Rounding Error Statistics as Numerics Signature

The current proliferation of application specific computer processors brings us many customized computer arithmetic designs with various precisions and/or numerical properties. Increasingly, application developers find themselves carrying out numerical quality assurance. The tools for this task are quite limited. A common method that requires computed result of a kernel operation on an example input to be accurate within a certain threshold is not robust: Not only is a good threshold hard to establish, but this very approach is fundamentally unreliable, as computation errors are so sensitive to minute computational differences that they can be quite different even using numerics of similar qualities. In this paper, we show that the statistics, rather than a few isolated instances, of computation errors are so robust that they can be thought of as signatures of the underlying numerics. We can therefore compared these statistics against reference signatures as a more robust quality assurance, or use observed statistics as diagnostic methods, or incorporate them during numerics and arithmetic design.