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Virtual Memory

Virtual Memory. 12. Virtual Memory Organization. Primary Memory. Secondary Memory. Memory Image for p i. Executable Image. Physical Address Space. B t : Virtual Address Space  Physical Address Space. Names, Virtual Addresses & Physical Addresses. Dynamically. Source Program.

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Virtual Memory

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  1. Operating Systems: A Modern Perspective, Chapter 12

  2. VirtualMemory 12 Operating Systems: A Modern Perspective, Chapter 12

  3. Virtual Memory Organization Primary Memory Secondary Memory Memory Image for pi Operating Systems: A Modern Perspective, Chapter 12

  4. Executable Image Physical Address Space Bt: Virtual Address Space  Physical Address Space Names, Virtual Addresses & Physical Addresses Dynamically Source Program Absolute Module Name Space Pi’s Virtual Address Space Operating Systems: A Modern Perspective, Chapter 12

  5. <1% 15% 35% 20% <1% 30% Execution time Locality Address Space for pi • Address space is logically partitioned • Text, data, stack • Initialization, main, error handle • Different parts have different reference patterns: Initialization code (used once) Code for 1 Code for 2 Code for 3 Code for error 1 Code for error 2 Code for error 3 Data & stack Operating Systems: A Modern Perspective, Chapter 12

  6. Virtual Memory • Every process has code and data locality • Code tends to execute in a few fragments at one time • Tend to reference same set of data structures • Dynamically load/unload currently-used address space fragments as the process executes • Uses dynamic address relocation/binding • Generalization of base-limit registers • Physical address corresponding to a compile-time address is not bound until run time Operating Systems: A Modern Perspective, Chapter 12

  7. Virtual Memory (cont) • Since binding changes with time, use a dynamic virtual address map, Bt Virtual Address Space Bt Operating Systems: A Modern Perspective, Chapter 12

  8. Physical Address Space 0 n-1 • Each address space is fragmented Primary Memory • Fragments of the virtual address space are dynamically loaded into primary memory at any given time Virtual Memory Secondary Memory Virtual Address Space for pi Virtual Address Space for pj Virtual Address Space for pk • Complete virtual address space is stored in secondary memory Operating Systems: A Modern Perspective, Chapter 12

  9. Address Formation • Translation system creates an address space, but its address are virtual instead of physical • A virtual address, x: • Is mapped to physical address y = Bt(x) if x is loaded at physical address y • Is mapped to W if x is not loaded • The map, Bt, changes as the process executes -- it is “time varying” • Bt: Virtual Address  Physical Address  {W} Operating Systems: A Modern Perspective, Chapter 12

  10. Size of Blocks of Memory • Virtual memory system transfers “blocks” of the address space to/from primary memory • Fixed size blocks: System-defined pages are moved back and forth between primary and secondary memory • Variable size blocks: Programmer-defined segments – corresponding to logical fragments – are the unit of movement • Paging is the commercially dominant form of virtual memory today Operating Systems: A Modern Perspective, Chapter 12

  11. Paging • A page is a fixed size, 2h, block of virtual addresses • A page frame is a fixed size, 2h, block of physical memory (the same size as a page) • When a virtual address, x, in page i is referenced by the CPU • If page i is loaded at page frame j, the virtual address is relocated to page frame j • If page is not loaded, the OS interrupts the process and loads the page into a page frame Operating Systems: A Modern Perspective, Chapter 12

  12. Addresses • Suppose there are G= 2g2h=2g+h virtual addresses and H=2j+h physical addresses assigned to a process • Each page/page frame is 2h addresses • There are 2g pages in the virtual address space • 2j page frames are allocated to the process • Rather than map individual addresses • Bt maps the 2g pages to the 2j page frames • That is, page_framej = Bt(pagei) • Address k in pagei corresponds to address k in page_framej Operating Systems: A Modern Perspective, Chapter 12

  13. Page-Based Address Translation • Let N = {d0, d1, … dn-1} be the pages • Let M = {b0, b1, …, bm-1} be page frames • Virtual address, i, satisfies 0i<G= 2g+h • Physical address, k = U2h+V (0V<G= 2h ) • U is page frame number • V is the line number within the page • Bt:[0:G-1]  <U, V>  {W} • Since every page is size c=2h • page number = U = i/c • line number = V = i mod c Operating Systems: A Modern Perspective, Chapter 12

