Quote:
Originally Posted by neomacdev
Hi,
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 Strassenlike 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!
Thanks.
For reference:
Strassen's Algorithm
https://en.wikipedia.org/wiki/Strassen_algorithm
Karatsuba's Algorithm
https://en.wikipedia.org/wiki/Karatsuba_algorithm

I'm not sure about the paper to which you refer but have you looked at Toom3?
It reduces 9 multiplies to 5.
Wikipedia has a good article under the algorithm's full name: ToomCook.
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 Toom3 implementation also.