DUE DATE: Friday, November 1, 2002, 5:00 pm

(no late submissions accepted)

Summary

This project acquaints students with techniques of array-processing used to implement a classic algorithm from antiquity, processing command-line arguments, and timing the program execution at runtime.

Write an assembly language program which generates a listing of all the prime numbers smaller than a given upper bound, based upon the famous Sieve of Eratosthenes. (A prime number is an integer, greater than one, which is not evenly divisible by any integers except itself and one. Examples of prime numbers are 2, 3, and 5. The number 4 is not a prime, since it has the number 2 as a factor.

In ancient times, the Greek mathematician Eratosthenes proposed the following simple algorithm for determining all the prime numbers smaller than an arbitrary positive number N.

• Make a list which includes all integers between 1 and N.
• For each integer in the list, remove all of its multiples.
• Those integers which remain in the list are the primes.

This algorithm (known as the 'sieve') has often been applied by computer scientists as a standard "benchmark" for evaluating the performance of a new processor or language compiler. As such, it would be useful to include a time measurement, and to inform the user at the end how long the sieve took to execute.

Your program should take a required argument, specifying the upper bound for the prime number search. It should also accept an option -v switch on the command line, which if present, should trigger a printout of the prime numbers that your program has found.

For example:

        $ ./sieve 1000
        There are 168 primes below 1000
        Search took 0 seconds
        $ ./sieve -v 100
        List of prime numbers below 100

        2       3       5       7       11      13      17      19
        23      29      31      37      41      43      47      53
        59      61      67      71      73      79      83      89
        97

        There are 25 primes below 100
        Search took 0 seconds

Notes

• In your assembly language program it will not be necessary to store the actual list of the numbers in memory. Instead, you should use an array of boolean values (0s and 1s) to indicate, for each array index, whether that index value is included in your list or not. (That is, the index into the array will give you the actual number and the array value at that index will indicate whether the number is prime or not.) For example, an array with the following ten boolean-values

           array:   0   0   1   1   0   1   0   1   0   0
  
                    ^   ^   ^   ^   ^   ^   ^   ^   ^   ^
           index:   0   1   2   3   4   5   6   7   8   9
  

  would serve to represent the list of all prime numbers smaller than ten.
• Since assembly language allows us to manipulate individual bits, the most efficient memory usage would be to represent each number as one bit. (See previous note.) You will find the bt family of instructions very useful in accomplishing this task.
• Theoretically, the upper bound is only limited by memory capacity of the computer. Your program should be able to use an upper bound of four billion. (Largest unsigned 32-bit number.) This will require at least 500 megabytes of memory, so you will have to use the machines in Harney 235 and Harney 535 for final testing.
• Time your program with an upper bound of four billion on a HR535 machines and on a HR235 machine and include your results in the printout your submit.
• To obtain nice-looking output (as shown above), you should print eight primes on one line and separate them with a horizontal tab. (ASCII code 09h)
• For this project, creating a Makefile is optional, but recommended.

Extra Credit

• There are numerous optimizations that can be made to this algorithm. (Of course, you should come up with them yourself.) Try to optimize your code for both memory usage and speed. Five fastest sieves (measured with an upper bound of four billion) will receive 15 points extra credit.

What to turn in

Please submit your source code, Makefile, object file, and executable to your submit directory for this class. (located under /home/submit/cs210.) In addition please submit a printout of your source code to the instructor.