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/* Soot - a J*va Optimization Framework
 * Copyright (C) 2000 Feng Qian
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the
 * Free Software Foundation, Inc., 59 Temple Place - Suite 330,
 * Boston, MA 02111-1307, USA.
 */

/*
 * Modified by the Sable Research Group and others 1997-1999.  
 * See the 'credits' file distributed with Soot for the complete list of
 * contributors.  (Soot is distributed at http://www.sable.mcgill.ca/soot)
 */

package soot.jimple.toolkits.annotation.arraycheck;
import soot.options.*;

import soot.* ;
import soot.toolkits.graph.*;
import soot.jimple.* ;

import java.util.* ;

class ArrayBoundsCheckerAnalysis 
{
    protected Map blockToBeforeFlow;
    protected Map unitToBeforeFlow;

    private final Map edgeMap;
    private final Set edgeSet;

    private HashMap stableRoundOfUnits;

    private ArrayRefBlockGraph graph;

    private final IntContainer zero = new IntContainer(0);

    private boolean fieldin = false;
    private HashMap> localToFieldRef;
    private HashMap> fieldToFieldRef;
    private final int strictness = 2;

    private boolean arrayin = false;

    private boolean csin = false;
    private HashMap> localToExpr;

    private boolean classfieldin = false;
    private ClassFieldAnalysis cfield;

    private boolean rectarray = false;
    private HashSet rectarrayset;
    private HashSet multiarraylocals;

    private final ArrayIndexLivenessAnalysis ailanalysis;

    /* A little bit different from ForwardFlowAnalysis */
    public ArrayBoundsCheckerAnalysis(Body body, 
                                      boolean takeClassField,
                                      boolean takeFieldRef,
                                      boolean takeArrayRef,
                                      boolean takeCSE,
                                      boolean takeRectArray)
    {
        classfieldin = takeClassField;
        fieldin = takeFieldRef;
        arrayin = takeArrayRef;
        csin = takeCSE;
        rectarray = takeRectArray;
        
        SootMethod thismethod = body.getMethod();

        if (Options.v().debug()) 
            G.v().out.println("ArrayBoundsCheckerAnalysis started on  "+thismethod.getName());

        ailanalysis = new ArrayIndexLivenessAnalysis(new ExceptionalUnitGraph(body), fieldin, arrayin, csin, rectarray);
        
        if (fieldin)
        {
            this.localToFieldRef = ailanalysis.getLocalToFieldRef();
            this.fieldToFieldRef = ailanalysis.getFieldToFieldRef();
        }
        
        if (arrayin)
        {
            if (rectarray)
            {
                this.multiarraylocals = ailanalysis.getMultiArrayLocals();
                this.rectarrayset = new HashSet();

                RectangularArrayFinder pgbuilder = RectangularArrayFinder.v();

                Iterator localIt = multiarraylocals.iterator();
                while (localIt.hasNext())
                {
                    Local local = localIt.next();
                    
                    MethodLocal mlocal = new MethodLocal(thismethod, local);
                    
                    if (pgbuilder.isRectangular(mlocal))
                        this.rectarrayset.add(local);
                }
            }
        }
        
        if (csin)
        {
            this.localToExpr = ailanalysis.getLocalToExpr();
        }

        if (classfieldin)
        {
            this.cfield = ClassFieldAnalysis.v();    
        }

        this.graph = new ArrayRefBlockGraph(body);

        blockToBeforeFlow = new HashMap(graph.size()*2+1, 0.7f);
        
        edgeMap = new HashMap(graph.size()*2+1, 0.7f);
        
        edgeSet = buildEdgeSet(graph);
        
        doAnalysis();
        
        convertToUnitEntry();
        
        if (Options.v().debug()) 
            G.v().out.println("ArrayBoundsCheckerAnalysis finished.");
    }

    private void convertToUnitEntry()
    {
        unitToBeforeFlow = new HashMap();
        Iterator blockIt = blockToBeforeFlow.keySet().iterator();
        while (blockIt.hasNext())
        {
            Block block = blockIt.next();
            Unit first = block.getHead();
            unitToBeforeFlow.put(first, blockToBeforeFlow.get(block));
        }
    }

    /** buildEdgeSet creates a set of edges from directed graph.
     */
    public Set buildEdgeSet(DirectedGraph dg)
    {
        HashSet edges = new HashSet();

