MAJ commentaire de la figure 1

diff --git a/figures/openMP-GPU.txt b/figures/openMP-GPU.txt
index 26e06964154b618a8b5495d004708340423a9a8a..8c7c5363dbc3a878ef8c6ca9de93c44fb9297507 100644 (file)
--- a/figures/openMP-GPU.txt
+++ b/figures/openMP-GPU.txt
@@ -4,9 +4,9 @@
 100000                         621.59          11                                              49.20           2360.15                  11                          
 150000                         1405.87         11                                              49.03           5805.67                  12
 250000                         5671.29         16                                              60.48           21550.902                16
 100000                         621.59          11                                              49.20           2360.15                  11                          
 150000                         1405.87         11                                              49.03           5805.67                  12
 250000                         5671.29         16                                              60.48           21550.902                16

-300000                         5635            11                                              40.55           21413                    11
-350000                         8366.34         12                                              52.40           31792.092                12
-400000                         15458.3         16                                              59.91           58741.54                 16
+300000                         5898.3          11                                              40.55           22413                    11
+350000                         8366.34         12                                              52.40           #31792.092               12
+400000                         15458.3         16                                              59.91           #58741.54                16

 
 
 # Second index block (index 1)
 
 
 # Second index block (index 1)

diff --git a/paper.tex b/paper.tex
index 04e13163673af29261f326e2e392a659b3890f81..d9d72c31c05b570457dfed406a93e3964c5efa97 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -642,7 +642,7 @@ E5620@2.40GHz and a GPU K40 (with 6 Go of ram).
 \subsection{Comparative study}
 In this section, we discuss the performance Ehrlich-Aberth method  of root finding polynomials implemented on CPUs and on GPUs.
 
 \subsection{Comparative study}
 In this section, we discuss the performance Ehrlich-Aberth method  of root finding polynomials implemented on CPUs and on GPUs.
 

-We performed a set of experiments on the sequential and the parallel algorithms, for both sparse and full polynomials and different sizes. We took into account the execution time,the  polynomial size and the number of threads per block performed by sum or each experiment on CPUs and on GPUs.
+We performed a set of experiments on the sequential and the parallel algorithms, for both sparse and full polynomials and different sizes. We took into account the execution time, the  polynomial size and the number of threads per block performed by sum or each experiment on CPUs and on GPUs.

 
 All experimental results obtained from the simulations are made in double precision data, for a convergence tolerance of the methods set to $10^{-7}$. Since we were more interested in the comparison of the performance behaviors of Ehrlich-Aberth and Durand-Kerner methods on CPUs versus on GPUs. The initialization values of the vector solution of the Ehrlich-Aberth method are given in section 2.2. 
 \subsubsection{The execution time in seconds of Ehrlich-Aberth algorithm on CPU core vs. on a Tesla GPU}
 
 All experimental results obtained from the simulations are made in double precision data, for a convergence tolerance of the methods set to $10^{-7}$. Since we were more interested in the comparison of the performance behaviors of Ehrlich-Aberth and Durand-Kerner methods on CPUs versus on GPUs. The initialization values of the vector solution of the Ehrlich-Aberth method are given in section 2.2. 
 \subsubsection{The execution time in seconds of Ehrlich-Aberth algorithm on CPU core vs. on a Tesla GPU}


@@ -656,7 +656,8 @@ All experimental results obtained from the simulations are made in double precis
 \end{figure}
 
 Figure 1 %%show a comparison of execution time between the parallel and sequential version of the Ehrlich-Aberth algorithm with sparse polynomial exceed 100000, 
 \end{figure}
 
 Figure 1 %%show a comparison of execution time between the parallel and sequential version of the Ehrlich-Aberth algorithm with sparse polynomial exceed 100000, 

-We report the execution times of the Ehrlich-Aberth method implemented on one core of the Quad-Core Xeon E5620 CPU and those of the same methods implemented on one Nvidia Tesla K40c GPU, with sparse polynomial degrees ranging from 100,000 to 1,000,000. We can see that the methods implemented on the GPU are faster than those implemented on the CPU. This is due to the GPU ability to compute the data-parallel functions faster than its CPU counterpart. However, the execution time for the sequential implementation exceed 16,000 s for 450,000 degrees polynomials, in counterpart  the GPU implementation for the same polynomials need only 350 s, more than again, with 1,000,000 polynomials degrees GPU implementation not reach 2,300 s degrees. While CPU implementation need more than 10 hours. We can also notice that the GPU implementation are almost 47 faster then those implementation on the CPU. Furthermore, we verify that the number of iterations is the same. This reduction of time allows us to compute roots of polynomial of more important degree at the same time than with a CPU.
+We report the execution times of the Ehrlich-Aberth method implemented on one core of the Quad-Core Xeon E5620 CPU and those of the same methods implemented on one Nvidia Tesla K40c GPU, with sparse polynomial degrees ranging from 100,000 to 1,000,000. We can see that the method implemented on the GPU are faster than those implemented on the CPU. This is due to the GPU ability to compute the data-parallel functions faster than its CPU counterpart. However, the execution time for the CPU implementation exceed 5,000 s for 250,000 degrees polynomials, in counterpart  the GPU implementation for the same polynomials not reach 100 s, more than again, % with 1,000,000 polynomials degrees GPU implementation not reach 2,300 s degrees. While CPU implementation need more than 10 hours.
+with an execution time under to 2500 s CPU implementation can resolve polynomials degrees of only 200,000 s, whereas GPU implementation can resolve polynomials more than 1,000,000 degrees. We can also notice that the GPU implementation are almost 47 faster then those implementation on the CPU. Furthermore, we verify that the number of iterations is the same. This reduction of time allows us to compute roots of polynomial of more important degree at the same time than with a CPU.

  
 
 
  
 
 


@@ -722,7 +723,7 @@ This figure show the execution time of the both algorithm EA and DK with sparse
 \begin{figure}[H]
 \centering
   \includegraphics[width=0.8\textwidth]{figures/openMP-GPU}
 \begin{figure}[H]
 \centering
   \includegraphics[width=0.8\textwidth]{figures/openMP-GPU}

-\caption{The execution time of Ehrlich-Aberth algorithm on OpenMP(1core, 4cores) and GPU(Tesla k40)}
+\caption{The execution time in seconds of Ehrlich-Aberth algorithm on OpenMP(1 core, 4 cores) vs. on a Tesla GPU}

 \label{fig:01}
 \end{figure}
 
 \label{fig:01}
 \end{figure}