.TH "ArrayLabels" 3 2024-02-29 OCamldoc "OCaml library"
.SH NAME
ArrayLabels \- Array operations.
.SH Module
Module   ArrayLabels
.SH Documentation
.sp
Module
.BI "ArrayLabels"
 : 
.B sig end

.sp
Array operations\&.
.sp
The labeled version of this module can be used as described in the
.ft B
StdLabels
.ft R
module\&.

.sp

.sp
.sp
.I type 
.B 'a
.I t 
= 
.B 'a array

.sp
An alias for the type of arrays\&.

.sp

.I val length 
: 
.B 'a array -> int
.sp
Return the length (number of elements) of the given array\&.

.sp

.I val get 
: 
.B 'a array -> int -> 'a
.sp

.ft B
get a n
.ft R
returns the element number 
.ft B
n
.ft R
of array 
.ft B
a
.ft R
\&.
The first element has number 0\&.
The last element has number 
.ft B
length a \- 1
.ft R
\&.
You can also write 
.ft B
a\&.(n)
.ft R
instead of 
.ft B
get a n
.ft R
\&.

.sp
.B "Raises Invalid_argument"
if 
.ft B
n
.ft R
is outside the range 0 to 
.ft B
(length a \- 1)
.ft R
\&.

.sp

.I val set 
: 
.B 'a array -> int -> 'a -> unit
.sp

.ft B
set a n x
.ft R
modifies array 
.ft B
a
.ft R
in place, replacing
element number 
.ft B
n
.ft R
with 
.ft B
x
.ft R
\&.
You can also write 
.ft B
a\&.(n) <\- x
.ft R
instead of 
.ft B
set a n x
.ft R
\&.

.sp
.B "Raises Invalid_argument"
if 
.ft B
n
.ft R
is outside the range 0 to 
.ft B
length a \- 1
.ft R
\&.

.sp

.I val make 
: 
.B int -> 'a -> 'a array
.sp

.ft B
make n x
.ft R
returns a fresh array of length 
.ft B
n
.ft R
,
initialized with 
.ft B
x
.ft R
\&.
All the elements of this new array are initially
physically equal to 
.ft B
x
.ft R
(in the sense of the 
.ft B
==
.ft R
predicate)\&.
Consequently, if 
.ft B
x
.ft R
is mutable, it is shared among all elements
of the array, and modifying 
.ft B
x
.ft R
through one of the array entries
will modify all other entries at the same time\&.

.sp
.B "Raises Invalid_argument"
if 
.ft B
n < 0
.ft R
or 
.ft B
n > Sys\&.max_array_length
.ft R
\&.
If the value of 
.ft B
x
.ft R
is a floating\-point number, then the maximum
size is only 
.ft B
Sys\&.max_array_length / 2
.ft R
\&.

.sp

.I val create_float 
: 
.B int -> float array
.sp

.ft B
create_float n
.ft R
returns a fresh float array of length 
.ft B
n
.ft R
,
with uninitialized data\&.

.sp
.B "Since"
4.03

.sp

.I val init 
: 
.B int -> f:(int -> 'a) -> 'a array
.sp

.ft B
init n ~f
.ft R
returns a fresh array of length 
.ft B
n
.ft R
,
with element number 
.ft B
i
.ft R
initialized to the result of 
.ft B
f i
.ft R
\&.
In other terms, 
.ft B
init n ~f
.ft R
tabulates the results of 
.ft B
f
.ft R
applied in order to the integers 
.ft B
0
.ft R
to 
.ft B
n\-1
.ft R
\&.

.sp
.B "Raises Invalid_argument"
if 
.ft B
n < 0
.ft R
or 
.ft B
n > Sys\&.max_array_length
.ft R
\&.
If the return type of 
.ft B
f
.ft R
is 
.ft B
float
.ft R
, then the maximum
size is only 
.ft B
Sys\&.max_array_length / 2
.ft R
\&.

.sp

.I val make_matrix 
: 
.B dimx:int -> dimy:int -> 'a -> 'a array array
.sp

.ft B
make_matrix ~dimx ~dimy e
.ft R
returns a two\-dimensional array
(an array of arrays) with first dimension 
.ft B
dimx
.ft R
and
second dimension 
.ft B
dimy
.ft R
\&. All the elements of this new matrix
are initially physically equal to 
.ft B
e
.ft R
\&.
The element (
.ft B
x,y
.ft R
) of a matrix 
.ft B
m
.ft R
is accessed
with the notation 
.ft B
m\&.(x)\&.(y)
.ft R
\&.

