Copyright	[2008..2017] Manuel M T Chakravarty Gabriele Keller [2009..2017] Trevor L. McDonell [2013..2017] Robert Clifton-Everest [2014..2014] Frederik M. Madsen
License	BSD3
Maintainer	Trevor L. McDonell <tmcdonell@cse.unsw.edu.au>
Stability	experimental
Portability	non-portable (GHC extensions)
Safe Haskell	None
Language	Haskell2010

Data.Array.Accelerate

Contents

The Accelerate Array Language
The Accelerate Expression Language
Foreign Function Interface (FFI)
Plain arrays
- Operations
- Getting data in
  - Function
  - Lists
Prelude re-exports

Description

Data.Array.Accelerate defines an embedded language of array computations for high-performance computing in Haskell. Computations on multi-dimensional, regular arrays are expressed in the form of parameterised collective operations such as maps, reductions, and permutations. These computations are online compiled and can be executed on a range of architectures.

Abstract interface:

The types representing array computations are only exported abstractly; client code can generate array computations and submit them for execution, but it cannot inspect these computations. This is to allow for more flexibility for future extensions of this library.

Stratified language:

Accelerate distinguishes the types of collective operations Acc from the type of scalar operations Exp to achieve a stratified language. Collective operations comprise many scalar computations that are executed in parallel, but scalar computations can not contain collective operations. This separation excludes nested, irregular data-parallelism statically; instead, Accelerate is limited to flat data-parallelism involving only regular, multi-dimensional arrays.

Optimisations:

Accelerate uses a number of scalar and array optimisations, including array fusion, in order to improve the performance of programs. Fusing a program entails combining successive traversals (loops) over an array into a single traversal, which reduces memory traffic and eliminates intermediate arrays.

Code execution:

Several backends are available which can be used to evaluate accelerate programs:

Data.Array.Accelerate.Interpreter: simple interpreter in Haskell as a reference implementation defining the semantics of the Accelerate language
accelerate-llvm-native: implementation supporting parallel execution on multicore CPUs (e.g. x86).
accelerate-llvm-ptx: implementation supporting parallel execution on CUDA-capable NVIDIA GPUs.

Examples:

A short tutorial-style example for generating a Mandelbrot set: http://www.acceleratehs.org/examples/mandelbrot.html
The accelerate-examples package demonstrates a range of computational kernels and several complete applications:
- Implementation of the canny edge detector
- Interactive Mandelbrot set generator
- N-body simulation of gravitational attraction between large bodies
- Implementation of the PageRank algorithm
- A simple, real-time, interactive ray tracer.
- A particle based simulation of stable fluid flows
- A cellular automaton simulation
- A "password recovery" tool, for dictionary attacks on MD5 hashes.
lulesh-accelerate is an implementation of the Livermore Unstructured Lagrangian Explicit Shock Hydrodynamics (LULESH) application. LULESH is representative of typical hydrodynamics codes, although simplified and hard-coded to solve the Sedov blast problem on an unstructured hexahedron mesh.
- For more information on LULESH: https://codesign.llnl.gov/lulesh.php.

Starting a new project:

Accelerate and its associated packages are available on both Hackage and Stackage. A project template is available to help create a new projects using the stack build tool. To create a new project using the template:

stack new PROJECT_NAME https://github.com/AccelerateHS/accelerate/raw/stable/accelerate.hsfiles

Additional components:

accelerate-io: Fast conversion between Accelerate arrays and other formats (e.g. Repa, Vector).
accelerate-fft: Fast Fourier transform, with FFI bindings to optimised implementations.
accelerate-blas: BLAS and LAPACK operations, with FFI bindings to optimised implementations.
accelerate-bignum: Fixed-width large integer arithmetic.
colour-accelerate: Colour representations in Accelerate (RGB, sRGB, HSV, and HSL).
gloss-accelerate: Generate gloss pictures from Accelerate.
gloss-raster-accelerate: Parallel rendering of raster images and animations.
lens-accelerate: Lens operators for Accelerate types.
linear-accelerate: Linear vector space types for Accelerate.
mwc-random-accelerate: Generate Accelerate arrays filled with high-quality pseudorandom numbers.

Contact:

Mailing list for both use and development discussion:
- mailto:accelerate-haskell@googlegroups.com
- http://groups.google.com/group/accelerate-haskell
Bug reports: https://github.com/AccelerateHS/accelerate/issues
Maintainers:
- Trevor L. McDonell: mailto:tmcdonell@cse.unsw.edu.au
- Manuel M T Chakravarty: mailto:chak@cse.unsw.edu.au

Tip:

Accelerate tends to stress GHC's garbage collector, so it helps to increase the default GC allocation sizes. This can be done when running an executable by specifying RTS options on the command line, for example:

./foo +RTS -A64M -n2M -RTS

You can make these settings the default by adding the following ghc-options to your .cabal file or similar:

ghc-options: -with-rtsopts=-n2M -with-rtsopts=-A64M

To specify RTS options you will also need to compile your program with -rtsopts.

Synopsis

data Acc a
data Array sh e
class (Typeable a, Typeable (ArrRepr a)) => Arrays a
type Scalar = Array DIM0
type Vector = Array DIM1
type Matrix = Array DIM2
type Segments = Vector
class (Show a, Typeable a, Typeable (EltRepr a), ArrayElt (EltRepr a)) => Elt a
data Z = Z
data tail :. head = tail :. head
type DIM0 = Z
type DIM1 = DIM0 :. Int
type DIM2 = DIM1 :. Int
type DIM3 = DIM2 :. Int
type DIM4 = DIM3 :. Int
type DIM5 = DIM4 :. Int
type DIM6 = DIM5 :. Int
type DIM7 = DIM6 :. Int
type DIM8 = DIM7 :. Int
type DIM9 = DIM8 :. Int
class (Elt sh, Elt (Any sh), Shape (EltRepr sh), FullShape sh ~ sh, CoSliceShape sh ~ sh, SliceShape sh ~ Z) => Shape sh
class (Elt sl, Shape (SliceShape sl), Shape (CoSliceShape sl), Shape (FullShape sl)) => Slice sl where
- type SliceShape sl :: *
- type CoSliceShape sl :: *
- type FullShape sl :: *
- sliceIndex :: sl -> SliceIndex (EltRepr sl) (EltRepr (SliceShape sl)) (EltRepr (CoSliceShape sl)) (EltRepr (FullShape sl))
data All = All
data Any sh = Any
(!) :: (Shape sh, Elt e) => Acc (Array sh e) -> Exp sh -> Exp e
(!!) :: (Shape sh, Elt e) => Acc (Array sh e) -> Exp Int -> Exp e
the :: Elt e => Acc (Scalar e) -> Exp e
null :: (Shape sh, Elt e) => Acc (Array sh e) -> Exp Bool
length :: Elt e => Acc (Vector e) -> Exp Int
shape :: (Shape sh, Elt e) => Acc (Array sh e) -> Exp sh
size :: (Shape sh, Elt e) => Acc (Array sh e) -> Exp Int
shapeSize :: Shape sh => Exp sh -> Exp Int
use :: Arrays arrays => arrays -> Acc arrays
unit :: Elt e => Exp e -> Acc (Scalar e)
generate :: (Shape sh, Elt a) => Exp sh -> (Exp sh -> Exp a) -> Acc (Array sh a)
fill :: (Shape sh, Elt e) => Exp sh -> Exp e -> Acc (Array sh e)
enumFromN :: (Shape sh, Num e, FromIntegral Int e) => Exp sh -> Exp e -> Acc (Array sh e)
enumFromStepN :: (Shape sh, Num e, FromIntegral Int e) => Exp sh -> Exp e -> Exp e -> Acc (Array sh e)
(++) :: forall sh e. (Slice sh, Shape sh, Elt e) => Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int) e)
concatOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Acc (Array sh e) -> Acc (Array sh e) -> Acc (Array sh e)
(?|) :: Arrays a => Exp Bool -> (Acc a, Acc a) -> Acc a
acond :: Arrays a => Exp Bool -> Acc a -> Acc a -> Acc a
awhile :: Arrays a => (Acc a -> Acc (Scalar Bool)) -> (Acc a -> Acc a) -> Acc a -> Acc a
class IfThenElse t where
- type EltT t a :: Constraint
- ifThenElse :: EltT t a => Exp Bool -> t a -> t a -> t a
(>->) :: (Arrays a, Arrays b, Arrays c) => (Acc a -> Acc b) -> (Acc b -> Acc c) -> Acc a -> Acc c
compute :: Arrays a => Acc a -> Acc a
indexed :: (Shape sh, Elt a) => Acc (Array sh a) -> Acc (Array sh (sh, a))
map :: (Shape sh, Elt a, Elt b) => (Exp a -> Exp b) -> Acc (Array sh a) -> Acc (Array sh b)
imap :: (Shape sh, Elt a, Elt b) => (Exp sh -> Exp a -> Exp b) -> Acc (Array sh a) -> Acc (Array sh b)
zipWith :: (Shape sh, Elt a, Elt b, Elt c) => (Exp a -> Exp b -> Exp c) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c)
zipWith3 :: (Shape sh, Elt a, Elt b, Elt c, Elt d) => (Exp a -> Exp b -> Exp c -> Exp d) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d)
zipWith4 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e) => (Exp a -> Exp b -> Exp c -> Exp d -> Exp e) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e)
zipWith5 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f) => (Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f)
zipWith6 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g) => (Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g)
zipWith7 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h) => (Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g -> Exp h) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h)
zipWith8 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i) => (Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g -> Exp h -> Exp i) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) -> Acc (Array sh i)
zipWith9 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i, Elt j) => (Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g -> Exp h -> Exp i -> Exp j) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) -> Acc (Array sh i) -> Acc (Array sh j)
izipWith :: (Shape sh, Elt a, Elt b, Elt c) => (Exp sh -> Exp a -> Exp b -> Exp c) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c)
izipWith3 :: (Shape sh, Elt a, Elt b, Elt c, Elt d) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d)
izipWith4 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d -> Exp e) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e)
izipWith5 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f)
izipWith6 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g)
izipWith7 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g -> Exp h) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h)
izipWith8 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g -> Exp h -> Exp i) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) -> Acc (Array sh i)
izipWith9 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i, Elt j) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g -> Exp h -> Exp i -> Exp j) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) -> Acc (Array sh i) -> Acc (Array sh j)
zip :: (Shape sh, Elt a, Elt b) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh (a, b))
zip3 :: (Shape sh, Elt a, Elt b, Elt c) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh (a, b, c))
zip4 :: (Shape sh, Elt a, Elt b, Elt c, Elt d) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh (a, b, c, d))
zip5 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh (a, b, c, d, e))
zip6 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh (a, b, c, d, e, f))
zip7 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh (a, b, c, d, e, f, g))
zip8 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) -> Acc (Array sh (a, b, c, d, e, f, g, h))
zip9 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) -> Acc (Array sh i) -> Acc (Array sh (a, b, c, d, e, f, g, h, i))
unzip :: (Shape sh, Elt a, Elt b) => Acc (Array sh (a, b)) -> (Acc (Array sh a), Acc (Array sh b))
unzip3 :: (Shape sh, Elt a, Elt b, Elt c) => Acc (Array sh (a, b, c)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c))
unzip4 :: (Shape sh, Elt a, Elt b, Elt c, Elt d) => Acc (Array sh (a, b, c, d)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c), Acc (Array sh d))
unzip5 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e) => Acc (Array sh (a, b, c, d, e)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c), Acc (Array sh d), Acc (Array sh e))
unzip6 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f) => Acc (Array sh (a, b, c, d, e, f)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c), Acc (Array sh d), Acc (Array sh e), Acc (Array sh f))
unzip7 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g) => Acc (Array sh (a, b, c, d, e, f, g)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c), Acc (Array sh d), Acc (Array sh e), Acc (Array sh f), Acc (Array sh g))
unzip8 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h) => Acc (Array sh (a, b, c, d, e, f, g, h)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c), Acc (Array sh d), Acc (Array sh e), Acc (Array sh f), Acc (Array sh g), Acc (Array sh h))
unzip9 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i) => Acc (Array sh (a, b, c, d, e, f, g, h, i)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c), Acc (Array sh d), Acc (Array sh e), Acc (Array sh f), Acc (Array sh g), Acc (Array sh h), Acc (Array sh i))
reshape :: (Shape sh, Shape sh', Elt e) => Exp sh -> Acc (Array sh' e) -> Acc (Array sh e)
flatten :: forall sh e. (Shape sh, Elt e) => Acc (Array sh e) -> Acc (Vector e)
replicate :: (Slice slix, Elt e) => Exp slix -> Acc (Array (SliceShape slix) e) -> Acc (Array (FullShape slix) e)
slice :: (Slice slix, Elt e) => Acc (Array (FullShape slix) e) -> Exp slix -> Acc (Array (SliceShape slix) e)
init :: forall sh e. (Slice sh, Shape sh, Elt e) => Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int) e)
tail :: forall sh e. (Slice sh, Shape sh, Elt e) => Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int) e)
take :: forall sh e. (Slice sh, Shape sh, Elt e) => Exp Int -> Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int) e)
drop :: forall sh e. (Slice sh, Shape sh, Elt e) => Exp Int -> Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int) e)
slit :: forall sh e. (Slice sh, Shape sh, Elt e) => Exp Int -> Exp Int -> Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int) e)
initOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Acc (Array sh e) -> Acc (Array sh e)
tailOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Acc (Array sh e) -> Acc (Array sh e)
takeOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Exp Int -> Acc (Array sh e) -> Acc (Array sh e)
dropOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Exp Int -> Acc (Array sh e) -> Acc (Array sh e)
slitOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Exp Int -> Exp Int -> Acc (Array sh e) -> Acc (Array sh e)
permute :: (Shape sh, Shape sh', Elt a) => (Exp a -> Exp a -> Exp a) -> Acc (Array sh' a) -> (Exp sh -> Exp sh') -> Acc (Array sh a) -> Acc (Array sh' a)
ignore :: Shape sh => Exp sh
scatter :: Elt e => Acc (Vector Int) -> Acc (Vector e) -> Acc (Vector e) -> Acc (Vector e)
backpermute :: (Shape sh, Shape sh', Elt a) => Exp sh' -> (Exp sh' -> Exp sh) -> Acc (Array sh a) -> Acc (Array sh' a)
gather :: (Shape sh, Elt e) => Acc (Array sh Int) -> Acc (Vector e) -> Acc (Array sh e)
reverse :: Elt e => Acc (Vector e) -> Acc (Vector e)
transpose :: Elt e => Acc (Array DIM2 e) -> Acc (Array DIM2 e)
reverseOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Acc (Array sh e) -> Acc (Array sh e)
transposeOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Lens' (Exp sh) (Exp Int) -> Acc (Array sh e) -> Acc (Array sh e)
filter :: forall sh e. (Shape sh, Slice sh, Elt e) => (Exp e -> Exp Bool) -> Acc (Array (sh :. Int) e) -> Acc (Vector e, Array sh Int)
fold :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array sh a)
fold1 :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Acc (Array (sh :. Int) a) -> Acc (Array sh a)
foldAll :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array sh a) -> Acc (Scalar a)
fold1All :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Acc (Array sh a) -> Acc (Scalar a)
foldSeg :: (Shape sh, Elt a, Elt i, IsIntegral i) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Segments i) -> Acc (Array (sh :. Int) a)
fold1Seg :: (Shape sh, Elt a, Elt i, IsIntegral i) => (Exp a -> Exp a -> Exp a) -> Acc (Array (sh :. Int) a) -> Acc (Segments i) -> Acc (Array (sh :. Int) a)
all :: (Shape sh, Elt e) => (Exp e -> Exp Bool) -> Acc (Array (sh :. Int) e) -> Acc (Array sh Bool)
any :: (Shape sh, Elt e) => (Exp e -> Exp Bool) -> Acc (Array (sh :. Int) e) -> Acc (Array sh Bool)
and :: Shape sh => Acc (Array (sh :. Int) Bool) -> Acc (Array sh Bool)
or :: Shape sh => Acc (Array (sh :. Int) Bool) -> Acc (Array sh Bool)
sum :: (Shape sh, Num e) => Acc (Array (sh :. Int) e) -> Acc (Array sh e)
product :: (Shape sh, Num e) => Acc (Array (sh :. Int) e) -> Acc (Array sh e)
minimum :: (Shape sh, Ord e) => Acc (Array (sh :. Int) e) -> Acc (Array sh e)
maximum :: (Shape sh, Ord e) => Acc (Array (sh :. Int) e) -> Acc (Array sh e)
scanl :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a)
scanl1 :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a)
scanl' :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a, Array sh a)
scanr :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a)
scanr1 :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a)
scanr' :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a, Array sh a)
prescanl :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a)
postscanl :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a)
prescanr :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a)
postscanr :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a)
scanlSeg :: forall sh e i. (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Exp e -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e)
scanl1Seg :: (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e)
scanl'Seg :: forall sh e i. (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Exp e -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e, Array (sh :. Int) e)
prescanlSeg :: (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Exp e -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e)
postscanlSeg :: (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Exp e -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e)
scanrSeg :: forall sh e i. (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Exp e -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e)
scanr1Seg :: (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e)
scanr'Seg :: forall sh e i. (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Exp e -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e, Array (sh :. Int) e)
prescanrSeg :: (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Exp e -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e)
postscanrSeg :: (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Exp e -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e)
stencil :: (Stencil sh a stencil, Elt b) => (stencil -> Exp b) -> Boundary (Array sh a) -> Acc (Array sh a) -> Acc (Array sh b)
stencil2 :: (Stencil sh a stencil1, Stencil sh b stencil2, Elt c) => (stencil1 -> stencil2 -> Exp c) -> Boundary (Array sh a) -> Acc (Array sh a) -> Boundary (Array sh b) -> Acc (Array sh b) -> Acc (Array sh c)
class (Elt (StencilRepr sh stencil), Stencil sh a (StencilRepr sh stencil)) => Stencil sh a stencil
data Boundary t
clamp :: Boundary (Array sh e)
mirror :: Boundary (Array sh e)
wrap :: Boundary (Array sh e)
function :: (Shape sh, Elt e) => (Exp sh -> Exp e) -> Boundary (Array sh e)
type Stencil3 a = (Exp a, Exp a, Exp a)
type Stencil5 a = (Exp a, Exp a, Exp a, Exp a, Exp a)
type Stencil7 a = (Exp a, Exp a, Exp a, Exp a, Exp a, Exp a, Exp a)
type Stencil9 a = (Exp a, Exp a, Exp a, Exp a, Exp a, Exp a, Exp a, Exp a, Exp a)
type Stencil3x3 a = (Stencil3 a, Stencil3 a, Stencil3 a)
type Stencil5x3 a = (Stencil5 a, Stencil5 a, Stencil5 a)
type Stencil3x5 a = (Stencil3 a, Stencil3 a, Stencil3 a, Stencil3 a, Stencil3 a)
type Stencil5x5 a = (Stencil5 a, Stencil5 a, Stencil5 a, Stencil5 a, Stencil5 a)
type Stencil3x3x3 a = (Stencil3x3 a, Stencil3x3 a, Stencil3x3 a)
type Stencil5x3x3 a = (Stencil5x3 a, Stencil5x3 a, Stencil5x3 a)
type Stencil3x5x3 a = (Stencil3x5 a, Stencil3x5 a, Stencil3x5 a)
type Stencil3x3x5 a = (Stencil3x3 a, Stencil3x3 a, Stencil3x3 a, Stencil3x3 a, Stencil3x3 a)
type Stencil5x5x3 a = (Stencil5x5 a, Stencil5x5 a, Stencil5x5 a)
type Stencil5x3x5 a = (Stencil5x3 a, Stencil5x3 a, Stencil5x3 a, Stencil5x3 a, Stencil5x3 a)
type Stencil3x5x5 a = (Stencil3x5 a, Stencil3x5 a, Stencil3x5 a, Stencil3x5 a, Stencil3x5 a)
type Stencil5x5x5 a = (Stencil5x5 a, Stencil5x5 a, Stencil5x5 a, Stencil5x5 a, Stencil5x5 a)
data Exp t
class Elt a => Eq a where
- (==) :: Exp a -> Exp a -> Exp Bool
- (/=) :: Exp a -> Exp a -> Exp Bool
class Eq a => Ord a where
- (<) :: Exp a -> Exp a -> Exp Bool
- (>) :: Exp a -> Exp a -> Exp Bool
- (<=) :: Exp a -> Exp a -> Exp Bool
- (>=) :: Exp a -> Exp a -> Exp Bool
- min :: Exp a -> Exp a -> Exp a
- max :: Exp a -> Exp a -> Exp a
- compare :: Exp a -> Exp a -> Exp Ordering
data Ordering
- = LT
- | EQ
- | GT
type Enum a = Enum (Exp a)
succ :: Enum a => a -> a
pred :: Enum a => a -> a
type Bounded a = (Elt a, Bounded (Exp a))
minBound :: Bounded a => a
maxBound :: Bounded a => a
type Num a = (Elt a, Num (Exp a))
(+) :: Num a => a -> a -> a
(-) :: Num a => a -> a -> a
(*) :: Num a => a -> a -> a
negate :: Num a => a -> a
abs :: Num a => a -> a
signum :: Num a => a -> a
fromInteger :: Num a => Integer -> Exp a
type Integral a = (Enum a, Real a, Integral (Exp a))
quot :: Integral a => a -> a -> a
rem :: Integral a => a -> a -> a
div :: Integral a => a -> a -> a
mod :: Integral a => a -> a -> a
quotRem :: Integral a => a -> a -> (a, a)
divMod :: Integral a => a -> a -> (a, a)
type Fractional a = (Num a, Fractional (Exp a))
(/) :: Fractional a => a -> a -> a
recip :: Fractional a => a -> a
fromRational :: Fractional a => Rational -> Exp a
type Floating a = (Fractional a, Floating (Exp a))
pi :: Floating a => a
sin :: Floating a => a -> a
cos :: Floating a => a -> a
tan :: Floating a => a -> a
asin :: Floating a => a -> a
acos :: Floating a => a -> a
atan :: Floating a => a -> a
sinh :: Floating a => a -> a
cosh :: Floating a => a -> a
tanh :: Floating a => a -> a
asinh :: Floating a => a -> a
acosh :: Floating a => a -> a
atanh :: Floating a => a -> a
exp :: Floating a => a -> a
sqrt :: Floating a => a -> a
log :: Floating a => a -> a
(**) :: Floating a => a -> a -> a
logBase :: Floating a => a -> a -> a
class (Real a, Fractional a) => RealFrac a where
- properFraction :: (Num b, ToFloating b a, IsIntegral b) => Exp a -> (Exp b, Exp a)
- truncate :: (Elt b, IsIntegral b) => Exp a -> Exp b
- round :: (Elt b, IsIntegral b) => Exp a -> Exp b
- ceiling :: (Elt b, IsIntegral b) => Exp a -> Exp b
- floor :: (Elt b, IsIntegral b) => Exp a -> Exp b
div' :: (RealFrac a, Elt b, IsIntegral b) => Exp a -> Exp a -> Exp b
mod' :: (Floating a, RealFrac a, ToFloating Int a) => Exp a -> Exp a -> Exp a
divMod' :: (Floating a, RealFrac a, Num b, IsIntegral b, ToFloating b a) => Exp a -> Exp a -> (Exp b, Exp a)
class (RealFrac a, Floating a) => RealFloat a where
- floatRadix :: Exp a -> Exp Int64
- floatDigits :: Exp a -> Exp Int
- floatRange :: Exp a -> (Exp Int, Exp Int)
- decodeFloat :: Exp a -> (Exp Int64, Exp Int)
- encodeFloat :: Exp Int64 -> Exp Int -> Exp a
- exponent :: Exp a -> Exp Int
- significand :: Exp a -> Exp a
- scaleFloat :: Exp Int -> Exp a -> Exp a
- isNaN :: Exp a -> Exp Bool
- isInfinite :: Exp a -> Exp Bool
- isDenormalized :: Exp a -> Exp Bool
- isNegativeZero :: Exp a -> Exp Bool
- isIEEE :: Exp a -> Exp Bool
- atan2 :: Exp a -> Exp a -> Exp a
class FromIntegral a b where
- fromIntegral :: Integral a => Exp a -> Exp b
class ToFloating a b where
- toFloating :: (Num a, Floating b) => Exp a -> Exp b
class Lift c e where
- type Plain e
- lift :: e -> c (Plain e)
class Lift c e => Unlift c e where
- unlift :: c (Plain e) -> e
lift1 :: (Unlift Exp a, Lift Exp b) => (a -> b) -> Exp (Plain a) -> Exp (Plain b)
lift2 :: (Unlift Exp a, Unlift Exp b, Lift Exp c) => (a -> b -> c) -> Exp (Plain a) -> Exp (Plain b) -> Exp (Plain c)
lift3 :: (Unlift Exp a, Unlift Exp b, Unlift Exp c, Lift Exp d) => (a -> b -> c -> d) -> Exp (Plain a) -> Exp (Plain b) -> Exp (Plain c) -> Exp (Plain d)
ilift1 :: (Exp Int -> Exp Int) -> Exp DIM1 -> Exp DIM1
ilift2 :: (Exp Int -> Exp Int -> Exp Int) -> Exp DIM1 -> Exp DIM1 -> Exp DIM1
ilift3 :: (Exp Int -> Exp Int -> Exp Int -> Exp Int) -> Exp DIM1 -> Exp DIM1 -> Exp DIM1 -> Exp DIM1
constant :: Elt t => t -> Exp t
fst :: forall a b. (Elt a, Elt b) => Exp (a, b) -> Exp a
afst :: forall a b. (Arrays a, Arrays b) => Acc (a, b) -> Acc a
snd :: forall a b. (Elt a, Elt b) => Exp (a, b) -> Exp b
asnd :: forall a b. (Arrays a, Arrays b) => Acc (a, b) -> Acc b
curry :: Lift f (f a, f b) => (f (Plain (f a), Plain (f b)) -> f c) -> f a -> f b -> f c
uncurry :: Unlift f (f a, f b) => (f a -> f b -> f c) -> f (Plain (f a), Plain (f b)) -> f c
(?) :: Elt t => Exp Bool -> (Exp t, Exp t) -> Exp t
caseof :: (Elt a, Elt b) => Exp a -> [(Exp a -> Exp Bool, Exp b)] -> Exp b -> Exp b
cond :: Elt t => Exp Bool -> Exp t -> Exp t -> Exp t
while :: Elt e => (Exp e -> Exp Bool) -> (Exp e -> Exp e) -> Exp e -> Exp e
iterate :: forall a. Elt a => Exp Int -> (Exp a -> Exp a) -> Exp a -> Exp a
sfoldl :: forall sh a b. (Shape sh, Slice sh, Elt a, Elt b) => (Exp a -> Exp b -> Exp a) -> Exp a -> Exp sh -> Acc (Array (sh :. Int) b) -> Exp a
(&&) :: Exp Bool -> Exp Bool -> Exp Bool
(||) :: Exp Bool -> Exp Bool -> Exp Bool
not :: Exp Bool -> Exp Bool
subtract :: Num a => Exp a -> Exp a -> Exp a
even :: Integral a => Exp a -> Exp Bool
odd :: Integral a => Exp a -> Exp Bool
gcd :: Integral a => Exp a -> Exp a -> Exp a
lcm :: Integral a => Exp a -> Exp a -> Exp a
(^) :: forall a b. (Num a, Integral b) => Exp a -> Exp b -> Exp a
(^^) :: (Fractional a, Integral b) => Exp a -> Exp b -> Exp a
index0 :: Exp Z
index1 :: Elt i => Exp i -> Exp (Z :. i)
unindex1 :: Elt i => Exp (Z :. i) -> Exp i
index2 :: (Elt i, Slice (Z :. i)) => Exp i -> Exp i -> Exp ((Z :. i) :. i)
unindex2 :: forall i. (Elt i, Slice (Z :. i)) => Exp ((Z :. i) :. i) -> Exp (i, i)
index3 :: (Elt i, Slice (Z :. i), Slice ((Z :. i) :. i)) => Exp i -> Exp i -> Exp i -> Exp (((Z :. i) :. i) :. i)
unindex3 :: forall i. (Elt i, Slice (Z :. i), Slice ((Z :. i) :. i)) => Exp (((Z :. i) :. i) :. i) -> Exp (i, i, i)
indexHead :: (Slice sh, Elt a) => Exp (sh :. a) -> Exp a
indexTail :: (Slice sh, Elt a) => Exp (sh :. a) -> Exp sh
toIndex :: Shape sh => Exp sh -> Exp sh -> Exp Int
fromIndex :: Shape sh => Exp sh -> Exp Int -> Exp sh
intersect :: Shape sh => Exp sh -> Exp sh -> Exp sh
ord :: Exp Char -> Exp Int
chr :: Exp Int -> Exp Char
boolToInt :: Exp Bool -> Exp Int
bitcast :: (Elt a, Elt b, IsScalar (EltRepr a), IsScalar (EltRepr b), BitSizeEq (EltRepr a) (EltRepr b)) => Exp a -> Exp b
foreignAcc :: (Arrays as, Arrays bs, Foreign asm) => asm (as -> bs) -> (Acc as -> Acc bs) -> Acc as -> Acc bs
foreignExp :: (Elt x, Elt y, Foreign asm) => asm (x -> y) -> (Exp x -> Exp y) -> Exp x -> Exp y
arrayRank :: Shape sh => sh -> Int
arrayShape :: Shape sh => Array sh e -> sh
arraySize :: Shape sh => sh -> Int
arrayReshape :: (Shape sh, Shape sh', Elt e) => sh -> Array sh' e -> Array sh e
indexArray :: Array sh e -> sh -> e
linearIndexArray :: Array sh e -> Int -> e
fromFunction :: (Shape sh, Elt e) => sh -> (sh -> e) -> Array sh e
fromFunctionM :: (Shape sh, Elt e) => sh -> (sh -> IO e) -> IO (Array sh e)
fromList :: (Shape sh, Elt e) => sh -> [e] -> Array sh e
toList :: forall sh e. Array sh e -> [e]
(.) :: (b -> c) -> (a -> b) -> a -> c
($) :: (a -> b) -> a -> b
error :: HasCallStack => [Char] -> a
undefined :: HasCallStack => a
const :: a -> b -> a
data Int
data Int8
data Int16
data Int32
data Int64
data Word
data Word8
data Word16
data Word32
data Word64
newtype Half = Half {
- getHalf :: CUShort
}
data Float
data Double
data Bool
- = False
- | True
data Char
data CFloat
data CDouble
data CShort
data CUShort
data CInt
data CUInt
data CLong
data CULong
data CLLong
data CULLong
data CChar
data CSChar
data CUChar
class Typeable a => IsScalar a
class (Num a, IsSingle a) => IsNum a
class IsBounded a
class (IsSingle a, IsNum a, IsBounded a) => IsIntegral a
class (Floating a, IsSingle a, IsNum a) => IsFloating a
class IsNonNum a

The Accelerate Array Language

Embedded array computations

data Acc a #

Accelerate is an embedded language that distinguishes between vanilla arrays (e.g. in Haskell memory on the CPU) and embedded arrays (e.g. in device memory on a GPU), as well as the computations on both of these. Since Accelerate is an embedded language, programs written in Accelerate are not compiled by the Haskell compiler (GHC). Rather, each Accelerate backend is a runtime compiler which generates and executes parallel SIMD code of the target language at application runtime.

The type constructor Acc represents embedded collective array operations. A term of type Acc a is an Accelerate program which, once executed, will produce a value of type a (an Array or a tuple of Arrays). Collective operations of type Acc a comprise many scalar expressions, wrapped in type constructor Exp, which will be executed in parallel. Although collective operations comprise many scalar operations executed in parallel, scalar operations cannot initiate new collective operations: this stratification between scalar operations in Exp and array operations in Acc helps statically exclude nested data parallelism, which is difficult to execute efficiently on constrained hardware such as GPUs.

A simple example

As a simple example, to compute a vector dot product we can write:

dotp :: Num a => Vector a -> Vector a -> Acc (Scalar a)
dotp xs ys =
  let
      xs' = use xs
      ys' = use ys
  in
  fold (+) 0 ( zipWith (*) xs' ys' )

The function dotp consumes two one-dimensional arrays (Vectors) of values, and produces a single (Scalar) result as output. As the return type is wrapped in the type Acc, we see that it is an embedded Accelerate computation - it will be evaluated in the object language of dynamically generated parallel code, rather than the meta language of vanilla Haskell.

As the arguments to dotp are plain Haskell arrays, to make these available to Accelerate computations they must be embedded with the use function.

An Accelerate backend is used to evaluate the embedded computation and return the result back to vanilla Haskell. Calling the run function of a backend will generate code for the target architecture, compile, and execute it. For example, the following backends are available:

accelerate-llvm-native: for execution on multicore CPUs
accelerate-llvm-ptx: for execution on NVIDIA CUDA-capable GPUs

See also Exp, which encapsulates embedded scalar computations.

Avoiding nested parallelism

As mentioned above, embedded scalar computations of type Exp can not initiate further collective operations.

Suppose we wanted to extend our above dotp function to matrix-vector multiplication. First, let's rewrite our dotp function to take Acc arrays as input (which is typically what we want):

dotp :: Num a => Acc (Vector a) -> Acc (Vector a) -> Acc (Scalar a)
dotp xs ys = fold (+) 0 ( zipWith (*) xs ys )

We might then be inclined to lift our dot-product program to the following (incorrect) matrix-vector product, by applying dotp to each row of the input matrix:

mvm_ndp :: Num a => Acc (Matrix a) -> Acc (Vector a) -> Acc (Vector a)
mvm_ndp mat vec =
  let Z :. rows :. cols  = unlift (shape mat)  :: Z :. Exp Int :. Exp Int
  in  generate (index1 rows)
               (\row -> the $ dotp vec (slice mat (lift (row :. All))))

Here, we use generate to create a one-dimensional vector by applying at each index a function to slice out the corresponding row of the matrix to pass to the dotp function. However, since both generate and slice are data-parallel operations, and moreover that slice depends on the argument row given to it by the generate function, this definition requires nested data-parallelism, and is thus not permitted. The clue that this definition is invalid is that in order to create a program which will be accepted by the type checker, we must use the function the to retrieve the result of the dotp operation, effectively concealing that dotp is a collective array computation in order to match the type expected by generate, which is that of scalar expressions. Additionally, since we have fooled the type-checker, this problem will only be discovered at program runtime.

In order to avoid this problem, we can make use of the fact that operations in Accelerate are rank polymorphic. The fold operation reduces along the innermost dimension of an array of arbitrary rank, reducing the rank (dimensionality) of the array by one. Thus, we can replicate the input vector to as many rows there are in the input matrix, and perform the dot-product of the vector with every row simultaneously:

mvm :: A.Num a => Acc (Matrix a) -> Acc (Vector a) -> Acc (Vector a)
mvm mat vec =
  let Z :. rows :. cols = unlift (shape mat) :: Z :. Exp Int :. Exp Int
      vec'              = A.replicate (lift (Z :. rows :. All)) vec
  in
  A.fold (+) 0 ( A.zipWith (*) mat vec' )

Note that the intermediate, replicated array vec' is never actually created in memory; it will be fused directly into the operation which consumes it. We discuss fusion next.

Fusion

Array computations of type Acc will be subject to array fusion; Accelerate will combine individual Acc computations into a single computation, which reduces the number of traversals over the input data and thus improves performance. As such, it is often useful to have some intuition on when fusion should occur.

The main idea is to first partition array operations into two categories:

Element-wise operations, such as map, generate, and backpermute. Each element of these operations can be computed independently of all others.
Collective operations such as fold, scanl, and stencil. To compute each output element of these operations requires reading multiple elements from the input array(s).

Element-wise operations fuse together whenever the consumer operation uses a single element of the input array. Element-wise operations can both fuse their inputs into themselves, as well be fused into later operations. Both these examples should fuse into a single loop:

If the consumer operation uses more than one element of the input array (typically, via generate indexing an array multiple times), then the input array will be completely evaluated first; no fusion occurs in this case, because fusing the first operation into the second implies duplicating work.

On the other hand, collective operations can fuse their input arrays into themselves, but on output always evaluate to an array; collective operations will not be fused into a later step. For example:

Here the element-wise sequence (use + generate + zipWith) will fuse into a single operation, which then fuses into the collective fold operation. At this point in the program the fold must now be evaluated. In the final step the map reads in the array produced by fold. As there is no fusion between the fold and map steps, this program consists of two "loops"; one for the use + generate + zipWith + fold step, and one for the final map step.

You can see how many operations will be executed in the fused program by Show-ing the Acc program, or by using the debugging option -ddump-dot to save the program as a graphviz DOT file.

As a special note, the operations unzip and reshape, when applied to a real array, are executed in constant time, so in this situation these operations will not be fused.

Tips

Since Acc represents embedded computations that will only be executed when evaluated by a backend, we can programatically generate these computations using the meta language Haskell; for example, unrolling loops or embedding input values into the generated code.
It is usually best to keep all intermediate computations in Acc, and only run the computation at the very end to produce the final result. This enables optimisations between intermediate results (e.g. array fusion) and, if the target architecture has a separate memory space, as is the case of GPUs, to prevent excessive data transfers.

