672 lines
36 KiB
Haskell
672 lines
36 KiB
Haskell
{-
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Tock: a compiler for parallel languages
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Copyright (C) 2007 University of Kent
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This program is free software; you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by the
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Free Software Foundation, either version 2 of the License, or (at your
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option) any later version.
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This program is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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General Public License for more details.
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You should have received a copy of the GNU General Public License along
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with this program. If not, see <http://www.gnu.org/licenses/>.
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-}
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module ArrayUsageCheck (checkArrayUsage, FlattenedExp(..), makeEquations, usageCheckPass, VarMap) where
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import Control.Monad.Error
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import Control.Monad.State
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import Data.Array.IArray
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import Data.List
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import qualified Data.Map as Map
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import Data.Maybe
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import qualified Data.Set as Set
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import qualified AST as A
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import CompState
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import Errors
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import FlowGraph
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import Metadata
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import Omega
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import Pass
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import ShowCode
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import Types
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import UsageCheck
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import Utils
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usageCheckPass :: Pass
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usageCheckPass t = do g' <- buildFlowGraph labelFunctions t
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g <- case g' of
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Left err -> die err
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Right g -> return g
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checkArrayUsage g
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return t
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checkArrayUsage :: forall m. (Die m, CSM m) => FlowGraph m (Maybe Decl, Vars) -> m ()
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checkArrayUsage graph = sequence_ $ checkPar checkArrayUsage' graph
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where
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checkArrayUsage' :: (Meta, ParItems (Maybe Decl, Vars)) -> m ()
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checkArrayUsage' (m,p) = mapM_ (checkIndexes m) $ Map.toList $
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groupArrayIndexes $ transformParItems snd p
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-- Returns (array name, list of written-to indexes, list of read-from indexes)
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groupArrayIndexes :: ParItems Vars -> Map.Map String (ParItems ([A.Expression], [A.Expression]))
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groupArrayIndexes vs = filterByKey $ transformParItems (uncurry (zipMap join) . (transformPair (makeList . writtenVars) (makeList . readVars)) . mkPair) vs
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where
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join :: Maybe [a] -> Maybe [a] -> Maybe ([a],[a])
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join x y = Just (fromMaybe [] x, fromMaybe [] y)
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flattenParItems :: ParItems a -> [a]
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flattenParItems (SeqItems xs) = xs
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flattenParItems (ParItems ps) = concatMap flattenParItems ps
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flattenParItems (RepParItem _ p) = flattenParItems p
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makeList :: Set.Set Var -> Map.Map String [A.Expression]
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makeList = Set.fold (maybe id (uncurry $ Map.insertWith (++)) . getArrayIndex) Map.empty
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filterByKey :: ParItems (Map.Map String ([A.Expression], [A.Expression])) -> Map.Map String (ParItems ([A.Expression], [A.Expression]))
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filterByKey p = Map.fromList $ map (\k -> (k, transformParItems (Map.findWithDefault ([],[]) k) p)) (concatMap Map.keys $ flattenParItems p)
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-- TODO this is quite hacky:
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getArrayIndex :: Var -> Maybe (String, [A.Expression])
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getArrayIndex (Var (A.SubscriptedVariable _ (A.Subscript _ e) (A.Variable _ n)))
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= Just (A.nameName n, [e])
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getArrayIndex _ = Nothing
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checkIndexes :: Meta -> (String,ParItems ([A.Expression],[A.Expression])) -> m ()
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checkIndexes m (arrName, indexes)
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= do userArrName <- getRealName (A.Name undefined undefined arrName)
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arrType <- typeOfName (A.Name undefined undefined arrName)
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(arrLength,checkable) <- case arrType of
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A.Array (A.Dimension d:_) _ -> return (d,True)
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A.Array (A.UnknownDimension:_) _ -> return (undefined, False)
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_ -> dieP m $ "Cannot usage check array \"" ++ userArrName ++ "\"; found to be of type: " ++ show arrType
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if not checkable
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then return ()
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else case makeEquations indexes (makeConstant emptyMeta arrLength) of
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Left err -> dieP m $ "Could not work with array indexes for array \"" ++ userArrName ++ "\": " ++ err
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Right [] -> return () -- No problems to work with
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Right problems ->
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case mapMaybe solve problems of
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-- No solutions; no worries!
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[] -> return ()
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(((lx,ly),varMapping,vm):_) ->
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do sol <- formatSolution varMapping (getCounterEqs vm)
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cx <- showCode lx
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cy <- showCode ly
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dieP m $ "Indexes of array \"" ++ userArrName ++ "\""
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++ "(\"" ++ cx ++ "\" and \"" ++ cy ++ "\") could overlap"
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++ if sol /= "" then " when: " ++ sol else ""
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solve :: (labels,vm,(EqualityProblem,InequalityProblem)) -> Maybe (labels,vm,VariableMapping)
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solve (ls,vm,(eq,ineq)) = case solveProblem eq ineq of
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Nothing -> Nothing
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Just vm' -> Just (ls,vm,vm')
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formatSolution :: VarMap -> Map.Map CoeffIndex Integer -> m String
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formatSolution varToIndex indexToConst = do names <- mapM valOfVar $ Map.assocs varToIndex
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return $ concat $ intersperse " , " $ catMaybes names
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where
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valOfVar (varExp,k) = case Map.lookup k indexToConst of
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Nothing -> return Nothing
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Just val -> do varExp' <- showFlattenedExp varExp
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return $ Just $ varExp' ++ " = " ++ show val
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-- TODO this is surely defined elsewhere already?
