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[mpi-energy.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 1ce2f6034c87f4cf2da2a87007c3943215805bc8..962a22b800097d80365ca9d4d5f5fee16f6d72a9 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -201,13 +201,13 @@ $P_{dyn}$ is related to the switching activity $\alpha$, load capacitance $C_L$,
 the supply voltage $V$ and operational frequency $f$ respectively as follow :
 \begin{equation}
   \label{eq:pd}
 the supply voltage $V$ and operational frequency $f$ respectively as follow :
 \begin{equation}
   \label{eq:pd}

-  P_{dyn} = \alpha \cdot C_L \cdot V^2 \cdot f
+ \textit P_{dyn} = \alpha \cdot C_L \cdot V^2 \cdot f

 \end{equation}
 The static power $P_{static}$ captures the leakage power consumption as well as
 the power consumption of peripheral devices like the I/O subsystem.
 \begin{equation}
   \label{eq:ps}
 \end{equation}
 The static power $P_{static}$ captures the leakage power consumption as well as
 the power consumption of peripheral devices like the I/O subsystem.
 \begin{equation}
   \label{eq:ps}

-  P_{static}  = V \cdot N \cdot K_{design} \cdot I_{leak}
+ \textit P_{static}  = V \cdot N \cdot K_{design} \cdot I_{leak}

 \end{equation}
 where V is the supply voltage, N is the number of transistors, $K_{design}$ is a
 design dependent parameter and $I_{leak}$ is a technology-dependent
 \end{equation}
 where V is the supply voltage, N is the number of transistors, $K_{design}$ is a
 design dependent parameter and $I_{leak}$ is a technology-dependent


@@ -216,7 +216,7 @@ of the dynamic and the static power multiply by the execution time for example
 see~\cite{36,15}.
 \begin{equation}
   \label{eq:eind}
 see~\cite{36,15}.
 \begin{equation}
   \label{eq:eind}

-  E_{ind} = ( P_{dyn} + P_{static} ) \cdot T
+  \textit E_{ind} = ( P_{dyn} + P_{static} ) \cdot T

 \end{equation}
 The dynamic voltage and frequency scaling (DVFS) is a process that allowed in
 modern processors to reduce the dynamic power by scaling down the voltage and
 \end{equation}
 The dynamic voltage and frequency scaling (DVFS) is a process that allowed in
 modern processors to reduce the dynamic power by scaling down the voltage and


@@ -229,7 +229,7 @@ expressed by scaling factor \emph S. The scale \emph S is the ratio between the
 maximum and the new frequency as in EQ~(\ref{eq:s}).
 \begin{equation}
   \label{eq:s}
 maximum and the new frequency as in EQ~(\ref{eq:s}).
 \begin{equation}
   \label{eq:s}

-  S = \frac{F_{max}}{F_{new}}
+ S = \frac{F_{max}}{F_{new}}

 \end{equation}
 The value of the scale $S$ is greater than 1 when changing the frequency to
 any new frequency value (\emph {P-state}) in governor.
 \end{equation}
 The value of the scale $S$ is greater than 1 when changing the frequency to
 any new frequency value (\emph {P-state}) in governor.


@@ -274,7 +274,7 @@ derivation for this equation (to be minimized) and set it to zero to produce the
 scaling factor as in EQ~(\ref{eq:sopt}).
 \begin{equation}
   \label{eq:sopt}
 scaling factor as in EQ~(\ref{eq:sopt}).
 \begin{equation}
   \label{eq:sopt}

-  S_{opt} = \sqrt[3]{\frac{2}{n} \cdot \frac{P_{dyn}}{P_{static}} \cdot
+ \textit  S_{opt} = \sqrt[3]{\frac{2}{n} \cdot \frac{P_{dyn}}{P_{static}} \cdot

     \left( 1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^3} \right) }
 \end{equation}
 
     \left( 1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^3} \right) }
 \end{equation}
 


@@ -307,7 +307,7 @@ any MPI program as a function of the new scaling factor as in the
 EQ~(\ref{eq:tnew}).
 \begin{equation}
   \label{eq:tnew}
 EQ~(\ref{eq:tnew}).
 \begin{equation}
   \label{eq:tnew}

-  T_{new} = T_{\textit{Max Comp Old}} \cdot S + T_{\textit{Max Comm Old}}
+ \textit  T_{new} = T_{\textit{Max Comp Old}} \cdot S + T_{\textit{Max Comm Old}}

