added concept of method context
[IRC.git] / Robust / src / Analysis / OwnershipAnalysis / OwnershipGraph.java
index 95b7a18a9836683481ba28ec38bdbaa58fcbc5b3..851b3e708ce1d159cd1554c16cd7edc4a3dcbf06 100644 (file)
@@ -8,6 +8,7 @@ import java.io.*;
 public class OwnershipGraph {
 
   private int allocationDepth;
+  private TypeUtil typeUtil;
 
   // there was already one other very similar reason
   // for traversing heap nodes that is no longer needed
@@ -18,10 +19,12 @@ public class OwnershipGraph {
 
   protected static TempDescriptor tdReturn = new TempDescriptor("_Return___");
 
+  protected static final int bogusParamIndexInt = -2;
+
 
   public Hashtable<Integer,        HeapRegionNode> id2hrn;
   public Hashtable<TempDescriptor, LabelNode     > td2ln;
-  public Hashtable<Integer,        Integer       > id2paramIndex;
+  public Hashtable<Integer,        Set<Integer>  > id2paramIndexSet;
   public Hashtable<Integer,        Integer       > paramIndex2id;
   public Hashtable<Integer,        TempDescriptor> paramIndex2tdQ;
 
@@ -30,14 +33,15 @@ public class OwnershipGraph {
 
 
 
-  public OwnershipGraph(int allocationDepth) {
+  public OwnershipGraph(int allocationDepth, TypeUtil typeUtil) {
     this.allocationDepth = allocationDepth;
+    this.typeUtil        = typeUtil;
 
-    id2hrn         = new Hashtable<Integer,        HeapRegionNode>();
-    td2ln          = new Hashtable<TempDescriptor, LabelNode     >();
-    id2paramIndex  = new Hashtable<Integer,        Integer       >();
-    paramIndex2id  = new Hashtable<Integer,        Integer       >();
-    paramIndex2tdQ = new Hashtable<Integer,        TempDescriptor>();
+    id2hrn           = new Hashtable<Integer,        HeapRegionNode>();
+    td2ln            = new Hashtable<TempDescriptor, LabelNode     >();
+    id2paramIndexSet = new Hashtable<Integer,        Set<Integer>  >();
+    paramIndex2id    = new Hashtable<Integer,        Integer       >();
+    paramIndex2tdQ   = new Hashtable<Integer,        TempDescriptor>();
 
     allocationSites = new HashSet <AllocationSite>();
   }
@@ -82,19 +86,23 @@ public class OwnershipGraph {
 
     if( alpha == null ) {
       if( isFlagged || isParameter ) {
-       alpha = new ReachabilitySet(new TokenTuple(id,
-                                                  !isSingleObject,
-                                                  TokenTuple.ARITY_ONE)
-                                   ).makeCanonical();
+       alpha = new ReachabilitySet(
+         new TokenTuple(id,
+                        !isSingleObject,
+                        TokenTuple.ARITY_ONE
+                        ).makeCanonical()
+         ).makeCanonical();
       } else {
-       alpha = new ReachabilitySet(new TokenTupleSet()
-                                   ).makeCanonical();
+       alpha = new ReachabilitySet(
+         new TokenTupleSet().makeCanonical()
+         ).makeCanonical();
       }
     }
 
     HeapRegionNode hrn = new HeapRegionNode(id,
                                             isSingleObject,
                                             isFlagged,
+                                           isParameter,
                                             isNewSummary,
                                             allocSite,
                                             alpha,
@@ -407,10 +415,39 @@ public class OwnershipGraph {
     HashSet<HeapRegionNode> nodesWithNewAlpha = new HashSet<HeapRegionNode>();
     HashSet<ReferenceEdge>  edgesWithNewBeta  = new HashSet<ReferenceEdge>();
 
+
+    // first look for possible strong updates and remove those edges
+    boolean strongUpdate = false;
+
     Iterator<ReferenceEdge> itrXhrn = lnX.iteratorToReferencees();
     while( itrXhrn.hasNext() ) {
       ReferenceEdge edgeX = itrXhrn.next();
-      HeapRegionNode hrnX  = edgeX.getDst();
+      HeapRegionNode hrnX = edgeX.getDst();
+
+      Iterator<ReferenceEdge> itrYhrn = lnY.iteratorToReferencees();
+      while( itrYhrn.hasNext() ) {
+       ReferenceEdge edgeY = itrYhrn.next();
+       HeapRegionNode hrnY = edgeY.getDst();
+
+       // we can do a strong update here if one of two cases holds     
+       if( f != null &&
+           hrnX.isSingleObject() &&
+           (   (hrnX.getNumReferencers() == 1)                           ||
+               ( lnX.getNumReferencees() == 1)
+           )
+         ) {
+         strongUpdate = true;
+         clearReferenceEdgesFrom( hrnX, f, false );
+       }
+      }
+    }
+
+    
+    // then do all token propagation
+    itrXhrn = lnX.iteratorToReferencees();
+    while( itrXhrn.hasNext() ) {
+      ReferenceEdge edgeX = itrXhrn.next();
+      HeapRegionNode hrnX = edgeX.getDst();
       ReachabilitySet betaX = edgeX.getBeta();
 
       ReachabilitySet R = hrnX.getAlpha().intersection(edgeX.getBeta() );
@@ -418,8 +455,8 @@ public class OwnershipGraph {
       Iterator<ReferenceEdge> itrYhrn = lnY.iteratorToReferencees();
       while( itrYhrn.hasNext() ) {
        ReferenceEdge edgeY = itrYhrn.next();
-       HeapRegionNode hrnY  = edgeY.getDst();
-       ReachabilitySet O     = edgeY.getBeta();
+       HeapRegionNode hrnY = edgeY.getDst();
+       ReachabilitySet O = edgeY.getBeta();
 
 
        // propagate tokens over nodes starting from hrnSrc, and it will
@@ -431,7 +468,8 @@ public class OwnershipGraph {
        // then propagate back just up the edges from hrn
        ChangeTupleSet Cx = R.unionUpArityToChangeSet(O);
 
-       HashSet<ReferenceEdge> todoEdges = new HashSet<ReferenceEdge>();
+
+       HashSet<ReferenceEdge> todoEdges = new HashSet<ReferenceEdge>();
 
        Hashtable<ReferenceEdge, ChangeTupleSet> edgePlannedChanges =
          new Hashtable<ReferenceEdge, ChangeTupleSet>();
@@ -446,64 +484,64 @@ public class OwnershipGraph {
        propagateTokensOverEdges(todoEdges,
                                 edgePlannedChanges,
                                 edgesWithNewBeta);
+      }
+    }
 
 
+    // apply the updates to reachability
+    Iterator<HeapRegionNode> nodeItr = nodesWithNewAlpha.iterator();
+    while( nodeItr.hasNext() ) {
+      nodeItr.next().applyAlphaNew();
+    }
+
+    Iterator<ReferenceEdge> edgeItr = edgesWithNewBeta.iterator();
+    while( edgeItr.hasNext() ) {
+      edgeItr.next().applyBetaNew();
+    }
 
-       //System.out.println( edgeY.getBetaNew() + "\nbeing pruned by\n" + hrnX.getAlpha() );
 
-       // create the actual reference edge hrnX.f -> hrnY
+    // then go back through and add the new edges
+    itrXhrn = lnX.iteratorToReferencees();
+    while( itrXhrn.hasNext() ) {
+      ReferenceEdge edgeX = itrXhrn.next();
+      HeapRegionNode hrnX = edgeX.getDst();
+
+      Iterator<ReferenceEdge> itrYhrn = lnY.iteratorToReferencees();
+      while( itrYhrn.hasNext() ) {
+       ReferenceEdge edgeY = itrYhrn.next();
+       HeapRegionNode hrnY = edgeY.getDst();
+
+       // prepare the new reference edge hrnX.f -> hrnY
        ReferenceEdge edgeNew = new ReferenceEdge(hrnX,
                                                  hrnY,
                                                  f,
                                                  false,
-                                                 edgeY.getBetaNew().pruneBy(hrnX.getAlpha() )
-                                                 //edgeY.getBeta().pruneBy( hrnX.getAlpha() )
+                                                 edgeY.getBeta().pruneBy( hrnX.getAlpha() )
                                                  );
-       addReferenceEdge(hrnX, hrnY, edgeNew);
-
-       /*
-          if( f != null ) {
-           // we can do a strong update here if one of two cases holds
-           // SAVE FOR LATER, WITHOUT STILL CORRECT
-           if( (hrnX.getNumReferencers() == 1)                           ||
-               ( lnX.getNumReferencees() == 1 && hrnX.isSingleObject() )
-             ) {
-               clearReferenceEdgesFrom( hrnX, f, false );
-           }
 
-           addReferenceEdge( hrnX, hrnY, edgeNew );
-
-          } else {
-           // if the field is null, or "any" field, then
-           // look to see if an any field already exists
-           // and merge with it, otherwise just add the edge
-           ReferenceEdge edgeExisting = hrnX.getReferenceTo( hrnY, f );
-
-           if( edgeExisting != null ) {
-               edgeExisting.setBetaNew(
-                 edgeExisting.getBetaNew().union( edgeNew.getBeta() )
-                                      );
-               // a new edge here cannot be reflexive, so existing will
-               // always be also not reflexive anymore
-               edgeExisting.setIsInitialParamReflexive( false );
-
-           } else {
-               addReferenceEdge( hrnX, hrnY, edgeNew );
-           }
-          }
-        */
+       // look to see if an edge with same field exists
+       // and merge with it, otherwise just add the edge
+       ReferenceEdge edgeExisting = hrnX.getReferenceTo( hrnY, f );
+       
+       if( edgeExisting != null ) {
+         edgeExisting.setBeta(
+                              edgeExisting.getBeta().union( edgeNew.getBeta() )
+                             );
+         // a new edge here cannot be reflexive, so existing will
+         // always be also not reflexive anymore
+         edgeExisting.setIsInitialParamReflexive( false );
+       } else {
+         addReferenceEdge( hrnX, hrnY, edgeNew );
+       }
       }
     }
 
-    Iterator<HeapRegionNode> nodeItr = nodesWithNewAlpha.iterator();
-    while( nodeItr.hasNext() ) {
-      nodeItr.next().applyAlphaNew();
-    }
 
-    Iterator<ReferenceEdge> edgeItr = edgesWithNewBeta.iterator();
-    while( edgeItr.hasNext() ) {
-      edgeItr.next().applyBetaNew();
-    }
+    // if there was a strong update, make sure to improve
+    // reachability with a global sweep
+    if( strongUpdate ) {      
+      globalSweep();
+    }  
   }
 
 
@@ -531,15 +569,17 @@ public class OwnershipGraph {
     // parameter labels, the index of the parameter they
     // are for is important when resolving method calls
     Integer newID = hrn.getID();
-    assert !id2paramIndex.containsKey(newID);
-    assert !id2paramIndex.containsValue(paramIndex);
-    id2paramIndex.put(newID, paramIndex);
+    assert !id2paramIndexSet.containsKey(newID);
+    Set s = new HashSet<Integer>();
+    s.add( paramIndex );
+    id2paramIndexSet.put(newID, s);
     paramIndex2id.put(paramIndex, newID);
     paramIndex2tdQ.put(paramIndex, tdParamQ);
 
     ReachabilitySet beta = new ReachabilitySet(new TokenTuple(newID,
                                                               true,
-                                                              TokenTuple.ARITY_ONE) );
+                                                              TokenTuple.ARITY_ONE).makeCanonical()
+                                               ).makeCanonical();
 
     // heap regions for parameters are always multiple object (see above)
     // and have a reference to themselves, because we can't know the
@@ -560,6 +600,94 @@ public class OwnershipGraph {
     addReferenceEdge(hrn,      hrn, edgeReflexive);
   }
 
