Chapter 28 | The bigarray library

The `bigarray` library implements large, multi-dimensional, numerical arrays. These arrays are called ``big arrays'' to distinguish them from the standard Caml arrays described in section 19.2. The main differences between ``big arrays'' and standard Caml arrays are as follows:

- Big arrays are not limited in size, unlike Caml arrays (`float array` are limited to 2097151 elements on a 32-bit platform, other `array` types to 4194303 elements).
- Big arrays are multi-dimensional. Any number of dimensions between 1 and 16 is supported. In contrast, Caml arrays are mono-dimensional and require encoding multi-dimensional arrays as arrays of arrays.
- Big arrays can only contain integers and floating-point numbers, while Caml arrays can contain arbitrary Caml data types. However, big arrays provide more space-efficient storage of integer and floating-point elements, in particular because they support ``small'' types such as single-precision floats and 8 and 16-bit integers, in addition to the standard Caml types of double-precision floats and 32 and 64-bit integers.
- The memory layout of big arrays is entirely compatible with that of arrays in C and Fortran, allowing large arrays to be passed back and forth between Caml code and C / Fortran code with no data copying at all.
- Big arrays 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.

Programs that use the `bigarray` library must be linked as follows:

            ocamlc other options bigarray.cma other files
            ocamlopt other options bigarray.cmxa other files

For interactive use of the `bigarray` library, do:

            ocamlmktop -o mytop bigarray.cma
            ./mytop

28.1 | Module `Bigarray`: large, multi-dimensional, numerical arrays

> This module implements multi-dimensional arrays of integers and floating-point numbers, thereafter referred to as ``big arrays''. The implementation allows efficient sharing of large numerical arrays between Caml code and C or Fortran numerical libraries.
> Concerning the naming conventions, 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`.
> Big arrays support all the Caml ad-hoc polymorphic operations: comparisons (`=`, `<>`, `<=`, etc, as well as `compare`); hashing (module `Hash`); and structured input-output (`output_value` and `input_value`, as well as the functions from the `Marshal` module).

Element kinds

    type float32_elt
    type float64_elt
    type int8_signed_elt
    type int8_unsigned_elt
    type int16_signed_elt
    type int16_unsigned_elt
    type int_elt
    type int32_elt
    type int64_elt
    type nativeint_elt

> Big arrays can contain elements of the following kinds:
> IEEE single precision (32 bits) floating-point numbers;
> IEEE double precision (64 bits) floating-point numbers;
> 8-bit integers (signed or unsigned);
> 16-bit integers (signed or unsigned);
> Caml integers (signed, 31 bits on 32-bit architectures, 63 bits on 64-bit architectures);
> 32-bit signed integers;
> 64-bit signed integers;
> platform-native signed integers (32 bits on 32-bit architectures, 64 bits on 64-bit architectures).
> Each element kind is represented at the type level by one of the abstract types defined above.

    type ('a, 'b) kind

> To each element kind is associated a Caml type, which is the type of Caml values that can be stored in the big array or read back from it. This type is not necessarily the same as the type of the array elements proper: for instance, a big array whose elements are of kind `float32_elt` contains 32-bit single precision floats, but reading or writing one of its elements from Caml uses the Caml type `float`, which is 64-bit double precision floats.
> The abstract type `('a, 'b) kind` captures this association of a Caml type `'a` for values read or written in the big array, and of an element kind `'b` which represents the actual contents of the big array. The following predefined values of type `kind` list all possible associations of Caml types with element kinds:

    val float32: (float, float32_elt) kind
    val float64: (float, float64_elt) kind
    val int8_signed: (int, int8_signed_elt) kind
    val int8_unsigned: (int, int8_unsigned_elt) kind
    val int16_signed: (int, int16_signed_elt) kind
    val int16_unsigned: (int, int16_unsigned_elt) kind
    val int: (int, int_elt) kind
    val int32: (int32, int32_elt) kind
    val int64: (int64, int64_elt) kind
    val nativeint: (nativeint, nativeint_elt) kind
    val char: (char, int8_unsigned_elt) kind

> As shown by the types of the values above, big arrays of kind `float32_elt` and `float64_elt` are accessed using the Caml type `float`. Big arrays of integer kinds are accessed using the smallest Caml integer type large enough to represent the array elements: `int` for 8- and 16-bit integer bigarrays, as well as Caml-integer bigarrays; `int32` for 32-bit integer bigarrays; `int64` for 64-bit integer bigarrays; and `nativeint` for platform-native integer bigarrays. Finally, big arrays 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`.

