From: couturie Date: Fri, 4 Nov 2011 20:33:32 +0000 (+0100) Subject: suite X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/commitdiff_plain/3a4d92d48d8e34ab9e636f7eb092235bcfa0215d suite --- diff --git a/prng_gpu.tex b/prng_gpu.tex index 39536c6..41e628a 100644 --- a/prng_gpu.tex +++ b/prng_gpu.tex @@ -56,15 +56,16 @@ generator (PRNG) needs to verify some features to be used by scientists. It is important to be able to generate pseudo-random numbers efficiently, the generation needs to be reproducible and a PRNG needs to satisfy many usual statistical properties. Finally, from our point a view, it is essential to prove -that a PRNG is chaotic. Devaney~\cite{Devaney} proposed a common mathematical -formulation of chaotic dynamical systems. Concerning the statistical tests, -TestU01the is the best-known public-domain statistical testing packages. So we -use it for all our PRNGs, especially the {\it BigCrush} which is based on the largest -serie of tests. +that a PRNG is chaotic. Concerning the statistical tests, TestU01 is the +best-known public-domain statistical testing package. So we use it for all our +PRNGs, especially the {\it BigCrush} which provides the largest serie of tests. +Concerning the chaotic properties, Devaney~\cite{Devaney} proposed a common +mathematical formulation of chaotic dynamical systems. In a previous work~\cite{bgw09:ip} we have proposed a new familly of chaotic -PRNG based on chaotic iterations (IC). In this paper we propose a faster -version which is also proven to be chaotic with the Devaney formulation. +PRNG based on chaotic iterations (IC). We have proven that these PRNGs are +chaotic in the Devaney's sense. In this paper we propose a faster version which +is also proven to be chaotic. Although graphics processing units (GPU) was initially designed to accelerate the manipulation of images, they are nowadays commonly used in many scientific @@ -92,8 +93,13 @@ chaotic. Concerning the speed of generation, they can generate about 3200000 random numbers per seconds on a GeForce 7800 GTX GPU (which is quite old now). In \cite{ZRKB10}, the authors propose different versions of efficient GPU PRNGs -based on Lagged Fibonacci, Hybrid Taus or Hybrid Taus. They have used these -PRNGs for Langevin simulations of biomolecules fully implemented on GPU. +based on Lagged Fibonacci, Hybrid Taus or Hybrid Taus. They have used these +PRNGs for Langevin simulations of biomolecules fully implemented on +GPU. Performance of the GPU versions are far better than those obtained with a +CPU and these PRNGs succeed to pass the {\it BigCrush} test of TestU01. There is +no mention that their PRNGs have chaos mathematical properties. + +To the best of our knowledge no GPU implementation have been proven to have chaotic properties. \section{Basic Recalls} \label{section:BASIC RECALLS}