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getRealName :: A.Name -> m String
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getRealName n = lookupName n >>* A.ndOrigName
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showFlattenedExp :: FlattenedExp -> m String
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showFlattenedExp (Const n) = return $ show n
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showFlattenedExp (Scale n ((A.Variable _ vn),vi))
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= do vn' <- getRealName vn >>* (\s -> if vi == 0 then s else s ++ replicate vi '\'' )
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case n of
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1 -> return vn'
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-1 -> return $ "-" ++ vn'
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_ -> return $ (show n) ++ "*" ++ vn'
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showFlattenedExp (Modulo top bottom)
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= do top' <- showFlattenedExpSet top
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bottom' <- showFlattenedExpSet bottom
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case onlyConst (Set.toList bottom) of
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Just _ -> return $ "(" ++ top' ++ " / " ++ bottom' ++ ")"
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Nothing -> return $ "((" ++ top' ++ " REM " ++ bottom' ++ ") - " ++ top' ++ ")"
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showFlattenedExp (Divide top bottom)
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= do top' <- showFlattenedExpSet top
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bottom' <- showFlattenedExpSet bottom
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return $ "(" ++ top' ++ " / " ++ bottom' ++ ")"
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showFlattenedExpSet :: Set.Set FlattenedExp -> m String
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showFlattenedExpSet s = liftM concat $ sequence $ intersperse (return " + ") $ map showFlattenedExp $ Set.toList s
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-- | A type for inside makeEquations:
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data FlattenedExp
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= Const Integer
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| Scale Integer (A.Variable, Int)
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| Modulo (Set.Set FlattenedExp) (Set.Set FlattenedExp)
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| Divide (Set.Set FlattenedExp) (Set.Set FlattenedExp)
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--TODO change the A.Variable to Var, and automatically derive Eq and Ord
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instance Eq FlattenedExp where
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a == b = EQ == compare a b
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instance Ord FlattenedExp where
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compare (Const _) (Const _) = EQ
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compare (Const _) _ = LT
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compare _ (Const _) = GT
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compare (Scale _ (lv,li)) (Scale _ (rv,ri)) = combineCompare [customVarCompare lv rv, compare li ri]
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compare (Scale {}) _ = LT
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compare _ (Scale {}) = GT
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compare (Modulo ltop lbottom) (Modulo rtop rbottom)
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= combineCompare [compare ltop rtop, compare lbottom rbottom]
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compare (Modulo {}) _ = LT
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compare _ (Modulo {}) = GT
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compare (Divide ltop lbottom) (Divide rtop rbottom)
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= combineCompare [compare ltop rtop, compare lbottom rbottom]
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onlyConst :: [FlattenedExp] -> Maybe Integer
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onlyConst [] = Just 0
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onlyConst ((Const n):es) = liftM2 (+) (return n) $ onlyConst es
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onlyConst _ = Nothing
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-- | A data type representing an array access. Each triple is (index, extra-equalities, extra-inequalities).
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-- A Single item can be paired with every other access.
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-- Each item of a Group cannot be paired with each other, but can be paired with each other access.
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-- With a Replicated, each item in the left branch can be paired with each item in the right branch.
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-- Each item in the left branch can be paired with each other, and each item in the left branch can
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-- be paired with all other items.
