change tables values to be all of them in the same long

[mpi-energy.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index efe0e3e201b490c2748737b7d68fb4d873498a00..c38368cd7b263869d14db8f8717eb45cd114a144 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -16,7 +16,6 @@
 %\usepackage[font={footnotesize,bt}]{caption}
 %\usepackage[font=scriptsize,labelfont=bf]{caption}
 \usepackage{lmodern}
 %\usepackage[font={footnotesize,bt}]{caption}
 %\usepackage[font=scriptsize,labelfont=bf]{caption}
 \usepackage{lmodern}

-

 \usepackage{todonotes}
 \newcommand{\AG}[2][inline]{\todo[color=green!50,#1]{\sffamily\small\textbf{AG:} #2}}
 
 \usepackage{todonotes}
 \newcommand{\AG}[2][inline]{\todo[color=green!50,#1]{\sffamily\small\textbf{AG:} #2}}
 


@@ -26,6 +25,12 @@
 \author{A. Badri \and J.-C. Charr \and R. Couturier \and A. Giersch}
 \maketitle
 
 \author{A. Badri \and J.-C. Charr \and R. Couturier \and A. Giersch}
 \maketitle
 

+\AG{``Optimal'' is a bit pretentious in the title}
+
+\begin{abstract}
+  \AG{FIXME}
+\end{abstract}
+

 \section{Introduction}
 
 The need for computing power is still increasing and it is not expected to slow
 \section{Introduction}
 
 The need for computing power is still increasing and it is not expected to slow


@@ -63,11 +68,11 @@ algorithm has ability to predict both energy consumption and execution time over
 all available scaling factors.  The prediction achieved depends on some
 computing time information, gathered at the beginning of the runtime.  We apply
 this algorithm to seven MPI benchmarks. These MPI programs are the NAS parallel
 all available scaling factors.  The prediction achieved depends on some
 computing time information, gathered at the beginning of the runtime.  We apply
 this algorithm to seven MPI benchmarks. These MPI programs are the NAS parallel

-penchmarks (NPB v3.3) developed by NASA~\cite{44}. Our experiments are executed
-using the simulator Simgrid/SMPI v3.10~\cite{45} over an homogeneous distributed
-memory architecture. Furthermore, we compare the proposed algorithm with
-Rauber's methods. The comparison's results show that our algorithm gives better
-energy-time trade off.
+benchmarks (NPB v3.3) developed by NASA~\cite{44}. Our experiments are executed
+using the simulator SimGrid/SMPI v3.10~\cite{Casanova:2008:SGF:1397760.1398183}
+over an homogeneous distributed memory architecture. Furthermore, we compare the
+proposed algorithm with Rauber's methods. The comparison's results show that our
+algorithm gives better energy-time trade off.

 
 \section{Related Works}
 
 
 \section{Related Works}
 


@@ -82,7 +87,7 @@ during the compilation phases as an example in Azevedo et al.~\cite{40}. He used
 intra-task algorithm to choose the DVFS setting when there are dependency points
 between tasks. While in~\cite{29}, Xie et al. used breadth-first search
 algorithm to do that. Their goal is saving energy with time limits. Another
 intra-task algorithm to choose the DVFS setting when there are dependency points
 between tasks. While in~\cite{29}, Xie et al. used breadth-first search
 algorithm to do that. Their goal is saving energy with time limits. Another

-approaches gathers and stores the runtime information for each DVFS state , then
+approaches gathers and stores the runtime information for each DVFS state, then

 used their methods offline to select the suitable DVFS that optimize energy-time
 trade offs. As an example~\cite{8}, Rountree et al. used liner programming
 algorithm, while in~\cite{38,34}, Cochran et al. used multi logistic regression
 used their methods offline to select the suitable DVFS that optimize energy-time
 trade offs. As an example~\cite{8}, Rountree et al. used liner programming
 algorithm, while in~\cite{38,34}, Cochran et al. used multi logistic regression


@@ -107,7 +112,7 @@ program used online for saving energy as in~\cite{1}, Lim et al. developed an
 algorithm that detects the communication sections and changes the frequency
 during these sections only. This approach changes the frequency many times
 because an iteration may contain more than one communication section. The domain
 algorithm that detects the communication sections and changes the frequency
 during these sections only. This approach changes the frequency many times
 because an iteration may contain more than one communication section. The domain

-of analytical modeling used for choosing the optimal frequency as in ~\cite{3},
+of analytical modeling used for choosing the optimal frequency as in~\cite{3},

 Rauber et al. developed an analytical mathematical model for determining the
 optimal frequency scaling factor for any number of concurrent tasks, without
 considering communication times. They set the slowest task to maximum frequency
 Rauber et al. developed an analytical mathematical model for determining the
 optimal frequency scaling factor for any number of concurrent tasks, without
 considering communication times. They set the slowest task to maximum frequency


@@ -159,7 +164,7 @@ where $T_i$ is the execution time of process $i$.
 
