# Amdahl equation and scalability

## Amdahl equation and scalability

Hello,

I have come to another interresting subject, the Amdahl's equation
that is equal to 1/(S+P/N)
(S:the percentage of the serial part,
P: percentage of the parallel part
N: the number of cores)

So we have to be smart, so follow with me,  i have read on some documents something that look like this: if the Serial partis 0.1% and the parallel part is 0.9% and we have 4 cores, so the Amdahl equation will equal  to 1/ 0.1 + 0.225 = 3X , so this will scale to 3X, but i don't agree with this , cause i think this Amdahl equation do not give a correct picture,so imagine that the serial part take 1 second and
the parallel part 9 seconds, that means S= 0.1% and P=0.9%,so with 4 cores you will say that this will run four P parts in 9 seconds
and four S parts in 4 seconds this will equal 13 seconds, but the serial part will run in 4*10 seconds , so the scalability will equal 40 seconds divide
by 13 seconds so this will scale to 3X, this is exactly what i have found with the Amdahl's equation. But the Amdahl's equation is not
so precise and it doesn't give a correct picture, cause i think the Amdhal equation is for only the ideal contention scenario as
i have just explain to you , but in a none contention scenario you will for example run four S parts in 1 seconds and four P parts in 9 seconds this will give a scalability equal to 40 seconds divide by 10 so this will scale to 4X in a none contention scenario, hence if you have less contention it will scale better than 3X , so this is why i say that the Amdahl equation doesn't give you a correct picture, and more than
that if in pratice the serial part is small and there is more randomness in the parallel part, you will have less contention i think, so the example that i just gave you will scale to much better than 3X , so hope you have undertood this important ideas that i am giving you.

"Amdahl's law, also known as Amdahl's argument,[1] is used to find the maximum expected improvement to an overall system"

http://en.wikipedia.org/wiki/Amdahl%27s_law

I think that's false, it's not the "maximum expected improvement to an overall system",  and i have explained to you why in my previous post , what i have explained is that the Amdahl equation gives you the scalability that you will have in an IDEAL CONTENTION SCENARIO , but if you have less contention it will scale much better, and in a none contention scenario it will have a perfect scalability,so  i have
proved to you and explainaed to you in my previous post that the Amdahl equation doesn't
give a correct picture. Hope you have understood my arguments and my ideas against  Amdahl's equation.

You will find my parallel libraries in the following website:

ttp://pages.videotron.com/aminer/

Thank you,
Amine Moulay Ramdane.

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