How Amdahl's low restricts supercomputer applications and building ever bigger supercomputers

Abstract: This paper reinterprets Amdahl's law in terms of execution time and applies this simple model to supercomputing. The systematic discussion results in practical formulas enabling to calculate expected running time using large number of processors from experimental runs using low number of processors, delivers a quantitative measure of computational efficiency of supercomputing applications. Through separating non-parallelizable contribution to fractions according to their origin, Amdahl's law enables to derive a timeline for supercomputers (quite similar to Moore's law) and describes why Amdahl's law limits the size of supercomputers. The paper validates that Amdahl's 50-years old model (with slight extension) correctly describes the performance limitations of the present supercomputers. Using some simple and reasonable assumptions, the absolute performance bound of supercomputers is concluded, furthermore that serious enhancements are still necessary to achieve the exaFLOPS dream value.