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366    Graph Coloring.
 This is a generic graph coloring library, abstracted over the type of
 the node keys, nodes and colors.

module GraphColor (
module GraphBase,
module GraphOps,
module GraphPpr,
colorGraph
)
where
import GraphBase
import GraphOps
import GraphPpr
import Unique
import UniqFM
import UniqSet
import Outputable
import Data.Maybe
import Data.List
  Try to color a graph with this set of colors.
 Uses Chaitin's algorithm to color the graph.
 The graph is scanned for nodes which are deamed 'trivially colorable'. These nodes
 are pushed onto a stack and removed from the graph.
 Once this process is complete the graph can be colored by removing nodes from
 the stack (ie in reverse order) and assigning them colors different to their neighbors.

colorGraph
:: ( Uniquable k, Uniquable cls, Uniquable color
, Eq color, Eq cls, Ord k
, Outputable k, Outputable cls, Outputable color)
=> Bool  ^ whether to do iterative coalescing
> Int  ^ how many times we've tried to color this graph so far.
> UniqFM (UniqSet color)  ^ map of (node class > set of colors available for this class).
> Triv k cls color  ^ fn to decide whether a node is trivially colorable.
> (Graph k cls color > k)  ^ fn to choose a node to potentially leave uncolored if nothing is trivially colorable.
> Graph k cls color  ^ the graph to color.
> ( Graph k cls color  the colored graph.
, UniqSet k  the set of nodes that we couldn't find a color for.
, UniqFM k )  map of regs (r1 > r2) that were coaleced
 r1 should be replaced by r2 in the source
colorGraph iterative spinCount colors triv spill graph0
= let
 If we're not doing iterative coalescing then do an aggressive coalescing first time
 around and then conservative coalescing for subsequent passes.

 Aggressive coalescing is a quick way to get rid of many regreg moves. However, if
 there is a lot of register pressure and we do it on every round then it can make the
 graph less colorable and prevent the algorithm from converging in a sensible number
 of cycles.

(graph_coalesced, kksCoalesce1)
= if iterative
then (graph0, [])
else if spinCount == 0
then coalesceGraph True triv graph0
else coalesceGraph False triv graph0
 run the scanner to slurp out all the trivially colorable nodes
 (and do coalescing if iterative coalescing is enabled)
(ksTriv, ksProblems, kksCoalesce2)
= colorScan iterative triv spill graph_coalesced
 If iterative coalescing is enabled, the scanner will coalesce the graph as does its business.
 We need to apply all the coalescences found by the scanner to the original
 graph before doing assignColors.

 Because we've got the whole, nonpruned graph here we turn on aggressive coalecing
 to force all the (conservative) coalescences found during scanning.

(graph_scan_coalesced, _)
= mapAccumL (coalesceNodes True triv) graph_coalesced kksCoalesce2
 color the trivially colorable nodes
 during scanning, keys of triv nodes were added to the front of the list as they were found
 this colors them in the reverse order, as required by the algorithm.
(graph_triv, ksNoTriv)
= assignColors colors graph_scan_coalesced ksTriv
 try and color the problem nodes
 problem nodes are the ones that were left uncolored because they weren't triv.
 theres a change we can color them here anyway.
(graph_prob, ksNoColor)
= assignColors colors graph_triv ksProblems
 if the trivially colorable nodes didn't color then something is probably wrong
 with the provided triv function.

in if not $ null ksNoTriv
then pprPanic "colorGraph: trivially colorable nodes didn't color!"  empty
( empty
$$ text "ksTriv = " <> ppr ksTriv
$$ text "ksNoTriv = " <> ppr ksNoTriv
$$ text "colors = " <> ppr colors
$$ empty
$$ dotGraph (\_ > text "white") triv graph_triv)
else ( graph_prob
, mkUniqSet ksNoColor  the nodes that didn't color (spills)
, if iterative
then (listToUFM kksCoalesce2)
else (listToUFM kksCoalesce1))
  Scan through the conflict graph separating out trivially colorable and
 potentially uncolorable (problem) nodes.

