Help for the Rational Arithmetic assignment

Here are some ideas that may help you approach this assignment. For detailed directions, see the instructions in the course packet and the checklist on the website.

• Create an initial version of RAT.c that implements each of the four required functions with code that simply prints the name of the function. For example, the RATshow function should look like this:

  void RATshow(Rational r)
  {
     printf("RATshow\n");
  }

  The other three functions will be a little more complicated, because they return a value. It may take a couple of tries to get the syntax right so that it compiles. Remember that since this file is an 'implementation', there is no main(), so you will have to compile it by typing 'gcc RAT.c RATtest.c' (where RATtest.c is the client program). Don't forget to type #include "RAT.h" at the top of your program. Otherwise, 'Rational' will be an undefined type.
  
  When you run this program, you should get a printout that starts with:

  RATinit
  RATinit
  RATadd
  RATshow
   + RATshow
   = RATshow

  You can trace through the code in RATtest.c to see that you print the name corresponding to each function called in this client.
  
  The purpose in doing this step is two-fold. First, it should help you better understand how the client and implementation relate. Second, you will now be able to work on the functions in your implementation one at a time. As you've probably learned by now, it's best to work on your programs in small steps. You can now do that, because you have a working implementation.

• Write RATinit and RATshow functions in RAT.c and test to see that they are working by running your client code. (Don't forget to remove the printf statements you wrote in the first step, above!) When you run this new version of you program, you should get a printout that looks something like:

  RATadd
  1/2 + 1/3 = 1/3
  RATadd
  8/9 + 1/9 = 1/9
  RATadd
  8/9 + 1/9 = 1/9
  RATadd
  1/200000000 + 1/300000000 = 1/300000000
  RATmul
  4/17 * 17/4 = 17/4
  RATmul
  3037141/3247033 * 3037547/3246599 = 3037547/3246599

• You may get different values for the 'results' of the add and multiply operations. But they won't be correct, because you haven't implemented RATadd and RATmul yet! So, the next steps are to write RATadd, test & debug it, write RATmul, test & debug it. Each of these functions should only require a few lines of code. It's definitely a good idea to work out a couple of simple fraction additions and multiplications on paper to get an idea of what your functions need to do. Also, you can always make a different version of RATtest.c in which you add or multiply different values. It shouldn't be too difficult to see how you can do that.
  
• On paper, outline your code for e.c and then create a new file: e.c to implement your ideas. Remember that you should only be using the functions RATinit, RATshow, RATadd, and RATmul to manipulate Rationals. It is incorrect to access x.p or x.q for any Rational variable x. A commonly asked question is, "Do I need to write the loop so that it stops before overflow occurs?" The answer is no, you can just set the client to print out the maximum number of terms that you can get without having overflow.
  
• The third part of the assignment is definitely the most difficult. In RATbetter.c, you need to write improved versions of your functions. You can use Euclid's algorithm (gcd) to find the greatest common divisor of two integers. Just add the code for the gcd function to RATbetter.c, and you can use it in your functions. Do not change RAT.h in any way: if you do, it will no longer work with RAT.c.
  
  Before you get started with this part of the assignment, I strongly urge you to add and multiply a few fractions on paper. Notice what you do to simplify your work, and think about how you could write code to do the same things. Make sure you vary the numbers you use in your fractions. You should improve RATinit, RATadd, and RATmult: it isn't necessary to use gcd in RATshow - WHY??
  
  Don't forget to test your code thoroughly with RATtest.c and possibly a test file of your own invntion. Also, verify that e.c still works with your new implementation. Check that you are able to get 13 terms without overfow. If you only get 9 terms, it's time to add some more fractions on paper...try adding 7/9 + 9/20 without producing any 3-digit number as an intermediate result.
  
  
  CORRECTION: Please ignore the statement above about adding 7/9 + 9/20. I wrote '+' but I meant '*'. An example of two numbers you can try to add without getting any 3 digit intermediate result is 7/10 + 4/15. Sorry for any confusion my error may have caused you!