Array layouts

    type c_layout
    type fortran_layout

> To facilitate interoperability with existing C and Fortran code, this library supports two different memory layouts for big arrays, 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 abstract types `c_layout` and `fortran_layout` respectively.

    type 'a layout

> The type `'a layout` represents one of the two supported memory layouts: C-style if `'a` is `c_layout`, Fortran-style if `'a` is `fortran_layout`.

    val c_layout: c_layout layout
    val fortran_layout: fortran_layout layout

> The abstract values `c_layout` and `fortran_layout` represent the two supported layouts at the level of values.

Generic arrays (of arbitrarily many dimensions)

    module Genarray: sig
      type ('a, 'b, 'c) t

> The type `Genarray.t` is the type of big arrays with variable numbers of dimensions. Any number of dimensions between 1 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 Caml 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 big arrays containing 32-bit floats in Fortran layout; reads and writes in this array use the Caml type `float`.

      external create:
        kind:('a, 'b) kind -> layout:'c layout -> dims:int array -> ('a, 'b, 'c) t

> `Genarray.create kind layout dimensions` returns a new big array 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 big array 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 big array of 32-bit integers, in C layout, having three dimensions, the three dimensions being 4, 6 and 8 respectively.
> Big arrays returned by `Genarray.create` are not initialized: the initial values of array elements is unspecified.
> `Genarray.create` raises `Invalid_arg` if the number of dimensions is not in the range 1 to 16 inclusive, or if one of the dimensions is negative.

      external num_dims: ('a, 'b, 'c) t -> int

> Return the number of dimensions of the given big array.

      external nth_dim: ('a, 'b, 'c) t -> int -> int

> `Genarray.nth_dim a n` returns the `n`-th dimension of the big array `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_arg` if `n` is less than 0 or greater or equal than `Genarray.num_dims a`.

      external get: ('a, 'b, 'c) t -> int array -> 'a

> Read an element of a generic big array. `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`. Raise `Invalid_arg` if the array `a` does not have exactly `N` dimensions, or if the coordinates are outside the array bounds.
> 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.)

      external set: ('a, 'b, 'c) t -> int array -> 'a -> unit

> Assign an element of a generic big array. `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_arg` 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 -> pos:int -> len:int -> ('a, 'b, c_layout) t

> Extract a sub-array of the given big array by restricting the first (left-most) dimension. `Genarray.sub_left a ofs len` returns a big array 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 big arrays in C layout. Raise `Invalid_arg` 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 ->
        pos:int -> len:int -> ('a, 'b, fortran_layout) t

> Extract a sub-array of the given big array by restricting the last (right-most) dimension. `Genarray.sub_right a ofs len` returns a big array 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 big arrays in Fortran layout. Raise `Invalid_arg` 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

> Extract a sub-array of lower dimension from the given big array 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 big arrays in C layout. Raise `Invalid_arg` 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

> Extract a sub-array of lower dimension from the given big array 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 big arrays in Fortran layout. Raise `Invalid_arg` if `M >= N`, or if `[|i1; ... ; iM|]` is outside the bounds of `a`.

      external blit: src:('a, 'b, 'c) t -> dst:('a, 'b, 'c) t -> unit

> Copy all elements of a big array in another big array. `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

> Set all elements of a big array to a given value. `Genarray.fill a v` stores the value `v` in all elements of the big array `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`.

      external map_file:
        Unix.file_descr -> kind:('a, 'b) kind -> layout:'c layout ->
        shared:bool -> dims:int array -> ('a, 'b, 'c) t

