public void MinCutTest()
{
Graph <BasicEdgeNode, BasicEdge> g = new Graph <BasicEdgeNode, BasicEdge>(BasicEdge.New);
// this graph is from Cormen et al, fig 27.1
BasicEdgeNode s = new BasicEdgeNode("s");
BasicEdgeNode v1 = new BasicEdgeNode("v1");
BasicEdgeNode v2 = new BasicEdgeNode("v2");
BasicEdgeNode v3 = new BasicEdgeNode("v3");
BasicEdgeNode v4 = new BasicEdgeNode("v4");
BasicEdgeNode t = new BasicEdgeNode("t");
g.Nodes.Add(s);
g.Nodes.Add(v1);
g.Nodes.Add(v2);
g.Nodes.Add(v3);
g.Nodes.Add(v4);
g.Nodes.Add(t);
Dictionary <BasicEdge, float> capacity = new Dictionary <BasicEdge, float>();
BasicEdge e;
e = g.AddEdge(s, v1);
capacity[e] = 16;
e = g.AddEdge(s, v2);
capacity[e] = 13;
e = g.AddEdge(v1, v2);
capacity[e] = 10;
e = g.AddEdge(v1, v3);
capacity[e] = 12;
e = g.AddEdge(v2, v1);
capacity[e] = 4;
e = g.AddEdge(v2, v4);
capacity[e] = 14;
e = g.AddEdge(v3, v2);
capacity[e] = 9;
e = g.AddEdge(v3, t);
capacity[e] = 20;
e = g.AddEdge(v4, v3);
capacity[e] = 7;
e = g.AddEdge(v4, t);
capacity[e] = 4;
var mc = new MinCut <BasicEdgeNode, BasicEdge>(g, e2 => capacity[e2]);
mc.Sources.Add(s);
mc.Sinks.Add(t);
// sourceGroup should be s,v1,v2,v4
Set <BasicEdgeNode> sourceGroup = mc.GetSourceGroup();
Console.WriteLine("sourceGroup = {0}", sourceGroup);
Assert.True(sourceGroup.Count == 4 && sourceGroup.ContainsAll(new BasicEdgeNode[] { s, v1, v2, v4 }));
mc.Sources.Add(v1);
mc.Sinks.Add(v3);
sourceGroup = mc.GetSourceGroup();
Console.WriteLine("sourceGroup = {0}", sourceGroup);
Assert.True(sourceGroup.Count == 4 && sourceGroup.ContainsAll(new BasicEdgeNode[] { s, v1, v2, v4 }));
capacity[g.GetEdge(v2, v4)] = 1;
sourceGroup = mc.GetSourceGroup();
Console.WriteLine("sourceGroup = {0}", sourceGroup);
Assert.True(sourceGroup.Count == 3 && sourceGroup.ContainsAll(new BasicEdgeNode[] { s, v1, v2 }));
}
public void MinCutCycleTest()
{
Graph <BasicEdgeNode, BasicEdge> g = new Graph <BasicEdgeNode, BasicEdge>(BasicEdge.New);
// cycle graph
BasicEdgeNode s = new BasicEdgeNode("s");
BasicEdgeNode v1 = new BasicEdgeNode("v1");
BasicEdgeNode v2 = new BasicEdgeNode("v2");
BasicEdgeNode t = new BasicEdgeNode("t");
g.Nodes.Add(s);
g.Nodes.Add(v1);
g.Nodes.Add(v2);
g.Nodes.Add(t);
Dictionary <BasicEdge, float> capacity = new Dictionary <BasicEdge, float>();
BasicEdge e;
e = g.AddEdge(s, v1);
capacity[e] = 16;
e = g.AddEdge(v1, v2);
capacity[e] = 10;
e = g.AddEdge(v2, s);
capacity[e] = 14;
var mc = new MinCut <BasicEdgeNode, BasicEdge>(g, e2 => capacity[e2]);
mc.Sources.Add(s);
mc.Sinks.Add(s);
// sourceGroup should be s,v1
