org.apache.lucene.util.packed

Class EliasFanoEncoder

java.lang.Object

org.apache.lucene.util.packed.EliasFanoEncoder

public class EliasFanoEncoder
extends Object

Encode a non decreasing sequence of non negative whole numbers in the Elias-Fano encoding that was introduced in the 1970's by Peter Elias and Robert Fano.

The Elias-Fano encoding is a high bits / low bits representation of a monotonically increasing sequence of numValues > 0 natural numbers x[i]

0 <= x[0] <= x[1] <= ... <= x[numValues-2] <= x[numValues-1] <= upperBound

where upperBound > 0 is an upper bound on the last value.
The Elias-Fano encoding uses less than half a bit per encoded number more than the smallest representation that can encode any monotone sequence with the same bounds.

The lower L bits of each x[i] are stored explicitly and contiguously in the lower-bits array, with L chosen as (log() base 2):

L = max(0, floor(log(upperBound/numValues)))

The upper bits are stored in the upper-bits array as a sequence of unary-coded gaps (x[-1] = 0):

(x[i]/2**L) - (x[i-1]/2**L)

The unary code encodes a natural number n by n 0 bits followed by a 1 bit: 0...01.
In the upper bits the total the number of 1 bits is numValues and the total number of 0 bits is:

floor(x[numValues-1]/2**L) <= upperBound/(2**max(0, floor(log(upperBound/numValues)))) <= 2*numValues

The Elias-Fano encoding uses at most

2 + ceil(log(upperBound/numValues))

bits per encoded number. With upperBound in these bounds (p is an integer):

2**p < x[numValues-1] <= upperBound <= 2**(p+1)

the number of bits per encoded number is minimized.

In this implementation the values in the sequence can be given as long, numValues = 0 and upperBound = 0 are allowed, and each of the upper and lower bit arrays should fit in a long[].
An index of positions of zero's in the upper bits is also built.

This implementation is based on this article:
Sebastiano Vigna, "Quasi Succinct Indices", June 19, 2012, sections 3, 4 and 9. Retrieved from http://arxiv.org/pdf/1206.4300 .

The articles originally describing the Elias-Fano representation are:
Peter Elias, "Efficient storage and retrieval by content and address of static files", J. Assoc. Comput. Mach., 21(2):246–260, 1974.
Robert M. Fano, "On the number of bits required to implement an associative memory", Memorandum 61, Computer Structures Group, Project MAC, MIT, Cambridge, Mass., 1971.

NOTE: This API is for internal purposes only and might change in incompatible ways in the next release.

Field Summary

Fields

Modifier and Type	Field and Description
static long	DEFAULT_INDEX_INTERVAL The default index interval for zero upper bits.

Constructor Summary

Constructors

Constructor and Description
EliasFanoEncoder(long numValues, long upperBound) Construct an Elias-Fano encoder using DEFAULT_INDEX_INTERVAL.
EliasFanoEncoder(long numValues, long upperBound, long indexInterval) Construct an Elias-Fano encoder.

Method Summary

Methods

Modifier and Type	Method and Description
void	encodeNext(long x) Call at most numValues times to encode a non decreasing sequence of non negative numbers.
boolean	equals(Object other)
EliasFanoDecoder	getDecoder() Returns an EliasFanoDecoder to access the encoded values.
long[]	getIndexBits() Expert.
long[]	getLowerBits() Expert.
long[]	getUpperBits() Expert.
int	hashCode()
static boolean	sufficientlySmallerThanBitSet(long numValues, long upperBound) Provide an indication that it is better to use an EliasFanoEncoder than a FixedBitSet to encode document identifiers.
String	toString()

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

DEFAULT_INDEX_INTERVAL

public static final long DEFAULT_INDEX_INTERVAL

The default index interval for zero upper bits.

See Also:

Constant Field Values

Constructor Detail

EliasFanoEncoder

public EliasFanoEncoder(long numValues,
                long upperBound,
                long indexInterval)

Construct an Elias-Fano encoder. After construction, call encodeNext(long) numValues times to encode a non decreasing sequence of non negative numbers.

Parameters:

numValues - The number of values that is to be encoded.

upperBound - At least the highest value that will be encoded. For space efficiency this should not exceed the power of two that equals or is the first higher than the actual maximum.
When numValues >= (upperBound/3) a FixedBitSet will take less space.

indexInterval - The number of high zero bits for which a single index entry is built. The index will have at most 2 * numValues / indexInterval entries and each index entry will use at most ceil(log2(3 * numValues)) bits, see EliasFanoEncoder.

Throws:

IllegalArgumentException - when:

• numValues is negative, or
• numValues is non negative and upperBound is negative, or
• the low bits do not fit in a long[]: (L * numValues / 64) > Integer.MAX_VALUE, or
• the high bits do not fit in a long[]: (2 * numValues / 64) > Integer.MAX_VALUE, or
• indexInterval < 2,
• the index bits do not fit in a long[]: (numValues / indexInterval * ceil(2log(3 * numValues)) / 64) > Integer.MAX_VALUE.

EliasFanoEncoder

public EliasFanoEncoder(long numValues,
                long upperBound)

Construct an Elias-Fano encoder using DEFAULT_INDEX_INTERVAL.

Method Detail

encodeNext

public void encodeNext(long x)

Call at most numValues times to encode a non decreasing sequence of non negative numbers.

Parameters:

x - The next number to be encoded.

Throws:

IllegalStateException - when called more than numValues times.

IllegalArgumentException - when:

• x is smaller than an earlier encoded value, or
• x is larger than upperBound.

sufficientlySmallerThanBitSet

public static boolean sufficientlySmallerThanBitSet(long numValues,
                                    long upperBound)

Provide an indication that it is better to use an EliasFanoEncoder than a FixedBitSet to encode document identifiers. This indication is not precise and may change in the future.
An EliasFanoEncoder is favoured when the size of the encoding by the EliasFanoEncoder (including some space for its index) is at most about 5/6 of the size of the FixedBitSet, this is the same as comparing estimates of the number of bits accessed by a pair of FixedBitSets and by a pair of non indexed EliasFanoDocIdSets when determining the intersections of the pairs.
A bit set is preferred when upperbound <= 256.
It is assumed that DEFAULT_INDEX_INTERVAL is used.

Parameters:

numValues - The number of document identifiers that is to be encoded. Should be non negative.

upperBound - The maximum possible value for a document identifier. Should be at least numValues.

getDecoder

public EliasFanoDecoder getDecoder()

Returns an EliasFanoDecoder to access the encoded values. Perform all calls to encodeNext(long) before calling getDecoder().

getLowerBits

public long[] getLowerBits()

Expert. The low bits.

getUpperBits

public long[] getUpperBits()

Expert. The high bits.

getIndexBits

public long[] getIndexBits()

Expert. The index bits.

toString

public String toString()

Overrides:

toString in class Object

equals

public boolean equals(Object other)

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object