abstract contract Timed {
    using SafeCast_2 for uint256;

    /// @notice the start timestamp of the timed period
    uint256 public startTime;

    /// @notice the duration of the timed period
    uint256 public duration;

    event DurationUpdate(uint256 _duration);

    event TimerReset(uint256 _startTime);

    constructor(uint256 _duration) public {
        _setDuration(_duration);
    }

    modifier duringTime() {
        require(isTimeStarted(), "Timed: time not started");
        require(!isTimeEnded(), "Timed: time ended");
        _;
    }

    modifier afterTime() {
        require(isTimeEnded(), "Timed: time not ended");
        _;
    }

    /// @notice return true if time period has ended
    function isTimeEnded() public view returns (bool) {
        return remainingTime() == 0;
    }

    /// @notice number of seconds remaining until time is up
    /// @return remaining
    function remainingTime() public view returns (uint256) {
        return duration - timeSinceStart(); // duration always >= timeSinceStart which is on [0,d]
    }

    /// @notice number of seconds since contract was initialized
    /// @return timestamp
    /// @dev will be less than or equal to duration
    function timeSinceStart() public view returns (uint256) {
        if (!isTimeStarted()) {
            return 0; // uninitialized
        }
        uint256 _duration = duration;
        // solhint-disable-next-line not-rely-on-time
        uint256 timePassed = block.timestamp - startTime; // block timestamp always >= startTime
        return timePassed > _duration ? _duration : timePassed;
    }

    function isTimeStarted() public view returns (bool) {
        return startTime != 0;
    }

    function _initTimed() internal {
        // solhint-disable-next-line not-rely-on-time
        startTime = block.timestamp;

        // solhint-disable-next-line not-rely-on-time
        emit TimerReset(block.timestamp);
    }

    function _setDuration(uint _duration) internal {
        duration = _duration;
        emit DurationUpdate(_duration);
    }
}
/// @title an abstract contract for timed events
/// @author Fei Protocol
function isTimeEnded() public view returns (bool) {
    return remainingTime() == 0;
}

/// @notice return true if time period has ended