.TH "Float.Array" 3 2024-02-29 OCamldoc "OCaml library"
.SH NAME
Float.Array \- Float arrays with packed representation.
.SH Module
Module   Float.Array
.SH Documentation
.sp
Module
.BI "Array"
 : 
.B sig end

.sp
Float arrays with packed representation\&.

.sp

.sp
.sp
.I type t 
= 
.B floatarray

.sp
The type of float arrays with packed representation\&.

.sp
.B "Since"
4.08

.sp

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

.sp

.I val get 
: 
.B t -> int -> float
.sp

.ft B
get a n
.ft R
returns the element number 
.ft B
n
.ft R
of floatarray 
.ft B
a
.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 t -> int -> float -> unit
.sp

.ft B
set a n x
.ft R
modifies floatarray 
.ft B
a
.ft R
in place, replacing element
number 
.ft B
n
.ft R
with 
.ft B
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 -> float -> t
.sp

.ft B
make n x
.ft R
returns a fresh floatarray of length 
.ft B
n
.ft R
, initialized with 
.ft B
x
.ft R
\&.

.sp
.B "Raises Invalid_argument"
if 
.ft B
n < 0
.ft R
or 
.ft B
n > Sys\&.max_floatarray_length
.ft R
\&.

.sp

.I val create 
: 
.B int -> t
.sp

.ft B
create n
.ft R
returns a fresh floatarray of length 
.ft B
n
.ft R
,
with uninitialized data\&.

.sp
.B "Raises Invalid_argument"
if 
.ft B
n < 0
.ft R
or 
.ft B
n > Sys\&.max_floatarray_length
.ft R
\&.

.sp

.I val init 
: 
.B int -> (int -> float) -> t
.sp

.ft B
init n f
.ft R
returns a fresh floatarray 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 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_floatarray_length
.ft R
\&.

.sp

.I val append 
: 
.B t -> t -> t
.sp

.ft B
append v1 v2
.ft R
returns a fresh floatarray containing the
concatenation of the floatarrays 
.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_floatarray_length
.ft R
\&.

.sp

.I val concat 
: 
.B t list -> t
.sp
Same as 
.ft B
Float\&.Array\&.append
.ft R
, but concatenates a list of floatarrays\&.

.sp

.I val sub 
: 
.B t -> int -> int -> t
.sp

.ft B
sub a pos len
.ft R
returns a fresh floatarray 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 floatarray 
.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 t -> t
.sp

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

.sp

.I val fill 
: 
.B t -> int -> int -> float -> unit
.sp

.ft B
fill a pos len x
.ft R
modifies the floatarray 
.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 t -> int -> t -> int -> int -> unit
.sp

.ft B
blit src src_pos dst dst_pos len
.ft R
copies 
.ft B
len
.ft R
elements
from floatarray 
.ft B
src
.ft R
, starting at element number 
.ft B
src_pos
.ft R
,
to floatarray 
.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 floatarray, 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 t -> float 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 float list -> t
.sp

.ft B
of_list l
.ft R
returns a fresh floatarray 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_floatarray_length
.ft R
\&.

.sp

.PP
.SS Iterators

.PP

.I val iter 
: 
.B (float -> unit) -> t -> 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 (int -> float -> unit) -> t -> unit
.sp
Same as 
.ft B
Float\&.Array\&.iter
.ft R
, but the
function is applied with the index of the element as first argument,
and the element itself as second argument\&.

.sp

.I val map 
: 
.B (float -> float) -> t -> t
.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 a floatarray with the results returned by 
.ft B
f
.ft R
\&.

.sp

.I val map_inplace 
: 
.B (float -> float) -> t -> 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 (int -> float -> float) -> t -> t
.sp
Same as 
.ft B
Float\&.Array\&.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 (int -> float -> float) -> t -> unit
.sp
Same as 
.ft B
Float\&.Array\&.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 ('acc -> float -> 'acc) -> 'acc -> t -> 'acc
.sp

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

.sp

.I val fold_right 
: 
.B (float -> 'acc -> 'acc) -> t -> '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 floatarray 
.ft B
a
.ft R
\&.

.sp

.PP
.SS Iterators on two arrays

.PP

.I val iter2 
: 
.B (float -> float -> unit) -> t -> t -> unit
.sp

.ft B
Array\&.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 "Raises Invalid_argument"
if the floatarrays are not the same size\&.

