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  2. Karatsuba algorithm - Wikipedia

    en.wikipedia.org/wiki/Karatsuba_algorithm

    The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. [ 1 ] [ 2 ] [ 3 ] It is a divide-and-conquer algorithm that reduces the multiplication of two n -digit numbers to three multiplications of n /2-digit numbers and, by repeating this reduction, to at most n log 2 ⁡ 3 ...

  3. Multiplication algorithm - Wikipedia

    en.wikipedia.org/wiki/Multiplication_algorithm

    Karatsuba's algorithm was the first known algorithm for multiplication that is asymptotically faster than long multiplication, [15] and can thus be viewed as the starting point for the theory of fast multiplications.

  4. Schönhage–Strassen algorithm - Wikipedia

    en.wikipedia.org/wiki/Schönhage–Strassen...

    The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers, published by Arnold Schönhage and Volker Strassen in 1971. [1] It works by recursively applying fast Fourier transform (FFT) over the integers modulo 2 n + 1 {\displaystyle 2^{n}+1} .

  5. Trachtenberg system - Wikipedia

    en.wikipedia.org/wiki/Trachtenberg_system

    Some of the algorithms Trachtenberg developed are ones for general multiplication, division and addition. Also, the Trachtenberg system includes some specialised methods for multiplying small numbers between 5 and 13. The section on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.

  6. Montgomery modular multiplication - Wikipedia

    en.wikipedia.org/wiki/Montgomery_modular...

    Classical modular multiplication reduces the double-width product ab using division by N and keeping only the remainder. This division requires quotient digit estimation and correction. The Montgomery form, in contrast, depends on a constant R > N which is coprime to N, and the only division necessary in Montgomery multiplication is division by R.

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