Harmonic analysis of random number generators
Computational Physics
2008-02-03 v1
Abstract
The spectral test of random number generators (R.R. Coveyou and R.D. McPherson, 1967) is generalized. The sequence of random numbers is analyzed explicitly, not just via their n-tupel distributions. We find that the mixed multiplicative generator with power of two modulus does not pass the extended test with an ideal result. Best qualities has a new generator with the recursion formula X(k+1)=a*X(k)+c*int(k/2) mod 2^d. We discuss the choice of the parameters a, c for very large moduli 2^d and present an implementation of the suggested generator with d=256, a=2^128+2^64+2^32+62181, c=(2^160+1)*11463.
Cite
@article{arxiv.physics/9610004,
title = {Harmonic analysis of random number generators},
author = {Oliver Schnetz},
journal= {arXiv preprint arXiv:physics/9610004},
year = {2008}
}
Comments
21 pages, LaTeX, AMSsymbols, 8 BigTeX figures