High Performance Linear Algebra Operations on Reconfigurable Systems

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Field-Programmable Gate Arrays (FPGAs) have become an attractive option for scientific computing. Several vendors have developed high performance reconfigurable systems which employ FPGAs for application acceleration. In this paper, we propose a BLAS (Basic Linear Algebra Subprograms) library for state-of-the-art reconfigurable systems. We study three data-intensive operations: dot product, matrix-vector multiply and dense matrix multiply. The first two operations are I/O bound, and our designs efficiently utilize the available memory bandwidth in the systems. As these operations require accumulation of sequentially delivered floating-point values, we develop a high performance reduction circuit. This circuit uses only one floating-point adder and buffers of moderate size. For matrix multiply operation, we propose a design which employs a linear array of FPGAs. This design exploits the memory hierarchy in the reconfigurable systems, and has very low memory bandwidth requirements. To illustrate our ideas, we have implemented our designs for Level 2 and Level 3 BLAS on Cray XD1.