# 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.

- Since 4.08

    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`.

- Raises `Invalid_argument` if `n` is outside the range 0 to `(length a - 1)`.

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

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

- Raises `Invalid_argument` if `n` is outside the range 0 to `(length a - 1)`.

    val make : int -> float -> t

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

- Raises `Invalid_argument` if `n < 0` or `n > Sys.max_floatarray_length`.

    val create : int -> t

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

- Raises `Invalid_argument` if `n < 0` or `n > Sys.max_floatarray_length`.

    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`.

- Raises `Invalid_argument` if `n < 0` or `n > Sys.max_floatarray_length`.

    val make_matrix : dimx:int -> dimy:int -> float -> t array

`make_matrix ~dimx ~dimy e` returns a two-dimensional array (an array of arrays) with first dimension `dimx` and second dimension `dimy`, where all elements are initialized with `e`.

- Since 5.2
- Raises `Invalid_argument` if `dimx` or `dimy` is negative or greater than `Sys.max_floatarray_length`.

    val init_matrix : dimx:int -> dimy:int -> f:(int -> int -> float) -> t array

`init_matrix ~dimx ~dimy ~f` returns a two-dimensional array (an array of arrays) with first dimension `dimx` and second dimension `dimy`, where the element at index (`x,y`) is initialized with `f x y`.

- Since 5.2
- Raises `Invalid_argument` if `dimx` or `dimy` is negative or greater than `Sys.max_floatarray_length`.

    val append : t -> t -> t

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

- Raises `Invalid_argument` if `length v1 + length v2 > Sys.max_floatarray_length`.

    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`.

- Raises `Invalid_argument` if `pos` and `len` do not designate a valid subarray of `a`; that is, if `pos < 0`, or `len < 0`, or `pos + len > length 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`.

- Raises `Invalid_argument` if `pos` and `len` do not designate a valid subarray of `a`.

    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.

- Raises `Invalid_argument` if `src_pos` and `len` do not designate a valid subarray of `src`, or if `dst_pos` and `len` do not designate a valid subarray of `dst`.

    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`.

- Raises `Invalid_argument` if the length of `l` is greater than `Sys.max_floatarray_length`.

## Comparison

    val equal : eq:(float -> float -> bool) ->
           t -> t -> bool

`equal eq a b` is `true` if and only if `a` and `b` have the same length `n` and for all `i` in [`0`;`n-1`], `eq a.(i) b.(i)` is `true`.

- Since 5.4

    val compare : cmp:(float -> float -> int) ->
           t -> t -> int

`compare cmp a b` compares `a` and `b` according to the shortlex order, that is, shorter arrays are smaller and equal-sized arrays are compared in lexicographic order using `cmp` to compare elements.

- Since 5.4

## 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 map_inplace : f:(float -> float) -> t -> unit

`map_inplace f a` applies function `f` to all elements of `a`, and updates their values in place.

- Since 5.1

    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 mapi_inplace : f:(int -> float -> float) -> t -> unit

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

- Since 5.1

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

`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 -> 'acc -> 'acc) -> t -> init:'acc -> 'acc

`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`.

- Raises `Invalid_argument` if the floatarrays are not the same size.

    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)|]`.

- Raises `Invalid_argument` if the floatarrays are not the same size.

## 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.

## Array searching

    val find_opt : f:(float -> bool) -> t -> float option

    val find_index : f:(float -> bool) -> t -> int option

`find_index ~f a` returns `Some i`, where `i` is the index of the first element of the array `a` that satisfies `f x`, if there is such an element.

It returns `None` if there is no such element.

- Since 5.1

    val find_map : f:(float -> 'a option) -> t -> 'a option

    val find_mapi : f:(int -> float -> 'a option) -> t -> 'a option

Same as `find_map`, but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument.

- Since 5.1

## Sorting and shuffling

    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 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.

    val shuffle : rand:(int -> int) -> t -> unit

`shuffle ~rand a` randomly permutes `a`'s elements using `rand` for randomness. The distribution of permutations is uniform.

`rand` must be such that a call to `rand n` returns a uniformly distributed random number in the range [`0`;`n-1`]. `Random.int` can be used for this (do not forget to initialize the generator).

- Since 5.2

## 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.