Discussion
Let f be the fraction of a computation (in terms of time) that is parallelizable, P the number of processors in the system, and \(s_p\) the speed up achievable in comparison with sequential execution – then the \(s_p\) can be calculated using the relation :
Answer: C
If a fraction f of the computation is parallelisable and P processors are used, the parallel part takes time f/P, while the serial part, 1 - f, remains. The speed up is the old time divided by the new time
\[ s_p = \frac{1}{(1 - f) + f/P} \]which is Amdahl's law. The first option has the term f/P subtracted, which would make the speed up larger than P, and the second and fourth options do not reduce to Amdahl's formula. The keyed answer is the third option.
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