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* Licensed to the Apache Software Foundation (ASF) under one
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* distributed with this work for additional information
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* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.cassandra.db;
import java.nio.ByteBuffer;
import java.util.Arrays;
import java.util.Collections;
import java.util.Iterator;
import org.apache.cassandra.config.DatabaseDescriptor;
import org.apache.cassandra.utils.AbstractIterator;
import org.apache.cassandra.utils.CassandraUInt;
import com.google.common.collect.Iterators;
import org.apache.cassandra.cache.IMeasurableMemory;
import org.apache.cassandra.db.rows.*;
import org.apache.cassandra.utils.ObjectSizes;
import org.apache.cassandra.utils.memory.ByteBufferCloner;
/**
* Data structure holding the range tombstones of a ColumnFamily.
*
* This is essentially a sorted list of non-overlapping (tombstone) ranges.
*
* A range tombstone has 4 elements: the start and end of the range covered,
* and the deletion infos (markedAt timestamp and local deletion time). The
* markedAt timestamp is what define the priority of 2 overlapping tombstones.
* That is, given 2 tombstones {@code [0, 10]@t1 and [5, 15]@t2, then if t2 > t1} (and
* are the tombstones markedAt values), the 2nd tombstone take precedence over
* the first one on [5, 10]. If such tombstones are added to a RangeTombstoneList,
* the range tombstone list will store them as [[0, 5]@t1, [5, 15]@t2].
*
* The only use of the local deletion time is to know when a given tombstone can
* be purged, which will be done by the purge() method.
*/
public class RangeTombstoneList implements Iterable, IMeasurableMemory
{
private static long EMPTY_SIZE = ObjectSizes.measure(new RangeTombstoneList(null, 0));
private final ClusteringComparator comparator;
// Note: we don't want to use a List for the markedAts and delTimes to avoid boxing. We could
// use a List for starts and ends, but having arrays everywhere is almost simpler.
private ClusteringBound[] starts;
private ClusteringBound[] ends;
private long[] markedAts;
private int[] delTimesUnsignedIntegers;
private long boundaryHeapSize;
private int size;
private RangeTombstoneList(ClusteringComparator comparator,
ClusteringBound[] starts,
ClusteringBound[] ends,
long[] markedAts,
int[] delTimesUnsignedIntegers,
long boundaryHeapSize,
int size)
{
assert starts.length == ends.length && starts.length == markedAts.length && starts.length == delTimesUnsignedIntegers.length;
this.comparator = comparator;
this.starts = starts;
this.ends = ends;
this.markedAts = markedAts;
this.delTimesUnsignedIntegers = delTimesUnsignedIntegers;
this.size = size;
this.boundaryHeapSize = boundaryHeapSize;
}
public RangeTombstoneList(ClusteringComparator comparator, int capacity)
{
this(comparator, new ClusteringBound[capacity], new ClusteringBound[capacity], new long[capacity], new int[capacity], 0, 0);
}
public boolean isEmpty()
{
return size == 0;
}
public int size()
{
return size;
}
public ClusteringComparator comparator()
{
return comparator;
}
public RangeTombstoneList copy()
{
return new RangeTombstoneList(comparator,
Arrays.copyOf(starts, size),
Arrays.copyOf(ends, size),
Arrays.copyOf(markedAts, size),
Arrays.copyOf(delTimesUnsignedIntegers, size),
boundaryHeapSize, size);
}
public RangeTombstoneList clone(ByteBufferCloner cloner)
{
RangeTombstoneList copy = new RangeTombstoneList(comparator,
new ClusteringBound[size],
new ClusteringBound[size],
Arrays.copyOf(markedAts, size),
Arrays.copyOf(delTimesUnsignedIntegers, size),
boundaryHeapSize, size);
for (int i = 0; i < size; i++)
{
copy.starts[i] = clone(starts[i], cloner);
copy.ends[i] = clone(ends[i], cloner);
}
return copy;
}
private static ClusteringBound clone(ClusteringBound bound, ByteBufferCloner cloner)
{
ByteBuffer[] values = new ByteBuffer[bound.size()];
for (int i = 0; i < values.length; i++)
values[i] = cloner.clone(bound.get(i), bound.accessor());
return new BufferClusteringBound(bound.kind(), values);
}
public void add(RangeTombstone tombstone)
{
add(tombstone.deletedSlice().start(),
tombstone.deletedSlice().end(),
tombstone.deletionTime().markedForDeleteAt(),
tombstone.deletionTime().localDeletionTimeUnsignedInteger);
}
/**
* Adds a new range tombstone.
