Diff for "AmdahlsLaw"

Differences between revisions 13 and 32 (spanning 19 versions)

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

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:

$$$Speedup Overall = \frac{Old~Execution~Time}{New~Execution~Time}$$$

This gives a new Execution time of

$$$New~Exec~Time = Old~Exec~Time( 1 - Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced})$$$

So we have

$$$Speedup Overall=\left(\frac{1}{1-Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced}}\right)$$$

Back to ComputerTerms

-  ⇤ ← Revision 13 as of 2005-06-27 22:22:36 → 
  Size: 1467
  Editor: yakko
  Comment:
+   ← Revision 32 as of 2020-01-23 23:15:20 → ⇥
  Size: 676
  Editor: scot
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 3:
-{{{#!latex2
\begin{equation} \label{eq:speedup}
   Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}
\end{equation}
}}}
+$$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$$
-Line 13:
+Line 9:
-{{{#!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}
}}}
+$$$Speedup Overall = \frac{Old~Execution~Time}{New~Execution~Time}$$$
-Line 22:
+Line 11:
-{{{
+This gives a new Execution time of
-Line 24:
+Line 13:
-                                                                    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)
+$$$New~Exec~Time = Old~Exec~Time( 1 - Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced})$$$
-Line 35:
+Line 16:
-
SpeedupOverall = --------------------------------------------
                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhanced
-Line 41:
+Line 17:
-}}}
+$$$Speedup Overall=\left(\frac{1}{1-Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced}}\right)$$$