Multiword and Multimodular Algorithms for Emulating High Accuracy with Low Precision

The growing availability of lower precision arithmetics has led to the development of mixed precision algorithms in numerical linear algebra. Most recently we have seen the emergence of AI-specialized hardware such as GPU accelerators implementing extremely fast matrix multiply--accumulate operations, but using extremely low precisions such as 16-, 8- or even 4-bit floating-point or integer formats. This motivates a new class of mixed precision algorithms aiming to emulate high accuracy with low precision computations. In this talk, we will review the dense and rapidly growing literature on precision emulation. We will notably compare two competing classes of methods respectively based on multiword and multimodular decompositions, and discuss in which situation each method is preferable.