A time and space-efficient implementation of vectors using
packed arrays, suitable for high performance use, both in terms
of large data quantities, or high speed requirements. Vectors
are encoded as strict arrays, held in a `ForeignPtr`

,
and can be passed between C and Haskell with little effort.

This module is intended to be imported `qualified`

, to avoid name
clashes with Prelude functions. eg.

import qualified Data.StorableVector as V

Original GHC implementation by Bryan O'Sullivan. Rewritten to use UArray by Simon Marlow. Rewritten to support slices and use ForeignPtr by David Roundy. Polished and extended by Don Stewart. Generalized to any Storable value by Spencer Janssen. Chunky lazy stream, also with chunk pattern control, mutable access in ST monad, Builder monoid by Henning Thieleman.

- data Vector a
- empty :: Storable a => Vector a
- singleton :: Storable a => a -> Vector a
- pack :: Storable a => [a] -> Vector a
- unpack :: Storable a => Vector a -> [a]
- packN :: Storable a => Int -> [a] -> (Vector a, [a])
- packWith :: Storable b => (a -> b) -> [a] -> Vector b
- unpackWith :: Storable a => (a -> b) -> Vector a -> [b]
- cons :: Storable a => a -> Vector a -> Vector a
- snoc :: Storable a => Vector a -> a -> Vector a
- append :: Storable a => Vector a -> Vector a -> Vector a
- head :: Storable a => Vector a -> a
- last :: Storable a => Vector a -> a
- tail :: Storable a => Vector a -> Vector a
- init :: Vector a -> Vector a
- null :: Vector a -> Bool
- length :: Vector a -> Int
- viewL :: Storable a => Vector a -> Maybe (a, Vector a)
- viewR :: Storable a => Vector a -> Maybe (Vector a, a)
- switchL :: Storable a => b -> (a -> Vector a -> b) -> Vector a -> b
- switchR :: Storable a => b -> (Vector a -> a -> b) -> Vector a -> b
- map :: (Storable a, Storable b) => (a -> b) -> Vector a -> Vector b
- reverse :: Storable a => Vector a -> Vector a
- intersperse :: Storable a => a -> Vector a -> Vector a
- transpose :: Storable a => [Vector a] -> [Vector a]
- foldl :: Storable a => (b -> a -> b) -> b -> Vector a -> b
- foldl' :: Storable a => (b -> a -> b) -> b -> Vector a -> b
- foldl1 :: Storable a => (a -> a -> a) -> Vector a -> a
- foldl1' :: Storable a => (a -> a -> a) -> Vector a -> a
- foldr :: Storable a => (a -> b -> b) -> b -> Vector a -> b
- foldr1 :: Storable a => (a -> a -> a) -> Vector a -> a
- concat :: Storable a => [Vector a] -> Vector a
- concatMap :: (Storable a, Storable b) => (a -> Vector b) -> Vector a -> Vector b
- monoidConcatMap :: (Storable a, Monoid m) => (a -> m) -> Vector a -> m
- any :: Storable a => (a -> Bool) -> Vector a -> Bool
- all :: Storable a => (a -> Bool) -> Vector a -> Bool
- maximum :: (Storable a, Ord a) => Vector a -> a
- minimum :: (Storable a, Ord a) => Vector a -> a
- scanl :: (Storable a, Storable b) => (a -> b -> a) -> a -> Vector b -> Vector a
- scanl1 :: Storable a => (a -> a -> a) -> Vector a -> Vector a
- scanr :: (Storable a, Storable b) => (a -> b -> b) -> b -> Vector a -> Vector b
- scanr1 :: Storable a => (a -> a -> a) -> Vector a -> Vector a
- mapAccumL :: (Storable a, Storable b) => (acc -> a -> (acc, b)) -> acc -> Vector a -> (acc, Vector b)
- mapAccumR :: (Storable a, Storable b) => (acc -> a -> (acc, b)) -> acc -> Vector a -> (acc, Vector b)
