{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE OverloadedStrings #-}
{-# OPTIONS_GHC -fno-warn-redundant-constraints #-}

-- | This module contains a representation for the index function based on
-- linear-memory accessor descriptors; see Zhu, Hoeflinger and David work.
module Futhark.IR.Mem.IxFun
  ( IxFun (..),
    Shape,
    LMAD (..),
    LMADDim (..),
    Monotonicity (..),
    index,
    mkExistential,
    iota,
    iotaOffset,
    permute,
    reshape,
    coerce,
    slice,
    flatSlice,
    rebase,
    shape,
    rank,
    linearWithOffset,
    rearrangeWithOffset,
    isDirect,
    isLinear,
    substituteInIxFun,
    existentialize,
    closeEnough,
    equivalent,
    dynamicEqualsLMAD,
  )
where

import Control.Category
import Control.Monad.Identity
import Control.Monad.State
import Control.Monad.Writer
import Data.Function (on, (&))
import Data.List (sort, sortBy, zip4, zipWith4)
import Data.List.NonEmpty (NonEmpty (..))
import qualified Data.List.NonEmpty as NE
import qualified Data.Map.Strict as M
import Data.Maybe (isJust)
import Futhark.Analysis.PrimExp
import Futhark.Analysis.PrimExp.Convert (substituteInPrimExp)
import Futhark.IR.Prop
import Futhark.IR.Syntax
  ( DimIndex (..),
    FlatDimIndex (..),
    FlatSlice (..),
    Slice (..),
    dimFix,
    flatSliceDims,
    flatSliceStrides,
    unitSlice,
  )
import Futhark.IR.Syntax.Core (Ext (..))
import Futhark.Transform.Rename
import Futhark.Transform.Substitute
import Futhark.Util.IntegralExp
import Futhark.Util.Pretty
import Prelude hiding (id, mod, (.))

-- | The shape of an index function.
type Shape num = [num]

type Indices num = [num]

type Permutation = [Int]

-- | The physical element ordering alongside a dimension, i.e. the
-- sign of the stride.
data Monotonicity
  = -- | Increasing.
    Inc
  | -- | Decreasing.
    Dec
  | -- | Unknown.
    Unknown
  deriving (Int -> Monotonicity -> ShowS
[Monotonicity] -> ShowS
Monotonicity -> String
(Int -> Monotonicity -> ShowS)
-> (Monotonicity -> String)
-> ([Monotonicity] -> ShowS)
-> Show Monotonicity
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [Monotonicity] -> ShowS
$cshowList :: [Monotonicity] -> ShowS
show :: Monotonicity -> String
$cshow :: Monotonicity -> String
showsPrec :: Int -> Monotonicity -> ShowS
$cshowsPrec :: Int -> Monotonicity -> ShowS
Show, Monotonicity -> Monotonicity -> Bool
(Monotonicity -> Monotonicity -> Bool)
-> (Monotonicity -> Monotonicity -> Bool) -> Eq Monotonicity
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Monotonicity -> Monotonicity -> Bool
$c/= :: Monotonicity -> Monotonicity -> Bool
== :: Monotonicity -> Monotonicity -> Bool
$c== :: Monotonicity -> Monotonicity -> Bool
Eq)

-- | A single dimension in an 'LMAD'.
data LMADDim num = LMADDim
  { forall num. LMADDim num -> num
ldStride :: num,
    forall num. LMADDim num -> num
ldShape :: num,
    forall num. LMADDim num -> Int
ldPerm :: Int,
    forall num. LMADDim num -> Monotonicity
ldMon :: Monotonicity
  }
  deriving (Int -> LMADDim num -> ShowS
[LMADDim num] -> ShowS
LMADDim num -> String
(Int -> LMADDim num -> ShowS)
-> (LMADDim num -> String)
-> ([LMADDim num] -> ShowS)
-> Show (LMADDim num)
forall num. Show num => Int -> LMADDim num -> ShowS
forall num. Show num => [LMADDim num] -> ShowS
forall num. Show num => LMADDim num -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [LMADDim num] -> ShowS
$cshowList :: forall num. Show num => [LMADDim num] -> ShowS
show :: LMADDim num -> String
$cshow :: forall num. Show num => LMADDim num -> String
showsPrec :: Int -> LMADDim num -> ShowS
$cshowsPrec :: forall num. Show num => Int -> LMADDim num -> ShowS
Show, LMADDim num -> LMADDim num -> Bool
(LMADDim num -> LMADDim num -> Bool)
-> (LMADDim num -> LMADDim num -> Bool) -> Eq (LMADDim num)
forall num. Eq num => LMADDim num -> LMADDim num -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: LMADDim num -> LMADDim num -> Bool
$c/= :: forall num. Eq num => LMADDim num -> LMADDim num -> Bool
== :: LMADDim num -> LMADDim num -> Bool
$c== :: forall num. Eq num => LMADDim num -> LMADDim num -> Bool
Eq)

-- | LMAD's representation consists of a general offset and for each dimension a
-- stride, number of elements (or shape), permutation, and
-- monotonicity. Note that the permutation is not strictly necessary in that the
-- permutation can be performed directly on LMAD dimensions, but then it is
-- difficult to extract the permutation back from an LMAD.
--
-- LMAD algebra is closed under composition w.r.t. operators such as
-- permute, index and slice.  However, other operations, such as
-- reshape, cannot always be represented inside the LMAD algebra.
--
-- It follows that the general representation of an index function is a list of
-- LMADS, in which each following LMAD in the list implicitly corresponds to an
-- irregular reshaping operation.
--
-- However, we expect that the common case is when the index function is one
-- LMAD -- we call this the "nice" representation.
--
-- Finally, the list of LMADs is kept in an @IxFun@ together with the shape of
-- the original array, and a bit to indicate whether the index function is
-- contiguous, i.e., if we instantiate all the points of the current index
-- function, do we get a contiguous memory interval?
--
-- By definition, the LMAD denotes the set of points (simplified):
--
--   \{ o + \Sigma_{j=0}^{k} ((i_j+r_j) `mod` n_j)*s_j,
--      \forall i_j such that 0<=i_j<n_j, j=1..k \}
data LMAD num = LMAD
  { forall num. LMAD num -> num
lmadOffset :: num,
    forall num. LMAD num -> [LMADDim num]
lmadDims :: [LMADDim num]
  }
  deriving (Int -> LMAD num -> ShowS
[LMAD num] -> ShowS
LMAD num -> String
(Int -> LMAD num -> ShowS)
-> (LMAD num -> String) -> ([LMAD num] -> ShowS) -> Show (LMAD num)
forall num. Show num => Int -> LMAD num -> ShowS
forall num. Show num => [LMAD num] -> ShowS
forall num. Show num => LMAD num -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [LMAD num] -> ShowS
$cshowList :: forall num. Show num => [LMAD num] -> ShowS
show :: LMAD num -> String
$cshow :: forall num. Show num => LMAD num -> String
showsPrec :: Int -> LMAD num -> ShowS
$cshowsPrec :: forall num. Show num => Int -> LMAD num -> ShowS
Show, LMAD num -> LMAD num -> Bool
(LMAD num -> LMAD num -> Bool)
-> (LMAD num -> LMAD num -> Bool) -> Eq (LMAD num)
forall num. Eq num => LMAD num -> LMAD num -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: LMAD num -> LMAD num -> Bool
$c/= :: forall num. Eq num => LMAD num -> LMAD num -> Bool
== :: LMAD num -> LMAD num -> Bool
$c== :: forall num. Eq num => LMAD num -> LMAD num -> Bool
Eq)

-- | 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.
data IxFun num = IxFun
  { forall num. IxFun num -> NonEmpty (LMAD num)
ixfunLMADs :: NonEmpty (LMAD num),
    forall num. IxFun num -> Shape num
base :: Shape num,
    -- | ignoring permutations, is the index function contiguous?
    forall num. IxFun num -> Bool
contiguous :: Bool
  }
  deriving (Int -> IxFun num -> ShowS
[IxFun num] -> ShowS
IxFun num -> String
(Int -> IxFun num -> ShowS)
-> (IxFun num -> String)
-> ([IxFun num] -> ShowS)
-> Show (IxFun num)
forall num. Show num => Int -> IxFun num -> ShowS
forall num. Show num => [IxFun num] -> ShowS
forall num. Show num => IxFun num -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [IxFun num] -> ShowS
$cshowList :: forall num. Show num => [IxFun num] -> ShowS
show :: IxFun num -> String
$cshow :: forall num. Show num => IxFun num -> String
showsPrec :: Int -> IxFun num -> ShowS
$cshowsPrec :: forall num. Show num => Int -> IxFun num -> ShowS
Show, IxFun num -> IxFun num -> Bool
(IxFun num -> IxFun num -> Bool)
-> (IxFun num -> IxFun num -> Bool) -> Eq (IxFun num)
forall num. Eq num => IxFun num -> IxFun num -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: IxFun num -> IxFun num -> Bool
$c/= :: forall num. Eq num => IxFun num -> IxFun num -> Bool
== :: IxFun num -> IxFun num -> Bool
$c== :: forall num. Eq num => IxFun num -> IxFun num -> Bool
Eq)

instance Pretty Monotonicity where
  ppr :: Monotonicity -> Doc
ppr = String -> Doc
text (String -> Doc) -> (Monotonicity -> String) -> Monotonicity -> Doc
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Monotonicity -> String
forall a. Show a => a -> String
show

instance Pretty num => Pretty (LMAD num) where
  ppr :: LMAD num -> Doc
ppr (LMAD num
offset [LMADDim num]
dims) =
    Doc -> Doc
braces (Doc -> Doc) -> Doc -> Doc
forall a b. (a -> b) -> a -> b
$
      [Doc] -> Doc
semisep
        [ Doc
"offset: " Doc -> Doc -> Doc
forall a. Semigroup a => a -> a -> a
<> Doc -> Doc
oneLine (num -> Doc
forall a. Pretty a => a -> Doc
ppr num
offset),
          Doc
"strides: " Doc -> Doc -> Doc
forall a. Semigroup a => a -> a -> a
<> (LMADDim num -> num) -> Doc
forall {b}. Pretty b => (LMADDim num -> b) -> Doc
p LMADDim num -> num
forall num. LMADDim num -> num
ldStride,
          Doc
"shape: " Doc -> Doc -> Doc
forall a. Semigroup a => a -> a -> a
<> (LMADDim num -> num) -> Doc
forall {b}. Pretty b => (LMADDim num -> b) -> Doc
p LMADDim num -> num
forall num. LMADDim num -> num
ldShape,
          Doc
"permutation: " Doc -> Doc -> Doc
forall a. Semigroup a => a -> a -> a
<> (LMADDim num -> Int) -> Doc
forall {b}. Pretty b => (LMADDim num -> b) -> Doc
p LMADDim num -> Int
forall num. LMADDim num -> Int
ldPerm,
          Doc
"monotonicity: " Doc -> Doc -> Doc
forall a. Semigroup a => a -> a -> a
<> (LMADDim num -> Monotonicity) -> Doc
forall {b}. Pretty b => (LMADDim num -> b) -> Doc
p LMADDim num -> Monotonicity
forall num. LMADDim num -> Monotonicity
ldMon
        ]
    where
      p :: (LMADDim num -> b) -> Doc
p LMADDim num -> b
f = Doc -> Doc
oneLine (Doc -> Doc) -> Doc -> Doc
forall a b. (a -> b) -> a -> b
$ Doc -> Doc
brackets (Doc -> Doc) -> Doc -> Doc
forall a b. (a -> b) -> a -> b
$ [Doc] -> Doc
commasep ([Doc] -> Doc) -> [Doc] -> Doc
forall a b. (a -> b) -> a -> b
$ (LMADDim num -> Doc) -> [LMADDim num] -> [Doc]
forall a b. (a -> b) -> [a] -> [b]
map (b -> Doc
forall a. Pretty a => a -> Doc
ppr (b -> Doc) -> (LMADDim num -> b) -> LMADDim num -> Doc
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. LMADDim num -> b
f) [LMADDim num]
dims

instance Pretty num => Pretty (IxFun num) where
  ppr :: IxFun num -> Doc
ppr (IxFun NonEmpty (LMAD num)
lmads Shape num
oshp Bool
cg) =
    Doc -> Doc
braces (Doc -> Doc) -> Doc -> Doc
forall a b. (a -> b) -> a -> b
$
      [Doc] -> Doc
semisep
        [ Doc
"base: " Doc -> Doc -> Doc
forall a. Semigroup a => a -> a -> a
<> Doc -> Doc
brackets ([Doc] -> Doc
commasep ([Doc] -> Doc) -> [Doc] -> Doc
forall a b. (a -> b) -> a -> b
$ (num -> Doc) -> Shape num -> [Doc]
forall a b. (a -> b) -> [a] -> [b]
map num -> Doc
forall a. Pretty a => a -> Doc
ppr Shape num
oshp),
          Doc
"contiguous: " Doc -> Doc -> Doc
forall a. Semigroup a => a -> a -> a
<> if Bool
cg then Doc
"true" else Doc
"false",
          Doc
"LMADs: " Doc -> Doc -> Doc
forall a. Semigroup a => a -> a -> a
<> Doc -> Doc
brackets ([Doc] -> Doc
commastack ([Doc] -> Doc) -> [Doc] -> Doc
forall a b. (a -> b) -> a -> b
$ NonEmpty Doc -> [Doc]
forall a. NonEmpty a -> [a]
NE.toList (NonEmpty Doc -> [Doc]) -> NonEmpty Doc -> [Doc]
forall a b. (a -> b) -> a -> b
$ (LMAD num -> Doc) -> NonEmpty (LMAD num) -> NonEmpty Doc
forall a b. (a -> b) -> NonEmpty a -> NonEmpty b
NE.map LMAD num -> Doc
forall a. Pretty a => a -> Doc
ppr NonEmpty (LMAD num)
lmads)
        ]

instance Substitute num => Substitute (LMAD num) where
  substituteNames :: Map VName VName -> LMAD num -> LMAD num
substituteNames Map VName VName
substs = (num -> num) -> LMAD num -> LMAD num
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((num -> num) -> LMAD num -> LMAD num)
-> (num -> num) -> LMAD num -> LMAD num
forall a b. (a -> b) -> a -> b
$ Map VName VName -> num -> num
forall a. Substitute a => Map VName VName -> a -> a
substituteNames Map VName VName
substs

instance Substitute num => Substitute (IxFun num) where
  substituteNames :: Map VName VName -> IxFun num -> IxFun num
substituteNames Map VName VName
substs = (num -> num) -> IxFun num -> IxFun num
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((num -> num) -> IxFun num -> IxFun num)
-> (num -> num) -> IxFun num -> IxFun num
forall a b. (a -> b) -> a -> b
$ Map VName VName -> num -> num
forall a. Substitute a => Map VName VName -> a -> a
substituteNames Map VName VName
substs

instance Substitute num => Rename (LMAD num) where
  rename :: LMAD num -> RenameM (LMAD num)
rename = LMAD num -> RenameM (LMAD num)
forall a. Substitute a => a -> RenameM a
substituteRename

instance Substitute num => Rename (IxFun num) where
  rename :: IxFun num -> RenameM (IxFun num)
rename = IxFun num -> RenameM (IxFun num)
forall a. Substitute a => a -> RenameM a
substituteRename

instance FreeIn num => FreeIn (LMAD num) where
  freeIn' :: LMAD num -> FV
freeIn' = (num -> FV) -> LMAD num -> FV
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap num -> FV
forall a. FreeIn a => a -> FV
freeIn'

instance FreeIn num => FreeIn (IxFun num) where
  freeIn' :: IxFun num -> FV
freeIn' = (num -> FV) -> IxFun num -> FV
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap num -> FV
forall a. FreeIn a => a -> FV
freeIn'

