Random number generation with multiple streams for sequential and parallel computing

International audienceWe provide a review of the state of the art on the design and implementation of random number generators (RNGs) for simulation, on both sequential and parallel computing environments. We focus on the need for multiple streams and substreams of random numbers, explain how they can be constructed and managed, review software libraries that offer them, and illustrate their usefulness via examples. We also review the basic quality criteria for good random number generators and their theoretical and empirical testing

Reliable Initialization of GPU-enabled Parallel Stochastic Simulations Using Mersenne Twister for Graphics Processors

International audienceParallel stochastic simulations tend to exploit more and more computing power and they are now also developed for General Purpose Graphics Process Units (GP-GPUs). Conse-quently, they need reliable random sources to feed their applications. We propose a survey of the current Pseudo Random Numbers Generators (PRNG) available on GPU. We give a particular focus to the recent Mersenne Twister for Graphics Processors (MTGP) that has just been released. Our work provides empirically checked statuses designed to initialize a particular configuration of this generator, in order to prevent any potential bias introduced by the parallelization of the PRNG

Generiranje pseudoslučajnih brojeva i testovi slučajnosti

U današnje vrijeme algoritmi za generiranje slučajnih brojeva postaju glavni izvor slučajnih brojeva, no oni su deterministički i periodički. Da bi algoritam bio prihvatljiv u nekim osjetljivim područjima poput kriptografije, gdje je nepredvidivost generiranih brojeva ključni zahtjev, on mora proći stroge testove slučajnosti. Ne postoji algoritam koji može proći baš sve testove slučajnosti. Isto tako, ako algoritam prođe sve testove slučajnosti, to ne znači da je on bez greške. Prolazak testova slučajnost može samo pojačati naše povjerenje u pojedini algoritam. Jedino generatori slučajnih brojeva koji koriste fenomene iz prirode mogu generirati stvarne slučajne brojeve, ali je njihova brzina generacije nedovoljna za današnje potrebe. Međutim, u praksi se najčešće koristi hibridni pristup, tj. koristi se pseudoslučajni generator čije se sjeme određuje pomoću generatora stvarnih slučajnih brojeva.In modern times, algorithms for generating random numbers are becoming the main source of random numbers. However, they are deterministic and periodic. An algorithm must pass strict tests of randomness in order to be acceptable for cryptographic and similar purposes, as unpredictability of generated numbers is the main requirement. There is no such algorithm that can pass all tests of randomness, but passing a number of tests can boost our faith in a certain algorithm. Also, if an algorithm has passed all tests of randomness, that does not mean it is flawless. Only random number generators that use some physical phenomenon can generate true random numbers. But, those generators are so slow that they cannot be used for modern purposes. In practice, hybrid approach has shown the best results, where the seed for a pseudorandom number generator is determined with a true random number generator

Des générateurs récursifs multiples combinés rapides avec des coefficients de la forme ±2p1 ±2p2

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal