Module Float.ArrayLabels

module ArrayLabels: sig .. end

Float arrays with packed representation (labeled functions).

type t = floatarray

The type of float arrays with packed representation.

val length : t -> int

Return the length (number of elements) of the given floatarray.

val get : t -> int -> float

get a n returns the element number n of floatarray a.

val set : t -> int -> float -> unit

set a n x modifies floatarray a in place, replacing element number n with x.

val make : int -> float -> t

make n x returns a fresh floatarray of length n, initialized with x.

val create : int -> t

create n returns a fresh floatarray of length n, with uninitialized data.

val init : int -> f:(int -> float) -> t

init n ~f returns a fresh floatarray of length n, with element number i initialized to the result of f i. In other terms, init n ~f tabulates the results of f applied to the integers 0 to n-1.

val append : t -> t -> t

append v1 v2 returns a fresh floatarray containing the concatenation of the floatarrays v1 and v2.

val concat : t list -> t

Same as Float.ArrayLabels.append, but concatenates a list of floatarrays.

val sub : t -> pos:int -> len:int -> t

sub a ~pos ~len returns a fresh floatarray of length len, containing the elements number pos to pos + len - 1 of floatarray a.

val copy : t -> t

copy a returns a copy of a, that is, a fresh floatarray containing the same elements as a.

val fill : t -> pos:int -> len:int -> float -> unit

fill a ~pos ~len x modifies the floatarray a in place, storing x in elements number pos to pos + len - 1.

val blit : src:t ->
       src_pos:int -> dst:t -> dst_pos:int -> len:int -> unit

blit ~src ~src_pos ~dst ~dst_pos ~len copies len elements from floatarray src, starting at element number src_pos, to floatarray dst, starting at element number dst_pos. It works correctly even if src and dst are the same floatarray, and the source and destination chunks overlap.

val to_list : t -> float list

to_list a returns the list of all the elements of a.

val of_list : float list -> t

of_list l returns a fresh floatarray containing the elements of l.

Iterators

val iter : f:(float -> unit) -> t -> unit

iter ~f a applies function f in turn to all the elements of a. It is equivalent to f a.(0); f a.(1); ...; f a.(length a - 1); ().

val iteri : f:(int -> float -> unit) -> t -> unit

Same as Float.ArrayLabels.iter, but the function is applied with the index of the element as first argument, and the element itself as second argument.

val map : f:(float -> float) -> t -> t

map ~f a applies function f to all the elements of a, and builds a floatarray with the results returned by f.

val mapi : f:(int -> float -> float) -> t -> t

Same as Float.ArrayLabels.map, but the function is applied to the index of the element as first argument, and the element itself as second argument.

val fold_left : f:('a -> float -> 'a) -> init:'a -> t -> 'a

fold_left ~f x ~init computes f (... (f (f x init.(0)) init.(1)) ...) init.(n-1), where n is the length of the floatarray init.

val fold_right : f:(float -> 'a -> 'a) -> t -> init:'a -> 'a

fold_right f a init computes f a.(0) (f a.(1) ( ... (f a.(n-1) init) ...)), where n is the length of the floatarray a.

Iterators on two arrays

val iter2 : f:(float -> float -> unit) ->
       t -> t -> unit

Array.iter2 ~f a b applies function f to all the elements of a and b.

val map2 : f:(float -> float -> float) ->
       t -> t -> t

map2 ~f a b applies function f to all the elements of a and b, and builds a floatarray with the results returned by f: [| f a.(0) b.(0); ...; f a.(length a - 1) b.(length b - 1)|].

Array scanning

val for_all : f:(float -> bool) -> t -> bool

for_all ~f [|a1; ...; an|] checks if all elements of the floatarray satisfy the predicate f. That is, it returns (f a1) && (f a2) && ... && (f an).

val exists : f:(float -> bool) -> t -> bool

exists f [|a1; ...; an|] checks if at least one element of the floatarray satisfies the predicate f. That is, it returns (f a1) || (f a2) || ... || (f an).

val mem : float -> set:t -> bool

mem a ~set is true if and only if there is an element of set that is structurally equal to a, i.e. there is an x in set such that compare a x = 0.

val mem_ieee : float -> set:t -> bool

Same as Float.ArrayLabels.mem, but uses IEEE equality instead of structural equality.

