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More on Squaring and Multiplying Large Integers
August 1994 (vol. 43 no. 8)
pp. 899-908

Methods of squaring and multiplying large integers are discussed. The obvious O(n/sup 2/) methods turn out to be best for small numbers. Existing O(n/sup log/ /sup 3/log/ /sup 2/)/spl ap/O(n/sup 1.585/) methods become better as the numbers get bigger. New methods that are O(/sup log5/log/ /sup 3/)/spl ap/0(n/sup 1.465/), O(n/sup log/ /sup 7/log/ /sup 4/)/spl ap/O(n/sup 1.404/), and O(n/sup log/ /sup 9/log/ /sup 5/)/spl ap/O(n/sup 1.365/) presented. In actual experiments, all of these methods turn out to be faster than FFT multipliers for numbers that can be quite large (<37,000,000 bits). Squaring seems to be fundamentally faster than multiplying but it is shown that T/sub multiplyspl les/2T/sub square/+O(n).

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Index Terms:
digital arithmetic; multiplying circuits; data handling; squaring; multiplying; large integers; FFT multipliers.
D. Zuras, "More on Squaring and Multiplying Large Integers," IEEE Transactions on Computers, vol. 43, no. 8, pp. 899-908, Aug. 1994, doi:10.1109/12.295852
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