> Memory mapping of a file as a big array. `Genarray.map_file fd kind layout shared dims` returns a big array of kind `kind`, layout `layout`, and dimensions as specified in `dims`. The data contained in this big array are the contents of the file referred to by the file descriptor `fd` (as opened previously with `Unix.openfile`, for example). If `shared` is `true`, all modifications performed on the array are reflected in the file. This requires that `fd` be opened with write permissions. If `shared` is `false`, modifications performed on the array are done in memory only, using copy-on-write of the modified pages; the underlying file is not affected.
> `Genarray.map_file` is much more efficient than reading the whole file in a big array, modifying that big array, and writing it afterwards.
> To adjust automatically the dimensions of the big array to the actual size of the file, the major dimension (that is, the first dimension for an array with C layout, and the last dimension for an array with Fortran layout) can be given as `-1`. `Genarray.map_file` then determines the major dimension from the size of the file. The file must contain an integral number of sub-arrays as determined by the non-major dimensions, otherwise `Failure` is raised.
> If all dimensions of the big array are given, the file size is matched against the size of the big array. If the file is larger than the big array, only the initial portion of the file is mapped to the big array. If the file is smaller than the big array, the file is automatically grown to the size of the big array. This requires write permissions on `fd`.

    end

One-dimensional arrays

> The `Array1` structure provides operations similar to those of `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 big arrays whose elements have Caml type `'a`, representation kind `'b`, and memory layout `'c`.

      val create:
        kind:('a, 'b) kind -> layout:'c layout -> dim: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 dim: ('a, 'b, 'c) t -> int

> Return the size (dimension) of the given one-dimensional big array.

      external get: ('a, 'b, 'c) t -> int -> 'a

> `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_arg` is raised.

      external set: ('a, 'b, 'c) t -> int -> 'a -> unit

> `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 `Array1.get`; otherwise, `Invalid_arg` is raised.

      external sub: ('a, 'b, 'c) t -> pos:int -> len:int -> ('a, 'b, 'c) t

> Extract a sub-array of the given one-dimensional big array. See `Genarray.sub_left` for more details.

      external blit: src:('a, 'b, 'c) t -> dst:('a, 'b, 'c) t -> unit

> Copy the first big array to the second big array. See `Genarray.blit` for more details.

      external fill: ('a, 'b, 'c) t -> 'a -> unit

> Fill the given big array with the given value. See `Genarray.fill` for more details.

      val of_array:
        kind:('a, 'b) kind -> layout:'c layout -> 'a array -> ('a, 'b, 'c) t

> Build a one-dimensional big array initialized from the given array.

      val map_file: Unix.file_descr -> kind:('a, 'b) kind -> layout:'c layout ->
                    shared:bool -> dim:int -> ('a, 'b, 'c) t

> Memory mapping of a file as a one-dimensional big array. See `Genarray.map_file` for more details.

    end

Two-dimensional arrays

> The `Array2` structure provides operations similar to those of `Genarray`, but specialized to the case of two-dimensional arrays.

    module Array2: sig
      type ('a, 'b, 'c) t

> The type of two-dimensional big arrays whose elements have Caml type `'a`, representation kind `'b`, and memory layout `'c`.

      val create:
        kind:('a, 'b) kind ->
        layout:'c layout -> dim1:int -> dim2:int -> ('a, 'b, 'c) t

> `Array2.create kind layout dim1 dim2` returns a new bigarray of two dimension, 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 `Genarray.create`.

      val dim1: ('a, 'b, 'c) t -> int

> Return the first dimension of the given two-dimensional big array.

      val dim2: ('a, 'b, 'c) t -> int

> Return the second dimension of the given two-dimensional big array.

      external get: ('a, 'b, 'c) t -> int -> int -> 'a

> `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 `Genarray.get`; otherwise, `Invalid_arg` is raised.

      external set: ('a, 'b, 'c) t -> int -> int -> 'a -> unit

> `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 `Genarray.set`; otherwise, `Invalid_arg` is raised.

      external sub_left:
        ('a, 'b, c_layout) t -> pos:int -> len:int -> ('a, 'b, c_layout) t

