X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hpcc2014.git/blobdiff_plain/e4b14590c5b948dac64c900d8d83e990a3f79122..8795c25e6f799826141cea21050391987f86f3ae:/hpcc.tex diff --git a/hpcc.tex b/hpcc.tex index 640f3ae..b33be48 100644 --- a/hpcc.tex +++ b/hpcc.tex @@ -135,35 +135,7 @@ iterative asynchronous algorithms to solve a given problem on a large-scale simulated environment challenges to find optimal configurations giving the best results with a lowest residual error and in the best of execution time. -<<<<<<< HEAD -To our knowledge, there is no existing work on the large-scale simulation of a -real AIAC application. The aim of this paper is twofold. First we give a first -approach of the simulation of AIAC algorithms using a simulation tool (i.e. the -SimGrid toolkit~\cite{SimGrid}). Second, we confirm the effectiveness of -asynchronous mode algorithms by comparing their performance with the synchronous -mode. More precisely, we had implemented a program for solving large -linear system of equations by numerical method GMRES (Generalized -Minimal Residual) \cite{ref1}. We show, that with minor modifications of the -initial MPI code, the SimGrid toolkit allows us to perform a test campaign of a -real AIAC application on different computing architectures. The simulated -results we obtained are in line with real results exposed in ??\AG[]{ref?}. -SimGrid had allowed us to launch the application from a modest computing -infrastructure by simulating different distributed architectures composed by -clusters nodes interconnected by variable speed networks. In the simulated environment, after setting appropriate -network and cluster parameters like the network bandwidth, latency or the processors power, -the experimental results have demonstrated a asynchronous execution time saving up to \np[\%]{40} in -compared to the synchronous mode. -\AG{Il faudrait revoir la phrase précédente (couper en deux?). Là, on peut - avoir l'impression que le gain de \np[\%]{40} est entre une exécution réelle - et une exécution simulée!} -\CER{La phrase a été modifiée} - -This article is structured as follows: after this introduction, the next section will give a brief description of -iterative asynchronous model. Then, the simulation framework SimGrid is presented with the settings to create various -distributed architectures. The algorithm of the multisplitting method based on GMRES \LZK{??? GMRES n'utilise pas la méthode de multisplitting! Sinon ne doit on pas expliquer le choix d'une méthode de multisplitting?} \CER{La phrase a été corrigée} written with MPI primitives and -its adaptation to SimGrid with SMPI (Simulated MPI) is detailed in the next section. At last, the experiments results -carried out will be presented before some concluding remarks and future works. -======= + To our knowledge, there is no existing work on the large-scale simulation of a real AIAC application. {\bf The contribution of the present paper can be summarised in two main points}. First we give a first approach of the @@ -196,7 +168,7 @@ based on GMRES to solve each block obtained of the splitting. This code is written with MPI primitives and its adaptation to SimGrid with SMPI (Simulated MPI) is detailed in the next section. At last, the simulation results carried out will be presented before some concluding remarks and future works. ->>>>>>> 6785b9ef58de0db67c33ca901c7813f3dfdc76e0 + \section{Motivations and scientific context} @@ -473,16 +445,14 @@ We did not encounter major blocking problems when adapting the multisplitting al debugging. Indeed, apart from the review of the program sequence for asynchronous exchanges between processors within a cluster or between clusters, the algorithm was executed successfully with SMPI and provided identical outputs as those obtained with direct execution under MPI. In synchronous mode, the