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(*
* This is my L-compressed DJ-graph data structure for optimal SSA
* construction. For the description of this algorithm, see:
* http://www.cs.nyu.edu/leunga/my-papers/linear-ssa.ps
* --Allen
*)
functor L_DJGraph (Dom : DOMINATOR_TREE) : DJ_GRAPH =
struct
structure G = Graph
structure Dom = Dom
structure A = Array
datatype exit_tree =
NODE of { name : int,
jedges : int list,
eedges : exit_tree list,
minVisitedLevel : int ref,
visited : int ref
}
datatype ('n,'e,'g) dj_graph =
DJGRAPH of
{ dom : ('n,'e,'g) Dom.dominator_tree,
trees : exit_tree list A.array,
stamp : int ref
}
fun error msg = MLRiscErrorMsg.error("L-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 debug = true
fun DJ(Dom as G.GRAPH dom) =
let val G.GRAPH cfg = Dom.cfg Dom
val N = #capacity dom ()
val [ENTRY] = #entries dom ()
val levelsMap = Dom.levelsMap Dom
val L = Dom.max_levels Dom
val trees = A.array(N, [])
val levels' = A.array(L, ~1)
val exitLevels' = A.array(L, ~1)
val T = A.array(L, [])
val J = A.array(L, [])
fun LTrees a =
let (* recurse *)
fun foreachDedge([]) = ()
| foreachDedge((_,b,_)::es) = (LTrees b; foreachDedge es)
val _ = foreachDedge(#out_edges dom a)
val lvl_a = A.sub(levelsMap, a)
(* partition J-edges *)
fun foreachJedge([], levels) = levels
| foreachJedge((_,b,_)::es, levels) =
let val lvl_b = A.sub(levelsMap, b)
in if lvl_b > lvl_a then (* non-J-edge *)
foreachJedge(es, levels)
else
let val _ =
if A.sub(exitLevels',lvl_b) = a then
A.update(J, lvl_b, b::A.sub(J, lvl_b))
else
(A.update(exitLevels',lvl_b,a);
A.update(J, lvl_b, [b])
)
val levels =
if A.sub(levels',lvl_b) = a then
levels
else
(A.update(T, lvl_b, []);
A.update(levels',lvl_b,a);
lvl_b::levels
)
in foreachJedge(es, levels)
end
end
val levels = foreachJedge(#out_edges cfg a, [])
(* partition subtrees *)
fun foreachDedge([], levels) = levels
| foreachDedge((_,b,_)::es, levels) =
let fun foreachTree([], levels) = levels
| foreachTree((l,t)::ts, levels) =
let val levels =
if l <= lvl_a then
if A.sub(levels',l) = a then
(A.update(T, l, t::A.sub(T, l)); levels)
else (A.update(levels',l,a);
A.update(T, l, [t]);
l::levels)
else levels
in foreachTree(ts, levels) end
val levels = foreachTree(A.sub(trees, b), levels)
in foreachDedge(es, levels)
end
val levels = foreachDedge(#out_edges dom a, levels)
(* Build Trees(a) *)
fun buildTrees([], trees_a) = trees_a
| buildTrees(l::levels, trees_a) =
let fun makeNode(succs) =
let val jedges = if A.sub(exitLevels',l) = a then
A.sub(J,l) else []
in (l,NODE{name=a, jedges=jedges, eedges=succs,
minVisitedLevel=ref 0, visited=ref 0})
end
val T_l =
case A.sub(T,l) of
[] => makeNode []
| ts as [t] => if A.sub(exitLevels',l) <> a then (l,t)
else makeNode ts
| ts => makeNode ts
in buildTrees(levels, T_l::trees_a)
end
val trees_a = buildTrees(levels, [])
in A.update(trees, a, trees_a)
end
fun bucketSort(trees) =
let val buckets = A.array(L, [])
val _ =
#forall_nodes dom
(fn (a,_) =>
let fun insert [] = ()
