// A Fast Algorithm for Finding Dominators in a Flowgraph
// T. Lengauer & R. Tarjan, ACM TOPLAS July 1979, pgs 121-141.
//
-// This implements the O(n*log(n)) versions of EVAL and LINK, because it turns
-// out that the theoretically slower O(n*log(n)) implementation is actually
-// faster than the almost-linear O(n*alpha(n)) version, even for large CFGs.
+// This implements both the O(n*ack(n)) and the O(n*log(n)) versions of EVAL and
+// LINK, but it turns out that the theoretically slower O(n*log(n))
+// implementation is actually faster than the "efficient" algorithm (even for
+// large CFGs) because the constant overheads are substantially smaller. The
+// lower-complexity version can be enabled with the following #define:
+//
+#define BALANCE_IDOM_TREE 0
//
//===----------------------------------------------------------------------===//
}
}
#else
- bool IsChildOfArtificialExit = (N != 0);
+ bool IsChilOfArtificialExit = (N != 0);
std::vector<std::pair<typename GraphT::NodeType*,
typename GraphT::ChildIteratorType> > Worklist;
//BBInfo[V].Child = 0; // Child[v] = 0
BBInfo.Size = 1; // Size[v] = 1
- if (IsChildOfArtificialExit)
+ if (IsChilOfArtificialExit)
BBInfo.Parent = 1;
- IsChildOfArtificialExit = false;
+ IsChilOfArtificialExit = false;
}
// store the DFS number of the current BB - the reference to BBInfo might
typename GraphT::NodeType *V) {
typename DominatorTreeBase<typename GraphT::NodeType>::InfoRec &VInfo =
DT.Info[V];
+#if !BALANCE_IDOM_TREE
+ // Higher-complexity but faster implementation
if (VInfo.Ancestor == 0)
return V;
Compress<GraphT>(DT, V);
return VInfo.Label;
+#else
+ // Lower-complexity but slower implementation
+ if (VInfo.Ancestor == 0)
+ return VInfo.Label;
+ Compress<GraphT>(DT, V);
+ GraphT::NodeType* VLabel = VInfo.Label;
+
+ GraphT::NodeType* VAncestorLabel = DT.Info[VInfo.Ancestor].Label;
+ if (DT.Info[VAncestorLabel].Semi >= DT.Info[VLabel].Semi)
+ return VLabel;
+ else
+ return VAncestorLabel;
+#endif
}
template<class GraphT>
void Link(DominatorTreeBase<typename GraphT::NodeType>& DT,
unsigned DFSNumV, typename GraphT::NodeType* W,
typename DominatorTreeBase<typename GraphT::NodeType>::InfoRec &WInfo) {
+#if !BALANCE_IDOM_TREE
+ // Higher-complexity but faster implementation
WInfo.Ancestor = DFSNumV;
+#else
+ // Lower-complexity but slower implementation
+ GraphT::NodeType* WLabel = WInfo.Label;
+ unsigned WLabelSemi = DT.Info[WLabel].Semi;
+ GraphT::NodeType* S = W;
+ InfoRec *SInfo = &DT.Info[S];
+
+ GraphT::NodeType* SChild = SInfo->Child;
+ InfoRec *SChildInfo = &DT.Info[SChild];
+
+ while (WLabelSemi < DT.Info[SChildInfo->Label].Semi) {
+ GraphT::NodeType* SChildChild = SChildInfo->Child;
+ if (SInfo->Size+DT.Info[SChildChild].Size >= 2*SChildInfo->Size) {
+ SChildInfo->Ancestor = S;
+ SInfo->Child = SChild = SChildChild;
+ SChildInfo = &DT.Info[SChild];
+ } else {
+ SChildInfo->Size = SInfo->Size;
+ S = SInfo->Ancestor = SChild;
+ SInfo = SChildInfo;
+ SChild = SChildChild;
+ SChildInfo = &DT.Info[SChild];
+ }
+ }
+
+ DominatorTreeBase::InfoRec &VInfo = DT.Info[V];
+ SInfo->Label = WLabel;
+
+ assert(V != W && "The optimization here will not work in this case!");
+ unsigned WSize = WInfo.Size;
+ unsigned VSize = (VInfo.Size += WSize);
+
+ if (VSize < 2*WSize)
+ std::swap(S, VInfo.Child);
+
+ while (S) {
+ SInfo = &DT.Info[S];
+ SInfo->Ancestor = V;
+ S = SInfo->Child;
+ }
+#endif
}
template<class FuncT, class NodeT>
// infinite loops). In these cases an artificial exit node is required.
MultipleRoots |= (DT.isPostDominator() && N != F.size());
- // When naively implemented, the Lengauer-Tarjan algorithm requires a separate
- // bucket for each vertex. However, this is unnecessary, because each vertex
- // is only placed into a single bucket (that of its semidominator), and each
- // vertex's bucket is processed before it is added to any bucket itself.
- //
- // Instead of using a bucket per vertex, we use a single array Buckets that
- // has two purposes. Before the vertex V with preorder number i is processed,
- // Buckets[i] stores the index of the first element in V's bucket. After V's
- // bucket is processed, Buckets[i] stores the index of the next element in the
- // bucket containing V, if any.
- std::vector<unsigned> Buckets;
- Buckets.resize(N + 1);
- for (unsigned i = 1; i <= N; ++i)
- Buckets[i] = i;
-
for (unsigned i = N; i >= 2; --i) {
typename GraphT::NodeType* W = DT.Vertex[i];
typename DominatorTreeBase<typename GraphT::NodeType>::InfoRec &WInfo =
DT.Info[W];
- // Step #2: Implicitly define the immediate dominator of vertices
- for (unsigned j = i; Buckets[j] != i; j = Buckets[j]) {
- typename GraphT::NodeType* V = DT.Vertex[Buckets[j]];
- typename GraphT::NodeType* U = Eval<GraphT>(DT, V);
- DT.IDoms[V] = DT.Info[U].Semi < i ? U : W;
- }
-
- // Step #3: Calculate the semidominators of all vertices
+ // Step #2: Calculate the semidominators of all vertices
// initialize the semi dominator to point to the parent node
WInfo.Semi = WInfo.Parent;
}
}
+ typename GraphT::NodeType* WParent = DT.Vertex[WInfo.Parent];
+
// If V is a non-root vertex and sdom(V) = parent(V), then idom(V) is
// necessarily parent(V). In this case, set idom(V) here and avoid placing
// V into a bucket.
- if (WInfo.Semi == WInfo.Parent) {
- DT.IDoms[W] = DT.Vertex[WInfo.Parent];
- } else {
- Buckets[i] = Buckets[WInfo.Semi];
- Buckets[WInfo.Semi] = i;
- }
+ if (WInfo.Semi == WInfo.Parent)
+ DT.IDoms[W] = WParent;
+ else
+ DT.Info[DT.Vertex[WInfo.Semi]].Bucket.push_back(W);
Link<GraphT>(DT, WInfo.Parent, W, WInfo);
- }
- if (N >= 1) {
- typename GraphT::NodeType* Root = DT.Vertex[1];
- for (unsigned j = 1; Buckets[j] != 1; j = Buckets[j]) {
- typename GraphT::NodeType* V = DT.Vertex[Buckets[j]];
- DT.IDoms[V] = Root;
+ // Step #3: Implicitly define the immediate dominator of vertices
+ std::vector<typename GraphT::NodeType*> &WParentBucket =
+ DT.Info[WParent].Bucket;
+ while (!WParentBucket.empty()) {
+ typename GraphT::NodeType* V = WParentBucket.back();
+ WParentBucket.pop_back();
+ typename GraphT::NodeType* U = Eval<GraphT>(DT, V);
+ DT.IDoms[V] = DT.Info[U].Semi < DT.Info[V].Semi ? U : WParent;
}
}