X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/blobdiff_plain/8f1af7e18d4d59611a7b16178ac5f32cfe541056..ecb1754c4e0d138d986131429812fb32f405953f:/prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index c5fbd5d..bf74539 100644
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -126,7 +126,16 @@ stringent statistical evaluation of a sequence claimed as random.
 This battery can be found in the well-known TestU01 package~\cite{LEcuyerS07}.
 Chaos, for its part, refers to the well-established definition of a
 chaotic dynamical system proposed by Devaney~\cite{Devaney}.
-
+\begin{color}{red}
+More precisely, each time we performed a test on a PRNG, we ran it
+twice in order to observe if all p-values are inside [0.01, 0.99]. In
+fact, we observed that few p-values (less than ten) are sometimes
+outside this interval but inside [0.001, 0.999], so that is why a
+second run allows us to confirm that the values outside are not for
+the same test. With this approach all our PRNGs pass the {\it
+  BigCrush} successfully and all p-values are at least once inside
+[0.01, 0.99].
+\end{color}
 
 In a previous work~\cite{bgw09:ip,guyeux10} we have proposed a post-treatment on PRNGs making them behave
 as a chaotic dynamical system. Such a post-treatment leads to a new category of
@@ -480,7 +489,7 @@ We have proposed in~\cite{bgw09:ip} a new family of generators that receives
 two PRNGs as inputs. These two generators are mixed with chaotic iterations, 
 leading thus to a new PRNG that 
 \begin{color}{red}
-should improves the statistical properties of each
+should improve the statistical properties of each
 generator taken alone. 
 Furthermore, the generator obtained by this way possesses various chaos properties that none of the generators used as input
 present.