Combining the Mersenne Twister and the Xorgens Designs

TL;DR

This paper introduces a new class of high-speed random number generators by combining Mersenne Twister and Xorgens designs, passing rigorous statistical tests and covering various state sizes and word lengths.

Contribution

It presents a novel hybrid generator design that achieves high speed and strong statistical properties, with comprehensive parameter tables and analysis of dimension gaps.

Findings

Generators passed all TestU01 statistical tests.

Achieved high speed comparable to original generators.

Covered a wide range of state sizes and word lengths.

Abstract

We combine the design of two \emph{random number generators}, \emph{Mersenne Twister} and \emph{Xorgens}, to obtain a new class of generators with heavy-weight characteristic polynomials (exceeded only by the {\sc well} generators) and high speed (comparable with the originals). Tables with parameter combinations are included for state sizes ranging from 521 to 44497 bits and each of the word lengths 32, 64, 128. These generators passed all tests of the \emph{TestU01}-package for each 32-bit integer part and each 64-bit derived real part of the output. We determine \emph{dimension gaps} for 32-bit words, neglecting the non-linear tempering, and compare with an alternative experimental linear tempering.