FLiMS: a fast lightweight 2-way merger for sorting

In this paper, we present FLiMS, a highly-efficient and simple parallel algorithm for merging two sorted lists residing in banked and/or wide memory. On FPGAs, its implementation uses fewer hardware resources than the state-of-the-art alternatives, due to the reduced number of comparators and elimination of redundant logic found on prior attempts. In combination with the distributed nature of the selector stage, a higher performance is achieved for the same amount of parallelism or higher. This is useful in many applications such as in parallel merge trees to achieve high-throughput sorting, where the resource utilisation of the merger is critical for building larger trees and internalising the workload for faster computation. Also presented are efficient variations of FLiMS for optimizing throughput for skewed datasets, achieving stable sorting or using fewer dequeue signals. FLiMS is also shown to perform well as conventional software on modern CPUs supporting single-instruction multiple-data (SIMD) instructions, surpassing the performance of some standard libraries for sorting

Database System Acceleration on FPGAs

Relational database systems provide various services and applications with an efficient means for storing, processing, and retrieving their data. The performance of these systems has a direct impact on the quality of service of the applications that rely on them. Therefore, it is crucial that database systems are able to adapt and grow in tandem with the demands of these applications, ensuring that their performance scales accordingly. In the past, Moore's law and algorithmic advancements have been sufficient to meet these demands. However, with the slowdown of Moore's law, researchers have begun exploring alternative methods, such as application-specific technologies, to satisfy the more challenging performance requirements. One such technology is field-programmable gate arrays (FPGAs), which provide ideal platforms for developing and running custom architectures for accelerating database systems. The goal of this thesis is to develop a domain-specific architecture that can enhance the performance of in-memory database systems when executing analytical queries. Our research is guided by a combination of academic and industrial requirements that seek to strike a balance between generality and performance. The former ensures that our platform can be used to process a diverse range of workloads, while the latter makes it an attractive solution for high-performance use cases. Throughout this thesis, we present the development of a system-on-chip for database system acceleration that meets our requirements. The resulting architecture, called CbMSMK, is capable of processing the projection, sort, aggregation, and equi-join database operators and can also run some complex TPC-H queries. CbMSMK employs a shared sort-merge pipeline for executing all these operators, which results in an efficient use of FPGA resources. This approach enables the instantiation of multiple acceleration cores on the FPGA, allowing it to serve multiple clients simultaneously. CbMSMK can process both arbitrarily deep and wide tables efficiently. The former is achieved through the use of the sort-merge algorithm which utilizes the FPGA RAM for buffering intermediate sort results. The latter is achieved through the use of KeRRaS, a novel variant of the forward radix sort algorithm introduced in this thesis. KeRRaS allows CbMSMK to process a table a few columns at a time, incrementally generating the final result through multiple iterations. Given that acceleration is a key objective of our work, CbMSMK benefits from many performance optimizations. For instance, multi-way merging is employed to reduce the number of merge passes required for the execution of the sort-merge algorithm, thus improving the performance of all our pipeline-breaking operators. Another example is our in-depth analysis of early aggregation, which led to the development of a novel cache-based algorithm that significantly enhances aggregation performance. Our experiments demonstrate that CbMSMK performs on average 5 times faster than the state-of-the-art CPU-based database management system MonetDB.:I Database Systems & FPGAs 1 INTRODUCTION 1.1 Databases & the Importance of Performance 1.2 Accelerators & FPGAs 1.3 Requirements 1.4 Outline & Summary of Contributions 2 BACKGROUND ON