8.4: Exercises

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Implement a subprogram which takes 4 numbers in the argument registers $a0...$a3, and returns the largest value and the average in $v0 and $v1 to the calling program. The program must be structured as follows:
```
Subprogram largestAndAverage($a1, $a2, $a3, $a4)
{
    int var0 = $a0, var1 = $a1, var2 = $a2, var3 = $a3;
    $s0 = getLarger($a1, $a2);
    $s0 = getLarger($s0, $a3);
    $v0 = getLarager(s0, $a4); // Largest is in $v0
    
    $v1 = (var0 + var1 + var2 + var3)/ 4; // Aversge is in $v1
    return;
}

Subprogram getLarger($a0, $a1) {    
    $v0 = $a0    
    if ($a1 > $a0)
        $v0 = $a1
    return;
}        
```
Note the use of the variables var0...var3. Because the values of $a0 and $a1 (at least) are changed on the call to getLarger, they will not be available when they are needed to calculate the average, and must be stored on the stack. To do this problem correctly, you must calculate the maximum value using the getLarger subprogram shown here, and it must be called before the average is calculated. This implies that at a minimum $a0 and $a1 must be stored on the stack, though I would suggest all four be stack variables as shown here.

It is possible to create a solution which does not require the use of the stack variables, for example by simply calculating the average first. Such solutions do not answer the issue of how to handle variables that change using the stack, and are thus incorrect.
In the utils.asm file, fix the PrintInt subprogram so that it can call the PrintNewLine subprogram to print a new line character.
Implement a subprogram that prompt the user for 3 numbers, finds the median (middle value) of the 3, and returns that value to the calling program.
Implement a subprogram that prompts a user to enter values from 0..100 until a sentinel value of -1 is entered. Return the average of the numbers to the calling program.
Implement a recursive program that takes in a number and finds the square of that number through addition. For example if the number 3 is entered, you would add 3+3+3=9. If 4 is entered you would add 4+4+4+4=16. This program must be implemented using recursion to add the numbers together.
Write a recursive function to calculate the summation of numbers from 1 to n. For example if the user enters 5, your program would add 1+2+3+4+5 and print out the answer 15.
Write a recursive program to calculate Fibonacci numbers. Use the definition of a Fibonacci number where F(n) = F(n-1) + F(n-2).
Write a recursive program to calculate factorial numbers. Use the definition of factorial as F(n) = n * F(n-1).