X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/blobdiff_plain/cc4c6aa868df1972b090ffcce36c865b8bf53644..8f1af7e18d4d59611a7b16178ac5f32cfe541056:/prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index bc40b2d..c5fbd5d 100644
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -13,6 +13,9 @@
 \usepackage[standard]{ntheorem}
 \usepackage{algorithmic}
 \usepackage{slashbox}
+\usepackage{ctable}
+\usepackage{tabularx}
+\usepackage{multirow}
 
 % Pour mathds : les ensembles IR, IN, etc.
 \usepackage{dsfont}
@@ -1007,6 +1010,53 @@ a^1 & \text{if}~  z^{n-1} = 0 .\end{array} \right. \end{array}\end{equation}
 
 
 
+\begin{table}
+\renewcommand{\arraystretch}{1.3}
+\caption{TestU01 Statistical Test}
+\label{TestU011}
+\centering
+  \begin{tabular}{lccccc}
+    \toprule
+Test name &Tests& Logistic 		& XORshift	& ISAAC\\
+Rabbit 				& 	38	&21  	 	&14	&0	 \\
+Alphabit 			&	17	&16 		&9	&0	 \\
+Pseudo DieHARD 			&126	&0 	 	&2	&0	\\
+FIPS\_140\_2 			&16	&0 		&0	&0	\\
+SmallCrush 			&15	&4 		&5	&0	 \\
+Crush 				&144	&95 		&57	&0	 \\
+Big Crush 			&160	&125 	 	&55	&0	 \\ \hline
+Failures 		&	&261 	 	&146	&0	 \\
+\bottomrule
+  \end{tabular}
+\end{table}
+
+
+
+\begin{table}
+\renewcommand{\arraystretch}{1.3}
+\caption{TestU01 Statistical Test for Old CI algorithms ($\mathsf{N}=4$)}
+\label{TestU01 for Old CI}
+\centering
+  \begin{tabular}{lcccc}
+    \toprule
+\multirow{3}*{Test name} & \multicolumn{4}{c}{Old CI}\\
+&Logistic& XORshift& ISAAC&ISAAC  \\ 
+&+& +& + & + \\ 
+&Logistic& XORshift& XORshift&ISAAC  \\ \cmidrule(r){2-5}
+Rabbit 				  	&7 	&2 	&0 	&0	 \\
+Alphabit 			 	& 3	&0 	&0 	&0	 \\
+DieHARD 		 	&0 	&0 	&0 	&0	\\
+FIPS\_140\_2 		 	&0 	&0	&0 	&0	\\
+SmallCrush 			 	&2 	&0	&0 	&0	 \\
+Crush 				 	&47 	&4 	&0 	&0	 \\
+Big Crush 			 	&79 	&3 	&0	&0	 \\ \hline
+Failures 	 		 	&138 	&9 	&0 	&0	 \\
+\bottomrule
+  \end{tabular}
+\end{table}
+
+
+
 
 
 \subsection{Statistical tests}
@@ -1106,25 +1156,32 @@ Threshold  value $m$& 19 & 7  & 2& 1 & 11& 9& 3& 4\\ \hline\hline
 \end{tabular}
 \end{table*}
 
+Finally, the TestU01 battery as been launched on three well-known generators 
+(a logistic map, a simple XORshift, and the cryptographically secure ISAAC, 
+see Table~\ref{TestU011}). These results can be compared with 
+Table~\ref{TestU01 for Old CI}, which gives the scores obtained by the
+Old CI PRNG that has received these generators.
+
+
 Next subsection gives a concrete implementation of this Xor CI PRNG, which will 
 new be simply called CIPRNG, or ``the proposed PRNG'', if this statement does not
 raise ambiguity.
 \end{color}
 
-\subsection{Efficient PRNG based on Chaotic Iterations}
+\subsection{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 
-improve the speed of the generator formerly presented in~\cite{bgw09:ip,guyeux10}. 
-The first idea is to consider
-that the provided strategy is a pseudorandom Boolean vector obtained by a
-given PRNG.
-An iteration of the system is simply the bitwise exclusive or between
-the last computed state and the current strategy.
-Topological properties of disorder exhibited by chaotic 
-iterations can be inherited by the inputted generator, we hope by doing so to 
-obtain some statistical improvements while preserving speed.
-
+%
+%Based on the proof presented in the previous section, it is now possible to 
+%improve the speed of the generator formerly presented in~\cite{bgw09:ip,guyeux10}. 
+%The first idea is to consider
+%that the provided strategy is a pseudorandom Boolean vector obtained by a
+%given PRNG.
+%An iteration of the system is simply the bitwise exclusive or between
+%the last computed state and the current strategy.
+%Topological properties of disorder exhibited by chaotic 
+%iterations can be inherited by the inputted generator, we hope by doing so to 
+%obtain some statistical improvements while preserving speed.
+%
 %%RAPH : j'ai virÃ© tout ca
 %% Let us give an example using 16-bits numbers, to clearly understand how the bitwise xor operations
 %% are
