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To report a compiler bug, one must often find a small test case that triggers the bug. The existing approach to automated test-case reduction, delta debugging, works by removing substrings of the original input; the result is a concatenation of substrings that delta cannot remove. We have found this approach less than ideal for reducing C programs because it typically yields test cases that are too large or even invalid (relying on undefined behavior). To obtain small and valid test cases consistently, we designed and implemented three new, domain-specific test-case reducers. The best of these is based on a novel framework in which a generic fixpoint computation invokes modular transformations that perform reduction operations. This reducer produces outputs that are, on average, more than 25 times smaller than those produced by our other reducers or by the existing reducer that is most commonly used by compiler developers. We conclude that effective program reduction requires more than straightforward delta debugging.

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In a setting where we have intervals for the values of floating-point variables x, a, and b, we are interested in improving these intervals when the floating-point equality x ⊕ a = b holds. This problem is common in constraint propagation, and called the inverse projection of the addition. It also appears in abstract interpretation for the analysis of programs containing IEEE 754 operations. We propose floating-point theorems that provide optimal bounds for all the intervals. Fast loop-free algorithms compute these optimal bounds using only floating-point computations at the target precision.

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Abstract. This article presents a causality analysis for a synchronous stream language with higher-order functions. This analysis takes the shape of a type system with rows. Rows were originally designed to add extensible records to the ML type system (Didier Rémy, Mitchell Wand). We also restate briefly the coiterative semantics for synchronous streams (Paul Caspi, Marc Pouzet), and prove the correctness of our analysis with respect to this semantics.