Mathemagix

Hoeven, Joris van der; Lecerf, Grégoire; Mourrain, Bernard; Trébuchet, Philippe; Berthomieu, Jérémy; Diatta, Daouda Niang; Mantzaflaris, Angelos

doi:10.1145/2110170.2110180

Cited by 16 publications

(13 citation statements)

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“…It would be interesting to know whether the new algorithms could be useful in practice. We have implemented an unoptimised version of the algorithm from section 8 in the Mathemagix system [29] and found our implementation to be an order of magnitude slower than the Gmp library [23]. There is certainly room for improvement, but we doubt that even a highly optimised implementation of the new algorithm will be competitive in the near future.…”

Section: O(log N)mentioning

confidence: 99%

Even faster integer multiplication

Harvey

Hoeven

Lecerf

2016

Journal of Complexity

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We give a new proof of Fürer's bound for the cost of multiplying n-bit integers in the bit complexity model. Unlike Fürer, our method does not require constructing special coecient rings with fast roots of unity. Moreover, we prove the more explicit bound O(n logn K log n ) with K = 8. We show that an optimised variant of Fürer's algorithm achieves only K = 16, suggesting that the new algorithm is faster than Fürer's by a factor of 2 log n . Assuming standard conjectures about the distribution of Mersenne primes, we give yet another algorithm that achieves K = 4.

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Section: O(log N)mentioning

confidence: 99%

Even faster integer multiplication

Harvey

Hoeven

Lecerf

2016

Journal of Complexity

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“…For these reasons, we have started the design of a new software system, Mathemagix [15,16], based on a compiled and strongly typed language, featuring signatures, dependent types, and overloading. Mathemagix is intended as a general purpose language, which supports both functional and imperative programming styles.…”

Section: Motivation Behind Mathemagixmentioning

confidence: 99%

Interfacing mathemagix with C++

Hoeven¹,

Lecerf²

2013

Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation

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“…It is also possible to mimic classical divide and conquer algorithms for right division, greatest common right divisors and least common left multiples, while using adjoints in order to perform the recursive operations on the appropriate side. Such algorithms were partially implemented inside Mathemagix [24] and we plan to analyze this technique in more details in a forthcoming paper.…”

Section: Introductionmentioning

confidence: 99%