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WALA/com.ibm.wala.core/src/com/ibm/wala/dataflow/IFDS/LocalPathEdges.java

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/*******************************************************************************
* Copyright (c) 2002 - 2006 IBM Corporation.
* All rights reserved. This program and the accompanying materials
* are made available under the terms of the Eclipse Public License v1.0
* which accompanies this distribution, and is available at
* http://www.eclipse.org/legal/epl-v10.html
*
* Contributors:
* IBM Corporation - initial API and implementation
*******************************************************************************/
package com.ibm.wala.dataflow.IFDS;
import java.util.Iterator;
import com.ibm.wala.util.collections.SparseVector;
import com.ibm.wala.util.intset.BasicNaturalRelation;
import com.ibm.wala.util.intset.BitVectorIntSet;
import com.ibm.wala.util.intset.IBinaryNaturalRelation;
import com.ibm.wala.util.intset.IntIterator;
import com.ibm.wala.util.intset.IntPair;
import com.ibm.wala.util.intset.IntSet;
import com.ibm.wala.util.intset.MutableSparseIntSet;
import com.ibm.wala.util.intset.SparseIntSet;
/**
* A set of path edges for a particular procedure entry s_p.
*/
public class LocalPathEdges {
/**
* Do paranoid error checking? (slow)
*/
private final static boolean PARANOID = false;
/**
* A map from integer (d2) -> (IBinaryNonNegativeIntRelation)
*
* For fact d2, paths[d2] gives a relation R=(n,d1) s.t. (<s_p, d1> -> <n,d2>) is a path edge.
*
* Note that we handle paths of the form <s_p, d1> -> <n,d1> specially, below. We also handle paths of the form <s_p, 0> -> <n,
* d1> specially below.
*
* We choose this somewhat convoluted representation for the following reasons: 1) of the (n, d1, d2) tuple-space, we expect the
* set of n to be dense for a given (d1,d2) pair. However the pairs should be sparse. So, we set up so n is the first dimension of
* the int-relations, which are designed to be dense in the first dimension 2) we need to support getInverse(), so we design
* lookup to get the d1's for an (n,d2) pair.
*
* Note that this representation is not good for merges. See below.
*
* TODO: more representation optimization. A special representation for triples? sparse representations for CFG? exploit shorts
* for ints?
*/
private final SparseVector<IBinaryNaturalRelation> paths = new SparseVector<>(1, 1.1f);
/**
* If this is non-null, it holds a redundant representation of the paths information, designed to make getReachable(II) faster.
* This is designed for algorithms that want to use frequent merges. While it's a shame to waste space, I don't want to compromise
* space or time of the non-merging IFDS solver, for which the original paths representation works well. Is there a better data
* structure tradeoff?
*
* A map from integer (d1) -&gt; (IBinaryNonNegativeIntRelation)
*
* For fact d1, paths[d1] gives a relation R=(n,d2) s.t. (&lt;s_p, d1&gt; -&gt; &lt;n,d2&gt;) is a path edge.
*
*
* We choose this somewhat convoluted representation for the following reasons: 1) of the (n, d1, d2) tuple-space, we expect the
* set of n to be dense for a given (d1,d2) pair. However the pairs should be sparse. So, we set up so n is the first dimension of
* the int-relations, which are designed to be dense in the first dimension 2) we need to support getReachable(), so we design
* lookup to get the d2's for an (n,d1) pair.
*/
private final SparseVector<IBinaryNaturalRelation> altPaths;
/**
* a map from integer d1 -&gt; int set.
*
* for fact d1, identityPaths[d1] gives the set of block numbers N s.t. for n \in N, &lt;s_p, d1&gt; -&gt; &lt;n, d1&gt; is a path edge.
*/
private final SparseVector<IntSet> identityPaths = new SparseVector<>(1, 1.1f);
/**
* a map from integer d2 -&gt; int set
*
* for fact d2, zeroPaths[d2] gives the set of block numbers N s.t. for n \in N, &lt;s_p, 0&gt; -&gt; &lt;n, d2&gt; is a path edge.
*/
private final SparseVector<IntSet> zeroPaths = new SparseVector<>(1, 1.1f);
/**
* @param fastMerge if true, the representation uses extra space in order to support faster merge operations
*/
public LocalPathEdges(boolean fastMerge) {
altPaths = fastMerge ? new SparseVector<>(1, 1.1f) : null;
}
/**
* Record that in this procedure we've discovered a same-level realizable path from (s_p,d_i) to (n,d_j)
*
* @param i
* @param n local block number of the basic block n
*
* @param j
*/
@SuppressWarnings("unused")
public void addPathEdge(int i, int n, int j) {
if (i == 0) {
addZeroPathEdge(n, j);
} else {
if (i == j) {
addIdentityPathEdge(i, n);
} else {
IBinaryNaturalRelation R = paths.get(j);
if (R == null) {
// we expect the first dimension of R to be dense, the second sparse
R = new BasicNaturalRelation(new byte[] { BasicNaturalRelation.SIMPLE_SPACE_STINGY }, BasicNaturalRelation.TWO_LEVEL);
paths.set(j, R);
}
R.add(n, i);
if (altPaths != null) {
IBinaryNaturalRelation R2 = altPaths.get(i);
if (R2 == null) {
// we expect the first dimension of R to be dense, the second sparse
R2 = new BasicNaturalRelation(new byte[] { BasicNaturalRelation.SIMPLE_SPACE_STINGY }, BasicNaturalRelation.TWO_LEVEL);
altPaths.set(i, R2);
}
R2.add(n, j);
}
if (TabulationSolver.DEBUG_LEVEL > 1) {
// System.err.println("recording path edge, now d2=" + j + " has been reached from " + R);
}
}
}
}
/**
* Record that in this procedure we've discovered a same-level realizable path from (s_p,i) to (n,i)
*
* @param n local block number of the basic block n
*/
@SuppressWarnings("unused")
private void addIdentityPathEdge(int i, int n) {
BitVectorIntSet s = (BitVectorIntSet) identityPaths.get(i);
if (s == null) {
s = new BitVectorIntSet();
identityPaths.set(i, s);
}
s.add(n);
if (altPaths != null) {
IBinaryNaturalRelation R2 = altPaths.get(i);
if (R2 == null) {
// we expect the first dimension of R to be dense, the second sparse
R2 = new BasicNaturalRelation(new byte[] { BasicNaturalRelation.SIMPLE_SPACE_STINGY }, BasicNaturalRelation.TWO_LEVEL);
altPaths.set(i, R2);
}
R2.add(n, i);
}
if (TabulationSolver.DEBUG_LEVEL > 1) {
System.err.println("recording self-path edge, now d1= " + i + " reaches " + s);
}
}
/**
* Record that in this procedure we've discovered a same-level realizable path from (s_p,0) to (n,d_j)
*
* @param n local block number of the basic block n
*
* @param j
*/
@SuppressWarnings("unused")
private void addZeroPathEdge(int n, int j) {
BitVectorIntSet z = (BitVectorIntSet) zeroPaths.get(j);
if (z == null) {
z = new BitVectorIntSet();
zeroPaths.set(j, z);
}
z.add(n);
if (altPaths != null) {
IBinaryNaturalRelation R = altPaths.get(0);
if (R == null) {
// we expect the first dimension of R to be dense, the second sparse
R = new BasicNaturalRelation(new byte[] { BasicNaturalRelation.SIMPLE_SPACE_STINGY }, BasicNaturalRelation.TWO_LEVEL);
altPaths.set(0, R);
}
R.add(n, j);
}
if (TabulationSolver.DEBUG_LEVEL > 1) {
System.err.println("recording 0-path edge, now d2= " + j + " reached at " + z);
}
}
/**
* N.B: If we're using the ZERO_PATH_SHORT_CIRCUIT, then we may have &lt;s_p, d1&gt; -&gt; &lt;n, d2&gt; implicitly represented since we also
* have &lt;s_p, 0&gt; -&gt; &lt;n,d2&gt;. However, getInverse() &lt;b&gt; will NOT &lt;/b&gt; return these implicit d1 bits in the result. This translates
* to saying that the caller had better not care about any other d1 other than d1==0 if d1==0 is present. This happens to be true
* in the single use of getInverse() in the tabulation solver, which uses getInverse() to propagate flow from an exit node back to
* the caller's return site(s). Since we know that we will see flow from fact 0 to the return sites(s), we don't care about other
* facts that may induce the same flow to the return site(s).
