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At least 37 records · Page 2

Computing rank‐revealing factorizations of matrices stored out‐of‐core

This paper describes efficient algorithms for computing rank-revealing factorizations of matrices that are too large to fit in main memory (RAM), and must instead be stored on slow external memory devices such as disks (out-of-core or out-of-memory). Traditional algorithms for computing rank-revealing factorizations (such as the column pivoted QR factorization and the singular value decomposition) are very communication intensive as they require many vector-vector and matrix-vector operations, which become prohibitively expensive when data is not in RAM. Randomization allows to reformulate new methods so that large contiguous blocks of the matrix are processed in bulk. The paper describes two distinct methods. The first is a blocked version of column pivoted Householder QR, organized as a “left-looking” method to minimize the number of the expensive write operations. The second method results employs a UTV factorization. It is organized as an algorithm-by-blocks to overlap computations and I/O operations. As it incorporates power iterations, it is much better at revealing the numerical rank. Numerical experiments on several computers demonstrate that the new algorithms are almost as fast when processing data stored on slow memory devices as traditional algorithms are for data stored in RAM.

97 MATHEMATICS AND COMPUTING↗

Novel Geometric Operations for Linear Programming

This report summarizes the work performed under the project "Linear Programming in Strongly Polynomial Time." Linear programming (LP) is a classic combinatorial optimization problem heavily used directly and as an enabling subroutine in integer programming (IP). Specifically IP is the same as LP except that some solution variables must take integer values (e.g. to represent yes/no decisions). Together LP and IP have many applications in resource allocation including general logistics, and infrastructure design and vulnerability analysis. The project was motivated by the PI's recent success developing methods to efficiently sample Voronoi vertices (essentially finding nearest neighbors in high-dimensional point sets) in arbitrary dimension. His method seems applicable to exploring the high-dimensional convex feasible space of an LP problem. Although the project did not provably find a strongly-polynomial algorithm, it explored multiple algorithm classes. The new medial simplex algorithms may still lead to solvers with improved provable complexity. We describe medial simplex algorithms and some relevant structural/complexity results. We also designed a novel parallel LP algorithm based on our geometric insights and implemented it in the Spoke-LP code. A major part of the computational step is many independent vector dot products. Our parallel algorithm distributes the problem constraints across processors. Current commercial and high-quality free LP solvers require all problem details to fit onto a single processor or multicore. Our new algorithm might enable the solution of problems too large for any current LP solvers. We describe our new algorithm, give preliminary proof-of-concept experiments, and describe a new generator for arbitrarily large LP instances.

97 MATHEMATICS AND COMPUTING↗

Mobile Thread Task Manager

The Mobile Thread Task Manager (MTTM) is being applied to parallelizing existing flight software to understand the benefits and to develop new techniques and architectural concepts for adapting software to multicore architectures. It allocates and load-balances tasks for a group of threads that migrate across processors to improve cache performance. In order to balance-load across threads, the MTTM augments a basic map-reduce strategy to draw jobs from a global queue. In a multicore processor, memory may be "homed" to the cache of a specific processor and must be accessed from that processor. The MTTB architecture wraps access to data with thread management to move threads to the home processor for that data so that the computation follows the data in an attempt to avoid L2 cache misses. Cache homing is also handled by a memory manager that translates identifiers to processor IDs where the data will be homed (according to rules defined by the user). The user can also specify the number of threads and processors separately, which is important for tuning performance for different patterns of computation and memory access. MTTM efficiently processes tasks in parallel on a multiprocessor computer. It also provides an interface to make it easier to adapt existing software to a multiprocessor environment.

