autres modifs

diff --git a/Revision.tex b/Revision.tex
index 8ac9590dcfa1ad8f81fd9eb2e0c48b65bf8970b3..a0f99c1716b0f597c16c2d705844c94c5f09754c 100644 (file)
--- a/Revision.tex
+++ b/Revision.tex
@@ -35,7 +35,7 @@ One minor piece that I didn't find addressed in the paper is the issue of how th
 Excellent excellent work!''
 
 \medskip
 Excellent excellent work!''
 
 \medskip

-In practice the seeds are generated using ISAAC which is a cryptographic PRNG. So the security of our seeds lies on the security of ISAAC. We think that this is enough to consider that our seeds are sufficiently secure.
+{\it In practice the seeds are generated using ISAAC which is a cryptographic PRNG. So the security of our seeds lies on the security of ISAAC. We think that this is enough to consider that our seeds are sufficiently secure.}

 
 \end{enumerate}
 
 
 \end{enumerate}
 


@@ -58,10 +58,10 @@ features their procedure to combine a few weaker but fast generators into a much
 longer period of the resultant generator compared to any of the input generators.''
 
 \medskip
 longer period of the resultant generator compared to any of the input generators.''
 
 \medskip

-We have added the following text in Section 4.2:\\
+{\it We have added the following text in Section 4.2:\\

 Obviously, when $S$ is periodic of period $p$, then $x$ is periodic too of
 period either $p$ or $2p$, depending on the fact that, after $p$ iterations,
 Obviously, when $S$ is periodic of period $p$, then $x$ is periodic too of
 period either $p$ or $2p$, depending on the fact that, after $p$ iterations,

-the state of the system may or not be the same than before these iterations.
+the state of the system may or not be the same than before these iterations.}

 \end{enumerate}
 
 
 \end{enumerate}
 
 


@@ -77,7 +77,7 @@ The paper is very well written and has only a few minor spelling mistakes, altho
 reworked by a native speaker.''
 
 \medskip
 reworked by a native speaker.''
 
 \medskip

-The paper has been reread by a native speaker
+{\it The paper has been reread by a native speaker.}

 
 \item ``The mathematical introductions are short and concise, enabling a reader to gather all relevant knowledge directly from this publication.
  This always raises the question of novelty of the paper, as new aspects are arising only at a later stage in the paper itself 
 
 \item ``The mathematical introductions are short and concise, enabling a reader to gather all relevant knowledge directly from this publication.
  This always raises the question of novelty of the paper, as new aspects are arising only at a later stage in the paper itself 


@@ -85,33 +85,33 @@ The paper has been reread by a native speaker
 While working through the paper a few minor questions arised:
 -      page 7, Algorithm 3: is the increment of i in the while loop implicit, or where is it incremented?''
 
 While working through the paper a few minor questions arised:
 -      page 7, Algorithm 3: is the increment of i in the while loop implicit, or where is it incremented?''
 

-In fact this is implicit with the ''while'' instruction.
+{\it In fact this is implicit with the ''while'' instruction.}

 
 \item ``In Algorithm 5 and 6 threadIdx is written sometimes as threadId''
 
 
 \item ``In Algorithm 5 and 6 threadIdx is written sometimes as threadId''
 

- We have uniformized that
+{\it We have uniformized that.}

 
  \item ``Page 19, Algorithm 6: there are 8 random numbers and their corresponding 8 states. You state that only a few of them are used, which is reflected in the algorithm itself. Are always the same ones used, or do you also rotate there?''
 
 
  \item ``Page 19, Algorithm 6: there are 8 random numbers and their corresponding 8 states. You state that only a few of them are used, which is reflected in the algorithm itself. Are always the same ones used, or do you also rotate there?''
 

-   In practice, 8 BBS random numbers are used but for each of them only the four last bits are used. So we used $8 \times 4=32$ bits. If we chose a bigger number of BBS, the computation would slower. That is why we have used 8 BBS which seems to be a good trade-off.
+{\it   In practice, 8 BBS random numbers are used but for each of them only the four last bits are used. So we used $8 \times 4=32$ bits. If we chose a bigger number of BBS, the computation would slower. That is why we have used 8 BBS which seems to be a good trade-off.}

    
  \item ``In the references starting on page 21, some references need a bit more work. Probably BibTeX did some magic there and needs 
    to be tweaked manually. Example Ref [7] nist needs to be NIST.''
 
    
  \item ``In the references starting on page 21, some references need a bit more work. Probably BibTeX did some magic there and needs 
    to be tweaked manually. Example Ref [7] nist needs to be NIST.''
 

