Namespaces
	Merit
	The methods in this namespace can compute the merit of a reduced lattice for a given projection and return it as a `Dbl`.

	Reductions
	Functions in this namespace perform lattice reductions.

Classes
class	AWCSWBLattice
	This class represents the lattice associated with either an AWC or a SWB random number generator. More...

class	Chrono
	This class acts as an interface to the system clock to compute the CPU time used by parts of a program. More...

class	ComboLattice
	This class represents a combined MRG. More...

class	FigureOfMerit
	This class is intended to store everything you might need after performing computations on a lattice. More...

class	IntFactorization
	The class `IntFactorization` implements the decomposition of integers in factors, preferably prime (see class `IntFactor`). More...

class	IntPrimitivity
	This class deals with primitive roots and primitive elements modulo an integer. More...

class	KorobovLattice
	This class implements lattice bases built from a Korobov lattice rule. More...

class	MeritList
	This class stores a certain number of `FigureOfMerit` objects. More...

class	MixmaxMMRG
	This class is used to manipulate easily MMRG of Mixmax types as described by Savvidy [CITE PAPER]. More...

class	MMRGLattice

class	ModInt

class	ModInt< NTL::ZZ >

class	ModInt< std::int64_t >

class	Modulus
	This class keeps parameters closely associated with a modulus of congruence. More...

class	MRGComponent
	This class is used to to test for full period length of generators and also to store a bit of information about generators without creating a lattice. More...

class	MRGLattice
	This class implements lattice basis built from multiple recursive linear congruential generators (MRGs). More...

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

class	ParamReaderExt
	Utility class used to read basic parameter fields in a configuration file. More...

class	PolyPE
	This class implements polynomials \(P(x)\) in \(\mathbb Z_m[X]\) defined as. More...

class	Primes
	This class provides methods to search for integers \(m\) that are prime, for which the integer \(r = (m^k-1)/(m-1)\) is also prime for a given \(k\), and possibly for which \((m-1)/2\) is also prime. More...

class	Projections
	A projection class that does exactly what we need when generating projections when testing a generator. More...

Enumerations
enum	DecompType { DECOMP, DECOMP_WRITE, DECOMP_READ, DECOMP_PRIME, NO_DECOMP }
	Given an integer \(r\), indicates what to do about the decomposition of \(r\) in its prime factors. More...

enum	GenType { LCG, MRG, MWC, KOROBOV, RANK1, MMRG, COMBO }
	Used to identify the type of a generator. More...

enum	ImplemCond { NO_COND, APP_FACT, POWER_TWO, EQUAL_COEF, ZERO_COEF }
	Indicates which type of conditions are imposed on the coefficients \(a_i\) of a recurrence. More...

enum	LacunaryType { NONE, SUBVECTOR, ARBITRARYINDICES }
	Indicates the type of lacunary projection used for MMRG: More...

enum	LatticeType { FULL, RECURRENT, ORBIT, PRIMEPOWER }
	Indicates whether to analyze the lattice generated by all possible states, or a sub-lattice generated by the set of recurrent states or by a sub-cycle of the generator. More...

enum	SearchMethod { EXHAUST, RANDOM }
	Indicates the search method used to find good multipliers \(a_i\). More...

Functions
template<typename Int , typename Dbl >
MRGLattice< Int, Dbl > *	getLatCombo (std::vector< MRGComponent< Int > * > &comp, int maxDim)
	This function computes and returns a `MRGLattice` that is the lattice of the combination of generators described in the `MRGComponent`s in the vector `comp`. More...

template MRGLattice< std::int64_t, double > *	getLatCombo (std::vector< MRGComponent< std::int64_t > * > &comp, int maxDim)

template MRGLattice< NTL::ZZ, double > *	getLatCombo (std::vector< MRGComponent< NTL::ZZ > * > &comp, int maxDim)

int	toDecomString (DecompType &decom, const std::string &decom_str)
	`decom = decom_str`. More...

int	toGenString (GenType &type, const string &type_str)

int	toGenString (GenType &type, const std::string &type_str)
	`type = type_str`. More...

std::string	toString (Chrono &timer)
	Returns the value of the duration from `timer`. More...

toString functions
Useful functions for printing the `enum` constants in this module. Returns the `enum` constants in this module as strings. Remarks Richard: These are global methods for now, but maybe `Const` should be a class containing these methods.
std::string	toStringGen (GenType)

std::string	toStringLattice (LatticeType)

std::string	toStringDecomp (DecompType)

std::string	toStringImplemCond (ImplemCond)

std::string	toStringSearchMethod (SearchMethod)

Enumeration Type Documentation

◆ DecompType

enum LatMRG::DecompType

Given an integer \(r\), indicates what to do about the decomposition of \(r\) in its prime factors.

DECOMP: means that the program will factorize \(r\).
DECOMP_WRITE: means that the program will factorize \(r\) and writes the factors in a file.
DECOMP_READ: means that \(r\) is already factorized, and the factors will be read from a file.
DECOMP_PRIME: means that \(r\) is prime. No factorization will be done. NO_DECOMP: The program will not need a decomposition. Used when not checking full generator period.

Enumerator
DECOMP
DECOMP_WRITE
DECOMP_READ
DECOMP_PRIME
NO_DECOMP

◆ GenType

enum LatMRG::GenType

Used to identify the type of a generator.

If a generator is of type MWC, it is converted to its corresponding MRG by the program.

