FFT-Based Dense Polynomial Arithmetic on Multi-cores

We report efficient implementation techniques for FFT-based dense multivariate polynomial arithmetic over finite fields, targeting multi-cores. We have extended a preliminary study dedicated to polynomial multiplication and obtained a complete set of efficient parallel routines in Cilk++ for polynom...

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Published inHigh Performance Computing Systems and Applications pp. 378 - 399
Main Authors Moreno Maza, Marc, Xie, Yuzhen
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2010
SeriesLecture Notes in Computer Science
Subjects
Cilk
multi-core
parallel multi-dimensional FFT/TFT
parallel normal form
Parallel polynomial arithmetic
parallel polynomial multiplication
Online AccessGet full text
ISBN3642126588
9783642126581
ISSN0302-9743
1611-3349
DOI10.1007/978-3-642-12659-8_28

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Abstract We report efficient implementation techniques for FFT-based dense multivariate polynomial arithmetic over finite fields, targeting multi-cores. We have extended a preliminary study dedicated to polynomial multiplication and obtained a complete set of efficient parallel routines in Cilk++ for polynomial arithmetic such as normal form computation. Since bivariate multiplication applied to balanced data is a good kernel for these routines, we provide an in-depth study on the performance and the cut-off criteria of our different implementations for this operation. We also show that, not only optimized parallel multiplication can improve the performance of higher-level algorithms such as normal form computation but also this composition is necessary for parallel normal form computation to reach peak performance on a variety of problems that we have tested.
AbstractList We report efficient implementation techniques for FFT-based dense multivariate polynomial arithmetic over finite fields, targeting multi-cores. We have extended a preliminary study dedicated to polynomial multiplication and obtained a complete set of efficient parallel routines in Cilk++ for polynomial arithmetic such as normal form computation. Since bivariate multiplication applied to balanced data is a good kernel for these routines, we provide an in-depth study on the performance and the cut-off criteria of our different implementations for this operation. We also show that, not only optimized parallel multiplication can improve the performance of higher-level algorithms such as normal form computation but also this composition is necessary for parallel normal form computation to reach peak performance on a variety of problems that we have tested.
Author Moreno Maza, Marc
Xie, Yuzhen
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Mewhort, Douglas J. K.
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Slater, Gary W.
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Snippet We report efficient implementation techniques for FFT-based dense multivariate polynomial arithmetic over finite fields, targeting multi-cores. We have...
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StartPage 378
SubjectTerms Cilk
multi-core
parallel multi-dimensional FFT/TFT
parallel normal form
Parallel polynomial arithmetic
parallel polynomial multiplication
Title FFT-Based Dense Polynomial Arithmetic on Multi-cores
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