Introduction to finite fields and their applications
Introduction to finite fields and their applications
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
ACM Transactions on Modeling and Computer Simulation (TOMACS)
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Maximally equidistributed combined Tausworthe generators
Mathematics of Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Monte Carlo Variance of Scrambled Net Quadrature
SIAM Journal on Numerical Analysis
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
On the L2-discrepancy for anchored boxes
Journal of Complexity
Beware of linear congruential generators with multipliers of the form a = ±2q ±2r
ACM Transactions on Mathematical Software (TOMS)
The k-distribution of generalized feedback shift register pseudorandom numbers
Communications of the ACM
On the performance of birthday spacings tests with certain families of random number generators
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
Combined generators with components from different families
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
The Multiple-Recursive Matrix Method for Pseudorandom Number Generation
Finite Fields and Their Applications
Fast random number generators based on linear recurrences modulo 2: overview and comparison
WSC '05 Proceedings of the 37th conference on Winter simulation
High Quality Uniform Random Number Generation Using LUT Optimised State-transition Matrices
Journal of VLSI Signal Processing Systems
TestU01: A C library for empirical testing of random number generators
ACM Transactions on Mathematical Software (TOMS)
Stateless key distribution for secure intra and inter-group multicast in mobile wireless network
Computer Networks: The International Journal of Computer and Telecommunications Networking
Comparison of Point Sets and Sequences for Quasi-Monte Carlo and for Random Number Generation
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Software Oriented Stream Ciphers Based upon FCSRs in Diversified Mode
INDOCRYPT '09 Proceedings of the 10th International Conference on Cryptology in India: Progress in Cryptology
Resolution-stationary random number generators
Mathematics and Computers in Simulation
A matrix approach for FCSR automata
Cryptography and Communications
Efficient update data generation for DBMS benchmarks
ICPE '12 Proceedings of the 3rd ACM/SPEC International Conference on Performance Engineering
GPU implementation of a scalable non-linear congruential generator for cryptography applications
Proceedings of the 23rd ACM international conference on Great lakes symposium on VLSI
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G. Marsaglia recently introduced a class of very fast xorshift random number generators, whose implementation uses three “xorshift” operations. They belong to a large family of generators based on linear recurrences modulo 2, which also includes shift-register generators, the Mersenne twister, and several others. In this article, we analyze the theoretical properties of xorshift generators, search for the best ones with respect to the equidistribution criterion, and test them empirically. We find that the vast majority of xorshift generators with only three xorshift operations, including those having good equidistribution, fail several simple statistical tests. We also discuss generators with more than three xorshifts.