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{-
Copyright (c) 2014 Joachim Breitner
A data structure for undirected graphs of variables
(or in plain terms: Sets of unordered pairs of numbers)
This is very specifically tailored for the use in CallArity. In particular it
stores the graph as a union of complete and complete bipartite graph, which
would be very expensive to store as sets of edges or as adjanceny lists.
It does not normalize the graphs. This means that g `unionUnVarGraph` g is
equal to g, but twice as expensive and large.
-}
module GHC.Data.Graph.UnVar
( UnVarSet
, emptyUnVarSet, mkUnVarSet, unionUnVarSet, unionUnVarSets
, extendUnVarSet, extendUnVarSetList, delUnVarSet, delUnVarSetList
, elemUnVarSet, isEmptyUnVarSet
, UnVarGraph
, emptyUnVarGraph
, unionUnVarGraph, unionUnVarGraphs
, completeGraph, completeBipartiteGraph
, neighbors
, hasLoopAt
, delNode
, domUFMUnVarSet
) where
import GHC.Prelude
import GHC.Types.Unique.FM( UniqFM, ufmToSet_Directly )
import GHC.Types.Var
import GHC.Utils.Outputable
import GHC.Types.Unique
import GHC.Word
import qualified GHC.Data.Word64Set as S
-- We need a type for sets of variables (UnVarSet).
-- We do not use VarSet, because for that we need to have the actual variable
-- at hand, and we do not have that when we turn the domain of a VarEnv into a UnVarSet.
-- Therefore, use a IntSet directly (which is likely also a bit more efficient).
-- Set of uniques, i.e. for adjacent nodes
newtype UnVarSet = UnVarSet S.Word64Set
deriving Eq
k :: Var -> Word64
k v = getKey (getUnique v)
domUFMUnVarSet :: UniqFM key elt -> UnVarSet
domUFMUnVarSet ae = UnVarSet $ ufmToSet_Directly ae
emptyUnVarSet :: UnVarSet
emptyUnVarSet = UnVarSet S.empty
elemUnVarSet :: Var -> UnVarSet -> Bool
elemUnVarSet v (UnVarSet s) = k v `S.member` s
isEmptyUnVarSet :: UnVarSet -> Bool
isEmptyUnVarSet (UnVarSet s) = S.null s
delUnVarSet :: UnVarSet -> Var -> UnVarSet
delUnVarSet (UnVarSet s) v = UnVarSet $ k v `S.delete` s
delUnVarSetList :: UnVarSet -> [Var] -> UnVarSet
delUnVarSetList s vs = s `minusUnVarSet` mkUnVarSet vs
minusUnVarSet :: UnVarSet -> UnVarSet -> UnVarSet
minusUnVarSet (UnVarSet s) (UnVarSet s') = UnVarSet $ s `S.difference` s'
sizeUnVarSet :: UnVarSet -> Int
sizeUnVarSet (UnVarSet s) = S.size s
mkUnVarSet :: [Var] -> UnVarSet
mkUnVarSet vs = UnVarSet $ S.fromList $ map k vs
extendUnVarSet :: Var -> UnVarSet -> UnVarSet
extendUnVarSet v (UnVarSet s) = UnVarSet $ S.insert (k v) s
extendUnVarSetList :: [Var] -> UnVarSet -> UnVarSet
extendUnVarSetList vs s = s `unionUnVarSet` mkUnVarSet vs
unionUnVarSet :: UnVarSet -> UnVarSet -> UnVarSet
unionUnVarSet (UnVarSet set1) (UnVarSet set2) = UnVarSet (set1 `S.union` set2)
unionUnVarSets :: [UnVarSet] -> UnVarSet
unionUnVarSets = foldl' (flip unionUnVarSet) emptyUnVarSet
instance Outputable UnVarSet where
ppr (UnVarSet s) = braces $
hcat $ punctuate comma [ ppr (mkUniqueGrimily i) | i <- S.toList s]
data UnVarGraph = CBPG !UnVarSet !UnVarSet -- ^ complete bipartite graph
| CG !UnVarSet -- ^ complete graph
| Union UnVarGraph UnVarGraph
| Del !UnVarSet UnVarGraph
emptyUnVarGraph :: UnVarGraph
emptyUnVarGraph = CG emptyUnVarSet
unionUnVarGraph :: UnVarGraph -> UnVarGraph -> UnVarGraph
{-
Premature optimisation, it seems.
