// File: src/AssimilatorFactory.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.13;

import "@openzeppelin/contracts/utils/Address.sol";

import "./assimilators/AssimilatorV3.sol";
import "./interfaces/IAssimilatorFactory.sol";
import "./interfaces/IOracle.sol";
import "./interfaces/ICurveFactory.sol";
import "./interfaces/IConfig.sol";

contract AssimilatorFactory is IAssimilatorFactory {
    using Address for address;

    event NewAssimilator(
        address indexed caller,
        bytes32 indexed id,
        address indexed assimilator,
        address oracle,
        address token,
        address quote
    );
    event AssimilatorRevoked(address indexed caller, bytes32 indexed id, address indexed assimilator);
    event CurveFactoryUpdated(address indexed caller, address indexed curveFactory);

    mapping(bytes32 => AssimilatorV3) public assimilators;

    address public curveFactory;
    address public config;

    modifier onlyCurveFactoryOrOwner() {
        require(msg.sender == curveFactory || msg.sender == owner(), "unauthorized");
        _;
    }

    modifier onlyOwner() {
        require(msg.sender == IConfig(config).getProtocolTreasury(), "unauthorized");
        _;
    }

    constructor(address _config) {
        require(_config.isContract(), "config-invalid!");
        config = _config;
    }

    function owner() public view returns (address) {
        return IConfig(config).getProtocolTreasury();
    }

    function setCurveFactory(address _curveFactory) external onlyOwner {
        require(_curveFactory != address(0), "curve-factory-invalid!");
        curveFactory = _curveFactory;
        emit CurveFactoryUpdated(msg.sender, curveFactory);
    }

    function getAssimilator(address _token, address _quote) external view override returns (AssimilatorV3) {
        bytes32 assimilatorID = keccak256(abi.encode(_token, _quote));
        return assimilators[assimilatorID];
    }

    function newAssimilator(address _quote, IOracle _oracle, address _token, uint256 _tokenDecimals)
        external
        override
        onlyCurveFactoryOrOwner
        returns (AssimilatorV3)
    {
        require(curveFactory != address(0), "curve-factory-not-set");
        bytes32 assimilatorID = keccak256(abi.encode(_token, _quote));
        if (address(assimilators[assimilatorID]) != address(0)) {
            revert("assimilator-already-exists");
        }
        AssimilatorV3 assimilator = new AssimilatorV3(
            ICurveFactory(curveFactory).wETH(),
            _quote,
            _oracle,
            _token,
            _tokenDecimals,
            IOracle(_oracle).decimals()
        );
        assimilators[assimilatorID] = assimilator;
        emit NewAssimilator(msg.sender, assimilatorID, address(assimilator), address(_oracle), _token, _quote);
        return assimilator;
    }

    function revokeAssimilator(address _token, address _quote) external onlyOwner {
        bytes32 assimilatorID = keccak256(abi.encode(_token, _quote));
        address _assimAddress = address(assimilators[assimilatorID]);
        assimilators[assimilatorID] = AssimilatorV3(address(0));
        emit AssimilatorRevoked(msg.sender, assimilatorID, address(_assimAddress));
    }
}

// File: lib/openzeppelin-contracts/contracts/utils/Address.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/Address.sol)

pragma solidity ^0.8.1;

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     *
     * Furthermore, `isContract` will also return true if the target contract within
     * the same transaction is already scheduled for destruction by `SELFDESTRUCT`,
     * which only has an effect at the end of a transaction.
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    function _revert(bytes memory returndata, string memory errorMessage) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            /// @solidity memory-safe-assembly
            assembly {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert(errorMessage);
        }
    }
}

// File: src/assimilators/AssimilatorV3.sol



// SPDX-License-Identifier: MIT

// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.8.13;

import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import "@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol";
import "@openzeppelin/contracts/utils/math/SafeMath.sol";
import "@openzeppelin/contracts/utils/math/Math.sol";

import "../lib/ABDKMath64x64.sol";
import "../interfaces/IAssimilator.sol";
import "../interfaces/IOracle.sol";
import "../interfaces/IWeth.sol";

contract AssimilatorV3 is IAssimilator {
    using ABDKMath64x64 for int128;
    using ABDKMath64x64 for uint256;

    using SafeMath for uint256;
    using SafeERC20 for IERC20Metadata;

    IERC20Metadata public immutable pairToken;

    IOracle public immutable oracle;
    IERC20Metadata public immutable token;
    uint256 public immutable oracleDecimals;
    uint256 public immutable tokenDecimals;
    uint256 public immutable pairTokenDecimals;

    address public immutable wETH;

    // solhint-disable-next-line
    constructor(
        address _wETH,
        address _pairToken,
        IOracle _oracle,
        address _token,
        uint256 _tokenDecimals,
        uint256 _oracleDecimals
    ) {
        wETH = _wETH;
        oracle = _oracle;
        token = IERC20Metadata(_token);
        oracleDecimals = _oracleDecimals;
        tokenDecimals = _tokenDecimals;
        pairToken = IERC20Metadata(_pairToken);
        pairTokenDecimals = pairToken.decimals();
    }

    function underlyingToken() external view override returns (address) {
        return address(token);
    }

    function getWeth() external view override returns (address) {
        return wETH;
    }

    function getRate() public view override returns (uint256) {
        (, int256 price,,,) = oracle.latestRoundData();
        require(price >= 0, "invalid price oracle");
        return uint256(price);
    }

    // takes raw eurs amount, transfers it in, calculates corresponding numeraire amount and returns it
    function intakeRawAndGetBalance(uint256 _amount)
        external
        payable
        override
        returns (int128 amount_, int128 balance_)
    {
        require(_amount > 0, "zero amount!");
        uint256 balanceBefore = token.balanceOf(address(this));
        token.safeTransferFrom(msg.sender, address(this), _amount);
        uint256 balanceAfter = token.balanceOf(address(this));
        uint256 diff = _amount - (balanceAfter - balanceBefore);
        if (diff > 0) {
            intakeMoreFromFoT(_amount, diff);
        }

        uint256 _balance = token.balanceOf(address(this));

        uint256 _rate = getRate();

        balance_ = ((_balance * _rate) / 10 ** oracleDecimals).divu(10 ** tokenDecimals);

        amount_ = ((_amount * _rate) / 10 ** oracleDecimals).divu(10 ** tokenDecimals);
    }

