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.
71 -- Because we've got the whole, non-pruned graph here we turn on aggressive coalecing
72 -- to force all the (conservative) coalescences found during scanning.
74 (graph_scan_coalesced, _)
75 = mapAccumL (coalesceNodes True triv) graph_coalesced kksCoalesce2
77 -- color the trivially colorable nodes
78 -- during scanning, keys of triv nodes were added to the front of the list as they were found
79 -- this colors them in the reverse order, as required by the algorithm.
80 (graph_triv, ksNoTriv)
81 = assignColors colors graph_scan_coalesced ksTriv
83 -- try and color the problem nodes
84 -- problem nodes are the ones that were left uncolored because they weren't triv.
85 -- theres a change we can color them here anyway.
86 (graph_prob, ksNoColor)
87 = assignColors colors graph_triv ksProblems
89 -- if the trivially colorable nodes didn't color then something is probably wrong
90 -- with the provided triv function.
92 in if not $ null ksNoTriv
93 then pprPanic "colorGraph: trivially colorable nodes didn't color!" empty
95 $$ text "ksTriv = " <> ppr ksTriv
96 $$ text "ksNoTriv = " <> ppr ksNoTriv
98 $$ dotGraph (\x -> text "white") triv graph1) -}
101 , mkUniqSet ksNoColor -- the nodes that didn't color (spills)
103 then (listToUFM kksCoalesce2)
104 else (listToUFM kksCoalesce1))
107 -- | Scan through the conflict graph separating out trivially colorable and
108 -- potentially uncolorable (problem) nodes.
110 -- Checking whether a node is trivially colorable or not is a resonably expensive operation,
111 -- so after a triv node is found and removed from the graph it's no good to return to the 'start'
112 -- of the graph and recheck a bunch of nodes that will probably still be non-trivially colorable.
114 -- To ward against this, during each pass through the graph we collect up a list of triv nodes
115 -- that were found, and only remove them once we've finished the pass. The more nodes we can delete
116 -- at once the more likely it is that nodes we've already checked will become trivially colorable
117 -- for the next pass.
119 -- TODO: add work lists to finding triv nodes is easier.
120 -- If we've just scanned the graph, and removed triv nodes, then the only
121 -- nodes that we need to rescan are the ones we've removed edges from.
124 :: ( Uniquable k, Uniquable cls, Uniquable color
126 , Outputable k, Outputable color)
127 => Bool -- ^ whether to do iterative coalescing
128 -> Triv k cls color -- ^ fn to decide whether a node is trivially colorable
129 -> (Graph k cls color -> k) -- ^ fn to choose a node to potentially leave uncolored if nothing is trivially colorable.
130 -> Graph k cls color -- ^ the graph to scan
132 -> ([k], [k], [(k, k)]) -- triv colorable nodes, problem nodes, pairs of nodes to coalesce
134 colorScan iterative triv spill graph
135 = colorScan_spin iterative triv spill graph [] [] []
137 colorScan_spin iterative triv spill graph
138 ksTriv ksSpill kksCoalesce
140 -- if the graph is empty then we're done
141 | isNullUFM $ graphMap graph
142 = (ksTriv, ksSpill, kksCoalesce)
145 -- Look for trivially colorable nodes.
146 -- If we can find some then remove them from the graph and go back for more.
149 <- scanGraph (\node -> triv (nodeClass node) (nodeConflicts node) (nodeExclusions node)
151 -- for iterative coalescing we only want non-move related
153 && (not iterative || isEmptyUniqSet (nodeCoalesce node)))
156 , ksTrivFound <- map nodeId nsTrivFound
157 , graph3 <- foldr (\k g -> let Just g' = delNode k g
161 = colorScan_spin iterative triv spill graph3
162 (ksTrivFound ++ ksTriv)
167 -- If we're doing iterative coalescing and no triv nodes are avaliable
168 -- then it's type for a coalescing pass.
170 = case coalesceGraph False triv graph of
172 -- we were able to coalesce something
173 -- go back and see if this frees up more nodes to be trivially colorable.
174 (graph2, kksCoalesceFound @(_:_))
175 -> colorScan_spin iterative triv spill graph2
176 ksTriv ksSpill (kksCoalesceFound ++ kksCoalesce)
179 -- nothing could be coalesced (or was triv),
180 -- time to choose a node to freeze and give up on ever coalescing it.