Clement, Bradley J.↗

High-Performance Spaceflight Computing (HPSC) Middleware Overview

High Performance Spacecraft Computing (HPSC) is a joint project between the National Aeronautics and Space Administration (NASA) and Air Force Research Lab (AFRL) to develop a high-performance multi-core radiation hardened flight processor. HPSC offers a new flight computing architecture to meet the needs of NASA missions through 2030 and beyond. Providing on the order of 100X the computational capacity of current flight processors for the same amount of power, the multicore architecture of the HPSC processor, or "Chiplet" provides unprecedented flexibility in a flight computing system by enabling the operating point to be set dynamically, trading among needs for computational performance, energy management and fault tolerance. The HPSC Chiplet is being developed by Boeing under contract to NASA, and is expected to provide prototypes in 2021. The HPSC Chiplet prototypes will be delivered with an evaluation board, system emulators, comprehensive system software, and a software development kit. In addition to the vendor deliverables, the AFRL is funding the development of a flexible Middleware to be developed by NASA Jet Propulsion Laboratory and NASA Goddard Space Flight Center. The HPSC Middleware provides a suite of thirteen high level services to manage the compute, memory and I/O resources of this complex device.This presentation will provide an overview of the HPSC project, including a hardware overview, system software overview, Middleware overview, and mission use cases. The hardware overview will provide a look at the 8 core High Performance Processing Subsystem (HPPS), the Real Time Processing Subsystem (RTPS), the Chiplet Configuration Management Subsystem, on chip peripherals, and high speed I/O. The system software overview will introduce the boot loaders, operating systems, device drivers, and software development environment. The Middleware overview will provide insight into the high-level services that will be provided to help mission developers manage the many resources and configurations made possible with the Chiplet. Finally, the presentation will provide a brief look at the mission use cases that can be enabled with this next generation architecture.

middleware↗

High Performance Spacecraft Computing (HPSC) Middleware Update

High Performance Spacecraft Computing (HPSC) is a joint project between the National Aeronautics and Space Administration (NASA) and Air Force Research Lab (AFRL) to develop a high-performance multi-core radiation hardened flight processor. HPSC offers a new flight computing architecture to meet the needs of NASA missions through 2030 and beyond. Providing on the order of 100X the computational capacity of current flight processors for the same amount of power, the multicore architecture of the HPSC processor, or "Chiplet" provides unprecedented flexibility in a flight computing system by enabling the operating point to be set dynamically, trading among needs for computational performance, energy management and fault tolerance. The HPSC Chiplet is being developed by Boeing under contract to NASA, and is expected to provide prototypes, an evaluation board, system emulators, comprehensive system software, and a software development kit. In addition to the vendor deliverables, the AFRL is funding the development of a flexible Middleware to be developed by NASA Jet Propulsion Laboratory and NASA Goddard Space Flight Center. The HPSC Middleware provides a suite of thirteen high level services to manage the compute, memory and I/O resources of this complex device.This presentation will provide an HPSC project update, an overview of the latest HPSC System Software release, an overview of HPSC Middleware Release 2, and a preview of the third HPSC Middleware release. The presentation will begin with a project update that will provide a look at the high-level changes since the project was introduced at the Flight Software Workshop last year. Next, the presentation will provide an overview of the current suite of HPSC System Software which includes the vendor provided bootloaders, operating systems, emulator, and development tools. Next, the HPSC Middleware progress will be presented, which includes an overview of the features and capabilities of HPSC Middleware Release 2, followed by a look at the reference flight software applications which utilize the Middleware. Finally, the presentation will give a preview of the HPSC Middleware Release 3.

Cudmore, Alan↗

The Importance of Scientific Visualization on Novel Hardware

Innovation in HPC hardware and adoption of heterogeneous systems has led to a variety of unique programming models. This has led to a challenge for scientific visualization software (and indeed all HPC software) to take full advantage of recent generations of supercomputing. Edge computing, where hardware is specialized for the needs of the particular application, exacerbates the problem. VTK-m has had many successes on this front by providing device-agnostic algorithms that compare favorably to implementations written to specific devices as shown in Table 1. However, VTK-m has focused mostly on GPU and traditional CPU multicore technology. There are numerous processor technologies, both existing and potential future, that are not being addressed by current R&D efforts.

