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 #8
End of Fixed Length Partions
4.2.1: Memory Management with Bitmaps
Divide memory into blocks and associate a bit with each block, used
to indicate if the corresponding block is free or allocated. To find
a chunk of size N blocks need to find N consecutive bits
indicating a free block.
The only design question is how much memory does one bit represent.
- Big: Serious internal fragmentation.
- Small: Many bits to store and process.
4.2.2: Memory Management with Linked Lists
- Each item on list gives the length and starting location of the
corresponding region of memory and says whether it is a Hole or Process.
- The items on the list are not taken from the memory to be
used by processes.
- Keep in order of starting address.
- Merge adjacent holes
- Double linked
Memory Management using Boundary Tags
- Use the same memory for list items as for processes
- Don't need an entry in linked list for blocks in use, just
the avail blocks are linked.
- For the blocks currently in use, just need a hole/process bit at
each end and the length. Keep this in the block itself.
- See Knuth, The Art of Computer Programming vol 1.
By far the most important and widely used memory management scheme in
- So far the schemes presented so far have had two properties:
- Each job is stored contiguously in memory. That is, the job is
contiguous in physical addresses.
- Each job cannot use more memory than exists in the system. That
is, the virtual addresses space cannot exceed the physical address
- Tanenbaum now attacks the second item. I wish to do both and start
with the first.
- Tanenbaum (and most of the world) uses the term ``paging'' to mean
what I call demand paging. This is unfortunate as it mixes together
- Paging (dicing the address space) to solve the placement
problem and essentially eliminate external fragmentation.
- Demand fetching, to permit the total memory requirements of
all loaded jobs to exceed the size of physical memory.
- Tanenbaum (and most of the world) uses the term virtual memory as
a synonym for demand paging. Again I consider this unfortunate.
- Demand paging is a fine term and is quite descriptive.
- Virtual memory ``should'' be used in contrast with physical
memory to describe any virtual to physical address translation.
** (non-demand) Paging
Simplest scheme to remove the requirement of contiguous physical
Example: Assume a decimal machine with
page size = frame size = 1000.
- Chop the program into fixed size pieces called
pages (invisible to the programmer).
- Chop the real memory into fixed size pieces called page
frames or simply frames.
- Size of a page (the page size) = size of a frame (the frame size).
- Sprinkle the pages into the frames.
- Keep a table (called the page table) having an
entry for each page. The page table entry or PTE for
page p contains the number of the frame f that contains page p.
Assume PTE 3 contains 459.
Then virtual address 3372 corresponds to physical address 459372.
Properties of (non-demand) paging.
- Entire job must be memory resident to run.
- No holes, i.e. no external fragmentation.
- If there are 50 frames available and the page size is 4KB than a
job requiring <= 200KB will fit, even if the available frames are
scattered over memory.
- Hence (non-demand) paging is useful.
- Introduces internal fragmentation approximately equal to 1/2 the
page size for every process (really every segment).
- Can have a job unable to run due to insufficient memory and
have some (but not enough) memory available. This is not
called external fragmentation since it is not due to memory being fragmented.
- Eliminates the placement question. All pages are equally
good since don't have external fragmentation.
- Replacement question remains.
- Since page boundaries occur at ``random'' points and can change from
run to run (the page size can change with no effect on the
program--other than performance), pages are not appropriate units of
memory to use for protection and sharing. This is discussed further
when we introduce segmentation.
- Each memory reference turns into 2 memory references
- Reference the page table
- Reference central memory
- This would be a disaster!
- Hence the MMU caches page#-->frame# translations. This cache is kept
near the processor and can be accessed rapidly.
- This cache is called a translation lookaside buffer (TLB) or
translation buffer (TB).
- For the above example, after referencing virtual address 3372,
there would be an entry in the TLB containing the mapping
- Hence a subsequent access to virtual address 3881 would be
translated to physical address 459881 without a memory reference.
Choice of page size is discuss below.
4.3: Virtual Memory (meaning fetch on demand)
Idea is that a program can execute even if only the active portion of its
address space is memory resident. That is, swap in and swap out
portions of a program. In a crude sense this can be called
- Can run a program larger than the total physical memory.
- Can increase the multiprogramming level since the total size of
the active, i.e. loaded, programs (running + ready + blocked) can
exceed the size of the physical memory.
- Since some portions of a program are rarely if ever used, it is
an inefficient use of memory to have them loaded all the time. Fetch on
demand will not load them if not used and will unload them during
replacement if they are not used for a long time (hopefully).
4.3.1: Paging (meaning demand paging)
Fetch pages from disk to memory when they are referenced, with a hope
of getting the most actively used pages in memory.
- Very common: dominates modern operating systems.
- Started by the Atlas system at Manchester University in the 60s
- Each PTE continues to have the frame number if the page is
- But what if the page is not loaded (exists only on disk)?
- The PTE has a flag indicating if it is loaded (can think of
the X in the diagram on the right as indicating that this flag is
- If not loaded, the location on disk could be kept in the PTE
(not shown in the diagram). But normally it is not
- When a reference is made to a non-loaded page (sometimes
called a non-existent page, but that is a bad name), the system
has a lot of work to do. We give more details
- Choose a free frame, if one exists.
- If not
- Choose a victim frame.
- More later on how to choose a victim.
- Called the replacement question
- Write victim back to disk if dirty,
- Update the victim PTE to show that it is not loaded
and, perhaps, where on disk it has been put.
- Copy the referenced page from disk to the free frame.
- Update the PTE of the referenced page to show that it is
loaded and give the frame number.
- Do the standard paging address translation (p#,off)-->(f#,off).
- Really not done quite this way
- There is ``always'' a free frame because ...
- There is a deamon active that checks the number of free frames
and if this is too low, chooses victims and ``pages them out''
(writing them back to disk if dirty).
- Choice of page size is discussed below.
4.3.2: Page tables
A discussion of page tables is also appropriate for (non-demand)
paging, but the issues are more acute with demand paging since the
tables can be much larger. Why?
- 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.
- 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.
- Big and fast are essentially incompatible.
- Big and fast and low cost is hopeless.
So we can't just say, put the page table in fast processor registers,
and let it be huge, and sell the system for $1500.
For now, put the (one-level) page table in main memory.
- Seems too slow since all memory references require two reference.
- TLB very helpful to reduce the average delay as mentioned above
(discussed later in more detail).
- The page might be too big.
- Currently we are considering contiguous virtual
addresses ranges (i.e. the virtual addresses have no holes).
- Typically put the stack at one end of virtual address and the
global (or static) data at the other end and let them grow towards
- The memory in between is unused.
- This unused memory can be huge (in address range) and hence
the page table will mostly contain unneeded PTEs.
- Works fine if the maximum virtual address size is small, which
was once true (e.g., the PDP-11 of the 1970s) but is no longer the
Contents of a PTE
Each page has a corresponding page table entry (PTE). The
information in a PTE is for use by the hardware. Information set by
and used by the OS is normally kept in other OS tables. The page
table format is determined by the hardware so access routines are not
portable. The following fields are often present.
- The valid bit. This tells if
the page is currently loaded (i.e., is in a frame). If set, the frame
pointer is valid. It is also called the presence or
presence/absence bit. If a page is accessed with the valid
bit zero, a page fault is generated by the hardware.
- The frame number. This is the main reason for the table. It is
needed for virtual to physical address translation.
- The Modified bit. Indicates that some part of the page
has been written since it was loaded. This is needed when the page is
evicted so the OS can know that the page must be written back to disk.
- 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).
- 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.