+  public void makeAliasedParamHeapRegionNode(TempDescriptor td) {
+    assert td != null;
+
+    LabelNode lnParam = getLabelNodeFromTemp(td);
+    HeapRegionNode hrn = createNewHeapRegionNode(null,
+                                                 false,
+                                                 false,
+                                                 false,
+                                                 true,
+                                                 null,
+                                                 null,
+                                                 "aliasedParams");
+
+
+    ReachabilitySet beta = new ReachabilitySet(new TokenTuple(hrn.getID(),
+                                                              true,
+                                                              TokenTuple.ARITY_ONE).makeCanonical()
+                                               ).makeCanonical();
+
+    // heap regions for parameters are always multiple object (see above)
+    // and have a reference to themselves, because we can't know the
+    // structure of memory that is passed into the method.  We're assuming
+    // the worst here.
+
+    ReferenceEdge edgeFromLabel =
+      new ReferenceEdge(lnParam, hrn, null, false, beta);
+
+    ReferenceEdge edgeReflexive =
+      new ReferenceEdge(hrn,     hrn, null, true,  beta);
+
+    addReferenceEdge(lnParam, hrn, edgeFromLabel);
+    addReferenceEdge(hrn,     hrn, edgeReflexive);
+  }
+
+  public void assignTempEqualToAliasedParam(TempDescriptor tdParam,
+                                           TempDescriptor tdAliased,
+                                           Integer paramIndex ) {
+
+    assert tdParam   != null;
+    assert tdAliased != null;
+
+    LabelNode lnParam   = getLabelNodeFromTemp(tdParam);
+    LabelNode lnAliased = getLabelNodeFromTemp(tdAliased);
+
+    // this is a non-program-accessible label that picks up beta
+    // info to be used for fixing a caller of this method
+    TempDescriptor tdParamQ = new TempDescriptor(tdParam+"specialQ");
+    LabelNode lnParamQ = getLabelNodeFromTemp(tdParamQ);
+
+    // the lnAliased should always only reference one node, and that
+    // heap region node is the aliased param blob
+    assert lnAliased.getNumReferencees() == 1;
+    HeapRegionNode hrnAliasBlob = lnAliased.iteratorToReferencees().next().getDst();
+
+    // keep track of heap regions that were created for
+    // parameter labels, the index of the parameter they
+    // are for is important when resolving method calls
+    Integer idAliased = hrnAliasBlob.getID();
+    Set s = id2paramIndexSet.get( idAliased );
+    if( s == null ) {
+      s = new HashSet<Integer>();
+    }
+    s.add( paramIndex );
+    id2paramIndexSet.put(idAliased, s);
+    paramIndex2id.put(paramIndex, idAliased);
+    paramIndex2tdQ.put(paramIndex, tdParamQ);
+
+    ReachabilitySet beta = new ReachabilitySet(new TokenTuple(idAliased,
+                                                              true,
+                                                              TokenTuple.ARITY_ONE).makeCanonical()
+                                               ).makeCanonical();
+
+    // heap regions for parameters are always multiple object (see above)
+    // and have a reference to themselves, because we can't know the
+    // structure of memory that is passed into the method.  We're assuming
+    // the worst here.
+
+    ReferenceEdge edgeFromLabel =
+      new ReferenceEdge(lnParam, hrnAliasBlob, null, false, beta);
+
+    ReferenceEdge edgeFromLabelQ =
+      new ReferenceEdge(lnParamQ, hrnAliasBlob, null, false, beta);
+
+    addReferenceEdge(lnParam,  hrnAliasBlob, edgeFromLabel);
+    addReferenceEdge(lnParamQ, hrnAliasBlob, edgeFromLabelQ);
+  }
+
+
 
   public void assignReturnEqualToTemp(TempDescriptor x) {
 
@@ -693,14 +821,16 @@ public class OwnershipGraph {
 
     // after tokens have been aged, reset newest node's reachability
     if( hrn0.isFlagged() ) {
-      hrn0.setAlpha(new ReachabilitySet(new TokenTupleSet(
-                                          new TokenTuple(hrn0)
-                                          )
-                                        ).makeCanonical()
+      hrn0.setAlpha(new ReachabilitySet(
+                      new TokenTupleSet(
+                        new TokenTuple(hrn0).makeCanonical()
+                        ).makeCanonical()
+                      ).makeCanonical()
                     );
     } else {
-      hrn0.setAlpha(new ReachabilitySet(new TokenTupleSet()
-                                        ).makeCanonical()
+      hrn0.setAlpha(new ReachabilitySet(
+                      new TokenTupleSet().makeCanonical()
+                      ).makeCanonical()
                     );
     }
   }
@@ -843,7 +973,7 @@ public class OwnershipGraph {
 
   protected void transferOnto(HeapRegionNode hrnA, HeapRegionNode hrnB) {
 
-    // clear references in and out of node i
+    // clear references in and out of node b
     clearReferenceEdgesFrom(hrnB, null, true);
     clearReferenceEdgesTo(hrnB, null, true);
 
@@ -882,12 +1012,109 @@ public class OwnershipGraph {
   }
 
 
+  public Set<Integer> calculateAliasedParamSet(FlatCall fc,
+                                              boolean isStatic,
+                                              FlatMethod fm) {
+
+    Hashtable<Integer, LabelNode> paramIndex2ln =
+      new Hashtable<Integer, LabelNode>();
+
+    Hashtable<Integer, HashSet<HeapRegionNode> > paramIndex2reachableCallerNodes =
+      new Hashtable<Integer, HashSet<HeapRegionNode> >();
+
+    for( int i = 0; i < fm.numParameters(); ++i ) {
+      Integer paramIndex = new Integer(i);
+
+      // now depending on whether the callee is static or not
+      // we need to account for a "this" argument in order to
+      // find the matching argument in the caller context
+      TempDescriptor argTemp_i;
+      if( isStatic ) {
+       argTemp_i = fc.getArg(paramIndex);
+      } else {
+       if( paramIndex.equals(0) ) {
+         argTemp_i = fc.getThis();
+       } else {
+         argTemp_i = fc.getArg(paramIndex - 1);
+       }
+      }
+
+      // in non-static methods there is a "this" pointer
+      // that should be taken into account
+      if( isStatic ) {
+       assert fc.numArgs()     == fm.numParameters();
+      } else {
+       assert fc.numArgs() + 1 == fm.numParameters();
+      }
+
+      LabelNode argLabel_i = getLabelNodeFromTemp(argTemp_i);
+      paramIndex2ln.put(paramIndex, argLabel_i);
+    }
+
+    Iterator lnArgItr = paramIndex2ln.entrySet().iterator();
+    while( lnArgItr.hasNext() ) {
+      Map.Entry me      = (Map.Entry)lnArgItr.next();
+      Integer index   = (Integer)   me.getKey();
+      LabelNode lnArg_i = (LabelNode) me.getValue();
+
+      // rewrite alpha for the nodes reachable from argument label i
+      HashSet<HeapRegionNode> reachableNodes = new HashSet<HeapRegionNode>();
+      HashSet<HeapRegionNode> todoNodes = new HashSet<HeapRegionNode>();
+
+      // to find all reachable nodes, start with label referencees
+      Iterator<ReferenceEdge> edgeArgItr = lnArg_i.iteratorToReferencees();
+      while( edgeArgItr.hasNext() ) {
+       ReferenceEdge edge = edgeArgItr.next();
+       todoNodes.add(edge.getDst() );
+      }
+
+      // then follow links until all reachable nodes have been found
+      while( !todoNodes.isEmpty() ) {
+       HeapRegionNode hrn = todoNodes.iterator().next();
+       todoNodes.remove(hrn);
+       reachableNodes.add(hrn);
+
+       Iterator<ReferenceEdge> edgeItr = hrn.iteratorToReferencees();
+       while( edgeItr.hasNext() ) {
+         ReferenceEdge edge = edgeItr.next();
+
+         if( !reachableNodes.contains(edge.getDst() ) ) {
+           todoNodes.add(edge.getDst() );
+         }
+       }
+      }
+
+      // save for later
+      paramIndex2reachableCallerNodes.put(index, reachableNodes);
+    }
+
+    Set<Integer> aliasedIndices = new HashSet<Integer>();
+
+    // check for arguments that are aliased
+    for( int i = 0; i < fm.numParameters(); ++i ) {
+      for( int j = 0; j < i; ++j ) {   
+       HashSet<HeapRegionNode> s1 = paramIndex2reachableCallerNodes.get( i );
+       HashSet<HeapRegionNode> s2 = paramIndex2reachableCallerNodes.get( j );
+
+       Set<HeapRegionNode> intersection = new HashSet<HeapRegionNode>(s1);
+       intersection.retainAll(s2);
+
+       if( !intersection.isEmpty() ) {
+         aliasedIndices.add( new Integer( i ) );
+         aliasedIndices.add( new Integer( j ) );
+       }
+      }
+    }
+
+    return aliasedIndices;
+  }
+
+
   public void resolveMethodCall(FlatCall fc,
                                 boolean isStatic,
                                 FlatMethod fm,
                                 OwnershipGraph ogCallee) {
 
-
     // define rewrite rules and other structures to organize
     // data by parameter/argument index
     Hashtable<Integer, ReachabilitySet> paramIndex2rewriteH =
@@ -899,6 +1126,9 @@ public class OwnershipGraph {
     Hashtable<Integer, ReachabilitySet> paramIndex2rewriteK =
       new Hashtable<Integer, ReachabilitySet>();
 
+    Hashtable<Integer, ReachabilitySet> paramIndex2rewrite_d =
+      new Hashtable<Integer, ReachabilitySet>();
+
     Hashtable<Integer, ReachabilitySet> paramIndex2rewriteD =
       new Hashtable<Integer, ReachabilitySet>();
 
@@ -909,10 +1139,10 @@ public class OwnershipGraph {
     Hashtable<Integer, TokenTuple> paramIndex2paramToken =
       new Hashtable<Integer, TokenTuple>();
 
-    Hashtable<TokenTuple, Integer> paramTokenStar2paramIndex =
+    Hashtable<TokenTuple, Integer> paramTokenPlus2paramIndex =
       new Hashtable<TokenTuple, Integer>();
 
-    Hashtable<Integer, TokenTuple> paramIndex2paramTokenStar =
+    Hashtable<Integer, TokenTuple> paramIndex2paramTokenPlus =
       new Hashtable<Integer, TokenTuple>();
 
     Hashtable<Integer, LabelNode> paramIndex2ln =
@@ -924,19 +1154,21 @@ public class OwnershipGraph {
 
