oracular (3) Bigarray.3o.gz

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NAME

       Bigarray - Large, multi-dimensional, numerical arrays.

Module

       Module   Bigarray

Documentation

       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 ).

   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 ).