Behavioral Non-portability in Scientific Numeric Computing

The precise semantics of floating-point arithmetic programs depends on the execution platform, including the compiler and the target hardware. Platform dependencies are particularly pronounced for arithmetic-intensive parallel numeric programs and infringe on the highly desirable goal of software portability (which is nonetheless promised by heterogeneous computing frameworks like OpenCL): the same program run on the same inputs on different platforms often produces different results. Serious doubts on the portability of numeric applications arise when these differences are behavioral, i.e. when they lead to changes in the control flow of a program. In this paper we present an algorithm that takes a numeric procedure and determines an input that may lead to different branching decisions depending on how the arithmetic in the procedure is compiled. We illustrate the algorithm on a diverse set of examples, characteristic of scientific numeric computing, where control flow divergence actually occurs across different execution platforms.