How computation errors relate to hardware and resources used
How Numerical Errors Scale with Hardware
Distributed, Parallel, and Cluster Computing
Summary
Computers make small mistakes when doing many calculations, and these mistakes can add up. This paper explains how to estimate the size of these mistakes based on how much computing power or energy is used. The authors combine known measures of algorithm speed with how well hardware can run tasks in parallel to compare different systems fairly. This helps people see which hardware or software setups produce fewer errors when given the same resources.
What this means in practice
- •For hardware engineers: Evaluate how different hardware designs affect calculation errors under fixed energy or resource limits.
- •For software developers: Compare accuracy of software algorithms fairly when running within the same computing or energy budget.
Authors
Niklas Baumgarten
Abstract
In this short technical note, we outline how to bound numerical errors with respect to computational resources. We consider algorithms with known complexity estimates that can be executed in parallel and combine these estimates with parallelization laws. We suppose that the proposed approach generalizes beyond the presented examples and argue that it provides a straightforward and fair framework for comparing algorithms, hardware systems, and software implementations. This is achieved by imposing identical resource or energy budgets on each configuration, and comparing the resulting numerical error evaluations.