Schönhage-Strassen Algorithm
An integer multiplication algorithm based on the fast Fourier transform, proposed by Schönhage and Strassen in 1971. It reduces complexity to O(n log n log log n) and remained one of the fastest asymptotically multiplication algorithms for a long period.
Timeline (last 90 days)
The Schönhage-Strassen algorithm transforms integer multiplication into polynomial multiplication and performs computation over a ring using the FFT.
The Schönhage-Strassen algorithm is one of the core algorithms for handling multiplication of very large integers in many high-precision computation libraries (such as GMP).
Toom-Cook and the FFT-based Schönhage-Strassen algorithm further approach n log n.
In 1971, Schönhage and Strassen introduced the fast Fourier transform (FFT), pushing the complexity of integer multiplication down to O(n log n log log n).
Shor算法将整数分解的复杂度从经典的亚指数级降至多项式级O((log N)³)
All Facts (5)
The Schönhage-Strassen algorithm transforms integer multiplication into polynomial multiplication and performs computation over a ring using the FFT.
50%UnverifiedThe Schönhage-Strassen algorithm is one of the core algorithms for handling multiplication of very large integers in many high-precision computation libraries (such as GMP).
50%UnverifiedToom-Cook and the FFT-based Schönhage-Strassen algorithm further approach n log n.
50%UnverifiedIn 1971, Schönhage and Strassen introduced the fast Fourier transform (FFT), pushing the complexity of integer multiplication down to O(n log n log log n).
50%UnverifiedShor算法将整数分解的复杂度从经典的亚指数级降至多项式级O((log N)³)
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