Introduce a sparse HyperLogLogPlusPlus class for cloning and serializing low cardinality buckets (#62480) (#62520)

Reduces the memory footprint of an HLL++ structure that uses Linear counting when cloning or deserialising the data structure.

server/src/main/java/org/elasticsearch/search/aggregations/metrics/AbstractHyperLogLog.java

@@ -784,17 +784,6 @@ public abstract class AbstractHyperLogLog extends AbstractCardinalityAlgorithm {
         addRunLen(bucketOrd, index, runLen);
     }
 
-    public void merge(long thisBucketOrd, AbstractHyperLogLog other, long otherBucketOrd) {
-        if (p != other.p) {
-            throw new IllegalArgumentException();
-        }
-        RunLenIterator iterator = other.getRunLens(otherBucketOrd);
-        for (int i = 0; i < m; ++i) {
-            iterator.next();
-            addRunLen(thisBucketOrd, i, iterator.value());
-        }
-    }
-
     static long index(long hash, int p) {
         return hash >>> (64 - p);
     }

server/src/main/java/org/elasticsearch/search/aggregations/metrics/AbstractHyperLogLogPlusPlus.java

@@ -0,0 +1,154 @@
+/*
+ * Licensed to Elasticsearch under one or more contributor
+ * license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright
+ * ownership. Elasticsearch licenses this file 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.elasticsearch.search.aggregations.metrics;
+
+import org.elasticsearch.common.io.stream.StreamInput;
+import org.elasticsearch.common.io.stream.StreamOutput;
+import org.elasticsearch.common.lease.Releasable;
+import org.elasticsearch.common.util.BigArrays;
+
+import java.io.IOException;
+import java.util.HashMap;
+import java.util.HashSet;
+import java.util.Map;
+import java.util.Objects;
+import java.util.Set;
+
+/**
+ * Base class for HLL++ algorithms.
+ *
+ * It contains methods for cloning and serializing the data structure.
+ */
+public abstract class AbstractHyperLogLogPlusPlus extends AbstractCardinalityAlgorithm implements Releasable {
+
+    public static final boolean LINEAR_COUNTING = false;
+    public static final boolean HYPERLOGLOG = true;
+
+    public AbstractHyperLogLogPlusPlus(int precision) {
+        super(precision);
+    }
+
+    /** Algorithm used in the given bucket */
+    protected abstract boolean getAlgorithm(long bucketOrd);
+
+    /** Get linear counting algorithm */
+    protected abstract AbstractLinearCounting.HashesIterator getLinearCounting(long bucketOrd);
+
+    /** Get HyperLogLog algorithm */
+    protected abstract AbstractHyperLogLog.RunLenIterator getHyperLogLog(long bucketOrd);
+
+    /** Get the number of data structures */
+    public abstract long maxOrd();
+
+    /** Collect a value in the given bucket */
+    public abstract void collect(long bucketOrd, long hash);
+
+
+    /** Clone the data structure at the given bucket */
+    public AbstractHyperLogLogPlusPlus clone(long bucketOrd, BigArrays bigArrays) {
+        if (getAlgorithm(bucketOrd) == LINEAR_COUNTING) {
+            // we use a sparse structure for linear counting
+            AbstractLinearCounting.HashesIterator iterator = getLinearCounting(bucketOrd);
+            int size = Math.toIntExact(iterator.size());
+            HyperLogLogPlusPlusSparse clone = new HyperLogLogPlusPlusSparse(precision(), bigArrays, size, 1);
+            while (iterator.next()) {
+                clone.addEncoded(0, iterator.value());
+            }
+            return clone;
+        } else {
+            HyperLogLogPlusPlus clone = new HyperLogLogPlusPlus(precision(), bigArrays, 1);
+            clone.merge(0, this, bucketOrd);
+            return clone;
+        }
+    }
+
+    private Object getComparableData(long bucketOrd) {
+        if (getAlgorithm(bucketOrd) == LINEAR_COUNTING) {
+            Set<Integer> values = new HashSet<>();
+            AbstractLinearCounting.HashesIterator iteratorValues = getLinearCounting(bucketOrd);
+            while (iteratorValues.next()) {
+                values.add(iteratorValues.value());
+            }
+            return values;
+        } else {
+            Map<Byte, Integer> values = new HashMap<>();
+            AbstractHyperLogLog.RunLenIterator iterator = getHyperLogLog(bucketOrd);
+            while (iterator.next()) {
+                byte runLength = iterator.value();
+                Integer numOccurances = values.get(runLength);
+                if (numOccurances == null) {
+                    values.put(runLength, 1);
+                } else {
+                    values.put(runLength, numOccurances + 1);
+                }
+            }
+            return values;
+        }
+    }
+
+    public void writeTo(long bucket, StreamOutput out) throws IOException {
+        out.writeVInt(precision());
+        if (getAlgorithm(bucket) == LINEAR_COUNTING) {
+            out.writeBoolean(LINEAR_COUNTING);
+            AbstractLinearCounting.HashesIterator hashes = getLinearCounting(bucket);
+            out.writeVLong(hashes.size());
+            while (hashes.next()) {
+                out.writeInt(hashes.value());
+            }
+        } else {
+            out.writeBoolean(HYPERLOGLOG);
+            AbstractHyperLogLog.RunLenIterator iterator = getHyperLogLog(bucket);
+            while (iterator.next()){
+                out.writeByte(iterator.value());
+            }
+        }
+    }
+
+    public static AbstractHyperLogLogPlusPlus readFrom(StreamInput in, BigArrays bigArrays) throws IOException {
+        final int precision = in.readVInt();
+        final boolean algorithm = in.readBoolean();
+        if (algorithm == LINEAR_COUNTING) {
+            // we use a sparse structure for linear counting
+            final long size = in.readVLong();
+            HyperLogLogPlusPlusSparse counts  = new HyperLogLogPlusPlusSparse(precision, bigArrays, Math.toIntExact(size), 1);
+            for (long i = 0; i < size; ++i) {
+                counts.addEncoded(0, in.readInt());
+            }
+            return counts;
+        } else {
+            HyperLogLogPlusPlus counts = new HyperLogLogPlusPlus(precision, bigArrays, 1);
+            final int registers = 1 << precision;
+            for (int i = 0; i < registers; ++i) {
+                counts.addRunLen(0, i, in.readByte());
+            }
+            return counts;
+        }
+    }
+
+    public boolean equals(long thisBucket, AbstractHyperLogLogPlusPlus other, long otherBucket) {
+        return Objects.equals(precision(), other.precision())
+            && Objects.equals(getAlgorithm(thisBucket), other.getAlgorithm(otherBucket))
+            && Objects.equals(getComparableData(thisBucket), other.getComparableData(otherBucket));
+    }
+
+    public int hashCode(long bucket) {
+        return Objects.hash(precision(), getAlgorithm(bucket), getComparableData(bucket));
+    }
+}

