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8 Generator Instantiations

8.1 BorlandRandGen

 The BorlandRandGen class implements the generator from the rand() function supplied in the Borland C++ v4.5 standard library. This generator is derived from the LinConRandGen class and is implemented in the file erndlcon.h. Although the generator itself retains 32 bits of seed, the output range is limited to 0-32767. The constructor for this class has the following prototype:

explicit BorlandRandGen( size_rand seed )

Requires a seed value. This seed defaults to 1 if none is supplied.

8.2 StdCRandGen

The StdCRandGen class implements the generator from the rand() function described in the ANSI C Standard ([7]). This generator is derived from the LinConRandGen class and is implemented in the file erndlcon.h. Although the generator itself retains 32 bits of seed, the output range is limited to 0-32767. The constructor for this class has the following prototype:

explicit StdCRandGen( size_rand seed )

Requires a seed value. This seed defaults to 1 if none is supplied.

8.3 BoroshNiederreiterRandGen

The generator implemented by the BoroshNiederreiterRandGen class is described in [4, pages 102-104]. It is derived from MultConRandGen and is implemented in the file erndmcon.h. This generator did very well on the spectral test for dimensions 2, 3, and 5, according to Knuth. The constructor for this class has the following prototype:

explicit BoroshNiederreiterRandGen( size_rand seed )

Requires a seed value. This seed defaults to 1 if none is supplied.

8.4 WatermanRandGen

The generator implemented by the WatermanRandGen class is described in [4, pages 102-104]. It is derived from MultConRandGen and is implemented in the file erndmcon.h. This generator did very well on the spectral test for dimensions 2, 3, 4, and 5, according to Knuth. The constructor for this class has the following prototype:

explicit WatermanRandGen( size_rand seed )

Requires a seed value. This seed defaults to 1 if none is supplied.

8.5 MarsagliaMCRandGen

The MarsagliaMCRandGen class implements a Multiplicative random number generator that was nominated by George Marsaglia as ``a candidate for the best of all multipliers'' according to [4]. This distinction was based on the spectral test for dimensions 2 through 5, and partly because the multiplier is easy to remember. It is derived from MultConRandGen and is implemented in the file erndlcon.h. The constructor for this class has the following prototype:

explicit MarsagliaMCRandGen( size_rand seed )

Requires a seed value. This seed defaults to 1 if none is supplied.

8.6 LavauxJanssensRandGen

The generator implemented by the LavauxJanssensRandGen class is described in [4, pages 102-104]. It is derived from MultConRandGen and is implemented in the file erndlcon.h. This generator did very well on the spectral test for dimensions 2 through 6, according to Knuth. The constructor for this class has the following prototype:

explicit LavauxJanssensRandGen( size_rand seed )

Requires a seed value. This seed defaults to 1 if none is supplied.

8.7 Knuth28RandGen

The Knuth28RandGen class is derived from SecConModRandGen and is implemented in the file erndsecm.h. In [4], this generator is described as having a period length of (231-1)2-1. The Knuth28RandGen class is based on the equation

Xn = (271828183Xn-1 - 314159269Xn-2) mod (231-1).

Although it does have a long period, this generator only did very well on dimensions 2 and 3 of the spectral test, according to Knuth. The constructor for this class has the following prototype:

explicit Knuth28RandGen( size_rand seed )

Requires a seed value. This seed defaults to 1 if none is supplied.

8.8 Knuth22RandGen

The generator implemented by the Knuth22RandGen class is described in [4, pages 102-104]. It is derived from MultConModRandGen and is implemented in the file erndmcnm.h. This generator did very well on the spectral test for dimension 2, according to Knuth. The constructor for this class has the following prototype:

explicit Knuth22RandGen( size_rand seed )

Requires a seed value. This seed defaults to 1 if none is supplied.

8.9 Knuth27RandGen

The generator implemented by the Knuth27RandGen class is described in [4, pages 102-104]. It is derived from MultConModRandGen and is implemented in the file erndmcnm.h. This generator did very well on the spectral test for dimensions 2 through 6, according to Knuth. The constructor for this class has the following prototype:

explicit Knuth27RandGen( size_rand seed )

Requires a seed value. This seed defaults to 1 if none is supplied.

8.10 MitchellMooreRandGen

The generator implemented by the MitchellMooreRandGen class is described in [4, page 26]. The class is derived from the LaggedFibonacciModRandGen and is implemented in the file erndlfib.h. This generator has a number of interesting properties. The least significant bits of any sequence generated by this generator will have a period of 255-1. The period has been found to be approximately 285-1. The MitchellMooreRandGen generator is based on the equation

Xn = (Xn-24 + Xn-55) mod m.

Knuth had reported that the main reason for not using this generator was a lack of theory regarding its operation. Since that time, research reported in [6] shows that generators of this type can be quite good. The constructor for this class has the following prototype:

explicit MitchellMooreRandGen( unsigned long mod, RandomGenerator *pRng )

Requires a pointer to a heap-based PRNG object. The MitchellMooreRandGen object owns this PRNG and deletes it when the object is destroyed. The mod parameter defines the modulus used in the calculations.

For further information, contact G. Wade Johnson (gwadej@anomaly.org).

© 1997 G. Wade Johnson. All rights reserved.
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