umontreal.iro.lecuyer.hups

Class F2wCycleBasedPolyLCG

java.lang.Object

umontreal.iro.lecuyer.hups.PointSet

umontreal.iro.lecuyer.hups.CycleBasedPointSet

umontreal.iro.lecuyer.hups.CycleBasedPointSetBase2

umontreal.iro.lecuyer.hups.F2wCycleBasedPolyLCG

public class F2wCycleBasedPolyLCG
extends CycleBasedPointSetBase2

This class creates a point set based upon a linear congruential sequence in the finite field F_2^w[z]/P(z). The recurrence is

q_n(z) = z^sq_n-1(z) mod P(z)

where P(z)∈F_2^w[z] has degree r and q_n(z) = q_{n, 1}z^r-1 + ^... + q_{n, r}∈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 F2wStructure. See the description of this class for more details on how the polynomial is stored.

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(y₁),…, φ(y_t-1) : (q_{0, 1},…,q_{0, r-1})∈F₂^rw}

where y_n = (q_{n, 1},…,q_{n, r}), q_{n, i} is the representation of q_{n, i} under the polynomial basis of F_2^w over F₂.

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
F2wCycleBasedPolyLCG(int w, int r, int modQ, int step, int nbcoeff, int[] coeff, int[] nocoeff) Constructs a point set with 2rw points.
F2wCycleBasedPolyLCG(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

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

F2wCycleBasedPolyLCG

public 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 F2wStructure for the meaning of the parameters.

F2wCycleBasedPolyLCG

public F2wCycleBasedPolyLCG(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