This class represents the lattice associated to a Multiply-with-carry (MWC) random number generator. More...

#include <latmrg/MWCLattice.h>

Inheritance diagram for LatMRG::MWCLattice< Int, Dbl >:

Public Types
typedef NTL::matrix< Int >	IntMat

typedef NTL::vector< Int >	IntVec

Public Types inherited from LatMRG::MRGLattice< Int, Dbl >
typedef Dbl	Dbl

typedef Int	Int

typedef NTL::matrix< Int >	IntMat

typedef NTL::vector< Int >	IntVec

Public Member Functions
	MWCLattice (const Int &b, const IntVec &e, int k, int maxDim=1)
	b is the modulo. More...

	MWCLattice (const Int &b, const Int &m, int maxDim=1)
	Another constructor with just `b` and `m`. More...

	MWCLattice (const MWCLattice< Int, Dbl > &Lat)
	Copy constructor. More...

	~MWCLattice ()
	Destructor. More...

const IntVec &	geteCoef () const
	The coefficients of the MWC generator. More...

const Int &	getMWCmod () const
	The modulo of the MWC generator this object represents. More...

int	getMWCorder () const
	The order of the MWC generator. More...

void	kill ()
	Cleans and releases memory used by this object. More...

MWCLattice< Int, Dbl > &	operator= (const MWCLattice< Int, Dbl > &Lat)
	Assigns `Lat` to this object. More...

std::string	toString () const override
	Gets all the information on the lattice in a string. More...

std::string	toStringCoef () const
	Gets the coefficients of the MRG that spawns the lattice in a string. More...

Public Member Functions inherited from LatMRG::MRGLattice< Int, Dbl >
	MRGLattice (const Int &m, const IntVec &a, int maxDim, int k, LatticeType latt, LatticeTester::NormType norm=LatticeTester::L2NORM)
	Constructor with modulus of congruence \(m\), order of the recurrence \(k\), multipliers \(a\), maximal dimension `MaxDim`, and lattice type `Latt`. More...

	MRGLattice (const Int &m, const Int &a, int maxDim, LatticeType latt, LatticeTester::NormType norm=LatticeTester::L2NORM)
	Alternative constructor for a LCG. More...

	MRGLattice (const Int &m, const IntVec &a, int maxDim, int k, IntVec &lac, LatticeType latt, LatticeTester::NormType norm=LatticeTester::L2NORM)
	As in the constructor above but the basis is built for the lacunary indices `lac`. More...

	MRGLattice (const MRGLattice< Int, Dbl > &Lat)
	Copy constructor. More...

	~MRGLattice ()
	Destructor. More...

virtual void	buildBasis (int d)
	Builds the basis in dimension \(d\). More...

Int &	getLac (int j)
	Returns the \(j\)-th lacunary index. More...

virtual void	incDim ()
	Increments the dimension of the basis by 1 by calling either `incDimBasis` or `incDimLaBasis`. More...

bool	isLacunary () const
	Returns `true` for the case of lacunary indices, returns `false` for non-lacunary indices. More...

void	kill ()
	Cleans and releases memory used by this object. More...

MRGLattice< Int, Dbl > &	operator= (const MRGLattice< Int, Dbl > &Lat)
	Assigns `Lat` to this object. More...

virtual void	setLac (const LatticeTester::Lacunary< Int > &lat)
	Sets the lacunary indices for this lattice to `lat`. More...

Int	getRho () const

Int	getLossRho () const

void	setRho (const Int &val)

void	setLossRho (const Int &val)

const IntVec &	getCoef () const
	Returns a non-mutable copy of the multipliers (coefficients) of the MRG. More...

std::string	toString () const override
	Returns the vector of multipliers \(A\) as a string. More...

void	setPower2 (std::vector< IntVec > &coeffs)
	Sets `m_power2` to true and sets `m_pow2_exp to`coeffs`. More...

void	buildProjection (LatticeTester::IntLattice< Int, Int, Dbl, Dbl > *lattice, const LatticeTester::Coordinates &proj) override
	Builds a projection for this lattice on the set in indices in `proj`. More...

Static Public Member Functions
static int	fullPeriod (const Int &b, const IntVec &e)
	This is a basic method to check if the MWC generator described by `b` and `e` has full period. More...

static int	validate (const Int &b, const IntVec &e)
	This checks if `b` and `e` are suitable parameters for a MWC generator. More...

Private Attributes
IntVec	m_eCoef
	The coefficients of the MWC generator. More...

