کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4608520 | 1631466 | 2016 | 30 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Even faster integer multiplication
ترجمه فارسی عنوان
حتی ضرب عدد صحیح سریعتر
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
We give a new algorithm for the multiplication of nn-bit integers in the bit complexity model, which is asymptotically faster than all previously known algorithms. More precisely, we prove that two nn-bit integers can be multiplied in time O(nlognKlog∗n), where K=8K=8 and log∗n=min{k∈N:log…k×logn⩽1}. Assuming standard conjectures about the distribution of Mersenne primes, we give yet another algorithm that achieves K=4K=4. The fastest previously known algorithm was due to Fürer, who proved the existence of a complexity bound of the above form for some finite KK. We show that an optimised variant of Fürer’s algorithm achieves only K=16K=16, suggesting that our new algorithm is faster than Fürer’s by a factor of 2log∗n2log∗n.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 36, October 2016, Pages 1–30
Journal: Journal of Complexity - Volume 36, October 2016, Pages 1–30
نویسندگان
David Harvey, Joris van der Hoeven, Grégoire Lecerf,