Paged VMM
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Paged Virtual Memory Management (VMM) (11/05/2003)
With the advent of 64-bit address architectures, the ancient principle of paged Virtual Memory
Management (VMM) experiences a revival in the early 2000s. Originally, the driving principle
for developing VMM systems (paged or segmented or both) was the hunger for more addressable
program memory than was available in physical memory. Scarceness was caused by the high cost
of memory. The early technology of core memories carried a high price tag due to the tedious
manual labor involved. Now the days of high cost per byte of memory are gone. But the days of
having insufficient physical memory have returned, with 64 bit addresses. What applications are
sufficiently served with just a few Gigabytes of physical memory? Only trivial ones 
Paged VMM is based on the idea that with small physical storage some memory areas can be
relocated out to disk, while others areas can be moved back from disc into memory when needed.
Disk space abounds while main memory is limited. This relocation in and out, called swapping,
can be handled transparently, thus imposing no additional constraint of the application
programmer. The system must detect situations in which an address references an object that is
on disk and must therefore perform the hidden swap-in automatically.
Paged VMM trades speed for address range. The loss in speed is caused by the need to map
logical-to-physical, and by the more than occasional disk accesses. A typical disk access can be
100s of 1000s to millions of times more expensive -in number of cycles- than a memory access
(load or a store operation). However, if virtual memory mapping allows large programs to run,
albeit slowly, that previously could not execute due to their high demands of memory, then the
trade-off seems worth the loss in speed. The real trade-off is: being able to execute programs
hungry for memory but slowly versus not executing them but swiftly.
Synopsis
 Steps of Paged Virtual Memory Management
 The Mapping Steps (Two-Level Mapping)
 Definitions
 History of Paging
 Goals and Methods of Paging
 An Unrealistic Paging Scheme
 A Realistic Paging Scheme for 32-bit Architecture
 Typical PD and PT Entries
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Steps of Paged Virtual Memory Management
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Instruction references a logical address
VMM determines, whether logical address maps onto a resident page
If yes, the memory access completes. In a system with L1 cache, such an access is fast
If such access is a store operation, (aka write) that fact is recorded
If not on a resident page, the corresponding swapped-out page is found on disk and
made available in memory, or else it is created the first time ever
Making a new page available requires finding memory space (page frame)
If such space can be allocated from unused memory (usually during initial program
execution), it is now reserved
If no page frame is available, a currently resident page is swapped out and the freed
space is reused for the new page
Should the page to be swapped out have be dirty, it must be written to disk
Otherwise a copy exists on disk already and the swap-out operation is empty
The Mapping Steps (Two-Level Mapping)
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Instruction references a logical address (la)
Processor finds start address of Page Directory (PD)
Logical address is partitioned into three bit fields, Page Directory Index, Page Table
(PT) Index, and Page Offset
Entry in PD is found by adding PD Index left-shifted by 2 to the start address of PD;
this yields a PT address
Add PT Index left-shifted by 2 to previously found PT address; this yields Page
Address
Add Page Offset to previously found Page Address; this yields byte address
Along the way there may have been 3 page faults
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Definitions
Demand Paging:
Policy that allocates a page in physical memory only if an address on that page is actually
referenced (demanded) in the executing program.
Dirty Bit:
Data structure (single-bit suffices) that tells whether the associated page was written after its
last swap-in (or creation).
Global Page:
A page that is used in more than one program; typically found in multi-programming
environment with shared pages.
Logical Address:
Address as defined by the architecture. Synonym on Intel architecture: Linear address.
Antonym: physical address.
Page:
A portion of logical memory that is fixed in size. The start address of a page is an integer
multiple of the page size. Antonym: Segment. A logical page is placed into a physical page
frame.
Page Frame:
A portion of physical memory that is fixed in size to one page. It starts at a boundary that is
evenly divisible by the page size. Total physical memory should be an integral multiple of
the page size.
Page Directory:
A list of addresses for Page Tables. Typically this directory consumes an integral number of
pages as well. In addition to page table addresses, each entry also contains information about
presence, access rights, written to or not, global, etc. similar to Page Table entries.
Page Directory Base Register (pdbr):
Resource (typically a register) that holds the address of the Page Directory page.
Page Table Base Register (ptbr):
Resource (typically a register) that holds the address of the Page Table. Used in a singlelevel paging scheme. In dual-level scheme use pdbr.
