Even faster integer multiplication

Abstract : 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 coefficient rings with ''fast'' roots of unity. Moreover, we establish the improved bound O(n log n 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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [49 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01022749
Contributor : Joris van der Hoeven <>
Submitted on : Wednesday, February 11, 2015 - 4:55:06 PM
Last modification on : Friday, November 15, 2019 - 2:08:04 PM
Long-term archiving on: Saturday, September 12, 2015 - 11:01:17 AM

File

mul3.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01022749, version 2

Collections

Citation

David Harvey, Joris van der Hoeven, Grégoire Lecerf. Even faster integer multiplication. 2014. ⟨hal-01022749v2⟩

Share

Metrics

Record views

361

Files downloads

291