X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper2.git/blobdiff_plain/769f5a935a7453b848ad1358a006be5949b7c52f..de1136ccefae31eda903086fc7310086c7a0ed57:/paper.tex

diff --git a/paper.tex b/paper.tex
index 6d8658f..2d47f22 100644
--- a/paper.tex
+++ b/paper.tex
@@ -109,7 +109,8 @@ In this paper we propose the parallelization of Ehrlich-Aberth method which has
 \item The parallel implementation of Ehrlich-Aberth algorithm on a multi-GPU platform with a distributed memory using MPI API, such that each GPU is attached and managed by a MPI process. The GPUs exchange their data by message-passing communications. 
  \end{itemize}
 This latter approach is more used on clusters to solve very complex problems that are too large for traditional supercomputers, which are very expensive to build and run.
-\LZK{Pas d'autres contributions possibles? J'ai supprimé les deux premiers points proposés précédemment.}
+\LZK{Pas d'autres contributions possibles? J'ai supprimé les deux premiers points proposés précédemment.
+\AS{La résolution du problème pour des polynomes pleins de degré 6M est une contribution aussi à mon avis}}
 
 The paper is organized as follows. In Section~\ref{sec2} we present three different parallel programming models OpenMP, MPI and CUDA. In Section~\ref{sec3} we present the implementation of the Ehrlich-Aberth algorithm on a single GPU. In Section~\ref{sec4} we present the parallel implementations of the Ehrlich-Aberth algorithm on multiple GPUs using the OpenMP and MPI approaches. In section~\ref{sec5} we present our experiments and discuss them. Finally, Section~\ref{sec6} concludes this paper and gives some hints for future research directions in this topic. 
 
@@ -239,8 +240,7 @@ Copy $P$, $P'$ and $Z$ from CPU to GPU\;
 \While{$\Delta Z_{max} > \epsilon$}{
   $Z^{prev}$ = KernelSave($Z,n$)\;
   $Z$ = KernelUpdate($P,P',Z,n$)\;
-  $\Delta Z$ = KernelComputeError($Z,Z^{prev},n$)\;
-  $\Delta Z_{max}$ = CudaMaxFunction($\Delta Z,n$)\;
+  $\Delta Z_{max}$ = KernelComputeError($Z,Z^{prev},n$)\;
 }
 Copy $Z$ from GPU to CPU\;
 \label{alg1-cuda}
@@ -285,27 +285,24 @@ arrays containing all the roots.
 \KwOut{$Z$ (solution vector of roots)}
 Initialize the polynomial $P$ and its derivative $P'$\;
 Set the initial values of vector $Z$\;
-Start of a parallel part with OpenMP ($Z$, $\Delta Z$, $\Delta
-Z_{max}$, $P$, $P'$ are shared variables)\;
+Start of a parallel part with OpenMP ($Z$, $\Delta Z_{max}$, $P$, $P'$ are shared variables)\;
 $id_{gpu}$ = cudaGetDevice()\;
 $n_{loc}$ = $n/ngpu$ (local size)\;
-%$idx$ = $id_{gpu}\times n_{loc}$ (local offset)\;
+$offset$ = $id_{gpu}\times n_{loc}$ (local offset)\;
 Copy $P$, $P'$ from CPU to GPU\;
 \While{$max > \epsilon$}{
   Copy $Z$ from CPU to GPU\;
   $Z^{prev}$ = KernelSave($Z,n$)\;
-  $Z_{loc}$ = KernelUpdate($P,P',Z,n_{loc}$)\;
-  $\Delta Z_{loc}$ = KernelComputeError($Z_{loc},Z^{prev}_{loc},n_{loc}$)\;
-  $\Delta Z_{max}[id_{gpu}]$ = CudaMaxFunction($\Delta Z_{loc},n_{loc}$)\;
-  Copy $Z_{loc}$ from GPU to $Z$ in CPU\;
+  $Z[offset]$ = KernelUpdate($P,P',Z,n_{loc}$)\;
+  $\Delta Z_{max}[id_{gpu}]$ = KernelComputeError($Z[offset],Z^{prev}[offset],n_{loc}$)\;
+  Copy $Z[offset]$ from GPU to $Z$ in CPU\;
   $max$ = MaxFunction($\Delta Z_{max},ngpu$)\; 
 }
 \label{alg2-cuda-openmp}
-\LZK{J'ai modifié l'algo. Le $P$ est mis shared. Qu'en est-il pour
-  $P'$?}\RC{Je l'ai rajouté. Bon sinon le n\_loc ne remplace pas
+\RC{Je l'ai rajouté. Bon sinon le n\_loc ne remplace pas
   vraiment un offset et une taille mais bon... et là il y a 4 lignes
   pour la convergence, c'est bcp ... Zloc, Zmax, max et
-  testconvergence. On pourrait faire mieux}
+  testconvergence. On pourrait faire mieux\LZK{Modifié, c'est bon!}}
 \end{algorithm}