1. Virtual Memory
© 2004, D. J. Foreman

2. Objectives Avoid copy/restore entire address space
Avoid unusable holes in memory
Increase program RAM past physical limits
Allocation based on virtual memory policy
Freedom from user requirements
Extended abstraction for users
Strategies
Paging - fixed sized blocks called pages
Segmentation - variable sized segments
© 2004, D. J. Foreman

3. Address Translation Mapping
Done at runtime
Only the part being used is loaded
Actually a small initial page-set > 1 page
Page size determined by the O/S
Instruction execution proceeds until an "addressing" or "missing data" fault
O/S gets control
Loads missing page
Re-start the instruction with new data address
© 2004, D. J. Foreman

4. Mapping -2 Formally: βt : vaddress  paddress  {Ω}
Βt is a time-varying map
t is the process's virtual time
Virtual memory manager implements the mapping. ANY mechanism is valid if it follows the definition.
βt(i) will be either:
Real address of virtual address i Ω
© 2004, D. J. Foreman

5. Concepts Entire virtual address space on disk
Small set of virtual addresses bound to real addresses at any instant
Virtual addresses are scattered
Frame size depends on hardware
Page size usually = frame size
Counter-example (OS/VS2 (2k) on VM (4k))
# frames computed from physical memory constraints
© 2004, D. J. Foreman

6. Computations Page size=2h & Frame size=2h
Usually constrained by hardware protection
Number of system pages: n = 2g
Number of process pages/frames: m = 2j
For a process:
Number virtual addresses: G= 2g2h = 2g+h
Number physical addresses: H=2j+h
FYI:
For Pentiums: g = 20 h=12 (page size=4K)
So G = 4 GB (max program size, including O/S)
© 2004, D. J. Foreman

7. Processing Ω If function returns Ω Significant overhead
Find location i on disk
Bring it into main memory
Re-translate i
Re-start the instruction
Significant overhead
O/S mode switch
Table search
I/O for missing address
© 2004, D. J. Foreman

8. Segmentation & Paging Segmentation Paging
Programs divided into segments
Location references are <seg#, offset>
I/O (Swap) whole segments (variable sized)
Programmer can control swapping
External fragmentation can occur
Paging
I/O (page) fixed-size blocks
Location references are linear
No programmer control of paging
© 2004, D. J. Foreman

9. Description of Translation
n = pages in virtual space
m =allocated frames
i is a virtual address 0<=i<=G G= 2g+h
k=a physical memory address =U*2h + V 0<=V<2h
c page size=2h
Page number =  (i/c) 
U is the page frame number
V=line number (offset in page) = i mod c
© 2004, D. J. Foreman

10. Policies Fetch - when to load a page
Replace - victim selection (when full)
Position (placement) - (when not full)
# allocated frames is constant
Page reference stream - numbers of the pages a P references in order of reference
© 2004, D. J. Foreman

11. Paging Algorithm Page fault occurs
Process with missing page is interrupted
Memory manager locates missing page
Page frame is unloaded (replacement policy)
Page is loaded into vacated page frame
Page table is updated
Process is restarted
© 2004, D. J. Foreman

12. Demand Paging Algorithms
Random - many 'missing page' faults
“perfect” - for comparisons only
Least Recently Used - if recently used, will be again, so dump the LRU page
Least Frequently Used - dump the most useless page - influenced by locality, slow to react
LRU, LFU are both Stack algorithms
© 2004, D. J. Foreman

13. Page Mgmt Structures Page # Disp A D K Frame # Virtual address PTE
A - Assigned
D - Dirty
K - Prot. Key
© 2004, D. J. Foreman

14. Page Table Lookup Pg# Disp Frame# Frame# Disp flags Page Table
1 entry per Page
flags
Frame#
Pg#
Process page-table ptr
(a register)
Frame#
Disp
© 2004, D. J. Foreman

15. Inverted Page Tables Useful for locating in-machine pages
Extract virtual page # (VPN) from address
Hash the VPN to an index
Search the table for this index
Each entry has VPN, frame# (PPN)
Efficient for small memories
Collisions must be resolved
Note: uses page#, not address
© 2004, D. J. Foreman

16. Inverted Page Tables -2 Regular page table Inverted table
Uses virtual page # directly
Entry per page
Inverted table
Uses virtual page # as hash input
Sparse lookup table
Finds frame if in memory
Followed by disk address lookup if needed
Entry per frame
© 2004, D. J. Foreman

17. Inverted Page Tables Pg# Disp HashedPg# PID link Frame# or link Frame#
Hashing Function
1 entry per Frame
Process page-table ptr
(a register)
Frame#
Disp
© 2004, D. J. Foreman

18. Translation Lookaside Buffer
Page#
Offset
If no TLB 'hit'
VPN
Full PTE
VPN
Frame #
TLB - h/w-cached
simultaneous
(associative) lookup
S/W lookup table
line by line lookup
hit
no hit
frame
offset
© 2004, D. J. Foreman