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Zunino, Claudio; Pompili, I.; Sanna, Andrea; Ciminiera, Luigi

doi:10.1002/spe.v37:8

Cited by 4 publications

(1 citation statement)

References 101 publications

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“…This work has proposed an inverse mapping from n-dimensions, and enhanced the encoding procedures suggested by Butz 5,6 . Chen 7 proposed mappings based on a replication process of the Hilbert square matrix rather than the bit-processing technique proposed by Fisher 12 . Liu and Schark 12 have implemented rotation matrices and vector functions in their three-dimensional Hilbert encoding/decoding approach.…”

Section: Space Filling Curvesmentioning

confidence: 99%

Locality properties of 3D data orderings with application to parallel molecular dynamics simulations

Al-Kharusi

Walker

2019

The International Journal of High Performance Computing Applica

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Application performance on graphical processing units (GPUs), in terms of execution speed and memory usage, depends on the efficient use of hierarchical memory. It is expected that enhancing data locality in molecular dynamic simulations will lower the cost of data movement across the GPU memory hierarchy. The work presented in this article analyses the spatial data locality and data reuse characteristics for row-major, Hilbert and Morton orderings and the impact these have on the performance of molecular dynamics simulations. A simple cache model is presented, and this is found to give results that are consistent with the timing results for the particle force computation obtained on NVidia GeForce GTX960 and Tesla P100 GPUs. Further analysis of the observed memory use, in terms of cache hits and the number of memory transactions, provides a more detailed explanation of execution behaviour for the different orderings. To the best of our knowledge, this is the first study to investigate memory analysis and data locality issues for molecular dynamics simulations of Lennard-Jones fluids on NVidia’s Maxwell and Tesla architectures.

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Section: Space Filling Curvesmentioning

confidence: 99%

Locality properties of 3D data orderings with application to parallel molecular dynamics simulations

Al-Kharusi

Walker

2019

The International Journal of High Performance Computing Applica

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Extending the limits for big data RSA cracking: Towards cache-oblivious TU decomposition

Salem

Arab

Yang

2020

Journal of Parallel and Distributed Computing

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A Novel Hilbert Curve for Cache-Locality Preserving Loops

Böhm

Perdacher

Plant

2021

IEEE Trans. Big Data

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Modern microprocessors offer a rich memory hierarchy including various levels of cache and registers. Some of these memories (like main memory, L3 cache) are big but slow and shared among all cores. Others (registers, L1 cache) are fast and exclusively assigned to a single core but small. Only if the data accesses have a high locality, we can avoid excessive data transfers between the memory hierarchy. In this paper we consider fundamental algorithms like matrix multiplication, K-Means, Cholesky decomposition as well as the algorithm by Floyd and Warshall typically operating in two or three nested loops. We propose to traverse these loops whenever possible not in the canonical order but in an order defined by a space-filling curve. This traversal order dramatically improves data locality over a wide granularity allowing not only to efficiently support a cache of a single, known size (cache conscious) but also a hierarchy of various caches where the effective size available to our algorithms may even be unknown (cache oblivious). We propose a new space-filling curve called Fast Unrestricted (FUR) Hilbert with the following advantages: (1) we overcome the usual limitation to square-like grid sizes where the side-length is a power of 2 or 3. Instead, our approach allows arbitrary loop boundaries for all variables. (2) FUR-Hilbert is non-recursive with a guaranteed constant worst case time complexity per loop iteration (in contrast to O(log(gridsize)) for previous methods). (3) Our non-recursive approach makes the application of our cache-oblivious loops in any host algorithm as easy as conventional loops and facilitates automatic optimization by the compiler. (4) We demonstrate that crucial algorithms like Cholesky decomposition as well as the algorithm by Floyd and Warshall by can be efficiently supported. (5) Extensive experiments on runtime efficiency, cache usage and energy consumption demonstrate the profit of our approach. We believe that future compilers could translate nested loops into cache-oblivious loops either fully automatic or by a user-guided analysis of the data dependency.

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Cited by 4 publications

References 101 publications

Locality properties of 3D data orderings with application to parallel molecular dynamics simulations

Locality properties of 3D data orderings with application to parallel molecular dynamics simulations

Extending the limits for big data RSA cracking: Towards cache-oblivious TU decomposition

A Novel Hilbert Curve for Cache-Locality Preserving Loops

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