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| \begin{equation} \label{eq:speedup} Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement} \end{equation} |
$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$ |
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| Start with stuff and [[latex2($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)]] (1) and more stuff over here. |
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| \begin{equation} SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time} \end{equation} \begin{equation} New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right) \end{equation} |
$$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$ |
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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:
Start with stuff and latex2($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$) (1) and more stuff over here.
$$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$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