    // takes raw eurs amount, transfers it in, calculates corresponding numeraire amount and returns it
    function intakeRaw(uint256 _amount) external payable override returns (int128 amount_) {
        require(_amount > 0, "zero amount!");
        uint256 balanceBefore = token.balanceOf(address(this));

        token.safeTransferFrom(msg.sender, address(this), _amount);

        uint256 balanceAfter = token.balanceOf(address(this));

        uint256 diff = _amount - (balanceAfter - balanceBefore);
        if (diff > 0) {
            intakeMoreFromFoT(_amount, diff);
        }

        uint256 _rate = getRate();

        amount_ = ((_amount * _rate) / 10 ** oracleDecimals).divu(10 ** tokenDecimals);
    }

    // takes a numeraire amount, calculates the raw amount of eurs, tr                                                                                                                                                                                                                                                                                        ansfers it in and returns the corresponding raw amount
    function intakeNumeraire(int128 _amount) external payable override returns (uint256 amount_) {
        uint256 _rate = getRate();
        // improve precision
        amount_ = Math.ceilDiv(_amount.mulu(10 ** (tokenDecimals + oracleDecimals + 18)), _rate * 1e18);
        require(amount_ > 0, "zero amount!");
        uint256 balanceBefore = token.balanceOf(address(this));

        token.safeTransferFrom(msg.sender, address(this), amount_);
        uint256 balanceAfter = token.balanceOf(address(this));
        uint256 diff = amount_ - (balanceAfter - balanceBefore);
        if (diff > 0) intakeMoreFromFoT(amount_, diff);
    }

    // takes a numeraire amount, calculates the raw amount of eurs, transfers it in and returns the corresponding raw amount
    function intakeNumeraireLPRatio(
        uint256 _minBaseAmount,
        uint256 _maxBaseAmount,
        uint256 _baseAmount,
        uint256 _minpairTokenAmount,
        uint256 _maxpairTokenAmount,
        uint256 _quoteAmount,
        address token0
    ) external payable override returns (uint256 amount_) {
        if (token0 == address(token)) {
            amount_ = _baseAmount;
        } else {
            amount_ = _quoteAmount;
        }

        require(amount_ > 0, "zero amount!");
        if (token0 == address(token)) {
            require(amount_ > _minBaseAmount && amount_ <= _maxBaseAmount, "Assimilator/LP Ratio imbalanced!");
        } else {
            require(amount_ > _minpairTokenAmount && amount_ <= _maxpairTokenAmount, "Assimilator/LP Ratio imbalanced!");
        }
        uint256 balanceBefore = token.balanceOf(address(this));
        token.safeTransferFrom(msg.sender, address(this), amount_);
        uint256 balanceAfter = token.balanceOf(address(this));
        uint256 diff = amount_ - (balanceAfter - balanceBefore);
        if (diff > 0) intakeMoreFromFoT(amount_, diff);
    }

    function intakeMoreFromFoT(uint256 amount_, uint256 diff) internal {
        require(amount_ > 0, "zero amount!");
        // handle FoT token
        uint256 feePercentage = diff.mul(1e5).div(amount_).add(1);
        uint256 additionalIntakeAmt = (diff * 1e5) / (1e5 - feePercentage);
        token.safeTransferFrom(msg.sender, address(this), additionalIntakeAmt);
    }

    // takes a raw amount of eurs and transfers it out, returns numeraire value of the raw amount
    function outputRawAndGetBalance(address _dst, uint256 _amount)
        external
        override
        returns (int128 amount_, int128 balance_)
    {
        require(_amount > 0, "zero amount!");
        uint256 _rate = getRate();

        token.safeTransfer(_dst, _amount);

        uint256 _balance = token.balanceOf(address(this));

        amount_ = ((_amount * _rate)).divu(10 ** (tokenDecimals + oracleDecimals));
        balance_ = ((_balance * _rate)).divu(10 ** (tokenDecimals + oracleDecimals));
    }

    // takes a raw amount of eurs and transfers it out, returns numeraire value of the raw amount
    function outputRaw(address _dst, uint256 _amount) external override returns (int128 amount_) {
        require(_amount > 0, "zero amount!");
        uint256 _rate = getRate();

        token.safeTransfer(_dst, _amount);

        amount_ = ((_amount * _rate)).divu(10 ** (tokenDecimals + oracleDecimals));
    }

    // takes a numeraire value of eurs, figures out the raw amount, transfers raw amount out, and returns raw amount
    function outputNumeraire(address _dst, int128 _amount, bool _toETH)
        external
        payable
        override
        returns (uint256 amount_)
    {
        uint256 _rate = getRate();

        amount_ = Math.ceilDiv(_amount.mulu(10 ** (tokenDecimals + oracleDecimals + 18)), _rate * 1e18);
        require(amount_ > 0, "zero amount!");
        if (_toETH) {
            IWETH(wETH).withdraw(amount_);
            (bool success,) = payable(_dst).call{value: amount_}("");
            require(success, "Assimilator/Transfer ETH Failed");
        } else {
            token.safeTransfer(_dst, amount_);
        }
    }

    // takes a numeraire amount and returns the raw amount
    function viewRawAmount(int128 _amount) external view override returns (uint256 amount_) {
        uint256 _rate = getRate();
        // improve precision
        amount_ = Math.ceilDiv(_amount.mulu(10 ** (tokenDecimals + oracleDecimals + 18)), _rate * 1e18);
    }

    function viewRawAmountLPRatio(uint256 _baseWeight, uint256 _pairTokenWeight, address _addr, int128 _amount)
        external
        view
        override
        returns (uint256 amount_)
    {
        uint256 _tokenBal = token.balanceOf(_addr);

        if (_tokenBal <= 0) return 0;

        _tokenBal = _tokenBal.mul(10 ** (18 + pairTokenDecimals)).div(_baseWeight);

        uint256 _pairTokenBal = pairToken.balanceOf(_addr).mul(10 ** (18 + tokenDecimals)).div(_pairTokenWeight);

        // Rate is in pair token decimals
        uint256 _rate = _pairTokenBal.mul(1e6).div(_tokenBal);

        amount_ = Math.ceilDiv(_amount.mulu(10 ** tokenDecimals * 1e6 * 1e18), _rate * 1e18);
    }

