Fast and Efficient Merge of Sorted Input Lists in Hardware Using List Offset Merge Sorters

TL;DR

This paper introduces List Offset Merge Sorters (LOMS), a hardware device that merges multiple sorted lists faster and more resource-efficiently than previous methods, especially in FPGA implementations.

Contribution

The paper presents LOMS, a novel hardware merge sort device that improves speed and resource efficiency over existing merge sorters like Bitonic and Odd-Even, and supports arbitrary list sizes.

Findings

LOMS 2-way merge sorter merges 64 values in 2.24 ns, 2.63 times faster than Batcher's sorter.

LOMS 3-way merge sorter merges 21 values in 3.4 ns, 1.36 times faster than previous state-of-the-art.

LOMS devices are resource-efficient, enabling larger merges within FPGA constraints.

Abstract

A new set of hardware merge sort devices are introduced here, which merge multiple sorted input lists into a single sorted output list in a fast and efficient manner. In each merge sorter, the values from the sorted input lists are arranged in an input 2-D setup array, but with the order of each sorted input list offset from the order of each of the other sorted input lists. In these new devices, called List Offset Merge Sorters (LOMS), a minimal set of column sort stages alternating with row sort stages process the input setup array into a final output array, now in the defined sorted order. LOMS 2-way sorters, which merge 2 sorted input lists, require only 2 merge stages and are significantly faster than Kenneth Batcher's previous state-of-the-art 2-way merge devices, Bitonic Merge Sorters and Odd-Even Merge Sorters. LOMS 2-way sorters utilize the recently-introduced Single-Stage 2-way Merge Sorters (S2MS) in their first stage. Both LOMS and S2MS devices can merge any mixture of input list sizes, while Batcher's merge sorters are difficult to design unless the 2 input lists are equal, and a power-of-2. By themselves, S2MS devices are the fastest 2-way merge sorters when implemented in this study's target FPGA devices, but they tend to use a large number of LUT resources. LOMS 2-way devices use fewer resources than comparable S2MS devices, enabling some large LOMS devices to be implemented in a given FPGA when comparable S2MS devices cannot fit in that FPGA. A List Offset 2-way sorter merges 2 lists, each with 32 values, into a sorted output list of those 64 values in 2.24 nS, a speedup of 2.63 versus a comparable Batcher device. A LOMS 3-way merge sorter, merging 3 sorted input lists with 7 values, fully merges the 21 values in 3.4 nS, a speedup of 1.36 versus the comparable state-of-the-art 3-way merge device.