◆ Purpose

update reserve status of pool

balance ⇒ state when token has already been transferred (latest version)

reserve ⇒ state before token is transferred (pre latest version)

To make reserve catch up with balance

◆ Input & Return value

(uint balance0, uint balance1, uint112 _reserve0, uint112 _reserve1) ⇒ none

◆ Example

balance0 = 51224550845936

balance1= 44552339419344963588195

reserve0 = 51224550843936

reserve1= 44552339419344963088195

◆ Code and Explain

function _update(uint balance0, uint balance1, uint112 _reserve0, uint112 _reserve1) private {
        require(balance0 <= uint112(-1) && balance1 <= uint112(-1), 'UniswapV2: OVERFLOW');
        
//--------- This code is used to get **TWAP**(I'll explain later) ------------

				uint32 blockTimestamp = uint32(block.timestamp % 2**32);
        uint32 timeElapsed = blockTimestamp - blockTimestampLast; // overflow is desired
        if (timeElapsed > 0 && _reserve0 != 0 && _reserve1 != 0) {
            // * never overflows, and + overflow is desired
            price0CumulativeLast += uint(UQ112x112.encode(_reserve1).uqdiv(_reserve0)) * timeElapsed;
            price1CumulativeLast += uint(UQ112x112.encode(_reserve0).uqdiv(_reserve1)) * timeElapsed;
        }

//---------------------------------------------------------------------
				
        reserve0 = uint112(balance0);
        reserve1 = uint112(balance1);
        blockTimestampLast = blockTimestamp; // TWAP
        emit Sync(reserve0, reserve1);
    }

◆ Resources

https://github.com/Uniswap/v2-core/blob/master/contracts/UniswapV2Pair.sol#L73

Trip to UniswapV2 Contracts