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Fast Parallel Multi-point Evaluation of Sparse Polynomials

Published: 23 July 2017 Publication History

Abstract

We present a parallel algorithm to evaluate a sparse polynomial in Zp[x0, ..., xn] into many bivariate images, based on the fast multi-point evaluation technique described by van der Hoeven and Lecerf [11]. We have implemented the fast parallel algorithm in Cilk C. We present benchmarks demonstrating good parallel speedup for multi-core computers.
Our algorithm was developed with a specific application in mind, namely, the sparse polynomial GCD algorithm of Hu and Monagan [6] which requires evaluations of this form. We present benchmarks showing a large speedup for the polynomial GCD problem.

References

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M. Ben-Or and P. Tiwari. A deterministic algorithm for sparse multivariate polynomial interpolation. In Proceedings of STOC '20, pages 301--309. ACM, 1988.
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E. Berlekamp. Factoring polynomials over large finite fields. Mathematics of Computation, 24(111):713--735, 1970.
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A. Bostan, G. Lecerf, and E. Schost. Tellegen's principle into practice. In Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, ISSAC '03, pages 37--44. ACM, 2003.
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J. Hu and M. Monagan. A fast parallel sparse polynomial gcd algorithm. In Proceedings of ISSAC '16, pages 271--278. ACM, 2016.
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E. Kaltofen, W. shin Lee, and A. Lobo. Early termination in ben-or/tiwari sparse interpolation and a hybrid of zippel's algorithm. In Proceedings of ISSAC 2000, pages 192--201. ACM Press, 2000.
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N. Moller and T. Granlund. Improved division by invariant integers. IEEE Transactions on Computers, 60(2):165--175, 2011.
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J. van der Hoeven. The truncated fourier transform and applications. In Proceedings of ISSAC '04, pages 290--296. ACM, 2004.
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J. van der Hoeven and G. Lecerf. On the bit-complexity of sparse polynomial and series multiplication. Journal of Symbolic Computation, 50:227--254, 2013.
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Cited By

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  • (2021)High‐performance SIMD modular arithmetic for polynomial evaluationConcurrency and Computation: Practice and Experience10.1002/cpe.627033:16Online publication date: 25-May-2021
  • (2020)A fast parallel sparse polynomial GCD algorithmJournal of Symbolic Computation10.1016/j.jsc.2020.06.001Online publication date: Jun-2020

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cover image ACM Other conferences
PASCO 2017: Proceedings of the International Workshop on Parallel Symbolic Computation
July 2017
91 pages
ISBN:9781450352888
DOI:10.1145/3115936
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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  • Heriot-Watt University: Heriot-Watt University

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Association for Computing Machinery

New York, NY, United States

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Published: 23 July 2017

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View all
  • (2021)High‐performance SIMD modular arithmetic for polynomial evaluationConcurrency and Computation: Practice and Experience10.1002/cpe.627033:16Online publication date: 25-May-2021
  • (2020)A fast parallel sparse polynomial GCD algorithmJournal of Symbolic Computation10.1016/j.jsc.2020.06.001Online publication date: Jun-2020

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