *)

  val of_array: ('a, 'b) kind -> 'c layout -> 'a array array -> ('a, 'b, 'c) t
  (** Build a two-dimensional Bigarray initialized from the
     given array of arrays.  *)

  external unsafe_get: ('a, 'b, 'c) t -> int -> int -> 'a
                     = "%caml_ba_unsafe_ref_2"
  (** Like {!Bigarray.Array2.get}, but bounds checking is not always
      performed. *)

  external unsafe_set: ('a, 'b, 'c) t -> int -> int -> 'a -> unit
                     = "%caml_ba_unsafe_set_2"
  (** Like {!Bigarray.Array2.set}, but bounds checking is not always
      performed. *)

end

(** {1 Three-dimensional arrays} *)

(** Three-dimensional arrays. The [Array3] structure provides operations
   similar to those of {!Bigarray.Genarray}, but specialized to the case
   of three-dimensional arrays. *)
module Array3 :
  sig
  type (!'a, !'b, !'c) t
  (** The type of three-dimensional Bigarrays whose elements have
     OCaml type ['a], representation kind ['b], and memory layout ['c]. *)

  val create: ('a, 'b) kind -> 'c layout -> int -> int -> int -> ('a, 'b, 'c) t
  (** [Array3.create kind layout dim1 dim2 dim3] returns a new Bigarray of
     three dimensions, whose size is [dim1] in the first dimension,
     [dim2] in the second dimension, and [dim3] in the third.
     [kind] and [layout] determine the array element kind and
     the array layout as described for {!Bigarray.Genarray.create}. *)

  val init: ('a, 'b) kind ->  'c layout -> int -> int -> int ->
            (int -> int -> int -> 'a) -> ('a, 'b, 'c) t
  (** [Array3.init kind layout dim1 dim2 dim3 f] returns a new Bigarray [b]
     of three dimensions, whose size is [dim1] in the first dimension,
     [dim2] in the second dimension, and [dim3] in the third.
     [kind] and [layout] determine the array element kind and the array
     layout as described for {!Bigarray.Genarray.create}.

     Each element [Array3.get b i j k] of the array is initialized to
     the result of [f i j k].

     In other words, [Array3.init kind layout dim1 dim2 dim3 f] tabulates
     the results of [f] applied to the indices of a new Bigarray whose
     layout is described by [kind], [layout], [dim1], [dim2] and [dim3].

     @since 4.12 *)

  external dim1: ('a, 'b, 'c) t -> int = "%caml_ba_dim_1"
  (** Return the first dimension of the given three-dimensional Bigarray. *)

  external dim2: ('a, 'b, 'c) t -> int = "%caml_ba_dim_2"
  (** Return the second dimension of the given three-dimensional Bigarray. *)

  external dim3: ('a, 'b, 'c) t -> int = "%caml_ba_dim_3"
  (** Return the third dimension of the given three-dimensional Bigarray. *)

  external kind: ('a, 'b, 'c) t -> ('a, 'b) kind = "caml_ba_kind"
  (** Return the kind of the given Bigarray. *)

  external layout: ('a, 'b, 'c) t -> 'c layout = "caml_ba_layout"
  (** Return the layout of the given Bigarray. *)


  val change_layout: ('a, 'b, 'c) t -> 'd layout -> ('a, 'b, 'd) t
  (** [Array3.change_layout a layout] returns a Bigarray with the
      specified [layout], sharing the data with [a] (and hence having
      the same dimensions as [a]). No copying of elements is involved: the
      new array and the original array share the same storage space.
      The dimensions are reversed, such that [get v [| a; b; c |]] in
      C layout becomes [get v [| c+1; b+1; a+1 |]] in Fortran layout.

      @since 4.06
  *)

  val size_in_bytes : ('a, 'b, 'c) t -> int
  (** [size_in_bytes a] is the number of elements in [a]
    multiplied by [a]'s {!kind_size_in_bytes}.

    @since 4.03 *)

  external get: ('a, 'b, 'c) t -> int -> int -> int -> 'a = "%caml_ba_ref_3"
  (** [Array3.get a x y z], also written [a.{x,y,z}],
     returns the element of [a] at coordinates ([x], [y], [z]).
     [x], [y] and [z] must be within the bounds of [a],
     as described for {!Bigarray.Genarray.get};
     otherwise, [Invalid_argument] is raised. *)

  external set: ('a, 'b, 'c) t -> int -> int -> int -> 'a -> unit
    = "%caml_ba_set_3"
  (** [Array3.set a x y v], or alternatively [a.{x,y,z} <- v],
     stores the value [v] at coordinates ([x], [y], [z]) in [a].
     [x], [y] and [z] must be within the bounds of [a],
     as described for {!Bigarray.Genarray.set};
     otherwise, [Invalid_argument] is raised. *)