Set <BasicEdgeNode> sourceGroup = mc.GetSourceGroup();
Console.WriteLine("sourceGroup = {0}", sourceGroup);
Assert.True(sourceGroup.Count == 2 && sourceGroup.ContainsAll(new BasicEdgeNode[] { s, v1 }));
mc.Sinks.Remove(s);
// test the case where t is not reachable from s
mc.Sinks.Add(t);
// sourceGroup should be s,v1,v2
sourceGroup = mc.GetSourceGroup();
Console.WriteLine("sourceGroup = {0}", sourceGroup);
Assert.True(sourceGroup.Count == 3 && sourceGroup.ContainsAll(new BasicEdgeNode[] { s, v1, v2 }));
// test IsSinkEdge
mc.Sinks.Remove(t);
e = g.GetEdge(v2, s);
mc.IsSinkEdge = edge => edge.Equals(e);
// sourceGroup should be s,v1
sourceGroup = mc.GetSourceGroup();
Console.WriteLine("sourceGroup = {0}", sourceGroup);
Assert.True(sourceGroup.Count == 2 && sourceGroup.ContainsAll(new BasicEdgeNode[] { s, v1 }));
}
/// <summary>
/// Test of solving an initializer scheduling problem as a min cut problem.
/// </summary>
//[Fact]
internal void MinCutTest3()
{
Graph <BasicEdgeNode, BasicEdge> g = new Graph <BasicEdgeNode, BasicEdge>(BasicEdge.New);
BasicEdgeNode s = new BasicEdgeNode("s");
BasicEdgeNode v1 = new BasicEdgeNode("v1");
BasicEdgeNode v2 = new BasicEdgeNode("v2");
BasicEdgeNode v3 = new BasicEdgeNode("v3");
BasicEdgeNode b1 = new BasicEdgeNode("b1");
BasicEdgeNode b2 = new BasicEdgeNode("b2");
BasicEdgeNode t = new BasicEdgeNode("t");
g.Nodes.Add(s);
g.Nodes.Add(v1);
g.Nodes.Add(v2);
g.Nodes.Add(v3);
g.Nodes.Add(b1);
g.Nodes.Add(b2);
g.Nodes.Add(t);
Dictionary <BasicEdge, float> capacity = new Dictionary <BasicEdge, float>();
foreach (var node in new[] { v1, v2, v3 })
{
BasicEdge e2 = g.AddEdge(s, node);
capacity[e2] = 1;
}
BasicEdgeNode[,] pairs =
{
{ v1, b1 },
{ v2, b1 },
{ v2, b2 },
{ v3, b2 }
};
for (int i = 0; i < pairs.GetLength(0); i++)
{
var source = pairs[i, 0];
var target = pairs[i, 1];
BasicEdge e2 = g.AddEdge(source, target);
capacity[e2] = 1;
}
BasicEdge e;
e = g.AddEdge(b1, t);
capacity[e] = 1.1f;
e = g.AddEdge(b2, t);
capacity[e] = 1.1f;
var mc = new MinCut <BasicEdgeNode, BasicEdge>(g, e2 => capacity[e2]);
mc.Sources.Add(s);
mc.Sinks.Add(t);
Set <BasicEdgeNode> sourceGroup = mc.GetSourceGroup();
Console.WriteLine("sourceGroup = {0}", sourceGroup);
}
protected override void DoConvertMethodBody(IList <IStatement> outputs, IList <IStatement> inputs)
{
List <int> whileNumberOfNode = new List <int>();
List <int> fusedCountOfNode = new List <int>();
List <List <IStatement> > containersOfNode = new List <List <IStatement> >();
// the code may have multiple while(true) loops, however these must be disjoint.
