Objects and classes - Data Structures and Problem Solving Using Java - page 87

The class that we write will represent rational numbers. A rational num-
ber stores a numerator and denominator, and we will use BigIntegers to repre-
sent the numerator and denominator. Thus our class will be aptly named
BigRational .
Figure 3.11 shows the BigRational class. The online code is fully com-
mented; we have omitted comments in order to allow the code to fit in the text
pages. Lines 5 and 6 are constants BigRational.ZERO and BigRational.ONE . We
also see that the data representation is two BigIntegers , num and den , and our
code will be implemented in a manner that guarantees that the denominator is
never negative. We provide four constructors, and two of the constructors are
implemented by using the this idiom. The other two constructors have more
complicated implementations shown in Figure 3.12. There we see that the
two-parameter BigRational constructor initializes the numerator and denomi-
nator as specified, but then must ensure that the denominator is not negative
(which is done by calling private method fixSigns ) and then reducing out
common factors (which is done by calling private method reduce ). We also
provide a check to ensure that 0/0 is not accepted as a BigRational , and this is
done in check00 which will throw an exception if there is an attempt to con-
struct such a BigRational . The details of check00 , fixSigns , and reduce are less
important than the fact that their use in a constructor and other methods
allows the designer of the class to guarantee that objects are always placed in
valid states.
The BigRational class also includes methods to return absolute values and
a negative. These are simple and shown in lines 24-27 of Figure 3.11. Note
that these methods return new BigRational objects, leaving the original intact.
add , subtract , multiply , and divide are listed in lines 29-36 of Figure 3.11
and implemented in Figure 3.13. The math is less interesting than a funda-
mental concept that because each of the four routines ends by creating a new
BigRational , and the BigRational constructor has calls to check00 , fixSigns ,
and reduce , the resulting answers are always in correct reduced form, and an
attempt to do a zero divide by zero would automatically be caught by check00 .
Finally, equals and toString are implemented in Figure 3.14. The signa-
ture for equals , as discussed earlier, requires a parameter of type Object . After
a standard instanceof test and type cast, we can compare numerators and
denominators. Notice that we use equals (not ==) to compare the numerators
and denominators, and also notice that since BigRational s are always in
reduced form, the test is relatively simple. For toString , which returns a
String representation of the BigRational , the implementation could be one
line, but we add code to handle infinity and -infinity, and also to not output the
denominator if it is 1.