        Iterator blockIt = dg.iterator();
        while (blockIt.hasNext())
        {
            Block s = blockIt.next();

            List preds = graph.getPredsOf(s);
            List succs = graph.getSuccsOf(s);

            /* Head units has in edge from itself to itself.*/
            if (preds.size() == 0)
            {
                edges.add(new FlowGraphEdge(s,s));
            }
            
            /* End units has out edge from itself to itself.*/
            if (succs.size() == 0)
            {
                edges.add(new FlowGraphEdge(s,s));
            }
            else
            {
                Iterator succIt = succs.iterator();
                while (succIt.hasNext())
                {
                    edges.add(new FlowGraphEdge(s, succIt.next()));
                }
            }
        }
        
        return edges;
    }
    
    public Object getFlowBefore(Object s)
    {
        return unitToBeforeFlow.get(s);
    }

    /* merge all preds' out set */
    private void mergebunch(Object ins[], Object s, Object prevOut, Object out)
    {
        WeightedDirectedSparseGraph prevgraph = (WeightedDirectedSparseGraph)prevOut,
            outgraph = (WeightedDirectedSparseGraph)out;

        WeightedDirectedSparseGraph[] ingraphs
            = new WeightedDirectedSparseGraph[ins.length];

        for (int i=0; i changedSuccs;

        /* An temporary object. */
        FlowGraphEdge tmpEdge = new FlowGraphEdge();

        /* If any output flow set has unknow value, it will be put in this set
         */
        HashSet unvisitedNodes = new HashSet(graph.size()*2+1, 0.7f);

        /* adjust livelocals set */
        {
            Iterator blockIt = graph.iterator();
            while (blockIt.hasNext())
            {
                Block block = (Block)blockIt.next();
                HashSet livelocals = (HashSet)ailanalysis.getFlowBefore(block.getHead());
                livelocals.add(zero);
            }
        }

        /* Set initial values and nodes to visit. */
        {
            stableRoundOfUnits = new HashMap();
            
            Iterator it = graph.iterator();

            while(it.hasNext())
            {
                Block block = (Block)it.next();

                unvisitedNodes.add(block);
                stableRoundOfUnits.put(block, new Integer(0));

                /* only take out the necessary node set. */
                HashSet livelocals = (HashSet)ailanalysis.getFlowBefore(block.getHead());
                
                blockToBeforeFlow.put(block, new WeightedDirectedSparseGraph(livelocals, false));                
            }

            Iterator edgeIt = edgeSet.iterator();
            while (edgeIt.hasNext())
            {
                FlowGraphEdge edge = edgeIt.next();
                
                Block target = (Block)edge.to;
                HashSet livelocals = (HashSet)ailanalysis.getFlowBefore(target.getHead());
                
                edgeMap.put(edge, new WeightedDirectedSparseGraph(livelocals, false));
            }
        }

        /* perform customized initialization. */
        {
            List headlist = graph.getHeads();
            Iterator headIt = headlist.iterator();

            while (headIt.hasNext())
            {
                Object head = headIt.next() ;
                FlowGraphEdge edge = new FlowGraphEdge(head, head);

                WeightedDirectedSparseGraph initgraph = 
                    edgeMap.get(edge) ;

                initgraph.setTop();
            }        
        }

        /* Perform fixed point flow analysis.
         */
        {
            WeightedDirectedSparseGraph beforeFlow = 
                new WeightedDirectedSparseGraph(null, false);

            //            DebugMsg.counter1 += allUnits.size();

            while(!changedUnits.isEmpty())
            {
                Block s = (Block) changedUnits.removeFirst();
                changedUnitsSet.remove(s);

                // DebugMsg.counter2++;

                /* previousAfterFlow, old-out, it is null initially */
                WeightedDirectedSparseGraph previousBeforeFlow = 
                    blockToBeforeFlow.get(s);
                
                beforeFlow.setVertexes(previousBeforeFlow.getVertexes());

                // Compute and store beforeFlow
                {
                    List preds = graph.getPredsOf(s);

                    /* the init node */
                    if (preds.size() == 0)
                    {
                        tmpEdge.changeEndUnits(s,s);
                        copy(edgeMap.get(tmpEdge), beforeFlow);
                    }
                    else if (preds.size() == 1)
                    {
                        tmpEdge.changeEndUnits(preds.get(0),s);
                        copy(edgeMap.get(tmpEdge), beforeFlow);
                        
