Package org.apache.hadoop.io.erasurecode.rawcoder.util

Class GaloisField

java.lang.Object

org.apache.hadoop.io.erasurecode.rawcoder.util.GaloisField

@Private
public class GaloisField
extends java.lang.Object

Implementation of Galois field arithmetic with 2^p elements. The input must be unsigned integers. It's ported from HDFS-RAID, slightly adapted.

Method Summary

Modifier and Type	Method	Description
int[]	add(int[] p, int[] q)	Compute the sum of two polynomials.
int	add(int x, int y)	Compute the sum of two fields
int	divide(int x, int y)	Compute the division of two fields
void	gaussianElimination(int[][] matrix)	Perform Gaussian elimination on the given matrix.
int	getFieldSize()	Return number of elements in the field
static GaloisField	getInstance()	Get the object performs Galois field arithmetic with default setting.
static GaloisField	getInstance(int fieldSize, int primitivePolynomial)	Get the object performs Galois field arithmetics.
int	getPrimitivePolynomial()	Return the primitive polynomial in GF(2)
int[]	multiply(int[] p, int[] q)	Compute the multiplication of two polynomials.
int	multiply(int x, int y)	Compute the multiplication of two fields
int	power(int x, int n)	Compute power n of a field
void	remainder(byte[][] dividend, int[] divisor)	The "bulk" version of the remainder.
void	remainder(byte[][] dividend, int[] offsets, int len, int[] divisor)	The "bulk" version of the remainder.
void	remainder(int[] dividend, int[] divisor)	Compute the remainder of a dividend and divisor pair.
void	remainder(java.nio.ByteBuffer[] dividend, int[] divisor)	The "bulk" version of the remainder, using ByteBuffer.
void	solveVandermondeSystem(int[] x, byte[][] y, int[] outputOffsets, int len, int dataLen)	A "bulk" version to the solving of Vandermonde System.
void	solveVandermondeSystem(int[] x, int[] y)	Given a Vandermonde matrix V[i][j]=x[j]^i and vector y, solve for z such that Vz=y.
void	solveVandermondeSystem(int[] x, int[] y, int len)	Given a Vandermonde matrix V[i][j]=x[j]^i and vector y, solve for z such that Vz=y.
void	solveVandermondeSystem(int[] x, java.nio.ByteBuffer[] y, int len)	A "bulk" version of the solveVandermondeSystem, using ByteBuffer.
void	substitute(byte[][] p, byte[] q, int x)	A "bulk" version of the substitute.
void	substitute(byte[][] p, int[] offsets, int len, byte[] q, int offset, int x)	A "bulk" version of the substitute.
int	substitute(int[] p, int x)	Substitute x into polynomial p(x).
void	substitute(java.nio.ByteBuffer[] p, int len, java.nio.ByteBuffer q, int x)	A "bulk" version of the substitute, using ByteBuffer.

Methods inherited from class java.lang.Object

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

Method Detail

getInstance

public static GaloisField getInstance(int fieldSize,
                                      int primitivePolynomial)

Get the object performs Galois field arithmetics.

Parameters:

fieldSize - size of the field

primitivePolynomial - a primitive polynomial corresponds to the size

Returns:

GaloisField.

getInstance

public static GaloisField getInstance()

Get the object performs Galois field arithmetic with default setting.

Returns:

GaloisField.

getFieldSize

public int getFieldSize()

Return number of elements in the field

Returns:

number of elements in the field

getPrimitivePolynomial

public int getPrimitivePolynomial()

Return the primitive polynomial in GF(2)

Returns:

primitive polynomial as a integer

add

public int add(int x,
               int y)

Compute the sum of two fields

Parameters:

x - input field

y - input field

Returns:

result of addition

multiply

public int multiply(int x,
                    int y)

Compute the multiplication of two fields

Parameters:

x - input field

y - input field

Returns:

result of multiplication

divide

public int divide(int x,
                  int y)

Compute the division of two fields

Parameters:

x - input field

y - input field

Returns:

x/y

power

public int power(int x,
                 int n)

Compute power n of a field

Parameters:

x - input field

n - power

Returns:

x^n

solveVandermondeSystem

public void solveVandermondeSystem(int[] x,
                                   int[] y)

Given a Vandermonde matrix V[i][j]=x[j]^i and vector y, solve for z such that Vz=y. The output z will be placed in y.

