it.unimi.dsi.util
Class IntHyperLogLogCounterArray

java.lang.Object
  it.unimi.dsi.util.IntHyperLogLogCounterArray

All Implemented Interfaces:

Serializable

public class IntHyperLogLogCounterArray
extends Object
implements Serializable

An array of approximate sets each represented using a HyperLogLog counter.

HyperLogLog counters represent the number of elements of a set in an approximate way. They have been introduced by Philippe Flajolet, Éric Fusy, Olivier Gandouet, and Freédeéric Meunier in “HyperLogLog: the analysis of a near-optimal cardinality estimation algorithm”, Proceedings of the 13th conference on analysis of algorithm (AofA 07), pages 127−146, 2007. They are an improvement over the basic idea of loglog counting, introduced by Marianne Durand and Philippe Flajolet in “Loglog counting of large cardinalities”, ESA 2003, 11th Annual European Symposium, volume 2832 of Lecture Notes in Computer Science, pages 605−617, Springer, 2003.

Each counter is composed by m registers, and each register is made of registerSize bits. The first number depends on the desired relative standard deviation, and its logarithm can be computed using log2NumberOfRegisters(double), whereas the second number depends on an upper bound on the number of distinct elements to be counted, and it can be computed using registerSize(long).

Actually, this class implements an array of counters. Each counter is completely independent, but they all use the same hash function. The reason for this design is that in our intended applications hundred of millions of counters are common, and the JVM overhead to create such a number of objects would be unbearable. This class allocates an array of LongArrayBitVectors, each containing CHUNK_SIZE registers, and can thus handle billions of billions of registers efficiently (in turn, this means being able to handle an array of millions of billions of high-precision counters).

When creating an instance, you can choose the size of the array (i.e., the number of counters) and the desired relative standard deviation (either explicitly or choosing the number of registers per counter). Then, you can add an element to a counter. At any time, you can count count (approximately) the number of distinct elements that have been added to a counter.

If you need to reuse this class multiple times, you can clear all registers, possibly setting a new seed. The seed is used to compute the hash function used by the HyperLogLog counters.

Author:

Paolo Boldi, Sebastiano Vigna

See Also:

Serialized Form

Field Summary

protected LongArrayBitVector[]	bitVector An array of bit vectors containing all registers.
static long	CHUNK_MASK The mask used to obtain an register offset in a chunk.
static int	CHUNK_SHIFT The logarithm of the maximum size in registers of a bit vector.
static long	CHUNK_SIZE The maximum size in registers of a bit vector.
protected int	counterShift The shift that selects the chunk corresponding to a counter.
protected int	counterSize The size in bits of each counter (registerSize * m).
protected int	log2m The logarithm of the number of registers per counter.
protected int	m The number of registers per counter.
protected int	mMinus1 The number of registers minus one.
protected LongBigList[]	registers registerSize-bit views of bitVector.
protected int	registerSize The size in bits of each register.
protected long	seed A seed for hashing.

Constructor Summary

IntHyperLogLogCounterArray(int arraySize, long n, double rsd)
Creates a new array of counters.

IntHyperLogLogCounterArray(int arraySize, long n, int log2m)
Creates a new array of counters.

IntHyperLogLogCounterArray(int arraySize, long n, int log2m, long seed)
Creates a new array of counters.

Method Summary

void	add(int k, int v) Adds an element to a counter.
protected int	chunk(int counter) Returns the chunk of a given counter.
void	clear() Clears all registers.
void	clear(long seed) Clears all registers and sets a new seed (e.g., using Util.randomSeed()).
double	count(int k) Estimates the number of distinct elements that have been added to a given counter so far.
protected double	count(long[] bits, long offset) Estimates the number of distinct elements that have been added to a given counter so far.
static int	log2NumberOfRegisters(double rsd) Returns the logarithm of the number of registers per counter that are necessary to attain a given relative standard deviation.
protected long	offset(int counter) Returns the bit offset of a given counter in its chunk.
LongBigList[]	registers() Returns the array of big lists of registers underlying this array of counters.
static int	registerSize(long n) Returns the register size in bits, given an upper bound on the number of distinct elements.
static double	relativeStandardDeviation(int log2m) Returns the relative standard deviation corresponding to a given logarithm of the number of registers per counter.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

CHUNK_SHIFT

public static final int CHUNK_SHIFT

The logarithm of the maximum size in registers of a bit vector.

