Schönhage–Strassen algorithm - Wikipedia, the free encyclopedia
The Schönhage–Strassen algorithm is based on the Fast Fourier transform (FFT) method of integer multiplication . This figure demonstrates multiplying 1234 × 5678 = 7006652 using the simple FFT method. Number-theoretic transforms in the integers modulo 337 are used, selecting 85 as an 8th root of unity. Base 10 is used in place of base 2w for illustrative purposes. Schönhage–Strassen improves on this by using negacyclic convolutions. The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers . It was developed by Arnold Schönhage and Volker Strassen in 1971. [1] The run-time bit complexity is, in Big O notation , O(n log n log log n) for two n-digit numbers. The algorithm uses recursive Fast Fourier transforms in rings with 22n + 1 elements, a specific type of number theoretic transform . The Schönhage–Strassen algorithm was the asymptotically fastest multiplication method known from 1971 until 2007, when a new method, Fürer's algorithm ,Read full article from Schönhage–Strassen algorithm - Wikipedia, the free encyclopedia
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