NOTE: These notes are by Allan Gottlieb, and are reproduced here, with superficial modifications, with his permission. "I" in this text generally refers to Prof. Gottlieb, except in regards to administrative matters.


================ Start Lecture #9 (Feb. 26) ================

Multilevel page tables

Recall the previous diagram. Most of the virtual memory is the unused space between the data and stack regions. However, with demand paging this space does not waste real memory. But the single large page table does waste real memory.

The idea of multi-level page tables (a similar idea is used in Unix inode-based file systems) is to add a level of indirection and have a page table containing pointers to page tables.

Do an example on the board

The VAX used a 2-level page table structure, but with some wrinkles (see Tanenbaum for details).

Naturally, there is no need to stop at 2 levels. In fact the SPARC has 3 levels and the Motorola 68030 has 4 (and the number of bits of Virtual Address used for P#1, P#2, P#3, and P#4 can be varied).

4.3.3: TLBs--Translation Lookaside Buffers (and General Associative Memory)

Note: Tanenbaum suggests that ``associative memory'' and ``translation lookaside buffer'' are synonyms. This is wrong. Associative memory is a general structure and translation lookaside buffer is a special case.

An associative memory is a content addressable memory. That is you access the memory by giving the value of some field and the hardware searches all the records and returns the record whose field contains the requested value.

For example

Name  | Animal | Mood     | Color
======+========+==========+======
Moris | Cat    | Finicky  | Grey
Fido  | Dog    | Friendly | Black
Izzy  | Iguana | Quiet    | Brown
Bud   | Frog   | Smashed  | Green
If the index field is Animal and Iguana is given, the associative memory returns
Izzy  | Iguana | Quiet    | Brown

A Translation Lookaside Buffer or TLB is an associate memory where the index field is the page number. The other fields include the frame number, dirty bit, valid bit, and others.

4.3.4: Inverted page tables

Keep a table indexed by frame number with the entry f containing the number of the page currently loaded in frame f.

4.4: Page Replacement Algorithms (PRAs)

These are solutions to the replacement question.

Good solutions take advantage of locality.

Pages belonging to processes that have terminated are of course perfect choices for victims.

Pages belonging to processes that have been blocked for a long time are good choices as well.

Random PRA

A lower bound on performance. Any decent scheme should do better.

4.4.1: The optimal page replacement algorithm (opt PRA) (aka Belady's min PRA)

Replace the page whose next reference will be furthest in the future.

4.4.2: The not recently used (NRU) PRA

Divide the frames into four classes and make a random selection from the lowest nonempty class.

  1. Not referenced, not modified
  2. Not referenced, modified
  3. Referenced, not modified
  4. Referenced, modified

Assumes that in each PTE there are two extra flags R (sometimes called U, for used) and M (often called D, for dirty).

Also assumes that a page in a lower priority class is cheaper to evict.

We again have the prisoner problem, we do a good job of making little ones out of big ones, but not the reverse. Need more resets.

Every k clock ticks, reset all R bits

What if the hardware doesn't set these bits?

4.4.3: FIFO PRA

Simple but poor since usage of the page is ignored.

Belady's Anomaly: Can have more frames yet generate more faults. Example given later.

4.4.4: Second chance PRA

Similar to the FIFO PRA but when time choosing a victim, if the page at the head of the queue has been referenced (R bit set), don't evict it. Instead reset R and move the page to the rear of the queue (so it looks new). The page is being a second chance.

What if all frames have been referenced?
Becomes the same as fifo (but takes longer).

Might want to turn off the R bit more often (say every k clock ticks).

4.4.5: Clock PRA

Same algorithm as 2nd chance, but a better (and I would say obvious) implementation: Use a circular list.

Do an example.

LIFO PRA

This is terrible! Why?
Ans: All but the last frame are frozen once loaded so you can replace only one frame. This is especially bad after a phase shift in the program when it is using all new pages.

4.4.6:Least Recently Used (LRU) PRA

When a page fault occurs, choose as victim that page that has been unused for the longest time, i.e. that has been least recently used.

LRU is definitely

Homework: 29, 23

A hardware cutsie in Tanenbaum

4.4.7: Simulating (Approximating) LRU in Software

The Not Frequently Used (NFU) PRA

R counter
110000000
001000000
110100000
111010000
001101000
000110100
110011010
111001101
001100110

The Aging PRA

NFU doesn't distinguish between old references and recent ones. The following modification does distinguish.

Homework: 25, 34

4.4.8: The Working Set Page Replacement Problem (Peter Denning)

The working set policy (Peter Denning)

The goal is to specify which pages a given process needs to have memory resident in order for the give process to run without too many page faults.

The idea of the working set policy is to ensure that each process keeps its working set in memory.

Interesting questions include:

... Various approximations to the working set, have been devised.

  1. 4.4.9: The WSClock Page Replacement Algorithm


  2. Page Fault Frequency (PFF): Described in 4.6 below.

4.4.10: Summary of Page Replacement Algorithms

AlgorithmComment
RandomPoor, used for comparison
OptimalUnimplementable, use for comparison
LIFOHorrible, useless
NRUCrude
FIFONot good ignores frequency of use
Second ChanceImprovement over FIFO
ClockBetter (natural) implementation of Second Chance
LRUGreat but impractical
NFUCrude LRU approximation
AgingBetter LRU approximation
Working SetGood, but expensive
WSClockGood approximation to working set