Comments on: Computer Algorithms: Karatsuba Fast Multiplication

By: Abelardo

Abelardo — Mon, 18 Sep 2017 11:18:35 +0000

Hello world,

Interesting article!

You mentioned:
“Finally xy will become:

xy = a * B^2m + b * B^m + c”

so, B² is a another way to multiply terms => B * B (yes, of course: B*B can be replaced by ‘B + B …’ ‘B’ times). Then, he didn’t get to avoid the 4th multiplication!!!???

By other hand, you can replace ‘m ^ n’ in a function which implements a sum:
1st step) It represents like a multiplication: m * m * m…. (n times)
and finally
2nd step) …like a sum (m * m) = m + m + … (several times).

Example:
2³ => 2 * 2 * 2 = (2 *2) * 2 = (4) * 2 = (2 + 2) + (2 + 2) = 8
3² => 3 * 3 = (3 + 3) + 3 = (6) + 3 = 9
4⁴ => 4 * 4 * 4 *4 = (4 + 4) + (4 + 4) + (4 + 4) + (4 + 4) + (4 + 4) …32 times!

Should many sum operations cause a problem to the cpu???

Nice blog!!!!

Best regards,
Abelardo

By: Shaikhul

Shaikhul — Tue, 11 Apr 2017 04:14:43 +0000

Hi Thanks for the nice explanation, it works for equal size of X and Y but doesn’t for different size of X and Y, it would be great if you could update the example with different size of X and Y.

By: Foysal Mamun

Foysal Mamun — Sat, 18 Feb 2017 20:37:31 +0000

Great help for me. Clean explanation.
Thanks.

By: samreen

samreen — Mon, 28 Mar 2016 16:35:05 +0000

thanks for good work

By: Himanshu

Himanshu — Fri, 31 Oct 2014 08:02:27 +0000

Hi,

Thanks for the article, it is really well explained with great examples.
But I tried implementing in java based on your code for PHP but you are considering different length for X and Y variable while dividing into two parts.
It was not working for me with different size(xlen/2, ylen/2) of X and Y so I tried with the min value of (xlen/2, ylen/2), and then its working fine.
Could you please tell me why this is not working in case of your logic.

Thanks for the great article

By: Dakota

Dakota — Sat, 05 Apr 2014 20:30:21 +0000

What will be the no of single digits multiplications to compute the product of two 6 digits numbers?

By: Nezza

Nezza — Mon, 10 Feb 2014 23:39:25 +0000

Hi there, this is very simple and easy to understand, thank you and you have done a grate job.

By: Niko

Niko — Fri, 24 May 2013 10:12:07 +0000

Hey that’s a very good article which you wrote there.
Thanks a lot.
I habe only a question, to say it better, a problem executing your code on PHP.
I dont’t get the correct result and i can not figure it out why. First of i got a fatal error because the function “sum()” does not exists. I implemented it but i dont know how exactly, becuase the parameters which are loaded in the sum() function are arrays.
If i got this right, we have to sum alla array-values and the the 2 sums again, and return it.
I hope this is still reading someone and could help me.

Thank you.

By: Priyanka Kumari

Priyanka Kumari — Thu, 09 May 2013 07:10:29 +0000

very neatly made us understand the algorithm…. gud wrk really helpful!!!

By: Stoimen

Stoimen — Mon, 11 Feb 2013 09:08:56 +0000

Of course, you can use the associative rule.