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On squaring and multiplying large integers

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1 Author(s)

Methods of squaring large integers are discussed. The obvious O(n 2) method turns out to be best for small numbers. The existing ≈ O(n1.585) method becomes better as the numbers get bigger. New methods that are ≈ O(n1.465) and ≈ O(n 2.404) are presented. All of these methods can be generalized to multiplication and turn out to be faster than a fast Fourier transform (FFT) multiplication for numbers that can be quite large (>3,000,000 b). Squaring seems to be fundamentally faster than multiplication, but it is shown that Tmult ⩽ 2Tsq + O(n)

Published in:

Computer Arithmetic, 1993. Proceedings., 11th Symposium on

Date of Conference:

29 Jun-2 Jul 1993