{-# LANGUAGE TypeOperators, FlexibleContexts, TypeFamilies, RankNTypes, ScopedTypeVariables #-} {-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, TypeSynonymInstances #-} {-# OPTIONS_GHC -fno-warn-missing-methods -fno-warn-orphans #-} -- | -- Module : Data.Array.Accelerate.Language -- Copyright : [2009..2011] Manuel M T Chakravarty, Gabriele Keller, Sean Lee, Trevor L. McDonell -- License : BSD3 -- -- Maintainer : Manuel M T Chakravarty -- Stability : experimental -- Portability : non-portable (GHC extensions) -- -- We use the dictionary view of overloaded operations (such as arithmetic and -- bit manipulation) to reify such expressions. With non-overloaded -- operations (such as, the logical connectives) and partially overloaded -- operations (such as comparisons), we use the standard operator names with a -- '*' attached. We keep the standard alphanumeric names as they can be -- easily qualified. -- module Data.Array.Accelerate.Language ( -- ** Array and scalar expressions Acc, Exp, -- re-exporting from 'Smart' -- ** Stencil specification Boundary(..), Stencil, -- re-exporting from 'Smart' -- ** Common stencil types Stencil3, Stencil5, Stencil7, Stencil9, Stencil3x3, Stencil5x3, Stencil3x5, Stencil5x5, Stencil3x3x3, Stencil5x3x3, Stencil3x5x3, Stencil3x3x5, Stencil5x5x3, Stencil5x3x5, Stencil3x5x5, Stencil5x5x5, -- ** Scalar introduction constant, -- re-exporting from 'Smart' -- ** Array construction use, unit, replicate, generate, fstA, sndA, pairA, -- ** Shape manipulation reshape, -- ** Extraction of subarrays slice, -- ** Map-like functions map, zipWith, -- ** Reductions fold, fold1, foldSeg, fold1Seg, -- ** Scan functions scanl, scanl', scanl1, scanr, scanr', scanr1, -- ** Permutations permute, backpermute, -- ** Stencil operations stencil, stencil2, -- ** Pipelining (>->), -- ** Array-level flow-control cond, (?|), -- ** Lifting and unlifting Lift(..), Unlift(..), lift1, lift2, ilift1, ilift2, -- ** Tuple construction and destruction fst, snd, curry, uncurry, -- ** Index construction and destruction index0, index1, unindex1, -- ** Conditional expressions (?), -- ** Array operations with a scalar result (!), the, shape, size, -- ** Methods of H98 classes that we need to redefine as their signatures change (==*), (/=*), (<*), (<=*), (>*), (>=*), max, min, bit, setBit, clearBit, complementBit, testBit, shift, shiftL, shiftR, rotate, rotateL, rotateR, truncate, round, floor, ceiling, -- ** Standard functions that we need to redefine as their signatures change (&&*), (||*), not, -- ** Conversions boolToInt, fromIntegral, -- ** Constants ignore -- Instances of Bounded, Enum, Eq, Ord, Bits, Num, Real, Floating, -- Fractional, RealFrac, RealFloat ) where -- avoid clashes with Prelude functions import Prelude hiding (replicate, zip, unzip, map, scanl, scanl1, scanr, scanr1, zipWith, filter, max, min, not, fst, snd, curry, uncurry, truncate, round, floor, ceiling, fromIntegral) -- standard libraries import Data.Bits (Bits((.&.), (.