1. Operating Systems COMP 4850/CISG 5550 Page Tables TLBs Inverted Page Tables Dr. James Money

2. Paging

3. Page Tables In the simplest cases, mapping of virtual addresses happens as we have described In the simplest cases, mapping of virtual addresses happens as we have described The virtual address is split into lower and higher order bits The virtual address is split into lower and higher order bits The higher order bits are grouped into a page number The higher order bits are grouped into a page number Splits might be of 3 or 5 bits instead of 4 Splits might be of 3 or 5 bits instead of 4

4. Page Tables The virtual page number is used as an index into the page table The virtual page number is used as an index into the page table From the entry in the page table, the page frame number is found From the entry in the page table, the page frame number is found The page frame number is attached to the high order bits to determine the physical address The page frame number is attached to the high order bits to determine the physical address

5. Page Tables The main purpose of the page table is to map virtual addresses to physical addresses The main purpose of the page table is to map virtual addresses to physical addresses Mathematically the page table is a function that takes a virtual page number and returns a physical frame number Mathematically the page table is a function that takes a virtual page number and returns a physical frame number

6. Page Tables There are two major issues to address There are two major issues to address –The page table can grow to be extremely large –The mapping of addresses must be fast

7. Page Tables The reason for large page tables is b/c most computers have at least 32 bits and many now have 64 The reason for large page tables is b/c most computers have at least 32 bits and many now have 64 With a 4KB page size, a 32 bit address space has 1 million pages With a 4KB page size, a 32 bit address space has 1 million pages With a 64 bit address space, there are more than one can imagine With a 64 bit address space, there are more than one can imagine Typically each process has its own page table with it’s own virtual address space Typically each process has its own page table with it’s own virtual address space

8. Page Tables The second point is needed b/c we do the virtual-to-physical mapping must be done with every memory reference The second point is needed b/c we do the virtual-to-physical mapping must be done with every memory reference Many times there are 1,2, or memory references per instruction Many times there are 1,2, or memory references per instruction If an instruction takes 4 nsec, the lookup must not exceed 1 nsec If an instruction takes 4 nsec, the lookup must not exceed 1 nsec

9. Page Tables The simplest design is to have the table as an array of fast hardware registers with an entry for each virtual page The simplest design is to have the table as an array of fast hardware registers with an entry for each virtual page This requires no memory references during mapping This requires no memory references during mapping This problem is this can be expensive($$!!) and slow with a context switch This problem is this can be expensive($$!!) and slow with a context switch

10. Page Tables The other end is to have the entire page table in memory The other end is to have the entire page table in memory There is a single register that points to start of the table There is a single register that points to start of the table Easy for a context switch Easy for a context switch Needs memory references to read page table Needs memory references to read page table

11. Multilevel Page Tables Many computers use a multilevel page system to alleviate the problem Many computers use a multilevel page system to alleviate the problem The basic idea is a two level tree with the top level being reference to leaf nodes with an array of page entries The basic idea is a two level tree with the top level being reference to leaf nodes with an array of page entries We partition the 32 bit virtual address into a PT1 field, a PT2 field, and the Offset field We partition the 32 bit virtual address into a PT1 field, a PT2 field, and the Offset field

12. Multilevel Page Tables

13. The idea is to not keep all the leaf page tables in memory when they are not needed The idea is to not keep all the leaf page tables in memory when they are not needed A page fault occurs when the top level entry has the Present bit is clear A page fault occurs when the top level entry has the Present bit is clear Either this is an illegal address or we need to allocate more pages to the process Either this is an illegal address or we need to allocate more pages to the process We can extend this scheme to three or four levels We can extend this scheme to three or four levels

14. Multilevel Page Tables For example, consider referencing the virtual address 0x00403004 For example, consider referencing the virtual address 0x00403004 This corresponds to PT1=1, PT2=2, and Offset=4 This corresponds to PT1=1, PT2=2, and Offset=4 The MMU uses PT1 as an index into the top level table and PT2 as the index into the appropriate second level table The MMU uses PT1 as an index into the top level table and PT2 as the index into the appropriate second level table

15. Page Table Entries We consider now the structure of a single entry for a page table We consider now the structure of a single entry for a page table This is highly machine dependent, but roughly the same from machine to machine This is highly machine dependent, but roughly the same from machine to machine A common size for an entry is 32 bits A common size for an entry is 32 bits

16. Page Table Entries The field contains The field contains –Page frame number –Present/absent bit –Protection – what kind of access is permitted –Modified/Referenced – keeps track of writes and read to a page frame –Caching disabled

