`std::ratio` module contains `BigRational` type, but the type is not usable by following reasons.
* `Ratio::new` requires `T: Copy + Num + Ord`, but `BigInt` is not implicitly copyable, because it contains unique vector.
* `BigInt` is not implements `Num`
So, I rewrite `Ratio` as follows.
* `Ratio` requires `T: Clone + Integer + Ord`.
* `Copy` -> `Clone`: to be able to use `BigRational`
* `Num` -> `Integer`: It is incorrect that a rational number constructed by two non-integer numbers.
* `BigInt` implements `Num` and `Orderable` which are required by `Integer` bound
fail!() used to require owned strings but can handle static strings
now. Also, it can pass its arguments to fmt!() on its own, no need for
the caller to call fmt!() itself.
`std::bigint` contains the following code.
```rust
borrow = *elem << (uint::bits - n_bits);
```
The code above contains a bug that the value of the right operand of the shift operator exceeds the size of the left operand,
because sizeof(*elem) == 32, and 0 <= n_bits < 32 in 64bit architecture.
If `--opt-level` option is not given to rustc, the code above runs as if the right operand is `(uint::bits - n_bits) % 32`,
but if --opt-level is given, `borrow` is always zero.
I wonder why this bug is not catched in the libstd's testsuite (I try the `rustc --test --opt-level=2 bigint.rs` before fixing the bug,
but the unittest passes normally.)
This pull request also removes the implicit vector copies in `bigint.rs`.
borrow = *elem << (uint::bits - n_bits);
The code above contains a bug that the value of the right operand of the shift operator exceeds the size of the left operand,
because sizeof(*elem) == 32, and 0 <= n_bits < 32 in 64bit architecture.
If `--opt-level` option is not given to rustc, the code above runs as if the right operand is `(uint::bits - n_bits) % 32`,
but if --opt-level is given, `borrow` is always zero.
I wonder why this bug is not catched in the libstd's testsuite (I try the `rustc --test --opt-level=2 bigint.rs` before fixing the bug,
but the unittest passes normally.)
Closes#3083.
This takes a similar approach to #5797 where a set is present on the `tcx` of used mutable definitions. Everything is by default warned about, and analyses must explicitly add mutable definitions to this set so they're not warned about.
Most of this was pretty straightforward, although there was one caveat that I ran into when implementing it. Apparently when the old modes are used (or maybe `legacy_modes`, I'm not sure) some different code paths are taken to cause spurious warnings to be issued which shouldn't be issued. I'm not really sure how modes even worked, so I was having a lot of trouble tracking this down. I figured that because they're a legacy thing that I'd just de-mode the compiler so that the warnings wouldn't be a problem anymore (or at least for the compiler).
Other than that, the entire compiler compiles without warnings of unused mutable variables. To prevent bad warnings, #5965 should be landed (which in turn is waiting on #5963) before landing this. I figured I'd stick it out for review anyway though.
