A program that has a sequential portion like this can never achieve perfect speedup, and in fact we can calculate the maximum achievable speedup for a given number of cores using Amdahl’s law. Amdahl’s law gives the maximum speedup as the ratio:
1 / ((1 - P) + P/N)
where P is the portion of the runtime that can be parallelized, and N is the number of processors available. In our case, P is (0.76 - 0.0167)/0.76 = 0.978, and the maximum speedup is 1.96. The sequential fraction here is too small to make a significant impact on the theoretical maximum speedup with two processors, but when we have more processors, say 64, it becomes much more important: 1 / ((1-0.978) + 0.978/64) = 26.8. So no matter what we do, this tiny sequential part of our program will limit the maximum speedup we can obtain with 64 processors to 26.8. In fact, even with 1,024 cores, we could achieve only around 44 speedup, and it is impossible to achieve a speedup of 46 no matter how many cores we have. **Amdahl’s law tells us that not only does parallel speedup become harder to achieve the more processors we add, but in practice most programs have a theoretical maximum amount of parallelism.**引自 Basic Parallelism: The Eval Monad
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