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A library for summarizing data in streams for which it is infeasible to store all events
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/*
* Copyright (C) 2012 Clearspring Technologies, Inc.
*
* Licensed 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 com.clearspring.analytics.stream.cardinality;
import java.io.ByteArrayInputStream;
import java.io.ByteArrayOutputStream;
import java.io.DataInput;
import java.io.DataInputStream;
import java.io.DataOutput;
import java.io.DataOutputStream;
import java.io.Externalizable;
import java.io.IOException;
import java.io.ObjectInput;
import java.io.ObjectInputStream;
import java.io.ObjectOutput;
import java.io.Serializable;
import com.clearspring.analytics.hash.MurmurHash;
import com.clearspring.analytics.util.Bits;
import com.clearspring.analytics.util.IBuilder;
/**
* Java implementation of HyperLogLog (HLL) algorithm from this paper:
*
* http://algo.inria.fr/flajolet/Publications/FlFuGaMe07.pdf
*
* HLL is an improved version of LogLog that is capable of estimating
* the cardinality of a set with accuracy = 1.04/sqrt(m) where
* m = 2^b. So we can control accuracy vs space usage by increasing
* or decreasing b.
*
* The main benefit of using HLL over LL is that it only requires 64%
* of the space that LL does to get the same accuracy.
*
* This implementation implements a single counter. If a large (millions)
* number of counters are required you may want to refer to:
*
* http://dsiutils.dsi.unimi.it/
*
* It has a more complex implementation of HLL that supports multiple counters
* in a single object, drastically reducing the java overhead from creating
* a large number of objects.
*
* This implementation leveraged a javascript implementation that Yammer has
* been working on:
*
* https://github.com/yammer/probablyjs
*
* Note that this implementation does not include the long range correction function
* defined in the original paper. Empirical evidence shows that the correction
* function causes more harm than good.
*
*
*
* Users have different motivations to use different types of hashing functions.
* Rather than try to keep up with all available hash functions and to remove
* the concern of causing future binary incompatibilities this class allows clients
* to offer the value in hashed int or long form. This way clients are free
* to change their hash function on their own time line. We recommend using Google's
* Guava Murmur3_128 implementation as it provides good performance and speed when
* high precision is required. In our tests the 32bit MurmurHash function included
* in this project is faster and produces better results than the 32 bit murmur3
* implementation google provides.
*
*/
public class HyperLogLog implements ICardinality, Serializable {
private final RegisterSet registerSet;
private final int log2m;
private final double alphaMM;
/**
* Create a new HyperLogLog instance using the specified standard deviation.
*
* @param rsd - the relative standard deviation for the counter.
* smaller values create counters that require more space.
*/
public HyperLogLog(double rsd) {
this(log2m(rsd));
}
private static int log2m(double rsd) {
return (int) (Math.log((1.106 / rsd) * (1.106 / rsd)) / Math.log(2));
}
private static double rsd(int log2m) {
return 1.106 / Math.sqrt(Math.exp(log2m * Math.log(2)));
}
private static void validateLog2m(int log2m) {
if (log2m < 0 || log2m > 30) {
throw new IllegalArgumentException("log2m argument is "
+ log2m + " and is outside the range [0, 30]");
}
}
/**
* Create a new HyperLogLog instance. The log2m parameter defines the accuracy of
* the counter. The larger the log2m the better the accuracy.
*
* accuracy = 1.04/sqrt(2^log2m)
*
* @param log2m - the number of bits to use as the basis for the HLL instance
*/
public HyperLogLog(int log2m) {
this(log2m, new RegisterSet(1 << log2m));
}
/**
* Creates a new HyperLogLog instance using the given registers. Used for unmarshalling a serialized
* instance and for merging multiple counters together.
*
* @param registerSet - the initial values for the register set
*/
@Deprecated
public HyperLogLog(int log2m, RegisterSet registerSet) {
validateLog2m(log2m);
this.registerSet = registerSet;
this.log2m = log2m;
int m = 1 << this.log2m;
alphaMM = getAlphaMM(log2m, m);
}
@Override
public boolean offerHashed(long hashedValue) {
// j becomes the binary address determined by the first b log2m of x
// j will be between 0 and 2^log2m
final int j = (int) (hashedValue >>> (Long.SIZE - log2m));
final int r = Long.numberOfLeadingZeros((hashedValue << this.log2m) | (1 << (this.log2m - 1)) + 1) + 1;
return registerSet.updateIfGreater(j, r);
}
@Override
public boolean offerHashed(int hashedValue) {
// j becomes the binary address determined by the first b log2m of x
// j will be between 0 and 2^log2m
final int j = hashedValue >>> (Integer.SIZE - log2m);
final int r = Integer.numberOfLeadingZeros((hashedValue << this.log2m) | (1 << (this.log2m - 1)) + 1) + 1;
return registerSet.updateIfGreater(j, r);
}
@Override
public boolean offer(Object o) {
final int x = MurmurHash.hash(o);
return offerHashed(x);
}
@Override
public long cardinality() {
double registerSum = 0;
int count = registerSet.count;
double zeros = 0.0;
for (int j = 0; j < registerSet.count; j++) {
int val = registerSet.get(j);
registerSum += 1.0 / (1 << val);
if (val == 0) {
zeros++;
}
}
double estimate = alphaMM * (1 / registerSum);
if (estimate <= (5.0 / 2.0) * count) {
// Small Range Estimate
return Math.round(linearCounting(count, zeros));
} else {
return Math.round(estimate);
}
}
@Override
public int sizeof() {
return registerSet.size * 4;
}
@Override
public byte[] getBytes() throws IOException {
ByteArrayOutputStream baos = new ByteArrayOutputStream();
DataOutput dos = new DataOutputStream(baos);
writeBytes(dos);
return baos.toByteArray();
}
private void writeBytes(DataOutput serializedByteStream) throws IOException {
serializedByteStream.writeInt(log2m);
serializedByteStream.writeInt(registerSet.size * 4);
for (int x : registerSet.readOnlyBits()) {
serializedByteStream.writeInt(x);
}
}
/**
* Add all the elements of the other set to this set.
