X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/blobdiff_plain/a6692cd736d836866212aae44ca8d787b63b1d01..c1ba143536007ddfded6ec4043d1a77536e27d75:/prng_gpu.tex?ds=inline

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 2a27439..6409faf 100644
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -44,17 +44,43 @@ 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, like  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.
+
+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
+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.
+
+
+
+
 Interet des itérations chaotiques pour générer des nombre alea\\
 Interet de générer des nombres alea sur GPU
-\alert{RC, un petit state-of-the-art sur les PRNGs sur GPU ?}
-...
 
 
+\section{Related works}
+
+In this section we review some GPU based PRNGs.
+\alert{RC, un petit state-of-the-art sur les PRNGs sur GPU ?}
+
 \section{Basic Recalls}
 \label{section:BASIC RECALLS}
 This section is devoted to basic definitions and terminologies in the fields of
@@ -410,7 +436,7 @@ 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{deuxième def}
 Let us consider the discrete dynamical systems in chaotic iterations having 
 the general form:
 
@@ -881,7 +907,7 @@ 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 +929,9 @@ Faire une courbe du nombre de random en fonction du nombre de threads,
 \section{The relativity of disorder}
 \label{sec:de la relativité du désordre}
 
+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{deuxième def}.
+
 \subsection{Impact of the topology's finenesse}
 
 Let us firstly introduce the following notations.