Hello,

More of my philosophy about my scalable algorithms of my Parallel C++ Conjugate Gradient Linear System Solver Library that scales very well and more of my thoughts..

I am a white arab from Morocco, and i think i am smart since i have also
invented many scalable algorithms and algorithms..

I think i am highly smart since I have passed two certified IQ tests and i have scored above 115 IQ, and I have just written the following:
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More of my philosophy about the new Zen 4 AMD Ryzen™ 9 7950X and more of my thoughts..

So i have just looked at the new Zen 4 AMD Ryzen™ 9 7950X CPU, and i invite you to look at it here:

https://www.amd.com/en/products/cpu/amd-ryzen-9-7950x

But notice carefully that the problem is with the number of supported memory channels, since it just support two memory channels, so it is not good, since for example my following Open source software project of Parallel C++ Conjugate Gradient Linear System Solver Library that scales very well is scaling around 8X on my 16 cores Intel Xeon with 2 NUMA nodes and with 8 memory channels, but it will not scale correctly on the
new Zen 4 AMD Ryzen™ 9 7950X CPU with just 2 memory channels since it is also memory-bound, and here is my Powerful Open source software project of Parallel C++ Conjugate Gradient Linear System Solver Library that scales very well and i invite you to take carefully a look at it:

https://sites.google.com/site/scalable68/scalable-parallel-c-conjugate-gradient-linear-system-solver-library

So i advice you to buy an an AMD Epyc CPU or an Intel Xeon CPU that supports 8 memory channels.

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And of course you can use the next Twelve DDR5 Memory Channels for Zen 4 AMD EPYC CPUs so that to scalable more my above algorithm, and read about it here:

https://www.tomshardware.com/news/amd-confirms-12-ddr5-memory-channels-on-genoa

And here is the simulation program that uses the probabilistic mechanism that i have talked about and that prove to you that my algorithm of my Parallel C++ Conjugate Gradient Linear System Solver Library is scalable:

If you look at my scalable parallel algorithm, it is dividing the each array of the matrix by 250 elements, and if you look carefully i am using two functions that consumes the greater part of all the CPU, it is the atsub() and asub(), and inside those functions i am using a probabilistic mechanism so that to render my algorithm scalable on NUMA architecture , and it also make it scale on the memory channels, what i am doing is scrambling the array parts using a probabilistic function and what i have noticed that this probabilistic mechanism is very efficient, to prove to you what i am saying , please look at the following simulation that i have done using a variable that contains the number of NUMA nodes, and what i have noticed that my simulation is giving almost a perfect scalability on NUMA architecture, for example let us give to the "NUMA_nodes" variable a value of 4, and to our array a value of 250, the simulation bellow will give a number of contention points of a quarter of the array, so if i am using 16 cores , in the worst case it will scale 4X throughput on NUMA architecture, because since i am using an array of 250 and there is a quarter of the array of contention points , so from the Amdahl's law this will give a scalability of almost 4X throughput on four NUMA nodes, and this will give almost a perfect scalability on more and more NUMA nodes, so my parallel algorithm is scalable on NUMA architecture and it also scale well on the memory channels,

Here is the simulation that i have done, please run it and you will notice yourself that my parallel algorithm is scalable on NUMA architecture.

Here it is:

---
program test;

uses math;

var tab,tab1,tab2,tab3:array of integer;
a,n1,k,i,n2,tmp,j,numa_nodes:integer;
begin

a:=250;
Numa_nodes:=4;

setlength(tab2,a);

for i:=0 to a-1
do
begin

tab2:=i mod numa_nodes;

end;

setlength(tab,a);

randomize;

for k:=0 to a-1
do tab:=k;

n2:=a-1;

for k:=0 to a-1
do
begin
n1:=random(n2);
tmp:=tab;
tab:=tab[n1];
tab[n1]:=tmp;
end;

setlength(tab1,a);

randomize;

for k:=0 to a-1
do tab1:=k;

n2:=a-1;

for k:=0 to a-1
do
begin
n1:=random(n2);
tmp:=tab1;
tab1:=tab1[n1];
tab1[n1]:=tmp;
end;

for i:=0 to a-1
do
if tab2[tab]=tab2[tab1] then
begin
inc(j);
writeln('A contention at: ',i);

end;

writeln('Number of contention points: ',j);
setlength(tab,0);
setlength(tab1,0);
setlength(tab2,0);
end.
---

And i invite you to read my thoughts about technology here:

https://groups.google.com/g/soc.culture.usa/c/N_UxX3OECX4

More of my philosophy about the problem with capacity planning of a website and more of my thoughts..

