LatMRG::Modulus< Int > Class Template Reference

This class offers a few tools to work with a modulus m. More...

Public Member Functions
	Modulus ()
	Modulus (const Int &m)
	Constructor with modulus of congruence \(m\).
	Modulus (long b, long e, long c)
	Constructor with value \(m =b^e + c\).
virtual	~Modulus ()
	Destructor.
void	init (const Int &m)
	Initializes with value \(m\).
void	init (long b, long e, long c)
	Initializes with value \(m =b^e + c\).
void	reduceM (const Int &a)
	Reduces the modulus \(m\) and sets the variable mRed to the reduced modulus.
bool	perMaxPowPrime (const Int &a)
	Assumes that \(m\) is a power of a prime \(p=b\) and that we have a multiplicative LCG ( \(k = 1\)).

Public Attributes
Int	m
	Value \(m\) of the modulus.
Int	mRed
	Reduced value of the modulus, in case m is a power of a prime.
bool	primeF
	This flag is true when \(m\) is prime, otherwise false.
bool	threeF
	When this flag is true, the value of \(m\) is built out of the three numbers \(b\), \(e\) and \(c\) as described below; otherwise, the flag is set false.
long	b
long	e
long	c
	When threeF is true, then \(m\) is given in the form \(m = b^e + c\); otherwise, \(b\), \(e\) and \(c\) are undefined.
Int	mRac
	\(\sqrt{\lfloor m \rfloor}\).
Int	mRacNeg
	\(-\sqrt{\lfloor m \rfloor}\).

Detailed Description

template<typename Int>
class LatMRG::Modulus< Int >

This class offers a few tools to work with a modulus m.

It keeps the value of m as an Int and its square root. It can also verify the max period conditions and compute the reduced modulus for the lattice structure over a single cycle, when m is a power of a prime. In the latter case, the modulus must be initialized as \(m =b^e + c\).

I am not sure if we should keep this class. It seems that what it contains should be move to where it is used. ********

Constructor & Destructor Documentation

Modulus() [1/3]

template<typename Int>

LatMRG::Modulus< Int >::Modulus

(

)

Modulus() [2/3]

template<typename Int>

LatMRG::Modulus< Int >::Modulus

(

const Int &

m

)

Constructor with modulus of congruence \(m\).

Modulus() [3/3]

template<typename Int>

LatMRG::Modulus< Int >::Modulus	(	long	b,
		long	e,
		long	c )

Constructor with value \(m =b^e + c\).

Restrictions: \(b>1\) and \(e > 0\).

~Modulus()

template<typename Int>

LatMRG::Modulus< Int >::~Modulus ( )

virtual

Destructor.

Member Function Documentation

init() [1/2]

template<typename Int>

void LatMRG::Modulus< Int >::init

(

const Int &

m

)

Initializes with value \(m\).

Computes mRac and mRacNeg.

init() [2/2]

template<typename Int>

void LatMRG::Modulus< Int >::init	(	long	b,
		long	e,
		long	c )

Initializes with value \(m =b^e + c\).

Restrictions: \(b>1\) and \(e > 0\). Computes mRac and mRacNeg.

reduceM()

template<typename Int>

void LatMRG::Modulus< Int >::reduceM

(

const Int &

a

)

Reduces the modulus \(m\) and sets the variable mRed to the reduced modulus.

The modulus must have the form \(m=p^e\). The multiplier of the LCG is \(a\).

perMaxPowPrime()

template<typename Int>

bool LatMRG::Modulus< Int >::perMaxPowPrime

(

const Int &

a

)

Assumes that \(m\) is a power of a prime \(p=b\) and that we have a multiplicative LCG ( \(k = 1\)).

Returns true iff the maximal period conditions are satisfied for this a. For b=2, this holds iff a mod 8 = 3 or 5.

Member Data Documentation

m

template<typename Int>

Int LatMRG::Modulus< Int >::m

Value \(m\) of the modulus.

mRed

template<typename Int>

Int LatMRG::Modulus< Int >::mRed

Reduced value of the modulus, in case m is a power of a prime.

Computed by reduceM.

primeF

template<typename Int>

bool LatMRG::Modulus< Int >::primeF

This flag is true when \(m\) is prime, otherwise false.

threeF

template<typename Int>

bool LatMRG::Modulus< Int >::threeF

When this flag is true, the value of \(m\) is built out of the three numbers \(b\), \(e\) and \(c\) as described below; otherwise, the flag is set false.

b

template<typename Int>

long LatMRG::Modulus< Int >::b

e

template<typename Int>

long LatMRG::Modulus< Int >::e

c

template<typename Int>

long LatMRG::Modulus< Int >::c

When threeF is true, then \(m\) is given in the form \(m = b^e + c\); otherwise, \(b\), \(e\) and \(c\) are undefined.

mRac

template<typename Int>

Int LatMRG::Modulus< Int >::mRac

\(\sqrt{\lfloor m \rfloor}\).

mRacNeg

template<typename Int>

Int LatMRG::Modulus< Int >::mRacNeg

\(-\sqrt{\lfloor m \rfloor}\).

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

• include/latmrg/Modulus.h