Parameters:

x - the vector which describe the Vandermonde matrix

y - right-hand side of the Vandermonde system equation. will be replaced the output in this vector

solveVandermondeSystem

public void solveVandermondeSystem(int[] x,
                                   int[] y,
                                   int len)

Given a Vandermonde matrix V[i][j]=x[j]^i and vector y, solve for z such that Vz=y. The output z will be placed in y.

Parameters:

x - the vector which describe the Vandermonde matrix

y - right-hand side of the Vandermonde system equation. will be replaced the output in this vector

len - consider x and y only from 0...len-1

solveVandermondeSystem

public void solveVandermondeSystem(int[] x,
                                   byte[][] y,
                                   int[] outputOffsets,
                                   int len,
                                   int dataLen)

A "bulk" version to the solving of Vandermonde System.

Parameters:

x - input x.

y - input y.

outputOffsets - input outputOffsets.

len - input len.

dataLen - input dataLen.

solveVandermondeSystem

public void solveVandermondeSystem(int[] x,
                                   java.nio.ByteBuffer[] y,
                                   int len)

A "bulk" version of the solveVandermondeSystem, using ByteBuffer.

Parameters:

x - input x.

y - input y.

len - input len.

multiply

public int[] multiply(int[] p,
                      int[] q)

Compute the multiplication of two polynomials. The index in the array corresponds to the power of the entry. For example p[0] is the constant term of the polynomial p.

Parameters:

p - input polynomial

q - input polynomial

Returns:

polynomial represents p*q

remainder

public void remainder(int[] dividend,
                      int[] divisor)

Compute the remainder of a dividend and divisor pair. The index in the array corresponds to the power of the entry. For example p[0] is the constant term of the polynomial p.

Parameters:

dividend - dividend polynomial, the remainder will be placed here when return

divisor - divisor polynomial

add

public int[] add(int[] p,
                 int[] q)

Compute the sum of two polynomials. The index in the array corresponds to the power of the entry. For example p[0] is the constant term of the polynomial p.

Parameters:

p - input polynomial

q - input polynomial

Returns:

polynomial represents p+q

substitute

public int substitute(int[] p,
                      int x)

Substitute x into polynomial p(x).

Parameters:

p - input polynomial

x - input field

Returns:

p(x)

substitute

public void substitute(byte[][] p,
                       byte[] q,
                       int x)

A "bulk" version of the substitute. Tends to be 2X faster than the "int" substitute in a loop.

Parameters:

p - input polynomial

q - store the return result

x - input field

substitute

public void substitute(byte[][] p,
                       int[] offsets,
                       int len,
                       byte[] q,
                       int offset,
                       int x)

A "bulk" version of the substitute. Tends to be 2X faster than the "int" substitute in a loop.

Parameters:

p - input polynomial

offsets - input offset.

len - input len.

q - store the return result

offset - input offset.

x - input field

substitute

public void substitute(java.nio.ByteBuffer[] p,
                       int len,
                       java.nio.ByteBuffer q,
                       int x)

A "bulk" version of the substitute, using ByteBuffer. Tends to be 2X faster than the "int" substitute in a loop.

Parameters:

p - input polynomial

q - store the return result

x - input field

len - input len.

remainder

public void remainder(byte[][] dividend,
                      int[] divisor)

The "bulk" version of the remainder. Warning: This function will modify the "dividend" inputs.

Parameters:

divisor - divisor.

dividend - dividend.

remainder

public void remainder(byte[][] dividend,
                      int[] offsets,
                      int len,
                      int[] divisor)

The "bulk" version of the remainder. Warning: This function will modify the "dividend" inputs.

Parameters:

dividend - dividend.

offsets - offsets.

len - len.

divisor - divisor.

remainder

public void remainder(java.nio.ByteBuffer[] dividend,
                      int[] divisor)

The "bulk" version of the remainder, using ByteBuffer. Warning: This function will modify the "dividend" inputs.

Parameters:

dividend - dividend.

divisor - divisor.

gaussianElimination

public void gaussianElimination(int[][] matrix)

Perform Gaussian elimination on the given matrix. This matrix has to be a fat matrix (number of rows > number of columns).

Parameters:

matrix - matrix.