Identifying volatile numeric expressions in numeric computing applications.

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.