server/src/main/java/org/elasticsearch/search/aggregations/metrics/AbstractLinearCounting.java

@@ -59,6 +59,7 @@ public abstract class AbstractLinearCounting extends AbstractCardinalityAlgorith
         return addEncoded(bucketOrd, k);
     }
 
+    @Override
     public long cardinality(long bucketOrd) {
         final long m = 1 << P2;
         final long v = m - size(bucketOrd);
@@ -92,7 +93,7 @@ public abstract class AbstractLinearCounting extends AbstractCardinalityAlgorith
         /**
          * number of elements in the iterator
          */
-        long size();
+        int size();
 
         /**
          * Moves the iterator to the next element if it exists.

server/src/main/java/org/elasticsearch/search/aggregations/metrics/CardinalityAggregator.java

@@ -157,13 +157,12 @@ public class CardinalityAggregator extends NumericMetricsAggregator.SingleValue
 
     @Override
     public InternalAggregation buildAggregation(long owningBucketOrdinal) {
-        if (counts == null || owningBucketOrdinal >= counts.maxBucket() || counts.cardinality(owningBucketOrdinal) == 0) {
+        if (counts == null || owningBucketOrdinal >= counts.maxOrd() || counts.cardinality(owningBucketOrdinal) == 0) {
             return buildEmptyAggregation();
         }
         // We need to build a copy because the returned Aggregation needs remain usable after
         // this Aggregator (and its HLL++ counters) is released.
-        HyperLogLogPlusPlus copy = new HyperLogLogPlusPlus(precision, BigArrays.NON_RECYCLING_INSTANCE, 1);
+        AbstractHyperLogLogPlusPlus copy = counts.clone(owningBucketOrdinal, BigArrays.NON_RECYCLING_INSTANCE);
-        copy.merge(0, counts, owningBucketOrdinal);
         return new InternalCardinality(name, copy, metadata());
     }
 

server/src/main/java/org/elasticsearch/search/aggregations/metrics/HyperLogLogPlusPlus.java

@@ -21,8 +21,6 @@ package org.elasticsearch.search.aggregations.metrics;
 
 import org.apache.lucene.util.BytesRef;
 import org.apache.lucene.util.packed.PackedInts;
-import org.elasticsearch.common.io.stream.StreamInput;
-import org.elasticsearch.common.io.stream.StreamOutput;
 import org.elasticsearch.common.lease.Releasable;
 import org.elasticsearch.common.lease.Releasables;
 import org.elasticsearch.common.util.BigArrays;
@@ -31,14 +29,8 @@ import org.elasticsearch.common.util.ByteArray;
 import org.elasticsearch.common.util.ByteUtils;
 import org.elasticsearch.common.util.IntArray;
 
