Tables of linear congruential generators of different sizes and good lattice structure

@article{LEcuyer1999TablesOL,
  title={Tables of linear congruential generators of different sizes and good lattice structure},
  author={Pierre L'Ecuyer},
  journal={Math. Comput.},
  year={1999},
  volume={68},
  pages={249-260}
}
  • P. L'Ecuyer
  • Published 1999
  • Mathematics, Computer Science
  • Math. Comput.
We provide sets of parameters for multiplicative linear congruential generators (MLCGs) of different sizes and good performance with respect to the spectral test. For ` = 8, 9, . . . , 64, 127, 128, we take as a modulus m the largest prime smaller than 2`, and provide a list of multipliers a such that the MLCG with modulus m and multiplier a has a good lattice structure in dimensions 2 to 32. We provide similar lists for power-of-two moduli m = 2`, for multiplicative and non-multiplicative LCGs… Expand
An analysis of linear congruential random number generators when multiplier restrictions exist
TLDR
An exhaustive search for the best spectral test performance in a full period linear congruential generator (LCG) with the largest prime modulus smaller than 2 b indicates differences exist among the numbers of possible multipliers for the three types of multiplier restrictions. Expand
Optimal Multipliers for Linear Congruential Pseudo-Random Number Generators with Prime Moduli: Parallel Computation and Properties
Two systematic search methods are employed to find multipliers for linear congruential pseudo-random number generation which are optimal with respect to an upper bound for the discrepancy of pairs ofExpand
Admissible and Asymptotically Optimal Linear Congruential Generators
TLDR
This paper presents several examples of admissible and asymptotical optimal sequences of multiplicators that give rise to well-directed search methods for LCGs with good equidistribution properties. Expand
Modulus of Linear Congruential Random Number Generator
This paper considers the problem of empirically analyzing the linear congruential generators (LCGs) with ten largest prime moduli smaller than 231. For each modulus, a computer exhaustive search isExpand
Parallel linear congruential generators with Sophie-Germain moduli
TLDR
The nature of the trade-off implicitly made in the choice of Mersenne primes is investigated by comparing them to parameterized Sophie-Germain prime modulus LCGs, a widely used random number generation suite for parallel, distributed, and grid-based Monte Carlo computations. Expand
Optimal Multipliers for Lcgs with Prime Moduli: Parallel Computation and Properties
Two systematic search methods are employed to nd multipliers for linear congru-ential pseudo-random number generation which are optimal with respect to an upper bound for the discrepancy of pairs ofExpand
Dimensionality of Spectral Test for a Linear Congruential Random Number Generator
Abstract This paper considers the successive dimensions of the spectral test for a linear congruential generator (LCG) based on three types of the upper bound on the center density. We conduct anExpand
Beware of linear congruential generators with multipliers of the form a = ±2q ±2r
TLDR
This note generalizes this algorithm, points out statistical weaknesses of these multipliers when used in a straightforward manner, and suggests in what context they could be used safely. Expand
Asymptotical behavior of linear congruential generators
TLDR
It is proved, f.e., that the classical spectral test can be described in terms of a special probability metric inducing a topology of weak convergence. Expand
A Method of Systematic Search for Optimal Multipliers in Congruential Random Number Generators
This paper presents a method of systematic search for optimal multipliers for congruential random number generators. The word-size of computers is a limiting factor for development of random numbers.Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 17 REFERENCES
Multiplicative congruential random number generators with modulus 2^{}: an exhaustive analysis for =32 and a partial analysis for =48
This paper presents the results of a search to find optimal maximal period multipliers for multiplicative congruential random number generators with moduli 2 32 and 2 48 . Here a multiplier is saidExpand
An Implementation of the Lattice and Spectral Tests for Multiple Recursive Linear Random Number Generators
TLDR
The implementation of theoretical tests to assess the structural properties of simple or combined linear congruential and multiple recursive random number generators are discussed and a package implementing the so-called spectral and lattice tests for such generators is described. Expand
Combination of multiplicative congruential random-number generators with safe prime modulus
TLDR
The authors recommend to make the modulus of each of the component generators a safe prime, and to chose the multipliers of the components so as to maximize the period and make the serial correlations small in absolute value. Expand
An Exhaustive Analysis of Multiplicative Congruential Random Number Generators with Modulus $2^{31} - 1$
This paper presents the results of an exhaustive search to find optimal full period multipliers for the multiplicative congruential random number generator with prime modulus $2^{31} - 1$. Here aExpand
A search for good multiple recursive random number generators
TLDR
An extensive computer search for good multiple recursive generators, in terms of their lattice structure and implementation speed, finds generators that are a little slower than the usual linear congruential generators, but have much longer periods and much better statistical properties. Expand
Efficient and portable combined random number generators
TLDR
An efficient way to combine two or more Multiplicative Linear Congruential Generators (MLCGs) is presented and a generator whose period is the least common multiple of the individual periods is produced. Expand
Sphere packings, I
  • T. Hales
  • Mathematics, Computer Science
  • Discret. Comput. Geom.
  • 1997
TLDR
A program to prove the Kepler conjecture on sphere packings is described and it is shown that every Delaunay star that satisfies a certain regularity condition satisfies the conjecture. Expand
Random number generation and Quasi-Monte Carlo methods
  • H. Niederreiter
  • Mathematics, Computer Science
  • CBMS-NSF regional conference series in applied mathematics
  • 1992
TLDR
This chapter discusses Monte Carlo methods and Quasi-Monte Carlo methods for optimization, which are used for numerical integration, and their applications in random numbers and pseudorandom numbers. Expand
Monte Carlo
TLDR
This lecture covers the other major method for generating atomic trajectories: the Monte Carlo (MC) approach, which rigorously generate correct thermodynamic properties as they are designed by construction to do so. Expand
The Art of Computer Programming
TLDR
The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid. Expand
...
1
2
...