private SortedSet <IRBlock> ConstructDominanceFrontierMapping(IRBlock x)
{
// Using Ron Cytron et al Algorithm
SortedSet <IRBlock> dfx = new SortedSet <IRBlock>();
// DF(X)local
foreach (IRBlock y in x.GetSuccessors())
{
if (!this.imediateDominator[y].Equals(x))
{
dfx.Add(y);
}
}
// DF(X)up
DominatorTreeNode xnode = this.blockToNodeMappings[x];
foreach (DominatorTreeNode z in xnode.GetDescendants())
{
foreach (IRBlock y in this.dominanceFrontiers[z.GetBlock()])
{
if (!this.imediateDominator[y].Equals(x))
{
dfx.Add(y);
}
}
}
return(dfx);
}
private void BuildDominatorTree()
{
// Using Aho & Ullman - The thoery of parsing and compilation Vol II ... Algorithm 11.5
IRBlock head = this.cfg.GetGraphHead();
SortedSet <IRBlock> V = this.cfg.GetSetOfAllBlocks();
SortedSet <IRBlock> VSansR = new SortedSet <IRBlock>();
VSansR.UnionWith(V);
VSansR.Remove(head); // remove head from the set of all blocks
// calculate which blocks dominates what list of blocks
Dictionary <IRBlock, SortedSet <IRBlock> > dominatesMapping = new Dictionary <IRBlock, SortedSet <IRBlock> >();
dominatesMapping[head] = VSansR;
foreach (IRBlock v in VSansR)
{
dominatesMapping[v] = CalculateDominatesSet(this.cfg, V, VSansR, v);
}
// use dominates sets to build the dominator tree
SortedSet <IRBlock> placed = new SortedSet <IRBlock>();
this.imediateDominator = new Dictionary <IRBlock, IRBlock>();
CalculateImediateDominators(head, dominatesMapping, placed);
this.rootNode = BuildTreeFromImediateDominators();
}
private static DominatorTreeNode BuildExpectedDominatorTree()
{
// this is silly replication but hey it makes life easy
IRBlock block1 = new IRBlock(1);
IRBlock block2 = new IRBlock(2);
IRBlock block3 = new IRBlock(3);
IRBlock block4 = new IRBlock(4);
IRBlock block5 = new IRBlock(5);
IRBlock block6 = new IRBlock(6);
IRBlock block7 = new IRBlock(7);
IRBlock block8 = new IRBlock(8);
IRBlock block9 = new IRBlock(9);
DominatorTreeNode node1 = new DominatorTreeNode(block1);
DominatorTreeNode node2 = new DominatorTreeNode(block2);
DominatorTreeNode node3 = new DominatorTreeNode(block3);
DominatorTreeNode node4 = new DominatorTreeNode(block4);
DominatorTreeNode node5 = new DominatorTreeNode(block5);
DominatorTreeNode node6 = new DominatorTreeNode(block6);
DominatorTreeNode node7 = new DominatorTreeNode(block7);
DominatorTreeNode node8 = new DominatorTreeNode(block8);
DominatorTreeNode node9 = new DominatorTreeNode(block9);
node1.AddDescendant(node2);
node2.AddDescendant(node3);
node3.AddDescendant(node4);
node3.AddDescendant(node5);
node4.AddDescendant(node6);
node4.AddDescendant(node7);
node4.AddDescendant(node9);
node5.AddDescendant(node8);
// node4.AddDescendant(node8);
return(node1);
}
public static SortedSet<IRBlock> CalculateDominatesSet(IRGraph cfg, SortedSet<IRBlock> V, SortedSet<IRBlock> VSansR, IRBlock v)
{
SortedSet<IRBlock> VSansv = new SortedSet<IRBlock>();
VSansv.UnionWith(V);
VSansv.Remove(v); // V - {v}
SortedSet<IRBlock> S = FindReachableBlocks(cfg, v.GetIndex());
VSansv.ExceptWith(S);