- mapIndexed :: (Storable a, Storable b) => (Int -> a -> b) -> Vector a -> Vector b
- replicate :: Storable a => Int -> a -> Vector a
- iterateN :: Storable a => Int -> (a -> a) -> a -> Vector a
- unfoldr :: Storable b => (a -> Maybe (b, a)) -> a -> Vector b
- unfoldrN :: Storable b => Int -> (a -> Maybe (b, a)) -> a -> (Vector b, Maybe a)
- unfoldrResultN :: Storable b => Int -> (a -> c) -> (a -> Either c (b, a)) -> a -> (Vector b, c)
- sample :: Storable a => Int -> (Int -> a) -> Vector a
- take :: Storable a => Int -> Vector a -> Vector a
- drop :: Storable a => Int -> Vector a -> Vector a
- splitAt :: Storable a => Int -> Vector a -> (Vector a, Vector a)
- takeWhile :: Storable a => (a -> Bool) -> Vector a -> Vector a
- dropWhile :: Storable a => (a -> Bool) -> Vector a -> Vector a
- span :: Storable a => (a -> Bool) -> Vector a -> (Vector a, Vector a)
- spanEnd :: Storable a => (a -> Bool) -> Vector a -> (Vector a, Vector a)
- break :: Storable a => (a -> Bool) -> Vector a -> (Vector a, Vector a)
- breakEnd :: Storable a => (a -> Bool) -> Vector a -> (Vector a, Vector a)
- group :: (Storable a, Eq a) => Vector a -> [Vector a]
- groupBy :: Storable a => (a -> a -> Bool) -> Vector a -> [Vector a]
- inits :: Storable a => Vector a -> [Vector a]
- tails :: Storable a => Vector a -> [Vector a]
- split :: (Storable a, Eq a) => a -> Vector a -> [Vector a]
- splitWith :: Storable a => (a -> Bool) -> Vector a -> [Vector a]
- tokens :: Storable a => (a -> Bool) -> Vector a -> [Vector a]
- join :: Storable a => Vector a -> [Vector a] -> Vector a
- isPrefixOf :: (Storable a, Eq a) => Vector a -> Vector a -> Bool
- isSuffixOf :: (Storable a, Eq a) => Vector a -> Vector a -> Bool
- elem :: (Storable a, Eq a) => a -> Vector a -> Bool
- notElem :: (Storable a, Eq a) => a -> Vector a -> Bool
- find :: Storable a => (a -> Bool) -> Vector a -> Maybe a
- filter :: Storable a => (a -> Bool) -> Vector a -> Vector a
- index :: Storable a => Vector a -> Int -> a
- elemIndex :: (Storable a, Eq a) => a -> Vector a -> Maybe Int
- elemIndices :: (Storable a, Eq a) => a -> Vector a -> [Int]
- elemIndexEnd :: (Storable a, Eq a) => a -> Vector a -> Maybe Int
- findIndex :: Storable a => (a -> Bool) -> Vector a -> Maybe Int
- findIndices :: Storable a => (a -> Bool) -> Vector a -> [Int]
- count :: (Storable a, Eq a) => a -> Vector a -> Int
- findIndexOrEnd :: Storable a => (a -> Bool) -> Vector a -> Int
- zip :: (Storable a, Storable b) => Vector a -> Vector b -> [(a, b)]
- zipWith :: (Storable a, Storable b, Storable c) => (a -> b -> c) -> Vector a -> Vector b -> Vector c
- zipWith3 :: (Storable a, Storable b, Storable c, Storable d) => (a -> b -> c -> d) -> Vector a -> Vector b -> Vector c -> Vector d
- zipWith4 :: (Storable a, Storable b, Storable c, Storable d, Storable e) => (a -> b -> c -> d -> e) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e
- unzip :: (Storable a, Storable b) => [(a, b)] -> (Vector a, Vector b)
- copy :: Storable a => Vector a -> Vector a
- hGet :: Storable a => Handle -> Int -> IO (Vector a)
- hPut :: Storable a => Handle -> Vector a -> IO ()
- readFile :: Storable a => FilePath -> IO (Vector a)
- writeFile :: Storable a => FilePath -> Vector a -> IO ()
- appendFile :: Storable a => FilePath -> Vector a -> IO ()

