Tuning FORM with large calculations

TL;DR

This paper introduces FORM's enhancements for handling extremely large symbolic calculations, focusing on large-file support and a tablebase that stores vast tables while loading only the needed elements on demand. It details a design that uses index-first loading, on-demand compilation, and gzipped storage, with the novel concept of stubbs to minimize unnecessary term manipulation. Through benchmark-like examples, it demonstrates handling intermediate expressions over multiple gigabytes and dynamic, file-backed table extension that enables reusing results across runs, including the tabulation of tens of thousands of integrals. The discussion also covers practical performance benefits, release notes for FORM 3.1, and considerations for future development, including potential open-source efforts and gaps such as GCD and factorization.

Abstract

Some recent additions to FORM are discussed. In particular large file support and the tablebases are presented.