execution of the program raised no particular issue but in asynchronous mode, the review of the sequence of MPI\_Isend, MPI\_Irecv and MPI\_Waitall instructions and with the addition of the primitive MPI\_Test was needed to avoid a memory fault due to an infinite loop resulting from the non-convergence of the algorithm. -\CER{On voulait en fait montrer la simplicité de l'adaptation de l'algo a SimGrid. Les problèmes rencontrés décrits dans ce paragraphe concerne surtout le mode async}\LZK{OK. J'aurais préféré avoir un peu plus de détails sur l'adaptation de la version async} -\CER{Le problème majeur sur l'adaptation MPI vers SMPI pour la partie asynchrone de l'algorithme a été le plantage en SMPI de Waitall après un Isend et Irecv. J'avais proposé un workaround en utilisant un MPI\_wait séparé pour chaque échange a la place d'un waitall unique pour TOUTES les échanges, une instruction qui semble bien fonctionner en MPI. Ce workaround aussi fonctionne bien. Mais après, tu as modifié le programme avec l'ajout d'un MPI\_Test, au niveau de la routine de détection de la convergence et du coup, l'échange global avec waitall a aussi fonctionné.} +%\CER{On voulait en fait montrer la simplicité de l'adaptation de l'algo a SimGrid. Les problèmes rencontrés décrits dans ce paragraphe concerne surtout le mode async}\LZK{OK. J'aurais préféré avoir un peu plus de détails sur l'adaptation de la version async} +%\CER{Le problème majeur sur l'adaptation MPI vers SMPI pour la partie asynchrone de l'algorithme a été le plantage en SMPI de Waitall après un Isend et Irecv. J'avais proposé un workaround en utilisant un MPI\_wait séparé pour chaque échange a la place d'un waitall unique pour TOUTES les échanges, une instruction qui semble bien fonctionner en MPI. Ce workaround aussi fonctionne bien. Mais après, tu as modifié le programme avec l'ajout d'un MPI\_Test, au niveau de la routine de détection de la convergence et du coup, l'échange global avec waitall a aussi fonctionné.} Note here that the use of SMPI functions optimizer for memory footprint and CPU usage is not recommended knowing that one wants to get real results by simulation. -As mentioned, upon this adaptation, the algorithm is executed as in the real life in the simulated environment after the following minor changes. First, all declared -global variables have been moved to local variables for each subroutine. In fact, global variables generate side effects arising from the concurrent access of -shared memory used by threads simulating each computing unit in the SimGrid architecture. Second, the alignment of certain types of variables such as ``long int'' had -also to be reviewed. -\AG{À propos de ces problèmes d'alignement, en dire plus si ça a un intérêt, ou l'enlever.} -\CER{Ce problème fait partie des modifications que j'ai dû faire dans l'adaptation du programme MPI vers SMPI. IL découle de la différence de la taille des mots en mémoire : en 32 bits, pour les variables declarees en long int, on garde dans les instructions de sortie (printf, sprintf, ...) le format \%lu sinon en 64 bits, on le substitue par \%llu.} - Finally, some compilation errors on MPI\_Waitall and MPI\_Finalize primitives have been fixed with the latest version of SimGrid. +As mentioned, upon this adaptation, the algorithm is executed as in the real life in the simulated environment after the following minor changes. First, the scope of all declared +global variables have been moved to local to subroutine. Indeed, global variables generate side effects arising from the concurrent access of +shared memory used by threads simulating each computing unit in the SimGrid architecture. +Second, some compilation errors on MPI\_Waitall and MPI\_Finalize primitives have been fixed with the latest version of SimGrid. +\AG{compilation or run-time error?