Cross-Loop Optimization of Arithmetic Intensity for Finite Element Local Assembly

We study and systematically evaluate a class of composable code transformations that improve arithmetic intensity in local assembly operations, which represent a significant fraction of the execution time in finite element methods. Their performance optimization is indeed a challenging issue. Even t...

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Bibliographic Details
Published in:ACM transactions on architecture and code optimization 2014-12, Vol.11 (4), p.1-25
Main Authors: Luporini, Fabio, Varbanescu, Ana Lucia, Rathgeber, Florian, Bercea, Gheorghe-Teodor, Ramanujam, J., Ham, David A., Kelly, Paul H. J.
Format: Article
Language:English
Subjects:
Arithmetic
Assembly
Compilers
Complexity
Finite element method
Mathematical analysis
Optimization
Transformations
Transformations (mathematics)
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Summary:We study and systematically evaluate a class of composable code transformations that improve arithmetic intensity in local assembly operations, which represent a significant fraction of the execution time in finite element methods. Their performance optimization is indeed a challenging issue. Even though affine loop nests are generally present, the short trip counts and the complexity of mathematical expressions, which vary among different problems, make it hard to determine an optimal sequence of successful transformations. Our investigation has resulted in the implementation of a compiler (called COFFEE) for local assembly kernels, fully integrated with a framework for developing finite element methods. The compiler manipulates abstract syntax trees generated from a domain-specific language by introducing domain-aware optimizations for instruction-level parallelism and register locality. Eventually, it produces C code including vector SIMD intrinsics. Experiments using a range of real-world finite element problems of increasing complexity show that significant performance improvement is achieved. The generality of the approach and the applicability of the proposed code transformations to other domains is also discussed.
ISSN:1544-3566
1544-3973
DOI:10.1145/2687415