Paging

1. Paging

2. Fragmentation Need for compaction/swapping A process size is limited by the available physical memory Dynamic growth of partition is troublesome No winning policy on allocation/deallocation Memory Partitioning Troubles P2 P3

3. The Basic Problem • A process needs a contiguous partition(s) But • Contiguity is difficult to manage Contiguity mandates the use of physical memory addressing (so far)

4. The Basic Solution • Give illusion of a contiguous address space • The actual allocation need not be contiguous • Use a Memory Management Unit (MMU) to translate from the illusion to reality

5. A solution: Virtual Addresses • Use n-bit to represent virtual or logical addresses • A process perceives an address space extending from address 0 to 2n-1 • MMU translates from virtual addresses to real ones • Processes no longer see real or physical addresses

6. Paged Memory • Subdivide the address space (both virtual and physical) to “pages” of equal size • Use MMU to map from virtual pages to physical ones • Physical pages are called frames

7. Paging: Example Virtual Physical Virtual 0 0 Process 1 Process 0

8. Key Facts • Virtual address spaces of different processes are independent • Two or more may have the same address range • Yet the mappings differentiate between them • A virtual page has no storage of its own • It must be backed by a physical frame (real page) that provides the actual storage • A contiguous virtual space need not be physically contiguous

9. Key Facts • Physical address space is independent of virtual address spaces • They can have different sizes • Allows process size to be independent of available physical memory size • Page size is always a power of 2, to simplify hardware addressing

10. Page Tables Virtual 0 Page Table

11. Indexed by virtual page number Contains frame number (if any) Contains protection bits Contains reference bit Page Table Structure Frame No. v w r x f m Frame No. v w r x f m Frame No. v w r x f m v: valid bit w: write bit r: read bit x: execute bit (rare) f: reference bit m: modified bit

12. Mapping Virtual to Real Addresses n bits Virtual address virtual page number offset s bits index into page table s bits frame no. offset p bits s: log (page size) Physical address

13. Example: PDP-11 Page size: 8K Up to 4M mem 16bits Virtual address vpn offset 13bits 13bits frame no. offset 8-entry page table 22bits Physical address (in hardware)

14. Weird Stuff: Free Page Management Virtual Physical Virtual Process 0 Process 1 Key fact: A memory frame cannot be accessed unless mapped Free space

15. Fun Stuff: Sharing Virtual Physical Virtual 0 0 Process 1 Process 0

16. Sharing • Processes can share pages by mapping their virtual pages to the same memory frame • In UNIX and Windows, code segments of processes running the same program to share the pages containing executables • saves a lot of memory • saves loading time for frequently run programs • Fine tuning using protection bits (rwx)

17. Fork Revisited: Copy-on-Write Virtual Physical Virtual W W W W W W Father Child

18. Copy-on-Write Fork • Initially no memory copying • Efficient • If an exec follows, no much harm • Page tables set the protection to disallow writes • If either father or child attempts to write, a page fault occurs

19. Copy-on-Write Virtual Physical Virtual W W W W W W Father Child

20. Requirements for Sharing • Page frames must have a reference count • Cannot be deallocated unless unmapped • Adds complexity to memory manager • Protection bits must be set properly

21. Page Table Implementation

22. Page Table Implementations Key issues: • Each instruction requires one or more memory accesses: • Mapping must be done very quickly • Where do we store the page table? • It is now part of the context, with implications on context switching • Hardware must support auxiliary bits

23. PDP-11 Example Revisited • Page table is small (8 entries) • Can be implemented in hardware • Moderate effect on context switching time • Each process will need an 8-entry array in its PCB to store page table when not running • Protections works fine But: what if address space is 32-bit

24. Page Table Size Problems Assume 16K page size and 32-bit address space Then: • For each process, there are 219 virtual pages • Page table size: 219 * 4 bytes/entry • Page table requires 2 Mbytes • Cannot be stored in hardware, slowing down the mapping from virtual to physical addressing

25. Solution1: Multi-Level Page Tables • Use two or three levels page tables • All entries in the topmost level must be there • Entries in lower levels are there only if needed • Store page tables in memory • Have one CPU register contain address of top-most level table

26. Example: SPARC Context 3-level page table index 1 index 2 index 3 offset 8 6 6 12 Page Level 1 Level 2 Level 3 Context table (up to 4K registers)

27. SPARC: Cont’d • Only level 1 table need be there entirely • 256 entries * 4 bytes/entry = 1K /process • Context switching is not affected • Just save and restore the context register/process • Second and third level tables are there only if necessary

28. Translation Lookaside Buffer • A small associative memory in processor • Contains recent mapping results • Typically 8 to 32 entries • If access is localized, works very well • Must be flushed on context switching • If TLB misses, then must resolve through page tables in main memory (slow)

29. Other Varieties • 2-level page table in VAX systems • 4-level page table in the 68030/68040 • Organize the cache memory by virtual addresses (instead of physical addresses) • Remove the TLB from critical path • Combine cache misses with address translations • e.g. MIPS 3000/4000

30. Solution 2: Inverted Page Tables Rationale: • Conventional per-process page tables depend on virtual memory size • Virtual address space is getting larger (e.g. 64 bits) • Size of physical memory projected is less than virtual memory in foreseeable future

31. Inverted Page Table Main Idea: • Global page table indexed by frame number • Each entry contains virtual address & pid • Use TLB to reduce the need to access PT • On a TLB miss: • Search page table for the <virtual address, pid> • Physical address is obtained from the index of the entry (frame number)

32. Indexed by frame number Entry contains virtual address and pid using the frame number (if any) Contains protection & reference Inverted Page Table Structure pid Virtual addr v w r x f m pid Virtual addr v w r x f m pid Virtual addr v w r x f m v: valid bit w: write bit r: read bit x: execute bit (rare) f: reference bit m: modified bit

33. Mapping Virtual to Real Addresses n bits Virtual address virtual page number offset s bits + pid: search key into inverted page table s bits frame no. offset p bits Physical address

34. Properties & Problems • Table size is independent of virtual address size, only function of physical memory size • TLB misses are expensive • We don’t know where to look • May require searching entire table (very bad) • Virtual memory more expensive • Sharing becomes very difficult

35. Organize Inverted Page Table as a hash table Search key <pid, vaddr> Search in hardware or software Examples: IBM 38, RS/6000, HP PA-RISC systems A Solution

36. Sharing & Inverted Page Tables • Size no longer limited, so no system implements it • Conceivably possible with a general hashing function • Requires an additional field in page table entry Frame no. pid Virtual addr v w r x f m Frame no. pid Virtual addr v w r x f m Frame no. pid Virtual addr v w r x f m