Implicit matrix multiplication with maximum accuracy on various transputer networks

Abstract

The majority of numerical algorithms employs floating-point vector and matrix operations. On a parallel computer these algorithms should be solved fastand reliably in order to avoid a time-consuming error analysis. The XSC-languages (high-level language extensions for eXtended Scientific Computation) are well-suited for this purpose since they support the design of numerical algorithms delivering correct and automatically verified results. This goal is attained by an arithmetic with maximum accuracy (especially for vector and matrix operations), highly accurate standard functions, and exact evaluation of dot product expressions. Within theESPRIT Parallel Computing Action, one XSC-language, PASCAL-XSC, was implemented on a Supercluster Transputer System under the operating system HELIOS. Parallel algorithms for computationally intensive and maximally accurate matrix operations were implemented and tested on various transputer architectures. We will sketch some features of these architectures and present some benchmarks for the algorithms used. These algorithms form a parallel C runtime library of PASCAL-XSC (or any other XSC-language that uses a C runtime library) and are called automatically. This can be considered a basis for implicit parallelization in an XSC-language.