CSCI 3323 (Principles of Operating Systems), Fall 2011:
Homework 4

Credit:

40 points.

Reading

Be sure you have read Chapter 3, sections 3.1 through 3.3.

Problems

Answer the following questions. You may write out your answers by hand or using a word processor or other program, but please submit hard copy, either in class or in my mailbox in the department office.

1. (5 points) Consider a computer system with 10,000 bytes of memory whose MMU uses the simple base register / limit register scheme described in section 3.2 of the textbook, and suppose memory is currently allocated as follows:
   • Locations 0-1999 are reserved for use by the operating system.
   • Process $A$ occupies locations 5000-6999.
   • Process $B$ occupies locations 7000-8999.
   • Other locations are free.

   Answer the following questions about this system.

   1. What value would need to be loaded into the base register if we performed a context switch to restart process $A$ ?

   2. What memory locations would correspond to the following virtual (program) addresses in process $A$ ?
      • 100

      • 4000

2. (5 points) Consider a computer system using paging to manage memory; suppose it has 64K ($2^{16}$ ) bytes of memory and a page size of 4K bytes, and suppose the page table for some process (call it process $A$ ) looks like the following.

   Page number	Present/absent bit	Page frame number
   0	1	5
   1	1	6
   2	1	2
   3	0	?
   4	0	?
   5	1	7
   6	0	?
   ...	0	?
   15	0	?

   Answer the following questions about this system.

   1. How many bits are required to represent a physical address (memory location) on this system? If each process has a maximum address space of 64K bytes, how many bits are required to represent a virtual (program) address?

   2. What memory locations would correspond to the following virtual (program) addresses for process $A$ ? (Here, the addresses will be given in hexadecimal, i.e., base 16, to make the needed calculations simpler. Your answers should also be in hexadecimal. Notice that if you find yourself converting between decimal and hexadecimal, you are doing the problem the hard way. Stop and think whether there is an easier way!)
      • 0x1420

      • 0x2ff0

      • 0x4008

      • 0x0010

   3. If we want to guarantee that this system could support 16 concurrent processes and give each an address space of 64K bytes, how much disk space would be required for storing out-of-memory pages? Explain your answer (i.e., show/explain how you calculated it). Assume that the first page frame is always in use by the operating system and will never be paged out. You may want to make additional assumptions; if you do, say what they are.

3. (5 points) Now consider a bigger computer system, one in which addresses (both physical and virtual) are 32 bits and the system has $2^{32}$ bytes of memory. Answer the following questions about this system. (You can express your answers in terms of powers of 2, if that is convenient.)
   1. What is the maximum size in bytes of a process's address space on this system?

   2. Is there a logical limit to how much main memory this system can make use of? That is, could we buy and install as much more memory as we like, assuming no hardware constraints? (Assume that the sizes of physical and virtual addresses don't change.)

   3. If page size is 4K ($2^{12}$ ) and each page table entry consists of a page frame number and four additional bits (present/absent, referenced, modified, and read-only), how much space is required for each process's page table? (You should express the size of each page table entry in bytes, not bits, assuming 8 bits per byte and rounding up if necessary.)

   4. Suppose instead the system uses a single inverted page table (as described in section 3.3.4 of the textbook), in which each entry consists of a page number, a process ID, and four additional bits (free/in-use, referenced, modified, and read-only), and at most 64 processes are allowed. How much space is needed for this inverted page table? (You should express the size of each page table entry in bytes, not bits, assuming 8 bits per byte and rounding up if necessary.) How does this compare to the amount of space needed for 64 regular page tables?

4. (5 points) Tanenbaum says, in one of the questions at the end of the chapter, that although the 8086 processor provided no support for virtual memory, there were companies that sold computer systems that used an unmodified 8086 processor and did paging. How do you think they managed this? (Hint: Think about the logical location of the MMU.)

5. (5 points) The operating system designers at Acme Computer Company have been asked to think of a way of reducing the amount of disk space needed for paging. One person proposes never saving pages that only contain program code, but simply paging them in directly from the file containing the executable. Will this work always, never, or sometimes? If ``sometimes'', when will it work and when will it not? (Hint: Search your recollections of CSCI 2321 -- or another source -- for a definition of ``self-modifying code''.)

6. (5 points) How long it takes to access all elements of a large data structure can depend on whether they're accessed in contiguous order (i.e., one after another in the order in which they're stored in memory), or in some other order. The classic example is a 2D array, in which performance of nested loops such as

   	for (int r = 0; r < ROWS; ++r)
   	  for (int c = 0; c < COLS; ++c)
   	    array[r][c] = foo(r,c);
   

   can change drastically for a large array if the order of the loops is reversed. Give an explanation for this phenomenon based on what you have learned from our discussion of memory management. For extra credit, give another explanation that is actually probably likelier to be true of current systems.

Programming Problems

Do the following programming problems. You will end up with at least one code file per problem. Submit your program source (and any other needed files) by sending mail to bmassing@cs.trinity.edu, with each file as an attachment. Please use a subject line that mentions the course number and the assignment (e.g., ``csci 3323 homework 4''). You can develop your programs on any system that provides the needed functionality, but I will test them on one of the department's Linux machines, so you should probably make sure they work in that environment before turning them in.

1. (10 points) Write a program or programs to demonstrate the phenomenon described in problem 6. Turn in your program(s) and output showing differences in execution time. (It's probably simplest to just put this output in a text file and send that together with your source code file(s).) Try to do this in a way that shows a non-trivial difference in execution time (so you will likely need to make the arrays or other data structures large). I'd prefer programs in C, C++, or Java, but anything that can be compiled and executed on one of the Linux lab machines is fine, as long as you tell me how to compile and execute what you turn in, if it's not C/C++ or Java. You don't have to develop and run your programs on one of the lab machines, but if you don't, (1) tell me what system you used instead, and (2) be sure your programs at least compile and run on one of the lab machines, even if they don't necessarily give the same timing results as on the system you used.

   Possibly helpful hints:

   • An easy way to measure how long program mypgm takes on a Linux system is to run it by typing time mypgm. Another way is to run it with /usr/bin/time mypgm. (This gives more/different information -- try it.) If you'd rather put something in the program itself to collect and print timing information, for C/C++ programs you could use the function in timer.h to obtain starting and ending times for the section of the code you want to time, or for Java programs you could use System.currentTimeMillis.
   • Your program doesn't have to use a 2D array (you might be able to think of some other data structure that produces the same result). If you do use a 2D array, though, keep in mind the following:
     • To the best of my knowledge, C and C++ allocate local variables on the stack, which may be limited in size. Dynamically allocated variables (i.e., those allocated with malloc or new) aren't subject to this limit.
     • Dynamic allocation of 2D arrays in C is full of pitfalls. It may be easier to just allocate a 1D array and fake accessing it as a 2D array (e.g., the element in x[i][j], if x is a 2D array, is at offset i*ncols+j).