instance Functor LMAD where
  fmap :: forall a b. (a -> b) -> LMAD a -> LMAD b
fmap a -> b
f = Identity (LMAD b) -> LMAD b
forall a. Identity a -> a
runIdentity (Identity (LMAD b) -> LMAD b)
-> (LMAD a -> Identity (LMAD b)) -> LMAD a -> LMAD b
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (a -> Identity b) -> LMAD a -> Identity (LMAD b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse (b -> Identity b
forall (f :: * -> *) a. Applicative f => a -> f a
pure (b -> Identity b) -> (a -> b) -> a -> Identity b
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. a -> b
f)

instance Functor IxFun where
  fmap :: forall a b. (a -> b) -> IxFun a -> IxFun b
fmap a -> b
f = Identity (IxFun b) -> IxFun b
forall a. Identity a -> a
runIdentity (Identity (IxFun b) -> IxFun b)
-> (IxFun a -> Identity (IxFun b)) -> IxFun a -> IxFun b
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (a -> Identity b) -> IxFun a -> Identity (IxFun b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse (b -> Identity b
forall (f :: * -> *) a. Applicative f => a -> f a
pure (b -> Identity b) -> (a -> b) -> a -> Identity b
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. a -> b
f)

instance Foldable LMAD where
  foldMap :: forall m a. Monoid m => (a -> m) -> LMAD a -> m
foldMap a -> m
f = Writer m (LMAD ()) -> m
forall w a. Writer w a -> w
execWriter (Writer m (LMAD ()) -> m)
-> (LMAD a -> Writer m (LMAD ())) -> LMAD a -> m
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (a -> WriterT m Identity ()) -> LMAD a -> Writer m (LMAD ())
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse (m -> WriterT m Identity ()
forall w (m :: * -> *). MonadWriter w m => w -> m ()
tell (m -> WriterT m Identity ())
-> (a -> m) -> a -> WriterT m Identity ()
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. a -> m
f)

instance Foldable IxFun where
  foldMap :: forall m a. Monoid m => (a -> m) -> IxFun a -> m
foldMap a -> m
f = Writer m (IxFun ()) -> m
forall w a. Writer w a -> w
execWriter (Writer m (IxFun ()) -> m)
-> (IxFun a -> Writer m (IxFun ())) -> IxFun a -> m
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (a -> WriterT m Identity ()) -> IxFun a -> Writer m (IxFun ())
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse (m -> WriterT m Identity ()
forall w (m :: * -> *). MonadWriter w m => w -> m ()
tell (m -> WriterT m Identity ())
-> (a -> m) -> a -> WriterT m Identity ()
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. a -> m
f)

instance Traversable LMAD where
  traverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> LMAD a -> f (LMAD b)
traverse a -> f b
f (LMAD a
offset [LMADDim a]
dims) =
    b -> [LMADDim b] -> LMAD b
forall num. num -> [LMADDim num] -> LMAD num
LMAD (b -> [LMADDim b] -> LMAD b) -> f b -> f ([LMADDim b] -> LMAD b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
offset f ([LMADDim b] -> LMAD b) -> f [LMADDim b] -> f (LMAD b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (LMADDim a -> f (LMADDim b)) -> [LMADDim a] -> f [LMADDim b]
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse LMADDim a -> f (LMADDim b)
f' [LMADDim a]
dims
    where
      f' :: LMADDim a -> f (LMADDim b)
f' (LMADDim a
s a
n Int
p Monotonicity
m) = b -> b -> Int -> Monotonicity -> LMADDim b
forall num. num -> num -> Int -> Monotonicity -> LMADDim num
LMADDim (b -> b -> Int -> Monotonicity -> LMADDim b)
-> f b -> f (b -> Int -> Monotonicity -> LMADDim b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
s f (b -> Int -> Monotonicity -> LMADDim b)
-> f b -> f (Int -> Monotonicity -> LMADDim b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f b
f a
n f (Int -> Monotonicity -> LMADDim b)
-> f Int -> f (Monotonicity -> LMADDim b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Int -> f Int
forall (f :: * -> *) a. Applicative f => a -> f a
pure Int
p f (Monotonicity -> LMADDim b) -> f Monotonicity -> f (LMADDim b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Monotonicity -> f Monotonicity
forall (f :: * -> *) a. Applicative f => a -> f a
pure Monotonicity
m

-- It is important that the traversal order here is the same as in
-- mkExistential.
instance Traversable IxFun where
  traverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> IxFun a -> f (IxFun b)
traverse a -> f b
f (IxFun NonEmpty (LMAD a)
lmads Shape a
oshp Bool
cg) =
    NonEmpty (LMAD b) -> Shape b -> Bool -> IxFun b
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (NonEmpty (LMAD b) -> Shape b -> Bool -> IxFun b)
-> f (NonEmpty (LMAD b)) -> f (Shape b -> Bool -> IxFun b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (LMAD a -> f (LMAD b))
-> NonEmpty (LMAD a) -> f (NonEmpty (LMAD b))
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse ((a -> f b) -> LMAD a -> f (LMAD b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse a -> f b
f) NonEmpty (LMAD a)
lmads f (Shape b -> Bool -> IxFun b)
-> f (Shape b) -> f (Bool -> IxFun b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (a -> f b) -> Shape a -> f (Shape b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse a -> f b
f Shape a
oshp f (Bool -> IxFun b) -> f Bool -> f (IxFun b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Bool -> f Bool
forall (f :: * -> *) a. Applicative f => a -> f a
pure Bool
cg

(++@) :: [a] -> NonEmpty a -> NonEmpty a
[a]
es ++@ :: forall a. [a] -> NonEmpty a -> NonEmpty a
++@ (a
ne :| [a]
nes) = case [a]
es of
  a
e : [a]
es' -> a
e a -> [a] -> NonEmpty a
forall a. a -> [a] -> NonEmpty a
:| [a]
es' [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
++ [a
ne] [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
++ [a]
nes
  [] -> a
ne a -> [a] -> NonEmpty a
forall a. a -> [a] -> NonEmpty a
:| [a]
nes

(@++@) :: NonEmpty a -> NonEmpty a -> NonEmpty a
(a
x :| [a]
xs) @++@ :: forall a. NonEmpty a -> NonEmpty a -> NonEmpty a
@++@ (a
y :| [a]
ys) = a
x a -> [a] -> NonEmpty a
forall a. a -> [a] -> NonEmpty a
:| [a]
xs [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
++ [a
y] [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
++ [a]
ys

invertMonotonicity :: Monotonicity -> Monotonicity
invertMonotonicity :: Monotonicity -> Monotonicity
invertMonotonicity Monotonicity
Inc = Monotonicity
Dec
invertMonotonicity Monotonicity
Dec = Monotonicity
Inc
invertMonotonicity Monotonicity
Unknown = Monotonicity
Unknown

lmadPermutation :: LMAD num -> Permutation
lmadPermutation :: forall num. LMAD num -> Permutation
lmadPermutation = (LMADDim num -> Int) -> [LMADDim num] -> Permutation
forall a b. (a -> b) -> [a] -> [b]
map LMADDim num -> Int
forall num. LMADDim num -> Int
ldPerm ([LMADDim num] -> Permutation)
-> (LMAD num -> [LMADDim num]) -> LMAD num -> Permutation
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. LMAD num -> [LMADDim num]
forall num. LMAD num -> [LMADDim num]
lmadDims

setLMADPermutation :: Permutation -> LMAD num -> LMAD num
setLMADPermutation :: forall num. Permutation -> LMAD num -> LMAD num
setLMADPermutation Permutation
perm LMAD num
lmad =
  LMAD num
lmad {lmadDims :: [LMADDim num]
lmadDims = (LMADDim num -> Int -> LMADDim num)
-> [LMADDim num] -> Permutation -> [LMADDim num]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith (\LMADDim num
dim Int
p -> LMADDim num
dim {ldPerm :: Int
ldPerm = Int
p}) (LMAD num -> [LMADDim num]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD num
lmad) Permutation
perm}

setLMADShape :: Shape num -> LMAD num -> LMAD num
setLMADShape :: forall num. Shape num -> LMAD num -> LMAD num
setLMADShape Shape num
shp LMAD num
lmad = LMAD num
lmad {lmadDims :: [LMADDim num]
lmadDims = (LMADDim num -> num -> LMADDim num)
-> [LMADDim num] -> Shape num -> [LMADDim num]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith (\LMADDim num
dim num
s -> LMADDim num
dim {ldShape :: num
ldShape = num
s}) (LMAD num -> [LMADDim num]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD num
lmad) Shape num
shp}

-- | Substitute a name with a PrimExp in an LMAD.
substituteInLMAD ::
  Ord a =>
  M.Map a (PrimExp a) ->
  LMAD (PrimExp a) ->
  LMAD (PrimExp a)
substituteInLMAD :: forall a.
Ord a =>
Map a (PrimExp a) -> LMAD (PrimExp a) -> LMAD (PrimExp a)
substituteInLMAD Map a (PrimExp a)
tab (LMAD PrimExp a
offset [LMADDim (PrimExp a)]
dims) =
  let offset' :: PrimExp a
offset' = Map a (PrimExp a) -> PrimExp a -> PrimExp a
forall v. Ord v => Map v (PrimExp v) -> PrimExp v -> PrimExp v
substituteInPrimExp Map a (PrimExp a)
tab PrimExp a
offset
      dims' :: [LMADDim (PrimExp a)]
dims' =
        (LMADDim (PrimExp a) -> LMADDim (PrimExp a))
-> [LMADDim (PrimExp a)] -> [LMADDim (PrimExp a)]
forall a b. (a -> b) -> [a] -> [b]
map
          ( \(LMADDim PrimExp a
s PrimExp a
n Int
p Monotonicity
m) ->
              PrimExp a
-> PrimExp a -> Int -> Monotonicity -> LMADDim (PrimExp a)
forall num. num -> num -> Int -> Monotonicity -> LMADDim num
LMADDim
                (Map a (PrimExp a) -> PrimExp a -> PrimExp a
forall v. Ord v => Map v (PrimExp v) -> PrimExp v -> PrimExp v
substituteInPrimExp Map a (PrimExp a)
tab PrimExp a
s)
                (Map a (PrimExp a) -> PrimExp a -> PrimExp a
forall v. Ord v => Map v (PrimExp v) -> PrimExp v -> PrimExp v
substituteInPrimExp Map a (PrimExp a)
tab PrimExp a
n)
                Int
p
                Monotonicity
m
          )
          [LMADDim (PrimExp a)]
dims
   in PrimExp a -> [LMADDim (PrimExp a)] -> LMAD (PrimExp a)
forall num. num -> [LMADDim num] -> LMAD num
LMAD PrimExp a
offset' [LMADDim (PrimExp a)]
dims'

-- | Substitute a name with a PrimExp in an index function.
substituteInIxFun ::
  Ord a =>
  M.Map a (TPrimExp t a) ->
  IxFun (TPrimExp t a) ->
  IxFun (TPrimExp t a)
substituteInIxFun :: forall a t.
Ord a =>
Map a (TPrimExp t a)
-> IxFun (TPrimExp t a) -> IxFun (TPrimExp t a)
substituteInIxFun Map a (TPrimExp t a)
tab (IxFun NonEmpty (LMAD (TPrimExp t a))
lmads Shape (TPrimExp t a)
oshp Bool
cg) =
  NonEmpty (LMAD (TPrimExp t a))
-> Shape (TPrimExp t a) -> Bool -> IxFun (TPrimExp t a)
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun
    ((LMAD (TPrimExp t a) -> LMAD (TPrimExp t a))
-> NonEmpty (LMAD (TPrimExp t a)) -> NonEmpty (LMAD (TPrimExp t a))
forall a b. (a -> b) -> NonEmpty a -> NonEmpty b
NE.map ((PrimExp a -> TPrimExp t a)
-> LMAD (PrimExp a) -> LMAD (TPrimExp t a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap PrimExp a -> TPrimExp t a
forall t v. PrimExp v -> TPrimExp t v
TPrimExp (LMAD (PrimExp a) -> LMAD (TPrimExp t a))
-> (LMAD (TPrimExp t a) -> LMAD (PrimExp a))
-> LMAD (TPrimExp t a)
-> LMAD (TPrimExp t a)
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Map a (PrimExp a) -> LMAD (PrimExp a) -> LMAD (PrimExp a)
forall a.
Ord a =>
Map a (PrimExp a) -> LMAD (PrimExp a) -> LMAD (PrimExp a)
substituteInLMAD Map a (PrimExp a)
tab' (LMAD (PrimExp a) -> LMAD (PrimExp a))
-> (LMAD (TPrimExp t a) -> LMAD (PrimExp a))
-> LMAD (TPrimExp t a)
-> LMAD (PrimExp a)
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (TPrimExp t a -> PrimExp a)
-> LMAD (TPrimExp t a) -> LMAD (PrimExp a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap TPrimExp t a -> PrimExp a
forall t v. TPrimExp t v -> PrimExp v
untyped) NonEmpty (LMAD (TPrimExp t a))
lmads)
    ((TPrimExp t a -> TPrimExp t a)
-> Shape (TPrimExp t a) -> Shape (TPrimExp t a)
forall a b. (a -> b) -> [a] -> [b]
map (PrimExp a -> TPrimExp t a
forall t v. PrimExp v -> TPrimExp t v
TPrimExp (PrimExp a -> TPrimExp t a)
-> (TPrimExp t a -> PrimExp a) -> TPrimExp t a -> TPrimExp t a
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Map a (PrimExp a) -> PrimExp a -> PrimExp a
forall v. Ord v => Map v (PrimExp v) -> PrimExp v -> PrimExp v
substituteInPrimExp Map a (PrimExp a)
tab' (PrimExp a -> PrimExp a)
-> (TPrimExp t a -> PrimExp a) -> TPrimExp t a -> PrimExp a
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. TPrimExp t a -> PrimExp a
forall t v. TPrimExp t v -> PrimExp v
untyped) Shape (TPrimExp t a)
oshp)
    Bool
cg
  where
    tab' :: Map a (PrimExp a)
tab' = (TPrimExp t a -> PrimExp a)
-> Map a (TPrimExp t a) -> Map a (PrimExp a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap TPrimExp t a -> PrimExp a
forall t v. TPrimExp t v -> PrimExp v
untyped Map a (TPrimExp t a)
tab

-- | Is this is a row-major array?
isDirect :: (Eq num, IntegralExp num) => IxFun num -> Bool
isDirect :: forall num. (Eq num, IntegralExp num) => IxFun num -> Bool
isDirect ixfun :: IxFun num
ixfun@(IxFun (LMAD num
offset [LMADDim num]
dims :| []) Shape num
oshp Bool
True) =
  let strides_expected :: Shape num
strides_expected = Shape num -> Shape num
forall a. [a] -> [a]
reverse (Shape num -> Shape num) -> Shape num -> Shape num
forall a b. (a -> b) -> a -> b
$ (num -> num -> num) -> num -> Shape num -> Shape num
forall b a. (b -> a -> b) -> b -> [a] -> [b]
scanl num -> num -> num
forall a. Num a => a -> a -> a
(*) num
1 (Shape num -> Shape num
forall a. [a] -> [a]
reverse (Shape num -> Shape num
forall a. [a] -> [a]
tail Shape num
oshp))
   in IxFun num -> Bool
forall num. IxFun num -> Bool
hasContiguousPerm IxFun num
ixfun
        Bool -> Bool -> Bool
&& Shape num -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length Shape num
oshp Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== [LMADDim num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [LMADDim num]
dims
        Bool -> Bool -> Bool
&& num
offset num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== num
0
        Bool -> Bool -> Bool
&& ((LMADDim num, Int, num, num) -> Bool)
-> [(LMADDim num, Int, num, num)] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all
          (\(LMADDim num
s num
n Int
p Monotonicity
_, Int
m, num
d, num
se) -> num
s num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== num
se Bool -> Bool -> Bool
&& num
n num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== num
d Bool -> Bool -> Bool
&& Int
p Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
m)
          ([LMADDim num]
-> Permutation
-> Shape num
-> Shape num
-> [(LMADDim num, Int, num, num)]
forall a b c d. [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)]
zip4 [LMADDim num]
dims [Int
0 .. [LMADDim num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [LMADDim num]
dims Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1] Shape num
oshp Shape num
strides_expected)
isDirect IxFun num
_ = Bool
False

