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CONCLUSIONS

The results of our assessment of inversive pseudorandom number generator s with prime moduli can be summarized as follows:

(i) the choice of parameters is simple, even trivial in the case of the EICG,

(ii) initialization is trivial,

(iii) the excellent theoretical and empirical properties of inversive methods remain stable under the variation of parameters, provided we have maximal period length,

(iv) the outstanding theoretical properties remain invariant under the compound approach,

(v) the EICG has remarkable splitting properties which have been tested extensively for disjoint substreams, with excellent numerical results,

(vi) hundreds of empirical results imply that we may work with considerably larger samples than in the case of LCG, and

(vii) the modular inversion involved causes acceptable slow-downs when generating pseudorandom number s: the time factor is less than 3.0 in comparison to the LCG, provided the simple guideline concerning the multipliers is respected (see Section 5).


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Peter Hellekalek