-import java.io.IOException;
 import java.nio.ByteBuffer;
 import java.nio.ByteOrder;
-import java.util.HashMap;
-import java.util.HashSet;
-import java.util.Map;
-import java.util.Objects;
-import java.util.Set;
 
 /**
  * Hyperloglog++ counter, implemented based on pseudo code from
@@ -56,11 +48,10 @@ import java.util.Set;
  *
  * It supports storing several HyperLogLogPlusPlus structures which are identified by a bucket number.
  */
-public final class HyperLogLogPlusPlus implements Releasable {
+public final class HyperLogLogPlusPlus extends AbstractHyperLogLogPlusPlus {
 
     private static final float MAX_LOAD_FACTOR = 0.75f;
-    private static final boolean LINEAR_COUNTING = false;
+
-    private static final boolean HYPERLOGLOG = true;
     public static final int DEFAULT_PRECISION = 14;
 
     private final BitArray algorithm;
@@ -85,35 +76,103 @@ public final class HyperLogLogPlusPlus implements Releasable {
         return 1L << precision;
     }
 
-
     public HyperLogLogPlusPlus(int precision, BigArrays bigArrays, long initialBucketCount) {
+        super(precision);
         hll = new HyperLogLog(bigArrays, initialBucketCount, precision);
         lc = new LinearCounting(bigArrays, initialBucketCount, precision, hll);
         algorithm = new BitArray(1, bigArrays);
     }
 
-    public int precision() {
+    @Override
-        return hll.precision();
+    public long maxOrd() {
-    }
-
-    public long maxBucket() {
         return hll.runLens.size() >>> hll.precision();
     }
 
-    public void merge(long thisBucket, HyperLogLogPlusPlus other, long otherBucket) {
+    @Override
+    public long cardinality(long bucketOrd) {
+        if (getAlgorithm(bucketOrd) == LINEAR_COUNTING) {
+            return lc.cardinality(bucketOrd);
+        } else {
+            return hll.cardinality(bucketOrd);
+        }
+    }
+
+    @Override
+    protected boolean getAlgorithm(long bucketOrd) {
+        return algorithm.get(bucketOrd);
+    }
+
+    @Override
+    protected AbstractLinearCounting.HashesIterator getLinearCounting(long bucketOrd) {
+        return lc.values(bucketOrd);
+    }
+
+    @Override
+    protected AbstractHyperLogLog.RunLenIterator getHyperLogLog(long bucketOrd) {
+        return hll.getRunLens(bucketOrd);
+    }
+
+    @Override
+    public void collect(long bucket, long hash) {
+        hll.ensureCapacity(bucket + 1);
+        if (algorithm.get(bucket) == LINEAR_COUNTING) {
+            final int newSize = lc.collect(bucket, hash);
+            if (newSize > lc.threshold) {
+                upgradeToHll(bucket);
+            }
+        } else {
+            hll.collect(bucket, hash);
+        }
+    }
+
+    @Override
+    public void close() {
+        Releasables.close(algorithm, hll, lc);
+    }
+
+    protected void addRunLen(long bucketOrd, int register, int runLen) {
+        if (algorithm.get(bucketOrd) == LINEAR_COUNTING) {
+            upgradeToHll(bucketOrd);
+        }
+        hll.addRunLen(0, register, runLen);
+    }
+
+    void upgradeToHll(long bucketOrd) {
+        hll.ensureCapacity(bucketOrd + 1);
+        final AbstractLinearCounting.HashesIterator hashes = lc.values(bucketOrd);
+        // We need to copy values into an arrays as we will override
+        // the values on the buffer
+        final IntArray values = lc.bigArrays.newIntArray(hashes.size());
+        try {
+            int i = 0;
+            while (hashes.next()) {
+                values.set(i++, hashes.value());
+            }
+            assert i == hashes.size();
+            hll.reset(bucketOrd);
+            for (long j = 0; j < values.size(); ++j) {
+                final int encoded = values.get(j);
+                hll.collectEncoded(bucketOrd, encoded);
+            }
+            algorithm.set(bucketOrd);
+        } finally {
+            Releasables.close(values);
+        }
+    }
+
+    public void merge(long thisBucket, AbstractHyperLogLogPlusPlus other, long otherBucket) {
         if (precision() != other.precision()) {
             throw new IllegalArgumentException();
         }
         hll.ensureCapacity(thisBucket + 1);
-        if (other.algorithm.get(otherBucket) == LINEAR_COUNTING) {
+        if (other.getAlgorithm(otherBucket) == LINEAR_COUNTING) {
-            merge(thisBucket, other.lc, otherBucket);
+            merge(thisBucket, other.getLinearCounting(otherBucket));
         } else {
-            merge(thisBucket, other.hll, otherBucket);
+            merge(thisBucket, other.getHyperLogLog(otherBucket));
         }
     }
 
