com.hjcenry.fec

类 Galois

java.lang.Object

com.hjcenry.fec.Galois

public final class Galois
extends Object

8-bit Galois Field This class implements multiplication, division, addition, subtraction, and exponentiation. The multiplication operation is in the inner loop of erasure coding, so it's been optimized. Having the class be "final" helps a little, and having the EXP_TABLE repeat the data, so there's no need to bound the sum of two logarithms to 255 helps a lot.

字段概要

字段

限定符和类型	字段和说明
(专用程序包) static byte[]	EXP_TABLE Inverse of the logarithm table.
static int	FIELD_SIZE The number of elements in the field.
static int	GENERATING_POLYNOMIAL The polynomial used to generate the logarithm table.
static short[]	LOG_TABLE Mapping from members of the Galois Field to their integer logarithms.
static byte[][]	MULTIPLICATION_TABLE A multiplication table for the Galois field.

构造器概要

构造器

构造器和说明
Galois()

方法概要

限定符和类型	方法和说明
static byte	add(byte a, byte b) Adds two elements of the field.
static Integer[]	allPossiblePolynomials() Returns a list of all polynomials that can be used to generate the field.
static byte	divide(byte a, byte b) Inverse of multiplication.
static byte	exp(byte a, int n) Computes a**n.
static byte[]	generateExpTable(short[] logTable) Generates the inverse log table.
static short[]	generateLogTable(int polynomial) Generates a logarithm table given a starting polynomial.
static byte[][]	generateMultiplicationTable() Generates a multiplication table as an array of byte arrays.
static byte	multiply(byte a, byte b) Multiplies two elements of the field.
static byte	subtract(byte a, byte b) Inverse of addition.

从类继承的方法 java.lang.Object

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

字段详细资料

FIELD_SIZE

public static final int FIELD_SIZE

The number of elements in the field.

另请参阅:

常量字段值

GENERATING_POLYNOMIAL

public static final int GENERATING_POLYNOMIAL

The polynomial used to generate the logarithm table. There are a number of polynomials that work to generate a Galois field of 256 elements. The choice is arbitrary, and we just use the first one. The possibilities are: 29, 43, 45, 77, 95, 99, 101, 105, 113, 135, 141, 169, 195, 207, 231, and 245.

另请参阅:

常量字段值

LOG_TABLE

public static final short[] LOG_TABLE

Mapping from members of the Galois Field to their integer logarithms. The entry for 0 is meaningless because there is no log of 0. This array is shorts, not bytes, so that they can be used directly to index arrays without casting. The values (except the non-value at index 0) are all really bytes, so they range from 0 to 255. This table was generated by java_tables.py, and the unit tests check it against the Java implementation.

EXP_TABLE

static final byte[] EXP_TABLE

Inverse of the logarithm table. Maps integer logarithms to members of the field. There is no entry for 255 because the highest log is 254. This table was generated by java_tables.py.

MULTIPLICATION_TABLE

public static byte[][] MULTIPLICATION_TABLE

A multiplication table for the Galois field. Using this table is an alternative to using the multiply() method, which uses log/exp table lookups.

构造器详细资料

Galois

public Galois()

方法详细资料

add

public static byte add(byte a,
                       byte b)

Adds two elements of the field. If you're in an inner loop, you should inline this function: it's just XOR.

subtract

public static byte subtract(byte a,
                            byte b)

Inverse of addition. If you're in an inner loop, you should inline this function: it's just XOR.

multiply

public static byte multiply(byte a,
                            byte b)

Multiplies two elements of the field.

divide

public static byte divide(byte a,
                          byte b)

Inverse of multiplication.

exp

public static byte exp(byte a,
                       int n)

Computes a**n. The result will be the same as multiplying a times itself n times.

参数:

a - A member of the field.

n - A plain-old integer.

返回:

The result of multiplying a by itself n times.

generateLogTable

public static short[] generateLogTable(int polynomial)

Generates a logarithm table given a starting polynomial.

generateExpTable

public static byte[] generateExpTable(short[] logTable)

Generates the inverse log table.

generateMultiplicationTable

public static byte[][] generateMultiplicationTable()

Generates a multiplication table as an array of byte arrays. To get the result of multiplying a and b: MULTIPLICATION_TABLE[a][b]

allPossiblePolynomials

public static Integer[] allPossiblePolynomials()

Returns a list of all polynomials that can be used to generate the field. This is never used in the code; it's just here for completeness.