new

diff --git a/mabase.bib b/mabase.bib
index ae0a8d5456e6f870e9b5f9adbefeedc1f6eb2f02..81621283a67827013aafe5dcf3535dabd8c79833 100644 (file)
--- a/mabase.bib
+++ b/mabase.bib
@@ -4267,6 +4267,14 @@ booktitle =      "Proceedings of the {ACM}/{SIGDA} 17th International
 @manual{Nvid10,
  author = {Nvidia},
  title = {Cuda cublas library},
 @manual{Nvid10,
  author = {Nvidia},
  title = {Cuda cublas library},

- year = {2010},
- Note = {Version 3.1},
+ year = {2011},
+ Note = {Version 4.0},

  }
  }

+
+@manual{curand11,
+ author = {Nvidia},
+ title = {Curand library},
+ year = {2011},
+ Note = {Version 4.0},
+ }
+

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 150e4342563c7ffba2d0d8086cd38847d623491c..2dfa78eea6ef6361c4d513340bdcc3cfeb299922 100644 (file)
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -44,9 +44,9 @@ Guyeux\thanks{Authors in alphabetic order}}
 \maketitle
 
 \begin{abstract}
 \maketitle
 
 \begin{abstract}

-In this paper we present a new produce pseudo-random numbers generator (PRNG) on
+In this paper we present a new pseudo-random numbers generator (PRNG) on

 graphics processing units  (GPU). This PRNG is based  on chaotic iterations.  it
 graphics processing units  (GPU). This PRNG is based  on chaotic iterations.  it

-is proven  to be chaotic  in the Devany's  formulation. We propose  an efficient
+is proven  to be chaotic  in the Devanay's  formulation. We propose  an efficient

 implementation  for  GPU which  succeeds  to  the  {\it BigCrush},  the  hardest
 batteries of test of TestU01.  Experimentations show that this PRNG can generate
 about 20 billions of random numbers  per second on Tesla C1060 and NVidia GTX280
 implementation  for  GPU which  succeeds  to  the  {\it BigCrush},  the  hardest
 batteries of test of TestU01.  Experimentations show that this PRNG can generate
 about 20 billions of random numbers  per second on Tesla C1060 and NVidia GTX280


@@ -59,7 +59,7 @@ cards.
 
 Random  numbers are  used in  many scientific  applications and  simulations. On
 finite  state machines,  as computers,  it is  not possible  to  generate random
 
 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
+numbers but only pseudo-random numbers. In practice, a good pseudo-random numbers

 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
 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


@@ -83,9 +83,7 @@ also provide  an efficient  PRNG for  GPU respecting based  on IC.  Such devices
 allows us to generated almost 20 billions of random numbers per second.
 
 In order  to establish  that our  PRNGs are chaotic  according to  the Devaney's
 allows us to generated almost 20 billions of random numbers per second.
 
 In order  to establish  that our  PRNGs are chaotic  according to  the Devaney's

-formulation, we  extend what we  have proposed in~\cite{guyeux10}.  Moreover, we
-define a  new distance to measure  the disorder in  the chaos and we  prove some
-interesting properties with this distance.
+formulation, we  extend what we  have proposed in~\cite{guyeux10}.

 
 The rest of this paper  is organised as follows. In Section~\ref{section:related
   works} we  review some GPU implementions  of PRNG.  Section~\ref{section:BASIC
 
 The rest of this paper  is organised as follows. In Section~\ref{section:related
   works} we  review some GPU implementions  of PRNG.  Section~\ref{section:BASIC


@@ -95,10 +93,7 @@ is   studied.    Section~\ref{sec:efficient    prng}   presents   an   efficient
 implementation of  our chaotic PRNG  on a CPU.   Section~\ref{sec:efficient prng
   gpu}   describes   the  GPU   implementation   of   our   chaotic  PRNG.    In
 Section~\ref{sec:experiments}     some    experimentations     are    presented.
 implementation of  our chaotic PRNG  on a CPU.   Section~\ref{sec:efficient prng
   gpu}   describes   the  GPU   implementation   of   our   chaotic  PRNG.    In
 Section~\ref{sec:experiments}     some    experimentations     are    presented.

-Section~\ref{sec:de  la  relativité du  désordre}  describes  the relativity  of
-disorder.   In Section~\ref{sec: chaos  order topology}  the proof  that chaotic
-iterations   can  be   described   by   iterations  on   a   real  interval   is
-established. Finally, we give a conclusion and some perspectives.
+ Finally, we give a conclusion and some perspectives.

