Efficient and portable combined Tausworthe random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Maximally equidistributed combined Tausworthe generators
Mathematics of Computation
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Tables of maximally equidistributed combined LFSR generators
Mathematics of Computation
An Asymptotically Random Tausworthe Sequence
Journal of the ACM (JACM)
The k-distribution of generalized feedback shift register pseudorandom numbers
Communications of the ACM
On the xorshift random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Improved long-period generators based on linear recurrences modulo 2
ACM Transactions on Mathematical Software (TOMS)
TestU01: A C library for empirical testing of random number generators
ACM Transactions on Mathematical Software (TOMS)
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Besides speed and period length, the quality of uniform random number generators (RNGs) is usually assessed by measuring the uniformity of their point sets, formed by taking vectors of successive output values over their entire period length. For F"2-linear generators, the commonly adopted measures of uniformity are based on the equidistribution of the most significant bits of the output. In this paper, we point out weaknesses of these measures and introduce generalizations that also give importance to the low-order (less significant) bits. These measures look at the equidistribution obtained when we permute the bits of each output value in a certain way. In a parameter search for good generators, a quality criterion based on these new measures of equidistribution helps to avoid generators that fail statistical tests targeting their low-order bits. We also introduce the notion of resolution-stationary generators, whose point sets are invariant under a multiplication by certain powers of 2, modulo 1. For such generators, least significant bits have the same equidistribution properties as the most significant ones. Tausworthe generators have this property. We finally show how an arbitrary F"2-linear generator can be made resolution-stationary by adding an appropriate linear transformation to the output. This provides new efficient ways of implementing high-quality and long-period Tausworthe generators.