LCG: the linear congruential generator with a carry.
MRG: the multiple-recursive generator.
MWC: the multiply-with-carry generator.
KOROBOV: the Korobov lattice. This is not used in LatMRG.
RANK1: the rank 1 lattice. This is not used in LatMRG
MMRG: the matrix multiple-recursive generator. A generator with a matrix multiplier.

Enumerator
LCG
MRG
MWC
KOROBOV
RANK1
MMRG
COMBO

◆ ImplemCond

enum LatMRG::ImplemCond

Indicates which type of conditions are imposed on the coefficients \(a_i\) of a recurrence.

NO_COND: no condition is imposed on the coefficients.
APP_FACT: the coefficients must satisfy the "approximate factoring" condition \(|a_i| (m\mod|a_i|) < m\). Congruential generators are easier to implement under this condition [20] .
POWER_TWO: the coefficients must be sums or differences of powers of 2.
EQUAL_COEF: all the coefficients must be equal by groups: a first group all equal to a first number, a second group all equal to a second number, and so on.
ZERO_COEF: all the coefficients must be equal to 0, except for a select fews.

Enumerator
NO_COND
APP_FACT
POWER_TWO
EQUAL_COEF
ZERO_COEF

◆ LacunaryType

enum LatMRG::LacunaryType

Indicates the type of lacunary projection used for MMRG:

NONE: no lacunary projection
SUBVECTOR: only the selected coordinates of each new random vector are kept
ARBITRARY: only the selected indices are kept.

Enumerator
NONE
SUBVECTOR
ARBITRARYINDICES

◆ LatticeType

enum LatMRG::LatticeType

Indicates whether to analyze the lattice generated by all possible states, or a sub-lattice generated by the set of recurrent states or by a sub-cycle of the generator.

FULL: The complete lattice, generated by all possible initial states, will be analyzed.
RECURRENT: If the (combined) generator has transient states, then the lattice analyzed will be the sub-lattice generated by the set of recurrent states.
ORBIT: The grid generated by the (forward) orbit of a state of the (combined) generator is analyzed. This state is specified as follows. On the following \(J\) lines, the initial state for each component must be given. This is an integer vector with a number of components equal to the order of the component.
PRIMEPOWER: In the case where some component is an MLCG whose modulus is a power of a prime \(p\), then the states visited over a single orbit (sub-cycle) of that component generate a sub-lattice (when \(a \equiv1 \bmod p\)) or belong to the union of \(p-1\) sub-lattices (otherwise). If LatticeType takes this value, and a component is a MLCG ( \(k=1\)), and if the modulus of that MLCG is given in the data file in the form (b): \((x y z)\) with \(z=0\) and \(x\) prime, then what is analyzed is one of those sub-lattices. This is done by dividing the modulus by the appropriate power of \(p\), as described in [17] . For example, if \(p=2\) and \(a \mod8 = 5\), then the modulus is divided by 4 as in [8], [13] .

Enumerator
FULL
RECURRENT
ORBIT
PRIMEPOWER

◆ SearchMethod

enum LatMRG::SearchMethod

Indicates the search method used to find good multipliers \(a_i\).

EXHAUST: the search will be exhaustive over the chosen regions.
RANDOM: the search will be random over the chosen regions.

Enumerator
EXHAUST
RANDOM

Function Documentation

◆ getLatCombo() [1/3]

template<typename Int , typename Dbl >

MRGLattice<Int, Dbl>* LatMRG::getLatCombo	(	std::vector< MRGComponent< Int > * > &	comp,
		int	maxDim
	)

This function computes and returns a MRGLattice that is the lattice of the combination of generators described in the MRGComponents in the vector comp.

This dynamically allocates memory to returned pointer. and needs to be deleted afterwards.

◆ getLatCombo() [2/3]

template MRGLattice< std::int64_t, double > * LatMRG::getLatCombo	(	std::vector< MRGComponent< std::int64_t > * > &	comp,
		int	maxDim
	)

◆ getLatCombo() [3/3]

template MRGLattice< NTL::ZZ, NTL::RR > * LatMRG::getLatCombo	(	std::vector< MRGComponent< NTL::ZZ > * > &	comp,
		int	maxDim
	)

◆ toDecomString()

int LatMRG::toDecomString	(	DecompType &	decom,
		const std::string &	decom_str
	)

decom = decom_str.

Does not change the value of decom if decom_str does not specify a valid value. Returns 0 if a change took place.

◆ toGenString() [1/2]

int LatMRG::toGenString	(	GenType &	type,
		const string &	type_str
	)

◆ toGenString() [2/2]

int LatMRG::toGenString	(	GenType &	type,
		const std::string &	type_str
	)

type = type_str.

Does not change the value of type if type_str does not specify a valid value. Returns 0 if a change took place.

◆ toString()

std::string LatMRG::toString ( Chrono & timer )

Returns the value of the duration from timer.

◆ toStringDecomp()

string LatMRG::toStringDecomp ( DecompType deco )

◆ toStringGen()

string LatMRG::toStringGen ( GenType gen )

◆ toStringImplemCond()

string LatMRG::toStringImplemCond ( ImplemCond cond )

◆ toStringLattice()

string LatMRG::toStringLattice ( LatticeType lat )

◆ toStringSearchMethod()

string LatMRG::toStringSearchMethod ( SearchMethod method )

Namespaces

Classes

Enumerations

Functions