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Numerical exceptions, which may be caused by overflow, operations likedivision by 0 or sqrt(-1), or convergence failures, are unavoidable in manycases, in particular when software is used on unforeseen and difficult inputs.As more aspects of society become automated, e.g., self-driving cars, healthmonitors, and cyber-physical systems more generally, it is becomingincreasingly important to design software that is resilient to exceptions, andthat responds to them in a consistent way. Consistency is needed to allow usersto build higher-level software that is also resilient and consistent (and so onrecursively). In this paper we explore the design space of consistent exceptionhandling for the widely used BLAS and LAPACK linear algebra libraries, pointingout a variety of instances of inconsistent exception handling in the currentversions, and propose a new design that balances consistency, complexity, easeof use, and performance. Some compromises are needed, because there arepreexisting inconsistencies that are outside our control, including in orbetween existing vendor BLAS implementations, different programming languages,and even compilers for the same programming language. And user requests fromour surveys are quite diverse. We also propose our design as a possible modelfor other numerical software, and welcome comments on our design choices.

Proposed Consistent Exception Handling for the BLAS and LAPACK