/*
*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*/
package org.apache.flex.abc.graph.algorithms;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.Stack;
import org.apache.flex.abc.graph.IBasicBlock;
/**
* An implementation of the O(n log n) Lengauer-Tarjan algorithm for building the
* <a href="http://en.wikipedia.org/wiki/Dominator_%28graph_theory%29">dominator tree</a>
* of a {@link org.apache.flex.abc.graph.IFlowgraph flowgraph}.
*/
public class DominatorTree
{
/**
* Construct a DominatorTree from a root.
* @param root the root of the graph.
*/
public DominatorTree(IBasicBlock root)
{
Collection<IBasicBlock> roots = new ArrayList<IBasicBlock>();
roots.add(root);
this.dfs(roots);
this.computeDominators();
}
/**
* Construct a DominatorTree from a collection of "roots."
* @param roots the collection of roots; one of these is
* the true root of the flowgraph, the others are exception
* handlers that would otherwise be unreachable.
*/
public DominatorTree(Collection<? extends IBasicBlock> roots)
{
this.dfs(roots);
this.computeDominators();
}
/**
* Semidominator numbers by block.
*/
private Map<IBasicBlock, Integer> semi = new HashMap<IBasicBlock, Integer>();
/**
* Parents by block.
*/
private Map<IBasicBlock, IBasicBlock> parent = new HashMap<IBasicBlock, IBasicBlock>();
/**
* Predecessors by block.
*/
private Multimap<IBasicBlock> pred = new Multimap<IBasicBlock>();
/**
* Blocks in DFS order; used to look up a block from its semidominator
* numbering.
*/
private ArrayList<IBasicBlock> vertex = new ArrayList<IBasicBlock>();
/**
* Blocks by semidominator block.
*/
private Multimap<IBasicBlock> bucket = new Multimap<IBasicBlock>();
/**
* idominator map, built iteratively.
*/
private Map<IBasicBlock, IBasicBlock> idom = new HashMap<IBasicBlock, IBasicBlock>();
/**
* Dominance frontiers of this dominator tree, built on demand.
*/
private Multimap<IBasicBlock> dominanceFrontiers = null;
/**
* Dominator tree, built on demand from the idominator map.
*/
private Multimap<IBasicBlock> dominatorTree = null;
/**
* Auxiliary data structure used by the O(m log n) eval/link implementation:
* ancestor relationships in the forest (the processed tree as it's built
* back up).
*/
private Map<IBasicBlock, IBasicBlock> ancestor = new HashMap<IBasicBlock, IBasicBlock>();
/**
* Auxiliary data structure used by the O(m log n) eval/link implementation:
* node with least semidominator seen during traversal of a path from node
* to subtree root in the forest.
*/
private Map<IBasicBlock, IBasicBlock> label = new HashMap<IBasicBlock, IBasicBlock>();
/**
* A topological traversal of the dominator tree, built on demand.
*/
private LinkedList<IBasicBlock> topologicalTraversalImpl = null;
/**
* Create and/or fetch the map of immediate dominators.
* @return the map from each block to its immediate dominator
* (if it has one).
*/
public Map<IBasicBlock, IBasicBlock> getIdoms()
{
return this.idom;
}
/**
* Compute and/or fetch the dominator tree as a Multimap.
* @return the dominator tree.
*/
public Multimap<IBasicBlock> getDominatorTree()
{
if ( this.dominatorTree == null )
{
this.dominatorTree = new Multimap<IBasicBlock>();
for ( IBasicBlock node: this.idom.keySet() )
dominatorTree.get(this.idom.get(node)).add(node);
}
return this.dominatorTree;
}
/**
* Compute and/or fetch the dominance frontiers as a Multimap.
* @return a Multimap where the set of nodes mapped to each key
* node is the set of nodes in the key node's dominance frontier.
*/
public Multimap<IBasicBlock> getDominanceFrontiers()
{
if ( this.dominanceFrontiers == null )
{
this.dominanceFrontiers = new Multimap<IBasicBlock>();
getDominatorTree(); // touch the dominator tree
for ( IBasicBlock x: reverseTopologicalTraversal() )
{
Set<IBasicBlock> dfx = this.dominanceFrontiers.get(x);
// Compute DF(local)
for ( IBasicBlock y: x.getSuccessors() )
if ( idom.get(y) != x )
dfx.add(y);
// Compute DF(up)
for ( IBasicBlock z : this.dominatorTree.get(x) )
for ( IBasicBlock y: this.dominanceFrontiers.get(z) )
if ( idom.get(y) != x )
dfx.add(y);
}
}
return this.dominanceFrontiers;
}
/**
* Create and/or fetch a topological traversal of the dominator tree,
* such that for every node, idom(node) appears before node.
* @return the topological traversal of the dominator tree,
* as an immutable List.
*/
public List<IBasicBlock> topologicalTraversal()
{
return Collections.unmodifiableList(getToplogicalTraversalImplementation());
}
/**
* Create and/or fetch a reverse topological traversal of the dominator tree,
* such that for every node, node appears before idom(node).
* @return a reverse topological traversal of the dominator tree,
* as an immutable List.
