Design of High-Speed Multiway Merge Sorting Networks Using Fast Single-Stage N-Sorters and N-Filters

Abstract

In hardware such as FPGAs, Kenneth Batcher's Odd-Even Merge Sort and Bitonic Merge Sort are the state-of-the-art methodologies used to quickly sort a list of more than 16 input values. Both sorting networks feature merges of 2 sorted input lists into a single sorted output list. For both, a full sort of 64 and 512 input values requires 21 and 45 serial stages, respectively. Multiway merge sorting networks described here require significantly fewer serial stages. For example, 8-way merge networks fully sort 64 and 512 input values in 9 and 20 serial stages, less than half the number of the respective 2-way networks. When the multiway merge sorting networks utilize the single-stage N -sorters recently defined by the authors, they are considerably faster than Batcher's networks. In the AMD-Xilinx Ultrascale+ xcvu9p FPGA, the two 8-way merge networks have speedups of 1.85 and 1.74 versus the comparable 2-way networks. A fully pipelined 3-way merge network in this FPGA is capable of fully sorting 500 million lists of 729 unsorted 32-bit values in one second. In software, multiway merge methods are used to find the median of certain pixel rectangles in images, since the median can be determined in fewer stages than are required to fully sort the rectangle. However, the software still requires a series of many 2-sorter operations to find a median. These multiway merge median methods are dramatically sped up in hardware, where the authors' new single-stage N -sorters and N -filters operate in parallel in each stage of the merge process.