} In total, the initial MPI program running on the simulation environment SMPI gave after a very simple adaptation the same results as those obtained in a real environment. We have successfully executed the code in synchronous mode using parallel GMRES algorithm compared with our multisplitting algorithm in asynchronous mode after few modifications. @@ -504,10 +474,6 @@ study that the results depend on the following parameters: compared to the asynchronous mode ($t_\text{sync} / t_\text{async}$) is defined as the \emph{relative gain}. So, our objective running the algorithm in SimGrid is to obtain a relative gain greater than 1. - \AG{$t_\text{async} / t_\text{sync} > 1$, l'objectif est donc que ça dure plus - longtemps (que ça aille moins vite) en asynchrone qu'en synchrone ? - Ce n'est pas plutôt l'inverse ?} - \CER{J'ai modifie la phrase.} \end{itemize} A priori, obtaining a relative gain greater than 1 would be difficult in a local @@ -524,7 +490,7 @@ The algorithm was run on a two clusters based network with 50 hosts each, totali factors have provided the results shown in Table~\ref{tab.cluster.2x50}. The algorithm convergence with a 3D matrix size ranging from $N_x = N_y = N_z = \text{62}$ to 150 elements (that is from $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} = -\text{\np{3375000}}$ entries), is obtained in asynchronous in average 2.5 times speeder than the synchronous mode. +\text{\np{3375000}}$ entries), is obtained in asynchronous in average 2.5 times faster than in the synchronous mode. \AG{Expliquer comment lire les tableaux.} \CER{J'ai reformulé la phrase par la lecture du tableau. Plus de détails seront lus dans la partie Interprétations et commentaires} % use the same column width for the following three tables @@ -540,51 +506,51 @@ $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} = \caption{2 clusters, each with 50 nodes} \label{tab.cluster.2x50} - \begin{mytable}{6} + \begin{mytable}{5} \hline - bandwidth (Mbits/s) - & 5 & 5 & 5 & 5 & 5 & 50 \\ + bandwidth (Mbit/s) + & 5 & 5 & 5 & 5 & 5 \\ \hline latency (ms) - & 0.02 & 0.02 & 0.02 & 0.02 & 0.02 & 0.02 \\ + & 0.02 & 0.02 & 0.02 & 0.02 & 0.02 \\ \hline power (GFlops) - & 1 & 1 & 1 & 1.5 & 1.5 & 1.5 \\ + & 1 & 1 & 1 & 1.5 & 1.5 \\ \hline - size - & 62 & 62 & 62 & 100 & 100 & 110 \\ + size $(n^3)$ + & 62 & 62 & 62 & 100 & 100 \\ \hline Precision - & \np{E-5} & \np{E-8} & \np{E-9} & \np{E-11} & \np{E-11} & \np{E-11} \\ + & \np{E-5} & \np{E-8} & \np{E-9} & \np{E-11} & \np{E-11} \\ \hline \hline Relative gain - & 2.52 & 2.55 & 2.52 & 2.57 & 2.54 & 2.53 \\ + & 2.52 & 2.55 & 2.52 & 2.57 & 2.54 \\ \hline \end{mytable} \bigskip - \begin{mytable}{6} + \begin{mytable}{5} \hline - bandwidth (Mbits/s) - & 50 & 50 & 50 & 50 \\ % & 10 & 10 \\ + bandwidth (Mbit/s) + & 50 & 50 & 50 & 50 & 50 \\ % & 10 & 10 \\ \hline latency (ms) - & 0.02 & 0.02 & 0.02 & 0.02 \\ % & 0.03 & 0.01 \\ + & 0.02 & 0.02 & 0.02 & 0.02 & 0.02 \\ % & 0.03 & 0.01 \\ \hline Power (GFlops) - & 1.5 & 1.5 & 1.5 & 1.5 \\ % & 1 & 1.5 \\ + & 1.5 & 1.5 & 1.5 & 1.5 & 1.5 \\ % & 1 & 1.5 \\ \hline - size - & 120 & 130 & 140 & 150 \\ % & 171 & 171 \\ + size $(n^3)$ + & 110 & 120 & 130 & 140 & 150 \\ % & 171 & 171 \\ \hline Precision - & \np{E-11} & \np{E-11} & \np{E-11} & \np{E-11} \\ % & \np{E-5} & \np{E-5} \\ + & \np{E-11} & \np{E-11} & \np{E-11} & \np{E-11} & \np{E-11} \\ % & \np{E-5} & \np{E-5} \\ \hline \hline Relative gain - & 2.51 & 2.58 & 2.55 & 2.54 \\ % & 1.59 & 1.29 \\ + & 2.53 & 2.51 & 2.58 & 2.55 & 2.54 \\ % & 1.59 & 1.29 \\ \hline \end{mytable} \end{table} @@ -656,31 +622,30 @@ Note that the program was run with the following parameters: \paragraph*{SMPI parameters} -~\\{}\AG{Donner un peu plus de précisions (plateforme en particulier).