Used existing operator for max.

[mpi-energy2.git] / Heter_paper.tex

diff --git a/Heter_paper.tex b/Heter_paper.tex
index c48c9275d34035f90937113f3f9788eef2e6332b..a31c0fbec3daac05e494d832b2bd23499cbca224 100644 (file)
--- a/Heter_paper.tex
+++ b/Heter_paper.tex
@@ -41,26 +41,17 @@
 \newcommand{\MaxDist}{\mathit{Max}\Dist}
 \newcommand{\MinTcm}{\mathit{Min}\Tcm}
 \newcommand{\Ntrans}{\Xsub{N}{trans}}
 \newcommand{\MaxDist}{\mathit{Max}\Dist}
 \newcommand{\MinTcm}{\mathit{Min}\Tcm}
 \newcommand{\Ntrans}{\Xsub{N}{trans}}

+\newcommand{\Pd}{\Xsub{P}{d}}

 \newcommand{\PdNew}{\Xsub{P}{dNew}}
 \newcommand{\PdOld}{\Xsub{P}{dOld}}
 \newcommand{\PdNew}{\Xsub{P}{dNew}}
 \newcommand{\PdOld}{\Xsub{P}{dOld}}

-%\newcommand{\Pdyn}{\Xsub{P}{dyn}}
-\newcommand{\Pd}{\Xsub{P}{d}}
-%\newcommand{\PnormInv}{\Xsub{P}{NormInv}}

 \newcommand{\Pnorm}{\Xsub{P}{Norm}}
 \newcommand{\Pnorm}{\Xsub{P}{Norm}}

-%\newcommand{\Pstates}{\Xsub{P}{states}}
-%\newcommand{\Pstatic}{\Xsub{P}{static}}

 \newcommand{\Ps}{\Xsub{P}{s}}
 \newcommand{\Scp}{\Xsub{S}{cp}}
 \newcommand{\Sopt}{\Xsub{S}{opt}}
 \newcommand{\Tcm}{\Xsub{T}{cm}}
 \newcommand{\Ps}{\Xsub{P}{s}}
 \newcommand{\Scp}{\Xsub{S}{cp}}
 \newcommand{\Sopt}{\Xsub{S}{opt}}
 \newcommand{\Tcm}{\Xsub{T}{cm}}

-%\newcommand{\Tcomp}{\Xsub{T}{comp}}
-\newcommand{\TcpOld}{\Xsub{T}{cpOld}}

 \newcommand{\Tcp}{\Xsub{T}{cp}}
 \newcommand{\Tcp}{\Xsub{T}{cp}}

-%\newcommand{\TmaxCommOld}{\Xsub{T}{Max Comm Old}}
-%\newcommand{\TmaxCompOld}{\Xsub{T}{Max Comp Old}}
-%\newcommand{\Tmax}{\Xsub{T}{max}}
+\newcommand{\TcpOld}{\Xsub{T}{cpOld}}

 \newcommand{\Tnew}{\Xsub{T}{New}}
 \newcommand{\Tnew}{\Xsub{T}{New}}

-%\newcommand{\Tnorm}{\Xsub{T}{Norm}}

 \newcommand{\Told}{\Xsub{T}{Old}} 
 
 \begin{document} 
 \newcommand{\Told}{\Xsub{T}{Old}} 
 
 \begin{document} 


@@ -647,7 +638,7 @@ maximum distance  between the  energy curve and  the performance curve  is while
     \If{(not the first frequency)}
           \State $F_i \gets F_i+\Fdiff_i,~i=1,\dots,N.$
     \EndIf 
     \If{(not the first frequency)}
           \State $F_i \gets F_i+\Fdiff_i,~i=1,\dots,N.$
     \EndIf 

-    \State $\Told \gets max_{~i=1,\dots,N } (\Tcp_i+\Tcm_i)$
+    \State $\Told \gets \max_{i=1,\dots,N} (\Tcp_i+\Tcm_i)$

     % \State $\Eoriginal \gets \sum_{i=1}^{N}{( \Pd_i \cdot  \Tcp_i)} +\sum_{i=1}^{N} {(\Ps_i \cdot \Told)}$
     \State $\Eoriginal \gets \sum_{i=1}^{N}{( \Pd_i \cdot  \Tcp_i + \Ps_i \cdot \Told)}$
     \State $\Sopt_{i} \gets 1,~i=1,\dots,N. $
     % \State $\Eoriginal \gets \sum_{i=1}^{N}{( \Pd_i \cdot  \Tcp_i)} +\sum_{i=1}^{N} {(\Ps_i \cdot \Told)}$
     \State $\Eoriginal \gets \sum_{i=1}^{N}{( \Pd_i \cdot  \Tcp_i + \Ps_i \cdot \Told)}$
     \State $\Sopt_{i} \gets 1,~i=1,\dots,N. $


@@ -657,7 +648,7 @@ maximum distance  between the  energy curve and  the performance curve  is while
         \State $F_i \gets F_i - \Fdiff_i,~i=1,\dots,N.$
         \State $S_i \gets \frac{\Fmax_i}{F_i},~i=1,\dots,N.$
         \EndIf
         \State $F_i \gets F_i - \Fdiff_i,~i=1,\dots,N.$
         \State $S_i \gets \frac{\Fmax_i}{F_i},~i=1,\dots,N.$
         \EndIf

-       \State $\Tnew \gets max_\textit{~i=1,\dots,N} (\Tcp_{i} \cdot S_{i}) + \MinTcm $
+       \State $\Tnew \gets \max_{i=1,\dots,N} (\Tcp_{i} \cdot S_{i}) + \MinTcm $

