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rng::Taus2 Class Reference

Maximally Equidistributed Combined Tausworthe generator. More...

#include <Random.h>

List of all members.

Public Methods
std::string	getName () const
	Get the name of this generator.
	Taus2 ()
	Construct a new generator with seed 0.
template<typename T> T	uniformInt (T lower, T upper)
	Return a random integer in the range lower to upper-1 (inclusive).
template<typename T> T	uniformInt (T upper)
	Equivalent to uniformInt(0, upper).
double	unit ()
	Return a random floating point value in the range [0, 1).
double	uniform (double lower, double upper)
	Return a random floating point value in the range [lower, upper).
void	setSeed (unsigned long int s)
	Reseed the random number generator.
void	getState (State &state) const
	Save the current state of the generator.
void	setState (State const &state)
	Restore the generator to a specific state saved with getState().

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Detailed Description

Maximally Equidistributed Combined Tausworthe generator.

This class was adapted from the c-implementation of the taus2 random number generator included in the GNU Scientific Library (rng/taus.c). That implementation is copyright (C) 1996, 1997, 1998, 1999, 2000 James Theiler, Brian Gough.

Comments from the GSL implementation follow:

This is a maximally equidistributed combined Tausworthe generator. The sequence is,

x_n = (s1_n ^ s2_n ^ s3_n)

s1_{n+1} = (((s1_n & 4294967294) <<12) ^ (((s1_n <<13) ^ s1_n) >>19)) s2_{n+1} = (((s2_n & 4294967288) << 4) ^ (((s2_n << 2) ^ s2_n) >>25)) s3_{n+1} = (((s3_n & 4294967280) <<17) ^ (((s3_n << 3) ^ s3_n) >>11))

computed modulo 2^32. In the three formulas above '^' means exclusive-or (C-notation), not exponentiation. Note that the algorithm relies on the properties of 32-bit unsigned integers (it is formally defined on bit-vectors of length 32). I have added a bitmask to make it work on 64 bit machines.

We initialize the generator with s1_1 .. s3_1 = s_n MOD m, where s_n = (69069 * s_{n-1}) mod 2^32, and s_0 = s is the user-supplied seed.

The theoretical value of x_{10007} is 2733957125. The subscript 10007 means (1) seed the generator with s=1 (2) do six warm-up iterations, (3) then do 10000 actual iterations.

The period of this generator is about 2^88.

From: P. L'Ecuyer, "Maximally Equidistributed Combined Tausworthe Generators", Mathematics of Computation, 65, 213 (1996), 203--213.

This is available on the net from L'Ecuyer's home page,

http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme.ps ftp://ftp.iro.umontreal.ca/pub/simulation/lecuyer/papers/tausme.ps

Update: April 2002

There is an erratum in the paper "Tables of Maximally Equidistributed Combined LFSR Generators", Mathematics of Computation, 68, 225 (1999), 261--269: http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme2.ps

... the k_j most significant bits of z_j must be non- zero, for each j. (Note: this restriction also applies to the computer code given in [4], but was mistakenly not mentioned in that paper.)

This affects the seeding procedure by imposing the requirement s1 > 1, s2 > 7, s3 > 15.

The generator taus2 has been added to satisfy this requirement. The original taus generator is unchanged.

Update: November 2002

There was a bug in the correction to the seeding procedure for s2. It affected the following seeds 254679140 1264751179 1519430319 2274823218 2529502358 3284895257 3539574397 (s2 < 8).

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Constructor & Destructor Documentation

rng::Taus2::Taus2 (    )  [inline]

Construct a new generator with seed 0.

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Member Function Documentation

std::string rng::Taus2::getName (    )  const [inline]

Get the name of this generator.

void rng::Taus2::getState (  State &    state )  const

Save the current state of the generator. The state can be restored at any time with setState().

void rng::Taus2::setSeed (  unsigned long int    s )

Reseed the random number generator. Parameters: s  the new seed.

void rng::Taus2::setState (  State const &    state )

Restore the generator to a specific state saved with getState(). The subsequent random numbers will be identical to the sequence following the corresponding getState() call.

double rng::Taus2::uniform (  double    lower, double    upper )  [inline]

Return a random floating point value in the range [lower, upper).

template<typename T> T rng::Taus2::uniformInt (  T    upper )  [inline]

Equivalent to uniformInt(0, upper).

template<typename T> T rng::Taus2::uniformInt (  T    lower, T    upper )  [inline]

Return a random integer in the range lower to upper-1 (inclusive). Parameters: lower  lower bound (inclusive) upper  upper bound (exclusive) Returns: a random integer int the range lower to upper-1 (inclusive)

double rng::Taus2::unit (    )  [inline]

Return a random floating point value in the range [0, 1).

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

• Random.h
• Random.cpp

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SimData version pre-0.4.0. For more information on SimData, visit the SimData Homepage. Generated on Tue Oct 14 12:06:43 2003, using Doxygen 1.2.18.