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 single coalescing
55 -- pass at the front. This won't be as good but should still eat up a
56 -- lot of the reg-reg moves.
57 (graph_coalesced, kksCoalesce1)
59 then coalesceGraph False triv graph0
62 -- run the scanner to slurp out all the trivially colorable nodes
63 -- (and do coalescing if iterative coalescing is enabled)
64 (ksTriv, ksProblems, kksCoalesce2)
65 = colorScan iterative triv spill graph_coalesced
67 -- If iterative coalescing is enabled, the scanner will coalesce the graph as does its business.
68 -- We need to apply all the coalescences found by the scanner to the original
69 -- graph before doing assignColors.
70 (graph_scan_coalesced, _)
71 = mapAccumL (coalesceNodes False triv) graph_coalesced kksCoalesce2
73 -- color the trivially colorable nodes
74 -- during scanning, keys of triv nodes were added to the front of the list as they were found
75 -- this colors them in the reverse order, as required by the algorithm.
76 (graph_triv, ksNoTriv)
77 = assignColors colors graph_scan_coalesced ksTriv
79 -- try and color the problem nodes
80 -- problem nodes are the ones that were left uncolored because they weren't triv.
81 -- theres a change we can color them here anyway.
82 (graph_prob, ksNoColor)
83 = assignColors colors graph_triv ksProblems
85 -- if the trivially colorable nodes didn't color then something is probably wrong
86 -- with the provided triv function.
88 in if not $ null ksNoTriv
89 then pprPanic "colorGraph: trivially colorable nodes didn't color!" empty
91 $$ text "ksTriv = " <> ppr ksTriv
92 $$ text "ksNoTriv = " <> ppr ksNoTriv
94 $$ dotGraph (\x -> text "white") triv graph1) -}
97 , mkUniqSet ksNoColor -- the nodes that didn't color (spills)
99 then (listToUFM kksCoalesce2)
100 else (listToUFM kksCoalesce1))
103 -- | Scan through the conflict graph separating out trivially colorable and
104 -- potentially uncolorable (problem) nodes.
106 -- Checking whether a node is trivially colorable or not is a resonably expensive operation,
107 -- so after a triv node is found and removed from the graph it's no good to return to the 'start'
108 -- of the graph and recheck a bunch of nodes that will probably still be non-trivially colorable.
110 -- To ward against this, during each pass through the graph we collect up a list of triv nodes
111 -- that were found, and only remove them once we've finished the pass. The more nodes we can delete
112 -- at once the more likely it is that nodes we've already checked will become trivially colorable
113 -- for the next pass.
115 -- TODO: add work lists to finding triv nodes is easier.
116 -- If we've just scanned the graph, and removed triv nodes, then the only
117 -- nodes that we need to rescan are the ones we've removed edges from.
120 :: ( Uniquable k, Uniquable cls, Uniquable color
122 , Outputable k, Outputable color)
123 => Bool -- ^ whether to do iterative coalescing
124 -> Triv k cls color -- ^ fn to decide whether a node is trivially colorable
125 -> (Graph k cls color -> k) -- ^ fn to choose a node to potentially leave uncolored if nothing is trivially colorable.
126 -> Graph k cls color -- ^ the graph to scan
128 -> ([k], [k], [(k, k)]) -- triv colorable nodes, problem nodes, pairs of nodes to coalesce
130 colorScan iterative triv spill graph
131 = colorScan_spin iterative triv spill graph [] [] []
133 colorScan_spin iterative triv spill graph
134 ksTriv ksSpill kksCoalesce
136 -- if the graph is empty then we're done
137 | isNullUFM $ graphMap graph
138 = (ksTriv, ksSpill, kksCoalesce)
141 -- Look for trivially colorable nodes.
142 -- If we can find some then remove them from the graph and go back for more.
145 <- scanGraph (\node -> triv (nodeClass node) (nodeConflicts node) (nodeExclusions node)
147 -- for iterative coalescing we only want non-move related
149 && (not iterative || isEmptyUniqSet (nodeCoalesce node)))
152 , ksTrivFound <- map nodeId nsTrivFound
153 , graph3 <- foldr delNode graph ksTrivFound
154 = colorScan_spin iterative triv spill graph3
155 (ksTrivFound ++ ksTriv)
160 -- If we're doing iterative coalescing and no triv nodes are avaliable
161 -- then it's type for a coalescing pass.
163 = case coalesceGraph False triv graph of
165 -- we were able to coalesce something
166 -- go back and see if this frees up more nodes to be trivially colorable.
