Differences between revisions 18 and 32 (spanning 14 versions)
Revision 18 as of 2005-06-27 22:26:15
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Editor: yakko
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Revision 32 as of 2020-01-23 23:15:20
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Editor: scot
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Deletions are marked like this. Additions are marked like this.
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{{{#!latex2
$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$
}}}
$$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$$
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[[latex($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)]] (1) $$$Speedup Overall = \frac{Old~Execution~Time}{New~Execution~Time}$$$
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{{{#!latex2
$$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$
}}}
This gives a new Execution time of
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{{{
or

                       Execution Time affected by Improvement
New Execution Time = -------------------------------------- + Execution Time unaffected
                            Amount of Improvement (x times)
$$$New~Exec~Time = Old~Exec~Time( 1 - Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced})$$$
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                                     1
SpeedupOverall = --------------------------------------------
                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhanced
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}}} $$$Speedup Overall=\left(\frac{1}{1-Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced}}\right)$$$

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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

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

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