1 research outputs found
Even faster integer multiplication
We give a new proof of F\"urer's bound for the cost of multiplying n-bit
integers in the bit complexity model. Unlike F\"urer, our method does not
require constructing special coefficient rings with "fast" roots of unity.
Moreover, we prove the more explicit bound O(n log n K^(log^* n))$ with K = 8.
We show that an optimised variant of F\"urer's algorithm achieves only K = 16,
suggesting that the new algorithm is faster than F\"urer'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