    // takes a raw amount and returns the numeraire amount
    function viewNumeraireAmount(uint256 _amount) external view override returns (int128 amount_) {
        uint256 _rate = getRate();

        amount_ = ((_amount * _rate) / 10 ** oracleDecimals).divu(10 ** tokenDecimals);
    }

    // views the numeraire value of the current balance of the reserve, in this case eurs
    function viewNumeraireBalance(address _addr) external view override returns (int128 balance_) {
        uint256 _rate = getRate();

        uint256 _balance = token.balanceOf(_addr);

        if (_balance <= 0) return ABDKMath64x64.fromUInt(0);

        balance_ = ((_balance * _rate) / 10 ** oracleDecimals).divu(10 ** tokenDecimals);
    }

    // views the numeraire value of the current balance of the reserve, in this case eurs
    function viewNumeraireAmountAndBalance(address _addr, uint256 _amount)
        external
        view
        override
        returns (int128 amount_, int128 balance_)
    {
        uint256 _rate = getRate();

        amount_ = ((_amount * _rate) / 10 ** oracleDecimals).divu(10 ** tokenDecimals);

        uint256 _balance = token.balanceOf(_addr);

        balance_ = ((_balance * _rate) / 10 ** oracleDecimals).divu(10 ** tokenDecimals);
    }

    // views the numeraire value of the current balance of the reserve, in this case eurs
    // instead of calculating with chainlink's "rate" it'll be determined by the existing
    // token ratio. This is in here to prevent LPs from losing out on future oracle price updates
    function viewNumeraireBalanceLPRatio(uint256 _baseWeight, uint256 _pairTokenWeight, address _addr)
        external
        view
        override
        returns (int128 balance_)
    {
        uint256 _tokenBal = token.balanceOf(_addr);

        if (_tokenBal <= 0) return ABDKMath64x64.fromUInt(0);

        uint256 _pairTokenBal = pairToken.balanceOf(_addr).mul(1e18).div(_pairTokenWeight);

        // Rate is in 1e6
        uint256 _rate = _pairTokenBal.mul(1e18).div(_tokenBal.mul(1e18).div(_baseWeight));

        balance_ = ((_tokenBal * _rate) / 10 ** pairTokenDecimals).divu(1e18);
    }

    function transferFee(int128 _amount, address _treasury) external payable override {
        uint256 _rate = getRate();
        if (_amount < 0) _amount = -(_amount);
        uint256 amount = _amount.mulu(10 ** (tokenDecimals + oracleDecimals + 18)) / (_rate * 1e18);
        token.safeTransfer(_treasury, amount);
    }
}

// File: src/interfaces/IAssimilatorFactory.sol



// SPDX-License-Identifier: MIT

// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.8.13;

import "../assimilators/AssimilatorV3.sol";
import "../interfaces/IOracle.sol";

interface IAssimilatorFactory {
    function getAssimilator(address _token, address _quote) external view returns (AssimilatorV3);

    function newAssimilator(address _quote, IOracle _oracle, address _token, uint256 _tokenDecimals)
        external
        returns (AssimilatorV3);
}

// File: src/interfaces/IOracle.sol



// SPDX-License-Identifier: MIT

// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.8.13;

interface IOracle {
    function acceptOwnership() external;

    function accessController() external view returns (address);

    function aggregator() external view returns (address);

    function confirmAggregator(address _aggregator) external;

    function decimals() external view returns (uint8);

    function description() external view returns (string memory);

    function getAnswer(uint256 _roundId) external view returns (int256);

    function getRoundData(uint80 _roundId)
        external
        view
        returns (uint80 roundId, int256 answer, uint256 startedAt, uint256 updatedAt, uint80 answeredInRound);

    function getTimestamp(uint256 _roundId) external view returns (uint256);

    function latestAnswer() external view returns (int256);

    function latestRound() external view returns (uint256);

    function latestRoundData()
        external
        view
        returns (uint80 roundId, int256 answer, uint256 startedAt, uint256 updatedAt, uint80 answeredInRound);

    function latestTimestamp() external view returns (uint256);

    function owner() external view returns (address);

    function phaseAggregators(uint16) external view returns (address);

    function phaseId() external view returns (uint16);

    function proposeAggregator(address _aggregator) external;

    function proposedAggregator() external view returns (address);

    function proposedGetRoundData(uint80 _roundId)
        external
        view
        returns (uint80 roundId, int256 answer, uint256 startedAt, uint256 updatedAt, uint80 answeredInRound);

    function proposedLatestRoundData()
        external
        view
        returns (uint80 roundId, int256 answer, uint256 startedAt, uint256 updatedAt, uint80 answeredInRound);

    function setController(address _accessController) external;

    function transferOwnership(address _to) external;

    function version() external view returns (uint256);
}

// File: src/interfaces/ICurveFactory.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.13;

import "./IAssimilatorFactory.sol";

interface ICurveFactory {
    function getProtocolFee() external view returns (int128);

    function getProtocolTreasury() external view returns (address);

    function assimilatorFactory() external view returns (IAssimilatorFactory);

    function wETH() external view returns (address);

    function isDFXCurve(address) external view returns (bool);
}

// File: src/interfaces/IConfig.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.13;

interface IConfig {
    function getGlobalFrozenState() external view returns (bool);

    function getProtocolFee() external view returns (int128);

    function getProtocolTreasury() external view returns (address);

    function setGlobalFrozen(bool) external;

    function updateProtocolTreasury(address) external;

    function updateProtocolFee(int128) external;
}

// File: lib/openzeppelin-contracts/contracts/token/ERC20/utils/SafeERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";
import "../extensions/IERC20Permit.sol";
import "../../../utils/Address.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    using Address for address;

    function safeTransfer(IERC20 token, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transfer.selector, to, value));
    }

    function safeTransferFrom(IERC20 token, address from, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transferFrom.selector, from, to, value));
    }

