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|
(*
* This is Reif and Tarjan's algorithm (SIAM J Computing 1981)
* for computing approximate birthpoints for expressions.
* For each basic block B,
* idef(x) = { defs(v_i) | i = 1 ... n in all paths
* idom(x) v_1 v_2 ... v_n x where n >= 1 and
* v_i <> idom(x) for all 1 <= i <= n
* }
* -- Allen
*)
structure IDefs : IDEFS =
struct
structure G = Graph
structure SL = SortedList
structure A = Array
structure Rev = ReversedGraphView
type var = int
fun compute_idefs {def_use, cfg} =
let val CFG as G.GRAPH cfg = cfg
val N = #capacity cfg ()
val DU = A.array(N,([],[]))
val _ = #forall_nodes cfg
(fn (b,b') => let val (d,u) = def_use(b,b')
in A.update(DU,b,(SL.uniq d,SL.uniq u))
end)
fun dump(name,a) =
(print(name^"=");
A.appi (fn (i,v) =>
print(Int.toString i ^ "=" ^Int.toString v^" "))
(a,0,NONE);
print "\n")
fun tarjan_lengauer(G.GRAPH cfg) =
let val [ENTRY] = #entries cfg ()
val vertex = A.array(N,~1)
val parent = A.array(N,~1)
val semi = A.array(N,~1)
val bucket = A.array(N,[])
val dom = A.array(N,~1)
val sdefuse = A.array(N,([],[]))
val idefuse = A.array(N,([],[]))
val ancestor = A.array(N,~1)
val treeparent = A.array(N,~1)
val label = A.array(N,~1)
fun dfs(p,n,i) =
if A.sub(semi,i) <> ~1 then n
else
(A.update(parent,i,p);
A.update(semi,i,n);
A.update(vertex,n,i);
A.update(label,i,i);
dfs'(i,n+1,#succ cfg i)
)
and dfs'(p,n,[]) = n
| dfs'(p,n,i::is) = dfs'(p,dfs(p,n,i),is)
val n = dfs(~1,0,ENTRY)
fun COMPRESS v =
if A.sub(ancestor,A.sub(ancestor,v)) <> ~1 then
(COMPRESS(A.sub(ancestor,v));
let val label_ancestor_v = A.sub(label,A.sub(ancestor,v))
val label_v = A.sub(label,v)
in if A.sub(semi,label_ancestor_v) <
A.sub(semi,label_v) then
A.update(label,v,label_ancestor_v)
else ()
end;
A.update(ancestor,v,A.sub(ancestor,A.sub(ancestor,v)))
)
else ()
fun LINK(v,w) = (A.update(ancestor,w,v);
A.update(treeparent,w,v))
fun EVAL v =
if A.sub(ancestor,v) = ~1 then v
else (COMPRESS v; A.sub(label,v))
fun EVALDEFUSE v =
let fun up(v,D,U) =
let val p = A.sub(treeparent,v)
in if p = ~1 then (D,U)
else let val (d,u) = A.sub(DU,v)
val (d',u') = A.sub(sdefuse,v)
in up(p,SL.merge(d,SL.merge(d',D)),
SL.merge(u,SL.merge(u',U)))
end
end
in
up(v,[],[])
end
fun step2_3 0 = ()
| step2_3 i =
let val w = A.sub(vertex,i)
val parent_w = A.sub(parent,w)
fun step2 [] = ()
| step2 ((v,_,_)::vs) =
let val u = EVAL v
val semi_u = A.sub(semi,u)
in if semi_u < A.sub(semi,w) then
A.update(semi,w,semi_u)
else ();
let val (d,u) = EVALDEFUSE v
val (d',u') = A.sub(sdefuse,w)
in A.update(sdefuse,w,(SL.merge(d,d'),
SL.merge(u,u')))
end;
step2 vs
end
val _ = step2(#in_edges cfg w)
val vertex_semi_w = A.sub(vertex,A.sub(semi,w))
val _ = A.update(bucket,vertex_semi_w,
w::A.sub(bucket,vertex_semi_w))
val _ = LINK(parent_w,w)
fun step3 [] = ()
| step3 (v::vs) =
let val u = EVAL v
in A.update(dom,v,if A.sub(semi,u) < A.sub(semi,v)
then u else parent_w);
let val (d,u) = A.sub(sdefuse,v)
val (d',u') = EVALDEFUSE(A.sub(parent,v))
in A.update(idefuse,v,(SL.merge(d,d'),
SL.merge(u,u')))
end;
step3 vs
end
val _ = step3 (A.sub(bucket,parent_w))
val _ = A.update(bucket,parent_w,[])
in step2_3(i-1)
end
val _ = step2_3(n-1)
(*
val _ = print("n = "^Int.toString n^"\n")
val _ = dump("vertex",vertex)
val _ = dump("parent",parent)
val _ = dump("semi",semi)
val _ = dump("dom",dom)
val _ = dump("ancestor",ancestor)
val _ = dump("label",label)
*)
fun step4 i =
if i = n then ()
else let val w = A.sub(vertex,i)
in if A.sub(dom,w) <> A.sub(vertex,A.sub(semi,w)) then
let val (d,u) = A.sub(idefuse,A.sub(dom,w))
val (d',u') = A.sub(idefuse,w)
in A.update(idefuse,w,(SL.merge(d,d'),
SL.merge(u,u')));
A.update(dom,w,A.sub(dom,A.sub(dom,w)))
end
else ();
step4(i+1)
end
val _ = step4 1
in idefuse
end
in
{idefuse = fn _ => tarjan_lengauer(CFG),
ipostdefuse = fn _ => tarjan_lengauer(Rev.rev_view CFG)
}
end
end
|
