Add modular exponentiation and modular inverse, closes #45

[dlesnoff]

Add powmod with all the comments made on the previous pull request.

[dlesnoff]

I finally made a rebase as the changes seemed too minor for a commit. I hope this will not break something, as I had to force push into my branch.

[dlesnoff]

I have added modular inverse for negative exponents in modular exponentiation. I fear that modular inverse is too slow as for now. It might be improved with a faster multiplication. Fixes #45.

[pietroppeter]

should we have base == zero return zero also for positive exponent? (and maybe we also check for exponent == 0 before and return 1 in that case)?
code would then be:

  if exponent == zero:
    return one
  if base == zero:
    return zero
  if exponent < 0:
    let baseInv = invmod(base, modulus)
    return powmod(baseInv, -exponent, modulus)

also: not sure if all those ifs would be better with an if..elif..else (even if they raise or return)

[dlesnoff]

Your propositiion removes a lot of unuseful computation for zero base and large positive exponent indeed.
I have not written it this way as zero does not appear as a specific case of the entire algorithm. The square and multiply algorithm would work with 0 as base too.
It is an edge case for modular inverse though and 0 has strictly speaking no modular inverse. As @konsumlamm has proposed to me to remove an if clause in previous PR, I think it is better to keep only edge cases in the first ifs (it improves readability).
Concerning multiple ifs rather than if .. elif .. else clause, I personnaly prefer to avoid else clause as it adds unuseful indentation for the rest of the algorithm. Maybe the compiler is able to do more compilation's optimization with if .. elif .. else clause. I do not think it improves a lot.

[konsumlamm]

I'm not fully done with reviewing, will finish that later (hopefully today).

[dlesnoff]

I have changed the modular exponentiation so that it uses an if..elif..else construct rather than only ifs.
I optimized a bit by using the isZero function rather than a modulus == 0.
I added some tests for two other edge cases (0^0 mod n == 1 and 0^1 mod n == 0).
I have tried to rebase on latest commit but I did this uncorrectly (I merged and rebased, while I should have done a simple rebase).

[dlesnoff]

Fix PR's history. The 5 different commits might be too much, wich ones should I keep ?

[konsumlamm]

Fix PR's history. The 5 different commits might be too much, wich ones should I keep ?

Don't worry, PRs get squashed anyway, it doesn't really matter how many commits your PR has.

[konsumlamm]

Now I'm done with reviewing. It took a little longer than expected.

[dlesnoff]

I believe there are some cases where invmod returns negative integers depending on the sign of the input. This needs more testing.

[dlesnoff]

Tried to rebase, then merge with current master branch. History is a mess. Please squash my commits before merging.

[dlesnoff]

I removed an example that used a custom modular exponentiation similar to my powmod function. I could have replaced with it with just one call to the function, it would not have been interesting.

[konsumlamm]

@dlesnoff can you rebase this, to resolve the conflicts?
@narimiran can we merge this soon, to avoid more conflicts? Unless you have any objections of course.

[dlesnoff]

merged the changes to resolve the conflicts.