Fast polynomial evaluation and composition

Guillaume Moroz 1
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : The library \emph{fast\_polynomial} for Sage compiles multivariate polynomials for subsequent fast evaluation. Several evaluation schemes are handled, such as Hörner, divide and conquer and new ones can be added easily. Notably, a new scheme is introduced that improves the classical divide and conquer scheme when the number of terms is not a pure power of two. Natively, the library handles polynomials over gmp big integers, boost intervals, python numeric types. And any type that supports addition and multiplication can extend the library thanks to the template design. Finally, the code is parallelized for the divide and conquer schemes, and memory allocation is localized and optimized for the different evaluation schemes. This extended abstract presents the concepts behind the \emph{fast\_polynomial} library. The sage package can be downloaded at \url{http://trac.sagemath.org/sage_trac/ticket/13358}.
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  • HAL Id : hal-00846961, version 3
  • ARXIV : 1307.5655

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Guillaume Moroz. Fast polynomial evaluation and composition. [Technical Report] RT-0453, Inria Nancy - Grand Est (Villers-lès-Nancy, France); INRIA. 2013. ⟨hal-00846961v3⟩

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