Instances

IfThenElse Acc #
Instance details Defined in Data.Array.Accelerate.Prelude Associated Types type EltT Acc a :: Constraint # Methods ifThenElse :: EltT Acc a => Exp Bool -> Acc a -> Acc a -> Acc a #
Unlift Acc (Acc a) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a)) -> Acc a #
Lift Acc (Acc a) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (Acc a) :: Type # Methods lift :: Acc a -> Acc (Plain (Acc a)) #
(Arrays a, Arrays b) => Unlift Acc (Acc a, Acc b) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b)) -> (Acc a, Acc b) #
(Lift Acc a, Lift Acc b, Arrays (Plain a), Arrays (Plain b)) => Lift Acc (a, b) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b) :: Type # Methods lift :: (a, b) -> Acc (Plain (a, b)) #
(Shape sh, Elt e) => Lift Acc (Array sh e) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (Array sh e) :: Type # Methods lift :: Array sh e -> Acc (Plain (Array sh e)) #
(Arrays a, Arrays b, Arrays c) => Unlift Acc (Acc a, Acc b, Acc c) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b, Acc c)) -> (Acc a, Acc b, Acc c) #
(Lift Acc a, Lift Acc b, Lift Acc c, Arrays (Plain a), Arrays (Plain b), Arrays (Plain c)) => Lift Acc (a, b, c) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b, c) :: Type # Methods lift :: (a, b, c) -> Acc (Plain (a, b, c)) #
(Arrays a, Arrays b, Arrays c, Arrays d) => Unlift Acc (Acc a, Acc b, Acc c, Acc d) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b, Acc c, Acc d)) -> (Acc a, Acc b, Acc c, Acc d) #
(Lift Acc a, Lift Acc b, Lift Acc c, Lift Acc d, Arrays (Plain a), Arrays (Plain b), Arrays (Plain c), Arrays (Plain d)) => Lift Acc (a, b, c, d) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b, c, d) :: Type # Methods lift :: (a, b, c, d) -> Acc (Plain (a, b, c, d)) #
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e) => Unlift Acc (Acc a, Acc b, Acc c, Acc d, Acc e) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b, Acc c, Acc d, Acc e)) -> (Acc a, Acc b, Acc c, Acc d, Acc e) #
(Lift Acc a, Lift Acc b, Lift Acc c, Lift Acc d, Lift Acc e, Arrays (Plain a), Arrays (Plain b), Arrays (Plain c), Arrays (Plain d), Arrays (Plain e)) => Lift Acc (a, b, c, d, e) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b, c, d, e) :: Type # Methods lift :: (a, b, c, d, e) -> Acc (Plain (a, b, c, d, e)) #
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f) => Unlift Acc (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f)) -> (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f) #
(Lift Acc a, Lift Acc b, Lift Acc c, Lift Acc d, Lift Acc e, Lift Acc f, Arrays (Plain a), Arrays (Plain b), Arrays (Plain c), Arrays (Plain d), Arrays (Plain e), Arrays (Plain f)) => Lift Acc (a, b, c, d, e, f) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b, c, d, e, f) :: Type # Methods lift :: (a, b, c, d, e, f) -> Acc (Plain (a, b, c, d, e, f)) #
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g) => Unlift Acc (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g)) -> (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g) #
(Lift Acc a, Lift Acc b, Lift Acc c, Lift Acc d, Lift Acc e, Lift Acc f, Lift Acc g, Arrays (Plain a), Arrays (Plain b), Arrays (Plain c), Arrays (Plain d), Arrays (Plain e), Arrays (Plain f), Arrays (Plain g)) => Lift Acc (a, b, c, d, e, f, g) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b, c, d, e, f, g) :: Type # Methods lift :: (a, b, c, d, e, f, g) -> Acc (Plain (a, b, c, d, e, f, g)) #
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h) => Unlift Acc (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h)) -> (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h) #
(Lift Acc a, Lift Acc b, Lift Acc c, Lift Acc d, Lift Acc e, Lift Acc f, Lift Acc g, Lift Acc h, Arrays (Plain a), Arrays (Plain b), Arrays (Plain c), Arrays (Plain d), Arrays (Plain e), Arrays (Plain f), Arrays (Plain g), Arrays (Plain h)) => Lift Acc (a, b, c, d, e, f, g, h) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b, c, d, e, f, g, h) :: Type # Methods lift :: (a, b, c, d, e, f, g, h) -> Acc (Plain (a, b, c, d, e, f, g, h)) #
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i) => Unlift Acc (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i)) -> (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i) #
(Lift Acc a, Lift Acc b, Lift Acc c, Lift Acc d, Lift Acc e, Lift Acc f, Lift Acc g, Lift Acc h, Lift Acc i, Arrays (Plain a), Arrays (Plain b), Arrays (Plain c), Arrays (Plain d), Arrays (Plain e), Arrays (Plain f), Arrays (Plain g), Arrays (Plain h), Arrays (Plain i)) => Lift Acc (a, b, c, d, e, f, g, h, i) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b, c, d, e, f, g, h, i) :: Type # Methods lift :: (a, b, c, d, e, f, g, h, i) -> Acc (Plain (a, b, c, d, e, f, g, h, i)) #
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i, Arrays j) => Unlift Acc (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j)) -> (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j) #
(Lift Acc a, Lift Acc b, Lift Acc c, Lift Acc d, Lift Acc e, Lift Acc f, Lift Acc g, Lift Acc h, Lift Acc i, Lift Acc j, Arrays (Plain a), Arrays (Plain b), Arrays (Plain c), Arrays (Plain d), Arrays (Plain e), Arrays (Plain f), Arrays (Plain g), Arrays (Plain h), Arrays (Plain i), Arrays (Plain j)) => Lift Acc (a, b, c, d, e, f, g, h, i, j) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b, c, d, e, f, g, h, i, j) :: Type # Methods lift :: (a, b, c, d, e, f, g, h, i, j) -> Acc (Plain (a, b, c, d, e, f, g, h, i, j)) #
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i, Arrays j, Arrays k) => Unlift Acc (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k)) -> (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k) #
(Lift Acc a, Lift Acc b, Lift Acc c, Lift Acc d, Lift Acc e, Lift Acc f, Lift Acc g, Lift Acc h, Lift Acc i, Lift Acc j, Lift Acc k, Arrays (Plain a), Arrays (Plain b), Arrays (Plain c), Arrays (Plain d), Arrays (Plain e), Arrays (Plain f), Arrays (Plain g), Arrays (Plain h), Arrays (Plain i), Arrays (Plain j), Arrays (Plain k)) => Lift Acc (a, b, c, d, e, f, g, h, i, j, k) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b, c, d, e, f, g, h, i, j, k) :: Type # Methods lift :: (a, b, c, d, e, f, g, h, i, j, k) -> Acc (Plain (a, b, c, d, e, f, g, h, i, j, k)) #
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i, Arrays j, Arrays k, Arrays l) => Unlift Acc (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k, Acc l) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k, Acc l)) -> (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k, Acc l) #
(Lift Acc a, Lift Acc b, Lift Acc c, Lift Acc d, Lift Acc e, Lift Acc f, Lift Acc g, Lift Acc h, Lift Acc i, Lift Acc j, Lift Acc k, Lift Acc l, Arrays (Plain a), Arrays (Plain b), Arrays (Plain c), Arrays (Plain d), Arrays (Plain e), Arrays (Plain f), Arrays (Plain g), Arrays (Plain h), Arrays (Plain i), Arrays (Plain j), Arrays (Plain k), Arrays (Plain l)) => Lift Acc (a, b, c, d, e, f, g, h, i, j, k, l) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b, c, d, e, f, g, h, i, j, k, l) :: Type # Methods lift :: (a, b, c, d, e, f, g, h, i, j, k, l) -> Acc (Plain (a, b, c, d, e, f, g, h, i, j, k, l)) #
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i, Arrays j, Arrays k, Arrays l, Arrays m) => Unlift Acc (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k, Acc l, Acc m) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k, Acc l, Acc m)) -> (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k, Acc l, Acc m) #
(Lift Acc a, Lift Acc b, Lift Acc c, Lift Acc d, Lift Acc e, Lift Acc f, Lift Acc g, Lift Acc h, Lift Acc i, Lift Acc j, Lift Acc k, Lift Acc l, Lift Acc m, Arrays (Plain a), Arrays (Plain b), Arrays (Plain c), Arrays (Plain d), Arrays (Plain e), Arrays (Plain f), Arrays (Plain g), Arrays (Plain h), Arrays (Plain i), Arrays (Plain j), Arrays (Plain k), Arrays (Plain l), Arrays (Plain m)) => Lift Acc (a, b, c, d, e, f, g, h, i, j, k, l, m) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b, c, d, e, f, g, h, i, j, k, l, m) :: Type # Methods lift :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Acc (Plain (a, b, c, d, e, f, g, h, i, j, k, l, m)) #
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i, Arrays j, Arrays k, Arrays l, Arrays m, Arrays n) => Unlift Acc (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k, Acc l, Acc m, Acc n) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k, Acc l, Acc m, Acc n)) -> (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k, Acc l, Acc m, Acc n) #
(Lift Acc a, Lift Acc b, Lift Acc c, Lift Acc d, Lift Acc e, Lift Acc f, Lift Acc g, Lift Acc h, Lift Acc i, Lift Acc j, Lift Acc k, Lift Acc l, Lift Acc m, Lift Acc n, Arrays (Plain a), Arrays (Plain b), Arrays (Plain c), Arrays (Plain d), Arrays (Plain e), Arrays (Plain f), Arrays (Plain g), Arrays (Plain h), Arrays (Plain i), Arrays (Plain j), Arrays (Plain k), Arrays (Plain l), Arrays (Plain m), Arrays (Plain n)) => Lift Acc (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b, c, d, e, f, g, h, i, j, k, l, m, n) :: Type # Methods lift :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Acc (Plain (a, b, c, d, e, f, g, h, i, j, k, l, m, n)) #
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i, Arrays j, Arrays k, Arrays l, Arrays m, Arrays n, Arrays o) => Unlift Acc (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k, Acc l, Acc m, Acc n, Acc o) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Acc (Plain (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k, Acc l, Acc m, Acc n, Acc o)) -> (Acc a, Acc b, Acc c, Acc d, Acc e, Acc f, Acc g, Acc h, Acc i, Acc j, Acc k, Acc l, Acc m, Acc n, Acc o) #
(Lift Acc a, Lift Acc b, Lift Acc c, Lift Acc d, Lift Acc e, Lift Acc f, Lift Acc g, Lift Acc h, Lift Acc i, Lift Acc j, Lift Acc k, Lift Acc l, Lift Acc m, Lift Acc n, Lift Acc o, Arrays (Plain a), Arrays (Plain b), Arrays (Plain c), Arrays (Plain d), Arrays (Plain e), Arrays (Plain f), Arrays (Plain g), Arrays (Plain h), Arrays (Plain i), Arrays (Plain j), Arrays (Plain k), Arrays (Plain l), Arrays (Plain m), Arrays (Plain n), Arrays (Plain o)) => Lift Acc (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) :: Type # Methods lift :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Acc (Plain (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)) #
Arrays arrs => Show (Acc arrs) #
Instance details Defined in Data.Array.Accelerate.Trafo Methods showsPrec :: Int -> Acc arrs -> ShowS # show :: Acc arrs -> String # showList :: [Acc arrs] -> ShowS #
Afunction (Acc a -> f) => Show (Acc a -> f) #
Instance details Defined in Data.Array.Accelerate.Trafo Methods showsPrec :: Int -> (Acc a -> f) -> ShowS # show :: (Acc a -> f) -> String # showList :: [Acc a -> f] -> ShowS #
type EltT Acc a #
Instance details Defined in Data.Array.Accelerate.Prelude type EltT Acc a = Arrays a
type Plain (Acc a) #
Instance details Defined in Data.Array.Accelerate.Lift type Plain (Acc a) = a

Arrays

data Array sh e #

Dense, regular, multi-dimensional arrays.

The Array is the core computational unit of Accelerate; all programs in Accelerate take zero or more arrays as input and produce one or more arrays as output. The Array type has two type parameters:

sh: is the shape of the array, tracking the dimensionality and extent of each dimension of the array; for example, DIM1 for one-dimensional Vectors, DIM2 for two-dimensional matrices, and so on.
e: represents the type of each element of the array; for example, Int, Float, et cetera.

Array data is store unboxed in an unzipped struct-of-array representation. Elements are laid out in row-major order (the right-most index of a Shape is the fastest varying). The allowable array element types are members of the Elt class, which roughly consists of:

Signed and unsigned integers (8, 16, 32, and 64-bits wide).
Floating point numbers (single and double precision)
Char
Bool
()
Shapes formed from Z and (:.)
Nested tuples of all of these, currently up to 15-elements wide.

Note that Array itself is not an allowable element type---there are no nested arrays in Accelerate, regular arrays only!

If device and host memory are separate, arrays will be transferred to the device when necessary (possibly asynchronously and in parallel with other tasks) and cached on the device if sufficient memory is available. Arrays are made available to embedded language computations via use.

Section "Getting data in" lists functions for getting data into and out of the Array type.

Instances

(Shape sh, Elt e) => Lift Acc (Array sh e) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (Array sh e) :: Type # Methods lift :: Array sh e -> Acc (Plain (Array sh e)) #
Elt e => IsList (Vector e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Associated Types type Item (Vector e) :: Type # Methods fromList :: [Item (Vector e)] -> Vector e # fromListN :: Int -> [Item (Vector e)] -> Vector e # toList :: Vector e -> [Item (Vector e)] #
Show (Vector e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods showsPrec :: Int -> Vector e -> ShowS # show :: Vector e -> String # showList :: [Vector e] -> ShowS #
Show (Scalar e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods showsPrec :: Int -> Scalar e -> ShowS # show :: Scalar e -> String # showList :: [Scalar e] -> ShowS #
(Eq sh, Eq e) => Eq (Array sh e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods (==) :: Array sh e -> Array sh e -> Bool # (/=) :: Array sh e -> Array sh e -> Bool #
Show (Array sh e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods showsPrec :: Int -> Array sh e -> ShowS # show :: Array sh e -> String # showList :: [Array sh e] -> ShowS #
Show (Array DIM2 e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods showsPrec :: Int -> Array DIM2 e -> ShowS # show :: Array DIM2 e -> String # showList :: [Array DIM2 e] -> ShowS #
NFData (Array sh e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods rnf :: Array sh e -> () #
(Shape sh, Elt e) => Arrays (Array sh e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: Array sh e -> ArraysR (ArrRepr (Array sh e)) flavour :: Array sh e -> ArraysFlavour (Array sh e) toArr :: ArrRepr (Array sh e) -> Array sh e fromArr :: Array sh e -> ArrRepr (Array sh e)
type Item (Vector e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type Item (Vector e) = e
type Plain (Array sh e) #
Instance details Defined in Data.Array.Accelerate.Lift type Plain (Array sh e) = Array sh e

class (Typeable a, Typeable (ArrRepr a)) => Arrays a #

Arrays consists of nested tuples of individual Arrays, currently up to 15-elements wide. Accelerate computations can thereby return multiple results.

Minimal complete definition

arrays, flavour, toArr, fromArr

Instances

Arrays () #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: () -> ArraysR (ArrRepr ()) flavour :: () -> ArraysFlavour () toArr :: ArrRepr () -> () fromArr :: () -> ArrRepr ()
(Arrays a, Arrays b) => Arrays (a, b) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b) -> ArraysR (ArrRepr (a, b)) flavour :: (a, b) -> ArraysFlavour (a, b) toArr :: ArrRepr (a, b) -> (a, b) fromArr :: (a, b) -> ArrRepr (a, b)
(Shape sh, Elt e) => Arrays (Array sh e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: Array sh e -> ArraysR (ArrRepr (Array sh e)) flavour :: Array sh e -> ArraysFlavour (Array sh e) toArr :: ArrRepr (Array sh e) -> Array sh e fromArr :: Array sh e -> ArrRepr (Array sh e)
(Arrays a, Arrays b, Arrays c) => Arrays (a, b, c) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c) -> ArraysR (ArrRepr (a, b, c)) flavour :: (a, b, c) -> ArraysFlavour (a, b, c) toArr :: ArrRepr (a, b, c) -> (a, b, c) fromArr :: (a, b, c) -> ArrRepr (a, b, c)
(Arrays a, Arrays b, Arrays c, Arrays d) => Arrays (a, b, c, d) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c, d) -> ArraysR (ArrRepr (a, b, c, d)) flavour :: (a, b, c, d) -> ArraysFlavour (a, b, c, d) toArr :: ArrRepr (a, b, c, d) -> (a, b, c, d) fromArr :: (a, b, c, d) -> ArrRepr (a, b, c, d)
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e) => Arrays (a, b, c, d, e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c, d, e) -> ArraysR (ArrRepr (a, b, c, d, e)) flavour :: (a, b, c, d, e) -> ArraysFlavour (a, b, c, d, e) toArr :: ArrRepr (a, b, c, d, e) -> (a, b, c, d, e) fromArr :: (a, b, c, d, e) -> ArrRepr (a, b, c, d, e)
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f) => Arrays (a, b, c, d, e, f) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c, d, e, f) -> ArraysR (ArrRepr (a, b, c, d, e, f)) flavour :: (a, b, c, d, e, f) -> ArraysFlavour (a, b, c, d, e, f) toArr :: ArrRepr (a, b, c, d, e, f) -> (a, b, c, d, e, f) fromArr :: (a, b, c, d, e, f) -> ArrRepr (a, b, c, d, e, f)
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g) => Arrays (a, b, c, d, e, f, g) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c, d, e, f, g) -> ArraysR (ArrRepr (a, b, c, d, e, f, g)) flavour :: (a, b, c, d, e, f, g) -> ArraysFlavour (a, b, c, d, e, f, g) toArr :: ArrRepr (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) fromArr :: (a, b, c, d, e, f, g) -> ArrRepr (a, b, c, d, e, f, g)
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h) => Arrays (a, b, c, d, e, f, g, h) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c, d, e, f, g, h) -> ArraysR (ArrRepr (a, b, c, d, e, f, g, h)) flavour :: (a, b, c, d, e, f, g, h) -> ArraysFlavour (a, b, c, d, e, f, g, h) toArr :: ArrRepr (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) fromArr :: (a, b, c, d, e, f, g, h) -> ArrRepr (a, b, c, d, e, f, g, h)
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i) => Arrays (a, b, c, d, e, f, g, h, i) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c, d, e, f, g, h, i) -> ArraysR (ArrRepr (a, b, c, d, e, f, g, h, i)) flavour :: (a, b, c, d, e, f, g, h, i) -> ArraysFlavour (a, b, c, d, e, f, g, h, i) toArr :: ArrRepr (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) fromArr :: (a, b, c, d, e, f, g, h, i) -> ArrRepr (a, b, c, d, e, f, g, h, i)
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i, Arrays j) => Arrays (a, b, c, d, e, f, g, h, i, j) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c, d, e, f, g, h, i, j) -> ArraysR (ArrRepr (a, b, c, d, e, f, g, h, i, j)) flavour :: (a, b, c, d, e, f, g, h, i, j) -> ArraysFlavour (a, b, c, d, e, f, g, h, i, j) toArr :: ArrRepr (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) fromArr :: (a, b, c, d, e, f, g, h, i, j) -> ArrRepr (a, b, c, d, e, f, g, h, i, j)
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i, Arrays j, Arrays k) => Arrays (a, b, c, d, e, f, g, h, i, j, k) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c, d, e, f, g, h, i, j, k) -> ArraysR (ArrRepr (a, b, c, d, e, f, g, h, i, j, k)) flavour :: (a, b, c, d, e, f, g, h, i, j, k) -> ArraysFlavour (a, b, c, d, e, f, g, h, i, j, k) toArr :: ArrRepr (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) fromArr :: (a, b, c, d, e, f, g, h, i, j, k) -> ArrRepr (a, b, c, d, e, f, g, h, i, j, k)
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i, Arrays j, Arrays k, Arrays l) => Arrays (a, b, c, d, e, f, g, h, i, j, k, l) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c, d, e, f, g, h, i, j, k, l) -> ArraysR (ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l)) flavour :: (a, b, c, d, e, f, g, h, i, j, k, l) -> ArraysFlavour (a, b, c, d, e, f, g, h, i, j, k, l) toArr :: ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) fromArr :: (a, b, c, d, e, f, g, h, i, j, k, l) -> ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l)
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i, Arrays j, Arrays k, Arrays l, Arrays m) => Arrays (a, b, c, d, e, f, g, h, i, j, k, l, m) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> ArraysR (ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l, m)) flavour :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> ArraysFlavour (a, b, c, d, e, f, g, h, i, j, k, l, m) toArr :: ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) fromArr :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l, m)
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i, Arrays j, Arrays k, Arrays l, Arrays m, Arrays n) => Arrays (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> ArraysR (ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n)) flavour :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> ArraysFlavour (a, b, c, d, e, f, g, h, i, j, k, l, m, n) toArr :: ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) fromArr :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n)
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i, Arrays j, Arrays k, Arrays l, Arrays m, Arrays n, Arrays o) => Arrays (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> ArraysR (ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)) flavour :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> ArraysFlavour (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) toArr :: ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) fromArr :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)
(Arrays a, Arrays b, Arrays c, Arrays d, Arrays e, Arrays f, Arrays g, Arrays h, Arrays i, Arrays j, Arrays k, Arrays l, Arrays m, Arrays n, Arrays o, Arrays p) => Arrays (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods arrays :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) -> ArraysR (ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p)) flavour :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) -> ArraysFlavour (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) toArr :: ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) fromArr :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) -> ArrRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p)

type Scalar = Array DIM0 #

Scalar arrays hold a single element

type Vector = Array DIM1 #

Vectors are one-dimensional arrays

type Matrix = Array DIM2 #

Matrices are two-dimensional arrays

type Segments = Vector #

Segment descriptor (vector of segment lengths).