*
* This method will be faster if the new tombstone sort after all the currently existing ones (this is a common use case),
* but it doesn't assume it.
*/
private void add(ClusteringBound start, ClusteringBound end, long markedAt, int delTimeUnsignedInteger)
{
if (isEmpty())
{
addInternal(0, start, end, markedAt, delTimeUnsignedInteger);
return;
}
int c = comparator.compare(ends[size-1], start);
// Fast path if we add in sorted order
if (c <= 0)
{
addInternal(size, start, end, markedAt, delTimeUnsignedInteger);
}
else
{
// Note: insertFrom expect i to be the insertion point in term of interval ends
int pos = Arrays.binarySearch(ends, 0, size, start, comparator);
insertFrom((pos >= 0 ? pos+1 : -pos-1), start, end, markedAt, delTimeUnsignedInteger);
}
boundaryHeapSize += start.unsharedHeapSize() + end.unsharedHeapSize();
}
/**
* Adds all the range tombstones of {@code tombstones} to this RangeTombstoneList.
*/
public void addAll(RangeTombstoneList tombstones)
{
if (tombstones.isEmpty())
return;
if (isEmpty())
{
copyArrays(tombstones, this);
return;
}
/*
* We basically have 2 techniques we can use here: either we repeatedly call add() on tombstones values,
* or we do a merge of both (sorted) lists. If this lists is bigger enough than the one we add, then
* calling add() will be faster, otherwise it's merging that will be faster.
*
* Let's note that during memtables updates, it might not be uncommon that a new update has only a few range
* tombstones, while the CF we're adding it to (the one in the memtable) has many. In that case, using add() is
* likely going to be faster.
*
* In other cases however, like when diffing responses from multiple nodes, the tombstone lists we "merge" will
* be likely sized, so using add() might be a bit inefficient.
*
* Roughly speaking (this ignore the fact that updating an element is not exactly constant but that's not a big
* deal), if n is the size of this list and m is tombstones size, merging is O(n+m) while using add() is O(m*log(n)).
*
* But let's not crank up a logarithm computation for that. Long story short, merging will be a bad choice only
* if this list size is lot bigger that the other one, so let's keep it simple.
*/
if (size > 10 * tombstones.size)
{
for (int i = 0; i < tombstones.size; i++)
add(tombstones.starts[i], tombstones.ends[i], tombstones.markedAts[i], tombstones.delTimesUnsignedIntegers[i]);
}
else
{
int i = 0;
int j = 0;
while (i < size && j < tombstones.size)
{
if (comparator.compare(tombstones.starts[j], ends[i]) < 0)
{
insertFrom(i, tombstones.starts[j], tombstones.ends[j], tombstones.markedAts[j], tombstones.delTimesUnsignedIntegers[j]);
j++;
}
else
{
i++;
}
}
// Addds the remaining ones from tombstones if any (note that addInternal will increment size if relevant).
for (; j < tombstones.size; j++)
addInternal(size, tombstones.starts[j], tombstones.ends[j], tombstones.markedAts[j], tombstones.delTimesUnsignedIntegers[j]);
}
}
/**
* Returns whether the given name/timestamp pair is deleted by one of the tombstone
* of this RangeTombstoneList.
*/
public boolean isDeleted(Clustering clustering, Cell cell)
{
int idx = searchInternal(clustering, 0, size);
// No matter what the counter cell's timestamp is, a tombstone always takes precedence. See CASSANDRA-7346.
return idx >= 0 && (cell.isCounterCell() || markedAts[idx] >= cell.timestamp());
}
/**
* Returns the DeletionTime for the tombstone overlapping {@code name} (there can't be more than one),
* or null if {@code name} is not covered by any tombstone.
