From: couturie Date: Thu, 3 Nov 2011 21:18:14 +0000 (+0100) Subject: suite X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/commitdiff_plain/960bbfb1dfac1653313d3028b758caf4ffedb672 suite --- diff --git a/mabase.bib b/mabase.bib index bb42b6a..59c6666 100644 --- a/mabase.bib +++ b/mabase.bib @@ -4189,5 +4189,45 @@ @comment{jabref-meta: selector_journal:} @comment{jabref-meta: selector_keywords:Chaos;Entropie Topologique;Tip -e;} + + + + +@InProceedings{Pang:2008:cec, + author = "Wai-Man Pang and Tien-Tsin Wong and Pheng-Ann Heng", + title = "Generating Massive High-Quality Random Numbers using + {GPU}", + booktitle = "2008 IEEE World Congress on Computational + Intelligence", + year = "2008", + editor = "Jun Wang", + address = "Hong Kong", + organization = "IEEE Computational Intelligence Society", + publisher = "IEEE Press", + +} + +@Article{LEcuyerS07, + title = "Test{U01}: {A} {C} library for empirical testing of + random number generators", + author = "Pierre L'Ecuyer and Richard J. Simard", + journal = "ACM Trans. Math. Softw", + year = "2007", + number = "4", + volume = "33", + bibdate = "2007-11-06", + bibsource = "DBLP, + http://dblp.uni-trier.de/db/journals/toms/toms33.html#LEcuyerS07", + URL = "http://doi.acm.org/10.1145/1268776.1268777", +} + +@Article{ZRKB10, + author = {A. Zhmurov, K. Rybnikov, Y. Kholodov, and V. Barsegov}, + title = {Generation of Random Numbers on Graphics Processors: Forced Indentation In Silico of the Bacteriophage HK97}, + journal = {J. Phys. Chem. B}, + year = {2011}, + volume = {115}, + number = {18}, + pages = {5278--5288}, +} diff --git a/prng_gpu.tex b/prng_gpu.tex index 6409faf..39536c6 100644 --- a/prng_gpu.tex +++ b/prng_gpu.tex @@ -34,7 +34,7 @@ \newcommand{\alert}[1]{\begin{color}{blue}\textit{#1}\end{color}} -\title{Efficient Generation of Pseudo-Random Bumbers based on Chaotic Iterations +\title{Efficient Generation of Pseudo-Random Numbers based on Chaotic Iterations on GPU} \begin{document} @@ -50,24 +50,27 @@ Guyeux\thanks{Authors in alphabetic order}} \section{Introduction} Random numbers are used in many scientific applications and simulations. On -finite state machines, like computers, it is not possible to generate random +finite state machines, as computers, it is not possible to generate random numbers but only pseudo-random numbers. In practice, a good pseudo-random number 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. +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. 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. Although graphics processing units (GPU) was initially designed to accelerate -the manipulation of image, they are nowadays commonly used in many scientific +the manipulation of images, they are nowadays commonly used in many scientific applications. Therefore, it is important to be able to generate pseudo-random -numbers in a GPU when a scientific application runs in a GPU. That is why we -also provie an efficient PRNG for GPU respecting based on IC. +numbers inside a GPU when a scientific application runs in a GPU. That is why we +also provide an efficient PRNG for GPU respecting based on IC. @@ -76,10 +79,21 @@ Interet des itérations chaotiques pour générer des nombre alea\\ Interet de générer des nombres alea sur GPU -\section{Related works} +\section{Related works on GPU based PRNGs} -In this section we review some GPU based PRNGs. -\alert{RC, un petit state-of-the-art sur les PRNGs sur GPU ?} +In the litterature many authors have work on defining GPU based PRNGs. We do not +want to be exhaustive and we just give the most significant works from our point +of view. + +In \cite{Pang:2008:cec}, the authors define a PRNG based on cellular automata +which does not require high precision integer arithmetics nor bitwise +operations. There is no mention of statistical tests nor proof that this PRNG is +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. \section{Basic Recalls} \label{section:BASIC RECALLS} @@ -751,17 +765,16 @@ unsigned int CIprng() { In listing~\ref{algo:seqCIprng} a sequential version of our chaotic iterations -based PRNG is presented. The xor operator is represented by -\textasciicircum. This function uses three classical 64-bits PRNG: the -\texttt{xorshift}, the \texttt{xor128} and the \texttt{xorwow}. In the -following, we call them xor-like PRNGSs. These three PRNGs are presented -in~\cite{Marsaglia2003}. As each xor-like PRNG used works with 64-bits and as -our PRNG works with 32-bits, the use of \texttt{(unsigned int)} selects the 32 -least significant bits whereas \texttt{(unsigned int)(t3$>>$32)} selects the 32 -most significants bits of the variable \texttt{t}. So to produce a random -number realizes 6 xor operations with 6 32-bits numbers produced by 3 64-bits -PRNG. This version successes the BigCrush of the TestU01 battery [P. L’ecuyer - and R. Simard. Testu01]. +based PRNG is presented. The xor operator is represented by \textasciicircum. +This function uses three classical 64-bits PRNG: the \texttt{xorshift}, the +\texttt{xor128} and the \texttt{xorwow}. In the following, we call them +xor-like PRNGSs. These three PRNGs are presented in~\cite{Marsaglia2003}. As +each xor-like PRNG used works with 64-bits and as our PRNG works with 32-bits, +the use of \texttt{(unsigned int)} selects the 32 least significant bits whereas +\texttt{(unsigned int)(t3$>>$32)} selects the 32 most significants bits of the +variable \texttt{t}. So to produce a random number realizes 6 xor operations +with 6 32-bits numbers produced by 3 64-bits PRNG. This version successes the +BigCrush of the TestU01 battery~\cite{LEcuyerS07}. \section{Efficient prng based on chaotic iterations on GPU}