To represent nested one-dimensional arrays, we use a flat array of data values in conjunction with a segment descriptor, which stores the lengths of the subarrays.

Array elements

class (Show a, Typeable a, Typeable (EltRepr a), ArrayElt (EltRepr a)) => Elt a #

The Elt class characterises the allowable array element types, and hence the types which can appear in scalar Accelerate expressions.

Accelerate arrays consist of simple atomic types as well as nested tuples thereof, stored efficiently in memory as consecutive unpacked elements without pointers. It roughly consists of:

Signed and unsigned integers (8, 16, 32, and 64-bits wide)
Floating point numbers (half, single, and double precision)
Char
Bool
()
Shapes formed from Z and (:.)
Nested tuples of all of these, currently up to 15-elements wide

Adding new instances for Elt consists of explaining to Accelerate how to map between your data type and a (tuple of) primitive values. For examples see:

Minimal complete definition

eltType, fromElt, toElt

Instances

Elt Bool #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Bool -> TupleType (EltRepr Bool) fromElt :: Bool -> EltRepr Bool toElt :: EltRepr Bool -> Bool
Elt Char #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Char -> TupleType (EltRepr Char) fromElt :: Char -> EltRepr Char toElt :: EltRepr Char -> Char
Elt Double #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Double -> TupleType (EltRepr Double) fromElt :: Double -> EltRepr Double toElt :: EltRepr Double -> Double
Elt Float #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Float -> TupleType (EltRepr Float) fromElt :: Float -> EltRepr Float toElt :: EltRepr Float -> Float
Elt Int #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Int -> TupleType (EltRepr Int) fromElt :: Int -> EltRepr Int toElt :: EltRepr Int -> Int
Elt Int8 #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Int8 -> TupleType (EltRepr Int8) fromElt :: Int8 -> EltRepr Int8 toElt :: EltRepr Int8 -> Int8
Elt Int16 #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Int16 -> TupleType (EltRepr Int16) fromElt :: Int16 -> EltRepr Int16 toElt :: EltRepr Int16 -> Int16
Elt Int32 #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Int32 -> TupleType (EltRepr Int32) fromElt :: Int32 -> EltRepr Int32 toElt :: EltRepr Int32 -> Int32
Elt Int64 #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Int64 -> TupleType (EltRepr Int64) fromElt :: Int64 -> EltRepr Int64 toElt :: EltRepr Int64 -> Int64
Elt Ordering #
Instance details Defined in Data.Array.Accelerate.Classes.Ord Methods eltType :: Ordering -> TupleType (EltRepr Ordering) fromElt :: Ordering -> EltRepr Ordering toElt :: EltRepr Ordering -> Ordering
Elt Word #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Word -> TupleType (EltRepr Word) fromElt :: Word -> EltRepr Word toElt :: EltRepr Word -> Word
Elt Word8 #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Word8 -> TupleType (EltRepr Word8) fromElt :: Word8 -> EltRepr Word8 toElt :: EltRepr Word8 -> Word8
Elt Word16 #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Word16 -> TupleType (EltRepr Word16) fromElt :: Word16 -> EltRepr Word16 toElt :: EltRepr Word16 -> Word16
Elt Word32 #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Word32 -> TupleType (EltRepr Word32) fromElt :: Word32 -> EltRepr Word32 toElt :: EltRepr Word32 -> Word32
Elt Word64 #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Word64 -> TupleType (EltRepr Word64) fromElt :: Word64 -> EltRepr Word64 toElt :: EltRepr Word64 -> Word64
Elt () #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: () -> TupleType (EltRepr ()) fromElt :: () -> EltRepr () toElt :: EltRepr () -> ()
Elt CChar #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: CChar -> TupleType (EltRepr CChar) fromElt :: CChar -> EltRepr CChar toElt :: EltRepr CChar -> CChar
Elt CSChar #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: CSChar -> TupleType (EltRepr CSChar) fromElt :: CSChar -> EltRepr CSChar toElt :: EltRepr CSChar -> CSChar
Elt CUChar #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: CUChar -> TupleType (EltRepr CUChar) fromElt :: CUChar -> EltRepr CUChar toElt :: EltRepr CUChar -> CUChar
Elt CShort #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: CShort -> TupleType (EltRepr CShort) fromElt :: CShort -> EltRepr CShort toElt :: EltRepr CShort -> CShort
Elt CUShort #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: CUShort -> TupleType (EltRepr CUShort) fromElt :: CUShort -> EltRepr CUShort toElt :: EltRepr CUShort -> CUShort
Elt CInt #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: CInt -> TupleType (EltRepr CInt) fromElt :: CInt -> EltRepr CInt toElt :: EltRepr CInt -> CInt
Elt CUInt #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: CUInt -> TupleType (EltRepr CUInt) fromElt :: CUInt -> EltRepr CUInt toElt :: EltRepr CUInt -> CUInt
Elt CLong #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: CLong -> TupleType (EltRepr CLong) fromElt :: CLong -> EltRepr CLong toElt :: EltRepr CLong -> CLong
Elt CULong #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: CULong -> TupleType (EltRepr CULong) fromElt :: CULong -> EltRepr CULong toElt :: EltRepr CULong -> CULong
Elt CLLong #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: CLLong -> TupleType (EltRepr CLLong) fromElt :: CLLong -> EltRepr CLLong toElt :: EltRepr CLLong -> CLLong
Elt CULLong #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: CULLong -> TupleType (EltRepr CULLong) fromElt :: CULLong -> EltRepr CULLong toElt :: EltRepr CULLong -> CULLong
Elt CFloat #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: CFloat -> TupleType (EltRepr CFloat) fromElt :: CFloat -> EltRepr CFloat toElt :: EltRepr CFloat -> CFloat
Elt CDouble #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: CDouble -> TupleType (EltRepr CDouble) fromElt :: CDouble -> EltRepr CDouble toElt :: EltRepr CDouble -> CDouble
Elt Half #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Half -> TupleType (EltRepr Half) fromElt :: Half -> EltRepr Half toElt :: EltRepr Half -> Half
Elt All #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: All -> TupleType (EltRepr All) fromElt :: All -> EltRepr All toElt :: EltRepr All -> All
Elt Z #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Z -> TupleType (EltRepr Z) fromElt :: Z -> EltRepr Z toElt :: EltRepr Z -> Z
Elt a => Elt (Maybe a) #
Instance details Defined in Data.Array.Accelerate.Data.Maybe Methods eltType :: Maybe a -> TupleType (EltRepr (Maybe a)) fromElt :: Maybe a -> EltRepr (Maybe a) toElt :: EltRepr (Maybe a) -> Maybe a
Elt (Complex Double) #
Instance details Defined in Data.Array.Accelerate.Data.Complex Methods eltType :: Complex Double -> TupleType (EltRepr (Complex Double)) fromElt :: Complex Double -> EltRepr (Complex Double) toElt :: EltRepr (Complex Double) -> Complex Double
Elt (Complex Float) #
Instance details Defined in Data.Array.Accelerate.Data.Complex Methods eltType :: Complex Float -> TupleType (EltRepr (Complex Float)) fromElt :: Complex Float -> EltRepr (Complex Float) toElt :: EltRepr (Complex Float) -> Complex Float
Elt (Complex CFloat) #
Instance details Defined in Data.Array.Accelerate.Data.Complex Methods eltType :: Complex CFloat -> TupleType (EltRepr (Complex CFloat)) fromElt :: Complex CFloat -> EltRepr (Complex CFloat) toElt :: EltRepr (Complex CFloat) -> Complex CFloat
Elt (Complex CDouble) #
Instance details Defined in Data.Array.Accelerate.Data.Complex Methods eltType :: Complex CDouble -> TupleType (EltRepr (Complex CDouble)) fromElt :: Complex CDouble -> EltRepr (Complex CDouble) toElt :: EltRepr (Complex CDouble) -> Complex CDouble
Elt (Complex Half) #
Instance details Defined in Data.Array.Accelerate.Data.Complex Methods eltType :: Complex Half -> TupleType (EltRepr (Complex Half)) fromElt :: Complex Half -> EltRepr (Complex Half) toElt :: EltRepr (Complex Half) -> Complex Half
Elt a => Elt (Min a) #
Instance details Defined in Data.Array.Accelerate.Data.Semigroup Methods eltType :: Min a -> TupleType (EltRepr (Min a)) fromElt :: Min a -> EltRepr (Min a) toElt :: EltRepr (Min a) -> Min a
Elt a => Elt (Max a) #
Instance details Defined in Data.Array.Accelerate.Data.Semigroup Methods eltType :: Max a -> TupleType (EltRepr (Max a)) fromElt :: Max a -> EltRepr (Max a) toElt :: EltRepr (Max a) -> Max a
Elt a => Elt (Sum a) #
Instance details Defined in Data.Array.Accelerate.Data.Monoid Methods eltType :: Sum a -> TupleType (EltRepr (Sum a)) fromElt :: Sum a -> EltRepr (Sum a) toElt :: EltRepr (Sum a) -> Sum a
Elt a => Elt (Product a) #
Instance details Defined in Data.Array.Accelerate.Data.Monoid Methods eltType :: Product a -> TupleType (EltRepr (Product a)) fromElt :: Product a -> EltRepr (Product a) toElt :: EltRepr (Product a) -> Product a
Shape sh => Elt (Any (sh :. Int)) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Any (sh :. Int) -> TupleType (EltRepr (Any (sh :. Int))) fromElt :: Any (sh :. Int) -> EltRepr (Any (sh :. Int)) toElt :: EltRepr (Any (sh :. Int)) -> Any (sh :. Int)
Elt (Any Z) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Any Z -> TupleType (EltRepr (Any Z)) fromElt :: Any Z -> EltRepr (Any Z) toElt :: EltRepr (Any Z) -> Any Z
(Elt a, Elt b) => Elt (Either a b) #
Instance details Defined in Data.Array.Accelerate.Data.Either Methods eltType :: Either a b -> TupleType (EltRepr (Either a b)) fromElt :: Either a b -> EltRepr (Either a b) toElt :: EltRepr (Either a b) -> Either a b
(Elt a, Elt b) => Elt (a, b) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b) -> TupleType (EltRepr (a, b)) fromElt :: (a, b) -> EltRepr (a, b) toElt :: EltRepr (a, b) -> (a, b)
(Elt t, Elt h) => Elt (t :. h) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (t :. h) -> TupleType (EltRepr (t :. h)) fromElt :: (t :. h) -> EltRepr (t :. h) toElt :: EltRepr (t :. h) -> t :. h
(Elt a, Elt b, Elt c) => Elt (a, b, c) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c) -> TupleType (EltRepr (a, b, c)) fromElt :: (a, b, c) -> EltRepr (a, b, c) toElt :: EltRepr (a, b, c) -> (a, b, c)
(Elt a, Elt b, Elt c, Elt d) => Elt (a, b, c, d) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c, d) -> TupleType (EltRepr (a, b, c, d)) fromElt :: (a, b, c, d) -> EltRepr (a, b, c, d) toElt :: EltRepr (a, b, c, d) -> (a, b, c, d)
(Elt a, Elt b, Elt c, Elt d, Elt e) => Elt (a, b, c, d, e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c, d, e) -> TupleType (EltRepr (a, b, c, d, e)) fromElt :: (a, b, c, d, e) -> EltRepr (a, b, c, d, e) toElt :: EltRepr (a, b, c, d, e) -> (a, b, c, d, e)
(Elt a, Elt b, Elt c, Elt d, Elt e, Elt f) => Elt (a, b, c, d, e, f) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c, d, e, f) -> TupleType (EltRepr (a, b, c, d, e, f)) fromElt :: (a, b, c, d, e, f) -> EltRepr (a, b, c, d, e, f) toElt :: EltRepr (a, b, c, d, e, f) -> (a, b, c, d, e, f)
(Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g) => Elt (a, b, c, d, e, f, g) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c, d, e, f, g) -> TupleType (EltRepr (a, b, c, d, e, f, g)) fromElt :: (a, b, c, d, e, f, g) -> EltRepr (a, b, c, d, e, f, g) toElt :: EltRepr (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
(Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h) => Elt (a, b, c, d, e, f, g, h) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c, d, e, f, g, h) -> TupleType (EltRepr (a, b, c, d, e, f, g, h)) fromElt :: (a, b, c, d, e, f, g, h) -> EltRepr (a, b, c, d, e, f, g, h) toElt :: EltRepr (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h)
(Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i) => Elt (a, b, c, d, e, f, g, h, i) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c, d, e, f, g, h, i) -> TupleType (EltRepr (a, b, c, d, e, f, g, h, i)) fromElt :: (a, b, c, d, e, f, g, h, i) -> EltRepr (a, b, c, d, e, f, g, h, i) toElt :: EltRepr (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i)
(Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i, Elt j) => Elt (a, b, c, d, e, f, g, h, i, j) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c, d, e, f, g, h, i, j) -> TupleType (EltRepr (a, b, c, d, e, f, g, h, i, j)) fromElt :: (a, b, c, d, e, f, g, h, i, j) -> EltRepr (a, b, c, d, e, f, g, h, i, j) toElt :: EltRepr (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j)
(Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i, Elt j, Elt k) => Elt (a, b, c, d, e, f, g, h, i, j, k) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c, d, e, f, g, h, i, j, k) -> TupleType (EltRepr (a, b, c, d, e, f, g, h, i, j, k)) fromElt :: (a, b, c, d, e, f, g, h, i, j, k) -> EltRepr (a, b, c, d, e, f, g, h, i, j, k) toElt :: EltRepr (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k)
(Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i, Elt j, Elt k, Elt l) => Elt (a, b, c, d, e, f, g, h, i, j, k, l) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c, d, e, f, g, h, i, j, k, l) -> TupleType (EltRepr (a, b, c, d, e, f, g, h, i, j, k, l)) fromElt :: (a, b, c, d, e, f, g, h, i, j, k, l) -> EltRepr (a, b, c, d, e, f, g, h, i, j, k, l) toElt :: EltRepr (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l)
(Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i, Elt j, Elt k, Elt l, Elt m) => Elt (a, b, c, d, e, f, g, h, i, j, k, l, m) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> TupleType (EltRepr (a, b, c, d, e, f, g, h, i, j, k, l, m)) fromElt :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> EltRepr (a, b, c, d, e, f, g, h, i, j, k, l, m) toElt :: EltRepr (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m)
(Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i, Elt j, Elt k, Elt l, Elt m, Elt n) => Elt (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> TupleType (EltRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n)) fromElt :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> EltRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n) toElt :: EltRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n)
(Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i, Elt j, Elt k, Elt l, Elt m, Elt n, Elt o) => Elt (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> TupleType (EltRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)) fromElt :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> EltRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) toElt :: EltRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)
(Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i, Elt j, Elt k, Elt l, Elt m, Elt n, Elt o, Elt p) => Elt (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) -> TupleType (EltRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p)) fromElt :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) -> EltRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) toElt :: EltRepr (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p)

Array shapes & indices

Operations in Accelerate take the form of collective operations over arrays of the type Array sh e. Much like the repa library, arrays in Accelerate are parameterised by a type sh which determines the dimensionality of the array and the type of each index, as well as the type of each element of the array e.

Shape types, and multidimensional array indices, are built like lists (technically; a heterogeneous snoc-list) using Z and (:.):

data Z = Z
data tail :. head = tail :. head

Here, the constructor Z corresponds to a shape with zero dimension (or a Scalar array, with one element) and is used to mark the end of the list. The constructor (:.) adds additional dimensions to the shape on the right. For example:

Z :. Int

is the type of the shape of a one-dimensional array (Vector) indexed by an Int, while:

Z :. Int :. Int

is the type of the shape of a two-dimensional array (a matrix) indexed by an Int in each dimension.

This style is used to construct both the type and value of the shape. For example, to define the shape of a vector of ten elements:

sh :: Z :. Int
sh = Z :. 10

Note that the right-most index is the innermost dimension. This is the fastest-varying index, and corresponds to the elements of the array which are adjacent in memory.

data Z #

Rank-0 index

Constructors

Z

Instances

Eq Z #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods (==) :: Z -> Z -> Bool # (/=) :: Z -> Z -> Bool #
Show Z #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods showsPrec :: Int -> Z -> ShowS # show :: Z -> String # showList :: [Z] -> ShowS #
Slice Z #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Associated Types type SliceShape Z :: Type # type CoSliceShape Z :: Type # type FullShape Z :: Type # Methods sliceIndex :: Z -> SliceIndex (EltRepr Z) (EltRepr (SliceShape Z)) (EltRepr (CoSliceShape Z)) (EltRepr (FullShape Z)) #
Shape Z #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods rank :: Z -> Int size :: Z -> Int empty :: Z ignore :: Z intersect :: Z -> Z -> Z union :: Z -> Z -> Z toIndex :: Z -> Z -> Int fromIndex :: Z -> Int -> Z iter :: Z -> (Z -> a) -> (a -> a -> a) -> a -> a iter1 :: Z -> (Z -> a) -> (a -> a -> a) -> a rangeToShape :: (Z, Z) -> Z shapeToRange :: Z -> (Z, Z) shapeToList :: Z -> [Int] listToShape :: [Int] -> Z sliceAnyIndex :: Z -> SliceIndex (EltRepr (Any Z)) (EltRepr Z) () (EltRepr Z) sliceNoneIndex :: Z -> SliceIndex (EltRepr Z) () (EltRepr Z) (EltRepr Z)
Elt Z #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Z -> TupleType (EltRepr Z) fromElt :: Z -> EltRepr Z toElt :: EltRepr Z -> Z
Unlift Exp Z #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Exp (Plain Z) -> Z #
Lift Exp Z #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain Z :: Type # Methods lift :: Z -> Exp (Plain Z) #
Elt e => Stencil DIM1 e (Exp e, Exp e, Exp e) #
Instance details Defined in Data.Array.Accelerate.Smart Associated Types type StencilRepr DIM1 (Exp e, Exp e, Exp e) :: Type Methods stencilPrj :: DIM1 -> e -> Exp (StencilRepr DIM1 (Exp e, Exp e, Exp e)) -> (Exp e, Exp e, Exp e)
Elt e => Stencil DIM1 e (Exp e, Exp e, Exp e, Exp e, Exp e) #
Instance details Defined in Data.Array.Accelerate.Smart Associated Types type StencilRepr DIM1 (Exp e, Exp e, Exp e, Exp e, Exp e) :: Type Methods stencilPrj :: DIM1 -> e -> Exp (StencilRepr DIM1 (Exp e, Exp e, Exp e, Exp e, Exp e)) -> (Exp e, Exp e, Exp e, Exp e, Exp e)
Elt e => Stencil DIM1 e (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e) #
Instance details Defined in Data.Array.Accelerate.Smart Associated Types type StencilRepr DIM1 (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e) :: Type Methods stencilPrj :: DIM1 -> e -> Exp (StencilRepr DIM1 (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e)) -> (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e)
Elt e => Stencil DIM1 e (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e) #
Instance details Defined in Data.Array.Accelerate.Smart Associated Types type StencilRepr DIM1 (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e) :: Type Methods stencilPrj :: DIM1 -> e -> Exp (StencilRepr DIM1 (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e)) -> (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e)
Elt e => IsList (Vector e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Associated Types type Item (Vector e) :: Type # Methods fromList :: [Item (Vector e)] -> Vector e # fromListN :: Int -> [Item (Vector e)] -> Vector e # toList :: Vector e -> [Item (Vector e)] #
Show (Vector e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods showsPrec :: Int -> Vector e -> ShowS # show :: Vector e -> String # showList :: [Vector e] -> ShowS #
Show (Scalar e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods showsPrec :: Int -> Scalar e -> ShowS # show :: Scalar e -> String # showList :: [Scalar e] -> ShowS #
Elt (Any Z) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Any Z -> TupleType (EltRepr (Any Z)) fromElt :: Any Z -> EltRepr (Any Z) toElt :: EltRepr (Any Z) -> Any Z
Show (Array DIM2 e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods showsPrec :: Int -> Array DIM2 e -> ShowS # show :: Array DIM2 e -> String # showList :: [Array DIM2 e] -> ShowS #
type SliceShape Z #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type SliceShape Z = Z
type CoSliceShape Z #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type CoSliceShape Z = Z
type FullShape Z #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type FullShape Z = Z
type Plain Z #
Instance details Defined in Data.Array.Accelerate.Lift type Plain Z = Z
type Item (Vector e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type Item (Vector e) = e

data tail :. head infixl 3 #

Increase an index rank by one dimension. The :. operator is used to construct both values and types.