Int	m_MWCmod
	The modulo of the MWC generator this object represents. More...

int	m_MWCorder
	The order of the MWC generator. More...

Additional Inherited Members
Protected Member Functions inherited from LatMRG::MRGLattice< Int, Dbl >
void	initStates ()
	Initializes a square matrix of order \(k\). More...

void	init ()
	Initializes some of the local variables. More...

void	initOrbit ()
	Initializes this object when the lattice type is `ORBIT`. More...

void	insertion (IntVec &Sta)

void	lemme2 (IntVec &Sta)

void	trace (char *msg, int d)
	For debugging purposes. More...

virtual void	incDimBasis ()
	Increments the basis by 1 in case of non-lacunary indices. More...

void	incDimLaBasis (int)
	Increments the basis by 1 in case of lacunary indices. More...

void	buildNaBasis (int d)
	Builds the basis of the MRG recurrence in case of non-lacunary indices. More...

void	buildLaBasis (int d)
	Builds the basis of the MRG recurrence in case of lacunary indices. More...

Protected Attributes inherited from LatMRG::MRGLattice< Int, Dbl >
IntVec	m_aCoef
	The coefficients of the recurrence. More...

bool *	m_ip
	When the flag `m_ip[i]` is `true`, the \(i\)-th diagonal element of matrix `m_sta` is non-zero (modulo \(m\)) and divides \(m\). More...

LatticeTester::Lacunary< Int >	m_lac
	Contains the lacunary indices when `LacunaryFlag` is `true`, otherwise is undefined. More...

bool	m_lacunaryFlag
	Is `true` in the case of lacunary indices, `false` otherwise. More...

LatticeType	m_latType
	Indicates which lattice or sublattice is analyzed. More...

IntMat	m_sta
	Matrix that contains the vectors that can be used to generate the basis for an arbitrary dimension. More...

Int	m_lossRho

Int	m_rho

Int	m_t4
	Work variables. More...

Int	m_t5

Int	m_t6

Int	m_t7

Int	m_t8

Int	m_e

IntVec	m_xi

Detailed Description

template<typename Int, typename Dbl>
class LatMRG::MWCLattice< Int, Dbl >

This class represents the lattice associated to a Multiply-with-carry (MWC) random number generator.

A MWC generator is defined by a recurrence of the form

\begin{align} x_n & = (e_1 x_{n-1} + \cdots + e_k x_{n-k} + c_{n-1})d\ \mathrm{mod} \ b \\ c_n & = \lfloor (e_0 x_n + e_1 x_{n-1} + \cdots + e_k x_{n-k} + c_{n-1} )/b \rfloor \\ u_n & = \sum_{i=1}^\infty x_{n+i-1} b^{-i} \end{align}

This generator can then be reprensented as an LCG and this class simply builds the correct MRGLattice object corresponding to a specific MWC generator. All the functions and attributes inherited by this class work as they would be expected to work on the lattice corresponding to that MRGLattice. For example, this means that the vector m_aCoef stores the coefficient of the LCG instead of the coefficients of the MWC generator.

This class simply implements a constructor and and the functions to compute the LCG equivalent to the MRG.

Member Typedef Documentation

◆ IntMat

template<typename Int , typename Dbl >

typedef NTL::matrix<Int> LatMRG::MWCLattice< Int, Dbl >::IntMat

◆ IntVec

template<typename Int , typename Dbl >

typedef NTL::vector<Int> LatMRG::MWCLattice< Int, Dbl >::IntVec

Constructor & Destructor Documentation

◆ MWCLattice() [1/3]

template<typename Int , typename Dbl >

LatMRG::MWCLattice< Int, Dbl >::MWCLattice	(	const Int &	b,
		const IntVec &	e,
		int	k,
		int	maxDim = `1`
	)

b is the modulo.

e is the vector of coefficients. k is the order of the recurrence.

It is recommended to verify that the parameters passed to this constructor work before using it, because the program will crash of validate(b, e) != 0.

◆ MWCLattice() [2/3]

template<typename Int , typename Dbl >

LatMRG::MWCLattice< Int, Dbl >::MWCLattice	(	const Int &	b,
		const Int &	m,
		int	maxDim = `1`
	)

Another constructor with just b and m.

Of course, b and m have to be valid.

◆ MWCLattice() [3/3]

template<typename Int , typename Dbl >

LatMRG::MWCLattice< Int, Dbl >::MWCLattice ( const MWCLattice< Int, Dbl > & Lat )

Copy constructor.