 The energy consumption by the processor consists of two powers metric: the
 dynamic and the static power. This general power formulation is used by many
 
 The energy consumption by the processor consists of two powers metric: the
 dynamic and the static power. This general power formulation is used by many

-researchers see ~\cite{9,3,15,26}. The dynamic power of the CMOS processors
+researchers see~\cite{9,3,15,26}. The dynamic power of the CMOS processors

 $P_{dyn}$ is related to the switching activity $\alpha$, load capacitance $C_L$,
 the supply voltage $V$ and operational frequency $f$ respectively as follow :
 \begin{equation}
 $P_{dyn}$ is related to the switching activity $\alpha$, load capacitance $C_L$,
 the supply voltage $V$ and operational frequency $f$ respectively as follow :
 \begin{equation}


@@ -248,7 +253,7 @@ frequency. Therefore, any DVFS operation for the energy reduction increase the
 execution time of the parallel program. As shown in EQ~(\ref{eq:energy}) the
 energy affected by the scaling factor $S$. This factor also has a great impact
 on the performance. When scaling down the frequency to the new value according
 execution time of the parallel program. As shown in EQ~(\ref{eq:energy}) the
 energy affected by the scaling factor $S$. This factor also has a great impact
 on the performance. When scaling down the frequency to the new value according

-to EQ(~\ref{eq:s}) lead to the value of the scale $S$ has inverse relation with
+to EQ~(\ref{eq:s}) lead to the value of the scale $S$ has inverse relation with

 new frequency value ($S \propto \frac{1}{F_{new}}$). Also when decrease the
 frequency value, the execution time increase. Then the new frequency value has
 inverse relation with time ($F_{new} \propto \frac{1}{T}$). This lead to the
 new frequency value ($S \propto \frac{1}{F_{new}}$). Also when decrease the
 frequency value, the execution time increase. Then the new frequency value has
 inverse relation with time ($F_{new} \propto \frac{1}{T}$). This lead to the


@@ -274,7 +279,7 @@ with the computation time without affecting the communication time. The
 communication time consists of the beginning times which an MPI calls for
 sending or receiving till the message is synchronously sent or received. In this
 paper we predict the execution time of the program for any new scaling factor
 communication time consists of the beginning times which an MPI calls for
 sending or receiving till the message is synchronously sent or received. In this
 paper we predict the execution time of the program for any new scaling factor

-value. Depending on this prediction we can produce our energy-performace scaling
+value. Depending on this prediction we can produce our energy-performance scaling

 method as we will show in the coming sections. In the next section we make an
 investigation study for the EQ~(\ref{eq:tnew}).
 
 method as we will show in the coming sections. In the next section we make an
 investigation study for the EQ~(\ref{eq:tnew}).
 


@@ -287,7 +292,9 @@ real execution time with the predicted execution time. Each program runs offline
 with all available scaling factors on 8 or 9 nodes to produce real execution
 time values. These scaling factors are computed by dividing the maximum
 frequency by the new one see EQ~(\ref{eq:s}). In all tests, we use the simulator
 with all available scaling factors on 8 or 9 nodes to produce real execution
 time values. These scaling factors are computed by dividing the maximum
 frequency by the new one see EQ~(\ref{eq:s}). In all tests, we use the simulator

-Simgrid/SMPI v3.10 to run the NAS programs.
+SimGrid/SMPI v3.10 to run the NAS programs.
+\AG{Fig.~\ref{fig:pred} is hard to read when printed in black and white,
+  especially the ``Normalize Real Perf.'' curve.}

 \begin{figure}[width=\textwidth,height=\textheight,keepaspectratio]
   \centering
   \includegraphics[scale=0.60]{cg_per.eps}
 \begin{figure}[width=\textwidth,height=\textheight,keepaspectratio]
   \centering
   \includegraphics[scale=0.60]{cg_per.eps}


