commenter l'influence du nombre de trheads par bloc

diff --git a/figures/Compar_EA_algorithm_CPU_GPU.txt b/figures/Compar_EA_algorithm_CPU_GPU.txt
index b2bf4a3ab71900e9c7fc136be28a6c70889e390b..71ce40d8b1d081b4a272fbdf2b4d6a04d2c60d54 100644 (file)
--- a/figures/Compar_EA_algorithm_CPU_GPU.txt
+++ b/figures/Compar_EA_algorithm_CPU_GPU.txt
@@ -1,8 +1,8 @@
 # Polynome with 256 threads per block en GPU
 # First data block (index 0)
 # Polynome with 256 threads per block en GPU
 # First data block (index 0)

-#Polynomial's degrees          times_CPU       nb iter         times_GPU       nb iter         Speed up
-100000                         621.59          11              12.45           16              49.20
-150000                         1405.87         11              28.67           17              49.03
+#Polynomial's degrees          times_CPU(4c)   nb iter         times_GPU       nb iter         Speed up        time_OpenMP(1c)     Nb_ietr
+100000                         621.59          11              12.45           16              49.20           2360.15                  11                          
+150000                         1405.87         11              28.67           17              49.03           5805.67                  12

 250000                         5671.29         16              93.76           20              60.48           
 300000                         5635            11              138.94          21              40.55
 350000                         8366.34         12              159.654         18              52.40
 250000                         5671.29         16              93.76           20              60.48           
 300000                         5635            11              138.94          21              40.55
 350000                         8366.34         12              159.654         18              52.40

diff --git a/paper.tex b/paper.tex
index 5cc9bdff518e1513e51aa40e8462f889e90e79da..fa4f62aadd5d1fab4ff89c1accd0b7db4120d0ad 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -63,9 +63,9 @@
 
 %% or include affiliations in footnotes:
 \author[mymainaddress]{Ghidouche Kahina\corref{mycorrespondingauthor}}
 
 %% or include affiliations in footnotes:
 \author[mymainaddress]{Ghidouche Kahina\corref{mycorrespondingauthor}}

-%%\ead[url]{kahina.ghidouche@gmail.com}
+%%\ead[url]{kahina.ghidouche@univ-bejaia.dz}

 \cortext[mycorrespondingauthor]{Corresponding author}
 \cortext[mycorrespondingauthor]{Corresponding author}

-\ead{kahina.ghidouche@gmail.com}
+\ead{kahina.ghidouche@univ-bejaia.dz}

 
 \author[mysecondaryaddress]{Couturier Raphael\corref{mycorrespondingauthor}}
 %%\cortext[mycorrespondingauthor]{Corresponding author}
 
 \author[mysecondaryaddress]{Couturier Raphael\corref{mycorrespondingauthor}}
 %%\cortext[mycorrespondingauthor]{Corresponding author}


@@ -75,8 +75,8 @@
 %%\cortext[mycorrespondingauthor]{Corresponding author}
 \ead{ar.sider@univ-bejaia.dz}
 
 %%\cortext[mycorrespondingauthor]{Corresponding author}
 \ead{ar.sider@univ-bejaia.dz}
 

-\address[mymainaddress]{Department of informatics,University of Bejaia,Algeria}
-\address[mysecondaryaddress]{FEMTO-ST Institute, University of Franche-Compté }
+\address[mymainaddress]{Laboratoire LIMED,Faculté des sciences exactes,Université de Bejaia,06000,Algeria}
+\address[mysecondaryaddress]{FEMTO-ST Institute,Université de Franche-Compté }

 
 \begin{abstract}
 Polynomials are mathematical algebraic structures that play a great role in science and engineering. But the process of solving them  for high and large degrees is computationally demanding and still not solved. In this paper, we present the results of a parallel implementation of the Ehrlich-Aberth algorithm for the problem root finding for
 
 \begin{abstract}
 Polynomials are mathematical algebraic structures that play a great role in science and engineering. But the process of solving them  for high and large degrees is computationally demanding and still not solved. In this paper, we present the results of a parallel implementation of the Ehrlich-Aberth algorithm for the problem root finding for


@@ -646,7 +646,8 @@ We report the execution times of the Ehrlich-Aberth method implemented on one co
 
 
 \subsubsection{Influence of the number of threads on the execution times of different polynomials (sparse and full)}
 
 
 \subsubsection{Influence of the number of threads on the execution times of different polynomials (sparse and full)}