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data ArrayAccess label =
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Group [(label, ArrayAccessType, (EqualityConstraintEquation, EqualityProblem, InequalityProblem))]
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| Replicated [ArrayAccess label] [ArrayAccess label]
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data ArrayAccessType = AAWrite | AARead
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parItemToArrayAccessM :: Monad m => ([(A.Replicator, Bool)] -> a -> m [(label, ArrayAccessType, (EqualityConstraintEquation, EqualityProblem, InequalityProblem))]) -> ParItems a -> m [ArrayAccess label]
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parItemToArrayAccessM f (SeqItems xs) = sequence [concatMapM (f []) xs >>* Group]
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parItemToArrayAccessM f (ParItems ps) = concatMapM (parItemToArrayAccessM f) ps
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parItemToArrayAccessM f (RepParItem rep p)
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= do normal <- parItemToArrayAccessM (\reps -> f ((rep,False):reps)) p
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mirror <- parItemToArrayAccessM (\reps -> f ((rep,True):reps)) p
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return [Replicated normal mirror]
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makeExpSet :: [FlattenedExp] -> Either String (Set.Set FlattenedExp)
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makeExpSet = foldM makeExpSet' Set.empty
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where
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makeExpSet' :: Set.Set FlattenedExp -> FlattenedExp -> Either String (Set.Set FlattenedExp)
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makeExpSet' accum (Const n) = return $ insert (addConst n) (Const n) accum
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makeExpSet' accum (Scale n v) = return $ insert (addScale n v) (Scale n v) accum
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makeExpSet' accum m@(Modulo {}) | Set.member m accum = throwError "Cannot have repeated REM items in an expression"
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| otherwise = return $ Set.insert m accum
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makeExpSet' accum d@(Divide {}) | Set.member d accum = throwError "Cannot have repeated (/) items in an expression"
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| otherwise = return $ Set.insert d accum
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insert :: (FlattenedExp -> Set.Set FlattenedExp -> Maybe (Set.Set FlattenedExp)) -> FlattenedExp -> Set.Set FlattenedExp -> Set.Set FlattenedExp
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insert f e s = case Set.fold insert' (Set.empty,False) s of
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(s',True) -> s'
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_ -> Set.insert e s
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where
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insert' :: FlattenedExp -> (Set.Set FlattenedExp, Bool) -> (Set.Set FlattenedExp, Bool)
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insert' e (s,b) = case f e s of
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Just s' -> (s', True)
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Nothing -> (Set.insert e s, False)
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addConst :: Integer -> FlattenedExp -> Set.Set FlattenedExp -> Maybe (Set.Set FlattenedExp)
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addConst x (Const n) s = Just $ Set.insert (Const (n + x)) s
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addConst _ _ _ = Nothing
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addScale :: Integer -> (A.Variable,Int) -> FlattenedExp -> Set.Set FlattenedExp -> Maybe (Set.Set FlattenedExp)
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addScale x (lv,li) (Scale n (rv,ri)) s
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| (EQ == customVarCompare lv rv) && (li == ri) = Just $ Set.insert (Scale (x + n) (rv,ri)) s
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| otherwise = Nothing
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addScale _ _ _ _ = Nothing
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type VarMap = Map.Map FlattenedExp Int
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-- | Given a list of (written,read) expressions, an expression representing the upper array bound, returns either an error
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-- (because the expressions can't be handled, typically) or a set of equalities, inequalities and mapping from
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-- (unique, munged) variable name to variable-index in the equations.
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--
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-- The general strategy is as follows.
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-- For every array index (here termed an "access"), we transform it into
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-- the usual [FlattenedExp] using the flatten function. Then we also transform
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-- any access that is in the mirror-side of a Replicated item into its mirrored version
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-- where each i is changed into i'. This is done by using vi=(variable "i",0)
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-- (in Scale _ vi) for the plain (normal) version, and vi=(variable "i",1)
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-- for the prime (mirror) version.
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--
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-- Then the equations have bounds added. The rules are fairly simple; if
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-- any of the transformed EqualityConstraintEquation representing an access
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-- have a non-zero i (and/or i'), the bound for that variable is added.
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-- So for example, an expression like "i = i' + 3" would have the bounds for
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-- both i and i' added (which would be near-identical, e.g. 1 <= i <= 6 and
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-- 1 <= i' <= 6).
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--
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-- The remainder of the work (correctly pairing equations) is done by
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-- squareAndPair.
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--
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-- TODO probably want to take this into the PassM monad at some point, to use the Meta in the error message
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-- TODO allow "background knowledge" in the form of other equalities and inequalities
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makeEquations :: ParItems ([A.Expression],[A.Expression]) -> A.Expression ->
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Either String [((A.Expression, A.Expression), VarMap, (EqualityProblem, InequalityProblem))]
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makeEquations accesses bound
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= do bound' <- flatten bound
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((v,h,repVarIndexes),s) <- (flip runStateT) Map.empty $
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do (accesses',repVars) <- flip runStateT [] $ parItemToArrayAccessM mkEq accesses
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high <- makeEquation bound (error "Type is irrelevant for upper bound") bound'
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>>= getSingleAccessItem "Multiple possible upper bounds not supported"
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return (accesses', high, nub repVars)
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return $ squareAndPair repVarIndexes s v (amap (const 0) h, addConstant (-1) h)
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where
