1. Operating Systems: A Modern Perspective, Chapter 12

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

5. Operating Systems: A Modern Perspective, Chapter 12
Locality
Address Space for pi
Address space is logically partitioned
Text, data, stack
Initialization, main, error handle
Different parts have different reference patterns:
30%
20%
35%
15%
<1%
Execution time
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. Operating Systems: A Modern Perspective, Chapter 12
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. Operating Systems: A Modern Perspective, Chapter 12
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. Operating Systems: A Modern Perspective, Chapter 12
Virtual Memory
Primary Memory
n-1
Physical Address Space
Fragments of the virtual address space are dynamically loaded into primary memory at any given time
Secondary Memory
Each address space is fragmented
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. Operating Systems: A Modern Perspective, Chapter 12
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. Operating Systems: A Modern Perspective, Chapter 12
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. Operating Systems: A Modern Perspective, Chapter 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. Operating Systems: A Modern Perspective, Chapter 12
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. Operating Systems: A Modern Perspective, Chapter 12
Random Replacement
Replaced page, y, is chosen from the m loaded page frames with probability 1/m
Let page reference stream, R =
Frame 1 2 2 2 2 3 2 1 3 2 1 3 2 1 3 1 3 1 3 1 2 1 2 3 2 3 2 6 2 4 6 2 4 5 2 7 5 2
No knowledge of R  not perform well
Easy to implement
13 page faults
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
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 =
Frame
AGE5(1) = ?
AGE5(0) = ?
AGE5(3) = ?
Operating Systems: A Modern Perspective, Chapter 12

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

43. Operating Systems: A Modern Perspective, Chapter 12
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
LRU
Frame
Operating Systems: A Modern Perspective, Chapter 12

44. Operating Systems: A Modern Perspective, Chapter 12
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
LRU
Frame
Operating Systems: A Modern Perspective, Chapter 12

45. Operating Systems: A Modern Perspective, Chapter 12
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
LRU
Frame
Operating Systems: A Modern Perspective, Chapter 12

46. Operating Systems: A Modern Perspective, Chapter 12
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
LRU
Frame
Operating Systems: A Modern Perspective, Chapter 12

47. Operating Systems: A Modern Perspective, Chapter 12
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
LRU
Frame
Operating Systems: A Modern Perspective, Chapter 12

48. Operating Systems: A Modern Perspective, Chapter 12
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
FIFO
Frame
Operating Systems: A Modern Perspective, Chapter 12

49. Operating Systems: A Modern Perspective, Chapter 12
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

51. Operating Systems: A Modern Perspective, Chapter 12
Working Set
Intuitively, the working set is the set of pages in the process’s locality
Somewhat imprecise
Time varying
Given k processes in memory, let mi(t) be # of pages frames allocated to pi at time t
mi(0) = 0
i=1k mi(t)  |primary memory|
Also have St(mi(t)) = St(mi(t-1))  Xt - Yt
Or, more simply S(mi(t)) = S(mi(t-1))  Xt - Yt
Operating Systems: A Modern Perspective, Chapter 12

52. Placed/Replaced Pages
S(mi(t)) = S(mi(t-1))  Xt - Yt
For the missing page
Allocate a new page frame
Xt = {rt} in the new page frame
How should Yt be defined?
Consider a parameter, w, called the window size
Determine BKWDt(y) for every yS(mi(t-1))
if BKWDt(y)  w, unload y and deallocate frame
if BKWDt(y) < w do not disturb y
Operating Systems: A Modern Perspective, Chapter 12

53. Figure 12‑11: The Working Set Windowri
R = … …
W=3
The “Window”
At virtual time i-1: working set = {0, 1}
At virtual time i: working set = {0, 1, 3}
Operating Systems: A Modern Perspective, Chapter 12

54. Operating Systems: A Modern Perspective, Chapter 12
Working Set Principle
Process pi should only be loaded and active if it can be allocated enough page frames to hold its entire working set
The size of the working set is estimated using w
Unfortunately, a “good” value of w depends on the size of the locality
Empirically this works with a fixed w
Operating Systems: A Modern Perspective, Chapter 12

55. Operating Systems: A Modern Perspective, Chapter 12
Example (w = 3)
Frame
0 0
# 1
Operating Systems: A Modern Perspective, Chapter 12

56. Operating Systems: A Modern Perspective, Chapter 12
Example (w = 4)
Frame
0 0
# 1
Operating Systems: A Modern Perspective, Chapter 12

57. Implementing the Working Set
Global LRU will behave similarly to a working set algorithm
Page fault
Add a page frame to one process
Take away a page frame from another process
Use LRU implementation idea
Reference bit for every page frame
Cleared periodically, set with each reference
Change allocation of some page frame with a clear reference bit
Clock algorithms use this technique by searching for cleared ref bits in a circular fashion
Operating Systems: A Modern Perspective, Chapter 12

58. Windows NT Paging System
Reference to Address k in Page i (User space)
Virtual Address
Space
Lookup (Page i, Addr k)
Reference (Page Frame j, Addr k)
Primary
Memory
Translate (Page i, Addr k) to (Page Frame j, Addr k)
Paging Disk
(Secondary Memory)
Supv space
User space
Operating Systems: A Modern Perspective, Chapter 12

59. Windows Address Translation
Virtual page number
Line number
Page Directory
Page Table
Byte Index a b A
Page Directory c B
Page Tables C
Target
Page
Target Byte
Operating Systems: A Modern Perspective, Chapter 12

60. Linux Virtual Address Translation
Operating Systems: A Modern Perspective, Chapter 12

61. Operating Systems: A Modern Perspective, Chapter 12
Segmentation
Unit of memory movement is:
Variably sized
Defined by the programmer
Two component addresses, <Seg#, offset>
Address translation is more complex than paging
Bt: segments x offsets  Physical Address  {W}
Bt(i, j) = k
Operating Systems: A Modern Perspective, Chapter 12

62. Inter Segment References
using segmentA …
call lab1
call [segmentC, lab20]
lab1: …
using segmentB
using segmentC
lab20: …
Operating Systems: A Modern Perspective, Chapter 12

63. Segment Address Translation
Bt: segments x offsets  physical address  {W}
Bt(i, j) = k
S: segments  segment addresses
Bt(S(segName), j) = k
N: offset names  offset addresses
Bt(S(segName), N(offsetName)) = k
Read implementation in Section 12.6
Operating Systems: A Modern Perspective, Chapter 12

64. Address Translation in Segmentation
<segmentName, offsetName> S N
segment #
offset ?
Limit Bt
Relocation
Missing segment +
Limit
Base P
To Memory Address Register
Operating Systems: A Modern Perspective, Chapter 12

65. Operating Systems: A Modern Perspective, Chapter 12
Implementation
Segmentation requires special hardware
Segment descriptor support
Segment base registers (segment, code, stack)
Translation hardware
Some of translation can be static
No dynamic offset name binding
Limited protection
Operating Systems: A Modern Perspective, Chapter 12

66. Operating Systems: A Modern Perspective, Chapter 12
Multics
Old, but still state-of-the-art segmentation
Uses linkage segments to support sharing
Uses dynamic offset name binding
Requires sophisticated memory management unit
See Section 12.6
Operating Systems: A Modern Perspective, Chapter 12

67. NT Memory-mapped Files
Secondary
memory
Ordinary file
Open the file
Create a section object (that maps file)
Identify point in address space to place the file
Executable
memory
Memory
mapped
files
Section
object
Operating Systems: A Modern Perspective, Chapter 12

68. NT Memory-mapped Files(2)
Operating Systems: A Modern Perspective, Chapter 12