# Module Stdlib.Bigarray

    module Bigarray: Bigarray

## 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).

    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 Element kinds.

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

## Array layouts

    type c_layout =

`|` | `C_layout_typ`

See `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 `Bigarray.c_layout` and `Bigarray.fortran_layout` respectively.

### 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

## Generic arrays (of arbitrarily many dimensions)

    module Genarray: sig .. end

## Zero-dimensional arrays

    module Array0: sig .. end

Zero-dimensional arrays.

## 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 Bigarrays and fixed-dimension Bigarrays

    val genarray_of_array0 : ('a, 'b, 'c) Array0.t -> ('a, 'b, 'c) Genarray.t

Return the generic Bigarray corresponding to the given zero-dimensional Bigarray.

- Since 4.05

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

Return the generic Bigarray corresponding to the given one-dimensional Bigarray.

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

Return the generic Bigarray corresponding to the given two-dimensional Bigarray.

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

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.

- Since 4.05
- Raises `Invalid_argument` if the generic Bigarray does not have exactly zero dimension.

    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.

- Raises `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.

- Raises `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.

- Raises `Invalid_argument` if the generic Bigarray does not have exactly three dimensions.

## 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.

## 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.

### 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`).

### 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.

### 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`).