Taxonomy of Small Floating-Point Formats
As part of my responsibilities as an industrial PhD student with PLSE and Intel, I develop and maintain, alongside my colleague and PLSE alumni Bill Zorn, a reference implementation of floating-point arithmetic. Hardware designers use this reference model to formally specify the behavior of floating point in hardware designs and verify the correctness of their implementations of these designs. Our library must not only have reasonable performance while simulating these designs and be consumable by formal verification tools for equivalence checking or property verification; but it must also correctly answer the often difficult question about floating point: “but what do it do?” With the prevalence of machine learning and its demand for ever smaller number formats for increased performance, we explored the interesting and often ridiculous world of small floating-point formats.