Proposed Consistent Exception Handling for the BLAS and LAPACK

TL;DR

This paper addresses the need for consistent exception handling in BLAS and LAPACK libraries, proposing a new design to improve resilience and uniformity in numerical computations amidst unavoidable exceptions.

Contribution

It introduces a novel design for exception handling in BLAS and LAPACK, balancing consistency, complexity, usability, and performance, and discusses its applicability to other numerical software.

Findings

Identifies inconsistencies in current exception handling implementations.

Proposes a new, balanced design for consistent exception handling.

Suggests the design as a model for broader numerical software applications.

Abstract

Numerical exceptions, which may be caused by overflow, operations like division by 0 or sqrt(-1), or convergence failures, are unavoidable in many cases, in particular when software is used on unforeseen and difficult inputs. As more aspects of society become automated, e.g., self-driving cars, health monitors, and cyber-physical systems more generally, it is becoming increasingly important to design software that is resilient to exceptions, and that responds to them in a consistent way. Consistency is needed to allow users to build higher-level software that is also resilient and consistent (and so on recursively). In this paper we explore the design space of consistent exception handling for the widely used BLAS and LAPACK linear algebra libraries, pointing out a variety of instances of inconsistent exception handling in the current versions, and propose a new design that balances consistency, complexity, ease of use, and performance. Some compromises are needed, because there are preexisting inconsistencies that are outside our control, including in or between existing vendor BLAS implementations, different programming languages, and even compilers for the same programming language. And user requests from our surveys are quite diverse. We also propose our design as a possible model for other numerical software, and welcome comments on our design choices.