 
 
 
 
 
 


@@ -134,6 +129,12 @@ efficient one because it provides the fastest number of generated random numbers
 per joule. Concerning the GPU,  authors can generate betweend 11 and 16GSample/s
 with a GTX 280  GPU. The drawback of this work is  that those PRNGs only succeed
 the {\it Crush} test which is easier than the {\it Big Crush} test.
 per joule. Concerning the GPU,  authors can generate betweend 11 and 16GSample/s
 with a GTX 280  GPU. The drawback of this work is  that those PRNGs only succeed
 the {\it Crush} test which is easier than the {\it Big Crush} test.

+
+Cuda  has developped  a  library for  the  generation of  random numbers  called
+Curand~\cite{curand11}.        Several       PRNGs        are       implemented:
+Xorwow~\cite{Marsaglia2003} and  some variants of Sobol. Some  tests report that
+the  fastest version provides  15GSample/s on  the new  Fermi C2050  card. Their
+PRNGs fail to succeed the whole tests of TestU01 on only one test.

 \newline
 \newline
 To the best of our knowledge no GPU implementation have been proven to have chaotic properties.
 \newline
 \newline
 To the best of our knowledge no GPU implementation have been proven to have chaotic properties.


@@ -413,7 +414,7 @@ It takes as input: a function $f$;
 an integer $b$, ensuring that the number of executed iterations is at least $b$
 and at most $2b+1$; and an initial configuration $x^0$.
 It returns the new generated configuration $x$.  Internally, it embeds two
 an integer $b$, ensuring that the number of executed iterations is at least $b$
 and at most $2b+1$; and an initial configuration $x^0$.
 It returns the new generated configuration $x$.  Internally, it embeds two

-\textit{XORshift}$(k)$ PRNGs \cite{Marsaglia2003} that returns integers
+\textit{XORshift}$(k)$ PRNGs~\cite{Marsaglia2003} that returns integers

 uniformly distributed
 into $\llbracket 1 ; k \rrbracket$.
 \textit{XORshift} is a category of very fast PRNGs designed by George Marsaglia,
 uniformly distributed
 into $\llbracket 1 ; k \rrbracket$.
 \textit{XORshift} is a category of very fast PRNGs designed by George Marsaglia,


@@ -860,6 +861,9 @@ and  random  number of  our  PRNG  is  equals to  $100,000\times  ((4+5+6)\times
 All the  tests performed  to pass the  BigCrush of TestU01  succeeded. Different
 number of threads, called \texttt{NumThreads} in our algorithm, have been tested
 upto $10$ millions.
 All the  tests performed  to pass the  BigCrush of TestU01  succeeded. Different
 number of threads, called \texttt{NumThreads} in our algorithm, have been tested
 upto $10$ millions.

+\newline
+\newline
+{\bf QUESTION : on laisse cette remarque, je suis mitigé !!!}

 
 \begin{remark}
 Algorithm~\ref{algo:gpu_kernel}  has  the  advantage to  manipulate  independent
 
 \begin{remark}
 Algorithm~\ref{algo:gpu_kernel}  has  the  advantage to  manipulate  independent


@@ -978,10 +982,10 @@ In  comparison,   Listing~\ref{algo:seqCIprng}  allows  us   to  generate  about
 
 
 
 
 
 

-\section{Cryptanalysis of the Proposed PRNG}
+%% \section{Cryptanalysis of the Proposed PRNG}

 
 
 
 

-Mettre ici la preuve de PCH
+%% Mettre ici la preuve de PCH

 
 %\section{The relativity of disorder}
 %\label{sec:de la relativité du désordre}
 
 %\section{The relativity of disorder}
 %\label{sec:de la relativité du désordre}


@@ -1515,6 +1519,18 @@ Mettre ici la preuve de PCH
 
 
 \section{Conclusion}
 
 
 \section{Conclusion}

+
+
+In  this  paper  we have  presented  a  new  class  of  PRNGs based  on  chaotic
+iterations. We have proven that these PRNGs are chaotic in the sense of Devenay. 
+
+An efficient implementation on GPU allows us to generate a huge number of pseudo
+random numbers  per second  (about 20Gsample/s). Our  PRNGs succeed to  pass the
+hardest batteries of test (TestU01).
+
+In future  work we plan  to extend our  work in order to  have cryptographically
+secure PRNGs because in some situations this property may be important.
+

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