|.), xor, complement)) -- friends import Data.Array.Accelerate.Type import Data.Array.Accelerate.Tuple import Data.Array.Accelerate.Array.Sugar hiding ((!), ignore, shape, size, index) import qualified Data.Array.Accelerate.Array.Sugar as Sugar import Data.Array.Accelerate.Smart import Data.Array.Accelerate.AST (Arrays) -- Array introduction -- ------------------ -- |Array inlet: makes an array available for processing using the Accelerate -- language; triggers asynchronous host->device transfer if necessary. -- use :: (Shape ix, Elt e) => Array ix e -> Acc (Array ix e) use = Acc . Use -- |Scalar inlet: injects a scalar (or a tuple of scalars) into a singleton -- array for use in the Accelerate language. -- unit :: Elt e => Exp e -> Acc (Scalar e) unit = Acc . Unit -- |Replicate an array across one or more dimensions as specified by the -- *generalised* array index provided as the first argument. -- -- For example, assuming 'arr' is a vector (one-dimensional array), -- -- > replicate (Z :.2 :.All :.3) arr -- -- yields a three dimensional array, where 'arr' is replicated twice across the -- first and three times across the third dimension. -- replicate :: (Slice slix, Elt e) => Exp slix -> Acc (Array (SliceShape slix) e) -> Acc (Array (FullShape slix) e) replicate = Acc $$ Replicate -- |Construct a new array by applying a function to each index. -- generate :: (Shape ix, Elt a) => Exp ix -> (Exp ix -> Exp a) -> Acc (Array ix a) generate = Acc $$ Generate -- Shape manipulation -- ------------------ -- |Change the shape of an array without altering its contents, where -- -- > precondition: size ix == size ix' -- reshape :: (Shape ix, Shape ix', Elt e) => Exp ix -> Acc (Array ix' e) -> Acc (Array ix e) reshape = Acc $$ Reshape -- Extraction of subarrays -- ----------------------- -- |Index an array with a *generalised* array index (supplied as the second -- argument). The result is a new array (possibly a singleton) containing -- all dimensions in their entirety. -- slice :: (Slice slix, Elt e) => Acc (Array (FullShape slix) e) -> Exp slix -> Acc (Array (SliceShape slix) e) slice = Acc $$ Index -- Map-like functions -- ------------------ -- |Apply the given function elementwise to the given array. -- map :: (Shape ix, Elt a, Elt b) => (Exp a -> Exp b) -> Acc (Array ix a) -> Acc (Array ix b) map = Acc $$ Map -- |Apply the given binary function elementwise to the two arrays. The extent of the resulting -- array is the intersection of the extents of the two source arrays. -- zipWith :: (Shape ix, Elt a, Elt b, Elt c) => (Exp a -> Exp b -> Exp c) -> Acc (Array ix a) -> Acc (Array ix b) -> Acc (Array ix c) zipWith = Acc $$$ ZipWith -- Reductions -- ---------- -- |Reduction of the innermost dimension of an array of arbitrary rank. The first argument needs to -- be an /associative/ function to enable an efficient parallel implementation. -- fold :: (Shape ix, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (ix:.Int) a) -> Acc (Array ix a) fold = Acc $$$ Fold -- |Variant of 'fold' that requires the reduced array to be non-empty and doesn't need an default -- value. -- fold1 :: (Shape ix, Elt a) => (Exp a -> Exp a -> Exp a) -> Acc (Array (ix:.Int) a) -> Acc (Array ix a) fold1 = Acc $$ Fold1 -- |Segmented reduction along the innermost dimension. Performs one individual reduction per -- segment of the source array. These reductions proceed in parallel. -- -- The source array must have at least rank 1. -- foldSeg :: (Shape ix, Elt a) => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Array (ix:.Int) a) -> Acc Segments -> Acc (Array (ix:.Int) a) foldSeg = Acc $$$$ FoldSeg -- |Variant of 'foldSeg' that requires /all/ segments of the reduced array to be non-empty and -- doesn't need a default value. -- -- The source array must have at least rank 1. -- fold1Seg :: (Shape ix, Elt