DATABASE SYSTEMS 2.1 Databases 2.1.1 Storage Model 2.1.2 Storage Medium 2.2 Database Operators 2.2.1 Projection 2.2.2 Filter 2.2.3 Sort 2.2.4 Aggregation 2.2.5 Join 2.2.6 Operator Classification 2.3 Database Queries 2.4 Impact of Acceleration 3 BACKGROUND ON FPGAS 3.1 FPGA 3.1.1 Logic Element 3.1.2 Block RAM (BRAM) 3.1.3 Digital Signal Processor (DSP) 3.1.4 IO Element 3.1.5 Programmable Interconnect 3.2 FPGADesignFlow 3.2.1 Specifications 3.2.2 RTL Description 3.2.3 Verification 3.2.4 Synthesis, Mapping, Placement, and Routing 3.2.5 TimingAnalysis 3.2.6 Bitstream Generation and FPGA Programming 3.3 Implementation Quality Metrics 3.4 FPGA Cards 3.5 Benefits of Using FPGAs 3.6 Challenges of Using FPGAs 4 RELATED WORK 4.1 Summary of Related Work 4.2 Platform Type 4.2.1 Accelerator Card 4.2.2 Coprocessor 4.2.3 Smart Storage 4.2.4 Network Processor 4.3 Implementation 4.3.1 Loop-based implementation 4.3.2 Sort-based Implementation 4.3.3 Hash-based Implementation 4.3.4 Mixed Implementation 4.4 A Note on Quantitative Performance Comparisons II Cache-Based Morphing Sort-Merge with KeRRaS (CbMSMK) 5 OBJECTIVES AND ARCHITECTURE OVERVIEW 5.1 From Requirements to Objectives 5.2 Architecture Overview 5.3 Outlineof Part II 6 COMPARATIVE ANALYSIS OF OPENCL AND RTL FOR SORT-MERGE PRIMITIVES ON FPGAS 6.1 Programming FPGAs 6.2 RelatedWork 6.3 Architecture 6.3.1 Global Architecture 6.3.2 Sorter Architecture 6.3.3 Merger Architecture 6.3.4 Scalability and Resource Adaptability 6.4 Experiments 6.4.1 OpenCL Sort-Merge Implementation 6.4.2 RTLSorters 6.4.3 RTLMergers 6.4.4 Hybrid OpenCL-RTL Sort-Merge Implementation 6.5 Summary & Discussion 7 RESOURCE-EFFICIENT ACCELERATION OF PIPELINE-BREAKING DATABASE OPERATORS ON FPGAS 7.1 The Case for Resource Efficiency 7.2 Related Work 7.3 Architecture 7.3.1 Sorters 7.3.2 Sort-Network 7.3.3 X:Y Mergers 7.3.4 Merge-Network 7.3.5 Join Materialiser (JoinMat) 7.4 Experiments 7.4.1 Experimental Setup 7.4.2 Implementation Description & Tuning 7.4.3 Sort Benchmarks 7.4.4 Aggregation Benchmarks 7.4.5 Join Benchmarks 7. Summary 8 KERRAS: COLUMN-ORIENTED WIDE TABLE PROCESSING ON FPGAS 8.1 The Scope of Database System Accelerators 8.2 Related Work 8.3 Key-Reduce Radix Sort(KeRRaS) 8.3.1 Time Complexity 8.3.2 Space Complexity (Memory Utilization) 8.3.3 Discussion and Optimizations 8.4 Architecture 8.4.1 MSM 8.4.2 MSMK: Extending MSM with KeRRaS 8.4.3 Payload, Aggregation and Join Processing 8.4.4 Limitations 8.5 Experiments 8.5.1 Experimental Setup 8.5.2 Datasets 8.5.3 MSMK vs. MSM 8.5.4 Payload-Less Benchmarks 8.5.5 Payload-Based Benchmarks 8.5.6 Flexibility 8.6 Summary 9 A STUDY OF EARLY AGGREGATION IN DATABASE QUERY PROCESSING ON FPGAS 9.1 Early Aggregation 9.2 Background & Related Work 9.2.1 Sort-Based Early Aggregation 9.2.2 Cache-Based Early Aggregation 9.3 Simulations 9.3.1 Datasets 9.3.2 Metrics 9.3.3 Sort-Based Versus Cache-Based Early Aggregation 9.3.4 Comparison of Set-Associative Caches 9.3.5 Comparison of Cache Structures 9.3.6 Comparison of Replacement Policies 9.3.7 Cache Selection Methodology 9.4 Cache System Architecture 9.4.1 Window Aggregator 9.4.2 Compressor & Hasher 9.4.3 Collision Detector 9.4.4 Collision Resolver 9.4.5 Cache 9.5 Experiments 9.5.1 Experimental Setup 9.5.2 Resource Utilization and Parameter Tuning 9.5.3 Datasets 9.5.4 Benchmarks on Synthetic Data 9.5.5 Benchmarks on Real Data 9.6 Summary 10 THE FULL PICTURE 10.1 System Architecture 10.2 Benchmarks 10.3 Meeting the Objectives III Conclusion 11 SUMMARY AND OUTLOOK ON FUTURE RESEARCH 11.1 Summary 11.2 Future Work BIBLIOGRAPHY LIST OF FIGURES LIST OF TABLE

Design of a GF(64)-LDPC Decoder Based on the EMS Algorithm

International audienceThis paper presents the architecture, performance and implementation results of a serial GF(64)-LDPC decoder based on a reduced-complexity version of the Extended Min-Sum algorithm. The main contributions of this work correspond to the variable node processing, the codeword decision and the elementary check node processing. Post-synthesis area results show that the decoder area is less than 20% of a Virtex 4 FPGA for a decoding throughput of 2.95 Mbps. The implemented decoder presents performance at less than 0.7 dB from the Belief Propagation algorithm for different code lengths and rates. Moreover, the proposed architecture can be easily adapted to decode very high Galois Field orders, such as GF(4096) or higher, by slightly modifying a marginal part of the design

Analysis of Hardware Sorting Units in Processor Design

Sorting is often computationally intensive and can cause the application in which it is used to run slowly. To date, the quickest software sorting implementations for an N element sorting problem runs at O(nlogn). Current techniques, beyond developing better algorithms, used to accelerate sorting include the use of multiple processors or moving the sorting operation to a GPU. The use of multiple processors or a GPU can lead to increased energy consumption and heat produced by the device as compared to a single-core GPU-less implementation. To address these problems, specialized instructions and hardware units can be added to the processors to accelerate the sorting operation directly. This thesis studies and records the performance implications from implementing a sorting accelerator into a modern RISC-V processor pipeline. This thesis also explores the additional energy and area costs of implementing such hardware units in the processor

Engineering faster sorters for small sets of items

Sorting a set of items is a task that can be useful by itself or as a building block for more complex operations. That is why a lot of effort has been put into finding sorting algorithms that sort large sets as efficiently as possible. But the more sophisticated and complex the algorithms become, the less efficient they are for small sets of items due to large constant factors. A relatively simple sorting algorithm that is often used as a base case sorter is insertion sort, because it has small code size and small constant factors influencing its execution time. We aim to determine if there is a faster way to sort small sets of items to provide an efficient base case sorter. We looked at sorting networks, at how they can improve the speed of sorting few elements, and how to implement them in an efficient manner using conditional moves. Since sorting networks need to be implemented explicitly for each set size, providing networks for larger sizes becomes less efficient due to increased code sizes. To also enable the sorting of slightly larger base cases, we adapted sample sort to Register Sample Sort, to break down those larger sets into sizes that can in turn be sorted by sorting networks. From our experiments we found that when sorting only small sets of integers, the sorting networks outperform insertion sort by a factor of at least 1.76 for any array size between six and 16, and by a factor of 2.72 on average across all machines and array sizes. When integrating sorting networks as a base case sorter into Quicksort, we achieved far less performance improvements over using insertion sort, which is probably due to the networks having a larger code size and cluttering the L1 instruction cache. The same effect occurs when including Register Sample Sort as a base case sorter for IPS4o. But for x86 machines that have a larger L1 instruction cache of 64 KiB or more, we obtained speedups of 12.7% when using sorting networks as a base case sorter in std::sort, and of 5%–6% when integrating Register Sample Sort as a base case sorter into IPS4o, each in comparison to using insertion sort as the base case sorter. In conclusion, the desired improvement in speed could only be achieved under special circumstances, but the results clearly show the potential of using conditional moves in the field of sorting algorithms

Hardware implementation aspects of polar decoders and ultra high-speed LDPC decoders

The goal of channel coding is to detect and correct errors that appear during the transmission of information. In the past few decades, channel coding has become an integral part of most communications standards as it improves the energy-efficiency of transceivers manyfold while only requiring a modest investment in terms of the required digital signal processing capabilities. The most commonly used channel codes in modern standards are low-density parity-check (LDPC) codes and Turbo codes, which were the first two types of codes to approach the capacity of several channels while still being practically implementable in hardware. The decoding algorithms for LDPC codes, in particular, are highly parallelizable and suitable for high-throughput applications. A new class of channel codes, called polar codes, was introduced recently. Polar codes have an explicit construction and low-complexity encoding and successive cancellation (SC) decoding algorithms. Moreover, polar codes are provably capacity achieving over a wide range of channels, making them very attractive from a theoretical perspective. Unfortunately, polar codes under standard SC decoding cannot compete with the LDPC and Turbo codes that are used in current standards in terms of their error-correcting performance. For this reason, several improved SC-based decoding algorithms have been introduced. The most prominent SC-based decoding algorithm is the successive cancellation list (SCL) decoding algorithm, which is powerful enough to approach the error-correcting performance of LDPC codes. The original SCL decoding algorithm was described in an arithmetic domain that is not well-suited for hardware implementations and is not clear how an efficient SCL decoder architecture can be implemented. To this end, in this thesis, we re-formulate the SCL decoding algorithm in two distinct arithmetic domains, we describe efficient hardware architectures to implement the resulting SCL decoders, and we compare the decoders with existing LDPC and Turbo decoders in terms of their error-correcting performance and their implementation efficiency. Due to the ongoing technology scaling, the feature sizes of integrated circuits keep shrinking at a remarkable pace. As transistors and memory cells keep shrinking, it becomes increasingly difficult and costly (in terms of both area and power) to ensure that the implemented digital circuits always operate correctly. Thus, manufactured digital signal processing circuits, including channel decoder circuits, may not always operate correctly. Instead of discarding these faulty dies or using costly circuit-level fault mitigation mechanisms, an alternative approach is to try to live with certain malfunctions, provided that the algorithm implemented by the circuit is sufficiently fault-tolerant. In this spirit, in this thesis we examine decoding of polar codes and LDPC codes under the assumption that the memories that are used within the decoders are not fully reliable. We show that, in both cases, there is inherent fault-tolerance and we also propose some methods to reduce the effect of memory faults on the error-correcting performance of the considered decoders