     // add a bogus entry with the identity rule for easy rewrite
     // of new callee nodes and edges, doesn't belong to any parameter
-    Integer bogusID = new Integer(-1);
-    Integer bogusIndex = new Integer(-1);
-    TokenTuple bogusToken = new TokenTuple(bogusID, true, TokenTuple.ARITY_ONE);
-    TokenTuple bogusTokenStar = new TokenTuple(bogusID, true, TokenTuple.ARITY_MANY);
+    Integer bogusID = new Integer(bogusParamIndexInt);
+    Integer bogusIndex = new Integer(bogusParamIndexInt);
+    TokenTuple bogusToken = new TokenTuple(bogusID, true, TokenTuple.ARITY_ONE).makeCanonical();
+    TokenTuple bogusTokenPlus = new TokenTuple(bogusID, true, TokenTuple.ARITY_ONEORMORE).makeCanonical();
     ReachabilitySet rsIdentity =
-      new ReachabilitySet(new TokenTupleSet(bogusToken).makeCanonical() ).makeCanonical();
+      new ReachabilitySet(
+        new TokenTupleSet(bogusToken).makeCanonical()
+        ).makeCanonical();
 
     paramIndex2rewriteH.put(bogusIndex, rsIdentity);
     paramIndex2rewriteJ.put(bogusIndex, rsIdentity);
     paramToken2paramIndex.put(bogusToken, bogusIndex);
     paramIndex2paramToken.put(bogusIndex, bogusToken);
-    paramTokenStar2paramIndex.put(bogusTokenStar, bogusIndex);
-    paramIndex2paramTokenStar.put(bogusIndex, bogusTokenStar);
+    paramTokenPlus2paramIndex.put(bogusTokenPlus, bogusIndex);
+    paramIndex2paramTokenPlus.put(bogusIndex, bogusTokenPlus);
 
 
     for( int i = 0; i < fm.numParameters(); ++i ) {
@@ -975,11 +1207,11 @@ public class OwnershipGraph {
       paramToken2paramIndex.put(p_i, paramIndex);
       paramIndex2paramToken.put(paramIndex, p_i);
 
-      TokenTuple p_i_star = new TokenTuple(hrnParam.getID(),
+      TokenTuple p_i_plus = new TokenTuple(hrnParam.getID(),
                                            true,
-                                           TokenTuple.ARITY_MANY).makeCanonical();
-      paramTokenStar2paramIndex.put(p_i_star, paramIndex);
-      paramIndex2paramTokenStar.put(paramIndex, p_i_star);
+                                           TokenTuple.ARITY_ONEORMORE).makeCanonical();
+      paramTokenPlus2paramIndex.put(p_i_plus, paramIndex);
+      paramIndex2paramTokenPlus.put(paramIndex, p_i_plus);
 
       // now depending on whether the callee is static or not
       // we need to account for a "this" argument in order to
@@ -988,7 +1220,7 @@ public class OwnershipGraph {
       if( isStatic ) {
        argTemp_i = fc.getArg(paramIndex);
       } else {
-       if( paramIndex == 0 ) {
+       if( paramIndex.equals(0) ) {
          argTemp_i = fc.getThis();
        } else {
          argTemp_i = fc.getArg(paramIndex - 1);
@@ -1006,13 +1238,15 @@ public class OwnershipGraph {
       LabelNode argLabel_i = getLabelNodeFromTemp(argTemp_i);
       paramIndex2ln.put(paramIndex, argLabel_i);
 
-      ReachabilitySet D_i = new ReachabilitySet().makeCanonical();
+      ReachabilitySet d_i = new ReachabilitySet().makeCanonical();
       Iterator<ReferenceEdge> edgeItr = argLabel_i.iteratorToReferencees();
       while( edgeItr.hasNext() ) {
        ReferenceEdge edge = edgeItr.next();
-       D_i = D_i.union(edge.getBeta() );
+       d_i = d_i.union(edge.getBeta());
       }
-      D_i = D_i.exhaustiveArityCombinations();
+      paramIndex2rewrite_d.put(paramIndex, d_i);
+
+      ReachabilitySet D_i = d_i.exhaustiveArityCombinations();
       paramIndex2rewriteD.put(paramIndex, D_i);
     }
 
@@ -1065,13 +1299,17 @@ public class OwnershipGraph {
       while( hrnItr.hasNext() ) {
        HeapRegionNode hrn = hrnItr.next();
 
-       rewriteCallerNodeAlpha(fm.numParameters(),
-                              index,
-                              hrn,
-                              paramIndex2rewriteH,
-                              paramIndex2rewriteD,
-                              paramIndex2paramToken,
-                              paramIndex2paramTokenStar);
+       rewriteCallerReachability(index,
+                                 hrn,
+                                 null,
+                                 paramIndex2rewriteH.get(index),
+                                 paramIndex2rewrite_d,
+                                 paramIndex2rewriteD,
+                                 paramIndex2paramToken.get(index),
+                                 paramToken2paramIndex,
+                                 paramTokenPlus2paramIndex,
+                                 false,
+                                 null);
 
        nodesWithNewAlpha.add(hrn);
 
@@ -1105,43 +1343,45 @@ public class OwnershipGraph {
        }
       }
 
-
       // update reachable edges
       Iterator<ReferenceEdge> edgeReachableItr = edgesReachable.iterator();
       while( edgeReachableItr.hasNext() ) {
        ReferenceEdge edgeReachable = edgeReachableItr.next();
 
-       rewriteCallerEdgeBeta(fm.numParameters(),
-                             index,
-                             edgeReachable,
-                             paramIndex2rewriteJ,
-                             paramIndex2rewriteD,
-                             paramIndex2paramToken,
-                             paramIndex2paramTokenStar,
-                             false,
-                             null);
+       rewriteCallerReachability(index,
+                                 null,
+                                 edgeReachable,
+                                 paramIndex2rewriteJ.get(index),
+                                 paramIndex2rewrite_d,
+                                 paramIndex2rewriteD,
+                                 paramIndex2paramToken.get(index),
+                                 paramToken2paramIndex,
+                                 paramTokenPlus2paramIndex,
+                                 false,
+                                 null);
 
        edgesWithNewBeta.add(edgeReachable);
       }
 
-
       // update upstream edges
-      Hashtable<ReferenceEdge, ChangeTupleSet> edgeUpstreamPlannedChanges
-      = new Hashtable<ReferenceEdge, ChangeTupleSet>();
+      Hashtable<ReferenceEdge, ChangeTupleSet> edgeUpstreamPlannedChanges =
+        new Hashtable<ReferenceEdge, ChangeTupleSet>();
 
       Iterator<ReferenceEdge> edgeUpstreamItr = edgesUpstream.iterator();
       while( edgeUpstreamItr.hasNext() ) {
        ReferenceEdge edgeUpstream = edgeUpstreamItr.next();
 
-       rewriteCallerEdgeBeta(fm.numParameters(),
-                             index,
-                             edgeUpstream,
-                             paramIndex2rewriteK,
-                             paramIndex2rewriteD,
-                             paramIndex2paramToken,
-                             paramIndex2paramTokenStar,
-                             true,
-                             edgeUpstreamPlannedChanges);
+       rewriteCallerReachability(index,
+                                 null,
+                                 edgeUpstream,
+                                 paramIndex2rewriteK.get(index),
+                                 paramIndex2rewrite_d,
+                                 paramIndex2rewriteD,
+                                 paramIndex2paramToken.get(index),
+                                 paramToken2paramIndex,
+                                 paramTokenPlus2paramIndex,
+                                 true,
+                                 edgeUpstreamPlannedChanges);
 
        edgesWithNewBeta.add(edgeUpstream);
       }
@@ -1164,7 +1404,6 @@ public class OwnershipGraph {
     }
 
 
-
     // verify the existence of allocation sites and their
     // shadows from the callee in the context of this caller graph
     // then map allocated nodes of callee onto the caller shadows
@@ -1172,6 +1411,9 @@ public class OwnershipGraph {
     Iterator<AllocationSite> asItr = ogCallee.allocationSites.iterator();
     while( asItr.hasNext() ) {
       AllocationSite allocSite  = asItr.next();
+
+      // grab the summary in the caller just to make sure
+      // the allocation site has nodes in the caller
       HeapRegionNode hrnSummary = getSummaryNode(allocSite);
 
       // assert that the shadow nodes have no reference edges
@@ -1182,8 +1424,6 @@ public class OwnershipGraph {
       assert hrnShadowSummary.getNumReferencees() == 0;
 
       // then bring g_ij onto g'_ij and rewrite
-      transferOnto(hrnSummary, hrnShadowSummary);
-
       HeapRegionNode hrnSummaryCallee = ogCallee.getSummaryNode(allocSite);
       hrnShadowSummary.setAlpha(toShadowTokens(ogCallee, hrnSummaryCallee.getAlpha() ) );
 
@@ -1191,13 +1431,17 @@ public class OwnershipGraph {
       // so rewrite and immediately commit--and they don't belong
       // to a particular parameter, so use a bogus param index
       // that pulls a self-rewrite out of H
-      rewriteCallerNodeAlpha(fm.numParameters(),
-                             bogusIndex,
-                             hrnShadowSummary,
-                             paramIndex2rewriteH,
-                             paramIndex2rewriteD,
-                             paramIndex2paramToken,
-                             paramIndex2paramTokenStar);
+      rewriteCallerReachability(bogusIndex,
+                                hrnShadowSummary,
+                                null,
+                                hrnShadowSummary.getAlpha(),
+                                paramIndex2rewrite_d,
+                                paramIndex2rewriteD,
+                                bogusToken,
+                                paramToken2paramIndex,
+                                paramTokenPlus2paramIndex,
+                                false,
+                                null);
 
       hrnShadowSummary.applyAlphaNew();
 
@@ -1213,19 +1457,21 @@ public class OwnershipGraph {
        assert hrnIthShadow.getNumReferencers() == 0;
        assert hrnIthShadow.getNumReferencees() == 0;
 
-       transferOnto(hrnIth, hrnIthShadow);
-
        assert ogCallee.id2hrn.containsKey(idIth);
        HeapRegionNode hrnIthCallee = ogCallee.id2hrn.get(idIth);
        hrnIthShadow.setAlpha(toShadowTokens(ogCallee, hrnIthCallee.getAlpha() ) );
 
-       rewriteCallerNodeAlpha(fm.numParameters(),
-                              bogusIndex,
-                              hrnIthShadow,
-                              paramIndex2rewriteH,
-                              paramIndex2rewriteD,
-                              paramIndex2paramToken,
-                              paramIndex2paramTokenStar);
+       rewriteCallerReachability(bogusIndex,
+                                 hrnIthShadow,
+                                 null,
+                                 hrnIthShadow.getAlpha(),
+                                 paramIndex2rewrite_d,
+                                 paramIndex2rewriteD,
+                                 bogusToken,
+                                 paramToken2paramIndex,
+                                 paramTokenPlus2paramIndex,
+                                 false,
+                                 null);
 
        hrnIthShadow.applyAlphaNew();
       }
@@ -1265,17 +1511,20 @@ public class OwnershipGraph {
                                                                    null,
                                                                    edgeCallee.getFieldDesc(),
                                                                    false,
-                                                                   toShadowTokens(ogCallee, edgeCallee.getBeta() )
+                                                                   toShadowTokens(ogCallee,
+                                                                                  edgeCallee.getBeta() )
                                                                    );
-         rewriteCallerEdgeBeta(fm.numParameters(),
-                               bogusIndex,
-                               edgeNewInCallerTemplate,
-                               paramIndex2rewriteJ,
-                               paramIndex2rewriteD,
-                               paramIndex2paramToken,
-                               paramIndex2paramTokenStar,
-                               false,
-                               null);
+         rewriteCallerReachability(bogusIndex,
+                                   null,
+                                   edgeNewInCallerTemplate,
+                                   edgeNewInCallerTemplate.getBeta(),
+                                   paramIndex2rewrite_d,
+                                   paramIndex2rewriteD,
+                                   bogusToken,
+                                   paramToken2paramIndex,
+                                   paramTokenPlus2paramIndex,
+                                   false,
+                                   null);
 
          edgeNewInCallerTemplate.applyBetaNew();
 
@@ -1292,46 +1541,26 @@ public class OwnershipGraph {
            getHRNSetThatPossiblyMapToCalleeHRN(ogCallee,
                                                edgeCallee.getDst(),
                                                paramIndex2reachableCallerNodes);
-         
+
 
          // make every possible pair of {srcSet} -> {dstSet} edges in the caller
          Iterator srcItr = possibleCallerSrcs.iterator();
          while( srcItr.hasNext() ) {
            HeapRegionNode src = (HeapRegionNode) srcItr.next();
 