-It is also interesting to see the influence of the number of threads per block on the execution time. For that, we notice that the maximum number of threads per block for the Nvidia Tesla K40c GPU is 1024, so we varied the number of threads per block from 8 to 1024. We took into account the execution time for both sparse and full polynomials of size 50000 and 500000 degrees.
+To optimize the performances of an algorithm on a GPU, it is necessary to maximize the use of cores GPU (maximize the number of threads executed in parallel) and to optimize the use of the various memoirs GPU. In fact, it is interesting to see the influence of the number of threads per block on the execution time of Ehrlich-Aberth algorithm. 
+For that, we notice that the maximum number of threads per block for the Nvidia Tesla K40c GPU is 1024, so we varied the number of threads per block from 8 to 1024. We took into account the execution time for both sparse and full polynomials of size 50000 and 500000 degrees.

 
 \begin{figure}[H]
 \centering
 
 \begin{figure}[H]
 \centering


@@ -655,7 +656,7 @@ It is also interesting to see the influence of the number of threads per block o
 \label{fig:01}
 \end{figure}
 
 \label{fig:01}
 \end{figure}
 

-The figure 2 show that, the best execution time for both sparse and full polynomial are given while the threads number varies between 64 and 256 threads per bloc. We notice that with small polynomials the number of threads per block is 64, Whereas, the large polynomials the number of threads per block is 256. However,In the following experiments we specify that the number of thread by block is 256.
+The figure 2 show that, the best execution time for both sparse and full polynomial are given when the threads number varies between 64 and 256 threads per bloc. We notice that with small polynomials the best number of threads per block is 64, Whereas, the large polynomials the best number of threads per block is 256. However,In the following experiments we specify that the number of thread by block is 256.

 
 \subsubsection{The impact of exp-log solution to compute very high degrees of  polynomial}
 
 
 \subsubsection{The impact of exp-log solution to compute very high degrees of  polynomial}
 


@@ -669,7 +670,7 @@ In this experiment we report the performance of log.exp solution describe in ~\r
 
 The figure 3, show a comparison between the execution time of the Ehrlich-Aberth algorithm applying log-exp solution and the execution time of the Ehrlich-Aberth algorithm without applying log-exp solution, with full and sparse polynomials degrees. We can see that the execution time for the both algorithms are the same while the full polynomials degrees are less than 4000 and full polynomials are less than 150,000. After,we show clearly that the classical version of Ehrlich-Aberth algorithm (without applying log.exp) stop to converge and can not solving any polynomial sparse or full. In counterpart, the new version of Ehrlich-Aberth algorithm (applying log.exp solution) can solve very high and large full polynomial exceed 100,000 degrees.
 
 
 The figure 3, show a comparison between the execution time of the Ehrlich-Aberth algorithm applying log-exp solution and the execution time of the Ehrlich-Aberth algorithm without applying log-exp solution, with full and sparse polynomials degrees. We can see that the execution time for the both algorithms are the same while the full polynomials degrees are less than 4000 and full polynomials are less than 150,000. After,we show clearly that the classical version of Ehrlich-Aberth algorithm (without applying log.exp) stop to converge and can not solving any polynomial sparse or full. In counterpart, the new version of Ehrlich-Aberth algorithm (applying log.exp solution) can solve very high and large full polynomial exceed 100,000 degrees.
 

-in fact, when the modulus of the roots are up than \textit{R} given in ~\ref{R},this exceed the limited number in the mantissa of floating points representations and can not compute the iterative function given in ~\ref{eq:Aberth-H-GS} to obtain the root solution, who justify the divergence of the classical Ehrlich-Aberth algorithm. However, applying log.exp solution given in ~\ref{sec2} took into account the limit of floating using the iterative function in(Eq.~\ref{Log_H1},Eq.~\ref{Log_H2}and allows to solve a very large polynomials degrees . 
+in fact, when the modulus of the roots are up than \textit{R} given in ~\ref{R},this exceed the limited number in the mantissa of floating points representations and can not compute the iterative function given in ~\ref{eq:Aberth-H-GS} to obtain the root solution, who justify the divergence of the classical Ehrlich-Aberth algorithm. However, applying log.exp solution given in ~\ref{sec2} took into account the limit of floating using the iterative function in(Eq.~\ref{Log_H1},Eq.~\ref{Log_H2} and allows to solve a very large polynomials degrees . 

 
 
 %\begin{figure}[H]
 
 
 %\begin{figure}[H]


@@ -703,4 +704,7 @@ This figure show the execution time of the both algorithm EA and DK with sparse
 
 \bibliography{mybibfile}
 
 
 \bibliography{mybibfile}
 

+
+\section{Conclusion and perspective}
+

 \end{document}
 \end{document}