return VSansv; // V - {v} - S
}
private static SortedSet<IRBlock> FindReachableBlocks(SortedSet<IRBlock> reachable, IRBlock block, int ignoreBlockIndex)
{
List<IRBlock> successors = block.GetSuccessors();
foreach (IRBlock successor in successors)
{
if ((!reachable.Contains(successor)) && (successor.GetIndex() != ignoreBlockIndex))
{
reachable.Add(successor);
FindReachableBlocks(reachable, successor, ignoreBlockIndex);
}
}
return reachable;
}
// TODO simplify this mess - blocks should know predcessors
public SortedSet <IRBlock> GetPredecessors(IRBlock block)
{
SortedSet <IRBlock> predecessors = new SortedSet <IRBlock>();
foreach (KeyValuePair <int, IRBlock> pair in this.blocks)
{
if (pair.Value.GetSuccessors().Contains(block))
{
predecessors.Add(pair.Value);
}
}
return(predecessors);
}
public void Print()
{
foreach (KeyValuePair <int, IRBlock> pair in this.blocks)
{
IRBlock block = pair.Value;
Console.WriteLine("Block " + block.GetIndex() + ":");
block.PrintStatements();
block.PrintSuccessors();
block.PrintLiveuseDef();
block.PrintLiveInOut();
block.PrintLiveouts();
Console.WriteLine();
}
}
private void CalculateImediateDominators(IRBlock block, Dictionary <IRBlock, SortedSet <IRBlock> > dominatesMapping, SortedSet <IRBlock> placed)
{
placed.Add(block);
foreach (IRBlock blocki in dominatesMapping[block])
{
if (!placed.Contains(blocki))
{
this.imediateDominator[blocki] = block;
CalculateImediateDominators(blocki, dominatesMapping, placed);
}
}
}
public static SortedSet <IRBlock> FindReachableBlocks(IRGraph cfg, int ignoreBlockIndex)
{
IRBlock head = cfg.GetGraphHead();
SortedSet <IRBlock> reachable = new SortedSet <IRBlock>();
reachable.Add(head);
// if you can't use head you should ge no where
if (head.GetIndex() == ignoreBlockIndex)
{
return(reachable);
}
return(FindReachableBlocks(reachable, head, ignoreBlockIndex));
}
public static void Main(string [] args)
{
IRBlock block1 = new IRBlock(1);
block1.AppendStatement(new IRTuple(IrOp.LABEL, "F$1"));
block1.AppendStatement(new IRTupleOneOpIdent(IrOp.STORE, "T", "R$2"));
block1.AppendStatement(new IRTupleOneOpIdent(IrOp.STORE, "A", "R$0"));
block1.AppendStatement(new IRTupleOneOpIdent(IrOp.STORE, "B", "R$1"));
block1.AppendStatement(new IRTupleOneOpImm <int>(IrOp.STORE, "C", 0));
block1.AppendStatement(new IRTupleOneOpIdent(IrOp.STORE, "D", "A"));
IRBlock block2 = new IRBlock(2);
block2.AppendStatement(new IRTuple(IrOp.LABEL, "L$1"));
block2.AppendStatement(new IRTupleTwoOp(IrOp.ADD, "C", "C", "B"));
block2.AppendStatement(new IRTupleOneOpImm <int>(IrOp.STORE, "T$1", 1));
block2.AppendStatement(new IRTupleTwoOp(IrOp.SUB, "D", "D", "T$1"));
block2.AppendStatement(new IRTupleOneOpImm <int>(IrOp.STORE, "T$2", 0));
block2.AppendStatement(new IRTupleTwoOp(IrOp.LTE, "T$3", "D", "T$2"));
block2.AppendStatement(new IRTupleOneOpIdent(IrOp.JMPF, "L$1", "T$3"));
IRBlock block3 = new IRBlock(3);
block3.AppendStatement(new IRTupleOneOpIdent(IrOp.STORE, "R$0", "C"));
block3.AppendStatement(new IRTupleOneOpIdent(IrOp.STORE, "R$2", "T"));