Page Fault:
Logical address references a page that is not resident. Consequently, space must be found for
the page referenced, and that page must be (created or) swapped in.
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Page Frame:
A physical piece of memory, of page-size, and page-size aligned, into which a page of actual
information can be placed.
Page Table:
A list of addresses of Pages. Typically each page table consumes an integral number of
pages. In addition to page addresses, each entry also contains information about presence,
access rights, written to or not, global, etc. similar to Page Directory entries.
Physical Memory:
Main memory actually available physically on a processor. Antonym: Logical memory.
Present Bit:
Single-bit data structure that tells, whether the associated page is resident or swapped out
onto disk.
Resident:
Attribute of memory object referenced by executing code: Object is physically in memory,
then it is resident, or is not in memory, then it is non-resident.
Swap-in:
Transfer of a page of information from secondary storage to primary storage (into a page
frame in memory); from disk to physical memory.
Swap-out:
Transfer of a page of information from primary to secondary storage; from physical memory
to disk.
Thrashing:
Excessive amount of swapping. When this happens, performance is severely degraded. This
is an indicator for the working set being too small.
Translation Look-Aside Buffer:
Special-purpose cache for storing Page Directory and Page Table entries.
Virtual Contiguity:
Memory management policy that separates physical from logical memory. In particular,
virtual contiguity creates the impression that two addresses are adjacent in main memory,
while in reality they are an arbitrary number of physical locations apart from one another.
Virtual Memory:
Memory management policy that separates physical from logical memory. In particular,
virtual memory can create the impression that a larger amount of memory is addressable than
is really available on the target.
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Working Set:
That number of allocated physical page frames that ensures that the program executes
without thrashing. The amount of physical memory to execute a system must exceed the
working set by the amount of memory necessary for all other system functions.
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History of Paging
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Invented about 1960 at University of Manchester for Atlas Computer
Used commercially in KDF-9 computer of English Electric Co.
Ever since claimed to have been invented by most computer manufacturers
In fact, KDF-9 was one of the major architectural milestones in computer history
aside from von Neumann’s and Atanasoff’s machines; incorporated first cache and
VMM, had hardware display for stack frame addresses, etc.
In the late 1960s to early 1980s, memory was expensive, processors were expensive
and getting fast, and programs grew large. Insufficient memories were common and
were one aspect of the growing Software Crisis of the late 1970s
16-bit minicomputers and 32-bit mainframes became common; also 18-bit address
architectures (CDC and Cyber) of 60-bit words were common
Paging grew increasingly popular: fast execution was gladly traded against large
address range at cost of slower performance
By mid 1980s, memories became cheaper, faster, large ones prevailed
By the late 1980s, memories had become cheaper yet, the address range remained 32bit, and large physical memories became possible and available
Several supercomputers were designed with operating systems that provided no
memory virtualization at all, no memory mapping. For example, Cray systems were
built without VMM. The Intel Hypercube NX ® operating system had no virtual
memory management
Just when VMM was falling into disfavor, the addressing limitation of 32 bits started
constraining programs. In the early 1990, 64-bit architectures started becoming
common-place, rather than an exception
Intermediate steps between architectural jumps: The Harris 3-byte system with 24-bit
addresses, not making the jump to 32 bit quite. The Pentium Pro ® with 36 bits in
extended addressing mode, not quite yet making the jump to 64 bit addresses. Even
the early Itanium ® family processors had only 44 physical address bits, not quite
making the jump to the physical 64 bit address space
By end of 1990s, 64-bit addresses were common, 64-bit integer arithmetic will be
performed in hardware, not longer via slow library extensions
Pentium Pro has 4kB pages by default, 4MB pages if page size extension (pse) bit is
set in normal addressing mode
However, if the physical address extension (pae) bit and pse bit are set, the default
page size changes from 4kB to 2 MB
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Goals and Methods of Paging (VMM)
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Make full logical (virtual) address space available, even if smaller physical memory
installed
Perform mapping transparently. Thus, if at a later time the target receives a larger
physical memory, the same program will run unchanged except faster
Map logical onto physical address, even if this costs some performance
Implement the mapping in a way that the overhead is small in relation to the total
program execution
A necessary requirement is a sufficiently large working set, but also:
This is accomplished by caching page directory- and page table entries
Or by placing complete page directory into a special cache
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An Unrealistic Paging Scheme
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Assume 32-bit architecture, byte-addressable, 4-byte words, 4kB page size
Single-level paging mechanism --later we’ll cover multi-level mapping
With 4kB page size, rightmost 12 bits of each page address are all 0, or implied
Page Table thus has (32-12 = 20) 220 entries, each entry typically 4 bytes
Page offset of 12 bits identifies each byte on a 4kB page
Logical
LogicalAddress
Address
Page
PageOffset
Offset(12)
(12)
Page
PageAddress
Address(20)
(20)
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With each Page Table entry consuming 4 bytes, results in page table of 4 MB
This is not a good paging scheme, since the scarce resource, physical memory,
consumes already a 4MB overhead. Note that Page Tables should be resident, as long
as some entries point to resident user pages
Thus the overhead may exceed the total available resource - memory
Moreover, almost all entries are empty; their associated pages do not exist yet,
pointers are null
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Page
PageOffset
Offset(12)
(12)
Page
PageAddress
Address(20)
(20)
Logical
LogicalAddress
Address
Page
PageTable
Table4MB
4MB
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User
UserPages
Pages4kB
4kB
Problem: The one data structure that should be resident is too large, consuming
all/most of the physical memory that is so scarce
So: break it into smaller units!