-           // check that if this source node has a definite type that
-           // it also has the appropriate field, otherwise prune this
-           AllocationSite asSrc = src.getAllocationSite();
-           if( asSrc != null ) {
-             boolean foundField = false;             
-             Iterator fieldsSrcItr = asSrc.getType().getClassDesc().getFields();
-             while( fieldsSrcItr.hasNext() ) {
-               FieldDescriptor fd = (FieldDescriptor) fieldsSrcItr.next();
-               if( fd == edgeCallee.getFieldDesc() ) {
-                 foundField = true;
-                 break;
-               }
-             }
-             if( !foundField ) {
-               // prune this source node possibility
-               continue;
-             }
+           if( !hasMatchingField(src, edgeCallee) ) {
+             // prune this source node possibility
+             continue;
            }
 
            Iterator dstItr = possibleCallerDsts.iterator();
            while( dstItr.hasNext() ) {
              HeapRegionNode dst = (HeapRegionNode) dstItr.next();
 
-             // check if this dst node has a definite type and
-             // if it matches the callee edge
-             AllocationSite asDst = dst.getAllocationSite();
-             if( asDst != null && edgeCallee.getFieldDesc() != null ) {
-               if( asDst.getType() == null && edgeCallee.getFieldDesc().getType() != null ) { continue; }
-               if( asDst.getType() != null && edgeCallee.getFieldDesc().getType() == null ) { continue; }
-               if( asDst.getType() != null && edgeCallee.getFieldDesc().getType() != null ) {
-                 if( !asDst.getType().equals( edgeCallee.getFieldDesc().getType() ) ) { continue; }
-               }
-             }       
+             if( !hasMatchingType(edgeCallee, dst) ) {
+               // prune
+               continue;
+             }
 
              // otherwise the caller src and dst pair can match the edge, so make it
              ReferenceEdge edgeNewInCaller = edgeNewInCallerTemplate.copy();
@@ -1353,11 +1582,11 @@ public class OwnershipGraph {
     }
 
 
-
     // return value may need to be assigned in caller
-    if( fc.getReturnTemp() != null ) {
+    TempDescriptor returnTemp = fc.getReturnTemp();
+    if( returnTemp != null && !returnTemp.getType().isImmutable() ) {
 
-      LabelNode lnLhsCaller = getLabelNodeFromTemp(fc.getReturnTemp() );
+      LabelNode lnLhsCaller = getLabelNodeFromTemp(returnTemp);
       clearReferenceEdgesFrom(lnLhsCaller, null, true);
 
       LabelNode lnReturnCallee = ogCallee.getLabelNodeFromTemp(tdReturn);
@@ -1366,21 +1595,24 @@ public class OwnershipGraph {
        ReferenceEdge edgeCallee = edgeCalleeItr.next();
 
        ReferenceEdge edgeNewInCallerTemplate = new ReferenceEdge(null,
-                                                                 null,
-                                                                 edgeCallee.getFieldDesc(),
-                                                                 false,
-                                                                 toShadowTokens(ogCallee, edgeCallee.getBeta() )
-                                                                 );
-       rewriteCallerEdgeBeta(fm.numParameters(),
-                             bogusIndex,
-                             edgeNewInCallerTemplate,
-                             paramIndex2rewriteJ,
-                             paramIndex2rewriteD,
-                             paramIndex2paramToken,
-                             paramIndex2paramTokenStar,
-                             false,
-                             null);
-       
+                                                                 null,
+                                                                 edgeCallee.getFieldDesc(),
+                                                                 false,
+                                                                 toShadowTokens(ogCallee,
+                                                                                edgeCallee.getBeta() )
+                                                                 );
+       rewriteCallerReachability(bogusIndex,
+                                 null,
+                                 edgeNewInCallerTemplate,
+                                 edgeNewInCallerTemplate.getBeta(),
+                                 paramIndex2rewrite_d,
+                                 paramIndex2rewriteD,
+                                 bogusToken,
+                                 paramToken2paramIndex,
+                                 paramTokenPlus2paramIndex,
+                                 false,
+                                 null);
+
        edgeNewInCallerTemplate.applyBetaNew();
 
 
@@ -1392,19 +1624,11 @@ public class OwnershipGraph {
        Iterator<HeapRegionNode> itrHrn = assignCallerRhs.iterator();
        while( itrHrn.hasNext() ) {
          HeapRegionNode hrnCaller = itrHrn.next();
-        
-         // check if this dst node has a definite type and
-         // if it matches the callee edge
-         // check if this dst node has a definite type and
-         // if it matches the callee edge
-         AllocationSite asDst = hrnCaller.getAllocationSite();
-         if( asDst != null && edgeCallee.getFieldDesc() != null ) {
-           if( asDst.getType() == null && edgeCallee.getFieldDesc().getType() != null ) { continue; }
-           if( asDst.getType() != null && edgeCallee.getFieldDesc().getType() == null ) { continue; }
-           if( asDst.getType() != null && edgeCallee.getFieldDesc().getType() != null ) {
-             if( !asDst.getType().equals( edgeCallee.getFieldDesc().getType() ) ) { continue; }
-           }
-         }           
+
+         if( !hasMatchingType(edgeCallee, hrnCaller) ) {
+           // prune
+           continue;
+         }
 
          // otherwise caller node can match callee edge, so make it
          ReferenceEdge edgeNewInCaller = edgeNewInCallerTemplate.copy();
@@ -1413,18 +1637,18 @@ public class OwnershipGraph {
 
          ReferenceEdge edgeExisting = lnLhsCaller.getReferenceTo(hrnCaller, edgeNewInCaller.getFieldDesc() );
          if( edgeExisting == null ) {
+
            // if this edge doesn't exist in the caller, create it
            addReferenceEdge(lnLhsCaller, hrnCaller, edgeNewInCaller);
          } else {
            // if it already exists, merge with it
            edgeExisting.setBeta(edgeExisting.getBeta().union(edgeNewInCaller.getBeta() ) );
-         }      
+         }
        }
       }
     }
 
 
-
     // merge the shadow nodes of allocation sites back down to normal capacity
     Iterator<AllocationSite> allocItr = ogCallee.allocationSites.iterator();
     while( allocItr.hasNext() ) {
@@ -1491,9 +1715,73 @@ public class OwnershipGraph {
        }
       }
     }
+
+    // improve reachability as much as possible
+    globalSweep();
   }
 
 
+  protected boolean hasMatchingField(HeapRegionNode src, ReferenceEdge edge) {
+
+    // if no allocation site, then it's a match-everything region
+    AllocationSite asSrc = src.getAllocationSite();
+    if( asSrc == null ) {
+      return true;
+    }
+
+    TypeDescriptor tdSrc = asSrc.getType();
+    assert tdSrc != null;
+
+    // if it's not a class, it doesn't have any fields to match
+    if( !tdSrc.isClass() ) {
+      return false;
+    }
+
+    Iterator fieldsSrcItr = tdSrc.getClassDesc().getFields();
+    while( fieldsSrcItr.hasNext() ) {
+      FieldDescriptor fd = (FieldDescriptor) fieldsSrcItr.next();
+      if( fd == edge.getFieldDesc() ) {
+       return true;
+      }
+    }
+
+    // otherwise it is a class with fields
+    // but we didn't find a match
+    return false;
+  }
+
+
+  protected boolean hasMatchingType(ReferenceEdge edge, HeapRegionNode dst) {
+
+    // if the region has no type, matches everything
+    AllocationSite asDst = dst.getAllocationSite();
+    if( asDst == null ) {
+      return true;
+    }
+
+    TypeDescriptor tdDst = asDst.getType();
+    assert tdDst != null;
+
+    // if the type is not a class don't match because
+    // primitives are copied, no memory aliases
+    ClassDescriptor cdDst = tdDst.getClassDesc();
+    if( cdDst == null ) {
+      return false;
+    }
+
+    // if the field is null, it matches everything
+    FieldDescriptor fd = edge.getFieldDesc();
+    if( fd == null ) {
+      return true;
+    }
+    TypeDescriptor tdFd = fd.getType();
+    assert tdFd != null;
+
+    return typeUtil.isSuperorType(tdFd, tdDst);
+  }
+
+
+
   protected void unshadowTokens(AllocationSite as, ReferenceEdge edge) {
     edge.setBeta(edge.getBeta().unshadowTokens(as) );
   }
@@ -1506,7 +1794,7 @@ public class OwnershipGraph {
   private ReachabilitySet toShadowTokens(OwnershipGraph ogCallee,
                                          ReachabilitySet rsIn) {
 
-    ReachabilitySet rsOut = new ReachabilitySet(rsIn);
+    ReachabilitySet rsOut = new ReachabilitySet(rsIn).makeCanonical();
 
     Iterator<AllocationSite> allocItr = ogCallee.allocationSites.iterator();
     while( allocItr.hasNext() ) {
@@ -1519,198 +1807,165 @@ public class OwnershipGraph {
   }
 
 
-  private void rewriteCallerNodeAlpha(int numParameters,
-                                      Integer paramIndex,
-                                      HeapRegionNode hrn,
-                                      Hashtable<Integer, ReachabilitySet> paramIndex2rewriteH,
-                                      Hashtable<Integer, ReachabilitySet> paramIndex2rewriteD,
-                                      Hashtable<Integer, TokenTuple> paramIndex2paramToken,
-                                      Hashtable<Integer, TokenTuple> paramIndex2paramTokenStar) {
+  private void rewriteCallerReachability(Integer paramIndex,
+                                         HeapRegionNode hrn,
+                                         ReferenceEdge edge,
+                                         ReachabilitySet rules,
+                                         Hashtable<Integer, ReachabilitySet> paramIndex2rewrite_d,
+                                         Hashtable<Integer, ReachabilitySet> paramIndex2rewriteD,
+                                         TokenTuple p_i,
+                                         Hashtable<TokenTuple, Integer> paramToken2paramIndex,
+                                         Hashtable<TokenTuple, Integer> paramTokenPlus2paramIndex,
+                                         boolean makeChangeSet,
+                                         Hashtable<ReferenceEdge, ChangeTupleSet> edgePlannedChanges) {
+    assert(hrn == null && edge != null) ||
+    (hrn != null && edge == null);
 
-    ReachabilitySet rules = paramIndex2rewriteH.get(paramIndex);
     assert rules != null;
+    assert p_i != null;
 
-    TokenTuple tokenToRewrite = paramIndex2paramToken.get(paramIndex);
-    assert tokenToRewrite != null;
-
-    ReachabilitySet r0 = new ReachabilitySet().makeCanonical();
-    Iterator<TokenTupleSet> ttsItr = rules.iterator();
-    while( ttsItr.hasNext() ) {
-      TokenTupleSet tts = ttsItr.next();
-      r0 = r0.union(tts.rewriteToken(tokenToRewrite,
-                                     hrn.getAlpha(),
-                                     false,
-                                     null) );
+    ReachabilitySet callerReachabilityCurrent;
+    if( hrn == null ) {
+      callerReachabilityCurrent = edge.getBeta();
+    } else {
+      callerReachabilityCurrent = hrn.getAlpha();
     }
 
-    ReachabilitySet r1 = new ReachabilitySet().makeCanonical();
-    ttsItr = r0.iterator();
-    while( ttsItr.hasNext() ) {
-      TokenTupleSet tts = ttsItr.next();
-      r1 = r1.union(rewriteDpass(numParameters,
-                                 paramIndex,
-                                 tts,
-                                 paramIndex2rewriteD,
-                                 paramIndex2paramToken,
-                                 paramIndex2paramTokenStar) );
-    }
+    ReachabilitySet callerReachabilityNew = new ReachabilitySet().makeCanonical();
 