-    private void merge(long thisBucket, AbstractLinearCounting other, long otherBucket) {
+    private void merge(long thisBucket, AbstractLinearCounting.HashesIterator values) {
-        final AbstractLinearCounting.HashesIterator values = other.values(otherBucket);
         while (values.next()) {
             final int encoded = values.value();
             if (algorithm.get(thisBucket) == LINEAR_COUNTING) {
@@ -127,124 +186,23 @@ public final class HyperLogLogPlusPlus implements Releasable {
         }
     }
 
-    private void merge(long thisBucket, AbstractHyperLogLog other, long otherBucket) {
+    private void merge(long thisBucket, AbstractHyperLogLog.RunLenIterator runLens) {
         if (algorithm.get(thisBucket) != HYPERLOGLOG) {
             upgradeToHll(thisBucket);
         }
-        hll.merge(thisBucket, other, otherBucket);
+        for (int i = 0; i < hll.m; ++i) {
+            runLens.next();
+            hll.addRunLen(thisBucket, i, runLens.value());
         }
-
-    public void collect(long bucket, long hash) {
-        hll.ensureCapacity(bucket + 1);
-        if (algorithm.get(bucket) == LINEAR_COUNTING) {
-            final int newSize = lc.collect(bucket, hash);
-            if (newSize > lc.threshold) {
-                upgradeToHll(bucket);
-            }
-        } else {
-            hll.collect(bucket, hash);
-        }
-    }
-
-    public long cardinality(long bucket) {
-        if (algorithm.get(bucket) == LINEAR_COUNTING) {
-            return lc.cardinality(bucket);
-        } else {
-            return hll.cardinality(bucket);
-        }
-    }
-
-    void upgradeToHll(long bucket) {
-        hll.ensureCapacity(bucket + 1);
-        final AbstractLinearCounting.HashesIterator hashes = lc.values(bucket);
-        // We need to copy values into an arrays as we will override
-        // the values on the buffer
-        final IntArray values = lc.bigArrays.newIntArray(hashes.size());
-        try {
-            int i = 0;
-            while (hashes.next()) {
-                values.set(i++, hashes.value());
-            }
-            assert i == hashes.size();
-            hll.reset(bucket);
-            for (long j = 0; j < values.size(); ++j) {
-                final int encoded = values.get(j);
-                hll.collectEncoded(bucket, encoded);
-            }
-            algorithm.set(bucket);
-        } finally {
-            Releasables.close(values);
-        }
-    }
-
-    @Override
-    public void close() {
-        Releasables.close(algorithm, hll, lc);
-    }
-
-    private Object getComparableData(long bucket) {
-        if (algorithm.get(bucket) == LINEAR_COUNTING) {
-            return lc.getComparableData(bucket);
-        } else {
-            return hll.getComparableData(bucket);
-        }
-    }
-
-    public int hashCode(long bucket) {
-        return Objects.hash(precision(), algorithm.get(bucket), getComparableData(bucket));
-    }
-
-    public boolean equals(long bucket, HyperLogLogPlusPlus other) {
-        return Objects.equals(precision(), other.precision())
-            && Objects.equals(algorithm.get(bucket), other.algorithm.get(bucket))
-            && Objects.equals(getComparableData(bucket), other.getComparableData(bucket));
-    }
-
-    public void writeTo(long bucket, StreamOutput out) throws IOException {
-        out.writeVInt(precision());
-        if (algorithm.get(bucket) == LINEAR_COUNTING) {
-            out.writeBoolean(LINEAR_COUNTING);
-            AbstractLinearCounting.HashesIterator hashes = lc.values(bucket);
-            out.writeVLong(hashes.size());
-            while (hashes.next()) {
-                out.writeInt(hashes.value());
-            }
-        } else {
-            out.writeBoolean(HYPERLOGLOG);
-            AbstractHyperLogLog.RunLenIterator iterator = hll.getRunLens(bucket);
-            while (iterator.next()){
-                out.writeByte(iterator.value());
-            }
-        }
-    }
-
-    public static HyperLogLogPlusPlus readFrom(StreamInput in, BigArrays bigArrays) throws IOException {
-        final int precision = in.readVInt();
-        HyperLogLogPlusPlus counts = new HyperLogLogPlusPlus(precision, bigArrays, 1);
-        final boolean algorithm = in.readBoolean();
-        if (algorithm == LINEAR_COUNTING) {
-            counts.algorithm.clear(0);
-            final long size = in.readVLong();
-            for (long i = 0; i < size; ++i) {
-                final int encoded = in.readInt();
-                counts.lc.addEncoded(0, encoded);
-            }
-        } else {
-            counts.algorithm.set(0);
-            for (int i = 0; i < counts.hll.m; ++i) {
-                counts.hll.addRunLen(0, i, in.readByte());
-            }
-        }
-        return counts;
     }
 
