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(*
* The algorithm for computing iterated dominance frontier.
* This is the algorithm by Sreedhar, Gao and Lee.
*
* --Allen
*)
functor DJGraph (Dom : DOMINATOR_TREE) : DJ_GRAPH =
struct
structure G = Graph
structure Dom = Dom
structure A = Array
type ('n,'e,'g) dj_graph = ('n,'e,'g) Dom.dominator_tree
fun error msg = MLRiscErrorMsg.error("DJGraph",msg)
val stats = false (* collect statistics? *)
val visitCount = MLRiscControl.getCounter "dj-visit-count"
val idfCount = MLRiscControl.getCounter "dj-IDF-count"
val idfSize = MLRiscControl.getCounter "dj-IDF-size"
val liveVisitCount = MLRiscControl.getCounter "dj-live-visit-count"
val maxBlockSize = MLRiscControl.getCounter "dj-max-block-size"
val totalBlockSize = MLRiscControl.getCounter "dj-total-block-size"
val debug = false
fun DJ x = x
(* Compute dominance frontier *)
fun DF (D as G.GRAPH dom) =
let val G.GRAPH cfg = Dom.cfg D
val L = Dom.max_levels D
val N = #capacity dom ()
val levels = Dom.levelsMap D
val in_phi = A.array(N,0) (* has appeared in the DF set? *)
val stamp = ref 0
fun new_stamp() = let val s = !stamp + 1 in stamp := s; s end
fun unmarked(marked,i,stamp : int) =
let val s = A.sub(marked,i)
in if s = stamp then false else (A.update(marked,i,stamp); true)
end
(*
* Compute the dominance frontiers of a node
* Dominance frontier of x:
* The set of all nodes y such that x dominates a predecessor
* of y but x doesn't strictly dominates y.
*)
fun DF x =
let val stamp = new_stamp()
val level_x = A.sub(levels,x)
fun walk(z, S) =
let fun scan((_,y,_)::es,S) =
if A.sub(levels,y) <= level_x andalso
unmarked(in_phi,y,stamp) then scan(es,y::S)
else scan(es,S)
| scan([],S) = S
val S = scan(#out_edges cfg z,S)
fun walkList([],S) = S
| walkList((_,z,_)::es,S) = walkList(es,walk(z,S))
in walkList(#out_edges dom z,S)
end
in walk(x,[])
end
in DF end
(* Compute iterated dominance frontier *)
fun IDFs (D as G.GRAPH dom) =
let val G.GRAPH cfg = Dom.cfg D
val L = Dom.max_levels D
val N = #capacity dom ()
val levels = Dom.levelsMap D
val in_phi = A.array(N,0) (* has appeared in the DF set? *)
val stamp = ref 0
fun new_stamp() = let val s = !stamp + 1 in stamp := s; s end
fun unmarked(marked,i,stamp : int) =
let val s = A.sub(marked,i)
in if s = stamp then false else (A.update(marked,i,stamp); true)
end
val in_alpha = A.array(N,0) (* has appeared in N_alpha? *)
val visited = A.array(N,0) (* has it been visited *)
val piggybank = A.array(L,[]) (* nodes in the piggy bank *)
val n = ref 0
(*
* This algorithm is described in POPL 95
*)
fun IDFs xs =
let val stamp = new_stamp()
val _ = if stats then (idfCount := !idfCount + 1; n := !visitCount)
else ()
fun init([],l) = l
| init(x::xs,l) =
let val l_x = A.sub(levels,x)
in A.update(in_alpha,x,stamp);
A.update(piggybank,l_x,x::A.sub(piggybank,l_x));
init(xs,if l < l_x then l_x else l)
end
fun visit(y,level_x,S) =
let fun scan([],S) = S
| scan((_,z,_)::es,S) =
let val level_z = A.sub(levels,z)
in if level_z <= level_x andalso unmarked(in_phi,z,stamp)
then (if A.sub(in_alpha,z) <> stamp
then A.update(piggybank,level_z,
z::A.sub(piggybank,level_z))
else ();