  14. Demand Paging Algorithm • Page fault occurs • Process with missing page is interrupted • Memory manager locates the missing page • Page frame is unloaded (replacement policy) • Page is loaded in the vacated page frame • Page table is updated • Process is restarted Operating Systems: A Modern Perspective, Chapter 12

  15. Modeling Page Behavior • Let R = r1, r2, r3, …, ri, … be a page reference stream • ri is the ith page # referenced by the process • The subscript is the virtual time for the process • Given a page frame allocation of m, the memory state at time t, St(m), is set of pages loaded • St(m) = St-1(m)  Xt - Yt • Xt is the set of fetched pages at time t • Yt is the set of replaced pages at time t Operating Systems: A Modern Perspective, Chapter 12

  16. More on Demand Paging • If rt was loaded at time t-1, St(m) = St-1(m) • If rt was not loaded at time t-1 and there were empty page frames • St(m) = St-1(m)  {rt} • If rt was not loaded at time t-1 and there were no empty page frames • St(m) = St-1(m)  {rt} - {y} • The alternative is prefetch paging Operating Systems: A Modern Perspective, Chapter 12

  17. Static Allocation, Demand Paging • Number of page frames is static over the life of the process • Fetch policy is demand • Since St(m) = St-1(m)  {rt} - {y}, the replacement policy must choose y -- which uniquely identifies the paging policy Operating Systems: A Modern Perspective, Chapter 12

  18. Address Translation with Paging g bits h bits Virtual Address Page # Line # “page table” Missing Page Bt j bits h bits Physical Address Frame # Line # CPU Memory MAR Operating Systems: A Modern Perspective, Chapter 12

  19. 13 page faults • No knowledge of R not perform well • Easy to implement Random Replacement • Replaced page, y, is chosen from the m loaded page frames with probability 1/m Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 1 2 2 2 0 2 0 3 2 1 3 2 1 3 2 1 0 3 1 0 3 1 0 3 1 2 0 1 2 0 3 2 0 3 2 0 6 2 4 6 2 4 5 2 7 5 2 Operating Systems: A Modern Perspective, Chapter 12

  20. Belady’s Optimal Algorithm • Replace page with maximal forward distance: yt = max xeS t-1(m)FWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 1 0 0 2 3 Operating Systems: A Modern Perspective, Chapter 12

  21. Belady’s Optimal Algorithm • Replace page with maximal forward distance: yt = max xeS t-1(m)FWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 1 0 0 2 3 FWD4(2) = 1 FWD4(0) = 2 FWD4(3) = 3 Operating Systems: A Modern Perspective, Chapter 12

  22. Belady’s Optimal Algorithm • Replace page with maximal forward distance: yt = max xeS t-1(m)FWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 2 1 0 0 0 2 31 FWD4(2) = 1 FWD4(0) = 2 FWD4(3) = 3 Operating Systems: A Modern Perspective, Chapter 12

  23. Belady’s Optimal Algorithm • Replace page with maximal forward distance: yt = max xeS t-1(m)FWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 2 2 2 1 0 0 0 0 0 2 31 1 1 Operating Systems: A Modern Perspective, Chapter 12

  24. Belady’s Optimal Algorithm • Replace page with maximal forward distance: yt = max xeS t-1(m)FWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 2 2 2 2 1 0 0 0 0 0 3 2 31 1 1 1 FWD7(2) = 2 FWD7(0) = 3 FWD7(1) = 1 Operating Systems: A Modern Perspective, Chapter 12

  25. Belady’s Optimal Algorithm • Replace page with maximal forward distance: yt = max xeS t-1(m)FWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 2 2 2 2 2 2 0 1 0 0 0 0 0 3 3 3 3 2 31 1 1 1 1 1 1 FWD10(2) =  FWD10(3) = 2 FWD10(1) = 3 Operating Systems: A Modern Perspective, Chapter 12

  26. Belady’s Optimal Algorithm • Replace page with maximal forward distance: yt = max xeS t-1(m)FWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 2 2 2 2 2 2 0 0 0 1 0 0 0 0 0 3 3 3 3 3 3 2 31 1 1 1 1 1 1 1 1 FWD13(0) =  FWD13(3) =  FWD13(1) =  Operating Systems: A Modern Perspective, Chapter 12