  external sub_left: ('a, 'b, c_layout) t -> int -> int -> ('a, 'b, c_layout) t
    = "caml_ba_sub"
  (** Extract a three-dimensional sub-array of the given
     three-dimensional Bigarray by restricting the first dimension.
     See {!Bigarray.Genarray.sub_left} for more details.  [Array3.sub_left]
     applies only to arrays with C layout. *)

  external sub_right:
    ('a, 'b, fortran_layout) t -> int -> int -> ('a, 'b, fortran_layout) t
    = "caml_ba_sub"
  (** Extract a three-dimensional sub-array of the given
     three-dimensional Bigarray by restricting the second dimension.
     See {!Bigarray.Genarray.sub_right} for more details.  [Array3.sub_right]
     applies only to arrays with Fortran layout. *)

  val slice_left_1:
    ('a, 'b, c_layout) t -> int -> int -> ('a, 'b, c_layout) Array1.t
  (** Extract a one-dimensional slice of the given three-dimensional
     Bigarray by fixing the first two coordinates.
     The integer parameters are the coordinates of the slice to
     extract.  See {!Bigarray.Genarray.slice_left} for more details.
     [Array3.slice_left_1] applies only to arrays with C layout. *)

  val slice_right_1:
    ('a, 'b, fortran_layout) t ->
    int -> int -> ('a, 'b, fortran_layout) Array1.t
  (** Extract a one-dimensional slice of the given three-dimensional
     Bigarray by fixing the last two coordinates.
     The integer parameters are the coordinates of the slice to
     extract.  See {!Bigarray.Genarray.slice_right} for more details.
     [Array3.slice_right_1] applies only to arrays with Fortran
     layout. *)

  val slice_left_2: ('a, 'b, c_layout) t -> int -> ('a, 'b, c_layout) Array2.t
  (** Extract a  two-dimensional slice of the given three-dimensional
     Bigarray by fixing the first coordinate.
     The integer parameter is the first coordinate of the slice to
     extract.  See {!Bigarray.Genarray.slice_left} for more details.
     [Array3.slice_left_2] applies only to arrays with C layout. *)

  val slice_right_2:
    ('a, 'b, fortran_layout) t -> int -> ('a, 'b, fortran_layout) Array2.t
  (** Extract a two-dimensional slice of the given
     three-dimensional Bigarray by fixing the last coordinate.
     The integer parameter is the coordinate of the slice
     to extract.  See {!Bigarray.Genarray.slice_right} for more details.
     [Array3.slice_right_2] applies only to arrays with Fortran
     layout. *)

  external blit: ('a, 'b, 'c) t -> ('a, 'b, 'c) t -> unit
    = "caml_ba_blit"
  (** Copy the first Bigarray to the second Bigarray.
     See {!Bigarray.Genarray.blit} for more details. *)

  external fill: ('a, 'b, 'c) t -> 'a -> unit = "caml_ba_fill"
  (** Fill the given Bigarray with the given value.
     See {!Bigarray.Genarray.fill} for more details. *)

  val of_array:
    ('a, 'b) kind -> 'c layout -> 'a array array array -> ('a, 'b, 'c) t
  (** Build a three-dimensional Bigarray initialized from the
     given array of arrays of arrays.  *)

  external unsafe_get: ('a, 'b, 'c) t -> int -> int -> int -> 'a
                     = "%caml_ba_unsafe_ref_3"
  (** Like {!Bigarray.Array3.get}, but bounds checking is not always
      performed. *)

  external unsafe_set: ('a, 'b, 'c) t -> int -> int -> int -> 'a -> unit
                     = "%caml_ba_unsafe_set_3"
  (** Like {!Bigarray.Array3.set}, but bounds checking is not always
      performed. *)

end

(** {1 Coercions between generic Bigarrays and fixed-dimension Bigarrays} *)

external genarray_of_array0 :
  ('a, 'b, 'c) Array0.t -> ('a, 'b, 'c) Genarray.t = "%identity"
(** Return the generic Bigarray corresponding to the given zero-dimensional
    Bigarray.
    @since 4.05 *)

external genarray_of_array1 :
  ('a, 'b, 'c) Array1.t -> ('a, 'b, 'c) Genarray.t = "%identity"
(** Return the generic Bigarray corresponding to the given one-dimensional
   Bigarray. *)

external genarray_of_array2 :
  ('a, 'b, 'c) Array2.t -> ('a, 'b, 'c) Genarray.t = "%identity"
(** Return the generic Bigarray corresponding to the given two-dimensional
   Bigarray. *)

