Module Float.Array

Float arrays with packed representation.

type t = floatarray

type t = floatarray;

The type of float arrays with packed representation.

since 4.08

val length : t -> int

let length: t => int;

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

val get : t -> int -> float

let 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

let 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

let 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

let 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 -> (int -> float) -> t

let init: int => (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 : int -> int -> float -> t array

let make_matrix: int => int => float => array(t);

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.

raises Invalid_argument if dimx or dimy is negative or greater than Sys.max_floatarray_length. since 5.2

val init_matrix : int -> int -> (int -> int -> float) -> t array

let init_matrix: int => int => (int => int => float) => array(t);

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.

raises Invalid_argument if dimx or dimy is negative or greater than Sys.max_floatarray_length. since 5.2

val append : t -> t -> t

let 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 sub : t -> int -> int -> t

let sub: t => int => 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

let copy: t => t;

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

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

let fill: t => int => 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 : t -> int -> t -> int -> int -> unit

let blit: t => int => t => int => 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

let to_list: t => list(float);

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

val of_list : float list -> t

let of_list: list(float) => 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 : (float -> float -> bool) -> t -> t -> bool

let equal: (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 : (float -> float -> int) -> t -> t -> int

let compare: (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 : (float -> unit) -> t -> unit

let iter: (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 : (int -> float -> unit) -> t -> unit

let iteri: (int => float => unit) => t => unit;

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

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

let map: (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 : (float -> float) -> t -> unit

let map_inplace: (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 : (int -> float -> float) -> t -> t

let mapi: (int => float => float) => t => t;

Same as 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 : (int -> float -> float) -> t -> unit

let mapi_inplace: (int => float => float) => t => unit;

Same as 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 : ('acc -> float -> 'acc) -> 'acc -> t -> 'acc

let fold_left: ('acc => float => 'acc) => '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 : (float -> 'acc -> 'acc) -> t -> 'acc -> 'acc

let fold_right: (float => 'acc => 'acc) => t => '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 : (float -> float -> unit) -> t -> t -> unit

let iter2: (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 : (float -> float -> float) -> t -> t -> t

let map2: (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 : (float -> bool) -> t -> bool

let for_all: (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 : (float -> bool) -> t -> bool

let exists: (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 -> t -> bool

let mem: float => 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 -> t -> bool

let mem_ieee: float => t => bool;

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

Array searching

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

let find_opt: (float => bool) => t => option(float);

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

let find_index: (float => bool) => t => option(int);

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 : (float -> 'a option) -> t -> 'a option

let find_map: (float => option('a)) => t => option('a);

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

let find_mapi: (int => float => option('a)) => t => option('a);

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

let sort: (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, Stdlib.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 : (float -> float -> int) -> t -> unit

let stable_sort: (float => float => int) => t => unit;

Same as 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 sort.

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

let fast_sort: (float => float => int) => t => unit;

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

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

let 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

let to_seq: t => Seq.t(float);

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

let to_seqi: t => Seq.t((int, float));

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

let of_seq: Seq.t(float) => t;

Create an array from the generator.

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

let map_to_array: (float => 'a) => t => array('a);

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 : ('a -> float) -> 'a array -> t

let map_from_array: ('a => float) => array('a) => 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.Array.make size 1.
let update a f () =
   Float.Array.iteri (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

let size = 100_000_000;
let a = Float.Array.make(size, 1.);
let update = (a, f, ()) =>
  Float.Array.iteri((i, x) => Float.Array.set(a, i, f(x)), a);
let d1 = Domain.spawn(update(a, x => x +. 1.));
let d2 = Domain.spawn(update(a, 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

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(() => Float.Array.blit(zeros, 0, res, 0, size));
let d2 = Domain.spawn(() => 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.