The results of numerical computations with floating point numbers depend on the execution platform, which we define as the hardware and the tools (compilers, etc.) supporting that hardware. One reason for the dependence is that compilers have significant freedom in deciding how to evaluate a floating point expression, as such evaluation is not standardized (not even in standards such as IEEE-754). Another reason is that hardware may or may not provide specialized instructions like Fused Multiply Add (FMA), and if it does, the compiler can take advantage of FMA functionality in different ways. We call an expression volatile if, for some input, its value differs across platform parameters. Differences can become particularly large across heterogeneous parallel architectures. This undermines the software portability promised by programming standards such as OpenCL and significantly impacts reproducibility of results in general. In this paper, we present a technique that predicts bounds on the output of a program containing volatile expressions when executed on different platforms. Using randomly selected inputs, we compare the bounds to results from running the code across a variety of platforms including CPUs and GPUs. Our results show that the theoretical bounds are relatively tight (within an order of magnitude) and can help users pinpoint where results should be stabilized, for instance by restricting expression reordering.
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