Design Search and Implementation of High-dimensional Efficient Long-cycle and Portable Uniform Random Variate Generator

Abstract

We propose a general class of uniform random variate generators with the nice property of High-dimension uniformity, Efficient, Long-cycle and Portable (HELP). It includes FMRG-k, proposed by Deng and Lin (2000), as a special class. FMRG-k, belonging to a wider class Multiple Recursive Generator (MRG), is a much more efficient generator than a general MRG. Here k is the degree of polynomial used in the recurrence relations. The value of k will determine the dimension of uniformity and the length of the cycle for MRG (and FMRG-k). In general, we prefer to find a larger value of k for FMRG-k because a larger k will improve the quality of the generator and it will not increase the computing time. We will first extend FMRG-k to a wider class, called HELP-k. We then discuss the main common problems in the search of HELP-k, for a large k. An efficient search algorithm will be discussed. In particular, we currently extend results by Deng and Lin (2000) for FMRG-k, from k 100. Listing of HELP-k and its C++/FORTRAN program implementation is also given. We offer HELP-k as an alternative to MT19937, a powerful random number generator proposed by Matumoto and Nishimura (1998). More recent results and detailed comparison will be also given.