Cache oblivious stencil computations

Frigo, Matteo; Strumpen, Volker

doi:10.1145/1088149.1088197

Cited by 153 publications

(144 citation statements)

References 3 publications

(2 reference statements)

Supporting

Mentioning

142

Contrasting

Order By: Relevance

“…Secondly, the low computationalintensity and reuse ratios. After gathering the set of data points, just one central point is computed and only the accessed data points in the sweep direction might be reused for the computation of the next central point [4].…”

Section: Boosting Numerical Codesmentioning

confidence: 99%

Unveiling WARIS Code, a Parallel and Multi-purpose FDM Framework

Cruz

Hanzich

Folch

et al. 2014

Lecture Notes in Computational Science and Engineering

View full text Add to dashboard Cite

Abstract. WARIS is an in-house multi-purpose framework focused on solving scientific problems using Finite Difference Methods as numerical scheme. Its framework was designed from scratch to solve in a parallel and efficient way Earth Science and Computational Fluid Dynamic problems on a wide variety of architectures. WARIS uses structured meshes to discretize the problem domains, as these are better suited for optimization in accelerator-based architectures. To succeed in such challenge, WARIS framework was initially designed to be modular in order to ease development cycles, portability, reusability and future extensions of the framework. In order to assess its performance, a code that solves the vectorial AdvectionDiffusion-Sedimentation equation has been ported to the WARIS framework. This problem appears in many geophysical applications, including atmospheric transport of passive substances. As an application example, we focus on atmospheric dispersion of volcanic ash, a case in which operational code performance is critical given the threat posed by this substance on aircraft engines. Preliminary results are very promising, performance has been improved by 8.2× with respect to the baseline code using a realistic case. This opens new perspectives for operational setups, including efficient ensemble forecast.

show abstract

Section: Boosting Numerical Codesmentioning

confidence: 99%

Unveiling WARIS Code, a Parallel and Multi-purpose FDM Framework

Cruz

Hanzich

Folch

et al. 2014

Lecture Notes in Computational Science and Engineering

View full text Add to dashboard Cite

show abstract

“…Periodic domains have also been tiled using rhombus shaped tiles [5,8,10]. These tiles overlap at their bases, causing two tiles to compute some duplicate results.…”

Section: Related Workmentioning

confidence: 99%

“…These benefits can be enough to overcome the extra time spent recomputing a portion of the iterations. Overlapping tiles can also be used to handle wraparound dependencies that are introduced due to periodic boundaries [5,8]. The presented techniques could feasibly be extended to handle the ring, cylinder, and torus domains.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Smashing: Folding Space to Tile through Time

Osheim

Strout

Rostron

et al. 2008

Languages and Compilers for Parallel Computing

View full text Add to dashboard Cite

Abstract. Partial differential equation solvers spend most of their computation time performing nearest neighbor (stencil) computations on grids that model spatial domains. Tiling is an effective performance optimization for improving the data locality and enabling course-grain parallelization for such computations. However, when the domains are periodic, tiling through time is not directly applicable due to wrap-around dependencies. It is possible to tile within the spatial domain, but tiling across time (i.e. time skewing) is not legal since no constant skewing can render all loops fully permutable. We introduce a technique called smashing that maps a periodic domain to computer memory without creating any wrap-around dependencies. For a periodic cylinder domain where time skewing improves performance, the performance of smashing is comparable to another method, circular skewing, which also handles the periodicity of a cylinder. Unlike circular skewing, smashing can remove wrap-around dependencies for an icosahedron model of earth's atmosphere.

show abstract

“…Tiling [19] [29] is often used to partition the stencil loops among multiple processing elements (PEs) for parallel execution, and we refer to a workload partition as a tile in this paper. Similar tiling techniques also help localize computation to optimize cache hit rate for an individual processor [13]. Tiling across multiple PEs introduces a problem because stencils along the boundary of a tile must obtain values that were computed remotely on other PEs, as shown in Figure 1(a).…”

Section: Introductionmentioning

confidence: 99%

A Performance Study for Iterative Stencil Loops on GPUs with Ghost Zone Optimizations

Meng

Skadron

2010

Int J Parallel Prog

View full text Add to dashboard Cite

Iterative stencil loops (ISLs) are used in many applications and tiling is a well-known technique to localize their computation. When ISLs are tiled across a parallel architecture, there are usually halo regions that need to be updated and exchanged among different processing elements (PEs). In addition, synchronization is often used to signal the completion of halo exchanges. Both communication and synchronization may incur significant overhead on parallel architectures with shared memory. This is especially true in the case of graphics processors (GPUs), which do not preserve the state of the per-core L1 storage across global synchronizations. To reduce these overheads, ghost zones can be created to replicate stencil operations, reducing communication and synchronization costs at the expense of redundantly computing some values on multiple PEs. However, the selection of the optimal ghost zone size depends on the characteristics of both the architecture and the application, and it has only been studied for message-passing systems in distributed environments. To automate this process on shared memory systems, we establish a performance model using NVIDIA's Tesla architecture as a case study and propose a framework that uses the performance model to automatically select the ghost zone size that performs best and generate appropriate code. The modeling is validated by four diverse ISL applications, for which the predicted ghost zone configurations are able to achieve a speedup no less than 95% of the optimal speedup.

show abstract

Cache oblivious stencil computations

Cited by 153 publications

References 3 publications

Unveiling WARIS Code, a Parallel and Multi-purpose FDM Framework

Unveiling WARIS Code, a Parallel and Multi-purpose FDM Framework

Smashing: Folding Space to Tile through Time

A Performance Study for Iterative Stencil Loops on GPUs with Ghost Zone Optimizations

Contact Info

Product

Resources

About