     private static class HyperLogLog extends AbstractHyperLogLog implements Releasable {
-
         private final BigArrays bigArrays;
         private final HyperLogLogIterator iterator;
         // array for holding the runlens.
         private ByteArray runLens;
 
+
         HyperLogLog(BigArrays bigArrays, long initialBucketCount, int precision) {
             super(precision);
             this.runLens =  bigArrays.newByteArray(initialBucketCount << precision);
@@ -268,20 +226,6 @@ public final class HyperLogLogPlusPlus implements Releasable {
             runLens.fill(bucketOrd << p, (bucketOrd << p) + m, (byte) 0);
         }
 
-        protected Object getComparableData(long bucketOrd) {
-            Map<Byte, Integer> values = new HashMap<>();
-            for (long i = 0; i < runLens.size(); i++) {
-                byte runLength = runLens.get((bucketOrd << p) + i);
-                Integer numOccurances = values.get(runLength);
-                if (numOccurances == null) {
-                    values.put(runLength, 1);
-                } else {
-                    values.put(runLength, numOccurances + 1);
-                }
-            }
-            return values;
-        }
-
         protected void ensureCapacity(long numBuckets) {
             runLens = bigArrays.grow(runLens, numBuckets << p);
         }
@@ -296,8 +240,8 @@ public final class HyperLogLogPlusPlus implements Releasable {
 
         private final HyperLogLog hll;
         private final int m, p;
-        private int pos;
+        int pos;
-        private long start;
+        long start;
         private byte value;
 
         HyperLogLogIterator(HyperLogLog hll, int p, int m) {
@@ -386,15 +330,6 @@ public final class HyperLogLogPlusPlus implements Releasable {
             return iterator;
         }
 
-        protected Object getComparableData(long bucketOrd) {
-            Set<Integer> values = new HashSet<>();
-            HashesIterator iteratorValues = values(bucketOrd);
-            while (iteratorValues.next()) {
-                values.add(iteratorValues.value());
-            }
-            return values;
-        }
-
         private long index(long bucketOrd, int index) {
             return (bucketOrd << p) + (index << 2);
         }
@@ -430,8 +365,8 @@ public final class HyperLogLogPlusPlus implements Releasable {
 
         private final LinearCounting lc;
         private final int capacity;
-        private int pos;
+        private int pos, size;
-        private long size, bucketOrd;
+        private long bucketOrd;
         private int value;
 
         LinearCountingIterator(LinearCounting lc, int capacity) {
@@ -439,14 +374,14 @@ public final class HyperLogLogPlusPlus implements Releasable {
             this.capacity = capacity;
         }
 
-        void reset(long bucketOrd, long size) {
+        void reset(long bucketOrd, int size) {
             this.bucketOrd = bucketOrd;
             this.size = size;
             this.pos = size == 0 ? capacity : 0;
         }
 
         @Override
-        public long size() {
+        public int size() {
             return size;
         }
 

server/src/main/java/org/elasticsearch/search/aggregations/metrics/HyperLogLogPlusPlusSparse.java