-   We have corrected that.
+{\it   We have corrected that.}

 
    \item ``Another nice aspect to consider in future might be different accelerator-based systems such as Intel Xeon Phi cards and speed measurements
  using such cards. As supercomputers tend to get more and more heterogeneous (Tianhe-2, Stampede) using other accelerators than GPGPUs,
  a Xeon Phi solution might be very beneficial for the community.''
 
 
    \item ``Another nice aspect to consider in future might be different accelerator-based systems such as Intel Xeon Phi cards and speed measurements
  using such cards. As supercomputers tend to get more and more heterogeneous (Tianhe-2, Stampede) using other accelerators than GPGPUs,
  a Xeon Phi solution might be very beneficial for the community.''
 

- Thank you for this remark, we have added that in the future work.
+{\it Thank you for this remark, we have added that in the future work.}

 
 
   \item ``With the strong mathematical focus, the authors could also think about submitting this paper to a different, more 
 mathematically oriented journal, as the focus on supercomputers and supercomputing capabilities is not as strong in this paper. 
 Nevertheless, I recommend the paper for publication.''
 
 
 
   \item ``With the strong mathematical focus, the authors could also think about submitting this paper to a different, more 
 mathematically oriented journal, as the focus on supercomputers and supercomputing capabilities is not as strong in this paper. 
 Nevertheless, I recommend the paper for publication.''
 

-In fact there are different parts in this paper, we have chosen the Journal of Supercomputing because, for previous submissions to this journal, we had interesting reviews and because this journal has a wide audience and is of really high standards.
+{\it In fact there are different parts in this paper, we have chosen the Journal of Supercomputing because, for previous submissions to this journal, we had interesting reviews and because this journal has a wide audience and is of really high standards.}

 \end{enumerate}
 
 
 \end{enumerate}
 
 

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 6ae1ef67161d651368535d85c39290de57654398..e90d0c241698897332ab973a12b42f73eefc0229 100644 (file)
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -18,7 +18,7 @@
 \usepackage{tabularx}
 \usepackage{multirow}
 
 \usepackage{tabularx}
 \usepackage{multirow}
 

-\usepackage{color}
+%\usepackage{color}

 
 % Pour mathds : les ensembles IR, IN, etc.
 \usepackage{dsfont}
 
 % Pour mathds : les ensembles IR, IN, etc.
 \usepackage{dsfont}


@@ -40,7 +40,7 @@
 \newcommand{\BN}{\mathds{B}^\mathsf{N}}
 \let\sur=\overline
 
 \newcommand{\BN}{\mathds{B}^\mathsf{N}}
 \let\sur=\overline
 

-\newcommand{\alert}[1]{\begin{color}{blue}\textit{#1}\end{color}}
+%\newcommand{\alert}[1]{\begin{color}{blue}\textit{#1}\end{color}}

 
 \begin{document}
 
 
 \begin{document}
 


@@ -58,7 +58,7 @@
 %% \ead{pierre-cyrille.heam@univ-fcomte.fr}
 
 \author{Christophe Guyeux \and  Rapha\"{e}l Couturier \and    Pierre-Cyrille Héam \and Jacques M. Bahi\\
 %% \ead{pierre-cyrille.heam@univ-fcomte.fr}
 
 \author{Christophe Guyeux \and  Rapha\"{e}l Couturier \and    Pierre-Cyrille Héam \and Jacques M. Bahi\\

-FEMTO-ST Institute, UMR  6174 CNRS,\\ University of Franche Comte, Belfort, France}
+FEMTO-ST Institute, UMR  6174 CNRS,\\ University of Bourgogne Franche Comte, Belfort, France}

 
 \maketitle
 
 
 \maketitle
 


@@ -194,9 +194,8 @@ original implementation of this PRNG is also proposed and experimented.
 Pseudorandom numbers are generated at a rate of 20GSamples/s, which is faster
 than in~\cite{conf/fpga/ThomasHL09,Marsaglia2003} (and with a better
 statistical behavior). Experiments are also provided using 
 Pseudorandom numbers are generated at a rate of 20GSamples/s, which is faster
 than in~\cite{conf/fpga/ThomasHL09,Marsaglia2003} (and with a better
 statistical behavior). Experiments are also provided using 

-\begin{color}{red} the well-known Blum-Blum-Shub
+ the well-known Blum-Blum-Shub

 (BBS) 
 (BBS) 

-\end{color}

 as the initial
 random generator. The generation speed is significantly weaker.
 %Note also that an original qualitative comparison between topological chaotic
 as the initial
 random generator. The generation speed is significantly weaker.
 %Note also that an original qualitative comparison between topological chaotic


@@ -724,11 +723,9 @@ the list of cells to update in the state $x^n$ of the system (represented
 as an integer having $\mathsf{N}$ bits too). More precisely, the $k-$th 
 component of this state (a binary digit) changes if and only if the $k-$th 
 digit in the binary decomposition of $S^n$ is 1.
 as an integer having $\mathsf{N}$ bits too). More precisely, the $k-$th 
 component of this state (a binary digit) changes if and only if the $k-$th 
 digit in the binary decomposition of $S^n$ is 1.

