
This Guy Just Found a Faster Way to Multiply - ToFab123
https://www.popularmechanics.com/science/a29514208/faster-way-multiply/
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rurban
No he didn't, he just proved the wellknown and widely implemented
Schoenhage–Strassen conjecture from 1971 to be correct. Which was O(n log log
n), now implemented for O(n log n).

Schoenhage–Strassen is used for multiplying large numbers with >30.000 digits.
Below Karatsuba is used, and for >trillion digits Fuerer could be used. What
he did was to improve Fuerer's method from 2007, nobody is using yet.

[https://en.wikipedia.org/wiki/F%C3%BCrer%27s_algorithm](https://en.wikipedia.org/wiki/F%C3%BCrer%27s_algorithm)

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dwrodri
From my understanding, this won't have any implications on the way ALUs are
designed, correct? I was taught that Russian Peasant multiplication[1] was the
most straightforward method for implementing multiplication efficiently on
hardware. I would have to imagine that performing a Fast Fourier Transform
(FFT from the paper) would add significant overhead. Can anyone more familiar
with ALU design confirm or deny this?

[1] =
[http://mathforum.org/dr.math/faq/faq.peasant.html](http://mathforum.org/dr.math/faq/faq.peasant.html)

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hinkley
Is my math off or is RP already nlogn?

Edit: I see my error. N is number of digits, not size of number. By our usual
definition of n, table multiplication is log10(n)², which is much smaller.

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acqq
The paper:

[https://hal.archives-ouvertes.fr/hal-02070778/document](https://hal.archives-
ouvertes.fr/hal-02070778/document)

