An exhaustive analysis of multiplicative congruential random number generators with modulus 231-1
SIAM Journal on Scientific and Statistical Computing
Random number generators: good ones are hard to find
Communications of the ACM
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A More Portable Fortran Random Number Generator
ACM Transactions on Mathematical Software (TOMS)
Coding the Lehmer pseudo-random number generator
Communications of the ACM
Uniform random number generators
Proceedings of the 30th conference on Winter simulation
Beware of linear congruential generators with multipliers of the form a = ±2q ±2r
ACM Transactions on Mathematical Software (TOMS)
Fast combined multiple recursive generators with multipliers of the form a = ±2q ±2r
Proceedings of the 32nd conference on Winter simulation
A system of high-dimensional, efficient, long-cycle and portable uniform random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient and portable multiple recursive generators of large order
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Parallel linear congruential generators with Sophie-Germain moduli
Parallel Computing
Eliminating Conflict Misses Using Prime Number-Based Cache Indexing
IEEE Transactions on Computers
TestU01: A C library for empirical testing of random number generators
ACM Transactions on Mathematical Software (TOMS)
Large-Order Multiple Recursive Generators with Modulus 231-1
INFORMS Journal on Computing
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The demand for random numbers in scientific applications is increasing. However, the most widely used multiplicative, congruential random-number generators with modulus 231 − 1 have a cycle length of about 2.1 × 109. Moreover, developing portable and efficient generators with a larger modulus such as 261 − 1 is more difficult than those with modulus 231 − 1. This article presents the development of multiplicative, congruential generators with modulus m = 2p − 1 and four forms of multipliers: 2k1 &minus 2k2, 2k1 + 2k2, m − 2k1 + 2k2, and m − 2k1 − 2k2, k1 k2. The multipliers for modulus 231 − 1 and 261 − 1 are measured by spectral tests, and the best ones are presented. The generators with these multipliers are portable and vary fast. They have also passed several empirical tests, including the frequency test, the run test, and the maximum-of-t test.