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|
(*
* The algorithm for computing iterated dominance
* frontier is my own algorithm which uses the $k$-compressed DJ-graph,
* which is a variant of DJ-graph due to Sreedhar, Gao and Lee. Here,
* I've set k=2. The algorithm using $k$-compressed DJ-graph is significantly
* faster than the DJ-graph version when |DF(x)| <= k.
*
* The write up will be in my thesis.
*
* --Allen
*)
functor K_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("K_DJGraph",msg)
val stats = true (* collect statistics? *)
val levelPrune = true
val domPrune = true
val pathPrune = true
val visitCount = MLRiscControl.getCounter "dj-visit-count"
val liveVisitCount = MLRiscControl.getCounter "dj-live-visit-count"
val debug = true
val K_max = 2
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_DF = 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_DF,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_DF = 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 *)
(*
* This algorithm is described in POPL 95
*)
fun IDFs xs =
let val stamp = new_stamp()
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_DF,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 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)
in visitAll(L,[])
end
in IDFs
end
(* Compute iterated dominance frontier intersected with liveness.
* This is my special algorithm! The idea is that when we find a
* new node b in IDF^+(S) we first check whether b is liveIn. If not,
* we can prune the search right there. If so, we continue as normal.
* Checking whether something is liveIn triggers the incremental liveness
* routine.
*
* -- Allen
*)
datatype kind = JOIN | DOM
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 minJLevels = A.array(N,10000000)
val djGraph = A.array(N,[]) (* path compressed dj graph *)
val liveIn = A.array(N,0) (* is a variable live in *)
val visited = A.array(N,0)
val strictly_dominates = Dom.dominates D
val K_inf = 255
fun compressDJGraph(X, lvl) =
let val nextLvl = lvl + 1
val stamp = ~X
(* merge join list, make sure there are no duplicates *)
fun mergeJoin(Z, E, n) =
if A.sub(visited, Z) = stamp orelse
A.sub(levels, Z) >= lvl then (E, n)
else (A.update(visited, Z, stamp);
(Z::E, n+1))
fun mergeJoins([], E, n) = (E, n)
| mergeJoins(Z::Zs, E, n) =
let val (E, n) = mergeJoin(Z, E, n)
in mergeJoins(Zs, E, n)
end
fun appendJoins([], E) = E
| appendJoins(Z::Zs, E) = appendJoins(Zs, (JOIN,Z)::E)
fun collapse([], DJ_X) = DJ_X
| collapse((e as (DOM,_))::Zs, DJ_X) = collapse(Zs, e::DJ_X)
| collapse((e as (JOIN,Z))::Zs, DJ_X) =
if A.sub(levels, Z) <= lvl then collapse(Zs, e::DJ_X)
else collapse(Zs, DJ_X)
(* L_X -- min level of all join edges in SubTree(X)
* DJ_X -- all dj-graph edges of X
* E_X -- all J-edges in SubTree(X) to level < lvl.
* K_X -- |E_X|
*)
fun walkDomSucc([], L_X, DJ_X, E_X, K_X) = (L_X, DJ_X, E_X, K_X)
| walkDomSucc((_,Y,_)::es, L_X, DJ_X, E_X, K_X) =
let val (L_Y, E_Y, K_Y) = compressDJGraph(Y, nextLvl)
val L_X = Int.min(L_X, L_Y)
in if pathPrune then
if L_Y >= nextLvl then
(* disconnect dom edge! *)
walkDomSucc(es, L_X, DJ_X, E_X, K_X)
else if K_Y <= K_max then
(* path compress! *)
let val (E_X, K_X) = mergeJoins(E_Y, E_X, K_X)
in walkDomSucc(es, L_X, appendJoins(E_Y, DJ_X), E_X, K_X)
end
else
let val Zs = A.sub(djGraph, Y)
in if length Zs <= K_max then
walkDomSucc(es, L_X, collapse(Zs,DJ_X), [], K_inf)
else
walkDomSucc(es, L_X, (DOM,Y)::DJ_X, [], K_inf)
end
else
walkDomSucc(es, L_X, (DOM,Y)::DJ_X, [], K_inf)
end
fun walkCFGSucc([], L_X, DJ_X, E_X, K_X) = (L_X, DJ_X, E_X, K_X)
| walkCFGSucc((_,Y,_)::es, L_X, DJ_X, E_X, K_X) =
let val L_X = Int.min(L_X, A.sub(levels, Y))
val (E_X, K_X) = mergeJoin(Y, E_X, K_X)
in walkCFGSucc(es, L_X, (JOIN,Y)::DJ_X, E_X, K_X)
end
val (L_X, DJ_X, E_X, K_X) =
walkDomSucc(#out_edges dom X, 10000000, [], [], 0)
val (L_X, DJ_X, E_X, K_X) =
walkCFGSucc(#out_edges cfg X, L_X, DJ_X, E_X, K_X)
in A.update(minJLevels, X, L_X);
A.update(djGraph, X, DJ_X);
(L_X, E_X, K_X)
end
val [ENTRY] = #entries dom ()
val _ = compressDJGraph(ENTRY, 0)
fun LiveIDFs {defs, localLiveIn=[]} = [] (* special case *)
| LiveIDFs {defs=xs, localLiveIn} =
let val stamp = new_stamp()
(* 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 foreach([],S) = S
| foreach((JOIN,z)::zs,S) =
let val level_z = A.sub(levels,z)
in if level_z <= level_x andalso
A.sub(in_phi,z) <> stamp andalso
isLive z
(* z is a new IDF^+ candidate;
* make sure it is live.
*)
then (A.update(in_phi,z,stamp);
if A.sub(in_alpha,z) <> stamp
then A.update(piggybank,level_z,
z::A.sub(piggybank,level_z))
else ();
foreach(zs,z::S)
)
else foreach(zs,S)
end
| foreach((DOM,z)::zs,S) =
foreach(zs,if isLive z andalso
A.sub(visited,z) <> stamp andalso
(not levelPrune orelse
A.sub(minJLevels,z) <= level_x)
then (A.update(visited,z,stamp);
visit(z,level_x,S)
)
else S)
in if stats then visitCount := !visitCount + 1 else ();
foreach(A.sub(djGraph, y),S)
end
fun visitAll(~1,S) = S
| visitAll(l,S) =
case A.sub(piggybank,l) of
[] => visitAll(l-1,S)
| x::xs =>
let val _ = A.update(piggybank,l,xs)
val _ = A.update(visited,x,stamp);
val S = visit(x, A.sub(levels, x), S)
in
visitAll(l,S)
end
fun domTest([x],uses) =
let fun loop [] = true
| loop(y::ys) = strictly_dominates(x,y) andalso loop ys
in loop uses end
| domTest _ = false
in if domPrune andalso domTest(xs,localLiveIn) then []
else
let val L = initDefs(xs, ~1)
in initLiveIn(localLiveIn);
visitAll(L, [])
end
end
in LiveIDFs
end
end
|