 \end{equation}
 The above equation shows that the scaling factor \emph S has linear relation
 with the computation time without affecting the communication time. The
 \end{equation}
 The above equation shows that the scaling factor \emph S has linear relation
 with the computation time without affecting the communication time. The


@@ -364,8 +364,8 @@ between the consumed energy with scaled frequency and the consumed energy
 without scaled frequency :
 \begin{multline}
   \label{eq:enorm}
 without scaled frequency :
 \begin{multline}
   \label{eq:enorm}

-  E_\textit{Norm} = \frac{E_{Reduced}}{E_{Original}}\\
-  {} = \frac{ P_{dyn} \cdot S_i^{-2} \cdot
+ \textit E_{Norm} = \frac{\textit E_{Reduced}}{\textit 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) +
                \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) +


@@ -381,9 +381,9 @@ without scaled frequency :
 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}

-  P_{Norm} = \frac{T_{New}}{T_{Old}}
+\textit  P_{Norm} = \frac{\textit T_{New}}{\textit T_{Old}}

           = \frac{T_{\textit{Max Comp Old}} \cdot S +
           = \frac{T_{\textit{Max Comp Old}} \cdot S +

-              T_{\textit{Max Comm Old}}}{T_{Old}}
+           T_{\textit{Max Comm Old}}}{\textit T_{Old}}

 \end{equation}
 The second problem is the optimization operation for both energy and performance
 is not in the same direction. In other words, the normalized energy and the
 \end{equation}
 The second problem is the optimization operation for both energy and performance
 is not in the same direction. In other words, the normalized energy and the


@@ -402,8 +402,8 @@ have the same direction. Therefore, we inverse the equation of normalize
 performance as follows :
 \begin{equation}
   \label{eq:pnorm_en}
 performance as follows :
 \begin{equation}
   \label{eq:pnorm_en}

-  P^{-1}_{Norm} = \frac{T_{Old}}{T_{New}}
-               = \frac{T_{Old}}{T_{\textit{Max Comp Old}} \cdot S +
+\textit  P^{-1}_{Norm} = \frac{\textit T_{Old}}{\textit T_{New}}
+               = \frac{\textit T_{Old}}{T_{\textit{Max Comp Old}} \cdot S +

                  T_{\textit{Max Comm Old}}}
 \end{equation}
 \begin{figure*}
                  T_{\textit{Max Comm Old}}}
 \end{equation}
 \begin{figure*}


@@ -424,8 +424,8 @@ in the same time, see figure~(\ref{fig:r1}). Then our objective function has the
 following form:
 \begin{equation}
   \label{eq:max}
 following form:
 \begin{equation}
   \label{eq:max}

-  \textit{MaxDist} = \max (\overbrace{P^{-1}_{Norm}}^{\text{Maximize}} -
-                           \overbrace{E_{Norm}}^{\text{Minimize}} )
+  \textit{MaxDist} = \max (\overbrace{\textit P^{-1}_{Norm}}^{\text{Maximize}} -
+                           \overbrace{\textit E_{Norm}}^{\text{Minimize}} )

 \end{equation}
 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
 \end{equation}
 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


@@ -489,9 +489,8 @@ in the MPI program.
  \For {$J:=1$ to $Some-Iterations \; $}
   \State -Computations Section.
    \State -Communications Section.
  \For {$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.
+   \If {$(J==1)$} 
+     \State -Gather all times of computation and communication from\par each node.

      \State -Call EPSA with these times.
      \State -Calculate the new frequency from optimal scale.
      \State -Set the new frequency to the system.
      \State -Call EPSA with these times.
      \State -Calculate the new frequency from optimal scale.
      \State -Set the new frequency to the system.


@@ -537,7 +536,7 @@ frequencies.
     \hline
     Max & Min & Backbone & Backbone&Link &Link& Sharing  \\
     Freq. & Freq. & Bandwidth & Latency & Bandwidth& Latency&Policy  \\ \hline
     \hline
     Max & Min & Backbone & Backbone&Link &Link& Sharing  \\
     Freq. & Freq. & Bandwidth & Latency & Bandwidth& Latency&Policy  \\ \hline

-    2.5 &800 & 2.25 GBps &$5\times 10^{-7} s$& 1 GBps & $5\times 10^{-5}$ 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}
     GHz& MHz&  & & &  &Duplex  \\\hline
   \end{tabular}
   \label{table:platform}


@@ -590,7 +589,7 @@ same time over all available scales.
     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
     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}
+  \end{tabular}        

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