Throwing Exceptions

File Factorials.java contains a program that calls the factorial method of the MathUtils class to compute the factorials of integers entered by the user. Save these files to your directory and study the code in both, then compile and run Factorials to see how it works. Try several positive integers, then try a negative number. You should find that it works for small positive integers (values < 17), but that it returns a large negative value for larger integers and that it always returns 1 for negative integers.

1. Returning 1 as the factorial of any negative integer is not correct -- mathematically, the factorial function is not defined for negative integers. To correct this, you could modify your factorial method to check if the argument is negative, but then what? The method must return a value, and even if it prints an error message, whatever value is returned could be misconstrued. Instead, it should throw an exception, indicating that something went wrong so it could not complete its calculation. You could define your own exception class, but there is already an exception appropriate for this situation -- IllegalArgumentException, which extends RuntimeException. Modify your program as follows:
   • Modify the header of the factorial method to indicate that factorial can throw an IllegalArgumentException.
   • Modify the body of factorial to check the value of the argument and, if it is negative, throw an IllegalArgumentException. Note that what you pass to throw is actually an instance of the IllegalArgumentException class, and that the constructor takes a String parameter. Use this parameter to be specific about what the problem is.
   • Compile and run your Factorials program after making these changes. Now when you enter a negative number, an exception will be thrown, terminating the program. The program ends because the exception is not caught, so it is thrown by the main method, causing a runtime error.
   • Modify the main method in your Factorials class to catch and print the exception thrown by factorial, but then continue with the loop. Think carefully about where you will need to put the try and catch.

2. Returning a negative number for values over 16 also is not correct. The problem is arithmetic overflow -- the factorial is bigger than can be represented by an int. This can also be thought of as an IllegalArgumentException -- this factorial method is only defined for arguments up to 16. Modify your code in factorial to check for an argument over 16 as well as for a negative argument. You should throw an IllegalArgumentException in either case, but pass different messages to the constructor so that the problem is clear.