umontreal.iro.lecuyer.util

Class ArithmeticMod

java.lang.Object

umontreal.iro.lecuyer.util.ArithmeticMod

public class ArithmeticMod
extends java.lang.Object

This class provides facilities to compute multiplications of scalars, of vectors and of matrices modulo m. All algorithms are present in three different versions. These allow operations on double, int and long. The int and long versions work exactly like the double ones.

Method Summary

Modifier and Type	Method and Description
static void	matMatModM(double[][] A, double[][] B, double[][] C, double m) Computes A×B mod m and puts the result in C.
static void	matMatModM(int[][] A, int[][] B, int[][] C, int m) Exactly like matMatModM using double, but with int instead of double.
static void	matMatModM(long[][] A, long[][] B, long[][] C, long m) Exactly like matMatModM using double, but with long instead of double.
static void	matPowModM(double[][] A, double[][] B, double m, int c) Computes Ac mod m and puts the result in B.
static void	matPowModM(int[][] A, int[][] B, int m, int c) Exactly like matPowModM using double, but with int instead of double.
static void	matPowModM(long[][] A, long[][] B, long m, int c) Exactly like matPowModM using double, but with long instead of double.
static void	matTwoPowModM(double[][] A, double[][] B, double m, int e) Computes A2e mod m and puts the result in B.
static void	matTwoPowModM(int[][] A, int[][] B, int m, int e) Exactly like matTwoPowModM using double, but with int instead of double.
static void	matTwoPowModM(long[][] A, long[][] B, long m, int e) Exactly like matTwoPowModM using double, but with long instead of double.
static void	matVecModM(double[][] A, double[] s, double[] v, double m) Computes the result of A×s mod m and puts the result in v.
static void	matVecModM(int[][] A, int[] s, int[] v, int m) Exactly like matVecModM using double, but with int instead of double.
static void	matVecModM(long[][] A, long[] s, long[] v, long m) Exactly like matVecModM using double, but with long instead of double.
static double	multModM(double a, double s, double c, double m) Computes (a×s + c) mod m.
static int	multModM(int a, int s, int c, int m) Computes (a×s + c) mod m.
static long	multModM(long a, long s, long c, long m) Computes (a×s + c) mod m.

Methods inherited from class java.lang.Object

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

Method Detail

multModM

public static double multModM(double a,
                              double s,
                              double c,
                              double m)

Computes (a×s + c) mod m. Where m must be smaller than 2³⁵. Works also if s or c are negative. The result is always positive (and thus always between 0 and m - 1).

Parameters:

a - the first factor of the multiplication

s - the second factor of the multiplication

c - the second term of the addition

m - the modulus

Returns:

the result of the multiplication and the addition modulo m

matVecModM

public static void matVecModM(double[][] A,
                              double[] s,
                              double[] v,
                              double m)

Computes the result of A×s mod m and puts the result in v. Where s and v are both column vectors. This method works even if s = v.

Parameters:

A - the multiplication matrix

s - the multiplied vector

v - the result of the multiplication

m - the modulus

matMatModM

public static void matMatModM(double[][] A,
                              double[][] B,
                              double[][] C,
                              double m)

Computes A×B mod m and puts the result in C. Works even if A = C, B = C or A = B = C.

Parameters:

A - the first factor of the multiplication

B - the second factor of the multiplication

C - the result of the multiplication

m - the modulus

matTwoPowModM

public static void matTwoPowModM(double[][] A,
                                 double[][] B,
                                 double m,
                                 int e)

Computes A^2e mod m and puts the result in B. Works even if A = B.

Parameters:

A - the matrix to raise to a power

B - the result of exponentiation

m - the modulus

e - the log₂ of the exponent

matPowModM

public static void matPowModM(double[][] A,
                              double[][] B,
                              double m,
                              int c)

Computes A^c mod m and puts the result in B. Works even if A = B.

Parameters:

A - the matrix to raise to a power

B - the result of the exponentiation

m - the modulus

c - the exponent

multModM

public static int multModM(int a,
                           int s,
                           int c,
                           int m)

Computes (a×s + c) mod m. Works also if s or c are negative. The result is always positive (and thus always between 0 and m - 1).

Parameters:

a - the first factor of the multiplication

s - the second factor of the multiplication

c - the second term of the addition

m - the modulus

Returns:

the result of the multiplication and the addition modulo m

matVecModM

public static void matVecModM(int[][] A,
                              int[] s,
                              int[] v,
                              int m)

Exactly like matVecModM using double, but with int instead of double.

Parameters:

A - the multiplication matrix

s - the multiplied vector

v - the result of the multiplication

m - the modulus

matMatModM

public static void matMatModM(int[][] A,
                              int[][] B,
                              int[][] C,
                              int m)

Exactly like matMatModM using double, but with int instead of double.

Parameters:

A - the first factor of the multiplication

B - the second factor of the multiplication

C - the result of the multiplication

m - the modulus

matTwoPowModM

public static void matTwoPowModM(int[][] A,
                                 int[][] B,
                                 int m,
                                 int e)

Exactly like matTwoPowModM using double, but with int instead of double.

Parameters:

A - the matrix to raise to a power

B - the result of exponentiation

m - the modulus

e - the log₂ of the exponent

matPowModM

public static void matPowModM(int[][] A,
                              int[][] B,
                              int m,
                              int c)

Exactly like matPowModM using double, but with int instead of double.

Parameters:

A - the matrix to raise to a power

B - the result of the exponentiation

m - the modulus

c - the exponent

multModM

public static long multModM(long a,
                            long s,
                            long c,
                            long m)

Computes (a×s + c) mod m. Works also if s or c are negative. The result is always positive (and thus always between 0 and m - 1).

Parameters:

a - the first factor of the multiplication

s - the second factor of the multiplication

c - the second term of the addition

m - the modulus

Returns:

the result of the multiplication and the addition modulo m

matVecModM

public static void matVecModM(long[][] A,
                              long[] s,
                              long[] v,
                              long m)

Exactly like matVecModM using double, but with long instead of double.

Parameters:

A - the multiplication matrix

s - the multiplied vector

v - the result of the multiplication

m - the modulus

matMatModM

public static void matMatModM(long[][] A,
                              long[][] B,
                              long[][] C,
                              long m)

Exactly like matMatModM using double, but with long instead of double.

Parameters:

A - the first factor of the multiplication

B - the second factor of the multiplication

C - the result of the multiplication

m - the modulus

matTwoPowModM

public static void matTwoPowModM(long[][] A,
                                 long[][] B,
                                 long m,
                                 int e)

Exactly like matTwoPowModM using double, but with long instead of double.

Parameters:

A - the matrix to raise to a power

B - the result of exponentiation

m - the modulus

e - the log₂ of the exponent

matPowModM

public static void matPowModM(long[][] A,
                              long[][] B,
                              long m,
                              int c)

Exactly like matPowModM using double, but with long instead of double.

Parameters:

A - the matrix to raise to a power

B - the result of the exponentiation

m - the modulus

c - the exponent