Diff for "AmdahlsLaw"

Differences between revisions 2 and 32 (spanning 30 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:

This gives a new Execution time of

So we have

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-  ⇤ ← Revision 2 as of 2004-01-25 18:27:14 → 
  Size: 1144
  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:
-{{{
           Performance for entire task using the enhancement when possible
Speedup = -----------------------------------------------------------------
              Performance for entire taks without using the enhancement
}}}
+$$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$$
-Line 13:
+Line 9:
-{{{
                  Old Execution Time
SpeedupOverall = --------------------
                  New Execution Time
+$$$Speedup Overall = \frac{Old~Execution~Time}{New~Execution~Time}$$$
-Line 18:
+Line 11:
-                                                                    FractionEnhanced
New Execution Time = Old Execution Time ( (1 - FractionEnhanced) + ------------------ )
                                                                    SpeedupEnhanced
+This gives a new Execution time of
-Line 22:
+Line 13:
--->
                                     1
SpeedupOverall = --------------------------------------------
                                         FractionEnhanced
               (1 - FractionEnhanced) + ------------------ )
                                         SpeedupEnhanced
+$$$New~Exec~Time = Old~Exec~Time( 1 - Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced})$$$
-Line 29:
+Line 15:
-}}}
+So we have

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