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(IERC20 token, address spender, uint256 value) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        require(
            (value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

    function safeIncreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 newAllowance = token.allowance(address(this), spender) + value;
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        unchecked {
            uint256 oldAllowance = token.allowance(address(this), spender);
            require(oldAllowance >= value, "SafeERC20: decreased allowance below zero");
            uint256 newAllowance = oldAllowance - value;
            _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
        }
    }

    function safePermit(
        IERC20Permit token,
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        uint256 nonceBefore = token.nonces(owner);
        token.permit(owner, spender, value, deadline, v, r, s);
        uint256 nonceAfter = token.nonces(owner);
        require(nonceAfter == nonceBefore + 1, "SafeERC20: permit did not succeed");
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We use {Address-functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

        bytes memory returndata = address(token).functionCall(data, "SafeERC20: low-level call failed");
        if (returndata.length > 0) {
            // Return data is optional
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}

// File: lib/openzeppelin-contracts/contracts/token/ERC20/extensions/IERC20Metadata.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Metadata.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";

/**
 * @dev Interface for the optional metadata functions from the ERC20 standard.
 *
 * _Available since v4.1._
 */
interface IERC20Metadata is IERC20 {
    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

    /**
     * @dev Returns the symbol of the token.
     */
    function symbol() external view returns (string memory);

    /**
     * @dev Returns the decimals places of the token.
     */
    function decimals() external view returns (uint8);
}

// File: lib/openzeppelin-contracts/contracts/utils/math/SafeMath.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (utils/math/SafeMath.sol)

pragma solidity ^0.8.0;

// CAUTION
// This version of SafeMath should only be used with Solidity 0.8 or later,
// because it relies on the compiler's built in overflow checks.

/**
 * @dev Wrappers over Solidity's arithmetic operations.
 *
 * NOTE: `SafeMath` is generally not needed starting with Solidity 0.8, since the compiler
 * now has built in overflow checking.
 */
library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            uint256 c = a + b;
            if (c < a) return (false, 0);
            return (true, c);
        }
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            if (b > a) return (false, 0);
            return (true, a - b);
        }
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
            // benefit is lost if 'b' is also tested.
            // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
            if (a == 0) return (true, 0);
            uint256 c = a * b;
            if (c / a != b) return (false, 0);
            return (true, c);
        }
    }

    /**
     * @dev Returns the division of two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            if (b == 0) return (false, 0);
            return (true, a / b);
        }
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            if (b == 0) return (false, 0);
            return (true, a % b);
        }
    }

    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        return a + b;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        return a - b;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        return a * b;
    }

    /**
     * @dev Returns the integer division of two unsigned integers, reverting on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator.
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        return a % b;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {trySub}.
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        unchecked {
            require(b <= a, errorMessage);
            return a - b;
        }
    }

    /**
     * @dev Returns the integer division of two unsigned integers, reverting with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        unchecked {
            require(b > 0, errorMessage);
            return a / b;
        }
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting with custom message when dividing by zero.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryMod}.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        unchecked {
            require(b > 0, errorMessage);
            return a % b;
        }
    }
}

// File: lib/openzeppelin-contracts/contracts/utils/math/Math.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1, "Math: mulDiv overflow");

            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10 ** 64) {
                value /= 10 ** 64;
                result += 64;
            }
            if (value >= 10 ** 32) {
                value /= 10 ** 32;
                result += 32;
            }
            if (value >= 10 ** 16) {
                value /= 10 ** 16;
                result += 16;
            }
            if (value >= 10 ** 8) {
                value /= 10 ** 8;
                result += 8;
            }
            if (value >= 10 ** 4) {
                value /= 10 ** 4;
                result += 4;
            }
            if (value >= 10 ** 2) {
                value /= 10 ** 2;
                result += 2;
            }
            if (value >= 10 ** 1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);
        }
    }
}

// File: src/lib/ABDKMath64x64.sol



// SPDX-License-Identifier: BSD-4-Clause
/*
 * ABDK Math 64.64 Smart Contract Library.  Copyright © 2019 by ABDK Consulting.
 * Author: Mikhail Vladimirov <mikhail.vladimirov@gmail.com>
 */
pragma solidity ^0.8.13;

/**
 * Smart contract library of mathematical functions operating with signed
 * 64.64-bit fixed point numbers.  Signed 64.64-bit fixed point number is
 * basically a simple fraction whose numerator is signed 128-bit integer and
 * denominator is 2^64.  As long as denominator is always the same, there is no
 * need to store it, thus in Solidity signed 64.64-bit fixed point numbers are
 * represented by int128 type holding only the numerator.
 */
library ABDKMath64x64 {
    /*
    * Minimum value signed 64.64-bit fixed point number may have. 
    */
    int128 private constant MIN_64x64 = -0x80000000000000000000000000000000;

    /*
    * Maximum value signed 64.64-bit fixed point number may have. 
    */
    int128 private constant MAX_64x64 = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

    /**
     * Convert signed 256-bit integer number into signed 64.64-bit fixed point
     * number.  Revert on overflow.
     *
     * @param x signed 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function fromInt(int256 x) internal pure returns (int128) {
        unchecked {
            require(x >= -0x8000000000000000 && x <= 0x7FFFFFFFFFFFFFFF);
            return int128(x << 64);
        }
    }

    /**
     * Convert signed 64.64 fixed point number into signed 64-bit integer number
     * rounding down.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64-bit integer number
     */
    function toInt(int128 x) internal pure returns (int64) {
        unchecked {
            return int64(x >> 64);
        }
    }

    /**
     * Convert unsigned 256-bit integer number into signed 64.64-bit fixed point
     * number.  Revert on overflow.
     *
     * @param x unsigned 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function fromUInt(uint256 x) internal pure returns (int128) {
        unchecked {
            require(x <= 0x7FFFFFFFFFFFFFFF);
            return int128(int256(x << 64));
        }
    }

    /**
     * Convert signed 64.64 fixed point number into unsigned 64-bit integer
     * number rounding down.  Revert on underflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return unsigned 64-bit integer number
     */
    function toUInt(int128 x) internal pure returns (uint64) {
        unchecked {
            require(x >= 0);
            return uint64(uint128(x >> 64));
        }
    }

    /**
     * Convert signed 128.128 fixed point number into signed 64.64-bit fixed point
     * number rounding down.  Revert on overflow.
     *
     * @param x signed 128.128-bin fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function from128x128(int256 x) internal pure returns (int128) {
        unchecked {
            int256 result = x >> 64;
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Convert signed 64.64 fixed point number into signed 128.128 fixed point
     * number.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 128.128 fixed point number
     */
    function to128x128(int128 x) internal pure returns (int256) {
        unchecked {
            return int256(x) << 64;
        }
    }

