Decrease Huffman Weights to u32

[JeremyRubin]

This builds on #699 but is the more bikesheddable part since it changes the API.

u32 of weight should be enough for any branch.
-- Bill Gates

[JeremyRubin]

rebased :)

[dr-orlovsky]

utACK 1518517

[Kixunil]

Looks legit but I'd like someone more experienced with probabilities than myself to confirm this is a good idea.

[JeremyRubin]

@Kixunil basically this restricts our "fidelity" in expressing relative probabilities to maximally 4 billion to one, and introduces a possible "optimization glitch" when we have more than 4 billion branches all of maximal weight (well formedness still fine).

I think it's very unlikely that we need to express something as more than 4 billion times more likely very often -- i.e. if you think you might use a signing path once per second for lightning, you'd use the other path once every 126 years.

I don't think this patch is critical, but some folks may not like using u128s internally.

[Kixunil]

Sounds good!

ACK 1518517

[JeremyRubin]

yeah to be clear i personally don't think this patch is needed, so it's really up to others if they think it's needed.

[dr-orlovsky]

Merging, since it has two ACKs for some time already and is quite trivial

[JeremyRubin]

I would like a post-merge ack i think maybe from @sanket1729 and @apoelstra if possible.

This was a follow up because there was some dissent on my use of u128 in a previous PR.

I know I authored it but i am neutral on this so i don't think the usual 2 acks works since usualy 2 acks is really 3, including the author's.

[apoelstra]

yep, concept ACK