  27. Belady’s Optimal Algorithm • Replace page with maximal forward distance: yt = max xeS t-1(m)FWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 2 2 2 2 2 2 0 0 0 0 4 4 4 1 0 0 0 0 0 3 3 3 3 3 3 6 6 6 7 2 31 1 1 1 1 1 1 1 1 1 1 5 5 10 page faults • Perfect knowledge of R perfect performance • Impossible to implement Operating Systems: A Modern Perspective, Chapter 12

  28. Least Recently Used (LRU) • Replace page with maximal forward distance: yt = max xeS t-1(m)BKWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 1 0 0 2 3 BKWD4(2) = 3 BKWD4(0) = 2 BKWD4(3) = 1 Operating Systems: A Modern Perspective, Chapter 12

  29. Least Recently Used (LRU) • Replace page with maximal forward distance: yt = max xeS t-1(m)BKWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 1 1 0 0 0 2 3 3 BKWD4(2) = 3 BKWD4(0) = 2 BKWD4(3) = 1 Operating Systems: A Modern Perspective, Chapter 12

  30. Least Recently Used (LRU) • Replace page with maximal forward distance: yt = max xeS t-1(m)BKWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 1 1 1 0 0 0 2 2 3 3 3 BKWD5(1) = 1 BKWD5(0) = 3 BKWD5(3) = 2 Operating Systems: A Modern Perspective, Chapter 12

  31. Least Recently Used (LRU) • Replace page with maximal forward distance: yt = max xeS t-1(m)BKWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 1 1 1 1 0 0 0 2 2 2 3 3 3 0 BKWD6(1) = 2 BKWD6(2) = 1 BKWD6(3) = 3 Operating Systems: A Modern Perspective, Chapter 12

  32. Least Recently Used (LRU) • Replace page with maximal forward distance: yt = max xeS t-1(m)BKWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 1 1 1 3 3 3 0 0 0 6 6 6 7 1 0 0 0 2 2 2 1 1 1 3 3 3 4 4 4 2 3 3 3 0 0 0 2 2 2 1 1 1 5 5 Operating Systems: A Modern Perspective, Chapter 12

  33. Least Recently Used (LRU) • Replace page with maximal forward distance: yt = max xeS t-1(m)BKWDt(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 2 2 2 2 3 2 2 2 2 6 6 6 6 1 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 2 3 3 3 3 3 3 3 3 3 3 3 3 5 5 3 1 1 1 1 1 1 1 1 1 1 1 1 7 • Backward distance is a good predictor of forward distance -- locality Operating Systems: A Modern Perspective, Chapter 12

  34. Least Frequently Used (LFU) • Replace page with minimum use: yt = min xeS t-1(m)FREQ(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 1 0 0 2 3 FREQ4(2) = 1 FREQ4(0) = 1 FREQ4(3) = 1 Operating Systems: A Modern Perspective, Chapter 12

  35. Least Frequently Used (LFU) • Replace page with minimum use: yt = min xeS t-1(m)FREQ(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 2 1 0 0 1 2 3 3 FREQ4(2) = 1 FREQ4(0) = 1 FREQ4(3) = 1 Operating Systems: A Modern Perspective, Chapter 12

  36. Least Frequently Used (LFU) • Replace page with minimum use: yt = min xeS t-1(m)FREQ(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 2 2 2 1 0 0 1 1 1 2 3 3 3 0 FREQ6(2) = 2 FREQ6(1) = 1 FREQ6(3) = 1 Operating Systems: A Modern Perspective, Chapter 12

  37. Least Frequently Used (LFU) • Replace page with minimum use: yt = min xeS t-1(m)FREQ(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 2 2 2 1 0 0 1 1 1 2 3 3 3 0 FREQ7(2) = ? FREQ7(1) = ? FREQ7(0) = ? Operating Systems: A Modern Perspective, Chapter 12

  38. First In First Out (FIFO) • Replace page that has been in memory the longest: yt = max xeS t-1(m)AGE(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 1 1 0 0 0 2 3 3 Operating Systems: A Modern Perspective, Chapter 12

  39. First In First Out (FIFO) • Replace page that has been in memory the longest: yt = max xeS t-1(m)AGE(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 1 0 0 2 3 AGE4(2) = 3 AGE4(0) = 2 AGE4(3) = 1 Operating Systems: A Modern Perspective, Chapter 12