@@ -304,7 +311,7 @@ frequencies. For more details on the characteristics of the platform refer to
 table~(\ref{table:platform}). This lead to 18 run states for each program. We
 use seven MPI programs of the NAS parallel benchmarks : CG, MG, EP, FT, BT, LU
 and SP. The average normalized errors between the predicted execution time and
 table~(\ref{table:platform}). This lead to 18 run states for each program. We
 use seven MPI programs of the NAS parallel benchmarks : CG, MG, EP, FT, BT, LU
 and SP. The average normalized errors between the predicted execution time and

-the real time (Simgrid time) for all programs is between 0.0032 to 0.0133. AS an
+the real time (SimGrid time) for all programs is between 0.0032 to 0.0133. AS an

 example, we are present the execution times of the NAS benchmarks as in the
 figure~(\ref{fig:pred}).
 
 example, we are present the execution times of the NAS benchmarks as in the
 figure~(\ref{fig:pred}).
 


@@ -321,13 +328,20 @@ between the consumed energy with scaled frequency and the consumed energy
 without scaled frequency :
 \begin{equation}
   \label{eq:enorm}
 without scaled frequency :
 \begin{equation}
   \label{eq:enorm}

-  E_{Norm} = \frac{E_{Reduced}}{E_{Orginal}}
+  E_\textit{Norm} = \frac{E_{Reduced}}{E_{Original}}

           = \frac{ P_{dyn} \cdot S_i^{-2} \cdot
                \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
                P_{static} \cdot T_1 \cdot S_i \cdot N  }{
               P_{dyn} \cdot \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
           = \frac{ P_{dyn} \cdot S_i^{-2} \cdot
                \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
                P_{static} \cdot T_1 \cdot S_i \cdot N  }{
               P_{dyn} \cdot \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +

-              P_{static} \cdot T_1\, \cdot N }
+              P_{static} \cdot T_1 \cdot N }

 \end{equation}
 \end{equation}

+\AG{Use \texttt{\textbackslash{}text\{xxx\}} or
+  \texttt{\textbackslash{}textit\{xxx\}} for all subscripted words in equations
+  (e.g. \mbox{\texttt{E\_\{\textbackslash{}text\{Norm\}\}}}).
+
+  Don't hesitate to define new commands :
+  \mbox{\texttt{\textbackslash{}newcommand\{\textbackslash{}ENorm\}\{E\_\{\textbackslash{}text\{Norm\}\}\}}}
+}

 By the same way we can normalize the performance as follows :
 \begin{equation}
   \label{eq:pnorm}
 By the same way we can normalize the performance as follows :
 \begin{equation}
   \label{eq:pnorm}


@@ -378,7 +392,7 @@ Then we can select the optimal scaling factor that satisfy the
 EQ~(\ref{eq:max}).  Our objective function can works with any energy model or
 static power values stored in a data file. Moreover, this function works in
 optimal way when the energy function has a convex form with frequency scaling
 EQ~(\ref{eq:max}).  Our objective function can works with any energy model or
 static power values stored in a data file. Moreover, this function works in
 optimal way when the energy function has a convex form with frequency scaling

-factor as shown in ~\cite{15,3,19}. Energy measurement model is not the
+factor as shown in~\cite{15,3,19}. Energy measurement model is not the

 objective of this paper and we choose Rauber's model as an example with two
 reasons that mentioned before.
 
 objective of this paper and we choose Rauber's model as an example with two
 reasons that mentioned before.
 


@@ -411,7 +425,7 @@ scaling factor for both energy and performance at the same time.
         \State $Dist = P_{NormInv} - E_{Norm}$
       \EndIf
     \EndFor
         \State $Dist = P_{NormInv} - E_{Norm}$
       \EndIf
     \EndFor

-    \State  $ Return \; \;  (S_{optimal})$
+    \State  Return $S_{optimal}$

   \end{algorithmic}
 \end{algorithm}
 The proposed EPSA algorithm works online during the execution time of the MPI
   \end{algorithmic}
 \end{algorithm}
 The proposed EPSA algorithm works online during the execution time of the MPI


@@ -425,21 +439,27 @@ optimal scaling factor. Then the program set the new frequency to the
 system. The algorithm is called just one time during the execution of the
 program. The following example shows where and when the EPSA algorithm is called
 in the MPI program :
 system. The algorithm is called just one time during the execution of the
 program. The following example shows where and when the EPSA algorithm is called
 in the MPI program :

