Figure out a good convention for normalizing rational numbers

[thestinger]

The gmp Mpq type does does it after each operation, and then exposes a raw interface for doing a few operations without normalizing. It only guarantees that operations are valid when the type is normalized. This leads to the most predictable performance with big integers, and avoids avoidable overflows for fixed size ones.

This would probably involve making the fields priv and using scary names for raw manipulation methods.

[pnkfelix]

Visited for bug triage, 2013jun24. The title of this bug makes this sound like a potentially open-ended task, but I interpret the description as being in favor of normalizing (by force, by doing it behind an enforced abstraction layer) after each operation (or at least all the standard arithmetic operations, in order to get predictable performance).

[huonw]

Triage: I'd agree with the description of normalising like GMP (after every operation) and exposing some low-level methods for when someone wants the library to trust them (maybe even making these unsafe?).

(Part of #4819, related to #8466.)

[flaper87]

Visiting for triage. @bjz may have more to add here.

(part of #10387)

[rust-highfive]

This issue has been moved to the RFCs repo: rust-lang/rfcs#332

[rust-highfive]

This issue has been moved to the RFCs repo: rust-num/num#6