Homework 4

Write a program which will demonstrate your ability to properly handle subroutine in MIPS assembly language. This program should generate a a list of 100 random integers between 0 and 1000. It should then sort this list. The list should be printed out. Finally you should demonstrate your search routine by searching for a series of numbers.

A random number generator

First you will need to write code to generate random numbers. Please implement both a void srand (x,y,s) and a int rand() function. Gruenberger and Jaffray in their 1965 book "Problems for Computer Solution" provide the following algorithm for generating random numbers:

srand

 Initialize x y and S to user supplied values.

rand

 x = x + x
 if (x > p) {
     x = x - p
 }
 y = y + y
 if (y > q) {
   y - y - q
 }
 S = S + x
 S = S + y
 Set the top bit of S to be 0.
 Return S.

A few notes from the text are in order here:

P and Q should be relatively prime. The used 999999893 and 999999883.
They used x= 314159265, y = 271828183, S = 0.
This isn't the best random number generator in the world, but it will do.
At one point in the text they discuss that the IBM 1620, the computer they were using for this book, could generate 100 numbers in a second. How many computations can you perform in a second? Assume a CPI of 1 and a processor speed of 1GHz.
The text includes "If there were a computer fast enough to generate and use a billion random numbers in a second..." . Is this a far fetched claim? Why or Why not?

Mod

You will need code to perform the mod operation. MIPS provides an integer divide instruction.

div $ra, $rb
$lo = $ra/$rb
$hi = $ra % $r

You don't have direct access to the high and low registers, you need to use

mfhi $reg
mflo $reg

To move the value from either high or low to a register of your choice. The code

addi     $t2, $zero, 20
addi     $t3, $zero, 3
div      $t2, $t3
mfhi     $t4

Should compute 20%3 (2) and store the results in register t4.

You should write a routine int mod(a,b) which will return a%b

Sort

You may implement any sort routine you wish.

Search

You must implement a binary search. Your routine must implement bool bsearch(int a[], int low, int high, int key). You must implement a recursive version of this search:

bool bsearch(int a[], int low, int high, int key) {
    if (low > high) {
       return false;
    }
    int mid = (low+high)/2
    if (a[mid] == key) {
       return true;
    } else if (a[mid] > key) {
       return (bsearch(a, low, mid-1, key));
    } else {
       return (bsearch(a, mid+1, high, key));
    }
}

The final product

Your program should implement the following code:


// other constants and procedures and such

void testSearch(int a[], int arraySize, int key) {
    cout << "Searching and " << key << " was ";
    if (!bsearch(a, 0, arraySize-1, key) {
       cout << "NOT " 
    }
    cout << "found." << endl;
}

int main() {
   srand(214159265,  271828183, 0)

   for (i=0;i<MAX;i++) {
      a[i] = rand() % SIZELIMIT
   }
   cout << "Before sorting: " << endl;
   printArray(a, MAX)
   sort(a, MAX) // the sort routine may take on other parameters.
   cout << "After sorting: " << endl;
   printArray(a, MAX)
   testSearch(a, MAX, a[4]);
   testSearch(a, MAX, a[4]+1);
}

Final Note

If you need help on any part of this assignment, ask for it.