3 -- This is a generic graph coloring library, abstracted over the type of
4 -- the node keys, nodes and colors.
6 {-# OPTIONS -fno-warn-missing-signatures #-}
30 -- | Try to color a graph with this set of colors.
31 -- Uses Chaitin's algorithm to color the graph.
32 -- The graph is scanned for nodes which are deamed 'trivially colorable'. These nodes
33 -- are pushed onto a stack and removed from the graph.
34 -- Once this process is complete the graph can be colored by removing nodes from
35 -- the stack (ie in reverse order) and assigning them colors different to their neighbors.
38 :: ( Uniquable k, Uniquable cls, Uniquable color
39 , Eq color, Eq cls, Ord k
40 , Outputable k, Outputable cls, Outputable color)
41 => Bool -- ^ whether to do iterative coalescing
42 -> UniqFM (UniqSet color) -- ^ map of (node class -> set of colors available for this class).
43 -> Triv k cls color -- ^ fn to decide whether a node is trivially colorable.
44 -> (Graph k cls color -> k) -- ^ fn to choose a node to potentially leave uncolored if nothing is trivially colorable.
45 -> Graph k cls color -- ^ the graph to color.
47 -> ( Graph k cls color -- the colored graph.
48 , UniqSet k -- the set of nodes that we couldn't find a color for.
49 , UniqFM k ) -- map of regs (r1 -> r2) that were coaleced
50 -- r1 should be replaced by r2 in the source
52 colorGraph iterative colors triv spill graph0
54 -- If we're not doing iterative coalescing then just do a conservative
55 -- coalescing stage at the front.
56 (graph_coalesced, kksCoalesce1)
58 then coalesceGraph True triv graph0
61 -- run the scanner to slurp out all the trivially colorable nodes
62 -- (and do coalescing if iterative coalescing is enabled)
63 (ksTriv, ksProblems, kksCoalesce2)
64 = colorScan iterative triv spill graph_coalesced
66 -- If iterative coalescing is enabled, the scanner will coalesce the graph as does its business.
67 -- We need to apply all the coalescences found by the scanner to the original
68 -- graph before doing assignColors.
70 -- Because we've got the whole, non-pruned graph here we turn on aggressive coalecing
71 -- to force all the (conservative) coalescences found during scanning.
73 (graph_scan_coalesced, _)
74 = mapAccumL (coalesceNodes True triv) graph_coalesced kksCoalesce2
76 -- color the trivially colorable nodes
77 -- during scanning, keys of triv nodes were added to the front of the list as they were found
78 -- this colors them in the reverse order, as required by the algorithm.
79 (graph_triv, ksNoTriv)
80 = assignColors colors graph_scan_coalesced ksTriv
82 -- try and color the problem nodes
83 -- problem nodes are the ones that were left uncolored because they weren't triv.
84 -- theres a change we can color them here anyway.
85 (graph_prob, ksNoColor)
86 = assignColors colors graph_triv ksProblems
88 -- if the trivially colorable nodes didn't color then something is probably wrong
89 -- with the provided triv function.
91 in if not $ null ksNoTriv
92 then pprPanic "colorGraph: trivially colorable nodes didn't color!" empty
94 $$ text "ksTriv = " <> ppr ksTriv
95 $$ text "ksNoTriv = " <> ppr ksNoTriv
97 $$ dotGraph (\x -> text "white") triv graph1) -}
100 , mkUniqSet ksNoColor -- the nodes that didn't color (spills)
102 then (listToUFM kksCoalesce2)
103 else (listToUFM kksCoalesce1))
106 -- | Scan through the conflict graph separating out trivially colorable and
107 -- potentially uncolorable (problem) nodes.
109 -- Checking whether a node is trivially colorable or not is a resonably expensive operation,
110 -- so after a triv node is found and removed from the graph it's no good to return to the 'start'
111 -- of the graph and recheck a bunch of nodes that will probably still be non-trivially colorable.
113 -- To ward against this, during each pass through the graph we collect up a list of triv nodes
114 -- that were found, and only remove them once we've finished the pass. The more nodes we can delete
115 -- at once the more likely it is that nodes we've already checked will become trivially colorable
116 -- for the next pass.
118 -- TODO: add work lists to finding triv nodes is easier.
119 -- If we've just scanned the graph, and removed triv nodes, then the only
120 -- nodes that we need to rescan are the ones we've removed edges from.
123 :: ( Uniquable k, Uniquable cls, Uniquable color
125 , Outputable k, Outputable color)
126 => Bool -- ^ whether to do iterative coalescing
127 -> Triv k cls color -- ^ fn to decide whether a node is trivially colorable
128 -> (Graph k cls color -> k) -- ^ fn to choose a node to potentially leave uncolored if nothing is trivially colorable.
129 -> Graph k cls color -- ^ the graph to scan
131 -> ([k], [k], [(k, k)]) -- triv colorable nodes, problem nodes, pairs of nodes to coalesce
133 colorScan iterative triv spill graph
134 = colorScan_spin iterative triv spill graph [] [] []
136 colorScan_spin iterative triv spill graph
137 ksTriv ksSpill kksCoalesce
139 -- if the graph is empty then we're done
140 | isNullUFM $ graphMap graph
141 = (ksTriv, ksSpill, kksCoalesce)
144 -- Look for trivially colorable nodes.
