Make gcdx agree with Julia.

[wbhart]

No description provided.

[thofma]

Given that this is quite a fundamental task, how big is the slow down?

[wbhart]

There's just one or in the worst case two extra exact divisions and an extra divrem, but only when the output isn't already normalised.

Generically the complexity of the gcd is much higher than for the divisions. For small integers, the time for the gcd dominates anyway. There is a small region in between the two cases where the division time could be 20% of the time.

In any event, I spent quite some time reducing the number of additional operations as much as possible. At least in the generic case the gcd is small and the exact divisions are a negligible cost. Obviously if the result is very far from reduced, the divrem is relatively expensive, otherwise it is cheap.

Flint never did this normalisation, whereas GMP and Julia do, so if we want it to be consistent, we have to do this normalisation in Nemo itself. So we don't have a lot of choice here.

Hmm, I just noticed that converting to BigInt, doing the gcdx there and converting back eliminates the cost entirely, and makes it faster for small integers. I think I might do that instead.