                        //                             widenGraphs(beforeFlow, previousBeforeFlow);
                    }
                    else 
                    {                    
                    /* has 2 or more preds, Updated by Feng. */
                        Object predFlows[] = new Object[preds.size()] ;
 
                        boolean allUnvisited = true;
                        Iterator predIt = preds.iterator();
                        
                        int index = 0 ;

                        int lastVisited = 0;

                        while(predIt.hasNext())
                        {
                            Object pred = predIt.next();

                                  tmpEdge.changeEndUnits(pred,s);
            
                            if (!unvisitedNodes.contains(pred))
                            {
                                allUnvisited = false;
                                lastVisited = index;
                            }

                            predFlows[index++] = edgeMap.get(tmpEdge);
                              }
                        // put the visited node as the first one

                        if (allUnvisited)
                        {
                            G.v().out.println("Warning : see all unvisited node");
                        }
                        else
                        {
                            Object tmp = predFlows[0];
                            predFlows[0] = predFlows[lastVisited];
                            predFlows[lastVisited] = tmp;
                        }

                        mergebunch(predFlows, s, previousBeforeFlow, beforeFlow); 
                    }
                    
                    copy(beforeFlow, previousBeforeFlow);
                }

                /* Compute afterFlow and store it.
                 * Now we do not have afterFlow, we only have the out edges.
                 * Different out edges may have different flow set.
                 * It returns back a list of succ units that edge has been
                 * changed.
                 */
                {
                    changedSuccs = flowThrough(beforeFlow, s);
                }

                {
                    for (int i = 0; i < changedSuccs.size(); i++)
                    {
                        Object succ = changedSuccs.get(i);
                        if (!changedUnitsSet.contains(succ))
                        {
                            changedUnits.add(succ);
                            changedUnitsSet.add(succ);
                        }
                    }
                }
                
                /* Decide to remove or add unit from/to unvisitedNodes set */
                {
                    unvisitedNodes.remove(s);
                }
            }
        }

        finish = new Date();
        if (Options.v().debug())
        {
            long runtime = finish.getTime()-start.getTime();
            long mins = runtime/60000;
            long secs = (runtime/60000)/1000;
            G.v().out.println("Doing analysis finished."
                               + " It took "+mins+" mins and "+secs+ "secs.");
        }
    }

    /* Flow go through a node, the output will be put into edgeMap, and also
     * the changed succ will be in a list to return back.
     */
    private List flowThrough(Object inValue, Object unit)
    {        
        ArrayList changedSuccs = new ArrayList();
      
        WeightedDirectedSparseGraph ingraph = 
            (WeightedDirectedSparseGraph)inValue;

        Block block = (Block)unit ;

        List succs = block.getSuccs();

        // leave out the last element.
        Unit s = block.getHead();
        Unit nexts = block.getSuccOf(s);
        while (nexts != null)
        {
            /* deal with array references */
            assertArrayRef(ingraph, s);

            /* deal with normal expressions. */
            assertNormalExpr(ingraph, s);

            s = nexts; 
            nexts = block.getSuccOf(nexts);
        }

        // at the end of block, it should update the out edges.
        if (s instanceof IfStmt)
        {
          if (!assertBranchStmt(ingraph, s, block, succs, changedSuccs))
            updateOutEdges(ingraph, block, succs, changedSuccs);
        }
        else
        {
            assertArrayRef(ingraph, s);
            assertNormalExpr(ingraph, s);
            updateOutEdges(ingraph, block, succs, changedSuccs);
        }

        return changedSuccs;
    }

    private void assertArrayRef(Object in, Unit unit)
    {
        if (!(unit instanceof AssignStmt))
            return;

        Stmt s = (Stmt)unit;

        WeightedDirectedSparseGraph ingraph = (WeightedDirectedSparseGraph)in;

        /*
        ArrayRef op = null;
       
        Value leftOp = ((AssignStmt)s).getLeftOp();
        Value rightOp = ((AssignStmt)s).getRightOp();

        if (leftOp instanceof ArrayRef)
            op = (ArrayRef)leftOp;

        if (rightOp instanceof ArrayRef)
            op = (ArrayRef)rightOp;

        if (op == null)
            return;
        */
        
        if (!s.containsArrayRef())
            return;

