Module CCArraySource
Array utils
Sourcetype 'a iter = ('a -> unit) -> unit Sourcetype 'a gen = unit -> 'a option Sourcetype 'a equal = 'a -> 'a -> bool Sourcetype 'a ord = 'a -> 'a -> int Arrays
An alias for the type of arrays.
Sourceval length : 'a array -> int Return the length (number of elements) of the given array.
Sourceval get : 'a array -> int -> 'a get a n returns the element number n of array a. The first element has number 0. The last element has number length a - 1. You can also write a.(n) instead of get a n.
Sourceval set : 'a array -> int -> 'a -> unit set a n x modifies array a in place, replacing element number n with x. You can also write a.(n) <- x instead of set a n x.
Sourceval make : int -> 'a -> 'a array make n x returns a fresh array of length n, initialized with x. All the elements of this new array are initially physically equal to x (in the sense of the == predicate). Consequently, if x is mutable, it is shared among all elements of the array, and modifying x through one of the array entries will modify all other entries at the same time.
Sourceval create_float : int -> float array create_float n returns a fresh float array of length n, with uninitialized data.
Sourceval init : int -> (int -> 'a) -> 'a array init n f returns a fresh array 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 in order to the integers 0 to n-1.
Sourceval make_matrix : int -> int -> 'a -> 'a array array make_matrix dimx dimy e returns a two-dimensional array (an array of arrays) with first dimension dimx and second dimension dimy. All the elements of this new matrix are initially physically equal to e. The element (x,y) of a matrix m is accessed with the notation m.(x).(y).
Sourceval init_matrix : int -> int -> (int -> int -> 'a) -> 'a array 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. The element (x,y) of a matrix m is accessed with the notation m.(x).(y).
Sourceval append : 'a array -> 'a array -> 'a array append v1 v2 returns a fresh array containing the concatenation of the arrays v1 and v2.
Sourceval concat : 'a array list -> 'a array Same as append, but concatenates a list of arrays.
Sourceval sub : 'a array -> int -> int -> 'a array sub a pos len returns a fresh array of length len, containing the elements number pos to pos + len - 1 of array a.
Sourceval copy : 'a array -> 'a array copy a returns a copy of a, that is, a fresh array containing the same elements as a.
Sourceval fill : 'a array -> int -> int -> 'a -> unit fill a pos len x modifies the array a in place, storing x in elements number pos to pos + len - 1.
Sourceval blit : 'a array -> int -> 'a array -> int -> int -> unit blit src src_pos dst dst_pos len copies len elements from array src, starting at element number src_pos, to array dst, starting at element number dst_pos. It works correctly even if src and dst are the same array, and the source and destination chunks overlap.
Sourceval to_list : 'a array -> 'a list to_list a returns the list of all the elements of a.
Sourceval of_list : 'a list -> 'a array of_list l returns a fresh array containing the elements of l.
Iterators
Sourceval iter : ('a -> unit) -> 'a array -> 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); ().
Sourceval iteri : (int -> 'a -> unit) -> 'a array -> unit Same as iter, but the function is applied to the index of the element as first argument, and the element itself as second argument.
Sourceval map : ('a -> 'b) -> 'a array -> 'b array map 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) |].
Sourceval mapi : (int -> 'a -> 'b) -> 'a array -> 'b array Same as map, but the function is applied to the index of the element as first argument, and the element itself as second argument.
Sourceval fold_left : ('acc -> 'a -> 'acc) -> 'acc -> 'a array -> 'acc fold_left f init a computes f (... (f (f init a.(0)) a.(1)) ...) a.(n-1), where n is the length of the array a.
Sourceval fold_left_map :
('acc -> 'a -> 'acc * 'b) ->
'acc ->
'a array ->
'acc * 'b array fold_left_map is a combination of fold_left and map that threads an accumulator through calls to f.
Sourceval fold_right : ('a -> 'acc -> 'acc) -> 'a array -> '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 array a.
Iterators on two arrays
Sourceval iter2 : ('a -> 'b -> unit) -> 'a array -> 'b array -> unit iter2 f a b applies function f to all the elements of a and b.