145 -- If we can find some then remove them from the graph and go back for more.
148 <- scanGraph (\node -> triv (nodeClass node) (nodeConflicts node) (nodeExclusions node)
150 -- for iterative coalescing we only want non-move related
152 && (not iterative || isEmptyUniqSet (nodeCoalesce node)))
155 , ksTrivFound <- map nodeId nsTrivFound
156 , graph2 <- foldr (\k g -> let Just g' = delNode k g
160 = colorScan_spin iterative triv spill graph2
161 (ksTrivFound ++ ksTriv)
166 -- If we're doing iterative coalescing and no triv nodes are avaliable
167 -- then it's time for a coalescing pass.
169 = case coalesceGraph False triv graph of
171 -- we were able to coalesce something
172 -- go back to Simplify and see if this frees up more nodes to be trivially colorable.
173 (graph2, kksCoalesceFound @(_:_))
174 -> colorScan_spin iterative triv spill graph2
175 ksTriv ksSpill (kksCoalesceFound ++ kksCoalesce)
178 -- nothing could be coalesced (or was triv),
179 -- time to choose a node to freeze and give up on ever coalescing it.
181 -> case freezeOneInGraph graph2 of
183 -- we were able to freeze something
184 -- hopefully this will free up something for Simplify
186 -> colorScan_spin iterative triv spill graph3
187 ksTriv ksSpill kksCoalesce
189 -- we couldn't find something to freeze either
192 -> colorScan_spill iterative triv spill graph3
193 ksTriv ksSpill kksCoalesce
197 = colorScan_spill iterative triv spill graph
198 ksTriv ksSpill kksCoalesce
202 -- we couldn't find any triv nodes or things to freeze or coalesce,
203 -- and the graph isn't empty yet.. We'll have to choose a spill
204 -- candidate and leave it uncolored.
206 colorScan_spill iterative triv spill graph
207 ksTriv ksSpill kksCoalesce
209 = let kSpill = spill graph
210 Just graph' = delNode kSpill graph
211 in colorScan_spin iterative triv spill graph'
212 ksTriv (kSpill : ksSpill) kksCoalesce
215 -- | Try to assign a color to all these nodes.
218 :: ( Uniquable k, Uniquable cls, Uniquable color, Eq color )
219 => UniqFM (UniqSet color) -- ^ map of (node class -> set of colors available for this class).
220 -> Graph k cls color -- ^ the graph
221 -> [k] -- ^ nodes to assign a color to.
222 -> ( Graph k cls color -- the colored graph
223 , [k]) -- the nodes that didn't color.
225 assignColors colors graph ks
226 = assignColors' colors graph [] ks
228 where assignColors' _ graph prob []
231 assignColors' colors graph prob (k:ks)
232 = case assignColor colors k graph of
234 -- couldn't color this node
235 Nothing -> assignColors' colors graph (k : prob) ks
237 -- this node colored ok, so do the rest
238 Just graph' -> assignColors' colors graph' prob ks
241 assignColor colors u graph
242 | Just c <- selectColor colors graph u
243 = Just (setColor u c graph)
250 -- | Select a color for a certain node
251 -- taking into account preferences, neighbors and exclusions.
252 -- returns Nothing if no color can be assigned to this node.
255 :: ( Uniquable k, Uniquable cls, Uniquable color, Eq color)
256 => UniqFM (UniqSet color) -- ^ map of (node class -> set of colors available for this class).
257 -> Graph k cls color -- ^ the graph
258 -> k -- ^ key of the node to select a color for.
261 selectColor colors graph u
262 = let -- lookup the node
263 Just node = lookupNode graph u
265 -- lookup the available colors for the class of this node.
267 = lookupUFM colors (nodeClass node)
269 -- find colors we can't use because they're already being used
270 -- by a node that conflicts with this one.
273 $ map (lookupNode graph)
277 colors_conflict = mkUniqSet
279 $ map nodeColor nsConflicts
281 -- the prefs of our neighbors
282 colors_neighbor_prefs
284 $ concat $ map nodePreference nsConflicts
286 -- colors that are still valid for us
287 colors_ok_ex = minusUniqSet colors_avail (nodeExclusions node)
288 colors_ok = minusUniqSet colors_ok_ex colors_conflict
290 -- the colors that we prefer, and are still ok
291 colors_ok_pref = intersectUniqSets
292 (mkUniqSet $ nodePreference node) colors_ok
294 -- the colors that we could choose while being nice to our neighbors
295 colors_ok_nice = minusUniqSet
296 colors_ok colors_neighbor_prefs
298 -- the best of all possible worlds..
301 colors_ok_nice colors_ok_pref
306 -- everyone is happy, yay!
307 | not $ isEmptyUniqSet colors_ok_pref_nice
308 , c : _ <- filter (\x -> elementOfUniqSet x colors_ok_pref_nice)
309 (nodePreference node)
312 -- we've got one of our preferences
313 | not $ isEmptyUniqSet colors_ok_pref
314 , c : _ <- filter (\x -> elementOfUniqSet x colors_ok_pref)
315 (nodePreference node)
318 -- it wasn't a preference, but it was still ok
319 | not $ isEmptyUniqSet colors_ok
320 , c : _ <- uniqSetToList colors_ok
323 -- no colors were available for us this time.
324 -- looks like we're going around the loop again..