 Checking whether a node is trivially colorable or not is a resonably expensive operation,
 so after a triv node is found and removed from the graph it's no good to return to the 'start'
 of the graph and recheck a bunch of nodes that will probably still be nontrivially colorable.

 To ward against this, during each pass through the graph we collect up a list of triv nodes
 that were found, and only remove them once we've finished the pass. The more nodes we can delete
 at once the more likely it is that nodes we've already checked will become trivially colorable
 for the next pass.

 TODO: add work lists to finding triv nodes is easier.
 If we've just scanned the graph, and removed triv nodes, then the only
 nodes that we need to rescan are the ones we've removed edges from.
colorScan
:: ( Uniquable k, Uniquable cls, Uniquable color
, Ord k, Eq cls
, Outputable k, Outputable cls)
=> Bool  ^ whether to do iterative coalescing
> Triv k cls color  ^ fn to decide whether a node is trivially colorable
> (Graph k cls color > k)  ^ fn to choose a node to potentially leave uncolored if nothing is trivially colorable.
> Graph k cls color  ^ the graph to scan
> ([k], [k], [(k, k)])  triv colorable nodes, problem nodes, pairs of nodes to coalesce
colorScan iterative triv spill graph
= colorScan_spin iterative triv spill graph [] [] []
colorScan_spin
:: ( Uniquable k, Uniquable cls, Uniquable color
, Ord k, Eq cls
, Outputable k, Outputable cls)
=> Bool
> Triv k cls color
> (Graph k cls color > k)
> Graph k cls color
> [k]
> [k]
> [(k, k)]
> ([k], [k], [(k, k)])
colorScan_spin iterative triv spill graph
ksTriv ksSpill kksCoalesce
 if the graph is empty then we're done
 isNullUFM $ graphMap graph
= (ksTriv, ksSpill, reverse kksCoalesce)
 Simplify:
 Look for trivially colorable nodes.
 If we can find some then remove them from the graph and go back for more.

 nsTrivFound@(_:_)
< scanGraph (\node > triv (nodeClass node) (nodeConflicts node) (nodeExclusions node)
 for iterative coalescing we only want nonmove related
 nodes here
&& (not iterative  isEmptyUniqSet (nodeCoalesce node)))
$ graph
, ksTrivFound < map nodeId nsTrivFound
, graph2 < foldr (\k g > let Just g' = delNode k g
in g')
graph ksTrivFound
= colorScan_spin iterative triv spill graph2
(ksTrivFound ++ ksTriv)
ksSpill
kksCoalesce
 Coalesce:
 If we're doing iterative coalescing and no triv nodes are avaliable
 then it's time for a coalescing pass.
 iterative
= case coalesceGraph False triv graph of
 we were able to coalesce something
 go back to Simplify and see if this frees up more nodes to be trivially colorable.
(graph2, kksCoalesceFound @(_:_))
> colorScan_spin iterative triv spill graph2
ksTriv ksSpill (reverse kksCoalesceFound ++ kksCoalesce)
 Freeze:
 nothing could be coalesced (or was triv),
 time to choose a node to freeze and give up on ever coalescing it.
(graph2, [])
> case freezeOneInGraph graph2 of
 we were able to freeze something
 hopefully this will free up something for Simplify
(graph3, True)
> colorScan_spin iterative triv spill graph3
ksTriv ksSpill kksCoalesce
 we couldn't find something to freeze either
 time for a spill
(graph3, False)
> colorScan_spill iterative triv spill graph3
ksTriv ksSpill kksCoalesce
 spill time
 otherwise
= colorScan_spill iterative triv spill graph
ksTriv ksSpill kksCoalesce
 Select:
 we couldn't find any triv nodes or things to freeze or coalesce,
 and the graph isn't empty yet.. We'll have to choose a spill
 candidate and leave it uncolored.