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setIndexVar :: A.Variable -> Int -> [FlattenedExp] -> [FlattenedExp]
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setIndexVar tv ti es = case mapAccumL (setIndexVar' tv ti) False es of
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(_, es') -> es'
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setIndexVar' :: A.Variable -> Int -> Bool -> FlattenedExp -> (Bool,FlattenedExp)
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setIndexVar' tv ti b s@(Scale n (v,_))
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| EQ == customVarCompare tv v = (True,Scale n (v,ti))
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| otherwise = (b,s)
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setIndexVar' _ _ b e = (b,e)
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makeEquationWithPossibleRepBounds :: [(A.Variable, EqualityConstraintEquation, EqualityConstraintEquation)] ->
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ArrayAccess label -> StateT (VarMap) (Either String) (ArrayAccess label)
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makeEquationWithPossibleRepBounds [] item = return item
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makeEquationWithPossibleRepBounds ((v,lower,upper):vars) item
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-- We fold over the variables, altering the items one at a time via mapM:
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= do item' <- makeEquationWithPossibleRepBounds vars item
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flip addPossibleRepBound' (v,0,lower,upper) item' >>=
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flip addPossibleRepBound' (v,1,lower,upper)
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addPossibleRepBound' :: ArrayAccess label ->
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(A.Variable, Int, EqualityConstraintEquation, EqualityConstraintEquation) ->
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StateT (VarMap) (Either String) (ArrayAccess label)
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addPossibleRepBound' (Group accesses) v = sequence [addPossibleRepBound acc v >>* (\acc' -> (l,t,acc')) | (l,t,acc) <- accesses ] >>* Group
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addPossibleRepBound' (Replicated acc0 acc1) v
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= do acc0' <- mapM (flip addPossibleRepBound' v) acc0
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acc1' <- mapM (flip addPossibleRepBound' v) acc1
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return $ Replicated acc0' acc1'
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addPossibleRepBound :: (EqualityConstraintEquation, EqualityProblem, InequalityProblem) ->
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(A.Variable, Int, EqualityConstraintEquation, EqualityConstraintEquation) ->
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StateT (VarMap) (Either String) (EqualityConstraintEquation, EqualityProblem, InequalityProblem)
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addPossibleRepBound (item,eq,ineq) (var,index,lower,upper)
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= do index <- varIndex (Scale 1 vi)
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let boundEqs = if arrayLookupWithDefault 0 item index /= 0
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then [add (index,1) $ amap negate lower,add (index,-1) upper]
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else []
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return (item,eq,ineq ++ boundEqs)
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where
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vi = (var,index)
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add :: (Int,Integer) -> Array Int Integer -> Array Int Integer
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add (ind,val) a = (makeSize (newMin, newMax) 0 a) // [(ind, (arrayLookupWithDefault 0 a ind) + val)]
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where
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newMin = minimum [fst $ bounds a, ind]
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newMax = maximum [snd $ bounds a, ind]
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mkEq :: [(A.Replicator, Bool)] -> ([A.Expression], [A.Expression]) -> StateT [(CoeffIndex, CoeffIndex)] (StateT VarMap (Either String)) [(A.Expression, ArrayAccessType, (EqualityConstraintEquation, EqualityProblem, InequalityProblem))]
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mkEq reps (ws,rs) = do repVarEqs <- mapM (liftF makeRepVarEq) reps
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concatMapM (mkEq' repVarEqs) (ws' ++ rs')
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where
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ws' = zip (repeat AAWrite) ws
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rs' = zip (repeat AARead) rs
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makeRepVarEq :: (A.Replicator, Bool) -> StateT VarMap (Either String) (A.Variable, EqualityConstraintEquation, EqualityConstraintEquation)
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makeRepVarEq (A.For m varName from for, _)
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= do from' <- lift (flatten from) >>= makeEquation from (error "Type is irrelevant for replication start")
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>>= getSingleAccessItem "Modulo or Divide not allowed in replication start"
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for' <- lift (flatten for) >>= makeEquation for (error "Type is irrelevant for replication count")
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>>= getSingleAccessItem "Modulo or Divide not allowed in replication count"
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return (A.Variable m varName, from', for')
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mkEq' :: [(A.Variable, EqualityConstraintEquation, EqualityConstraintEquation)] -> (ArrayAccessType, A.Expression) -> StateT [(CoeffIndex,CoeffIndex)] (StateT VarMap (Either String)) [(A.Expression, ArrayAccessType, (EqualityConstraintEquation, EqualityProblem, InequalityProblem))]
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mkEq' repVarEqs (aat, e)
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= do f <- lift . lift $ flatten e
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f' <- foldM mirrorFlaggedVars f reps
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g <- lift $ makeEquationWithPossibleRepBounds repVarEqs =<< makeEquation e aat f'
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case g of
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Group g' -> return g'
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_ -> throwError "Replicated group found unexpectedly"
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mirrorFlaggedVars :: [FlattenedExp] -> (A.Replicator,Bool) -> StateT [(CoeffIndex,CoeffIndex)] (StateT VarMap (Either String)) [FlattenedExp]
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mirrorFlaggedVars exp (_,False) = return exp
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mirrorFlaggedVars exp (A.For m varName from for, True)
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= do varIndexes <- lift $ seqPair (varIndex (Scale 1 (var,0)), varIndex (Scale 1 (var,1)))
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modify (varIndexes :)
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return $ setIndexVar var 1 exp
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where
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var = A.Variable m varName
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-- Note that in all these functions, the divisor should always be positive!
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-- Takes an expression, and transforms it into an expression like:
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-- (e_0 + e_1 + e_2) / d
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-- where d is a constant (non-zero!) integer, and each e_k
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-- is either a const, a var, const * var, or (const * var) % const [TODO].