*/
public DeletionTime searchDeletionTime(Clustering name)
{
int idx = searchInternal(name, 0, size);
return idx < 0 ? null : DeletionTime.buildUnsafeWithUnsignedInteger(markedAts[idx], delTimesUnsignedIntegers[idx]);
}
public RangeTombstone search(Clustering name)
{
int idx = searchInternal(name, 0, size);
return idx < 0 ? null : rangeTombstone(idx);
}
/*
* Return is the index of the range covering name if name is covered. If the return idx is negative,
* no range cover name and -idx-1 is the index of the first range whose start is greater than name.
*
* Note that bounds are not in the range if they fall on its boundary.
*/
private int searchInternal(ClusteringPrefix name, int startIdx, int endIdx)
{
if (isEmpty())
return -1;
int pos = Arrays.binarySearch(starts, startIdx, endIdx, name, comparator);
if (pos >= 0)
{
// Equality only happens for bounds (as used by forward/reverseIterator), and bounds are equal only if they
// are the same or complementary, in either case the bound itself is not part of the range.
return -pos - 1;
}
else
{
// We potentially intersect the range before our "insertion point"
int idx = -pos-2;
if (idx < 0)
return -1;
return comparator.compare(name, ends[idx]) < 0 ? idx : -idx-2;
}
}
public int dataSize()
{
int dataSize = TypeSizes.sizeof(size);
for (int i = 0; i < size; i++)
{
dataSize += starts[i].dataSize() + ends[i].dataSize();
dataSize += TypeSizes.sizeof(markedAts[i]);
dataSize += TypeSizes.sizeof(delTimesUnsignedIntegers[i]);
}
return dataSize;
}
public long maxMarkedAt()
{
long max = Long.MIN_VALUE;
for (int i = 0; i < size; i++)
max = Math.max(max, markedAts[i]);
return max;
}
public void collectStats(EncodingStats.Collector collector)
{
for (int i = 0; i < size; i++)
{
collector.updateTimestamp(markedAts[i]);
collector.updateLocalDeletionTime(CassandraUInt.toLong(delTimesUnsignedIntegers[i]));
}
}
public void updateAllTimestamp(long timestamp)
{
for (int i = 0; i < size; i++)
markedAts[i] = timestamp;
}
private RangeTombstone rangeTombstone(int idx)
{
return new RangeTombstone(Slice.make(starts[idx], ends[idx]), DeletionTime.buildUnsafeWithUnsignedInteger(markedAts[idx], delTimesUnsignedIntegers[idx]));
}
private RangeTombstone rangeTombstoneWithNewStart(int idx, ClusteringBound newStart)
{
return new RangeTombstone(Slice.make(newStart, ends[idx]), DeletionTime.buildUnsafeWithUnsignedInteger(markedAts[idx], delTimesUnsignedIntegers[idx]));
}
private RangeTombstone rangeTombstoneWithNewEnd(int idx, ClusteringBound newEnd)
{
return new RangeTombstone(Slice.make(starts[idx], newEnd), DeletionTime.buildUnsafeWithUnsignedInteger(markedAts[idx], delTimesUnsignedIntegers[idx]));
}
private RangeTombstone rangeTombstoneWithNewBounds(int idx, ClusteringBound newStart, ClusteringBound newEnd)
{
return new RangeTombstone(Slice.make(newStart, newEnd), DeletionTime.buildUnsafeWithUnsignedInteger(markedAts[idx], delTimesUnsignedIntegers[idx]));
}
public Iterator iterator()
{
return iterator(false);
}
@SuppressWarnings("resource")
public Iterator iterator(boolean reversed)
{
return reversed
? new AbstractIterator()
{
private int idx = size - 1;
protected RangeTombstone computeNext()
{
if (idx < 0)
return endOfData();
return rangeTombstone(idx--);
}
}
: new AbstractIterator()
{
private int idx;
protected RangeTombstone computeNext()
{
if (idx >= size)
return endOfData();
return rangeTombstone(idx++);
}
};
}
public Iterator iterator(final Slice slice, boolean reversed)
{
return reversed ? reverseIterator(slice) : forwardIterator(slice);
}
private Iterator forwardIterator(final Slice slice)
{
int startIdx = slice.start().isBottom() ? 0 : searchInternal(slice.start(), 0, size);
final int start = startIdx < 0 ? -startIdx-1 : startIdx;
if (start >= size)
return Collections.emptyIterator();
int finishIdx = slice.end().isTop() ? size - 1 : searchInternal(slice.end(), start, size);
// if stopIdx is the first range after 'slice.end()' we care only until the previous range
final int finish = finishIdx < 0 ? -finishIdx-2 : finishIdx;
if (start > finish)
return Collections.emptyIterator();
if (start == finish)
{
// We want to make sure the range are stricly included within the queried slice as this
// make it easier to combine things when iterating over successive slices.
