# Module Bigarray

    module Bigarray: sig .. end

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

Big arrays can contain elements of the following kinds:

- 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`),
- Caml integers (signed, 31 bits on 32-bit architectures, 63 bits on 64-bit architectures) (`Bigarray.int_elt`),
- 32-bit signed integer (`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 abstract types defined below.

    type float32_elt

    type float64_elt

    type complex32_elt

    type complex64_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

    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

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`.

    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, big arrays of kind `float32_elt` and `float64_elt` are accessed using the Caml type `float`. Big arrays of complex kinds `complex32_elt`, `complex64_elt` are accessed with the Caml type `Complex.t`. 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

See `Bigarray.fortran_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 `Bigarray.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 `Bigarray.c_layout`, Fortran-style if `'a` is `Bigarray.fortran_layout`.
Supported layouts

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

    val c_layout : c_layout layout

    val fortran_layout : fortran_layout layout

###### Generic arrays (of arbitrarily many dimensions)

    module Genarray: sig .. end

###### One-dimensional arrays

    module Array1: sig .. end

One-dimensional arrays.

###### Two-dimensional arrays

    module Array2: sig .. end

Two-dimensional arrays.

###### Three-dimensional arrays

    module Array3: sig .. end

Three-dimensional arrays.

###### Coercions between generic big arrays and fixed-dimension big arrays

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

Return the generic big array corresponding to the given one-dimensional big array.

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

Return the generic big array corresponding to the given two-dimensional big array.

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

Return the generic big array corresponding to the given 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_argument` 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_argument` 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_argument` if the generic big array does not have exactly three dimensions.

###### Re-shaping big arrays

    val reshape : ('a, 'b, 'c) Genarray.t ->
           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_argument` is raised.

    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.