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.

Parallel Programming Paradigms

“…The limits to parallel processing implied by the law but also the limits of the law's basic assumptions have been discussed extensively in the literature, by designers of parallel systems and algorithms; for example, cf. [24][25][26][27][28][29][30][31]. We make the following remarks.…”

“…An appropriate rate, sometimes called isoefficiency [33], could indeed be neither of the two extremes, namely the constant problem size of Amdahl and the linear increase suggested in [32]; cf. [24] for a discussion.…”

An empirical high level performance model for future many-cores

“…In [7], Juurlink et al extend Gustafson's law to symmetric, asymmetric and dynamic multicores to predict multicore performance. They claimed that neither the parallel fraction remains constant as assumed by the Amdahl's law nor it grows linearly as assumed by Gustafson's Law.…”

Impact of Serial Scaling of Multi-threaded Programs in Many-Core Era

“…In [4], Juurlink et al extend Gustafson's law to symmetric, asymmetric and dynamic multicores to predict multicore performance. They claim that neither the parallel fraction remains constant as assumed by the Amdahl's law nor it grows linearly as assumed by Gustafson's Law and proposed a Generalized Scaled Speedup model with parallel scaling factor Scale(P)= √ P .…”