a) => (Exp a -> Exp a -> Exp a) -> Acc (Array (ix:.Int) a) -> Acc Segments -> Acc (Array (ix:.Int) a) fold1Seg = Acc $$$ Fold1Seg -- Scan functions -- -------------- -- |'Data.List'-style left-to-right scan, but with the additional restriction that the first -- argument needs to be an /associative/ function to enable an efficient parallel implementation. -- The initial value (second argument) may be arbitrary. -- scanl :: Elt a => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Vector a) -> Acc (Vector a) scanl = Acc $$$ Scanl -- |Variant of 'scanl', where the final result of the reduction is returned separately. -- Denotationally, we have -- -- > scanl' f e arr = (crop 0 (len - 1) res, unit (res!len)) -- > where -- > len = shape arr -- > res = scanl f e arr -- scanl' :: Elt a => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Vector a) -> (Acc (Vector a), Acc (Scalar a)) scanl' = unpair . Acc $$$ Scanl' -- |'Data.List' style left-to-right scan without an intial value (aka inclusive scan). Again, the -- first argument needs to be an /associative/ function. Denotationally, we have -- -- > scanl1 f e arr = crop 1 len res -- > where -- > len = shape arr -- > res = scanl f e arr -- scanl1 :: Elt a => (Exp a -> Exp a -> Exp a) -> Acc (Vector a) -> Acc (Vector a) scanl1 = Acc $$ Scanl1 -- |Right-to-left variant of 'scanl'. -- scanr :: Elt a => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Vector a) -> Acc (Vector a) scanr = Acc $$$ Scanr -- |Right-to-left variant of 'scanl\''. -- scanr' :: Elt a => (Exp a -> Exp a -> Exp a) -> Exp a -> Acc (Vector a) -> (Acc (Vector a), Acc (Scalar a)) scanr' = unpair . Acc $$$ Scanr' -- |Right-to-left variant of 'scanl1'. -- scanr1 :: Elt a => (Exp a -> Exp a -> Exp a) -> Acc (Vector a) -> Acc (Vector a) scanr1 = Acc $$ Scanr1 -- Permutations -- ------------ -- |Forward permutation specified by an index mapping. 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/. Eltents that are mapped to -- the magic value 'ignore' by the permutation function are being dropped. -- permute :: (Shape ix, Shape ix', Elt a) => (Exp a -> Exp a -> Exp a) -- ^combination function -> Acc (Array ix' a) -- ^array of default values -> (Exp ix -> Exp ix') -- ^permutation -> Acc (Array ix a) -- ^permuted array -> Acc (Array ix' a) permute = Acc $$$$ Permute -- |Backward permutation -- backpermute :: (Shape ix, Shape ix', Elt a) => Exp ix' -- ^shape of the result array -> (Exp ix' -> Exp ix) -- ^permutation -> Acc (Array ix a) -- ^permuted array -> Acc (Array ix' a) backpermute = Acc $$$ Backpermute -- Stencil operations -- ------------------ -- Common stencil types -- -- DIM1 stencil type 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) -- DIM2 stencil type 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) -- DIM3 stencil type 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) -- |Map a stencil over an array. In contrast to 'map', the domain of a stencil function is an -- entire /neighbourhood/ of each array element. Neighbourhoods are sub-arrays centred around a -- focal point. They are not necessarily rectangular, but they are symmetric in each dimension -- and have an extent of at least three in each dimensions — due to the symmetry requirement, the -- extent is necessarily odd. The focal point is the array position that is determined by the -- stencil. -- -- For those array positions where the neighbourhood extends