.sp
.B "Raises Invalid_argument"
if 
.ft B
dimx
.ft R
or 
.ft B
dimy
.ft R
is negative or
greater than 
.ft B
Sys\&.max_array_length
.ft R
\&.
If the value of 
.ft B
e
.ft R
is a floating\-point number, then the maximum
size is only 
.ft B
Sys\&.max_array_length / 2
.ft R
\&.

.sp

.I val append 
: 
.B 'a array -> 'a array -> 'a array
.sp

.ft B
append v1 v2
.ft R
returns a fresh array containing the
concatenation of the arrays 
.ft B
v1
.ft R
and 
.ft B
v2
.ft R
\&.

.sp
.B "Raises Invalid_argument"
if
.ft B
length v1 + length v2 > Sys\&.max_array_length
.ft R
\&.

.sp

.I val concat 
: 
.B 'a array list -> 'a array
.sp
Same as 
.ft B
ArrayLabels\&.append
.ft R
, but concatenates a list of arrays\&.

.sp

.I val sub 
: 
.B 'a array -> pos:int -> len:int -> 'a array
.sp

.ft B
sub a ~pos ~len
.ft R
returns a fresh array of length 
.ft B
len
.ft R
,
containing the elements number 
.ft B
pos
.ft R
to 
.ft B
pos + len \- 1
.ft R
of array 
.ft B
a
.ft R
\&.

.sp
.B "Raises Invalid_argument"
if 
.ft B
pos
.ft R
and 
.ft B
len
.ft R
do not
designate a valid subarray of 
.ft B
a
.ft R
; that is, if
.ft B
pos < 0
.ft R
, or 
.ft B
len < 0
.ft R
, or 
.ft B
pos + len > length a
.ft R
\&.

.sp

.I val copy 
: 
.B 'a array -> 'a array
.sp

.ft B
copy a
.ft R
returns a copy of 
.ft B
a
.ft R
, that is, a fresh array
containing the same elements as 
.ft B
a
.ft R
\&.

.sp

.I val fill 
: 
.B 'a array -> pos:int -> len:int -> 'a -> unit
.sp

.ft B
fill a ~pos ~len x
.ft R
modifies the array 
.ft B
a
.ft R
in place,
storing 
.ft B
x
.ft R
in elements number 
.ft B
pos
.ft R
to 
.ft B
pos + len \- 1
.ft R
\&.

.sp
.B "Raises Invalid_argument"
if 
.ft B
pos
.ft R
and 
.ft B
len
.ft R
do not
designate a valid subarray of 
.ft B
a
.ft R
\&.

.sp

.I val blit 
: 
.B src:'a array -> src_pos:int -> dst:'a array -> dst_pos:int -> len:int -> unit
.sp

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

.sp
.B "Raises Invalid_argument"
if 
.ft B
src_pos
.ft R
and 
.ft B
len
.ft R
do not
designate a valid subarray of 
.ft B
src
.ft R
, or if 
.ft B
dst_pos
.ft R
and 
.ft B
len
.ft R
do not
designate a valid subarray of 
.ft B
dst
.ft R
\&.

.sp

.I val to_list 
: 
.B 'a array -> 'a list
.sp

.ft B
to_list a
.ft R
returns the list of all the elements of 
.ft B
a
.ft R
\&.

.sp

.I val of_list 
: 
.B 'a list -> 'a array
.sp

.ft B
of_list l
.ft R
returns a fresh array containing the elements
of 
.ft B
l
.ft R
\&.

.sp
.B "Raises Invalid_argument"
if the length of 
.ft B
l
.ft R
is greater than
.ft B
Sys\&.max_array_length
.ft R
\&.

.sp

.PP
.SS Iterators

.PP

.I val iter 
: 
.B f:('a -> unit) -> 'a array -> unit
.sp

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

.sp

.I val iteri 
: 
.B f:(int -> 'a -> unit) -> 'a array -> unit
.sp
Same as 
.ft B
ArrayLabels\&.iter
.ft R
, but the
function is applied to the index of the element as first argument,
and the element itself as second argument\&.

.sp

.I val map 
: 
.B f:('a -> 'b) -> 'a array -> 'b array
.sp

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

.sp

.I val map_inplace 
: 
.B f:('a -> 'a) -> 'a array -> unit
.sp

.ft B
map_inplace ~f a
.ft R
applies function 
.ft B
f
.ft R
to all elements of 
.ft B
a
.ft R
,
and updates their values in place\&.

