This commit adds `cargo update` to the distclean target in the
makefile. This updates the Cargo.lock file when clearing the
deps directory.
In addition, it adds a faster implementation of the Sieve of
Eratosthenes for use by `src/factor/gen_table.rs` and `test/factor.rs`.
This change does the following:
1. Updates the arithmetic functions in `src/factor/numeric.rs` to
correctly handle all cases up to 2^64. When numbers are larger
than 2^63, we fall back to slightly slower routines that check
for and handle overflow.
2. Since the arithmetic functions will now not overflow, we no longer
need the safety net trial division implementation. We now always
use Pollard's rho after eliminating small (<=13 bit) primes.
3. Slight tweak in `src/factor/gen_table.rs` to generate the first
1027 primes, which means we test every prime of 13 or fewer bits
before going into Pollard's rho. Includes corresponding update in
`src/factor/prime_table.rs` and the Makefile to reflect this.
4. Add a new test that generates random numbers with exclusively
large (14 to 50 bit) prime factors. This exercises the possible
overflow paths.
5. Add another new test that checks the `is_prime()` function against
a few dozen 64-bit primes. Again this is to exercise possible
overflow paths.
Add a test for `factor`.
This commit also pulls factor's Sieve implementation into its own module
so that the factor test can use it.
Finally, slight refactoring for clarity in gen_table.rs.
This commit builds upon @wikol's Pollard rho implementation.
It adds the following:
1. A generator for prime inverse tables. With these, we can do
very fast divisibility tests (a single multiply and comparison)
for small primes (presently, the first 1000 primes are in the
table, which means all numbers of ~26 bits or less can be
factored very quickly.
2. Always try prime inverse tables before jumping into Pollard's
rho method or using trial division.
3. Since we have eliminated all small factors by the time we're
done with the table division, only use slow trial division when
the number is big enough to cause overflow issues in Pollard's
rho, and jump out of trial division and into Pollard's rho as
soon as the number is small enough.
4. Updates the Makefile to regenerate the prime table if it's not
up-to-date.
