    ui = _getUtility(xi, yi);
    uf = _getUtility(xf, yf);
    uint256 result = Math.mulDiv(uint256(uf), uint256(si), uint256(ui));
    require(result < INT_MAX);
    int256 sf = int256(result);
        ui = _getUtility(xi, yi);
        uf = _getUtility(xf, yf);

        uint256 result = Math.mulDiv(uint256(uf), uint256(si), uint256(ui));
        require(result < INT_MAX);   
        int256 sf = int256(result);

        // apply fee to the computed amount
        computedAmount = _applyFeeByRounding(sf - si, feeDirection);
        require(sf >= MIN_BALANCE);
        int256 result = _reserveTokenSpecified(
            withdrawnToken,
            -int256(withdrawnAmount),
            FEE_UP,
            int256(totalSupply),
            int256(xBalance),
            int256(yBalance)
        );
    uint256 result = Math.mulDiv(uint256(uf), uint256(si), uint256(ui));
    require(result < INT_MAX);
    int256 sf = int256(result);

    require(sf >= MIN_BALANCE); 