| insert((l,t)::ts) =
(A.update(buckets,l,(a,t)::A.sub(buckets,l)); insert ts)
in insert(A.sub(trees,a))
end)
val trees = A.array(N, [])
fun collect(l) =
if l >= L then ()
else let fun dist [] = ()
| dist((a,t)::ts) =
(A.update(trees,a,t::A.sub(trees,a)); dist ts)
in dist(A.sub(buckets, l));
collect(l+1)
end
in collect 0;
trees
end
val _ = LTrees ENTRY (* build Trees *)
val trees = bucketSort(trees) (* sort trees *)
in DJGRAPH{dom=Dom, trees=trees, stamp=ref 0}
end
(* Compute dominance frontier *)
fun DF _ = error "DF"
fun IDFs _ = error "IDFs"
fun LiveIDFs (DJGRAPH{trees, dom, stamp, ...}) =
let val G.GRAPH cfg = Dom.cfg dom
val levelsMap = Dom.levelsMap dom
val N = #capacity cfg ()
val inphi = A.array(N, 0)
val inalpha = A.array(N, 0)
val live = A.array(N, 0)
fun newStamp() =
let val s = Word.toIntX(Word.fromInt(!stamp) + 0w1)
in stamp := s; s
end
fun LiveIDFs{defs, localLiveIn=[]} = []
| LiveIDFs{defs, localLiveIn} =
let val stamp = newStamp()
fun initDefs([]) = ()
| initDefs(x::xs) = (A.update(inalpha, x, stamp); initDefs xs)
fun markLiveIn(b) =
let fun markPred [] = ()
| markPred((j,_,_)::es) =
(if A.sub(live,j) <> stamp andalso
A.sub(inalpha,j) <> stamp then
markLiveIn j
else ();
markPred es
)
in (* m := !m + 1; *)
A.update(live,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(live, b) = stamp
fun unmarked(X,b) = A.sub(X,b) <> stamp
fun mark(X,b) = A.update(X,b,stamp)
fun visit(x, queue, IDF) =
let val level_x = A.sub(levelsMap, x)
fun walk(NODE{name=y, jedges, eedges, visited, minVisitedLevel},
queue, IDF) =
let fun foreachJedge([], queue, IDF) = (queue, IDF)
| foreachJedge(z::es, queue, IDF) =
if isLive z andalso unmarked(inphi,z)
then (mark(inphi, z);
foreachJedge
(es,
if unmarked(inalpha,z) then z::queue else queue,
z::IDF)
)
else foreachJedge(es, queue, IDF)
fun foreachEEdge([], queue, IDF) = (queue, IDF)
| foreachEEdge((z as NODE{name=z',...})::es, queue, IDF) =
if isLive z' then
let val (queue, IDF) = walk(z, queue, IDF)
in foreachEEdge(es, queue, IDF) end
else
foreachEEdge(es, queue, IDF)
in if !visited = stamp then (* visited before *)
(minVisitedLevel := Int.min(!minVisitedLevel, level_x);
(queue, IDF)
)
else
(minVisitedLevel := level_x; (* non-visited *)
visited := stamp;
let val (queue, IDF) = foreachJedge(jedges, queue, IDF)
in foreachEEdge(eedges, queue, IDF) end
)
end
fun ancestorHasBeenProcessed
(NODE{visited, minVisitedLevel, ...}) =
!visited = stamp andalso !minVisitedLevel < level_x
fun foreachTree([], queue, IDF) = (queue, IDF)
| foreachTree(t::ts, queue, IDF) =
if ancestorHasBeenProcessed t then (queue, IDF)
else let val (queue, IDF) = walk(t, queue, IDF)
in foreachTree(ts, queue, IDF) end
in foreachTree(A.sub(trees, x), queue, IDF)
end
fun visitAll([], IDF) = IDF
| visitAll(x::queue, IDF) =
let val (queue, IDF) = visit(x, queue, IDF)
in visitAll(queue, IDF) end
in initDefs defs;
initLiveIn localLiveIn;
visitAll(defs, [])
end
in LiveIDFs
end
end
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