Testing a numerical library's exception handling is often left to its regression tests. However, designing floating-point inputs that exercise exceptional behavior is difficult. Further-more, existing input generation techniques are designed with the view that any exception-causing input is of interest when most are unremarkable from the standpoint of exception handling: most functions should handle exceptions correctly by construction, i.e., by returning exceptional values (NaN,$+\text{Inf})$due to IEEE 754's mandate that most operations propagate such values. To test library exception handling, we propose an approach which - given only a set of regression test executables and a set of function prototypes - cheaply identifies potential failures via exception-spoofing and then reifies these failures using an off-the-shelf SMT solver that generates concrete inputs inducing buggy behavior. We implement this approach in a prototype tool Excvate,present an evaluation that targets 26 BLAS functions across three implementations, two compilers, and multiple compiler optimizations, and ultimately identify exception-handling failures in five functions in multiple BLAS versions.

As computer system technology approaches the end of Moore's law, new computing paradigms that improve performance become a necessity. One such paradigm is approximate computing (AC). AC can present significant performance improvements, but a challenge lies in providing confidence that approximations will not overly degrade the application output quality. In AC, application domain experts manually identify code regions amenable to approximation. However, automatically guiding a developer where to apply AC is still a challenge. We propose Puppeteer, a novel method to rank code regions based on amenability to approximation. Puppeteer uses uncertainty quantification methods to measure the sensitivity of application outputs to approximation errors. A developer annotates possible application code regions and Puppeteer estimates the sensitivity of each region. Puppeteer successfully identifies insensitive regions on different benchmarks. We utilize AC on these regions and we obtain speedups of$1.18\times, 1.8\times$, and$1.3\times$for HPCCG. DCT, and BlackScholes, respectively.

Numerical libraries constitute the building blocks for software applications that perform numerical calculations. Thus, it is paramount that such libraries provide accurate and consistent results. To that end, this paper addresses the problem of finding discrepancies between synonymous functions in different numerical libraries as a means of identifying incorrect behavior. Our approach automatically finds such synonymous functions, synthesizes testing drivers, and executes differential tests to discover meaningful discrepancies across numerical libraries. We implement our approach in a tool named FPDiff, and provide an evaluation on four popular numerical libraries: GNU Scientific Library (GSL), SciPy, mpmath, and jmat. FPDiff finds a total of 126 equivalence classes with a 95.8% precision and 79% recall, and discovers 655 instances in which an input produces a set of disagreeing outputs between function synonyms, 150 of which we found to represent 125 unique bugs. We have reported all bugs to library maintainers; so far, 30 bugs have been fixed, 9 have been found to be previously known, and 25 more have been acknowledged by developers.