We give an overview on Paclib, a library for parallel algebraic computation on shared memory multiprocessors. Paclib is essentially a package of C functions that provide the basic objects and methods of computer algebra in a parallel context. The Paclib programming model supports concurrency, shared memory communication, non-determinism and speculative parallelism. The system is based on a heap management kernel with parallelized garbage collection that is portable among most Unix machines. We present the successful application of paclib for the parallelization of several algebraic algorithms and discuss the achieved results. 1 Introduction Scientific computing is a rich source of challenging problems such as the solution of systems of partial differential equations. Classical numerical methods operate with efficient finite-precision (floating point) arithmetic and thus quickly yield approximative solutions. However, often one is also interested in certain qualitative aspects like s...

: We describe the design and implementation of pD, a parallel variant of a small functional language that serves as a programming interface for the parallel computer algebra package PACLIB. pD provides several facilities to express parallel algorithms in a flexible way on different levels of abstraction. The compiler translates a pD module into statically typed parallel C code with explicit task creation and synchronization constructs. This target code can be linked with the PACLIB kernel, the multi-processor runtime system of the computer algebra library SACLIB. The parallelization of several computer algebra algorithms on a shared memory multi-processor demonstrates the elegance and efficiency of this approach. Keywords: Para-Functional Programming, Computer Algebra, Compilation. 1 Introduction We present in this paper a small functional language D and its para-functional variant pD that is used as a parallel programming interface for the computer algebra package PACLIB. Parallelism...

We describe how a para-functional programming language is applied to implementing parallel computer algebra algorithms on a shared memory multiprocessor. The language we use is pD, a small functional language that we have developed as a high-level programming interface for the parallel computer algebra package PACLIB. pD provides several facilities to express parallel algorithms in a flexible way on different levels of abstraction. The compiler translates a pD program into parallel C code with explicit task creation and synchronization constructs. The implemented para-functional programs perform as efficient as manually coded parallel C programs. 1 Introduction While most computer algebra algorithms [3] are based on the concept of pure functions, real-world computer algebra programs are for performance reasons usually written in a low-level imperative style (typically in C). Consequently, there is little resemblance between the notation in which the mathematical theory is formulated a...

We describe the design of a parallel algorithm for the exact solution of linear equation systems with integer coefficients and the implementation of this algorithm on a shared memory multiprocessor. An efficient solution of the original problem is difficult since the coefficients grow during the computation and arithmetic becomes very time-consuming. Therefore we transform the problem into a problem of determinant computation and apply a modular approach: the system is mapped into several finite fields where the determinants can be efficiently computed. The subresults are combined to yield the original determinants and to compute the solutions of the system. Several parallel versions of this algorithm have been developed and implemented on a shared memory multiprocessor. The programs are applied to equation systems of different characteristics and the results are analyzed and compared. Keywords: Parallel algorithms, scientific computing, computer algebra, shared memory machines. Fund...

We describe the design and implementation of pD, a parallel variant of the small functional language D. In particular, we show the compilation techniques that we apply to translate a pD program with para-functional annotations into statically typed parallel C code that corresponds (with restrictions) in structure and quality to a program written by a human programmer. The generated code can be linked with the PACLIB kernel, the multi-processor runtime system for the computer algebra library SACLIB. This allows to develop parallel computer algebra applications in an elegant and efficient manner. Supported by the FWF grant S5302-PHY "Parallel Symbolic Computation". Contents 1 Introduction 4 2 The Pseudo-Functional Core Language 6 2.1 Abstract Syntax : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.2 Examples : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 2.3 Semantic Algebras : : : : : : : : : : : : : : : : : : : : : : : : : : : : :...