feat: AMM

[benesjan]

This is an implementation of a Uni v2 style DEX pool. One of the main goals of this PR was to figure out what kind of token flows we will need.

Note for reviewers

I put a lot of comments and some questions in the code. The code does not yet compile as the token is not yet updated with the flows we need but I have a high confidence that it's very close to final.

Problems

There were a couple problems I have stumbled upon:

1. The need for having the liquidity token be separate from the DEX/pair contract itself. This is because we don't have inheritance in Noir and copying the contract code into the DEX is not something I am willing to go through.
2. We don't have a large enough integer type that is not terrible - (U128 is too cumbersome to use because of #8271). I currently use u64 everywhere but that is not sufficiently large for DeFi.

[benesjan]

• #9934
• #8644 👈
• #9950
• #9943
• master

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[nventuro]

Superceded by https://github.com/AztecProtocol/aztec-packages/pull/8644