SSJ  3.2.1
Stochastic Simulation in Java
Public Member Functions | List of all members
CycleBasedLFSR Class Reference

LFSR generators produce numbers by generating a sequence of bits from a linear recurrence modulo 2, and forming fractional numbers by taking blocks of successive bits. More...

Inheritance diagram for CycleBasedLFSR:
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Collaboration diagram for CycleBasedLFSR:
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Public Member Functions

 CycleBasedLFSR (int step1, int nbcoeff1, int [] nocoeff1)
 
 CycleBasedLFSR (int step1, int step2, int nbcoeff1, int nbcoeff2, int [] nocoeff1, int [] nocoeff2)
 Constructs a point set based on a combination of two polynomials in base 2 with \(2^{k_1 + k_2}\) points. More...
 
 CycleBasedLFSR (String filename, int no)
 Constructs a point set after reading its parameters from file filename; the parameters associated with number no of filename corresponds to the no-th polynomial. More...
 
String toString ()
 This method returns a string containing the polynomials and the stepping parameters.
 
- 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)
 Adds a random shift 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 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 point set. 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 setStream (RandomStream stream)
 Sets the random stream used to generate random shifts to stream. More...
 
RandomStream getStream ()
 Returns the random stream used to generate random shifts. More...
 
void randomize (PointSetRandomization rand)
 Randomizes the point set using the given rand. More...
 
void addRandomShift (int d1, int d2, RandomStream stream)
 This method does nothing for this generic class. More...
 
void addRandomShift (RandomStream stream)
 This method does nothing for this generic class. More...
 
void addRandomShift (int d1, int d2)
 Similar to addRandomShift(d1, d2, stream), with the current random stream.
 
void addRandomShift ()
 Similar to addRandomShift(0, d2, stream) with the current random stream and d2 the dimension of the current random shift.
 
void clearRandomShift ()
 Erases the current random shift, if any.
 
void randomize (int fromDim, int toDim, RandomStream stream)
 By default, this method simply calls addRandomShift (fromDim, toDim, stream), which does nothing.
 
void randomize (RandomStream stream)
 By default, this method simply calls randomize(0, dim, stream).
 
void randomize (int d1, int d2)
 By default, this method simply calls addRandomShift(d1, d2).
 
void randomize ()
 By default, this method simply calls addRandomShift().
 
void unrandomize ()
 By default, this method simply calls clearRandomShift().
 
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]
 
int dim = 0
 
int numPoints = 0
 
int dimShift = 0
 
int capacityShift = 0
 
RandomStream shiftStream
 
- Static Protected Attributes inherited from PointSet
static final int MAXBITS = 31
 

Detailed Description

LFSR generators produce numbers by generating a sequence of bits from a linear recurrence modulo 2, and forming fractional numbers by taking blocks of successive bits.

More precisely, let \(\mathbb F_2\) denote the finite field with two elements (say, 0 and 1). Let \(P(z) = z^k - a_1 z^{k-1} - \cdots- a_k\) be a polynomial with coefficients in \(\mathbb F_2\), and consider the recurrence

\[ x_n = a_1 x_{n-1} + \cdots+ a_k x_{n-k}, \tag{mrg} \]

whose characteristic polynomial is \(P(z)\). It should be understood that in ( mrg ) all computations are performed in \(\mathbb F_2\) (this can be identified with working in integer arithmetic modulo 2). Suppose that \(\mathbf{s}_0 = (x_0,…,x_{k-1})\in\{0,1\}^k\) is fixed and define

\[ u_n = \sum_{i=1}^L x_{ns+i-1} 2^{-i}, \tag{taus} \]

where \(s\) and \(L\) are positive integers. If \(P\) is primitive, \(\mathbf{s}_0\not0\), and \(\rho= 2^k-1\) is coprime to \(s\), then the sequences ( mrg ) and ( taus ) are both purely periodic with period \(\rho\). Computing \(u_n\) from \(u_{n-1}\) involves performing \(s\) steps of the recurrence ( mrg ).

Suppose now that we have \(J\) LFSR recurrences, the \(j\)-th one having a primitive characteristic polynomial \(P_j(z)\) of degree \(k_j\), and step size \(s_j\). Let \(\{x_{j,n},  n\ge0\}\) be the \(j\)-th LFSR sequence, and define \(x_n = (x_{1,n} + \cdots+ x_{J,n}) \mod2\) and \(u_n\) as in ( taus ). Equivalently, if \(\{u_{j,n},  n\ge0\}\) is the output sequence from the \(j\)-th LFSR, then \(u_n = u_{1,n}\oplus\cdots\oplus u_{J,n}\) where \(\oplus\) denotes the bitwise exclusive-or in the binary expansion. The sequence \(\{x_n\}\) is called the combined LFSR sequence and a generator that produces this \(\{u_n\}\) is called a combined LFSR generator.

Constructor & Destructor Documentation

◆ CycleBasedLFSR() [1/2]

CycleBasedLFSR ( int  step1,
int  step2,
int  nbcoeff1,
int  nbcoeff2,
int []  nocoeff1,
int []  nocoeff2 
)

Constructs a point set based on a combination of two polynomials in base 2 with \(2^{k_1 + k_2}\) points.

The meaning of the parameters is the same as in the case of one polynomial.

◆ CycleBasedLFSR() [2/2]

CycleBasedLFSR ( String  filename,
int  no 
)

Constructs a point set after reading its parameters from file filename; the parameters associated with number no of filename corresponds to the no-th polynomial.

The existing files and the number of polynomials they contain are in the table below. The name of the files describe the number of polynomials \(J\) in the combined LFSR and the number of points \(2^k\) generated. For example, the parameters in file j1_k11.dat are based on \(J = 1\) polynomial and generates \(2^k = 2^{11}\) points, while those in file j2_k17.dat are based on a combination of \(J=2\) polynomials and generates \(2^k = 2^{17}\) points. Thus to use the 3-th combined LFSR of file j2_k17.dat, one must use CycleBasedLFSR("j2_k17", 3).

Filename Num. of polynomials
j1_k11.dat 1
j2_k17.dat 6
j2_k19.dat 4

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