Dense Arithmetic over Finite Fields with the CUMODP Library

Sardar Anisul Haquen, Xin Li, Farnam Mansouri, Marc Moreno Maza, Wei Pan, Ning Xie
University of Western Ontario, Canada
4th International Congress on Mathematical Software (ICMS), Lecture Notes in Computer Science, volume 8592, pages 725-732, 2014


   title={Dense Arithmetic over Finite Fields with the CUMODP Library},

   author={Haque, Sardar Anisul and Li, Xin and Mansouri, Farnam and Maza, Marc Moreno and Pan, Wei and Xie, Ning},

   booktitle={Mathematical Software–ICMS 2014},





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CUMODP is a CUDA library for exact computations with dense polynomials over finite fields. A variety of operations like multiplication, division, computation of subresultants, multi-point evaluation, interpolation and many others are provided. These routines are primarily designed to offer GPU support to polynomial system solvers and a bivariate system solver is part of the library. Algorithms combine FFT-based and plain arithmetic, while the implementation strategy emphasizes reducing parallelism overheads and optimizing hardware usage.
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