Operating Systems

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.

• Since modern machine have a smaller physical address space than virtual address space, the table is smaller.
• But on a TLB miss, must search the inverted page table.
• Would be hopelessly slow except that some tricks are employed.
• The book mentions some but not all of the tricks, we are officially skipping this topic.

4.4: Page Replacement Algorithms (PRAs)

These are solutions to the replacement question.

Good solutions take advantage of locality.

• Temporal locality: If a word is referenced now, it is likely to be referenced in the near future.
  • This argues for caching referenced words, i.e. keeping the referenced word near the processor for a while.
• Spatial locality: If a word is referenced now, nearby words are likely to be referenced in the near future.
  • This argues for prefetching words around the currently referenced word.
• These are lumped together into locality: If any word in a page is referenced, each word in the page is “likely” to be referenced.
  • So it is good to bring in the entire page on a miss and to keep the page in memory for a while.
• When programs begin there is no history so nothing to base locality on. At this point the paging system is said to be undergoing a “cold start”.
• Programs exhibit “phase changes”, when the set of pages referenced changes abruptly (similar to a cold start). At the point of a phase change, many page faults occur because locality is poor.

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.

• Also called Belady's min algorithm.
• Provably optimal. That is, generates the fewest number of page faults.
• Unimplementable: Requires predicting the future.
• Good upper bound on performance.

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.

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

• If not referenced, probably will not referenced again soon and hence is a good candidate for eviction.
• If not modified, do not have to write it out so the cost of the eviction is lower.
• When a page is brought in, OS resets R and M (i.e. R=M=0)
• On a read, hardware sets R.
• On a write, hardware sets R and M.

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

• Why not reset M?
  Answer: Must have M accurate to know if victim needs to be written back
• Could have two M bits one accurate and one reset, but I don't know of any system (or proposal) that does so.

What if the hardware doesn't set these bits?

• OS can use tricks
• When the bits are reset, make the PTE indicate the page is not resident (i.e. lie). On the page fault, set the appropriate bit(s).

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.

The natural implementation is to have a queue of nodes each pointing to a page.

• When a page is loaded, a node referring to the page is appended to the tail of the queue.
• When a page needs to be evicted, the head node is removed and the page referenced is chosen as the victim.

4.4.4: Second chance PRA

Similar to the FIFO PRA, but altered so that a page recently referenced is given a second chance.

• When a page is loaded, a node referring to the page is appended to the tail of the queue. The R bit of the page is naturally cleared.
• When a page needs to be evicted, the head node is removed and the page referenced is the potential victim.
• If the R bit on this page is cleared (the page hasn't been referenced recently), then the page is the victim.
• If the R bit is set, then the bit is cleared, the node referring to this page is appended to the rear of the queue (so it appears to have just been loaded), and the current head node becomes the potential victim.
• What if all the R bits are set?
• We will move each page from the front to the rear and will arrive at the initial condition but with all the R bits now clear. Hence we will remove the same page as fifo would have removed, but will have spent more time doing so.
• Might want to periodically clear all the R bits so that a long ago reference is forgotten (but so is a recent reference).

4.4.5: Clock PRA

Same algorithm as 2nd chance, but a better implementation for the nodes: Use a circular list with a single pointer serving as both head and tail.

Let us begin by assuming that the number of pages loaded is constant.

• So the size of the node list in 2nd chance is constant.
• Use a circular list for the nodes and have a pointer pointing to the head entry. Think of the list as the hours on a clock and the pointer as the hour hand.
• Since the number of nodes is constant, the operation we need to support is replace the “oldest” page by a new page.
• Examine the node pointed to by the (hour) hand. If the R bit of the corresponding page is set, we give the page a second chance: clear the R bit, move the hour hand (now P looks freshly loaded), and examine the next node.
• Eventually we will reach a node whose corresponding R bit is clear. The corresponding page is the victim.
• Replace the victim with the new page (may involve 2 I/Os as always).
• Update the node to refer to this new page.
• Move the hand forward another hour so that the new page is at the rear.

What if the number of pages is not constant?

• We now have to support inserting a node right before the hour hand (the rear of the queue) and removing the node pointed to by the hour hand.
• The natural solution is to double link the circular list.
• In this case insertion and deletion are a little slower than for the primitive 2nd chance (double linked lists have more pointer updates for insert and delete).
• So the trade-off is that if there are mostly inserts and deletes and granting 2nd chances is not too common, use the original 2nd chance implementation. If there are mostly replacements and you often give nodes a 2nd chance, use clock.

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

• Implementable: The past is knowable.
• Good: Simulation studies have shown this.
• Difficult. Essentially need to either:
  1. Keep a time stamp in each PTE, updated on each reference and scan all the PTEs when choosing a victim to find the PTE with the oldest timestamp.
  2. Keep the PTEs in a linked list in usage order, which means on each reference moving the PTE to the end of the list

Homework: 29, 23

A hardware cutsie in Tanenbaum

• For n pages, keep an nxn bit matrix.
• On a reference to page i, set row i to all 1s and col i to all 0s
• At any time the 1 bits in the rows are ordered by inclusion. I.e. one row's 1s are a subset of another row's 1s, which is a subset of a third. (Tanenbaum forgets to mention this.)
• So the row with the fewest 1s is a subset of all the others and is hence least recently used.
• This row also has the smallest value, when treated as an unsigned binary number. So the hardware can do a comparison of the rows rather than counting the number of 1 bits.
• Cute, but still impractical.

4.4.7: Simulating (Approximating) LRU in Software

The Not Frequently Used (NFU) PRA

• Include a counter in each PTE (and have R in each PTE).
• Set counter to zero when page is brought into memory.
• For each PTE, every k clock ticks.
  1. Add R to counter.
  2. Clear R.
• Choose as victim the PTE with lowest count.

The Aging PRA

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

• Include a counter in each PTE (and have R in each PTE).
• Set counter to zero when page is brought into memory.
• For each PTE, every k clock ticks.
  1. Shift counter right one bit.
  2. Insert R as new high order bit (HOB).
  3. Clear R.
• Choose as victim the PTE with lowest count.

Homework: 25, 34