F2wCycleBasedPolyLCG Class Reference

This class creates a point set based upon a linear congruential sequence in the finite field \(\mathbb F_{2^w}[z]/P(z)\). More...

Inheritance diagram for F2wCycleBasedPolyLCG:

Collaboration diagram for F2wCycleBasedPolyLCG:

Public Member Functions
	F2wCycleBasedPolyLCG (int w, int r, int modQ, int step, int nbcoeff, int coeff[], int nocoeff[])
	Constructs a point set with \(2^{rw}\) points. More...
	F2wCycleBasedPolyLCG (String filename, int no)
	Constructs a point set after reading its parameters from file filename; the parameters are located at line numbered no of filename. More...
String	toString ()
Public Member Functions inherited from CycleBasedPointSetBase2
double	getCoordinate (int i, int j)
PointSetIterator	iterator ()
void	addRandomShift (int d1, int d2, RandomStream stream)
	Adds a random digital shift in base 2 to all the points of the point set, using stream stream to generate the random numbers, for coordinates d1 to d2 - 1. More...
void	clearRandomShift ()
	Erases the current digital random shift, if any.
String	formatPoints ()
Public Member Functions inherited from CycleBasedPointSet
double	getCoordinate (int i, int j)
void	addRandomShift (int d1, int d2, RandomStream stream)
	Same as the same method in PointSet. More...
void	clearRandomShift ()
	Erases the current random shift, if any.
int	getDimension ()
PointSetIterator	iterator ()
String	toString ()
String	formatPoints ()
Public Member Functions inherited from PointSet
int	getDimension ()
	Returns the dimension (number of available coordinates) of the points. More...
int	getNumPoints ()
	Returns the number of points. More...
abstract double	getCoordinate (int i, int j)
	Returns \(u_{i,j}\), the coordinate \(j\) of the point \(i\). More...
PointSetIterator	iterator ()
	Constructs and returns a point set iterator. More...
void	randomize (PointSetRandomization rand)
	Randomizes this point set using the given rand. More...
void	addRandomShift (int d1, int d2, RandomStream stream)
	By default, this method generates a random shift in the protected double[] array shift, to be used eventually for a random shift modulo 1. More...
void	addRandomShift (RandomStream stream)
	Same as addRandomShift(0, dim, stream), where dim is the dimension of the point set. More...
void	addRandomShift (int d1, int d2)
	Refreshes the random shift (generates new uniform values for the random shift coordinates) for coordinates d1 to d2-1, using the saved shiftStream.
void	addRandomShift ()
	Same as addRandomShift(0, dim), where dim is the dimension of the point set.
void	clearRandomShift ()
	Erases the current random shift, if any.
String	toString ()
	Formats a string that contains information about the point set. More...
String	formatPoints ()
	Same as invoking formatPoints(n, d) with \(n\) and \(d\) equal to the number of points and the dimension of this object, respectively. More...
String	formatPoints (int n, int d)
	Formats a string that displays the same information as returned by toString, together with the first \(d\) coordinates of the first \(n\) points. More...
String	formatPoints (PointSetIterator iter)
	Same as invoking formatPoints(iter, n, d) with \(n\) and \(d\) equal to the number of points and the dimension, respectively. More...
String	formatPoints (PointSetIterator iter, int n, int d)
	Same as invoking formatPoints(n, d), but prints the points by calling iter repeatedly. More...
String	formatPointsBase (int b)
	Similar to formatPoints(), but the points coordinates are printed in base \(b\). More...
String	formatPointsBase (int n, int d, int b)
	Similar to formatPoints(n, d), but the points coordinates are printed in base \(b\). More...
String	formatPointsBase (PointSetIterator iter, int b)
	Similar to formatPoints(iter), but the points coordinates are printed in base \(b\). More...
String	formatPointsBase (PointSetIterator iter, int n, int d, int b)
	Similar to formatPoints(iter, n, d), but the points coordinates are printed in base \(b\). More...
String	formatPointsNumbered ()
	Same as invoking formatPointsNumbered(n, d) with \(n\) and \(d\) equal to the number of points and the dimension, respectively. More...
String	formatPointsNumbered (int n, int d)
	Same as invoking formatPoints(n,d), except that the points are numbered. More...

