Tighter bounds for IntMap and IntSet merge

[meooow25]

Closes #1011

[meooow25]

It would be good to get some more eyes on this.

[Lysxia]

Your analysis looks good to me.

It may be worth explicitly defining $n$ as the min and $m$ as the max of the two sizes, otherwise at first glance it looks like there is something asymmetric going on.

[meooow25]

$O(\min(n, m \log \frac{2^W}{m})), m \leq n$

It does say $m \leq n$, in the same manner as Set and Map.

Though maybe you mean one may mistakenly think $m$ and $n$ are the first and second maps?

[Lysxia]

Yes that's what I mean.

[meooow25]

Hmm that goes for Set and Map too. And I'm not sure how to make it better.

$O(\min(\max(m,n), \min(m,n) \log \frac{2^W}{\min(m,n)}))$ looks terrible.

[Lysxia]

How about a top level comment under the "Combine" header, with a slight change of naming:

Most of these combining functions have complexity $O(\min(N, n \log(\frac{2^W}{n})))$, where $n$ is the minimum of the sizes of the arguments and $N$ is their maximum.

[meooow25]

The "Combine" section might not be enough, since a few functions like isSubmapOf are elsewhere. But I like the idea, we can put this comment at the top of the module instead.

I'll make a separate PR for it (with Set and Map too).

Edit: Oh and I would like to keep the $m$ and $n$ names (rather than $n$ and $N$) because the terms are from the "Parallel Ordered Sets Using Join" paper and it's nice to be consistent. $N$ is also used to denote a maximum value in #957, which could be confusing.