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

TL;DR

This paper reinterprets Amdahl's law in terms of execution time to analyze supercomputer performance limits, providing formulas to predict scalability and explaining why increasing supercomputer size faces fundamental constraints.

Contribution

It offers a practical reinterpretation of Amdahl's law for supercomputing, enabling performance prediction and highlighting inherent scalability limitations.

Findings

Amdahl's law accurately models current supercomputer performance.

Supercomputer size is fundamentally limited by non-parallelizable tasks.

Achieving exaFLOPS requires significant breakthroughs beyond current models.

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.