.sp
.B "Since"
5.1

.sp

.I val mapi 
: 
.B f:(int -> 'a -> 'b) -> 'a array -> 'b array
.sp
Same as 
.ft B
ArrayLabels\&.map
.ft R
, but the
function is applied to the index of the element as first argument,
and the element itself as second argument\&.

.sp

.I val mapi_inplace 
: 
.B f:(int -> 'a -> 'a) -> 'a array -> unit
.sp
Same as 
.ft B
ArrayLabels\&.map_inplace
.ft R
, but the function is applied to the index of the
element as first argument, and the element itself as second argument\&.

.sp
.B "Since"
5.1

.sp

.I val fold_left 
: 
.B f:('acc -> 'a -> 'acc) -> init:'acc -> 'a array -> 'acc
.sp

.ft B
fold_left ~f ~init a
.ft R
computes
.ft B
f (\&.\&.\&. (f (f init a\&.(0)) a\&.(1)) \&.\&.\&.) a\&.(n\-1)
.ft R
,
where 
.ft B
n
.ft R
is the length of the array 
.ft B
a
.ft R
\&.

.sp

.I val fold_left_map 
: 
.B f:('acc -> 'a -> 'acc * 'b) -> init:'acc -> 'a array -> 'acc * 'b array
.sp

.ft B
fold_left_map
.ft R
is a combination of 
.ft B
ArrayLabels\&.fold_left
.ft R
and 
.ft B
ArrayLabels\&.map
.ft R
that threads an
accumulator through calls to 
.ft B
f
.ft R
\&.

.sp
.B "Since"
4.13

.sp

.I val fold_right 
: 
.B f:('a -> 'acc -> 'acc) -> 'a array -> init:'acc -> 'acc
.sp

.ft B
fold_right ~f a ~init
.ft R
computes
.ft B
f a\&.(0) (f a\&.(1) ( \&.\&.\&. (f a\&.(n\-1) init) \&.\&.\&.))
.ft R
,
where 
.ft B
n
.ft R
is the length of the array 
.ft B
a
.ft R
\&.

.sp

.PP
.SS Iterators on two arrays

.PP

.I val iter2 
: 
.B f:('a -> 'b -> unit) -> 'a array -> 'b array -> unit
.sp

.ft B
iter2 ~f a b
.ft R
applies function 
.ft B
f
.ft R
to all the elements of 
.ft B
a
.ft R
and 
.ft B
b
.ft R
\&.

.sp
.B "Since"
4.05

.sp
.B "Raises Invalid_argument"
if the arrays are not the same size\&.

.sp

.I val map2 
: 
.B f:('a -> 'b -> 'c) -> 'a array -> 'b array -> 'c array
.sp

.ft B
map2 ~f a b
.ft R
applies function 
.ft B
f
.ft R
to all the elements of 
.ft B
a
.ft R
and 
.ft B
b
.ft R
, and builds an array with the results returned by 
.ft B
f
.ft R
:
.ft B
[| f a\&.(0) b\&.(0); \&.\&.\&.; f a\&.(length a \- 1) b\&.(length b \- 1)|]
.ft R
\&.

.sp
.B "Since"
4.05

.sp
.B "Raises Invalid_argument"
if the arrays are not the same size\&.

.sp

.PP
.SS Array scanning

.PP

.I val for_all 
: 
.B f:('a -> bool) -> 'a array -> bool
.sp

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

.sp
.B "Since"
4.03

.sp

.I val exists 
: 
.B f:('a -> bool) -> 'a array -> bool
.sp

.ft B
exists ~f [|a1; \&.\&.\&.; an|]
.ft R
checks if at least one element of
the array satisfies the predicate 
.ft B
f
.ft R
\&. That is, it returns
.ft B
(f a1) || (f a2) || \&.\&.\&. || (f an)
.ft R
\&.

.sp
.B "Since"
4.03

.sp

.I val for_all2 
: 
.B f:('a -> 'b -> bool) -> 'a array -> 'b array -> bool
.sp
Same as 
.ft B
ArrayLabels\&.for_all
.ft R
, but for a two\-argument predicate\&.

.sp
.B "Since"
4.11

.sp
.B "Raises Invalid_argument"
if the two arrays have different lengths\&.

.sp

.I val exists2 
: 
.B f:('a -> 'b -> bool) -> 'a array -> 'b array -> bool
.sp
Same as 
.ft B
ArrayLabels\&.exists
.ft R
, but for a two\-argument predicate\&.