past the boundaries of the source -- array, a boundary condition determines the contents of the out-of-bounds neighbourhood -- positions. -- stencil :: (Shape ix, Elt a, Elt b, Stencil ix a stencil) => (stencil -> Exp b) -- ^stencil function -> Boundary a -- ^boundary condition -> Acc (Array ix a) -- ^source array -> Acc (Array ix b) -- ^destination array stencil = Acc $$$ Stencil -- |Map a binary stencil of an array. The extent of the resulting array is the intersection of -- the extents of the two source arrays. -- stencil2 :: (Shape ix, Elt a, Elt b, Elt c, Stencil ix a stencil1, Stencil ix b stencil2) => (stencil1 -> stencil2 -> Exp c) -- ^binary stencil function -> Boundary a -- ^boundary condition #1 -> Acc (Array ix a) -- ^source array #1 -> Boundary b -- ^boundary condition #2 -> Acc (Array ix b) -- ^source array #2 -> Acc (Array ix c) -- ^destination array stencil2 = Acc $$$$$ Stencil2 -- Composition of array computations -- --------------------------------- -- |Pipelining of two array computations. -- -- Denotationally, we have -- -- > (acc1 >-> acc2) arrs = let tmp = acc1 arrs in acc2 tmp -- -- Operationally, the array computations 'acc1' and 'acc2' will not share any subcomputations, -- neither between each other nor with the environment. This makes them truly independent stages -- that only communicate by way of the result of 'acc1' which is being fed as an argument to 'acc2'. -- infixl 1 >-> (>->) :: (Arrays a, Arrays b, Arrays c) => (Acc a -> Acc b) -> (Acc b -> Acc c) -> (Acc a -> Acc c) (>->) = Acc $$$ Pipe -- Flow control constructs -- ----------------------- -- |An array-level if-then-else construct. -- cond :: (Arrays a) => Exp Bool -- ^if-condition -> Acc a -- ^then-array -> Acc a -- ^else-array -> Acc a cond = Acc $$$ Acond -- |Infix version of 'cond'. -- infix 0 ?| (?|) :: (Arrays a) => Exp Bool -> (Acc a, Acc a) -> Acc a c ?| (t, e) = cond c t e -- Construction and destruction of array pairs -- ------------------------------------------- -- |Extract the first component of an array pair. -- fstA :: (Shape sh1, Shape sh2, Elt e1, Elt e2) => Acc (Array sh1 e1, Array sh2 e2) -> Acc (Array sh1 e1) fstA = Acc . FstArray -- |Extract the second component of an array pair. -- sndA :: (Shape sh1, Shape sh2, Elt e1, Elt e2) => Acc (Array sh1 e1, Array sh2 e2) -> Acc (Array sh2 e2) sndA = Acc . SndArray -- |Create an array pair from two separate arrays. -- pairA :: (Shape sh1, Shape sh2, Elt e1, Elt e2) => Acc (Array sh1 e1) -> Acc (Array sh2 e2) -> Acc (Array sh1 e1, Array sh2 e2) pairA = Acc $$ PairArrays -- Lifting scalar expressions -- -------------------------- class Lift e where type Plain e -- |Lift the given value into 'Exp'. The value may already contain subexpressions in 'Exp'. -- lift :: e -> Exp (Plain e) class Lift e => Unlift e where -- |Unlift the outmost constructor through 'Exp'. This is only possible if the constructor is -- fully determined by its type - i.e., it is a singleton. -- unlift :: Exp (Plain e) -> e -- instances for indices instance Lift () where type Plain () = () lift _ = Tuple NilTup instance Unlift () where unlift _ = () instance Lift Z where type Plain Z = Z lift _ = IndexNil instance Unlift Z where unlift _ = Z instance (Slice (Plain ix), Lift ix) => Lift (ix :. Int) where type Plain (ix :. Int) = Plain ix :. Int lift (ix:.i) = IndexCons (lift ix) (Const i) instance (Slice (Plain ix), Lift ix) => Lift (ix :. All) where type Plain (ix :. All) = Plain ix :. All lift (ix:.i) = IndexCons (lift ix) (Const i) instance (Elt e, Slice (Plain ix), Lift ix) => Lift (ix :. Exp e) where type Plain (ix :. Exp e) = Plain ix :. e lift (ix:.i) = IndexCons (lift ix) i instance (Elt e, Slice (Plain ix), Unlift ix) => Unlift (ix :. Exp e) where unlift e = unlift (IndexTail e) :. IndexHead e instance Shape sh => Lift (Any sh) where type Plain (Any sh) = Any sh lift Any = IndexAny -- instances for numeric types instance Lift Int where type Plain Int = Int lift = Const instance Lift Int8 where type Plain Int8 = Int8 lift = Const instance Lift Int16 where type Plain Int16 = Int16 lift = Const instance Lift Int32 where type Plain Int32 = Int32 lift = Const instance Lift Int64 where type Plain Int64 = Int64 lift = Const instance Lift Word where type Plain Word = Word lift = Const instance Lift Word8 where type Plain Word8 = Word8 lift = Const instance Lift Word16 where type Plain Word16 = Word16 lift = Const instance Lift Word32 where type Plain Word32 = Word32 lift = Const instance Lift Word64 where type Plain Word64 = Word64 lift = Const {- instance Lift CShort where type Plain CShort = CShort lift = Const instance Lift CUShort where type Plain CUShort = CUShort lift = Const instance Lift CInt where type Plain CInt = CInt lift = Const instance Lift CUInt where type Plain CUInt = CUInt lift = Const instance Lift CLong where type Plain CLong = CLong lift = Const instance Lift CULong where type Plain CULong = CULong lift = Const instance Lift CLLong where type Plain CLLong = CLLong lift = Const instance Lift CULLong where type Plain CULLong = CULLong lift = Const -} instance Lift Float where type Plain Float = Float lift = Const instance Lift Double where type Plain Double = Double lift = Const {- instance Lift CFloat where type Plain CFloat = CFloat lift = Const instance Lift CDouble where type Plain CDouble = CDouble lift = Const -} instance Lift Bool where type Plain Bool = Bool lift = Const instance Lift Char where type Plain Char = Char lift = Const {- instance Lift CChar where type Plain CChar = CChar lift = Const instance Lift CSChar where type Plain CSChar = CSChar lift = Const instance Lift CUChar where type Plain CUChar = CUChar lift = Const -} -- Instances for tuples instance (Lift a, Lift b, Elt (Plain a), Elt (Plain b)) => Lift (a, b) where type Plain (a, b) = (Plain a, Plain b) lift (x, y) = tup2 (lift x, lift y) instance (Elt a, Elt b) => Unlift (Exp a, Exp b) where unlift = untup2 instance (Lift a, Lift b, Lift c, Elt (Plain a), Elt (Plain b), Elt (Plain c)) => Lift (a, b, c) where type Plain (a, b, c) = (Plain a, Plain b, Plain c) lift (x, y, z) = tup3 (lift x, lift y, lift z) instance (Elt a, Elt b, Elt c) => Unlift (Exp a, Exp b, Exp c) where unlift = untup3 instance (Lift a, Lift b, Lift c, Lift d, Elt (Plain a), Elt (Plain b), Elt (Plain c), Elt (Plain d)) => Lift (a, b, c, d) where type Plain (a, b, c, d) = (Plain a, Plain b, Plain c, Plain d) lift (x, y, z, u) = tup4 (lift x, lift y, lift z, lift u) instance (Elt a, Elt b, Elt c, Elt d) => Unlift (Exp a, Exp b, Exp c, Exp d) where unlift = untup4 instance (Lift a, Lift b, Lift c, Lift d, Lift e, Elt (Plain a), Elt (Plain b), Elt (Plain c), Elt (Plain d), Elt (Plain e)) => Lift (a, b, c, d, e) where type Plain (a, b, c, d, e) = (Plain a, Plain b, Plain c, Plain d, Plain e) lift (x, y, z, u, v) = tup5 (lift