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More on squaring and multiplying large integers

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1 Author(s)
Zuras, D. ; Hewlett-Packard Co., Cupertino, CA, USA

Methods of squaring and multiplying large integers are discussed. The obvious O(n2) methods turn out to be best for small numbers. Existing O(nlog 3log/ 2)≈O(n1.585) methods become better as the numbers get bigger. New methods that are O(log5log/ 3 )≈0(n1.465), O(nlog 7log/ 4)≈O(n1.404), and O(nlog 9log/ 5)≈O(n1.365) 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 Tmultiply⩽2Tsquare+O(n)

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Computers, IEEE Transactions on  (Volume:43 ,  Issue: 8 )