.sp
.B "Since"
4.11

.sp
.B "Raises Invalid_argument"
if the two arrays have different lengths\&.

.sp

.I val mem 
: 
.B 'a -> set:'a array -> bool
.sp

.ft B
mem a ~set
.ft R
is true if and only if 
.ft B
a
.ft R
is structurally equal
to an element of 
.ft B
l
.ft R
(i\&.e\&. there is an 
.ft B
x
.ft R
in 
.ft B
l
.ft R
such that
.ft B
compare a x = 0
.ft R
)\&.

.sp
.B "Since"
4.03

.sp

.I val memq 
: 
.B 'a -> set:'a array -> bool
.sp
Same as 
.ft B
ArrayLabels\&.mem
.ft R
, but uses physical equality
instead of structural equality to compare list elements\&.

.sp
.B "Since"
4.03

.sp

.I val find_opt 
: 
.B f:('a -> bool) -> 'a array -> 'a option
.sp

.ft B
find_opt ~f a
.ft R
returns the first element of the array 
.ft B
a
.ft R
that satisfies
the predicate 
.ft B
f
.ft R
, or 
.ft B
None
.ft R
if there is no value that satisfies 
.ft B
f
.ft R
in the
array 
.ft B
a
.ft R
\&.

.sp
.B "Since"
4.13

.sp

.I val find_index 
: 
.B f:('a -> bool) -> 'a array -> int option
.sp

.ft B
find_index ~f a
.ft R
returns 
.ft B
Some i
.ft R
, where 
.ft B
i
.ft R
is the index of the first
element of the array 
.ft B
a
.ft R
that satisfies 
.ft B
f x
.ft R
, if there is such an
element\&.
.sp
It returns 
.ft B
None
.ft R
if there is no such element\&.

.sp
.B "Since"
5.1

.sp

.I val find_map 
: 
.B f:('a -> 'b option) -> 'a array -> 'b option
.sp

.ft B
find_map ~f a
.ft R
applies 
.ft B
f
.ft R
to the elements of 
.ft B
a
.ft R
in order, and returns the
first result of the form 
.ft B
Some v
.ft R
, or 
.ft B
None
.ft R
if none exist\&.

.sp
.B "Since"
4.13

.sp

.I val find_mapi 
: 
.B f:(int -> 'a -> 'b option) -> 'a array -> 'b option
.sp
Same as 
.ft B
find_map
.ft R
, but the predicate is applied to the index of
the element as first argument (counting from 0), and the element
itself as second argument\&.

.sp
.B "Since"
5.1

.sp

.PP
.SS Arrays of pairs

.PP

.I val split 
: 
.B ('a * 'b) array -> 'a array * 'b array
.sp

.ft B
split [|(a1,b1); \&.\&.\&.; (an,bn)|]
.ft R
is 
.ft B
([|a1; \&.\&.\&.; an|], [|b1; \&.\&.\&.; bn|])
.ft R
\&.

.sp
.B "Since"
4.13

.sp

.I val combine 
: 
.B 'a array -> 'b array -> ('a * 'b) array
.sp

.ft B
combine [|a1; \&.\&.\&.; an|] [|b1; \&.\&.\&.; bn|]
.ft R
is 
.ft B
[|(a1,b1); \&.\&.\&.; (an,bn)|]
.ft R
\&.
Raise 
.ft B
Invalid_argument
.ft R
if the two arrays have different lengths\&.

.sp
.B "Since"
4.13

.sp

.PP
.SS Sorting

.PP

.I val sort 
: 
.B cmp:('a -> 'a -> int) -> 'a array -> unit
.sp
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, 
.ft B
compare
.ft R
is
a suitable comparison function\&. After calling 
.ft B
sort
.ft R
, the
array is sorted in place in increasing order\&.
.ft B
sort
.ft R
is guaranteed to run in constant heap space
and (at most) logarithmic stack space\&.
.sp
The current implementation uses Heap Sort\&.  It runs in constant
stack space\&.
.sp
Specification of the comparison function:
Let 
.ft B
a
.ft R
be the array and 
.ft B
cmp
.ft R
the comparison function\&.  The following
must be true for all 
.ft B
x
.ft R
, 
.ft B
y
.ft R
, 
.ft B
z
.ft R
in 
.ft B
a
.ft R
:
.sp
\-  
.ft B
cmp x y
.ft R
> 0 if and only if 
.ft B
cmp y x
.ft R
< 0
.sp
\-  if 
.ft B
cmp x y
.ft R
>= 0 and 
.ft B
cmp y z
.ft R
>= 0 then 
.ft B
cmp x z
.ft R
>= 0

