contract DividendPayingToken is
    ERC20,
    DividendPayingTokenInterface,
    DividendPayingTokenOptionalInterface
{
    using SafeMath for uint256;
    using SafeMathUint for uint256;
    using SafeMathInt for int256;

    // With `magnitude`, we can properly distribute dividends even if the amount of received ether is small.
    // For more discussion about choosing the value of `magnitude`,
    //  see https://github.com/ethereum/EIPs/issues/1726#issuecomment-472352728
    uint256 internal constant magnitude = 2**128;

    uint256 internal magnifiedDividendPerShare;

    // About dividendCorrection:
    // If the token balance of a `_user` is never changed, the dividend of `_user` can be computed with:
    //   `dividendOf(_user) = dividendPerShare * balanceOf(_user)`.
    // When `balanceOf(_user)` is changed (via minting/burning/transferring tokens),
    //   `dividendOf(_user)` should not be changed,
    //   but the computed value of `dividendPerShare * balanceOf(_user)` is changed.
    // To keep the `dividendOf(_user)` unchanged, we add a correction term:
    //   `dividendOf(_user) = dividendPerShare * balanceOf(_user) + dividendCorrectionOf(_user)`,
    //   where `dividendCorrectionOf(_user)` is updated whenever `balanceOf(_user)` is changed:
    //   `dividendCorrectionOf(_user) = dividendPerShare * (old balanceOf(_user)) - (new balanceOf(_user))`.
    // So now `dividendOf(_user)` returns the same value before and after `balanceOf(_user)` is changed.
    mapping(address => int256) internal magnifiedDividendCorrections;
    mapping(address => uint256) internal withdrawnDividends;

    uint256 public totalDividendsDistributed;

    constructor(string memory _name, string memory _symbol)
        ERC20(_name, _symbol)
    {}

    /// @dev Distributes dividends whenever ether is paid to this contract.
    receive() external payable {
        distributeDividends();
    }

    /// @notice Distributes ether to token holders as dividends.
    /// @dev It reverts if the total supply of tokens is 0.
    /// It emits the `DividendsDistributed` event if the amount of received ether is greater than 0.
    /// About undistributed ether:
    ///   In each distribution, there is a small amount of ether not distributed,
    ///     the magnified amount of which is
    ///     `(msg.value * magnitude) % totalSupply()`.
    ///   With a well-chosen `magnitude`, the amount of undistributed ether
    ///     (de-magnified) in a distribution can be less than 1 wei.
    ///   We can actually keep track of the undistributed ether in a distribution
    ///     and try to distribute it in the next distribution,
    ///     but keeping track of such data on-chain costs much more than
    ///     the saved ether, so we don't do that.
    function distributeDividends() public payable override {
        require(totalSupply() > 0);

        if (msg.value > 0) {
            magnifiedDividendPerShare = magnifiedDividendPerShare.add(
                (msg.value).mul(magnitude) / totalSupply()
            );
            emit DividendsDistributed(msg.sender, msg.value);

            totalDividendsDistributed = totalDividendsDistributed.add(
                msg.value
            );
        }
    }

    /// @notice Withdraws the ether distributed to the sender.
    /// @dev It emits a `DividendWithdrawn` event if the amount of withdrawn ether is greater than 0.
    function withdrawDividend() public virtual override {
        _withdrawDividendOfUser(payable(msg.sender));
    }

    /// @notice Withdraws the ether distributed to the sender.
    /// @dev It emits a `DividendWithdrawn` event if the amount of withdrawn ether is greater than 0.
    function _withdrawDividendOfUser(address payable user)
        internal
        virtual
        returns (uint256)
    {
        uint256 _withdrawableDividend = withdrawableDividendOf(user);
        if (_withdrawableDividend > 0) {
            withdrawnDividends[user] = withdrawnDividends[user].add(
                _withdrawableDividend
            );
            emit DividendWithdrawn(user, _withdrawableDividend);
            (bool success, ) = user.call{
                value: _withdrawableDividend,
                gas: 3000
            }("");

            if (!success) {
                withdrawnDividends[user] = withdrawnDividends[user].sub(
                    _withdrawableDividend
                );
                return 0;
            }

            return _withdrawableDividend;
        }

        return 0;
    }

    /// @notice View the amount of dividend in wei that an address can withdraw.
    /// @param _owner The address of a token holder.
    /// @return The amount of dividend in wei that `_owner` can withdraw.
    function dividendOf(address _owner) public view override returns (uint256) {
        return withdrawableDividendOf(_owner);
    }

