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Register a new userEfficient Realization of Givens Rotation through Algorithm-Architecture Co-design for Acceleration of QR Factorization
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Added by
Farhad Merchant
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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We present efficient realization of Generalized Givens Rotation (GGR) based QR factorization that achieves 3-100x better performance in terms of Gflops/watt over state-of-the-art realizations on multicore, and General Purpose Graphics Processing Units (GPGPUs). GGR is an improvement over classical Givens Rotation (GR) operation that can annihilate multiple elements of rows and columns of an input matrix simultaneously. GGR takes 33% lesser multiplications compared to GR. For custom implementation of GGR, we identify macro operations in GGR and realize them on a Reconfigurable Data-path (RDP) tightly coupled to pipeline of a Processing Element (PE). In PE, GGR attains speed-up of 1.1x over Modified Householder Transform (MHT) presented in the literature. For parallel realization of GGR, we use REDEFINE, a scalable massively parallel Coarse-grained Reconfigurable Architecture, and show that the speed-up attained is commensurate with the hardware resources in REDEFINE. GGR also outperforms General Matrix Multiplication (gemm) by 10% in-terms of Gflops/watt which is counter-intuitive.
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We present efficient realization of Householder Transform (HT) based QR factorization through algorithm-architecture co-design where we achieve performance improvement of 3-90x in-terms of Gflops/watt over state-of-the-art multicore, General Purpose Graphics Processing Units (GPGPUs), Field Programmable Gate Arrays (FPGAs), and ClearSpeed CSX700. Theoretical and experimental analysis of classical HT is performed for opportunities to exhibit higher degree of parallelism where parallelism is quantified as a number of parallel operations per level in the Directed Acyclic Graph (DAG) of the transform. Based on theoretical analysis of classical HT, an opportunity re-arrange computations in the classical HT is identified that results in Modified HT (MHT) where it is shown that MHT exhibits 1.33x times higher parallelism than classical HT. Experiments in off-the-shelf multicore and General Purpose Graphics Processing Units (GPGPUs) for HT and MHT suggest that MHT is capable of achieving slightly better or equal performance compared to classical HT based QR factorization realizations in the optimized software packages for Dense Linear Algebra (DLA). We implement MHT on a customized platform for Dense Linear Algebra (DLA) and show that MHT achieves 1.3x better performance than native implementation of classical HT on the same accelerator. For custom realization of HT and MHT based QR factorization, we also identify macro operations in the DAGs of HT and MHT that are realized on a Reconfigurable Data-path (RDP). We also observe that due to re-arrangement in the computations in MHT, custom realization of MHT is capable of achieving 12% better performance improvement over multicore and GPGPUs than the performance improvement reported by General Matrix Multiplication (GEMM) over highly tuned DLA software packages for multicore and GPGPUs which is counter-intuitive.
In this paper, we present efficient realization of Kalman Filter (KF) that can achieve up to 65% of the theoretical peak performance of underlying architecture platform. KF is realized using Modified Faddeeva Algorithm (MFA) as a basic building block due to its versatility and REDEFINE Coarse Grained Reconfigurable Architecture (CGRA) is used as a platform for experiments since REDEFINE is capable of supporting realization of a set algorithmic compute structures at run-time on a Reconfigurable Data-path (RDP). We perform several hardware and software based optimizations in the realization of KF to achieve 116% improvement in terms of Gflops over the first realization of KF. Overall, with the presented approach for KF, 4-105x performance improvement in terms of Gflops/watt over several academically and commercially available realizations of KF is attained. In REDEFINE, we show that our implementation is scalable and the performance attained is commensurate with the underlying hardware resources
Personalized PageRank (PPR) is a graph algorithm that evaluates the importance of the surrounding nodes from a source node. Widely used in social network related applications such as recommender systems, PPR requires real-time responses (latency) for a better user experience. Existing works either focus on algorithmic optimization for improving precision while neglecting hardware implementations or focus on distributed global graph processing on large-scale systems for improving throughput rather than response time. Optimizing low-latency local PPR algorithm with a tight memory budget on edge devices remains unexplored. In this work, we propose a memory-efficient, low-latency PPR solution, namely MeLoPPR, with largely reduced memory requirement and a flexible trade-off between latency and precision. MeLoPPR is composed of stage decomposition and linear decomposition and exploits the node score sparsity: Through stage and linear decomposition, MeLoPPR breaks the computation on a large graph into a set of smaller sub-graphs, that significantly saves the computation memory; Through sparsity exploitation, MeLoPPR selectively chooses the sub-graphs that contribute the most to the precision to reduce the required computation. In addition, through software/hardware co-design, we propose a hardware implementation on a hybrid CPU and FPGA accelerating platform, that further speeds up the sub-graph computation. We evaluate the proposed MeLoPPR on memory-constrained devices including a personal laptop and Xilinx Kintex-7 KC705 FPGA using six real-world graphs. First, MeLoPPR demonstrates significant memory saving by 1.5x to 13.4x on CPU and 73x to 8699x on FPGA. Second, MeLoPPR allows flexible trade-offs between precision and execution time: when the precision is 80%, the speedup on CPU is up to 15x and up to 707x on FPGA; when the precision is around 90%, the speedup is up to 70x on FPGA.
