Hello,


USL for Delphi and FreePascal was updated to version 2.5

Now you can draw a beautiful graph of the USL law

Here is how:

I have included also usl_graph.exe and its source code,
us_graph.exe will draw a graph of the predicted scalability
of the USL law, please type at the commmand prompt:

usl_graph data.csv -g 5 449

You have to give two parameters to the -g option, this will
draw a graph with a step=d(x)=5 between two successive
data points , and it will draw a graph up to the peak number
that is x=449

You can save after that your graph to the clipboard and
open the paint program on windows and save it after that.

You will find the Delphi XE source code of the usl_graph.exe
on the source directory of the zipfile for the Delphi XE versions.

You can download my USL programs from:

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


Author: Amine Moulay Ramdane.

Email: aminer@videotron.ca


Description:

This program analyzes system performance data with the Universal
Scalability Law, and it compiles with Delphi XE versions and
FreePascal.

You have to supply the performance data as a csv file format,
please take a look at the supplied csv file called "data.csv",
the first line of the names of the colomuns of the csv file must
be commented by "#" character, the names of the columns are
mandatory.

Just compile the usl.pas program and run it by executing it
on the command prompt like this: usl data.csv

The Universal Scalability Law (USL) was developed by Dr. Neil J.
Gunther. It can be used to analyze system performance data in order to
learn more about the scalability limitations of the system.

Details are presented in the book *Guerrilla Capacity Planning*.

Authors of Universal Scalability Law website:

http://www.perfdynamics.com/

Please take a look at the source code in the zip file:

When you compile the usl.pas , please type this at
the command prompt:

usl data.csv

Here is the output of my program:

Peak number is: 449.188
Predicted scalability peak is: 18.434
Coefficient of determination R-squared is: 0.995

The peak number is the peak number of cores (look inside the csv file)
that will give the Predicted scalability peak that is: 18.434X

I have included also usl_graph.exe and its source code,
us_graph.exe will draw a graph of the predicted scalability
of the USL law, please type at the commmand prompt:

usl_graph data.csv -g 5 449

You have to give two parameters to the -g option, this will draw a graph
with a step=d(x)=5 between two successive data points , and it will draw
a graph up to the peak number that is x=449

You can save after that your graph to the clipboard and open the
paint program on windows and save it after that.

I have used a polynomial regression and i have done other approximations
to find the predicted scalability peak when the derivative must equal an approximation of 0 and this when the USL coefficient beta equal 0. This
is all about mathematics.

You have two options:

You can type at the command prompt: usl data.csv -p 20

the -p option will give you the scalability for the data point 20

and you can type at the command prompt: usl data.csv -d 0.2 10

the -d option will give you the derivative of the USL equation at delta(y)/delta(x)=0.2 (it must be between 0 and 1) with a step
delta(x)=10 that will output a good approximation of a number and a
derivative to better optimize the criterion of the cost for a
better QoS.

I will a little bit explain my USL program...

If you have took a look at this link:

https://cran.r-project.org/web/packages/usl/vignettes/usl.pdf

You will notice that the performance data for the raytracer in the
link above is the same as the performance data inside the data.csv
file inside my zip file of my USL software..

And as you have noticed in the link above the peak scalability
number is at: 449 processors.

So if you run my program against this same performance data
like this at the command prompt:

usl data.csv

So the output is of my program is:

--
Peak number is: 449.188
Predicted scalability peak is: 18.434
Coefficient of determination R-squared is: 0.995
--

So as you have noticed that the peak number that
is the peak number of processors is: 449.188
this is the same result as the link above.

So my program is working correctly.

But this is not the end of the story..

You have to optimize the criterion of the cost for a better QoS,
and for this i have supplied you with a second option called -d that
you have to run for that, so you have to type at the command
prompt:

usl data.csv -d 0.3 0.1


the 0.3 is the slope of the secant with a step 0.1, so since the step
is 0.1 so this will approximate a derivative of the USL equation that
equal 0.3, so here is the output of my program when you run
it with -d 0.3 0.1:

--
Peak number is: 449.188
Predicted scalability peak is: 18.434
Coefficient of determination R-squared is: 0.995
The derivative of the USL equation at delta(y)/delta(x)=0.300 with a
step delta(x)=0.100, gives a good approximation of a number and a
derivative delta(y)/delta (x) of: 16.600 and 0.300
--

So as you have noticed that a good approximation for the
derivative of the USL equation will arrive at the 16.600 cores
and this gives also a derivative of the secant that approximate the
derivative of the USL equation.

So to optimize more the criterion of the cost for a better QoS,
you have to choose a good delta(y)/delta(x) to optimize the criterion
of the cost of your system and you have to balance better between
the performance and the cost.

I have tested more my USL for Delphi and FreePascal and it is working perfectly. But to make it work best with multicores, you have to choose
the first column of the number of cores of the csv to: 1,2,4,8,
16 without going up to 32 and it will work ok, don't choose 1,2,3,4,5
because this will not be a good approximation and this will cause problems.

How can you be sure that my USL program for Delphi and FreePascal works correctly ?

Please take a look at this link:

https://cran.r-project.org/web/packages/usl/vignettes/usl.pdf

Notice the raytracer performance data, when they have analysed it, it
gives a peak scalability at: 449

So try to run my program inside the zip against the the same raytracer performance data that you will find inside the data.csv file inside the
zip, and this will give the same peak scalability at: 449.

So as you have noticed, my program is working for this performance data
of the raytracer, so i think that you can be confident with my program.

I have included a 32 bit windows executable called usl.exe inside the
zip, please read the readme file to know how to use it, it is a very
powerful tool.

- Platform: Win32 ,Win64,Linux,OSX


Thank you,
Amine Moulay Ramdane.

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