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',
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 'big arrays' and standard OCaml arrays are as follows:

- Big arrays 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.)
- Big arrays 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.
- Big arrays can only contain integers and floating-point numbers, while OCaml arrays can contain arbitrary OCaml data types.
- Big arrays 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 big arrays 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.
- 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.

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 OCaml ad-hoc polymorphic operations:

- comparisons (
`=`

,`<>`

,`<=`

, etc, as well as`compare`

); - hashing (module
`Hash`

); - and structured input-output (the functions from the
`Marshal`

module, as well as`output_value`

and`input_value`

).

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`

), - 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 `

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 : ` |

`|` |
`Float64 : ` |

`|` |
`Int8_signed : ` |

`|` |
`Int8_unsigned : ` |

`|` |
`Int16_signed : ` |

`|` |
`Int16_unsigned : ` |

`|` |
`Int32 : ` |

`|` |
`Int64 : ` |

`|` |
`Int : ` |

`|` |
`Nativeint : ` |

`|` |
`Complex32 : ` |

`|` |
`Complex64 : ` |

`|` |
`Char : ` |

To each element kind is associated an OCaml type, which is
the type of OCaml 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 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 big array,
and of an element kind `'b`

which represents the actual contents
of the big array. 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 to write 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`

.

`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 OCaml type `float`

. Big arrays of complex kinds
`complex32_elt`

, `complex64_elt`

are accessed with the OCaml type
`Complex.t`

. Big arrays 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, 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`

.

`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**4.03.0

`type `

c_layout =

`|` |
`C_layout_typ` |

`type `

fortran_layout =

`|` |
`Fortran_layout_typ` |

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
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 : ` |

`|` |
`Fortran_layout : ` |

`val c_layout : ``c_layout layout`

`val fortran_layout : ``fortran_layout layout`

module Genarray:`sig`

..`end`

module Array0:`sig`

..`end`

Zero-dimensional arrays.

module Array1:`sig`

..`end`

One-dimensional arrays.

module Array2:`sig`

..`end`

Two-dimensional arrays.

module Array3:`sig`

..`end`

Three-dimensional arrays.

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

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

**Since**4.05.0

`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 array0_of_genarray : ``('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array0.t`

Return the zero-dimensional big array corresponding to the given
generic big array. Raise `Invalid_argument`

if the generic big array
does not have exactly zero dimension.

**Since**4.05.0

`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.

`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_0 : ``('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array0.t`

Specialized version of `Bigarray.reshape`

for reshaping to
zero-dimensional arrays.

**Since**4.05.0

`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.