Basic Linear Algebra Subprograms (BLAS) play key role in high performance and scientific computing applications. Experimentally, yesteryear multicore and General Purpose Graphics Processing Units (GPGPUs) are capable of achieving up to 15 to 57% of the theoretical peak performance at 65W to 240W respectively for compute bound operations like Double/Single Precision General Matrix Multiplication (XGEMM). For bandwidth bound operations like Single/Double precision Matrix-vector Multiplication (XGEMV) the performance is merely 5 to 7% of the theoretical peak performance in multicores and GPGPUs respectively. Achieving performance in BLAS requires moving away from conventional wisdom and evolving towards customized accelerator tailored for BLAS through algorithm-architecture co-design. In this paper, we present acceleration of Level-1 (vector operations), Level-2 (matrix-vector operations), and Level-3 (matrix-matrix operations) BLAS through algorithm architecture co-design on a Coarse-grained Reconfigurable Architecture (CGRA). We choose REDEFINE CGRA as a platform for our experiments since REDEFINE can be adapted to support domain of interest through tailor-made Custom Function Units (CFUs). For efficient sequential realization of BLAS, we present design of a Processing Element (PE) and perform micro-architectural enhancements in the PE to achieve up-to 74% of the theoretical peak performance of PE in DGEMM, 40% in DGEMV and 20% in double precision inner product (DDOT). We attach this PE to REDEFINE CGRA as a CFU and show the scalability of our solution. Finally, we show performance improvement of 3-140x in PE over commercially available Intel micro-architectures, ClearSpeed CSX700, FPGA, and Nvidia GPGPUs.
Innovations in Next-Generation Sequencing are enabling generation of DNA sequence data at ever faster rates and at very low cost. Large sequencing centers typically employ hundreds of such systems. Such high-throughput and low-cost generation of data underscores the need for commensurate acceleration in downstream computational analysis of the sequencing data. A fundamental step in downstream analysis is mapping of the reads to a long reference DNA sequence, such as a reference human genome. Sequence mapping is a compute-intensive step that accounts for more than 30% of the overall time of the GATK workflow. BWA-MEM is one of the most widely used tools for sequence mapping and has tens of thousands of users. In this work, we focus on accelerating BWA-MEM through an efficient architecture aware implementation, while maintaining identical output. The volume of data requires distributed computing environment, usually deploying multicore processors. Since the application can be easily parallelized for distributed memory systems, we focus on performance improvements on a single socket multicore processor. BWA-MEM run time is dominated by three kernels, collectively responsible for more than 85% of the overall compute time. We improved the performance of these kernels by 1) improving cache reuse, 2) simplifying the algorithms, 3) replacing small fragmented memory allocations with a few large contiguous ones, 4) software prefetching, and 5) SIMD utilization wherever applicable - and massive reorganization of the source code enabling these improvements. As a result, we achieved nearly 2x, 183x, and 8x speedups on the three kernels, respectively, resulting in up to 3.5x and 2.4x speedups on end-to-end compute time over the original BWA-MEM on single thread and single socket of Intel Xeon Skylake processor. To the best of our knowledge, this is the highest reported speedup over BWA-MEM.
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