Data.StorableVector

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.

The Vector type

data Vector a

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

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

Instances

Typeable1 Vector

(Storable a, Eq a) => Eq (Vector a)

Data a => Data (Vector a)

(Storable a, Show a) => Show (Vector a)

Storable a => Monoid (Vector a)

Introducing and eliminating Vectors

empty :: Storable a => Vector a

O(1) The empty Vector

singleton :: Storable a => a -> Vector a

O(1) Construct a Vector containing a single element

pack :: Storable a => [a] -> Vector a

O(n) Convert a '[a]' into a 'Vector a'.

unpack :: Storable a => Vector a -> [a]

O(n) Converts a 'Vector a' to a '[a]'.

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

O(n) Convert first n elements of a '[a]' into a 'Vector a'.

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

O(n) Convert a list into a Vector using a conversion function

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

O(n) Convert a Vector into a list using a conversion function

Basic interface

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

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

snoc :: Storable a => Vector a -> a -> Vector a

O(n) Append an element to the end of a Vector

append :: Storable a => Vector a -> Vector a -> Vector a

O(n) Append two Vectors

head :: Storable a => Vector a -> a

O(1) Extract the first element of a Vector, which must be non-empty. An exception will be thrown in the case of an empty Vector.

last :: Storable a => Vector a -> a

O(1) Extract the last element of a Vector, which must be finite and non-empty. An exception will be thrown in the case of an empty Vector.

tail :: Storable a => Vector a -> Vector a

O(1) Extract the elements after the head of a Vector, which must be non-empty. An exception will be thrown in the case of an empty Vector.

init :: Vector a -> Vector a

O(1) Return all the elements of a Vector except the last one. An exception will be thrown in the case of an empty Vector.

null :: Vector a -> Bool

O(1) Test whether a Vector is empty.

length :: Vector a -> Int

O(1) length returns the length of a Vector as an 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

Transforming Vectors

map :: (Storable a, Storable b) => (a -> b) -> Vector a -> Vector b

O(n) map f xs is the Vector obtained by applying f to each element of xs.

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

O(n) reverse xs efficiently returns the elements of xs in reverse order.

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

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.

transpose :: Storable a => [Vector a] -> [Vector a]

The transpose function transposes the rows and columns of its Vector argument.

Reducing Vectors (folds)

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

foldl, applied to a binary operator, a starting value (typically the left-identity of the operator), and a Vector, reduces the Vector using the binary operator, from left to right. This function is subject to array fusion.

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

'foldl\'' is like foldl, but strict in the accumulator.

foldl1 :: Storable a => (a -> a -> a) -> Vector a -> a

foldl1 is a variant of foldl that has no starting value argument, and thus must be applied to non-empty Vectors. This function is subject to array fusion. An exception will be thrown in the case of an empty Vector.

foldl1' :: Storable a => (a -> a -> a) -> Vector a -> a

'foldl1\'' is like foldl1, but strict in the accumulator. An exception will be thrown in the case of an empty Vector.

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

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.

foldr1 :: Storable a => (a -> a -> a) -> Vector a -> a

foldr1 is a variant of foldr that has no starting value argument, and thus must be applied to non-empty Vectors An exception will be thrown in the case of an empty Vector.

Special folds

concat :: Storable a => [Vector a] -> Vector a

O(n) Concatenate a list of Vectors.

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

Map a function over a Vector and concatenate the results

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

This is like mconcat . map f, but in many cases the result of f will not be storable.

any :: Storable a => (a -> Bool) -> Vector a -> Bool

O(n) Applied to a predicate and a Vector, any determines if any element of the Vector satisfies the predicate.

all :: Storable a => (a -> Bool) -> Vector a -> Bool

O(n) Applied to a predicate and a Vector, all determines if all elements of the Vector satisfy the predicate.

maximum :: (Storable a, Ord a) => Vector a -> a

O(n) maximum returns the maximum value from a Vector This function will fuse. An exception will be thrown in the case of an empty Vector.

minimum :: (Storable a, Ord a) => Vector a -> a

O(n) minimum returns the minimum value from a Vector This function will fuse. An exception will be thrown in the case of an empty Vector.

Building Vectors

Scans

scanl :: (Storable a, Storable b) => (a -> b -> a) -> a -> Vector b -> Vector a

scanl is similar to foldl, but returns a list of successive reduced values from the left. This function will fuse.

 scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]

Note that

 last (scanl f z xs) == foldl f z xs.

scanl1 :: Storable a => (a -> a -> a) -> Vector a -> Vector a

scanl1 is a variant of scanl that has no starting value argument. This function will fuse.

 scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]

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

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

scanr1 :: Storable a => (a -> a -> a) -> Vector a -> Vector a

scanr1 is a variant of scanr that has no starting value argument.

Accumulating maps

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

The mapAccumL function behaves like a combination of map and foldl; it applies a function to each element of a Vector, passing an accumulating parameter from left to right, and returning a final value of this accumulator together with the new list.

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

The mapAccumR function behaves like a combination of map and foldr; it applies a function to each element of a Vector, passing an accumulating parameter from right to left, and returning a final value of this accumulator together with the new Vector.

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

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

Unfolding Vectors

replicate :: Storable a => Int -> a -> Vector a

O(n) replicate n x is a Vector of length n with x the value of every element.

iterateN :: Storable a => Int -> (a -> a) -> a -> Vector a

O(n) iterateN n f x is a Vector of length n where the elements of x are generated by repeated application of f.

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

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)

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)

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 a

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

take :: Storable a => Int -> Vector a -> Vector a

O(1) take n, applied to a Vector xs, returns the prefix of xs of length n, or xs itself if n > length xs.

drop :: Storable a => Int -> Vector a -> Vector a

O(1) drop n xs returns the suffix of xs after the first n elements, or empty if n > length xs.

splitAt :: Storable a => Int -> Vector a -> (Vector a, Vector a)

O(1) splitAt n xs is equivalent to (take n xs, drop n xs).

takeWhile :: Storable a => (a -> Bool) -> Vector a -> Vector a

takeWhile, applied to a predicate p and a Vector xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p.

dropWhile :: Storable a => (a -> Bool) -> Vector a -> Vector a

dropWhile p xs returns the suffix remaining after takeWhile p xs.

span :: Storable a => (a -> Bool) -> Vector a -> (Vector a, Vector a)

span p xs breaks the Vector into two segments. It is equivalent to (takeWhile p xs, dropWhile p xs)

spanEnd :: Storable a => (a -> Bool) -> Vector a -> (Vector a, Vector a)

spanEnd behaves like span but from the end of the Vector. We have

 spanEnd (not.isSpace) "x y z" == ("x y ","z")

and

 spanEnd (not . isSpace) ps
    ==
 let (x,y) = span (not.isSpace) (reverse ps) in (reverse y, reverse x)

break :: Storable a => (a -> Bool) -> Vector a -> (Vector a, Vector a)

break p is equivalent to span (not . p).

breakEnd :: Storable a => (a -> Bool) -> Vector a -> (Vector a, Vector a)

breakEnd behaves like break but from the end of the Vector

breakEnd p == spanEnd (not.p)

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

The group function takes a Vector and returns a list of Vectors 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 (==)

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

The groupBy function is the non-overloaded version of group.

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

O(n) Return all initial segments of the given Vector, shortest first.

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

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]

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 Vectors that are slices of the original.

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

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]

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

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

Joining strings

join :: Storable a => Vector a -> [Vector a] -> Vector a

O(n) The join function takes a Vector and a list of Vectors and concatenates the list after interspersing the first argument between each element of the list.

Predicates

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

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 -> Bool

O(n) The isSuffixOf function takes two Vectors and returns True iff the first is a suffix of the second.

The following holds:

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

Searching Vectors

Searching by equality

elem :: (Storable a, Eq a) => a -> Vector a -> Bool

O(n) elem is the Vector membership predicate.

notElem :: (Storable a, Eq a) => a -> Vector a -> Bool

O(n) notElem is the inverse of elem

Searching with a predicate

find :: Storable a => (a -> Bool) -> Vector a -> Maybe a

O(n) The find function takes a predicate and a Vector, and returns the first element in matching the predicate, or Nothing if there is no such element.

 find f p = case findIndex f p of Just n -> Just (p ! n) ; _ -> Nothing

filter :: Storable a => (a -> Bool) -> Vector a -> Vector a

O(n) filter, applied to a predicate and a Vector, returns a Vector containing those elements that satisfy the predicate. This function is subject to array fusion.

Indexing Vectors

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

O(1) Vector index (subscript) operator, starting from 0.

elemIndex :: (Storable a, Eq a) => a -> Vector a -> Maybe Int

O(n) The elemIndex function returns the index of the first element in the given Vector which is equal to the query element, or Nothing if there is no such element.

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

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 Int

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)

findIndex :: Storable a => (a -> Bool) -> Vector a -> Maybe Int

The findIndex function takes a predicate and a Vector and returns the index of the first element in the Vector satisfying the predicate.

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

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 -> Int

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 -> Int

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

Zipping and unzipping Vectors

zip :: (Storable a, Storable b) => Vector a -> Vector b -> [(a, b)]

O(n) zip takes two Vectors and returns a list of corresponding pairs of elements. If one input Vector is short, excess elements of the longer Vector are discarded. This is equivalent to a pair of unpack operations.

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

zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two Vectors to produce the list of corresponding sums.

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

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 e

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

unzip :: (Storable a, Storable b) => [(a, b)] -> (Vector a, Vector b)

O(n) unzip transforms a list of pairs of elements into a pair of Vectors. Note that this performs two pack operations.

copy :: Storable a => Vector a -> Vector a

O(n) Make a copy of the Vector with its own storage. This is mainly useful to allow the rest of the data pointed to by the Vector to be garbage collected, for example if a large string has been read in, and only a small part of it is needed in the rest of the program.

Interleaved Vectors

sieve :: Storable a => Int -> Vector a -> Vector a

O(ln)/ sieve selects every nth element.

deinterleave :: Storable a => Int -> Vector a -> [Vector a]

O(n) Returns n sieved vectors with successive starting elements. deinterleave 3 (pack ['a'..'k']) = [pack adgj, pack behk, pack cfi] This is the same as sliceHorizontal.

interleave :: Storable a => [Vector a] -> Vector a

O(n) Almost the inverse of deinterleave. Restriction is that all input vector must have equal length. interleave [pack adgj, pack behk, pack cfil] = pack ['a'..'l']

IO

hGet :: Storable a => Handle -> Int -> IO (Vector a)

Read a Vector directly from the specified Handle. This is far more efficient than reading the characters into a list and then using pack.

hPut :: Storable a => Handle -> Vector a -> IO ()

Outputs a Vector to the specified Handle.

readFile :: Storable a => FilePath -> IO (Vector a)

Read an entire file strictly into a Vector. This is far more efficient than reading the characters into a String and then using pack. It also may be more efficient than opening the file and reading it using hGet. Files are read using 'binary mode' on Windows.

writeFile :: Storable a => FilePath -> Vector a -> IO ()

Write a Vector to a file.

appendFile :: Storable a => FilePath -> Vector a -> IO ()

Append a Vector to a file.