    /// @notice View the amount of dividend in wei that an address can withdraw.
    /// @param _owner The address of a token holder.
    /// @return The amount of dividend in wei that `_owner` can withdraw.
    function withdrawableDividendOf(address _owner)
        public
        view
        override
        returns (uint256)
    {
        return accumulativeDividendOf(_owner).sub(withdrawnDividends[_owner]);
    }

    /// @notice View the amount of dividend in wei that an address has withdrawn.
    /// @param _owner The address of a token holder.
    /// @return The amount of dividend in wei that `_owner` has withdrawn.
    function withdrawnDividendOf(address _owner)
        public
        view
        override
        returns (uint256)
    {
        return withdrawnDividends[_owner];
    }

    /// @notice View the amount of dividend in wei that an address has earned in total.
    /// @dev accumulativeDividendOf(_owner) = withdrawableDividendOf(_owner) + withdrawnDividendOf(_owner)
    /// = (magnifiedDividendPerShare * balanceOf(_owner) + magnifiedDividendCorrections[_owner]) / magnitude
    /// @param _owner The address of a token holder.
    /// @return The amount of dividend in wei that `_owner` has earned in total.
    function accumulativeDividendOf(address _owner)
        public
        view
        override
        returns (uint256)
    {
        return
            magnifiedDividendPerShare
                .mul(balanceOf(_owner))
                .toInt256Safe()
                .add(magnifiedDividendCorrections[_owner])
                .toUint256Safe() / magnitude;
    }

    /// @dev Internal function that transfer tokens from one address to another.
    /// Update magnifiedDividendCorrections to keep dividends unchanged.
    /// @param from The address to transfer from.
    /// @param to The address to transfer to.
    /// @param value The amount to be transferred.
    function _transfer(
        address from,
        address to,
        uint256 value
    ) internal virtual override {
        require(false);

        int256 _magCorrection = magnifiedDividendPerShare
            .mul(value)
            .toInt256Safe();
        magnifiedDividendCorrections[from] = magnifiedDividendCorrections[from]
            .add(_magCorrection);
        magnifiedDividendCorrections[to] = magnifiedDividendCorrections[to].sub(
            _magCorrection
        );
    }

    /// @dev Internal function that mints tokens to an account.
    /// Update magnifiedDividendCorrections to keep dividends unchanged.
    /// @param account The account that will receive the created tokens.
    /// @param value The amount that will be created.
    function _mint(address account, uint256 value) internal override {
        super._mint(account, value);

        magnifiedDividendCorrections[account] = magnifiedDividendCorrections[
            account
        ].sub((magnifiedDividendPerShare.mul(value)).toInt256Safe());
    }

    /// @dev Internal function that burns an amount of the token of a given account.
    /// Update magnifiedDividendCorrections to keep dividends unchanged.
    /// @param account The account whose tokens will be burnt.
    /// @param value The amount that will be burnt.
    function _burn(address account, uint256 value) internal override {
        super._burn(account, value);

        magnifiedDividendCorrections[account] = magnifiedDividendCorrections[
            account
        ].add((magnifiedDividendPerShare.mul(value)).toInt256Safe());
    }

    function _setBalance(address account, uint256 newBalance) internal {
        uint256 currentBalance = balanceOf(account);

        if (newBalance > currentBalance) {
            uint256 mintAmount = newBalance.sub(currentBalance);
            _mint(account, mintAmount);
        } else if (newBalance < currentBalance) {
            uint256 burnAmount = currentBalance.sub(newBalance);
            _burn(account, burnAmount);
        }
    }
}
function _burn(address account, uint256 value) internal override {
    super._burn(account, value);

    magnifiedDividendCorrections[account] = magnifiedDividendCorrections[
        account
    ].add((magnifiedDividendPerShare.mul(value)).toInt256Safe());
}

/// @dev Internal function that burns an amount of the token of a given account.
/// Update magnifiedDividendCorrections to keep dividends unchanged.
/// @param account The account whose tokens will be burnt.
/// @param value The amount that will be burnt.