Parallelizing the Symbolic Manipulation Program FORM Part I: Workstation Clusters and Message Passing

TL;DR

The present paper is the first of a series of papers reporting the parallelization of the symbolic manipulation program FORM on different parallel architectures using workstation clusters using dedicated network hardware and the messages passing libraries.

Abstract

The present paper is the first of a series of papers reporting on the parallelization of the symbolic manipulation program FORM on different parallel architectures. Part I deals with workstation clusters using dedicated network hardware and the messages passing libraries (MPI and PVM). After a short introduction to the sequential version of FORM a detailed analysis of the different platforms used is given and the structure of the parallel version of FORM is explained. The forthcoming part II will describe the parallelization of FORM on SMP (symmetrical multi-processing) architectures.

Figures (14)

• Figure 1: Example for the internal representation of $-\frac{2}{5}a^5$ as a series of words (short integers). The first number gives the total length (number of words) 8 of the term. The following numbers represent a subterm of type 1 (symbol) with total length 4. The number of the symbol $a$ in the symbol table is 3 and the exponent is 5. The subterm is followed by the coefficient with length 3 (absolute value of last number) and negative sign (sign of last number). The numerator is 2 and the denominator 5.
• Figure 2: The data flow during preprocessing and compiling.
• Figure 3: Schematic picture of a generation tree.
• Figure 4: The tree of losers algorithm for integers. A number of pre-sorted integer streams are merged together in a tree-like structure, yielding the so-called loser (the smallest element) at the root of the tree.
• Figure 5: The different stages of the sorting procedure.