last version

[book_gpu.git] / BookGPU / Chapters / chapter18 / ch18.tex

diff --git a/BookGPU/Chapters/chapter18/ch18.tex b/BookGPU/Chapters/chapter18/ch18.tex
index 71d2b84ee02307ade24a3af9a91df0c9e0bb82e8..5f0df4b43f0742532c38ab044207665948d37965 100755 (executable)
--- a/BookGPU/Chapters/chapter18/ch18.tex
+++ b/BookGPU/Chapters/chapter18/ch18.tex
@@ -13,14 +13,14 @@ generated by either a deterministic and reproducible algorithm called
 a pseudorandom number generator (PRNG)\index{PRNG}, or by a physical nondeterministic 
 process having all the characteristics of a random noise, called a truly random number
 generator (TRNG). In this chapter, we focus on
 a pseudorandom number generator (PRNG)\index{PRNG}, or by a physical nondeterministic 
 process having all the characteristics of a random noise, called a truly random number
 generator (TRNG). In this chapter, we focus on

-reproducible generators, useful for instance in MonteCarlo-based
+reproducible generators, useful for instance in Monte Carlo-based

 simulators.  These domains need PRNGs that are statistically
 irreproachable.  In some fields such as in numerical simulations,
 speed is a strong requirement that is usually attained by using
 parallel architectures. In that case, a recurrent problem is that a
 deflation of the statistical qualities is often reported, when the
 parallelization of a good PRNG is realized.  This
 simulators.  These domains need PRNGs that are statistically
 irreproachable.  In some fields such as in numerical simulations,
 speed is a strong requirement that is usually attained by using
 parallel architectures. In that case, a recurrent problem is that a
 deflation of the statistical qualities is often reported, when the
 parallelization of a good PRNG is realized.  This

-is why adhoc PRNGs for each possible architecture must be found to
+is why ad hoc PRNGs for each possible architecture must be found to

 achieve both speed and randomness.  On the other hand, speed is not
 the main requirement in cryptography: the most important point is to
 define \emph{secure} generators able to withstand malicious
 achieve both speed and randomness.  On the other hand, speed is not
 the main requirement in cryptography: the most important point is to
 define \emph{secure} generators able to withstand malicious


@@ -81,7 +81,7 @@ naive and improved efficient generators for CPU and for GPU.
 These generators are finally experimented in Section~\ref{sec:experiments}.
 
 
 These generators are finally experimented in Section~\ref{sec:experiments}.
 
 

-\section{Basic remindees}
+\section{Basic reminders}

 \label{section:BASIC RECALLS}
 
 This section is devoted to basic definitions and terminologies in the fields of
 \label{section:BASIC RECALLS}
 
 This section is devoted to basic definitions and terminologies in the fields of


@@ -93,7 +93,7 @@ with basic notions on topology (see for instance~\cite{Devaney}).
 
 
 Chaos theory studies the behavior of dynamical systems that are perfectly predictable, yet appear to be wildly amorphous and meaningless. 
 
 
 Chaos theory studies the behavior of dynamical systems that are perfectly predictable, yet appear to be wildly amorphous and meaningless. 

-Chaotic systems\index{chaotic systems} are highly sensitive to initial conditions, 
+Chaotic systems\index{chaotic!systems} are highly sensitive to initial conditions, 

 which is popularly referred to as the butterfly effect. 
 In other words, small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes, 
 in general rendering long-term prediction impossible  \cite{kellert1994wake}. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved \cite{kellert1994wake}. That is, the deterministic nature of these systems does not make them predictable \cite{kellert1994wake,Werndl01032009}. This behavior is known as deterministic chaos, or simply chaos. It has been well-studied in mathematics and
 which is popularly referred to as the butterfly effect. 
 In other words, small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes, 
 in general rendering long-term prediction impossible  \cite{kellert1994wake}. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved \cite{kellert1994wake}. That is, the deterministic nature of these systems does not make them predictable \cite{kellert1994wake,Werndl01032009}. This behavior is known as deterministic chaos, or simply chaos. It has been well-studied in mathematics and


@@ -149,7 +149,7 @@ When $f$ is chaotic, then the system $(\mathcal{X}, f)$ is chaotic and quoting D
 
 
 
 
 
 

-\subsection{Chaotic iterations}\index{chaotic iterations}
+\subsection{Chaotic iterations}\index{chaotic!iterations}

 \label{subsection:Chaotic iterations}
 
 Let us now introduce an example of a dynamical systems family that has
 \label{subsection:Chaotic iterations}
 
 Let us now introduce an example of a dynamical systems family that has


@@ -247,31 +247,12 @@ satisfies the Devaney's definition of chaos.
 