ClusteringBound s = comparator.compare(starts[start], slice.start()) < 0 ? slice.start() : starts[start];
ClusteringBound e = comparator.compare(slice.end(), ends[start]) < 0 ? slice.end() : ends[start];
if (Slice.isEmpty(comparator, s, e))
return Collections.emptyIterator();
return Iterators.singletonIterator(rangeTombstoneWithNewBounds(start, s, e));
}
return new AbstractIterator()
{
private int idx = start;
protected RangeTombstone computeNext()
{
if (idx >= size || idx > finish)
return endOfData();
// We want to make sure the range are stricly included within the queried slice as this
// make it easier to combine things when iterating over successive slices. This means that
// for the first and last range we might have to "cut" the range returned.
if (idx == start && comparator.compare(starts[idx], slice.start()) < 0)
return rangeTombstoneWithNewStart(idx++, slice.start());
if (idx == finish && comparator.compare(slice.end(), ends[idx]) < 0)
return rangeTombstoneWithNewEnd(idx++, slice.end());
return rangeTombstone(idx++);
}
};
}
private Iterator reverseIterator(final Slice slice)
{
int startIdx = slice.end().isTop() ? size - 1 : searchInternal(slice.end(), 0, size);
// if startIdx is the first range after 'slice.end()' we care only until the previous range
final int start = startIdx < 0 ? -startIdx-2 : startIdx;
if (start < 0)
return Collections.emptyIterator();
int finishIdx = slice.start().isBottom() ? 0 : searchInternal(slice.start(), 0, start + 1); // include same as finish
// if stopIdx is the first range after 'slice.end()' we care only until the previous range
final int finish = finishIdx < 0 ? -finishIdx-1 : finishIdx;
if (start < finish)
return Collections.emptyIterator();
if (start == finish)
{
// We want to make sure the range are stricly included within the queried slice as this
// make it easier to combine things when iterator over successive slices.
ClusteringBound s = comparator.compare(starts[start], slice.start()) < 0 ? slice.start() : starts[start];
ClusteringBound e = comparator.compare(slice.end(), ends[start]) < 0 ? slice.end() : ends[start];
if (Slice.isEmpty(comparator, s, e))
return Collections.emptyIterator();
return Iterators.singletonIterator(rangeTombstoneWithNewBounds(start, s, e));
}
return new AbstractIterator()
{
private int idx = start;
protected RangeTombstone computeNext()
{
if (idx < 0 || idx < finish)
return endOfData();
// We want to make sure the range are stricly included within the queried slice as this
// make it easier to combine things when iterator over successive slices. This means that
// for the first and last range we might have to "cut" the range returned.
if (idx == start && comparator.compare(slice.end(), ends[idx]) < 0)
return rangeTombstoneWithNewEnd(idx--, slice.end());
if (idx == finish && comparator.compare(starts[idx], slice.start()) < 0)
return rangeTombstoneWithNewStart(idx--, slice.start());
return rangeTombstone(idx--);
}
};
}
@Override
public boolean equals(Object o)
{
if(!(o instanceof RangeTombstoneList))
return false;
RangeTombstoneList that = (RangeTombstoneList)o;
if (size != that.size)
return false;
for (int i = 0; i < size; i++)
{
if (!starts[i].equals(that.starts[i]))
return false;
if (!ends[i].equals(that.ends[i]))
return false;
if (markedAts[i] != that.markedAts[i])
return false;
if (delTimesUnsignedIntegers[i] != that.delTimesUnsignedIntegers[i])
return false;
}
return true;
}
@Override
public final int hashCode()
{
int result = size;
for (int i = 0; i < size; i++)
{
result += starts[i].hashCode() + ends[i].hashCode();
result += (int)(markedAts[i] ^ (markedAts[i] >>> 32));
result += delTimesUnsignedIntegers[i];
}
return result;
}
private static void copyArrays(RangeTombstoneList src, RangeTombstoneList dst)
{
dst.grow(src.size);
System.arraycopy(src.starts, 0, dst.starts, 0, src.size);
System.arraycopy(src.ends, 0, dst.ends, 0, src.size);
System.arraycopy(src.markedAts, 0, dst.markedAts, 0, src.size);
System.arraycopy(src.delTimesUnsignedIntegers, 0, dst.delTimesUnsignedIntegers, 0, src.size);
dst.size = src.size;
dst.boundaryHeapSize = src.boundaryHeapSize;
}
/*
* Inserts a new element starting at index i. This method assumes that:
* ends[i-1] <= start < ends[i]
* (note that start can be equal to ends[i-1] in the case where we have a boundary, i.e. for instance
* ends[i-1] is the exclusive end of X and start is the inclusive start of X).
