computeProfitMaximizingTrade in uniswap

Question

I'm trying to understand how uniswap can compute the best trade. I found the code here : https://github.com/Uniswap/v2-periphery/blob/master/contracts/libraries/UniswapV2LiquidityMathLibrary.sol

   function computeProfitMaximizingTrade(
    uint256 truePriceTokenA,
    uint256 truePriceTokenB,
    uint256 reserveA,
    uint256 reserveB
) pure internal returns (bool aToB, uint256 amountIn) {
    aToB = FullMath.mulDiv(reserveA, truePriceTokenB, reserveB) < truePriceTokenA;

    uint256 invariant = reserveA.mul(reserveB);

    uint256 leftSide = Babylonian.sqrt(
        FullMath.mulDiv(
            invariant.mul(1000),
            aToB ? truePriceTokenA : truePriceTokenB,
            (aToB ? truePriceTokenB : truePriceTokenA).mul(997)
        )
    );
    uint256 rightSide = (aToB ? reserveA.mul(1000) : reserveB.mul(1000)) / 997;

    if (leftSide < rightSide) return (false, 0);

    // compute the amount that must be sent to move the price to the profit-maximizing price
    amountIn = leftSide.sub(rightSide);
}

Why they use price to determinate aToB ? I don't understand the formula

Answer 1

This code does not compute the best trade on Uniswap. It's used to calculate the profit you can make between Uniswap and another market.

Take a look at here: https://github.com/Uniswap/v2-periphery/issues/103#issuecomment-933029929