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HDFS-13223. Reduce DiffListBySkipList memory usage. Contributed by Shashikant Banerjee

This commit is contained in:
Tsz-Wo Nicholas Sze 2018-03-06 12:23:03 -08:00
parent 9276ef0665
commit 871d0d39fa
4 changed files with 261 additions and 103 deletions
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218
hadoop-hdfs-project/hadoop-hdfs/src/main/java/org/apache/hadoop/hdfs/server/namenode/snapshot/DiffListBySkipList.java
View File

@ -17,6 +17,7 @@
*/
package org.apache.hadoop.hdfs.server.namenode.snapshot;
import com.google.common.base.Preconditions;
import org.apache.hadoop.hdfs.server.namenode.INodeDirectory;
import org.apache.hadoop.hdfs.server.namenode.snapshot.
DirectoryWithSnapshotFeature.DirectoryDiff;
@ -30,9 +31,7 @@ import java.util.ArrayList;
import java.util.Iterator;
import java.util.Arrays;
import java.util.Collections;
import java.util.Random;
import java.util.Objects;
import java.util.concurrent.ThreadLocalRandom;
/**
* SkipList is an implementation of a data structure for storing a sorted list
@ -72,7 +71,20 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
public static final Logger LOG =
LoggerFactory.getLogger(DiffListBySkipList.class);
static String childrenDiff2String(ChildrenDiff diff) {
if (diff == null) {
return "null";
}
return "@" + Integer.toHexString(System.identityHashCode(diff));
}
static String skip2String(SkipListNode skipTo, ChildrenDiff diff) {
return "->" + skipTo + ":diff=" + childrenDiff2String(diff);
}
private static class SkipDiff {
static final SkipDiff[] EMPTY_ARRAY = {};
/**
* The references to the subsequent nodes.
*/
@ -104,7 +116,7 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
@Override
public String toString() {
return "->" + skipTo + (diff == null? " (diff==null)": "");
return skip2String(skipTo, diff);
}
}
@ -112,17 +124,19 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
* SkipListNode is an implementation of a DirectoryDiff List node,
* which stores a Directory Diff and references to subsequent nodes.
*/
private final static class SkipListNode implements Comparable<Integer> {
final static class SkipListNode implements Comparable<Integer> {
/**
* The data element stored in this node.
*/
private DirectoryDiff diff;
private final DirectoryDiff diff;
/** Next node. */
private SkipListNode next;
/**
* List containing combined children diffs over a skip interval.
* Array containing combined children diffs over a skip interval.
*/
private List<SkipDiff> skipDiffList;
private SkipDiff[] skips;
/**
* Constructs a new instance of SkipListNode with the specified data element
@ -132,20 +146,28 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
*/
SkipListNode(DirectoryDiff diff, int level) {
this.diff = diff;
skipDiffList = new ArrayList<>(level + 1);
this.skips = level > 0? new SkipDiff[level]: SkipDiff.EMPTY_ARRAY;
for(int i = 0; i < skips.length; i++) {
skips[i] = new SkipDiff(null);
}
}
/**
* Returns the level of this SkipListNode.