*
* A RangeTombstoneList is a list of range [s_0, e_0]...[s_n, e_n] such that:
* - s_i is a start bound and e_i is a end bound
* - s_i < e_i
* - e_i <= s_i+1
* Basically, range are non overlapping and in order.
*/
private void insertFrom(int i, ClusteringBound start, ClusteringBound end, long markedAt, int delTimeUnsignedInternal)
{
while (i < size)
{
assert start.isStart() && end.isEnd();
assert i == 0 || comparator.compare(ends[i-1], start) <= 0;
assert comparator.compare(start, ends[i]) < 0;
if (Slice.isEmpty(comparator, start, end))
return;
// Do we overwrite the current element?
if (markedAt > markedAts[i])
{
// We do overwrite.
// First deal with what might come before the newly added one.
if (comparator.compare(starts[i], start) < 0)
{
ClusteringBound newEnd = start.invert();
if (!Slice.isEmpty(comparator, starts[i], newEnd))
{
addInternal(i, starts[i], newEnd, markedAts[i], delTimesUnsignedIntegers[i]);
i++;
setInternal(i, start, ends[i], markedAts[i], delTimesUnsignedIntegers[i]);
}
}
// now, start <= starts[i]
// Does the new element stops before the current one,
int endCmp = comparator.compare(end, starts[i]);
if (endCmp < 0)
{
// Here start <= starts[i] and end < starts[i]
// This means the current element is before the current one.
addInternal(i, start, end, markedAt, delTimeUnsignedInternal);
return;
}
// Do we overwrite the current element fully?
int cmp = comparator.compare(ends[i], end);
if (cmp <= 0)
{
// We do overwrite fully:
// update the current element until it's end and continue on with the next element (with the new inserted start == current end).
// If we're on the last element, or if we stop before the next start, we set the current element and are done
// Note that the comparison below is inclusive: if a end equals a start, this means they form a boundary, or
// in other words that they are for the same element but one is inclusive while the other exclusive. In which case we know
// we're good with the next element
if (i == size-1 || comparator.compare(end, starts[i+1]) <= 0)
{
setInternal(i, start, end, markedAt, delTimeUnsignedInternal);
return;
}
setInternal(i, start, starts[i+1].invert(), markedAt, delTimeUnsignedInternal);
start = starts[i+1];
i++;
}
else
{
// We don't overwrite fully. Insert the new interval, and then update the now next
// one to reflect the not overwritten parts. We're then done.
addInternal(i, start, end, markedAt, delTimeUnsignedInternal);
i++;
ClusteringBound newStart = end.invert();
if (!Slice.isEmpty(comparator, newStart, ends[i]))
{
setInternal(i, newStart, ends[i], markedAts[i], delTimesUnsignedIntegers[i]);
}
return;
}
}
else
{
// we don't overwrite the current element
// If the new interval starts before the current one, insert that new interval
if (comparator.compare(start, starts[i]) < 0)
{
// If we stop before the start of the current element, just insert the new interval and we're done;
// otherwise insert until the beginning of the current element
if (comparator.compare(end, starts[i]) <= 0)
{
addInternal(i, start, end, markedAt, delTimeUnsignedInternal);
return;
}
ClusteringBound newEnd = starts[i].invert();
if (!Slice.isEmpty(comparator, start, newEnd))
{
addInternal(i, start, newEnd, markedAt, delTimeUnsignedInternal);
i++;
}
}
// After that, we're overwritten on the current element but might have
// some residual parts after ...
