Update.

[mpi-energy.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 9c374ba8c8b4d56d6ca1346ca15f2942f2f41b28..f87dd56ddf5bff938dfc081f4accd0030c1cb202 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -285,11 +285,11 @@ function of the scaling factor $S$, as in EQ~\eqref{eq:energy}.
     \left( T_1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^2} \right) +
       \Pstatic \cdot T_1 \cdot S_1 \cdot N
 \end{equation}
-where $N$ is the number of parallel nodes, $T_i$ and $S_i$ for $i=1,\dots,N$ are
-the execution times and scaling factors of the sorted tasks.  Therefore, $T_1$ is
+where $N$ is the number of parallel nodes, $T_i$ for $i=1,\dots,N$ are
+the execution times of the sorted tasks.  Therefore, $T_1$ is
 the time of the slowest task, and $S_1$ its scaling factor which should be the
 highest because they are proportional to the time values $T_i$.  The scaling
-factors are computed as in EQ~\eqref{eq:si}.
+factors $S_i$ are computed as in EQ~\eqref{eq:si}.
 \begin{equation}
   \label{eq:si}
   S_i = S \cdot \frac{T_1}{T_i}
@@ -345,18 +345,18 @@ the consumed energy with scaled frequency and the consumed energy without scaled
 frequency:
 \begin{multline}
   \label{eq:enorm}
-  \Enorm(S) = \frac{ \Ereduced}{\Eoriginal} \\
-         {} = \frac{\Pdyn \cdot S^{-2} \cdot
+  \Enorm = \frac{ \Ereduced}{\Eoriginal} \\
+      {} = \frac{\Pdyn \cdot S_1^{-2} \cdot
              \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
-               \Pstatic \cdot T_1 \cdot S \cdot N}{
+               \Pstatic \cdot T_1 \cdot S_1 \cdot N}{
              \Pdyn \cdot \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
                \Pstatic \cdot T_1 \cdot N }
 \end{multline}
 In the same way we can normalize the performance as follows:
 \begin{equation}
   \label{eq:pnorm}
-  \Pnorm(S) = \frac{\Tnew}{\Told}
-            = \frac{\TmaxCompOld \cdot S + \TmaxCommOld}{
+  \Pnorm = \frac{\Tnew}{\Told}
+         = \frac{\TmaxCompOld \cdot S + \TmaxCommOld}{
              \TmaxCompOld + \TmaxCommOld}
 \end{equation}
 The second problem is that the optimization operation for both energy and
@@ -377,7 +377,7 @@ direction.  Therefore, we inverse the equation of the normalized performance as
 follows:
 \begin{equation}
   \label{eq:pnorm_en}
-  \Pnorm^{-1}(S) = \frac{ \Told}{ \Tnew}
+  \Pnorm^{-1} = \frac{ \Told}{ \Tnew}
                = \frac{\TmaxCompOld +
                  \TmaxCommOld}{\TmaxCompOld \cdot S +
                  \TmaxCommOld}
@@ -433,10 +433,13 @@ the objective function described above.
     \For {$j = 2$ to $\Pstates$}
       \State $\Fnew \gets \Fnew - \Fdiff$
       \State $S \gets \Fmax / \Fnew$
+      \State $S_i \gets S \cdot \frac{T_1}{T_i}
+                  = \frac{\Fmax}{\Fnew} \cdot \frac{T_1}{T_i}$
+             for $i=1,\dots,N$
       \State $\Enorm \gets
-          \frac{\Pdyn \cdot S^{-2} \cdot
+          \frac{\Pdyn \cdot S_1^{-2} \cdot
                   \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
-                  \Pstatic \cdot T_1 \cdot S \cdot N }{
+                  \Pstatic \cdot T_1 \cdot S_1 \cdot N }{
                 \Pdyn \cdot
                   \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
                   \Pstatic \cdot T_1 \cdot N }$