Hello........

I will make my proof more precise...

For bigger serial parts of the Amdahl's law my reasonning is correct and
here it is:

If the serial part of the Amdahl's law is bigger, you have more
chance probabilistically to get contention on the serial part
with fewer threads and fewer cores with the USL methodology,
and this contention will enable the nonlinear regression to
approximate more the predicted scalability, because this
mathematical fact will deviate the graph of the nonlinear
regression in a more right direction up to a farther predicted
scalability, so this enable the nonlinear regression to predict
scalability farther, so this reasonning will make the USL methodology to succeed on a more bigger serial parts of the Amdahl's law.

But for smaller serial parts of the Amdahl's law, i will make my
proof more precise by example..

On smaller serial parts of the Amdahl's law, let's imagine
the serial part is 1/8 the overall parallel program, so this
1/8 has a probability of happening empirically on the overall
number of parallel applications, and this 1/8 can cause contention
on fewer cores and fewer threads using the USL methodology, but this 1/8
is not the only one in the distribution of probability, because we have
other that are 1/9 and 1/10 and 1/11 that has a
probability to happen empirically... and my reasonning
by mathematical probability and by making a better approximation
will make us affirm that there is a higher chance to get a more smaller
serial parts than 1/8 , so this is all about mathematical probability,
and my reasonning with mathematical probability that i am making makes
the nonlinear regression of the USL methodology to succeed in predicting
much farther.

Hence from the above proof, the bigger parts of the Amdahl's law
that causes more contention with fewer threads an fewer cores using
the USL methodology and the much smaller parts of the Amdahl's law has a
much higher chance to happen than the rest, so since they have a higher
chance to happen that means mathematically that USL methodology is
successful in predicting scalability and that means that it is a really
a great tool.


I have included the 32 bit and 64 bit windows executables of my
programs inside the zip file to easy the job for you.

You can download my USL programs version 3.0 with the source code from:

https://sites.google.com/site/aminer68/universal-scalability-law-for-delphi-and-freepascal


Thank you,
Amine Moulay Ramdane.

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