High-Performance QR Decomposition for FPGAs

Abstract

QR decomposition (QRD) is of increasing importance for many current applications, such as wireless and radar. Data dependencies in known algorithms and approaches, combined with the data access patterns used in many of these methods, restrict the achievable performance in software programmable targets. Some FPGA architectures now incorporate hard floating-point (HFP) resources, and in combination with distributed memories, as well as the flexibility of internal connectivity, can support high-performance matrix arithmetic. In this work, we present the mapping to parallel structures with inter-vector connectivity of a new QRD algorithm. Based on a Modified Gram-Schmidt (MGS) algorithm, this new algorithm has a different loop organization, but the dependent functional sequences are unchanged, so error analysis and numerical stability are unaffected. This work has a theoretical sustained-to-peak performance close to 100% for large matrices, which is roughly three times the functional density of the previously best known implementations. Mapped to an Intel Arria 10 device, we achieve 80us for a 256x256 single precision real matrix, for a 417 GFLOP equivalent. This corresponds to a 95% sustained to peak ratio, for the portion of the device used for this work.