} -\CER {Précisions ajoutées} - \begin{itemize} \item HOSTFILE: Text file containing the list of the processors units name. Here 100 hosts; \item PLATFORM: XML file description of the platform architecture : two clusters (cluster1 and cluster2) with the following characteristics : - - - Processor unit power : 1.5 GFlops; - - - Intracluster network : bandwidth = 1,25 Gbits/s and latency = 5E-05 ms; - - - Intercluster network : bandwidth = 5 Mbits/s and latency = 5E-03 ms; + \begin{itemize} + \item Processor unit power: \np[GFlops]{1.5}; + \item Intracluster network bandwidth: \np[Gbit/s]{1.25} and latency: + \np[$\mu$s]{0.05}; + \item Intercluster network bandwidth: \np[Mbit/s]{5} and latency: + \np[$\mu$s]{5}; + \end{itemize} \end{itemize} \paragraph*{Arguments of the program} \begin{itemize} - \item Description of the cluster architecture matching the format ; - \item Maximum number of iterations; - \item Precisions on the residual error; - \item Matrix size $N_x$, $N_y$ and $N_z$; - \item Matrix diagonal value: \np{1.0} (See (3)); - \item Matrix off-diagonal value: $-\frac{1}{6}$ (See(3)); - \item Communication mode: Asynchronous. +\item Description of the cluster architecture matching the format ; +\item Maximum number of iterations; +\item Precisions on the residual error; +\item Matrix size $N_x$, $N_y$ and $N_z$; +\item Matrix diagonal value: \np{1.0} (See~(\ref{eq:03})); +\item Matrix off-diagonal value: \np{-1}/\np{6} (See~(\ref{eq:03})); +\item Communication mode: asynchronous. \end{itemize} \paragraph*{Interpretations and comments} @@ -696,7 +661,7 @@ obtained in asynchronous mode for a matrix size of 62 elements. It is noticed th stable even we vary the residual error precision from \np{E-5} to \np{E-9}. By increasing the matrix size up to 100 elements, it was necessary to increase the CPU power of \np[\%]{50} to \np[GFlops]{1.5} to get the algorithm convergence and the same order of asynchronous mode efficiency. Maintaining such processor power but increasing network throughput inter cluster up to -\np[Mbit/s]{50}, the result of efficiency with a relative gain of 2.5\AG[]{2.5 ?} is obtained with +\np[Mbit/s]{50}, the result of efficiency with a relative gain of 2.5 is obtained with high external precision of \np{E-11} for a matrix size from 110 to 150 side elements. @@ -715,10 +680,10 @@ elements. %obtained with a bandwidth of \np[Mbit/s]{1} as shown in %Table~\ref{tab.cluster.3x67}. -\RC{Est ce qu'on sait expliquer pourquoi il y a une telle différence entre les résultats avec 2 et 3 clusters... Avec 3 clusters, ils sont pas très bons... Je me demande s'il ne faut pas les enlever...} -\RC{En fait je pense avoir la réponse à ma remarque... On voit avec les 2 clusters que le gain est d'autant plus grand qu'on choisit une bonne précision. Donc, plusieurs solutions, lancer rapidement un long test pour confirmer ca, ou enlever des tests... ou on ne change rien :-)} -\LZK{Ma question est: le bandwidth et latency sont ceux inter-clusters ou pour les deux inter et intra cluster??} -\CER{Définitivement, les paramètres réseaux variables ici se rapportent au réseau INTER cluster.} +%\RC{Est ce qu'on sait expliquer pourquoi il y a une telle différence entre les résultats avec 2 et 3 clusters... Avec 3 clusters, ils sont pas très bons... Je me demande s'il ne faut pas les enlever...} +%\RC{En fait je pense avoir la réponse à ma remarque... On voit avec les 2 clusters que le gain est d'autant plus grand qu'on choisit une bonne précision. Donc, plusieurs solutions, lancer rapidement un long test pour confirmer ca, ou enlever des tests... ou on ne change rien :-)} +%\LZK{Ma question est: le bandwidth et latency sont ceux inter-clusters ou pour les deux inter et intra cluster??} +%\CER{Définitivement, les paramètres réseaux variables ici se rapportent au réseau INTER cluster.} \section{Conclusion} The experimental results on executing a parallel iterative algorithm in asynchronous mode on an environment simulating a large scale of virtual