    /**
     * Calculate x + y.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function add(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            int256 result = int256(x) + y;
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Calculate x - y.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function sub(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            int256 result = int256(x) - y;
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Calculate x * y rounding down.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function mul(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            int256 result = int256(x) * y >> 64;
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Calculate x * y rounding towards zero, where x is signed 64.64 fixed point
     * number and y is signed 256-bit integer number.  Revert on overflow.
     *
     * @param x signed 64.64 fixed point number
     * @param y signed 256-bit integer number
     * @return signed 256-bit integer number
     */
    function muli(int128 x, int256 y) internal pure returns (int256) {
        unchecked {
            if (x == MIN_64x64) {
                require(
                    y >= -0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
                        && y <= 0x1000000000000000000000000000000000000000000000000
                );
                return -y << 63;
            } else {
                bool negativeResult = false;
                if (x < 0) {
                    x = -x;
                    negativeResult = true;
                }
                if (y < 0) {
                    y = -y; // We rely on overflow behavior here
                    negativeResult = !negativeResult;
                }
                uint256 absoluteResult = mulu(x, uint256(y));
                if (negativeResult) {
                    require(absoluteResult <= 0x8000000000000000000000000000000000000000000000000000000000000000);
                    return -int256(absoluteResult); // We rely on overflow behavior here
                } else {
                    require(absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
                    return int256(absoluteResult);
                }
            }
        }
    }

    /**
     * Calculate x * y rounding down, where x is signed 64.64 fixed point number
     * and y is unsigned 256-bit integer number.  Revert on overflow.
     *
     * @param x signed 64.64 fixed point number
     * @param y unsigned 256-bit integer number
     * @return unsigned 256-bit integer number
     */
    function mulu(int128 x, uint256 y) internal pure returns (uint256) {
        unchecked {
            if (y == 0) return 0;

            require(x >= 0);

            uint256 lo = (uint256(int256(x)) * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)) >> 64;
            uint256 hi = uint256(int256(x)) * (y >> 128);

            require(hi <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
            hi <<= 64;

            require(hi <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF - lo);
            return hi + lo;
        }
    }

    /**
     * Calculate x / y rounding towards zero.  Revert on overflow or when y is
     * zero.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function div(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            require(y != 0);
            int256 result = (int256(x) << 64) / y;
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Calculate x / y rounding towards zero, where x and y are signed 256-bit
     * integer numbers.  Revert on overflow or when y is zero.
     *
     * @param x signed 256-bit integer number
     * @param y signed 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function divi(int256 x, int256 y) internal pure returns (int128) {
        unchecked {
            require(y != 0);

            bool negativeResult = false;
            if (x < 0) {
                x = -x; // We rely on overflow behavior here
                negativeResult = true;
            }
            if (y < 0) {
                y = -y; // We rely on overflow behavior here
                negativeResult = !negativeResult;
            }
            uint128 absoluteResult = divuu(uint256(x), uint256(y));
            if (negativeResult) {
                require(absoluteResult <= 0x80000000000000000000000000000000);
                return -int128(absoluteResult); // We rely on overflow behavior here
            } else {
                require(absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
                return int128(absoluteResult); // We rely on overflow behavior here
            }
        }
    }

    /**
     * Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
     * integer numbers.  Revert on overflow or when y is zero.
     *
     * @param x unsigned 256-bit integer number
     * @param y unsigned 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function divu(uint256 x, uint256 y) internal pure returns (int128) {
        unchecked {
            require(y != 0);
            uint128 result = divuu(x, y);
            require(result <= uint128(MAX_64x64));
            return int128(result);
        }
    }

    /**
     * Calculate -x.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function neg(int128 x) internal pure returns (int128) {
        unchecked {
            require(x != MIN_64x64);
            return -x;
        }
    }

    /**
     * Calculate |x|.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function abs(int128 x) internal pure returns (int128) {
        unchecked {
            require(x != MIN_64x64);
            return x < 0 ? -x : x;
        }
    }

    /**
     * Calculate 1 / x rounding towards zero.  Revert on overflow or when x is
     * zero.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function inv(int128 x) internal pure returns (int128) {
        unchecked {
            require(x != 0);
            int256 result = int256(0x100000000000000000000000000000000) / x;
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Calculate arithmetics average of x and y, i.e. (x + y) / 2 rounding down.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function avg(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            return int128((int256(x) + int256(y)) >> 1);
        }
    }

    /**
     * Calculate geometric average of x and y, i.e. sqrt (x * y) rounding down.
     * Revert on overflow or in case x * y is negative.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function gavg(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            int256 m = int256(x) * int256(y);
            require(m >= 0);
            require(m < 0x4000000000000000000000000000000000000000000000000000000000000000);
            return int128(sqrtu(uint256(m)));
        }
    }

    /**
     * Calculate x^y assuming 0^0 is 1, where x is signed 64.64 fixed point number
     * and y is unsigned 256-bit integer number.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y uint256 value
     * @return signed 64.64-bit fixed point number
     */
    function pow(int128 x, uint256 y) internal pure returns (int128) {
        unchecked {
            bool negative = x < 0 && y & 1 == 1;

            uint256 absX = uint128(x < 0 ? -x : x);
            uint256 absResult;
            absResult = 0x100000000000000000000000000000000;

            if (absX <= 0x10000000000000000) {
                absX <<= 63;
                while (y != 0) {
                    if (y & 0x1 != 0) {
                        absResult = absResult * absX >> 127;
                    }
                    absX = absX * absX >> 127;

                    if (y & 0x2 != 0) {
                        absResult = absResult * absX >> 127;
                    }
                    absX = absX * absX >> 127;

                    if (y & 0x4 != 0) {
                        absResult = absResult * absX >> 127;
                    }
                    absX = absX * absX >> 127;

                    if (y & 0x8 != 0) {
                        absResult = absResult * absX >> 127;
                    }
                    absX = absX * absX >> 127;

