Optimizing Polynomial Expressions by Algebraic Factorization and Common Subexpression Elimination

Hosangadi, Anup; Fallah, Farzan; Kastner, Ryan

doi:10.1109/tcad.2006.875712

Cited by 35 publications

(45 citation statements)

References 19 publications

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“…Our factorizer is based on the work of Hosangadi et al on factorizing sets of multivariate polynomial expressions [Hosangadi et al 2006]. Most importantly, it is capable of finding factorizations that employ distributivity.…”

Section: Polynomial Factorisation and Common Sub-expression Eliminationmentioning

confidence: 99%

“…For conciseness, we do not describe the kernel extraction algorithm here, it is detailed in [Hosangadi et al 2006]. The algorithm computes the set of all possible kernel expressions for each SOP.…”

Section: The Following Definitionsmentioning

confidence: 99%

“…Hosangadi et al do not describe an algorithm to find the best scoring matrix covering in [Hosangadi et al 2006]. They do however note that it is analogous to the rectangle covering problem described in [Brayton et al 1987], which is NP-hard.…”

Section: The Following Definitionsmentioning

confidence: 99%

“…The techniques we have adapted from Hosangadi et al [Hosangadi et al 2006] require the solution of a covering problem which is NP-Hard [Brayton et al 1987]. Our technique of decomposing rational coefficients increases the size of this search space further.…”

Section: Scalabilitymentioning

confidence: 99%

“…We use existing work by Hosangadi et al [Hosangadi et al 2006] on polynomial common subexpression elimination (CSE) to find factorizations that exploit the distributivity of multiplication over addition. We extend this work to take account of numerical relationships that would be opaque to the original Hosangadi et al algorithms.…”

Section: Introductionmentioning

confidence: 99%

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Optimized code generation for finite element local assembly using symbolic manipulation

Russell

2013

ACM Trans. Math. Softw.

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Automated code generators for finite element local assembly have facilitated exploration of alternative implementation strategies within generated code. However, even for a theoretical performance indicator such as operation count, an optimal strategy for local assembly is unknown. We explore a code generation strategy based on symbolic integration and polynomial common sub-expression elimination (CSE). We present our implementation of a local assembly code generator using these techniques. We systematically evaluate the approach, measuring operation count, execution time and numerical error using a benchmark suite of synthetic variational forms, comparing against the FEniCS Form Compiler (FFC). Our benchmark forms span complexities chosen to expose the performance characteristics of different code generation approaches. We show that it is possible with additional computational cost, to consistently achieve much of, and sometimes substantially exceed, the performance of alternative approaches without compromising precision. Although the approach of using symbolic integration and CSE for optimizing local assembly is not new, we distinguish our work through our strategies for maintaining numerical precision and detecting common sub-expressions. We discuss the benefits of the symbolic approach for inferring numerical relationships, and analyze the relationship to other proposed techniques which also have greater computational complexity than those of FFC.

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Section: Polynomial Factorisation and Common Sub-expression Eliminationmentioning

confidence: 99%

Section: The Following Definitionsmentioning

confidence: 99%

Section: The Following Definitionsmentioning

confidence: 99%

Section: Scalabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations