Diff for "AmdahlsLaw"

Differences between revisions 7 and 24 (spanning 17 versions)

latex2($$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$) }}}

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:

latex2($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)

This gives a new Execution time of

latex2($$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$)

So we have latex2($$SpeedupOverall=\frac{1}{1-FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}})

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-  ⇤ ← Revision 7 as of 2005-06-27 22:15:58 → 
  Size: 1569
  Editor: yakko
  Comment:
+   ← Revision 24 as of 2005-06-28 01:18:43 → ⇥
  Size: 709
  Editor: yakko
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 3:
-{{{#!latex
\begin{equation}
   Speedup = \frac{Performance~for~entire~task~using~the~enhancement~when~possible}{Performance~for~entire~task~without~enhancement}
\end(equation}
}}}

{{{
           Performance for entire task using the enhancement when possible
Speedup = -----------------------------------------------------------------
              Performance for entire taks without using the enhancement
+[[latex2($$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$)]]
-Line 19:
+Line 10:
-{{{
                  Old Execution Time
SpeedupOverall = --------------------
                  New Execution Time
+[[latex2($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)]]
-Line 24:
+Line 12:
-                                                                    FractionEnhanced
New Execution Time = Old Execution Time ( (1 - FractionEnhanced) + ------------------ )
                                                                    SpeedupEnhanced
+This gives a new Execution time of
-Line 28:
+Line 14:
-or

                       Execution Time affected by Improvement
New Execution Time =   --------------------------------------  + Execution Time unaffected
                            Amount of Improvement (x times)
+[[latex2($$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$)]]
-Line 35:
+Line 17:
-
SpeedupOverall = --------------------------------------------
                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhanced

}}}
+[[latex2($$SpeedupOverall=\frac{1}{1-FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}})]]