X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/mpi-energy.git/blobdiff_plain/b2cc9a1514a726fba321b6a0928b8c7a3ac5078b..0ca453cf546b2a56b2b987f75ab16d61ec87ffba:/paper.tex diff --git a/paper.tex b/paper.tex index 29f175b..373e18b 100644 --- a/paper.tex +++ b/paper.tex @@ -16,7 +16,6 @@ %\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}} @@ -329,7 +328,7 @@ between the consumed energy with scaled frequency and the consumed energy without scaled frequency : \begin{equation} \label{eq:enorm} - E_{Norm} = \frac{E_{Reduced}}{E_{Original}} + 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 }{ @@ -438,24 +437,29 @@ for each task from the first iteration only. When these times are measured, the MPI program calls the EPSA algorithm to choose the new frequency using the 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 : -\begin{minipage}{\textwidth} -\AG{Use the same format as for Algorithm~\ref{EPSA}} -\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} +program. The DVFS algorithm~(\ref{dvfs}) shows where and when the EPSA algorithm is called +in the MPI program. +%\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 \; $} + \State -Computations Section. + \State -Communications Section. + \If {$(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 @@ -493,7 +497,7 @@ frequencies. \hline Max & Min & Backbone & Backbone&Link &Link& Sharing \\ Freq. & Freq. & Bandwidth & Latency & Bandwidth& Latency&Policy \\ \hline - 2.5 &800 & 2.25 GBps &5E-7 s & 1 GBps & 5E-5 s&Full \\ + 2.5 &800 & 2.25 GBps &$5\times 10^{-7} s$& 1 GBps & $5\times 10^{-5}$ s&Full \\ GHz& MHz& & & & &Duplex \\\hline \end{tabular} \label{table:platform} @@ -539,13 +543,13 @@ same time over all available scales. \hline Program & Optimal & Energy & Performance&Energy-Perf.\\ Name & Scaling Factor& Saving \%&Degradation \% &Distance \\ \hline - CG & 1.56 &39.23 & 14.88 & 24.35\\ \hline - MG & 1.47 &34.97&21.7& 13.27 \\ \hline + CG & 1.56 &39.23&14.88 &24.35\\ \hline + MG & 1.47 &34.97&21.70 &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 @@ -575,39 +579,39 @@ benchmarks programs for classes A,B and C. \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 - $Rauber_{E-P}$&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 - $Rauber_{E}$&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 - $Rauber_{E}$&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 - $Rauber_{E-P}$&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 - 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 - 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 @@ -622,8 +626,8 @@ benchmarks programs for classes A,B and C. 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 @@ -631,24 +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 - $Rauber_{E-P}$&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 - $Rauber_{E-P}$&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 - 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 - $Rauber_{E}$&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 @@ -666,31 +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 - $Rauber_{E}$&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 - $Rauber_{E-P}$&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 @@ -726,7 +730,8 @@ than the first. \label{fig:compare} \end{figure} -\AG{\texttt{bibtex} gives many errors, please correct them} +\AG{\texttt{bibtex} gives many errors, please correct them !! Its correct } +\clearpage \bibliographystyle{plain} \bibliography{my_reference} \end{document} @@ -735,7 +740,7 @@ than the first. %%% mode: latex %%% TeX-master: t %%% fill-column: 80 -%%% ispell-local-dictionary: "american" +%%%ispell-local-dictionary: "american" %%% End: % LocalWords: Badri Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber