Breaking Sequential Dependencies in FPGA-Based Sparse LU Factorization

Abstract

Substitution, and reassociation of irregular sparse LU factorization can deliver up to 31% additional speedup over an existing state-of-the-art parallel FPGA implementation where further parallelization was deemed virtually impossible. The state-of-the-art implementation is already capable of delivering 3× acceleration over CPU-based sparse LU solvers. Sparse LU factorization is a well-known computational bottleneck in many existing scientific and engineering applications and is notoriously hard to parallelize due to inherent sequential dependencies in the computation graph. In this paper, we show how to break these alleged inherent dependencies using depth-limited substitution, and reassociation of the resulting computation. This is a work-parallelism tradeoff that is well-suited for implementation on FPGA-based token dataflow architectures. Such compute organizations are capable of fast parallel processing of large irregular graphs extracted from the sparse LU computation. We manage and control the growth in additional work due to substitution through careful selection of substitution depth. We exploit associativity in the generated graphs to restructure long compute chains into reduction trees.