Sparse linear algebra is an important kernel in many different applications. Among various sparse general matrix-matrix multiplication (SpGEMM) algorithms, Gustavson’s column-wise SpGEMM has good locality when reading input matrix and can be easily parallelized by distributing the computation of different columns of an output matrix to different processors. However, the sparse accumulation (SPA) step in column-wise SpGEMM, which merges partial sums from each of the multiplications by the row indices, is still a performance bottleneck. The state-of-the-art software implementation uses a hash table for partial sum search in the SPA, which makes SPA the largest contributor to the execution time of SpGEMM. There are three reasons that cause the SPA to become the bottleneck: (1) hash probing requires data-dependent branches that are difficult for a branch predictor to predict correctly; (2) the accumulation of partial sum is dependent on the results of the hash probing, which makes it difficult to hide the hash probing latency; and (3) hash collision requires time-consuming linear search and optimizations to reduce these collisions require an accurate estimation of the number of non-zeros in each column of the output matrix. This work proposes ASA architecture to accelerate the SPA. ASA overcomes the challenges of SPA by (1) executing the partial sum search and accumulate with a single instruction through ISA extension to eliminate data-dependent branches in hash probing, (2) using a dedicated on-chip cache to perform the search and accumulation in a pipelined fashion, (3) relying on the parallel search capability of a set-associative cache to reduce search latency, and (4) delaying the merging of overflowed entries. As a result, ASA achieves an average of 2.25× and 5.05× speedup as compared to the state-of-the-art software implementation of a Markov clustering application and its SpGEMM kernel, respectively. As compared to a state-of-the-art hashing accelerator design, ASA achieves an average of 1.95× speedup in the SpGEMM kernel.
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Efficient local locking for massively multithreaded in-memory hash-based operators
Abstract The join and group-by aggregation are two memory intensive operators that are affecting the performance of relational databases. Hashing is a common approach used to implement both operators. Recent paradigm shifts in multi-core processor architectures have reinvigorated research into how the join and group-by aggregation operators can leverage these advances. However, the poor spatial locality of the hashing approach has hindered performance on multi-core processor architectures which rely on using large cache hierarchies for latency mitigation. Multithreaded architectures can better cope with poor spatial locality by masking memory latency with many outstanding requests. Nevertheless, the number of parallel threads, even in the most advanced multithreaded processors, such as UltraSPARC, is not enough to fully cover the main memory access latency. In this paper, we explore the hardware re-configurability of FPGAs to enable deeper execution pipelines that maintain hundreds (instead of tens) of outstanding memory requests across four FPGAs-drastically increasing concurrency and throughput. We present two end-to-end in-memory accelerators for the join and group-by aggregation operators using FPGAs. Both accelerators use massive multithreading to mask long memory delays of traversing linked-list data structures, while concurrently managing hundreds of thread states across four FPGAs locally. We explore how content addressable memories can be intermixed within our multithreaded designs to act as a synchronizing cache , which enforces locks and merges jobs together before they are written to memory. Throughput results for our hash-join operator accelerator show a speedup between 2 $$\times $$ × and 3.4 $$\times $$ × over the best multi-core approaches with comparable memory bandwidths on uniform and skewed datasets. The accelerator for the hash-based group-by aggregation operator demonstrates that leveraging CAMs achieves average speedup of 3.3 $$\times $$ × with a best case of 9.4 $$\times $$ × in terms of throughput over CPU implementations across five types of data distributions.
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- Award ID(s):
- 1838222
- NSF-PAR ID:
- 10313677
- Date Published:
- Journal Name:
- The VLDB Journal
- Volume:
- 30
- Issue:
- 3
- ISSN:
- 1066-8888
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s00778-020-00642-5