See Also:

Constant Field Values

CHUNK_SIZE

public static final long CHUNK_SIZE

The maximum size in registers of a bit vector.

See Also:

Constant Field Values

CHUNK_MASK

public static final long CHUNK_MASK

The mask used to obtain an register offset in a chunk.

See Also:

Constant Field Values

bitVector

protected final LongArrayBitVector[] bitVector

An array of bit vectors containing all registers.

registers

protected final LongBigList[] registers

registerSize-bit views of bitVector.

log2m

protected final int log2m

The logarithm of the number of registers per counter.

m

protected final int m

The number of registers per counter.

mMinus1

protected final int mMinus1

The number of registers minus one.

registerSize

protected final int registerSize

The size in bits of each register.

counterSize

protected final int counterSize

The size in bits of each counter (registerSize * m).

counterShift

protected final int counterShift

The shift that selects the chunk corresponding to a counter.

seed

protected long seed

A seed for hashing.

Constructor Detail

IntHyperLogLogCounterArray

public IntHyperLogLogCounterArray(int arraySize,
                                  long n,
                                  double rsd)

Creates a new array of counters.

Parameters:

arraySize - the number of counters.

n - the expected number of elements.

rsd - the relative standard deviation.

IntHyperLogLogCounterArray

public IntHyperLogLogCounterArray(int arraySize,
                                  long n,
                                  int log2m)

Creates a new array of counters.

Parameters:

arraySize - the number of counters.

n - the expected number of elements.

log2m - the logarithm of the number of registers per counter.

IntHyperLogLogCounterArray

public IntHyperLogLogCounterArray(int arraySize,
                                  long n,
                                  int log2m,
                                  long seed)

Creates a new array of counters.

Parameters:

arraySize - the number of counters.

n - the expected number of elements.

log2m - the logarithm of the number of registers per counter.

seed - the seed used to compute the hash function.

Method Detail

log2NumberOfRegisters

public static int log2NumberOfRegisters(double rsd)

Returns the logarithm of the number of registers per counter that are necessary to attain a given relative standard deviation.

Parameters:

rsd - the relative standard deviation to be attained.

Returns:

the logarithm of the number of registers that are necessary to attain relative standard deviation rsd.

relativeStandardDeviation

public static double relativeStandardDeviation(int log2m)

Returns the relative standard deviation corresponding to a given logarithm of the number of registers per counter.

Parameters:

log2m - the logarithm of the number of registers.

Returns:

the resulting relative standard deviation.

registerSize

public static int registerSize(long n)

Returns the register size in bits, given an upper bound on the number of distinct elements.

Parameters:

n - an upper bound on the number of distinct elements.

Returns:

the register size in bits.

chunk

protected int chunk(int counter)

Returns the chunk of a given counter.

Parameters:

counter - a counter.

Returns:

its chunk.

offset

protected long offset(int counter)

Returns the bit offset of a given counter in its chunk.

Parameters:

counter - a counter.

Returns:

the starting bit of the given counter in its chunk.

clear

public void clear(long seed)

Clears all registers and sets a new seed (e.g., using Util.randomSeed()).

Parameters:

seed - the new seed used to compute the hash function

clear

public void clear()

Clears all registers.

add

public void add(int k,
                int v)

Adds an element to a counter.

Parameters:

k - the index of the counter.

v - the element to be added.

registers

public LongBigList[] registers()

Returns the array of big lists of registers underlying this array of counters.

The main purpose of this method is debugging, as it makes comparing the evolution of the state of two implementations easy.

Returns:

the array of big lists of registers underlying this array of counters.

count

protected double count(long[] bits,
                       long offset)

Estimates the number of distinct elements that have been added to a given counter so far.

Parameters:

bits - the bit array containing the counter.

offset - the starting bit position of the counter in bits.

Returns:

an approximation of the number of distinct elements that have been added to counter so far.

count

public double count(int k)

Estimates the number of distinct elements that have been added to a given counter so far.

Parameters:

k - the index of the counter.

Returns:

an approximation of the number of distinct elements that have been added to counter k so far.