*/
public int level() {
return skipDiffList.size() - 1;
return skips.length;
}
void trim() {
for (int level = level();
level > 0 && getSkipNode(level) == null; level--) {
skipDiffList.remove(level);
int n = skips.length - 1;
for (; n >= 0 && skips[n] == null; n--) {
continue;
}
n++;
if (n < skips.length) {
skips = n > 0 ? Arrays.copyOf(skips, n) : SkipDiff.EMPTY_ARRAY;
}
}
@ -179,40 +201,66 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
}
public void setSkipDiff(ChildrenDiff cDiff, int level) {
if (level < skipDiffList.size()) {
skipDiffList.get(level).setDiff(cDiff);
} else {
skipDiffList.add(new SkipDiff(cDiff));
Preconditions.checkArgument(level > 0);
resize(level);
skips[level - 1].setDiff(cDiff);
}
void setSkipDiff4Target(
SkipListNode target, int startLevel, ChildrenDiff childrenDiff) {
for(int i = startLevel; i <= level(); i++) {
if (getSkipNode(i) != target) {
return;
}
setSkipDiff(childrenDiff, i);
}
}
private void resize(int newLevel) {
int i = skips.length;
if (i < newLevel) {
skips = Arrays.copyOf(skips, newLevel);
for (; i < newLevel; i++) {
skips[i] = new SkipDiff(null);
}
}
}
public void setSkipTo(SkipListNode node, int level) {
for (int i = skipDiffList.size(); i <= level; i++) {
skipDiffList.add(new SkipDiff(null));
if (level == 0) {
next = node;
} else {
resize(level);
skips[level - 1].setSkipTo(node);
}
skipDiffList.get(level).setSkipTo(node);
}
public ChildrenDiff getChildrenDiff(int level) {
if (level == 0) {
return diff.getChildrenDiff();
return diff != null? diff.getChildrenDiff(): null;
} else {
return skipDiffList.get(level).getDiff();
return skips[level - 1].getDiff();
}
}
SkipListNode getSkipNode(int level) {
if (level >= skipDiffList.size()) {
return null;
} else {
return skipDiffList.get(level).getSkipTo();
}
return level == 0? next
: level <= skips.length? skips[level - 1].getSkipTo()
: null;
}
@Override
public String toString() {
return diff != null ? "" + diff.getSnapshotId() : "?";
}
StringBuilder appendTo(StringBuilder b) {
b.append(this).append(": ").append(skip2String(next, getChildrenDiff(0)));
for(int i = 0; i < skips.length; i++) {
b.append(", ").append(skips[i]);
}
return b;
}
}
/**
@ -220,17 +268,7 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
* The list will grow linearly once a new Directory diff gets added.
* All the list inteface defined methods provide a linear view of the list.
*/
private List<SkipListNode> skipNodeList;
/**
* The max no of skipLevels.
*/
private final int maxSkipLevels;
/**
* The no of diffs after which the level promotion happens.
*/
private final int skipInterval;
private final List<SkipListNode> skipNodeList;
/**
* The head node to the list.
@ -240,11 +278,9 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
/**
* Constructs a new, empty instance of SkipList.
*/
public DiffListBySkipList(int capacity, int interval, int skipLevel) {
public DiffListBySkipList(int capacity) {
skipNodeList = new ArrayList<>(capacity);
head = new SkipListNode(null, 0);
this.maxSkipLevels = skipLevel;
this.skipInterval = interval;
}
/**
@ -254,13 +290,9 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
*/
@Override
public void addFirst(DirectoryDiff diff) {
final int nodeLevel = randomLevel(skipInterval, maxSkipLevels);
final int nodeLevel = DirectoryDiffListFactory.randomLevel();
final SkipListNode[] nodePath = new SkipListNode[nodeLevel + 1];
Arrays.fill(nodePath, head);
for (int level = head.level() + 1; level <= nodeLevel; level++) {
head.skipDiffList.add(new SkipDiff(null));
}
final SkipListNode newNode = new SkipListNode(diff, nodeLevel);
for (int level = 0; level <= nodeLevel; level++) {
@ -316,15 +348,10 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
*/
@Override
public boolean addLast(DirectoryDiff diff) {
final int nodeLevel = randomLevel(skipInterval, maxSkipLevels);
final int headLevel = head.level();
final int nodeLevel = DirectoryDiffListFactory.randomLevel();
final SkipListNode[] nodePath = findPreviousNodes(null, nodeLevel);
for (int level = headLevel + 1; level <= nodeLevel; level++) {
head.skipDiffList.add(new SkipDiff(null));
nodePath[level] = head;
}
final SkipListNode current = new SkipListNode(diff, nodeLevel);
final SkipListNode newNode = new SkipListNode(diff, nodeLevel);
for (int level = 0; level <= nodeLevel; level++) {
if (level > 0 && nodePath[level] != head) {
// suppose the list is like:
@ -339,22 +366,24 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
// level 0:head-> s1->s2->s3->s4->s5->s6->s7->s8->s9---->s10
// At level 1, we combine s5, s6, s7, s8, s9 and store as s5'
// At level 2, we combine s1', s3', s5' and form s1'' and store at s1.
