...and correct some implementations in Rational.
Although it was possible to implement many of the simpler algorithms using a two's complement representation, it proved to be difficult to implement multiplication or division without taking the absolute value. Some reading suggests that most (if not all) arbitrary-precision integer implementations use sign-and-magnitude representation. Thus, I have switched back to that representation (which was one option that I had already explored).
This PR contains working implementations of comparison, addition, subtraction, long multiplication, and negation. Additional testing is required to verify correctness.
No attempt has yet been made to implement division or bit shifting, and no updated implementation is included for other bitwise operations. It remains unclear to me whether generic use of such operations always assumes two's complement representation, or whether it is appropriate to simply perform these bitwise operations on the native sign-and-magnitude representation.
Future directions include implementation of more sophisticated multiplication algorithms such as Karatsuba.
Xiaodi Wu