Sourceval map2 : ('a -> 'b -> 'c) -> 'a array -> 'b array -> 'c array map2 f a b applies function f to all the elements of a and b, and builds an array with the results returned by f: [| f a.(0) b.(0); ...; f a.(length a - 1) b.(length b - 1)|].
Array scanning
Sourceval for_all : ('a -> bool) -> 'a array -> bool for_all f [|a1; ...; an|] checks if all elements of the array satisfy the predicate f. That is, it returns (f a1) && (f a2) && ... && (f an).
Sourceval exists : ('a -> bool) -> 'a array -> bool exists f [|a1; ...; an|] checks if at least one element of the array satisfies the predicate f. That is, it returns (f a1) || (f a2) || ... || (f an).
Sourceval memq : 'a -> 'a array -> bool Same as mem, but uses physical equality instead of structural equality to compare array elements.
Sourceval find_opt : ('a -> bool) -> 'a array -> 'a option find_opt f a returns the first element of the array a that satisfies the predicate f, or None if there is no value that satisfies f in the array a.
Sourceval find_index : ('a -> bool) -> 'a array -> 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.
Sourceval find_mapi : (int -> 'a -> 'b option) -> 'a array -> 'b 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.
Arrays of pairs
Sourceval split : ('a * 'b) array -> 'a array * 'b array split [|(a1,b1); ...; (an,bn)|] is ([|a1; ...; an|], [|b1; ...; bn|]).
Sourceval combine : 'a array -> 'b array -> ('a * 'b) array combine [|a1; ...; an|] [|b1; ...; bn|] is [|(a1,b1); ...; (an,bn)|]. Raise Invalid_argument if the two arrays have different lengths.
Sorting and shuffling
Sourceval sort : ('a -> 'a -> int) -> 'a array -> unit Sort an array 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 array 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
Sourceval stable_sort : ('a -> 'a -> int) -> 'a array -> 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 array of length n/2, where n is the length of the array. It is usually faster than the current implementation of sort.
Sourceval fast_sort : ('a -> 'a -> int) -> 'a array -> unit Arrays and Sequences
Iterate on the array, in increasing order, yielding indices along elements. Modifications of the array during iteration will be reflected in the sequence.
Create an array from the generator
Arrays and concurrency safety
Care must be taken when concurrently accessing arrays from multiple domains: accessing an array will never crash a program, but unsynchronized accesses might yield surprising (non-sequentially-consistent) results.
Atomicity
Every 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 = Array.make size 1
let d1 = Domain.spawn (fun () ->
Array.iteri (fun i x -> a.(i) <- x + 1) a
)
let d2 = Domain.spawn (fun () ->
Array.iteri (fun i x -> a.(i) <- 2 * x + 1) a
)
let () = Domain.join d1; Domain.join d2
After executing this code, each field of the 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 for float arrays).
Float arrays
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 = Array.make size 0.
let max_floats = Array.make size Float.max_float
let res = Array.copy zeros
let d1 = Domain.spawn (fun () -> Array.blit zeros 0 res 0 size)
let d2 = Domain.spawn (fun () -> Array.blit max_floats 0 res 0 size)
let () = Domain.join d1; Domain.join d2
the res 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.
empty is the empty array, physically equal to [||].
equal eq a1 a2 is true if the lengths of a1 and a2 are the same and if their corresponding elements test equal, using eq.
compare cmp a1 a2 compares arrays a1 and a2 using the function comparison cmp.
Sourceval swap : 'a t -> int -> int -> unit swap a i j swaps elements at indices i and j.
Sourceval get_safe : 'a t -> int -> 'a option get_safe a i returns Some a.(i) if i is a valid index.
Sourceval map_inplace : ('a -> 'a) -> 'a t -> unit map_inplace f a replace all elements of a by its image by f.
Sourceval mapi_inplace : (int -> 'a -> 'a) -> 'a t -> unit mapi_inplace f a replace all elements of a by its image by f.
