A Novel Computational Model for GPUs with Applications to Efficient Algorithms

Abstract

We propose a novel computational model for GPUs. Known parallel computational models such as the PRAM model are not appropriate for evaluating GPU-based algorithms. Our model, called AGPU, abstracts the essence of current GPU architectures such as global and shared memory, memory coalescing and bank conflicts. Using our model, we can evaluate asymptotic behavior of GPU algorithms more efficiently than the known models and we can develop algorithms that run fast on real GPU devices.As a showcase, we analyze the asymptotic behavior of basic existing algorithms including reduction, prefix scan, and comparison sorting. We further develop new algorithms by detecting and resolving performance bottlenecks of the existing algorithms. Our reduction algorithm has the optimal time and I/O complexities and works with non-commutative operators. Our comparison sorting algorithm has the optimal I/O complexity. Additionally, we show our algorithms run faster than the existing algorithms not only in theory but also in practice.

Analysis-driven Engineering of Comparison-based Sorting Algorithms on GPUs

“…We consider two state-of-the-art GPU-efficient sorting algorithms: modernGPU (MGPU) [3] pairwise mergesort and the multiway mergesort presented by Koike and Sadakane [21]. For each algorithm, we analytically identify performance bottlenecks.…”

“…The work of Afshani and Sitchinava [1] focuses on shared memory only and presents an algorithm that sorts small inputs in shared memory without bank conflicts. Koike and Sadakane [21] also present a GPU sorting algorithm that minimizes global memory accesses using a multiway mergesort that is also bank conflict-free (we analyze their algorithm Section 4.2).…”

“…Bank conflicts. It is well-known [1,21,33] that when utilizing shared memory, an algorithm must be careful to avoid bank conflicts, as they negatively impact performance. Yet, sometimes completely eliminating bank conflicts requires an algorithm with higher complexity, and the increase in the number of operations can offsets the benefit of removing bank conflicts.…”

“…One of the arguments why samplesort of Leischner et al [23] is not the fastest in practice could be attributed to large number of bank conflicts in shared memory. Therefore, Koike and Sadakane [21] developed a bank conflict free multi-way mergesort algorithm. Unfortunately, we could not obtain the source code of their implementation to compare it to MGPU experimentally.…”

“…Thread occupancy, multiplicity and ILP. Using I/O complexity analysis of the External Memory model [2], it can be shown that the multiway mergesort of Koike and Sadakane [21] achieves asymptotically optimal global memory accesses, while MGPU mergesort does not. However, the I/O complexity analysis ignores many other performance factors that are significant for GPUs.…”