Diff for "AmdahlsLaw"

Differences between revisions 11 and 29 (spanning 18 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 11 as of 2005-06-27 22:18:40 → 
  Size: 1555
  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
\begin{equation} \label{eq:speedup}
   Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}
\end{equation}
}}}


{{{
           Performance for entire task using the enhancement when possible
Speedup = -----------------------------------------------------------------
              Performance for entire taks without using the enhancement
}}}
+[[latex($$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$)]]
-Line 20:
+Line 9:
-{{{
                  Old Execution Time
SpeedupOverall = --------------------
                  New Execution Time
+[[latex($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)]] (1)
-Line 25:
+Line 11:
-                                                                    FractionEnhanced
New Execution Time = Old Execution Time ( (1 - FractionEnhanced) + ------------------ )
                                                                    SpeedupEnhanced
+This gives a new Execution time of
-Line 29:
+Line 13:
-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 36:
+Line 16:
-
SpeedupOverall = --------------------------------------------
                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhanced
-Line 42:
+Line 17:
-}}}
+[[latex($$SpeedupOverall=\left(\frac{1}{1-FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}}\right)$$)]]