-\begin{color}{red} 

 Obviously, when $S$ is periodic of period $p$, then $x$ is periodic too of
 period either $p$ or $2p$, depending on the fact that, after $p$ iterations,
 the state of the system may or not be the same as before these iterations.
 Obviously, when $S$ is periodic of period $p$, then $x$ is periodic too of
 period either $p$ or $2p$, depending on the fact that, after $p$ iterations,
 the state of the system may or not be the same as before these iterations.

-\end{color}

 
 The single basic component presented in Eq.~\ref{equation Oplus} is of 
 ordinary use as a good elementary brick in various PRNGs. It corresponds
 
 The single basic component presented in Eq.~\ref{equation Oplus} is of 
 ordinary use as a good elementary brick in various PRNGs. It corresponds


@@ -1494,13 +1491,12 @@ then   the  memory   required   to  store all of the  internals   variables  of
 PRNGs\footnote{we multiply this number by $2$ in order to count 32-bits numbers}
 and  the pseudorandom  numbers generated by  our  PRNG,  is  equal to  $100,000\times  ((4+5+6)\times
 2+(1+100))=1,310,000$ 32-bits numbers, that is, approximately $52$Mb.
 PRNGs\footnote{we multiply this number by $2$ in order to count 32-bits numbers}
 and  the pseudorandom  numbers generated by  our  PRNG,  is  equal to  $100,000\times  ((4+5+6)\times
 2+(1+100))=1,310,000$ 32-bits numbers, that is, approximately $52$Mb.

-\begin{color}{red}

 Remark that the only requirement regarding the seed regarding the security of our PRNG is
 that it must be randomly picked. Indeed, the asymptotic security of BBS guarantees
 that, as the seed length increases, no polynomial time statistical test can 
 distinguish the pseudorandom sequences from truly random sequences with non-negligible probability,
 see, \emph{e.g.},~\cite{Sidorenko:2005:CSB:2179218.2179250}.
 Remark that the only requirement regarding the seed regarding the security of our PRNG is
 that it must be randomly picked. Indeed, the asymptotic security of BBS guarantees
 that, as the seed length increases, no polynomial time statistical test can 
 distinguish the pseudorandom sequences from truly random sequences with non-negligible probability,
 see, \emph{e.g.},~\cite{Sidorenko:2005:CSB:2179218.2179250}.

-\end{color}
+

 
 This generator is able to pass the whole BigCrush battery of tests, for all
 the versions that have been tested depending on their number of threads 
 
 This generator is able to pass the whole BigCrush battery of tests, for all
 the versions that have been tested depending on their number of threads 


@@ -2123,16 +2119,16 @@ In future  work we plan to extend this research, building a parallel PRNG for  c
 grid computing. Topological properties of the various proposed generators will be investigated,
 and the use of other categories of PRNGs as input will be studied too. The improvement
 of Blum-Goldwasser will be deepened.
 grid computing. Topological properties of the various proposed generators will be investigated,
 and the use of other categories of PRNGs as input will be studied too. The improvement
 of Blum-Goldwasser will be deepened.

-\begin{color}{red}

 Another aspect to consider might be different accelerator-based systems like 
 Intel Xeon Phi cards and speed measurements using such cards: as heterogeneity of
 supercomputers tends to increase using other accelerators than GPGPUs,
 a Xeon Phi solution might be interesting to investigate.
 Another aspect to consider might be different accelerator-based systems like 
 Intel Xeon Phi cards and speed measurements using such cards: as heterogeneity of
 supercomputers tends to increase using other accelerators than GPGPUs,
 a Xeon Phi solution might be interesting to investigate.

-\end{color}

  Finally, we
 will try to enlarge the quantity of pseudorandom numbers generated per second either
 in a simulation context or in a cryptographic one.
 
  Finally, we
 will try to enlarge the quantity of pseudorandom numbers generated per second either
 in a simulation context or in a cryptographic one.
 

+\section*{Acknowledgment}
+This work is  partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).

 
 
 \bibliographystyle{plain} 
 
 
 \bibliographystyle{plain}