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 scientific numeric programs and infringe on the highly desirable goal of software portability (which is in fact promised by heterogeneous computing frameworks like OpenCL): the same program run on the same inputs on different platforms can produce different results. So far so bad.
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 work I will present an algorithm that takes a numeric procedure and determines an input that is likely to lead to different decisions depending merely on how the arithmetic in the procedure is compiled. Our implementation of the algorithm requires minimal intervention by the user. I will illustrate its operation on examples characteristic of scientific numeric computing, where control flow divergence actually occurs across different execution platforms.
Time permitting, I will also sketch how to prove the /absence/ of inputs that may lead to control flow divergence, i.e. how to prove programs /stable/ (in one of the many senses of this word). This is ongoing work.
Thomas Wahl is an Assistant Professor at Northeastern University. This is joint work with Yijia Gu, Mahsa Bayati, and Miriam Leeser at Northeastern.