Functions

Goals

This laboratory exercise provides initial practice with functions and passing values as parameters within C programs.

Consider the program quadratic.c that solves the quadratic formula ax² + bx + c = 0, while illustrating several common variations for simple functions.

`void` and non-`void` Functions

Copy quadratic.c to your account, compile and run it, and review the code to determine how it works.
1. Procedure printEquation has a void return type. Parameters are passed into printEquation, but nothing is passed back. What will happen if the statement
```
return coeff2+coeff1+coeff0;
```
  is inserted at the end of this procedure?
2. Verify your prediction by making the modification and compiling the code. Explain the result.
3. Restore the program to its original state.
4. Procedure printEquation is called in both procedures displayExample1 and displayExample2 with just a simple statement, such as:
```
printEquation (1.0, -3.0, 2.0);
```
  Predict what will happen if you try to assign the result of printEquation to a variable, such as
```
double value = printEquation(1.0, -3.0, 2.0);
```
  After making your prediction, verify whether you were correct by making the change and compiling the code. Explain the results.
5. Restore the program again to its original state.
6. Procedure computeDiscriminant returns a double. Sometimes beginning programmers separate the call to a function from the assignment of the return value. Here are two examples:
  
  Attempt 1:
```
double discriminant;
computeDiscriminant (a, b, c);
```
  Attempt 2:
```
computeDiscriminant (a, b, c);
double discriminant;
```
  Try each of these attempts within procedure printRoots.
  - Does the code compile?
    - First, use "make" to compile.
    - Next, try using the following command to manually compile your modified program:
```
clang -lm -o quadratic quadratic.c
```
  - Does the compiled program give the desired result?
  When you are finished, restore the program to its original state.
7. Change the body of computeDiscriminant to the following
```
printf ("r = %lf, s = %lf, t = %lf\n", r, s, t);
return sqrt (s*s - 4*r*t);
```
  Compile and run the program.
  - Describe what is printed by the overall program. What might you conclude about what happens when printing is done in the middle of a computation? For example, how does this impact the overall program's output?
  - Can you identify any guidelines regarding the advisability of including print statements in functions designed for computation (e.g., computeDiscriminant)?
  Restore the program to its original state.

Writing Numeric Functions

Within a new C program, define and use the following functions:
- Function computeCircumference that takes a circle's radius as parameter and returns the circumference of the circle.
- Function computeArea that takes a radius as parameter and returns the area of the circle with that radius.
Note: In some extended versions of C, you can access the constant M_PI by including the library header math.h. Alternately, one can define their own constant or implicitly calculate the value with an inverse trigonometric function.

The Perils of Global Variables

Global variables are variables declared outside any particular function. In terms of our stack model of computation, they exist in a separate part of memory called the static region, which you can draw in your diagrams as a collection of variable-value pairs separate from the stack. They tend to be problematic and are generally to be avoided (unless they are declared constants with the keyword const. Instead, you should favor explicitly passing data between function calls using parameters and return values.

To better understand the confusions global variables can cause, consider the following program.

#include <stdio.h>

int glob = 10;

void
g (void) {
    // Point (B)---first call to g()
    for (int i = 0; i < glob; i++) {
        printf("%d ", i);
    }
    printf("\n");
    glob += 1;
    // Point (C)---final call to g()
} // g

int
f (void) {
    for (int i = 0; i < glob; i += 2) {
        // Point (A)---first iteration of the for-loop
        g();
        printf("===\n");
    }
    return glob;
} // f

int
main (void) {
    int ret = f();
    printf("%d\n",ret);                
    // Point (D)
} // main

Predict what the program will print.
Verify your prediction by compiling and running the code. If your prediction was incorrect, trace the execution of the program by recording and updating the stack diagram (including the static region) as you trace the code's execution.

Functions, Values as Parameters, and Robot Motion

Program yoyo.c uses the function yoyo to control a Scribbler 2 robot.

Copy yoyo.c to your account, compile and run it, and review to code to determine how it works.
1. Explain what the program does.
  - What movements does the robot make? Why?
  - What output is printed? Why?
2. In the main program, duplicate the line
```
result = yoyo (repetitions);
```
  (I.e., this line should appear twice in succession.)
  
  Does making this call twice change how many times the robot yoyos in each call? Why or why not?
3. In the main program, replace the line
```
result = yoyo (repetitions);
```
  by
```
repetitions = yoyo (repetitions);
repetitions = yoyo (repetitions);
```
  Does making this call twice change how many times the robot yoyos in each call? Why or why not?
4. In C (as in Scheme), variables declared within a function are separate from variables declared elsewhere (e.g., in main). In the original program, change the name of the repetitions variable to reps throughout the main procedure. Compile and run the program.
  
  Does changing yoyo's variable reps have any impact on the variable reps in the main procedure?
5. Again, return to the original program. This time nest the call to yoyo in the main procedure. That is, the call to yoyo will become:
```
yoyo (yoyo (repetitions));
```
  - Make a prediction of what will happen with the above nested call.
  - Test out your nested call and explain what happened.
Recall the reading's discussion of memory diagrams. Draw a sequence of stack diagrams for program quadratic.c from Step 1.
Important: To benefit from this exercise, you must actually draw these diagrams. It is not a mental exercise.
Consider the program value-params.c.
1. Copy the program to your account, compile, and run it.
2. Draw stack diagrams for the program state when each print statement is executed. Be sure you can explain the running of the program at each step, based upon this series of diagrams.