X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper2.git/blobdiff_plain/a055895aab68dd582363f108223327a760bea1ff..769f5a935a7453b848ad1358a006be5949b7c52f:/paper.tex?ds=sidebyside

diff --git a/paper.tex b/paper.tex
index 2ee181a..6d8658f 100644
--- a/paper.tex
+++ b/paper.tex
@@ -1,17 +1,8 @@
-
-
-
 \documentclass[conference]{IEEEtran}
-
 \usepackage[ruled,vlined]{algorithm2e}
-
-
 \hyphenation{op-tical net-works semi-conduc-tor}
-
 \bibliographystyle{IEEEtran}
 
-
-
 \usepackage{amsfonts}
 \usepackage[utf8]{inputenc}
 \usepackage[T1]{fontenc}
@@ -26,8 +17,6 @@
   \todo[color=orange!10,#1]{\sffamily\textbf{AS:} #2}\xspace}
 
 
-
-
 \begin{document}
 
 \title{Two parallel implementations of Ehrlich-Aberth algorithm for root-finding of polynomials on multiple GPUs with OpenMP and MPI}
@@ -123,7 +112,7 @@ This latter approach is more used on clusters to solve very complex problems tha
 \LZK{Pas d'autres contributions possibles? J'ai supprimÃ© les deux premiers points proposÃ©s prÃ©cÃ©demment.}
 
 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. 
-%\LZK{A revoir toute cette organization: je viens de la revoir}
+
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -247,20 +236,15 @@ implementation of Ehrlich-Aberth method.
 Initialize the polynomial $P$ and its derivative $P'$\;
 Set the initial values of vector $Z$\;
 Copy $P$, $P'$ and $Z$ from CPU to GPU\;
-\While{\emph{not convergence}}{
+\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($\Delta Z,n$)\;
-  TestConvergence($\Delta Z_{max},\epsilon$)\;
 }
 Copy $Z$ from GPU to CPU\;
 \label{alg1-cuda}
-\LZK{J'ai modifiÃ© l'algo. Sinon, est ce qu'on doit mettre en paramÃ¨tre
-  $Z^{prev}$ ou $Z$ tout court (dans le cas oÃ¹ on exploite
-  l'asynchronisme des threads cuda!) pour le Kernel\_Update? }
-\RC{Le $Z_{prev}$ sert Ã  calculer l'erreur donc j'ai remis Z. La ligne
-avec TestConvergence ca fait une ligne de plus.}
+\RC{La ligne avec TestConvergence ca fait une ligne de plus.\LZK{Oui j'ai hÃ©sitÃ© Ã  l'ajouter. On peut faire le test dans la condition de while mais quelle est la valeur initiale de $\Delta Z_{max}$?! Ou bien on s'en fiche?}}
 \end{algorithm}
 
  
@@ -307,15 +291,14 @@ $id_{gpu}$ = cudaGetDevice()\;
 $n_{loc}$ = $n/ngpu$ (local size)\;
 %$idx$ = $id_{gpu}\times n_{loc}$ (local offset)\;
 Copy $P$, $P'$ from CPU to GPU\;
-\While{\emph{not convergence}}{
+\While{$max > \epsilon$}{
   Copy $Z$ from CPU to GPU\;
   $Z^{prev}$ = KernelSave($Z,n$)\;
-  $Z_{loc}$ = KernelUpdate($P,P',Z^{prev},n_{loc}$)\;
+  $Z_{loc}$ = 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\;
-  $max$ = MaxFunction($\Delta Z_{max},ngpu$)\;
-  TestConvergence($max,\epsilon$)\;
+  $max$ = MaxFunction($\Delta Z_{max},ngpu$)\; 
 }
 \label{alg2-cuda-openmp}
 \LZK{J'ai modifiÃ© l'algo. Le $P$ est mis shared. Qu'en est-il pour