# The `Vector`

type

A space-efficient representation of a vector, supporting many efficient operations.

Instances of Eq, Ord, Read, Show, Data, Typeable

# Introducing and eliminating `Vector`

s

packN :: Storable a => Int -> [a] -> (Vector a, [a])Source

*O(n)* Convert first `n`

elements of a '[a]' into a 'Vector a'.

packWith :: Storable b => (a -> b) -> [a] -> Vector bSource

*O(n)* Convert a list into a `Vector`

using a conversion function

unpackWith :: Storable a => (a -> b) -> Vector a -> [b]Source

*O(n)* Convert a `Vector`

into a list using a conversion function

# Basic interface

cons :: Storable a => a -> Vector a -> Vector aSource

*O(n)* `cons`

is analogous to (:) for lists, but of different
complexity, as it requires a memcpy.

# Transforming `Vector`

s

reverse :: Storable a => Vector a -> Vector aSource

*O(n)* `reverse`

`xs`

efficiently returns the elements of `xs`

in reverse order.

intersperse :: Storable a => a -> Vector a -> Vector aSource

*O(n)* The `intersperse`

function takes a element and a
`Vector`

and `intersperses' that element between the elements of
the `Vector`

. It is analogous to the intersperse function on
Lists.

# Reducing `Vector`

s (folds)

foldl' :: Storable a => (b -> a -> b) -> b -> Vector a -> bSource

'foldl\'' is like `foldl`

, but strict in the accumulator.

foldr :: Storable a => (a -> b -> b) -> b -> Vector a -> bSource

`foldr`

, applied to a binary operator, a starting value
(typically the right-identity of the operator), and a `Vector`

,
reduces the `Vector`

using the binary operator, from right to left.
However, it is not the same as `foldl`

applied to the reversed vector.
Actually `foldr`

starts processing with the first element,
and thus can be used for efficiently building a singly linked list
by `foldr (:) [] vec`

.
Unfortunately `foldr`

is quite slow for low-level loops,
since GHC (up to 6.12.1) cannot detect the loop.

## Special folds

concatMap :: (Storable a, Storable b) => (a -> Vector b) -> Vector a -> Vector bSource

Map a function over a `Vector`

and concatenate the results

monoidConcatMap :: (Storable a, Monoid m) => (a -> m) -> Vector a -> mSource

This is like `mconcat . map f`

,
but in many cases the result of `f`

will not be storable.

# Building `Vector`

s

## Scans

scanr :: (Storable a, Storable b) => (a -> b -> b) -> b -> Vector a -> Vector bSource

scanr is the right-to-left dual of scanl.

## Accumulating maps

mapAccumL :: (Storable a, Storable b) => (acc -> a -> (acc, b)) -> acc -> Vector a -> (acc, Vector b)Source

mapAccumR :: (Storable a, Storable b) => (acc -> a -> (acc, b)) -> acc -> Vector a -> (acc, Vector b)Source

mapIndexed :: (Storable a, Storable b) => (Int -> a -> b) -> Vector a -> Vector bSource

*O(n)* map functions, provided with the index at each position

## Unfolding `Vector`

s

unfoldr :: Storable b => (a -> Maybe (b, a)) -> a -> Vector bSource

*O(n)*, where *n* is the length of the result. The `unfoldr`

function is analogous to the List 'unfoldr'. `unfoldr`

builds a
`Vector`

from a seed value. The function takes the element and
returns `Nothing`

if it is done producing the 'Vector or returns
`Just`

`(a,b)`

, in which case, `a`

is the next element in the `Vector`

,
and `b`

is the seed value for further production.

Examples:

unfoldr (\x -> if x <= 5 then Just (x, x + 1) else Nothing) 0 == pack [0, 1, 2, 3, 4, 5]

unfoldrN :: Storable b => Int -> (a -> Maybe (b, a)) -> a -> (Vector b, Maybe a)Source

*O(n)* Like `unfoldr`

, `unfoldrN`

builds a `Vector`

from a seed
value. However, the length of the result is limited by the first
argument to `unfoldrN`

. This function is more efficient than `unfoldr`

when the maximum length of the result is known.

The following equation relates `unfoldrN`

and `unfoldr`

:

fst (unfoldrN n f s) == take n (unfoldr f s)

unfoldrResultN :: Storable b => Int -> (a -> c) -> (a -> Either c (b, a)) -> a -> (Vector b, c)Source

*O(n)* Like `unfoldrN`

this function builds a `Vector`

from a seed value with limited size.
Additionally it returns a value, that depends on the state,
but is not necessarily the state itself.
If end of vector and end of the generator coincide,
then the result is as if only the end of vector is reached.

Example:

unfoldrResultN 30 Char.ord (\c -> if c>'z' then Left 1000 else Right (c, succ c)) 'a'

The following equation relates `unfoldrN`

and `unfoldrResultN`

:

unfoldrN n f s == unfoldrResultN n Just (maybe (Left Nothing) Right . f) s

It is not possible to express `unfoldrResultN`

in terms of `unfoldrN`

.

sample :: Storable a => Int -> (Int -> a) -> Vector aSource

*O(n)*, where *n* is the length of the result.
This function constructs a vector by evaluating a function
that depends on the element index.
It is a special case of `unfoldrN`

and can in principle be parallelized.

