X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/blobdiff_plain/a6692cd736d836866212aae44ca8d787b63b1d01..960bbfb1dfac1653313d3028b758caf4ffedb672:/prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 2a27439..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}
 
@@ -44,17 +44,57 @@ Guyeux\thanks{Authors in alphabetic order}}
 \maketitle
 
 \begin{abstract}
-This is the abstract
+
 \end{abstract}
 
 \section{Introduction}
 
+Random  numbers are  used in  many scientific  applications and  simulations. On
+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. 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  images, they are nowadays commonly  used in many scientific
+applications. Therefore,  it is important  to be able to  generate pseudo-random
+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.
+
+
+
+
 Interet des itÃ©rations chaotiques pour gÃ©nÃ©rer des nombre alea\\
 Interet de gÃ©nÃ©rer des nombres alea sur GPU
-\alert{RC, un petit state-of-the-art sur les PRNGs sur GPU ?}
-...
 
 
+\section{Related works on GPU based PRNGs}
+
+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}
 This section is devoted to basic definitions and terminologies in the fields of
@@ -410,7 +450,7 @@ use of more general chaotic iterations to generate pseudo-random numbers
 faster, does not deflate their topological chaos properties.
 
 \subsection{Proofs of Chaos of the General Formulation of the Chaotic Iterations}
-
+\label{deuxiÃ¨me def}
 Let us consider the discrete dynamical systems in chaotic iterations having 
 the general form:
 
@@ -725,17 +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$>>$32)} selects the 32
-most  significants bits  of the  variable \texttt{t}.   So to  produce  a random
-number realizes  6 xor operations with  6 32-bits numbers produced  by 3 64-bits
-PRNG.  This version successes the  BigCrush of the TestU01 battery [P.  Lâecuyer
-  and R. Simard. Testu01].
+based PRNG is  presented.  The xor operator is  represented by \textasciicircum.
+This  function uses  three classical  64-bits PRNG:  the  \texttt{xorshift}, the
+\texttt{xor128}  and  the  \texttt{xorwow}.   In  the following,  we  call  them
+xor-like PRNGSs.   These three PRNGs are  presented in~\cite{Marsaglia2003}.  As
+each xor-like PRNG  used works with 64-bits and as our  PRNG works with 32-bits,
+the use of \texttt{(unsigned int)} selects the 32 least significant bits whereas
+\texttt{(unsigned int)(t3$>>$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}
 
@@ -881,7 +920,7 @@ Devaney's formulation of a chaotic behavior.
 
 \section{Experiments}
 
-Differents experiments have been performed in order to measure the generation
+Different experiments have been performed in order to measure the generation
 speed.
 \begin{figure}[t]
 \begin{center}
@@ -903,6 +942,9 @@ Faire une courbe du nombre de random en fonction du nombre de threads,
 \section{The relativity of disorder}
 \label{sec:de la relativitÃ© du dÃ©sordre}
 
+In the next two sections, we investigate the impact of the choices that have
+lead to the definitions of measures in Sections \ref{sec:chaotic iterations} and \ref{deuxiÃ¨me def}.
+
 \subsection{Impact of the topology's finenesse}
 
 Let us firstly introduce the following notations.
