Numo

⚠️ WARNING: This code has not yet been audited. Use at your own risk.

Overview

Numo is a dynamic, automated market maker that provides continuous liquidity to onchain FX markets. Numo's specialized curve can offer more efficient exchange of FX and market make a variety of derivative products such as futures, forwards, and exotic option instruments without oracles.

Try it out! Send money from one currency to another at the best rates possible and instantly with numo.cash.

Advantages

• ✅ Any FX pair
• 🌍 Globally accessible
• 🤝 Instant settlement

Architecture

Numo is a Uniswap V4 hook that inherits OpenZeppelin's BaseCustomCurve contract from their uniswap-hooks library. Thus enabling Numo to interact with the V4 poolmanager for optimal routing and inherit much of their battle tested code without needing use the concentrated liquidity logic.

Log-Normal Market Maker

A log-normal curve is beter suited for FX over hyperbolic curves implemented by Uniswap as FX exchange rates exhbit log-normal behavior. Instead of overriding beforeSwap completey, Numo uses _getUnspecifiedAmount to implement the curve defined as:

$$ \varphi(x, y, L; \mu, \sigma) = \Phi^{-1} \left(\frac{x}{L} \right) + \Phi^{-1} \left(\frac{y}{\mu L} \right) + \sigma $$

where:

• $\Phi^{-1}$ is the inverse Gaussian cumulative distribution function (CDF).
• $L$ represents the total liquidity of the pool.
• $x$ and $y$ represent the reserves scaled by liquidity.
• $\mu$, the mean and $\sigma$, the width define the distribution of liquidity.

As liquidity $L$ increases, both reserves scale proportionally, maintaining a log-normal liquidity distribution.

Acknowledgements

The smart contract suite is inspired by Primitive's Log-Normal DFMM implementation and the replicating market makers paper that first showed the relationship between liquidity and the trading curve of an AMM.

Setup

Requires forge to be installed already.

forge install

Testing

forge test -vvv

Coverage

forge coverage --report lcov
cmd + shift + p -> Coverage Gutters: Display Coverage

Gas benchmarks

View gas usage

forge snapshot --gas-report

Compare gas usage

forge snapshot --diff

Update dependencies

git submodule update --init --recursive

Deployments

Network	Factory Address
Base	0x82360b9a2076a09ea8abe2b3e11aed89de3a02d1

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