Stable Single-Stage 2-Way Merge Sorters

Fast number sorting in hardware takes advantage of simultaneous parallel operations to quickly sort an unordered list of values. When sorting more than 2 values, multistage sorting networks have been the state-of-the-art devices used for fast hardware sorting. Such sorting networks use numerous 2-sorters operating in parallel in each process stage. After the first overall process stage, which produces sorted lists of length 2, each additional set of network stages implement a 2-way merge of increasingly larger sorted input lists. These sorting networks are not designed to produce a stable merge sort, in which the stable order of the 2 input lists is preserved. This work introduces a system that is used to create hardware devices which perform a 2-way merge sort, using single-stage operations which preserve the stable order of the 2 sorted input lists. These single-stage devices tend to be significantly faster than the equivalent current start-of-the-art 2-way merge sorters. The single-stage merge of two 32-valued input lists, into a sorted output list with 64 values, has a speedup of 3.55 versus comparable Batcher 6-stage 2-way merge sorters. Single-stage 2-way Merge Sorters are now the new state-of-the-art for fast 2-way merge sorting in hardware.