                    y >>= 4;
                }

                absResult >>= 64;
            } else {
                uint256 absXShift = 63;
                if (absX < 0x1000000000000000000000000) {
                    absX <<= 32;
                    absXShift -= 32;
                }
                if (absX < 0x10000000000000000000000000000) {
                    absX <<= 16;
                    absXShift -= 16;
                }
                if (absX < 0x1000000000000000000000000000000) {
                    absX <<= 8;
                    absXShift -= 8;
                }
                if (absX < 0x10000000000000000000000000000000) {
                    absX <<= 4;
                    absXShift -= 4;
                }
                if (absX < 0x40000000000000000000000000000000) {
                    absX <<= 2;
                    absXShift -= 2;
                }
                if (absX < 0x80000000000000000000000000000000) {
                    absX <<= 1;
                    absXShift -= 1;
                }

                uint256 resultShift = 0;
                while (y != 0) {
                    require(absXShift < 64);

                    if (y & 0x1 != 0) {
                        absResult = absResult * absX >> 127;
                        resultShift += absXShift;
                        if (absResult > 0x100000000000000000000000000000000) {
                            absResult >>= 1;
                            resultShift += 1;
                        }
                    }
                    absX = absX * absX >> 127;
                    absXShift <<= 1;
                    if (absX >= 0x100000000000000000000000000000000) {
                        absX >>= 1;
                        absXShift += 1;
                    }

                    y >>= 1;
                }

                require(resultShift < 64);
                absResult >>= 64 - resultShift;
            }
            int256 result = negative ? -int256(absResult) : int256(absResult);
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Calculate sqrt (x) rounding down.  Revert if x < 0.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function sqrt(int128 x) internal pure returns (int128) {
        unchecked {
            require(x >= 0);
            return int128(sqrtu(uint256(int256(x)) << 64));
        }
    }

    /**
     * Calculate binary logarithm of x.  Revert if x <= 0.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function log_2(int128 x) internal pure returns (int128) {
        unchecked {
            require(x > 0);

            int256 msb = 0;
            int256 xc = x;
            if (xc >= 0x10000000000000000) {
                xc >>= 64;
                msb += 64;
            }
            if (xc >= 0x100000000) {
                xc >>= 32;
                msb += 32;
            }
            if (xc >= 0x10000) {
                xc >>= 16;
                msb += 16;
            }
            if (xc >= 0x100) {
                xc >>= 8;
                msb += 8;
            }
            if (xc >= 0x10) {
                xc >>= 4;
                msb += 4;
            }
            if (xc >= 0x4) {
                xc >>= 2;
                msb += 2;
            }
            if (xc >= 0x2) msb += 1; // No need to shift xc anymore

            int256 result = msb - 64 << 64;
            uint256 ux = uint256(int256(x)) << uint256(127 - msb);
            for (int256 bit = 0x8000000000000000; bit > 0; bit >>= 1) {
                ux *= ux;
                uint256 b = ux >> 255;
                ux >>= 127 + b;
                result += bit * int256(b);
            }

            return int128(result);
        }
    }

    /**
     * Calculate natural logarithm of x.  Revert if x <= 0.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function ln(int128 x) internal pure returns (int128) {
        unchecked {
            require(x > 0);

            return int128(int256(uint256(int256(log_2(x))) * 0xB17217F7D1CF79ABC9E3B39803F2F6AF >> 128));
        }
    }

    /**
     * Calculate binary exponent of x.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function exp_2(int128 x) internal pure returns (int128) {
        unchecked {
            require(x < 0x400000000000000000); // Overflow

            if (x < -0x400000000000000000) return 0; // Underflow

            uint256 result = 0x80000000000000000000000000000000;