block1.AddSuccessor(block2);
block2.AddSuccessor(block2);
block2.AddSuccessor(block3);
List <IRBlock> blocks = new List <IRBlock>();
blocks.Add(block1);
blocks.Add(block2);
blocks.Add(block3);
foreach (IRBlock irb in blocks)
{
irb.ComputeLiveuseDef();
irb.ComputeLiveouts();
Console.WriteLine("B" + irb.GetIndex() + ":");
irb.PrintStatements();
irb.PrintSuccessors();
irb.PrintLiveuseDef();
irb.PrintLiveouts();
Console.WriteLine();
}
}
// Establish pointers between each block in the graph and its successor blocks
private void LinkSuccessors(SortedDictionary <int, int> firsts, SortedDictionary <int, int> lasts)
{
foreach (KeyValuePair <int, IRBlock> pair in this.blocks)
{
IRBlock block = pair.Value;
IRTuple tup = block.GetLast(); // Get last statement in block
if (tup.getOp() == IrOp.JMP)
{
foreach (KeyValuePair <int, IRBlock> pair0 in this.blocks)
{
IRBlock block0 = pair0.Value;
IRTuple tup0 = block0.GetFirst();
if (tup0.getOp() == IrOp.LABEL && tup0.getDest() == tup.getDest())
{
block.AddSuccessor(block0);
}
}
}
else if (tup.getOp() == IrOp.JMPF)
{
foreach (KeyValuePair <int, IRBlock> pair0 in this.blocks)
{
IRBlock block0 = pair0.Value;
IRTuple tup0 = block0.GetFirst();
if (tup0.getOp() == IrOp.LABEL && tup0.getDest() == ((IRTupleOneOpIdent)tup).getDest())
{
block.AddSuccessor(block0);
}
else if (firsts[block0.GetIndex()] == lasts[block.GetIndex()] + 1)
{
block.AddSuccessor(block0);
}
}
}
else
{
foreach (KeyValuePair <int, IRBlock> pair0 in this.blocks)
{
IRBlock block0 = pair0.Value;
if (firsts[block0.GetIndex()] == lasts[block.GetIndex()] + 1)
{
block.AddSuccessor(block0);
}
}
}
}
}
public static void Main(string [] args)
{
IRBlock block1 = new IRBlock(1);
block1.AppendStatement(new IRTuple(IrOp.LABEL, "F$1"));
block1.AppendStatement(new IRTupleOneOpIdent(IrOp.STORE, "T", "R$2"));
block1.AppendStatement(new IRTupleOneOpIdent(IrOp.STORE, "A", "R$0"));
block1.AppendStatement(new IRTupleOneOpIdent(IrOp.STORE, "B", "R$1"));
block1.AppendStatement(new IRTupleOneOpImm<int>(IrOp.STORE, "C", 0));
block1.AppendStatement(new IRTupleOneOpIdent(IrOp.STORE, "D", "A"));
IRBlock block2 = new IRBlock(2);
block2.AppendStatement(new IRTuple(IrOp.LABEL, "L$1"));
block2.AppendStatement(new IRTupleTwoOp(IrOp.ADD, "C", "C", "B"));
block2.AppendStatement(new IRTupleOneOpImm<int>(IrOp.STORE, "T$1", 1));
block2.AppendStatement(new IRTupleTwoOp(IrOp.SUB, "D", "D", "T$1"));
block2.AppendStatement(new IRTupleOneOpImm<int>(IrOp.STORE, "T$2", 0));
block2.AppendStatement(new IRTupleTwoOp(IrOp.LTE, "T$3", "D", "T$2"));
block2.AppendStatement(new IRTupleOneOpIdent(IrOp.JMPF, "L$1", "T$3"));
IRBlock block3 = new IRBlock(3);
block3.AppendStatement(new IRTupleOneOpIdent(IrOp.STORE, "R$0", "C"));
block3.AppendStatement(new IRTupleOneOpIdent(IrOp.STORE, "R$2", "T"));
block1.AddSuccessor(block2);
block2.AddSuccessor(block2);
block2.AddSuccessor(block3);
List<IRBlock> blocks = new List<IRBlock>();
blocks.Add(block1);
blocks.Add(block2);
blocks.Add(block3);
