factor_one and friends

[hvds]

Hi Dana, we've discussed this from time to time, I finally got round to having a go at implementing it - moving the core of factor() out to a new function factor_one() that returns one factor at a time. This will add a slight overhead for the additional calls, and management of the factor_state structure; but will give direct benefits for some of the functions that call factor() (is_semiprime, is_smooth, is_rough, is_powerful), and I think offers opportunities for further improvement.

• add_factor now also takes an exponent, the two macros are removed;
• fs_init, fs_close added to help with management of the factor_state structure;
• removed the secondary power_factor() check; not sure how important that is, but can work on bringing it back if needed
• the primary power_factor check no longer recurses, just sets a multiplier for exponents;
• bonus function is_tau(n, k) returns true if tau(n) == k (should it be called has_divisors?);
• handling 32-bit overflow on khi*khi needs more thought: maybe tlim should become mpz_t, or maybe khi should be reduced on 32-bit targets;
• is_tau() needs more tests.

I'm not in a rush for this, I think it'd be a good idea to release what's currently in the repo before merging this, and it needs some polish in any case. In particular, I don't know which FS_LARGE tests are worth repeating after a factor is found, and which should be skipped - that could be handled either by adding more FS states or, say, by having a bitmask of tests to try (probably also copied with the pending factors onto the tofac_stack).

I'd welcome your thoughts.

[hvds]

Note that MPU t/26-issquarefree.t found the missing mpz_init when factorizing 815373060690029363516051578884163974. That appears to be the only test case across MPU and MPUG that reaches that point (finding a composite factor directly).