-\begin{minipage}{\textwidth}
-\begin{lstlisting}[frame=tb]
-FOR J:=1 to Some_iterations Do
-   -Computations Section.
-   -Communications Section.
-   IF (J==1) THEN
-     -Gather all times of computation and communication
-      from each node.
-     -Call EPSA with these times.
-     -Calculate the new frequency from optimal scale.
-     -Set the new frequency to the system.
-   ENDIF
-ENDFOR
-\end{lstlisting}
-\end{minipage}
+%\begin{minipage}{\textwidth}
+%\AG{Use the same format as for Algorithm~\ref{EPSA}}
+
+\begin{algorithm}[d]
+  \caption{DVFS}
+  \label{dvfs}
+  \begin{algorithmic}
+ \For {$J:=1$ to $Some_iterations Do$}
+  \State -Computations Section.
+   \State -Communications Section.
+   \If {$(J==1)$} 
+     \State -Gather all times of computation and\par
+        \State      communication from each node.
+     \State -Call EPSA with these times.
+     \State -Calculate the new frequency from optimal scale.
+     \State -Set the new frequency to the system.
+   \EndIf
+\EndFor
+\end{algorithmic}
+\end{algorithm}
+\clearpage

 After obtaining the optimal scale factor from the EPSA algorithm. The program
 calculates the new frequency $F_i$ for each task proportionally to its time
 value $T_i$. By substitution of the EQ~(\ref{eq:s}) in the EQ~(\ref{eq:si}), we
 After obtaining the optimal scale factor from the EPSA algorithm. The program
 calculates the new frequency $F_i$ for each task proportionally to its time
 value $T_i$. By substitution of the EQ~(\ref{eq:s}) in the EQ~(\ref{eq:si}), we


@@ -451,27 +471,28 @@ can calculate the new frequency $F_i$ as follows :
 According to this equation all the nodes may have the same frequency value if
 they have balanced workloads. Otherwise, they take different frequencies when
 have imbalanced workloads. Then EQ~(\ref{eq:fi}) works in adaptive way to change
 According to this equation all the nodes may have the same frequency value if
 they have balanced workloads. Otherwise, they take different frequencies when
 have imbalanced workloads. Then EQ~(\ref{eq:fi}) works in adaptive way to change

-the freguency according to the nodes workloads.
+the frequency according to the nodes workloads.

 
 \section{Experimental Results}
 
 
 \section{Experimental Results}
 

-The proposed ESPA algorithm was applied to seven MPI programs of the NAS
-benchmarks (EP ,CG , MG ,FT , BT, LU and SP). We work on three classes (A, B and
+The proposed EPSA algorithm was applied to seven MPI programs of the NAS
+benchmarks (EP, CG, MG, FT, BT, LU and SP). We work on three classes (A, B and

 C) for each program. Each program runs on specific number of processors
 proportional to the size of the class.  Each class represents the problem size
 ascending from the class A to C. Additionally, depending on some speed up points
 for each class we run the classes A, B and C on 4, 8 or 9 and 16 nodes
 C) for each program. Each program runs on specific number of processors
 proportional to the size of the class.  Each class represents the problem size
 ascending from the class A to C. Additionally, depending on some speed up points
 for each class we run the classes A, B and C on 4, 8 or 9 and 16 nodes

-respectively. Our experiments are executed on the simulator Simgrid/SMPI
+respectively. Our experiments are executed on the simulator SimGrid/SMPI

 v3.10. We design a platform file that simulates a cluster with one core per
 node. This cluster is a homogeneous architecture with distributed memory. The
 v3.10. We design a platform file that simulates a cluster with one core per
 node. This cluster is a homogeneous architecture with distributed memory. The

-detailed characteristics of our platform file are shown in
-thetable~(\ref{table:platform}). Each node in the cluster has 18 frequency
-values from 2.5 GHz to 800 MHz with 100 MHz difference between each two
-successive frequencies.
+detailed characteristics of our platform file are shown in the
+table~(\ref{table:platform}). Each node in the cluster has 18 frequency values
+from 2.5 GHz to 800 MHz with 100 MHz difference between each two successive
+frequencies.

 \begin{table}[ht]
   \caption{Platform File Parameters}
   % title of Table
   \centering
 \begin{table}[ht]
   \caption{Platform File Parameters}
   % title of Table
   \centering