// Note : the last element(elemnt being added) diff is not added while
// Note : the last element(element being added) diff is not added while
// combining the diffs.
ChildrenDiff combined = combineDiff(nodePath[level], current, level);
ChildrenDiff combined = combineDiff(nodePath[level], newNode, level);
if (combined != null) {
nodePath[level].setSkipDiff(combined, level);
}
}
nodePath[level].setSkipTo(current, level);
current.setSkipTo(null, level);
nodePath[level].setSkipTo(newNode, level);
newNode.setSkipTo(null, level);
}
return skipNodeList.add(current);
return skipNodeList.add(newNode);
}
private static ChildrenDiff combineDiff(SkipListNode from, SkipListNode to,
int level) {
ChildrenDiff combined = null;
ChildrenDiff first = null;
SkipListNode cur = from;
for (int i = level - 1; i >= 0; i--) {
while (cur != to) {
@ -362,14 +391,20 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
if (next == null) {
break;
}
if (combined == null) {
combined = new ChildrenDiff();
if (first == null) {
first = cur.getChildrenDiff(i);
} else {
if (combined == null) {
combined = new ChildrenDiff();
combined.combinePosterior(first, null);
}
combined.combinePosterior(cur.getChildrenDiff(i), null);
}
combined.combinePosterior(cur.getChildrenDiff(i), null);
cur = next;
}
}
return combined;
return combined != null? combined: first;
}
/**
@ -383,6 +418,10 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
return skipNodeList.get(index).getDiff();
}
SkipListNode getSkipListNode(int i) {
return skipNodeList.get(i);
}
/**
* Removes the element at the specified position in this list.
*
@ -391,12 +430,20 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
*/
@Override
public DirectoryDiff remove(int index) {
SkipListNode node = getNode(index);
final SkipListNode node = getNode(index);
int headLevel = head.level();
int nodeLevel = node.level();
final SkipListNode[] nodePath = findPreviousNodes(node, nodeLevel);
for (int level = 0; level <= nodeLevel; level++) {
if (nodePath[level] != head && level > 0) {
final SkipListNode previous = nodePath[level];
final SkipListNode next = node.getSkipNode(level);
if (level == 0) {
if (next != null) {
previous.setSkipDiff4Target(next, 1, previous.getChildrenDiff(0));
}
} else if (previous != head) {
// if the last snapshot is deleted, for all the skip level nodes
// pointing to the last one, the combined children diff at each level
// > 0 should be made null and skip pointers will be updated to null.
@ -404,8 +451,8 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
// the diff of deleted node at each level to the previous skip level
// node at that level and the skip pointers will be updated to point to
// the skip nodes of the deleted node.
if (index == size() - 1) {
nodePath[level].setSkipDiff(null, level);
if (next == null) {
previous.setSkipDiff(null, level);
} else {
/* Ideally at level 0, the deleted diff will be combined with
* the previous diff , and deleted inodes will be cleaned up
@ -414,12 +461,23 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
* {@link AbstractINodeDiffList#deleteSnapshotDiff} function.
*/
if (node.getChildrenDiff(level) != null) {
nodePath[level].getChildrenDiff(level)
.combinePosterior(node.getChildrenDiff(level), null);
final ChildrenDiff combined;
if (previous == nodePath[level - 1]
&& next == node.getSkipNode(level - 1)) {
combined = nodePath[level - 1].getChildrenDiff(level - 1);
previous.setSkipDiff4Target(next, level + 1, combined);
} else if (next == previous.getSkipNode(level + 1)) {
combined = previous.getChildrenDiff(level + 1);
} else {
combined = new ChildrenDiff();
combined.combinePosterior(previous.getChildrenDiff(level), null);
combined.combinePosterior(node.getChildrenDiff(level), null);
}
previous.setSkipDiff(combined, level);
}
}
}
nodePath[level].setSkipTo(node.getSkipNode(level), level);
previous.setSkipTo(next, level);
}
if (nodeLevel == headLevel) {
head.trim();
@ -478,24 +536,6 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
return skipNodeList.get(index);
}
/**
* Returns the level of the skipList node.