*
* @param n local block number of a basic block n
* @param d2
* @return the sparse int set of d1 s.t. {@literal <s_p, d1> -> <n, d2>} are recorded as path edges. null if none found
*/
public IntSet getInverse(int n, int d2) {
IBinaryNaturalRelation R = paths.get(d2);
BitVectorIntSet s = (BitVectorIntSet) identityPaths.get(d2);
BitVectorIntSet z = (BitVectorIntSet) zeroPaths.get(d2);
if (R == null) {
if (s == null) {
if (z == null) {
return null;
} else {
return z.contains(n) ? SparseIntSet.singleton(0) : null;
}
} else {
if (s.contains(n)) {
if (z == null) {
return SparseIntSet.singleton(d2);
} else {
return z.contains(n) ? SparseIntSet.pair(0, d2) : SparseIntSet.singleton(d2);
}
} else {
return null;
}
}
} else {
if (s == null) {
if (z == null) {
return R.getRelated(n);
} else {
if (z.contains(n)) {
IntSet related = R.getRelated(n);
if (related == null) {
return SparseIntSet.singleton(0);
} else {
MutableSparseIntSet result = MutableSparseIntSet.make(related);
result.add(0);
return result;
}
} else {
return R.getRelated(n);
}
}
} else {
if (s.contains(n)) {
IntSet related = R.getRelated(n);
if (related == null) {
if (z == null || !z.contains(n)) {
return SparseIntSet.singleton(d2);
} else {
return SparseIntSet.pair(0, d2);
}
} else {
MutableSparseIntSet result = MutableSparseIntSet.make(related);
result.add(d2);
if (z != null && z.contains(n)) {
result.add(0);
}
return result;
}
} else {
if (z == null || !z.contains(n)) {
return R.getRelated(n);
} else {
IntSet related = R.getRelated(n);
MutableSparseIntSet result = (related == null) ? MutableSparseIntSet.makeEmpty() : MutableSparseIntSet.make(related);
result.add(0);
return result;
}
}
}
}
}
/**
* @param i
* @param n local block number of a basic block n
* @param j
* @return true iff we have a path edge {@literal <s_p,i> -> <n, j>}
*/
public boolean contains(int i, int n, int j) {
if (n < 0) {
throw new IllegalArgumentException("invalid n: " + n);
}
if (i == 0) {
BitVectorIntSet z = (BitVectorIntSet) zeroPaths.get(j);
if (z != null && z.contains(n)) {
return true;
} else {
return false;
}
} else {
if (i == j) {
BitVectorIntSet s = (BitVectorIntSet) identityPaths.get(i);
if (s != null && s.contains(n)) {
return true;
} else {
return false;
}
} else {
IBinaryNaturalRelation R = paths.get(j);
if (R == null) {
return false;
}
return R.contains(n, i);
}
}
}
/**
*
* @param n
* @return set of d2 s.t. d1 -&gt; d2 is a path edge for node n.
*/
public IntSet getReachable(int n, int d1) {
if (PARANOID) {
assert getReachableSlow(n, d1).sameValue(getReachableFast(n, d1));
}
return (altPaths == null) ? getReachableSlow(n, d1) : getReachableFast(n, d1);
}
/**
* Note that this is really slow!!!
*
* @return set of d2 s.t. d1 -&gt; d2 is a path edge for node n
*/
private IntSet getReachableSlow(int n, int d1) {
MutableSparseIntSet result = MutableSparseIntSet.makeEmpty();
if (paths.size() > 0) {
// this is convoluted on purpose for efficiency: to avoid random access to
// the sparse vector, we do parallel iteration with the vector's indices
// and contents. TODO: better data structure?
Iterator<IBinaryNaturalRelation> contents = paths.iterator();
for (IntIterator it = paths.iterateIndices(); it.hasNext();) {
int d2 = it.next();
IBinaryNaturalRelation R = contents.next();
if (R != null && R.contains(n, d1)) {
result.add(d2);
}
}
}
if (identityPaths.size() > 0) {
BitVectorIntSet s = (BitVectorIntSet) identityPaths.get(d1);
if (s != null && s.contains(n)) {
result.add(d1);
}
}
if (d1 == 0 && zeroPaths.size() > 0) {
// this is convoluted on purpose for efficiency: to avoid random access to
// the sparse vector, we do parallel iteration with the vector's indices
// and contents. TODO: better data structure?
Iterator<IntSet> contents = zeroPaths.iterator();
for (IntIterator it = zeroPaths.iterateIndices(); it.hasNext();) {
int d2 = it.next();
IntSet s = contents.next();
if (s != null && s.contains(n)) {
result.add(d2);
}
}
}
return result;
}
/**
* @return set of d2 s.t. d1 -&gt; d2 is a path edge for node n
*/
private IntSet getReachableFast(int n, int d1) {
IBinaryNaturalRelation R = altPaths.get(d1);
if (R != null) {
return R.getRelated(n);
}
return null;
}
/**
* TODO: optimize this based on altPaths
*
* @param n the local block number of a node
* @return set of d2 s.t \exists d1 s.t. d1 -&gt; d2 is a path edge for node n
*/
public IntSet getReachable(int n) {
MutableSparseIntSet result = MutableSparseIntSet.makeEmpty();
if (paths.size() > 0) {
// this is convoluted on purpose for efficiency: to avoid random access to
// the sparse vector, we do parallel iteration with the vector's indices
// and contents. TODO: better data structure?
Iterator<IBinaryNaturalRelation> contents = paths.iterator();
for (IntIterator it = paths.iterateIndices(); it.hasNext();) {
int d2 = it.next();
IBinaryNaturalRelation R = contents.next();
if (R != null && R.anyRelated(n)) {
result.add(d2);
}
}
}
if (identityPaths.size() > 0) {
// this is convoluted on purpose for efficiency: to avoid random access to
// the sparse vector, we do parallel iteration with the vector's indices
// and contents. TODO: better data structure?
Iterator<IntSet> contents = identityPaths.iterator();
for (IntIterator it = identityPaths.iterateIndices(); it.hasNext();) {
int d1 = it.next();
IntSet s = contents.next();
if (s != null && s.contains(n)) {
result.add(d1);
}
}
}
if (zeroPaths.size() > 0) {
// this is convoluted on purpose for efficiency: to avoid random access to
// the sparse vector, we do parallel iteration with the vector's indices
// and contents. TODO: better data structure?
Iterator<IntSet> contents = zeroPaths.iterator();
for (IntIterator it = zeroPaths.iterateIndices(); it.hasNext();) {
int d2 = it.next();
IntSet s = contents.next();
if (s != null && s.contains(n)) {
result.add(d2);
}
}
}
return result;
}
/**
* TODO: optimize this
*
* @return set of node numbers that are reached by any fact
*/
public IntSet getReachedNodeNumbers() {
MutableSparseIntSet result = MutableSparseIntSet.makeEmpty();
if (paths.size() > 0) {
for (IBinaryNaturalRelation R : paths) {
for (IntPair p : R) {
result.add(p.getX());
}
}
}
if (identityPaths.size() > 0) {
for (IntSet s : identityPaths) {
result.addAll(s);
}
}
if (zeroPaths.size() > 0) {
for (IntSet s : zeroPaths) {
result.addAll(s);
}
}
return result;
}
}
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