-- | Does the index function have an ascending permutation?
hasContiguousPerm :: IxFun num -> Bool
hasContiguousPerm :: forall num. IxFun num -> Bool
hasContiguousPerm (IxFun (LMAD num
lmad :| []) Shape num
_ Bool
_) =
  let perm :: Permutation
perm = LMAD num -> Permutation
forall num. LMAD num -> Permutation
lmadPermutation LMAD num
lmad
   in Permutation
perm Permutation -> Permutation -> Bool
forall a. Eq a => a -> a -> Bool
== Permutation -> Permutation
forall a. Ord a => [a] -> [a]
sort Permutation
perm
hasContiguousPerm IxFun num
_ = Bool
False

-- | The index space of the index function.  This is the same as the
-- shape of arrays that the index function supports.
shape :: (Eq num, IntegralExp num) => IxFun num -> Shape num
shape :: forall num. (Eq num, IntegralExp num) => IxFun num -> Shape num
shape (IxFun (LMAD num
lmad :| [LMAD num]
_) Shape num
_ Bool
_) =
  Permutation -> Shape num -> Shape num
forall a. Permutation -> [a] -> [a]
permuteFwd (LMAD num -> Permutation
forall num. LMAD num -> Permutation
lmadPermutation LMAD num
lmad) (Shape num -> Shape num) -> Shape num -> Shape num
forall a b. (a -> b) -> a -> b
$ LMAD num -> Shape num
forall num. (Eq num, IntegralExp num) => LMAD num -> Shape num
lmadShapeBase LMAD num
lmad

-- | Shape of an LMAD.
lmadShape :: (Eq num, IntegralExp num) => LMAD num -> Shape num
lmadShape :: forall num. (Eq num, IntegralExp num) => LMAD num -> Shape num
lmadShape LMAD num
lmad = Permutation -> [num] -> [num]
forall a. Permutation -> [a] -> [a]
permuteInv (LMAD num -> Permutation
forall num. LMAD num -> Permutation
lmadPermutation LMAD num
lmad) ([num] -> [num]) -> [num] -> [num]
forall a b. (a -> b) -> a -> b
$ LMAD num -> [num]
forall num. (Eq num, IntegralExp num) => LMAD num -> Shape num
lmadShapeBase LMAD num
lmad

-- | Shape of an LMAD, ignoring permutations.
lmadShapeBase :: (Eq num, IntegralExp num) => LMAD num -> Shape num
lmadShapeBase :: forall num. (Eq num, IntegralExp num) => LMAD num -> Shape num
lmadShapeBase = (LMADDim num -> num) -> [LMADDim num] -> [num]
forall a b. (a -> b) -> [a] -> [b]
map LMADDim num -> num
forall num. LMADDim num -> num
ldShape ([LMADDim num] -> [num])
-> (LMAD num -> [LMADDim num]) -> LMAD num -> [num]
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. LMAD num -> [LMADDim num]
forall num. LMAD num -> [LMADDim num]
lmadDims

-- | Compute the flat memory index for a complete set @inds@ of array indices
-- and a certain element size @elem_size@.
index ::
  (IntegralExp num, Eq num) =>
  IxFun num ->
  Indices num ->
  num
index :: forall num.
(IntegralExp num, Eq num) =>
IxFun num -> Indices num -> num
index = NonEmpty (LMAD num) -> Indices num -> num
forall num.
(IntegralExp num, Eq num) =>
NonEmpty (LMAD num) -> Indices num -> num
indexFromLMADs (NonEmpty (LMAD num) -> Indices num -> num)
-> (IxFun num -> NonEmpty (LMAD num))
-> IxFun num
-> Indices num
-> num
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. IxFun num -> NonEmpty (LMAD num)
forall num. IxFun num -> NonEmpty (LMAD num)
ixfunLMADs
  where
    indexFromLMADs ::
      (IntegralExp num, Eq num) =>
      NonEmpty (LMAD num) ->
      Indices num ->
      num
    indexFromLMADs :: forall num.
(IntegralExp num, Eq num) =>
NonEmpty (LMAD num) -> Indices num -> num
indexFromLMADs (LMAD num
lmad :| []) Indices num
inds = LMAD num -> Indices num -> num
forall num.
(IntegralExp num, Eq num) =>
LMAD num -> Indices num -> num
indexLMAD LMAD num
lmad Indices num
inds
    indexFromLMADs (LMAD num
lmad1 :| LMAD num
lmad2 : [LMAD num]
lmads) Indices num
inds =
      let i_flat :: num
i_flat = LMAD num -> Indices num -> num
forall num.
(IntegralExp num, Eq num) =>
LMAD num -> Indices num -> num
indexLMAD LMAD num
lmad1 Indices num
inds
          new_inds :: Indices num
new_inds = Indices num -> num -> Indices num
forall num. IntegralExp num => [num] -> num -> [num]
unflattenIndex (Permutation -> Indices num -> Indices num
forall a. Permutation -> [a] -> [a]
permuteFwd (LMAD num -> Permutation
forall num. LMAD num -> Permutation
lmadPermutation LMAD num
lmad2) (Indices num -> Indices num) -> Indices num -> Indices num
forall a b. (a -> b) -> a -> b
$ LMAD num -> Indices num
forall num. (Eq num, IntegralExp num) => LMAD num -> Shape num
lmadShapeBase LMAD num
lmad2) num
i_flat
       in NonEmpty (LMAD num) -> Indices num -> num
forall num.
(IntegralExp num, Eq num) =>
NonEmpty (LMAD num) -> Indices num -> num
indexFromLMADs (LMAD num
lmad2 LMAD num -> [LMAD num] -> NonEmpty (LMAD num)
forall a. a -> [a] -> NonEmpty a
:| [LMAD num]
lmads) Indices num
new_inds
    indexLMAD ::
      (IntegralExp num, Eq num) =>
      LMAD num ->
      Indices num ->
      num
    indexLMAD :: forall num.
(IntegralExp num, Eq num) =>
LMAD num -> Indices num -> num
indexLMAD lmad :: LMAD num
lmad@(LMAD num
off [LMADDim num]
dims) Indices num
inds =
      let prod :: num
prod =
            Indices num -> num
forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
sum (Indices num -> num) -> Indices num -> num
forall a b. (a -> b) -> a -> b
$
              (num -> num -> num) -> Indices num -> Indices num -> Indices num
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith
                num -> num -> num
forall num. (Eq num, IntegralExp num) => num -> num -> num
flatOneDim
                ((LMADDim num -> num) -> [LMADDim num] -> Indices num
forall a b. (a -> b) -> [a] -> [b]
map LMADDim num -> num
forall num. LMADDim num -> num
ldStride [LMADDim num]
dims)
                (Permutation -> Indices num -> Indices num
forall a. Permutation -> [a] -> [a]
permuteInv (LMAD num -> Permutation
forall num. LMAD num -> Permutation
lmadPermutation LMAD num
lmad) Indices num
inds)
       in num
off num -> num -> num
forall a. Num a => a -> a -> a
+ num
prod

-- | iota with offset.
iotaOffset :: IntegralExp num => num -> Shape num -> IxFun num
iotaOffset :: forall num. IntegralExp num => num -> Shape num -> IxFun num
iotaOffset num
o Shape num
ns = NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (Monotonicity -> num -> Shape num -> LMAD num
forall num.
IntegralExp num =>
Monotonicity -> num -> [num] -> LMAD num
makeRotIota Monotonicity
Inc num
o Shape num
ns LMAD num -> [LMAD num] -> NonEmpty (LMAD num)
forall a. a -> [a] -> NonEmpty a
:| []) Shape num
ns Bool
True

-- | iota.
iota :: IntegralExp num => Shape num -> IxFun num
iota :: forall num. IntegralExp num => Shape num -> IxFun num
iota = num -> Shape num -> IxFun num
forall num. IntegralExp num => num -> Shape num -> IxFun num
iotaOffset num
0

-- | Create a contiguous single-LMAD index function that is
-- existential in everything, with the provided permutation,
-- monotonicity, and contiguousness.
mkExistential :: Int -> [(Int, Monotonicity)] -> Bool -> Int -> IxFun (Ext a)
mkExistential :: forall a.
Int -> [(Int, Monotonicity)] -> Bool -> Int -> IxFun (Ext a)
mkExistential Int
basis_rank [(Int, Monotonicity)]
perm Bool
contig Int
start =
  NonEmpty (LMAD (Ext a)) -> Shape (Ext a) -> Bool -> IxFun (Ext a)
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (LMAD (Ext a) -> NonEmpty (LMAD (Ext a))
forall a. a -> NonEmpty a
NE.singleton LMAD (Ext a)
forall {a}. LMAD (Ext a)
lmad) Shape (Ext a)
forall {a}. [Ext a]
basis Bool
contig
  where
    basis :: [Ext a]
basis = Int -> [Ext a] -> [Ext a]
forall a. Int -> [a] -> [a]
take Int
basis_rank ([Ext a] -> [Ext a]) -> [Ext a] -> [Ext a]
forall a b. (a -> b) -> a -> b
$ (Int -> Ext a) -> Permutation -> [Ext a]
forall a b. (a -> b) -> [a] -> [b]
map Int -> Ext a
forall a. Int -> Ext a
Ext [Int
start Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
1 Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
dims_rank Int -> Int -> Int
forall a. Num a => a -> a -> a
* Int
2 ..]
    dims_rank :: Int
dims_rank = [(Int, Monotonicity)] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [(Int, Monotonicity)]
perm
    lmad :: LMAD (Ext a)
lmad = Ext a -> [LMADDim (Ext a)] -> LMAD (Ext a)
forall num. num -> [LMADDim num] -> LMAD num
LMAD (Int -> Ext a
forall a. Int -> Ext a
Ext Int
start) ([LMADDim (Ext a)] -> LMAD (Ext a))
-> [LMADDim (Ext a)] -> LMAD (Ext a)
forall a b. (a -> b) -> a -> b
$ ((Int, Monotonicity) -> Int -> LMADDim (Ext a))
-> [(Int, Monotonicity)] -> Permutation -> [LMADDim (Ext a)]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith (Int, Monotonicity) -> Int -> LMADDim (Ext a)
forall {a}. (Int, Monotonicity) -> Int -> LMADDim (Ext a)
onDim [(Int, Monotonicity)]
perm [Int
0 ..]
    onDim :: (Int, Monotonicity) -> Int -> LMADDim (Ext a)
onDim (Int
p, Monotonicity
mon) Int
i =
      Ext a -> Ext a -> Int -> Monotonicity -> LMADDim (Ext a)
forall num. num -> num -> Int -> Monotonicity -> LMADDim num
LMADDim (Int -> Ext a
forall a. Int -> Ext a
Ext (Int
start Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
1 Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
* Int
2)) (Int -> Ext a
forall a. Int -> Ext a
Ext (Int
start Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
2 Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
* Int
2)) Int
p Monotonicity
mon

-- | Permute dimensions.
permute ::
  IntegralExp num =>
  IxFun num ->
  Permutation ->
  IxFun num
permute :: forall num.
IntegralExp num =>
IxFun num -> Permutation -> IxFun num
permute (IxFun (LMAD num
lmad :| [LMAD num]
lmads) Shape num
oshp Bool
cg) Permutation
perm_new =
  let perm_cur :: Permutation
perm_cur = LMAD num -> Permutation
forall num. LMAD num -> Permutation
lmadPermutation LMAD num
lmad
      perm :: Permutation
perm = (Int -> Int) -> Permutation -> Permutation
forall a b. (a -> b) -> [a] -> [b]
map (Permutation
perm_cur Permutation -> Int -> Int
forall a. [a] -> Int -> a
!!) Permutation
perm_new
   in NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (Permutation -> LMAD num -> LMAD num
forall num. Permutation -> LMAD num -> LMAD num
setLMADPermutation Permutation
perm LMAD num
lmad LMAD num -> [LMAD num] -> NonEmpty (LMAD num)
forall a. a -> [a] -> NonEmpty a
:| [LMAD num]
lmads) Shape num
oshp Bool
cg

-- | Handle the case where a slice can stay within a single LMAD.
sliceOneLMAD ::
  (Eq num, IntegralExp num) =>
  IxFun num ->
  Slice num ->
  Maybe (IxFun num)
sliceOneLMAD :: forall num.
(Eq num, IntegralExp num) =>
IxFun num -> Slice num -> Maybe (IxFun num)
sliceOneLMAD (IxFun (lmad :: LMAD num
lmad@(LMAD num
_ [LMADDim num]
ldims) :| [LMAD num]
lmads) Shape num
oshp Bool
cg) (Slice [DimIndex num]
is) = do
  let perm :: Permutation
perm = LMAD num -> Permutation
forall num. LMAD num -> Permutation
lmadPermutation LMAD num
lmad
      is' :: [DimIndex num]
is' = Permutation -> [DimIndex num] -> [DimIndex num]
forall a. Permutation -> [a] -> [a]
permuteInv Permutation
perm [DimIndex num]
is
      cg' :: Bool
cg' = Bool
cg Bool -> Bool -> Bool
&& LMAD num -> Slice num -> Bool
forall num.
(Eq num, IntegralExp num) =>
LMAD num -> Slice num -> Bool
slicePreservesContiguous LMAD num
lmad ([DimIndex num] -> Slice num
forall d. [DimIndex d] -> Slice d
Slice [DimIndex num]
is')
  let lmad' :: LMAD num
lmad' = (LMAD num -> (DimIndex num, LMADDim num) -> LMAD num)
-> LMAD num -> [(DimIndex num, LMADDim num)] -> LMAD num
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl LMAD num -> (DimIndex num, LMADDim num) -> LMAD num
forall num.
(Eq num, IntegralExp num) =>
LMAD num -> (DimIndex num, LMADDim num) -> LMAD num
sliceOne (num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD (LMAD num -> num
forall num. LMAD num -> num
lmadOffset LMAD num
lmad) []) ([(DimIndex num, LMADDim num)] -> LMAD num)
-> [(DimIndex num, LMADDim num)] -> LMAD num
forall a b. (a -> b) -> a -> b
$ [DimIndex num] -> [LMADDim num] -> [(DimIndex num, LMADDim num)]
forall a b. [a] -> [b] -> [(a, b)]
zip [DimIndex num]
is' [LMADDim num]
ldims
      -- need to remove the fixed dims from the permutation
      perm' :: Permutation
perm' =
        Permutation -> Permutation -> Permutation
forall {t :: * -> *} {b} {t :: * -> *}.
(Foldable t, Ord b, Foldable t, Num b) =>
t b -> t b -> [b]
updatePerm Permutation
perm (Permutation -> Permutation) -> Permutation -> Permutation
forall a b. (a -> b) -> a -> b
$
          ((Int, DimIndex num) -> Int)
-> [(Int, DimIndex num)] -> Permutation
forall a b. (a -> b) -> [a] -> [b]
map (Int, DimIndex num) -> Int
forall a b. (a, b) -> a
fst ([(Int, DimIndex num)] -> Permutation)
-> [(Int, DimIndex num)] -> Permutation
forall a b. (a -> b) -> a -> b
$
            ((Int, DimIndex num) -> Bool)
-> [(Int, DimIndex num)] -> [(Int, DimIndex num)]
forall a. (a -> Bool) -> [a] -> [a]
filter (Maybe num -> Bool
forall a. Maybe a -> Bool
isJust (Maybe num -> Bool)
-> ((Int, DimIndex num) -> Maybe num)
-> (Int, DimIndex num)
-> Bool
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. DimIndex num -> Maybe num
forall d. DimIndex d -> Maybe d
dimFix (DimIndex num -> Maybe num)
-> ((Int, DimIndex num) -> DimIndex num)
-> (Int, DimIndex num)
-> Maybe num
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (Int, DimIndex num) -> DimIndex num
forall a b. (a, b) -> b
snd) ([(Int, DimIndex num)] -> [(Int, DimIndex num)])
-> [(Int, DimIndex num)] -> [(Int, DimIndex num)]
forall a b. (a -> b) -> a -> b
$
              Permutation -> [DimIndex num] -> [(Int, DimIndex num)]
forall a b. [a] -> [b] -> [(a, b)]
zip [Int
0 .. [DimIndex num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [DimIndex num]
is' Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1] [DimIndex num]
is'

