X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/7f0014c901a78db6eabc4e705b0fb6f0dd7b681e..d68696e794f5a194dfd430a8397b1e6d55525843:/paper.tex?ds=inline diff --git a/paper.tex b/paper.tex index cdbc6e7..94bdb91 100644 --- a/paper.tex +++ b/paper.tex @@ -92,14 +92,27 @@ %% Lilia Ziane Khodja: Department of Aerospace \& Mechanical Engineering\\ Non Linear Computational Mechanics\\ University of Liege\\ Liege, Belgium. Email: l.zianekhodja@ulg.ac.be \begin{abstract} -ABSTRACT + The behavior of multicore applications is always a challenge to predict, especially with a new architecture for which no experiment has been performed. With some applications, it is difficult, if not impossible, to build accurate performance models. That is why another solution is to use a simulation tool which allows us to change many parameters of the architecture (network bandwidth, latency, number of processors) and to simulate the execution of such applications. We have decided to use SimGrid as it enables to benchmark MPI applications. + +In this paper, we focus our attention on two parallel iterative algorithms based +on the Multisplitting algorithm and we compare them to the GMRES algorithm. +These algorithms are used to solve libear systems. Two different variantsof the Multisplitting are +studied: one using synchronoous iterations and another one with asynchronous +iterations. For each algorithm we have tested different parameters to see their +influence. We strongly recommend people interested by investing into a new +expensive hardware architecture to benchmark their applications using a +simulation tool before. + + + + \end{abstract} \keywords{Algorithm; distributed; iterative; asynchronous; simulation; simgrid; performance} \maketitle -\section{Introduction} +\section{Introduction} \section{The asynchronous iteration model} @@ -196,17 +209,17 @@ The algorithm in Figure~\ref{alg:02} includes the procedure of the residual mini \subsection{Simulation of two-stage methods using SimGrid framework} \label{sec:04.02} -One of our objectives when simulating the application in SIMGRID is, as in real life, to get accurate results (solutions of the problem) but also ensure the test reproducibility under the same conditions.According our experience, very few modifications are required to adapt a MPI program to run in SIMGRID simulator using SMPI (Simulator MPI).The first modification is to include SMPI libraries and related header files (smpi.h). The second and important modification is to eliminate all global variables in moving them to local subroutine or using a Simgrid selector called "runtime automatic switching" (smpi/privatize\_global\_variables). Indeed, global variables can generate side effects on runtime between the threads running in the same process, generated by the Simgrid to simulate the grid environment.The last modification on the MPI program pointed out for some cases, the review of the sequence of the MPI\_Isend, MPI\_Irecv and MPI\_Waitall instructions which might cause an infinite loop. +One of our objectives when simulating the application in SIMGRID is, as in real life, to get accurate results (solutions of the problem) but also ensure the test reproducibility under the same conditions. According our experience, very few modifications are required to adapt a MPI program to run in SIMGRID simulator using SMPI (Simulator MPI).The first modification is to include SMPI libraries and related header files (smpi.h). The second and important modification is to eliminate all global variables in moving them to local subroutine or using a Simgrid selector called "runtime automatic switching" (smpi/privatize\_global\_variables). Indeed, global variables can generate side effects on runtime between the threads running in the same process, generated by the Simgrid to simulate the grid environment.The last modification on the MPI program pointed out for some cases, the review of the sequence of the MPI\_Isend, MPI\_Irecv and MPI\_Waitall instructions which might cause an infinite loop. \paragraph{SIMGRID Simulator parameters} \begin{itemize} - \item HOSTFILE: Hosts description file. - \item PLATFORM: File describing the platform architecture : clusters (CPU power, + \item hostfile: Hosts description file. + \item plarform: File describing the platform architecture : clusters (CPU power, \dots{}), intra cluster network description, inter cluster network (bandwidth bw, -lat latency, \dots{}). - \item ARCHI : Grid computational description (Number of clusters, Number of +latency lat, \dots{}). + \item archi : Grid computational description (Number of clusters, Number of nodes/processors for each cluster). \end{itemize} @@ -216,43 +229,38 @@ In addition, the following arguments are given to the programs at runtime: \begin{itemize} \item Maximum number of inner and outer iterations; \item Inner and outer precisions; - \item Matrix size (NX, NY and NZ); + \item Matrix size (N$_{x}$, N$_{y}$ and N$_{z}$); \item Matrix diagonal value = 6.0; \item Execution Mode: synchronous or asynchronous. \end{itemize} -At last, note that the two solver algorithms have been executed with the Simgrid selector --cfg=smpi/running\_power which determine the computational power (here 19GFlops) of the simulator host machine. +At last, note that the two solver algorithms have been executed with the Simgrid selector -cfg=smpi/running\_power which determine the computational power (here 19GFlops) of the simulator host machine. %%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%% -\section{Experimental, Results and Comments} +\section{Experimental Results} \subsection{Setup study and Methodology} To conduct our study, we have put in place the following methodology -which can be reused with any grid-enabled applications. +which can be reused for any grid-enabled applications. \textbf{Step 1} : Choose with the end users the class of algorithms or the application to be tested. Numerical parallel iterative algorithms -have been chosen for the study in the paper. +have been chosen for the study in this paper. \\ \textbf{Step 2} : Collect the software materials needed for the -experimentation. In our case, we have three variants algorithms for the -resolution of three 3D-Poisson problem: (1) using the classical GMRES alias Algo-1 in this -paper, (2) using the multisplitting method alias Algo-2 and (3) an -enhanced version of the multisplitting method as Algo-3. In addition, -SIMGRID simulator has been chosen to simulate the behaviors of the -distributed applications. SIMGRID is running on the Mesocentre -datacenter in Franche-Comte University $[$10$]$ but also in a virtual -machine on a laptop. +experimentation. In our case, we have two variants algorithms for the +resolution of three 3D-Poisson problem: (1) using the classical GMRES (Algo-1)(2) and the multisplitting method (Algo-2). In addition, SIMGRID simulator has been chosen to simulate the behaviors of the +distributed applications. SIMGRID is running on the Mesocentre datacenter in Franche-Comte University but also in a virtual machine on a laptop. \\ \textbf{Step 3} : Fix the criteria which will be used for the future results comparison and analysis. In the scope of this study, we retain in one hand the algorithm execution mode (synchronous and asynchronous) and in the other hand the execution time and the number of iterations of -the application before obtaining the convergence. +the application before obtaining the convergence. \\ \textbf{Step 4 }: Setup up the different grid testbeds environment which will be simulated in the simulator tool to run the program. The @@ -261,15 +269,15 @@ grid containing 2 clusters with 16 hosts (processors/cores) each -, 4x8, 4x16, 8x8 and 2x50. The network has been designed to operate with a bandwidth equals to 10Gbits (resp. 1Gbits/s) and a latency of 8E-6 microseconds (resp. 5E-5) for the intra-clusters links (resp. -inter-clusters backbone links). +inter-clusters backbone links). \\ -\textbf{Step 5}: Process an extensive and comprehensive testings +\textbf{Step 5}: Conduct an extensive and comprehensive testings within these configurations in varying the key parameters, especially the CPU power capacity, the network parameters and also the size of the -input matrix. Note that some parameters should be invariant to allow the -comparison like some program input arguments. +input matrix. Note that some parameters should be fixed to be invariant to allow the +comparison like some program input arguments. \\ -{Step 6} : Collect and analyze the output results. +\textbf{Step 6} : Collect and analyze the output results. \subsection{Factors impacting distributed applications performance in a grid environment} @@ -286,7 +294,7 @@ Another important factor impacting the overall performance of the application is the network configuration. Two main network parameters can modify drastically the program output results : (i) the network bandwidth (bw=bits/s) also known as "the data-carrying capacity" -$[$13$]$ of the network is defined as the maximum of data that can pass +of the network is defined as the maximum of data that can pass from one point to another in a unit of time. (ii) the network latency (lat : microsecond) defined as the delay from the start time to send the data from a source and the final time the destination have finished to @@ -314,15 +322,15 @@ In the scope of this paper, our first objective is to demonstrate the Algo-2 (Multisplitting method) shows a better performance in grid architecture compared with Algo-1 (Classical GMRES) both running in \textbf{\textit{synchronous mode}}. Better algorithm performance -should mean a less number of iterations output and a less execution time +should means a less number of iterations output and a less execution time before reaching the convergence. For a systematic study, the experiments should figure out that, for various grid parameters values, the simulator will confirm the targeted outcomes, particularly for poor and slow networks, focusing on the impact on the communication performance -on the chosen class of algorithm $[$12$]$. +on the chosen class of algorithm. The following paragraphs present the test conditions, the output results -and our comments. +and our comments.\\ \textit{3.a Executing the algorithms on various computational grid @@ -334,26 +342,27 @@ architecture scaling up the input matrix size} \begin{tabular}{r c } \hline Grid & 2x16, 4x8, 4x16 and 8x8\\ %\hline - Network & N2 : bw=1Gbs-lat=5E-05 \\ %\hline - Input matrix size & N$_{x}$ =150 x 150 x 150 and\\ %\hline - - & N$_{x}$ =170 x 170 x 170 \\ \hline + Network & N2 : bw=1Gbits/s - lat=\np{5E-5} \\ %\hline + Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ %\hline + - & N$_{x}$ x N$_{y}$ x N$_{z}$ =170 x 170 x 170 \\ \hline \end{tabular} -\end{footnotesize} +Table 1 : Clusters x Nodes with N$_{x}$=150 or N$_{x}$=170 \\ +\end{footnotesize} - Table 1 : Clusters x Nodes with NX=150 or NX=170 + %\RCE{J'ai voulu mettre les tableaux des données mais je pense que c'est inutile et ça va surcharger} -The results in figure 1 show the non-variation of the number of +The results in figure 3 show the non-variation of the number of iterations of classical GMRES for a given input matrix size; it is not the case for the multisplitting method. -%\begin{wrapfigure}{l}{60mm} +%\begin{wrapfigure}{l}{100mm} \begin{figure} [ht!] \centering -\includegraphics[width=60mm]{cluster_x_nodes_nx_150_and_nx_170.pdf} +\includegraphics[width=100mm]{cluster_x_nodes_nx_150_and_nx_170.pdf} \caption{Cluster x Nodes NX=150 and NX=170} %\label{overflow}} \end{figure} @@ -367,7 +376,7 @@ experiment concludes the low sensitivity of the multisplitting method (compared with the classical GMRES) when scaling up to higher input matrix size. -\textit{3.b Running on various computational grid architecture} +\textit{\\3.b Running on various computational grid architecture\\} % environment \begin{footnotesize} @@ -378,16 +387,16 @@ matrix size. - & N2 : bw=1Gbs-lat=5E-05 \\ Input matrix size & N$_{x}$ =150 x 150 x 150\\ \hline \\ \end{tabular} -\end{footnotesize} +Table 2 : Clusters x Nodes - Networks N1 x N2 \\ -%Table 2 : Clusters x Nodes - Networks N1 x N2 -%\RCE{idem pour tous les tableaux de donnees} + \end{footnotesize} -%\begin{wrapfigure}{l}{60mm} + +%\begin{wrapfigure}{l}{100mm} \begin{figure} [ht!] \centering -\includegraphics[width=60mm]{cluster_x_nodes_n1_x_n2.pdf} +\includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf} \caption{Cluster x Nodes N1 x N2} %\label{overflow}} \end{figure} @@ -401,7 +410,7 @@ performance was