Statistical Testing of Additive Congruential Random Number (ACORN) Generators

Royal Society meeting on Numerical algorithms for high-performance computational science, 2019

The Royal Society, London.

R S Wikramaratna

8 – 9 April 2019


ACORN generators represents an approach to generating uniformly distributed pseudo-random numbers which is straightforward to implement for arbitrarily large order k and modulus M=230t (integer t). They give long period sequences which can be proven theoretically to approximate to uniformity in up to k dimensions. The standard TestU01 Crush and BigCrush Statistical Test Suites are used to demonstrate for ACORN generators with order 8≤k≤25 that the statistical performance improves as the modulus increases from 260 to 2120. With M=2120 and k≥9, ACORN generators passed all the tests for each of 7 initialisations. The only constraint on initialisation was that the seed be an odd integer less than the modulus; this gives more than 2119 different sequences each of length at least 2120, which might reasonably be expected to pass all of the tests in these test suites. An ACORN generator might also be expected to pass any more demanding tests for p-dimensional uniformity that may be required in the future, simply by choosing k≥p and modulus M=230t for sufficiently large t. This contrasts with corresponding results obtained for the widely-used Mersenne Twister MT19937 generator, which consistently failed on two of the tests in both the Crush and BigCrush test suites.

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