external genarray_of_array3 :
  ('a, 'b, 'c) Array3.t -> ('a, 'b, 'c) Genarray.t = "%identity"
(** Return the generic Bigarray corresponding to the given three-dimensional
   Bigarray. *)

val array0_of_genarray : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array0.t
(** Return the zero-dimensional Bigarray corresponding to the given
   generic Bigarray.
   @raise Invalid_argument if the generic Bigarray
   does not have exactly zero dimension.
   @since 4.05 *)

val array1_of_genarray : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array1.t
(** Return the one-dimensional Bigarray corresponding to the given
   generic Bigarray.
   @raise Invalid_argument if the generic Bigarray
   does not have exactly one dimension. *)

val array2_of_genarray : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array2.t
(** Return the two-dimensional Bigarray corresponding to the given
   generic Bigarray.
   @raise Invalid_argument if the generic Bigarray
   does not have exactly two dimensions. *)

val array3_of_genarray : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array3.t
(** Return the three-dimensional Bigarray corresponding to the given
   generic Bigarray.
   @raise Invalid_argument if the generic Bigarray
   does not have exactly three dimensions. *)


(** {1 Re-shaping Bigarrays} *)

val reshape : ('a, 'b, 'c) Genarray.t -> int array -> ('a, 'b, 'c) Genarray.t
(** [reshape b [|d1;...;dN|]] converts the Bigarray [b] to a
   [N]-dimensional array of dimensions [d1]...[dN].  The returned
   array and the original array [b] share their data
   and have the same layout.  For instance, assuming that [b]
   is a one-dimensional array of dimension 12, [reshape b [|3;4|]]
   returns a two-dimensional array [b'] of dimensions 3 and 4.
   If [b] has C layout, the element [(x,y)] of [b'] corresponds
   to the element [x * 3 + y] of [b].  If [b] has Fortran layout,
   the element [(x,y)] of [b'] corresponds to the element
   [x + (y - 1) * 4] of [b].
   The returned Bigarray must have exactly the same number of
   elements as the original Bigarray [b].  That is, the product
   of the dimensions of [b] must be equal to [i1 * ... * iN].
   Otherwise, [Invalid_argument] is raised. *)

val reshape_0 : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array0.t
(** Specialized version of {!Bigarray.reshape} for reshaping to
   zero-dimensional arrays.
   @since 4.05 *)

val reshape_1 : ('a, 'b, 'c) Genarray.t -> int -> ('a, 'b, 'c) Array1.t
(** Specialized version of {!Bigarray.reshape} for reshaping to
   one-dimensional arrays. *)

val reshape_2 : ('a, 'b, 'c) Genarray.t -> int -> int -> ('a, 'b, 'c) Array2.t
(** Specialized version of {!Bigarray.reshape} for reshaping to
   two-dimensional arrays. *)

val reshape_3 :
  ('a, 'b, 'c) Genarray.t -> int -> int -> int -> ('a, 'b, 'c) Array3.t
(** Specialized version of {!Bigarray.reshape} for reshaping to
    three-dimensional arrays. *)

(** {1:bigarray_concurrency Bigarrays and concurrency safety}

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

    {2:bigarray_atomicity Atomicity}

    Every bigarray operation that accesses more than one array element is not
    atomic. This includes slicing, bliting, and filling bigarrays.

    For example, consider the following program:
{[open Bigarray
let size = 100_000_000
let a = Array1.init Int C_layout size (fun _ -> 1)
let update f a () =
  for i = 0 to size - 1 do a.{i} <- f a.{i} done
let d1 = Domain.spawn (update (fun x -> x + 1) a)
let d2 = Domain.spawn (update (fun x -> 2 * x + 1) a)
let () = Domain.join d1; Domain.join d2
]}

    After executing this code, each field of the bigarray [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:bigarray_data_race Data races}

    If two domains only access disjoint parts of the bigarray, 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 bigarray
    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 bigarray 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.

    {2:bigarrarray_data_race_tearing Tearing}

    Bigarrays have a distinct caveat in the presence of data races:
    concurrent bigarray operations might produce surprising values due to
    tearing. More precisely, the interleaving of partial writes and reads might
    create values that would not exist with a sequential execution.
    For instance, at the end of
{[let res = Array1.init Complex64 c_layout size (fun _ -> Complex.zero)
let d1 = Domain.spawn (fun () -> Array1.fill res Complex.one)
let d2 = Domain.spawn (fun () -> Array1.fill res Complex.i)
let () = Domain.join d1; Domain.join d2
]}
    the [res] bigarray might contain values that are neither [Complex.i]
    nor [Complex.one] (for instance [1 + i]).
*)