Diff for "AmdahlsLaw"

Differences between revisions 2 and 14 (spanning 12 versions)

$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$

See SpeedUp

Notice that we are talking about the entire task here and that performance (speedup) is defined in terms of execution time! So we have to define the following:

\begin{equation}
   SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}
\end{equation}
\begin{equation}
   New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)
\end{equation}

                                                                    FractionEnhanced
New Execution Time = Old Execution Time ( (1 - FractionEnhanced) + ------------------ )
                                                                    SpeedupEnhanced

or

                       Execution Time affected by Improvement
New Execution Time =   --------------------------------------  + Execution Time unaffected
                            Amount of Improvement (x times) 

So we have
                                     1
SpeedupOverall = --------------------------------------------
                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhanced

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-  ⇤ ← Revision 2 as of 2004-01-25 18:27:14 → 
  Size: 1144
  Editor: yakko
  Comment:
+   ← Revision 14 as of 2005-06-27 22:23:22 → ⇥
  Size: 1415
  Editor: yakko
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 3:
-{{{
           Performance for entire task using the enhancement when possible
Speedup = -----------------------------------------------------------------
              Performance for entire taks without using the enhancement
+{{{#!latex2
$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$
-Line 13:
+Line 11:
+{{{#!latex2
\begin{equation}
   SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}
\end{equation}
\begin{equation}
   New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)
\end{equation}
}}}
-Line 14:
+Line 21:
-                  Old Execution Time
SpeedupOverall = --------------------
                  New Execution Time
-Line 22:
+Line 26:
--->
+or

                       Execution Time affected by Improvement
New Execution Time =   --------------------------------------  + Execution Time unaffected
                            Amount of Improvement (x times) 

So we have
-Line 25:
+Line 35:
-                                         FractionEnhanced
               (1 - FractionEnhanced) + ------------------ )
                                         SpeedupEnhanced
+                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhanced