Shared-Memory Range-Tiled CDF Sort for Small-Range Integer Keys on GPUs

Abstract

We study unstable integer sorting on GPUs for arrays whose elements lie in a known integer range. Focusing on counting-sort-based methods that determine the output interval of each value from its frequency and the prefix sums of the frequencies, we propose and evaluate Range-Tiled CDF sort (RT-CDF), which partitions the possible value range into small intervals, called tiles, that fit in shared memory. For each tile, RT-CDF constructs a histogram, computes its prefix sum as a local CDF, and directly generates the output array from the local CDF. We compare RT-CDF against three baselines: CUB DeviceRadixSort, whose processed bit range is restricted to $[0,\lceil {\log }_{2}R\rceil )$ to exploit the known range size $R$; Ref-H-P sort; and an implementation based on the algorithm of Kolonias et al. Experiments on an NVIDIA GeForce RTX 4090 with range sizes from $R=2^7$ to $2^{18}$, input sizes from $n=10^6$ to $10^9$, and uniformly distributed, normally distributed, and all-equal inputs show that RT-CDF outperforms the baselines over a broad set of conditions for small to medium ranges, achieving a maximum speedup of 4.39 over the fastest baseline. For $R=2^{18}$, however, at least one baseline outperforms RT-CDF for every evaluated input size and input distribution, showing that the cost of histogram construction limits the applicability of RT-CDF to larger ranges.

arXiv comment44 pages, 14 figures, 17 tables