// therefore we treat 'while' as one container, but give each loop a different 'while number'.
int outerWhileCount = 0;
int currentOuterWhileNumber = 0;
int currentFusedCount = 0;
List <Set <IVariableDeclaration> > loopVarsOfWhileNumber = new List <Set <IVariableDeclaration> >();
// build the dependency graph
var g = new DependencyGraph2(context, inputs, DependencyGraph2.BackEdgeHandling.Ignore,
delegate(IWhileStatement iws)
{
if (iws is IFusedBlockStatement)
{
if (iws.Condition is IVariableReferenceExpression)
{
currentFusedCount++;
}
}
else
{
outerWhileCount++;
currentOuterWhileNumber = outerWhileCount;
}
},
delegate(IWhileStatement iws)
{
if (iws is IFusedBlockStatement)
{
if (iws.Condition is IVariableReferenceExpression)
{
currentFusedCount--;
}
}
else
{
currentOuterWhileNumber = 0;
}
},
delegate(IConditionStatement ics)
{
},
delegate(IConditionStatement ics)
{
},
delegate(IStatement ist, int targetIndex)
{
int whileNumber = currentOuterWhileNumber;
whileNumberOfNode.Add(whileNumber);
fusedCountOfNode.Add(currentFusedCount);
List <IStatement> containers = new List <IStatement>();
LoopMergingTransform.UnwrapStatement(ist, containers);
containersOfNode.Add(containers);
for (int i = 0; i < currentFusedCount; i++)
{
if (containers[i] is IForStatement ifs)
{
var loopVar = Recognizer.LoopVariable(ifs);
if (loopVarsOfWhileNumber.Count <= whileNumber)
{
while (loopVarsOfWhileNumber.Count <= whileNumber)
{
loopVarsOfWhileNumber.Add(new Set <IVariableDeclaration>());
}
}
Set <IVariableDeclaration> loopVars = loopVarsOfWhileNumber[whileNumber];
loopVars.Add(loopVar);
}
}
});
var nodes = g.nodes;
var dependencyGraph = g.dependencyGraph;
for (int whileNumber = 1; whileNumber < loopVarsOfWhileNumber.Count; whileNumber++)
{
foreach (var loopVar in loopVarsOfWhileNumber[whileNumber])
{
// Any statement (in the while loop) that has a forward descendant and a backward descendant will be cloned, so we want to minimize the number of such nodes.
// The free variables in this problem are the loop directions at the leaf statements, since all other loop directions are forced by these.
// We find the optimal labeling of the free variables by solving a min cut problem on a special network.
// The network is constructed so that the cost of a cut is equal to the number of statements that will be cloned.
// The network has 2 nodes for every statement: an in-node and an out-node.
// For a non-leaf statement, there is a capacity 1 edge from the in-node to out-node. This edge is cut when the statement is cloned.
// For a leaf statement, there is an infinite capacity edge in both directions, or equivalently a single node.
// If statement A depends on statement B, then there is an infinite capacity edge from in-A to in-B, and from out-B to out-A,
// representing the fact that cloning A requires cloning B, but not the reverse.
// If a statement must appear with a forward loop, it is connected to the source.
// If a statement must appear with a backward loop, it is connected to the sink.
