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// SPDX-License-Identifier: GPL-3.0

/// @title The CNNouns DAO auction house

/*********************************
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// LICENSE
// NounsAuctionHouse.sol is a modified version of Zora's AuctionHouse.sol:
// https://github.com/ourzora/auction-house/blob/54a12ec1a6cf562e49f0a4917990474b11350a2d/contracts/AuctionHouse.sol
//
// AuctionHouse.sol source code Copyright Zora licensed under the GPL-3.0 license.
// With modifications by Nounders DAO.
// With modifications by CNNouns DAO.

pragma solidity ^0.8.6;

import { PausableUpgradeable } from '@openzeppelin/contracts-upgradeable/security/PausableUpgradeable.sol';
import { ReentrancyGuardUpgradeable } from '@openzeppelin/contracts-upgradeable/security/ReentrancyGuardUpgradeable.sol';
import { OwnableUpgradeable } from '@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol';
import { IERC20 } from '@openzeppelin/contracts/token/ERC20/IERC20.sol';
import { ABDKMathQuad } from 'abdk-libraries-solidity/ABDKMathQuad.sol';
import { INounsAuctionHouse } from './interfaces/INounsAuctionHouse.sol';
import { INounsToken } from './interfaces/INounsToken.sol';
import { IWETH } from './interfaces/IWETH.sol';

contract NounsAuctionHouse is INounsAuctionHouse, PausableUpgradeable, ReentrancyGuardUpgradeable, OwnableUpgradeable {
    // The Nouns ERC721 token contract
    INounsToken public nouns;

    // The address of the WETH contract
    address public weth;

    // The minimum amount of time left in an auction after a new bid is created
    uint256 public timeBuffer;

    // The minimum price accepted in an auction
    uint256 public reservePrice;

    // The minimum percentage difference between the last bid amount and the current bid
    uint8 public minBidIncrementPercentage;

    // The base duration of a single auction
    uint256 public baseDuration;

    // The origin date for calculating duration
    uint256 public origin;

    // The active auction
    INounsAuctionHouse.Auction public auction;

    /**
     * @notice Initialize the auction house and base contracts,
     * populate configuration values, and pause the contract.
     * @dev This function can only be called once.
     */
    function initialize(
        INounsToken _nouns,
        address _weth,
        uint256 _timeBuffer,
        uint256 _reservePrice,
        uint8 _minBidIncrementPercentage,
        uint256 _baseDuration
    ) external initializer {
        __Pausable_init();
        __ReentrancyGuard_init();
        __Ownable_init();

        _pause();

        nouns = _nouns;
        weth = _weth;
        timeBuffer = _timeBuffer;
        reservePrice = _reservePrice;
        minBidIncrementPercentage = _minBidIncrementPercentage;
        baseDuration = _baseDuration;
        origin = block.timestamp;
    }

    /**
     * @notice Settle the current auction, mint a new Noun, and put it up for auction.
     */
    function settleCurrentAndCreateNewAuction() external override nonReentrant whenNotPaused {
        _settleAuction();
        _createAuction();
    }

    /**
     * @notice Settle the current auction.
     * @dev This function can only be called when the contract is paused.
     */
    function settleAuction() external override whenPaused nonReentrant {
        _settleAuction();
    }

    /**
     * @notice Create a bid for a Noun, with a given amount.
     * @dev This contract only accepts payment in ETH.
     */
    function createBid(uint256 nounId) external payable override nonReentrant {
        INounsAuctionHouse.Auction memory _auction = auction;

        require(_auction.nounId == nounId, 'Noun not up for auction');
        require(block.timestamp < _auction.endTime, 'Auction expired');
        require(msg.value >= reservePrice, 'Must send at least reservePrice');
        require(
            msg.value >= _auction.amount + ((_auction.amount * minBidIncrementPercentage) / 100),
            'Must send more than last bid by minBidIncrementPercentage amount'
        );

        address payable lastBidder = _auction.bidder;

        // Refund the last bidder, if applicable
        if (lastBidder != address(0)) {
            _safeTransferETHWithFallback(lastBidder, _auction.amount);
        }

        auction.amount = msg.value;
        auction.bidder = payable(msg.sender);

        // Extend the auction if the bid was received within `timeBuffer` of the auction end time
        bool extended = _auction.endTime - block.timestamp < timeBuffer;
        if (extended) {
            auction.endTime = _auction.endTime = block.timestamp + timeBuffer;
        }

        emit AuctionBid(_auction.nounId, msg.sender, msg.value, extended);

        if (extended) {
            emit AuctionExtended(_auction.nounId, _auction.endTime);
        }
    }

    /**
     * @notice Pause the Nouns auction house.
     * @dev This function can only be called by the owner when the
     * contract is unpaused. While no new auctions can be started when paused,
     * anyone can settle an ongoing auction.
     */
    function pause() external override onlyOwner {
        _pause();
    }

    /**
     * @notice Unpause the Nouns auction house.
     * @dev This function can only be called by the owner when the
     * contract is paused. If required, this function will start a new auction.
     */
    function unpause() external override onlyOwner {
        _unpause();

        if (auction.startTime == 0 || auction.settled) {
            _createAuction();
        }
    }

    /**
     * @notice Set the auction time buffer.
     * @dev Only callable by the owner.
     */
    function setTimeBuffer(uint256 _timeBuffer) external override onlyOwner {
        timeBuffer = _timeBuffer;

        emit AuctionTimeBufferUpdated(_timeBuffer);
    }

    /**
     * @notice Set the auction reserve price.
     * @dev Only callable by the owner.
     */
    function setReservePrice(uint256 _reservePrice) external override onlyOwner {
        reservePrice = _reservePrice;

        emit AuctionReservePriceUpdated(_reservePrice);
    }

    /**
     * @notice Set the auction minimum bid increment percentage.
     * @dev Only callable by the owner.
     */
    function setMinBidIncrementPercentage(uint8 _minBidIncrementPercentage) external override onlyOwner {
        minBidIncrementPercentage = _minBidIncrementPercentage;

        emit AuctionMinBidIncrementPercentageUpdated(_minBidIncrementPercentage);
    }

    /**
     * @notice Calculate a next auction duration.
     */
    function _calcDuration(uint256 _timestamp) internal view returns (uint256) {
        // It implements a geometric sequence that doubles in 4 years with
        // an upper limit of 1.4 years
        uint256 interval = _timestamp - origin;
        if (interval >= 1135296000) {
            return 44236800;
        } else if (interval < 0) {
            interval = 0;
        }

        bytes16 x = ABDKMathQuad.fromUInt(interval);
        x = ABDKMathQuad.div(x, ABDKMathQuad.fromUInt(1460 * 86400));
        x = ABDKMathQuad.pow_2(x);
        x = ABDKMathQuad.mul(x, ABDKMathQuad.fromUInt(baseDuration));
        return ABDKMathQuad.toUInt(x);
    }

    /**
     * @notice Create an auction.
     * @dev Store the auction details in the `auction` state variable and emit an AuctionCreated event.
     * If the mint reverts, the minter was updated without pausing this contract first. To remedy this,
     * catch the revert and pause this contract.
     */
    function _createAuction() internal {
        try nouns.mint() returns (uint256 nounId) {
            uint256 startTime = block.timestamp;
            uint256 endTime = startTime + _calcDuration(startTime);

            auction = Auction({
                nounId: nounId,
                amount: 0,
                startTime: startTime,
                endTime: endTime,
                bidder: payable(0),
                settled: false
            });

            emit AuctionCreated(nounId, startTime, endTime);
        } catch Error(string memory) {
            _pause();
        }
    }

    /**
     * @notice Settle an auction, finalizing the bid and paying out to the owner.
     * @dev If there are no bids, the Noun is burned.
     */
    function _settleAuction() internal {
        INounsAuctionHouse.Auction memory _auction = auction;

        require(_auction.startTime != 0, "Auction hasn't begun");
        require(!_auction.settled, 'Auction has already been settled');
        require(block.timestamp >= _auction.endTime, "Auction hasn't completed");

        auction.settled = true;

        if (_auction.bidder == address(0)) {
            nouns.burn(_auction.nounId);
        } else {
            nouns.transferFrom(address(this), _auction.bidder, _auction.nounId);
        }

        if (_auction.amount > 0) {
            _safeTransferETHWithFallback(owner(), _auction.amount);
        }

        emit AuctionSettled(_auction.nounId, _auction.bidder, _auction.amount);
    }

    /**
     * @notice Transfer ETH. If the ETH transfer fails, wrap the ETH and try send it as WETH.
     */
    function _safeTransferETHWithFallback(address to, uint256 amount) internal {
        if (!_safeTransferETH(to, amount)) {
            IWETH(weth).deposit{ value: amount }();
            IERC20(weth).transfer(to, amount);
        }
    }

    /**
     * @notice Transfer ETH and return the success status.
     * @dev This function only forwards 30,000 gas to the callee.
     */
    function _safeTransferETH(address to, uint256 value) internal returns (bool) {
        (bool success, ) = to.call{ value: value, gas: 30_000 }(new bytes(0));
        return success;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (security/Pausable.sol)

pragma solidity ^0.8.0;

import "../utils/ContextUpgradeable.sol";
import "../proxy/utils/Initializable.sol";

/**
 * @dev Contract module which allows children to implement an emergency stop
 * mechanism that can be triggered by an authorized account.
 *
 * This module is used through inheritance. It will make available the
 * modifiers `whenNotPaused` and `whenPaused`, which can be applied to
 * the functions of your contract. Note that they will not be pausable by
 * simply including this module, only once the modifiers are put in place.
 */
abstract contract PausableUpgradeable is Initializable, ContextUpgradeable {
    /**
     * @dev Emitted when the pause is triggered by `account`.
     */
    event Paused(address account);

    /**
     * @dev Emitted when the pause is lifted by `account`.
     */
    event Unpaused(address account);

    bool private _paused;

    /**
     * @dev Initializes the contract in unpaused state.
     */
    function __Pausable_init() internal initializer {
        __Context_init_unchained();
        __Pausable_init_unchained();
    }

    function __Pausable_init_unchained() internal initializer {
        _paused = false;
    }

    /**
     * @dev Returns true if the contract is paused, and false otherwise.
     */
    function paused() public view virtual returns (bool) {
        return _paused;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is not paused.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    modifier whenNotPaused() {
        require(!paused(), "Pausable: paused");
        _;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is paused.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    modifier whenPaused() {
        require(paused(), "Pausable: not paused");
        _;
    }

    /**
     * @dev Triggers stopped state.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    function _pause() internal virtual whenNotPaused {
        _paused = true;
        emit Paused(_msgSender());
    }

    /**
     * @dev Returns to normal state.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    function _unpause() internal virtual whenPaused {
        _paused = false;
        emit Unpaused(_msgSender());
    }
    uint256[49] private __gap;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (security/ReentrancyGuard.sol)

pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuardUpgradeable is Initializable {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.

    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;

    uint256 private _status;

    function __ReentrancyGuard_init() internal initializer {
        __ReentrancyGuard_init_unchained();
    }

    function __ReentrancyGuard_init_unchained() internal initializer {
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and making it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        // On the first call to nonReentrant, _notEntered will be true
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

        // Any calls to nonReentrant after this point will fail
        _status = _ENTERED;

        _;

        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = _NOT_ENTERED;
    }
    uint256[49] private __gap;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../utils/ContextUpgradeable.sol";
import "../proxy/utils/Initializable.sol";

/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract OwnableUpgradeable is Initializable, ContextUpgradeable {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    function __Ownable_init() internal initializer {
        __Context_init_unchained();
        __Ownable_init_unchained();
    }

    function __Ownable_init_unchained() internal initializer {
        _transferOwnership(_msgSender());
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
        _;
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _transferOwnership(newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
    uint256[49] private __gap;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @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 `recipient`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address recipient, 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 `sender` to `recipient` 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 sender,
        address recipient,
        uint256 amount
    ) external returns (bool);

    /**
     * @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);
}

// SPDX-License-Identifier: BSD-4-Clause
/*
 * ABDK Math Quad Smart Contract Library.  Copyright © 2019 by ABDK Consulting.
 * Author: Mikhail Vladimirov <[email protected]>
 */
pragma solidity ^0.8.0;

