Bigarray - Large, multi-dimensional, numerical arrays.
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 '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 compare );
-hashing (module Hash );
-and structured input-output (the functions from the Marshal module, as well as
output_value and input_value ).
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 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
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 .
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, 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 .
Since 4.03.0
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.
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
module Genarray : sig end
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.
Since 4.05.0
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 Bigarray.Array2 and Bigarray.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 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.
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.
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 4.05.0
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 4.05.0
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.
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 4.05.0
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.