Polymorphic Matrices in Paladin

Scientific programmers are eager to take advantage of the computational power offered by Distributed Computing Systems (DCSs), but axe generally reluctant to undertake the porting of their application programs onto such machines. The DCS commercially available today are indeed widely believed to be difficult to use, which should not be a surprise since they axe traditionally prqgrammed with software tools dating back to the days of punch cards and paper tape. We claim that provided modern object oriented technologies are used, these computers can be programmed easily and efficiently. In EPEE, our Eiffel Parallel Execution Environment, we propose to use a kind of parallelism known as data-parallelism, encapsulated within classes of the Eiffel sequential object-oriented language, using the SPMD (Single Program Multiple Data) programming model. We describe our method for designing with this environment PALADIN, an object-oriented linear algebra library for DCSs. We show how dynamic binding and polymorphism can be used to solve the problems set by the dynamic aspects of the distribution of linear algebra objects such as matrices and vectors. 1 I n t r o d u c t i o n Distributed computing systems (DCSs)nalso called distributed memory parallel computers or multiprocessors---consist of hundreds or thousands of processors and are now commercially available. An example of this kind of DCS is the Intel Paragon supercomputer, a distributed-memory multicomputer with architecture that can accommodate more than a thousand heterogeneous nodes connected in a twodimensional rectangular mesh (see Figure 1). Its computation nodes are based on Intel i860 processors, and communicate by passing messages over a high-speed internal interconnect network. These kinds of multiprocessors provide orders of magnitude more raw power than traditional supercomputers at lower costs. They enable the development of previously infeasible applications (called grand challenges) in various scientific domains, such as materials science (for the aerospace and automobile industries), molecular biology, high-energy physics (Quantic Chromo-Dynamic), and global climate modeling. Although the physical world they model is inherently parallel, scientific programmers used to rely on sequential techniques and algorithms to solve their problems, because these algorithms e.g., the N-body problem) often present a better computational complexity than possible direct solutions. Their interest in concurrency only results from their desire to improve the performance of sequential algorithms applied