  IxFun num -> Maybe (IxFun num)
forall (f :: * -> *) a. Applicative f => a -> f a
pure (IxFun num -> Maybe (IxFun num)) -> IxFun num -> Maybe (IxFun num)
forall a b. (a -> b) -> a -> b
$ NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (Permutation -> LMAD num -> LMAD num
forall num. Permutation -> LMAD num -> LMAD num
setLMADPermutation Permutation
perm' LMAD num
lmad' LMAD num -> [LMAD num] -> NonEmpty (LMAD num)
forall a. a -> [a] -> NonEmpty a
:| [LMAD num]
lmads) Shape num
oshp Bool
cg'
  where
    updatePerm :: t b -> t b -> [b]
updatePerm t b
ps t b
inds = (b -> [b]) -> t b -> [b]
forall (t :: * -> *) a b. Foldable t => (a -> [b]) -> t a -> [b]
concatMap b -> [b]
decrease t b
ps
      where
        decrease :: b -> [b]
decrease b
p =
          let f :: a -> b -> a
f a
n b
i
                | b
i b -> b -> Bool
forall a. Eq a => a -> a -> Bool
== b
p = -a
1
                | b
i b -> b -> Bool
forall a. Ord a => a -> a -> Bool
> b
p = a
n
                | a
n a -> a -> Bool
forall a. Eq a => a -> a -> Bool
/= -a
1 = a
n a -> a -> a
forall a. Num a => a -> a -> a
+ a
1
                | Bool
otherwise = a
n
              d :: b
d = (b -> b -> b) -> b -> t b -> b
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl b -> b -> b
forall {a}. (Num a, Eq a) => a -> b -> a
f b
0 t b
inds
           in [b
p b -> b -> b
forall a. Num a => a -> a -> a
- b
d | b
d b -> b -> Bool
forall a. Eq a => a -> a -> Bool
/= -b
1]

    -- XXX: TODO: what happens to r on a negative-stride slice; is there
    -- such a case?
    sliceOne ::
      (Eq num, IntegralExp num) =>
      LMAD num ->
      (DimIndex num, LMADDim num) ->
      LMAD num
    sliceOne :: forall num.
(Eq num, IntegralExp num) =>
LMAD num -> (DimIndex num, LMADDim num) -> LMAD num
sliceOne (LMAD num
off [LMADDim num]
dims) (DimFix num
i, LMADDim num
s num
_x Int
_ Monotonicity
_) =
      num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD (num
off num -> num -> num
forall a. Num a => a -> a -> a
+ num -> num -> num
forall num. (Eq num, IntegralExp num) => num -> num -> num
flatOneDim num
s num
i) [LMADDim num]
dims
    sliceOne (LMAD num
off [LMADDim num]
dims) (DimSlice num
_ num
ne num
_, LMADDim num
0 num
_ Int
p Monotonicity
_) =
      num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD num
off ([LMADDim num]
dims [LMADDim num] -> [LMADDim num] -> [LMADDim num]
forall a. [a] -> [a] -> [a]
++ [num -> num -> Int -> Monotonicity -> LMADDim num
forall num. num -> num -> Int -> Monotonicity -> LMADDim num
LMADDim num
0 num
ne Int
p Monotonicity
Unknown])
    sliceOne (LMAD num
off [LMADDim num]
dims) (DimIndex num
dmind, dim :: LMADDim num
dim@(LMADDim num
_ num
n Int
_ Monotonicity
_))
      | DimIndex num
dmind DimIndex num -> DimIndex num -> Bool
forall a. Eq a => a -> a -> Bool
== num -> num -> DimIndex num
forall d. Num d => d -> d -> DimIndex d
unitSlice num
0 num
n = num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD num
off ([LMADDim num]
dims [LMADDim num] -> [LMADDim num] -> [LMADDim num]
forall a. [a] -> [a] -> [a]
++ [LMADDim num
dim])
    sliceOne (LMAD num
off [LMADDim num]
dims) (DimIndex num
dmind, LMADDim num
s num
n Int
p Monotonicity
m)
      | DimIndex num
dmind DimIndex num -> DimIndex num -> Bool
forall a. Eq a => a -> a -> Bool
== num -> num -> num -> DimIndex num
forall d. d -> d -> d -> DimIndex d
DimSlice (num
n num -> num -> num
forall a. Num a => a -> a -> a
- num
1) num
n (-num
1) =
          let off' :: num
off' = num
off num -> num -> num
forall a. Num a => a -> a -> a
+ num -> num -> num
forall num. (Eq num, IntegralExp num) => num -> num -> num
flatOneDim num
s (num
n num -> num -> num
forall a. Num a => a -> a -> a
- num
1)
           in num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD num
off' ([LMADDim num]
dims [LMADDim num] -> [LMADDim num] -> [LMADDim num]
forall a. [a] -> [a] -> [a]
++ [num -> num -> Int -> Monotonicity -> LMADDim num
forall num. num -> num -> Int -> Monotonicity -> LMADDim num
LMADDim (num
s num -> num -> num
forall a. Num a => a -> a -> a
* (-num
1)) num
n Int
p (Monotonicity -> Monotonicity
invertMonotonicity Monotonicity
m)])
    sliceOne (LMAD num
off [LMADDim num]
dims) (DimSlice num
b num
ne num
0, LMADDim num
s num
_ Int
p Monotonicity
_) =
      num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD (num
off num -> num -> num
forall a. Num a => a -> a -> a
+ num -> num -> num
forall num. (Eq num, IntegralExp num) => num -> num -> num
flatOneDim num
s num
b) ([LMADDim num]
dims [LMADDim num] -> [LMADDim num] -> [LMADDim num]
forall a. [a] -> [a] -> [a]
++ [num -> num -> Int -> Monotonicity -> LMADDim num
forall num. num -> num -> Int -> Monotonicity -> LMADDim num
LMADDim num
0 num
ne Int
p Monotonicity
Unknown])
    sliceOne (LMAD num
off [LMADDim num]
dims) (DimSlice num
bs num
ns num
ss, LMADDim num
s num
_ Int
p Monotonicity
m) =
      let m' :: Monotonicity
m' = case num -> Maybe Int
forall e. IntegralExp e => e -> Maybe Int
sgn num
ss of
            Just Int
1 -> Monotonicity
m
            Just (-1) -> Monotonicity -> Monotonicity
invertMonotonicity Monotonicity
m
            Maybe Int
_ -> Monotonicity
Unknown
       in num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD (num
off num -> num -> num
forall a. Num a => a -> a -> a
+ num
s num -> num -> num
forall a. Num a => a -> a -> a
* num
bs) ([LMADDim num]
dims [LMADDim num] -> [LMADDim num] -> [LMADDim num]
forall a. [a] -> [a] -> [a]
++ [num -> num -> Int -> Monotonicity -> LMADDim num
forall num. num -> num -> Int -> Monotonicity -> LMADDim num
LMADDim (num
ss num -> num -> num
forall a. Num a => a -> a -> a
* num
s) num
ns Int
p Monotonicity
m'])

    slicePreservesContiguous ::
      (Eq num, IntegralExp num) =>
      LMAD num ->
      Slice num ->
      Bool
    slicePreservesContiguous :: forall num.
(Eq num, IntegralExp num) =>
LMAD num -> Slice num -> Bool
slicePreservesContiguous (LMAD num
_ [LMADDim num]
dims) (Slice [DimIndex num]
slc) =
      -- remove from the slice the LMAD dimensions that have stride 0.
      -- If the LMAD was contiguous in mem, then these dims will not
      -- influence the contiguousness of the result.
      -- Also normalize the input slice, i.e., 0-stride and size-1
      -- slices are rewritten as DimFixed.
      let ([LMADDim num]
dims', [DimIndex num]
slc') =
            [(LMADDim num, DimIndex num)] -> ([LMADDim num], [DimIndex num])
forall a b. [(a, b)] -> ([a], [b])
unzip ([(LMADDim num, DimIndex num)] -> ([LMADDim num], [DimIndex num]))
-> [(LMADDim num, DimIndex num)] -> ([LMADDim num], [DimIndex num])
forall a b. (a -> b) -> a -> b
$
              ((LMADDim num, DimIndex num) -> Bool)
-> [(LMADDim num, DimIndex num)] -> [(LMADDim num, DimIndex num)]
forall a. (a -> Bool) -> [a] -> [a]
filter ((num -> num -> Bool
forall a. Eq a => a -> a -> Bool
/= num
0) (num -> Bool)
-> ((LMADDim num, DimIndex num) -> num)
-> (LMADDim num, DimIndex num)
-> Bool
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. LMADDim num -> num
forall num. LMADDim num -> num
ldStride (LMADDim num -> num)
-> ((LMADDim num, DimIndex num) -> LMADDim num)
-> (LMADDim num, DimIndex num)
-> num
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (LMADDim num, DimIndex num) -> LMADDim num
forall a b. (a, b) -> a
fst) ([(LMADDim num, DimIndex num)] -> [(LMADDim num, DimIndex num)])
-> [(LMADDim num, DimIndex num)] -> [(LMADDim num, DimIndex num)]
forall a b. (a -> b) -> a -> b
$
                [LMADDim num] -> [DimIndex num] -> [(LMADDim num, DimIndex num)]
forall a b. [a] -> [b] -> [(a, b)]
zip [LMADDim num]
dims ([DimIndex num] -> [(LMADDim num, DimIndex num)])
-> [DimIndex num] -> [(LMADDim num, DimIndex num)]
forall a b. (a -> b) -> a -> b
$
                  (DimIndex num -> DimIndex num) -> [DimIndex num] -> [DimIndex num]
forall a b. (a -> b) -> [a] -> [b]
map DimIndex num -> DimIndex num
forall num.
(Eq num, IntegralExp num) =>
DimIndex num -> DimIndex num
normIndex [DimIndex num]
slc
          -- Check that:
          -- 1. a clean split point exists between Fixed and Sliced dims
          -- 2. the outermost sliced dim has +/- 1 stride.
          -- 3. the rest of inner sliced dims are full.
          (Bool
_, Bool
success) =
            ((Bool, Bool) -> (DimIndex num, LMADDim num) -> (Bool, Bool))
-> (Bool, Bool) -> [(DimIndex num, LMADDim num)] -> (Bool, Bool)
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl
              ( \(Bool
found, Bool
res) (DimIndex num
slcdim, LMADDim num
_ num
n Int
_ Monotonicity
_) ->
                  case (DimIndex num
slcdim, Bool
found) of
                    (DimFix {}, Bool
True) -> (Bool
found, Bool
False)
                    (DimFix {}, Bool
False) -> (Bool
found, Bool
res)
                    (DimSlice num
_ num
_ num
ds, Bool
False) ->
                      -- outermost sliced dim: +/-1 stride
                      let res' :: Bool
res' = (num
ds num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== num
1 Bool -> Bool -> Bool
|| num
ds num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== -num
1)
                       in (Bool
True, Bool
res Bool -> Bool -> Bool
&& Bool
res')
                    (DimSlice num
_ num
ne num
ds, Bool
True) ->
                      -- inner sliced dim: needs to be full
                      let res' :: Bool
res' = (num
n num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== num
ne) Bool -> Bool -> Bool
&& (num
ds num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== num
1 Bool -> Bool -> Bool
|| num
ds num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== -num
1)
                       in (Bool
found, Bool
res Bool -> Bool -> Bool
&& Bool
res')
              )
              (Bool
False, Bool
True)
              ([(DimIndex num, LMADDim num)] -> (Bool, Bool))
-> [(DimIndex num, LMADDim num)] -> (Bool, Bool)
forall a b. (a -> b) -> a -> b
$ [DimIndex num] -> [LMADDim num] -> [(DimIndex num, LMADDim num)]
forall a b. [a] -> [b] -> [(a, b)]
zip [DimIndex num]
slc' [LMADDim num]
dims'
       in Bool
success

    normIndex ::
      (Eq num, IntegralExp num) =>
      DimIndex num ->
      DimIndex num
    normIndex :: forall num.
(Eq num, IntegralExp num) =>
DimIndex num -> DimIndex num
normIndex (DimSlice num
b num
1 num
_) = num -> DimIndex num
forall d. d -> DimIndex d
DimFix num
b
    normIndex (DimSlice num
b num
_ num
0) = num -> DimIndex num
forall d. d -> DimIndex d
DimFix num
b
    normIndex DimIndex num
d = DimIndex num
d

-- | Slice an index function.
slice ::
  (Eq num, IntegralExp num) =>
  IxFun num ->
  Slice num ->
  IxFun num
slice :: forall num.
(Eq num, IntegralExp num) =>
IxFun num -> Slice num -> IxFun num
slice ixfun :: IxFun num
ixfun@(IxFun (lmad :: LMAD num
lmad@(LMAD num
_ [LMADDim num]
_) :| [LMAD num]
lmads) Shape num
oshp Bool
cg) Slice num
dim_slices
  -- Avoid identity slicing.
  | Slice num -> [DimIndex num]
forall d. Slice d -> [DimIndex d]
unSlice Slice num
dim_slices [DimIndex num] -> [DimIndex num] -> Bool
forall a. Eq a => a -> a -> Bool
== (num -> DimIndex num) -> Shape num -> [DimIndex num]
forall a b. (a -> b) -> [a] -> [b]
map (num -> num -> DimIndex num
forall d. Num d => d -> d -> DimIndex d
unitSlice num
0) (IxFun num -> Shape num
forall num. (Eq num, IntegralExp num) => IxFun num -> Shape num
shape IxFun num
ixfun) = IxFun num
ixfun
  | Just IxFun num
ixfun' <- IxFun num -> Slice num -> Maybe (IxFun num)
forall num.
(Eq num, IntegralExp num) =>
IxFun num -> Slice num -> Maybe (IxFun num)
sliceOneLMAD IxFun num
ixfun Slice num
dim_slices = IxFun num
ixfun'
  | Bool
otherwise =
      case IxFun num -> Slice num -> Maybe (IxFun num)
forall num.
(Eq num, IntegralExp num) =>
IxFun num -> Slice num -> Maybe (IxFun num)
sliceOneLMAD (Shape num -> IxFun num
forall num. IntegralExp num => Shape num -> IxFun num
iota (LMAD num -> Shape num
forall num. (Eq num, IntegralExp num) => LMAD num -> Shape num
lmadShape LMAD num
lmad)) Slice num
dim_slices of
        Just (IxFun (LMAD num
lmad' :| []) Shape num
_ Bool
cg') ->
          NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (LMAD num
lmad' LMAD num -> [LMAD num] -> NonEmpty (LMAD num)
forall a. a -> [a] -> NonEmpty a
:| LMAD num
lmad LMAD num -> [LMAD num] -> [LMAD num]
forall a. a -> [a] -> [a]
: [LMAD num]
lmads) Shape num
oshp (Bool
cg Bool -> Bool -> Bool
&& Bool
cg')
        Maybe (IxFun num)
_ -> String -> IxFun num
forall a. HasCallStack => String -> a
error String
"slice: reached impossible case"

-- | Flat-slice an index function.
flatSlice ::
  (Eq num, IntegralExp num) =>
  IxFun num ->
  FlatSlice num ->
  IxFun num
flatSlice :: forall num.
(Eq num, IntegralExp num) =>
IxFun num -> FlatSlice num -> IxFun num
flatSlice ixfun :: IxFun num
ixfun@(IxFun (LMAD num
offset (LMADDim num
dim : [LMADDim num]
dims) :| [LMAD num]
lmads) Shape num
oshp Bool
cg) (FlatSlice num
new_offset [FlatDimIndex num]
is)
  | IxFun num -> Bool
forall num. IxFun num -> Bool
hasContiguousPerm IxFun num
ixfun =
      let lmad :: LMAD num
lmad =
            num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD
              (num
offset num -> num -> num
forall a. Num a => a -> a -> a
+ num
new_offset num -> num -> num
forall a. Num a => a -> a -> a
* LMADDim num -> num
forall num. LMADDim num -> num
ldStride LMADDim num
dim)
              ((FlatDimIndex num -> LMADDim num)
-> [FlatDimIndex num] -> [LMADDim num]
forall a b. (a -> b) -> [a] -> [b]
map (num -> FlatDimIndex num -> LMADDim num
forall {num}.
(Eq num, Num num) =>
num -> FlatDimIndex num -> LMADDim num
helper (num -> FlatDimIndex num -> LMADDim num)
-> num -> FlatDimIndex num -> LMADDim num
forall a b. (a -> b) -> a -> b
$ LMADDim num -> num
forall num. LMADDim num -> num
ldStride LMADDim num
dim) [FlatDimIndex num]
is [LMADDim num] -> [LMADDim num] -> [LMADDim num]
forall a. Semigroup a => a -> a -> a
<> [LMADDim num]
dims)
              LMAD num -> (LMAD num -> LMAD num) -> LMAD num
forall a b. a -> (a -> b) -> b
& Permutation -> LMAD num -> LMAD num
forall num. Permutation -> LMAD num -> LMAD num
setLMADPermutation [Int
0 ..]
       in NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (LMAD num
lmad LMAD num -> [LMAD num] -> NonEmpty (LMAD num)
forall a. a -> [a] -> NonEmpty a
:| [LMAD num]
lmads) Shape num
oshp Bool
cg
  where
    helper :: num -> FlatDimIndex num -> LMADDim num
helper num
s0 (FlatDimIndex num
n num
s) =
      let new_mon :: Monotonicity
new_mon = if num
s0 num -> num -> num
forall a. Num a => a -> a -> a
* num
s num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== num
1 then Monotonicity
Inc else Monotonicity
Unknown
       in num -> num -> Int -> Monotonicity -> LMADDim num
forall num. num -> num -> Int -> Monotonicity -> LMADDim num
LMADDim (num
s0 num -> num -> num
forall a. Num a => a -> a -> a
* num
s) num
n Int
0 Monotonicity
new_mon
flatSlice (IxFun (LMAD num
lmad :| [LMAD num]
lmads) Shape num
oshp Bool
cg) s :: FlatSlice num
s@(FlatSlice num
new_offset [FlatDimIndex num]
_) =
  NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD (num
new_offset num -> num -> num
forall a. Num a => a -> a -> a
* num
base_stride) ([LMADDim num]
new_dims [LMADDim num] -> [LMADDim num] -> [LMADDim num]
forall a. Semigroup a => a -> a -> a
<> [LMADDim num]
tail_dims) LMAD num -> [LMAD num] -> NonEmpty (LMAD num)
forall a. a -> [a] -> NonEmpty a
:| LMAD num
lmad LMAD num -> [LMAD num] -> [LMAD num]
forall a. a -> [a] -> [a]
: [LMAD num]
lmads) Shape num
oshp Bool
cg
  where
    tail_shapes :: Shape num
tail_shapes = Shape num -> Shape num
forall a. [a] -> [a]
tail (Shape num -> Shape num) -> Shape num -> Shape num
forall a b. (a -> b) -> a -> b
$ LMAD num -> Shape num
forall num. (Eq num, IntegralExp num) => LMAD num -> Shape num
lmadShape LMAD num
lmad
    base_stride :: num
base_stride = Shape num -> num
forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
product Shape num
tail_shapes
    tail_strides :: Shape num
tail_strides = Shape num -> Shape num
forall a. [a] -> [a]
tail (Shape num -> Shape num) -> Shape num -> Shape num
forall a b. (a -> b) -> a -> b
$ (num -> num -> num) -> num -> Shape num -> Shape num
forall a b. (a -> b -> b) -> b -> [a] -> [b]
scanr num -> num -> num
forall a. Num a => a -> a -> a
(*) num
1 Shape num
tail_shapes
    tail_dims :: [LMADDim num]
tail_dims = (num -> num -> Int -> Monotonicity -> LMADDim num)
-> Shape num
-> Shape num
-> Permutation
-> [Monotonicity]
-> [LMADDim num]
forall a b c d e.
(a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]
zipWith4 num -> num -> Int -> Monotonicity -> LMADDim num
forall num. num -> num -> Int -> Monotonicity -> LMADDim num
LMADDim Shape num
tail_strides Shape num
tail_shapes [Shape num -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length Shape num
new_shapes ..] (Monotonicity -> [Monotonicity]
forall a. a -> [a]
repeat Monotonicity
Inc)
    new_shapes :: Shape num
new_shapes = FlatSlice num -> Shape num
forall d. FlatSlice d -> [d]
flatSliceDims FlatSlice num
s
    new_strides :: Shape num
new_strides = (num -> num) -> Shape num -> Shape num
forall a b. (a -> b) -> [a] -> [b]
map (num -> num -> num
forall a. Num a => a -> a -> a
* num
base_stride) (Shape num -> Shape num) -> Shape num -> Shape num
forall a b. (a -> b) -> a -> b
$ FlatSlice num -> Shape num
forall d. FlatSlice d -> [d]
flatSliceStrides FlatSlice num
s
    new_dims :: [LMADDim num]
new_dims = (num -> num -> Int -> Monotonicity -> LMADDim num)
-> Shape num
-> Shape num
-> Permutation
-> [Monotonicity]
-> [LMADDim num]
forall a b c d e.
(a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]
zipWith4 num -> num -> Int -> Monotonicity -> LMADDim num
forall num. num -> num -> Int -> Monotonicity -> LMADDim num
LMADDim Shape num
new_strides Shape num
new_shapes [Int
0 ..] (Monotonicity -> [Monotonicity]
forall a. a -> [a]
repeat Monotonicity
Inc)

-- | Handle the case where a reshape operation can stay inside a single LMAD.
--
-- There are four conditions that all must hold for the result of a reshape
-- operation to remain in the one-LMAD domain:
--
--   (1) the permutation of the underlying LMAD must leave unchanged
--       the LMAD dimensions that were *not* reshape coercions.
--   (2) the repetition of dimensions of the underlying LMAD must
--       refer only to the coerced-dimensions of the reshape operation.
--   (3) finally, the underlying memory is contiguous (and monotonous).
--
-- If any of these conditions do not hold, then the reshape operation will
-- conservatively add a new LMAD to the list, leading to a representation that
-- provides less opportunities for further analysis.
reshapeOneLMAD ::
  (Eq num, IntegralExp num) =>
  IxFun num ->
  Shape num ->
  Maybe (IxFun num)
reshapeOneLMAD :: forall num.
(Eq num, IntegralExp num) =>
IxFun num -> Shape num -> Maybe (IxFun num)
reshapeOneLMAD ixfun :: IxFun num
ixfun@(IxFun (lmad :: LMAD num
lmad@(LMAD num
off [LMADDim num]
dims) :| [LMAD num]
lmads) Shape num
oldbase Bool
cg) Shape num
newshape = do
  let perm :: Permutation
perm = LMAD num -> Permutation
forall num. LMAD num -> Permutation
lmadPermutation LMAD num
lmad
      dims_perm :: [LMADDim num]
dims_perm = Permutation -> [LMADDim num] -> [LMADDim num]
forall a. Permutation -> [a] -> [a]
permuteFwd Permutation
perm [LMADDim num]
dims
      mid_dims :: [LMADDim num]
mid_dims = Int -> [LMADDim num] -> [LMADDim num]
forall a. Int -> [a] -> [a]
take ([LMADDim num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [LMADDim num]
dims) [LMADDim num]
dims_perm
      mon :: Monotonicity
mon = IxFun num -> Monotonicity
forall num. (Eq num, IntegralExp num) => IxFun num -> Monotonicity
ixfunMonotonicity IxFun num
ixfun

  Bool -> Maybe ()
forall (f :: * -> *). Alternative f => Bool -> f ()
guard (Bool -> Maybe ()) -> Bool -> Maybe ()
forall a b. (a -> b) -> a -> b
$
    -- checking conditions (2)
    (LMADDim num -> Bool) -> [LMADDim num] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (\(LMADDim num
s num
_ Int
_ Monotonicity
_) -> num
s num -> num -> Bool
forall a. Eq a => a -> a -> Bool
/= num
0) [LMADDim num]
mid_dims
      Bool -> Bool -> Bool
&&
      -- checking condition (1)
      Int -> Permutation -> Bool
forall {a}. (Eq a, Num a, Enum a) => a -> [a] -> Bool
consecutive Int
0 ((LMADDim num -> Int) -> [LMADDim num] -> Permutation
forall a b. (a -> b) -> [a] -> [b]
map LMADDim num -> Int
forall num. LMADDim num -> Int
ldPerm [LMADDim num]
mid_dims)
      Bool -> Bool -> Bool
&&
      -- checking condition (3)
      IxFun num -> Bool
forall num. IxFun num -> Bool
hasContiguousPerm IxFun num
ixfun
      Bool -> Bool -> Bool
&& Bool
cg
      Bool -> Bool -> Bool
&& (Monotonicity
mon Monotonicity -> Monotonicity -> Bool
forall a. Eq a => a -> a -> Bool
== Monotonicity
Inc Bool -> Bool -> Bool
|| Monotonicity
mon Monotonicity -> Monotonicity -> Bool
forall a. Eq a => a -> a -> Bool
== Monotonicity
Dec)

  -- make new permutation
  let rsh_len :: Int
rsh_len = Shape num -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length Shape num
newshape
      diff :: Int
diff = Shape num -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length Shape num
newshape Int -> Int -> Int
forall a. Num a => a -> a -> a
- [LMADDim num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [LMADDim num]
dims
      iota_shape :: Permutation
iota_shape = [Int
0 .. Shape num -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length Shape num
newshape Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1]
      perm' :: Permutation
perm' =
        (Int -> Int) -> Permutation -> Permutation
forall a b. (a -> b) -> [a] -> [b]
map
          ( \Int
i ->
              let ind :: Int
ind = Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
diff
               in if (Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= Int
0) Bool -> Bool -> Bool
&& (Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
rsh_len)
                    then Int
i -- already checked mid_dims not affected
                    else LMADDim num -> Int
forall num. LMADDim num -> Int
ldPerm ([LMADDim num]
dims [LMADDim num] -> Int -> LMADDim num
forall a. [a] -> Int -> a
!! Int
ind) Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
diff
          )
          Permutation
iota_shape
      -- split the dimensions
      ([(Int, num)]
support_inds, [a]
repeat_inds) =
        (([(Int, num)], [a]) -> (num, Int) -> ([(Int, num)], [a]))
-> ([(Int, num)], [a]) -> [(num, Int)] -> ([(Int, num)], [a])
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl
          (\([(Int, num)]
sup, [a]
rpt) (num
shpdim, Int
ip) -> ((Int
ip, num
shpdim) (Int, num) -> [(Int, num)] -> [(Int, num)]
forall a. a -> [a] -> [a]
: [(Int, num)]
sup, [a]
rpt))
          ([], [])
          ([(num, Int)] -> ([(Int, num)], [a]))
-> [(num, Int)] -> ([(Int, num)], [a])
forall a b. (a -> b) -> a -> b
$ [(num, Int)] -> [(num, Int)]
forall a. [a] -> [a]
reverse
          ([(num, Int)] -> [(num, Int)]) -> [(num, Int)] -> [(num, Int)]
forall a b. (a -> b) -> a -> b
$ Shape num -> Permutation -> [(num, Int)]
forall a b. [a] -> [b] -> [(a, b)]
zip Shape num
newshape Permutation
perm'

      (Permutation
sup_inds, Shape num
support) = [(Int, num)] -> (Permutation, Shape num)
forall a b. [(a, b)] -> ([a], [b])
unzip ([(Int, num)] -> (Permutation, Shape num))
-> [(Int, num)] -> (Permutation, Shape num)
forall a b. (a -> b) -> a -> b
$ ((Int, num) -> (Int, num) -> Ordering)
-> [(Int, num)] -> [(Int, num)]
forall a. (a -> a -> Ordering) -> [a] -> [a]
sortBy (Int -> Int -> Ordering
forall a. Ord a => a -> a -> Ordering
compare (Int -> Int -> Ordering)
-> ((Int, num) -> Int) -> (Int, num) -> (Int, num) -> Ordering
forall b c a. (b -> b -> c) -> (a -> b) -> a -> a -> c
`on` (Int, num) -> Int
forall a b. (a, b) -> a
fst) [(Int, num)]
support_inds
      ([a]
rpt_inds, [b]
repeats) = [(a, b)] -> ([a], [b])
forall a b. [(a, b)] -> ([a], [b])
unzip [(a, b)]
forall a. [a]
repeat_inds
      LMAD num
off' [LMADDim num]
dims_sup = Monotonicity -> num -> Shape num -> LMAD num
forall num.
IntegralExp num =>
Monotonicity -> num -> [num] -> LMAD num
makeRotIota Monotonicity
mon num
off Shape num
support
      repeats' :: [LMADDim num]
repeats' = (num -> LMADDim num) -> Shape num -> [LMADDim num]
forall a b. (a -> b) -> [a] -> [b]
map (\num
n -> num -> num -> Int -> Monotonicity -> LMADDim num
forall num. num -> num -> Int -> Monotonicity -> LMADDim num
LMADDim num
0 num
n Int
0 Monotonicity
Unknown) Shape num
forall a. [a]
repeats
      dims' :: [LMADDim num]
dims' =
        ((Int, LMADDim num) -> LMADDim num)
-> [(Int, LMADDim num)] -> [LMADDim num]
forall a b. (a -> b) -> [a] -> [b]
map (Int, LMADDim num) -> LMADDim num
forall a b. (a, b) -> b
snd ([(Int, LMADDim num)] -> [LMADDim num])
-> [(Int, LMADDim num)] -> [LMADDim num]
forall a b. (a -> b) -> a -> b
$
          ((Int, LMADDim num) -> (Int, LMADDim num) -> Ordering)
-> [(Int, LMADDim num)] -> [(Int, LMADDim num)]
forall a. (a -> a -> Ordering) -> [a] -> [a]
sortBy (Int -> Int -> Ordering
forall a. Ord a => a -> a -> Ordering
compare (Int -> Int -> Ordering)
-> ((Int, LMADDim num) -> Int)
-> (Int, LMADDim num)
-> (Int, LMADDim num)
-> Ordering
forall b c a. (b -> b -> c) -> (a -> b) -> a -> a -> c
`on` (Int, LMADDim num) -> Int
forall a b. (a, b) -> a
fst) ([(Int, LMADDim num)] -> [(Int, LMADDim num)])
-> [(Int, LMADDim num)] -> [(Int, LMADDim num)]
forall a b. (a -> b) -> a -> b
$
            Permutation -> [LMADDim num] -> [(Int, LMADDim num)]
forall a b. [a] -> [b] -> [(a, b)]
zip Permutation
sup_inds [LMADDim num]
dims_sup [(Int, LMADDim num)]
-> [(Int, LMADDim num)] -> [(Int, LMADDim num)]
forall a. [a] -> [a] -> [a]
++ Permutation -> [LMADDim num] -> [(Int, LMADDim num)]
forall a b. [a] -> [b] -> [(a, b)]
zip Permutation
forall a. [a]
rpt_inds [LMADDim num]
repeats'
      lmad' :: LMAD num
lmad' = num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD num
off' [LMADDim num]
dims'
  IxFun num -> Maybe (IxFun num)
forall (f :: * -> *) a. Applicative f => a -> f a
pure (IxFun num -> Maybe (IxFun num)) -> IxFun num -> Maybe (IxFun num)
forall a b. (a -> b) -> a -> b
$ NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (Permutation -> LMAD num -> LMAD num
forall num. Permutation -> LMAD num -> LMAD num
setLMADPermutation Permutation
perm' LMAD num
lmad' LMAD num -> [LMAD num] -> NonEmpty (LMAD num)
forall a. a -> [a] -> NonEmpty a
:| [LMAD num]
lmads) Shape num
oldbase Bool
cg
  where
    consecutive :: a -> [a] -> Bool
consecutive a
_ [] = Bool
True
    consecutive a
i [a
p] = a
i a -> a -> Bool
forall a. Eq a => a -> a -> Bool
== a
p
    consecutive a
i [a]
ps = [Bool] -> Bool
forall (t :: * -> *). Foldable t => t Bool -> Bool
and ([Bool] -> Bool) -> [Bool] -> Bool
forall a b. (a -> b) -> a -> b
$ (a -> a -> Bool) -> [a] -> [a] -> [Bool]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith a -> a -> Bool
forall a. Eq a => a -> a -> Bool
(==) [a]
ps [a
i, a
i a -> a -> a
forall a. Num a => a -> a -> a
+ a
1 ..]

