Diff for "AmdahlsLaw"

Differences between revisions 3 and 31 (spanning 28 versions)

<<latex($$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$)>>

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:

<<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 3 as of 2004-01-25 18:27:27 → 
  Size: 1150
  Editor: yakko
  Comment:
+   ← Revision 31 as of 2008-10-24 02:24:20 → ⇥
  Size: 720
  Editor: 209-142-131-35
  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
}}}
+<<latex($$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$)>>
-Line 13:
+Line 9:
-{{{
                  Old Execution Time
SpeedupOverall = --------------------
                  New Execution Time
+<<latex($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)>> (1)
-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
+<<latex($$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$)>>
-Line 29:
+Line 15:
-}}}
+So we have

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