*/
public Iterable<IBasicBlock> reverseTopologicalTraversal()
{
return new Iterable<IBasicBlock>()
{
@Override
public Iterator<IBasicBlock> iterator()
{
return getToplogicalTraversalImplementation().descendingIterator();
}
};
}
/**
* Depth-first search the graph and initialize data structures.
* @param roots the root(s) of the flowgraph. One of these is
* the start block, the others are exception handlers.
*/
private void dfs(Collection<? extends IBasicBlock> roots)
{
Iterator<IBasicBlock> it = new DepthFirstPreorderIterator(roots);
while ( it.hasNext() )
{
IBasicBlock node = it.next();
if ( !semi.containsKey(node) )
{
vertex.add(node);
// Initial assumption: the node's semidominator is itself.
semi.put(node, semi.size());
label.put(node, node);
for (IBasicBlock child : node.getSuccessors())
{
pred.get(child).add(node);
if (!semi.containsKey(child))
{
parent.put(child, node);
}
}
}
}
}
/**
* Steps 2, 3, and 4 of Lengauer-Tarjan.
*/
private void computeDominators()
{
int lastSemiNumber = semi.size() - 1;
for (int i = lastSemiNumber; i > 0; i--)
{
IBasicBlock w = vertex.get(i);
IBasicBlock p = this.parent.get(w);
// step 2: compute semidominators
// for each v in pred(w)...
int semidominator = semi.get(w);
for (IBasicBlock v : pred.get(w))
semidominator = Math.min(semidominator, semi.get(eval(v)));
semi.put(w, semidominator);
bucket.get(vertex.get(semidominator)).add(w);
// Link w into the forest via its parent, p
link(p, w);
// step 3: implicitly compute idominators
// for each v in bucket(parent(w)) ...
for (IBasicBlock v : bucket.get(p))
{
IBasicBlock u = eval(v);
if (semi.get(u) < semi.get(v))
idom.put(v, u);
else
idom.put(v, p);
}
bucket.get(p).clear();
}
// step 4: explicitly compute idominators
for (int i = 1; i <= lastSemiNumber; i++)
{
IBasicBlock w = vertex.get(i);
if (idom.get(w) != vertex.get((semi.get(w))))
idom.put(w, idom.get(idom.get(w)));
}
}
/**
* Extract the node with the least-numbered semidominator in the (processed)
* ancestors of the given node.
*
* @param v - the node of interest.
* @return "If v is the root of a tree in the forest, return v. Otherwise,
* let r be the root of the tree which contains v. Return any vertex u != r
* of miniumum semi(u) on the path r-*v."
*/
private IBasicBlock eval(IBasicBlock v)
{
// This version of Lengauer-Tarjan implements
// eval(v) as a path-compression procedure.
compress(v);
return label.get(v);
}
/**
* Traverse ancestor pointers back to a subtree root, then propagate the
* least semidominator seen along this path through the "label" map.
*/
private void compress(IBasicBlock v)
{
Stack<IBasicBlock> worklist = new Stack<IBasicBlock>();
worklist.add(v);
IBasicBlock a = this.ancestor.get(v);
// Traverse back to the subtree root.
while ( this.ancestor.containsKey(a) )
{
worklist.push(a);
a = this.ancestor.get(a);
}
// Propagate semidominator information forward.
IBasicBlock ancestor = worklist.pop();
int leastSemi = semi.get(label.get(ancestor));
while ( !worklist.empty() )
{
IBasicBlock descendent = worklist.pop();
int currentSemi = semi.get(label.get(descendent));
if ( currentSemi > leastSemi)
label.put(descendent, label.get(ancestor));
else
leastSemi = currentSemi;
// Prepare to process the next iteration.
ancestor = descendent;
}
}
/**
* Simple version of link(parent,child) simply links the child into the
* parent's forest, with no attempt to balance the subtrees or otherwise
* optimize searching.
*/
private void link(IBasicBlock parent, IBasicBlock child)
{
this.ancestor.put(child, parent);
}
/**
* Multimap maps a key to a set of values.
*/
@SuppressWarnings("serial")
public static class Multimap<T> extends HashMap<T, Set<T>>
{
/**
* Fetch the set for a given key, creating it if necessary.
*
* @param key - the key.
* @return the set of values mapped to the key.
*/
@SuppressWarnings("unchecked")
@Override
public Set<T> get(Object key)
{
if (!this.containsKey(key))
this.put((T)key, new HashSet<T>());
return super.get(key);
}
}
/**
* Create/fetch the topological traversal of the dominator tree.
* @return {@link this.topologicalTraversal}, the traversal of
* the dominator tree such that for any node n with a dominator,
* n appears before idom(n).
*/
private LinkedList<IBasicBlock> getToplogicalTraversalImplementation()
{
if ( this.topologicalTraversalImpl == null )
{
this.topologicalTraversalImpl = new LinkedList<IBasicBlock>();
for ( IBasicBlock node: this.vertex )
{
int idx = this.topologicalTraversalImpl.indexOf(this.idom.get(node));
if ( idx != -1 )
this.topologicalTraversalImpl.add(idx+1,node);
else
this.topologicalTraversalImpl.add(node);
}
}
return this.topologicalTraversalImpl;
}
}