From deaad9c91bd56f904fe3c5ff93664431a18d4f44 Mon Sep 17 00:00:00 2001
From: Arnaud Giersch <arnaud.giersch@univ-fcomte.fr>
Date: Fri, 23 May 2014 15:32:51 +0200
Subject: [PATCH] Correct formulae and algorithm.

---
 paper.tex | 19 ++++++++-----------
 1 file changed, 8 insertions(+), 11 deletions(-)

diff --git a/paper.tex b/paper.tex
index 618e7ad..9c374ba 100644
--- a/paper.tex
+++ b/paper.tex
@@ -345,18 +345,18 @@ the consumed energy with scaled frequency and the consumed energy without scaled
 frequency:
 \begin{multline}
   \label{eq:enorm}
-  \Enorm = \frac{ \Ereduced}{\Eoriginal} \\
-      {} = \frac{\Pdyn \cdot S_1^{-2} \cdot
+  \Enorm(S) = \frac{ \Ereduced}{\Eoriginal} \\
+         {} = \frac{\Pdyn \cdot S^{-2} \cdot
              \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
-               \Pstatic \cdot T_1 \cdot S_1 \cdot N}{
+               \Pstatic \cdot T_1 \cdot S \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 = \frac{\Tnew}{\Told}
-         = \frac{\TmaxCompOld \cdot S + \TmaxCommOld}{
+  \Pnorm(S) = \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} = \frac{ \Told}{ \Tnew}
+  \Pnorm^{-1}(S) = \frac{ \Told}{ \Tnew}
                = \frac{\TmaxCompOld +
                  \TmaxCommOld}{\TmaxCompOld \cdot S +
                  \TmaxCommOld}
@@ -433,13 +433,10 @@ 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 $\Enorm \gets
-          \frac{\Pdyn \cdot S_1^{-2} \cdot
+          \frac{\Pdyn \cdot S^{-2} \cdot
                   \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
-                  \Pstatic \cdot T_1 \cdot S_1 \cdot N }{
+                  \Pstatic \cdot T_1 \cdot S \cdot N }{
                 \Pdyn \cdot
                   \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
                   \Pstatic \cdot T_1 \cdot N }$
-- 
2.39.5