A convolve-and-merge approach for exact computations on high-performance reconfigurable computers

Authors:
Esam El-Araby;Ivan Gonzalez;Sergio Lopez-Buedo;Tarek El-Ghazawi
Affiliations:
Department of Electrical Engineering and Computer Science, The Catholic University of America, Washington, DC;Departments of Computer Engineering at Escuela Politecnica Superior of Universidad Autonoma de Madrid, Madrid, Spain;Departments of Computer Engineering at Escuela Politecnica Superior of Universidad Autonoma de Madrid, Madrid, Spain;Department of Electrical and Computer Engineering, The George Washington University, Washington, DC
Venue:
International Journal of Reconfigurable Computing - Special issue on High-Performance Reconfigurable Computing
Year:
2012

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Abstract

This work presents an approach for accelerating arbitrary-precision arithmetic on high-performance reconfigurable computers (HPRCs). Although faster and smaller, fixed-precision arithmetic has inherent rounding and overflow problems that can cause errors in scientific or engineering applications. This recurring phenomenon is usually referred to as numerical nonrobustness. Therefore, there is an increasing interest in the paradigmof exact computation, based on arbitrary-precision arithmetic. There are a number of libraries and/or languages supporting this paradigm, for example, the GNUmultiprecision (GMP) library. However, the performance of computations is significantly reduced in comparison to that of fixed-precision arithmetic. In order to reduce this performance gap, this paper investigates the acceleration of arbitrary-precision arithmetic on HPRCs. A Convolve-And-MErge approach is proposed, that implements virtual convolution schedules derived from the formal representation of the arbitraryprecision multiplication problem. Additionally, dynamic (nonlinear) pipeline techniques are also exploited in order to achieve speedups ranging from 5x (addition) to 9x (multiplication), while keeping resource usage of the reconfigurable device low, ranging from 11% to 19%.