colorScan_spill
:: ( Uniquable k, Uniquable cls, Uniquable color
, Ord k, Eq cls
, Outputable k, Outputable cls)
=> Bool
> Triv k cls color
> (Graph k cls color > k)
> Graph k cls color
> [k]
> [k]
> [(k, k)]
> ([k], [k], [(k, k)])
colorScan_spill iterative triv spill graph
ksTriv ksSpill kksCoalesce
= let kSpill = spill graph
Just graph' = delNode kSpill graph
in colorScan_spin iterative triv spill graph'
ksTriv (kSpill : ksSpill) kksCoalesce
  Try to assign a color to all these nodes.
assignColors
:: ( Uniquable k, Uniquable cls, Uniquable color
, Eq color, Outputable cls)
=> UniqFM (UniqSet color)  ^ map of (node class > set of colors available for this class).
> Graph k cls color  ^ the graph
> [k]  ^ nodes to assign a color to.
> ( Graph k cls color  the colored graph
, [k])  the nodes that didn't color.
assignColors colors graph ks
= assignColors' colors graph [] ks
where assignColors' _ graph prob []
= (graph, prob)
assignColors' colors graph prob (k:ks)
= case assignColor colors k graph of
 couldn't color this node
Nothing > assignColors' colors graph (k : prob) ks
 this node colored ok, so do the rest
Just graph' > assignColors' colors graph' prob ks
assignColor colors u graph
 Just c < selectColor colors graph u
= Just (setColor u c graph)
 otherwise
= Nothing
  Select a color for a certain node
 taking into account preferences, neighbors and exclusions.
 returns Nothing if no color can be assigned to this node.

selectColor
:: ( Uniquable k, Uniquable cls, Uniquable color
, Eq color, Outputable cls)
=> UniqFM (UniqSet color)  ^ map of (node class > set of colors available for this class).
> Graph k cls color  ^ the graph
> k  ^ key of the node to select a color for.
> Maybe color
selectColor colors graph u
= let  lookup the node
Just node = lookupNode graph u
 lookup the available colors for the class of this node.
colors_avail
= case lookupUFM colors (nodeClass node) of
Nothing > pprPanic "selectColor: no colors available for class " (ppr (nodeClass node))
Just cs > cs
 find colors we can't use because they're already being used
 by a node that conflicts with this one.
Just nsConflicts
= sequence
$ map (lookupNode graph)
$ uniqSetToList
$ nodeConflicts node
colors_conflict = mkUniqSet
$ catMaybes
$ map nodeColor nsConflicts
 the prefs of our neighbors
colors_neighbor_prefs
= mkUniqSet
$ concat $ map nodePreference nsConflicts
 colors that are still valid for us
colors_ok_ex = minusUniqSet colors_avail (nodeExclusions node)
colors_ok = minusUniqSet colors_ok_ex colors_conflict
 the colors that we prefer, and are still ok
colors_ok_pref = intersectUniqSets
(mkUniqSet $ nodePreference node) colors_ok
 the colors that we could choose while being nice to our neighbors
colors_ok_nice = minusUniqSet
colors_ok colors_neighbor_prefs
 the best of all possible worlds..
colors_ok_pref_nice
= intersectUniqSets
colors_ok_nice colors_ok_pref
 make the decision
chooseColor
 everyone is happy, yay!
 not $ isEmptyUniqSet colors_ok_pref_nice
, c : _ < filter (\x > elementOfUniqSet x colors_ok_pref_nice)
(nodePreference node)
= Just c
 we've got one of our preferences
 not $ isEmptyUniqSet colors_ok_pref
, c : _ < filter (\x > elementOfUniqSet x colors_ok_pref)
(nodePreference node)
= Just c
 it wasn't a preference, but it was still ok
 not $ isEmptyUniqSet colors_ok
, c : _ < uniqSetToList colors_ok
= Just c
 no colors were available for us this time.
 looks like we're going around the loop again..
 otherwise
= Nothing
in chooseColor
