-In Listing~\ref{algo:seqCIPRNG} a sequential version of the proposed PRNG based on chaotic iterations
- is presented. The xor operator is represented by \textasciicircum.
-This function uses three classical 64-bits PRNGs, namely the \texttt{xorshift}, the
-\texttt{xor128}, and the \texttt{xorwow}~\cite{Marsaglia2003}. In the following, we call them
-``xor-like PRNGs''.
-As
-each xor-like PRNG uses 64-bits whereas our proposed generator works with 32-bits,
-we use the command \texttt{(unsigned int)}, that selects the 32 least significant bits of a given integer, and the code
-\texttt{(unsigned int)(t3$>>$32)} in order to obtain the 32 most significant bits of \texttt{t}.
-
-So producing a pseudorandom number needs 6 xor operations
-with 6 32-bits numbers that are provided by 3 64-bits PRNGs. This version successfully passes the
+In Listing~\ref{algo:seqCIPRNG} a sequential version of the proposed PRNG based
+on chaotic iterations is presented. The xor operator is represented by
+\textasciicircum. This function uses three classical 64-bits PRNGs, namely the
+\texttt{xorshift}, the \texttt{xor128}, and the
+\texttt{xorwow}~\cite{Marsaglia2003}. In the following, we call them ``xor-like
+PRNGs''. As each xor-like PRNG uses 64-bits whereas our proposed generator
+works with 32-bits, we use the command \texttt{(unsigned int)}, that selects the
+32 least significant bits of a given integer, and the code \texttt{(unsigned
+ int)(t$>>$32)} in order to obtain the 32 most significant bits of \texttt{t}.
+
+So producing a pseudorandom number needs 6 xor operations with 6 32-bits numbers
+that are provided by 3 64-bits PRNGs. This version successfully passes the
stringent BigCrush battery of tests~\cite{LEcuyerS07}.
\section{Efficient PRNGs based on Chaotic Iterations on GPU}
contains the indexes of all threads and for which a combination has been
performed.
-In Algorithm~\ref{algo:gpu_kernel2}, two combination arrays are used.
-The variable \texttt{offset} is computed using the value of
+In Algorithm~\ref{algo:gpu_kernel2}, two combination arrays are used. The
+variable \texttt{offset} is computed using the value of
\texttt{combination\_size}. Then we can compute \texttt{o1} and \texttt{o2}
-representing the indexes of the other threads whose results are used
-by the current one. In this algorithm, we consider that a 64-bits xor-like
-PRNG has been chosen, and so its two 32-bits parts are used.
+representing the indexes of the other threads whose results are used by the
+current one. In this algorithm, we consider that a 32-bits xor-like PRNG has
+been chosen. In practice, we use the xor128 proposed in~\cite{Marsaglia2003} in
+which unsigned longs (64 bits) have been replaced by unsigned integers (32
+bits).
This version also can pass the whole {\it BigCrush} battery of tests.
\KwIn{InternalVarXorLikeArray: array with internal variables of 1 xor-like PRNGs
in global memory\;
NumThreads: Number of threads\;
-tab1, tab2: Arrays containing combinations of size combination\_size\;}
+array\_comb1, array\_comb2: Arrays containing combinations of size combination\_size\;}
\KwOut{NewNb: array containing random numbers in global memory}
\If{threadId is concerned} {
retrieve data from InternalVarXorLikeArray[threadId] in local variables including shared memory and x\;
offset = threadIdx\%combination\_size\;
- o1 = threadIdx-offset+tab1[offset]\;
- o2 = threadIdx-offset+tab2[offset]\;
+ o1 = threadIdx-offset+array\_comb1[offset]\;
+ o2 = threadIdx-offset+array\_comb2[offset]\;
\For{i=1 to n} {
t=xor-like()\;
t=t $\wedge$ shmem[o1] $\wedge$ shmem[o2]\;
\KwIn{InternalVarBBSArray: array with internal variables of the 8 BBS
in global memory\;
NumThreads: Number of threads\;
-tab: 2D Arrays containing 16 combinations (in first dimension) of size combination\_size (in second dimension)\;}
+array\_comb: 2D Arrays containing 16 combinations (in first dimension) of size combination\_size (in second dimension)\;
+
+}
\KwOut{NewNb: array containing random numbers in global memory}
\If{threadId is concerned} {
retrieve data from InternalVarBBSArray[threadId] in local variables including shared memory and x\;
we consider that bbs1 ... bbs8 represent the internal states of the 8 BBS numbers\;
offset = threadIdx\%combination\_size\;
- o1 = threadIdx-offset+tab[bbs1\&7][offset]\;
- o2 = threadIdx-offset+tab[8+bbs2\&7][offset]\;
+ o1 = threadIdx-offset+array\_comb[bbs1\&7][offset]\;
+ o2 = threadIdx-offset+array\_comb[8+bbs2\&7][offset]\;
\For{i=1 to n} {
t<<=4\;
t|=BBS1(bbs1)\&15\;
