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[Dominators] Use Semi-NCA instead of SLT to calculate dominators
Summary: This patch makes GenericDomTreeConstruction use the Semi-NCA algorithm instead of Simple Lengauer-Tarjan. As described in `RFC: Dynamic dominators`, Semi-NCA offers slightly better performance than SLT. What's more important, it can be extended to perform incremental updates on already constructed dominator trees. The patch passes check-all, llvm test suite and is able to boostrap clang. I also wasn't able to observe any compilation time regressions. Reviewers: sanjoy, dberlin, chandlerc, grosser Reviewed By: dberlin Subscribers: llvm-commits Differential Revision: https://reviews.llvm.org/D34258 git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@306437 91177308-0d34-0410-b5e6-96231b3b80d8
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@ -10,10 +10,11 @@
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///
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/// Generic dominator tree construction - This file provides routines to
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/// construct immediate dominator information for a flow-graph based on the
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/// algorithm described in this document:
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/// Semi-NCA algorithm described in this dissertation:
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///
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/// A Fast Algorithm for Finding Dominators in a Flowgraph
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/// T. Lengauer & R. Tarjan, ACM TOPLAS July 1979, pgs 121-141.
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/// Linear-Time Algorithms for Dominators and Related Problems
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/// Loukas Georgiadis, Princeton University, November 2005, pp. 21-23:
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/// ftp://ftp.cs.princeton.edu/reports/2005/737.pdf
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///
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/// This implements the O(n*log(n)) versions of EVAL and LINK, because it turns
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/// out that the theoretically slower O(n*log(n)) implementation is actually
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@ -169,39 +170,22 @@ void Calculate(DominatorTreeBaseByGraphTraits<GraphTraits<NodeT>> &DT,
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N = DFSPass<GraphT>(DT, DT.Roots[0], N);
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}
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// it might be that some blocks did not get a DFS number (e.g., blocks of
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// It might be that some blocks did not get a DFS number (e.g., blocks of
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// infinite loops). In these cases an artificial exit node is required.
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MultipleRoots |= (DT.isPostDominator() && N != GraphTraits<FuncT*>::size(&F));
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// When naively implemented, the Lengauer-Tarjan algorithm requires a separate
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// bucket for each vertex. However, this is unnecessary, because each vertex
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// is only placed into a single bucket (that of its semidominator), and each
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// vertex's bucket is processed before it is added to any bucket itself.
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//
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// Instead of using a bucket per vertex, we use a single array Buckets that
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// has two purposes. Before the vertex V with preorder number i is processed,
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// Buckets[i] stores the index of the first element in V's bucket. After V's
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// bucket is processed, Buckets[i] stores the index of the next element in the
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// bucket containing V, if any.
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SmallVector<unsigned, 32> Buckets;
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Buckets.resize(N + 1);
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for (unsigned i = 1; i <= N; ++i)
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Buckets[i] = i;
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// Initialize IDoms to spanning tree parents.
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for (unsigned i = 1; i <= N; ++i) {
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const NodePtr V = DT.Vertex[i];
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DT.IDoms[V] = DT.Vertex[DT.Info[V].Parent];
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}
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// Step #2: Calculate the semidominators of all vertices.
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for (unsigned i = N; i >= 2; --i) {
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NodePtr W = DT.Vertex[i];
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auto &WInfo = DT.Info[W];
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// Step #2: Implicitly define the immediate dominator of vertices
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for (unsigned j = i; Buckets[j] != i; j = Buckets[j]) {
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NodePtr V = DT.Vertex[Buckets[j]];
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NodePtr U = Eval<GraphT>(DT, V, i + 1);
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DT.IDoms[V] = DT.Info[U].Semi < i ? U : W;
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}
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// Step #3: Calculate the semidominators of all vertices
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// initialize the semi dominator to point to the parent node
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// Initialize the semi dominator to point to the parent node.
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WInfo.Semi = WInfo.Parent;
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for (const auto &N : inverse_children<NodeT>(W))
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if (DT.Info.count(N)) { // Only if this predecessor is reachable!
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@ -209,32 +193,22 @@ void Calculate(DominatorTreeBaseByGraphTraits<GraphTraits<NodeT>> &DT,
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if (SemiU < WInfo.Semi)
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WInfo.Semi = SemiU;
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}
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// If V is a non-root vertex and sdom(V) = parent(V), then idom(V) is
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// necessarily parent(V). In this case, set idom(V) here and avoid placing
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// V into a bucket.
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if (WInfo.Semi == WInfo.Parent) {
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DT.IDoms[W] = DT.Vertex[WInfo.Parent];
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} else {
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Buckets[i] = Buckets[WInfo.Semi];
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Buckets[WInfo.Semi] = i;
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}
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}
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if (N >= 1) {
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NodePtr Root = DT.Vertex[1];
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for (unsigned j = 1; Buckets[j] != 1; j = Buckets[j]) {
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NodePtr V = DT.Vertex[Buckets[j]];
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DT.IDoms[V] = Root;
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}
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}
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// Step #4: Explicitly define the immediate dominator of each vertex
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// Step #3: Explicitly define the immediate dominator of each vertex.
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// IDom[i] = NCA(SDom[i], SpanningTreeParent(i)).
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// Note that the parents were stored in IDoms and later got invalidated during
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// path compression in Eval.
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for (unsigned i = 2; i <= N; ++i) {
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NodePtr W = DT.Vertex[i];
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NodePtr &WIDom = DT.IDoms[W];
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if (WIDom != DT.Vertex[DT.Info[W].Semi])
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WIDom = DT.IDoms[WIDom];
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const NodePtr W = DT.Vertex[i];
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const auto &WInfo = DT.Info[W];
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const unsigned SDomNum = DT.Info[DT.Vertex[WInfo.Semi]].DFSNum;
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NodePtr WIDomCandidate = DT.IDoms[W];
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while (DT.Info[WIDomCandidate].DFSNum > SDomNum)
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WIDomCandidate = DT.IDoms[WIDomCandidate];
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DT.IDoms[W] = WIDomCandidate;
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}
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if (DT.Roots.empty()) return;
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