scan(es,z::S))
else scan(es,S)
end
fun visitSucc([],S) = S
| visitSucc((_,z,_)::es,S) =
visitSucc(es,if unmarked(visited,z,stamp)
then visit(z,level_x,S) else S)
val S = scan(#out_edges cfg y,S)
in if stats then visitCount := !visitCount + 1 else ();
visitSucc(#out_edges dom y,S)
end
fun visitAll(~1,S) = S
| visitAll(l,S) =
case A.sub(piggybank,l) of
[] => visitAll(l-1,S)
| x::xs => (A.update(visited,x,stamp);
A.update(piggybank,l,xs);
visitAll(l,visit(x,A.sub(levels,x),S)))
val L = init(xs,~1)
val IDF = visitAll(L,[])
in if stats then
(idfSize := !idfSize + length IDF;
maxBlockSize := Int.max(!maxBlockSize, N);
totalBlockSize := !totalBlockSize + N
)
else ();
if debug then print("N="^Int.toString N^" visits="^
Int.toString(!visitCount - !n)^"\n") else ();
IDF
end
in IDFs
end
fun LiveIDFs(D as G.GRAPH dom) =
let val G.GRAPH cfg = Dom.cfg D
val L = Dom.max_levels D
val N = #capacity dom ()
val levels = Dom.levelsMap D
val in_phi = A.array(N,0) (* has appeared in the DF set? *)
val stamp = ref 0
fun new_stamp() = let val s = !stamp + 2 in stamp := s; s end
val in_alpha = A.array(N,0) (* has appeared in N_alpha? *)
val piggybank = A.array(L,[]) (* nodes in the piggy bank *)
val liveIn = A.array(N,0) (* is a variable live in *)
val visited = A.array(N,0)
fun unmarked(marked,i,stamp : int) =
let val s = A.sub(marked,i)
in if s = stamp then false else (A.update(marked,i,stamp); true)
end
fun LiveIDFs {defs, localLiveIn=[]} = [] (* special case *)
| LiveIDFs {defs=xs, localLiveIn} =
let val stamp = new_stamp()
val _ = if stats then idfCount := !idfCount + 1 else ()
(* val n = ref 0
val m = ref 0 *)
fun initDefs([],maxLvl) = maxLvl
| initDefs(x::xs,maxLvl) =
let val lvl_x = A.sub(levels,x)
in A.update(in_alpha,x,stamp);
A.update(piggybank,lvl_x,x::A.sub(piggybank,lvl_x));
initDefs(xs,if maxLvl < lvl_x then lvl_x else maxLvl)
end
fun markLiveIn(b) =
let fun markPred [] = ()
| markPred((j,_,_)::es) =
(if A.sub(liveIn,j) <> stamp andalso
A.sub(in_alpha,j) <> stamp then
markLiveIn j
else ();
markPred es
)
in (* m := !m + 1; *)
A.update(liveIn,b,stamp);
if stats then liveVisitCount := !liveVisitCount + 1 else ();
markPred(#in_edges cfg b)
end
fun initLiveIn [] = ()
| initLiveIn(x::xs) = (markLiveIn x; initLiveIn xs)
fun isLive b = A.sub(liveIn,b) = stamp
fun visit(y,level_x,S) =
let fun scan([],S) = S
| scan((_,z,_)::es,S) =
let val level_z = A.sub(levels,z)
in if level_z <= level_x andalso
isLive z andalso
unmarked(in_phi,z,stamp)
then (if A.sub(in_alpha,z) <> stamp
then A.update(piggybank,level_z,
z::A.sub(piggybank,level_z))
else ();
scan(es,z::S))
else scan(es,S)
end
fun visitSucc([],S) = S
| visitSucc((_,z,_)::es,S) =
visitSucc(es,if isLive z andalso unmarked(visited,z,stamp)
then visit(z,level_x,S) else S)
val S = scan(#out_edges cfg y,S)
in visitSucc(#out_edges dom y,S)
end
fun visitAll(~1,S) = S
| visitAll(l,S) =
case A.sub(piggybank,l) of
[] => visitAll(l-1,S)
| x::xs => (A.update(visited,x,stamp);
A.update(piggybank,l,xs);
visitAll(l,visit(x,A.sub(levels,x),S)))
val L = initDefs(xs, ~1)
in initLiveIn(localLiveIn);
visitAll(L, [])
end
in LiveIDFs
end
end
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