        ArrayRef op = s.getArrayRef();
        

        Value base = (op).getBase();
        Value index = (op).getIndex();

        HashSet livelocals = (HashSet)ailanalysis.getFlowAfter(s);
        if (!livelocals.contains(base) && !livelocals.contains(index))
            return;
        
        if (index instanceof IntConstant)
        {
            int weight = ((IntConstant)index).value;
            weight = -1-weight;

            ingraph.addEdge(base, zero, weight);
        }
        else
        {
            // add two edges.
            // index <= a.length -1;
            ingraph.addEdge(base, index, -1);

            // index >= 0
            ingraph.addEdge(index, zero, 0);
        }
    }

    private void assertNormalExpr(Object in, Unit s)
    {

        WeightedDirectedSparseGraph ingraph = (WeightedDirectedSparseGraph)in;

        /* If it is a contains invoke expr, the parameter should be analyzed. */
        if (fieldin)
        {
            Stmt stmt = (Stmt)s;
            if (stmt.containsInvokeExpr())
            {
                HashSet tokills = new HashSet();
                Value expr = stmt.getInvokeExpr();
                List parameters = ((InvokeExpr)expr).getArgs();
                
                /* kill only the locals in hierarchy. */
                if (strictness == 0)
                {
                    Hierarchy hierarchy = Scene.v().getActiveHierarchy();

                    for (int i=0; i keyIt = localToFieldRef.keySet().iterator();
                            while (keyIt.hasNext())
                            {
                                Value local = (Value)keyIt.next();

                                Type ltype = local.getType();
                                
                                SootClass lclass = ((RefType)ltype).getSootClass();

                                if (hierarchy.isClassSuperclassOfIncluding(pclass, lclass) ||
                                    hierarchy.isClassSuperclassOfIncluding(lclass, pclass))
                                {
                                    HashSet toadd = localToFieldRef.get(local);
                                    tokills.addAll(toadd);
                                }                                    
                            }
                        }
                    }
                    
                    if (expr instanceof InstanceInvokeExpr)
                    {
                        Value base = ((InstanceInvokeExpr)expr).getBase();
                        Type type = base.getType();
                        if (type instanceof RefType)
                        {
                            SootClass pclass = ((RefType)type).getSootClass();

                            /* then we are looking for the possible types. */
                            Iterator keyIt = localToFieldRef.keySet().iterator();
                            while (keyIt.hasNext())
                            {
                                Value local = (Value)keyIt.next();

                                Type ltype = local.getType();
                                
                                SootClass lclass = ((RefType)ltype).getSootClass();

                                if (hierarchy.isClassSuperclassOfIncluding(pclass, lclass) ||
                                    hierarchy.isClassSuperclassOfIncluding(lclass, pclass))
                                {
                                    HashSet toadd = localToFieldRef.get(local);
                                    tokills.addAll(toadd);
                                }                                    
                            }
                        }
                    }
                }
                else
                    /* kill all instance field reference. */ 
                if (strictness == 1)
                {
                    boolean killall = false;
                    if (expr instanceof InstanceInvokeExpr)
                        killall = true;
                    else
                    {
                        for (int i=0; i keyIt = localToFieldRef.keySet().iterator();
                        while (keyIt.hasNext())
                        {
                            HashSet toadd = localToFieldRef.get(keyIt.next());
                            tokills.addAll(toadd);
                        }                            
                    }
                }
                else
                if (strictness == 2)
                {
                    //                    tokills.addAll(allFieldRefs);
                    HashSet vertexes = ingraph.getVertexes();
                    Iterator nodeIt = vertexes.iterator();
                    while (nodeIt.hasNext())
                    {
                        Object node = nodeIt.next();
                        if (node instanceof FieldRef)
                            ingraph.killNode(node);
                    }
                }

                /*
                Iterator killIt = tokills.iterator();
                while (killIt.hasNext())
                    ingraph.killNode(killIt.next());
                */
            }
        }

        if (arrayin)
        {
            Stmt stmt = (Stmt)s;

            if (stmt.containsInvokeExpr())
            {
                if (strictness == 2)
                {
                    /*
                    Iterator killIt = allArrayRefs.iterator();
                    while (killIt.hasNext())
                    {
                        ingraph.killNode(killIt.next());
                    }
                    */
                    HashSet vertexes = ingraph.getVertexes();
                    Iterator nodeIt = vertexes.iterator();
                    while (nodeIt.hasNext())
                    {
                        Object node = nodeIt.next();
                        if (node instanceof ArrayRef)
                            ingraph.killNode(node);

                        /*
                        if (rectarray)
                            if (node instanceof Array2ndDimensionSymbol)
                                ingraph.killNode(node);
                        */
                    }
                }
            }
        }

        if (!(s instanceof AssignStmt))
            return;

        Value leftOp = ((AssignStmt)s).getLeftOp();
        Value rightOp = ((AssignStmt)s).getRightOp();


        HashSet livelocals = (HashSet)ailanalysis.getFlowAfter(s);

        if (fieldin)
        {
            if (leftOp instanceof Local)
            {
                HashSet fieldrefs = localToFieldRef.get(leftOp);
                
                if (fieldrefs != null)
                {
                    Iterator refsIt = fieldrefs.iterator();
                    while (refsIt.hasNext())
                    {
                        Object ref = refsIt.next();
                        if (livelocals.contains(ref))
                            ingraph.killNode(ref);
                    }
                }
            }
            else
            if (leftOp instanceof InstanceFieldRef)
            {
                SootField field = ((InstanceFieldRef)leftOp).getField();
                
                HashSet fieldrefs = fieldToFieldRef.get(field);
                
                if (fieldrefs != null)
                {
                    Iterator refsIt = fieldrefs.iterator();
                    while (refsIt.hasNext())
                    {
                        Object ref = refsIt.next();
                        if (livelocals.contains(ref))
                            ingraph.killNode(ref);
                    }
                }                
            }
        }

        if (arrayin)
        {
            /* a = ..;  kill all references of a;
               i = ..;  kill all references with index i;
            */
            if (leftOp instanceof Local)
            {
                /*
                HashSet arrayrefs = (HashSet)localToArrayRef.get(leftOp);
                
                if (arrayrefs != null)
                {
                    Iterator refsIt = arrayrefs.iterator();
                    while (refsIt.hasNext())
                    {
                        Object ref = refsIt.next();
                        ingraph.killNode(ref);
                    }
                }
                */
                HashSet vertexes = ingraph.getVertexes();
                Iterator nodeIt = vertexes.iterator();
                while (nodeIt.hasNext())
                {
                    Object node = nodeIt.next();
                    if (node instanceof ArrayRef)
                    {
                        Value base = ((ArrayRef)node).getBase();
                        Value index = ((ArrayRef)node).getIndex();
                        
                        if (base.equals(leftOp) || index.equals(leftOp))
                            ingraph.killNode(node);                        
                    }

                    if (rectarray)
                    {
                        if (node instanceof Array2ndDimensionSymbol)
                        {
                            Object base = ((Array2ndDimensionSymbol)node).getVar();
                            if (base.equals(leftOp))
                                ingraph.killNode(node);
                        }
                    }
                }
            }
            else
                /* kill all array references */
            if (leftOp instanceof ArrayRef)
            {
                /*
                Iterator allrefsIt = allArrayRefs.iterator();
                while (allrefsIt.hasNext())
                {
                    Object ref = allrefsIt.next();
                    ingraph.killNode(ref);
                }
                */
                HashSet vertexes = ingraph.getVertexes();
                {
                    Iterator nodeIt = vertexes.iterator();
                    while (nodeIt.hasNext())
                    {
                        Object node = nodeIt.next();
                        if (node instanceof ArrayRef)
                            ingraph.killNode(node);
                    }
                }

                /* only when multiarray was given a new value to its sub dimension, we kill all second dimensions of arrays */
                /*
                if (rectarray)
                {
                    Value base = ((ArrayRef)leftOp).getBase();

                    if (multiarraylocals.contains(base))
                    {
                        Iterator nodeIt = vertexes.iterator();
                        while (nodeIt.hasNext())
                        {
                            Object node = nodeIt.next();
                            if (node instanceof Array2ndDimensionSymbol)
                                ingraph.killNode(node);
                        }
                    }
                }
                */
            }
        }

        if ( !livelocals.contains(leftOp) && !livelocals.contains(rightOp))
            return;

        // i = i;
        if (rightOp.equals(leftOp))
            return;

        if (csin)
        {
            HashSet exprs = localToExpr.get(leftOp);
            if (exprs != null)
            {
                Iterator exprIt = exprs.iterator();
                while (exprIt.hasNext())
                {
                    ingraph.killNode(exprIt.next());
                }
            }
        }


        // i = i + c; is special
        if (rightOp instanceof AddExpr)
        {
            Value op1 = ((AddExpr)rightOp).getOp1();
            Value op2 = ((AddExpr)rightOp).getOp2();

            if (op1 == leftOp && op2 instanceof IntConstant)
            {
                int inc_w = ((IntConstant)op2).value;
                ingraph.updateWeight(leftOp, inc_w);
                return;
            }
            else
            if (op2 == leftOp && op1 instanceof IntConstant)
            {
                int inc_w = ((IntConstant)op1).value;
                ingraph.updateWeight(leftOp, inc_w);
                return;
            }
        }
        
        // i = i - c; is also special
        if (rightOp instanceof SubExpr)
        {
            Value op1 = ((SubExpr)rightOp).getOp1();
            Value op2 = ((SubExpr)rightOp).getOp2();

            if ((op1 == leftOp) && (op2 instanceof IntConstant))
            {
                int inc_w = - ((IntConstant)op2).value;
                ingraph.updateWeight(leftOp, inc_w);
                return;
            }
        }

        // i = j; i = j + c; i = c + j; need two operations, kill node and add new relationship.
        // kill left hand side,

        ingraph.killNode(leftOp);

        // add new relationship.

        // i = c;
        if (rightOp instanceof IntConstant)
        {
            int inc_w = ((IntConstant)rightOp).value;
            ingraph.addMutualEdges(zero, leftOp, inc_w);
            return;
        }

        // i = j;
        if (rightOp instanceof Local)
        {
            ingraph.addMutualEdges(rightOp, leftOp, 0);
            return;
        }

        if (rightOp instanceof FieldRef)
        {
            if (fieldin)
            {
                ingraph.addMutualEdges(rightOp, leftOp, 0);
            }

            if (classfieldin)
            {            
                SootField field = ((FieldRef)rightOp).getField();
                IntValueContainer flength = (IntValueContainer)cfield.getFieldInfo(field);

                if (flength != null)
                {
                    if (flength.isInteger())
                    {
                        ingraph.addMutualEdges(zero, leftOp, flength.getValue());
                    }
                }        
            }

            return;
        }

        /*
        if (rectarray)
        {
            Type leftType = leftOp.getType();

            if ((leftType instanceof ArrayType) && (rightOp instanceof ArrayRef))
            {
                Local base = (Local)((ArrayRef)rightOp).getBase();
                
                SymbolArrayLength sv = (SymbolArrayLength)lra_analysis.getSymbolLengthAt(base, s);
                if (sv != null)
                {
                    ingraph.addMutualEdges(leftOp, sv.next(), 0);
                }
            }
        }
        */

        if (arrayin)
        {
            if (rightOp instanceof ArrayRef)
            {
                ingraph.addMutualEdges(rightOp, leftOp, 0);

                if (rectarray)
                {
                    Value base = ((ArrayRef)rightOp).getBase();

                    if (rectarrayset.contains(base))
                    {
                        ingraph.addMutualEdges(leftOp, Array2ndDimensionSymbol.v(base), 0);
                    }
                }

                return;
            }
        }

        if (csin)
        {
            Value rhs = rightOp;

            if (rhs instanceof BinopExpr)
            {
                Value op1 = ((BinopExpr)rhs).getOp1();
                Value op2 = ((BinopExpr)rhs).getOp2();

                if (rhs instanceof AddExpr)
                {
                    if ((op1 instanceof Local) &&
                        (op2 instanceof Local))
                    {
                        ingraph.addMutualEdges(rhs, leftOp, 0);
                        return;
                    }
                }
                else
                if (rhs instanceof MulExpr)
                {
                    if ((op1 instanceof Local) ||
                        (op2 instanceof Local))
                    {
                        ingraph.addMutualEdges(rhs, leftOp, 0);
                        return;
                    }                    
                }
                else
                if (rhs instanceof SubExpr)
                {
                    if (op2 instanceof Local)
                    {
                        ingraph.addMutualEdges(rhs, leftOp, 0);
                        return;
                    }
                }
            }
        }


