RAIVE: runtime assessment of floating-point instability by vectorization

Abstract

Floating point representation has limited precision and inputs to floating point programs may also have errors. Consequently, during execution, errors are introduced, propagated, and accumulated, leading to unreliable outputs. We call this the instability problem. We propose RAIVE, a technique that identifies output variations of a floating point execution in the presence of instability. RAIVE transforms every floating point value to a vector of multiple values – the values added to create the vector are obtained by introducing artifi- cial errors that are upper bounds of actual errors. The propagation of artificial errors models the propagation of actual errors. When values in vectors result in discrete execution differences (e.g., following different paths), the execution is forked to capture the resulting output variations. Our evaluation shows that RAIVE can precisely capture output variations. Its overhead (340%) is 2.43 times lower than the state of the art