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-- If the expression cannot be transformed into such a format, an error is returned
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flatten :: A.Expression -> Either String [FlattenedExp]
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flatten (A.Literal _ _ (A.IntLiteral _ n)) = return [Const (read n)]
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flatten (A.ExprVariable _ v) = return [Scale 1 (v,0)]
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flatten (A.Dyadic m op lhs rhs) | op == A.Add = combine' (flatten lhs) (flatten rhs)
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| op == A.Subtr = combine' (flatten lhs) (liftM (scale (-1)) $ flatten rhs)
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| op == A.Mul = multiplyOut' (flatten lhs) (flatten rhs)
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| op == A.Rem = liftM2L Modulo (flatten lhs) (flatten rhs)
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| op == A.Div = liftM2L Divide (flatten lhs) (flatten rhs)
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| otherwise = throwError ("Unhandleable operator found in expression: " ++ show op)
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where
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-- liftM2L :: (Ord a, Ord b, Monad m) => (Set.Set a -> Set.Set b -> c) -> m [a] -> m [b] -> m [c]
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liftM2L f x y = liftM singleton $ liftM2 f (x >>= makeExpSet) (y >>= makeExpSet)
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--TODO we need to handle lots more different expression types in future.
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multiplyOut' :: Either String [FlattenedExp] -> Either String [FlattenedExp] -> Either String [FlattenedExp]
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multiplyOut' x y = do {x' <- x; y' <- y; multiplyOut x' y'}
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multiplyOut :: [FlattenedExp] -> [FlattenedExp] -> Either String [FlattenedExp]
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multiplyOut lhs rhs = mapM (uncurry mult) pairs
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where
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pairs = product2 (lhs,rhs)
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mult :: FlattenedExp -> FlattenedExp -> Either String FlattenedExp
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mult (Const x) (Const y) = return $ Const (x*y)
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mult (Scale n v) (Const x) = return $ Scale (n*x) v
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mult (Const x) (Scale n v) = return $ Scale (n*x) v
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mult (Scale _ v) (Scale _ v')
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= throwError $ "Cannot deal with non-linear equations; during flattening found: "
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++ show v ++ " * " ++ show v'
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-- TODO test and handle modulo and divide here
|
|
|
|
-- | Scales a flattened expression by the given integer scaling.
|
|
scale :: Integer -> [FlattenedExp] -> [FlattenedExp]
|
|
scale sc = map scale'
|
|
where
|
|
scale' (Const n) = Const (n * sc)
|
|
scale' (Scale n v) = Scale (n * sc) v
|
|
-- TODO test the other cases then write them
|
|
|
|
-- | An easy way of applying combine to two monadic returns
|
|
combine' :: Either String [FlattenedExp] -> Either String [FlattenedExp] -> Either String [FlattenedExp]
|
|
combine' = liftM2 combine
|
|
|
|
-- | Combines (adds) two flattened expressions.
|
|
combine :: [FlattenedExp] -> [FlattenedExp] -> [FlattenedExp]
|
|
combine = (++)
|
|
flatten other = throwError ("Unhandleable item found in expression: " ++ show other)
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|
|
|
-- | The "square" refers to making all equations the length of the longest
|
|
-- one, and the pair refers to pairing each in a list of array accesses (e.g.
|
|
-- [0, 5, i + 2]) into all possible pairings ([0 == 5, 0 == i + 2, 5 == i + 2])
|
|
--
|
|
-- There are two complications to this function.
|
|
--
|
|
-- Firstly, the array accesses are not actually given in a plain list, but
|
|
-- instead a list of lists. This is because for things like modulo, there are
|
|
-- groups of possible accesses that should not be paired against each other.
|
|
-- For example, you may have something like [0,x,-x] as the three possible
|
|
-- options for a modulo. You want to pair the accesses against other accesses
|
|
-- (e.g. y + 6), but not against each other. So the arguments are passed in
|
|
-- in groups: [[0,x,-x],[y + 6]] and groups are paired against each other,
|
|
-- but not against themselves. This all refers to the third argument to the
|
|
-- function. Each item is actually a triple of (item, equalities, inequalities)
|
|
-- because the modulo aspect adds additional constraints.
|
|
--
|
|
-- The other complication comes from replicated variables.
|
|
-- The first argument is a list of (plain,prime) coefficient indexes
|
|
-- that effectively labels the indexes related to replicated variables.
|
|
-- squareAndPair does two things with this information:
|
|
-- 1. It discards all equations that feature only the prime version of
|
|
-- a variable. You might have passed in the accesses as [[i],[i'],[3]].
|
|
-- (Altering the grouping would not be able to solve this particular problem)
|
|
-- The pairings generated would be [i == i', i == 3, i' == 3]. But the
|
|
-- last two are in effect identical. Therefore we drop the i' prime
|
|
-- version, because it has i' but not i. In contrast, the first item
|
|
-- (i == i') is retained because it features both i and i'.
|
|
-- 2. For every equation that features both i and i', it adds
|
|
-- the inequality "i <= i' - 1". Because all possible combinations of
|
|
-- accesses are examined, in the case of [i,i + 1,i', i' + 1], the pairing
|
|
-- will produce both "i = i' + 1" and "i + 1 = i'" so there is no need
|
|
-- to vary the inequality itself.