+  \AG{Use e.g. $5\times 10^{-7}$ instead of 5E-7}

   \begin{tabular}{ | l | l | l |l | l |l |l |  p{2cm} |}
     \hline
     Max & Min & Backbone & Backbone&Link &Link& Sharing  \\
   \begin{tabular}{ | l | l | l |l | l |l |l |  p{2cm} |}
     \hline
     Max & Min & Backbone & Backbone&Link &Link& Sharing  \\


@@ -483,7 +504,7 @@ successive frequencies.
 \end{table}
 Depending on the EQ~(\ref{eq:energy}), we measure the energy consumption for all
 the NAS MPI programs while assuming the power dynamic is equal to 20W and the
 \end{table}
 Depending on the EQ~(\ref{eq:energy}), we measure the energy consumption for all
 the NAS MPI programs while assuming the power dynamic is equal to 20W and the

-power static is equal to 4W for all experiments. We run the proposed ESPA
+power static is equal to 4W for all experiments. We run the proposed EPSA

 algorithm for all these programs. The results showed that the algorithm selected
 different scaling factors for each program depending on the communication
 features of the program as in the figure~(\ref{fig:nas}). This figure shows that
 algorithm for all these programs. The results showed that the algorithm selected
 different scaling factors for each program depending on the communication
 features of the program as in the figure~(\ref{fig:nas}). This figure shows that


@@ -515,6 +536,9 @@ same time over all available scales.
   \caption{Optimal Scaling Factors Results}
   % title of Table
   \centering
   \caption{Optimal Scaling Factors Results}
   % title of Table
   \centering

+  \AG{Use the same number of decimals for all numbers in a column,
+    and vertically align the numbers along the decimal points.
+    The same for all the following tables.}

   \begin{tabular}{ | l | l | l |l | l | p{2cm} |}
     \hline
     Program & Optimal & Energy  & Performance&Energy-Perf.\\
   \begin{tabular}{ | l | l | l |l | l | p{2cm} |}
     \hline
     Program & Optimal & Energy  & Performance&Energy-Perf.\\


@@ -522,10 +546,10 @@ same time over all available scales.
     CG & 1.56 &39.23 & 14.88 & 24.35\\ \hline
     MG & 1.47 &34.97&21.7& 13.27   \\ \hline
     EP & 1.04 &22.14&20.73 &1.41\\ \hline
     CG & 1.56 &39.23 & 14.88 & 24.35\\ \hline
     MG & 1.47 &34.97&21.7& 13.27   \\ \hline
     EP & 1.04 &22.14&20.73 &1.41\\ \hline

-    LU & 1.388 &35.83&22.49 &13.34\\ \hline
-    BT & 1.315 &29.6&21.28 &8.32\\ \hline
-    SP & 1.388 &33.48 &21.36&12.12\\ \hline
-    FT & 1.47 &34.72 &19&15.72\\ \hline
+    LU & 1.38 &35.83&22.49 &13.34\\ \hline
+    BT & 1.31 &29.60&21.28 &8.32\\ \hline
+    SP & 1.38 &33.48 &21.36&12.12\\ \hline
+    FT & 1.47 &34.72 &19.00&15.72\\ \hline

   \end{tabular}
   \label{table:factors results}
   % is used to refer this table in the text
   \end{tabular}
   \label{table:factors results}
   % is used to refer this table in the text


@@ -555,39 +579,39 @@ benchmarks programs for classes A,B and C.
   \caption{Comparing Results for  The NAS Class A}
   % title of Table
   \centering
   \caption{Comparing Results for  The NAS Class A}
   % title of Table
   \centering

-  \begin{tabular}{ | l | l | l |l | l |l|  }
+  \begin{tabular}{ | l | l | l |l | l | l|  }

     \hline
     Method&Program&Factor& Energy& Performance &Energy-Perf.\\
     name &name&value& Saving \%&Degradation \% &Distance
     \\ \hline
     % \rowcolor[gray]{0.85}
     EPSA&CG & 1.56 &37.02 & 13.88 & 23.14\\ \hline
     \hline
     Method&Program&Factor& Energy& Performance &Energy-Perf.\\
     name &name&value& Saving \%&Degradation \% &Distance
     \\ \hline
     % \rowcolor[gray]{0.85}
     EPSA&CG & 1.56 &37.02 & 13.88 & 23.14\\ \hline

-    $Rauber_{E-P}$&CG &2.14 &42.77 & 25.27 & 17.5\\ \hline
+    $Rauber_{E-P}$&CG &2.14 &42.77 & 25.27 & 17.50\\ \hline