*
* @param skipInterval The max interval after which the next level promotion
* should happen.
* @param maxLevel Maximum no of skip levels
* @return A value in the range 0 to maxLevel-1.
*/
static int randomLevel(int skipInterval, int maxLevel) {
final Random r = ThreadLocalRandom.current();
for (int level = 0; level < maxLevel; level++) {
// skip to the next level with probability 1/skipInterval
if (r.nextInt(skipInterval) > 0) {
return level;
}
}
return maxLevel;
}
/**
* This function returns the minimal set of diffs required to combine in
@ -535,10 +575,10 @@ public class DiffListBySkipList implements DiffList<DirectoryDiff> {
@Override
public String toString() {
final StringBuilder b = new StringBuilder(getClass().getSimpleName());
b.append(" head: ").append(head).append(head.skipDiffList);
final StringBuilder b = new StringBuilder().append(" head: ");
head.appendTo(b);
for (SkipListNode n : skipNodeList) {
b.append("\n ").append(n).append(n.skipDiffList);
n.appendTo(b.append("\n "));
}
return b.toString();
}

30
hadoop-hdfs-project/hadoop-hdfs/src/main/java/org/apache/hadoop/hdfs/server/namenode/snapshot/DirectoryDiffListFactory.java
View File

@ -17,9 +17,11 @@
*/
package org.apache.hadoop.hdfs.server.namenode.snapshot;
import org.apache.commons.logging.Log;
import org.apache.hadoop.hdfs.server.namenode.snapshot.DirectoryWithSnapshotFeature.DirectoryDiff;
import org.slf4j.Logger;
import java.util.Random;
import java.util.concurrent.ThreadLocalRandom;
import java.util.function.IntFunction;
/** For creating {@link DiffList} for {@link DirectoryDiff}. */
@ -28,9 +30,12 @@ public abstract class DirectoryDiffListFactory {
return constructor.apply(capacity);
}
public static void init(int skipInterval, int maxLevels, Log log) {
public static void init(int interval, int maxSkipLevels, Logger log) {
DirectoryDiffListFactory.skipInterval = interval;
DirectoryDiffListFactory.maxLevels = maxSkipLevels;
if (maxLevels > 0) {
constructor = c -> new DiffListBySkipList(c, skipInterval, maxLevels);
constructor = c -> new DiffListBySkipList(c);
log.info("SkipList is enabled with skipInterval=" + skipInterval
+ ", maxLevels=" + maxLevels);
} else {
@ -42,5 +47,24 @@ public abstract class DirectoryDiffListFactory {
private static volatile IntFunction<DiffList<DirectoryDiff>> constructor
= c -> new DiffListByArrayList<>(c);
private static volatile int skipInterval;
private static volatile int maxLevels;
/**
* Returns the level of a skip list node.
* @return A value in the range 0 to maxLevels.
*/
public static int randomLevel() {
final Random r = ThreadLocalRandom.current();
for (int level = 0; level < maxLevels; level++) {
// skip to the next level with probability 1/skipInterval
if (r.nextInt(skipInterval) > 0) {
return level;
}
}
return maxLevels;
}
private DirectoryDiffListFactory() {}
}

7
hadoop-hdfs-project/hadoop-hdfs/src/main/java/org/apache/hadoop/hdfs/server/namenode/snapshot/SnapshotManager.java
View File

@ -36,8 +36,6 @@ import java.util.concurrent.atomic.AtomicInteger;
import javax.management.ObjectName;
import com.google.common.annotations.VisibleForTesting;
import org.apache.commons.logging.Log;
import org.apache.commons.logging.LogFactory;
import org.apache.hadoop.conf.Configuration;
import org.apache.hadoop.hdfs.DFSConfigKeys;
import org.apache.hadoop.hdfs.DFSUtil;
@ -60,6 +58,8 @@ import org.apache.hadoop.hdfs.server.namenode.LeaseManager;
import org.apache.hadoop.metrics2.util.MBeans;
import com.google.common.base.Preconditions;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
/**
* Manage snapshottable directories and their snapshots.
@ -74,7 +74,8 @@ import com.google.common.base.Preconditions;
* if necessary.
*/
public class SnapshotManager implements SnapshotStatsMXBean {
public static final Log LOG = LogFactory.getLog(SnapshotManager.class);
public static final Logger LOG =
LoggerFactory.getLogger(SnapshotManager.class);
private final FSDirectory fsdir;
private boolean captureOpenFiles;

109
hadoop-hdfs-project/hadoop-hdfs/src/test/java/org/apache/hadoop/hdfs/server/namenode/snapshot/TestDiffListBySkipList.java
View File

@ -27,6 +27,7 @@ import org.apache.hadoop.hdfs.server.namenode.INode;
import org.apache.hadoop.hdfs.server.namenode.INodeDirectory;
import org.apache.hadoop.hdfs.server.namenode.snapshot.DirectoryWithSnapshotFeature.ChildrenDiff;
import org.apache.hadoop.hdfs.server.namenode.snapshot.DirectoryWithSnapshotFeature.DirectoryDiff;
import org.apache.hadoop.hdfs.server.namenode.snapshot.DiffListBySkipList.SkipListNode;
import org.apache.hadoop.hdfs.util.ReadOnlyList;
import org.junit.After;
import org.junit.Assert;
@ -36,13 +37,16 @@ import org.junit.Test;
import java.util.Collections;
import java.util.List;
import java.util.concurrent.ThreadLocalRandom;
import java.util.function.IntFunction;
import java.util.function.ToIntBiFunction;
import java.util.function.ToIntFunction;
/**
* This class tests the DirectoryDiffList API's.
*/
public class TestDiffListBySkipList {
static final int NUM_SNAPSHOTS = 100;
static final int MAX_LEVEL = 5;
static {
SnapshotTestHelper.disableLogs();
}
@ -71,6 +75,11 @@ public class TestDiffListBySkipList {
}
}
static DiffListBySkipList newDiffListBySkipList() {
DirectoryDiffListFactory.init(3, MAX_LEVEL, DiffListBySkipList.LOG);
return new DiffListBySkipList(0);
}
static void assertList(List<INode> expected, List<INode> computed) {
Assert.assertEquals(expected.size(), computed.size());
for (int index = 0; index < expected.size(); index++) {
@ -114,6 +123,8 @@ public class TestDiffListBySkipList {
}
}
}
assertSkipList(skip);
}
private static ChildrenDiff getCombined(
@ -146,7 +157,7 @@ public class TestDiffListBySkipList {
final Path root = new Path("/testAddLast" + n);
DiffListBySkipList.LOG.info("run " + root);
final DiffListBySkipList skipList = new DiffListBySkipList(0, 3, 5);
final DiffListBySkipList skipList = newDiffListBySkipList();
final DiffList<DirectoryDiff> arrayList = new DiffListByArrayList<>(0);
INodeDirectory dir = addDiff(n, skipList, arrayList, root);
// verify that the both the children list obtained from hdfs and
@ -180,7 +191,7 @@ public class TestDiffListBySkipList {
DiffList<DirectoryDiff> diffs = dir.getDiffs().asList();
List<INode> childrenList = ReadOnlyList.Util.asList(dir.getChildrenList(
diffs.get(0).getSnapshotId()));
final DiffListBySkipList skipList = new DiffListBySkipList(0, 3, 5);
final DiffListBySkipList skipList = newDiffListBySkipList();
final DiffList<DirectoryDiff> arrayList = new DiffListByArrayList<>(0);
for (int i = diffs.size() - 1; i >= 0; i--) {
final DirectoryDiff d = diffs.get(i);
@ -208,6 +219,7 @@ public class TestDiffListBySkipList {
skipList.addLast(d);
arrayList.addLast(d);
}
DiffListBySkipList.LOG.info("skipList: " + skipList);
return dir;
}
@ -228,19 +240,26 @@ public class TestDiffListBySkipList {
testRemove("Random", n, i -> ThreadLocalRandom.current().nextInt(n - i));
}
static void testRemove(String name, int n, IntFunction<Integer> indexFunction)
static void testRemove(String name, int n,
