On Extending Amdahl's law to Learn Computer Performance

TL;DR

This paper extends Amdahl's law to multiple resources and uses machine learning to model performance, achieving over 95% accuracy across various benchmarks and hardware platforms.

Contribution

It introduces a multivariable extension of Amdahl's law and transforms performance modeling into a regression problem for machine learning applications.

Findings

Models achieve over 95% cross-validated accuracy

Extension of Amdahl's law accommodates multiple resources

Applicable across diverse benchmarks and hardware platforms

Abstract

The problem of learning parallel computer performance is investigated in the context of multicore processors. Given a fixed workload, the effect of varying system configuration on performance is sought. Conventionally, the performance speedup due to a single resource enhancement is formulated using Amdahl's law. However, in case of multiple configurable resources the conventional formulation results in several disconnected speedup equations that cannot be combined together to determine the overall speedup. To solve this problem, we propose to (1) extend Amdahl's law to accommodate multiple configurable resources into the overall speedup equation, and (2) transform the speedup equation into a multivariable regression problem suitable for machine learning. Using experimental data from fifty-eight tests spanning two benchmarks (SPECCPU 2017 and PCMark 10) and four hardware platforms (Intel Xeon 8180M, AMD EPYC 7702P, Intel CoffeeLake 8700K, and AMD Ryzen 3900X), analytical models are developed and cross-validated. Findings indicate that in most cases, the models result in an average cross-validated accuracy higher than 95%, thereby validating the proposed extension of Amdahl's law. The proposed methodology enables rapid generation of multivariable analytical models to support future industrial development, optimization, and simulation needs.