-    hrn.setAlphaNew(hrn.getAlphaNew().union(r1) );
-  }
+    // for initializing structures in this method
+    TokenTupleSet ttsEmpty = new TokenTupleSet().makeCanonical();
 
+    // use this to construct a change set if required; the idea is to
+    // map every partially rewritten token tuple set to the set of
+    // caller-context token tuple sets that were used to generate it
+    Hashtable<TokenTupleSet, HashSet<TokenTupleSet> > rewritten2source =
+      new Hashtable<TokenTupleSet, HashSet<TokenTupleSet> >();
+    rewritten2source.put(ttsEmpty, new HashSet<TokenTupleSet>() );
 
-  private void rewriteCallerEdgeBeta(int numParameters,
-                                     Integer paramIndex,
-                                     ReferenceEdge edge,
-                                     Hashtable<Integer, ReachabilitySet> paramIndex2rewriteJorK,
-                                     Hashtable<Integer, ReachabilitySet> paramIndex2rewriteD,
-                                     Hashtable<Integer, TokenTuple> paramIndex2paramToken,
-                                     Hashtable<Integer, TokenTuple> paramIndex2paramTokenStar,
-                                     boolean makeChangeSet,
-                                     Hashtable<ReferenceEdge, ChangeTupleSet> edgePlannedChanges) {
 
-    ReachabilitySet rules = paramIndex2rewriteJorK.get(paramIndex);
-    assert rules != null;
+    Iterator<TokenTupleSet> rulesItr = rules.iterator();
+    while(rulesItr.hasNext()) {
+      TokenTupleSet rule = rulesItr.next();
 
-    TokenTuple tokenToRewrite = paramIndex2paramToken.get(paramIndex);
-    assert tokenToRewrite != null;
+      ReachabilitySet rewrittenRule = new ReachabilitySet(ttsEmpty).makeCanonical();
 
-    ChangeTupleSet cts0 = new ChangeTupleSet().makeCanonical();
+      Iterator<TokenTuple> ruleItr = rule.iterator();
+      while(ruleItr.hasNext()) {
+       TokenTuple ttCallee = ruleItr.next();
 
-    Iterator<TokenTupleSet> ttsItr = rules.iterator();
-    while( ttsItr.hasNext() ) {
-      TokenTupleSet tts = ttsItr.next();
+       // compute the possibilities for rewriting this callee token
+       ReachabilitySet ttCalleeRewrites = null;
+       boolean callerSourceUsed = false;
 
-      Hashtable<TokenTupleSet, TokenTupleSet> forChangeSet =
-        new Hashtable<TokenTupleSet, TokenTupleSet>();
+       if( ttCallee.equals(p_i) ) {
+         // replace the arity-one token of the current parameter with the reachability
+         // information from the caller edge
+         ttCalleeRewrites = callerReachabilityCurrent;
+         callerSourceUsed = true;
 
-      ReachabilitySet rTemp = tts.rewriteToken(tokenToRewrite,
-                                               edge.getBeta(),
-                                               true,
-                                               forChangeSet);
+       } else if( paramToken2paramIndex.containsKey(ttCallee) ) {
+         // use little d
+         Integer paramIndex_j = paramToken2paramIndex.get(ttCallee);
+         assert paramIndex_j != null;
+         ttCalleeRewrites = paramIndex2rewrite_d.get(paramIndex_j);
+         assert ttCalleeRewrites != null;
 
-      Iterator fcsItr = forChangeSet.entrySet().iterator();
-      while( fcsItr.hasNext() ) {
-       Map.Entry me = (Map.Entry)fcsItr.next();
-       TokenTupleSet ttsMatch = (TokenTupleSet) me.getKey();
-       TokenTupleSet ttsAdd   = (TokenTupleSet) me.getValue();
+       } else if( paramTokenPlus2paramIndex.containsKey(ttCallee) ) {
+         // worse, use big D
+         Integer paramIndex_j = paramTokenPlus2paramIndex.get(ttCallee);
+         assert paramIndex_j != null;
+         ttCalleeRewrites = paramIndex2rewriteD.get(paramIndex_j);
+         assert ttCalleeRewrites != null;
 
-       ChangeTuple ct = new ChangeTuple(ttsMatch,
-                                        ttsAdd
-                                        ).makeCanonical();
+       } else {
+         // otherwise there's no need for a rewrite, just pass this one on
+         TokenTupleSet ttsCaller = new TokenTupleSet(ttCallee).makeCanonical();
+         ttCalleeRewrites = new ReachabilitySet(ttsCaller).makeCanonical();
+       }
 
-       cts0 = cts0.union(ct);
-      }
-    }
+       // branch every version of the working rewritten rule with
+       // the possibilities for rewriting the current callee token
+       ReachabilitySet rewrittenRuleWithTTCallee = new ReachabilitySet().makeCanonical();
 
+       Iterator<TokenTupleSet> rewrittenRuleItr = rewrittenRule.iterator();
+       while( rewrittenRuleItr.hasNext() ) {
+         TokenTupleSet ttsRewritten = rewrittenRuleItr.next();
 
-    ReachabilitySet r1 = new ReachabilitySet().makeCanonical();
-    ChangeTupleSet cts1 = new ChangeTupleSet().makeCanonical();
+         Iterator<TokenTupleSet> ttCalleeRewritesItr = ttCalleeRewrites.iterator();
+         while( ttCalleeRewritesItr.hasNext() ) {
+           TokenTupleSet ttsBranch = ttCalleeRewritesItr.next();
 
-    Iterator<ChangeTuple> ctItr = cts0.iterator();
-    while( ctItr.hasNext() ) {
-      ChangeTuple ct = ctItr.next();
+           TokenTupleSet ttsRewrittenNext = ttsRewritten.unionUpArity(ttsBranch);
 
-      ReachabilitySet rTemp = rewriteDpass(numParameters,
-                                           paramIndex,
-                                           ct.getSetToAdd(),
-                                           paramIndex2rewriteD,
-                                           paramIndex2paramToken,
-                                           paramIndex2paramTokenStar
-                                           ).makeCanonical();
-      r1 = r1.union(rTemp);
+           if( makeChangeSet ) {
+             // in order to keep the list of source token tuple sets
+             // start with the sets used to make the partially rewritten
+             // rule up to this point
+             HashSet<TokenTupleSet> sourceSets = rewritten2source.get(ttsRewritten);
+             assert sourceSets != null;
 
-      if( makeChangeSet ) {
-       assert edgePlannedChanges != null;
+             // make a shallow copy for possible modification
+             sourceSets = (HashSet<TokenTupleSet>)sourceSets.clone();
 
-       Iterator<TokenTupleSet> ttsTempItr = rTemp.iterator();
-       while( ttsTempItr.hasNext() ) {
-         TokenTupleSet tts = ttsTempItr.next();
+             // if we used something from the caller to rewrite it, remember
+             if( callerSourceUsed ) {
+               sourceSets.add(ttsBranch);
+             }
 
-         ChangeTuple ctFinal = new ChangeTuple(ct.getSetToMatch(),
-                                               tts
-                                               ).makeCanonical();
+             // set mapping for the further rewritten rule
+             rewritten2source.put(ttsRewrittenNext, sourceSets);
+           }
 
-         cts1 = cts1.union(ctFinal);
+           rewrittenRuleWithTTCallee =
+             rewrittenRuleWithTTCallee.union(ttsRewrittenNext);
+         }
        }
+
+       // now the rewritten rule's possibilities have been extended by
+       // rewriting the current callee token, remember result
+       rewrittenRule = rewrittenRuleWithTTCallee;
       }
-    }
 
-    if( makeChangeSet ) {
-      edgePlannedChanges.put(edge, cts1);
+      // the rule has been entirely rewritten into the caller context
+      // now, so add it to the new reachability information
+      callerReachabilityNew =
+        callerReachabilityNew.union(rewrittenRule);
     }
 
-    edge.setBetaNew(edge.getBetaNew().union(r1) );
-  }
-
-
-  private ReachabilitySet rewriteDpass(int numParameters,
-                                       Integer paramIndex,
-                                       TokenTupleSet ttsIn,
-                                       Hashtable<Integer, ReachabilitySet> paramIndex2rewriteD,
-                                       Hashtable<Integer, TokenTuple> paramIndex2paramToken,
-                                       Hashtable<Integer, TokenTuple> paramIndex2paramTokenStar) {
-
-    ReachabilitySet rsOut = new ReachabilitySet().makeCanonical();
-
-    boolean rewritten = false;
-
-    for( int j = 0; j < numParameters; ++j ) {
-      Integer paramIndexJ = new Integer(j);
-      ReachabilitySet D_j = paramIndex2rewriteD.get(paramIndexJ);
-      assert D_j != null;
-
-      if( paramIndexJ != paramIndex ) {
-       TokenTuple tokenToRewriteJ = paramIndex2paramToken.get(paramIndexJ);
-       assert tokenToRewriteJ != null;
-       if( ttsIn.containsTuple(tokenToRewriteJ) ) {
-         ReachabilitySet r = ttsIn.rewriteToken(tokenToRewriteJ,
-                                                D_j,
-                                                false,
-                                                null);
-         Iterator<TokenTupleSet> ttsItr = r.iterator();
-         while( ttsItr.hasNext() ) {
-           TokenTupleSet tts = ttsItr.next();
-           rsOut = rsOut.union(rewriteDpass(numParameters,
-                                            paramIndex,
-                                            tts,
-                                            paramIndex2rewriteD,
-                                            paramIndex2paramToken,
-                                            paramIndex2paramTokenStar) );
-           rewritten = true;
-         }
+    if( makeChangeSet ) {
+      ChangeTupleSet callerChangeSet = new ChangeTupleSet().makeCanonical();
+
+      // each possibility for the final reachability should have a set of
+      // caller sources mapped to it, use to create the change set
+      Iterator<TokenTupleSet> callerReachabilityItr = callerReachabilityNew.iterator();
+      while( callerReachabilityItr.hasNext() ) {
+       TokenTupleSet ttsRewrittenFinal = callerReachabilityItr.next();
+       HashSet<TokenTupleSet> sourceSets = rewritten2source.get(ttsRewrittenFinal);
+       assert sourceSets != null;
+
+       Iterator<TokenTupleSet> sourceSetsItr = sourceSets.iterator();
+       while( sourceSetsItr.hasNext() ) {
+         TokenTupleSet ttsSource = sourceSetsItr.next();
+
+         callerChangeSet =
+           callerChangeSet.union(new ChangeTuple(ttsSource, ttsRewrittenFinal) );
        }
       }
 
-      TokenTuple tokenStarToRewriteJ = paramIndex2paramTokenStar.get(paramIndexJ);
-      assert tokenStarToRewriteJ != null;
-      if( ttsIn.containsTuple(tokenStarToRewriteJ) ) {
-       ReachabilitySet r = ttsIn.rewriteToken(tokenStarToRewriteJ,
-                                              D_j,
-                                              false,
-                                              null);
-       Iterator<TokenTupleSet> ttsItr = r.iterator();
-       while( ttsItr.hasNext() ) {
-         TokenTupleSet tts = ttsItr.next();
-         rsOut = rsOut.union(rewriteDpass(numParameters,
-                                          paramIndex,
-                                          tts,
-                                          paramIndex2rewriteD,
-                                          paramIndex2paramToken,
-                                          paramIndex2paramTokenStar) );
-         rewritten = true;
-       }
-      }
+      assert edgePlannedChanges != null;
+      edgePlannedChanges.put(edge, callerChangeSet);
     }
 