Sourceval fold : ('a -> 'b -> 'a) -> 'a -> 'b t -> 'a fold f init a computes f (… (f (f init a.(0)) a.(1)) …) a.(n-1), where n is the length of the array a. Same as Array.fold_left
Sourceval foldi : ('a -> int -> 'b -> 'a) -> 'a -> 'b t -> 'a foldi f init a is just like fold, but it also passes in the index of each element as the second argument to the folded function f.
Sourceval fold_while : ('a -> 'b -> 'a * [ `Stop | `Continue ]) -> 'a -> 'b t -> 'a fold_while f init a folds left on array a until a stop condition via ('a, `Stop) is indicated by the accumulator.
Sourceval fold_map : ('acc -> 'a -> 'acc * 'b) -> 'acc -> 'a t -> 'acc * 'b t fold_map f init a is a fold_left-like function, but it also maps the array to another array.
Sourceval scan_left : ('acc -> 'a -> 'acc) -> 'acc -> 'a t -> 'acc t scan_left f init a returns the array [|init; f init x0; f (f init a.(0)) a.(1); …|] .
Sourceval reverse_in_place : 'a t -> unit reverse_in_place a reverses the array a in place.
Sourceval sorted : ('a -> 'a -> int) -> 'a t -> 'a array sorted f a makes a copy of a and sorts it with f.
Sourceval sort_indices : ('a -> 'a -> int) -> 'a t -> int array sort_indices f a returns a new array b, with the same length as a, such that b.(i) is the index at which the i-th element of sorted f a appears in a. a is not modified.
In other words, map (fun i -> a.(i)) (sort_indices f a) = sorted f a. sort_indices yields the inverse permutation of sort_ranking.
Sourceval sort_ranking : ('a -> 'a -> int) -> 'a t -> int array sort_ranking f a returns a new array b, with the same length as a, such that b.(i) is the index at which the i-th element of a appears in sorted f a. a is not modified.
In other words, map (fun i -> (sorted f a).(i)) (sort_ranking f a) = a. sort_ranking yields the inverse permutation of sort_indices.
In the absence of duplicate elements in a, we also have lookup_exn a.(i) (sorted a) = (sorted_ranking a).(i).
Sourceval mem : ?eq:('a -> 'a -> bool) -> 'a -> 'a t -> bool mem ~eq x a return true if x is present in a. Linear time.
Sourceval find_map : ('a -> 'b option) -> 'a t -> 'b option find_map f a returns Some y if there is an element x such that f x = Some y. Otherwise returns None.
Sourceval find_map_i : (int -> 'a -> 'b option) -> 'a t -> 'b option find_map_i f a is like find_map, but the index of the element is also passed to the predicate function f.
Sourceval find_idx : ('a -> bool) -> 'a t -> (int * 'a) option find_idx f a returns Some (i,x) where x is the i-th element of a, and f x holds. Otherwise returns None.
Sourceval lookup : cmp:'a ord -> 'a -> 'a t -> int option lookup ~cmp key a lookups the index of some key key in a sorted array a. Undefined behavior if the array a is not sorted wrt ~cmp. Complexity: O(log (n)) (dichotomic search).
Sourceval lookup_exn : cmp:'a ord -> 'a -> 'a t -> int lookup_exn ~cmp key a is like lookup, but
Sourceval bsearch :
cmp:('a -> 'a -> int) ->
'a ->
'a t ->
[ `All_lower | `All_bigger | `Just_after of int | `Empty | `At of int ] bsearch ~cmp key a finds the index of the object key in the array a, provided a is sorted using cmp. If the array is not sorted, the result is not specified (may raise Invalid_argument).
Complexity: O(log n) where n is the length of the array a (dichotomic search).
Sourceval for_all2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool for_all2 f [|a1; …; an|] [|b1; …; bn|] is true if each pair of elements ai bi satisfies the predicate f. That is, it returns (f a1 b1) && (f a2 b2) && … && (f an bn).
Sourceval exists2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool exists2 f [|a1; …; an|] [|b1; …; bn|] is true if any pair of elements ai bi satisfies the predicate f. That is, it returns (f a1 b1) || (f a2 b2) || … || (f an bn).
