modif

diff --git a/prng_gpu.tex b/prng_gpu.tex
index d95e87f0e69d9d47dab61d8e1e8cb708628cf177..5b07118a5f04aaeae8bc521e7aa1998e4d324321 100644 (file)
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -44,6 +44,14 @@ Guyeux\thanks{Authors in alphabetic order}}
 \maketitle
 
 \begin{abstract}
+In this paper we present a new produce pseudo-random numbers generator (PRNG) on
+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
+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
+cards.
+
 
 \end{abstract}
 
@@ -63,7 +71,7 @@ Concerning  the  chaotic properties,  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). We  have proven  that these  PRNGs are
+PRNG  based on  chaotic iterations. We  have proven  that these  PRNGs are
 chaotic in the Devaney's sense.  In this paper we propose a faster version which
 is also proven to be chaotic.
 
@@ -75,18 +83,22 @@ 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
-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}.  Moreover, we
+define a  new distance to measure  the disorder in  the chaos and we  prove some
+interesting properties with this distance.
 
 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 RECALLS}  gives some  basic recalls  on  Devanay's formation  of chaos  and
-chaotic iterations. In Section~\ref{sec:pseudo-random} the proof of chaos of our
-PRNGs  is  studied.   Section~\ref{sec:efficient  prng}  presents  an  efficient
+  works} we  review some GPU implementions  of PRNG.  Section~\ref{section:BASIC
+  RECALLS} gives some basic recalls  on Devanay's formation of chaos and chaotic
+iterations. In  Section~\ref{sec:pseudo-random} the proof of chaos  of our PRNGs
+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.
 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.
+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.
 
 
 
@@ -748,29 +760,7 @@ x \oplus S^i&=&1&1&0&1&1&1&0&0&0&1&1&1&0&1&0&1\\
  \end{array}
 $$
 
-%% \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\textasciicircum (unsigned int)t1;\\
-%%   x = x\textasciicircum (unsigned int)(t2$>>$32);\\
-%%   x = x\textasciicircum (unsigned int)(t3$>>$32);\\
-%%   x = x\textasciicircum (unsigned int)t2;\\
-%%   x = x\textasciicircum (unsigned int)(t1$>>$32);\\
-%%   x = x\textasciicircum (unsigned int)t3;\\
-%%   return x;\\
-%% \}
-%% \end{minipage}
-%% }
-%% \end{center}
-%% \caption{sequential Chaotic Iteration PRNG}
-%% \label{algo:seqCIprng}
-%% \end{figure}
+
 
 
 
@@ -828,7 +818,7 @@ The principe consists in assigning the computation of a PRNG as in 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~\ref{Jenkins96}  to  initalize  all  the
+have  chosen  to  use  the  ISAAC  PRNG~\cite{Jenkins96}  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