Multiplication

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Problem Description

Multiplication is one of the four elementary mathematical operations of arithmetic; with the others being addition; subtraction and division.

Bounds Chart

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Step Chart

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Improvement Table

Complexity Classes Algorithm Paper Links Lower Bounds Paper Links
Exp/Factorial
Polynomial > 3
Cubic
Quadratic Karatsuba Algorithm (1962)

Toom-3 (1969)

[ Long Multiplication (1940)]

Schönhage–Strassen algorithm (1971)

Furer's algorithm (2007)

De 2008 (2008)

Harvey; Hoeven; Lecerf (2015)

Covanov and Thomé (2015)

Covanov and Thomé (2016)

Harvey; Hoeven; Lecerf (2018)

nlogn Harvey; Hoeven (2019)
Linear
logn