Class EliasFanoEncoder

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

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]/2L) <= upperBound/(2max(0, floor(log(upperBound/numValues)))) <= 2numValues

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):

2p < 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):246â€"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.

Inheritance

System.Object

EliasFanoEncoder

Inherited Members

System.Object.Equals(System.Object, System.Object)

System.Object.GetType()

System.Object.MemberwiseClone()

System.Object.ReferenceEquals(System.Object, System.Object)

Namespace: Lucene.Net.Util.Packed

Assembly: Lucene.Net.dll

Syntax

public class EliasFanoEncoder

Constructors

EliasFanoEncoder(Int64, Int64)

Construct an Elias-Fano encoder using DEFAULT_INDEX_INTERVAL.

Declaration

public EliasFanoEncoder(long numValues, long upperBound)

Parameters

Type	Name	Description
System.Int64	numValues
System.Int64	upperBound

EliasFanoEncoder(Int64, Int64, Int64)

Construct an Elias-Fano encoder. After construction, call EncodeNext(Int64) numValues times to encode a non decreasing sequence of non negative numbers.

Declaration

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

Parameters

Type	Name	Description
System.Int64	numValues	The number of values that is to be encoded.
System.Int64	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.
System.Int64	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.

Exceptions

Type

Condition

System.ArgumentException

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) > System.Int32.MaxValue, or the high bits do not fit in a long[]: (2 * numValues / 64) > System.Int32.MaxValue, or indexInterval < 2, the index bits do not fit in a long[]: (numValues / indexInterval * ceil(2log(3 * numValues)) / 64) > System.Int32.MaxValue.

Fields

DEFAULT_INDEX_INTERVAL

The default index interval for zero upper bits.

Declaration

public const long DEFAULT_INDEX_INTERVAL = 256L

Field Value

Type	Description
System.Int64

Properties

IndexBits

Expert. The index bits.

Declaration

public virtual long[] IndexBits { get; }

Property Value

Type	Description
System.Int64[]

LowerBits

Expert. The low bits.

Declaration

public virtual long[] LowerBits { get; }

Property Value

Type	Description
System.Int64[]

UpperBits

Expert. The high bits.

Declaration

public virtual long[] UpperBits { get; }

Property Value

Type	Description
System.Int64[]

Methods

EncodeNext(Int64)

Call at most Lucene.Net.Util.Packed.EliasFanoEncoder.numValues times to encode a non decreasing sequence of non negative numbers.

Declaration

public virtual void EncodeNext(long x)

Parameters

Type	Name	Description
System.Int64	x	The next number to be encoded.

Exceptions

Type	Condition
System.InvalidOperationException	when called more than Lucene.Net.Util.Packed.EliasFanoEncoder.numValues times.
System.ArgumentOutOfRangeException	when: x is smaller than an earlier encoded value, or x is larger than Lucene.Net.Util.Packed.EliasFanoEncoder.upperBound.

Equals(Object)

Declaration

public override bool Equals(object other)

Parameters

Type	Name	Description
System.Object	other

Returns

Type	Description
System.Boolean

Overrides

System.Object.Equals(System.Object)

GetDecoder()

Returns an EliasFanoDecoder to access the encoded values. Perform all calls to EncodeNext(Int64) before calling GetDecoder().

Declaration

public virtual EliasFanoDecoder GetDecoder()

Returns

Type	Description
EliasFanoDecoder

GetHashCode()

Declaration

public override int GetHashCode()

Returns

Type	Description
System.Int32

Overrides

System.Object.GetHashCode()

SufficientlySmallerThanBitSet(Int64, Int64)

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 favored 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.

Declaration

public static bool SufficientlySmallerThanBitSet(long numValues, long upperBound)

Parameters

Type	Name	Description
System.Int64	numValues	The number of document identifiers that is to be encoded. Should be non negative.
System.Int64	upperBound	The maximum possible value for a document identifier. Should be at least numValues.

Returns

Type	Description
System.Boolean

ToString()

Declaration

public override string ToString()

Returns

Type	Description
System.String

Overrides

System.Object.ToString()