|
|
squareAndPair ::
|
|
[(CoeffIndex, CoeffIndex)] ->
|
|
VarMap ->
|
|
[ArrayAccess label] ->
|
|
(EqualityConstraintEquation, EqualityConstraintEquation) ->
|
|
[((label, label), VarMap, (EqualityProblem, InequalityProblem))]
|
|
squareAndPair repVars s v lh
|
|
= [(labels, s,squareEquations (eq,ineq ++ concat (applyAll (eq,ineq) (map addExtra repVars))))
|
|
| (labels, eq,ineq) <- pairEqsAndBounds v lh
|
|
,and (map (primeImpliesPlain (eq,ineq)) repVars)
|
|
]
|
|
where
|
|
itemPresent :: CoeffIndex -> [Array CoeffIndex Integer] -> Bool
|
|
itemPresent x = any (\a -> arrayLookupWithDefault 0 a x /= 0)
|
|
|
|
primeImpliesPlain :: (EqualityProblem,InequalityProblem) -> (CoeffIndex,CoeffIndex) -> Bool
|
|
primeImpliesPlain (eq,ineq) (plain,prime) =
|
|
if itemPresent prime (eq ++ ineq)
|
|
-- There are primes, check all the plains are present:
|
|
then itemPresent plain (eq ++ ineq)
|
|
-- No prime, therefore fine:
|
|
else True
|
|
|
|
addExtra :: (CoeffIndex, CoeffIndex) -> (EqualityProblem,InequalityProblem) -> InequalityProblem
|
|
addExtra (plain,prime) (eq, ineq)
|
|
| itemPresent plain (eq ++ ineq) && itemPresent prime (eq ++ ineq) = extraIneq
|
|
| otherwise = []
|
|
where
|
|
extraIneq :: InequalityProblem
|
|
-- prime >= plain + 1 (prime - plain - 1 >= 0)
|
|
extraIneq = [simpleArray [(prime,1), (plain,-1), (0, -1)]]
|
|
|
|
getSingleAccessItem :: MonadTrans m => String -> ArrayAccess label -> m (Either String) EqualityConstraintEquation
|
|
getSingleAccessItem _ (Group [(_,_,(acc,_,_))]) = lift $ return acc
|
|
getSingleAccessItem err _ = lift $ throwError err
|
|
|
|
-- | Odd helper function for getting/asserting the first item of a triple from a singleton list inside a monad transformer (!)
|
|
getSingleItem :: MonadTrans m => String -> [(a,b,c)] -> m (Either String) a
|
|
getSingleItem _ [(item,_,_)] = lift $ return item
|
|
getSingleItem err _ = lift $ throwError err
|
|
|
|
-- | Finds the index associated with a particular variable; either by finding an existing index
|
|
-- or allocating a new one.
|
|
varIndex :: FlattenedExp -> StateT (VarMap) (Either String) Int
|
|
varIndex (Scale _ (var@(A.Variable _ (A.Name _ _ varName)),vi))
|
|
= do st <- get
|
|
let (st',ind) = case Map.lookup (Scale 1 (var,vi)) st of
|
|
Just val -> (st,val)
|
|
Nothing -> let newId = (1 + (maximum $ 0 : Map.elems st)) in
|
|
(Map.insert (Scale 1 (var,vi)) newId st, newId)
|
|
put st'
|
|
return ind
|
|
varIndex mod@(Modulo top bottom)
|
|
= do st <- get
|
|
let (st',ind) = case Map.lookup mod st of
|
|
Just val -> (st,val)
|
|
Nothing -> let newId = (1 + (maximum $ 0 : Map.elems st)) in
|
|
(Map.insert mod newId st, newId)
|
|
put st'
|
|
return ind
|
|
|
|
-- | Pairs all possible combinations of the list of equations.
|
|
pairEqsAndBounds :: [ArrayAccess label] -> (EqualityConstraintEquation, EqualityConstraintEquation) -> [((label,label),EqualityProblem, InequalityProblem)]
|
|
pairEqsAndBounds items bounds = (concatMap (uncurry pairEqs) . allPairs) items ++ concatMap pairRep items
|
|
where
|
|
pairEqs :: ArrayAccess label
|
|
-> ArrayAccess label
|
|
-> [((label,label),EqualityProblem, InequalityProblem)]
|
|
pairEqs (Group accs) (Group accs') = mapMaybe (uncurry pairEqs'') $ product2 (accs,accs')
|
|
pairEqs (Replicated rA rB) lacc
|
|
= concatMap (pairEqs lacc) rA
|
|
pairEqs lacc (Replicated rA rB)
|
|
= concatMap (pairEqs lacc) rA
|
|
|
|
-- Used to pair the items of a single instance of PAR replication with each other
|
|
pairRep :: ArrayAccess label -> [((label,label),EqualityProblem, InequalityProblem)]
|
|
pairRep (Replicated rA rB) = concatMap (uncurry pairEqs) (product2 (rA,rB))
|
|
++ concatMap (uncurry pairEqs) (allPairs rA)
|
|
pairRep _ = []
|
|
|
|
pairEqs'' :: (label, ArrayAccessType,(EqualityConstraintEquation, EqualityProblem, InequalityProblem))