The maximal dimension of the created basis is set equal to Lat’s current dimension.

◆ ~MWCLattice()

template<typename Int , typename Dbl >

LatMRG::MWCLattice< Int, Dbl >::~MWCLattice ( )

Destructor.

Member Function Documentation

◆ fullPeriod()

template<typename Int , typename Dbl >

static int LatMRG::MWCLattice< Int, Dbl >::fullPeriod	(	const Int &	b,
		const IntVec &	e
	)

inlinestatic

This is a basic method to check if the MWC generator described by b and e has full period.

Todo:: finish this

◆ geteCoef()

template<typename Int , typename Dbl >

const IntVec& LatMRG::MWCLattice< Int, Dbl >::geteCoef ( ) const

inline

The coefficients of the MWC generator.

We have that m_eCoef[i] = e_i. The MWC equations mean that if the order is k, the generator has k+1 coefficients.

◆ getMWCmod()

template<typename Int , typename Dbl >

const Int& LatMRG::MWCLattice< Int, Dbl >::getMWCmod ( ) const

inline

The modulo of the MWC generator this object represents.

◆ getMWCorder()

template<typename Int , typename Dbl >

int LatMRG::MWCLattice< Int, Dbl >::getMWCorder ( ) const

inline

The order of the MWC generator.

An order of k means that the generator has k+1 coefficients.

◆ kill()

template<typename Int , typename Dbl >

void LatMRG::MWCLattice< Int, Dbl >::kill ( )

Cleans and releases memory used by this object.

◆ operator=()

template<typename Int , typename Dbl >

MWCLattice< Int, Dbl > & LatMRG::MWCLattice< Int, Dbl >::operator= ( const MWCLattice< Int, Dbl > & Lat )

Assigns Lat to this object.

The maximal dimension of this basis is set equal to Lat’s current dimension.

◆ toString()

template<typename Int , typename Dbl >

std::string LatMRG::MWCLattice< Int, Dbl >::toString ( ) const

override

Gets all the information on the lattice in a string.

This contains the type of generator and the coefficients.

◆ toStringCoef()

template<typename Int , typename Dbl >

std::string LatMRG::MWCLattice< Int, Dbl >::toStringCoef ( ) const

virtual

Gets the coefficients of the MRG that spawns the lattice in a string.

Reimplemented from LatMRG::MRGLattice< Int, Dbl >.

◆ validate()

template<typename Int , typename Dbl >

static int LatMRG::MWCLattice< Int, Dbl >::validate	(	const Int &	b,
		const IntVec &	e
	)

inlinestatic

This checks if b and e are suitable parameters for a MWC generator.

It is recommended to call this function before building a MWCLattice object because the program will exit if the condition verified here is not met.

This basically just checks that gcd(b, e[0]) = 1 and returns 1 if it is false and 0 if it checks out.

Member Data Documentation

◆ m_eCoef

template<typename Int , typename Dbl >

IntVec LatMRG::MWCLattice< Int, Dbl >::m_eCoef

private

The coefficients of the MWC generator.

We have that m_eCoef[i] = e_i. The MWC equations mean that if the order is k, the generator has k+1 coefficients.

◆ m_MWCmod

template<typename Int , typename Dbl >

Int LatMRG::MWCLattice< Int, Dbl >::m_MWCmod

private

The modulo of the MWC generator this object represents.

◆ m_MWCorder

template<typename Int , typename Dbl >

int LatMRG::MWCLattice< Int, Dbl >::m_MWCorder

private

The order of the MWC generator.

An order of k means that the generator has k+1 coefficients.

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

include/latmrg/MWCLattice.h

Public Types

Public Member Functions

Static Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<typename Int, typename Dbl> class LatMRG::MWCLattice< Int, Dbl >

Member Typedef Documentation

◆ IntMat

◆ IntVec

Constructor & Destructor Documentation

◆ MWCLattice() [1/3]

◆ MWCLattice() [2/3]

◆ MWCLattice() [3/3]

◆ ~MWCLattice()

Member Function Documentation

◆ fullPeriod()

◆ geteCoef()

◆ getMWCmod()

◆ getMWCorder()

◆ kill()

◆ operator=()

◆ toString()

◆ toStringCoef()

◆ validate()

Member Data Documentation

◆ m_eCoef

◆ m_MWCmod

◆ m_MWCorder

template<typename Int, typename Dbl>
class LatMRG::MWCLattice< Int, Dbl >