     $Rauber_{E}$&CG &2.14 &42.77&26.46&16.31\\ \hline
 
     EPSA&MG & 1.47 &27.66&16.82&10.84\\ \hline
     $Rauber_{E-P}$&MG &2.14&34.45&31.84&2.61\\ \hline
     $Rauber_{E}$&CG &2.14 &42.77&26.46&16.31\\ \hline
 
     EPSA&MG & 1.47 &27.66&16.82&10.84\\ \hline
     $Rauber_{E-P}$&MG &2.14&34.45&31.84&2.61\\ \hline

-    $Rauber_{E}$&MG &2.14&34.48&33.65&0.8 \\ \hline
+    $Rauber_{E}$&MG &2.14&34.48&33.65&0.80 \\ \hline

 
     EPSA&EP &1.19 &25.32&20.79&4.53\\ \hline
     $Rauber_{E-P}$&EP&2.05&41.45&55.67&-14.22\\ \hline
 
     EPSA&EP &1.19 &25.32&20.79&4.53\\ \hline
     $Rauber_{E-P}$&EP&2.05&41.45&55.67&-14.22\\ \hline

-    $Rauber_{E}$&EP&2.05&42.09&57.59&-15.5\\ \hline
+    $Rauber_{E}$&EP&2.05&42.09&57.59&-15.50\\ \hline

 
     EPSA&LU&1.56& 39.55 &19.38& 20.17\\ \hline
 
     EPSA&LU&1.56& 39.55 &19.38& 20.17\\ \hline

-    $Rauber_{E-P}$&LU&2.14&45.62&27&18.62 \\ \hline
+    $Rauber_{E-P}$&LU&2.14&45.62&27.00&18.62 \\ \hline

     $Rauber_{E}$&LU&2.14&45.66&33.01&12.65\\ \hline
 
     $Rauber_{E}$&LU&2.14&45.66&33.01&12.65\\ \hline
 

-    EPSA&BT&1.315& 29.6&20.53&9.07 \\ \hline
-    $Rauber_{E-P}$&BT&2.1&45.53&49.63&-4.1\\ \hline
-    $Rauber_{E}$&BT&2.1&43.93&52.86&-8.93\\ \hline
+    EPSA&BT&1.31& 29.60&20.53&9.07 \\ \hline
+    $Rauber_{E-P}$&BT&2.10&45.53&49.63&-4.10\\ \hline
+    $Rauber_{E}$&BT&2.10&43.93&52.86&-8.93\\ \hline

 
 

-    EPSA&SP&1.388& 33.51&15.65&17.86 \\ \hline
-    $Rauber_{E-P}$&SP&2.11&45.62&42.52&3.1\\ \hline
+    EPSA&SP&1.38& 33.51&15.65&17.86 \\ \hline
+    $Rauber_{E-P}$&SP&2.11&45.62&42.52&3.10\\ \hline

     $Rauber_{E}$&SP&2.11&45.78&43.09&2.69\\ \hline
 
     $Rauber_{E}$&SP&2.11&45.78&43.09&2.69\\ \hline
 

-    EPSA&FT&1.25& 25&10.8&14.2 \\ \hline
-    $Rauber_{E-P}$&FT&2.1&39.29&34.3&4.99 \\ \hline
-    $Rauber_{E}$&FT&2.1&37.56&38.21&-0.65\\ \hline
+    EPSA&FT&1.25&25.00&10.80&14.20 \\ \hline
+    $Rauber_{E-P}$&FT&2.10&39.29&34.30&4.99 \\ \hline
+    $Rauber_{E}$&FT&2.10&37.56&38.21&-0.65\\ \hline

   \end{tabular}
   \label{table:compare Class A}
   % is used to refer this table in the text
   \end{tabular}
   \label{table:compare Class A}
   % is used to refer this table in the text


@@ -602,8 +626,8 @@ benchmarks programs for classes A,B and C.
     name &name&value& Saving \%&Degradation \% &Distance
     \\ \hline
     % \rowcolor[gray]{0.85}
     name &name&value& Saving \%&Degradation \% &Distance
     \\ \hline
     % \rowcolor[gray]{0.85}

-    EPSA&CG & 1.66 &39.23&16.63&22.6   \\ \hline
-    $Rauber_{E-P}$&CG &2.15 &45.34&27.6&17.74\\ \hline
+    EPSA&CG & 1.66 &39.23&16.63&22.60   \\ \hline
+    $Rauber_{E-P}$&CG &2.15 &45.34&27.60&17.74\\ \hline

