Suppose the frequency for the sequential portion of the computation is f s, the frequency for the parallel portion is f p, and the time it takes to carry out the sequential portion of the computation is t.
Based on the Amdahl's law[12], the sequential portion of a task limits the speed-up in parallelized implementation.
Suppose the parallel portion of the computation is distributed to n cores, and the sequential portion of the computation is carried out by core 1.
Similar to the 2-core case, the saved energy comes from the cores which do not carry out the sequential portion of the computation.
Based on the Amdahl's law, the sequential portion of a task limits the maximum speed-up of the parallelized implementation.
Specifically, for a given computation which involves a sequential portion and a parallel portion, the optimal frequencies for the two portions can be derived, which can achieve minimum power consumption while maintaining the same performance as running the computation sequentially on a single core.
This computation has a sequential portion in which the manager gathers all information about the bodies, and sends it to all worker actors, and a parallel portion is that each individual body calculates its new position, and sends a reply message to the manager.
Based on equation 8, we get the value t which minimizes E: t ∗ = s s + p N 2 / 3. Therefore, the optimal frequencies for the sequential portion and parallel portion of the computation are: f s ∗ = s t ∗ = s + p N 2 / 3 (9).
\, Both Amdahl's law and Gustafson's law assume that the running time of the sequential portion of the program is independent of the number of processors.
If the sequential portion of a program accounts for 10% of the runtime (\alpha=0.1), we can get no more than a 10× speed-up, regardless of how many processors are added.
