115 research outputs found

    Fast Linear Programming through Transprecision Computing on Small and Sparse Data

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    A plethora of program analysis and optimization techniques rely on linear programming at their heart. However, such techniques are often considered too slow for production use. While today’s best solvers are optimized for complex problems with thousands of dimensions, linear programming, as used in compilers, is typically applied to small and seemingly trivial problems, but to many instances in a single compilation run. As a result, compilers do not benefit from decades of research on optimizing large-scale linear programming. We design a simplex solver targeted at compilers. A novel theory of transprecision computation applied from individual elements to full data-structures provides the computational foundation. By carefully combining it with optimized representations for small and sparse matrices and specialized small-coefficient algorithms, we (1) reduce memory traffic, (2) exploit wide vectors, and (3) use low-precision arithmetic units effectively. We evaluate our work by embedding our solver into a state-of-the-art integer set library and implement one essential operation, coalescing, on top of our transprecision solver. Our evaluation shows more than an order-of-magnitude speedup on the core simplex pivot operation and a mean speedup of 3.2x (vs. GMP) and 4.6x (vs. IMath) for the optimized coalescing operation. Our results demonstrate that our optimizations exploit the wide SIMD instructions of modern microarchitectures effectively. We expect our work to provide foundations for a future integer set library that uses transprecision arithmetic to accelerate compiler analyses.ISSN:2475-142

    GHOST: Building blocks for high performance sparse linear algebra on heterogeneous systems

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    While many of the architectural details of future exascale-class high performance computer systems are still a matter of intense research, there appears to be a general consensus that they will be strongly heterogeneous, featuring "standard" as well as "accelerated" resources. Today, such resources are available as multicore processors, graphics processing units (GPUs), and other accelerators such as the Intel Xeon Phi. Any software infrastructure that claims usefulness for such environments must be able to meet their inherent challenges: massive multi-level parallelism, topology, asynchronicity, and abstraction. The "General, Hybrid, and Optimized Sparse Toolkit" (GHOST) is a collection of building blocks that targets algorithms dealing with sparse matrix representations on current and future large-scale systems. It implements the "MPI+X" paradigm, has a pure C interface, and provides hybrid-parallel numerical kernels, intelligent resource management, and truly heterogeneous parallelism for multicore CPUs, Nvidia GPUs, and the Intel Xeon Phi. We describe the details of its design with respect to the challenges posed by modern heterogeneous supercomputers and recent algorithmic developments. Implementation details which are indispensable for achieving high efficiency are pointed out and their necessity is justified by performance measurements or predictions based on performance models. The library code and several applications are available as open source. We also provide instructions on how to make use of GHOST in existing software packages, together with a case study which demonstrates the applicability and performance of GHOST as a component within a larger software stack.Comment: 32 pages, 11 figure

    Analytical Query Processing Using Heterogeneous SIMD Instruction Sets

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    Numerous applications gather increasing amounts of data, which have to be managed and queried. Different hardware developments help to meet this challenge. The grow-ing capacity of main memory enables database systems to keep all their data in memory. Additionally, the hardware landscape is becoming more diverse. A plethora of homo-geneous and heterogeneous co-processors is available, where heterogeneity refers not only to a different computing power, but also to different instruction set architectures. For instance, modern Intel® CPUs offer different instruction sets supporting the Single Instruction Multiple Data (SIMD) paradigm, e.g. SSE, AVX, and AVX512. Database systems have started to exploit SIMD to increase performance. However, this is still a challenging task, because existing algorithms were mainly developed for scalar processing and because there is a huge variety of different instruction sets, which were never standardized and have no unified interface. This requires to completely rewrite the source code for porting a system to another hardware architecture, even if those archi-tectures are not fundamentally different and designed by the same company. Moreover, operations on large registers, which are the core principle of SIMD processing, behave counter-intuitively in several cases. This is especially true for analytical query process-ing, where different memory access patterns and data dependencies caused by the com-pression of data, challenge the limits of the SIMD principle. Finally, there are physical constraints to the use of such instructions affecting the CPU frequency scaling, which is further influenced by the use of multiple cores. This is because the supply power of a CPU is limited, such that not all transistors can be powered at the same time. Hence, there is a complex relationship between performance and power, and therefore also between performance and energy consumption. This thesis addresses the specific challenges, which are introduced by the application of SIMD in general, and the heterogeneity of SIMD ISAs in particular. Hence, the goal of this thesis is to exploit the potential of heterogeneous SIMD ISAs for increasing the performance as well as the energy-efficiency

    Ansor : Generating High-Performance Tensor Programs for Deep Learning

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    High-performance tensor programs are crucial to guarantee efficient execution of deep neural networks. However, obtaining performant tensor programs for different operators on various hardware platforms is notoriously challenging. Currently, deep learning systems rely on vendor-provided kernel libraries or various search strategies to get performant tensor programs. These approaches either require significant engineering effort to develop platform-specific optimization code or fall short of finding high-performance programs due to restricted search space and ineffective exploration strategy. We present Ansor, a tensor program generation framework for deep learning applications. Compared with existing search strategies, Ansor explores many more optimization combinations by sampling programs from a hierarchical representation of the search space. Ansor then fine-tunes the sampled programs with evolutionary search and a learned cost model to identify the best programs. Ansor can find high-performance programs that are outside the search space of existing state-of-the-art approaches. In addition, Ansor utilizes a task scheduler to simultaneously optimize multiple subgraphs in deep neural networks. We show that Ansor improves the execution performance of deep neural networks relative to the state-of-the-art on the Intel CPU, ARM CPU, and NVIDIA GPU by up to 3.8×3.8\times, 2.6×2.6\times, and 1.7×1.7\times, respectively.Comment: Published in OSDI 202

    Modular SIMD arithmetic in Mathemagix

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    Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography, and error correcting codes. Although recent microprocessors typically offer a wide range of highly optimized arithmetic functions, modular integer operations still require dedicated implementations. In this article, we survey existing algorithms for modular integer arithmetic, and present detailed vectorized counterparts. We also present several applications, such as fast modular Fourier transforms and multiplication of integer polynomials and matrices. The vectorized algorithms have been implemented in C++ inside the free computer algebra and analysis system Mathemagix. The performance of our implementation is illustrated by various benchmarks

    Efficient Storage of Genomic Sequences in High Performance Computing Systems

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    ABSTRACT: In this dissertation, we address the challenges of genomic data storage in high performance computing systems. In particular, we focus on developing a referential compression approach for Next Generation Sequence data stored in FASTQ format files. The amount of genomic data available for researchers to process has increased exponentially, bringing enormous challenges for its efficient storage and transmission. General-purpose compressors can only offer limited performance for genomic data, thus the need for specialized compression solutions. Two trends have emerged as alternatives to harness the particular properties of genomic data: non-referential and referential compression. Non-referential compressors offer higher compression rations than general purpose compressors, but still below of what a referential compressor could theoretically achieve. However, the effectiveness of referential compression depends on selecting a good reference and on having enough computing resources available. This thesis presents one of the first referential compressors for FASTQ files. We first present a comprehensive analytical and experimental evaluation of the most relevant tools for genomic raw data compression, which led us to identify the main needs and opportunities in this field. As a consequence, we propose a novel compression workflow that aims at improving the usability of referential compressors. Subsequently, we discuss the implementation and performance evaluation for the core of the proposed workflow: a referential compressor for reads in FASTQ format that combines local read-to-reference alignments with a specialized binary-encoding strategy. The compression algorithm, named UdeACompress, achieved very competitive compression ratios when compared to the best compressors in the current state of the art, while showing reasonable execution times and memory use. In particular, UdeACompress outperformed all competitors when compressing long reads, typical of the newest sequencing technologies. Finally, we study the main aspects of the data-level parallelism in the Intel AVX-512 architecture, in order to develop a parallel version of the UdeACompress algorithms to reduce the runtime. Through the use of SIMD programming, we managed to significantly accelerate the main bottleneck found in UdeACompress, the Suffix Array Construction

    GPU-Accelerated and CPU SIMD Optimized Monte Carlo Simulation of φ4 Model

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    In this contribution we describe an efficient GPU implementation of the Monte-Carlo simulation of the Ginzburg-Landau model. We achieve the performance close to 50 % of the peak performance of the used GPU. We compare this performance with a parallelized and vectorized CPU code and discuss the observed differences
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