Diff for "AmdahlsLaw"

Differences between revisions 14 and 29 (spanning 15 versions)

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:

latex($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$) (1)

This gives a new Execution time of

latex($$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$)

So we have

latex($$SpeedupOverall=\left(\frac{1}{1-FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}}\right)$$)

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-  ⇤ ← Revision 14 as of 2005-06-27 22:23:22 → 
  Size: 1415
  Editor: yakko
  Comment:
+   ← Revision 29 as of 2008-10-24 02:23:30 → ⇥
  Size: 720
  Editor: 209-142-131-35
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 3:
-{{{#!latex2
$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$
}}}
+[[latex($$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$)]]
-Line 11:
+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}
}}}
+[[latex($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)]] (1)
-Line 20:
+Line 11:
-{{{
+This gives a new Execution time of
-Line 22:
+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)
+[[latex($$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$)]]
-Line 33:
+Line 16:
-
SpeedupOverall = --------------------------------------------
                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhanced
-Line 39:
+Line 17:
-}}}
+[[latex($$SpeedupOverall=\left(\frac{1}{1-FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}}\right)$$)]]