@@ -0,0 +1,205 @@
+/*
+ * Licensed to Elasticsearch under one or more contributor
+ * license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright
+ * ownership. Elasticsearch licenses this file 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.elasticsearch.search.aggregations.metrics;
+
+import org.elasticsearch.common.lease.Releasable;
+import org.elasticsearch.common.lease.Releasables;
+import org.elasticsearch.common.util.BigArrays;
+import org.elasticsearch.common.util.IntArray;
+
+/**
+ * AbstractHyperLogLogPlusPlus instance that only supports linear counting. The maximum number of hashes supported
+ * by the structure is determined at construction time.
+ *
+ * This structure expects all the added values to be distinct and therefore there are no checks
+ * if an element has been previously added.
+ */
+final class HyperLogLogPlusPlusSparse extends AbstractHyperLogLogPlusPlus implements Releasable {
+
+    private final LinearCounting lc;
+
+    /**
+     * Create an sparse HLL++ algorithm where capacity is the maximum number of hashes this structure can hold
+     * per bucket.
+     */
+    HyperLogLogPlusPlusSparse(int precision, BigArrays bigArrays, int capacity, int initialSize) {
+        super(precision);
+        this.lc = new LinearCounting(precision, bigArrays, capacity, initialSize);
+    }
+
+    @Override
+    public long maxOrd() {
+        return lc.sizes.size();
+    }
+
+    @Override
+    public long cardinality(long bucketOrd) {
+        return lc.cardinality(bucketOrd);
+    }
+
+    @Override
+    protected boolean getAlgorithm(long bucketOrd) {
+        return LINEAR_COUNTING;
+    }
+
+    @Override
+    protected AbstractLinearCounting.HashesIterator getLinearCounting(long bucketOrd) {
+        return lc.values(bucketOrd);
+    }
+
+    @Override
+    protected AbstractHyperLogLog.RunLenIterator getHyperLogLog(long bucketOrd) {
+        throw new IllegalArgumentException("Implementation does not support HLL structures");
+    }
+
+    @Override
+    public void collect(long bucket, long hash) {
+        lc.collect(bucket, hash);
+    }
+
+    @Override
+    public void close() {
+        Releasables.close(lc);
+    }
+
+    protected void addEncoded(long bucket, int encoded) {
+        lc.addEncoded(bucket, encoded);
+    }
+
+    private static class LinearCounting extends AbstractLinearCounting implements Releasable {
+
+        private final int capacity;
+        private final BigArrays bigArrays;
+        private final LinearCountingIterator iterator;
+        // We are actually using HyperLogLog's runLens array but interpreting it as a hash set for linear counting.
+        // Number of elements stored.
+        private IntArray values;
+        private IntArray sizes;
+
+        LinearCounting(int p, BigArrays bigArrays, int capacity, int initialSize) {
+            super(p);
+            this.bigArrays = bigArrays;
+            this.capacity = capacity;
+            values = bigArrays.newIntArray(initialSize * capacity);
+            sizes = bigArrays.newIntArray(initialSize * capacity);
+            iterator = new LinearCountingIterator(this, capacity);
+        }
+
+        @Override
+        protected int addEncoded(long bucketOrd, int encoded) {
+            assert encoded != 0;
+            return set(bucketOrd, encoded);
+        }
+
+        @Override
+        protected int size(long bucketOrd) {
+            if (bucketOrd >= sizes.size()) {
+                return 0;
+            }
+            final int size = sizes.get(bucketOrd);
+            assert size == recomputedSize(bucketOrd);
+            return size;
+        }
+
+        @Override
+        protected HashesIterator values(long bucketOrd) {
+            iterator.reset(bucketOrd, size(bucketOrd));
+            return iterator;
+        }
+
+        private long index(long bucketOrd, int index) {
+            return (bucketOrd * capacity) + index;
+        }
+
+        private int get(long bucketOrd, int index) {
+            long globalIndex = index(bucketOrd, index);
+            if (values.size() < globalIndex) {
+                return 0;
+            }
+            return values.get(globalIndex);
+        }
+
+        private int set(long bucketOrd, int value) {
+            int size = size(bucketOrd);
+            if (size == 0) {
+                sizes = bigArrays.grow(sizes, bucketOrd + 1);
+                values = bigArrays.grow(values, (bucketOrd * capacity)  + capacity);
+            }
+            values.set(index(bucketOrd, size), value);
+            return sizes.increment(bucketOrd, 1);
+        }
+
+        private int recomputedSize(long bucketOrd) {
+            for (int i = 0; i < capacity; ++i) {
+                final int v = get(bucketOrd, i);
+                if (v == 0) {
+                    return i;
+                }
+            }
+            return capacity;
+        }
+
+        @Override
+        public void close() {
+            Releasables.close(values, sizes);
+        }
+    }
+
+    private static class LinearCountingIterator implements AbstractLinearCounting.HashesIterator {
+
+        private final LinearCounting lc;
+        private final int capacity;
+        long start;
+        long end;
+        private int value, size;
+        private long pos;
+
+        LinearCountingIterator(LinearCounting lc, int capacity) {
+            this.lc = lc;
+            this.capacity = capacity;
+        }
+
+        void reset(long bucketOrd, int size) {
+            this.start = bucketOrd * capacity;
+            this.size = size;
+            this.end = start + size;
+            this.pos = start;
+        }
+
+        @Override
+        public int size() {
+            return size;
+        }
+
+        @Override
+        public boolean next() {
+            if (pos < end) {
+               value = lc.values.get(pos++);
+               return true;
+            }
+            return false;
+        }
+
+        @Override
+        public int value() {
+            return value;
+        }
+    }
+}

server/src/main/java/org/elasticsearch/search/aggregations/metrics/InternalCardinality.java