97 MATHEMATICS AND COMPUTING↗

Roofline scaling trajectories: A method for parallel application and architectural performance analysis

The end of Dennard scaling signaled a shift in HPC supercomputer architectures from systems built from single-core processor architectures to systems built from multicore and eventually manycore architectures. This transition substantially complicated performance optimization and analysis as new programming models were created, new scaling methodologies deployed, and on-chip contention became a bottleneck to performance. Existing distributed memory performance models like logP and logGP were unable to capture this contention. The Roofline model was created to address this contention and its interplay with locality. However, to date, the Roofline model has focused on full-node concurrency. In this paper, we extend the Roofline model to capture the effects of concurrency on data locality and on-chip contention. We demonstrate the value of this new technique by evaluating the NAS parallel benchmarks on both multicore and manycore architectures under both strong-And weak-scaling regimes. In order to quantify the interplay between programming model and locality, we evaluate scaling under both the OpenMP and flat MPI programming models.

Ibrahim, K↗

A System to Provide Deterministic Flight Software Operation and Maximize Multicore Processing Performance: The Safe and Precise Landing – Integrated Capabilities Evolution (SPLICE) Datapath

A method and design are described for a system that processes multiple data streams, utilizing a multicore asymmetric processing architecture, that eliminates data interrupts to the application processors. The design supports a deterministic environment for flight software in NASA’s Safe and Precise Landing – Integrated Capabilities Evolution (SPLICE) project. The SPLICE project develops sensor, algorithm, and compute technologies for Precision Landing and Hazard Avoidance (PL&HA) capabilities. The compute technology for SPLICE is the Descent and Landing Computer (DLC). The DLC hosts several SPLICE algorithms with high computational resource requirements that must be executed in a real-time and deterministic manner. The software runs on a custom Single Board Computer (SBC), with a Xilinx Ultrascale+ Multiprocessor System-on-a-Chip (MPSoC). Input data for the flight software is from a variety of sensors, unique with respect to data rate and packet size. A data path between the SPLICE sensors and algorithms is designed to efficiently deliver this data to the flight software using the MPSoC asymmetric processing cores and Field Programmable Gate Array (FPGA) fabric. This is implemented in a manner that isolates the application processors running the flight software from interrupts associated with the input data. By leveraging real-time processors on the MPSoC, and a structure with the appropriate interfaces in the shared memory on the SBC, the flight software can use the full set of application processors. The available utilization for each processor in this set is also maximized for the SPLICE applications, providing a sufficiently deterministic execution environment without the cost and overhead of a real-time operating system.

heterogeneous processing system↗

SequenceL: Automated Parallel Algorithms Derived from CSP-NT Computational Laws

With the introduction of new parallel architectures like the cell and multicore chips from IBM, Intel, AMD, and ARM, as well as the petascale processing available for highend computing, a larger number of programmers will need to write parallel codes. Adding the parallel control structure to the sequence, selection, and iterative control constructs increases the complexity of code development, which often results in increased development costs and decreased reliability. SequenceL is a high-level programming language that is, a programming language that is closer to a human s way of thinking than to a machine s. Historically, high-level languages have resulted in decreased development costs and increased reliability, at the expense of performance. In recent applications at JSC and in industry, SequenceL has demonstrated the usual advantages of high-level programming in terms of low cost and high reliability. SequenceL programs, however, have run at speeds typically comparable with, and in many cases faster than, their counterparts written in C and C++ when run on single-core processors. Moreover, SequenceL is able to generate parallel executables automatically for multicore hardware, gaining parallel speedups without any extra effort from the programmer beyond what is required to write the sequen tial/singlecore code. A SequenceL-to-C++ translator has been developed that automatically renders readable multithreaded C++ from a combination of a SequenceL program and sample data input. The SequenceL language is based on two fundamental computational laws, Consume-Simplify- Produce (CSP) and Normalize-Trans - pose (NT), which enable it to automate the creation of parallel algorithms from high-level code that has no annotations of parallelism whatsoever. In our anecdotal experience, SequenceL development has been in every case less costly than development of the same algorithm in sequential (that is, single-core, single process) C or C++, and an order of magnitude less costly than development of comparable parallel code. Moreover, SequenceL not only automatically parallelizes the code, but since it is based on CSP-NT, it is provably race free, thus eliminating the largest quality challenge the parallelized software developer faces.