182 -> case freezeOneInGraph graph2 of
184 -- we were able to freeze something
185 -- hopefully this will free up something for Simplify
187 -> colorScan_spin iterative triv spill graph3
188 ksTriv ksSpill kksCoalesce
190 -- we couldn't find something to freeze either
193 -> colorScan_spill iterative triv spill graph3
194 ksTriv ksSpill kksCoalesce
198 = colorScan_spill iterative triv spill graph
199 ksTriv ksSpill kksCoalesce
203 -- we couldn't find any triv nodes or things to freeze or coalesce,
204 -- and the graph isn't empty yet.. We'll have to choose a spill
205 -- candidate and leave it uncolored.
207 colorScan_spill iterative triv spill graph
208 ksTriv ksSpill kksCoalesce
210 = let kSpill = spill graph
211 Just graph' = delNode kSpill graph
212 in colorScan_spin iterative triv spill graph'
213 ksTriv (kSpill : ksSpill) kksCoalesce
216 -- | Try to assign a color to all these nodes.
219 :: ( Uniquable k, Uniquable cls, Uniquable color, Eq color )
220 => UniqFM (UniqSet color) -- ^ map of (node class -> set of colors available for this class).
221 -> Graph k cls color -- ^ the graph
222 -> [k] -- ^ nodes to assign a color to.
223 -> ( Graph k cls color -- the colored graph
224 , [k]) -- the nodes that didn't color.
226 assignColors colors graph ks
227 = assignColors' colors graph [] ks
229 where assignColors' _ graph prob []
232 assignColors' colors graph prob (k:ks)
233 = case assignColor colors k graph of
235 -- couldn't color this node
236 Nothing -> assignColors' colors graph (k : prob) ks
238 -- this node colored ok, so do the rest
239 Just graph' -> assignColors' colors graph' prob ks
242 assignColor colors u graph
243 | Just c <- selectColor colors graph u
244 = Just (setColor u c graph)
251 -- | Select a color for a certain node
252 -- taking into account preferences, neighbors and exclusions.
253 -- returns Nothing if no color can be assigned to this node.
256 :: ( Uniquable k, Uniquable cls, Uniquable color, Eq color)
257 => UniqFM (UniqSet color) -- ^ map of (node class -> set of colors available for this class).
258 -> Graph k cls color -- ^ the graph
259 -> k -- ^ key of the node to select a color for.
262 selectColor colors graph u
263 = let -- lookup the node
264 Just node = lookupNode graph u
266 -- lookup the available colors for the class of this node.
268 = lookupUFM colors (nodeClass node)
270 -- find colors we can't use because they're already being used
271 -- by a node that conflicts with this one.
274 $ map (lookupNode graph)
278 colors_conflict = mkUniqSet
280 $ map nodeColor nsConflicts
282 -- the prefs of our neighbors
283 colors_neighbor_prefs
285 $ concat $ map nodePreference nsConflicts
287 -- colors that are still valid for us
288 colors_ok_ex = minusUniqSet colors_avail (nodeExclusions node)
289 colors_ok = minusUniqSet colors_ok_ex colors_conflict
291 -- the colors that we prefer, and are still ok
292 colors_ok_pref = intersectUniqSets
293 (mkUniqSet $ nodePreference node) colors_ok
295 -- the colors that we could choose while being nice to our neighbors
296 colors_ok_nice = minusUniqSet
297 colors_ok colors_neighbor_prefs
299 -- the best of all possible worlds..
302 colors_ok_nice colors_ok_pref
307 -- everyone is happy, yay!
308 | not $ isEmptyUniqSet colors_ok_pref_nice
309 , c : _ <- filter (\x -> elementOfUniqSet x colors_ok_pref_nice)
310 (nodePreference node)
313 -- we've got one of our preferences
314 | not $ isEmptyUniqSet colors_ok_pref
315 , c : _ <- filter (\x -> elementOfUniqSet x colors_ok_pref)
316 (nodePreference node)
319 -- it wasn't a preference, but it was still ok
320 | not $ isEmptyUniqSet colors_ok
321 , c : _ <- uniqSetToList colors_ok
324 -- no colors were available for us this time.
325 -- looks like we're going around the loop again..