*
* This operation does not imply a loss of precision.
*
* @param other A compatible Hyperloglog instance (same log2m)
* @throws CardinalityMergeException if other is not compatible
*/
public void addAll(HyperLogLog other) throws CardinalityMergeException {
if (this.sizeof() != other.sizeof()) {
throw new HyperLogLogMergeException("Cannot merge estimators of different sizes");
}
registerSet.merge(other.registerSet);
}
@Override
public ICardinality merge(ICardinality... estimators) throws CardinalityMergeException {
HyperLogLog merged = new HyperLogLog(log2m, new RegisterSet(this.registerSet.count));
merged.addAll(this);
if (estimators == null) {
return merged;
}
for (ICardinality estimator : estimators) {
if (!(estimator instanceof HyperLogLog)) {
throw new HyperLogLogMergeException("Cannot merge estimators of different class");
}
HyperLogLog hll = (HyperLogLog) estimator;
merged.addAll(hll);
}
return merged;
}
private Object writeReplace() {
return new SerializationHolder(this);
}
/**
* This class exists to support Externalizable semantics for
* HyperLogLog objects without having to expose a public
* constructor, public write/read methods, or pretend final
* fields aren't final.
*
* In short, Externalizable allows you to skip some of the more
* verbose meta-data default Serializable gets you, but still
* includes the class name. In that sense, there is some cost
* to this holder object because it has a longer class name. I
* imagine people who care about optimizing for that have their
* own work-around for long class names in general, or just use
* a custom serialization framework. Therefore we make no attempt
* to optimize that here (eg. by raising this from an inner class
* and giving it an unhelpful name).
*/
private static class SerializationHolder implements Externalizable {
HyperLogLog hyperLogLogHolder;
public SerializationHolder(HyperLogLog hyperLogLogHolder) {
this.hyperLogLogHolder = hyperLogLogHolder;
}
/**
* required for Externalizable
*/
public SerializationHolder() {
}
@Override
public void writeExternal(ObjectOutput out) throws IOException {
hyperLogLogHolder.writeBytes(out);
}
@Override
public void readExternal(ObjectInput in) throws IOException, ClassNotFoundException {
hyperLogLogHolder = Builder.build(in);
}
private Object readResolve() {
return hyperLogLogHolder;
}
}
public static class Builder implements IBuilder, Serializable {
private static final long serialVersionUID = -2567898469253021883L;
private final double rsd;
private transient int log2m;
/**
* Uses the given RSD percentage to determine how many bytes the constructed HyperLogLog will use.
*
* @deprecated Use {@link #withRsd(double)} instead. This builder's constructors did not match the (already
* themselves ambiguous) constructors of the HyperLogLog class, but there is no way to make them match without
* risking behavior changes downstream.
*/
@Deprecated
public Builder(double rsd) {
this.log2m = log2m(rsd);
validateLog2m(log2m);
this.rsd = rsd;
}
/** This constructor is private to prevent behavior change for ambiguous usages. (Legacy support). */
private Builder(int log2m) {
this.log2m = log2m;
validateLog2m(log2m);
this.rsd = rsd(log2m);
}
private void readObject(ObjectInputStream in) throws IOException, ClassNotFoundException {
in.defaultReadObject();
this.log2m = log2m(rsd);
}
@Override
public HyperLogLog build() {
return new HyperLogLog(log2m);
}
@Override
public int sizeof() {
int k = 1 << log2m;
return RegisterSet.getBits(k) * 4;
}
public static Builder withLog2m(int log2m) {
return new Builder(log2m);
}
public static Builder withRsd(double rsd) {
return new Builder(rsd);
}
public static HyperLogLog build(byte[] bytes) throws IOException {
ByteArrayInputStream bais = new ByteArrayInputStream(bytes);
return build(new DataInputStream(bais));
}
public static HyperLogLog build(DataInput serializedByteStream) throws IOException {
int log2m = serializedByteStream.readInt();
int byteArraySize = serializedByteStream.readInt();
return new HyperLogLog(log2m,
new RegisterSet(1 << log2m, Bits.getBits(serializedByteStream, byteArraySize)));
}
}
@SuppressWarnings("serial")
protected static class HyperLogLogMergeException extends CardinalityMergeException {
public HyperLogLogMergeException(String message) {
super(message);
}
}
protected static double getAlphaMM(final int p, final int m) {
// See the paper.
switch (p) {
case 4:
return 0.673 * m * m;
case 5:
return 0.697 * m * m;
case 6:
return 0.709 * m * m;
default:
return (0.7213 / (1 + 1.079 / m)) * m * m;
}
}
protected static double linearCounting(int m, double V) {
return m * Math.log(m / V);
}
}