X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/blobdiff_plain/9000a5dc19eb61806daa88858a42b7a433da0c5d..7350647ed60074e4d6b4e25a68dac9cd91a268e1:/prng_gpu.tex?ds=sidebyside diff --git a/prng_gpu.tex b/prng_gpu.tex index 19adf22..c48aeda 100644 --- a/prng_gpu.tex +++ b/prng_gpu.tex @@ -74,11 +74,11 @@ numbers inside a GPU when a scientific application runs in a GPU. That is why we also provide an efficient PRNG for GPU respecting based on IC. Such devices allows us to generated almost 20 billions of random numbers per second. -In order to establish +In order to establish that our PRNGs are chaotic according to the Devaney's +formulation, we extend what we have proposed in~\cite{guyeux10}. Moreover, we define a new distance to measure the disorder in the chaos and we prove some interesting properties with this distance. The rest of this paper is organised as follows. In Section~\ref{section:related - works} we review some GPU implementions of PRNG. Section~\ref{sec:chaotic - iterations} gives some basic recalls on Devanay's formation of chaos and + works} we review some GPU implementions of PRNG. Section~\ref{section:BASIC RECALLS} gives some basic recalls on Devanay's formation of chaos and chaotic iterations. In Section~\ref{sec:pseudo-random} the proof of chaos of our PRNGs is studied. Section~\ref{sec:efficient prng} presents an efficient implementation of our chaotic PRNG on a CPU. Section~\ref{sec:efficient prng @@ -817,8 +817,8 @@ the larger the number of threads is, the more local memory is used and the less branching instructions are used (if, while, ...), the better performance is obtained on GPU. So with algorithm \ref{algo:seqCIprng} presented in the previous section, it is possible to build a similar program which computes PRNG -on GPU. In the CUDA [ref] environment, threads have a local identificator, -called \texttt{ThreadIdx} relative to the block containing them. +on GPU. In the CUDA~\cite{Nvid10} environment, threads have a local +identificator, called \texttt{ThreadIdx} relative to the block containing them. \subsection{Naive version for GPU} @@ -828,14 +828,14 @@ The principe consists in assigning the computation of a PRNG as in sequential to each thread of the GPU. Of course, it is essential that the three xor-like PRNGs used for our computation have different parameters. So we chose them randomly with another PRNG. As the initialisation is performed by the CPU, we -have chosen to use the ISAAC PRNG [ref] to initalize all the parameters for the -GPU version of our PRNG. The implementation of the three xor-like PRNGs is -straightforward as soon as their parameters have been allocated in the GPU -memory. Each xor-like PRNGs used works with an internal number $x$ which keeps -the last generated random numbers. Other internal variables are also used by the -xor-like PRNGs. More precisely, the implementation of the xor128, the xorshift -and the xorwow respectively require 4, 5 and 6 unsigned long as internal -variables. +have chosen to use the ISAAC PRNG~\ref{Jenkins96} to initalize all the +parameters for the GPU version of our PRNG. The implementation of the three +xor-like PRNGs is straightforward as soon as their parameters have been +allocated in the GPU memory. Each xor-like PRNGs used works with an internal +number $x$ which keeps the last generated random numbers. Other internal +variables are also used by the xor-like PRNGs. More precisely, the +implementation of the xor128, the xorshift and the xorwow respectively require +4, 5 and 6 unsigned long as internal variables. \begin{algorithm} @@ -895,7 +895,7 @@ which represent the indexes of the other threads for which the results are used by the current thread. In the algorithm, we consider that a 64-bits xor-like PRNG is used, that is why both 32-bits parts are used. -This version also succeed to the BigCrush batteries of tests. +This version also succeeds to the {\it BigCrush} batteries of tests. \begin{algorithm} @@ -954,22 +954,34 @@ Devaney's formulation of a chaotic behavior. \section{Experiments} \label{sec:experiments} -Different experiments have been performed in order to measure the generation -speed. -\begin{figure}[t] +Different experiments have been performed in order to measure the generation +speed. We have used a computer equiped with Tesla C1060 NVidia GPU card and an +Intel Xeon E5530 cadenced at 2.40 GHz for our experiments. + +In Figure~\ref{fig:time_gpu} we compare the number of random numbers generated +per second. In order to obtain the optimal number we remove the storage of +random numbers in the GPU memory. This step is time consumming and slows down +the random number generation. Moreover, if you are interested by applications +that consome random number directly when they are generated, their storage is +completely useless. In this figure we can see that when the number of threads is +greater than approximately 30,000 upto 5 millions the number of random numbers +generated per second is almost constant. With the naive version, it is between +2.5 and 3GSample/s. With the optimized version, it is almost equals to +20GSample/s. + +\begin{figure}[htbp] \begin{center} \includegraphics[scale=.7]{curve_time_gpu.pdf} \end{center} \caption{Number of random numbers generated per second} -\label{fig:time_naive_gpu} +\label{fig:time_gpu} \end{figure} -First of all we have compared the time to generate X random numbers with both -the CPU version and the GPU version. +In comparison, Listing~\ref{algo:seqCIprng} allows us to generate about +138MSample/s with only one core of the Xeon E5530. + -Faire une courbe du nombre de random en fonction du nombre de threads, -éventuellement en fonction du nombres de threads par bloc.