|
|
-> (label, ArrayAccessType,(EqualityConstraintEquation, EqualityProblem, InequalityProblem))
|
|
-> Maybe ((label,label), EqualityProblem, InequalityProblem)
|
|
pairEqs'' (lx,x,x') (ly,y,y') = case pairEqs' (x,x') (y,y') of
|
|
Just (eq,ineq) -> Just ((lx,ly),eq,ineq)
|
|
Nothing -> Nothing
|
|
|
|
pairEqs' :: (ArrayAccessType,(EqualityConstraintEquation, EqualityProblem, InequalityProblem))
|
|
-> (ArrayAccessType,(EqualityConstraintEquation, EqualityProblem, InequalityProblem))
|
|
-> Maybe (EqualityProblem, InequalityProblem)
|
|
pairEqs' (AARead,_) (AARead,_) = Nothing
|
|
pairEqs' (_,(ex,eqX,ineqX)) (_,(ey,eqY,ineqY)) = Just ([arrayZipWith' 0 (-) ex ey] ++ eqX ++ eqY, ineqX ++ ineqY ++ getIneqs bounds [ex,ey])
|
|
|
|
-- | Given a (low,high) bound (typically: array dimensions), and a list of equations ex,
|
|
-- forms the possible inequalities:
|
|
-- * ex >= low
|
|
-- * ex <= high
|
|
getIneqs :: (EqualityConstraintEquation, EqualityConstraintEquation) -> [EqualityConstraintEquation] -> [InequalityConstraintEquation]
|
|
getIneqs (low, high) = concatMap getLH
|
|
where
|
|
-- eq >= low => eq - low >= 0
|
|
-- eq <= high => high - eq >= 0
|
|
|
|
getLH :: EqualityConstraintEquation -> [InequalityConstraintEquation]
|
|
getLH eq = [eq `addEq` (amap negate low),high `addEq` amap negate eq]
|
|
addEq :: EqualityConstraintEquation -> EqualityConstraintEquation -> EqualityConstraintEquation
|
|
addEq = arrayZipWith' 0 (+)
|
|
|
|
-- | Given an expression, forms equations (and accompanying additional equation-sets) and returns it
|
|
makeEquation :: label -> ArrayAccessType -> [FlattenedExp] -> StateT VarMap (Either String) (ArrayAccess label)
|
|
makeEquation l t summedItems
|
|
= do eqs <- process summedItems
|
|
let eqs' = map (transformTriple mapToArray (map mapToArray) (map mapToArray)) eqs :: [(EqualityConstraintEquation, EqualityProblem, InequalityProblem)]
|
|
return $ case eqs' of
|
|
-- [acc] -> Single (l,t,acc)
|
|
_ -> Group [(l,t,e) | e <- eqs']
|
|
where
|
|
process :: [FlattenedExp] -> StateT VarMap (Either String) [(Map.Map Int Integer,[Map.Map Int Integer], [Map.Map Int Integer])]
|
|
process = foldM makeEquation' empty
|
|
|
|
makeEquation' :: [(Map.Map Int Integer,[Map.Map Int Integer], [Map.Map Int Integer])] -> FlattenedExp -> StateT (VarMap) (Either String) [(Map.Map Int Integer,[Map.Map Int Integer], [Map.Map Int Integer])]
|
|
makeEquation' m (Const n) = return $ add (0,n) m
|
|
makeEquation' m sc@(Scale n v) = varIndex sc >>* (\ind -> add (ind, n) m)
|
|
makeEquation' m mod@(Modulo top bottom)
|
|
= do top' <- process $ Set.toList top
|
|
top'' <- getSingleItem "Modulo or divide not allowed in the numerator of Modulo" top'
|
|
bottom' <- process $ Set.toList bottom
|
|
topIndex <- varIndex mod
|
|
case onlyConst (Set.toList bottom) of
|
|
Just bottomConst ->
|
|
let add_x_plus_my = zipMap plus top'' . zipMap plus (Map.fromList [(topIndex,bottomConst)]) in
|
|
return $
|
|
-- The zero option (x = 0, x REM y = 0):
|
|
( map (transformTriple id (++ [top'']) id) m)
|
|
++
|
|
-- The top-is-positive option:
|
|
( map (transformTriple add_x_plus_my id (++
|
|
-- x >= 1
|
|
[zipMap plus (Map.fromList [(0,-1)]) top''
|
|
-- m <= 0
|
|
,Map.fromList [(topIndex,-1)]
|
|
-- x + my + 1 - |y| <= 0
|
|
,Map.map negate $ add_x_plus_my $ Map.fromList [(0,1 - bottomConst)]
|
|
-- x + my >= 0
|
|
,add_x_plus_my $ Map.empty])
|
|
) m) ++
|
|
-- The top-is-negative option:
|
|
( map (transformTriple add_x_plus_my id (++
|
|
-- x <= -1
|
|
[add' (0,-1) $ Map.map negate top''
|
|
-- m >= 0
|
|
,Map.fromList [(topIndex,1)]
|
|
-- x + my - 1 + |y| >= 0
|
|
,add_x_plus_my $ Map.fromList [(0,bottomConst - 1)]
|
|
-- x + my <= 0
|
|
,Map.map negate $ add_x_plus_my Map.empty])
|
|
) m)
|
|
_ ->
|
|
