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x86 Paging Tutorial Multi-level paging scheme numerical translation example Updated 2025-07-16
Page directory given to process by the OS:
entry index entry address page table address present
----------- ---------------- ------------------ --------
0 CR3 + 0 * 4 0x10000 1
1 CR3 + 1 * 4 0
2 CR3 + 2 * 4 0x80000 1
3 CR3 + 3 * 4 0
...
2^10-1 CR3 + 2^10-1 * 4 0Page tables given to process by the OS at
PT1 = 0x10000000 (0x10000 * 4K):entry index entry address page address present
----------- ---------------- ------------ -------
0 PT1 + 0 * 4 0x00001 1
1 PT1 + 1 * 4 0
2 PT1 + 2 * 4 0x0000D 1
... ...
2^10-1 PT1 + 2^10-1 * 4 0x00005 1Page tables given to process by the OS at where
PT2 = 0x80000000 (0x80000 * 4K):entry index entry address page address present
----------- --------------- ------------ ------------
0 PT2 + 0 * 4 0x0000A 1
1 PT2 + 1 * 4 0x0000C 1
2 PT2 + 2 * 4 0
...
2^10-1 PT2 + 0x3FF * 4 0x00003 1PT1 and PT2: initial position of page table 1 and page table 2 for process 1 on RAM.With that setup, the following translations would happen:
linear 10 10 12 split physical
-------- -------------- ----------
00000001 000 000 001 00001001
00001001 000 001 001 page fault
003FF001 000 3FF 001 00005001
00400000 001 000 000 page fault
00800001 002 000 001 0000A001
00801004 002 001 004 0000C004
00802004 002 002 004 page fault
00B00001 003 000 000 page faultLet's translate the linear address
0x00801004 step by step:- In binary the linear address is:
0 0 8 0 1 0 0 4 0000 0000 1000 0000 0001 0000 0000 0100 - Grouping as
10 | 10 | 12gives:which gives:0000000010 0000000001 000000000100 0x2 0x1 0x4So the hardware looks for entry 2 of the page directory.page directory entry = 0x2 page table entry = 0x1 offset = 0x4 - The page directory table says that the page table is located at
0x80000 * 4K = 0x80000000. This is the first RAM access of the process. - Finally, the paging hardware adds the offset, and the final address is
0x0000C004.
The Intel manual gives a picture of this translation process in the image "Linear-Address Translation to a 4-KByte Page using 32-Bit Paging": Figure 1. "x86 page translation process"
x86 page translation process
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Ciro Santilli used it for the 2D version of his Ciro's 2D reinforcement learning games.
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Lawrence Krauss explains Gauge symmetry by Joe Rogan (2017)
Source. While most of this is useless as you would expect from the channel, it does give one key idea: you can change charge locally, but things somehow still work out.
And this has something to do with the general intuition of special relativity that only local measures make much sense, as evidenced by Einstein synchronization.
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x86 Paging Tutorial PAE and PSE page table schemes Updated 2025-07-16
If either PAE and PSE are active, different paging level schemes are used:
- no PAE and no PSE:
10 | 10 | 12 - no PAE and PSE:
10 | 22.22 is the offset within the 4Mb page, since 22 bits address 4Mb. - PAE and no PSE:
2 | 9 | 9 | 12The design reason why 9 is used twice instead of 10 is that now entries cannot fit anymore into 32 bits, which were all filled up by 20 address bits and 12 meaningful or reserved flag bits.The reason is that 20 bits are not enough anymore to represent the address of page tables: 24 bits are now needed because of the 4 extra wires added to the processor.Therefore, the designers decided to increase entry size to 64 bits, and to make them fit into a single page table it is necessary reduce the number of entries to 2^9 instead of 2^10. - PAE and PSE:
2 | 9 | 21
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Cirodance Updated 2025-07-16
During his teenage years, Ciro created an innovative new dance style combining elements of the various corporal practices that he studied a bit of across the years:
- Kung Fu/Taichi
- Brazilian Axé and Capoeira
- Breakdance
- Yoga
- Modern dance
Ciro later called this style Cirodance.
Ciro's legendary dance style was famous during his university years, when Ciro would go to parties and dance like made while mostly unsuccessfully trying to woo girls.
Ciro has always been critical of dancing conditions in University parties, where people would always be cramped up doing boring non-creative moves. Rather, Ciro would go to to the edges of the dance floor to have enough space for his amazing moves. There is a perhaps a parallel between such tendencies and Ciro's highly innovative personality. Also perhaps being cramped would have helped wooing said girls.
Ciro later quit dancing, to a large extent because it is too hard to find suitable dancing locations outside: Europe is too cold much of the year, also ground conditions have to be perfect, and no patience to book a dance room somewhere. Kid's playgrounds are ideal, but Ciro is afraid of dancing there because kids parent's would freak out.
Therefore, all evidence of Cirodance seems to have disappeared into the depths of the Internet. There used to be a notorious video on YouTube from around June 2010 entitled "A Piriguete da Poli !!" ("Poli's bitch" in Portuguese) with comment "Sem comentarios... foi a atraçao da cervejada" (No comments... was the main attraction of the beer party) dancing the Piriguete by MC Papo Brazilian Funk carioca song. But the video was removed at some point, they were likely afraid of getting sued, the URL was www.youtube.com/watch?v=T969azGjIeE as shown at www.facebook.com/cirosantilli/posts/133333123357495, but this was before Ciro noticed that every good thing on the web goes down and became an obsessive web archiver. But in any case, the title gives an idea of the amazing style of Ciro's furor poeticus Axé performance on that day. If the video owner ever reads this message, please please restore the video, or send Ciro a copy. TODO: which channel was it on? Knowing that Ciro would be able to try and contact them.
One legendary episode linked to Cirodance was when Ciro was living in Paris and jobless around 2014 (but not destitute as he leached from his girlfriend). Cirodance was his main physical activity at the time, and Place de la République, where the skateboarders hung out due to the perfect wide concrete floor and relatively close to Bastille where Ciro lived, was the perfect place for it. One cold dark winter evening, Ciro was practicing Cirodance with his headphones and crappy clothes (dirty public square floor, remember), when someone took him for a homeless person and offered him a bowl of soup! It must be said that Place de la République had many events of giving food to the poor. Ciro was a bit stunned, declined, and continued dancing. And so that was the day when a prestigious Polytechnicien was mistaken for a homeless person. And Ciro liked that.
As of 2021, Googling "cirodance" leads to www.youtube.com/watch?v=tyvv4ddL2so "Ciro Dance" in which comedian "Ciro Priello" (no Wikipedia page at the time) participates in a comedy show with a "silly dance" (TODO this likely has a name) described in the comments as:
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