Amdahl's law for predicting the future of multicores considered harmful

Abstract

Several recent works predict the future of multicore systems or identify scalability bottlenecks based on Amdahl's law. Amdahl's law implicitly assumes, however, that the problem size stays constant, but in most cases more cores are used to solve larger and more complex problems. There is a related law known as Gustafson's law which assumes that runtime, not the problem size, is constant. In other words, it is assumed that the runtime on p cores is the same as the runtime on 1 core and that the parallel part of an application scales linearly with the number of cores. We apply Gustafson's law to symmetric, asymmetric, and dynamic multicores and show that this leads to fundamentally different results than when Amdahl's law is applied. We also generalize Amdahl's and Gustafson's law and study how this quantitatively effects the dimensioning of future multicore systems.