-    if( !rewritten ) {
-      rsOut = rsOut.union(ttsIn);
+    if( hrn == null ) {
+      edge.setBetaNew(edge.getBetaNew().union(callerReachabilityNew) );
+    } else {
+      hrn.setAlphaNew(hrn.getAlphaNew().union(callerReachabilityNew) );
     }
-
-    return rsOut;
   }
 
 
+
   private HashSet<HeapRegionNode>
   getHRNSetThatPossiblyMapToCalleeHRN(OwnershipGraph ogCallee,
                                       HeapRegionNode hrnCallee,
@@ -1719,9 +1974,9 @@ public class OwnershipGraph {
 
     HashSet<HeapRegionNode> possibleCallerHRNs = new HashSet<HeapRegionNode>();
 
-    Integer paramIndexCallee = ogCallee.id2paramIndex.get(hrnCallee.getID() );
+    Set<Integer> paramIndicesCallee = ogCallee.id2paramIndexSet.get( hrnCallee.getID() );
 
-    if( paramIndexCallee == null ) {
+    if( paramIndicesCallee == null ) {
       // this is a node allocated in the callee then and it has
       // exactly one shadow node in the caller to map to
       AllocationSite as = hrnCallee.getAllocationSite();
@@ -1751,8 +2006,12 @@ public class OwnershipGraph {
     } else {
       // this is a node that was created to represent a parameter
       // so it maps to a whole mess of heap regions
-      assert paramIndex2reachableCallerNodes.containsKey(paramIndexCallee);
-      possibleCallerHRNs = paramIndex2reachableCallerNodes.get(paramIndexCallee);
+      Iterator<Integer> itrIndex = paramIndicesCallee.iterator();
+      while( itrIndex.hasNext() ) {
+       Integer paramIndexCallee = itrIndex.next();
+       assert paramIndex2reachableCallerNodes.containsKey(paramIndexCallee);
+       possibleCallerHRNs.addAll( paramIndex2reachableCallerNodes.get(paramIndexCallee) );
+      }
     }
 
     return possibleCallerHRNs;
@@ -1760,6 +2019,207 @@ public class OwnershipGraph {
 
 
 
+  ////////////////////////////////////////////////////
+  //
+  //  This global sweep is an optional step to prune
+  //  reachability sets that are not internally
+  //  consistent with the global graph.  It should be
+  //  invoked after strong updates or method calls.
+  //
+  ////////////////////////////////////////////////////
+  protected void globalSweep() {
+
+    // a work set for performing the sweep
+    Hashtable<HeapRegionNode, HashSet<TokenTupleSet> > workSet = 
+      new Hashtable<HeapRegionNode, HashSet<TokenTupleSet> >();
+
+    // first initialize every alphaNew for a flagged region
+    // (or parameter region) to a set with just that token
+    Set hrns = id2hrn.entrySet();
+    Iterator itrHrns = hrns.iterator();
+    while( itrHrns.hasNext() ) {
+      Map.Entry me = (Map.Entry)itrHrns.next();
+      Integer token = (Integer) me.getKey();
+      HeapRegionNode hrn = (HeapRegionNode) me.getValue();
+
+      // assert that this node and incoming edges have clean alphaNew
+      // and betaNew sets, respectively
+      ReachabilitySet rsEmpty = new ReachabilitySet().makeCanonical();
+      assert rsEmpty.equals( hrn.getAlphaNew() );
+
+      Iterator<ReferenceEdge> itrRes = hrn.iteratorToReferencers();
+      while( itrRes.hasNext() ) {
+       ReferenceEdge edge = itrRes.next();
+       assert rsEmpty.equals( edge.getBetaNew() );
+      }      
+      
+      TokenTuple tt     = new TokenTuple( token, !hrn.isSingleObject(), TokenTuple.ARITY_ONE        ).makeCanonical();
+      TokenTuple ttPlus = new TokenTuple( token, !hrn.isSingleObject(), TokenTuple.ARITY_ONEORMORE  ).makeCanonical();
+      TokenTuple ttStar = new TokenTuple( token, !hrn.isSingleObject(), TokenTuple.ARITY_ZEROORMORE ).makeCanonical();
+
+      TokenTupleSet tts      = new TokenTupleSet( tt     ).makeCanonical();
+      TokenTupleSet ttsPlus  = new TokenTupleSet( ttPlus ).makeCanonical();
+      TokenTupleSet ttsStar  = new TokenTupleSet( ttStar ).makeCanonical();
+      TokenTupleSet ttsEmpty = new TokenTupleSet(        ).makeCanonical();
+
+      if( hrn.isFlagged() || hrn.isParameter() ) {
+       HashSet<TokenTupleSet> subWorkSet = new HashSet<TokenTupleSet>();
+       subWorkSet.add( tts     );
+       subWorkSet.add( ttsPlus );
+       subWorkSet.add( ttsStar );
+       workSet.put( hrn, subWorkSet );
+       
+       hrn.setAlphaNew( new ReachabilitySet( tts ).makeCanonical() );
+      } else {
+       hrn.setAlphaNew( new ReachabilitySet( ttsEmpty ).makeCanonical() );
+      }
+    }
+
+    // then propagate tokens forward one step at a time
+    while( !workSet.isEmpty() ) {
+      HeapRegionNode hrn = workSet.keySet().iterator().next();
+
+      HashSet<TokenTupleSet> subWorkSet = workSet.get( hrn );
+      assert subWorkSet != null;
+      
+      if( subWorkSet.isEmpty() ) {
+       // we're currently done with sub work at this heap region, although
+       // more work may get queued up later, but remove it for now and continue
+       workSet.remove( hrn );
+       continue;
+      }
+      
+      TokenTupleSet tts = subWorkSet.iterator().next();
+      subWorkSet.remove( tts );
+
+      // try to push this TokenTupleSet over all outgoing edges
+      Iterator<ReferenceEdge> itrRes = hrn.iteratorToReferencees();
+      while( itrRes.hasNext() ) {
+       ReferenceEdge edge = itrRes.next();
+
+       if( edge.getBeta().containsSuperSet( tts ) ) {
+         HeapRegionNode dst = edge.getDst();
+
+         // make a set of possible contributions this token
+         // might have on the alpha set here
+         HashSet<TokenTupleSet> ttsNewSet = new HashSet<TokenTupleSet>();
+
+         Iterator<TokenTupleSet> itrDstAlphaNew = dst.getAlphaNew().iterator();
+         while( itrDstAlphaNew.hasNext() ) {
+           TokenTupleSet ttsDstAlphaNew = itrDstAlphaNew.next();
+           ttsNewSet.add( tts.unionUpArity( ttsDstAlphaNew ) );
+         }
+
+         // only add this to the dst alpha new if it is in the beta of
+         // the edge we crossed to get here, and then only continue the
+         // propagation if it isn't already in the dst alpha new
+         Iterator<TokenTupleSet> itrNewSet = ttsNewSet.iterator();
+         while( itrNewSet.hasNext() ) {
+           TokenTupleSet ttsNew = itrNewSet.next();
+
+           if( edge.getBeta().containsSuperSet( ttsNew ) &&
+               !dst.getAlphaNew().contains( ttsNew ) ) {
+             
+             // okay, this is a valid propagation, and add to the
+             // work set to further propagate it
+             dst.setAlphaNew( dst.getAlphaNew().union( ttsNew ) );
+                     
+             HashSet<TokenTupleSet> subWorkSetDst = workSet.get( dst );
+             if( subWorkSetDst == null ) {
+               subWorkSetDst = new HashSet<TokenTupleSet>();         
+             }
+
+             subWorkSetDst.add( ttsNew );
+             workSet.put( dst, subWorkSetDst );
+           }
+         }
+       }
+      }
+    }
+
+    // now prepare work sets to propagate token sets backwards
+    // from heap regions across all edges
+    assert workSet.isEmpty();
+    hrns = id2hrn.entrySet();
+    itrHrns = hrns.iterator();
+    while( itrHrns.hasNext() ) {
+      Map.Entry me = (Map.Entry)itrHrns.next();
+      HeapRegionNode hrn = (HeapRegionNode) me.getValue();
+
+      HashSet<TokenTupleSet> subWorkSet = new HashSet<TokenTupleSet>();
+
+      Iterator<TokenTupleSet> itrAlphaNewSets = hrn.getAlphaNew().iterator();
+      while( itrAlphaNewSets.hasNext() ) {
+       TokenTupleSet tts = itrAlphaNewSets.next();
+       subWorkSet.add( tts );
+      }
+
+      workSet.put( hrn, subWorkSet );
+    }
+
+    // propagate token sets backwards across edges one step at a time
+    while( !workSet.isEmpty() ) {
+      HeapRegionNode hrn = workSet.keySet().iterator().next();
+
+      HashSet<TokenTupleSet> subWorkSet = workSet.get( hrn );
+      assert subWorkSet != null;
+      
+      if( subWorkSet.isEmpty() ) {
+       // we're currently done with sub work at this heap region, although
+       // more work may get queued up later, but remove it for now and continue
+       workSet.remove( hrn );
+       continue;
+      }
+      
+      TokenTupleSet tts = subWorkSet.iterator().next();
+      subWorkSet.remove( tts );
+
+      // try to push this TokenTupleSet back up incoming edges
+      Iterator<ReferenceEdge> itrRes = hrn.iteratorToReferencers();
+      while( itrRes.hasNext() ) {
+       ReferenceEdge edge = itrRes.next();
+       if( edge.getBeta().containsWithZeroes( tts ) && 
+           !edge.getBetaNew().contains( tts ) ) {
+         // okay, this is a valid propagation, and add to the
+         // work set to further propagate it
+         edge.setBetaNew( edge.getBetaNew().union( tts ) );
+                     
+         OwnershipNode src = edge.getSrc();
+         if( src instanceof HeapRegionNode ) {
+
+           HashSet<TokenTupleSet> subWorkSetSrc = workSet.get( (HeapRegionNode) src );
+           if( subWorkSetSrc == null ) {
+             subWorkSetSrc = new HashSet<TokenTupleSet>();           
+           }
+           
+           subWorkSetSrc.add( tts );
+           workSet.put( (HeapRegionNode) src, subWorkSetSrc );
+         }       
+       }         
+      }
+    }    
+
+    // apply alphaNew and betaNew to all nodes and edges
+    HashSet<ReferenceEdge> res = new HashSet<ReferenceEdge>();
+
+    Iterator<HeapRegionNode> nodeItr = id2hrn.values().iterator();
+    while( nodeItr.hasNext() ) {
+      HeapRegionNode hrn = nodeItr.next();
+      hrn.applyAlphaNew();
+      Iterator<ReferenceEdge> itrRes = hrn.iteratorToReferencers();
+      while( itrRes.hasNext() ) {
+       res.add( itrRes.next() );
+      }
+    }
+
+    Iterator<ReferenceEdge> edgeItr = res.iterator();
+    while( edgeItr.hasNext() ) {
+      edgeItr.next().applyBetaNew();
+    }
+  }  
+
+
+
   ////////////////////////////////////////////////////
   // in merge() and equals() methods the suffix A
   // represents the passed in graph and the suffix
@@ -1952,18 +2412,18 @@ public class OwnershipGraph {
   // same number of parameters, or if one or both parameter
   // index tables are empty
   protected void mergeId2paramIndex(OwnershipGraph og) {
-    if( id2paramIndex.size() == 0 ) {
-      id2paramIndex  = og.id2paramIndex;
-      paramIndex2id  = og.paramIndex2id;
-      paramIndex2tdQ = og.paramIndex2tdQ;
+    if( id2paramIndexSet.size() == 0 ) {
+      id2paramIndexSet = og.id2paramIndexSet;
+      paramIndex2id    = og.paramIndex2id;
+      paramIndex2tdQ   = og.paramIndex2tdQ;
       return;
     }
 
