Pair: Reserve Updates and TWAP Oracle

Key takeaway: Uniswap V2's TWAP oracle accumulates price0CumulativeLast and price1CumulativeLast on every reserve update, encoded in a custom UQ112x112 fixed-point format (224 bits, 112 integer + 112 fractional). The _update() function holds two opposite arithmetic regimes in one body: reserve writes must revert on overflow (the uint112 cast is guarded by require), while accumulator increments must allow overflow so modular subtraction over an oracle window produces the correct average price.

What You Are Building

The _update() function is called after every mint, burn, and swap. It does two things: store the new reserves and accumulate prices for the TWAP (time-weighted average price) oracle. This is one of the most elegant pieces of Uniswap V2. A few lines of code give the entire DeFi ecosystem a manipulation-resistant price feed, and the design decisions behind each line are worth understanding deeply.