     $Rauber_{E}$&CG &2.15 &45.34&28.88&16.46\\ \hline
 
     EPSA&MG & 1.47 &34.98&18.35&16.63\\ \hline
     $Rauber_{E}$&CG &2.15 &45.34&28.88&16.46\\ \hline
 
     EPSA&MG & 1.47 &34.98&18.35&16.63\\ \hline


@@ -611,24 +635,24 @@ benchmarks programs for classes A,B and C.
     $Rauber_{E}$&MG &2.14&43.56&37.07&6.49 \\ \hline
 
     EPSA&EP &1.08 &20.29&17.15&3.14 \\ \hline
     $Rauber_{E}$&MG &2.14&43.56&37.07&6.49 \\ \hline
 
     EPSA&EP &1.08 &20.29&17.15&3.14 \\ \hline

-    $Rauber_{E-P}$&EP&2&42.38&56.88&-14.5\\ \hline
-    $Rauber_{E}$&EP&2&39.73&59.94&-20.21\\ \hline
+    $Rauber_{E-P}$&EP&2.00&42.38&56.88&-14.50\\ \hline
+    $Rauber_{E}$&EP&2.00&39.73&59.94&-20.21\\ \hline

 
     EPSA&LU&1.47&38.57&21.34&17.23 \\ \hline
 
     EPSA&LU&1.47&38.57&21.34&17.23 \\ \hline

-    $Rauber_{E-P}$&LU&2.1&43.62&36.51&7.11 \\ \hline
-    $Rauber_{E}$&LU&2.1&43.61&38.54&5.07 \\ \hline
+    $Rauber_{E-P}$&LU&2.10&43.62&36.51&7.11 \\ \hline
+    $Rauber_{E}$&LU&2.10&43.61&38.54&5.07 \\ \hline

 
 

-    EPSA&BT&1.315& 29.59&20.88&8.71\\ \hline
-    $Rauber_{E-P}$&BT&2.1&44.53&53.05&-8.52\\ \hline
-    $Rauber_{E}$&BT&2.1&42.93&52.806&-9.876\\ \hline
+    EPSA&BT&1.31& 29.59&20.88&8.71\\ \hline
+    $Rauber_{E-P}$&BT&2.10&44.53&53.05&-8.52\\ \hline
+    $Rauber_{E}$&BT&2.10&42.93&52.80&-9.87\\ \hline

 
 

-    EPSA&SP&1.388&33.44&19.24&14.2 \\ \hline
-    $Rauber_{E-P}$&SP&2.15&45.69&43.2&2.49\\ \hline
+    EPSA&SP&1.38&33.44&19.24&14.20 \\ \hline
+    $Rauber_{E-P}$&SP&2.15&45.69&43.20&2.49\\ \hline

     $Rauber_{E}$&SP&2.15&45.41&44.47&0.94\\ \hline
 
     $Rauber_{E}$&SP&2.15&45.41&44.47&0.94\\ \hline
 

-    EPSA&FT&1.388&34.4&14.57&19.83 \\ \hline
+    EPSA&FT&1.38&34.40&14.57&19.83 \\ \hline

     $Rauber_{E-P}$&FT&2.13&42.98&37.35&5.63 \\ \hline
     $Rauber_{E-P}$&FT&2.13&42.98&37.35&5.63 \\ \hline

-    $Rauber_{E}$&FT&2.13&43.04&37.9&5.14\\ \hline
+    $Rauber_{E}$&FT&2.13&43.04&37.90&5.14\\ \hline

   \end{tabular}
   \label{table:compare Class B}
   % is used to refer this table in the text
   \end{tabular}
   \label{table:compare Class B}
   % is used to refer this table in the text


@@ -646,31 +670,31 @@ benchmarks programs for classes A,B and C.
     % \rowcolor[gray]{0.85}
     EPSA&CG & 1.56 &39.23&14.88&24.35  \\ \hline
     $Rauber_{E-P}$&CG &2.15 &45.36&25.89&19.47\\ \hline
     % \rowcolor[gray]{0.85}
     EPSA&CG & 1.56 &39.23&14.88&24.35  \\ \hline
     $Rauber_{E-P}$&CG &2.15 &45.36&25.89&19.47\\ \hline

-    $Rauber_{E}$&CG &2.15 &45.36&26.7&18.66\\ \hline
+    $Rauber_{E}$&CG &2.15 &45.36&26.70&18.66\\ \hline

 
 

