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Architecture Independent Massive Parallelization of DivideandConquer Algorithms
 Mathematics of Program Construction, Lecture Notes in Computer Science 947
, 1995
"... . We present a strategy to develop, in a functional setting, correct, efficient and portable DivideandConquer (DC) programs for massively parallel architectures. Starting from an operational DC program, mapping sequences to sequences, we apply a set of semantics preserving transformation rules, wh ..."
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Cited by 9 (1 self)
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. We present a strategy to develop, in a functional setting, correct, efficient and portable DivideandConquer (DC) programs for massively parallel architectures. Starting from an operational DC program, mapping sequences to sequences, we apply a set of semantics preserving transformation rules, which transform the parallel control structure of DC into a sequential control flow, thereby making the implicit data parallelism in a DC scheme explicit. In the next phase of our strategy, the parallel architecture is fully expressed, where `architecture dependent' higherorder functions are introduced. Then  due to the rising communication complexities on particular architectures  topology dependent communication patterns are optimized in order to reduce the overall communication costs. The advantages of this approach are manifold and are demonstrated with a set of nontrivial examples. 1 Introduction It is wellknown that the main problems in exploiting the power of modern parallel sys...
From Transformations to Methodology in Parallel Program Development: A Case Study
 Microprocessing and Microprogramming
, 1996
"... The BirdMeertens formalism (BMF) of higherorder functions over lists is a mathematical framework supporting formal derivation of algorithms from functional specifications. This paper reports results of a case study on the systematic use of BMF in the process of parallel program development. We dev ..."
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The BirdMeertens formalism (BMF) of higherorder functions over lists is a mathematical framework supporting formal derivation of algorithms from functional specifications. This paper reports results of a case study on the systematic use of BMF in the process of parallel program development. We develop a parallel program for polynomial multiplication, starting with a straightforward mathematical specification and arriving at the target processor topology together with a program for each processor of it. The development process is based on formal transformations; design decisions concerning data partitioning, processor interconnections, etc. are governed by formal type analysis and performance estimation rather than made ad hoc. The parallel target implementation is parameterized for an arbitrary number of processors; for the particular number, the target program is both time and costoptimal. We compare our results with systolic solutions to polynomial multiplication.