Diff for "AmdahlsLaw"

Differences between revisions 7 and 15 (spanning 8 versions)

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

See SpeedUp

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:

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

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

or

                       Execution Time affected by Improvement
New Execution Time =   --------------------------------------  + Execution Time unaffected
                            Amount of Improvement (x times) 

So we have
                                     1
SpeedupOverall = --------------------------------------------
                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhanced

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-  ⇤ ← Revision 7 as of 2005-06-27 22:15:58 → 
  Size: 1569
  Editor: yakko
  Comment:
+   ← Revision 15 as of 2005-06-27 22:24:50 → ⇥
  Size: 1105
  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 11:
+{{{#!latex2
$$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$
}}}

{{{#!latex2
$$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$
}}}
 Line 20:
-                  Old Execution Time
SpeedupOverall = --------------------
                  New Execution Time

                                                                    FractionEnhanced
New Execution Time = Old Execution Time ( (1 - FractionEnhanced) + ------------------ )
                                                                    SpeedupEnhanced