I think i am highly smart since I have passed two certified IQ tests and i have scored above 115 IQ, and i have just invented a new methodology
that simplifies a lot capacity planning of a website that can be of a
three-tier architecture with the web servers and with the applications servers and with the database servers, but i have to explain more so that you understand the big problem with capacity planning of a website, so when you want to for example to use web testing, the problem is
how to choose for example the correct distribution of the read and write and delete transactions on the database of a website ? so if it is not
realistic you can go beyond the knee of the curve and get a not acceptable waiting time, and the Mean value analysis (MVA) algorithm has
the same problem, so how to solve the problem ? so as you are noticing
it is why i have come with my new methodology that uses mathematics that
solves the problem. And read my previous thoughts:

More of my philosophy about website capacity planning and about Quality of service and more of my thoughts..

I think i am highly smart since I have passed two certified IQ tests and i have scored above 115 IQ, so i think that you have to lower to a certain level the QoS (quality of service) of a website, since you have to fix the limit of the number of connections that we allow to the website so that to not go beyond the knee of the curve, and of course i will soon show you my mathematical calculations of my new methodology of how to do capacity planning of a website, and of course
you have to know that that we have to do capacity planning using
mathematics so that to know the average waiting time etc. and this
permits us to calculate the number of connections that we allow to the website.

More of my philosophy about the Mean value analysis (MVA) algorithm and more of my thoughts..

I think i am highly smart since I have passed two certified IQ tests and i have scored above 115 IQ, and i have just read the following paper
about the Mean value analysis (MVA) algorithm, and i invite you to read it carefully:

https://www.cs.ucr.edu/~mart/204/MVA.pdf

But i say that i am understanding easily the above paper of Mean value analysis (MVA) algorithm, but i say that the above paper doesn't say that since you have to empirically collect the visit ratio and and the average demand of each class, so it is not so practical, since i say that you can and you have for example to calculate the "tendency" by also for example rendering the not memoryless service of for example the database to a memoryless service, but don't worry since i will soon make you understand my powerful methodology with all the mathematical calculations that easy for you the job and that makes it much more practical.

More of my philosophy about formal methods and about Leslie Lamport and more of my thoughts..

I think i am highly smart since I have passed two certified IQ tests and i have scored "above" 115 IQ, and I have just looked at the following video about the man who revolutionized computer science with math, and i invite you to look at it:

https://www.youtube.com/watch?v=rkZzg7Vowao

So i say that in mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. And Leslie Lamport the known scientist is saying in the above video the following: "An algorithm without a proof is conjecture, and if you are proving things, that means using mathematics.", so then i think that Leslie Lamport the known scientist is not thinking correctly by saying so, since i think that you can also prove an algorithm by highering much more the probability of the success of the proof without using mathematics to prove the algorithm, and i say that a proof has not to be just a conclusion as a boolean logic of true or false, since i think that a proof can be a conclusion in fuzzy logic and by logical analogy it looks like how race detectors in the very agressive mode don't detect all the data races, so then they miss a really small number of real races , so it is like a very high probability of really detecting real races, so read my below thoughts about it so that yo understand my views. And i think that the second mistake of Leslie Lamport the known scientist is that he is wanting us to use formal methods, but read the following interesting article below about why don't people use formal methods:

And I invite you to read the following new article of the known computer expert in the above video called Leslie Lamport , and that says programmers need to use math by using formal methods, and how Lamport discuss some of his work, such as the TLA+ specification language (developed by Lamport over the past few decades, the TLA+ [Temporal Logic of Actions] specification language allows engineers to describe objectives of a program in a precise and mathematical way), and also cited some of the reasons why he gives a prominent place to mathematics in programming.