// ... unless we don't extend beyond it.
if (comparator.compare(end, ends[i]) <= 0)
return;
start = ends[i].invert();
i++;
}
}
// If we got there, then just insert the remainder at the end
addInternal(i, start, end, markedAt, delTimeUnsignedInternal);
}
private int capacity()
{
return starts.length;
}
/*
* Adds the new tombstone at index i, growing and/or moving elements to make room for it.
*/
private void addInternal(int i, ClusteringBound start, ClusteringBound end, long markedAt, int delTimeUnsignedInteger)
{
assert i >= 0;
if (size == capacity())
growToFree(i);
else if (i < size)
moveElements(i);
setInternal(i, start, end, markedAt, delTimeUnsignedInteger);
size++;
}
/*
* Grow the arrays, leaving index i "free" in the process.
*/
private void growToFree(int i)
{
// Introduce getRangeTombstoneResizeFactor
int newLength = (int) Math.ceil(capacity() * DatabaseDescriptor.getRangeTombstoneListGrowthFactor());
// Fallback to the original calculation if the newLength calculated from the resize factor is not valid.
if (newLength <= capacity())
newLength = ((capacity() * 3) / 2) + 1;
grow(i, newLength);
}
/*
* Grow the arrays to match newLength capacity.
*/
private void grow(int newLength)
{
if (capacity() < newLength)
grow(-1, newLength);
}
private void grow(int i, int newLength)
{
starts = grow(starts, size, newLength, i);
ends = grow(ends, size, newLength, i);
markedAts = grow(markedAts, size, newLength, i);
delTimesUnsignedIntegers = grow(delTimesUnsignedIntegers, size, newLength, i);
}
private static ClusteringBound[] grow(ClusteringBound[] a, int size, int newLength, int i)
{
if (i < 0 || i >= size)
return Arrays.copyOf(a, newLength);
ClusteringBound[] newA = new ClusteringBound[newLength];
System.arraycopy(a, 0, newA, 0, i);
System.arraycopy(a, i, newA, i+1, size - i);
return newA;
}
private static long[] grow(long[] a, int size, int newLength, int i)
{
if (i < 0 || i >= size)
return Arrays.copyOf(a, newLength);
long[] newA = new long[newLength];
System.arraycopy(a, 0, newA, 0, i);
System.arraycopy(a, i, newA, i+1, size - i);
return newA;
}
private static int[] grow(int[] a, int size, int newLength, int i)
{
if (i < 0 || i >= size)
return Arrays.copyOf(a, newLength);
int[] newA = new int[newLength];
System.arraycopy(a, 0, newA, 0, i);
System.arraycopy(a, i, newA, i+1, size - i);
return newA;
}
/*
* Move elements so that index i is "free", assuming the arrays have at least one free slot at the end.
*/
private void moveElements(int i)
{
if (i >= size)
return;
System.arraycopy(starts, i, starts, i+1, size - i);
System.arraycopy(ends, i, ends, i+1, size - i);
System.arraycopy(markedAts, i, markedAts, i+1, size - i);
System.arraycopy(delTimesUnsignedIntegers, i, delTimesUnsignedIntegers, i+1, size - i);
// we set starts[i] to null to indicate the position is now empty, so that we update boundaryHeapSize
// when we set it
starts[i] = null;
}
private void setInternal(int i, ClusteringBound start, ClusteringBound end, long markedAt, int delTimeUnsignedInteger)
{
if (starts[i] != null)
boundaryHeapSize -= starts[i].unsharedHeapSize() + ends[i].unsharedHeapSize();
starts[i] = start;
ends[i] = end;
markedAts[i] = markedAt;
delTimesUnsignedIntegers[i] = delTimeUnsignedInteger;
boundaryHeapSize += start.unsharedHeapSize() + end.unsharedHeapSize();
}
@Override
public long unsharedHeapSize()
{
return EMPTY_SIZE
+ boundaryHeapSize
+ ObjectSizes.sizeOfArray(starts)
+ ObjectSizes.sizeOfArray(ends)
+ ObjectSizes.sizeOfArray(markedAts)
+ ObjectSizes.sizeOfArray(delTimesUnsignedIntegers);
}
}