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| \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 |
$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$ |
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| {{{#!latex2 $$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$ }}} \n {{{#!latex2 $$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$ }}} |
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| Old Execution Time SpeedupOverall = -------------------- New Execution Time FractionEnhanced New Execution Time = Old Execution Time ( (1 - FractionEnhanced) + ------------------ ) SpeedupEnhanced |
Back to ComputerTerms
$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$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:
$$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$\n
$$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$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) + ------------------ )
SpeedupEnhancedBack to ComputerTerms