Operating Systems

Start Lecture #7

Remark: Lab 3 (banker) assigned. It is due in 2 NYU weeks, which is 3 calendar weeks.

** (non-demand) Paging

Simplest scheme to remove the requirement of contiguous physical memory.

Example: Assume a decimal machine with page size = frame size = 1000.
Assume PTE 3 contains 459.
Then virtual address 3372 corresponds to physical address 459372.

Properties of (non-demand) paging (without segmentation).

Address translation

Choice of page size is discuss below.

Homework: Using the page table of Fig. 3.9, give the physical address corresponding to each of the following virtual addresses.

  1. 20
  2. 4100
  3. 8300

3.3 Virtual Memory (meaning Fetch on Demand)

The idea is to enable a program to execute even if only the active portion of its address space is memory resident. That is, we are to swap in and swap out portions of a program. In a crude sense this could be called automatic overlays.

Advantages

Disadvantages

The Memory Management Unit and Virtual to Physical Address Translation

The memory management unit is a piece of hardware in the processor that translates virtual addresses (i.e., the addresses in the program) into physical addresses (i.e., real hardware addresses in the memory). The memory management unit is abbreviated as and normally referred to as the MMU.

(The idea of an MMU and virtual to physical address translation applies equally well to non-demand paging and in olden days the meaning of paging and virtual memory included that case as well. Sadly, in my opinion, modern usage of the term paging and virtual memory are limited to fetch-on-demand memory systems, typically some form of demand paging.)

** 3.3.1 Paging (Meaning Demand Paging)

The idea is to fetch pages from disk to memory when they are referenced, with a hope of getting the most actively used pages in memory. The choice of page size is discussed below.

Paging is very common: More complicated variants, multilevel-level paging and paging plus segmentation (both of which we will discuss), dominates modern operating systems.

Started by the Atlas system at Manchester University in the 60s (Fortheringham).

Each PTE continues to contain the frame number if the page is loaded. But what if the page is not loaded (exists only on disk)?


Really not done quite this way

Homework: 9.

3.3.2 Page tables

A discussion of page tables is also appropriate for (non-demand) paging, but the issues are more acute with demand paging and the tables can be much larger. Why?

  1. The total size of the active processes is no longer limited to the size of physical memory. Since the total size of the processes is greater, the total size of the page tables is greater and hence concerns over the size of the page table are more acute.
  2. With demand paging an important question is the choice of a victim page to page out. Data in the page table can be useful in this choice.

We must be able access to the page table very quickly since it is needed for every memory access.

Unfortunate laws of hardware.

So we can't just say, put the page table in fast processor registers, and let it be huge, and sell the system for $1000.

The simplest solution is to put the page table in main memory. However it seems to be both too slow and two big.

  1. This solution seems too slow since all memory references now require two reference.
  2. We will soon see how to speed up the references and for many programs eliminate extra reference by using a TLB.
  3. This solution seems too big.
  4. A fix is to use multiple levels of mapping. We will see two examples below: multilevel page tables and segmentation plus paging.

Structure of a Page Table Entry

Each page has a corresponding page table entry (PTE). The information in a PTE is used by the hardware and its format is machine dependent; thus the OS routines that access PTEs are not portable.f Information set by and used by the OS is normally kept in other OS tables.

(Actually some systems, those with software TLB reload, do not require hardware access to the page table.)

The page table is index by the page number; thus the page number is not stored in the table.

The following fields are often present in a PTE.

  1. The valid bit. This tells if the page is currently loaded (i.e., is in a frame). If set, the frame number is valid. It is also called the presence or presence/absence bit. If a page is accessed with the valid bit unset, a page fault is generated by the hardware.

  2. The frame number. This field is the main reason for the table. It gives the virtual to physical address translation.

  3. The Modified bit. Indicates that some part of the page has been written since it was loaded. This is needed if the page is evicted so that the OS can tell if the page must be written back to disk.

  4. The referenced bit. Indicates that some word in the page has been referenced. Used to select a victim: unreferenced pages make good victims by the locality property (discussed below).

  5. Protection bits. For example one can mark text pages as execute only. This requires that boundaries between regions with different protection are on page boundaries. Normally many consecutive (in logical address) pages have the same protection so many page protection bits are redundant. Protection is more naturally done with segmentation, but in many current systems, it is done with paging (since the systems don't utilize segmentation, even though the hardware supports it).

We will soon understand why the disk address of non-resident pages is not in the PTE: a PTE is loaded into the TLB, which is used for address translation for resident pages, page faults trap to the OS.

3.3.3 Speeding Up Paging

As mentioned above the simple scheme of storing the page table in its entirety in central memory alone appears to be both too slow and too big. We address both these issues here, but note that a second solution to the size question (segmentation) is discussed later.

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 concept of which translation lookaside buffer is a specific example.

An associative memory is a content addressable memory. That is you access the memory by giving the value of some field (called an index) and the hardware searches all the records and returns the record whose index 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, etc. Note that unlike the situation with a the page table, the page number is stored in the TLB; indeed it is the index field.

A TLB is small and expensive but at least it is fast. When the page number is in the TLB, the frame number is returned very quickly.

On a miss, a TLB reload is performed. The page number is looked up in the page table. The record found is placed in the TLB and a victim is discarded (not really discarded, dirty and referenced bits are copied back to the PTE). There is no placement question since all TLB entries are accessed at the same time and hence are equally suitable. But there is a replacement question.

As the size of the TLB has grown, some processors have switched from single-level, fully-associative, unified TLBs to multi-level, set-associative, separate instruction and data, TLBs.

We are actually discussing caching, but using different terminology.

Software TLB Management

The words above assume that, on a TLB miss, the MMU (i.e., hardware and not the OS) loads the TLB with the needed PTE and then performs the virtual to physical address translation. This implies that the OS need not be concerned with TLB misses.

Some newer systems do this in software, i.e., the OS is involved.

Homework: 15.

Multilevel page tables

Recall the diagram above showing the data and stack growing towards each other. 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 i-node-based file systems, which we study later when we do I/O) is to add a level of indirection and have a page table containing pointers to page tables.

This idea can be extended to three or more levels. The largest I know of has four levels. We will be content with two levels.

Address Translation With a 2-Level Page Table

For a two level page table the virtual address is divided into three pieces 

    +-----+-----+-------+
    | P#1 | P#2 | Offset|
    +-----+-----+-------+

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).

Inverted Page Tables

For many systems the virtual address range is much bigger that the size of physical memory. In particular, with 64-bit addresses, the range is 264 bytes, which is 16 million terabytes. If the page size is 4KB and a PTE is 4 bytes, a full page table would be 16 thousand terabytes.

A two level table would still need 16 terabytes for the first level table, which is stored in memory. A three level table reduces this to 16 gigabytes, which is still large and only a 4-level table gives a reasonable memory footprint of 16 megabytes.

An alternative is to instead keep a table indexed by frame number. The content of entry f contains the number of the page currently loaded in frame f. This is often called a frame table as well as an inverted page table.

Now there is one entry per frame. Again using 4KB pages and 4 byte PTEs, we see that the table would be a constant 0.1% of the size of real memory.

But on a TLB miss, the system must search the inverted page table, which would be hopelessly slow except that some tricks are employed. Specifically, hashing is used.

Also it is often convenient to have an inverted table as we will see when we study global page replacement algorithms. Some systems keep both page and inverted page tables.

3.4 Page Replacement Algorithms (PRAs)

These are solutions to the replacement question. Good solutions take advantage of locality when choosing the victim page to replace.

  1. 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.
  2. 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.
  3. Temporal and spacial locality 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 in which 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.

3.4.1 The Optimal Page Replacement Algorithm

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

3.4.2 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).

Based on the belief that a page in a lower priority class is a better victim.

We again have the prisoner problem: We do a good job of making little ones out of big ones, but not the reverse. We need more resets so every k clock ticks, the OS resets all R bits.

Why not reset M as well?
Answer: If a dirty page has a clear M, we will not copy the page back to disk and thus the only accurate version of the page is lost!

I suppose one 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?
Answer: The OS can uses tricks. When the bits are reset, the PTE is made to indicate that the page is not resident (which is a lie). On the ensuing page fault, the OS sets the appropriate bit(s).

We ignore the tricks and assume the hardware does set the bits.

3.4.3 FIFO PRA

Simple but poor since usage of the page is ignored.

Belady's Anomaly: Can have more frames yet generate more faults. An example is given later.

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

3.4.4 Second chance PRA

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

3.4.5 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.

Thus when the number of loaded pages is constant, the algorithm is just like 2nd chance except that only the one pointer (the clock hand) is updated.

What if the number of pages is not constant?

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 as now the program is references mostly new pages but only one frame is available to hold them.