mev-beta/docs/uniswap-pricing.md

Uniswap V3 Pricing Documentation

This document explains the Uniswap V3 pricing model and how it's implemented in the MEV bot.

Core Concepts

Ticks

In Uniswap V3, prices are represented as ticks. A tick is defined as:

tick = log√1.0001(√P)

Where P is the price of token1 in terms of token0.

Ticks are integers that range from -887272 to 887272.

sqrtPriceX96

Prices are stored internally as sqrtPriceX96, which is:

sqrtPriceX96 = √P * 2^96

This allows for precise fixed-point arithmetic without floating-point operations.

Liquidity

Liquidity in a pool is represented as a uint128 value that determines the depth of the pool at a given price.

Mathematical Relationships

Converting between representations

1. Tick to sqrtPriceX96:

   sqrtPriceX96 = 1.0001^(tick/2) * 2^96
   

2. sqrtPriceX96 to Tick:

   tick = log_1.0001(sqrtPriceX96 / 2^96)^2
   

3. Price to Tick:

   tick = log_1.0001(price)
   

Implementation Details

Our Go implementation uses the math/big package for precision and handles the fixed-point arithmetic required for Uniswap V3 calculations.

Key functions:

• SqrtPriceX96ToPrice: Converts sqrtPriceX96 to a floating-point price
• PriceToSqrtPriceX96: Converts a floating-point price to sqrtPriceX96
• TickToSqrtPriceX96 : Converts a tick to sqrtPriceX96
• SqrtPriceX96ToTick : Converts sqrtPriceX96 to a tick