The Rise of Multiprecision Arithmetic

"There is a growing demand for and availability of multiprecision arithmetic: floating point arithmetic supporting multiple, possibly arbitrary, precisions. For an increasing body of applications, including in supernova simulations, electromagnetic scattering theory, and computational number theory, double precision arithmetic is insufficient to provide results of the required accuracy. On the other hand, for climate modelling and deep learning half precision (about four significant decimal digits) has been shown to be sufficient in some studies. We discuss a number of topics involving multiprecision arithmetic, including:• The need for, availability of, and ways to exploit, higher precision arithmetic (e.g., quadruple precision arithmetic).• How to derive linear algebra algorithms that will run in any precision, as opposed to be being optimized (as some key algorithms are) for double precision.• For solving linear systems with the use of iterative refinement, the benefits of suitably combining three different precisions of arithmetic (say, half, single, and double).• How a new form of preconditioned iterative refinement can be used to solve very ill conditioned sparse linear systems to high accuracy."