Additional Inherited Members
Protected Member Functions inherited from CycleBasedPointSet
void	addCycle (AbstractList c)
	Adds the cycle c to the list of all cycles. More...
Protected Attributes inherited from CycleBasedPointSetBase2
int	numBits
double	normFactor
Protected Attributes inherited from CycleBasedPointSet
int	numCycles = 0
ObjectArrayList	cycles = new ObjectArrayList()
Protected Attributes inherited from PointSet
double	EpsilonHalf = 1.0 / Num.TWOEXP[55]
	To avoid 0 for nextCoordinate when random shifting, we add this to each coordinate.
int	dim = 0
	Dimension of the points.
int	numPoints = 0
	Number of points.
int	dimShift = 0
	Current dimension of the shift. More...
int	capacityShift = 0
	Number of array elements in the shift vector, always >= dimShift.
double []	shift
	This is the shift vector as a double[] array, which contains the current random shift in case we apply a random shift modulo 1. More...
RandomStream	shiftStream
	Stream used to generate the random shifts. More...
Static Protected Attributes inherited from PointSet
static final int	MAXBITS = 31
	Since Java has no unsigned type, the 32nd bit cannot be used efficiently, so we have only 31 bits. More...

Detailed Description

This class creates a point set based upon a linear congruential sequence in the finite field \(\mathbb F_{2^w}[z]/P(z)\).

The recurrence is

\[ q_n(z) = z^s q_{n-1}(z) \mod P(z) \]

where \(P(z)\in\mathbb F_{2^w}[z]\) has degree \(r\) and \(q_n(z) = q_{n,1} z^{r-1} + \cdots+ q_{n,r} \in\mathbb F_{2^w}[z]/P(z)\). The parameter \(s\) is called the stepping parameter of the recurrence. The polynomial \(P(z)\) is not necessarily the characteristic polynomial of this recurrence, but it can still be used to store the parameters of the recurrence. In the implementation, it is stored in an object of the class umontreal.ssj.hups.F2wStructure. See the description of this class for more details on how the polynomial is stored.

Let \(\mathbf{x} = (x^{(0)}, …, x^{(p-1)}) \in\mathbb F_2^p\) be a \(p\)-bit vector. Let us define the function \(\phi(\mathbf{x}) = \sum_{i=1}^p 2^{-i} x^{(i-1)}\). The point set in \(t\) dimensions produced by this class is

\[ \{ (\phi(\mathbf{y}_0),\phi(\mathbf{y}_1),…,\phi(\mathbf{y}_{t-1}): (\mathbf{q}_{0,1},…,\mathbf{q}_{0,r-1})\in\mathbb F_2^{rw}\} \]

where \(\mathbf{y}_n = (\mathbf{q}_{n,1},…,\mathbf{q}_{n,r})\), \(\mathbf{q}_{n,i}\) is the representation of \(q_{n,i}\) under the polynomial basis of \(\mathbb F_{2^w}\) over \(\mathbb F_2\).

Constructor & Destructor Documentation

F2wCycleBasedPolyLCG() [1/2]

F2wCycleBasedPolyLCG	(	int	w,
		int	r,
		int	modQ,
		int	step,
		int	nbcoeff,
		int	coeff[],
		int	nocoeff[]
	)

Constructs a point set with \(2^{rw}\) points.

See the description of the class umontreal.ssj.hups.F2wStructure for the meaning of the parameters. Constructs and stores the set of cycles for an LCG with modulus n and multiplier a. If pgcd(a, n) = 1, this constructs a full-period LCG which has two cycles, one containing 0 and one, the LCG period.

Parameters

n	required number of points and modulo of the LCG
a	generator a of the LCG

F2wCycleBasedPolyLCG() [2/2]

F2wCycleBasedPolyLCG	(	String	filename,
		int	no
	)

Constructs a point set after reading its parameters from file filename; the parameters are located at line numbered no of filename.

The available files are listed in the description of class umontreal.ssj.hups.F2wStructure.

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

• F2wCycleBasedPolyLCG.java