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{{{#!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 \begin{equation} \label{eq:speedup} Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement} \end{equation} |
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{{{#!latex2 \begin{equation} SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time} \end{equation} \begin{equation} New~Execution~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right) \end{equation} }}} |
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Old Execution Time SpeedupOverall = -------------------- New Execution Time |
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\begin{equation} \label{eq:speedup} Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement} \end{equation}
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:
\begin{equation} SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time} \end{equation} \begin{equation} New~Execution~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right) \end{equation}
FractionEnhanced New Execution Time = Old Execution Time ( (1 - FractionEnhanced) + ------------------ ) SpeedupEnhanced 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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