This class implements methods and fields needed by the classes. More...

Public Member Functions
String	toString ()
	This method returns a string containing the polynomial \(P(z)\) and the stepping parameter.

Static Public Member Functions
static void	print (String filename)
	Prints the content of file filename.

Package Functions
	F2wStructure (int w, int r, int modQ, int step, int nbcoeff, int coeff[], int nocoeff[])
	Constructs a F2wStructure object that contains the parameters of a polynomial in \(\mathbb F_{2^w}[z]\), as well as a stepping parameter.
	F2wStructure (String filename, int no)
	Constructs a polynomial in \(\mathbb F_{2^w}[z]\) after reading its parameters from file filename; the parameters of this polynomial are stored at line number no of filename.
int	getLog2N ()
	This method returns the product \(rw\).
int	multiply (int a, int b)
	Method that multiplies two elements in \(\mathbb F_{2^w}\).

Detailed Description

This class implements methods and fields needed by the classes.

umontreal.ssj.hups.F2wNetLFSR, umontreal.ssj.hups.F2wNetPolyLCG, umontreal.ssj.hups.F2wCycleBasedLFSR and umontreal.ssj.hups.F2wCycleBasedPolyLCG. It also stores the parameters of these point sets which will contain \(2^{rw}\) points (see the meaning of \(r\) and \(w\) below). The parameters can be stored as a polynomial \(P(z)\) over \(\mathbb F_{2^w}[z]\)

\[ P(z) = z^r + \sum_{i=1}^r b_i z^{r-i} \]

where \(b_i\in\mathbb F_{2^w}\) for \(i=1,…,r\). Let \(\zeta\) be the root of an irreducible polynomial \(Q(z)\in\mathbb F_2[z]\). It is well known that \(\zeta\) is a generator of the finite field \(\mathbb F_{2^w}\). The elements of \(\mathbb F_{2^w}\) are represented using the polynomial ordered basis \((1,\zeta,…,\zeta^{w-1})\).

In this class, only the non-zero coefficients of \(P(z)\) are stored. It is stored as

\[ P(z) = z^{\mathtt{r}} + \sum_{i=0}^{\mathtt{nbcoeff}} {\mathtt{coeff[}}i{\mathtt{]}} z^{{\mathtt{nocoeff[}}i{\mathtt{]}}} \]

where the coefficients in coeff[] represent the non-zero coefficients \(b_i\) of \(P(z)\) using the polynomial basis. The finite field \(\mathbb F_{2^w}\) used is defined by the polynomial

\[ Q(z) = z^w + \sum_{i=1}^w a_i z^{w-i} \]

where \(a_i\in\mathbb F_2\), for \(i=1,…,w\). Polynomial \(Q\) is stored as the bit vector modQ = \((a_w,…,a_1)\).

The class also stores the parameter step that is used by the classes umontreal.ssj.hups.F2wNetLFSR, umontreal.ssj.hups.F2wNetPolyLCG, umontreal.ssj.hups.F2wCycleBasedLFSR and umontreal.ssj.hups.F2wCycleBasedPolyLCG. This parameter is such that the implementation of the recurrence will output a value at every step iterations.

Additional Information

Directory LFSR_equid_max
Filename	Num of poly.
f2wR2_W5.dat	2358
f2wR2_W6.dat	1618
f2wR2_W7.dat	507
f2wR2_W8.dat	26
f2wR2_W9.dat	3
f2wR3_W4.dat	369
f2wR3_W5.dat	26
f2wR3_W6.dat	1
f2wR4_W3.dat	117
f2wR4_W4.dat	1
f2wR5_W2.dat	165
f2wR5_W3.dat	1
f2wR6_W2.dat	36
f2wR6_W3.dat	1
f2wR7_W2.dat	10
f2wR8_W2.dat	11
f2wR9_W2.dat	1

Directory LFSR_equid_sum
Filename	Num of poly.
f2wR2_W5.dat	2276
f2wR2_W6.dat	1121
f2wR2_W7.dat	474
f2wR2_W8.dat	37
f2wR2_W9.dat	6
f2wR3_W4.dat	381
f2wR3_W5.dat	65
f2wR3_W6.dat	7
f2wR4_W3.dat	154
f2wR4_W4.dat	2
f2wR5_W2.dat	688
f2wR5_W3.dat	5
f2wR6_W2.dat	70
f2wR6_W3.dat	1
f2wR7_W2.dat	9
f2wR8_W2.dat	3
f2wR9_W2.dat	3

Directory LFSR_mindist_max
Filename	Num of poly.
f2wR2_W5.dat	1
f2wR2_W6.dat	1
f2wR2_W7.dat	2
f2wR2_W8.dat	2
f2wR2_W9.dat	1
f2wR3_W4.dat	2
f2wR3_W5.dat	2
f2wR3_W6.dat	1
f2wR4_W3.dat	1
f2wR4_W4.dat	1
f2wR5_W2.dat	2
f2wR5_W3.dat	1
f2wR6_W2.dat	4
f2wR6_W3.dat	1
f2wR7_W2.dat	1
f2wR8_W2.dat	1
f2wR9_W2.dat	1

Directory LFSR_mindist_sum
Filename	Num of poly.
f2wR2_W5.dat	1
f2wR2_W6.dat	1
f2wR2_W7.dat	1
f2wR2_W8.dat	1
f2wR2_W9.dat	1
f2wR3_W4.dat	1
f2wR3_W5.dat	1
f2wR3_W6.dat	1
f2wR4_W3.dat	1
f2wR4_W4.dat	2
f2wR5_W2.dat	2
f2wR5_W3.dat	2
f2wR6_W2.dat	1
f2wR6_W3.dat	1
f2wR7_W2.dat	2
f2wR8_W2.dat	1
f2wR9_W2.dat	2

Directory LFSR_tvalue_max
Filename	Num of poly.
f2wR2_W5.dat	7
f2wR2_W6.dat	1
f2wR2_W7.dat	1
f2wR2_W8.dat	1
f2wR2_W9.dat	1
f2wR3_W4.dat	1
f2wR3_W5.dat	1
f2wR3_W6.dat	1
f2wR4_W3.dat	2
f2wR4_W4.dat	1
f2wR5_W2.dat	14
f2wR5_W3.dat	1
f2wR6_W2.dat	2
f2wR6_W3.dat	1
f2wR7_W2.dat	1
f2wR8_W2.dat	1
f2wR9_W2.dat	1

Directory LFSR_tvalue_sum
Filename	Num of poly.
f2wR2_W5.dat	15
f2wR2_W6.dat	1
f2wR2_W7.dat	1
f2wR2_W8.dat	2
f2wR2_W9.dat	1
f2wR3_W4.dat	1
f2wR3_W5.dat	1
f2wR3_W6.dat	1
f2wR4_W3.dat	2
f2wR4_W4.dat	1
f2wR5_W2.dat	13
f2wR5_W3.dat	2
f2wR6_W2.dat	12
f2wR6_W3.dat	1
f2wR7_W2.dat	1
f2wR8_W2.dat	1
f2wR9_W2.dat	1

Definition at line 439 of file F2wStructure.java.

Constructor & Destructor Documentation

◆ F2wStructure() [1/2]

umontreal.ssj.hups.F2wStructure.F2wStructure	(	int	w,
		int	r,
		int	modQ,
		int	step,
		int	nbcoeff,
		int	coeff[],
		int	nocoeff[] )

package

Constructs a F2wStructure object that contains the parameters of a polynomial in \(\mathbb F_{2^w}[z]\), as well as a stepping parameter.

Definition at line 500 of file F2wStructure.java.

◆ F2wStructure() [2/2]

umontreal.ssj.hups.F2wStructure.F2wStructure	(	String	filename,
		int	no )

package

Constructs a polynomial in \(\mathbb F_{2^w}[z]\) after reading its parameters from file filename; the parameters of this polynomial are stored at line number no of filename.

The files are kept in different directories depending on the criteria used in the searches for the parameters defining the polynomials. The different criteria for the searches and the theory behind it are described in [191], [193] . The existing files and the number of polynomials they contain are given in the following tables. The first table below contains files in subdirectory LFSR_equid_max. The name of each file indicates the value of \(r\) and \(w\) for the polynomials. For example, file f2wR2_W5.dat in directory LFSR_equid_max contains the parameters of 2358 polynomials with \(r=2\) and \(w=5\). For example, to use the 5-th polynomial of file f2wR2_W5.dat, one may call F2wStructure("f2wR2_W5.dat", 5). The files of parameters have been stored at the address http://simul.iro.umontreal.ca/ssj/dataF2w/Panneton/. The files should be copied in the user directory, and passed as parameter to the constructor.

Definition at line 524 of file F2wStructure.java.

Member Function Documentation

◆ getLog2N()

int umontreal.ssj.hups.F2wStructure.getLog2N ( )

package

This method returns the product \(rw\).

Definition at line 568 of file F2wStructure.java.

◆ multiply()

int umontreal.ssj.hups.F2wStructure.multiply	(	int	a,
		int	b )

package

Method that multiplies two elements in \(\mathbb F_{2^w}\).

Definition at line 575 of file F2wStructure.java.

◆ print()

void umontreal.ssj.hups.F2wStructure.print ( String filename )

static

Prints the content of file filename.

See the constructor above for the conditions on filename.

Definition at line 638 of file F2wStructure.java.

◆ toString()

String umontreal.ssj.hups.F2wStructure.toString ( )

This method returns a string containing the polynomial \(P(z)\) and the stepping parameter.

Definition at line 667 of file F2wStructure.java.

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

src/main/java/umontreal/ssj/hups/F2wStructure.java

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Static Public Member Functions

Package Functions

Detailed Description

Additional Information

Constructor & Destructor Documentation

◆ F2wStructure() [1/2]

◆ F2wStructure() [2/2]

Member Function Documentation

◆ getLog2N()

◆ multiply()

◆ print()

◆ toString()