Disadvantage of additional mapping: more memory accesses
Advantage: Avoiding large 4MB Page Table
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A Realistic Paging Scheme for 32-bit Architecture
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Again: 32-bit architecture, byte-addressable, 4-byte words, 4kB page size
Two-level paging mechanism, consisting of Page Directory and Page Tables in
addition to user pages
With 4kB page size, again rightmost 12 bits of any page address 0  implied
Mechanism to determine a physical address:
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Have HW register point to Page Directory
Or else implement Page Directory as a special-purpose cache
Or place PD into a-priori known memory location
But there must be a way to locate the PD, best without extra memory access
Design principle: have user pages, pages of Page Tables, and pages of Page Directory
look the same: all consume a page frame each
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Every logical address is broken into three parts: two indices + one offset
Note that Page Directory Index is indeed an index; to find the entry in PD, first << 2
(multiply by 4), add this to the start address of PD, then PD entry found
Similarly, Page Table Index is an index; to find the entry: << 2 and add result to the
start address of PT found in previous step, thus entry in PT found
The PT entry holds the address of the user page, rightmost 12 bit implied all 0
The rightmost 12 bits of a logical address define the page offset within the found user
page
Since pages are 4 kB in size, 12 bits suffice to identify any byte in a page
Given that the address of a user page is found, add the offset to its address, and the
final byte address is identified
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PD Index
PT Index
Page Offset
Logical
LogicalAddress
Address
pdbr
pdbr
User
UserPages
Pages
Page
PageDirectory
Directory
Page
PageTables
Tables
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Disadvantage: Multiple memory accesses, total of 3
In fact, any of these total 3 accesses could cause page faults, resulting in 3 swap-ins
Performance loss could be tremendous; i.e. several decimal orders of magnitude
slower than a single memory access
Thus some of these data structures must be cached
In Intel Pentium Pro ® the Translation Look-Aside Buffer (TLB) is a special purpose
cache of PD or PT entries
Also possible to cache the complete PD, since contained in size O( 4 kB )
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Typical PD and PT Entries
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Entries in PD and PT need 20 bits for address; lower 12 bits implied
Other 12 bits can be used for additional information
P-Bit: Is referenced page present? (aka resident)
R/W/E bit: Can referenced page be read, written, executed, all?
User/Supervisor bit: OS dependent, is page reserved for privileged code?
Typically the P-Bit is positioned for quick, easy access: rightmost bit in 4-byte word
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Some information is unique to PD or PT
For example, P-Bit not needed in PD entries, if Page Tables must be present
On systems with varying page sizes, page size information must be recorded
See examples below:
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Page Directory Entry
Unused -- Bits
Page Table Address
Accessed Bit
User/Supervisor
Read/Write
Present Bit
If the Operating System exercises a policy to not ever swap-out Page Tables, then the respective
PT entries in the PD do not need to track the fact that a PT was modified (i.e. the Dirty bit).
Hence there may be reasons that PT and PD entries have minor differences. But in general, the
format and structure of PTs and PDs are identical, and the size of user pages, PTs and PDs are
identical.
Page Table Entry
User Page Address
Dirty Bit
Accessed Bit
User/Supervisor
Read/Write
Present Bit
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