Mersenne twister

A new algorithm called Mersenne Twister (MT) is proposed for generating uniform pseudorandom numbers. For a particular choice of parameters, the algorithm provides a super astronomical period of 219937 - 1 and 623-dimensional equidistribution up to 32-bit accuracy, while using a working area of only 624 words. This is a new variant of the previously proposed generators, TGFSR, modified so as to admit a Mersenne-prime period. The characteristic polynomial has many terms. The distribution up to v bits accuracy for 1 ≤ v ≤ 32 is also shown to be good. An algorithm is also given that checks the primitivity of the characteristic polynomial of MT with computational complexity O(p2) where p is the degree of the polynomial. We implemented this generator in portable C-code. It passed several stringent statistical tests, including diehard. Its speed is comparable to other modern generators. Its merits are due to the efficient algorithms that are unique to polynomial calculations over the two-element field

Pseudo-Random Streams for Distributed and Parallel Stochastic Simulations on GP-GPU

International audienceRandom number generation is a key element of stochastic simulations. It has been widely studied for sequential applications purposes, enabling us to reliably use pseudo-random numbers in this case. Unfortunately, we cannot be so enthusiastic when dealing with parallel stochastic simulations. Many applications still neglect random stream parallelization, leading to potentially biased results. In particular parallel execution platforms, such as Graphics Processing Units (GPUs), add their constraints to those of Pseudo-Random Number Generators (PRNGs) used in parallel. This results in a situation where potential biases can be combined with performance drops when parallelization of random streams has not been carried out rigorously. Here, we propose criteria guiding the design of good GPU-enabled PRNGs. We enhance our comments with a study of the techniques aiming to parallelize random streams correctly, in the context of GPU-enabled stochastic simulations

Abstract Good random number generators are (not so) easy to find

Every random number generator has its advantages and deficiencies. There are no ``safe' ' generators. The practitioner's problem is how to decide which random number generator will suit his needs best. In this paper, we will discuss criteria for good random number generators: theoretical support, empirical evidence and practical aspects. We will study several recent algorithms that perform better than most generators in actual use. We will compare the different methods and supply numerical results as well as selected pointers and links to important literature and other sources. Additional information on random number generation, including the code of most algorithms discussed in this paper is available from our web-server under th

On Weyl sums and skew products over irrational rotations

AbstractLet ϕ : [0, 1] → R have a Lipschitz-continuous derivative on [0, 1], ∫10 ϕ(t)dt = 0, let α ϵ R\Q and write ϕn(x) = ϕ(x) + ϕ({x + α}) + ⋯ + ϕ({x + (n − 1)α}), n ϵ N, x ϵ [0, 1[. In this paper results on the boundedness and the limit points of the sequence (ϕn(x))n ⩾ 1 are given. Further, ergodicity of the skew product (x, y) ↦ (x + α, y + ϕ(x)) on RZ×R is proved for certain classes of ϕ and α