            if (x & 0x8000000000000000 > 0) {
                result = result * 0x16A09E667F3BCC908B2FB1366EA957D3E >> 128;
            }
            if (x & 0x4000000000000000 > 0) {
                result = result * 0x1306FE0A31B7152DE8D5A46305C85EDEC >> 128;
            }
            if (x & 0x2000000000000000 > 0) {
                result = result * 0x1172B83C7D517ADCDF7C8C50EB14A791F >> 128;
            }
            if (x & 0x1000000000000000 > 0) {
                result = result * 0x10B5586CF9890F6298B92B71842A98363 >> 128;
            }
            if (x & 0x800000000000000 > 0) {
                result = result * 0x1059B0D31585743AE7C548EB68CA417FD >> 128;
            }
            if (x & 0x400000000000000 > 0) {
                result = result * 0x102C9A3E778060EE6F7CACA4F7A29BDE8 >> 128;
            }
            if (x & 0x200000000000000 > 0) {
                result = result * 0x10163DA9FB33356D84A66AE336DCDFA3F >> 128;
            }
            if (x & 0x100000000000000 > 0) {
                result = result * 0x100B1AFA5ABCBED6129AB13EC11DC9543 >> 128;
            }
            if (x & 0x80000000000000 > 0) {
                result = result * 0x10058C86DA1C09EA1FF19D294CF2F679B >> 128;
            }
            if (x & 0x40000000000000 > 0) {
                result = result * 0x1002C605E2E8CEC506D21BFC89A23A00F >> 128;
            }
            if (x & 0x20000000000000 > 0) {
                result = result * 0x100162F3904051FA128BCA9C55C31E5DF >> 128;
            }
            if (x & 0x10000000000000 > 0) {
                result = result * 0x1000B175EFFDC76BA38E31671CA939725 >> 128;
            }
            if (x & 0x8000000000000 > 0) {
                result = result * 0x100058BA01FB9F96D6CACD4B180917C3D >> 128;
            }
            if (x & 0x4000000000000 > 0) {
                result = result * 0x10002C5CC37DA9491D0985C348C68E7B3 >> 128;
            }
            if (x & 0x2000000000000 > 0) {
                result = result * 0x1000162E525EE054754457D5995292026 >> 128;
            }
            if (x & 0x1000000000000 > 0) {
                result = result * 0x10000B17255775C040618BF4A4ADE83FC >> 128;
            }
            if (x & 0x800000000000 > 0) {
                result = result * 0x1000058B91B5BC9AE2EED81E9B7D4CFAB >> 128;
            }
            if (x & 0x400000000000 > 0) {
                result = result * 0x100002C5C89D5EC6CA4D7C8ACC017B7C9 >> 128;
            }
            if (x & 0x200000000000 > 0) {
                result = result * 0x10000162E43F4F831060E02D839A9D16D >> 128;
            }
            if (x & 0x100000000000 > 0) {
                result = result * 0x100000B1721BCFC99D9F890EA06911763 >> 128;
            }
            if (x & 0x80000000000 > 0) {
                result = result * 0x10000058B90CF1E6D97F9CA14DBCC1628 >> 128;
            }
            if (x & 0x40000000000 > 0) {
                result = result * 0x1000002C5C863B73F016468F6BAC5CA2B >> 128;
            }
            if (x & 0x20000000000 > 0) {
                result = result * 0x100000162E430E5A18F6119E3C02282A5 >> 128;
            }
            if (x & 0x10000000000 > 0) {
                result = result * 0x1000000B1721835514B86E6D96EFD1BFE >> 128;
            }
            if (x & 0x8000000000 > 0) {
                result = result * 0x100000058B90C0B48C6BE5DF846C5B2EF >> 128;
            }
            if (x & 0x4000000000 > 0) {
                result = result * 0x10000002C5C8601CC6B9E94213C72737A >> 128;
            }
            if (x & 0x2000000000 > 0) {
                result = result * 0x1000000162E42FFF037DF38AA2B219F06 >> 128;
            }
            if (x & 0x1000000000 > 0) {
                result = result * 0x10000000B17217FBA9C739AA5819F44F9 >> 128;
            }
            if (x & 0x800000000 > 0) {
                result = result * 0x1000000058B90BFCDEE5ACD3C1CEDC823 >> 128;
            }
            if (x & 0x400000000 > 0) {
                result = result * 0x100000002C5C85FE31F35A6A30DA1BE50 >> 128;
            }
            if (x & 0x200000000 > 0) {
                result = result * 0x10000000162E42FF0999CE3541B9FFFCF >> 128;
            }
            if (x & 0x100000000 > 0) {
                result = result * 0x100000000B17217F80F4EF5AADDA45554 >> 128;
            }
            if (x & 0x80000000 > 0) {
                result = result * 0x10000000058B90BFBF8479BD5A81B51AD >> 128;
            }
            if (x & 0x40000000 > 0) {
                result = result * 0x1000000002C5C85FDF84BD62AE30A74CC >> 128;
            }
            if (x & 0x20000000 > 0) {
                result = result * 0x100000000162E42FEFB2FED257559BDAA >> 128;
            }
            if (x & 0x10000000 > 0) {
                result = result * 0x1000000000B17217F7D5A7716BBA4A9AE >> 128;
            }
            if (x & 0x8000000 > 0) {
                result = result * 0x100000000058B90BFBE9DDBAC5E109CCE >> 128;
            }
            if (x & 0x4000000 > 0) {
                result = result * 0x10000000002C5C85FDF4B15DE6F17EB0D >> 128;
            }
            if (x & 0x2000000 > 0) {
                result = result * 0x1000000000162E42FEFA494F1478FDE05 >> 128;
            }
            if (x & 0x1000000 > 0) {
                result = result * 0x10000000000B17217F7D20CF927C8E94C >> 128;
            }
            if (x & 0x800000 > 0) {
                result = result * 0x1000000000058B90BFBE8F71CB4E4B33D >> 128;
            }
            if (x & 0x400000 > 0) {
                result = result * 0x100000000002C5C85FDF477B662B26945 >> 128;
            }
            if (x & 0x200000 > 0) {
                result = result * 0x10000000000162E42FEFA3AE53369388C >> 128;
            }
            if (x & 0x100000 > 0) {
                result = result * 0x100000000000B17217F7D1D351A389D40 >> 128;
            }
            if (x & 0x80000 > 0) {
                result = result * 0x10000000000058B90BFBE8E8B2D3D4EDE >> 128;
            }
            if (x & 0x40000 > 0) {
                result = result * 0x1000000000002C5C85FDF4741BEA6E77E >> 128;
            }
            if (x & 0x20000 > 0) {
                result = result * 0x100000000000162E42FEFA39FE95583C2 >> 128;
            }
            if (x & 0x10000 > 0) {
                result = result * 0x1000000000000B17217F7D1CFB72B45E1 >> 128;
            }
            if (x & 0x8000 > 0) {
                result = result * 0x100000000000058B90BFBE8E7CC35C3F0 >> 128;
            }
            if (x & 0x4000 > 0) {
                result = result * 0x10000000000002C5C85FDF473E242EA38 >> 128;
            }
            if (x & 0x2000 > 0) {
                result = result * 0x1000000000000162E42FEFA39F02B772C >> 128;
            }
            if (x & 0x1000 > 0) {
                result = result * 0x10000000000000B17217F7D1CF7D83C1A >> 128;
            }
            if (x & 0x800 > 0) {
                result = result * 0x1000000000000058B90BFBE8E7BDCBE2E >> 128;
            }
            if (x & 0x400 > 0) {
                result = result * 0x100000000000002C5C85FDF473DEA871F >> 128;
            }
            if (x & 0x200 > 0) {
                result = result * 0x10000000000000162E42FEFA39EF44D91 >> 128;
            }
            if (x & 0x100 > 0) {
                result = result * 0x100000000000000B17217F7D1CF79E949 >> 128;
            }
            if (x & 0x80 > 0) {
                result = result * 0x10000000000000058B90BFBE8E7BCE544 >> 128;
            }
            if (x & 0x40 > 0) {
                result = result * 0x1000000000000002C5C85FDF473DE6ECA >> 128;
            }
            if (x & 0x20 > 0) {
                result = result * 0x100000000000000162E42FEFA39EF366F >> 128;
            }
            if (x & 0x10 > 0) {
                result = result * 0x1000000000000000B17217F7D1CF79AFA >> 128;
            }
            if (x & 0x8 > 0) {
                result = result * 0x100000000000000058B90BFBE8E7BCD6D >> 128;
            }
            if (x & 0x4 > 0) {
                result = result * 0x10000000000000002C5C85FDF473DE6B2 >> 128;
            }
            if (x & 0x2 > 0) {
                result = result * 0x1000000000000000162E42FEFA39EF358 >> 128;
            }
            if (x & 0x1 > 0) {
                result = result * 0x10000000000000000B17217F7D1CF79AB >> 128;
            }

            result >>= uint256(int256(63 - (x >> 64)));
            require(result <= uint256(int256(MAX_64x64)));

            return int128(int256(result));
        }
    }

    /**
     * Calculate natural exponent of x.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function exp(int128 x) internal pure returns (int128) {
        unchecked {
            require(x < 0x400000000000000000); // Overflow

            if (x < -0x400000000000000000) return 0; // Underflow

            return exp_2(int128(int256(x) * 0x171547652B82FE1777D0FFDA0D23A7D12 >> 128));
        }
    }

