This was the CPU architecure that saved AMD in the 2010's, see also: Video "How AMD went from nearly Bankrupt to Booming by Brandon Yen (2021)"
x86 Paging Tutorial Hardware implementation by 
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01Paging is implemented by the CPU hardware itself.
Paging could be implemented in software, but that would be too slow, because every single RAM memory access uses it!
Operating systems must setup and control paging by communicating to the CPU hardware. This is done mostly via:
- the CR3 register, which tells the CPU where the page table is in RAM memory
- writing the correct paging data structures to the RAM pointed to the CR3 register.Using RAM data structures is a common technique when lots of data must be transmitted to the CPU as it would cost too much to have such a large CPU register.The format of the configuration data structures is fixed by the hardware, but it is up to the OS to set up and manage those data structures on RAM correctly, and to tell the hardware where to find them (via
cr3).Then some heavy caching is done to ensure that the RAM access will be fast, in particular using the TLB.Another notable example of RAM data structure used by the CPU is the IDT which sets up interrupt handlers. - CR3 cannot be modified in ring 3. The OS runs in ring 0. See also:
- the page table structures are made invisible to the process using paging itself!
Processes can however make requests to the OS that cause the page tables to be modified, notably:
- stack size changes
brkandmmapcalls, see also: stackoverflow.com/questions/6988487/what-does-brk-system-call-do/31082353#31082353
The kernel then decides if the request will be granted or not in a controlled manner.
Physical address extension.
With 32 bits, only 4GB RAM can be addressed.
This started becoming a limitation for large servers, so Intel introduced the PAE mechanism to Pentium Pro.
Page table structure is also altered if PAE is on. The exact way in which it is altered depends on weather PSE is on or off.
x86 Paging Tutorial Memory management unit by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01Paging is done by the Memory Management Unit (MMU) part of the CPU.
It was later integrated into the CPU, but the term MMU still used.
As of 2022:
- www.ox.ac.uk/students/fees-funding/fees/rates gives study fees. Almost all courses are about 9k pounds / academic year. Courses take minimum 3 years, with an optional 4th year masters. The costs of masters can be higher however, though most aren't much.It is funny to note how Public Policy is comically priced at 45,890 for a course without laboratories, how can a country be so corrupt? :-) It was later brought to Ciro's attention that the reason is that those courses are not usually paid by individuals, but by their employers...Another eye popping one is Mathematical & Computational Finance MSc for £36,370.
- www.ox.ac.uk/students/fees-funding/living-costs gives living costs, an average 12k for the usual 9 month period
- there is the Crankstart scholarship: www.ox.ac.uk/admissions/undergraduate/student-life/help-with-the-cost/crankstart-scholarships which gives 5k/year to students whose families have less than 27k/year income, and values decrease from there to 60k/year income where they become zero.It is funny to note that the scholarship was previously named after a Welsh billionaire who studied there and donated and his wife, Michael Moritz and wife Harriet Heyman. It is actually the Welsh who are creating those scholarships for the English! It is so funny to see. His background is quite amazing, from historian to journalist to venture capitalist.It was later renamed Crankstart after the Crankstart Foundation, presumably to help gather funds from others, but it is just still led by Michael.It does appear that most/all of the natural sciences ones are reasonably priced, perhaps they are subsided.
The median household income at the time was 31k[ref]. Clearly, putting one child through university with that income would be basically impossible, you would pay 19 - 5 = 14k/year, almost half of your income. Two children would be impossible. Remember how each family needs to have two children minimum to perpetuate life?
- cherwell.org/2023/10/02/27000-for-a-library-card/ £27,000 for a library card? published on the Cherwell
Divisions of the University of Oxford by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01 University of California, Santa Barbara by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01 The derivative is the generator of the translation group by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01The way to think about this is:
- the translation group operates on the argument of a function
- the generator is an operator that operates on itself
So let's take the exponential map:and we notice that this is exactly the Taylor series of around the identity element of the translation group, which is 0! Therefore, if behaves nicely enough, within some radius of convergence around the origin we have for finite :
This example shows clearly how the exponential map applied to a (differential) operator can generate finite (non-infinitesimal) Translation!
Dropped in favor of SVG 2.
Organization developing superconducting quantum computer by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01Good shortcuts and user experience.
No waveform viewer: github.com/otsaloma/gaupol/issues/49 so unusable.
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