foreach (IRBlock irb in blocks)
{
irb.ComputeLiveuseDef();
irb.ComputeLiveouts();
Console.WriteLine("B" + irb.GetIndex() + ":");
irb.PrintStatements();
irb.PrintSuccessors();
irb.PrintLiveuseDef();
irb.PrintLiveouts();
Console.WriteLine();
}
}
// Compute LiveIn and LiveOut for each block in this graph
private void ComputeBlockLiveness()
{
bool converged = true;
do
{
converged = true;
foreach (KeyValuePair <int, IRBlock> pair in this.blocks)
{
IRBlock block = pair.Value;
HashSet <Ident> oldlivein = new HashSet <Ident>(block.GetLiveIn());
HashSet <Ident> oldliveout = new HashSet <Ident>(block.GetLiveOut());
block.UpdateLiveness();
if (!block.GetLiveIn().SetEquals(oldlivein) || !block.GetLiveOut().SetEquals(oldliveout))
{
converged = false;
}
}
} while(!converged);
}
/*
* Helper Methods
*/
private static IRGraph BuildSampleCFG()
{
IRBlock block1 = new IRBlock(1);
IRBlock block2 = new IRBlock(2);
IRBlock block3 = new IRBlock(3);
IRBlock block4 = new IRBlock(4);
IRBlock block5 = new IRBlock(5);
IRBlock block6 = new IRBlock(6);
IRBlock block7 = new IRBlock(7);
IRBlock block8 = new IRBlock(8);
IRBlock block9 = new IRBlock(9);
block1.AddSuccessor(block2);
block2.AddSuccessor(block3);
block3.AddSuccessor(block4);
block3.AddSuccessor(block5);
block4.AddSuccessor(block6);
block4.AddSuccessor(block7);
block5.AddSuccessor(block8);
block6.AddSuccessor(block9);
block7.AddSuccessor(block9);
block9.AddSuccessor(block3);
List <IRBlock> blocks = new List <IRBlock>();
blocks.Add(block1);
blocks.Add(block2);
blocks.Add(block3);
blocks.Add(block4);
blocks.Add(block5);
blocks.Add(block6);
blocks.Add(block7);
blocks.Add(block8);
blocks.Add(block9);
IRGraph cfg = new IRGraph(blocks);
return(cfg);
}
public DominatorTreeNode GetNode(IRBlock block)
{
return(this.blockToNodeMappings[block]);
}
private static void Search(IRBlock block, DominatorTree dominatorTree, Dictionary <Ident, int> count, Dictionary <Ident, Stack <int> > stack)
{
// Algorithm from Ron Cytron et al to rename variables into SSA form
foreach (IRTuple irt in block.GetStatements())
{
Console.Write("Type: " + irt.GetType() + " ");
irt.Print();
Console.WriteLine();
if (irt.getOp() != IrOp.PHI)
{
foreach (Ident v in irt.GetUsedVars())
{
Console.WriteLine("Renaming variable: " + v);
int i = stack[v].Peek();
RenameTupleSourcesHelper(irt, v, i); // replace uses of v with vi in statement
}
}
foreach (Ident a in irt.GetDefinedVars())
{
count[a] = count[a] + 1;
int i = count[a];
stack[a].Push(i);
irt.setDest(RenameVar(a, i)); // replace definitions of a with ai in statement
}
}
// rename Phi function arguments in the successors
List <IRBlock> successors = block.GetSuccessors();
for (int i = 0; i < successors.Count; i++)
{
foreach (IRTuple stmt in block.GetStatements())
{
if (stmt.getOp() == IrOp.PHI)
{
IRTupleManyOp phi = (IRTupleManyOp)stmt;
Ident v = phi.GetSources()[i];
int numbering = stack[v].Peek();
phi.SetSource(i, RenameVar(v, numbering));
}
}
}
// for each descendant do the Search(X) renaming process
