new

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

diff --git a/BookGPU/Chapters/chapter18/ch18.tex b/BookGPU/Chapters/chapter18/ch18.tex
index 71d2b84ee02307ade24a3af9a91df0c9e0bb82e8..7c2a3931d7f91c39a8f01f39ecb8d4e59bb1d50b 100755 (executable)
--- a/BookGPU/Chapters/chapter18/ch18.tex
+++ b/BookGPU/Chapters/chapter18/ch18.tex
@@ -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


@@ -247,26 +247,7 @@ 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
 
 
 In Listing~\ref{algo:seqCIPRNG} a sequential  version of the proposed PRNG based


@@ -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]\;