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Modern Operating Systems by Herbert...
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##### Page 258
SEC. 3.5
DESIGN ISSUES FOR PAGING SYSTEMS
227
must lie somewhere in between.
By taking the first derivative with respect to
p
and
equating it to zero, we get the equation
se
/
p
2
+
1/2
=
0
From this equation we can derive a formula that gives the optimum page size (con-
sidering only memory wasted in fragmentation and page table size).
The result is:
p
=√
⎯⎯
2
se
For
s
=
1MB and
e
=
8 bytes per page table entry, the optimum page size is 4 KB.
Commercially available computers have used page sizes ranging from 512 bytes to
64 KB.
A typical value used to be 1 KB, but nowadays 4 KB is more common.
3.5.4 Separate Instruction and Data Spaces
Most computers have a single address space that holds both programs and data,
as shown in Fig. 3-24(a). If this address space is large enough, everything works
fine. However, if it’s too small, it forces programmers to stand on their heads to fit
space
2
32
0
Data
Program
(a)
I space
D space
2
32
0
Program
Unused page
Data
(b)
Figure 3-24.
(a) One address space. (b) Separate I and D spaces.
One solution, pioneered on the (16-bit) PDP-11, is to have separate address
spaces for instructions (program text) and data, called
I-space
and
D-space
, re-
spectively, as illustrated in Fig. 3-24(b). Each address space runs from 0 to some
maximum, typically 2
16
1 or 2
32
1. The linker must know when separate I-
and D-spaces are being used, because when they are, the data are relocated to vir-
In a computer with this kind of design, both address spaces can be paged, inde-
pendently from one another. Each one has its own page table, with its own map-
ping of virtual pages to physical page frames. When the hardware wants to fetch an
instruction, it knows that it must use I-space and the I-space page table. Similarly,
data must go through the D-space page table.
Other than this distinction, having
separate I- and D-spaces does not introduce any special complications for the oper-
ating system and it does double the available address space.

##### Page 259
228
MEMORY MANAGEMENT
CHAP. 3
While address spaces these days are large, their sizes used to be a serious prob-
lem. Even today, though, separate I- and D-spaces are still common.
However,
rather than for the normal address spaces, they are now used to divide the L1
cache. After all, in the L1 cache, memory is still plenty scarce.
3.5.5 Shared Pages
Another design issue is sharing.
In a large multiprogramming system, it is
common for several users to be running the same program at the same time. Even a
single user may be running several programs that use the same library.
It is clearly
more efficient to share the pages, to avoid having two copies of the same page in
memory at the same time. One problem is that not all pages are sharable.
In partic-
ular, pages that are read-only, such as program text, can be shared, but for data
pages sharing is more complicated.
If separate I- and D-spaces are supported, it is relatively straightforward to
share programs by having two or more processes use the same page table for their
I-space but different page tables for their D-spaces. Typically in an implementation
that supports sharing in this way, page tables are data structures independent of the
process table. Each process then has two pointers in its process table: one to the I-
space page table and one to the D-space page table, as shown in Fig. 3-25. When
the scheduler chooses a process to run, it uses these pointers to locate the ap-
propriate page tables and sets up the MMU using them. Even without separate I-
and D-spaces, processes can share programs (or sometimes, libraries), but the
mechanism is more complicated.
When two or more processes share some code, a problem occurs with the shar-
ed pages. Suppose that processes
A
and
B
are both running the editor and sharing
its pages.
If the scheduler decides to remove
A
from memory, evicting all its pages
and filling the empty page frames with some other program will cause
B
to gener-
ate a large number of page faults to bring them back in again.
Similarly, when
A
terminates, it is essential to be able to discover that the
pages are still in use so that their disk space will not be freed by accident. Search-
ing all the page tables to see if a page is shared is usually too expensive, so special
data structures are needed to keep track of shared pages, especially if the unit of
sharing is the individual page (or run of pages), rather than an entire page table.
Sharing data is trickier than sharing code, but it is not impossible.
In particu-
lar, in UNIX, after a
fork
system call, the parent and child are required to share
both program text and data.
In a paged system, what is often done is to give each
of these processes its own page table and have both of them point to the same set
of pages. Thus no copying of pages is done at
fork
time. However, all the data
pages are mapped into both processes as READ ONLY.
As long as both processes just read their data, without modifying it, this situa-
tion can continue.
As soon as either process updates a memory word, the violation
of the read-only protection causes a trap to the operating system.
A copy is then

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