Method of spectral tests of multiplicative congruential random number generators

摘要

The present invention discloses a new method of spectral tests, on multiplicative congruential generator (d,z,n) or (d,z) comprising an odd integer d for the modulus and an integer z coprime with d for the multiplier and an integer n coprime with d for the seed and generating the sequence of integers {n k :‰¡nz k-1 mod(d)| 1‰¤n k ‰¤d, k=1,2,···} consecutively and giving the output random number sequence by realizing the arithmetic {v k :=n k /d| 0‰¤v k ‰¤1, k=1,2, ···}, the new method being based on the valuation of the geometrical form of the lattice G L (d,z), wherein L consecutive integer outputs of the generator (d,z,n) {Q k :=(n k ,n k+1 ,···,n k+L-1 )| k=1,2, ···} take their seats, through the computation of the largest distance » L (d,z) between parallel and neighboring lattice hyperplanes of G L (d,z) and evaluating Á L '(d,z):=» L (d,z)/M L (d) of the generator (d,z) on the basis of new reference values M L (d):=L -1/2 (L+1) (L-1)/(2L) d (L-1)/L , L‰¥3, and judging (d,z) to be passable if conditions 1<Á L '(d,z)1| 3‰¤L‰¤6}.