Constructors

tail :. head infixl 3

Instances

Elt e => Stencil DIM1 e (Exp e, Exp e, Exp e) #
Instance details Defined in Data.Array.Accelerate.Smart Associated Types type StencilRepr DIM1 (Exp e, Exp e, Exp e) :: Type Methods stencilPrj :: DIM1 -> e -> Exp (StencilRepr DIM1 (Exp e, Exp e, Exp e)) -> (Exp e, Exp e, Exp e)
Elt e => Stencil DIM1 e (Exp e, Exp e, Exp e, Exp e, Exp e) #
Instance details Defined in Data.Array.Accelerate.Smart Associated Types type StencilRepr DIM1 (Exp e, Exp e, Exp e, Exp e, Exp e) :: Type Methods stencilPrj :: DIM1 -> e -> Exp (StencilRepr DIM1 (Exp e, Exp e, Exp e, Exp e, Exp e)) -> (Exp e, Exp e, Exp e, Exp e, Exp e)
Elt e => Stencil DIM1 e (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e) #
Instance details Defined in Data.Array.Accelerate.Smart Associated Types type StencilRepr DIM1 (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e) :: Type Methods stencilPrj :: DIM1 -> e -> Exp (StencilRepr DIM1 (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e)) -> (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e)
Elt e => Stencil DIM1 e (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e) #
Instance details Defined in Data.Array.Accelerate.Smart Associated Types type StencilRepr DIM1 (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e) :: Type Methods stencilPrj :: DIM1 -> e -> Exp (StencilRepr DIM1 (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e)) -> (Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e, Exp e)
(Elt e, Slice (Plain ix), Unlift Exp ix) => Unlift Exp (ix :. Exp e) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Exp (Plain (ix :. Exp e)) -> ix :. Exp e #
(Elt e, Slice ix) => Unlift Exp (Exp ix :. Exp e) #
Instance details Defined in Data.Array.Accelerate.Lift Methods unlift :: Exp (Plain (Exp ix :. Exp e)) -> Exp ix :. Exp e #
(Elt e, Slice (Plain ix), Lift Exp ix) => Lift Exp (ix :. Exp e) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (ix :. Exp e) :: Type # Methods lift :: (ix :. Exp e) -> Exp (Plain (ix :. Exp e)) #
(Slice (Plain ix), Lift Exp ix) => Lift Exp (ix :. All) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (ix :. All) :: Type # Methods lift :: (ix :. All) -> Exp (Plain (ix :. All)) #
(Slice (Plain ix), Lift Exp ix) => Lift Exp (ix :. Int) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (ix :. Int) :: Type # Methods lift :: (ix :. Int) -> Exp (Plain (ix :. Int)) #
Elt e => IsList (Vector e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Associated Types type Item (Vector e) :: Type # Methods fromList :: [Item (Vector e)] -> Vector e # fromListN :: Int -> [Item (Vector e)] -> Vector e # toList :: Vector e -> [Item (Vector e)] #
Show (Vector e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods showsPrec :: Int -> Vector e -> ShowS # show :: Vector e -> String # showList :: [Vector e] -> ShowS #
Shape sh => Elt (Any (sh :. Int)) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Any (sh :. Int) -> TupleType (EltRepr (Any (sh :. Int))) fromElt :: Any (sh :. Int) -> EltRepr (Any (sh :. Int)) toElt :: EltRepr (Any (sh :. Int)) -> Any (sh :. Int)
(Eq tail, Eq head) => Eq (tail :. head) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods (==) :: (tail :. head) -> (tail :. head) -> Bool # (/=) :: (tail :. head) -> (tail :. head) -> Bool #
Show (Array DIM2 e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods showsPrec :: Int -> Array DIM2 e -> ShowS # show :: Array DIM2 e -> String # showList :: [Array DIM2 e] -> ShowS #
(Show sh, Show sz) => Show (sh :. sz) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods showsPrec :: Int -> (sh :. sz) -> ShowS # show :: (sh :. sz) -> String # showList :: [sh :. sz] -> ShowS #
Slice sl => Slice (sl :. Int) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Associated Types type SliceShape (sl :. Int) :: Type # type CoSliceShape (sl :. Int) :: Type # type FullShape (sl :. Int) :: Type # Methods sliceIndex :: (sl :. Int) -> SliceIndex (EltRepr (sl :. Int)) (EltRepr (SliceShape (sl :. Int))) (EltRepr (CoSliceShape (sl :. Int))) (EltRepr (FullShape (sl :. Int))) #
Slice sl => Slice (sl :. All) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Associated Types type SliceShape (sl :. All) :: Type # type CoSliceShape (sl :. All) :: Type # type FullShape (sl :. All) :: Type # Methods sliceIndex :: (sl :. All) -> SliceIndex (EltRepr (sl :. All)) (EltRepr (SliceShape (sl :. All))) (EltRepr (CoSliceShape (sl :. All))) (EltRepr (FullShape (sl :. All))) #
Shape sh => Shape (sh :. Int) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods rank :: (sh :. Int) -> Int size :: (sh :. Int) -> Int empty :: sh :. Int ignore :: sh :. Int intersect :: (sh :. Int) -> (sh :. Int) -> sh :. Int union :: (sh :. Int) -> (sh :. Int) -> sh :. Int toIndex :: (sh :. Int) -> (sh :. Int) -> Int fromIndex :: (sh :. Int) -> Int -> sh :. Int iter :: (sh :. Int) -> ((sh :. Int) -> a) -> (a -> a -> a) -> a -> a iter1 :: (sh :. Int) -> ((sh :. Int) -> a) -> (a -> a -> a) -> a rangeToShape :: (sh :. Int, sh :. Int) -> sh :. Int shapeToRange :: (sh :. Int) -> (sh :. Int, sh :. Int) shapeToList :: (sh :. Int) -> [Int] listToShape :: [Int] -> sh :. Int sliceAnyIndex :: (sh :. Int) -> SliceIndex (EltRepr (Any (sh :. Int))) (EltRepr (sh :. Int)) () (EltRepr (sh :. Int)) sliceNoneIndex :: (sh :. Int) -> SliceIndex (EltRepr (sh :. Int)) () (EltRepr (sh :. Int)) (EltRepr (sh :. Int))
(Elt t, Elt h) => Elt (t :. h) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: (t :. h) -> TupleType (EltRepr (t :. h)) fromElt :: (t :. h) -> EltRepr (t :. h) toElt :: EltRepr (t :. h) -> t :. h
(Stencil (sh :. Int) a row2, Stencil (sh :. Int) a row1, Stencil (sh :. Int) a row0) => Stencil ((sh :. Int) :. Int) a (row2, row1, row0) #
Instance details Defined in Data.Array.Accelerate.Smart Associated Types type StencilRepr ((sh :. Int) :. Int) (row2, row1, row0) :: Type Methods stencilPrj :: ((sh :. Int) :. Int) -> a -> Exp (StencilRepr ((sh :. Int) :. Int) (row2, row1, row0)) -> (row2, row1, row0)
(Stencil (sh :. Int) a row1, Stencil (sh :. Int) a row2, Stencil (sh :. Int) a row3, Stencil (sh :. Int) a row4, Stencil (sh :. Int) a row5) => Stencil ((sh :. Int) :. Int) a (row1, row2, row3, row4, row5) #
Instance details Defined in Data.Array.Accelerate.Smart Associated Types type StencilRepr ((sh :. Int) :. Int) (row1, row2, row3, row4, row5) :: Type Methods stencilPrj :: ((sh :. Int) :. Int) -> a -> Exp (StencilRepr ((sh :. Int) :. Int) (row1, row2, row3, row4, row5)) -> (row1, row2, row3, row4, row5)
(Stencil (sh :. Int) a row1, Stencil (sh :. Int) a row2, Stencil (sh :. Int) a row3, Stencil (sh :. Int) a row4, Stencil (sh :. Int) a row5, Stencil (sh :. Int) a row6, Stencil (sh :. Int) a row7) => Stencil ((sh :. Int) :. Int) a (row1, row2, row3, row4, row5, row6, row7) #
Instance details Defined in Data.Array.Accelerate.Smart Associated Types type StencilRepr ((sh :. Int) :. Int) (row1, row2, row3, row4, row5, row6, row7) :: Type Methods stencilPrj :: ((sh :. Int) :. Int) -> a -> Exp (StencilRepr ((sh :. Int) :. Int) (row1, row2, row3, row4, row5, row6, row7)) -> (row1, row2, row3, row4, row5, row6, row7)
(Stencil (sh :. Int) a row1, Stencil (sh :. Int) a row2, Stencil (sh :. Int) a row3, Stencil (sh :. Int) a row4, Stencil (sh :. Int) a row5, Stencil (sh :. Int) a row6, Stencil (sh :. Int) a row7, Stencil (sh :. Int) a row8, Stencil (sh :. Int) a row9) => Stencil ((sh :. Int) :. Int) a (row1, row2, row3, row4, row5, row6, row7, row8, row9) #
Instance details Defined in Data.Array.Accelerate.Smart Associated Types type StencilRepr ((sh :. Int) :. Int) (row1, row2, row3, row4, row5, row6, row7, row8, row9) :: Type Methods stencilPrj :: ((sh :. Int) :. Int) -> a -> Exp (StencilRepr ((sh :. Int) :. Int) (row1, row2, row3, row4, row5, row6, row7, row8, row9)) -> (row1, row2, row3, row4, row5, row6, row7, row8, row9)
type Item (Vector e) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type Item (Vector e) = e
type SliceShape (sl :. Int) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type SliceShape (sl :. Int) = SliceShape sl
type SliceShape (sl :. All) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type SliceShape (sl :. All) = SliceShape sl :. Int
type CoSliceShape (sl :. Int) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type CoSliceShape (sl :. Int) = CoSliceShape sl :. Int
type CoSliceShape (sl :. All) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type CoSliceShape (sl :. All) = CoSliceShape sl
type FullShape (sl :. Int) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type FullShape (sl :. Int) = FullShape sl :. Int
type FullShape (sl :. All) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type FullShape (sl :. All) = FullShape sl :. Int
type Plain (ix :. Exp e) #
Instance details Defined in Data.Array.Accelerate.Lift type Plain (ix :. Exp e) = Plain ix :. e
type Plain (ix :. All) #
Instance details Defined in Data.Array.Accelerate.Lift type Plain (ix :. All) = Plain ix :. All
type Plain (ix :. Int) #
Instance details Defined in Data.Array.Accelerate.Lift type Plain (ix :. Int) = Plain ix :. Int

type DIM0 = Z #

type DIM1 = DIM0 :. Int #

type DIM2 = DIM1 :. Int #

type DIM3 = DIM2 :. Int #

type DIM4 = DIM3 :. Int #

type DIM5 = DIM4 :. Int #

type DIM6 = DIM5 :. Int #

type DIM7 = DIM6 :. Int #

type DIM8 = DIM7 :. Int #

type DIM9 = DIM8 :. Int #

class (Elt sh, Elt (Any sh), Shape (EltRepr sh), FullShape sh ~ sh, CoSliceShape sh ~ sh, SliceShape sh ~ Z) => Shape sh #

Shapes and indices of multi-dimensional arrays

Minimal complete definition

sliceAnyIndex, sliceNoneIndex

Instances

Shape Z #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods rank :: Z -> Int size :: Z -> Int empty :: Z ignore :: Z intersect :: Z -> Z -> Z union :: Z -> Z -> Z toIndex :: Z -> Z -> Int fromIndex :: Z -> Int -> Z iter :: Z -> (Z -> a) -> (a -> a -> a) -> a -> a iter1 :: Z -> (Z -> a) -> (a -> a -> a) -> a rangeToShape :: (Z, Z) -> Z shapeToRange :: Z -> (Z, Z) shapeToList :: Z -> [Int] listToShape :: [Int] -> Z sliceAnyIndex :: Z -> SliceIndex (EltRepr (Any Z)) (EltRepr Z) () (EltRepr Z) sliceNoneIndex :: Z -> SliceIndex (EltRepr Z) () (EltRepr Z) (EltRepr Z)
Shape sh => Shape (sh :. Int) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods rank :: (sh :. Int) -> Int size :: (sh :. Int) -> Int empty :: sh :. Int ignore :: sh :. Int intersect :: (sh :. Int) -> (sh :. Int) -> sh :. Int union :: (sh :. Int) -> (sh :. Int) -> sh :. Int toIndex :: (sh :. Int) -> (sh :. Int) -> Int fromIndex :: (sh :. Int) -> Int -> sh :. Int iter :: (sh :. Int) -> ((sh :. Int) -> a) -> (a -> a -> a) -> a -> a iter1 :: (sh :. Int) -> ((sh :. Int) -> a) -> (a -> a -> a) -> a rangeToShape :: (sh :. Int, sh :. Int) -> sh :. Int shapeToRange :: (sh :. Int) -> (sh :. Int, sh :. Int) shapeToList :: (sh :. Int) -> [Int] listToShape :: [Int] -> sh :. Int sliceAnyIndex :: (sh :. Int) -> SliceIndex (EltRepr (Any (sh :. Int))) (EltRepr (sh :. Int)) () (EltRepr (sh :. Int)) sliceNoneIndex :: (sh :. Int) -> SliceIndex (EltRepr (sh :. Int)) () (EltRepr (sh :. Int)) (EltRepr (sh :. Int))

class (Elt sl, Shape (SliceShape sl), Shape (CoSliceShape sl), Shape (FullShape sl)) => Slice sl where #

Slices, aka generalised indices, as n-tuples and mappings of slice indices to slices, co-slices, and slice dimensions

Associated Types

type SliceShape sl :: * #

type CoSliceShape sl :: * #

type FullShape sl :: * #

Methods

sliceIndex :: sl -> SliceIndex (EltRepr sl) (EltRepr (SliceShape sl)) (EltRepr (CoSliceShape sl)) (EltRepr (FullShape sl)) #

Instances

Slice Z #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Associated Types type SliceShape Z :: Type # type CoSliceShape Z :: Type # type FullShape Z :: Type # Methods sliceIndex :: Z -> SliceIndex (EltRepr Z) (EltRepr (SliceShape Z)) (EltRepr (CoSliceShape Z)) (EltRepr (FullShape Z)) #
Shape sh => Slice (Any sh) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Associated Types type SliceShape (Any sh) :: Type # type CoSliceShape (Any sh) :: Type # type FullShape (Any sh) :: Type # Methods sliceIndex :: Any sh -> SliceIndex (EltRepr (Any sh)) (EltRepr (SliceShape (Any sh))) (EltRepr (CoSliceShape (Any sh))) (EltRepr (FullShape (Any sh))) #
Slice sl => Slice (sl :. Int) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Associated Types type SliceShape (sl :. Int) :: Type # type CoSliceShape (sl :. Int) :: Type # type FullShape (sl :. Int) :: Type # Methods sliceIndex :: (sl :. Int) -> SliceIndex (EltRepr (sl :. Int)) (EltRepr (SliceShape (sl :. Int))) (EltRepr (CoSliceShape (sl :. Int))) (EltRepr (FullShape (sl :. Int))) #
Slice sl => Slice (sl :. All) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Associated Types type SliceShape (sl :. All) :: Type # type CoSliceShape (sl :. All) :: Type # type FullShape (sl :. All) :: Type # Methods sliceIndex :: (sl :. All) -> SliceIndex (EltRepr (sl :. All)) (EltRepr (SliceShape (sl :. All))) (EltRepr (CoSliceShape (sl :. All))) (EltRepr (FullShape (sl :. All))) #

data All #

Marker for entire dimensions in slice and replicate descriptors.

Occurrences of All indicate the dimensions into which the array's existing extent will be placed unchanged.

See slice and replicate for examples.

Constructors

All

Instances

Eq All #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods (==) :: All -> All -> Bool # (/=) :: All -> All -> Bool #
Show All #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods showsPrec :: Int -> All -> ShowS # show :: All -> String # showList :: [All] -> ShowS #
Elt All #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: All -> TupleType (EltRepr All) fromElt :: All -> EltRepr All toElt :: EltRepr All -> All
(Slice (Plain ix), Lift Exp ix) => Lift Exp (ix :. All) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (ix :. All) :: Type # Methods lift :: (ix :. All) -> Exp (Plain (ix :. All)) #
Slice sl => Slice (sl :. All) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Associated Types type SliceShape (sl :. All) :: Type # type CoSliceShape (sl :. All) :: Type # type FullShape (sl :. All) :: Type # Methods sliceIndex :: (sl :. All) -> SliceIndex (EltRepr (sl :. All)) (EltRepr (SliceShape (sl :. All))) (EltRepr (CoSliceShape (sl :. All))) (EltRepr (FullShape (sl :. All))) #
type SliceShape (sl :. All) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type SliceShape (sl :. All) = SliceShape sl :. Int
type CoSliceShape (sl :. All) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type CoSliceShape (sl :. All) = CoSliceShape sl
type FullShape (sl :. All) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type FullShape (sl :. All) = FullShape sl :. Int
type Plain (ix :. All) #
Instance details Defined in Data.Array.Accelerate.Lift type Plain (ix :. All) = Plain ix :. All

data Any sh #

Marker for arbitrary dimensions in slice and replicate descriptors.

Any can be used in the leftmost position of a slice instead of Z, indicating that any dimensionality is admissible in that position.

See slice and replicate for examples.

