* factor::Factors: Derive implementations of Eq and PartialEq
* factors::Factors: Implement quickcheck::Arbitrary
This generates uniformly-distributed integers with known factorisations,
and will enable further testing.
* factor: Test against random numbers with known factorisations
* factor::Factors::arbitrary: Simplify method signature
* factor::numeric::gcd: Rename test against the Euclidean algorithm
* factor::numeric::gcd: Add various property-based tests
* factor::numeric::modular_inverse: Rename test
* factor::numeric::modular_inverse: Add test on random values
* factor::numeric: Start refactoring into multiple submodules
No change to the module's interface, but it should make it much easier to
keep the tests right next to the code they are related to.
Moreover, build.rs' dependency is now limited to numeric::{modular_inverse,
traits}, meaning that the rest of it can use build-time generated tables etc.
* factor::numeric: Move gcd (and its test) to a submodule
* factor::numeric: Move Montgomery arithmetic to its own module
Finally hollowed-out numeric.rs
* factor: Move numeric.rs to numeric/mod.rs
* factor::numeric: Fix an erroneous lint on obsolete Rust versions
Ignoring a value of that type is a bug: they are only produced by
`miller_rabbin::test`, which is a pure, but expensive, function.
As such, an ignored value is always either a mistake, or an easy
optimisation opportunity (just remove the useless call to `test`).
Also add a property-based test against the Euclidean implementation.
numeric::gcd got ~50-65% faster, according to criterion. The effect on the
overall system is small, but later PRs will use a lot more GCD computations.
- `DoubleInt::Double` renamed to `DoubleWidth`
- `{as,from}_double()` renamed to `{as,from}_double_width()`.
This should hopefully clarify that this is not a “double precision”
floating-point type, but an integer type with a larger range (used
for storing intermediate results, typ. from a multiplication)
Montgomery only works for odd n, so attempting to construct an instance
for an even number results in a panic!
The most obvious solution is to special-case even numbers.
test() takes a modulus that is known to not be even or <2 (otherwise the
Montgomery value could not be constructed), so those checks can be hoisted
into is_prime() and out of the critical path.
Montgomery<_> only works for odd n, so attempting to construct an instance
for an even number results in a panic!
The most obvious solution is to special-case even numbers.
