Fix a bug in factorization function causing infinite loops in rare cases

[pivis]

There is a small bug in factorization function when it gets to factors above 10M and starts calling pollard_rho. If it can't find a factor using f(x)=x^2+c (mod n) with c==1 it is supposed to update c to some other random value. But initialization accidentally got in the loop body and would always reset c back to 1.

Since pollard_rho is only called to get factors larger than 10M at the point, and the fact that c=1 usually works it is quite rare for this bug to surface, but in the rare case when c=1 doesn't work it causes the infinite loop. Example would be galois.GF(2400610585866217) which requires factorization of 2400610585866217 - 1 = 2^3 * 3 * 100025441077759 = 2^3 * 3 * 10000537 * 10002007.

[codecov]

Codecov Report

Base: 96.38% // Head: 96.38% // No change to project coverage 👍

Coverage data is based on head (64f3cf2) compared to base (648aa06).
Patch coverage: 100.00% of modified lines in pull request are covered.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #450   +/-   ##
=======================================
  Coverage   96.38%   96.38%           
=======================================
  Files          42       42           
  Lines        5533     5533           
=======================================
  Hits         5333     5333           
  Misses        200      200           

Impacted Files	Coverage Δ
src/galois/_prime.py	93.53% <100.00%> (ø)

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[mhostetter]

Thanks for looking into this. That's a bit of an embarrassing bug, but you're absolutely right!

I'm inclined to merge this and immediately push a bug fix release 0.3.1. Then I will respond to your comments/suggestions about improving prime factoring generally #187 (comment).

Thanks again for the PR!

[mhostetter]

Performance improvements:

In [1]: import galois

# Before PR
In [2]: %time galois.GF(2400610585866217)
# Never returns...

# After PR
In [2]: %time galois.GF(2400610585866217)
Wall time: 96 ms
Out[2]: <class 'galois.GF(2400610585866217)'>