Sourceval fold2 : ('acc -> 'a -> 'b -> 'acc) -> 'acc -> 'a t -> 'b t -> 'acc fold2 f init a b fold on two arrays a and b stepwise. It computes f (… (f init a1 b1) …) an bn.
shuffle a randomly shuffles the array a, in place.
shuffle_with rs a randomly shuffles the array a (like shuffle) but a specialized random state rs is used to control the random numbers being produced during shuffling (for reproducibility).
random_choose a rs randomly chooses an element of a.
Sourceval to_string : ?sep:string -> ('a -> string) -> 'a array -> string to_string ~sep item_to_string a print a to a string using sep as a separator between elements of a.
to_iter a returns an iter of the elements of an array a. The input array a is shared with the sequence and modification of it will result in modification of the iterator.
to_seq a returns a Seq.t of the elements of an array a. The input array a is shared with the sequence and modification of it will result in modification of the sequence. Renamed from to_std_seq since 3.0.
to_gen a returns a gen of the elements of an array a.
IO
pp ~pp_start ~pp_stop ~pp_sep pp_item ppf a formats the array a on ppf. Each element is formatted with pp_item, pp_start is called at the beginning, pp_stop is called at the end, pp_sep is called between each elements. By defaults pp_start and pp_stop does nothing and pp_sep defaults to (fun out -> Format.fprintf out ",@ ").
pp_i ~pp_start ~pp_stop ~pp_sep pp_item ppf a prints the array a on ppf. The printing function pp_item is giving both index and element. pp_start is called at the beginning, pp_stop is called at the end, pp_sep is called between each elements. By defaults pp_start and pp_stop does nothing and pp_sep defaults to (fun out -> Format.fprintf out ",@ ").
rev a copies the array a and reverses it in place.
Sourceval filter : ('a -> bool) -> 'a t -> 'a t filter f a filters elements out of the array a. Only the elements satisfying the given predicate f will be kept.
Sourceval filter_map : ('a -> 'b option) -> 'a t -> 'b t filter_map f [|a1; …; an|] calls (f a1) … (f an) and returns an array b consisting of all elements bi such as f ai = Some bi. When f returns None, the corresponding element of a is discarded.
Sourceval monoid_product : ('a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t monoid_product f a b passes all combinaisons of tuples from the two arrays a and b to the function f.
Sourceval flat_map : ('a -> 'b t) -> 'a t -> 'b array flat_map f a transforms each element of a into an array, then flattens.
Sourceval except_idx : 'a t -> int -> 'a list except_idx a i removes the element of a at given index i, and returns the list of the other elements.
Generic Functions
Sourceval sort_generic :
(module MONO_ARRAY with type elt = 'elt and type t = 'arr) ->
cmp:('elt -> 'elt -> int) ->
'arr ->
unit sort_generic (module M) ~cmp a sorts the array a, without allocating (eats stack space though). Performance might be lower than Array.sort.
Infix Operators
It is convenient to openCCArray.Infix to access the infix operators without cluttering the scope too much.
include module type of Infix
Sourceval (>>=) : 'a t -> ('a -> 'b t) -> 'b t a >>= f is the infix version of flat_map.
Sourceval (>>|) : 'a t -> ('a -> 'b) -> 'b t a >>| f is the infix version of map.
Sourceval (>|=) : 'a t -> ('a -> 'b) -> 'b t a >|= f is the infix version of map.
Sourceval (--) : int -> int -> int t x -- y creates an array containing integers in the range x .. y. Bounds included.
Sourceval (--^) : int -> int -> int t x --^ y creates an array containing integers in the range x .. y. Right bound excluded.
Let operators on OCaml >= 4.08.0, nothing otherwise
Sourceval (let+) : 'a array -> ('a -> 'b) -> 'b array Sourceval (and+) : 'a array -> 'b array -> ('a * 'b) array Sourceval (let*) : 'a array -> ('a -> 'b array) -> 'b array Sourceval (and*) : 'a array -> 'b array -> ('a * 'b) array