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\title{Efficient generation of pseudo random numbers based on chaotic iterations on GPU}
\begin{document}
\maketitle

\begin{abstract}
This is the abstract
\end{abstract}

\section{Introduction}

Interet des itérations chaotiques pour générer des nombre alea\\
Interet de générer des nombres alea sur GPU
...

\section{Chaotic iterations}

Présentation des itérations chaotiques

\section{Efficient prng based on chaotic iterations}

On parle du séquentiel avec des nombres 64 bits\\

Faire le lien avec le paragraphe précédent (je considère que la stratégie s'appelle $S^i$\\

In  order to  implement efficiently  a PRNG  based on  chaotic iterations  it is
possible to improve  previous works [ref]. One solution  consists in considering
that the  strategy used $S^i$  contains all the  bits for which the  negation is
achieved out. Then instead of applying  the negation on these bits we can simply
apply the  xor operator between  the current number  and the strategy  $S^i$. In
order to obtain the strategy we also use a classical PRNG.

\begin{figure}[htbp]
\begin{center}
\fbox{
\begin{minipage}{14cm}
unsigned int CIprng() \{\\
  static unsigned int x = 123123123;\\
  unsigned long t1 = xorshift();\\
  unsigned long t2 = xor128();\\
  unsigned long t3 = xorwow();\\
  x = x\^\ (unsigned int)t1;\\
  x = x\^\ (unsigned int)(t2$>>$32);\\
  x = x\^\ (unsigned int)(t3$>>$32);\\
  x = x\^\ (unsigned int)t2;\\
  x = x\^\ (unsigned int)(t1$>>$32);\\
  x = x\^\ (unsigned int)t3;\\
  return x;\\
\}
\end{minipage}
}
\end{center}
\caption{sequential Chaotic Iteration PRNG}
\label{algo:seqCIprng}
\end{figure}

In Figure~\ref{algo:seqCIprng}  a sequential  version of our  chaotic iterations
based PRNG  is presented.  This version  uses three classical  64-bits PRNG: the
\texttt{xorshift},  the \texttt{xor128}  and the  \texttt{xorwow}.   These three
PRNGs  are  presented in~\cite{Marsaglia2003}.  As  each  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 bits most significants bits of the variable \texttt{t}.

\section{Efficient prng based on chaotic iterations on GPU}

On parle du passage du sequentiel au GPU

\section{Experiments}

On passe le BigCrush\\
On donne des temps de générations sur GPU/CPU\\
On donne des temps de générations de nombre sur GPU puis on rappatrie sur CPU / CPU ? bof bof, on verra

\section{Lyapunov}

\section{Conclusion}
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