Constructors

Any

Instances

Shape sh => Lift Exp (Any sh) #
Instance details Defined in Data.Array.Accelerate.Lift Associated Types type Plain (Any sh) :: Type # Methods lift :: Any sh -> Exp (Plain (Any sh)) #
Eq (Any sh) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods (==) :: Any sh -> Any sh -> Bool # (/=) :: Any sh -> Any sh -> Bool #
Show (Any sh) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods showsPrec :: Int -> Any sh -> ShowS # show :: Any sh -> String # showList :: [Any sh] -> ShowS #
Shape sh => Slice (Any sh) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Associated Types type SliceShape (Any sh) :: Type # type CoSliceShape (Any sh) :: Type # type FullShape (Any sh) :: Type # Methods sliceIndex :: Any sh -> SliceIndex (EltRepr (Any sh)) (EltRepr (SliceShape (Any sh))) (EltRepr (CoSliceShape (Any sh))) (EltRepr (FullShape (Any sh))) #
Shape sh => Elt (Any (sh :. Int)) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Any (sh :. Int) -> TupleType (EltRepr (Any (sh :. Int))) fromElt :: Any (sh :. Int) -> EltRepr (Any (sh :. Int)) toElt :: EltRepr (Any (sh :. Int)) -> Any (sh :. Int)
Elt (Any Z) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar Methods eltType :: Any Z -> TupleType (EltRepr (Any Z)) fromElt :: Any Z -> EltRepr (Any Z) toElt :: EltRepr (Any Z) -> Any Z
type SliceShape (Any sh) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type SliceShape (Any sh) = sh
type CoSliceShape (Any sh) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type CoSliceShape (Any sh) = Z
type FullShape (Any sh) #
Instance details Defined in Data.Array.Accelerate.Array.Sugar type FullShape (Any sh) = sh
type Plain (Any sh) #
Instance details Defined in Data.Array.Accelerate.Lift type Plain (Any sh) = Any sh

Array access

Element indexing

(!) :: (Shape sh, Elt e) => Acc (Array sh e) -> Exp sh -> Exp e infixl 9 #

Multidimensional array indexing. Extract the value from an array at the specified zero-based index.

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> runExp $ use mat ! constant (Z:.1:.2)
12

(!!) :: (Shape sh, Elt e) => Acc (Array sh e) -> Exp Int -> Exp e infixl 9 #

Extract the value from an array at the specified linear index. Multidimensional arrays in Accelerate are stored in row-major order with zero-based indexing.

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> runExp $ use mat !! 12
12

the :: Elt e => Acc (Scalar e) -> Exp e #

Extract the element of a singleton array.

the xs  ==  xs ! Z

Shape information

null :: (Shape sh, Elt e) => Acc (Array sh e) -> Exp Bool #

Test whether an array is empty.

length :: Elt e => Acc (Vector e) -> Exp Int #

Get the length of a vector.

shape :: (Shape sh, Elt e) => Acc (Array sh e) -> Exp sh #

Extract the shape (extent) of an array.

size :: (Shape sh, Elt e) => Acc (Array sh e) -> Exp Int #

The number of elements in the array

shapeSize :: Shape sh => Exp sh -> Exp Int #

The number of elements that would be held by an array of the given shape.

Construction

Introduction

use :: Arrays arrays => arrays -> Acc arrays #

Make an array from vanilla Haskell available for processing within embedded Accelerate computations.

Depending upon which backend is used to eventually execute array computations, use may entail data transfer (e.g. to a GPU).

use is overloaded so that it can accept tuples of Arrays:

>>> let vec = fromList (Z:.10) [0..] :: Vector Int
>>> vec
Vector (Z :. 10) [0,1,2,3,4,5,6,7,8,9]

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> let vec' = use vec         :: Acc (Vector Int)
>>> let mat' = use mat         :: Acc (Matrix Int)
>>> let tup  = use (vec, mat)  :: Acc (Vector Int, Matrix Int)

unit :: Elt e => Exp e -> Acc (Scalar e) #

Construct a singleton (one element) array from a scalar value (or tuple of scalar values).

Initialisation

generate :: (Shape sh, Elt a) => Exp sh -> (Exp sh -> Exp a) -> Acc (Array sh a) #

Construct a new array by applying a function to each index.

For example, the following will generate a one-dimensional array (Vector) of three floating point numbers:

>>> run $ generate (index1 3) (\_ -> 1.2) :: Vector Float
Vector (Z :. 3) [1.2,1.2,1.2]

Or equivalently:

>>> run $ fill (constant (Z :. 3)) 1.2 :: Vector Float
Vector (Z :. 3) [1.2,1.2,1.2]

The following will create a vector with the elements [1..10]:

>>> run $ generate (index1 10) (\ix -> unindex1 ix + 1) :: Vector Int
Vector (Z :. 10) [1,2,3,4,5,6,7,8,9,10]

NOTE:

Using generate, it is possible to introduce nested data parallelism, which will cause the program to fail.

If the index given by the scalar function is then used to dispatch further parallel work, whose result is returned into Exp terms by array indexing operations such as (!) or the, the program will fail with the error: ./Data/Array/Accelerate/Trafo/Sharing.hs:447 (convertSharingExp): inconsistent valuation @ shared 'Exp' tree ....

fill :: (Shape sh, Elt e) => Exp sh -> Exp e -> Acc (Array sh e) #

Create an array where all elements are the same value.

>>> run $ fill (constant (Z:.10)) 0 :: Vector Float
Vector (Z :. 10) [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]

Enumeration

enumFromN :: (Shape sh, Num e, FromIntegral Int e) => Exp sh -> Exp e -> Acc (Array sh e) #

Create an array of the given shape containing the values x, x+1, etc. (in row-major order).

>>> run $ enumFromN (constant (Z:.5:.10)) 0 :: Matrix Int
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

enumFromStepN #

Arguments

:: (Shape sh, Num e, FromIntegral Int e)
=> Exp sh
-> Exp e	x: start
-> Exp e	y: step
-> Acc (Array sh e)

Create an array of the given shape containing the values x, x+y, x+y+y etc. (in row-major order).

>>> run $ enumFromStepN (constant (Z:.5:.10)) 0 0.5 :: Matrix Float
Matrix (Z :. 5 :. 10)
  [  0.0,  0.5,  1.0,  1.5,  2.0,  2.5,  3.0,  3.5,  4.0,  4.5,
     5.0,  5.5,  6.0,  6.5,  7.0,  7.5,  8.0,  8.5,  9.0,  9.5,
    10.0, 10.5, 11.0, 11.5, 12.0, 12.5, 13.0, 13.5, 14.0, 14.5,
    15.0, 15.5, 16.0, 16.5, 17.0, 17.5, 18.0, 18.5, 19.0, 19.5,
    20.0, 20.5, 21.0, 21.5, 22.0, 22.5, 23.0, 23.5, 24.0, 24.5]

Concatenation

(++) :: forall sh e. (Slice sh, Shape sh, Elt e) => Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int) e) infixr 5 #

Concatenate innermost component of two arrays. The extent of the lower dimensional component is the intersection of the two arrays.

>>> let m1 = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> m1
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> let m2 = fromList (Z:.10:.3) [0..] :: Matrix Int
>>> m2
Matrix (Z :. 10 :. 3)
  [  0,  1,  2,
     3,  4,  5,
     6,  7,  8,
     9, 10, 11,
    12, 13, 14,
    15, 16, 17,
    18, 19, 20,
    21, 22, 23,
    24, 25, 26,
    27, 28, 29]

>>> run $ use m1 ++ use m2
Matrix (Z :. 5 :. 13)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,  0,  1,  2,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,  3,  4,  5,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,  6,  7,  8,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,  9, 10, 11,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 12, 13, 14]

concatOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Acc (Array sh e) -> Acc (Array sh e) -> Acc (Array sh e) #

Generalised version of '(++)' where the argument Lens' specifies which dimension to concatenate along.

Appropriate lenses are available from lens-accelerate.

>>> let m1 = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> m1
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> let m2 = fromList (Z:.10:.5) [0..] :: Matrix Int
>>> m2
Matrix (Z :. 10 :. 5)
  [  0,  1,  2,  3,  4,
     5,  6,  7,  8,  9,
    10, 11, 12, 13, 14,
    15, 16, 17, 18, 19,
    20, 21, 22, 23, 24,
    25, 26, 27, 28, 29,
    30, 31, 32, 33, 34,
    35, 36, 37, 38, 39,
    40, 41, 42, 43, 44,
    45, 46, 47, 48, 49]

>>> run $ concatOn _1 (use m1) (use m2)
Matrix (Z :. 5 :. 15)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,  0,  1,  2,  3,  4,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,  5,  6,  7,  8,  9,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 10, 11, 12, 13, 14,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 15, 16, 17, 18, 19,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 20, 21, 22, 23, 24]

>>> run $ concatOn _2 (use m1) (use m2)
Matrix (Z :. 15 :. 5)
  [  0,  1,  2,  3,  4,
    10, 11, 12, 13, 14,
    20, 21, 22, 23, 24,
    30, 31, 32, 33, 34,
    40, 41, 42, 43, 44,
     0,  1,  2,  3,  4,
     5,  6,  7,  8,  9,
    10, 11, 12, 13, 14,
    15, 16, 17, 18, 19,
    20, 21, 22, 23, 24,
    25, 26, 27, 28, 29,
    30, 31, 32, 33, 34,
    35, 36, 37, 38, 39,
    40, 41, 42, 43, 44,
    45, 46, 47, 48, 49]

Composition

Flow control

(?|) :: Arrays a => Exp Bool -> (Acc a, Acc a) -> Acc a infix 0 #

Infix version of acond. If the predicate evaluates to True, the first component of the tuple is returned, else the second.

Enabling the RebindableSyntax extension will allow you to use the standard if-then-else syntax instead.

acond #

Arguments

:: Arrays a
=> Exp Bool	if-condition
-> Acc a	then-array
-> Acc a	else-array
-> Acc a

An array-level if-then-else construct.

Enabling the RebindableSyntax extension will allow you to use the standard if-then-else syntax instead.

awhile #

Arguments

:: Arrays a
=> (Acc a -> Acc (Scalar Bool))	keep evaluating while this returns `True`
-> (Acc a -> Acc a)	function to apply
-> Acc a	initial value
-> Acc a

An array-level while construct. Continue to apply the given function, starting with the initial value, until the test function evaluates to False.

class IfThenElse t where #

For use with -XRebindableSyntax, this class provides ifThenElse lifted to both scalar and array types.

Associated Types

type EltT t a :: Constraint #

Methods

ifThenElse :: EltT t a => Exp Bool -> t a -> t a -> t a #

Instances

IfThenElse Exp #
Instance details Defined in Data.Array.Accelerate.Prelude Associated Types type EltT Exp a :: Constraint # Methods ifThenElse :: EltT Exp a => Exp Bool -> Exp a -> Exp a -> Exp a #
IfThenElse Acc #
Instance details Defined in Data.Array.Accelerate.Prelude Associated Types type EltT Acc a :: Constraint # Methods ifThenElse :: EltT Acc a => Exp Bool -> Acc a -> Acc a -> Acc a #

Controlling execution

(>->) :: (Arrays a, Arrays b, Arrays c) => (Acc a -> Acc b) -> (Acc b -> Acc c) -> Acc a -> Acc c infixl 1 #

Pipelining of two array computations. The first argument will be fully evaluated before being passed to the second computation. This can be used to prevent the argument being fused into the function, for example.

Denotationally, we have

(acc1 >-> acc2) arrs = let tmp = acc1 arrs
                       in  tmp `seq` acc2 tmp

For an example use of this operation see the compute function.

compute :: Arrays a => Acc a -> Acc a #

Force an array expression to be evaluated, preventing it from fusing with other operations. Forcing operations to be computed to memory, rather than being fused into their consuming function, can sometimes improve performance. For example, computing a matrix transpose could provide better memory locality for the subsequent operation. Preventing fusion to split large operations into several simpler steps could also help by reducing register pressure.

Preventing fusion also means that the individual operations are available to be executed concurrently with other kernels. In particular, consider using this if you have a series of operations that are compute bound rather than memory bound.

Here is the synthetic example:

loop :: Exp Int -> Exp Int
loop ticks =
  let clockRate = 900000   -- kHz
  in  while (\i -> i < clockRate * ticks) (+1) 0

test :: Acc (Vector Int)
test =
  zip3
    (compute $ map loop (use $ fromList (Z:.1) [10]))
    (compute $ map loop (use $ fromList (Z:.1) [10]))
    (compute $ map loop (use $ fromList (Z:.1) [10]))

Without the use of compute, the operations are fused together and the three long-running loops are executed sequentially in a single kernel. Instead, the individual operations can now be executed concurrently, potentially reducing overall runtime.

Element-wise operations

Indexing

indexed :: (Shape sh, Elt a) => Acc (Array sh a) -> Acc (Array sh (sh, a)) #

Pair each element with its index

>>> let xs = fromList (Z:.5) [0..] :: Vector Float
>>> run $ indexed (use xs)
Vector (Z :. 5) [(Z :. 0,0.0),(Z :. 1,1.0),(Z :. 2,2.0),(Z :. 3,3.0),(Z :. 4,4.0)]

>>> let mat = fromList (Z:.3:.4) [0..] :: Matrix Float
>>> run $ indexed (use mat)
Matrix (Z :. 3 :. 4)
  [ (Z :. 0 :. 0,0.0), (Z :. 0 :. 1,1.0),  (Z :. 0 :. 2,2.0),  (Z :. 0 :. 3,3.0),
    (Z :. 1 :. 0,4.0), (Z :. 1 :. 1,5.0),  (Z :. 1 :. 2,6.0),  (Z :. 1 :. 3,7.0),
    (Z :. 2 :. 0,8.0), (Z :. 2 :. 1,9.0), (Z :. 2 :. 2,10.0), (Z :. 2 :. 3,11.0)]

Mapping

map :: (Shape sh, Elt a, Elt b) => (Exp a -> Exp b) -> Acc (Array sh a) -> Acc (Array sh b) #

Apply the given function element-wise to an array. Denotationally we have:

map f [x1, x2, ... xn] = [f x1, f x2, ... f xn]

>>> let xs = fromList (Z:.10) [0..] :: Vector Int
>>> xs
Vector (Z :. 10) [0,1,2,3,4,5,6,7,8,9]

>>> run $ map (+1) (use xs)
Vector (Z :. 10) [1,2,3,4,5,6,7,8,9,10]

imap :: (Shape sh, Elt a, Elt b) => (Exp sh -> Exp a -> Exp b) -> Acc (Array sh a) -> Acc (Array sh b) #

Apply a function to every element of an array and its index

Zipping

zipWith :: (Shape sh, Elt a, Elt b, Elt c) => (Exp a -> Exp b -> Exp c) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) #

Apply the given binary function element-wise to the two arrays. The extent of the resulting array is the intersection of the extents of the two source arrays.

>>> let xs = fromList (Z:.3:.5) [0..] :: Matrix Int
>>> xs
Matrix (Z :. 3 :. 5)
  [  0,  1,  2,  3,  4,
     5,  6,  7,  8,  9,
    10, 11, 12, 13, 14]

>>> let ys = fromList (Z:.5:.10) [1..] :: Matrix Int
>>> ys
Matrix (Z :. 5 :. 10)
  [  1,  2,  3,  4,  5,  6,  7,  8,  9, 10,
    11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
    21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
    31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
    41, 42, 43, 44, 45, 46, 47, 48, 49, 50]

>>> run $ zipWith (+) (use xs) (use ys)
Matrix (Z :. 3 :. 5)
  [  1,  3,  5,  7,  9,
    16, 18, 20, 22, 24,
    31, 33, 35, 37, 39]

zipWith3 :: (Shape sh, Elt a, Elt b, Elt c, Elt d) => (Exp a -> Exp b -> Exp c -> Exp d) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) #

Zip three arrays with the given function, analogous to zipWith.

zipWith4 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e) => (Exp a -> Exp b -> Exp c -> Exp d -> Exp e) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) #

Zip four arrays with the given function, analogous to zipWith.

zipWith5 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f) => (Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) #

Zip five arrays with the given function, analogous to zipWith.

zipWith6 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g) => (Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) #

Zip six arrays with the given function, analogous to zipWith.

zipWith7 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h) => (Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g -> Exp h) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) #

Zip seven arrays with the given function, analogous to zipWith.

zipWith8 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i) => (Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g -> Exp h -> Exp i) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) -> Acc (Array sh i) #

Zip eight arrays with the given function, analogous to zipWith.

zipWith9 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i, Elt j) => (Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g -> Exp h -> Exp i -> Exp j) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) -> Acc (Array sh i) -> Acc (Array sh j) #

Zip nine arrays with the given function, analogous to zipWith.

izipWith :: (Shape sh, Elt a, Elt b, Elt c) => (Exp sh -> Exp a -> Exp b -> Exp c) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) #

Zip two arrays with a function that also takes the element index

izipWith3 :: (Shape sh, Elt a, Elt b, Elt c, Elt d) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) #

Zip three arrays with a function that also takes the element index, analogous to izipWith.

izipWith4 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d -> Exp e) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) #

Zip four arrays with the given function that also takes the element index, analogous to zipWith.

izipWith5 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) #

Zip five arrays with the given function that also takes the element index, analogous to zipWith.

izipWith6 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) #

Zip six arrays with the given function that also takes the element index, analogous to zipWith.

izipWith7 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g -> Exp h) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) #

Zip seven arrays with the given function that also takes the element index, analogous to zipWith.

izipWith8 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g -> Exp h -> Exp i) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) -> Acc (Array sh i) #

Zip eight arrays with the given function that also takes the element index, analogous to zipWith.

izipWith9 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i, Elt j) => (Exp sh -> Exp a -> Exp b -> Exp c -> Exp d -> Exp e -> Exp f -> Exp g -> Exp h -> Exp i -> Exp j) -> Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) -> Acc (Array sh i) -> Acc (Array sh j) #

Zip nine arrays with the given function that also takes the element index, analogous to zipWith.

zip :: (Shape sh, Elt a, Elt b) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh (a, b)) #

Combine the elements of two arrays pairwise. The shape of the result is the intersection of the two argument shapes.

>>> let m1 = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> let m2 = fromList (Z:.10:.5) [0..] :: Matrix Float
>>> run $ zip (use m1) (use m2)
Matrix (Z :. 5 :. 5)
  [   (0,0.0),   (1,1.0),   (2,2.0),   (3,3.0),   (4,4.0),
     (10,5.0),  (11,6.0),  (12,7.0),  (13,8.0),  (14,9.0),
    (20,10.0), (21,11.0), (22,12.0), (23,13.0), (24,14.0),
    (30,15.0), (31,16.0), (32,17.0), (33,18.0), (34,19.0),
    (40,20.0), (41,21.0), (42,22.0), (43,23.0), (44,24.0)]

zip3 :: (Shape sh, Elt a, Elt b, Elt c) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh (a, b, c)) #

Take three arrays and return an array of triples, analogous to zip.

zip4 :: (Shape sh, Elt a, Elt b, Elt c, Elt d) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh (a, b, c, d)) #

Take four arrays and return an array of quadruples, analogous to zip.

zip5 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh (a, b, c, d, e)) #

Take five arrays and return an array of five-tuples, analogous to zip.

zip6 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh (a, b, c, d, e, f)) #

Take six arrays and return an array of six-tuples, analogous to zip.

zip7 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh (a, b, c, d, e, f, g)) #

Take seven arrays and return an array of seven-tuples, analogous to zip.

zip8 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) -> Acc (Array sh (a, b, c, d, e, f, g, h)) #

Take seven arrays and return an array of seven-tuples, analogous to zip.

zip9 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i) => Acc (Array sh a) -> Acc (Array sh b) -> Acc (Array sh c) -> Acc (Array sh d) -> Acc (Array sh e) -> Acc (Array sh f) -> Acc (Array sh g) -> Acc (Array sh h) -> Acc (Array sh i) -> Acc (Array sh (a, b, c, d, e, f, g, h, i)) #

Take seven arrays and return an array of seven-tuples, analogous to zip.