-    EPSA&MG & 1.47 &34.97&21.697&13.273\\ \hline
-    $Rauber_{E-P}$&MG &2.15&43.65&40.45&3.2 \\ \hline
+    EPSA&MG & 1.47 &34.97&21.69&13.27\\ \hline
+    $Rauber_{E-P}$&MG &2.15&43.65&40.45&3.20 \\ \hline

     $Rauber_{E}$&MG &2.15&43.64&41.38&2.26 \\ \hline
 
     EPSA&EP &1.04 &22.14&20.73&1.41 \\ \hline
     $Rauber_{E}$&MG &2.15&43.64&41.38&2.26 \\ \hline
 
     EPSA&EP &1.04 &22.14&20.73&1.41 \\ \hline

-    $Rauber_{E-P}$&EP&1.92&39.4&56.33&-16.93\\ \hline
-    $Rauber_{E}$&EP&1.92&38.1&56.35&-18.25\\ \hline
+    $Rauber_{E-P}$&EP&1.92&39.40&56.33&-16.93\\ \hline
+    $Rauber_{E}$&EP&1.92&38.10&56.35&-18.25\\ \hline

 
 

-    EPSA&LU&1.388&35.83&22.49&13.34 \\ \hline
-    $Rauber_{E-P}$&LU&2.15&44.97&41&3.97 \\ \hline
-    $Rauber_{E}$&LU&2.15&44.97&41.8&3.17 \\ \hline
+    EPSA&LU&1.38&35.83&22.49&13.34 \\ \hline
+    $Rauber_{E-P}$&LU&2.15&44.97&41.00&3.97 \\ \hline
+    $Rauber_{E}$&LU&2.15&44.97&41.80&3.17 \\ \hline

 
 

-    EPSA&BT&1.315& 29.6&21.28&8.32\\ \hline
-    $Rauber_{E-P}$&BT&2.13&45.6&49.84&-4.24\\ \hline
-    $Rauber_{E}$&BT&2.13&44.9&55.16&-10.26\\ \hline
+    EPSA&BT&1.31& 29.60&21.28&8.32\\ \hline
+    $Rauber_{E-P}$&BT&2.13&45.60&49.84&-4.24\\ \hline
+    $Rauber_{E}$&BT&2.13&44.90&55.16&-10.26\\ \hline

 
 

-    EPSA&SP&1.388&33.48&21.35&12.12\\ \hline
-    $Rauber_{E-P}$&SP&2.1&45.69&43.6&2.09\\ \hline
-    $Rauber_{E}$&SP&2.1&45.75&44.1&1.65\\ \hline
+    EPSA&SP&1.38&33.48&21.35&12.12\\ \hline
+    $Rauber_{E-P}$&SP&2.10&45.69&43.60&2.09\\ \hline
+    $Rauber_{E}$&SP&2.10&45.75&44.10&1.65\\ \hline

 
 

-    EPSA&FT&1.47&34.72&19&15.72 \\ \hline
-    $Rauber_{E-P}$&FT&2.04&39.4&37.1&2.3\\ \hline
-    $Rauber_{E}$&FT&2.04&39.35&37.7&1.65\\ \hline
+    EPSA&FT&1.47&34.72&19.00&15.72 \\ \hline
+    $Rauber_{E-P}$&FT&2.04&39.40&37.10&2.30\\ \hline
+    $Rauber_{E}$&FT&2.04&39.35&37.70&1.65\\ \hline

   \end{tabular}
 \label{table:compare Class C}
 % is used to refer this table in the text
   \end{tabular}
 \label{table:compare Class C}
 % is used to refer this table in the text


@@ -706,6 +730,8 @@ than the first.
   \label{fig:compare}
 \end{figure}
 
   \label{fig:compare}
 \end{figure}
 

+\AG{\texttt{bibtex} gives many errors, please correct them}
+\clearpage

 \bibliographystyle{plain}
 \bibliography{my_reference}
 \end{document}
 \bibliographystyle{plain}
 \bibliography{my_reference}
 \end{document}


@@ -714,5 +740,8 @@ than the first.
 %%% mode: latex
 %%% TeX-master: t
 %%% fill-column: 80
 %%% mode: latex
 %%% TeX-master: t
 %%% fill-column: 80

-%%% ispell-local-dictionary: "american"
+%%%ispell-local-dictionary: "american"

 %%% End:
 %%% End:

+
+%  LocalWords:  Badri Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber
+%  LocalWords:  CMOS EQ EPSA