# package monomorphic

Library

Module

Module type

Parameter

Class

Class type

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 `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`

).

## Element kinds

Bigarrays 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`

), - 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 ('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`

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
| Int8_signed -> 0 | Int8_unsigned -> 0
| Int16_signed -> 0 | Int16_unsigned -> 0
| Int32 -> 0l | Int64 -> 0L
| Int -> 0 | Nativeint -> 0n
| Char -> '\000'
```

`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`

.

See `Bigarray.char`

.

See `Bigarray.char`

.

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 `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`

.

## Array layouts

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.

`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. 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.

## One-dimensional arrays

`module Array1 : sig ... end`

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.

## Two-dimensional arrays

`module Array2 : sig ... end`

Two-dimensional arrays. The `Array2`

structure provides operations similar to those of `Bigarray.Genarray`

, but specialized to the case of two-dimensional arrays.

## Three-dimensional arrays

`module Array3 : sig ... end`

Three-dimensional arrays. The `Array3`

structure provides operations similar to those of `Bigarray.Genarray`

, but specialized to the case of 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.

`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.

`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.

`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.

`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.

## 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.

`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`

).