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-rwxr-xr-xbackend/IRC.v122
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diff --git a/backend/IRC.v b/backend/IRC.v
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-Require Import Recdef.
-Require Import FSetInterface.
-Require Import InterfGraphMapImp.
-Require Import OrderedOption.
-Require Import FMapAVL.
-Require Import IRC_termination.
-Require Import IRC_graph.
-Require Import IRC_Graph_Functions.
-Require Import Edges.
-
-Import Edge RegFacts Props OTFacts.
-
-(* Definition of Register options *)
-
-Module OptionReg := OrderedOpt Register.
-
-(* Definition of the type of colorings *)
-
-Definition Coloring := Register.t -> OptionReg.t.
-
-(* Map used to build a coloring of the graph.
- A coloring is a the function find applied to the map *)
-
-Module ColorMap := FMapAVL.Make Register.
-
-(* Function to complete a coloring by giving the
- same color to coalesced vertices *)
-
-Definition complete_coloring e col : ColorMap.t Register.t :=
-let x := snd_ext e in let y := fst_ext e in
-match ColorMap.find y col with
-| None => col
-| Some c => ColorMap.add x c col
-end.
-
-(* Function to compute forbidden colors when completing the coloring
- for simplified or spilled registers (optimistic spilling) *)
-
-Section add_monad.
-
-Definition vertex_add_monad (o : option Register.t) (VS : VertexSet.t) :=
-match o with
-|Some v => VertexSet.add v VS
-|None => VS
-end.
-
-Variable A : Type.
-
-Lemma monad_fold : forall f a l s,
-VertexSet.Equal (fold_left
- (fun (x : VertexSet.t) (e : A) => vertex_add_monad (f e) x)
- (a :: l) s)
- (vertex_add_monad (f a)
- (fold_left (fun (x : VertexSet.t) (e : A) => vertex_add_monad (f e) x) l s)).
-
-Proof.
-intros f a l s;apply fold_left_assoc.
-intros y z e;unfold vertex_add_monad.
-destruct (f y);destruct (f z);[apply add_add|intuition|intuition|intuition].
-intros e1 e2 y H. unfold vertex_add_monad.
-destruct (f y);intuition.
-apply Dec.F.add_m; intuition.
-Qed.
-
-End add_monad.
-
-Definition forbidden_colors x col g :=
-VertexSet.fold (fun v => vertex_add_monad (ColorMap.find v col))
- (interference_adj x g)
- VertexSet.empty.
-
-(* Function to complete the coloring for simplified or spilled vertices.
- Calls forbidden_colors. Is choosing yet any available color *)
-
-Definition available_coloring ircg x (col : ColorMap.t Register.t) :=
-let g := (irc_g ircg) in let palette := (pal ircg) in
-match (VertexSet.choose (VertexSet.diff palette (forbidden_colors x col g))) with
-| None => col
-| Some c => ColorMap.add x c col
-end.
-
-(* Definition of the empty coloring as the coloring where the only
- colored vertices are the precolored ones *)
-
-Definition precoloring_map g :=
-VertexSet.fold (fun x => ColorMap.add x x) (precolored g) (ColorMap.empty Register.t).
-
-Function IRC_map (g : irc_graph)
-{measure irc_measure g} : ColorMap.t Register.t :=
-match simplify g with
-|Some rg' => let (r,g') := rg' in available_coloring g r (IRC_map g')
-|None => match coalesce g with
- |Some eg' => let (e,g') := eg' in complete_coloring e (IRC_map g')
- |None => match freeze g with
- |Some rg' => let (r,g') := rg' in IRC_map g'
- |None => match spill g with
- |Some rg' => let (r,g') := rg' in available_coloring g r (IRC_map g')
- |None => precoloring_map (irc_g g)
- end
- end
- end
-end.
-
-Proof.
-intros. apply (simplify_dec g r g' teq).
-intros. apply (coalesce_dec g e g' teq0).
-intros. apply (freeze_dec g r g' teq1).
-intros. apply (spill_dec g r g' teq2).
-Qed.
-
-(* Definition of the transformation from a map to a coloring,
- simply by using find *)
-
-Definition map_to_coloring (colmap : ColorMap.t Register.t) :=
-fun x => ColorMap.find x colmap.
-
-(* Final definition of iterated register coalescing *)
-
-Definition IRC g palette :=
-let g' := graph_to_IRC_graph g palette in map_to_coloring (IRC_map g').
-
-Definition precoloring g := map_to_coloring (precoloring_map g).