 %       \State $\Ereduced \gets \sum_{i=1}^{N}{(S_i^{-2} \cdot \Pd_i \cdot  \Tcp_i)} + \sum_{i=1}^{N} {(\Ps_i \cdot \rlap{\Tnew)}} $
        \State $\Ereduced \gets \sum_{i=1}^{N}{(S_i^{-2} \cdot \Pd_i \cdot  \Tcp_i + \Ps_i \cdot \rlap{\Tnew)}} $
        \State $\Pnorm \gets \frac{\Told}{\Tnew}$
 %       \State $\Ereduced \gets \sum_{i=1}^{N}{(S_i^{-2} \cdot \Pd_i \cdot  \Tcp_i)} + \sum_{i=1}^{N} {(\Ps_i \cdot \rlap{\Tnew)}} $
        \State $\Ereduced \gets \sum_{i=1}^{N}{(S_i^{-2} \cdot \Pd_i \cdot  \Tcp_i + \Ps_i \cdot \rlap{\Tnew)}} $
        \State $\Pnorm \gets \frac{\Told}{\Tnew}$


@@ -1139,6 +1130,24 @@ degradation.
   \label{table:res_s2}
 \end{table}
 
   \label{table:res_s2}
 \end{table}
 

+\begin{table}[!t]
+ \caption{Comparing the proposed algorithm}
+ \centering
+\begin{tabular}{|*{7}{r|}}
+\hline
+Program & \multicolumn{2}{c|}{Energy saving \%} & \multicolumn{2}{c|}{Perf.  degradation \%} & \multicolumn{2}{c|}{Distance} \\ \cline{2-7} 
+name    & EDP             & MaxDist          & EDP            & MaxDist           & EDP          & MaxDist        \\ \hline
+CG      & 27.58           & 31.25            & 5.82           & 7.12              & 21.76        & 24.13          \\ \hline
+MG      & 29.49           & 33.78            & 3.74           & 6.41              & 25.75        & 27.37          \\ \hline
+LU      & 19.55           & 28.33            & 0.0            & 0.01              & 19.55        & 28.22          \\ \hline
+EP      & 28.40           & 27.04            & 4.29           & 0.49              & 24.11        & 26.55          \\ \hline
+BT      & 27.68           & 32.32            & 6.45           & 7.87              & 21.23        & 24.43          \\ \hline
+SP      & 20.52           & 24.73            & 5.21           & 2.78              & 15.31         & 21.95         \\ \hline
+FT      & 27.03           & 31.02            & 2.75           & 2.54              & 24.28        & 28.48           \\ \hline
+
+\end{tabular}
+\label{table:compare_EDP}
+\end{table}

 
 \begin{figure}[!t]
   \centering
 
 \begin{figure}[!t]
   \centering


@@ -1151,7 +1160,12 @@ degradation.
   \caption{The comparison of the three power scenarios}
 \end{figure}  
 
   \caption{The comparison of the three power scenarios}
 \end{figure}  
 

-
+\begin{figure}[!t]
+  \centering
+   \includegraphics[scale=0.5]{fig/compare_EDP.pdf}
+  \caption{Trade-off comparison for NAS benchmarks class C}
+  \label{fig:compare_EDP}
+\end{figure}

 
 
 \subsection{The comparison of the proposed scaling algorithm }
 
 
 \subsection{The comparison of the proposed scaling algorithm }


@@ -1188,39 +1202,6 @@ because it maximizes the distance  between the energy saving and the performance
 degradation values while giving the same weight for both metrics.
 
 
 degradation values while giving the same weight for both metrics.
 
 

-
-
-\begin{table}[!t]
- \caption{Comparing the proposed algorithm}
- \centering
-\begin{tabular}{|*{7}{r|}}
-\hline
-Program & \multicolumn{2}{c|}{Energy saving \%} & \multicolumn{2}{c|}{Perf.  degradation \%} & \multicolumn{2}{c|}{Distance} \\ \cline{2-7} 
-name    & EDP             & MaxDist          & EDP            & MaxDist           & EDP          & MaxDist        \\ \hline
-CG      & 27.58           & 31.25            & 5.82           & 7.12              & 21.76        & 24.13          \\ \hline
-MG      & 29.49           & 33.78            & 3.74           & 6.41              & 25.75        & 27.37          \\ \hline
-LU      & 19.55           & 28.33            & 0.0            & 0.01              & 19.55        & 28.22          \\ \hline
-EP      & 28.40           & 27.04            & 4.29           & 0.49              & 24.11        & 26.55          \\ \hline
-BT      & 27.68           & 32.32            & 6.45           & 7.87              & 21.23        & 24.43          \\ \hline
-SP      & 20.52           & 24.73            & 5.21           & 2.78              & 15.31         & 21.95         \\ \hline
-FT      & 27.03           & 31.02            & 2.75           & 2.54              & 24.28        & 28.48           \\ \hline
-
-\end{tabular}
-\label{table:compare_EDP}
-\end{table}
-
-
-
-
-
-\begin{figure}[!t]
-  \centering
-   \includegraphics[scale=0.5]{fig/compare_EDP.pdf}
-  \caption{Trade-off comparison for NAS benchmarks class C}
-  \label{fig:compare_EDP}
-\end{figure}
-
-

 \section{Conclusion}
 \label{sec.concl} 
 In this paper, a new online frequency selecting algorithm has been presented. It
 \section{Conclusion}
 \label{sec.concl} 
 In this paper, a new online frequency selecting algorithm has been presented. It