Unzipping

unzip :: (Shape sh, Elt a, Elt b) => Acc (Array sh (a, b)) -> (Acc (Array sh a), Acc (Array sh b)) #

The converse of zip, but the shape of the two results is identical to the shape of the argument.

If the argument array is manifest in memory, unzip is a no-op.

unzip3 :: (Shape sh, Elt a, Elt b, Elt c) => Acc (Array sh (a, b, c)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c)) #

Take an array of triples and return three arrays, analogous to unzip.

unzip4 :: (Shape sh, Elt a, Elt b, Elt c, Elt d) => Acc (Array sh (a, b, c, d)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c), Acc (Array sh d)) #

Take an array of quadruples and return four arrays, analogous to unzip.

unzip5 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e) => Acc (Array sh (a, b, c, d, e)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c), Acc (Array sh d), Acc (Array sh e)) #

Take an array of 5-tuples and return five arrays, analogous to unzip.

unzip6 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f) => Acc (Array sh (a, b, c, d, e, f)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c), Acc (Array sh d), Acc (Array sh e), Acc (Array sh f)) #

Take an array of 6-tuples and return six arrays, analogous to unzip.

unzip7 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g) => Acc (Array sh (a, b, c, d, e, f, g)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c), Acc (Array sh d), Acc (Array sh e), Acc (Array sh f), Acc (Array sh g)) #

Take an array of 7-tuples and return seven arrays, analogous to unzip.

unzip8 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h) => Acc (Array sh (a, b, c, d, e, f, g, h)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c), Acc (Array sh d), Acc (Array sh e), Acc (Array sh f), Acc (Array sh g), Acc (Array sh h)) #

Take an array of 8-tuples and return eight arrays, analogous to unzip.

unzip9 :: (Shape sh, Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i) => Acc (Array sh (a, b, c, d, e, f, g, h, i)) -> (Acc (Array sh a), Acc (Array sh b), Acc (Array sh c), Acc (Array sh d), Acc (Array sh e), Acc (Array sh f), Acc (Array sh g), Acc (Array sh h), Acc (Array sh i)) #

Take an array of 8-tuples and return eight arrays, analogous to unzip.

Modifying Arrays

Shape manipulation

reshape :: (Shape sh, Shape sh', Elt e) => Exp sh -> Acc (Array sh' e) -> Acc (Array sh e) #

Change the shape of an array without altering its contents. The size of the source and result arrays must be identical.

precondition: shapeSize sh == shapeSize sh'

If the argument array is manifest in memory, reshape is a no-op. If the argument is to be fused into a subsequent operation, reshape corresponds to an index transformation in the fused code.

flatten :: forall sh e. (Shape sh, Elt e) => Acc (Array sh e) -> Acc (Vector e) #

Flatten the given array of arbitrary dimension into a one-dimensional vector. As with reshape, this operation performs no work.

Replication

replicate :: (Slice slix, Elt e) => Exp slix -> Acc (Array (SliceShape slix) e) -> Acc (Array (FullShape slix) e) #

Replicate an array across one or more dimensions as specified by the generalised array index provided as the first argument.

For example, given the following vector:

>>> let vec = fromList (Z:.10) [0..] :: Vector Int
>>> vec
Vector (Z :. 10) [0,1,2,3,4,5,6,7,8,9]

...we can replicate these elements to form a two-dimensional array either by replicating those elements as new rows:

>>> run $ replicate (constant (Z :. (4::Int) :. All)) (use vec)
Matrix (Z :. 4 :. 10)
  [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
    0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
    0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
    0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

...or as columns:

>>> run $ replicate (lift (Z :. All :. (4::Int))) (use vec)
Matrix (Z :. 10 :. 4)
  [ 0, 0, 0, 0,
    1, 1, 1, 1,
    2, 2, 2, 2,
    3, 3, 3, 3,
    4, 4, 4, 4,
    5, 5, 5, 5,
    6, 6, 6, 6,
    7, 7, 7, 7,
    8, 8, 8, 8,
    9, 9, 9, 9]

Replication along more than one dimension is also possible. Here we replicate twice across the first dimension and three times across the third dimension:

>>> run $ replicate (constant (Z :. (2::Int) :. All :. (3::Int))) (use vec)
Array (Z :. 2 :. 10 :. 3) [0,0,0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,0,0,0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9]

The marker Any can be used in the slice specification to match against some arbitrary dimension. For example, here Any matches against whatever shape type variable sh takes.

>>> :{
  let rep0 :: (Shape sh, Elt e) => Exp Int -> Acc (Array sh e) -> Acc (Array (sh :. Int) e)
      rep0 n a = replicate (lift (Any :. n)) a
:}

>>> let x = unit 42 :: Acc (Scalar Int)
>>> run $ rep0 10 x
Vector (Z :. 10) [42,42,42,42,42,42,42,42,42,42]

>>> run $ rep0 5 (use vec)
Matrix (Z :. 10 :. 5)
  [ 0, 0, 0, 0, 0,
    1, 1, 1, 1, 1,
    2, 2, 2, 2, 2,
    3, 3, 3, 3, 3,
    4, 4, 4, 4, 4,
    5, 5, 5, 5, 5,
    6, 6, 6, 6, 6,
    7, 7, 7, 7, 7,
    8, 8, 8, 8, 8,
    9, 9, 9, 9, 9]

Of course, Any and All can be used together.

>>> :{
  let rep1 :: (Shape sh, Elt e) => Exp Int -> Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int :. Int) e)
      rep1 n a = replicate (lift (Any :. n :. All)) a
:}

>>> run $ rep1 5 (use vec)
Matrix (Z :. 5 :. 10)
  [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
    0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
    0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
    0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
    0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Extracting sub-arrays

slice :: (Slice slix, Elt e) => Acc (Array (FullShape slix) e) -> Exp slix -> Acc (Array (SliceShape slix) e) #

Index an array with a generalised array index, supplied as the second argument. The result is a new array (possibly a singleton) containing the selected dimensions (Alls) in their entirety.

slice is the opposite of replicate, and can be used to cut out entire dimensions. For example, for the two dimensional array mat:

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

...will can select a specific row to yield a one dimensional result by fixing the row index (2) while allowing the column index to vary (via All):

>>> run $ slice (use mat) (constant (Z :. (2::Int) :. All))
Vector (Z :. 10) [20,21,22,23,24,25,26,27,28,29]

A fully specified index (with no Alls) returns a single element (zero dimensional array).

>>> run $ slice (use mat) (constant (Z :. 4 :. 2 :: DIM2))
Scalar Z [42]

The marker Any can be used in the slice specification to match against some arbitrary (lower) dimension. Here Any matches whatever shape type variable sh takes:

>>> :{
  let
      sl0 :: (Shape sh, Elt e) => Acc (Array (sh:.Int) e) -> Exp Int -> Acc (Array sh e)
      sl0 a n = slice a (lift (Any :. n))
:}

>>> let vec = fromList (Z:.10) [0..] :: Vector Int
>>> run $ sl0 (use vec) 4
Scalar Z [4]

>>> run $ sl0 (use mat) 4
Vector (Z :. 5) [4,14,24,34,44]

Of course, Any and All can be used together.

>>> :{
  let sl1 :: (Shape sh, Elt e) => Acc (Array (sh:.Int:.Int) e) -> Exp Int -> Acc (Array (sh:.Int) e)
      sl1 a n = slice a (lift (Any :. n :. All))
:}

>>> run $ sl1 (use mat) 4
Vector (Z :. 10) [40,41,42,43,44,45,46,47,48,49]

>>> let cube = fromList (Z:.3:.4:.5) [0..] :: Array DIM3 Int
>>> cube
Array (Z :. 3 :. 4 :. 5) [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59]

>>> run $ sl1 (use cube) 2
Matrix (Z :. 3 :. 5)
  [ 10, 11, 12, 13, 14,
    30, 31, 32, 33, 34,
    50, 51, 52, 53, 54]

init :: forall sh e. (Slice sh, Shape sh, Elt e) => Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int) e) #

Yield all but the elements in the last index of the innermost dimension.

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> run $ init (use mat)
Matrix (Z :. 5 :. 9)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,
    10, 11, 12, 13, 14, 15, 16, 17, 18,
    20, 21, 22, 23, 24, 25, 26, 27, 28,
    30, 31, 32, 33, 34, 35, 36, 37, 38,
    40, 41, 42, 43, 44, 45, 46, 47, 48]

tail :: forall sh e. (Slice sh, Shape sh, Elt e) => Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int) e) #

Yield all but the first element along the innermost dimension of an array. The innermost dimension must not be empty.

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> run $ tail (use mat)
Matrix (Z :. 5 :. 9)
  [  1,  2,  3,  4,  5,  6,  7,  8,  9,
    11, 12, 13, 14, 15, 16, 17, 18, 19,
    21, 22, 23, 24, 25, 26, 27, 28, 29,
    31, 32, 33, 34, 35, 36, 37, 38, 39,
    41, 42, 43, 44, 45, 46, 47, 48, 49]

take :: forall sh e. (Slice sh, Shape sh, Elt e) => Exp Int -> Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int) e) #

Yield the first n elements in the innermost dimension of the array (plus all lower dimensional elements).

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> run $ take 5 (use mat)
Matrix (Z :. 5 :. 5)
  [  0,  1,  2,  3,  4,
    10, 11, 12, 13, 14,
    20, 21, 22, 23, 24,
    30, 31, 32, 33, 34,
    40, 41, 42, 43, 44]

drop :: forall sh e. (Slice sh, Shape sh, Elt e) => Exp Int -> Acc (Array (sh :. Int) e) -> Acc (Array (sh :. Int) e) #

Yield all but the first n elements along the innermost dimension of the array (plus all lower dimensional elements).

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> run $ drop 7 (use mat)
Matrix (Z :. 5 :. 3)
  [  7,  8,  9,
    17, 18, 19,
    27, 28, 29,
    37, 38, 39,
    47, 48, 49]

slit #

Arguments

:: (Slice sh, Shape sh, Elt e)
=> Exp Int	starting index
-> Exp Int	length
-> Acc (Array (sh :. Int) e)
-> Acc (Array (sh :. Int) e)

Yield a slit (slice) of the innermost indices of an array. Denotationally, we have:

slit i n = take n . drop i

initOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Acc (Array sh e) -> Acc (Array sh e) #

Generalised version of init where the argument Lens' specifies which dimension to operate over.

Appropriate lenses are available from lens-accelerate.

Since: 1.2.0.0

tailOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Acc (Array sh e) -> Acc (Array sh e) #

Generalised version of tail where the argument Lens' specifies which dimension to operate over.

Appropriate lenses are available from lens-accelerate.

Since: 1.2.0.0

takeOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Exp Int -> Acc (Array sh e) -> Acc (Array sh e) #

Generalised version of take where the argument Lens' specifies which dimension to operate over.

Appropriate lenses are available from lens-accelerate.

Since: 1.2.0.0

dropOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Exp Int -> Acc (Array sh e) -> Acc (Array sh e) #

Generalised version of drop where the argument Lens' specifies which dimension to operate over.

Appropriate lenses are available from lens-accelerate.

Since: 1.2.0.0

slitOn #

Arguments

:: (Shape sh, Elt e)
=> Lens' (Exp sh) (Exp Int)
-> Exp Int	starting index
-> Exp Int	length
-> Acc (Array sh e)
-> Acc (Array sh e)

Generalised version of drop where the argument Lens' specifies which dimension to operate over.

Appropriate lenses are available from lens-accelerate.

Since: 1.2.0.0

Permutations

Forward permutation (scatter)

permute #

Arguments

:: (Shape sh, Shape sh', Elt a)
=> (Exp a -> Exp a -> Exp a)	combination function
-> Acc (Array sh' a)	array of default values
-> (Exp sh -> Exp sh')	index permutation function
-> Acc (Array sh a)	array of source values to be permuted
-> Acc (Array sh' a)

Generalised forward permutation operation (array scatter).

Forward permutation specified by a function mapping indices from the source array to indices in the result array. The result array is initialised with the given defaults and any further values that are permuted into the result array are added to the current value using the given combination function.

The combination function must be associative and commutative. Elements that are mapped to the magic index ignore by the permutation function are dropped.

The combination function is given the new value being permuted as its first argument, and the current value of the array as its second.

For example, we can use permute to compute the occurrence count (histogram) for an array of values in the range [0,10):

>>> :{
  let histogram :: Acc (Vector Int) -> Acc (Vector Int)
      histogram xs =
        let zeros = fill (constant (Z:.10)) 0
            ones  = fill (shape xs)         1
        in
        permute (+) zeros (\ix -> index1 (xs!ix)) ones
:}

>>> let xs = fromList (Z :. 20) [0,0,1,2,1,1,2,4,8,3,4,9,8,3,2,5,5,3,1,2] :: Vector Int
>>> run $ histogram (use xs)
Vector (Z :. 10) [2,4,4,3,2,2,0,0,2,1]

As a second example, note that the dimensionality of the source and destination arrays can differ. In this way, we can use permute to create an identity matrix by overwriting elements along the diagonal:

>>> :{
  let identity :: Num a => Exp Int -> Acc (Matrix a)
      identity n =
        let zeros = fill (index2 n n) 0
            ones  = fill (index1 n)   1
        in
        permute const zeros (\(unindex1 -> i) -> index2 i i) ones
:}

>>> run $ identity 5 :: Matrix Int
Matrix (Z :. 5 :. 5)
  [ 1, 0, 0, 0, 0,
    0, 1, 0, 0, 0,
    0, 0, 1, 0, 0,
    0, 0, 0, 1, 0,
    0, 0, 0, 0, 1]

Note:

Regarding array fusion:

The permute operation will always be evaluated; it can not be fused into a later step.
Since the index permutation function might not cover all positions in the output array (the function is not surjective), the array of default values must be evaluated. However, other operations may fuse into this.
The array of source values can fuse into the permutation operation.
If the array of default values is only used once, it will be updated in-place.

Regarding the defaults array:

If you are sure that the default values are not necessary---they are not used by the combination function and every element will be overwritten---a default array created by filling with the value undef will give you a new uninitialised array.

ignore :: Shape sh => Exp sh #

Magic index identifying elements that are ignored in a forward permutation.

scatter #

Arguments

:: Elt e
=> Acc (Vector Int)	destination indices to scatter into
-> Acc (Vector e)	default values
-> Acc (Vector e)	source values
-> Acc (Vector e)

Overwrite elements of the destination by scattering the values of the source array according to the given index mapping.

Note that if the destination index appears more than once in the mapping the result is undefined.

>>> let to    = fromList (Z :. 6) [1,3,7,2,5,8] :: Vector Int
>>> let input = fromList (Z :. 7) [1,9,6,4,4,2,5] :: Vector Int
>>> run $ scatter (use to) (fill (constant (Z:.10)) 0) (use input)
Vector (Z :. 10) [0,1,4,9,0,4,0,6,2,0]

Backward permutation (gather)

backpermute #

Arguments

:: (Shape sh, Shape sh', Elt a)
=> Exp sh'	shape of the result array
-> (Exp sh' -> Exp sh)	index permutation function
-> Acc (Array sh a)	source array
-> Acc (Array sh' a)

Generalised backward permutation operation (array gather).

Backward permutation specified by a function mapping indices in the destination array to indices in the source array. Elements of the output array are thus generated by reading from the corresponding index in the source array.

For example, backpermute can be used to transpose a matrix; at every index Z:.y:.x in the result array, we get the value at that index by reading from the source array at index Z:.x:.y:

>>> :{
  let swap :: Exp DIM2 -> Exp DIM2
      swap = lift1 f
        where
          f :: Z :. Exp Int :. Exp Int -> Z :. Exp Int :. Exp Int
          f (Z:.y:.x) = Z :. x :. y
:}

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> let mat' = use mat
>>> run $ backpermute (swap (shape mat')) swap mat'
Matrix (Z :. 10 :. 5)
  [ 0, 10, 20, 30, 40,
    1, 11, 21, 31, 41,
    2, 12, 22, 32, 42,
    3, 13, 23, 33, 43,
    4, 14, 24, 34, 44,
    5, 15, 25, 35, 45,
    6, 16, 26, 36, 46,
    7, 17, 27, 37, 47,
    8, 18, 28, 38, 48,
    9, 19, 29, 39, 49]

gather #

Arguments

:: (Shape sh, Elt e)
=> Acc (Array sh Int)	index of source at each index to gather
-> Acc (Vector e)	source values
-> Acc (Array sh e)

Gather elements from a source array by reading values at the given indices.

>>> let input = fromList (Z:.9) [1,9,6,4,4,2,0,1,2] :: Vector Int
>>> let from  = fromList (Z:.6) [1,3,7,2,5,3] :: Vector Int
>>> run $ gather (use from) (use input)
Vector (Z :. 6) [9,4,1,6,2,4]

Specialised permutations

reverse :: Elt e => Acc (Vector e) -> Acc (Vector e) #

Reverse the elements of a vector.

transpose :: Elt e => Acc (Array DIM2 e) -> Acc (Array DIM2 e) #

Transpose the rows and columns of a matrix.

reverseOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Acc (Array sh e) -> Acc (Array sh e) #

Generalised version of reverse where the argument Lens' specifies which dimension to reverse.

Appropriate lenses are available from lens-accelerate.

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> run $ reverseOn _1 (use mat)
Matrix (Z :. 5 :. 10)
  [  9,  8,  7,  6,  5,  4,  3,  2,  1,  0,
    19, 18, 17, 16, 15, 14, 13, 12, 11, 10,
    29, 28, 27, 26, 25, 24, 23, 22, 21, 20,
    39, 38, 37, 36, 35, 34, 33, 32, 31, 30,
    49, 48, 47, 46, 45, 44, 43, 42, 41, 40]

>>> run $ reverseOn _2 (use mat)
Matrix (Z :. 5 :. 10)
  [ 40, 41, 42, 43, 44, 45, 46, 47, 48, 49,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
     0,  1,  2,  3,  4,  5,  6,  7,  8,  9]

Since: 1.2.0.0

transposeOn :: (Shape sh, Elt e) => Lens' (Exp sh) (Exp Int) -> Lens' (Exp sh) (Exp Int) -> Acc (Array sh e) -> Acc (Array sh e) #

Generalised version of transpose where the argument Lens's specify which two dimensions to transpose.

Appropriate lenses are available from lens-accelerate.