    /**
     * Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
     * integer numbers.  Revert on overflow or when y is zero.
     *
     * @param x unsigned 256-bit integer number
     * @param y unsigned 256-bit integer number
     * @return unsigned 64.64-bit fixed point number
     */
    function divuu(uint256 x, uint256 y) private pure returns (uint128) {
        unchecked {
            require(y != 0);

            uint256 result;

            if (x <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF) {
                result = (x << 64) / y;
            } else {
                uint256 msb = 192;
                uint256 xc = x >> 192;
                if (xc >= 0x100000000) {
                    xc >>= 32;
                    msb += 32;
                }
                if (xc >= 0x10000) {
                    xc >>= 16;
                    msb += 16;
                }
                if (xc >= 0x100) {
                    xc >>= 8;
                    msb += 8;
                }
                if (xc >= 0x10) {
                    xc >>= 4;
                    msb += 4;
                }
                if (xc >= 0x4) {
                    xc >>= 2;
                    msb += 2;
                }
                if (xc >= 0x2) msb += 1; // No need to shift xc anymore

                result = (x << 255 - msb) / ((y - 1 >> msb - 191) + 1);
                require(result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);

                uint256 hi = result * (y >> 128);
                uint256 lo = result * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);

                uint256 xh = x >> 192;
                uint256 xl = x << 64;

                if (xl < lo) xh -= 1;
                xl -= lo; // We rely on overflow behavior here
                lo = hi << 128;
                if (xl < lo) xh -= 1;
                xl -= lo; // We rely on overflow behavior here

                assert(xh == hi >> 128);

                result += xl / y;
            }

            require(result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
            return uint128(result);
        }
    }

    /**
     * Calculate sqrt (x) rounding down, where x is unsigned 256-bit integer
     * number.
     *
     * @param x unsigned 256-bit integer number
     * @return unsigned 128-bit integer number
     */
    function sqrtu(uint256 x) private pure returns (uint128) {
        unchecked {
            if (x == 0) {
                return 0;
            } else {
                uint256 xx = x;
                uint256 r = 1;
                if (xx >= 0x100000000000000000000000000000000) {
                    xx >>= 128;
                    r <<= 64;
                }
                if (xx >= 0x10000000000000000) {
                    xx >>= 64;
                    r <<= 32;
                }
                if (xx >= 0x100000000) {
                    xx >>= 32;
                    r <<= 16;
                }
                if (xx >= 0x10000) {
                    xx >>= 16;
                    r <<= 8;
                }
                if (xx >= 0x100) {
                    xx >>= 8;
                    r <<= 4;
                }
                if (xx >= 0x10) {
                    xx >>= 4;
                    r <<= 2;
                }
                if (xx >= 0x8) r <<= 1;
                r = (r + x / r) >> 1;
                r = (r + x / r) >> 1;
                r = (r + x / r) >> 1;
                r = (r + x / r) >> 1;
                r = (r + x / r) >> 1;
                r = (r + x / r) >> 1;
                r = (r + x / r) >> 1; // Seven iterations should be enough
                uint256 r1 = x / r;
                return uint128(r < r1 ? r : r1);
            }
        }
    }
}

// File: src/interfaces/IAssimilator.sol



// SPDX-License-Identifier: MIT

// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.8.13;

interface IAssimilator {
    function oracleDecimals() external view returns (uint256);

    function underlyingToken() external view returns (address);

    function getWeth() external view returns (address);

    function tokenDecimals() external view returns (uint256);

    function getRate() external view returns (uint256);

    function intakeRaw(uint256 amount) external payable returns (int128);

    function intakeRawAndGetBalance(uint256 amount) external payable returns (int128, int128);

    function intakeNumeraire(int128 amount) external payable returns (uint256);

    function intakeNumeraireLPRatio(uint256, uint256, uint256, uint256, uint256, uint256, address)
        external
        payable
        returns (uint256);

    function outputRaw(address dst, uint256 amount) external returns (int128);

    function outputRawAndGetBalance(address dst, uint256 amount) external returns (int128, int128);

    function outputNumeraire(address dst, int128 amount, bool toETH) external payable returns (uint256);

    function viewRawAmount(int128) external view returns (uint256);

    function viewRawAmountLPRatio(uint256, uint256, address, int128) external view returns (uint256);

    function viewNumeraireAmount(uint256) external view returns (int128);

    function viewNumeraireBalanceLPRatio(uint256, uint256, address) external view returns (int128);

    function viewNumeraireBalance(address) external view returns (int128);

    function viewNumeraireAmountAndBalance(address, uint256) external view returns (int128, int128);

    function transferFee(int128, address) external payable;
}

// File: src/interfaces/IWeth.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.13;

interface IWETH {
    function deposit() external payable;

    function transfer(address to, uint256 value) external returns (bool);

    function withdraw(uint256) external;
}

// File: lib/openzeppelin-contracts/contracts/token/ERC20/IERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);

    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the amount of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves `amount` tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 amount) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `from` to `to` using the
     * allowance mechanism. `amount` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(address from, address to, uint256 amount) external returns (bool);
}

// File: lib/openzeppelin-contracts/contracts/token/ERC20/extensions/IERC20Permit.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Permit.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on {IERC20-approve}, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 */
interface IERC20Permit {
    /**
     * @dev Sets `value` as the allowance of `spender` over ``owner``'s tokens,
     * given ``owner``'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     */
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

    /**
     * @dev Returns the current nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases ``owner``'s nonce by one. This
     * prevents a signature from being used multiple times.
     */
    function nonces(address owner) external view returns (uint256);

    /**
     * @dev Returns the domain separator used in the encoding of the signature for {permit}, as defined by {EIP712}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view returns (bytes32);
}