When the process changes,
cr3 change to point to the page table of the new current process.A simple and naive solution would be to completely invalidate the TLB whenever the
cr3 changes.However, this is would not be very efficient, because it often happens that we switch back to process 1 before process 2 has completely used up the entire TLB cache entries.
The solution for this is to use so called "Address Space Identifiers" (ASID) as mentioned in sources such as:
Basically, the OS assigns a different ASID for each process, and then TLB entries are automatically also tagged with that ASID. This way when the process makes an access, the TLB can determine if a hit is actually for the current process, or if it is an old address coincidence with another process.
x86 Paging Tutorial Single level paging scheme visualization by 
Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16This is how the memory could look like in a single level paging scheme:
Links Data Physical address
+-----------------------+ 2^32 - 1
| |
. .
| |
+-----------------------+ page0 + 4k
| data of page 0 |
+---->+-----------------------+ page0
| | |
| . .
| | |
| +-----------------------+ pageN + 4k
| | data of page N |
| +->+-----------------------+ pageN
| | | |
| | . .
| | | |
| | +-----------------------+ CR3 + 2^20 * 4
| +--| entry[2^20-1] = pageN |
| +-----------------------+ CR3 + 2^20 - 1 * 4
| | |
| . many entires .
| | |
| +-----------------------+ CR3 + 2 * 4
| +--| entry[1] = page1 |
| | +-----------------------+ CR3 + 1 * 4
+-----| entry[0] = page0 |
| +-----------------------+ <--- CR3
| | |
| . .
| | |
| +-----------------------+ page1 + 4k
| | data of page 1 |
+->+-----------------------+ page1
| |
. .
| |
+-----------------------+ 0Notice that:
- the CR3 register points to the first entry of the page table
- the page table is just a large array with 2^20 page table entries
- each entry is 4 bytes big, so the array takes up 4 MiB
- each page table contains the physical address a page
- each page is a 4 KiB aligned 4 KiB chunk of memory that user processes may use
- we have 2^20 table entries. Since each page is 4 KiB == 2^12, this covers the whole 4 GiB (2^32) of 32-bit memory
The exact format of table entries is fixed by the hardware.
The page table is then an array of
struct.On this simplified example, the page table entries contain only two fields:so in this example the hardware designers could have chosen the size of the page table to b
bits function
----- -----------------------------------------
20 physical address of the start of the page
1 present flag21 instead of 32 as we've used so far.All real page table entries have other fields, notably fields to set pages to read-only for Copy-on-write. This will be explained elsewhere.
It would be impractical to align things at 21 bits since memory is addressable by bytes and not bits. Therefore, even in only 21 bits are needed in this case, hardware designers would probably choose 32 to make access faster, and just reserve bits the remaining bits for later usage. The actual value on x86 is 32 bits.
Here is a screenshot from the Intel manual image "Formats of CR3 and Paging-Structure Entries with 32-Bit Paging" showing the structure of a page table in all its glory: Figure 1. "x86 page entry format".
The fields are explained in the manual just after.
Addresses are now split as:
| directory (10 bits) | table (10 bits) | offset (12 bits) |Then:
- The top table is called a "directory of page tables".
cr3now points to the location on RAM of the page directory of the current process instead of page tables.Page directory entries are very similar to page table entries except that they point to the physical addresses of page tables instead of physical addresses of pages.Each directory entry also takes up 4 bytes, just like page entries, so that makes 4 KiB per process minimum.Page directory entries also contain a valid flag: if invalid, the OS does not allocate a page table for that entry, and saves memory.Each process has one and only one page directory associated to it (and pointed to bycr3), so it will contain at least2^10 = 1Kpage directory entries, much better than the minimum 1M entries required on a single-level scheme. - Second level entries are also called page tables like the single level scheme.Each page table has only
2^10 = 1Kpage table entries instead of2^20for the single paging scheme. - the offset is again not used for translation, it only gives the offset within a page
One reason for using 10 bits on the first two levels (and not, say,
12 | 8 | 12 ) is that each Page Table entry is 4 bytes long. Then the 2^10 entries of Page directories and Page Tables will fit nicely into 4Kb pages. This means that it faster and simpler to allocate and deallocate pages for that purpose.This is particularly important in SQL: Nested set model in SQL, as it is an efficient way to transverse trees there, since querying parents every time would require multiple disk accesses.
The ASCII art visualizations from stackoverflow.com/questions/192220/what-is-the-most-efficient-elegant-way-to-parse-a-flat-table-into-a-tree/194031#194031 are worth reproducing.
As the sets:
__________________________________________________________________________
| Root 1 |
| ________________________________ ________________________________ |
| | Child 1.1 | | Child 1.2 | |
| | ___________ ___________ | | ___________ ___________ | |
| | | C 1.1.1 | | C 1.1.2 | | | | C 1.2.1 | | C 1.2.2 | | |
1 2 3___________4 5___________6 7 8 9___________10 11__________12 13 14
| |________________________________| |________________________________| |
|__________________________________________________________________________|Consider the following nested set:
0, 8, root
1, 7, mathematics
2, 3, geometry
3, 6, calculus
4, 5, derivative
5, 6, integral
6, 7, algebra
7, 8, physicsThe minimalism, serverlessness/lack of temporary caches/lack of permission management, Hipp's religious obsession with efficiency, the use of their own pure Fossil version control[ref]. Wait, scrap that last one. Pure beauty!
Official Git mirror: github.com/sqlite/sqlite
Create a table
sqlite3 db.sqlite3 "
CREATE TABLE 'IntegerNames' (int0 INT, char0 CHAR(16));
INSERT INTO 'IntegerNames' (int0, char0) VALUES (2, 'two'), (3, 'three'), (5, 'five'), (7, 'seven');
"List tables:output:
sqlite3 db.sqlite3 '.tables'IntegerNamesShow schema of a table:outputs the query that would generate that table:
sqlite3 db.sqlite3 '.schema IntegerNames'CREATE TABLE IF NOT EXISTS 'IntegerNames' (int0 INT, char0 CHAR(16));Introduction to Spintronics by Aurélien Manchon (2020) spin-transfer torque section
. Source. Describes how how spin-transfer torque was used in magnetoresistive RAM
More comments at: Video "Introduction to Spintronics by Aurélien Manchon (2020)".
The Google Story suggests that this practice existed in academia, where it was brought from. But I can't find external references to it easily:
At Google, the preference is for working in small teams of three, with individual employees expected to allot 20 percent of their time to exploring whatever ideas interest them most. The notion of "20 percent time" is borrowed from the academic world, where professors are given one day a week to pursue private interests.
Answers suggest hat you basically pick a random large odd number, and add 2 to it until your selected primality test passes.
The prime number theorem tells us that the probability that a number between 1 and is a prime number is .
Bibliography:
This is a bit "formal hocus pocus first, action later". But withing that category, it is just barely basic enough that 2021 Ciro can understand something.
By: Tobias J. Osborne.
Lecture notes transcribed by a student: github.com/avstjohn/qft
18 1h30 lectures.
Followup course: Advanced quantum field theory lecture by Tobias Osborne (2017).
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