-- | Reshape an index function.
reshape ::
  (Eq num, IntegralExp num) =>
  IxFun num ->
  Shape num ->
  IxFun num
reshape :: forall num.
(Eq num, IntegralExp num) =>
IxFun num -> Shape num -> IxFun num
reshape IxFun num
ixfun Shape num
new_shape
  | Just IxFun num
ixfun' <- IxFun num -> Shape num -> Maybe (IxFun num)
forall num.
(Eq num, IntegralExp num) =>
IxFun num -> Shape num -> Maybe (IxFun num)
reshapeOneLMAD IxFun num
ixfun Shape num
new_shape = IxFun num
ixfun'
reshape (IxFun (LMAD num
lmad0 :| [LMAD num]
lmad0s) Shape num
oshp Bool
cg) Shape num
new_shape =
  case Shape num -> IxFun num
forall num. IntegralExp num => Shape num -> IxFun num
iota Shape num
new_shape of
    IxFun (LMAD num
lmad :| []) Shape num
_ Bool
_ -> NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (LMAD num
lmad LMAD num -> [LMAD num] -> NonEmpty (LMAD num)
forall a. a -> [a] -> NonEmpty a
:| LMAD num
lmad0 LMAD num -> [LMAD num] -> [LMAD num]
forall a. a -> [a] -> [a]
: [LMAD num]
lmad0s) Shape num
oshp Bool
cg
    IxFun num
_ -> String -> IxFun num
forall a. HasCallStack => String -> a
error String
"reshape: reached impossible case"

-- | Coerce an index function to look like it has a new shape.
-- Dynamically the shape must be the same.
coerce ::
  (Eq num, IntegralExp num) =>
  IxFun num ->
  Shape num ->
  IxFun num
coerce :: forall num.
(Eq num, IntegralExp num) =>
IxFun num -> Shape num -> IxFun num
coerce (IxFun (LMAD num
lmad :| [LMAD num]
lmads) Shape num
oshp Bool
cg) Shape num
new_shape =
  NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (LMAD num -> LMAD num
onLMAD LMAD num
lmad LMAD num -> [LMAD num] -> NonEmpty (LMAD num)
forall a. a -> [a] -> NonEmpty a
:| [LMAD num]
lmads) Shape num
oshp Bool
cg
  where
    onLMAD :: LMAD num -> LMAD num
onLMAD (LMAD num
offset [LMADDim num]
dims) = num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD num
offset ([LMADDim num] -> LMAD num) -> [LMADDim num] -> LMAD num
forall a b. (a -> b) -> a -> b
$ (LMADDim num -> num -> LMADDim num)
-> [LMADDim num] -> Shape num -> [LMADDim num]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith LMADDim num -> num -> LMADDim num
forall {num}. LMADDim num -> num -> LMADDim num
onDim [LMADDim num]
dims Shape num
new_shape
    onDim :: LMADDim num -> num -> LMADDim num
onDim LMADDim num
ld num
d = LMADDim num
ld {ldShape :: num
ldShape = num
d}

-- | The number of dimensions in the domain of the input function.
rank ::
  IntegralExp num =>
  IxFun num ->
  Int
rank :: forall num. IntegralExp num => IxFun num -> Int
rank (IxFun (LMAD num
_ [LMADDim num]
sss :| [LMAD num]
_) Shape num
_ Bool
_) = [LMADDim num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [LMADDim num]
sss

-- | Handle the case where a rebase operation can stay within m + n - 1 LMADs,
-- where m is the number of LMADs in the index function, and n is the number of
-- LMADs in the new base.  If both index function have only on LMAD, this means
-- that we stay within the single-LMAD domain.
--
-- We can often stay in that domain if the original ixfun is essentially a
-- slice, e.g. `x[i, (k1,m,s1), (k2,n,s2)] = orig`.
--
-- XXX: TODO: handle repetitions in both lmads.
--
-- How to handle repeated dimensions in the original?
--
--   (a) Shave them off of the last lmad of original
--   (b) Compose the result from (a) with the first
--       lmad of the new base
--   (c) apply a repeat operation on the result of (b).
--
-- However, I strongly suspect that for in-place update what we need is actually
-- the INVERSE of the rebase function, i.e., given an index function new-base
-- and another one orig, compute the index function ixfun0 such that:
--
--   new-base == rebase ixfun0 ixfun, or equivalently:
--   new-base == ixfun o ixfun0
--
-- because then I can go bottom up and compose with ixfun0 all the index
-- functions corresponding to the memory block associated with ixfun.
rebaseNice ::
  (Eq num, IntegralExp num) =>
  IxFun num ->
  IxFun num ->
  Maybe (IxFun num)
rebaseNice :: forall num.
(Eq num, IntegralExp num) =>
IxFun num -> IxFun num -> Maybe (IxFun num)
rebaseNice
  new_base :: IxFun num
new_base@(IxFun (LMAD num
lmad_base :| [LMAD num]
lmads_base) Shape num
_ Bool
cg_base)
  ixfun :: IxFun num
ixfun@(IxFun NonEmpty (LMAD num)
lmads Shape num
shp Bool
cg) = do
    let (LMAD num
lmad :| [LMAD num]
lmads') = NonEmpty (LMAD num) -> NonEmpty (LMAD num)
forall a. NonEmpty a -> NonEmpty a
NE.reverse NonEmpty (LMAD num)
lmads
        dims :: [LMADDim num]
dims = LMAD num -> [LMADDim num]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD num
lmad
        perm :: Permutation
perm = LMAD num -> Permutation
forall num. LMAD num -> Permutation
lmadPermutation LMAD num
lmad
        perm_base :: Permutation
perm_base = LMAD num -> Permutation
forall num. LMAD num -> Permutation
lmadPermutation LMAD num
lmad_base

    Bool -> Maybe ()
forall (f :: * -> *). Alternative f => Bool -> f ()
guard (Bool -> Maybe ()) -> Bool -> Maybe ()
forall a b. (a -> b) -> a -> b
$
      -- Core rebase condition.
      IxFun num -> Shape num
forall num. IxFun num -> Shape num
base IxFun num
ixfun Shape num -> Shape num -> Bool
forall a. Eq a => a -> a -> Bool
== IxFun num -> Shape num
forall num. (Eq num, IntegralExp num) => IxFun num -> Shape num
shape IxFun num
new_base
        -- Conservative safety conditions: ixfun is contiguous and has known
        -- monotonicity for all dimensions.
        Bool -> Bool -> Bool
&& Bool
cg
        Bool -> Bool -> Bool
&& (LMADDim num -> Bool) -> [LMADDim num] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all ((Monotonicity -> Monotonicity -> Bool
forall a. Eq a => a -> a -> Bool
/= Monotonicity
Unknown) (Monotonicity -> Bool)
-> (LMADDim num -> Monotonicity) -> LMADDim num -> Bool
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. LMADDim num -> Monotonicity
forall num. LMADDim num -> Monotonicity
ldMon) [LMADDim num]
dims
        -- XXX: We should be able to handle some basic cases where both index
        -- functions have non-trivial permutations.
        Bool -> Bool -> Bool
&& (IxFun num -> Bool
forall num. IxFun num -> Bool
hasContiguousPerm IxFun num
ixfun Bool -> Bool -> Bool
|| IxFun num -> Bool
forall num. IxFun num -> Bool
hasContiguousPerm IxFun num
new_base)
        -- We need the permutations to be of the same size if we want to compose
        -- them.  They don't have to be of the same size if the ixfun has a trivial
        -- permutation.  Supporting this latter case allows us to rebase when ixfun
        -- has been created by slicing with fixed dimensions.
        Bool -> Bool -> Bool
&& (Permutation -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length Permutation
perm Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Permutation -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length Permutation
perm_base Bool -> Bool -> Bool
|| IxFun num -> Bool
forall num. IxFun num -> Bool
hasContiguousPerm IxFun num
ixfun)
        -- To not have to worry about ixfun having non-1 strides, we also check that
        -- it is a row-major array (modulo permutation, which is handled
        -- separately).  Accept a non-full innermost dimension.  XXX: Maybe this can
        -- be less conservative?
        Bool -> Bool -> Bool
&& [Bool] -> Bool
forall (t :: * -> *). Foldable t => t Bool -> Bool
and
          ( (num -> LMADDim num -> Bool -> Bool)
-> Shape num -> [LMADDim num] -> [Bool] -> [Bool]
forall a b c d. (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
zipWith3
              (\num
sn LMADDim num
ld Bool
inner -> num
sn num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== LMADDim num -> num
forall num. LMADDim num -> num
ldShape LMADDim num
ld Bool -> Bool -> Bool
|| (Bool
inner Bool -> Bool -> Bool
&& LMADDim num -> num
forall num. LMADDim num -> num
ldStride LMADDim num
ld num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== num
1))
              Shape num
shp
              [LMADDim num]
dims
              (Int -> Bool -> [Bool]
forall a. Int -> a -> [a]
replicate ([LMADDim num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [LMADDim num]
dims Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1) Bool
False [Bool] -> [Bool] -> [Bool]
forall a. [a] -> [a] -> [a]
++ [Bool
True])
          )

    -- Compose permutations, reverse strides and adjust offset if necessary.
    let perm_base' :: Permutation
perm_base' =
          if IxFun num -> Bool
forall num. IxFun num -> Bool
hasContiguousPerm IxFun num
ixfun
            then Permutation
perm_base
            else (Int -> Int) -> Permutation -> Permutation
forall a b. (a -> b) -> [a] -> [b]
map (Permutation
perm Permutation -> Int -> Int
forall a. [a] -> Int -> a
!!) Permutation
perm_base
        lmad_base' :: LMAD num
lmad_base' = Permutation -> LMAD num -> LMAD num
forall num. Permutation -> LMAD num -> LMAD num
setLMADPermutation Permutation
perm_base' LMAD num
lmad_base
        dims_base :: [LMADDim num]
dims_base = LMAD num -> [LMADDim num]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD num
lmad_base'
        n_fewer_dims :: Int
n_fewer_dims = [LMADDim num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [LMADDim num]
dims_base Int -> Int -> Int
forall a. Num a => a -> a -> a
- [LMADDim num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [LMADDim num]
dims
        ([LMADDim num]
dims_base', Shape num
offs_contrib) =
          [(LMADDim num, num)] -> ([LMADDim num], Shape num)
forall a b. [(a, b)] -> ([a], [b])
unzip ([(LMADDim num, num)] -> ([LMADDim num], Shape num))
-> [(LMADDim num, num)] -> ([LMADDim num], Shape num)
forall a b. (a -> b) -> a -> b
$
            (LMADDim num -> LMADDim num -> (LMADDim num, num))
-> [LMADDim num] -> [LMADDim num] -> [(LMADDim num, num)]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith
              ( \(LMADDim num
s1 num
n1 Int
p1 Monotonicity
_) (LMADDim num
_ num
_ Int
_ Monotonicity
m2) ->
                  let (num
s', num
off')
                        | Monotonicity
m2 Monotonicity -> Monotonicity -> Bool
forall a. Eq a => a -> a -> Bool
== Monotonicity
Inc = (num
s1, num
0)
                        | Bool
otherwise = (num
s1 num -> num -> num
forall a. Num a => a -> a -> a
* (-num
1), num
s1 num -> num -> num
forall a. Num a => a -> a -> a
* (num
n1 num -> num -> num
forall a. Num a => a -> a -> a
- num
1))
                   in (num -> num -> Int -> Monotonicity -> LMADDim num
forall num. num -> num -> Int -> Monotonicity -> LMADDim num
LMADDim num
s' num
n1 (Int
p1 Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
n_fewer_dims) Monotonicity
Inc, num
off')
              )
              -- If @dims@ is morally a slice, it might have fewer dimensions than
              -- @dims_base@.  Drop extraneous outer dimensions.
              (Int -> [LMADDim num] -> [LMADDim num]
forall a. Int -> [a] -> [a]
drop Int
n_fewer_dims [LMADDim num]
dims_base)
              [LMADDim num]
dims
        off_base :: num
off_base = LMAD num -> num
forall num. LMAD num -> num
lmadOffset LMAD num
lmad_base' num -> num -> num
forall a. Num a => a -> a -> a
+ Shape num -> num
forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
sum Shape num
offs_contrib
        lmad_base'' :: LMAD num
lmad_base''
          | LMAD num -> num
forall num. LMAD num -> num
lmadOffset LMAD num
lmad num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== num
0 = num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD num
off_base [LMADDim num]
dims_base'
          | Bool
otherwise =
              -- If the innermost dimension of the ixfun was not full (but still
              -- had a stride of 1), add its offset relative to the new base.
              Shape num -> LMAD num -> LMAD num
forall num. Shape num -> LMAD num -> LMAD num
setLMADShape
                (LMAD num -> Shape num
forall num. (Eq num, IntegralExp num) => LMAD num -> Shape num
lmadShape LMAD num
lmad)
                ( num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD
                    (num
off_base num -> num -> num
forall a. Num a => a -> a -> a
+ LMADDim num -> num
forall num. LMADDim num -> num
ldStride ([LMADDim num] -> LMADDim num
forall a. [a] -> a
last [LMADDim num]
dims_base) num -> num -> num
forall a. Num a => a -> a -> a
* LMAD num -> num
forall num. LMAD num -> num
lmadOffset LMAD num
lmad)
                    [LMADDim num]
dims_base'
                )
        new_base' :: IxFun num
new_base' = NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (LMAD num
lmad_base'' LMAD num -> [LMAD num] -> NonEmpty (LMAD num)
forall a. a -> [a] -> NonEmpty a
:| [LMAD num]
lmads_base) Shape num
shp Bool
cg_base
        IxFun NonEmpty (LMAD num)
lmads_base' Shape num
_ Bool
_ = IxFun num
new_base'
        lmads'' :: NonEmpty (LMAD num)
lmads'' = [LMAD num]
lmads' [LMAD num] -> NonEmpty (LMAD num) -> NonEmpty (LMAD num)
forall a. [a] -> NonEmpty a -> NonEmpty a
++@ NonEmpty (LMAD num)
lmads_base'
    IxFun num -> Maybe (IxFun num)
forall (f :: * -> *) a. Applicative f => a -> f a
pure (IxFun num -> Maybe (IxFun num)) -> IxFun num -> Maybe (IxFun num)
forall a b. (a -> b) -> a -> b
$ NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun NonEmpty (LMAD num)
lmads'' Shape num
shp (Bool
cg Bool -> Bool -> Bool
&& Bool
cg_base)

