Toom–Cook multiplication

The Toom - Cook algorithm is an efficient algorithm for multiplication of two integers, the divide and rule works on the principle. It was first described by Andrei Toom, later improved by Cook and published in his doctoral thesis.

It exists in two versions. The variant with a fixed pitch has a term of complexity, which is a fixed constant that depends only on the pitch, but not from the input length. The variant with variable pitch has runtime complexity.

The algorithm is a generalization of the Karatsuba algorithm and significantly faster than the naive algorithm, the school method (or the Russian peasant multiplication in the binary system ), has the runtime complexity. However, for sufficiently large numbers it is slower than the Schönhage -Strassen algorithm is its running time complexity and is considered from the perspective of complexity theory as the fastest, practically applied, the algorithm for multiplication of integers.

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