DominatorTreeNode node = dominatorTree.GetNode(block);
foreach (DominatorTreeNode descendant in node.GetDescendants())
{
Search(descendant.GetBlock(), dominatorTree, count, stack);
}
// pop stack phase
foreach (IRTuple irt in block.GetStatements())
{
foreach (Ident v in irt.GetDefinedVars())
{
stack[v].Pop();
}
}
}
/*
* Helper Methods
*/
private static IRGraph BuildSampleCFG()
{
IRBlock block1 = new IRBlock(1);
IRBlock block2 = new IRBlock(2);
IRBlock block3 = new IRBlock(3);
IRBlock block4 = new IRBlock(4);
IRBlock block5 = new IRBlock(5);
IRBlock block6 = new IRBlock(6);
IRBlock block7 = new IRBlock(7);
IRBlock block8 = new IRBlock(8);
IRBlock block9 = new IRBlock(9);
block1.AddSuccessor(block2);
block2.AddSuccessor(block3);
block3.AddSuccessor(block4);
block3.AddSuccessor(block5);
block4.AddSuccessor(block6);
block4.AddSuccessor(block7);
block5.AddSuccessor(block8);
block6.AddSuccessor(block9);
block7.AddSuccessor(block9);
block9.AddSuccessor(block3);
List<IRBlock> blocks = new List<IRBlock>();
blocks.Add(block1);
blocks.Add(block2);
blocks.Add(block3);
blocks.Add(block4);
blocks.Add(block5);
blocks.Add(block6);
blocks.Add(block7);
blocks.Add(block8);
blocks.Add(block9);
IRGraph cfg = new IRGraph(blocks);
return cfg;
}
public DominatorTreeNode GetNode(IRBlock block)
{
return this.blockToNodeMappings[block];
}
public SortedSet<IRBlock> GetDominanceFrontier(IRBlock block)
{
return this.dominanceFrontiers[block];
}
private static void Search(IRBlock block, DominatorTree dominatorTree, Dictionary<Ident, int> count, Dictionary<Ident, Stack<int>> stack)
{
// Algorithm from Ron Cytron et al to rename variables into SSA form
foreach (IRTuple irt in block.GetStatements())
{
Console.Write("Type: " + irt.GetType() + " ");
irt.Print();
Console.WriteLine();
if (irt.getOp() != IrOp.PHI) {
foreach (Ident v in irt.GetUsedVars()) {
Console.WriteLine("Renaming variable: " + v);
int i = stack[v].Peek();
RenameTupleSourcesHelper(irt, v, i); // replace uses of v with vi in statement
}
}
foreach (Ident a in irt.GetDefinedVars()) {
count[a] = count[a] + 1;
int i = count[a];
stack[a].Push(i);
irt.setDest(RenameVar(a, i)); // replace definitions of a with ai in statement
}
}
// rename Phi function arguments in the successors
List<IRBlock> successors = block.GetSuccessors();
for (int i = 0; i < successors.Count; i++)
{
foreach (IRTuple stmt in block.GetStatements())
{
if (stmt.getOp() == IrOp.PHI)
{
IRTupleManyOp phi = (IRTupleManyOp)stmt;
Ident v = phi.GetSources()[i];
int numbering = stack[v].Peek();
phi.SetSource(i, RenameVar(v, numbering));
}
}
}
// for each descendant do the Search(X) renaming process
DominatorTreeNode node = dominatorTree.GetNode(block);
foreach (DominatorTreeNode descendant in node.GetDescendants())
{
Search(descendant.GetBlock(), dominatorTree, count, stack);
}
// pop stack phase
foreach (IRTuple irt in block.GetStatements())
{
foreach (Ident v in irt.GetDefinedVars())
stack[v].Pop();
}
}
private SortedSet<IRBlock> ConstructDominanceFrontierMapping(IRBlock x)
{
// Using Ron Cytron et al Algorithm
SortedSet<IRBlock> dfx = new SortedSet<IRBlock>();
// DF(X)local
foreach (IRBlock y in x.GetSuccessors())
{
if(!this.imediateDominator[y].Equals(x))
{
dfx.Add(y);
}
}
// DF(X)up
DominatorTreeNode xnode = this.blockToNodeMappings[x];
foreach (DominatorTreeNode z in xnode.GetDescendants())
{
foreach (IRBlock y in this.dominanceFrontiers[z.GetBlock()])
{
if(!this.imediateDominator[y].Equals(x))
dfx.Add(y);
}
}
return dfx;
}
private void CalculateImediateDominators(IRBlock block, Dictionary<IRBlock, SortedSet<IRBlock>> dominatesMapping, SortedSet<IRBlock> placed)
{
placed.Add(block);
foreach (IRBlock blocki in dominatesMapping[block])
{
if(!placed.Contains(blocki))
{
this.imediateDominator[blocki] = block;
CalculateImediateDominators(blocki, dominatesMapping, placed);
}
}
}
public static SortedSet <IRBlock> CalculateDominatesSet(IRGraph cfg, SortedSet <IRBlock> V, SortedSet <IRBlock> VSansR, IRBlock v)
{
SortedSet <IRBlock> VSansv = new SortedSet <IRBlock>();
VSansv.UnionWith(V);
VSansv.Remove(v); // V - {v}
SortedSet <IRBlock> S = FindReachableBlocks(cfg, v.GetIndex());
VSansv.ExceptWith(S);
return(VSansv); // V - {v} - S
}
private static DominatorTreeNode BuildExpectedDominatorTree()
{
// this is silly replication but hey it makes life easy
IRBlock block1 = new IRBlock(1);
IRBlock block2 = new IRBlock(2);
IRBlock block3 = new IRBlock(3);
IRBlock block4 = new IRBlock(4);
IRBlock block5 = new IRBlock(5);
IRBlock block6 = new IRBlock(6);
IRBlock block7 = new IRBlock(7);
IRBlock block8 = new IRBlock(8);
IRBlock block9 = new IRBlock(9);
DominatorTreeNode node1 = new DominatorTreeNode(block1);
DominatorTreeNode node2 = new DominatorTreeNode(block2);
DominatorTreeNode node3 = new DominatorTreeNode(block3);
DominatorTreeNode node4 = new DominatorTreeNode(block4);
DominatorTreeNode node5 = new DominatorTreeNode(block5);
DominatorTreeNode node6 = new DominatorTreeNode(block6);
DominatorTreeNode node7 = new DominatorTreeNode(block7);
DominatorTreeNode node8 = new DominatorTreeNode(block8);
DominatorTreeNode node9 = new DominatorTreeNode(block9);
node1.AddDescendant(node2);
node2.AddDescendant(node3);
node3.AddDescendant(node4);
node3.AddDescendant(node5);
node4.AddDescendant(node6);
node4.AddDescendant(node7);
node4.AddDescendant(node9);
node5.AddDescendant(node8);
// node4.AddDescendant(node8);
return node1;
}
private static SortedSet <IRBlock> FindReachableBlocks(SortedSet <IRBlock> reachable, IRBlock block, int ignoreBlockIndex)
{
List <IRBlock> successors = block.GetSuccessors();
foreach (IRBlock successor in successors)
{
if ((!reachable.Contains(successor)) && (successor.GetIndex() != ignoreBlockIndex))
{
reachable.Add(successor);
FindReachableBlocks(reachable, successor, ignoreBlockIndex);
}
}
return(reachable);
}
public DominatorTreeNode(IRBlock block)
{
this.block = block;
this.descendants = new SortedSet <DominatorTreeNode>();
}
public SortedSet <IRBlock> GetDominanceFrontier(IRBlock block)
{
return(this.dominanceFrontiers[block]);
}