/**
 * Smart contract library of mathematical functions operating with IEEE 754
 * quadruple-precision binary floating-point numbers (quadruple precision
 * numbers).  As long as quadruple precision numbers are 16-bytes long, they are
 * represented by bytes16 type.
 */
library ABDKMathQuad {
  /*
   * 0.
   */
  bytes16 private constant POSITIVE_ZERO = 0x00000000000000000000000000000000;

  /*
   * -0.
   */
  bytes16 private constant NEGATIVE_ZERO = 0x80000000000000000000000000000000;

  /*
   * +Infinity.
   */
  bytes16 private constant POSITIVE_INFINITY = 0x7FFF0000000000000000000000000000;

  /*
   * -Infinity.
   */
  bytes16 private constant NEGATIVE_INFINITY = 0xFFFF0000000000000000000000000000;

  /*
   * Canonical NaN value.
   */
  bytes16 private constant NaN = 0x7FFF8000000000000000000000000000;

  /**
   * Convert signed 256-bit integer number into quadruple precision number.
   *
   * @param x signed 256-bit integer number
   * @return quadruple precision number
   */
  function fromInt (int256 x) internal pure returns (bytes16) {
    unchecked {
      if (x == 0) return bytes16 (0);
      else {
        // We rely on overflow behavior here
        uint256 result = uint256 (x > 0 ? x : -x);

        uint256 msb = mostSignificantBit (result);
        if (msb < 112) result <<= 112 - msb;
        else if (msb > 112) result >>= msb - 112;

        result = result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 16383 + msb << 112;
        if (x < 0) result |= 0x80000000000000000000000000000000;

        return bytes16 (uint128 (result));
      }
    }
  }

  /**
   * Convert quadruple precision number into signed 256-bit integer number
   * rounding towards zero.  Revert on overflow.
   *
   * @param x quadruple precision number
   * @return signed 256-bit integer number
   */
  function toInt (bytes16 x) internal pure returns (int256) {
    unchecked {
      uint256 exponent = uint128 (x) >> 112 & 0x7FFF;

      require (exponent <= 16638); // Overflow
      if (exponent < 16383) return 0; // Underflow

      uint256 result = uint256 (uint128 (x)) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF |
        0x10000000000000000000000000000;

      if (exponent < 16495) result >>= 16495 - exponent;
      else if (exponent > 16495) result <<= exponent - 16495;

      if (uint128 (x) >= 0x80000000000000000000000000000000) { // Negative
        require (result <= 0x8000000000000000000000000000000000000000000000000000000000000000);
        return -int256 (result); // We rely on overflow behavior here
      } else {
        require (result <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
        return int256 (result);
      }
    }
  }

  /**
   * Convert unsigned 256-bit integer number into quadruple precision number.
   *
   * @param x unsigned 256-bit integer number
   * @return quadruple precision number
   */
  function fromUInt (uint256 x) internal pure returns (bytes16) {
    unchecked {
      if (x == 0) return bytes16 (0);
      else {
        uint256 result = x;

        uint256 msb = mostSignificantBit (result);
        if (msb < 112) result <<= 112 - msb;
        else if (msb > 112) result >>= msb - 112;

        result = result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 16383 + msb << 112;

        return bytes16 (uint128 (result));
      }
    }
  }

  /**
   * Convert quadruple precision number into unsigned 256-bit integer number
   * rounding towards zero.  Revert on underflow.  Note, that negative floating
   * point numbers in range (-1.0 .. 0.0) may be converted to unsigned integer
   * without error, because they are rounded to zero.
   *
   * @param x quadruple precision number
   * @return unsigned 256-bit integer number
   */
  function toUInt (bytes16 x) internal pure returns (uint256) {
    unchecked {
      uint256 exponent = uint128 (x) >> 112 & 0x7FFF;

      if (exponent < 16383) return 0; // Underflow

      require (uint128 (x) < 0x80000000000000000000000000000000); // Negative

      require (exponent <= 16638); // Overflow
      uint256 result = uint256 (uint128 (x)) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF |
        0x10000000000000000000000000000;

      if (exponent < 16495) result >>= 16495 - exponent;
      else if (exponent > 16495) result <<= exponent - 16495;

      return result;
    }
  }

  /**
   * Convert signed 128.128 bit fixed point number into quadruple precision
   * number.
   *
   * @param x signed 128.128 bit fixed point number
   * @return quadruple precision number
   */
  function from128x128 (int256 x) internal pure returns (bytes16) {
    unchecked {
      if (x == 0) return bytes16 (0);
      else {
        // We rely on overflow behavior here
        uint256 result = uint256 (x > 0 ? x : -x);

