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Amdahl equation and scalability

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  Amdahl equation and scalability aminer <aminer@toto.net> - 2013-10-09 16:25 -0700
    Re: Amdahl equation and scalability Ben Bacarisse <ben.usenet@bsb.me.uk> - 2013-10-10 14:47 +0100

#3887 — Amdahl equation and scalability

Hello,

I have come to another interresting subject, the Amdahl 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 part is 0.1% and 
the parallel part is 0.9% and we have 4 cores, so the Amdahl equatoin
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 , 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 equation. But the Amdhal 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.



Thank you,
Amine Moulay Ramdane.

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#3897

aminer <aminer@toto.net> writes:

since you post too much stuff, I don't normally read your posts, but
Robert's reply made me take a look...

> I have come to another interresting subject, the Amdahl 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)

S and P are fractions.  If you write these as percentages you need to
remember to divide by 100.  Personally, I prefer to write (1-S) rather
than P since S+P must equal 1.

> So we have to be smart, so follow with me,  i have read on some
> documents something that look like this: if the Serial part is 0.1%
> and the parallel part is 0.9% and we have 4 cores, so the Amdahl
> equatoin
> will equal  to 1/ 0.1 + 0.225 = 3X , so this will scale to 3X,

You need parentheses there: 1/(0.1 + 0.225).

> 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 , 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 equation.

This is all wrong, though the numbers come out right.  Your use of % is
wrong and there are not four serial parts.  The serial part of the
programs takes 1 second.  On one core, the parallel part takes 9
seconds, so on 4 cores its takes (no less than) 2.25 seconds.  Thus the
(minimum) total time on four cores is 1 + 2.25 = 3.25 seconds.  The
speed-up is therefore 10/3.25.  I can't follow where you get 13 and 40
from, though there happen to be in the right ratio.

> But the Amdhal 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,

No these numbers are wrong.  What's more the Amdahl law already applies
to the "no contention" situation -- it give a maximum possible speed-up
where the processors can always be optimally used.

> 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.

I think you've got confused about it somewhere, because your numbers are
wrong.

-- 
Ben.

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