-    if( og.id2paramIndex.size() == 0 ) {
+    if( og.id2paramIndexSet.size() == 0 ) {
       return;
     }
 
-    assert id2paramIndex.size() == og.id2paramIndex.size();
+    assert id2paramIndexSet.size() == og.id2paramIndexSet.size();
   }
 
   protected void mergeAllocationSites(OwnershipGraph og) {
@@ -2198,11 +2658,10 @@ public class OwnershipGraph {
 
 
   protected boolean areId2paramIndexEqual(OwnershipGraph og) {
-    return id2paramIndex.size() == og.id2paramIndex.size();
+    return id2paramIndexSet.size() == og.id2paramIndexSet.size();
   }
 
-
-  public boolean hasPotentialAlias( Integer paramIndex1, Integer paramIndex2 ) {
+  public boolean hasPotentialAlias(Integer paramIndex1, Integer paramIndex2) {
 
     // get parameter's heap region
     assert paramIndex2id.containsKey(paramIndex1);
@@ -2214,12 +2673,16 @@ public class OwnershipGraph {
 
     // get tokens for this parameter
     TokenTuple p1 = new TokenTuple(hrnParam1.getID(),
-                                  true,
-                                  TokenTuple.ARITY_ONE).makeCanonical();
+                                   true,
+                                   TokenTuple.ARITY_ONE).makeCanonical();
+
+    TokenTuple pPlus1 = new TokenTuple(hrnParam1.getID(),
+                                       true,
+                                       TokenTuple.ARITY_ONEORMORE).makeCanonical();
 
     TokenTuple pStar1 = new TokenTuple(hrnParam1.getID(),
-                                      true,
-                                      TokenTuple.ARITY_MANY).makeCanonical();    
+                                       true,
+                                       TokenTuple.ARITY_ZEROORMORE).makeCanonical();
 
 
     // get tokens for the other parameter
@@ -2231,17 +2694,21 @@ public class OwnershipGraph {
     assert hrnParam2 != null;
 
     TokenTuple p2 = new TokenTuple(hrnParam2.getID(),
-                                  true,
-                                  TokenTuple.ARITY_ONE).makeCanonical();
+                                   true,
+                                   TokenTuple.ARITY_ONE).makeCanonical();
+
+    TokenTuple pPlus2 = new TokenTuple(hrnParam2.getID(),
+                                       true,
+                                       TokenTuple.ARITY_ONEORMORE).makeCanonical();
 
     TokenTuple pStar2 = new TokenTuple(hrnParam2.getID(),
-                                      true,
-                                      TokenTuple.ARITY_MANY).makeCanonical();    
+                                       true,
+                                       TokenTuple.ARITY_ZEROORMORE).makeCanonical();
 
 
     // get special label p_q for first parameter
     TempDescriptor tdParamQ1 = paramIndex2tdQ.get(paramIndex1);
-    assert tdParamQ1 != null;    
+    assert tdParamQ1 != null;
     LabelNode lnParamQ1 = td2ln.get(tdParamQ1);
     assert lnParamQ1 != null;
 
@@ -2254,16 +2721,39 @@ public class OwnershipGraph {
     ReachabilitySet beta1 = edgeSpecialQ1.getBeta();
     assert beta1 != null;
 
-    if( beta1.containsTupleSetWithBoth( p1,     p2     ) ) { return true; }
-    if( beta1.containsTupleSetWithBoth( pStar1, p2     ) ) { return true; }
-    if( beta1.containsTupleSetWithBoth( p1,     pStar2 ) ) { return true; }
-    if( beta1.containsTupleSetWithBoth( pStar1, pStar2 ) ) { return true; }
-    
+    if( beta1.containsTupleSetWithBoth(p1,     p2) ) {
+      return true;
+    }
+    if( beta1.containsTupleSetWithBoth(pPlus1, p2) ) {
+      return true;
+    }
+    if( beta1.containsTupleSetWithBoth(pStar1, p2) ) {
+      return true;
+    }
+    if( beta1.containsTupleSetWithBoth(p1,     pPlus2) ) {
+      return true;
+    }
+    if( beta1.containsTupleSetWithBoth(pPlus1, pPlus2) ) {
+      return true;
+    }
+    if( beta1.containsTupleSetWithBoth(pStar1, pPlus2) ) {
+      return true;
+    }
+    if( beta1.containsTupleSetWithBoth(p1,     pStar2) ) {
+      return true;
+    }
+    if( beta1.containsTupleSetWithBoth(pPlus1, pStar2) ) {
+      return true;
+    }
+    if( beta1.containsTupleSetWithBoth(pStar1, pStar2) ) {
+      return true;
+    }
+
     return false;
   }
 
 
-  public boolean hasPotentialAlias( Integer paramIndex, AllocationSite as ) {
+  public boolean hasPotentialAlias(Integer paramIndex, AllocationSite as) {
 
     // get parameter's heap region
     assert paramIndex2id.containsKey(paramIndex);
@@ -2275,16 +2765,20 @@ public class OwnershipGraph {
 
     // get tokens for this parameter
     TokenTuple p = new TokenTuple(hrnParam.getID(),
-                                 true,
-                                 TokenTuple.ARITY_ONE).makeCanonical();
+                                  true,
+                                  TokenTuple.ARITY_ONE).makeCanonical();
+
+    TokenTuple pPlus = new TokenTuple(hrnParam.getID(),
+                                      true,
+                                      TokenTuple.ARITY_ONEORMORE).makeCanonical();
 
     TokenTuple pStar = new TokenTuple(hrnParam.getID(),
-                                     true,
-                                     TokenTuple.ARITY_MANY).makeCanonical();    
+                                      true,
+                                      TokenTuple.ARITY_ZEROORMORE).makeCanonical();
 
     // get special label p_q
     TempDescriptor tdParamQ = paramIndex2tdQ.get(paramIndex);
-    assert tdParamQ != null;    
+    assert tdParamQ != null;
     LabelNode lnParamQ = td2ln.get(tdParamQ);
     assert lnParamQ != null;
 
@@ -2299,49 +2793,101 @@ public class OwnershipGraph {
 
     // get tokens for summary node
     TokenTuple gs = new TokenTuple(as.getSummary(),
-                                 true,
-                                 TokenTuple.ARITY_ONE).makeCanonical();
+                                   true,
+                                   TokenTuple.ARITY_ONE).makeCanonical();
+
+    TokenTuple gsPlus = new TokenTuple(as.getSummary(),
+                                       true,
+                                       TokenTuple.ARITY_ONEORMORE).makeCanonical();
 
     TokenTuple gsStar = new TokenTuple(as.getSummary(),
-                                      true,
-                                      TokenTuple.ARITY_MANY).makeCanonical();    
+                                       true,
+                                       TokenTuple.ARITY_ZEROORMORE).makeCanonical();
 
-    if( beta.containsTupleSetWithBoth( p,     gs     ) ) { return true; }
-    if( beta.containsTupleSetWithBoth( pStar, gs     ) ) { return true; }
-    if( beta.containsTupleSetWithBoth( p,     gsStar ) ) { return true; }
-    if( beta.containsTupleSetWithBoth( pStar, gsStar ) ) { return true; }
+
+    if( beta.containsTupleSetWithBoth(p,     gs) ) {
+      return true;
+    }
+    if( beta.containsTupleSetWithBoth(pPlus, gs) ) {
+      return true;
+    }
+    if( beta.containsTupleSetWithBoth(pStar, gs) ) {
+      return true;
+    }
+    if( beta.containsTupleSetWithBoth(p,     gsPlus) ) {
+      return true;
+    }
+    if( beta.containsTupleSetWithBoth(pPlus, gsPlus) ) {
+      return true;
+    }
+    if( beta.containsTupleSetWithBoth(pStar, gsPlus) ) {
+      return true;
+    }
+    if( beta.containsTupleSetWithBoth(p,     gsStar) ) {
+      return true;
+    }
+    if( beta.containsTupleSetWithBoth(pPlus, gsStar) ) {
+      return true;
+    }
+    if( beta.containsTupleSetWithBoth(pStar, gsStar) ) {
+      return true;
+    }
 
     // check for other nodes
     for( int i = 0; i < as.getAllocationDepth(); ++i ) {
 
-      // the other nodes of an allocation site are single, no stars
+      // the other nodes of an allocation site are single, no plus
       TokenTuple gi = new TokenTuple(as.getIthOldest(i),
-                                    false,
-                                    TokenTuple.ARITY_ONE).makeCanonical();
+                                     false,
+                                     TokenTuple.ARITY_ONE).makeCanonical();
+
+      TokenTuple giStar = new TokenTuple(as.getIthOldest(i),
+                                         false,
+                                         TokenTuple.ARITY_ZEROORMORE).makeCanonical();
+
+      if( beta.containsTupleSetWithBoth(p,     gi) ) {
+       return true;
+      }
+      if( beta.containsTupleSetWithBoth(pPlus, gi) ) {
+       return true;
+      }
+      if( beta.containsTupleSetWithBoth(pStar, gi) ) {
+       return true;
+      }
+      if( beta.containsTupleSetWithBoth(p,     giStar) ) {
+       return true;
+      }
+      if( beta.containsTupleSetWithBoth(pPlus, giStar) ) {
+       return true;
+      }
+      if( beta.containsTupleSetWithBoth(pStar, giStar) ) {
+       return true;
+      }
+    }
 
-      if( beta.containsTupleSetWithBoth( p,     gi     ) ) { return true; }
-      if( beta.containsTupleSetWithBoth( pStar, gi     ) ) { return true; }
-    }    
-    
     return false;
   }
 
 
-  public boolean hasPotentialAlias( AllocationSite as1, AllocationSite as2 ) {
+  public boolean hasPotentialAlias(AllocationSite as1, AllocationSite as2) {
 
     // get tokens for summary nodes
     TokenTuple gs1 = new TokenTuple(as1.getSummary(),
-                                   true,
-                                   TokenTuple.ARITY_ONE).makeCanonical();
-    
+                                    true,
+                                    TokenTuple.ARITY_ONE).makeCanonical();
+
+    TokenTuple gsPlus1 = new TokenTuple(as1.getSummary(),
+                                        true,
+                                        TokenTuple.ARITY_ONEORMORE).makeCanonical();
+
     TokenTuple gsStar1 = new TokenTuple(as1.getSummary(),
-                                       true,
-                                       TokenTuple.ARITY_MANY).makeCanonical();
-    
+                                        true,
+                                        TokenTuple.ARITY_ZEROORMORE).makeCanonical();
+
     // get summary node's alpha
     Integer idSum1 = as1.getSummary();
-    assert id2hrn.containsKey( idSum1 );
-    HeapRegionNode hrnSum1 = id2hrn.get( idSum1 );
+    assert id2hrn.containsKey(idSum1);
+    HeapRegionNode hrnSum1 = id2hrn.get(idSum1);
     assert hrnSum1 != null;
     ReachabilitySet alphaSum1 = hrnSum1.getAlpha();
     assert alphaSum1 != null;
@@ -2349,121 +2895,209 @@ public class OwnershipGraph {
 
     // and for the other one
     TokenTuple gs2 = new TokenTuple(as2.getSummary(),
-                                   true,
-                                   TokenTuple.ARITY_ONE).makeCanonical();
-    
+                                    true,
+                                    TokenTuple.ARITY_ONE).makeCanonical();
+
+    TokenTuple gsPlus2 = new TokenTuple(as2.getSummary(),
+                                        true,
+                                        TokenTuple.ARITY_ONEORMORE).makeCanonical();
+
     TokenTuple gsStar2 = new TokenTuple(as2.getSummary(),
-                                       true,
-                                       TokenTuple.ARITY_MANY).makeCanonical();
-    
+                                        true,
+                                        TokenTuple.ARITY_ZEROORMORE).makeCanonical();
+
     // get summary node's alpha
     Integer idSum2 = as2.getSummary();
-    assert id2hrn.containsKey( idSum2 );
-    HeapRegionNode hrnSum2 = id2hrn.get( idSum2 );
+    assert id2hrn.containsKey(idSum2);
+    HeapRegionNode hrnSum2 = id2hrn.get(idSum2);
     assert hrnSum2 != null;
     ReachabilitySet alphaSum2 = hrnSum2.getAlpha();
     assert alphaSum2 != null;
 