x, lift y, lift z, lift u, lift v) instance (Elt a, Elt b, Elt c, Elt d, Elt e) => Unlift (Exp a, Exp b, Exp c, Exp d, Exp e) where unlift = untup5 instance (Lift a, Lift b, Lift c, Lift d, Lift e, Lift f, Elt (Plain a), Elt (Plain b), Elt (Plain c), Elt (Plain d), Elt (Plain e), Elt (Plain f)) => Lift (a, b, c, d, e, f) where type Plain (a, b, c, d, e, f) = (Plain a, Plain b, Plain c, Plain d, Plain e, Plain f) lift (x, y, z, u, v, w) = tup6 (lift x, lift y, lift z, lift u, lift v, lift w) instance (Elt a, Elt b, Elt c, Elt d, Elt e, Elt f) => Unlift (Exp a, Exp b, Exp c, Exp d, Exp e, Exp f) where unlift = untup6 instance (Lift a, Lift b, Lift c, Lift d, Lift e, Lift f, Lift g, Elt (Plain a), Elt (Plain b), Elt (Plain c), Elt (Plain d), Elt (Plain e), Elt (Plain f), Elt (Plain g)) => Lift (a, b, c, d, e, f, g) where type Plain (a, b, c, d, e, f, g) = (Plain a, Plain b, Plain c, Plain d, Plain e, Plain f, Plain g) lift (x, y, z, u, v, w, r) = tup7 (lift x, lift y, lift z, lift u, lift v, lift w, lift r) instance (Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g) => Unlift (Exp a, Exp b, Exp c, Exp d, Exp e, Exp f, Exp g) where unlift = untup7 instance (Lift a, Lift b, Lift c, Lift d, Lift e, Lift f, Lift g, Lift h, Elt (Plain a), Elt (Plain b), Elt (Plain c), Elt (Plain d), Elt (Plain e), Elt (Plain f), Elt (Plain g), Elt (Plain h)) => Lift (a, b, c, d, e, f, g, h) where type Plain (a, b, c, d, e, f, g, h) = (Plain a, Plain b, Plain c, Plain d, Plain e, Plain f, Plain g, Plain h) lift (x, y, z, u, v, w, r, s) = tup8 (lift x, lift y, lift z, lift u, lift v, lift w, lift r, lift s) instance (Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h) => Unlift (Exp a, Exp b, Exp c, Exp d, Exp e, Exp f, Exp g, Exp h) where unlift = untup8 instance (Lift a, Lift b, Lift c, Lift d, Lift e, Lift f, Lift g, Lift h, Lift i, Elt (Plain a), Elt (Plain b), Elt (Plain c), Elt (Plain d), Elt (Plain e), Elt (Plain f), Elt (Plain g), Elt (Plain h), Elt (Plain i)) => Lift (a, b, c, d, e, f, g, h, i) where type Plain (a, b, c, d, e, f, g, h, i) = (Plain a, Plain b, Plain c, Plain d, Plain e, Plain f, Plain g, Plain h, Plain i) lift (x, y, z, u, v, w, r, s, t) = tup9 (lift x, lift y, lift z, lift u, lift v, lift w, lift r, lift s, lift t) instance (Elt a, Elt b, Elt c, Elt d, Elt e, Elt f, Elt g, Elt h, Elt i) => Unlift (Exp a, Exp b, Exp c, Exp d, Exp e, Exp f, Exp g, Exp h, Exp i) where unlift = untup9 -- Instance for scalar Accelerate expressions instance Lift (Exp e) where type Plain (Exp e) = e lift = id -- Helpers to lift functions -- |Lift a unary function into 'Exp'. -- lift1 :: (Unlift e1, Lift e2) => (e1 -> e2) -> Exp (Plain e1) -> Exp (Plain e2) lift1 f = lift . f . unlift -- |Lift a binary function into 'Exp'. -- lift2 :: (Unlift e1, Unlift e2, Lift e3) => (e1 -> e2 -> e3) -> Exp (Plain e1) -> Exp (Plain e2) -> Exp (Plain e3) lift2 f x y = lift $ f (unlift x) (unlift y) -- |Lift a unary function to a computation over rank-1 indices. -- ilift1 :: (Exp Int -> Exp Int) -> Exp (Z :. Int) -> Exp (Z :. Int) ilift1 f = lift1 (\(Z:.i) -> Z :. f i) -- |Lift a binary function to a computation over rank-1 indices. -- ilift2 :: (Exp Int -> Exp Int -> Exp Int) -> Exp (Z :. Int) -> Exp (Z :. Int) -> Exp (Z :. Int) ilift2 f = lift2 (\(Z:.i) (Z:.j) -> Z :. f i j) -- Helpers to lift tuples -- |Extract the first component of a pair. -- fst :: forall a b. (Elt a, Elt b) => Exp (a, b) -> Exp a fst e = let (x, _:: Exp b) = unlift e in x -- |Extract the second component of a pair. -- snd :: forall a b. (Elt a, Elt b) => Exp (a, b) -> Exp b snd e = let (_ :: Exp a, y) = unlift e in y -- |Converts an uncurried function to a curried function. -- curry :: (Elt a, Elt b) => (Exp (a, b) -> Exp c) -> Exp a -> Exp b -> Exp c curry f x y = f (lift (x, y)) -- |Converts a curried function to a function on pairs. -- uncurry :: (Elt a, Elt b) => (Exp a -> Exp b -> Exp c) -> Exp (a, b) -> Exp c uncurry f t = let (x, y) = unlift t in f x y -- Helpers to lift shapes and indices -- |The one index for a rank-0 array. -- index0 :: Exp Z index0 = lift Z -- |Turn an 'Int' expression into a rank-1 indexing expression. -- index1 :: Exp Int -> Exp (Z:. Int) index1 = lift . (Z:.) -- |Turn an 'Int' expression into a rank-1 indexing expression. -- unindex1 :: Exp (Z:. Int) -> Exp Int unindex1 ix = let Z:.i = unlift ix in i -- Conditional expressions -- ----------------------- -- |Conditional expression. -- infix 0 ? (?) :: Elt t => Exp Bool -> (Exp t, Exp t) -> Exp t c ? (t, e) = Cond c t e -- Array operations with a scalar result -- ------------------------------------- -- |Expression form that extracts a scalar from an array. -- infixl 9 ! (!) :: (Shape ix, Elt e) => Acc (Array ix e) -> Exp ix -> Exp e (!) = IndexScalar -- |Extraction of the element in a singleton array. -- the :: Elt e => Acc (Scalar e) -> Exp e the = (!index0) -- |Expression form that yields the shape of an array. -- shape :: (Shape ix, Elt e) => Acc (Array ix e) -> Exp ix shape = Shape -- |Expression form that yields the size of an array. -- size :: (Shape ix, Elt e) => Acc (Array ix e) -> Exp Int size = Size -- Instances of all relevant H98 classes -- ------------------------------------- instance (Elt t, IsBounded t) => Bounded (Exp t) where minBound = mkMinBound maxBound = mkMaxBound instance (Elt t, IsScalar t) => Enum (Exp t) -- succ = mkSucc -- pred = mkPred -- FIXME: ops instance (Elt t, IsScalar t) => Prelude.Eq (Exp t) where -- FIXME: instance makes no sense with standard signatures (==) = error "Prelude.Eq.== applied to EDSL types" instance (Elt t, IsScalar t) => Prelude.Ord (Exp t) where -- FIXME: instance makes no sense with standard signatures compare = error "Prelude.Ord.compare applied to EDSL types" instance (Elt t, IsNum t, IsIntegral t) => Bits (Exp t) where (.&.) = mkBAnd (.|.) = mkBOr xor = mkBXor complement = mkBNot -- FIXME: argh, the rest have fixed types in their signatures shift, shiftL, shiftR :: (Elt t, IsIntegral t) => Exp t -> Exp Int -> Exp t shift x i = i ==* 0 ? (x, i <* 0 ? (x `shiftR` (-i), x `shiftL` i)) shiftL = mkBShiftL shiftR = mkBShiftR rotate, rotateL, rotateR :: (Elt t, IsIntegral t) => Exp t -> Exp Int -> Exp t rotate x i = i ==* 0 ? (x, i <* 0 ? (x `rotateR` (-i), x `rotateL` i)) rotateL = mkBRotateL rotateR = mkBRotateR bit :: (Elt t, IsIntegral t) => Exp Int -> Exp t bit x = 1 `shiftL` x setBit, clearBit, complementBit :: (Elt t, IsIntegral t) => Exp t -> Exp Int -> Exp t x `setBit` i = x .|. bit i x `clearBit` i = x .&. complement (bit i) x `complementBit` i = x `xor` bit i testBit :: (Elt t, IsIntegral t) => Exp t -> Exp Int -> Exp Bool x `testBit` i = (x .