increased in a factor of 2. The results depict also that when the network speed drops down, the difference between the execution times can reach more than 25\%. -\textit{\\\\\\\\\\\\\\\\\\3.c Network latency impacts on performance} +\textit{\\3.c Network latency impacts on performance\\} % environment \begin{footnotesize} @@ -411,14 +420,16 @@ times can reach more than 25\%. Network & N1 : bw=1Gbs \\ %\hline Input matrix size & N$_{x}$ =150 x 150 x 150\\ \hline\\ \end{tabular} + +Table 3 : Network latency impact \\ + \end{footnotesize} -Table 3 : Network latency impact \begin{figure} [ht!] \centering -\includegraphics[width=60mm]{network_latency_impact_on_execution_time.pdf} +\includegraphics[width=100mm]{network_latency_impact_on_execution_time.pdf} \caption{Network latency impact on execution time} %\label{overflow}} \end{figure} @@ -434,7 +445,7 @@ a less rate increase. Consequently, in the worst case (lat=6.10$^{-5 the multisplitting, even though, the performance was on the same order of magnitude with a latency of 8.10$^{-6}$. -\textit{3.d Network bandwidth impacts on performance} +\textit{\\3.d Network bandwidth impacts on performance\\} % environment \begin{footnotesize} @@ -444,13 +455,15 @@ of magnitude with a latency of 8.10$^{-6}$. Network & N1 : bw=1Gbs - lat=5E-05 \\ %\hline Input matrix size & N$_{x}$ =150 x 150 x 150\\ \hline \end{tabular} + +Table 4 : Network bandwidth impact \\ + \end{footnotesize} -Table 4 : Network bandwidth impact \begin{figure} [ht!] \centering -\includegraphics[width=60mm]{network_bandwith_impact_on_execution_time.pdf} +\includegraphics[width=100mm]{network_bandwith_impact_on_execution_time.pdf} \caption{Network bandwith impact on execution time} %\label{overflow} \end{figure} @@ -463,7 +476,7 @@ algorithms. However, and again in this case, the multisplitting method presents a better performance in the considered bandwidth interval with a gain of 40\% which is only around 24\% for classical GMRES. -\textit{3.e Input matrix size impacts on performance} +\textit{\\3.e Input matrix size impacts on performance\\} % environment \begin{footnotesize} @@ -473,13 +486,14 @@ a gain of 40\% which is only around 24\% for classical GMRES. Network & N2 : bw=1Gbs - lat=5E-05 \\ %\hline Input matrix size & N$_{x}$ = From 40 to 200\\ \hline \end{tabular} +Table 5 : Input matrix size impact\\ + \end{footnotesize} -Table 5 : Input matrix size impact \begin{figure} [ht!] \centering -\includegraphics[width=60mm]{pb_size_impact_on_execution_time.pdf} +\includegraphics[width=100mm]{pb_size_impact_on_execution_time.pdf} \caption{Pb size impact on execution time} %\label{overflow}} \end{figure} @@ -498,7 +512,7 @@ the best and the optimal targeted environment for the application deployment when focusing on the problem size scale up. Note that the same test has been done with the grid 2x16 getting the same conclusion. -\textit{3.f CPU Power impact on performance} +\textit{\\3.f CPU Power impact on performance\\} % environment \begin{footnotesize} @@ -508,13 +522,14 @@ same test has been done with the grid 2x16 getting the same conclusion. Network & N2 : bw=1Gbs - lat=5E-05 \\ %\hline Input matrix size & N$_{x}$ = 150 x 150 x 150\\ \hline \end{tabular} +Table 6 : CPU Power impact \\ + \end{footnotesize} -Table 6 : CPU Power impact \begin{figure} [ht!] \centering -\includegraphics[width=60mm]{cpu_power_impact_on_execution_time.pdf} +\includegraphics[width=100mm]{cpu_power_impact_on_execution_time.pdf} \caption{CPU Power impact on execution time} %\label{overflow}} \end{figure} @@ -554,7 +569,7 @@ best combination of the grid resources (CPU, Network, input matrix size, classical GMRES time. -The test conditions are summarized in the table below : +The test conditions are summarized in the table below : \\ % environment \begin{footnotesize} @@ -565,7 +580,7 @@ The test conditions are summarized in the table below : Intra-Network & bw=1.25 Gbits - lat=5E-05 \\ %\hline Inter-Network & bw=5 Mbits - lat=2E-02\\ Input matrix size & N$_{x}$ = From 62 to 150\\ %\hline - Residual error precision: 10$^{-5}$ to 10$^{-9}$\\ \hline + Residual error precision: 10$^{-5}$ to 10$^{-9}$\\ \hline \\ \end{tabular} \end{footnotesize}