Basic Linear Algebra Operations in SLI Arithmetic

Symmetric level-index arithmetic was introduced to overcome recognized limitations of oating-point systems, most notably overrow and un-derrow. The original recursive algorithms for arithmetic operations could be parallelized to some extent, particularly when applied to extended sums or products, and a SIMD software implementation of some of these algorithms is described. The main purpose of this paper is to present parallel SLI algorithms for arithmetic and basic linear algebra operations. 1. Introduction This paper reports on a continuing project to develop, implement and apply parallel algorithms for SLI (symmetric level-index) arithmetic. The algorithms are being developed with a view toward a possible future implementation in hardware but at this stage they are being coded for a particular SIMD (single instruction, multiple data) computer system, a DEC MasPar MP-1