Toward a Theory of Algorithm-Architecture Co-design

摘要

We are carrying out a research program that asks whether there is a useful mathematical framework for reasoning at a high-level about the behavior of an algorithm on a supercomputer with respect to the physical constraints of energy, power, and die area. By "high-level," we mean that we wish to explicitly relate characteristics of an algorithm, such as its inherent parallelism or memory and communication behavior, with parameters of an architecture, such as the number of cores, structure of the memory hierarchy, or network topology. Our ultimate goal is to say, in broad but also quantitative terms, how macroscopic changes to an architecture might affect the execution time, scalability, accuracy, and power-efficiency of a computation; and, conversely, identify what classes of computation might best match a given architecture. The approach we shall outline marries abstract algorithmic complexity analysis with caps on power and die area, which are arguably the central first-order constraints on the extreme-scale systems of 2018 and beyond [1, 16, 21, 29, 41]. We refer to our approach as one of algorithm-architecture co-design.