@@ -32,9 +32,9 @@ import java.util.Map;
 import java.util.Objects;
 
 public final class InternalCardinality extends InternalNumericMetricsAggregation.SingleValue implements Cardinality {
-    private final HyperLogLogPlusPlus counts;
+    private final AbstractHyperLogLogPlusPlus counts;
 
-    InternalCardinality(String name, HyperLogLogPlusPlus counts, Map<String, Object> metadata) {
+    InternalCardinality(String name, AbstractHyperLogLogPlusPlus counts, Map<String, Object> metadata) {
         super(name, metadata);
         this.counts = counts;
     }
@@ -46,7 +46,7 @@ public final class InternalCardinality extends InternalNumericMetricsAggregation
         super(in);
         format = in.readNamedWriteable(DocValueFormat.class);
         if (in.readBoolean()) {
-            counts = HyperLogLogPlusPlus.readFrom(in, BigArrays.NON_RECYCLING_INSTANCE);
+            counts = AbstractHyperLogLogPlusPlus.readFrom(in, BigArrays.NON_RECYCLING_INSTANCE);
         } else {
             counts = null;
         }
@@ -78,34 +78,30 @@ public final class InternalCardinality extends InternalNumericMetricsAggregation
         return counts == null ? 0 : counts.cardinality(0);
     }
 
-    public HyperLogLogPlusPlus getCounts() {
+    public AbstractHyperLogLogPlusPlus getCounts() {
         return counts;
     }
 
     @Override
     public InternalAggregation reduce(List<InternalAggregation> aggregations, ReduceContext reduceContext) {
-        InternalCardinality reduced = null;
+        HyperLogLogPlusPlus reduced = null;
         for (InternalAggregation aggregation : aggregations) {
             final InternalCardinality cardinality = (InternalCardinality) aggregation;
             if (cardinality.counts != null) {
                 if (reduced == null) {
-                    reduced = new InternalCardinality(name, new HyperLogLogPlusPlus(cardinality.counts.precision(),
+                    reduced = new HyperLogLogPlusPlus(cardinality.counts.precision(),
-                            BigArrays.NON_RECYCLING_INSTANCE, 1), getMetadata());
+                        BigArrays.NON_RECYCLING_INSTANCE, 1);
                 }
-                reduced.merge(cardinality);
+                reduced.merge(0, cardinality.counts, 0);
             }
         }
 
         if (reduced == null) { // all empty
             return aggregations.get(0);
         } else {
-            return reduced;
+            return new InternalCardinality(name, reduced, getMetadata());
-        }
-    }
 
-    public void merge(InternalCardinality other) {
+        }
-        assert counts != null && other != null;
-        counts.merge(0, other.counts, 0);
     }
 
     @Override
@@ -127,10 +123,10 @@ public final class InternalCardinality extends InternalNumericMetricsAggregation
         if (super.equals(obj) == false) return false;
 
         InternalCardinality other = (InternalCardinality) obj;
-        return counts.equals(0, other.counts);
+        return counts.equals(0, other.counts, 0);
     }
 
-    HyperLogLogPlusPlus getState() {
+    AbstractHyperLogLogPlusPlus getState() {
         return counts;
     }
 }

server/src/test/java/org/elasticsearch/search/aggregations/metrics/HyperLogLogPlusPlusSparseTests.java

