X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/blobdiff_plain/807fde0ea31c414c79ee3922e51251371e227185..6f71a8e8c76974cada0ce140b630cb1c38835336:/prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index db219a1..27702e8 100644
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -724,6 +724,11 @@ the list of cells to update in the state $x^n$ of the system (represented
 as an integer having $\mathsf{N}$ bits too). More precisely, the $k-$th 
 component of this state (a binary digit) changes if and only if the $k-$th 
 digit in the binary decomposition of $S^n$ is 1.
+\begin{color}{red} 
+Obviously, when $S$ is periodic of period $p$, then $x$ is periodic too of
+period either $p$ or $2p$, depending of the fact that, after $p$ iterations,
+the state of the system may or not be the same than before these iterations.
+\end{color}
 
 The single basic component presented in Eq.~\ref{equation Oplus} is of 
 ordinary use as a good elementary brick in various PRNGs. It corresponds
@@ -1539,20 +1544,20 @@ NumThreads: Number of threads\;
 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\;
+\If{threadIdx is concerned} {
+  retrieve data from InternalVarXorLikeArray[threadIdx] in local variables including shared memory and x\;
   offset = threadIdx\%combination\_size\;
   o1 = threadIdx-offset+array\_comb1[offset]\;
   o2 = threadIdx-offset+array\_comb2[offset]\;
   \For{i=1 to n} {
     t=xor-like()\;
     t=t\textasciicircum shmem[o1]\textasciicircum shmem[o2]\;
-    shared\_mem[threadId]=t\;
+    shared\_mem[threadIdx]=t\;
     x = x\textasciicircum t\;
 
-    store the new PRNG in NewNb[NumThreads*threadId+i]\;
+    store the new PRNG in NewNb[NumThreads*threadIdx+i]\;
   }
-  store internal variables in InternalVarXorLikeArray[threadId]\;
+  store internal variables in InternalVarXorLikeArray[threadIdx]\;
 }
 \end{small}
 \caption{Main kernel for the chaotic iterations based PRNG GPU efficient
@@ -1942,8 +1947,8 @@ array\_shift[4]=\{0,1,3,7\}\;
 }
 
 \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\;
+\If{threadIdx is concerned} {
+  retrieve data from InternalVarBBSArray[threadIdx] 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+array\_comb[bbs1\&7][offset]\;
@@ -1962,12 +1967,12 @@ array\_shift[4]=\{0,1,3,7\}\;
     t$<<$=shift\;
     t|=BBS2(bbs2)\&array\_shift[shift]\;
     t=t\textasciicircum  shmem[o1]\textasciicircum     shmem[o2]\;
-    shared\_mem[threadId]=t\;
+    shared\_mem[threadIdx]=t\;
     x = x\textasciicircum   t\;
 
-    store the new PRNG in NewNb[NumThreads*threadId+i]\;
+    store the new PRNG in NewNb[NumThreads*threadIdx+i]\;
   }
-  store internal variables in InternalVarXorLikeArray[threadId] using a rotation\;
+  store internal variables in InternalVarXorLikeArray[threadIdx] using a rotation\;
 }
 \end{small}
 \caption{main kernel for the BBS based PRNG GPU}