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

diff --git a/BookGPU/Chapters/chapter18/ch18.tex b/BookGPU/Chapters/chapter18/ch18.tex
index d161c762743db39f988c5184b14a94ae4f4b22b0..9e92d3e1965faba93e0b0cd9c275cb890352c8e4 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


@@ -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


@@ -252,7 +252,7 @@ satisfies the Devaney's definition of chaos.
 
 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