@@ -0,0 +1,78 @@
+/*
+ * Licensed to Elasticsearch under one or more contributor
+ * license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright
+ * ownership. Elasticsearch licenses this file 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.elasticsearch.search.aggregations.metrics;
+
+import com.carrotsearch.hppc.BitMixer;
+import org.elasticsearch.common.io.stream.BytesStreamOutput;
+import org.elasticsearch.common.util.BigArrays;
+import org.elasticsearch.test.ESTestCase;
+
+import java.io.IOException;
+
+import static org.elasticsearch.search.aggregations.metrics.AbstractHyperLogLog.MAX_PRECISION;
+import static org.elasticsearch.search.aggregations.metrics.AbstractHyperLogLog.MIN_PRECISION;
+
+public class HyperLogLogPlusPlusSparseTests extends ESTestCase {
+
+    public void testEquivalence() throws IOException {
+        final int p = randomIntBetween(MIN_PRECISION, MAX_PRECISION);
+        final HyperLogLogPlusPlus single = new HyperLogLogPlusPlus(p, BigArrays.NON_RECYCLING_INSTANCE, 0);
+        final int numBuckets = randomIntBetween(2, 100);
+        final int numValues = randomIntBetween(1, 100000);
+        final int maxValue = randomIntBetween(1, randomBoolean() ? 1000: 1000000);
+        for (int i = 0; i < numValues; ++i) {
+            final int n = randomInt(maxValue);
+            final long hash = BitMixer.mix64(n);
+            single.collect(randomInt(numBuckets), hash);
+        }
+        for (int i = 0; i < numBuckets; i++) {
+            // test clone
+            AbstractHyperLogLogPlusPlus clone = single.clone(i, BigArrays.NON_RECYCLING_INSTANCE);
+            if (single.getAlgorithm(i) == AbstractHyperLogLogPlusPlus.LINEAR_COUNTING) {
+                assertTrue(clone instanceof HyperLogLogPlusPlusSparse);
+            } else {
+                assertTrue(clone instanceof HyperLogLogPlusPlus);
+            }
+            checkEquivalence(single, i, clone, 0);
+            // test serialize
+            BytesStreamOutput out = new BytesStreamOutput();
+            single.writeTo(i, out);
+            clone = AbstractHyperLogLogPlusPlus.readFrom(out.bytes().streamInput(), BigArrays.NON_RECYCLING_INSTANCE);
+            if (single.getAlgorithm(i) == AbstractHyperLogLogPlusPlus.LINEAR_COUNTING) {
+                assertTrue(clone instanceof HyperLogLogPlusPlusSparse);
+            } else {
+                assertTrue(clone instanceof HyperLogLogPlusPlus);
+            }
+            checkEquivalence(single, i, clone, 0);
+            // test merge
+            final HyperLogLogPlusPlus merge = new HyperLogLogPlusPlus(p, BigArrays.NON_RECYCLING_INSTANCE, 0);
+            merge.merge(0, clone, 0);
+            checkEquivalence(merge, 0, clone, 0);
+        }
+    }
+
+    private void checkEquivalence(AbstractHyperLogLogPlusPlus first, int firstBucket,
+                                  AbstractHyperLogLogPlusPlus second, int secondBucket) {
+        assertEquals(first.hashCode(firstBucket), second.hashCode(secondBucket));
+        assertEquals(first.cardinality(firstBucket), second.cardinality(0));
+        assertTrue(first.equals(firstBucket, second, secondBucket));
+        assertTrue(second.equals(secondBucket, first, firstBucket));
+    }
+}

server/src/test/java/org/elasticsearch/search/aggregations/metrics/InternalCardinalityTests.java

@@ -90,7 +90,7 @@ public class InternalCardinalityTests extends InternalAggregationTestCase<Intern
     @Override
     protected InternalCardinality mutateInstance(InternalCardinality instance) {
         String name = instance.getName();
-        HyperLogLogPlusPlus state = instance.getState();
+        AbstractHyperLogLogPlusPlus state = instance.getState();
         Map<String, Object> metadata = instance.getMetadata();
         switch (between(0, 2)) {
         case 0:

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/cumulativecardinality/CumulativeCardinalityPipelineAggregator.java

@@ -16,6 +16,7 @@ import org.elasticsearch.search.aggregations.InternalMultiBucketAggregation;
 import org.elasticsearch.search.aggregations.bucket.MultiBucketsAggregation;
 import org.elasticsearch.search.aggregations.bucket.MultiBucketsAggregation.Bucket;
 import org.elasticsearch.search.aggregations.bucket.histogram.HistogramFactory;
+import org.elasticsearch.search.aggregations.metrics.AbstractHyperLogLogPlusPlus;
 import org.elasticsearch.search.aggregations.metrics.HyperLogLogPlusPlus;
 import org.elasticsearch.search.aggregations.metrics.InternalCardinality;
 import org.elasticsearch.search.aggregations.pipeline.AbstractPipelineAggregationBuilder;
@@ -68,7 +69,7 @@ public class CumulativeCardinalityPipelineAggregator extends PipelineAggregator
         try {
             long cardinality = 0;
             for (InternalMultiBucketAggregation.InternalBucket bucket : buckets) {
-                HyperLogLogPlusPlus bucketHll = resolveBucketValue(histo, bucket, bucketsPaths()[0]);
+                AbstractHyperLogLogPlusPlus bucketHll = resolveBucketValue(histo, bucket, bucketsPaths()[0]);
                 if (hll == null && bucketHll != null) {
                     // We have to create a new HLL because otherwise it will alter the
                     // existing cardinality sketch and bucket value
@@ -94,7 +95,7 @@ public class CumulativeCardinalityPipelineAggregator extends PipelineAggregator
         }
     }
 
-    private HyperLogLogPlusPlus resolveBucketValue(MultiBucketsAggregation agg,
+    private AbstractHyperLogLogPlusPlus resolveBucketValue(MultiBucketsAggregation agg,
                                                            InternalMultiBucketAggregation.InternalBucket bucket,
                                                            String aggPath) {
         List<String> aggPathsList = AggregationPath.parse(aggPath).getPathElementsAsStringList();