Cooke, Daniel↗

A System to Provide Deterministic Flight Software Operation and Maximize Multicore Processing Performance: The Safe and Precise Landing – Integrated Capabilities Evolution (SPLICE) Datapath

A method and design are described for a system that processes multiple data streams, utilizing a multicore asymmetric processing architecture, that eliminates data interrupts to the application processors. The design supports a deterministic environment for flight software in NASA’s Safe and Precise Landing – Integrated Capabilities Evolution (SPLICE) project. The SPLICE project develops sensor, algorithm, and compute technologies for Precision Landing and Hazard Avoidance (PL&HA) capabilities. The compute technology for SPLICE is the Descent and Landing Computer (DLC). The DLC hosts several SPLICE algorithms with high computational resource requirements that must be executed in a real-time and deterministic manner. The software runs on a custom Single Board Computer (SBC), with a Xilinx Ultrascale+ Multiprocessor System-on-a-Chip (MPSoC). Input data for the flight software is from a variety of sensors, unique with respect to data rate and packet size. A data path between the SPLICE sensors and algorithms is designed to efficiently deliver this data to the flight software using the MPSoC asymmetric processing cores and Field Programmable Gate Array (FPGA) fabric. This is implemented in a manner that isolates the application processors running the flight software from interrupts associated with the input data. By leveraging real-time processors on the MPSoC, and a structure with the appropriate interfaces in the shared memory on the SBC, the flight software can use the full set of application processors. The available utilization for each processor in this set is also maximized for the SPLICE applications, providing a sufficiently deterministic execution environment without the cost and overhead of a real-time operating system.

David K. Rutishauser↗

Understanding HPC Benchmark Performance on Intel Broadwell and Cascade Lake Processors

Hardware platforms in high performance computing are constantly getting more complex to handle even when considering multicore CPUs alone. Numerous features and configuration options in the hardware and the software environment that are relevant for performance are not even known to most application users or developers. Microbenchmarks, i.e., simple codes that fathom a particular aspect of the hardware, can help to shed light on such issues, but only if they are well understood and if the results can be reconciled with known facts or performance models. The insight gained from microbenchmarks may then be applied to real applications for performance analysis or optimization. In this paper we investigate two modern Intel x86 server CPU architectures in depth: Broadwell EP and Cascade Lake SP. We highlight relevant hardware configuration settings that can have a decisive impact on code performance and show how to properly measure on-chip and off-chip data transfer bandwidths. The new victim L3 cache of Cascade Lake and its advanced replacement policy receive due attention. Finally we use DGEMM, sparse matrix-vector multiplication, and the HPCG benchmark to make a connection to relevant application scenarios.

97 MATHEMATICS AND COMPUTING↗

A Flexible-blocking Based Approach for Performance Tuning of Matrix Multiplication Routines for Large Matrices with Edge Cases

Efficient and scalable matrix operations are being highly demanding in the recent era of Machine Learning, Deep Learning, and Big Data Analytics. The two commonly used matrix-matrix operations in the Basic Linear Algebra Subprograms (BLAS) specification are General Matrix-Matrix multiplication (GEMM) and Symmetric Rank-k update (SYRK). The SYRK routine is a specialization of the GEMM routine, where half of the multiplications are skipped as the resultant matrix is known to be symmetric. Fortunately, several linear algebra libraries implement these BLAS routines quite efficiently. The libraries usually partition the input matrices into blocks and place them in processor caches, thus improving performance by leveraging the caches. However, the contemporary libraries are highly optimized for squarish matrices, but the performance degrades significantly for the matrices with edge case (strictly thin or strictly fat shapes) in the multicore machine. The primary reason is that the current state-of-the-art libraries make fixed block shapes based on a processor architecture, and do not consider the shape of the input matrices. In this paper, we propose a new blocking approach, we name it Flexible-blocking, to mitigate the scalability issues. In contrast to the contemporary libraries, our approach formulates the blocks of the input matrices based on the shapes of the matrices as well as the number of threads used in the implementation. Our proposed technique shows noticeable performance improvement on multicore shared-memory machines for the edge case matrices.

