This class provides facilities to compute multiplications of scalars, of vectors and of matrices modulo m. More...

Static Public Member Functions
Methods using `double`
static double	multModM (double a, double s, double c, double m)
	Computes \((a \times s + c) \bmod m\). More...

static void	matVecModM (double A[][], double s[], double v[], double m)
	Computes the result of \(\mathtt{A} \times\mathtt{\mathbf{s}} \bmod m\) and puts the result in `v`. More...

static void	matMatModM (double A[][], double B[][], double C[][], double m)
	Computes \(\mathtt{A} \times\mathtt{B} \bmod m\) and puts the result in `C`. More...

static void	matTwoPowModM (double A[][], double B[][], double m, int e)
	Computes \(\mathtt{A}^{2^{\mathtt{e}}} \bmod m\) and puts the result in `B`. More...

static void	matPowModM (double A[][], double B[][], double m, int c)
	Computes \(\mathtt{A}^c \bmod m\) and puts the result in `B`. More...

Methods using `int`
static int	multModM (int a, int s, int c, int m)
	Computes \((a \times s + c) \bmod m\). More...

static void	matVecModM (int A[][], int s[], int v[], int m)
	Exactly like matVecModM(double[][],double[],double[],double) using `double`, but with `int` instead of `double`. More...

static void	matMatModM (int A[][], int B[][], int C[][], int m)
	Exactly like matMatModM(double[][],double[][],double[][],double) using `double`, but with `int` instead of `double`. More...

static void	matTwoPowModM (int A[][], int B[][], int m, int e)
	Exactly like matTwoPowModM(double[][],double[][],double,int) using `double`, but with `int` instead of `double`. More...

static void	matPowModM (int A[][], int B[][], int m, int c)
	Exactly like matPowModM(double[][],double[][],double,int) using `double`, but with `int` instead of `double`. More...

Methods using `long`
static long	multModM (long a, long s, long c, long m)
	Computes \((a \times s + c) \bmod m\). More...

static void	matVecModM (long A[][], long s[], long v[], long m)
	Exactly like matVecModM(double[][],double[],double[],double) using `double`, but with `long` instead of `double`. More...

static void	matMatModM (long A[][], long B[][], long C[][], long m)
	Exactly like matMatModM(double[][],double[][],double[][],double) using `double`, but with `long` instead of `double`. More...

static void	matTwoPowModM (long A[][], long B[][], long m, int e)
	Exactly like matTwoPowModM(double[][],double[][],double,int) using `double`, but with `long` instead of `double`. More...

static void	matPowModM (long A[][], long B[][], long m, int c)
	Exactly like matPowModM(double[][],double[][],double,int) using `double`, but with `long` instead of `double`. More...

Detailed Description

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.

Member Function Documentation

◆ matMatModM() [1/3]

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

static

Computes \(\mathtt{A} \times\mathtt{B} \bmod m\) 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

◆ matMatModM() [2/3]

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

static

Exactly like matMatModM(double[][],double[][],double[][],double) 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

◆ matMatModM() [3/3]

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

static

Exactly like matMatModM(double[][],double[][],double[][],double) 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

◆ matPowModM() [1/3]

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

static

Computes \(\mathtt{A}^c \bmod m\) 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

◆ matPowModM() [2/3]

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

static

Exactly like matPowModM(double[][],double[][],double,int) 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

◆ matPowModM() [3/3]

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

static

Exactly like matPowModM(double[][],double[][],double,int) 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

◆ matTwoPowModM() [1/3]

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

static

Computes \(\mathtt{A}^{2^{\mathtt{e}}} \bmod m\) 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 \(\log_2\) of the exponent

◆ matTwoPowModM() [2/3]

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

static

Exactly like matTwoPowModM(double[][],double[][],double,int) 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 \(\log_2\) of the exponent

◆ matTwoPowModM() [3/3]

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

static

Exactly like matTwoPowModM(double[][],double[][],double,int) 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 \(\log_2\) of the exponent

◆ matVecModM() [1/3]

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

static

Computes the result of \(\mathtt{A} \times\mathtt{\mathbf{s}} \bmod m\) 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

◆ matVecModM() [2/3]

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

static

Exactly like matVecModM(double[][],double[],double[],double) 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

◆ matVecModM() [3/3]

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

static

Exactly like matVecModM(double[][],double[],double[],double) 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

◆ multModM() [1/3]

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

static

Computes \((a \times s + c) \bmod m\).

Where m must be smaller than \(2^{35}\). 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

◆ multModM() [2/3]

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

static

Computes \((a \times s + c) \bmod m\).

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

◆ multModM() [3/3]

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

static

Computes \((a \times s + c) \bmod m\).

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

The documentation for this class was generated from the following file:

ArithmeticMod.java

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ matMatModM() [1/3]

◆ matMatModM() [2/3]

◆ matMatModM() [3/3]

◆ matPowModM() [1/3]

◆ matPowModM() [2/3]

◆ matPowModM() [3/3]

◆ matTwoPowModM() [1/3]

◆ matTwoPowModM() [2/3]

◆ matTwoPowModM() [3/3]

◆ matVecModM() [1/3]

◆ matVecModM() [2/3]

◆ matVecModM() [3/3]

◆ multModM() [1/3]

◆ multModM() [2/3]

◆ multModM() [3/3]