        // i = j + c; or i = c + j;
        if (rightOp instanceof AddExpr)
        {
            Value op1 = ((AddExpr)rightOp).getOp1();
            Value op2 = ((AddExpr)rightOp).getOp2();

            if ( (op1 instanceof Local) && (op2 instanceof IntConstant) )
            {
                int inc_w = ((IntConstant)op2).value;
                ingraph.addMutualEdges(op1, leftOp, inc_w);
                return;
            }

            if ( (op2 instanceof Local) && (op1 instanceof IntConstant) )
            {
                int inc_w = ((IntConstant)op1).value;
                ingraph.addMutualEdges(op2, leftOp, inc_w);
                return;
            }
        }

        // only i = j - c was considered. 
        if (rightOp instanceof SubExpr)
        {
            Value op1 = ((SubExpr)rightOp).getOp1();
            Value op2 = ((SubExpr)rightOp).getOp2();

            if ((op1 instanceof Local) && (op2 instanceof IntConstant))
            {
                int inc_w = - ((IntConstant)op2).value;
                ingraph.addMutualEdges(op1, leftOp, inc_w);
                return;
            }
        }
        
        // new experessions can also generate relationship
        // a = new A[i]; a = new A[c];
        if (rightOp instanceof NewArrayExpr)
        {
            Value size = ((NewArrayExpr)rightOp).getSize();
            if (size instanceof Local)
            {
                ingraph.addMutualEdges(size, leftOp, 0);
                return;
            }

            if (size instanceof IntConstant)
            {
                int inc_w = ((IntConstant)size).value;
                ingraph.addMutualEdges(zero, leftOp, inc_w);
                return;
            }
        }

        // a = new A[i][].. ; a = new A[c]...;
        if (rightOp instanceof NewMultiArrayExpr)
        {
            Value size = ((NewMultiArrayExpr)rightOp).getSize(0);
            if (size instanceof Local)
            {
                ingraph.addMutualEdges(size, leftOp, 0);
            }
            else
            if (size instanceof IntConstant)
            {
                int inc_w = ((IntConstant)size).value;
                ingraph.addMutualEdges(zero, leftOp, inc_w);
            }

            if (arrayin && rectarray)
            {
                if (((NewMultiArrayExpr)rightOp).getSizeCount() > 1)
                {
                    size = ((NewMultiArrayExpr)rightOp).getSize(1);
                    if (size instanceof Local)
                    {
                        ingraph.addMutualEdges(size, Array2ndDimensionSymbol.v(leftOp), 0);
                    }
                    else
                    if (size instanceof IntConstant)
                    {
                        int inc_w = ((IntConstant)size).value;
                        ingraph.addMutualEdges(zero, Array2ndDimensionSymbol.v(leftOp), inc_w);
                    }
                }
            }

            return;
        }

        // i = a.length
        if (rightOp instanceof LengthExpr)
        {
            Value base = ((LengthExpr)rightOp).getOp();
            ingraph.addMutualEdges(base, leftOp, 0);
            return;
        }
    }

  /* assert the branch statement
   * return true, if the out condition changed,
   *        false, otherwise
   */
    private boolean assertBranchStmt(Object in,
                                     Unit s, Block current,
                                     List succs,
                                     List changedSuccs)
    {
        IfStmt ifstmt = (IfStmt)s;

        // take out the condition.
        Value cmpcond = ifstmt.getCondition();

        if (!(cmpcond instanceof ConditionExpr))
            return false;

        // how may succs?
        if (succs.size() != 2) {
          return false;
        }

        Stmt targetUnit = ifstmt.getTarget();
        Block targetBlock = (Block)succs.get(0);
        Block nextBlock = (Block)succs.get(1);

        if (!targetUnit.equals(targetBlock.getHead()))
        {
            Block swap = targetBlock;
            targetBlock = nextBlock;
            nextBlock = swap;
        }

        Value op1 = ((ConditionExpr)cmpcond).getOp1();
        Value op2 = ((ConditionExpr)cmpcond).getOp2();

        HashSet livelocals = (HashSet)ailanalysis.getFlowAfter(s);

        if (!livelocals.contains(op1) && !livelocals.contains(op2))
            return false;

