\section{Efficient prng based on chaotic iterations}
-On parle du séquentiel avec des nombres 64 bits\\
-
-
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 contains all the bits for which the negation is
-achieved out. Then instead of applying the negation on these bits we can simply
+achieved out. Then in order to apply the negation on these bits we can simply
apply the xor operator between the current number and the strategy. In
order to obtain the strategy we also use a classical PRNG.
+Here is an example with 16-bits numbers showing how the bit operations are
+applied. Suppose that $x$ and the strategy $S^i$ are defined in binary mode.
+Then the following table shows the result of $x$ xor $S^i$.
+$$
+\begin{array}{|cc|cccccccccccccccc|}
+\hline
+x &=&1&0&1&1&1&0&1&0&1&0&0&1&0&0&1&0\\
+\hline
+S^i &=&0&1&1&0&0&1&1&0&1&1&1&0&0&1&1&1\\
+\hline
+x \oplus S^i&=&1&1&0&1&1&1&0&0&0&1&1&1&0&1&0&1\\
+\hline
+
+\hline
+ \end{array}
+$$
+
%% \begin{figure}[htbp]
%% \begin{center}
%% \fbox{
In listing~\ref{algo:seqCIprng} a sequential version of our chaotic iterations
-based PRNG is presented. This version uses three classical 64-bits PRNG: the
+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
sequential to each thread of the GPU. Of course, it is essential that the three
xor-like PRNGs used for our computation have different parameters. So we chose
them randomly with another PRNG. As the initialisation is performed by the CPU,
-we have chosen to use the ISAAC PRNG to initalize all the parameters for the GPU
-version of our PRNG. The implementation of the three xor-like PRNGs is
+we have chosen to use the ISAAC PRNG [ref] to initalize all the parameters for
+the GPU version of our PRNG. The implementation of the three xor-like PRNGs is
straightforward as soon as their parameters have been allocated in the GPU
memory. Each xor-like PRNGs used works with an internal number $x$ which keeps
the last generated random numbers. Other internal variables are also used by the
and random number of our PRNG is equals to $100,000\times ((4+5+6)\times
2+(1+100))=1,310,000$ 32-bits numbers, i.e. about $52$Mb.
+All the tests performed to pass the BigCrush of TestU01 succeeded. Different
+number of threads have been tested upto $10$ millions.
+
\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
+Differents experiments have been performed in order to measure the generation speed.
+
+
+First of all we have compared the time to generate X random numbers with both the CPU version and the GPU version.
+
+Faire une courbe du nombre de random en fonction du nombre de threads, éventuellement en fonction du nombres de threads par bloc.
\section{Conclusion}