17. Page Table Entries

18. Note the disk address to hold the page is not in memory or part of the page table Note the disk address to hold the page is not in memory or part of the page table This is b/c the OS handles this information internally in its software tables This is b/c the OS handles this information internally in its software tables The page table only has to hold information on virtual -> physical mappings for processes The page table only has to hold information on virtual -> physical mappings for processes

19. TLBs Most paging systems keep page tables in memory due to their large size Most paging systems keep page tables in memory due to their large size In register to register instructions, there is no paging hit In register to register instructions, there is no paging hit Since the rate of the memory access is the limiting factor, making two references reduces performance by 2/3 Since the rate of the memory access is the limiting factor, making two references reduces performance by 2/3

20. TLBs The solution is based on the fact there are a large number of close by memory references The solution is based on the fact there are a large number of close by memory references This results in a little number of page references This results in a little number of page references The rest are used rarely The rest are used rarely

21. TLBs The solution is to equip a device to handle the mapping without going through the page table The solution is to equip a device to handle the mapping without going through the page table This device is called the Translation Lookaside Buffer (TLB) or associate memory This device is called the Translation Lookaside Buffer (TLB) or associate memory This is kept inside the MMU and has a small number of entries(8-64) This is kept inside the MMU and has a small number of entries(8-64)

22. TLBs

23. TLBs How does this work? How does this work? The MMU first looks in the TLB by comparing all entries simultaneously The MMU first looks in the TLB by comparing all entries simultaneously If an entry is found and the protection is appropriate, then the entry is used without going to the page table If an entry is found and the protection is appropriate, then the entry is used without going to the page table If there is a protection problem, then a protection fault is issued If there is a protection problem, then a protection fault is issued

24. TLBs If the entry is not in the TLB, the MMU does a normal page lookup If the entry is not in the TLB, the MMU does a normal page lookup It replaces an entry in the TLB with the page lookup just issued It replaces an entry in the TLB with the page lookup just issued If that page is used again, then it will read the page frame from the TLB If that page is used again, then it will read the page frame from the TLB

25. Software TLB Management So far the management of the TLB has been done by the MMU itself So far the management of the TLB has been done by the MMU itself This was true in the past This was true in the past Many modern RISC CPUs do this management in software Many modern RISC CPUs do this management in software On these systems, a TLB fault is issued for handling the TLB miss On these systems, a TLB fault is issued for handling the TLB miss

26. Software TLB Management The OS needs to find the page table entry, evict the least used one, and load the new TLB entry The OS needs to find the page table entry, evict the least used one, and load the new TLB entry This has to be done fast since there are many TLB misses to a page fault This has to be done fast since there are many TLB misses to a page fault If the TLB size is large(64), then there is no problem b/c the misses are far in between If the TLB size is large(64), then there is no problem b/c the misses are far in between

27. Inverted Page Tables With 32 bit computers, with 4KB page size, a full table might require 4MB With 32 bit computers, with 4KB page size, a full table might require 4MB This can be a problem on 64 bit address systems This can be a problem on 64 bit address systems We now need 2 52 entries We now need 2 52 entries If each entry is 8 bytes, we need to use 30 million gigabytes If each entry is 8 bytes, we need to use 30 million gigabytes

28. Inverted Page Tables We need a different solution We need a different solution One solution is called an inverted page table One solution is called an inverted page table In this design, there is one entry per page frame in real memory rather than one entry per virtual page In this design, there is one entry per page frame in real memory rather than one entry per virtual page In the same scenario with 256MB of RAM, we need only 65536 entries In the same scenario with 256MB of RAM, we need only 65536 entries

29. Inverted Page Tables Each entry keeps track of which (process,virtual page) belongs to the frame Each entry keeps track of which (process,virtual page) belongs to the frame Now the virtual to physical mapping is hard to perform Now the virtual to physical mapping is hard to perform When a process references virtual page p, it must search the inverted page table for an entry of the form (n,p) When a process references virtual page p, it must search the inverted page table for an entry of the form (n,p)

30. Inverted Page Tables The way around this again it to use the TLB The way around this again it to use the TLB When the TLB holds the heavily used pages, then this work happens as fast as regular page tables When the TLB holds the heavily used pages, then this work happens as fast as regular page tables However, on a miss, the search must be done in software However, on a miss, the search must be done in software

31. Inverted Page Tables One way to do this search is to use a hash table with chaining One way to do this search is to use a hash table with chaining If the hash table has as many entries as frames, then the chains will only have one entry each If the hash table has as many entries as frames, then the chains will only have one entry each Once the entry is found, the entry is put in the TLB Once the entry is found, the entry is put in the TLB

32. Inverted Page Tables