Feldspar.Vector

A high-level interface to the operations in the core language (Feldspar.Core). Many of the functions defined here are imitations of Haskell's list operations, and to a first approximation they behave accordingly.

A symbolic vector (Vector) can be thought of as a representation of a parallel core array. This view is made precise by the function freezeVector, which converts a symbolic vector to a core vector using parallel.

Vector is instantiated under the Computable class, which means that symbolic vectors can be used quite seamlessly with the interface in Feldspar.Core.

Unlike core arrays vectors don't use any physical memory. All operations on vectors are "fused" which means that intermediate vectors are removed. As an example, the following function uses only constant space despite using two intermediate vectors of length n.

 sumSq n = sum (map (^2) (1...n))

Memory is only introduced when a vector is explicitly written to memory using the function memorize or converted to a core array using freezeVector. The function vector for creating a vector also allocates memory.

Note also that most operations only introduce a small constant overhead on the vector. The exceptions are

• dropWhile
• fold
• fold1
• Functions that introduce storage (see above)
• "Folding" functions: sum, maximum, etc.

These functions introduce overhead that is linear in the length of the vector.

Finally, note that freezeVector can be introduced implicitly by functions overloaded by the Computable class. This means that, for example, printCore f, where f :: Vector (Data Int) -> Vector (Data Int), will introduce storage for the input and output of f.

Types

type Ix = Int

Vector index

data Vector a

Symbolic vector

Constructors

Indexed

Fields

length :: Data Length

index :: Data Ix -> a

Instances

RandomAccess (Vector a)

Storable a => Computable (Vector (Data a))

Storable a => Computable (Vector (Vector (Data a)))

type DVector a = Vector (Data a)

Short-hand for non-nested parallel vector

Construction/conversion

freezeVector :: Storable a => Vector (Data a) -> Data [a]

Converts a non-nested vector to a core vector.

unfreezeVector :: Storable a => Data Length -> Data [a] -> Vector (Data a)

Converts a non-nested core vector to a parallel vector.

memorize :: Storable a => Vector (Data a) -> Vector (Data a)

Optimizes vector lookup by computing all elements and storing them in a core array.

indexed :: Data Length -> (Data Ix -> a) -> Vector a

vector :: Storable a => [a] -> Vector (Data a)

Constructs a non-nested vector. The elements are stored in a core vector.

modifyLength :: (Data Length -> Data Length) -> Vector a -> Vector a

setLength :: Data Length -> Vector a -> Vector a

boundVector :: Int -> Vector a -> Vector a

Operations

(++) :: Computable a => Vector a -> Vector a -> Vector a

Introduces an ifThenElse for each element; use with care!

take :: Data Int -> Vector a -> Vector a

drop :: Data Int -> Vector a -> Vector a

dropWhile :: (a -> Data Bool) -> Vector a -> Vector a

splitAt :: Data Int -> Vector a -> (Vector a, Vector a)

head :: Vector a -> a

last :: Vector a -> a

tail :: Vector a -> Vector a

init :: Vector a -> Vector a

tails :: Vector a -> Vector (Vector a)

inits :: Vector a -> Vector (Vector a)

inits1 :: Vector a -> Vector (Vector a)

permute :: (Data Length -> Data Ix -> Data Ix) -> Vector a -> Vector a

reverse :: Vector a -> Vector a

replicate :: Data Int -> a -> Vector a

enumFromTo :: Data Int -> Data Int -> Vector (Data Int)

(...) :: Data Int -> Data Int -> Vector (Data Int)

zip :: Vector a -> Vector b -> Vector (a, b)

unzip :: Vector (a, b) -> (Vector a, Vector b)

map :: (a -> b) -> Vector a -> Vector b

zipWith :: (a -> b -> c) -> Vector a -> Vector b -> Vector c

fold :: Computable a => (a -> b -> a) -> a -> Vector b -> a

Corresponds to foldl.

fold1 :: Computable a => (a -> a -> a) -> Vector a -> a

Corresponds to foldl1.

sum :: Numeric a => Vector (Data a) -> Data a

maximum :: Ord a => Vector (Data a) -> Data a

minimum :: Ord a => Vector (Data a) -> Data a

scalarProd :: Numeric a => Vector (Data a) -> Vector (Data a) -> Data a

Scalar product of two vectors