IC220 Spring 2008 Project #1: Fabulous Fibonacci Due Wed Feb 6

This project must be completed independently (unlike regular assignments).

This means collaboration between students is not permitted. Online sources (aside from IC220’s website) are also prohibited. You may consult your notes, textbook, and the instructor. See the instructor for help or clarification.

Background: You have already had experience with writing simple MIPS programs and testing them with SPIM. In this project you will review and integrate your understanding of:

1. General MIPS programming

2. Function calls

3. Recursion

Task: Write a recursive MIPS program that computes a term in the Fibonacci sequence. This sequence of numbers
(0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …) can be computed with the following recursive function:

int fibonacci (int N) {

if (N < 2)

return N;

else

return fibonacci(N-1) + fibonacci(N-2);

}

Thus, Fib(0) = 0, Fib(1) = 1, Fib(2) = 1, Fib(3) = 2, …. Fib(10) = 55. Be sure you aren’t off by 1 in the sequence.

There are much more efficient ways to compute the Fibonacci series, but to solidify your understanding of recursion and the stack you are required to have a recursive solution.

Specifics: Starter code is provided: FibonacciStarter.asm. Start with this!!!! You should do the following with this code:

1. Modify the main function to:

Print a welcome message that includes your name

Call the fibonacci procedure to compute the Fibonacci term requested by the user

Print the calculated term after it has been returned to the main function

2. Write a procedure called fibonacci that:

Recursively calculates the Nth Fibonacci term, where N comes from the argument passed in register $a0.

Returns the value in $v0.

You do not have to write this function from scratch – translate the C code given above!

3. Test your code with SPIM.

Sample screen shot of completed program:

Tips:

1. Start early! Recursion can be tricky. Allow time to get help from the instructor if needed.

2. But don’t make this harder than it needs to be! Your primary task is to simply translate the C code above to a MIPS function. While this function is recursive, really this is just another example of a nested procedure – follow the rules for nested procedures and recursion will take care of itself.

3. You will need to use the stack. Be sure you begin, make sure you understand how to do this and what will need to be saved and restored with the stack.

4. This assignment requires you to write only about 30 carefully chosen assembly instructions. If you have many more than that, you probably are misunderstanding what should be done.

5. The following material may be helpful to you:

· Lecture notes on MIPS procedure calls, and SPIM

· Lab #1, where you first used SPIM

· SPIM reference material: http://www.usna.edu/Users/cs/lmcdowel/courses/ic220/spim/

6. Use Alt-PrintScreen to generate a screenshot.

7. An error message like “Can’t add 8 bytes to Lstack” means you are stuck in infinite recursion.

8. Use the starter code!

(more on back)

Deliverables: (1 through 3 handed in, stapled together in the following order)

1) A cover sheet with your feedback. (10 pts)

2) Screenshot showing your program computing Fib(10) (10 pts)

3) Printout of your recursive assembly code (60 pts)

4) .asm file saved to your X drive (20 pts)

Place this file in your IC220 directory. Name it Project1-section-lastname.asm

(e.g., Project1-2001-smith.asm).

Extra credit (up to 5 pts each):

1. Write a new program to calculate the Fibonacci numbers in a non-recursive manner. Turn in this program and a screenshot showing the calculation of Fib(30).

2. Write a new program to calculate the Fibonacci numbers using the floating point registers to keep track of the calculations (you can assume that you only have to deal with numbers with no fractional part). Why might you want to do this?