from ETHGlobal Paris 2023, built with Uniswap v4 Hooks 🦄
Why not use TWAP? lower-liquidity pools are prone to manipulation!
| Algorithm | Gas (Read) |
|---|---|
| Quickselect | comically a lot (hundreds of thousands) |
| Frugal-2U | comically a lot (but less than QS) |
| Running Frugal-2U | 4812 |
| Quickselect Time-weighted | TBD |
| Frugal-2U Time-weighted | TBD |
Methodology: obtain 50 unique tick observations by running swaps in both directions. Each swap is spaced 12 seconds apart. Use
gasleft()before and after reading the median
The classic: given a sequence of unordered ticks, fetch the median with the quickselect algorithm
- Uses an O(logn) algorithm on-read
- Depends on tick observations written to storage
Approximates the median using Frugal-2U from a sequence of numbers (naive implementation)
Frugal median algorithm compares new numbers against the current approximation and updates the approximation according to a dynamic step
- Uses the frugal median-approximation algorithm
- Depends on tick observations written to storage
The gas-optimized implementation of the frugal median approximation: calculating an on-going approximation of the median
- Uses the frugal median-approxiation algorithm
- Stores the running median (approximated) in direct storage
- additional research™️ required for windowed support
In the frugal median algorithm, the dynamic step can be modified to favor stabilization or responsiveness/accuracy. The repo uses 1-tick as a step, but the implementation is set up for additional experimentation
The repo is in its early stages and did not have sufficient time to implement time-weighted medians. Time-weighted medians are likely to better represent the price since they account for the duration of a tick (price observation). The repo currently treats unique price observations as having equivalent durations.
src/
├── RunningFrugalMedianHook.sol Running median approximation
├── TickObserver.sol store tick observations for windowed median reads
├── lens
│ ├── FrugalMedianLens.sol read TickObserver and approximate median
│ └── MedianLens.sol read TickObserver and calculate true median
└── lib
├── FrugalMedianLibrary.sol median approximation library
├── MedianLibrary.sol median calculation library (quickselect)
└── RingBufferLibrary.sol optimized ring buffer for price observations
test/
├── FrugalMedianLens.t.sol test the naive frugal median
├── MedianLens.t.sol test the true median (quickselect)
├── RunningMedian.t.sol test the running median approximation
├── TickObserver.t.sol test the tick observer
├── implementation
│ ├── ... Uniswap overrides for testing
├── median
│ ├── FrugalMedianTest.t.sol test frugal median algo
│ └── MedianLibrary.t.sol test quickselect algo
└── utils
├── HookTest.sol
└── RingBuffer.t.sol test ring buffer
Additional resources:
v4-periphery contains advanced hook implementations that serve as a great reference
requires foundry
forge install
forge test
Credits