        WeightedDirectedSparseGraph ingraph = (WeightedDirectedSparseGraph)in;

        WeightedDirectedSparseGraph targetgraph = ingraph.dup();

        // EqExpr, GeExpr, GtExpr, LeExpr, LtExpr, NeExpr 
        if ((cmpcond instanceof EqExpr) ||
            (cmpcond instanceof NeExpr) )
        {
            Object node1 = op1, node2 = op2;
            int weight = 0;
            if (node1 instanceof IntConstant)
            {
                      weight = ((IntConstant)node1).value;
                node1 = zero;
            }
            if (node2 instanceof IntConstant)
            {
                weight = ((IntConstant)node2).value;
                node2 = zero;
            }

            if (node1 == node2)
                return false;
            
            if (cmpcond instanceof EqExpr)
                targetgraph.addMutualEdges(node1, node2, weight);
            else
                ingraph.addMutualEdges(node1, node2, weight);
        }
        else
            // i > j
        if ((cmpcond instanceof GtExpr) ||
            // i >= j
            (cmpcond instanceof GeExpr) )
        {
            Object node1 = op1, node2 = op2;
            int weight = 0;
            
            if (node1 instanceof IntConstant)
            {
                weight += ((IntConstant)node1).value;
                node1 = zero;
            }

            if (node2 instanceof IntConstant)
            {
                weight -= ((IntConstant)node2).value;
                node2 = zero;
            }
            
            if (node1 == node2)
                return false;

            if (cmpcond instanceof GtExpr)
            {
                targetgraph.addEdge(node1, node2, weight-1);
                ingraph.addEdge(node2, node1, -weight);
            }
            else
            {
                targetgraph.addEdge(node1, node2, weight);
                ingraph.addEdge(node2, node1, -weight-1);                                
            }
        }
        else
            // i < j 
        if ((cmpcond instanceof LtExpr) ||
            (cmpcond instanceof LeExpr) )
        {
            Object node1 = op1, node2 = op2;
            int weight = 0;
            
            if (node1 instanceof IntConstant)
            {
                weight -= ((IntConstant)node1).value;
                node1 = zero;
            }

            if (node2 instanceof IntConstant)
            {
                weight += ((IntConstant)node2).value;
                node2 = zero;
            }

            if (node1 == node2)
                return false;
            
            if (cmpcond instanceof LtExpr)
            {
                targetgraph.addEdge(node2, node1, weight-1);
                ingraph.addEdge(node1, node2, -weight);
            }
            else
            {
                targetgraph.addEdge(node2, node1, weight);
                ingraph.addEdge(node1, node2, -weight-1);
            }
        }
        else
            return false;

        // update out edges and changed succs.
        // targetgraph -> targetBlock

        FlowGraphEdge targetEdge = new FlowGraphEdge(current, targetBlock);
        WeightedDirectedSparseGraph prevtarget = edgeMap.get(targetEdge);
        boolean changed = false;

               targetgraph.makeShortestPathGraph();

        WeightedDirectedSparseGraph tmpgraph =
            new WeightedDirectedSparseGraph(prevtarget.getVertexes(), true);

        copy(targetgraph, tmpgraph);

        if (!tmpgraph.equals(prevtarget))
        {
            prevtarget.replaceAllEdges(tmpgraph);
            changed = true;
        }

        if (changed)
            changedSuccs.add(targetBlock);

        
        // ingraph -> nextBlock
        FlowGraphEdge nextEdge = new FlowGraphEdge(current, nextBlock);
        WeightedDirectedSparseGraph prevnext = edgeMap.get(nextEdge);
        changed = false;

               ingraph.makeShortestPathGraph();

        tmpgraph = new WeightedDirectedSparseGraph(prevnext.getVertexes(), true);
            
        copy(ingraph, tmpgraph);

        if (!tmpgraph.equals(prevnext))
        {
            prevnext.replaceAllEdges(tmpgraph);
            changed = true;
        }

        if (changed)
            changedSuccs.add(nextBlock);                

        return true;

    }

    private void updateOutEdges(Object in,
                                Block current,
                                List succs,
                                List changedSuccs)
    {
        WeightedDirectedSparseGraph ingraph = (WeightedDirectedSparseGraph)in;

               ingraph.makeShortestPathGraph();

        for (int i=0; i