umontreal.iro.lecuyer.hups

Class F2wCycleBasedLFSR

java.lang.Object

umontreal.iro.lecuyer.hups.PointSet

umontreal.iro.lecuyer.hups.CycleBasedPointSet

umontreal.iro.lecuyer.hups.CycleBasedPointSetBase2

umontreal.iro.lecuyer.hups.F2wCycleBasedLFSR

public class F2wCycleBasedLFSR
extends CycleBasedPointSetBase2

This class creates a point set based upon a linear feedback shift register sequence. The recurrence used to produce the point set is

m_n = ∑_i=1^rb_im_n-i

where m_n∈F_2^w, n >= 0 and b_i∈F_2^w. There is a polynomial in F_2^w[z] associated with this recurrence called the characteristic polynomial. It is

P(z) = z^r + ∑_i=1^rb_iz^r-i.

In the implementation, this polynomial is stored in an object F2wStructure.

Let x = (x⁽⁰⁾,…, x^(p-1))∈F₂^p be a p-bit vector. Let us define the function φ(x) = ∑_i=1^p2^-ix^(i-1). The point set in t dimensions produced by this class is

{(φ(y₀), φ(y_s),…, φ(y_s(t-1)) : (v₀,…,v_r-1)∈F₂^rw}

where y_n = trunc_h(v_n,v_n+1,…), v_n is the representation of m_n under the polynomial basis of F_2^w over F₂, and h = w floor(31/w). The parameter s is called the stepping parameter of the recurrence.

Nested Class Summary

Nested classes/interfaces inherited from class umontreal.iro.lecuyer.hups.CycleBasedPointSetBase2

CycleBasedPointSetBase2.CycleBasedPointSetBase2Iterator

Nested classes/interfaces inherited from class umontreal.iro.lecuyer.hups.CycleBasedPointSet

CycleBasedPointSet.CycleBasedPointSetIterator

Constructor Summary

Constructors

Constructor and Description
F2wCycleBasedLFSR(int w, int r, int modQ, int step, int nbcoeff, int[] coeff, int[] nocoeff) Constructs a point set with 2rw points.
F2wCycleBasedLFSR(java.lang.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.

Method Summary

Methods

Modifier and Type	Method and Description
java.lang.String	toString() Formats a string that contains information about the point set.

Methods inherited from class umontreal.iro.lecuyer.hups.CycleBasedPointSetBase2

addRandomShift, clearRandomShift, formatPoints, getCoordinate, iterator

Methods inherited from class umontreal.iro.lecuyer.hups.CycleBasedPointSet

getDimension

Methods inherited from class umontreal.iro.lecuyer.hups.PointSet

addRandomShift, addRandomShift, addRandomShift, formatPoints, formatPoints, formatPoints, formatPointsBase, formatPointsBase, formatPointsBase, formatPointsBase, formatPointsNumbered, formatPointsNumbered, getNumPoints, getStream, randomize, randomize, randomize, randomize, randomize, setStream, unrandomize

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

F2wCycleBasedLFSR

public F2wCycleBasedLFSR(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 F2wStructure for the meaning of the parameters.

F2wCycleBasedLFSR

public F2wCycleBasedLFSR(java.lang.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 F2wStructure.

Method Detail

toString

public java.lang.String toString()

Description copied from class: PointSet

Formats a string that contains information about the point set.

Overrides:

toString in class CycleBasedPointSet

Returns:

string representation of the point set information