unionUnVarGraph (UnVarGraph [CBPG s1 s2]) (UnVarGraph [CG s3, CG s4])
| s1 == s3 && s2 == s4
= pprTrace "unionUnVarGraph fired" empty $
completeGraph (s1 `unionUnVarSet` s2)
unionUnVarGraph (UnVarGraph [CBPG s1 s2]) (UnVarGraph [CG s3, CG s4])
| s2 == s3 && s1 == s4
= pprTrace "unionUnVarGraph fired2" empty $
completeGraph (s1 `unionUnVarSet` s2)
-}
unionUnVarGraph a b
| is_null a = b
| is_null b = a
| otherwise = Union a b
unionUnVarGraphs :: [UnVarGraph] -> UnVarGraph
unionUnVarGraphs = foldl' unionUnVarGraph emptyUnVarGraph
-- completeBipartiteGraph A B = { {a,b} | a ∈ A, b ∈ B }
completeBipartiteGraph :: UnVarSet -> UnVarSet -> UnVarGraph
completeBipartiteGraph s1 s2 = prune $ CBPG s1 s2
completeGraph :: UnVarSet -> UnVarGraph
completeGraph s = prune $ CG s
-- (v' ∈ neighbors G v) <=> v--v' ∈ G
neighbors :: UnVarGraph -> Var -> UnVarSet
neighbors = go
where
go (Del d g) v
| v `elemUnVarSet` d = emptyUnVarSet
| otherwise = go g v `minusUnVarSet` d
go (Union g1 g2) v = go g1 v `unionUnVarSet` go g2 v
go (CG s) v = if v `elemUnVarSet` s then s else emptyUnVarSet
go (CBPG s1 s2) v = (if v `elemUnVarSet` s1 then s2 else emptyUnVarSet) `unionUnVarSet`
(if v `elemUnVarSet` s2 then s1 else emptyUnVarSet)
-- hasLoopAt G v <=> v--v ∈ G
hasLoopAt :: UnVarGraph -> Var -> Bool
hasLoopAt = go
where
go (Del d g) v
| v `elemUnVarSet` d = False
| otherwise = go g v
go (Union g1 g2) v = go g1 v || go g2 v
go (CG s) v = v `elemUnVarSet` s
go (CBPG s1 s2) v = v `elemUnVarSet` s1 && v `elemUnVarSet` s2
delNode :: UnVarGraph -> Var -> UnVarGraph
delNode (Del d g) v = Del (extendUnVarSet v d) g
delNode g v
| is_null g = emptyUnVarGraph
| otherwise = Del (mkUnVarSet [v]) g
-- | Resolves all `Del`, by pushing them in, and simplifies `∅ ∪ … = …`
prune :: UnVarGraph -> UnVarGraph
prune = go emptyUnVarSet
where
go :: UnVarSet -> UnVarGraph -> UnVarGraph
go dels (Del dels' g) = go (dels `unionUnVarSet` dels') g
go dels (Union g1 g2)
| is_null g1' = g2'
| is_null g2' = g1'
| otherwise = Union g1' g2'
where
g1' = go dels g1
g2' = go dels g2
go dels (CG s) = CG (s `minusUnVarSet` dels)
go dels (CBPG s1 s2) = CBPG (s1 `minusUnVarSet` dels) (s2 `minusUnVarSet` dels)
-- | Shallow empty check.
is_null :: UnVarGraph -> Bool
is_null (CBPG s1 s2) = isEmptyUnVarSet s1 || isEmptyUnVarSet s2
is_null (CG s) = isEmptyUnVarSet s
is_null _ = False
instance Outputable UnVarGraph where
ppr (Del d g) = text "Del" <+> ppr (sizeUnVarSet d) <+> parens (ppr g)
ppr (Union a b) = text "Union" <+> parens (ppr a) <+> parens (ppr b)
ppr (CG s) = text "CG" <+> ppr (sizeUnVarSet s)
ppr (CBPG a b) = text "CBPG" <+> ppr (sizeUnVarSet a) <+> ppr (sizeUnVarSet b)
|