> Extract a two-dimensional sub-array of the given two-dimensional big array by restricting the first dimension. See `Genarray.sub_left` for more details. `Array2.sub_left` applies only to arrays with C layout.

      external sub_right:
        ('a, 'b, fortran_layout) t ->
        pos:int -> len:int -> ('a, 'b, fortran_layout) t

> Extract a two-dimensional sub-array of the given two-dimensional big array by restricting the second dimension. See `Genarray.sub_right` for more details. `Array2.sub_right` applies only to arrays with Fortran layout.

      val slice_left:
        ('a, 'b, c_layout) t -> x:int -> ('a, 'b, c_layout) Array1.t

> Extract a row (one-dimensional slice) of the given two-dimensional big array. The integer parameter is the index of the row to extract. See `Genarray.slice_left` for more details. `Array2.slice_left` applies only to arrays with C layout.

      val slice_right:
        ('a, 'b, fortran_layout) t -> y:int -> ('a, 'b, fortran_layout) Array1.t

> Extract a column (one-dimensional slice) of the given two-dimensional big array. The integer parameter is the index of the column to extract. See `Genarray.slice_right` for more details. `Array2.slice_right` applies only to arrays with Fortran layout.

      external blit: src:('a, 'b, 'c) t -> dst:('a, 'b, 'c) t -> unit

> Copy the first big array to the second big array. See `Genarray.blit` for more details.

      external fill: ('a, 'b, 'c) t -> 'a -> unit

> Fill the given big array with the given value. See `Genarray.fill` for more details.

      val of_array:
        kind:('a, 'b) kind -> layout:'c layout -> 'a array array -> ('a, 'b, 'c) t

> Build a two-dimensional big array initialized from the given array of arrays.

      val map_file: Unix.file_descr -> kind:('a, 'b) kind -> layout:'c layout ->
                    shared:bool -> dim1:int -> dim2:int -> ('a, 'b, 'c) t

> Memory mapping of a file as a two-dimensional big array. See `Genarray.map_file` for more details.

    end

Three-dimensional arrays

> The `Array3` structure provides operations similar to those of `Genarray`, but specialized to the case of three-dimensional arrays.

    module Array3: sig
      type ('a, 'b, 'c) t

> The type of three-dimensional big arrays whose elements have Caml type `'a`, representation kind `'b`, and memory layout `'c`.

      val create:
        kind:('a, 'b) kind -> layout:'c layout ->
        dim1:int -> dim2:int -> dim3:int -> ('a, 'b, 'c) t

> `Array3.create kind layout dim1 dim2 dim3` returns a new bigarray of three dimension, 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 `Genarray.create`.

      val dim1: ('a, 'b, 'c) t -> int

> Return the first dimension of the given three-dimensional big array.

      val dim2: ('a, 'b, 'c) t -> int

> Return the second dimension of the given three-dimensional big array.

      val dim3: ('a, 'b, 'c) t -> int

> Return the third dimension of the given three-dimensional big array.

      external get: ('a, 'b, 'c) t -> int -> int -> int -> 'a

> `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 `Genarray.get`; otherwise, `Invalid_arg` is raised.

      external set: ('a, 'b, 'c) t -> int -> int -> int -> 'a -> unit

> `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 `Genarray.set`; otherwise, `Invalid_arg` is raised.

      external sub_left:
        ('a, 'b, c_layout) t -> pos:int -> len:int -> ('a, 'b, c_layout) t

> Extract a three-dimensional sub-array of the given three-dimensional big array by restricting the first dimension. See `Genarray.sub_left` for more details. `Array3.sub_left` applies only to arrays with C layout.

      external sub_right:
        ('a, 'b, fortran_layout) t ->
        pos:int -> len:int -> ('a, 'b, fortran_layout) t

> Extract a three-dimensional sub-array of the given three-dimensional big array by restricting the second dimension. See `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 -> x:int -> y:int -> ('a, 'b, c_layout) Array1.t