do bottom'' <- getSingleItem "Modulo or divide not allowed in the divisor of Modulo" bottom'
|
|
return $
|
|
-- The zero option (x = 0, x REM y = 0):
|
|
(map (transformTriple id (++ [top'']) id) m)
|
|
-- The rest:
|
|
++ twinItems True True (top'', topIndex) bottom''
|
|
++ twinItems True False (top'', topIndex) bottom''
|
|
++ twinItems False True (top'', topIndex) bottom''
|
|
++ twinItems False False (top'', topIndex) bottom''
|
|
where
|
|
-- Each pair for modulo (variable divisor) depending on signs of x and y (in x REM y):
|
|
twinItems :: Bool -> Bool -> (Map.Map Int Integer,Int) -> Map.Map Int Integer ->
|
|
[(Map.Map Int Integer,[Map.Map Int Integer], [Map.Map Int Integer])]
|
|
twinItems xPos yPos (top,topIndex) bottom
|
|
= (map (transformTriple (zipMap plus top) id
|
|
(++ [xEquation]
|
|
++ [xLowerBound False]
|
|
++ [xUpperBound False])) m)
|
|
++ (map (transformTriple (zipMap plus top . add' (topIndex,1)) id
|
|
(++ [xEquation]
|
|
++ [xLowerBound True]
|
|
++ [xUpperBound True]
|
|
-- We want to add the bounds for a and y as follows:
|
|
-- xPos yPos | Equation
|
|
-- T T | -y - a >= 0
|
|
-- T F | y - a >= 0
|
|
-- F T | a - y >= 0
|
|
-- F F | a + y >= 0
|
|
-- Therefore the sign of a is (not xPos), the sign of y is (not yPos)
|
|
++ [add' (topIndex,if xPos then -1 else 1) (signEq (not yPos) bottom)])) m)
|
|
where
|
|
-- x >= 1 or x <= -1 (rearranged: -1 + x >= 0 or -1 - x >= 0)
|
|
xEquation = add' (0,-1) (signEq xPos top)
|
|
-- We include (x [+ a] >= 0 or x [+ a] <= 0) even though they are redundant in some cases (addA = False):
|
|
xLowerBound addA = signEq xPos $ (if addA then add' (topIndex,1) else id) top
|
|
-- We want to add the bounds as follows:
|
|
-- xPos yPos | Equation
|
|
-- T T | y - 1 - x - a >= 0
|
|
-- T F | -y - 1 - x - a >= 0
|
|
-- F T | x + a - 1 + y >= 0
|
|
-- F F | x + a - y - 1 >= 0
|
|
-- Therefore the sign of y in the equation is yPos, the sign of x and a is (not xPos)
|
|
xUpperBound addA = add' (0,-1) $ zipMap plus (signEq (not xPos) ((if addA then add' (topIndex,1) else id) top)) (signEq yPos bottom)
|
|
|
|
signEq sign eq = if sign then eq else Map.map negate eq
|
|
|
|
makeEquation' m (Divide top bottom) = throwError "TODO Divide"
|
|
|
|
empty :: [(Map.Map Int Integer,[Map.Map Int Integer], [Map.Map Int Integer])]
|
|
empty = [(Map.empty,[],[])]
|
|
|
|
plus :: Num n => Maybe n -> Maybe n -> Maybe n
|
|
plus x y = Just $ (fromMaybe 0 x) + (fromMaybe 0 y)
|
|
|
|
add' :: (Int,Integer) -> Map.Map Int Integer -> Map.Map Int Integer
|
|
add' (m,n) = Map.insertWith (+) m n
|
|
|
|
add :: (Int,Integer) -> [(Map.Map Int Integer,a,b)] -> [(Map.Map Int Integer,a,b)]
|
|
add (m,n) = map $ transformTriple (Map.insertWith (+) m n) id id
|
|
|
|
-- | Converts a map to an array. Any missing elements in the middle of the bounds are given the value zero.
|
|
-- Could probably be moved to Utils
|
|
mapToArray :: (IArray a v, Num v, Num k, Ord k, Ix k) => Map.Map k v -> a k v
|
|
mapToArray m = accumArray (+) 0 (0, highest') . Map.assocs $ m
|
|
where
|
|
highest' = maximum $ 0 : Map.keys m
|
|
|
|
makeSize :: ({- Show i, Show e, -} IArray a e, Ix i, Enum i) => (i,i) -> e -> a i e -> a i e
|
|
makeSize size def arr = array size [(i,arrayLookupWithDefault def arr i) | i <- [fst size .. snd size]]
|
|
|
|
|
|
-- | Given a pair of equation sets, makes all the equations in the lists be the length
|
|
-- of the longest equation. All missing elements are of course given value zero.
|
|
squareEquations :: ([Array CoeffIndex Integer],[Array CoeffIndex Integer]) -> ([Array CoeffIndex Integer],[Array CoeffIndex Integer])
|
|
squareEquations (eqs,ineqs) = uncurry transformPair (mkPair $ map $ makeSize (0,highest) 0) (eqs,ineqs)
|
|
|
|
where
|
|
highest = maximum $ 0 : (concatMap indices $ eqs ++ ineqs)
|
|
|