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Old 2019-07-30, 01:40   #2
tServo's Avatar
May 2009
near the Tannhäuser Gate

31E16 Posts

Originally Posted by neomacdev View Post

This question is not Mersenne prime related, nor prime related at all.

There is a series of optimized algorithms for Matrix Multiplication ala Strassen's Algorithm for performing 2x2 x 2x2 Matrix multiplication in only 7 scalar multiplications rather than the standard 8. And there is Karatsuba's algorithm for performing large integer multiplication which reduces the number of single digit multiplications from n^2 to n^1.58.

I vaguely recall I saw a reference to a Mathematics paper that, if I recall correctly, stated for every Strassen-like accelerated matrix multiplication algorithm there was a corresponding accelerated integer multiplication algorithm like Karatsuba. Is anyone framiliar with this paper? Can you provide a citation or link? I have tried searching, but must not be using the correct terms as I can't locate it. Or perhaps I've imagined the entire thing!


For reference:

Strassen's Algorithm

Karatsuba's Algorithm
I'm not sure about the paper to which you refer but have you looked at Toom-3?
It reduces 9 multiplies to 5.
Wikipedia has a good article under the algorithm's full name: Toom-Cook.
Also, check the link the article has to Marco Bodrato's web site. He has some good stuff.
The freely available big integer system call LibTomMath has a Toom-3 implementation also.
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