  Constant-product market making functions were first introduced by Hayden
Adams in 2017 to create Uniswap, a decentralised exchange on Ethereum. This
enables users to exchange assets at any given rate. Some variations such as
Balancer and Curve were later introduced. In this paper, we analyse the maths
that rule this type of protocol. We show that splitting a trade in multiple
smaller trades does not impact the final exchange rate. We also show that the
protocol is safer and more profitable when no one recompounds their fees.
