From 893deb2477f17914ca2f0420009697c0925d5cbe Mon Sep 17 00:00:00 2001 From: cguyeux Date: Thu, 20 Sep 2012 17:54:33 +0200 Subject: [PATCH 1/1] lkfjlkfdjqlf --- prng_gpu.tex | 29 ++++++++++------------------- 1 file changed, 10 insertions(+), 19 deletions(-) diff --git a/prng_gpu.tex b/prng_gpu.tex index 25214fd..32055e7 100644 --- a/prng_gpu.tex +++ b/prng_gpu.tex @@ -192,12 +192,11 @@ The remainder of this paper is organized as follows. In Section~\ref{section:re and on an iteration process called ``chaotic iterations'' on which the post-treatment is based. The proposed PRNG and its proof of chaos are given in Section~\ref{sec:pseudorandom}. - -Section~\ref{The generation of pseudorandom sequence} illustrates the statistical -improvement related to the chaotic iteration based post-treatment, for -our previously released PRNGs and a new efficient +Section~\ref{sec:efficient PRNG} %{The generation of pseudorandom sequence} %illustrates the statistical +%improvement related to the chaotic iteration based post-treatment, for +%our previously released PRNGs and + contains a new efficient implementation on CPU. - Section~\ref{sec:efficient PRNG gpu} describes and evaluates theoretically the GPU implementation. Such generators are experimented in @@ -726,15 +725,7 @@ investigated in Annex~\ref{A-deuxième def}, leading to the following result. \begin{theorem} \label{t:chaos des general} - The general chaotic iterations defined by - \begin{equation} - x_i^n=\left\{ - \begin{array}{ll} - x_i^{n-1} & \text{ if } i \notin \mathcal{S}^n \\ - \left(f(x^{n-1})\right)_{S^n} & \text{ if }i \in \mathcal{S}^n. - \end{array}\right. - \label{general CIs} - \end{equation} + The general chaotic iterations defined in Equation~\ref{eq:generalIC} satisfy the Devaney's property of chaos. \end{theorem} @@ -998,10 +989,10 @@ satisfy %%RAF : mis en supplementary -\section{Statistical Improvements Using Chaotic Iterations} -\label{The generation of pseudorandom sequence} -The content is this section is given in Section~\ref{A-The generation of pseudorandom sequence} of the annex document. - +%\section{Statistical Improvements Using Chaotic Iterations} +%\label{The generation of pseudorandom sequence} +%The content is this section is given in Section~\ref{A-The generation of pseudorandom sequence} of the annex document. +The reasons to desire chaos to achieve randomness are given in Annex~\ref{A-The generation of pseudorandom sequence}. %% \label{The generation of pseudorandom sequence} @@ -1325,7 +1316,7 @@ The content is this section is given in Section~\ref{A-The generation of pseudor %% raise ambiguity. -\subsection{First Efficient Implementation of a PRNG based on Chaotic Iterations} +\section{First Efficient Implementation of a PRNG based on Chaotic Iterations} \label{sec:efficient PRNG} % %Based on the proof presented in the previous section, it is now possible to -- 2.39.5