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> run $ transposeOn _1 _2 (use mat)
Matrix (Z :. 10 :. 5)
  [ 0, 10, 20, 30, 40,
    1, 11, 21, 31, 41,
    2, 12, 22, 32, 42,
    3, 13, 23, 33, 43,
    4, 14, 24, 34, 44,
    5, 15, 25, 35, 45,
    6, 16, 26, 36, 46,
    7, 17, 27, 37, 47,
    8, 18, 28, 38, 48,
    9, 19, 29, 39, 49]

>>> let box = fromList (Z:.2:.3:.5) [0..] :: Array DIM3 Int
>>> box
Array (Z :. 2 :. 3 :. 5) [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]

>>> run $ transposeOn _1 _2 (use box)
Array (Z :. 2 :. 5 :. 3) [0,5,10,1,6,11,2,7,12,3,8,13,4,9,14,15,20,25,16,21,26,17,22,27,18,23,28,19,24,29]

>>> run $ transposeOn _2 _3 (use box)
Array (Z :. 3 :. 2 :. 5) [0,1,2,3,4,15,16,17,18,19,5,6,7,8,9,20,21,22,23,24,10,11,12,13,14,25,26,27,28,29]

>>> run $ transposeOn _1 _3 (use box)
Array (Z :. 5 :. 3 :. 2) [0,15,5,20,10,25,1,16,6,21,11,26,2,17,7,22,12,27,3,18,8,23,13,28,4,19,9,24,14,29]

Since: 1.2.0.0

Filtering

filter :: forall sh e. (Shape sh, Slice sh, Elt e) => (Exp e -> Exp Bool) -> Acc (Array (sh :. Int) e) -> Acc (Vector e, Array sh Int) #

Drop elements that do not satisfy the predicate. Returns the elements which pass the predicate, together with a segment descriptor indicating how many elements along each outer dimension were valid.

>>> let vec = fromList (Z :. 10) [1..10] :: Vector Int
>>> vec
Vector (Z :. 10) [1,2,3,4,5,6,7,8,9,10]

>>> run $ filter even (use vec)
(Vector (Z :. 5) [2,4,6,8,10],Scalar Z [5])

>>> let mat = fromList (Z :. 4 :. 10) [1,2,3,4,5,6,7,8,9,10,1,1,1,1,1,2,2,2,2,2,2,4,6,8,10,12,14,16,18,20,1,3,5,7,9,11,13,15,17,19] :: Matrix Int
>>> mat
Matrix (Z :. 4 :. 10)
  [ 1, 2, 3, 4,  5,  6,  7,  8,  9, 10,
    1, 1, 1, 1,  1,  2,  2,  2,  2,  2,
    2, 4, 6, 8, 10, 12, 14, 16, 18, 20,
    1, 3, 5, 7,  9, 11, 13, 15, 17, 19]

>>> run $ filter odd (use mat)
(Vector (Z :. 20) [1,3,5,7,9,1,1,1,1,1,1,3,5,7,9,11,13,15,17,19],Vector (Z :. 4) [5,5,0,10])

Folding

fold :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array sh a) #

Reduction of the innermost dimension of an array of arbitrary rank.

The shape of the result obeys the property:

shape (fold f z xs) == indexTail (shape xs)

The first argument needs to be an associative function to enable an efficient parallel implementation. The initial element does not need to be an identity element of the combination function.

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> run $ fold (+) 42 (use mat)
Vector (Z :. 5) [87,187,287,387,487]

Reductions with non-commutative operators are supported. For example, the following computes the maximum segment sum problem along each innermost dimension of the array.

https://en.wikipedia.org/wiki/Maximum_subarray_problem

>>> :{
  let maximumSegmentSum
          :: forall sh e. (Shape sh, Num e, Ord e)
          => Acc (Array (sh :. Int) e)
          -> Acc (Array sh e)
      maximumSegmentSum
        = map (\v -> let (x,_,_,_) = unlift v :: (Exp e, Exp e, Exp e, Exp e) in x)
        . fold1 f
        . map g
        where
          f :: (Num a, Ord a) => Exp (a,a,a,a) -> Exp (a,a,a,a) -> Exp (a,a,a,a)
          f x y =
            let (mssx, misx, mcsx, tsx) = unlift x
                (mssy, misy, mcsy, tsy) = unlift y
            in
            lift ( mssx `max` (mssy `max` (mcsx+misy))
                 , misx `max` (tsx+misy)
                 , mcsy `max` (mcsx+tsy)
                 , tsx+tsy
                 )
          --
          g :: (Num a, Ord a) => Exp a -> Exp (a,a,a,a)
          g x = let y = max x 0
                in  lift (y,y,y,x)
:}

>>> let vec = fromList (Z:.10) [-2,1,-3,4,-1,2,1,-5,4,0] :: Vector Int
>>> run $ maximumSegmentSum (use vec)
Scalar Z [6]

See also Fold, which can be a useful way to compute multiple results from a single reduction.

fold1 :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Acc (Array (sh :. Int) a) -> Acc (Array sh a) #

Variant of fold that requires the innermost dimension of the array to be non-empty and doesn't need an default value.

The shape of the result obeys the property:

shape (fold f z xs) == indexTail (shape xs)

The first argument needs to be an associative function to enable an efficient parallel implementation, but does not need to be commutative.

foldAll :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array sh a) -> Acc (Scalar a) #

Reduction of an array of arbitrary rank to a single scalar value. The first argument needs to be an associative function to enable efficient parallel implementation. The initial element does not need to be an identity element.

>>> let vec = fromList (Z:.10) [0..] :: Vector Float
>>> run $ foldAll (+) 42 (use vec)
Scalar Z [87.0]

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Float
>>> run $ foldAll (+) 0 (use mat)
Scalar Z [1225.0]

fold1All :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Acc (Array sh a) -> Acc (Scalar a) #

Variant of foldAll that requires the reduced array to be non-empty and does not need a default value. The first argument must be an associative function.

Segmented reductions

foldSeg :: (Shape sh, Elt a, Elt i, IsIntegral i) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Segments i) -> Acc (Array (sh :. Int) a) #

Segmented reduction along the innermost dimension of an array. The segment descriptor specifies the lengths of the logical sub-arrays, each of which is reduced independently. The innermost dimension must contain at least as many elements as required by the segment descriptor (sum thereof).

>>> let seg = fromList (Z:.4) [1,4,0,3] :: Segments Int
>>> seg
Vector (Z :. 4) [1,4,0,3]

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> run $ foldSeg (+) 0 (use mat) (use seg)
Matrix (Z :. 5 :. 4)
  [  0,  10, 0,  18,
    10,  50, 0,  48,
    20,  90, 0,  78,
    30, 130, 0, 108,
    40, 170, 0, 138]

fold1Seg :: (Shape sh, Elt a, Elt i, IsIntegral i) => (Exp a -> Exp a -> Exp a) -> Acc (Array (sh :. Int) a) -> Acc (Segments i) -> Acc (Array (sh :. Int) a) #

Variant of foldSeg that requires all segments of the reduced array to be non-empty and doesn't need a default value. The segment descriptor specifies the length of each of the logical sub-arrays.

Specialised reductions

all :: (Shape sh, Elt e) => (Exp e -> Exp Bool) -> Acc (Array (sh :. Int) e) -> Acc (Array sh Bool) #

Check if all elements along the innermost dimension satisfy a predicate.

>>> let mat = fromList (Z :. 4 :. 10) [1,2,3,4,5,6,7,8,9,10,1,1,1,1,1,2,2,2,2,2,2,4,6,8,10,12,14,16,18,20,1,3,5,7,9,11,13,15,17,19] :: Matrix Int
>>> mat
Matrix (Z :. 4 :. 10)
  [ 1, 2, 3, 4,  5,  6,  7,  8,  9, 10,
    1, 1, 1, 1,  1,  2,  2,  2,  2,  2,
    2, 4, 6, 8, 10, 12, 14, 16, 18, 20,
    1, 3, 5, 7,  9, 11, 13, 15, 17, 19]

>>> run $ all even (use mat)
Vector (Z :. 4) [False,False,True,False]

any :: (Shape sh, Elt e) => (Exp e -> Exp Bool) -> Acc (Array (sh :. Int) e) -> Acc (Array sh Bool) #

Check if any element along the innermost dimension satisfies the predicate.

>>> let mat = fromList (Z :. 4 :. 10) [1,2,3,4,5,6,7,8,9,10,1,1,1,1,1,2,2,2,2,2,2,4,6,8,10,12,14,16,18,20,1,3,5,7,9,11,13,15,17,19] :: Matrix Int
>>> mat
Matrix (Z :. 4 :. 10)
  [ 1, 2, 3, 4,  5,  6,  7,  8,  9, 10,
    1, 1, 1, 1,  1,  2,  2,  2,  2,  2,
    2, 4, 6, 8, 10, 12, 14, 16, 18, 20,
    1, 3, 5, 7,  9, 11, 13, 15, 17, 19]

>>> run $ any even (use mat)
Vector (Z :. 4) [True,True,True,False]

and :: Shape sh => Acc (Array (sh :. Int) Bool) -> Acc (Array sh Bool) #

Check if all elements along the innermost dimension are True.

or :: Shape sh => Acc (Array (sh :. Int) Bool) -> Acc (Array sh Bool) #

Check if any element along the innermost dimension is True.

sum :: (Shape sh, Num e) => Acc (Array (sh :. Int) e) -> Acc (Array sh e) #

Compute the sum of elements along the innermost dimension of the array. To find the sum of the entire array, flatten it first.

>>> let mat = fromList (Z:.2:.5) [0..] :: Matrix Int
>>> run $ sum (use mat)
Vector (Z :. 2) [10,35]

product :: (Shape sh, Num e) => Acc (Array (sh :. Int) e) -> Acc (Array sh e) #

Compute the product of the elements along the innermost dimension of the array. To find the product of the entire array, flatten it first.

>>> let mat = fromList (Z:.2:.5) [0..] :: Matrix Int
>>> run $ product (use mat)
Vector (Z :. 2) [0,15120]

minimum :: (Shape sh, Ord e) => Acc (Array (sh :. Int) e) -> Acc (Array sh e) #

Yield the minimum element along the innermost dimension of the array. To find find the minimum element of the entire array, flatten it first.

The array must not be empty. See also fold1.

>>> let mat = fromList (Z :. 3 :. 4) [1,4,3,8, 0,2,8,4, 7,9,8,8] :: Matrix Int
>>> mat
Matrix (Z :. 3 :. 4)
  [ 1, 4, 3, 8,
    0, 2, 8, 4,
    7, 9, 8, 8]

>>> run $ minimum (use mat)
Vector (Z :. 3) [1,0,7]

maximum :: (Shape sh, Ord e) => Acc (Array (sh :. Int) e) -> Acc (Array sh e) #

Yield the maximum element along the innermost dimension of the array. To find the maximum element of the entire array, flatten it first.

The array must not be empty. See also fold1.

>>> let mat = fromList (Z :. 3 :. 4) [1,4,3,8, 0,2,8,4, 7,9,8,8] :: Matrix Int
>>> mat
Matrix (Z :. 3 :. 4)
  [ 1, 4, 3, 8,
    0, 2, 8, 4,
    7, 9, 8, 8]

>>> run $ maximum (use mat)
Vector (Z :. 3) [8,8,9]

Scans (prefix sums)

scanl :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a) #

Data.List style left-to-right scan along the innermost dimension of an arbitrary rank array. The first argument needs to be an associative function to enable efficient parallel implementation. The initial value (second argument) may be arbitrary.

>>> let vec = fromList (Z :. 10) [0..] :: Vector Int
>>> run $ scanl (+) 10 (use vec)
Vector (Z :. 11) [10,10,11,13,16,20,25,31,38,46,55]

>>> let mat = fromList (Z :. 4 :. 10) [0..] :: Matrix Int
>>> run $ scanl (+) 0 (use mat)
Matrix (Z :. 4 :. 11)
  [ 0,  0,  1,  3,   6,  10,  15,  21,  28,  36,  45,
    0, 10, 21, 33,  46,  60,  75,  91, 108, 126, 145,
    0, 20, 41, 63,  86, 110, 135, 161, 188, 216, 245,
    0, 30, 61, 93, 126, 160, 195, 231, 268, 306, 345]

scanl1 :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a) #

Data.List style left-to-right scan along the innermost dimension without an initial value (aka inclusive scan). The innermost dimension of the array must not be empty. The first argument must be an associative function.

>>> let mat = fromList (Z:.4:.10) [0..] :: Matrix Int
>>> run $ scanl1 (+) (use mat)
Matrix (Z :. 4 :. 10)
  [  0,  1,  3,   6,  10,  15,  21,  28,  36,  45,
    10, 21, 33,  46,  60,  75,  91, 108, 126, 145,
    20, 41, 63,  86, 110, 135, 161, 188, 216, 245,
    30, 61, 93, 126, 160, 195, 231, 268, 306, 345]

scanl' :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a, Array sh a) #

Variant of scanl, where the last element (final reduction result) along each dimension is returned separately. Denotationally we have:

scanl' f e arr = (init res, unit (res!len))
  where
    len = shape arr
    res = scanl f e arr

>>> let vec       = fromList (Z:.10) [0..] :: Vector Int
>>> let (res,sum) = run $ scanl' (+) 0 (use vec)
>>> res
Vector (Z :. 10) [0,0,1,3,6,10,15,21,28,36]
>>> sum
Scalar Z [45]

>>> let mat        = fromList (Z:.4:.10) [0..] :: Matrix Int
>>> let (res,sums) = run $ scanl' (+) 0 (use mat)
>>> res
Matrix (Z :. 4 :. 10)
  [ 0,  0,  1,  3,   6,  10,  15,  21,  28,  36,
    0, 10, 21, 33,  46,  60,  75,  91, 108, 126,
    0, 20, 41, 63,  86, 110, 135, 161, 188, 216,
    0, 30, 61, 93, 126, 160, 195, 231, 268, 306]
>>> sums
Vector (Z :. 4) [45,145,245,345]

scanr :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a) #

Right-to-left variant of scanl.

scanr1 :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a) #

Right-to-left variant of scanl1.

scanr' :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a, Array sh a) #

Right-to-left variant of scanl'.

prescanl :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a) #

Left-to-right pre-scan (aka exclusive scan). As for scan, the first argument must be an associative function. Denotationally, we have:

prescanl f e = afst . scanl' f e

>>> let vec = fromList (Z:.10) [1..10] :: Vector Int
>>> run $ prescanl (+) 0 (use vec)
Vector (Z :. 10) [0,1,3,6,10,15,21,28,36,45]

postscanl :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a) #

Left-to-right post-scan, a variant of scanl1 with an initial value. As with scanl1, the array must not be empty. Denotationally, we have:

postscanl f e = map (e `f`) . scanl1 f

>>> let vec = fromList (Z:.10) [1..10] :: Vector Int
>>> run $ postscanl (+) 42 (use vec)
Vector (Z :. 10) [43,45,48,52,57,63,70,78,87,97]

prescanr :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a) #

Right-to-left pre-scan (aka exclusive scan). As for scan, the first argument must be an associative function. Denotationally, we have:

prescanr f e = afst . scanr' f e

postscanr :: (Shape sh, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (sh :. Int) a) -> Acc (Array (sh :. Int) a) #

Right-to-left postscan, a variant of scanr1 with an initial value. Denotationally, we have:

postscanr f e = map (e `f`) . scanr1 f

Segmented scans

scanlSeg :: forall sh e i. (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Exp e -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e) #

Segmented version of scanl along the innermost dimension of an array. The innermost dimension must have at least as many elements as the sum of the segment descriptor.

>>> let seg = fromList (Z:.4) [1,4,0,3] :: Segments Int
>>> seg
Vector (Z :. 4) [1,4,0,3]

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> run $ scanlSeg (+) 0 (use mat) (use seg)
Matrix (Z :. 5 :. 12)
  [ 0,  0, 0,  1,  3,   6,  10, 0, 0,  5, 11,  18,
    0, 10, 0, 11, 23,  36,  50, 0, 0, 15, 31,  48,
    0, 20, 0, 21, 43,  66,  90, 0, 0, 25, 51,  78,
    0, 30, 0, 31, 63,  96, 130, 0, 0, 35, 71, 108,
    0, 40, 0, 41, 83, 126, 170, 0, 0, 45, 91, 138]

scanl1Seg :: (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e) #

Segmented version of scanl1 along the innermost dimension.

As with scanl1, the total number of elements considered, in this case given by the sum of segment descriptor, must not be zero. The input vector must contain at least this many elements.

Zero length segments are allowed, and the behaviour is as if those entries were not present in the segment descriptor; that is:

scanl1Seg f xs [n,0,0] == scanl1Seg f xs [n]   where n /= 0

>>> let seg = fromList (Z:.4) [1,4,0,3] :: Segments Int
>>> seg
Vector (Z :. 4) [1,4,0,3]

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> run $ scanl1Seg (+) (use mat) (use seg)
Matrix (Z :. 5 :. 8)
  [  0,  1,  3,   6,  10,  5, 11,  18,
    10, 11, 23,  36,  50, 15, 31,  48,
    20, 21, 43,  66,  90, 25, 51,  78,
    30, 31, 63,  96, 130, 35, 71, 108,
    40, 41, 83, 126, 170, 45, 91, 138]

scanl'Seg :: forall sh e i. (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Exp e -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e, Array (sh :. Int) e) #

Segmented version of scanl' along the innermost dimension of an array. The innermost dimension must have at least as many elements as the sum of the segment descriptor.

The first element of the resulting tuple is a vector of scanned values. The second element is a vector of segment scan totals and has the same size as the segment vector.

>>> let seg = fromList (Z:.4) [1,4,0,3] :: Segments Int
>>> seg
Vector (Z :. 4) [1,4,0,3]

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> let (res,sums) = run $ scanl'Seg (+) 0 (use mat) (use seg)
>>> res
Matrix (Z :. 5 :. 8)
  [ 0, 0,  1,  3,   6, 0,  5, 11,
    0, 0, 11, 23,  36, 0, 15, 31,
    0, 0, 21, 43,  66, 0, 25, 51,
    0, 0, 31, 63,  96, 0, 35, 71,
    0, 0, 41, 83, 126, 0, 45, 91]
>>> sums
Matrix (Z :. 5 :. 4)
  [  0,  10, 0,  18,
    10,  50, 0,  48,
    20,  90, 0,  78,
    30, 130, 0, 108,
    40, 170, 0, 138]

prescanlSeg :: (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Exp e -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e) #

Segmented version of prescanl.

postscanlSeg :: (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Exp e -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e) #

Segmented version of postscanl.

scanrSeg :: forall sh e i. (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Exp e -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e) #

Segmented version of scanr along the innermost dimension of an array. The innermost dimension must have at least as many elements as the sum of the segment descriptor.

>>> let seg = fromList (Z:.4) [1,4,0,3] :: Segments Int
>>> seg
Vector (Z :. 4) [1,4,0,3]

>>> let mat = fromList (Z:.5:.10) [0..] :: Matrix Int
>>> mat
Matrix (Z :. 5 :. 10)
  [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
    10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
    20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
    30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49]

>>> run $ scanrSeg (+) 0 (use mat) (use seg)
Matrix (Z :. 5 :. 12)
  [  2, 0,  18,  15, 11,  6, 0, 0,  24, 17,  9, 0,
    12, 0,  58,  45, 31, 16, 0, 0,  54, 37, 19, 0,
    22, 0,  98,  75, 51, 26, 0, 0,  84, 57, 29, 0,
    32, 0, 138, 105, 71, 36, 0, 0, 114, 77, 39, 0,
    42, 0, 178, 135, 91, 46, 0, 0, 144, 97, 49, 0]

scanr1Seg :: (Shape sh, Slice sh, Elt e, Integral i, Bits i, FromIntegral i Int) => (Exp e -> Exp e -> Exp e) -> Acc (Array (sh :. Int) e) -> Acc (Segments i) -> Acc (Array (sh :. Int) e) #

Segmented version of scanr1.

>>>