Examples:

sample 26 (\x -> chr(ord 'a'+x)) == pack "abcdefghijklmnopqrstuvwxyz"

# Substrings

## Breaking strings

group :: (Storable a, Eq a) => Vector a -> [Vector a]Source

The `group`

function takes a `Vector`

and returns a list of
`Vector`

s such that the concatenation of the result is equal to the
argument. Moreover, each sublist in the result contains only equal
elements. For example,

group "Mississippi" = ["M","i","ss","i","ss","i","pp","i"]

It is a special case of `groupBy`

, which allows the programmer to
supply their own equality test. It is about 40% faster than
*groupBy (==)*

inits :: Storable a => Vector a -> [Vector a]Source

*O(n)* Return all initial segments of the given `Vector`

, shortest first.

tails :: Storable a => Vector a -> [Vector a]Source

*O(n)* Return all final segments of the given `Vector`

, longest first.

## Breaking into many substrings

split :: (Storable a, Eq a) => a -> Vector a -> [Vector a]Source

*O(n)* Break a `Vector`

into pieces separated by the
argument, consuming the delimiter. I.e.

split '\n' "a\nb\nd\ne" == ["a","b","d","e"] split 'a' "aXaXaXa" == ["","X","X","X"] split 'x' "x" == ["",""]

and

join [c] . split c == id split == splitWith . (==)

As for all splitting functions in this library, this function does
not copy the substrings, it just constructs new `Vector`

s that
are slices of the original.

splitWith :: Storable a => (a -> Bool) -> Vector a -> [Vector a]Source

*O(n)* Splits a `Vector`

into components delimited by
separators, where the predicate returns True for a separator element.
The resulting components do not contain the separators. Two adjacent
separators result in an empty component in the output. eg.

splitWith (=='a') "aabbaca" == ["","","bb","c",""] splitWith (=='a') [] == []

tokens :: Storable a => (a -> Bool) -> Vector a -> [Vector a]Source

Like `splitWith`

, except that sequences of adjacent separators are
treated as a single separator. eg.

tokens (=='a') "aabbaca" == ["bb","c"]

## Joining strings

# Predicates

isPrefixOf :: (Storable a, Eq a) => Vector a -> Vector a -> BoolSource

*O(n)* The `isPrefixOf`

function takes two `Vector`

and returns `True`

iff the first is a prefix of the second.

isSuffixOf :: (Storable a, Eq a) => Vector a -> Vector a -> BoolSource

*O(n)* The `isSuffixOf`

function takes two `Vector`

s and returns `True`

iff the first is a suffix of the second.

The following holds:

isSuffixOf x y == reverse x `isPrefixOf` reverse y

# Searching `Vector`

s

## Searching by equality

## Searching with a predicate

# Indexing `Vector`

s

index :: Storable a => Vector a -> Int -> aSource

*O(1)* `Vector`

index (subscript) operator, starting from 0.

elemIndices :: (Storable a, Eq a) => a -> Vector a -> [Int]Source

*O(n)* The `elemIndices`

function extends `elemIndex`

, by returning
the indices of all elements equal to the query element, in ascending order.

elemIndexEnd :: (Storable a, Eq a) => a -> Vector a -> Maybe IntSource

*O(n)* The `elemIndexEnd`

function returns the last index of the
element in the given `Vector`

which is equal to the query
element, or `Nothing`

if there is no such element. The following
holds:

elemIndexEnd c xs == (-) (length xs - 1) `fmap` elemIndex c (reverse xs)

findIndices :: Storable a => (a -> Bool) -> Vector a -> [Int]Source

The `findIndices`

function extends `findIndex`

, by returning the
indices of all elements satisfying the predicate, in ascending order.

count :: (Storable a, Eq a) => a -> Vector a -> IntSource

count returns the number of times its argument appears in the `Vector`

count = length . elemIndices

But more efficiently than using length on the intermediate list.

findIndexOrEnd :: Storable a => (a -> Bool) -> Vector a -> IntSource

`findIndexOrEnd`

is a variant of findIndex, that returns the length
of the string if no element is found, rather than Nothing.

# Zipping and unzipping `Vector`

s

zipWith :: (Storable a, Storable b, Storable c) => (a -> b -> c) -> Vector a -> Vector b -> Vector cSource

zipWith3 :: (Storable a, Storable b, Storable c, Storable d) => (a -> b -> c -> d) -> Vector a -> Vector b -> Vector c -> Vector dSource

Like `zipWith`

but for three input vectors

zipWith4 :: (Storable a, Storable b, Storable c, Storable d, Storable e) => (a -> b -> c -> d -> e) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector eSource

Like `zipWith`

but for four input vectors
If you need even more input vectors,
you might write a function yourselve using unfoldrN and viewL.