&. bit i) /=* 0 instance (Elt t, IsNum t) => Num (Exp t) where (+) = mkAdd (-) = mkSub (*) = mkMul negate = mkNeg abs = mkAbs signum = mkSig fromInteger = constant . fromInteger instance (Elt t, IsNum t) => Real (Exp t) -- FIXME: Why did we include this class? We won't need `toRational' until -- we support rational numbers in AP computations. instance (Elt t, IsIntegral t) => Integral (Exp t) where quot = mkQuot rem = mkRem div = mkIDiv mod = mkMod -- quotRem = -- divMod = -- toInteger = -- makes no sense instance (Elt t, IsFloating t) => Floating (Exp t) where pi = mkPi sin = mkSin cos = mkCos tan = mkTan asin = mkAsin acos = mkAcos atan = mkAtan asinh = mkAsinh acosh = mkAcosh atanh = mkAtanh exp = mkExpFloating sqrt = mkSqrt log = mkLog (**) = mkFPow logBase = mkLogBase instance (Elt t, IsFloating t) => Fractional (Exp t) where (/) = mkFDiv recip = mkRecip fromRational = constant . fromRational instance (Elt t, IsFloating t) => RealFrac (Exp t) -- FIXME: add other ops instance (Elt t, IsFloating t) => RealFloat (Exp t) where atan2 = mkAtan2 -- FIXME: add other ops -- Methods from H98 classes, where we need other signatures -- -------------------------------------------------------- infix 4 ==*, /=*, <*, <=*, >*, >=* -- |Equality lifted into Accelerate expressions. -- (==*) :: (Elt t, IsScalar t) => Exp t -> Exp t -> Exp Bool (==*) = mkEq -- |Inequality lifted into Accelerate expressions. -- (/=*) :: (Elt t, IsScalar t) => Exp t -> Exp t -> Exp Bool (/=*) = mkNEq -- compare :: a -> a -> Ordering -- we have no enumerations at the moment -- compare = ... -- |Smaller-than lifted into Accelerate expressions. -- (<*) :: (Elt t, IsScalar t) => Exp t -> Exp t -> Exp Bool (<*) = mkLt -- |Greater-or-equal lifted into Accelerate expressions. -- (>=*) :: (Elt t, IsScalar t) => Exp t -> Exp t -> Exp Bool (>=*) = mkGtEq -- |Greater-than lifted into Accelerate expressions. -- (>*) :: (Elt t, IsScalar t) => Exp t -> Exp t -> Exp Bool (>*) = mkGt -- |Smaller-or-equal lifted into Accelerate expressions. -- (<=*) :: (Elt t, IsScalar t) => Exp t -> Exp t -> Exp Bool (<=*) = mkLtEq -- |Determine the maximum of two scalars. -- max :: (Elt t, IsScalar t) => Exp t -> Exp t -> Exp t max = mkMax -- |Determine the minimum of two scalars. -- min :: (Elt t, IsScalar t) => Exp t -> Exp t -> Exp t min = mkMin -- |Conversions from the RealFrac class -- truncate :: (Elt a, Elt b, IsFloating a, IsIntegral b) => Exp a -> Exp b truncate = mkTruncate round :: (Elt a, Elt b, IsFloating a, IsIntegral b) => Exp a -> Exp b round = mkRound floor :: (Elt a, Elt b, IsFloating a, IsIntegral b) => Exp a -> Exp b floor = mkFloor ceiling :: (Elt a, Elt b, IsFloating a, IsIntegral b) => Exp a -> Exp b ceiling = mkCeiling -- Non-overloaded standard functions, where we need other signatures -- ----------------------------------------------------------------- -- |Conjunction -- infixr 3 &&* (&&*) :: Exp Bool -> Exp Bool -> Exp Bool (&&*) = mkLAnd -- |Disjunction -- infixr 2 ||* (||*) :: Exp Bool -> Exp Bool -> Exp Bool (||*) = mkLOr -- |Negation -- not :: Exp Bool -> Exp Bool not = mkLNot -- Conversions -- ----------- -- |Convert a Boolean value to an 'Int', where 'False' turns into '0' and 'True' -- into '1'. -- boolToInt :: Exp Bool -> Exp Int boolToInt = mkBoolToInt -- |General coercion from integral types -- fromIntegral :: (Elt a, Elt b, IsIntegral a, IsNum b) => Exp a -> Exp b fromIntegral = mkFromIntegral -- Constants -- --------- -- |Magic value identifying elements that are ignored in a forward permutation -- ignore :: Shape ix => Exp ix ignore = constant Sugar.ignore