     // does either one report reachability from the other tokens?
-    if( alphaSum1.containsTuple( gsStar2 ) ) { return true; }
-    if( alphaSum2.containsTuple( gsStar1 ) ) { return true; }
+    if( alphaSum1.containsTuple(gsPlus2) ) {
+      return true;
+    }
+    if( alphaSum1.containsTuple(gsStar2) ) {
+      return true;
+    }
+    if( alphaSum2.containsTuple(gsPlus1) ) {
+      return true;
+    }
+    if( alphaSum2.containsTuple(gsStar1) ) {
+      return true;
+    }
 
-    // only check non-star token if they are different sites
+    // only check ONE token if they are different sites
     if( as1 != as2 ) {
-      if( alphaSum1.containsTuple( gs2 ) ) { return true; }
-      if( alphaSum2.containsTuple( gs1 ) ) { return true; }
+      if( alphaSum1.containsTuple(gs2) ) {
+       return true;
+      }
+      if( alphaSum2.containsTuple(gs1) ) {
+       return true;
+      }
     }
 
 
     // check sum2 against alloc1 nodes
     for( int i = 0; i < as1.getAllocationDepth(); ++i ) {
       Integer idI1 = as1.getIthOldest(i);
-      assert id2hrn.containsKey( idI1 );
-      HeapRegionNode hrnI1 = id2hrn.get( idI1 );
+      assert id2hrn.containsKey(idI1);
+      HeapRegionNode hrnI1 = id2hrn.get(idI1);
       assert hrnI1 != null;
       ReachabilitySet alphaI1 = hrnI1.getAlpha();
       assert alphaI1 != null;
 
       // the other nodes of an allocation site are single, no stars
       TokenTuple gi1 = new TokenTuple(as1.getIthOldest(i),
-                                     false,
-                                     TokenTuple.ARITY_ONE).makeCanonical();
+                                      false,
+                                      TokenTuple.ARITY_ONE).makeCanonical();
 
-      if( alphaSum2.containsTuple( gi1     ) ) { return true; }
-      if( alphaI1.containsTuple  ( gs2     ) ) { return true; }
-      if( alphaI1.containsTuple  ( gsStar2 ) ) { return true; }
-    }    
+      TokenTuple giStar1 = new TokenTuple(as1.getIthOldest(i),
+                                          false,
+                                          TokenTuple.ARITY_ZEROORMORE).makeCanonical();
+
+      if( alphaSum2.containsTuple(gi1) ) {
+       return true;
+      }
+      if( alphaSum2.containsTuple(giStar1) ) {
+       return true;
+      }
+      if(   alphaI1.containsTuple(gs2) ) {
+       return true;
+      }
+      if(   alphaI1.containsTuple(gsPlus2) ) {
+       return true;
+      }
+      if(   alphaI1.containsTuple(gsStar2) ) {
+       return true;
+      }
+    }
 
     // check sum1 against alloc2 nodes
     for( int i = 0; i < as2.getAllocationDepth(); ++i ) {
       Integer idI2 = as2.getIthOldest(i);
-      assert id2hrn.containsKey( idI2 );
-      HeapRegionNode hrnI2 = id2hrn.get( idI2 );
+      assert id2hrn.containsKey(idI2);
+      HeapRegionNode hrnI2 = id2hrn.get(idI2);
       assert hrnI2 != null;
       ReachabilitySet alphaI2 = hrnI2.getAlpha();
       assert alphaI2 != null;
 
       TokenTuple gi2 = new TokenTuple(as2.getIthOldest(i),
-                                     false,
-                                     TokenTuple.ARITY_ONE).makeCanonical();
+                                      false,
+                                      TokenTuple.ARITY_ONE).makeCanonical();
 
-      if( alphaSum1.containsTuple( gi2     ) ) { return true; }
-      if( alphaI2.containsTuple  ( gs1     ) ) { return true; }
-      if( alphaI2.containsTuple  ( gsStar1 ) ) { return true; }
+      TokenTuple giStar2 = new TokenTuple(as2.getIthOldest(i),
+                                          false,
+                                          TokenTuple.ARITY_ZEROORMORE).makeCanonical();
+
+      if( alphaSum1.containsTuple(gi2) ) {
+       return true;
+      }
+      if( alphaSum1.containsTuple(giStar2) ) {
+       return true;
+      }
+      if(   alphaI2.containsTuple(gs1) ) {
+       return true;
+      }
+      if(   alphaI2.containsTuple(gsPlus1) ) {
+       return true;
+      }
+      if(   alphaI2.containsTuple(gsStar1) ) {
+       return true;
+      }
 
       // while we're at it, do an inner loop for alloc2 vs alloc1 nodes
-      for( int j = 0; j < as1.getAllocationDepth(); ++j ) {    
+      for( int j = 0; j < as1.getAllocationDepth(); ++j ) {
        Integer idI1 = as1.getIthOldest(j);
-       
-       // if these are the same site, don't look for the same token, no alias
+
+       // if these are the same site, don't look for the same token, no alias.
        // different tokens of the same site could alias together though
-       if( idI1 == idI2 ) { continue; }
+       if( idI1 == idI2 ) {
+         continue;
+       }
 
-       HeapRegionNode hrnI1 = id2hrn.get( idI1 );
+       HeapRegionNode hrnI1 = id2hrn.get(idI1);
        ReachabilitySet alphaI1 = hrnI1.getAlpha();
        TokenTuple gi1 = new TokenTuple(as1.getIthOldest(j),
-                                       false,
-                                       TokenTuple.ARITY_ONE).makeCanonical();  
-       if( alphaI2.containsTuple( gi1 ) ) { return true; }
-       if( alphaI1.containsTuple( gi2 ) ) { return true; }
-      }    
+                                       false,
+                                       TokenTuple.ARITY_ONE).makeCanonical();
+
+       TokenTuple giStar1 = new TokenTuple(as1.getIthOldest(j),
+                                           false,
+                                           TokenTuple.ARITY_ZEROORMORE).makeCanonical();
+
+       if( alphaI2.containsTuple(gi1) ) {
+         return true;
+       }
+       if( alphaI2.containsTuple(giStar1) ) {
+         return true;
+       }
+       if( alphaI1.containsTuple(gi2) ) {
+         return true;
+       }
+       if( alphaI1.containsTuple(giStar2) ) {
+         return true;
+       }
+      }
     }
-    
+
     return false;
   }
 
 
   // for writing ownership graphs to dot files
-  public void writeGraph(Descriptor methodDesc,
+  public void writeGraph(MethodContext mc,
                          FlatNode fn,
                          boolean writeLabels,
                          boolean labelSelect,
                          boolean pruneGarbage,
-                         boolean writeReferencers
+                         boolean writeReferencers,
+                         boolean writeParamMappings
                          ) throws java.io.IOException {
     writeGraph(
-      methodDesc.getSymbol() +
-      methodDesc.getNum() +
+      mc.toString() +
       fn.toString(),
       writeLabels,
       labelSelect,
       pruneGarbage,
-      writeReferencers
+      writeReferencers,
+      writeParamMappings
       );
   }
 
-  public void writeGraph(Descriptor methodDesc,
+  public void writeGraph(MethodContext mc,
+                         boolean writeLabels,
+                         boolean labelSelect,
+                         boolean pruneGarbage,
+                         boolean writeReferencers,
+                         boolean writeParamMappings
+                         ) throws java.io.IOException {
+
+    writeGraph(mc+"COMPLETE",
+               writeLabels,
+               labelSelect,
+               pruneGarbage,
+               writeReferencers,
+               writeParamMappings
+               );
+  }
+
+  public void writeGraph(MethodContext mc,
+                         Integer numUpdate,
                          boolean writeLabels,
                          boolean labelSelect,
                          boolean pruneGarbage,
-                         boolean writeReferencers
+                         boolean writeReferencers,
+                         boolean writeParamMappings
                          ) throws java.io.IOException {
 
-    writeGraph(methodDesc+"COMPLETE",
+    writeGraph(mc+"COMPLETE"+String.format("%05d", numUpdate),
                writeLabels,
                labelSelect,
                pruneGarbage,
-               writeReferencers
+               writeReferencers,
+               writeParamMappings
                );
   }
 
@@ -2471,7 +3105,8 @@ public class OwnershipGraph {
                          boolean writeLabels,
                          boolean labelSelect,
                          boolean pruneGarbage,
-                         boolean writeReferencers
+                         boolean writeReferencers,
+                         boolean writeParamMappings
                          ) throws java.io.IOException {
 
     // remove all non-word characters from the graph name so
@@ -2480,17 +3115,20 @@ public class OwnershipGraph {
 
     BufferedWriter bw = new BufferedWriter(new FileWriter(graphName+".dot") );
     bw.write("digraph "+graphName+" {\n");
-    //bw.write( "  size=\"7.5,10\";\n" );
 
     HashSet<HeapRegionNode> visited = new HashSet<HeapRegionNode>();
 
     // then visit every heap region node
-    if( !pruneGarbage ) {
-      Set s = id2hrn.entrySet();
-      Iterator i = s.iterator();
-      while( i.hasNext() ) {
-       Map.Entry me  = (Map.Entry)i.next();
-       HeapRegionNode hrn = (HeapRegionNode) me.getValue();
+    Set s = id2hrn.entrySet();
+    Iterator i = s.iterator();
+    while( i.hasNext() ) {
+      Map.Entry me  = (Map.Entry)i.next();
+      HeapRegionNode hrn = (HeapRegionNode) me.getValue();
+      if( !pruneGarbage ||
+          hrn.isFlagged() ||
+          hrn.getDescription().startsWith("param")
+          ) {
+
        if( !visited.contains(hrn) ) {
          traverseHeapRegionNodes(VISIT_HRN_WRITE_FULL,
                                  hrn,
@@ -2504,11 +3142,21 @@ public class OwnershipGraph {
 
     bw.write("  graphTitle[label=\""+graphName+"\",shape=box];\n");
 
+    if( writeParamMappings ) {
+      Set df = paramIndex2id.entrySet();
+      Iterator ih = df.iterator();
+      while( ih.hasNext() ) {
+       Map.Entry meh = (Map.Entry)ih.next();
+       Integer pi = (Integer) meh.getKey();
+       Integer id = (Integer) meh.getValue();
+       bw.write("  pindex"+pi+"[label=\""+pi+" to "+id+"\",shape=box];\n");
+      }
+    }
 
     // then visit every label node, useful for debugging
     if( writeLabels ) {
-      Set s = td2ln.entrySet();
-      Iterator i = s.iterator();
+      s = td2ln.entrySet();
+      i = s.iterator();
       while( i.hasNext() ) {
        Map.Entry me = (Map.Entry)i.next();
        LabelNode ln = (LabelNode) me.getValue();
@@ -2523,7 +3171,7 @@ public class OwnershipGraph {
          }
        }
 
-       bw.write(ln.toString() + ";\n");
+       //bw.write("  "+ln.toString() + ";\n");
 
        Iterator<ReferenceEdge> heapRegionsItr = ln.iteratorToReferencees();
        while( heapRegionsItr.hasNext() ) {