-- | Rebase an index function on top of a new base.
rebase ::
  (Eq num, IntegralExp num) =>
  IxFun num ->
  IxFun num ->
  IxFun num
rebase :: forall num.
(Eq num, IntegralExp num) =>
IxFun num -> IxFun num -> IxFun num
rebase new_base :: IxFun num
new_base@(IxFun NonEmpty (LMAD num)
lmads_base Shape num
shp_base Bool
cg_base) ixfun :: IxFun num
ixfun@(IxFun NonEmpty (LMAD num)
lmads Shape num
shp Bool
cg)
  | Just IxFun num
ixfun' <- IxFun num -> IxFun num -> Maybe (IxFun num)
forall num.
(Eq num, IntegralExp num) =>
IxFun num -> IxFun num -> Maybe (IxFun num)
rebaseNice IxFun num
new_base IxFun num
ixfun = IxFun num
ixfun'
  -- In the general case just concatenate LMADs since this refers to index
  -- function composition, which is always safe.
  | Bool
otherwise =
      let (NonEmpty (LMAD num)
lmads_base', Shape num
shp_base') =
            if IxFun num -> Shape num
forall num. IxFun num -> Shape num
base IxFun num
ixfun Shape num -> Shape num -> Bool
forall a. Eq a => a -> a -> Bool
== IxFun num -> Shape num
forall num. (Eq num, IntegralExp num) => IxFun num -> Shape num
shape IxFun num
new_base
              then (NonEmpty (LMAD num)
lmads_base, Shape num
shp_base)
              else
                let IxFun NonEmpty (LMAD num)
lmads' Shape num
shp_base'' Bool
_ = IxFun num -> Shape num -> IxFun num
forall num.
(Eq num, IntegralExp num) =>
IxFun num -> Shape num -> IxFun num
reshape IxFun num
new_base Shape num
shp
                 in (NonEmpty (LMAD num)
lmads', Shape num
shp_base'')
       in NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (NonEmpty (LMAD num)
lmads NonEmpty (LMAD num) -> NonEmpty (LMAD num) -> NonEmpty (LMAD num)
forall a. NonEmpty a -> NonEmpty a -> NonEmpty a
@++@ NonEmpty (LMAD num)
lmads_base') Shape num
shp_base' (Bool
cg Bool -> Bool -> Bool
&& Bool
cg_base)

-- | 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.
linearWithOffset ::
  (Eq num, IntegralExp num) =>
  IxFun num ->
  num ->
  Maybe num
linearWithOffset :: forall num.
(Eq num, IntegralExp num) =>
IxFun num -> num -> Maybe num
linearWithOffset ixfun :: IxFun num
ixfun@(IxFun (LMAD num
lmad :| []) Shape num
_ Bool
cg) num
elem_size
  | IxFun num -> Bool
forall num. IxFun num -> Bool
hasContiguousPerm IxFun num
ixfun Bool -> Bool -> Bool
&& Bool
cg Bool -> Bool -> Bool
&& IxFun num -> Monotonicity
forall num. (Eq num, IntegralExp num) => IxFun num -> Monotonicity
ixfunMonotonicity IxFun num
ixfun Monotonicity -> Monotonicity -> Bool
forall a. Eq a => a -> a -> Bool
== Monotonicity
Inc =
      num -> Maybe num
forall a. a -> Maybe a
Just (num -> Maybe num) -> num -> Maybe num
forall a b. (a -> b) -> a -> b
$ LMAD num -> num
forall num. LMAD num -> num
lmadOffset LMAD num
lmad num -> num -> num
forall a. Num a => a -> a -> a
* num
elem_size
linearWithOffset IxFun num
_ num
_ = Maybe num
forall a. Maybe a
Nothing

-- | Similar restrictions to @linearWithOffset@ except for transpositions, which
-- are returned together with the offset.
rearrangeWithOffset ::
  (Eq num, IntegralExp num) =>
  IxFun num ->
  num ->
  Maybe (num, [(Int, num)])
rearrangeWithOffset :: forall num.
(Eq num, IntegralExp num) =>
IxFun num -> num -> Maybe (num, [(Int, num)])
rearrangeWithOffset (IxFun (LMAD num
lmad :| []) Shape num
oshp Bool
cg) num
elem_size = do
  -- Note that @cg@ describes whether the index function is
  -- contiguous, *ignoring permutations*.  This function requires that
  -- functionality.
  let perm :: Permutation
perm = LMAD num -> Permutation
forall num. LMAD num -> Permutation
lmadPermutation LMAD num
lmad
      perm_contig :: Permutation
perm_contig = [Int
0 .. Permutation -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length Permutation
perm Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1]
  num
offset <-
    IxFun num -> num -> Maybe num
forall num.
(Eq num, IntegralExp num) =>
IxFun num -> num -> Maybe num
linearWithOffset
      (NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
forall num. NonEmpty (LMAD num) -> Shape num -> Bool -> IxFun num
IxFun (Permutation -> LMAD num -> LMAD num
forall num. Permutation -> LMAD num -> LMAD num
setLMADPermutation Permutation
perm_contig LMAD num
lmad LMAD num -> [LMAD num] -> NonEmpty (LMAD num)
forall a. a -> [a] -> NonEmpty a
:| []) Shape num
oshp Bool
cg)
      num
elem_size
  (num, [(Int, num)]) -> Maybe (num, [(Int, num)])
forall (f :: * -> *) a. Applicative f => a -> f a
pure (num
offset, Permutation -> Shape num -> [(Int, num)]
forall a b. [a] -> [b] -> [(a, b)]
zip Permutation
perm (Permutation -> Shape num -> Shape num
forall a. Permutation -> [a] -> [a]
permuteFwd Permutation
perm (LMAD num -> Shape num
forall num. (Eq num, IntegralExp num) => LMAD num -> Shape num
lmadShapeBase LMAD num
lmad)))
rearrangeWithOffset IxFun num
_ num
_ = Maybe (num, [(Int, num)])
forall a. Maybe a
Nothing

-- | Is this a row-major array starting at offset zero?
isLinear :: (Eq num, IntegralExp num) => IxFun num -> Bool
isLinear :: forall num. (Eq num, IntegralExp num) => IxFun num -> Bool
isLinear = (Maybe num -> Maybe num -> Bool
forall a. Eq a => a -> a -> Bool
== num -> Maybe num
forall a. a -> Maybe a
Just num
0) (Maybe num -> Bool)
-> (IxFun num -> Maybe num) -> IxFun num -> Bool
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (IxFun num -> num -> Maybe num) -> num -> IxFun num -> Maybe num
forall a b c. (a -> b -> c) -> b -> a -> c
flip IxFun num -> num -> Maybe num
forall num.
(Eq num, IntegralExp num) =>
IxFun num -> num -> Maybe num
linearWithOffset num
1

permuteFwd :: Permutation -> [a] -> [a]
permuteFwd :: forall a. Permutation -> [a] -> [a]
permuteFwd Permutation
ps [a]
elems = (Int -> a) -> Permutation -> [a]
forall a b. (a -> b) -> [a] -> [b]
map ([a]
elems [a] -> Int -> a
forall a. [a] -> Int -> a
!!) Permutation
ps

permuteInv :: Permutation -> [a] -> [a]
permuteInv :: forall a. Permutation -> [a] -> [a]
permuteInv Permutation
ps [a]
elems = ((Int, a) -> a) -> [(Int, a)] -> [a]
forall a b. (a -> b) -> [a] -> [b]
map (Int, a) -> a
forall a b. (a, b) -> b
snd ([(Int, a)] -> [a]) -> [(Int, a)] -> [a]
forall a b. (a -> b) -> a -> b
$ ((Int, a) -> (Int, a) -> Ordering) -> [(Int, a)] -> [(Int, a)]
forall a. (a -> a -> Ordering) -> [a] -> [a]
sortBy (Int -> Int -> Ordering
forall a. Ord a => a -> a -> Ordering
compare (Int -> Int -> Ordering)
-> ((Int, a) -> Int) -> (Int, a) -> (Int, a) -> Ordering
forall b c a. (b -> b -> c) -> (a -> b) -> a -> a -> c
`on` (Int, a) -> Int
forall a b. (a, b) -> a
fst) ([(Int, a)] -> [(Int, a)]) -> [(Int, a)] -> [(Int, a)]
forall a b. (a -> b) -> a -> b
$ Permutation -> [a] -> [(Int, a)]
forall a b. [a] -> [b] -> [(a, b)]
zip Permutation
ps [a]
elems

flatOneDim ::
  (Eq num, IntegralExp num) =>
  num ->
  num ->
  num
flatOneDim :: forall num. (Eq num, IntegralExp num) => num -> num -> num
flatOneDim num
s num
i
  | num
s num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== num
0 = num
0
  | Bool
otherwise = num
i num -> num -> num
forall a. Num a => a -> a -> a
* num
s

-- | Generalised iota with user-specified offset and rotates.
makeRotIota ::
  IntegralExp num =>
  Monotonicity ->
  -- | Offset
  num ->
  -- | Shape
  [num] ->
  LMAD num
makeRotIota :: forall num.
IntegralExp num =>
Monotonicity -> num -> [num] -> LMAD num
makeRotIota Monotonicity
mon num
off [num]
ns
  | Monotonicity
mon Monotonicity -> Monotonicity -> Bool
forall a. Eq a => a -> a -> Bool
== Monotonicity
Inc Bool -> Bool -> Bool
|| Monotonicity
mon Monotonicity -> Monotonicity -> Bool
forall a. Eq a => a -> a -> Bool
== Monotonicity
Dec =
      let rk :: Int
rk = [num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [num]
ns
          ss0 :: [num]
ss0 = [num] -> [num]
forall a. [a] -> [a]
reverse ([num] -> [num]) -> [num] -> [num]
forall a b. (a -> b) -> a -> b
$ Int -> [num] -> [num]
forall a. Int -> [a] -> [a]
take Int
rk ([num] -> [num]) -> [num] -> [num]
forall a b. (a -> b) -> a -> b
$ (num -> num -> num) -> num -> [num] -> [num]
forall b a. (b -> a -> b) -> b -> [a] -> [b]
scanl num -> num -> num
forall a. Num a => a -> a -> a
(*) num
1 ([num] -> [num]) -> [num] -> [num]
forall a b. (a -> b) -> a -> b
$ [num] -> [num]
forall a. [a] -> [a]
reverse [num]
ns
          ss :: [num]
ss =
            if Monotonicity
mon Monotonicity -> Monotonicity -> Bool
forall a. Eq a => a -> a -> Bool
== Monotonicity
Inc
              then [num]
ss0
              else (num -> num) -> [num] -> [num]
forall a b. (a -> b) -> [a] -> [b]
map (num -> num -> num
forall a. Num a => a -> a -> a
* (-num
1)) [num]
ss0
          ps :: Permutation
ps = (Int -> Int) -> Permutation -> Permutation
forall a b. (a -> b) -> [a] -> [b]
map Int -> Int
forall a b. (Integral a, Num b) => a -> b
fromIntegral [Int
0 .. Int
rk Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1]
          fi :: [Monotonicity]
fi = Int -> Monotonicity -> [Monotonicity]
forall a. Int -> a -> [a]
replicate Int
rk Monotonicity
mon
       in num -> [LMADDim num] -> LMAD num
forall num. num -> [LMADDim num] -> LMAD num
LMAD num
off ([LMADDim num] -> LMAD num) -> [LMADDim num] -> LMAD num
forall a b. (a -> b) -> a -> b
$ (num -> num -> Int -> Monotonicity -> LMADDim num)
-> [num] -> [num] -> Permutation -> [Monotonicity] -> [LMADDim num]
forall a b c d e.
(a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]
zipWith4 num -> num -> Int -> Monotonicity -> LMADDim num
forall num. num -> num -> Int -> Monotonicity -> LMADDim num
LMADDim [num]
ss [num]
ns Permutation
ps [Monotonicity]
fi
  | Bool
otherwise = String -> LMAD num
forall a. HasCallStack => String -> a
error String
"makeRotIota: requires Inc or Dec"

-- | Check monotonicity of an index function.
ixfunMonotonicity ::
  (Eq num, IntegralExp num) =>
  IxFun num ->
  Monotonicity
ixfunMonotonicity :: forall num. (Eq num, IntegralExp num) => IxFun num -> Monotonicity
ixfunMonotonicity (IxFun (LMAD num
lmad :| [LMAD num]
lmads) Shape num
_ Bool
_) =
  let mon0 :: Monotonicity
mon0 = LMAD num -> Monotonicity
forall num. (Eq num, IntegralExp num) => LMAD num -> Monotonicity
lmadMonotonicityRots LMAD num
lmad
   in if (LMAD num -> Bool) -> [LMAD num] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all ((Monotonicity -> Monotonicity -> Bool
forall a. Eq a => a -> a -> Bool
== Monotonicity
mon0) (Monotonicity -> Bool)
-> (LMAD num -> Monotonicity) -> LMAD num -> Bool
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. LMAD num -> Monotonicity
forall num. (Eq num, IntegralExp num) => LMAD num -> Monotonicity
lmadMonotonicityRots) [LMAD num]
lmads
        then Monotonicity
mon0
        else Monotonicity
Unknown
  where
    lmadMonotonicityRots ::
      (Eq num, IntegralExp num) =>
      LMAD num ->
      Monotonicity
    lmadMonotonicityRots :: forall num. (Eq num, IntegralExp num) => LMAD num -> Monotonicity
lmadMonotonicityRots (LMAD num
_ [LMADDim num]
dims)
      | (LMADDim num -> Bool) -> [LMADDim num] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (Monotonicity -> LMADDim num -> Bool
forall num.
(Eq num, IntegralExp num) =>
Monotonicity -> LMADDim num -> Bool
isMonDim Monotonicity
Inc) [LMADDim num]
dims = Monotonicity
Inc
      | (LMADDim num -> Bool) -> [LMADDim num] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (Monotonicity -> LMADDim num -> Bool
forall num.
(Eq num, IntegralExp num) =>
Monotonicity -> LMADDim num -> Bool
isMonDim Monotonicity
Dec) [LMADDim num]
dims = Monotonicity
Dec
      | Bool
otherwise = Monotonicity
Unknown

    isMonDim ::
      (Eq num, IntegralExp num) =>
      Monotonicity ->
      LMADDim num ->
      Bool
    isMonDim :: forall num.
(Eq num, IntegralExp num) =>
Monotonicity -> LMADDim num -> Bool
isMonDim Monotonicity
mon (LMADDim num
s num
_ Int
_ Monotonicity
ldmon) =
      num
s num -> num -> Bool
forall a. Eq a => a -> a -> Bool
== num
0 Bool -> Bool -> Bool
|| Monotonicity
mon Monotonicity -> Monotonicity -> Bool
forall a. Eq a => a -> a -> Bool
== Monotonicity
ldmon

