Interfacing mathemagix with C++

Larrieu

Mathematical Aspects of Computer and Information Sciences

2017

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The efficient multiplication of polynomials over the finite field 2 is a fundamental problem in computer science with several applications to geometric error correcting codes and algebraic crypto-systems. In this paper we report on a new algorithm that leads to a practical speed-up of about two over previously available implementations. Our current implementation assumes a modern AVX2 and CLMUL enabled processor.

Section: Implementation Detailsmentioning

confidence: 99%

Implementing Fast Carryless Multiplication

Larrieu

Mathematical Aspects of Computer and Information Sciences

2017

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“…Those for our polynomial products in F 2 k [x] are in polynomial_f2k_amd64_avx_clmul.mmx. Let us recall here that Mathemagix functions can also be easily exported to C++ [24].…”

Section: Timingsmentioning

confidence: 99%

Fast Polynomial Multiplication over F₂₆₀

Harvey

Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation

2016

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Can post-SchönhageStrassen multiplication algorithms be competitive in practice for large input sizes? So far, the GMP library still outperforms all implementations of the recent, asymptotically more ecient algorithms for integer multiplication by Fürer, DeKururSahaSaptharishi, and ourselves. In this paper, we show how central ideas of our recent asymptotically fast algorithms turn out to be of practical interest for multiplication of polynomials over nite fields of characteristic two. Our Mathemagix implementation is based on the automatic generation of assembly codelets. It outperforms existing implementations in large degree, especially for polynomial matrix multiplication over nite elds.

“…Our implementation is divided into C++ and Mathemagix libraries. Import/export mechanisms between these two languages are rather easy, as described in [7,8]. The C++ library Multimix contains several implementations of multivariate polynomials, including SLPs (type slp_polynomial defined in slp_polynomial.hpp), naive interpreted evaluation (slp_polynomial_naive.hpp), compilation into dynamic libraries loaded via dlopen (slp_polynomial_compiled.hpp), and fast JIT compilation.…”

Section: Software Overviewmentioning

confidence: 99%

Evaluating Straight-Line Programs over Balls

2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH)

2016

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Interval arithmetic achieves numerical reliability for a wide range of applications, at the price of a performance penalty. For applications to homotopy continuation, one key ingredient is the efficient and reliable evaluation of complex polynomials represented by straight-line programs. This is best achieved using ball arithmetic, a variant of interval arithmetic. In this article, we describe strategies for reducing the performance penalty of basic operations on balls. We also show how to bound the effect of rounding errors at the global level of evaluating a straight-line program. This allows us to introduce a new and faster "transient" variant of ball arithmetic.