Hello,

More of my philosophy about matrix-matrix multiplication and about scalability and more of my thoughts..

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

I think that the time complexity of the Strassen algorithm for matrix-matrix multiplication is around O(N^2.8074), and the time complexity of the naive algorithm is O(N^3) , so it is not a significant difference, so i think i will soon implement the parallel Blocked matrix-matrix multiplication and i will implement it with a new algorithm that also uses intel AVX512 and that uses fused multiply-add and of course it will use the assembler instructions below of prefetching into caches so that to gain a 22% speed, so i think that overall it will have around the same speed as parallel BLAS, and i say that Pipelining greatly increases throughput in modern CPUs such as x86 CPUs, and another common pipelining scenario is the FMA or fused multiply-add, which is a fundamental part of the instruction set for some processors.. The basic load-operate-store sequence simply lengthens by one step to become load-multiply-add-store. The FMA is possible only if the hardware supports it, as it does in the case of the Intel Xeon Phi, for example, as well as in Skylake etc.

More of my philosophy about matrix-vector multiplication of large matrices and about scalability and more of my thoughts..

The matrix-vector multiplication of large matrices is completly limited by the memory bandwidth as i have just said it, read it below, so vector extensions like using SSE or AVX are usually not necessary for matrix-vector multiplication of large matrices. It is interesting that
matrix-matrix-multiplications don't have these kind of problems with memory bandwidth. Companies like Intel or AMD typically usually show benchmarks of matrix-matrix multiplications and they show how nice they scale on many more cores, but they never show matrix-vector multiplications, and notice that my Powerful Open source software project of Parallel C++ Conjugate Gradient Linear System Solver Library that scales very well is also memory-bound and the matrices for it are usually big, but my new algorithm of it is efficiently cache-aware and efficiently NUMA-aware, and i have implemented it for the dense and sparse matrices.

More of my philosophy about the efficient Matrix-Vector multiplication algorithm in MPI and about scalability and more of my thoughts..

Matrix-vector multiplication is an absolutely fundamental operation, with countless applications in computer science and scientific computing. Efficient algorithms for matrix-vector multiplication are of paramount importance, and notice that for matrix-vector multiplication, n^2 time is certainly required for an n × n dense matrix, but you have to be smart, since in MPI computing for also the supercomputer exascale systems, doesn't only take into account this n^2 time, since it has to also be efficiently be cache-aware, and it has to also have a good complexity for the how much memory is used by the parallel processes in MPI, since notice carefully with me that you have also to not send both a row of the matrix and the vector the the parallel processes of MPI, but you have to know how to reduce efficiently this complexity by for example dividing each row of the matrix and by dividing the vector and sending a part of the row of the matrix and a part of the vector to the parallel processes of MPI, and i think that in an efficient algorithm for Matrix-Vector multiplication, time for addition is dominated by the communication time, and of course that my implementation of my Powerful Open source software of Parallel C++ Conjugate Gradient Linear System Solver Library that scales very well is also smart, since it is efficiently cache-aware and efficiently NUMA-aware, and it implements both the dense and the sparse, and of course as i am showing below, it is scaling well on the memory channels, so it is scaling well in my 16 cores dual Xeon with 8 memory channels as i am showing below, and it will scale well on 16 sockets HPE NONSTOP X SYSTEMS or the 16 sockets HPE Integrity Superdome X with above 512 cores and with 64 memory channels, so i invite you to read carefully and to download my Open source software project of Parallel C++ Conjugate Gradient Linear System Solver Library that scales very well from my website here:

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

MPI will continue to be a viable programming model on exascale supercomputer systems, so i will soon implement many algorithms in MPI for Delphi and Freepascal and i will provide you with them, i am currently
implementing an efficient Matrix-Vector multiplication algorithm in MPI
and you have to know that an efficient Matrix-Vector multiplication algorithm is really important for scientific applications, and of course i will also soon implement many other interesting algorithms in MPI for Delphi and Freepascal and i will provide you with them, so stay tuned !
More of my philosophy about the memory bottleneck and about scalability
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 am also specialized in parallel computing, and i know that the large cache can reduce Amdahl’s Law bottleneck – main memory, but you have to understand what i am saying, since my Open source project below of my Powerful Open source software project of Parallel C++ Conjugate Gradient Linear System Solver Library that scales very well is also memory-bound and the matrices for it are usually big, and since also the sparse linear system solvers are ubiquitous in high performance computing (HPC) and often are the most computational intensive parts in scientific computing codes. A few of the many applications relying on sparse linear solvers include fusion energy simulation, space weather simulation, climate modeling, and environmental modeling, and finite element method, and large-scale reservoir simulations to enhance oil recovery by the oil and gas industry. So it is why i am speaking about the how many memory channels comes in the 16 sockets HPE NONSTOP X SYSTEMS or the 16 sockets HPE Integrity Superdome X, so as you notice that they can come with more than 512 cores and with 64 memory channels. Also i have just benchmarked my Scalable Varfiler and it is scaling above 7x on my 16 cores Dual Xeon processor, and it is scaling well since i have 8 memory channels, and i invite you to look at my powerful Scalable Varfiler carefully in the following web link:

https://sites.google.com/site/scalable68/scalable-parallel-varfiler

More of my philosophy about the how many memory channels in the 16 sockets HPE NONSTOP X SYSTEMS and more of my thoughts..

I think i was right by saying that the 16 sockets HPE NONSTOP X SYSTEMS or the 16 sockets HPE Integrity Superdome X have around 2 to 4 memory channels per socket on x86 with Intel Xeons, and it means that they have 32 or 64 memory channels.

You can read here the FAQ from Hewlett Packard Enterprise from USA so that to notice it:

https://bugzilla.redhat.com/show_bug.cgi?id=1346327

And it says the following:

"How many memory channels per socket for specific CPU?

Each of the 8 blades has 2 CPU sockets.
Each CPU socket has 2 memory channels each connecting to 2 memory controllers that contain 6 Dimms each."

So i think that it can also support 4 memory channels per CPU socket with Intel Xeons.

More of my philosophy about the highest availability with HPE NONSTOP X SYSTEMS from Hewlett Packard Enterprise from USA and more of my thoughts..

I have just talked, read it below, about the 16 sockets HPE Integrity Superdome X from Hewlett Packard Enterprise from USA, but so that
to be the highest "availability" on x86 architecture, i advice you to buy the
16 sockets HPE NONSTOP X SYSTEMS from Hewlett Packard Enterprise from USA, and read about it here:

https://www.hpe.com/hpe-external-resources/4aa4-2000-2999/enw/4aa4-2988?resourceTitle=Engineered+for+the+highest+availability+with+HPE+Integrity+NonStop+family+of+systems+brochure&download=true

And here is more of my thoughts about the history of HP NonStop on x86:

More of my philosophy about HP and about the Tandem team and more of my thoughts..

I invite you to read the following interesting article so that
to notice how HP was smart by also acquiring Tandem Computers, Inc.
with there "NonStop" systems and by learning from the Tandem team
that has also Extended HP NonStop to x86 Server Platform, you can read about it in my below writing and you can read about Tandem Computers here: https://en.wikipedia.org/wiki/Tandem_Computers , so notice that Tandem Computers, Inc. was the dominant manufacturer of fault-tolerant computer systems for ATM networks, banks, stock exchanges, telephone switching centers, and other similar commercial transaction processing applications requiring maximum uptime and zero data loss:

https://www.zdnet.com/article/tandem-returns-to-its-hp-roots/

More of my philosophy about HP "NonStop" to x86 Server Platform fault-tolerant computer systems and more..

Now HP to Extend HP NonStop to x86 Server Platform

HP announced in 2013 plans to extend its mission-critical HP NonStop technology to x86 server architecture, providing the 24/7 availability required in an always-on, globally connected world, and increasing customer choice.

Read the following to notice it:

https://www8.hp.com/us/en/hp-news/press-release.html?id=1519347#.YHSXT-hKiM8

And today HP provides HP NonStop to x86 Server Platform, and here is
an example, read here: