Safe Haskell | Safe-Inferred |
---|---|
Language | Haskell2010 |
This module contains a representation for the index function based on linear-memory accessor descriptors; see Zhu, Hoeflinger and David work.
Synopsis
- data IxFun num = IxFun {
- ixfunLMADs :: NonEmpty (LMAD num)
- base :: Shape num
- ixfunContig :: Bool
- index :: (IntegralExp num, Eq num) => IxFun num -> Indices num -> num
- iota :: IntegralExp num => Shape num -> IxFun num
- permute :: IntegralExp num => IxFun num -> Permutation -> IxFun num
- rotate :: (Eq num, IntegralExp num) => IxFun num -> Indices num -> IxFun num
- reshape :: (Eq num, IntegralExp num) => IxFun num -> ShapeChange num -> IxFun num
- slice :: (Eq num, IntegralExp num) => IxFun num -> Slice num -> IxFun num
- rebase :: (Eq num, IntegralExp num) => IxFun num -> IxFun num -> IxFun num
- shape :: (Eq num, IntegralExp num) => IxFun num -> Shape num
- rank :: IntegralExp num => IxFun num -> Int
- linearWithOffset :: (Eq num, IntegralExp num) => IxFun num -> num -> Maybe num
- rearrangeWithOffset :: (Eq num, IntegralExp num) => IxFun num -> num -> Maybe (num, [(Int, num)])
- isDirect :: (Eq num, IntegralExp num) => IxFun num -> Bool
- isLinear :: (Eq num, IntegralExp num) => IxFun num -> Bool
- substituteInIxFun :: Ord a => Map a (TPrimExp t a) -> IxFun (TPrimExp t a) -> IxFun (TPrimExp t a)
- leastGeneralGeneralization :: Eq v => IxFun (PrimExp v) -> IxFun (PrimExp v) -> Maybe (IxFun (PrimExp (Ext v)), [(PrimExp v, PrimExp v)])
- existentialize :: (IntExp t, Eq v, Pretty v) => IxFun (TPrimExp t v) -> State [TPrimExp t v] (Maybe (IxFun (TPrimExp t (Ext v))))
- closeEnough :: IxFun num -> IxFun num -> Bool
Documentation
An index function is a mapping from a multidimensional array
index space (the domain) to a one-dimensional memory index space.
Essentially, it explains where the element at position [i,j,p]
of
some array is stored inside the flat one-dimensional array that
constitutes its memory. For example, we can use this to
distinguish row-major and column-major representations.
An index function is represented as a sequence of LMAD
s.
IxFun | |
|
Instances
Functor IxFun Source # | |
Foldable IxFun Source # | |
Defined in Futhark.IR.Mem.IxFun fold :: Monoid m => IxFun m -> m # foldMap :: Monoid m => (a -> m) -> IxFun a -> m # foldMap' :: Monoid m => (a -> m) -> IxFun a -> m # foldr :: (a -> b -> b) -> b -> IxFun a -> b # foldr' :: (a -> b -> b) -> b -> IxFun a -> b # foldl :: (b -> a -> b) -> b -> IxFun a -> b # foldl' :: (b -> a -> b) -> b -> IxFun a -> b # foldr1 :: (a -> a -> a) -> IxFun a -> a # foldl1 :: (a -> a -> a) -> IxFun a -> a # elem :: Eq a => a -> IxFun a -> Bool # maximum :: Ord a => IxFun a -> a # minimum :: Ord a => IxFun a -> a # | |
Traversable IxFun Source # | |
Eq num => Eq (IxFun num) Source # | |
Show num => Show (IxFun num) Source # | |
Generic (IxFun num) Source # | |
Pretty num => Pretty (IxFun num) Source # | |
SexpIso num => SexpIso (IxFun num) Source # | |
Defined in Futhark.IR.Mem.IxFun sexpIso :: SexpGrammar (IxFun num) # | |
FreeIn num => FreeIn (IxFun num) Source # | |
Substitute num => Substitute (IxFun num) Source # | |
Defined in Futhark.IR.Mem.IxFun | |
Substitute num => Rename (IxFun num) Source # | |
type Rep (IxFun num) Source # | |
Defined in Futhark.IR.Mem.IxFun |
index :: (IntegralExp num, Eq num) => IxFun num -> Indices num -> num Source #
Compute the flat memory index for a complete set inds
of array indices
and a certain element size elem_size
.
iota :: IntegralExp num => Shape num -> IxFun num Source #
iota.
rotate :: (Eq num, IntegralExp num) => IxFun num -> Indices num -> IxFun num Source #
Rotate an index function.
reshape :: (Eq num, IntegralExp num) => IxFun num -> ShapeChange num -> IxFun num Source #
Reshape an index function.
slice :: (Eq num, IntegralExp num) => IxFun num -> Slice num -> IxFun num Source #
Slice an index function.
rebase :: (Eq num, IntegralExp num) => IxFun num -> IxFun num -> IxFun num Source #
Rebase an index function on top of a new base.
rank :: IntegralExp num => IxFun num -> Int Source #
The number of dimensions in the domain of the input function.
linearWithOffset :: (Eq num, IntegralExp num) => IxFun num -> num -> Maybe num Source #
If the memory support of the index function is contiguous and row-major (i.e., no transpositions, repetitions, rotates, etc.), then this should return the offset from which the memory-support of this index function starts.
rearrangeWithOffset :: (Eq num, IntegralExp num) => IxFun num -> num -> Maybe (num, [(Int, num)]) Source #
Similar restrictions to linearWithOffset
except for transpositions, which
are returned together with the offset.
isLinear :: (Eq num, IntegralExp num) => IxFun num -> Bool Source #
Is this a row-major array starting at offset zero?
substituteInIxFun :: Ord a => Map a (TPrimExp t a) -> IxFun (TPrimExp t a) -> IxFun (TPrimExp t a) Source #
Substitute a name with a PrimExp in an index function.
leastGeneralGeneralization :: Eq v => IxFun (PrimExp v) -> IxFun (PrimExp v) -> Maybe (IxFun (PrimExp (Ext v)), [(PrimExp v, PrimExp v)]) Source #
Generalization (anti-unification)
Anti-unification of two index functions is supported under the following conditions: 0. Both index functions are represented by ONE lmad (assumed common case!) 1. The support array of the two indexfuns have the same dimensionality (we can relax this condition if we use a 1D support, as we probably should!) 2. The contiguous property and the per-dimension monotonicity are the same (otherwise we might loose important information; this can be relaxed!) 3. Most importantly, both index functions correspond to the same permutation (since the permutation is represented by INTs, this restriction cannot be relaxed, unless we move to a gated-LMAD representation!)
existentialize :: (IntExp t, Eq v, Pretty v) => IxFun (TPrimExp t v) -> State [TPrimExp t v] (Maybe (IxFun (TPrimExp t (Ext v)))) Source #
closeEnough :: IxFun num -> IxFun num -> Bool Source #
When comparing index functions as part of the type check in KernelsMem, we may run into problems caused by the simplifier. As index functions can be generalized over if-then-else expressions, the simplifier might hoist some of the code from inside the if-then-else (computing the offset of an array, for instance), but now the type checker cannot verify that the generalized index function is valid, because some of the existentials are computed somewhere else. To Work around this, we've had to relax the KernelsMem type-checker a bit, specifically, we've introduced this function to verify whether two index functions are "close enough" that we can assume that they match. We use this instead of `ixfun1 == ixfun2` and hope that it's good enough.