oracular (3) Stdlib.Bigarray.3o.gz
NAME
Stdlib.Bigarray - no description
Module
Module Stdlib.Bigarray
Documentation
Module Bigarray
: (module Stdlib__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 .
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. 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
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 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.
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.
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 ).