Differences between revisions 3 and 32 (spanning 29 versions)
Revision 3 as of 2004-01-25 18:27:27
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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.
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{{{
           Performance for entire task using the enhancement when possible
Speedup = -----------------------------------------------------------------
              Performance for entire taks without using the enhancement
}}}
$$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$$
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{{{
                  Old Execution Time
SpeedupOverall = --------------------
                  New Execution Time
$$$Speedup Overall = \frac{Old~Execution~Time}{New~Execution~Time}$$$
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                                                                    FractionEnhanced
New Execution Time = Old Execution Time ( (1 - FractionEnhanced) + ------------------ )
                                                                    SpeedupEnhanced
This gives a new Execution time of
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-->
                                     1
SpeedupOverall = --------------------------------------------
                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhanced
$$$New~Exec~Time = Old~Exec~Time( 1 - Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced})$$$
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}}} So we have

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

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

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:

$$$Speedup Overall = \frac{Old~Execution~Time}{New~Execution~Time}$$$

This gives a new Execution time of

$$$New~Exec~Time = Old~Exec~Time( 1 - Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced})$$$

So we have

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

Back to ComputerTerms

AmdahlsLaw (last edited 2020-01-23 23:15:20 by scot)