> Extract a one-dimensional slice of the given three-dimensional big array by fixing the first two coordinates. The integer parameters are the coordinates of the slice to extract. See `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 -> y:int -> z:int ->
            ('a, 'b, fortran_layout) Array1.t

> Extract a one-dimensional slice of the given three-dimensional big array by fixing the last two coordinates. The integer parameters are the coordinates of the slice to extract. See `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 -> x:int -> ('a, 'b, c_layout) Array2.t

> Extract a two-dimensional slice of the given three-dimensional big array by fixing the first coordinate. The integer parameter is the first coordinate of the slice to extract. See `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 -> z:int -> ('a, 'b, fortran_layout) Array2.t

> Extract a two-dimensional slice of the given three-dimensional big array by fixing the last coordinate. The integer parameter is the coordinate of the slice to extract. See `Genarray.slice_right` for more details. `Array3.slice_right_2` applies only to arrays with Fortran layout.

      external blit: src:('a, 'b, 'c) t -> dst:('a, 'b, 'c) t -> unit

> Copy the first big array to the second big array. See `Genarray.blit` for more details.

      external fill: ('a, 'b, 'c) t -> 'a -> unit

> Fill the given big array with the given value. See `Genarray.fill` for more details.

      val of_array:
            kind:('a, 'b) kind -> layout:'c layout ->
            'a array array array -> ('a, 'b, 'c) t

> Build a three-dimensional big array initialized from the given array of arrays of arrays.

      val map_file: Unix.file_descr -> kind:('a, 'b) kind -> layout:'c layout ->
                 shared:bool -> dim1:int -> dim2:int -> dim3:int -> ('a, 'b, 'c) t

> Memory mapping of a file as a three-dimensional big array. See `Genarray.map_file` for more details.

    end

Coercions between generic big arrays and fixed-dimension big arrays

    val genarray_of_array1: ('a, 'b, 'c) Array1.t -> ('a, 'b, 'c) Genarray.t
    val genarray_of_array2: ('a, 'b, 'c) Array2.t -> ('a, 'b, 'c) Genarray.t
    val genarray_of_array3: ('a, 'b, 'c) Array3.t -> ('a, 'b, 'c) Genarray.t

> Return the generic big array corresponding to the given one-dimensional, two-dimensional or three-dimensional big array.

    val array1_of_genarray: ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array1.t

> Return the one-dimensional big array corresponding to the given generic big array. Raise `Invalid_arg` if the generic big array does not have exactly one dimension.

    val array2_of_genarray: ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array2.t

> Return the two-dimensional big array corresponding to the given generic big array. Raise `Invalid_arg` if the generic big array does not have exactly two dimensions.

    val array3_of_genarray: ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array3.t

> Return the three-dimensional big array corresponding to the given generic big array. Raise `Invalid_arg` if the generic big array does not have exactly three dimensions.

Re-shaping big arrays

    val reshape:
          ('a, 'b, 'c) Genarray.t -> dims:int array -> ('a, 'b, 'c) Genarray.t

> `reshape b [|d1;...;dN|]` converts the big array `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 big array must have exactly the same number of elements as the original big array `b`. That is, the product of the dimensions of `b` must be equal to `i1 * ... * iN`. Otherwise, `Invalid_arg` is raised.

    val reshape_1:
          ('a, 'b, 'c) Genarray.t -> dim:int -> ('a, 'b, 'c) Array1.t

> Specialized version of `reshape` for reshaping to one-dimensional arrays.

    val reshape_2:
          ('a, 'b, 'c) Genarray.t -> dim1:int -> dim2:int -> ('a, 'b, 'c) Array2.t

> Specialized version of `reshape` for reshaping to two-dimensional arrays.

    val reshape_3:
          ('a, 'b, 'c) Genarray.t -> dim1:int -> dim2:int -> dim3:int ->
          ('a, 'b, 'c) Array3.t

> Specialized version of `reshape` for reshaping to three-dimensional arrays.

28.2 | Big arrays in the Caml-C interface

C stub code that interface C or Fortran code with Caml code, as described in chapter 17, can exploit big arrays as follows.

28.2.1 | Include file

The include file `<caml/bigarray.h>` must be included in the C stub file. It declares the functions, constants and macros discussed below.

28.2.2 | Accessing a Caml bigarray from C or Fortran

If v is a Caml `value` representing a big array, the expression `Data``_``bigarray``_``val(`v`)` returns a pointer to the data part of the array. This pointer is of type `void *` and can be cast to the appropriate C type for the array (e.g. `double []`, `char [][10]`, etc).
Various characteristics of the Caml big array can be consulted from C as follows:

C expression | Returns
`Bigarray``_``val(`v`)->num``_``dims` | number of dimensions
`Bigarray``_``val(`v`)->dim[`i`]` | i-th dimension
`Bigarray``_``val(`v`)->flags` `&``BIGARRAY``_``KIND``_``MASK` | kind of array elements

The kind of array elements is one of the following constants:

Constant | Element kind
`BIGARRAY``_``FLOAT32` | 32-bit single-precision floats
`BIGARRAY``_``FLOAT64` | 64-bit double-precision floats
`BIGARRAY``_``SINT8` | 8-bit signed integers
`BIGARRAY``_``UINT8` | 8-bit unsigned integers
`BIGARRAY``_``SINT16` | 16-bit signed integers
`BIGARRAY``_``UINT16` | 16-bit unsigned integers
`BIGARRAY``_``INT32` | 32-bit signed integers
`BIGARRAY``_``INT64` | 64-bit signed integers
`BIGARRAY``_``CAML``_``INT` | 31- or 63-bit signed integers
`BIGARRAY``_``NATIVE``_``INT` | 32- or 64-bit (platform-native) integers

The following example shows the passing of a two-dimensional big array to a C function and a Fortran function.

        extern void my_c_function(double * data, int dimx, int dimy);
        extern void my_fortran_function_(double * data, int * dimx, int * dimy);

        value caml_stub(value bigarray)
        {
          int dimx = Bigarray_val(bigarray)->dim[0];
          int dimy = Bigarray_val(bigarray)->dim[1];
          /* C passes scalar parameters by value */
          my_c_function(Data_bigarray_val(bigarray), dimx, dimy);
          /* Fortran passes all parameters by reference */
          my_fortran_function_(Data_bigarray_val(bigarray), &dimx, &dimy);
          return Val_unit;
        }

28.2.3 | Wrapping a C or Fortran array as a Caml big array

A pointer p to an already-allocated C or Fortran array can be wrapped and returned to Caml as a big array using the `alloc``_``bigarray` or `alloc``_``bigarray``_``dims` functions.

- `alloc``_``bigarray(`kind `|` layout, numdims, p, dims`)`
  Return a Caml big array wrapping the data pointed to by p. kind is the kind of array elements (one of the `BIGARRAY``_` kind constants above). layout is `BIGARRAY``_``C``_``LAYOUT` for an array with C layout and `BIGARRAY``_``FORTRAN``_``LAYOUT` for an array with Fortran layout. numdims is the number of dimensions in the array. dims is an array of numdims long integers, giving the sizes of the array in each dimension.
- `alloc``_``bigarray``_``dims(`kind `|` layout, numdims, p, `(long)` dim1, `(long)` dim2, ..., `(long)` dimnumdims`)`
  Same as `alloc``_``bigarray`, but the sizes of the array in each dimension are listed as extra arguments in the function call, rather than being passed as an array.

The following example illustrates how statically-allocated C and Fortran arrays can be made available to Caml.

        extern long my_c_array[100][200];
        extern float my_fortran_array_[300][400];

        value caml_get_c_array(value unit)
        {
          long dims[2];
          dims[0] = 100; dims[1] = 200;
          return alloc_bigarray(BIGARRAY_NATIVEINT | BIGARRAY_C_LAYOUT,
                                2, my_c_array, dims);
        }

        value caml_get_fortran_array(value unit)
        {
          return alloc_bigarray_dims(BIGARRAY_FLOAT32 | BIGARRAY_FORTRAN_LAYOUT,
                                     2, my_fortran_array_, 300L, 400L);
        }