Publications

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Matrix-vector products are ubiquitous in high-performance scientific applications and have a growing set of occurrences in advanced data analysis activities. Achieving high performance for these kernels is therefore paramount, in part, because these operations can consume vast amounts of application execution time. In this report we document the development of several sparse-matrix vector product kernel implementations using a variety of programming models and approaches. Each kernel is run on a broad set of matrices selected to demonstrate the wide variety of matrix structure and sparsity that is possible with a single, generic kernel. For benchmarking and performance analysis, we utilize leading computing architectures for the NNSA/ASC program including Intel's Knights Landing processor and IBM's POWER8.

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A challenge in computer architecture is that processors often cannot be fed data from DRAM as fast as CPUs can consume it. Therefore, many applications are memory-bandwidth bound. With this motivation and the realization that traditional architectures (with all DRAM reachable only via bus) are insufficient to feed groups of modern processing units, vendors have introduced a variety of non-DDR 3D memory technologies (Hybrid Memory Cube (HMC),Wide I/O 2, High Bandwidth Memory (HBM)). These offer higher bandwidth and lower power by stacking DRAM chips on the processor or nearby on a silicon interposer. We will call these solutions “near-memory,” and if user-addressable, “scratchpad.” High-performance systems on the market now offer two levels of main memory: near-memory on package and traditional DRAM further away. In the near term we expect the latencies near-memory and DRAM to be similar. Thus, it is natural to think of near-memory as another module on the DRAM level of the memory hierarchy. Vendors are expected to offer modes in which the near memory is used as cache, but we believe that this will be inefficient. In this paper, we explore the design space for a user-controlled multi-level main memory. Our work identifies situations in which rewriting application kernels can provide significant performance gains when using near-memory. We present algorithms designed for two-level main memory, using divide-and-conquer to partition computations and streaming to exploit data locality. We consider algorithms for the fundamental application of sorting and for the data analysis kernel k-means. Our algorithms asymptotically reduce memory-block transfers under certain architectural parameter settings. We use and extend Sandia National Laboratories’ SST simulation capability to demonstrate the relationship between increased bandwidth and improved algorithmic performance. Memory access counts from simulations corroborate predicted performance improvements for our sorting algorithm. In contrast, the k-means algorithm is generally CPU bound and does not improve when using near-memory except under extreme conditions. These conditions require large instances that rule out SST simulation, but we demonstrate improvements by running on a customized machine with high and low bandwidth memory. These case studies in co-design serve as positive and cautionary templates, respectively, for the major task of optimizing the computational kernels of many fundamental applications for two-level main memory systems.

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DRAM technology is the main building block of main memory, however, DRAM scaling is becoming very challenging. The main issues for DRAM scaling are the increasing error rates with each new generation, the geometric and physical constraints of scaling the capacitor part of the DRAM cells, and the high power consumption caused by the continuous need for refreshing cell values. At the same time, emerging Non- Volatile Memory (NVM) technologies, such as Phase-Change Memory (PCM), are emerging as promising replacements for DRAM. NVMs, when compared to current technologies e.g., NAND-based ash, have latencies comparable to DRAM. Additionally, NVMs are non-volatile, which eliminates the need for refresh power and enables persistent memory applications. Finally, NVMs have promising densities and the potential for multi-level cell (MLC) storage.

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Emerging novel architectures for shared memory parallel computing are incorporating increasingly creative innovations to deliver higher memory performance. A notable exemplar of this phenomenon is the Multi-Channel DRAM (MCDRAM) that is included in the Intel® XeonPhi™ processors. In this paper, we examine techniques to use OpenMP to exploit the high bandwidth of MCDRAM by staging data. In particular, we implement double buffering using OpenMP sections and tasks to explicitly manage movement of data into MCDRAM. We compare our double-buffered approach to a non-buffered implementation and to Intel’s cache mode, in which the system manages the MCDRAM as a transparent cache. We also demonstrate the sensitivity of performance to parameters such as dataset size and the distribution of threads between compute and copy operations.

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