ToIntFunction<Integer> indexFunction) throws Exception {
testRemove(name, n, (skipList, i) -> indexFunction.applyAsInt(i));
}
static void testRemove(String name, int n,
ToIntBiFunction<DiffListBySkipList, Integer> indexFunction)
throws Exception {
final Path root = new Path("/testRemove" + name + n);
DiffListBySkipList.LOG.info("run " + root);
final DiffListBySkipList skipList = new DiffListBySkipList(0, 3, 5);
final DiffListBySkipList skipList = newDiffListBySkipList();
final DiffList<DirectoryDiff> arrayList = new DiffListByArrayList<>(0);
final INodeDirectory dir = addDiff(n, skipList, arrayList, root);
Assert.assertEquals(n, arrayList.size());
Assert.assertEquals(n, skipList.size());
for(int i = 0; i < n; i++) {
final int index = indexFunction.apply(i);
for (int i = 0; i < n; i++) {
DiffListBySkipList.LOG.debug("i={}: {}", i, skipList);
final int index = indexFunction.applyAsInt(skipList, i);
final DirectoryDiff diff = remove(index, skipList, arrayList);
hdfs.deleteSnapshot(root, "s" + diff.getSnapshotId());
verifyChildrenList(skipList, dir);
@ -248,10 +267,58 @@ public class TestDiffListBySkipList {
}
}
@Test
public void testRemoveFromLowerLevel() throws Exception {
testRemove("FromLowerLevel", NUM_SNAPSHOTS,
new ToIntBiFunction<DiffListBySkipList, Integer>() {
private int level = 0;
@Override
public int applyAsInt(DiffListBySkipList skipList, Integer integer) {
for (; level <= MAX_LEVEL; level++) {
final int index = findIndex(skipList, level);
if (index != -1) {
return index;
}
}
return -1;
}
});
}
@Test
public void testRemoveFromUpperLevel() throws Exception {
testRemove("FromUpperLevel", NUM_SNAPSHOTS,
new ToIntBiFunction<DiffListBySkipList, Integer>() {
private int level = MAX_LEVEL;
@Override
public int applyAsInt(DiffListBySkipList skipList, Integer integer) {
for(; level >= 0; level--) {
final int index = findIndex(skipList, level);
if (index != -1) {
return index;
}
DiffListBySkipList.LOG.info("change from level " + level);
}
return -1;
}
});
}
static int findIndex(DiffListBySkipList skipList, int level) {
for (int i = 0; i < skipList.size(); i++) {
if (skipList.getSkipListNode(i).level() == level) {
return i;
}
}
return -1;
}
static DirectoryDiff remove(int i, DiffListBySkipList skip,
DiffList<DirectoryDiff> array) {
DiffListBySkipList.LOG.info("remove " + i);
final DirectoryDiff expected = array.remove(i);
DiffListBySkipList.LOG
.info("remove " + i + ", snapshotId=" + expected.getSnapshotId());
final DirectoryDiff computed = skip.remove(i);
assertDirectoryDiff(expected, computed);
return expected;
@ -261,4 +328,30 @@ public class TestDiffListBySkipList {
DirectoryDiff computed) {
Assert.assertEquals(expected.getSnapshotId(), computed.getSnapshotId());
}
static void assertSkipList(DiffListBySkipList skipList) {
for(int i = 0; i < skipList.size(); i++) {
assertSkipListNode(skipList.getSkipListNode(i));
}
}
static void assertSkipListNode(SkipListNode n) {
for (int i = 1; i <= n.level(); i++) {
final SkipListNode target = n.getSkipNode(i);
final ChildrenDiff diff = n.getChildrenDiff(i);
if (target == null) {
if (diff != null) {
throw new AssertionError(
"Target is null but children diff is not at i=" + i + n
.appendTo(new StringBuilder(": ")));
}
} else if (target == n.getSkipNode(i - 1)) {
if (diff != n.getChildrenDiff(i - 1)) {
throw new AssertionError(
"Same target but different children diff at i=" + i + n
.appendTo(new StringBuilder(": ")));
}
}
}
}
}