When 
.ft B
sort
.ft R
returns, 
.ft B
a
.ft R
contains the same elements as before,
reordered in such a way that for all i and j valid indices of 
.ft B
a
.ft R
:
.sp
\-  
.ft B
cmp a\&.(i) a\&.(j)
.ft R
>= 0 if and only if i >= j


.sp

.I val stable_sort 
: 
.B cmp:('a -> 'a -> int) -> 'a array -> unit
.sp
Same as 
.ft B
ArrayLabels\&.sort
.ft R
, 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\&.
.sp
The current implementation uses Merge Sort\&. It uses a temporary array of
length 
.ft B
n/2
.ft R
, where 
.ft B
n
.ft R
is the length of the array\&.  It is usually faster
than the current implementation of 
.ft B
ArrayLabels\&.sort
.ft R
\&.

.sp

.I val fast_sort 
: 
.B cmp:('a -> 'a -> int) -> 'a array -> unit
.sp
Same as 
.ft B
ArrayLabels\&.sort
.ft R
or 
.ft B
ArrayLabels\&.stable_sort
.ft R
, whichever is
faster on typical input\&.

.sp

.PP
.SS Arrays and Sequences

.PP

.I val to_seq 
: 
.B 'a array -> 'a Seq.t
.sp
Iterate on the array, in increasing order\&. Modifications of the
array during iteration will be reflected in the sequence\&.

.sp
.B "Since"
4.07

.sp

.I val to_seqi 
: 
.B 'a array -> (int * 'a) Seq.t
.sp
Iterate on the array, in increasing order, yielding indices along elements\&.
Modifications of the array during iteration will be reflected in the
sequence\&.

.sp
.B "Since"
4.07

.sp

.I val of_seq 
: 
.B 'a Seq.t -> 'a array
.sp
Create an array from the generator

.sp
.B "Since"
4.07

.sp

.PP
.SS Arrays and concurrency safety
.sp
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\&.
.sp
.SS Atomicity
.sp
Every array operation that accesses more than one array element is not
atomic\&. This includes iteration, scanning, sorting, splitting and
combining arrays\&.
.sp
For example, consider the following program:
.EX
.ft B
let size = 100_000_000
.br
\&let a = ArrayLabels\&.make size 1
.br
\&let d1 = Domain\&.spawn (fun () \->
.br
\&   ArrayLabels\&.iteri ~f:(fun i x \-> a\&.(i) <\- x + 1) a
.br
\&)
.br
\&let d2 = Domain\&.spawn (fun () \->
.br
\&  ArrayLabels\&.iteri ~f:(fun i x \-> a\&.(i) <\- 2 * x + 1) a
.br
\&)
.br
\&let () = Domain\&.join d1; Domain\&.join d2
.br
\&
.ft R
.EE
.sp
After executing this code, each field of the array 
.ft B
a
.ft R
is either 
.ft B
2
.ft R
, 
.ft B
3
.ft R
,
.ft B
4
.ft R
or 
.ft B
5
.ft R
\&. If atomicity is required, then the user must implement their own
synchronization (for example, using 
.ft B
Mutex\&.t
.ft R
)\&.
.sp
.SS Data races
.sp
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\&.
.sp
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\&.
.sp
Whenever possible, data races should be avoided by using synchronization to
mediate the accesses to the array elements\&.
.sp
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)\&.
.sp
.SS Float arrays
.sp
Float arrays have two supplementary caveats in the presence of data races\&.
.sp
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\&.
.sp
For instance, at the end of
.EX
.ft B
let zeros = Array\&.make size 0\&.
.br
\&let max_floats = Array\&.make size Float\&.max_float
.br
\&let res = Array\&.copy zeros
.br
\&let d1 = Domain\&.spawn (fun () \-> Array\&.blit zeros 0 res 0 size)
.br
\&let d2 = Domain\&.spawn (fun () \-> Array\&.blit max_floats 0 res 0 size)
.br
\&let () = Domain\&.join d1; Domain\&.join d2
.br
\&
.ft R
.EE
the 
.ft B
res
.ft R
array might contain values that are neither 
.ft B
0\&.
.ft R
nor 
.ft B
max_float
.ft R
\&.
.sp
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\&.
.PP