 
 
 
 
 

-\lstset{language=C,caption={C code of the sequential PRNG based on chaotic iterations},label={algo:seqCIPRNG}}
-\begin{small}
-\begin{lstlisting}
-
-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{lstlisting}
-\end{small}
-
+\lstinputlisting[label=algo:seqCIPRNG,caption={C code of the sequential PRNG based on chaotic iterations}]{Chapters/chapter18/code2.cu}

 
 
 In Listing~\ref{algo:seqCIPRNG} a sequential  version of the proposed PRNG based
 on  chaotic  iterations  is  presented, which extends the generator family 
 
 
 In Listing~\ref{algo:seqCIPRNG} a sequential  version of the proposed PRNG based
 on  chaotic  iterations  is  presented, which extends the generator family 

-formerly presented in~\cite{bgw09:ip,guyeux10}.   The xor  operator  is  represented  by
+formerly presented in~\cite{bgw09:ip,guyeux10}.   The \texttt{xor}  operator  is  represented  by

 \textasciicircum.  This function uses  three classical 64-bit PRNGs, namely the
 \texttt{xorshift},         the          \texttt{xor128},         and         the
 \texttt{xorwow}~\cite{Marsaglia2003}.  In the following, we call them ``xor-like
 \textasciicircum.  This function uses  three classical 64-bit PRNGs, namely the
 \texttt{xorshift},         the          \texttt{xor128},         and         the
 \texttt{xorwow}~\cite{Marsaglia2003}.  In the following, we call them ``xor-like


@@ -298,8 +279,7 @@ simultaneously. In general,  the larger the number of  threads is, the
 more local  memory is  used, and the  less branching  instructions are
 used  (if,  while,  etc.) and so,  the  better the  performances  on  GPU  are.
 Obviously, having these requirements in  mind, it is possible to build
 more local  memory is  used, and the  less branching  instructions are
 used  (if,  while,  etc.) and so,  the  better the  performances  on  GPU  are.
 Obviously, having these requirements in  mind, it is possible to build

-a   program    similar   to    the   one   presented    in  Listing 
-\ref{algo:seqCIPRNG}, which computes  pseudorandom numbers on GPU.  To
+a   program    similar   to    the   one   presented    in  Listing~\ref{algo:seqCIPRNG}, which computes  pseudorandom numbers on GPU.  To

 do  so,  we  must   first  recall  that  in  the  CUDA~\cite{Nvid10}
 environment,    threads    have     a    local    identifier    called
 \texttt{ThreadIdx},  which   is  relative  to   the  block  containing
 do  so,  we  must   first  recall  that  in  the  CUDA~\cite{Nvid10}
 environment,    threads    have     a    local    identifier    called
 \texttt{ThreadIdx},  which   is  relative  to   the  block  containing


@@ -337,7 +317,7 @@ NumThreads: number of threads\;}
 \If{threadIdx is concerned by the computation} {
   retrieve data from InternalVarXorLikeArray[threadIdx] in local variables\;
   \For{i=1 to n} {
 \If{threadIdx is concerned by the computation} {
   retrieve data from InternalVarXorLikeArray[threadIdx] in local variables\;
   \For{i=1 to n} {

-    compute a new PRNG as in Listing\ref{algo:seqCIPRNG}\;
+    compute a new PRNG as in Listing~\ref{algo:seqCIPRNG}\;

     store the new PRNG in NewNb[NumThreads*threadIdx+i]\;
   }
   store internal variables in InternalVarXorLikeArray[threadIdx]\;
     store the new PRNG in NewNb[NumThreads*threadIdx+i]\;
   }
   store internal variables in InternalVarXorLikeArray[threadIdx]\;


@@ -411,7 +391,7 @@ array\_comb1, array\_comb2: Arrays containing combinations of size combination\_
   store internal variables in InternalVarXorLikeArray[threadIdx]\;
 }
 \end{small}
   store internal variables in InternalVarXorLikeArray[threadIdx]\;
 }
 \end{small}

-\caption{Main kernel for the chaotic iterations based PRNG GPU efficient
+\caption{main kernel for the chaotic iterations based PRNG GPU efficient

 version\label{IR}}
 \label{algo:gpu_kernel2} 
 \end{algorithm}
 version\label{IR}}
 \label{algo:gpu_kernel2} 
 \end{algorithm}