167 (graph2, kksCoalesceFound @(_:_))
168 -> colorScan_spin iterative triv spill graph2
169 ksTriv ksSpill (kksCoalesceFound ++ kksCoalesce)
172 -- nothing could be coalesced (or was triv),
173 -- time to choose a node to freeze and give up on ever coalescing it.
175 -> case freezeOneInGraph graph2 of
177 -- we were able to freeze something
178 -- hopefully this will free up something for Simplify
180 -> colorScan_spin iterative triv spill graph3
181 ksTriv ksSpill kksCoalesce
183 -- we couldn't find something to freeze either
186 -> colorScan_spill iterative triv spill graph3
187 ksTriv ksSpill kksCoalesce
191 = colorScan_spill iterative triv spill graph
192 ksTriv ksSpill kksCoalesce
196 -- we couldn't find any triv nodes or things to freeze or coalesce,
197 -- and the graph isn't empty yet.. We'll have to choose a spill
198 -- candidate and leave it uncolored.
200 colorScan_spill iterative triv spill graph
201 ksTriv ksSpill kksCoalesce
203 = let kSpill = spill graph
204 graph' = delNode kSpill graph
205 in colorScan_spin iterative triv spill graph'
206 ksTriv (kSpill : ksSpill) kksCoalesce
209 -- | Try to assign a color to all these nodes.
212 :: ( Uniquable k, Uniquable cls, Uniquable color, Eq color )
213 => UniqFM (UniqSet color) -- ^ map of (node class -> set of colors available for this class).
214 -> Graph k cls color -- ^ the graph
215 -> [k] -- ^ nodes to assign a color to.
216 -> ( Graph k cls color -- the colored graph
217 , [k]) -- the nodes that didn't color.
219 assignColors colors graph ks
220 = assignColors' colors graph [] ks
222 where assignColors' _ graph prob []
225 assignColors' colors graph prob (k:ks)
226 = case assignColor colors k graph of
228 -- couldn't color this node
229 Nothing -> assignColors' colors graph (k : prob) ks
231 -- this node colored ok, so do the rest
232 Just graph' -> assignColors' colors graph' prob ks
235 assignColor colors u graph
236 | Just c <- selectColor colors graph u
237 = Just (setColor u c graph)
244 -- | Select a color for a certain node
245 -- taking into account preferences, neighbors and exclusions.
246 -- returns Nothing if no color can be assigned to this node.
249 :: ( Uniquable k, Uniquable cls, Uniquable color, Eq color)
250 => UniqFM (UniqSet color) -- ^ map of (node class -> set of colors available for this class).
251 -> Graph k cls color -- ^ the graph
252 -> k -- ^ key of the node to select a color for.
255 selectColor colors graph u
256 = let -- lookup the node
257 Just node = lookupNode graph u
259 -- lookup the available colors for the class of this node.
261 = lookupUFM colors (nodeClass node)
263 -- find colors we can't use because they're already being used
264 -- by a node that conflicts with this one.
267 $ map (lookupNode graph)
271 colors_conflict = mkUniqSet
273 $ map nodeColor nsConflicts
275 -- the prefs of our neighbors
276 colors_neighbor_prefs
278 $ concat $ map nodePreference nsConflicts
280 -- colors that are still valid for us
281 colors_ok_ex = minusUniqSet colors_avail (nodeExclusions node)
282 colors_ok = minusUniqSet colors_ok_ex colors_conflict
284 -- the colors that we prefer, and are still ok
285 colors_ok_pref = intersectUniqSets
286 (mkUniqSet $ nodePreference node) colors_ok
288 -- the colors that we could choose while being nice to our neighbors
289 colors_ok_nice = minusUniqSet
290 colors_ok colors_neighbor_prefs
292 -- the best of all possible worlds..
295 colors_ok_nice colors_ok_pref
300 -- everyone is happy, yay!
301 | not $ isEmptyUniqSet colors_ok_pref_nice
302 , c : _ <- filter (\x -> elementOfUniqSet x colors_ok_pref_nice)
303 (nodePreference node)
306 -- we've got one of our preferences
307 | not $ isEmptyUniqSet colors_ok_pref
308 , c : _ <- filter (\x -> elementOfUniqSet x colors_ok_pref)
309 (nodePreference node)
312 -- it wasn't a preference, but it was still ok
313 | not $ isEmptyUniqSet colors_ok
314 , c : _ <- uniqSetToList colors_ok
317 -- no colors were available for us this time.
318 -- looks like we're going around the loop again..