© 2004, D. J. Foreman 1

Virtual Memory

© 2004, D. J. Foreman 2

ObjectivesAvoid copy/restore entire address spaceAvoid unusable holes in memoryIncrease program RAM past physical limitsAllocation 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 MappingDone at runtimeOnly 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 -2Formally: 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

ConceptsEntire virtual address space on diskSmall set of virtual addresses bound to

real addresses at any instantVirtual addresses are scatteredPage size depends on hardwarePage size usually = frame size

■ Counter-example (OS/VS2 (2k) on VM (4k))# page frames computed from physical

memory constraints

© 2004, D. J. Foreman 6

Computations Page size=2h & Page 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= 2g2h = 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 ΩIf function returns Ω

■ Find location i on disk■ Bring it into main memory■ Re-translate i■ Re-start the instruction

Significant overhead■ O/S context switch■ Table search■ I/O for missing address

© 2004, D. J. Foreman 8

Segmentation & PagingSegmentation

■ 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 Translationn = pages in virtual spacem =allocated framesi 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 numberV=line number (offset in page) = i mod c

© 2004, D. J. Foreman 10

PoliciesFetch - when to load a pageReplace - 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

1. Page fault occurs

2. Process with missing page is interrupted

3. Memory manager locates missing page

4. Page frame is unloaded (replacement policy)

5. Page is loaded into vacated page frame

6. Page table is updated

7. Process is restarted

© 2004, D. J. Foreman 12

Demand Paging AlgorithmsRandom - many 'missing page' faults“perfect” - for comparisons onlyLeast Recently Used - if recently used, will

be again, so dump the LRU pageLeast 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 - AssignedD - DirtyK - Prot. Key

© 2004, D. J. Foreman 14

Page Table LookupPg# Disp

flags Frame#

Process page-table ptr

(a register)

Frame# Disp

Page Table1 entry per Page

Pg#

© 2004, D. J. Foreman 15

Inverted Page TablesUseful for locating in-machine pagesExtract virtual page # (VPN) from addressHash the VPN to an indexSearch the table for this indexEach entry has VPN, frame# (PPN)Efficient for small memoriesCollisions must be resolved

Note: uses page#, not address

© 2004, D. J. Foreman 16

Inverted Page Tables -2Regular page 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

HashedPg#

PID link

Frame# or link

1 entry per Frame

Pg# Disp

Hashing Function

Frame# Disp

Process page-table ptr

(a register)

© 2004, D. J. Foreman 18

Translation Lookaside Buffer

VPN Full PTE

TLB - h/w-cachedsimultaneous (associative) lookup

VPN Frame #

S/W lookup tableline by line lookup

frame offset

If no TLB 'hit'

Page# Offset

hit no hit