ParFORM: Parallel Version of the Symbolic Manipulation Program FORM

TL;DR

The paper addresses accelerating symbolic computations on very large expressions in FORM by introducing ParFORM, a MPI-based master–slave parallelization that distributes term-level work across processors while preserving compatibility with existing FORM programs. It details the architecture, data-flow, and the merging of sorted term streams, highlighting the reliance on local-term operations to enable parallelism. Benchmark results with the BAICER packet on heterogeneous hardware demonstrate near-linear speedups up to 8–12 processors and substantial reductions in wall-clock time, sometimes turning multi-year tasks into weeks. The findings underscore the practical potential of parallel symbolic manipulation for complex perturbative calculations in quantum field theory, while acknowledging problem-dependent limits and overheads.

Abstract

After an introduction to the sequential version of FORM and the mechanisms behind, we report on the status of our project of parallelization. We have now a parallel version of FORM running on Cluster- and SMP-architectures. This version can be used to run arbitrary FORM programs in parallel.

Figures (4)

• Figure 1: The fragment of a typical FORM program. In the first module, the expression $expr = ax+x^2$ is introduced, and then the substitution $x \to a+b$ is performed. In the second module, only terms in which the degree of $b$ is exactly 1 are multiplied by $4a/b$ (there is only one such term in the expression).
• Figure 2: General conception of ParFORM.
• Figure 3: Computing time and speedup for the test program BAICER on Compaq-AlphaServer with 8x Alpha (EV67) processors 700 MHz.
• Figure 4: Computing time and speedup for the test program BAICER on the SGI Altix 3700 server with 32x Itanium2 processors (1.3 GHz).