.sp

.I val map2 
: 
.B (float -> float -> float) -> t -> t -> t
.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 a floatarray 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 "Raises Invalid_argument"
if the floatarrays are not the same size\&.

.sp

.PP
.SS Array scanning

.PP

.I val for_all 
: 
.B (float -> bool) -> t -> bool
.sp

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

.sp

.I val exists 
: 
.B (float -> bool) -> t -> bool
.sp

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

.sp

.I val mem 
: 
.B float -> t -> bool
.sp

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

.sp

.I val mem_ieee 
: 
.B float -> t -> bool
.sp
Same as 
.ft B
Float\&.Array\&.mem
.ft R
, but uses IEEE equality instead of structural equality\&.

.sp

.PP
.SS Array searching

.PP

.I val find_opt 
: 
.B (float -> bool) -> t -> float option
.sp

.sp

.I val find_index 
: 
.B (float -> bool) -> t -> 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 (float -> 'a option) -> t -> 'a option
.sp

.sp

.I val find_mapi 
: 
.B (int -> float -> 'a option) -> t -> 'a 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 Sorting

.PP

.I val sort 
: 
.B (float -> float -> int) -> t -> unit
.sp
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, 
.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 floatarray 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 (float -> float -> int) -> t -> unit
.sp
Same as 
.ft B
Float\&.Array\&.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
floatarray of length 
.ft B
n/2
.ft R
, where 
.ft B
n
.ft R
is the length of the floatarray\&.
It is usually faster than the current implementation of 
.ft B
Float\&.Array\&.sort
.ft R
\&.

.sp

.I val fast_sort 
: 
.B (float -> float -> int) -> t -> unit
.sp
Same as 
.ft B
Float\&.Array\&.sort
.ft R
or 
.ft B
Float\&.Array\&.stable_sort
.ft R
, whichever is faster
on typical input\&.

.sp

.PP
.SS Float arrays and Sequences

.PP

.I val to_seq 
: 
.B t -> float Seq.t
.sp
Iterate on the floatarray, in increasing order\&. Modifications of the
floatarray during iteration will be reflected in the sequence\&.

.sp

.I val to_seqi 
: 
.B t -> (int * float) Seq.t
.sp
Iterate on the floatarray, in increasing order, yielding indices along
elements\&. Modifications of the floatarray during iteration will be
reflected in the sequence\&.

.sp

.I val of_seq 
: 
.B float Seq.t -> t
.sp
Create an array from the generator\&.

.sp

.I val map_to_array 
: 
.B (float -> 'a) -> t -> 'a array
.sp

.ft B
map_to_array 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_from_array 
: 
.B ('a -> float) -> 'a array -> t
.sp

.ft B
map_from_array f a
.ft R
applies function 
.ft B
f
.ft R
to all the elements of 
.ft B
a
.ft R
,
and builds a floatarray with the results returned by 
.ft B
f
.ft R
\&.

.sp

.PP
.SS Arrays and concurrency safety
.sp
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\&.
.sp
.SS Atomicity
.sp
Every float 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 = Float\&.Array\&.make size 1\&.
.br
\&  let update a f () =
.br
\&     Float\&.Array\&.iteri (fun i x \-> Float\&.Array\&.set a i (f x)) a
.br
\&  let d1 = Domain\&.spawn (update a (fun x \-> x +\&. 1\&.))
.br
\&  let d2 = Domain\&.spawn (update a (fun x \->  2\&. *\&. x +\&. 1\&.))
.br
\&  let () = Domain\&.join d1; Domain\&.join d2
.br
\&  
.ft R
.EE
.sp
After executing this code, each field of the float 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\&.
.sp
.SS Tearing 
.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 = Float\&.Array\&.make size 0\&.
.br
\&  let max_floats = Float\&.Array\&.make size Float\&.max_float
.br
\&  let res = Float\&.Array\&.copy zeros
.br
\&  let d1 = Domain\&.spawn (fun () \-> Float\&.Array\&.blit zeros 0 res 0 size)
.br
\&  let d2 = Domain\&.spawn (fun () \-> Float\&.Array\&.blit max_floats 0 res 0 size)
.br
\&  let () = Domain\&.join d1; Domain\&.join d2
.br
\&  
.ft R
.EE
.sp
the 
.ft B
res
.ft R
float 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