  40. First In First Out (FIFO) • Replace page that has been in memory the longest: yt = max xeS t-1(m)AGE(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 1 1 0 0 0 2 3 3 AGE4(2) = 3 AGE4(0) = 2 AGE4(3) = 1 Operating Systems: A Modern Perspective, Chapter 12

  41. First In First Out (FIFO) • Replace page that has been in memory the longest: yt = max xeS t-1(m)AGE(x) Let page reference stream,R = 2031203120316457 Frame 2 0 3 1 2 0 3 1 2 0 3 1 6 4 5 7 0 2 2 2 1 1 0 0 0 2 3 3 AGE5(1) = ? AGE5(0) = ? AGE5(3) = ? Operating Systems: A Modern Perspective, Chapter 12

  42. Belady’s Anomaly Let page reference stream,R = 012301401234 Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 3 3 3 4 4 4 4 4 4 1 1 1 1 0 0 0 0 0 2 2 2 2 2 2 2 1 1 1 1 1 3 3 Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 0 0 0 4 4 4 4 3 3 1 1 1 1 1 1 1 0 0 0 0 4 2 2 2 2 2 2 2 1 1 1 1 3 3 3 3 3 3 3 2 2 2 • FIFO with m = 3 has 9 faults • FIFO with m = 4 has 10 faults Operating Systems: A Modern Perspective, Chapter 12

  43. Stack Algorithms • Some algorithms are well-behaved • Inclusion Property: Pages loaded at time t with m is also loaded at time t with m+1 Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 3 1 1 1 1 2 2 2 LRU Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 0 1 1 1 1 2 2 2 3 3 Operating Systems: A Modern Perspective, Chapter 12

  44. Stack Algorithms • Some algorithms are well-behaved • Inclusion Property: Pages loaded at time t with m is also loaded at time t with m+1 Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 3 3 1 1 1 1 1 2 2 2 0 LRU Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 0 0 1 1 1 1 1 2 2 2 2 3 3 3 Operating Systems: A Modern Perspective, Chapter 12

  45. Stack Algorithms • Some algorithms are well-behaved • Inclusion Property: Pages loaded at time t with m is also loaded at time t with m+1 Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 3 3 3 1 1 1 1 0 0 2 2 2 2 1 LRU Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 Operating Systems: A Modern Perspective, Chapter 12

  46. Stack Algorithms • Some algorithms are well-behaved • Inclusion Property: Pages loaded at time t with m is also loaded at time t with m+1 Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 3 3 3 4 1 1 1 1 0 0 0 2 2 2 2 1 1 LRU Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 2 2 2 2 2 4 3 3 3 3 3 Operating Systems: A Modern Perspective, Chapter 12

  47. Stack Algorithms • Some algorithms are well-behaved • Inclusion Property: Pages loaded at time t with m is also loaded at time t with m+1 Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 3 3 3 4 4 4 2 2 2 1 1 1 1 0 0 0 0 0 0 3 3 2 2 2 2 1 1 1 1 1 1 4 LRU Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 0 0 0 0 0 0 0 0 4 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 4 4 4 4 3 3 3 3 3 3 3 3 3 2 2 2 Operating Systems: A Modern Perspective, Chapter 12

  48. Stack Algorithms • Some algorithms are well-behaved • Inclusion Property: Pages loaded at time t with m is also loaded at time t with m+1 Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 3 3 3 4 4 4 4 4 4 1 1 1 1 0 0 0 0 0 2 2 2 2 2 2 2 1 1 1 1 1 3 3 FIFO Frame 0 1 2 3 0 1 4 0 1 2 3 4 0 0 0 0 0 0 0 4 4 4 4 3 3 1 1 1 1 1 1 1 0 0 0 0 4 2 2 2 2 2 2 2 1 1 1 1 3 3 3 3 3 3 3 2 2 2 Operating Systems: A Modern Perspective, Chapter 12

  49. Implementation • LRU has become preferred algorithm • Difficult to implement • Must record when each page was referenced • Difficult to do in hardware • Approximate LRU with a reference bit • Periodically reset • Set for a page when it is referenced • Dirty bit Operating Systems: A Modern Perspective, Chapter 12

  50. Dynamic Paging Algorithms • The amount of physical memory -- the number of page frames -- varies as the process executes • How much memory should be allocated? • Fault rate must be “tolerable” • Will change according to the phase of process • Need to define a placement & replacement policy • Contemporary models based on working set Operating Systems: A Modern Perspective, Chapter 12

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