Hossain, Md Mosharaf↗

Accelerated Adaptive MGS Phase Retrieval

The Modified Gerchberg-Saxton (MGS) algorithm is an image-based wavefront-sensing method that can turn any science instrument focal plane into a wavefront sensor. MGS characterizes optical systems by estimating the wavefront errors in the exit pupil using only intensity images of a star or other point source of light. This innovative implementation of MGS significantly accelerates the MGS phase retrieval algorithm by using stream-processing hardware on conventional graphics cards. Stream processing is a relatively new, yet powerful, paradigm to allow parallel processing of certain applications that apply single instructions to multiple data (SIMD). These stream processors are designed specifically to support large-scale parallel computing on a single graphics chip. Computationally intensive algorithms, such as the Fast Fourier Transform (FFT), are particularly well suited for this computing environment. This high-speed version of MGS exploits commercially available hardware to accomplish the same objective in a fraction of the original time. The exploit involves performing matrix calculations in nVidia graphic cards. The graphical processor unit (GPU) is hardware that is specialized for computationally intensive, highly parallel computation. From the software perspective, a parallel programming model is used, called CUDA, to transparently scale multicore parallelism in hardware. This technology gives computationally intensive applications access to the processing power of the nVidia GPUs through a C/C++ programming interface. The AAMGS (Accelerated Adaptive MGS) software takes advantage of these advanced technologies, to accelerate the optical phase error characterization. With a single PC that contains four nVidia GTX-280 graphic cards, the new implementation can process four images simultaneously to produce a JWST (James Webb Space Telescope) wavefront measurement 60 times faster than the previous code.

Lam, Raymond K.↗

Compute Element and Interface Box for the Hazard Detection System

The Autonomous Landing and Hazard Avoidance Technology (ALHAT) program is building a sensor that enables a spacecraft to evaluate autonomously a potential landing area to generate a list of hazardous and safe landing sites. It will also provide navigation inputs relative to those safe sites. The Hazard Detection System Compute Element (HDS-CE) box combines a field-programmable gate array (FPGA) board for sensor integration and timing, with a multicore computer board for processing. The FPGA does system-level timing and data aggregation, and acts as a go-between, removing the real-time requirements from the processor and labeling events with a high resolution time. The processor manages the behavior of the system, controls the instruments connected to the HDS-CE, and services the "heavy lifting" computational requirements for analyzing the potential landing spots.

Villalpando, Carlos Y.↗

High-Performance Sparse Matrix-Matrix Products on Intel KNL and Multicore Architectures

Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is vastly used in areas ranging from traditional numerical applications to recent big data analysis and machine learning. While many SpGEMM algorithms have been proposed, hardware specific optimizations for multi- and many-core processors are lacking and a detailed analysis of their performance under various use cases and matrices is not available. We firstly identify and mitigate multiple bottlenecks with memory management and thread scheduling on Intel Xeon Phi (Knights Landing or KNL). Specifically targeting multi- and many-core processors, we develop a hash-table-based algorithm and optimize a heap-based shared-memory SpGEMM algorithm. We investigate their performance together with other publicly available codes. Different from the literature, our evaluation also includes use cases that are representative of real graph algorithms, such as multi-source breadth-first search or triangle counting. Our hash-table and heap-based algorithms are showing significant speedups from libraries in the majority of the cases while different algorithms dominate the other scenarios with different matrix size, sparsity, compression factor and operation type. We wrap up in-depth evaluation results and make a recipe to give the best SpGEMM algorithm for target scenario. In conclusion, a critical finding is that hash-table-based SpGEMM gets a significant performance boost if the nonzeros are not required to be sorted within each row of the output matrix.

97 MATHEMATICS AND COMPUTING↗