Sorting

val sort : cmp:(float -> float -> int) -> t -> unit

Sort a floatarray in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see below for a complete specification). For example, compare is a suitable comparison function. After calling sort, the array is sorted in place in increasing order. sort is guaranteed to run in constant heap space and (at most) logarithmic stack space.

The current implementation uses Heap Sort. It runs in constant stack space.

Specification of the comparison function: Let a be the floatarray and cmp the comparison function. The following must be true for all x, y, z in a :

  • cmp x y > 0 if and only if cmp y x < 0
  • if cmp x y >= 0 and cmp y z >= 0 then cmp x z >= 0

When sort returns, a contains the same elements as before, reordered in such a way that for all i and j valid indices of a :

  • cmp a.(i) a.(j) >= 0 if and only if i >= j
val stable_sort : cmp:(float -> float -> int) -> t -> unit

Same as Float.ArrayLabels.sort, but the sorting algorithm is stable (i.e. elements that compare equal are kept in their original order) and not guaranteed to run in constant heap space.

The current implementation uses Merge Sort. It uses a temporary floatarray of length n/2, where n is the length of the floatarray. It is usually faster than the current implementation of Float.ArrayLabels.sort.

val fast_sort : cmp:(float -> float -> int) -> t -> unit

Same as Float.ArrayLabels.sort or Float.ArrayLabels.stable_sort, whichever is faster on typical input.

Float arrays and Sequences

val to_seq : t -> float Seq.t

Iterate on the floatarray, in increasing order. Modifications of the floatarray during iteration will be reflected in the sequence.

val to_seqi : t -> (int * float) Seq.t

Iterate on the floatarray, in increasing order, yielding indices along elements. Modifications of the floatarray during iteration will be reflected in the sequence.

val of_seq : float Seq.t -> t

Create an array from the generator.

val map_to_array : f:(float -> 'a) -> t -> 'a array

map_to_array ~f a applies function f to all the elements of a, and builds an array with the results returned by f: [| f a.(0); f a.(1); ...; f a.(length a - 1) |].

val map_from_array : f:('a -> float) -> 'a array -> t

map_from_array ~f a applies function f to all the elements of a, and builds a floatarray with the results returned by f.

Arrays and concurrency safety

Care must be taken when concurrently accessing float arrays from multiple domains: accessing an array will never crash a program, but unsynchronized accesses might yield surprising (non-sequentially-consistent) results.

Atomicity

Every float array operation that accesses more than one array element is not atomic. This includes iteration, scanning, sorting, splitting and combining arrays.

For example, consider the following program:

let size = 100_000_000
  let a = Float.ArrayLabels.make size 1.
  let update a f () =
     Float.ArrayLabels.iteri ~f:(fun i x -> Float.Array.set a i (f x)) a
  let d1 = Domain.spawn (update a (fun x -> x +. 1.))
  let d2 = Domain.spawn (update a (fun x ->  2. *. x +. 1.))
  let () = Domain.join d1; Domain.join d2

After executing this code, each field of the float array 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 array, 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 array 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 array 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. Nevertheless, even in the presence of data races, a read operation will return the value of some prior write to that location with a few exceptions.

Tearing

Float arrays have two supplementary caveats in the presence of data races.

First, the blit operation might copy an array byte-by-byte. Data races between such a blit operation and another operation might produce surprising values due to tearing: partial writes interleaved with other operations can create float values that would not exist with a sequential execution.

For instance, at the end of

let zeros = Float.Array.make size 0.
  let max_floats = Float.Array.make size Float.max_float
  let res = Float.Array.copy zeros
  let d1 = Domain.spawn (fun () -> Float.Array.blit zeros 0 res 0 size)
  let d2 = Domain.spawn (fun () -> Float.Array.blit max_floats 0 res 0 size)
  let () = Domain.join d1; Domain.join d2

the res float array might contain values that are neither 0. nor max_float.

Second, on 32-bit architectures, getting or setting a field involves two separate memory accesses. In the presence of data races, the user may observe tearing on any operation.