منابع مشابه
Even faster integer multiplication
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 ...
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Let n > 1 and let u and v be integers in the interval 0 6 u, v < 2. We write M(n) for the cost of computing the full product of u and v, which is just the usual 2n-bit product uv. Unless otherwise specified, by ‘cost’ we mean the number of bit operations, under a model such as the multitape Turing machine [12]. In this paper we are interested in two types of truncated product. The low product o...
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For almost 35 years, Schönhage-Strassen’s algorithm has been the fastest algorithm known for multiplying integers, with a time complexity O(n · log n · log log n) for multiplying n-bit inputs. In 2007, Fürer proved that there exists K > 1 and an algorithm performing this operation in O(n · log n · Klog∗ ). Recent work showed that this complexity estimate can be made more precise with K = 8, and...
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Assuming a conjectural upper bound for the least prime in an arithmetic progression, we show that n-bit integers may be multiplied in O(n logn 4 ∗ n) bit operations.
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2016
ISSN: 0885-064X
DOI: 10.1016/j.jco.2016.03.001