// construct a capacitated graph
int inNodeStart = 0;
int outNodeStart = inNodeStart + dependencyGraph.Nodes.Count;
int sourceNode = outNodeStart + dependencyGraph.Nodes.Count;
int sinkNode = sourceNode + 1;
int cutNodeCount = sinkNode + 1;
Func <NodeIndex, int> getInNode = node => node + inNodeStart;
Func <NodeIndex, int> getOutNode = node => node + outNodeStart;
IndexedGraph network = new IndexedGraph(cutNodeCount);
const float infinity = 1000000f;
List <float> capacity = new List <float>();
List <NodeIndex> nodesOfInterest = new List <NodeIndex>();
foreach (var node in dependencyGraph.Nodes)
{
if (whileNumberOfNode[node] != whileNumber)
{
continue;
}
NodeIndex source = node;
List <IStatement> containersOfSource = containersOfNode[source];
bool hasLoopVar = containersOfSource.Any(container => container is IForStatement && Recognizer.LoopVariable((IForStatement)container) == loopVar);
if (!hasLoopVar)
{
continue;
}
nodesOfInterest.Add(node);
IStatement sourceSt = nodes[source];
var readAfterWriteEdges = dependencyGraph.EdgesOutOf(source).Where(edge => !g.isWriteAfterRead[edge]);
bool isLeaf = true;
int inNode = getInNode(node);
int outNode = getOutNode(node);
foreach (var target in readAfterWriteEdges.Select(dependencyGraph.TargetOf))
{
List <IStatement> containersOfTarget = containersOfNode[target];
IStatement targetSt = nodes[target];
ForEachMatchingLoopVariable(containersOfSource, containersOfTarget, (loopVar2, afs, bfs) =>
{
if (loopVar2 == loopVar)
{
int inTarget = getInNode(target);
int outTarget = getOutNode(target);
network.AddEdge(inTarget, inNode);
capacity.Add(infinity);
network.AddEdge(outNode, outTarget);
capacity.Add(infinity);
isLeaf = false;
}
});
}
if (isLeaf)
{
if (debug)
{
log.Add($"loopVar={loopVar.Name} leaf {sourceSt}");
}
network.AddEdge(inNode, outNode);
capacity.Add(infinity);
network.AddEdge(outNode, inNode);
capacity.Add(infinity);
}
else
{
network.AddEdge(inNode, outNode);
capacity.Add(1f);
}
int fusedCount = fusedCountOfNode[node];
Direction desiredDirectionOfSource = GetDesiredDirection(loopVar, containersOfSource, fusedCount);
if (desiredDirectionOfSource == Direction.Forward)
{
if (debug)
{
log.Add($"loopVar={loopVar.Name} forward {sourceSt}");
}
network.AddEdge(sourceNode, inNode);
capacity.Add(infinity);
}
else if (desiredDirectionOfSource == Direction.Backward)
{
if (debug)
{
log.Add($"loopVar={loopVar.Name} backward {sourceSt}");
}
network.AddEdge(outNode, sinkNode);
capacity.Add(infinity);
}
}
network.IsReadOnly = true;
// compute the min cut
MinCut <NodeIndex, EdgeIndex> mc = new MinCut <EdgeIndex, EdgeIndex>(network, e => capacity[e]);
mc.Sources.Add(sourceNode);
mc.Sinks.Add(sinkNode);
Set <NodeIndex> sourceGroup = mc.GetSourceGroup();
foreach (NodeIndex node in nodesOfInterest)
{
IStatement sourceSt = nodes[node];
bool forwardIn = sourceGroup.Contains(getInNode(node));
bool forwardOut = sourceGroup.Contains(getOutNode(node));
if (forwardIn != forwardOut)
{
if (debug)
{
log.Add($"loopVar={loopVar.Name} will clone {sourceSt}");
}
}
else if (forwardIn)
{
if (debug)
{
log.Add($"loopVar={loopVar.Name} wants forward {sourceSt}");
}
}
else
{
if (debug)
{
log.Add($"loopVar={loopVar.Name} wants backward {sourceSt}");
}
var containers = containersOfNode[node];
bool isForwardLoop = true;
foreach (var container in containers)
{
if (container is IForStatement)
{
IForStatement ifs = (IForStatement)container;
if (Recognizer.LoopVariable(ifs) == loopVar)
{
isForwardLoop = Recognizer.IsForwardLoop(ifs);
}
}
}
if (isForwardLoop)
{
Set <IVariableDeclaration> loopVarsToReverse;
if (!loopVarsToReverseInStatement.TryGetValue(sourceSt, out loopVarsToReverse))
{
// TODO: re-use equivalent sets
loopVarsToReverse = new Set <IVariableDeclaration>();
loopVarsToReverseInStatement.Add(sourceSt, loopVarsToReverse);
}
loopVarsToReverse.Add(loopVar);
}
}
}
}
}
base.DoConvertMethodBody(outputs, inputs);
}