-- | Turn all the leaves of the index function into 'Ext's.
existentialize ::
  IxFun (TPrimExp Int64 a) ->
  IxFun (TPrimExp Int64 (Ext b))
existentialize :: forall a b.
IxFun (TPrimExp Int64 a) -> IxFun (TPrimExp Int64 (Ext b))
existentialize IxFun (TPrimExp Int64 a)
ixfun = State Int (IxFun (TPrimExp Int64 (Ext b)))
-> Int -> IxFun (TPrimExp Int64 (Ext b))
forall s a. State s a -> s -> a
evalState ((TPrimExp Int64 a -> StateT Int Identity (TPrimExp Int64 (Ext b)))
-> IxFun (TPrimExp Int64 a)
-> State Int (IxFun (TPrimExp Int64 (Ext b)))
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse (StateT Int Identity (TPrimExp Int64 (Ext b))
-> TPrimExp Int64 a -> StateT Int Identity (TPrimExp Int64 (Ext b))
forall a b. a -> b -> a
const StateT Int Identity (TPrimExp Int64 (Ext b))
forall {t} {a}. StateT Int Identity (TPrimExp t (Ext a))
mkExt) IxFun (TPrimExp Int64 a)
ixfun) Int
0
  where
    mkExt :: StateT Int Identity (TPrimExp t (Ext a))
mkExt = do
      Int
i <- StateT Int Identity Int
forall s (m :: * -> *). MonadState s m => m s
get
      Int -> StateT Int Identity ()
forall s (m :: * -> *). MonadState s m => s -> m ()
put (Int -> StateT Int Identity ()) -> Int -> StateT Int Identity ()
forall a b. (a -> b) -> a -> b
$ Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
1
      TPrimExp t (Ext a) -> StateT Int Identity (TPrimExp t (Ext a))
forall (f :: * -> *) a. Applicative f => a -> f a
pure (TPrimExp t (Ext a) -> StateT Int Identity (TPrimExp t (Ext a)))
-> TPrimExp t (Ext a) -> StateT Int Identity (TPrimExp t (Ext a))
forall a b. (a -> b) -> a -> b
$ PrimExp (Ext a) -> TPrimExp t (Ext a)
forall t v. PrimExp v -> TPrimExp t v
TPrimExp (PrimExp (Ext a) -> TPrimExp t (Ext a))
-> PrimExp (Ext a) -> TPrimExp t (Ext a)
forall a b. (a -> b) -> a -> b
$ Ext a -> PrimType -> PrimExp (Ext a)
forall v. v -> PrimType -> PrimExp v
LeafExp (Int -> Ext a
forall a. Int -> Ext a
Ext Int
i) PrimType
int64

-- | 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.
closeEnough :: IxFun num -> IxFun num -> Bool
closeEnough :: forall num. IxFun num -> IxFun num -> Bool
closeEnough IxFun num
ixf1 IxFun num
ixf2 =
  ([num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length (IxFun num -> [num]
forall num. IxFun num -> Shape num
base IxFun num
ixf1) Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== [num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length (IxFun num -> [num]
forall num. IxFun num -> Shape num
base IxFun num
ixf2))
    Bool -> Bool -> Bool
&& (NonEmpty (LMAD num) -> Int
forall a. NonEmpty a -> Int
NE.length (IxFun num -> NonEmpty (LMAD num)
forall num. IxFun num -> NonEmpty (LMAD num)
ixfunLMADs IxFun num
ixf1) Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== NonEmpty (LMAD num) -> Int
forall a. NonEmpty a -> Int
NE.length (IxFun num -> NonEmpty (LMAD num)
forall num. IxFun num -> NonEmpty (LMAD num)
ixfunLMADs IxFun num
ixf2))
    Bool -> Bool -> Bool
&& ((LMAD num, LMAD num) -> Bool)
-> NonEmpty (LMAD num, LMAD num) -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (LMAD num, LMAD num) -> Bool
forall num. (LMAD num, LMAD num) -> Bool
closeEnoughLMADs (NonEmpty (LMAD num)
-> NonEmpty (LMAD num) -> NonEmpty (LMAD num, LMAD num)
forall a b. NonEmpty a -> NonEmpty b -> NonEmpty (a, b)
NE.zip (IxFun num -> NonEmpty (LMAD num)
forall num. IxFun num -> NonEmpty (LMAD num)
ixfunLMADs IxFun num
ixf1) (IxFun num -> NonEmpty (LMAD num)
forall num. IxFun num -> NonEmpty (LMAD num)
ixfunLMADs IxFun num
ixf2))
    -- This treats ixf1 as the "declared type" that we are matching against.
    Bool -> Bool -> Bool
&& (IxFun num -> Bool
forall num. IxFun num -> Bool
contiguous IxFun num
ixf1 Bool -> Bool -> Bool
forall a. Ord a => a -> a -> Bool
<= IxFun num -> Bool
forall num. IxFun num -> Bool
contiguous IxFun num
ixf2)
  where
    closeEnoughLMADs :: (LMAD num, LMAD num) -> Bool
    closeEnoughLMADs :: forall num. (LMAD num, LMAD num) -> Bool
closeEnoughLMADs (LMAD num
lmad1, LMAD num
lmad2) =
      [LMADDim num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length (LMAD num -> [LMADDim num]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD num
lmad1) Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== [LMADDim num] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length (LMAD num -> [LMADDim num]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD num
lmad2)
        Bool -> Bool -> Bool
&& (LMADDim num -> Int) -> [LMADDim num] -> Permutation
forall a b. (a -> b) -> [a] -> [b]
map LMADDim num -> Int
forall num. LMADDim num -> Int
ldPerm (LMAD num -> [LMADDim num]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD num
lmad1)
          Permutation -> Permutation -> Bool
forall a. Eq a => a -> a -> Bool
== (LMADDim num -> Int) -> [LMADDim num] -> Permutation
forall a b. (a -> b) -> [a] -> [b]
map LMADDim num -> Int
forall num. LMADDim num -> Int
ldPerm (LMAD num -> [LMADDim num]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD num
lmad2)

-- | Returns true if two 'IxFun's are equivalent.
--
-- Equivalence in this case is defined as having the same number of LMADs, with
-- each pair of LMADs matching in permutation, offsets, strides and rotations.
equivalent :: Eq num => IxFun num -> IxFun num -> Bool
equivalent :: forall num. Eq num => IxFun num -> IxFun num -> Bool
equivalent IxFun num
ixf1 IxFun num
ixf2 =
  NonEmpty (LMAD num) -> Int
forall a. NonEmpty a -> Int
NE.length (IxFun num -> NonEmpty (LMAD num)
forall num. IxFun num -> NonEmpty (LMAD num)
ixfunLMADs IxFun num
ixf1) Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== NonEmpty (LMAD num) -> Int
forall a. NonEmpty a -> Int
NE.length (IxFun num -> NonEmpty (LMAD num)
forall num. IxFun num -> NonEmpty (LMAD num)
ixfunLMADs IxFun num
ixf2)
    Bool -> Bool -> Bool
&& ((LMAD num, LMAD num) -> Bool)
-> NonEmpty (LMAD num, LMAD num) -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (LMAD num, LMAD num) -> Bool
forall {b}. Eq b => (LMAD b, LMAD b) -> Bool
equivalentLMADs (NonEmpty (LMAD num)
-> NonEmpty (LMAD num) -> NonEmpty (LMAD num, LMAD num)
forall a b. NonEmpty a -> NonEmpty b -> NonEmpty (a, b)
NE.zip (IxFun num -> NonEmpty (LMAD num)
forall num. IxFun num -> NonEmpty (LMAD num)
ixfunLMADs IxFun num
ixf1) (IxFun num -> NonEmpty (LMAD num)
forall num. IxFun num -> NonEmpty (LMAD num)
ixfunLMADs IxFun num
ixf2))
  where
    equivalentLMADs :: (LMAD b, LMAD b) -> Bool
equivalentLMADs (LMAD b
lmad1, LMAD b
lmad2) =
      [LMADDim b] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length (LMAD b -> [LMADDim b]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD b
lmad1) Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== [LMADDim b] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length (LMAD b -> [LMADDim b]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD b
lmad2)
        Bool -> Bool -> Bool
&& (LMADDim b -> Int) -> [LMADDim b] -> Permutation
forall a b. (a -> b) -> [a] -> [b]
map LMADDim b -> Int
forall num. LMADDim num -> Int
ldPerm (LMAD b -> [LMADDim b]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD b
lmad1)
          Permutation -> Permutation -> Bool
forall a. Eq a => a -> a -> Bool
== (LMADDim b -> Int) -> [LMADDim b] -> Permutation
forall a b. (a -> b) -> [a] -> [b]
map LMADDim b -> Int
forall num. LMADDim num -> Int
ldPerm (LMAD b -> [LMADDim b]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD b
lmad2)
        Bool -> Bool -> Bool
&& LMAD b -> b
forall num. LMAD num -> num
lmadOffset LMAD b
lmad1
          b -> b -> Bool
forall a. Eq a => a -> a -> Bool
== LMAD b -> b
forall num. LMAD num -> num
lmadOffset LMAD b
lmad2
        Bool -> Bool -> Bool
&& (LMADDim b -> b) -> [LMADDim b] -> [b]
forall a b. (a -> b) -> [a] -> [b]
map LMADDim b -> b
forall num. LMADDim num -> num
ldStride (LMAD b -> [LMADDim b]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD b
lmad1)
          [b] -> [b] -> Bool
forall a. Eq a => a -> a -> Bool
== (LMADDim b -> b) -> [LMADDim b] -> [b]
forall a b. (a -> b) -> [a] -> [b]
map LMADDim b -> b
forall num. LMADDim num -> num
ldStride (LMAD b -> [LMADDim b]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD b
lmad2)

-- | Dynamically determine if two 'LMADDim' are equal.
--
-- True if the dynamic values of their constituents are equal.
dynamicEqualsLMADDim :: Eq num => LMADDim (TPrimExp t num) -> LMADDim (TPrimExp t num) -> TPrimExp Bool num
dynamicEqualsLMADDim :: forall num t.
Eq num =>
LMADDim (TPrimExp t num)
-> LMADDim (TPrimExp t num) -> TPrimExp Bool num
dynamicEqualsLMADDim LMADDim (TPrimExp t num)
dim1 LMADDim (TPrimExp t num)
dim2 =
  LMADDim (TPrimExp t num) -> TPrimExp t num
forall num. LMADDim num -> num
ldStride LMADDim (TPrimExp t num)
dim1 TPrimExp t num -> TPrimExp t num -> TPrimExp Bool num
forall t v. TPrimExp t v -> TPrimExp t v -> TPrimExp Bool v
.==. LMADDim (TPrimExp t num) -> TPrimExp t num
forall num. LMADDim num -> num
ldStride LMADDim (TPrimExp t num)
dim2
    TPrimExp Bool num -> TPrimExp Bool num -> TPrimExp Bool num
forall v. TPrimExp Bool v -> TPrimExp Bool v -> TPrimExp Bool v
.&&. LMADDim (TPrimExp t num) -> TPrimExp t num
forall num. LMADDim num -> num
ldShape LMADDim (TPrimExp t num)
dim1 TPrimExp t num -> TPrimExp t num -> TPrimExp Bool num
forall t v. TPrimExp t v -> TPrimExp t v -> TPrimExp Bool v
.==. LMADDim (TPrimExp t num) -> TPrimExp t num
forall num. LMADDim num -> num
ldShape LMADDim (TPrimExp t num)
dim2
    TPrimExp Bool num -> TPrimExp Bool num -> TPrimExp Bool num
forall v. TPrimExp Bool v -> TPrimExp Bool v -> TPrimExp Bool v
.&&. Bool -> TPrimExp Bool num
forall v. Bool -> TPrimExp Bool v
fromBool (LMADDim (TPrimExp t num) -> Int
forall num. LMADDim num -> Int
ldPerm LMADDim (TPrimExp t num)
dim1 Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== LMADDim (TPrimExp t num) -> Int
forall num. LMADDim num -> Int
ldPerm LMADDim (TPrimExp t num)
dim2)
    TPrimExp Bool num -> TPrimExp Bool num -> TPrimExp Bool num
forall v. TPrimExp Bool v -> TPrimExp Bool v -> TPrimExp Bool v
.&&. Bool -> TPrimExp Bool num
forall v. Bool -> TPrimExp Bool v
fromBool (LMADDim (TPrimExp t num) -> Monotonicity
forall num. LMADDim num -> Monotonicity
ldMon LMADDim (TPrimExp t num)
dim1 Monotonicity -> Monotonicity -> Bool
forall a. Eq a => a -> a -> Bool
== LMADDim (TPrimExp t num) -> Monotonicity
forall num. LMADDim num -> Monotonicity
ldMon LMADDim (TPrimExp t num)
dim2)

-- | Dynamically determine if two 'LMAD' are equal.
--
-- True if offset and constituent 'LMADDim' are equal.
dynamicEqualsLMAD :: Eq num => LMAD (TPrimExp t num) -> LMAD (TPrimExp t num) -> TPrimExp Bool num
dynamicEqualsLMAD :: forall num t.
Eq num =>
LMAD (TPrimExp t num) -> LMAD (TPrimExp t num) -> TPrimExp Bool num
dynamicEqualsLMAD LMAD (TPrimExp t num)
lmad1 LMAD (TPrimExp t num)
lmad2 =
  LMAD (TPrimExp t num) -> TPrimExp t num
forall num. LMAD num -> num
lmadOffset LMAD (TPrimExp t num)
lmad1 TPrimExp t num -> TPrimExp t num -> TPrimExp Bool num
forall t v. TPrimExp t v -> TPrimExp t v -> TPrimExp Bool v
.==. LMAD (TPrimExp t num) -> TPrimExp t num
forall num. LMAD num -> num
lmadOffset LMAD (TPrimExp t num)
lmad2
    TPrimExp Bool num -> TPrimExp Bool num -> TPrimExp Bool num
forall v. TPrimExp Bool v -> TPrimExp Bool v -> TPrimExp Bool v
.&&. ((LMADDim (TPrimExp t num), LMADDim (TPrimExp t num))
 -> TPrimExp Bool num -> TPrimExp Bool num)
-> TPrimExp Bool num
-> [(LMADDim (TPrimExp t num), LMADDim (TPrimExp t num))]
-> TPrimExp Bool num
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr
      (TPrimExp Bool num -> TPrimExp Bool num -> TPrimExp Bool num
forall v. TPrimExp Bool v -> TPrimExp Bool v -> TPrimExp Bool v
(.&&.) (TPrimExp Bool num -> TPrimExp Bool num -> TPrimExp Bool num)
-> ((LMADDim (TPrimExp t num), LMADDim (TPrimExp t num))
    -> TPrimExp Bool num)
-> (LMADDim (TPrimExp t num), LMADDim (TPrimExp t num))
-> TPrimExp Bool num
-> TPrimExp Bool num
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (LMADDim (TPrimExp t num)
 -> LMADDim (TPrimExp t num) -> TPrimExp Bool num)
-> (LMADDim (TPrimExp t num), LMADDim (TPrimExp t num))
-> TPrimExp Bool num
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry LMADDim (TPrimExp t num)
-> LMADDim (TPrimExp t num) -> TPrimExp Bool num
forall num t.
Eq num =>
LMADDim (TPrimExp t num)
-> LMADDim (TPrimExp t num) -> TPrimExp Bool num
dynamicEqualsLMADDim)
      TPrimExp Bool num
forall v. TPrimExp Bool v
true
      ([LMADDim (TPrimExp t num)]
-> [LMADDim (TPrimExp t num)]
-> [(LMADDim (TPrimExp t num), LMADDim (TPrimExp t num))]
forall a b. [a] -> [b] -> [(a, b)]
zip (LMAD (TPrimExp t num) -> [LMADDim (TPrimExp t num)]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD (TPrimExp t num)
lmad1) (LMAD (TPrimExp t num) -> [LMADDim (TPrimExp t num)]
forall num. LMAD num -> [LMADDim num]
lmadDims LMAD (TPrimExp t num)
lmad2))