Designing Scalable FPGA-Based Reduction Circuits Using Pipelined Floating-Point Cores

The use of pipelined floating-point arithmetic cores to create high-performance FPGA-based computational kernels has introduced a new class of problems that do not exist when using single-cycle arithmetic cores. In particular, the data hazards associated with pipelined floating-point reduction circuits can limit the scalability or severely reduce the performance of an otherwise high-performance computational kernel. The inability to efficiently execute the reduction in hardware coupled with memory bandwidth issues may even negate the performance gains derived from hardware acceleration of the kernel. In this paper we introduce a method for developing scalable floating-point reduction circuits that run in optimal time while requiring only ϴ(lg (n)) space and a single pipelined floating-point unit. Using a Xilinx Virtex-II Pro as the target device, we implement reference instances of our reduction method and present the FPGA design statistics supporting our scalability claims.