The Objective

The Background

Although the square and cube of a number are very easy to calculate, finding the square root of a number, or actually the approximation of the squareroot, can be quite time consuming, especially if done by hand. Using a computer, we can calculate square roots by using a successive approximation algorithm. There are many such algorithms, but the one you will be using for this project is shown below:

The square root of a number n can be approximated by repeated calculation using the formula

where an initial guess of 1.0 will be the starting value of lastGuess. A value for nextGuess should then be computed using the formula given above. The difference between nextGuess and lastGuess should then be checked to see if those two values are almost identical. If they are, nextGuess is accepted as the square root of the number; otherwise, the value of nextGuess becomes the new value of lastGuess and the process is repeated (another value is computed for nextGuess, the difference checked, and so on). The loop should be repeated until the difference is less than 0.005

The Task

After printing the program explanation and getting a positive real number from the user, you will display a menu that will allow the user to choose which operations to do. The choices include :

• squaring the number
• cubing the number
• finding the approximate square root of the number
• finding the precise square root of the number
• finding the difference between the approximate and precise square roots
• getting a new number from the user
• OR quitting the program.

You will be expected to write eight functions, other than main, for this project.

Here are the function prototypes :

void PrintGreeting (void); void PrintMenu (void); int GetValidInt (int min, int max); double GetPositiveValue (void); double FindSquare (double n); double FindCube (double n); double FindApproxSqRt (double n); double FindDifference (double n);

You MUST use these function prototypes, as shown, without modification.

Function Descriptions:

• PrintGreeting() - should print a message to the user, explaining what the program will do. Since this function returns nothing, it can also be called a procedure.

• PrintMenu() - should print the menu to the screen

• GetValidInt() - should prompt the user for an integer within the range of min to max, inclusive, that are passed in as arguments, ensure the integer entered is within that range and return it. It may be necessary to have initial prompting done in the caling function that says what this value is, i.e. In this example, the initial prompt might be, "Your Choice: ". See the sample output for clarification.

• GetPositiveValue() - should prompt the user for a positive number, ensure that it is a positive real number and return it. Like GetValidInt() this function should be a module and so initial prompting may be necessary in the calling function to clarify what the value is, and the prompt within the function should just ask for a positive value. See the sample output for clarification.

• FindSquare() - This function will take a positive real number as its single argument, n, and return n-squared.

• FindCube() - This function will take a positive real number as its single argument, n, and return n-cubed.

• FindApproxSqRt() - This function will find the approximate square root of a number, n, by performing repeated calculations using the formula given above.

• FindDifference() - This function will take a positive value as its single argument, n, and find the difference between the approximate square root, calculated by your function FindApproxSqRt(), and the precise square root, the value returned from the sqrt() function found in the math library. It should compare these values and return the absolute value of the difference.

Sample Run

More Details

• You MUST use the prototypes as shown without any modification.
• You MUST use separate compilation. Your files must be named proj1.c, exponents.c and exponents.h, where proj1.c should contain main(), exponents.c should contain the function definitions and exponents.h should contain the function prototypes for the functions found in exponents.c
• You MUST use symbolic constants for all numeric values, therefore you will need the following #defines :
  #define MIN 1 #define MAX 7 #define SQUARE 1 #define CUBE 2 #define APPROX_SQRT 3 #define SQRT 4 #define DIFFERENCE 5 #define NEW_NUM 6 #define QUIT 7
• The design for this project is to be given in lecture on Wednesday, 9/26/07 and Thursday, 9/27/07. Your project MUST be written as it is designed in class.

Compiling the Pieces & Linking

• Separate compilation requires the -c flag to compile without linking : gcc -Wall -ansi -c proj1.c gcc -Wall -ansi -c exponents.c
• Since we are using the sqrt() function from the math library, we need to use the -lm flag to explicitly link to the math library. None of the other libraries we'll use will need explicit linking. gcc proj1.o exponents.o -lm

Submitting the Program

To submit the files you should use the command:

submit cs201 Proj1 proj1.c exponents.c exponents.h

You can check your submission by using the command:

submitls cs201 Proj1