        uint256 msb = mostSignificantBit (result);
        if (msb < 112) result <<= 112 - msb;
        else if (msb > 112) result >>= msb - 112;

        result = result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 16255 + msb << 112;
        if (x < 0) result |= 0x80000000000000000000000000000000;

        return bytes16 (uint128 (result));
      }
    }
  }

  /**
   * Convert quadruple precision number into signed 128.128 bit fixed point
   * number.  Revert on overflow.
   *
   * @param x quadruple precision number
   * @return signed 128.128 bit fixed point number
   */
  function to128x128 (bytes16 x) internal pure returns (int256) {
    unchecked {
      uint256 exponent = uint128 (x) >> 112 & 0x7FFF;

      require (exponent <= 16510); // Overflow
      if (exponent < 16255) return 0; // Underflow

      uint256 result = uint256 (uint128 (x)) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF |
        0x10000000000000000000000000000;

      if (exponent < 16367) result >>= 16367 - exponent;
      else if (exponent > 16367) result <<= exponent - 16367;

      if (uint128 (x) >= 0x80000000000000000000000000000000) { // Negative
        require (result <= 0x8000000000000000000000000000000000000000000000000000000000000000);
        return -int256 (result); // We rely on overflow behavior here
      } else {
        require (result <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
        return int256 (result);
      }
    }
  }

  /**
   * Convert signed 64.64 bit fixed point number into quadruple precision
   * number.
   *
   * @param x signed 64.64 bit fixed point number
   * @return quadruple precision number
   */
  function from64x64 (int128 x) internal pure returns (bytes16) {
    unchecked {
      if (x == 0) return bytes16 (0);
      else {
        // We rely on overflow behavior here
        uint256 result = uint128 (x > 0 ? x : -x);

        uint256 msb = mostSignificantBit (result);
        if (msb < 112) result <<= 112 - msb;
        else if (msb > 112) result >>= msb - 112;

        result = result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 16319 + msb << 112;
        if (x < 0) result |= 0x80000000000000000000000000000000;

        return bytes16 (uint128 (result));
      }
    }
  }

  /**
   * Convert quadruple precision number into signed 64.64 bit fixed point
   * number.  Revert on overflow.
   *
   * @param x quadruple precision number
   * @return signed 64.64 bit fixed point number
   */
  function to64x64 (bytes16 x) internal pure returns (int128) {
    unchecked {
      uint256 exponent = uint128 (x) >> 112 & 0x7FFF;

      require (exponent <= 16446); // Overflow
      if (exponent < 16319) return 0; // Underflow

      uint256 result = uint256 (uint128 (x)) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF |
        0x10000000000000000000000000000;

      if (exponent < 16431) result >>= 16431 - exponent;
      else if (exponent > 16431) result <<= exponent - 16431;

      if (uint128 (x) >= 0x80000000000000000000000000000000) { // Negative
        require (result <= 0x80000000000000000000000000000000);
        return -int128 (int256 (result)); // We rely on overflow behavior here
      } else {
        require (result <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
        return int128 (int256 (result));
      }
    }
  }

  /**
   * Convert octuple precision number into quadruple precision number.
   *
   * @param x octuple precision number
   * @return quadruple precision number
   */
  function fromOctuple (bytes32 x) internal pure returns (bytes16) {
    unchecked {
      bool negative = x & 0x8000000000000000000000000000000000000000000000000000000000000000 > 0;

      uint256 exponent = uint256 (x) >> 236 & 0x7FFFF;
      uint256 significand = uint256 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

      if (exponent == 0x7FFFF) {
        if (significand > 0) return NaN;
        else return negative ? NEGATIVE_INFINITY : POSITIVE_INFINITY;
      }

      if (exponent > 278526)
        return negative ? NEGATIVE_INFINITY : POSITIVE_INFINITY;
      else if (exponent < 245649)
        return negative ? NEGATIVE_ZERO : POSITIVE_ZERO;
      else if (exponent < 245761) {
        significand = (significand | 0x100000000000000000000000000000000000000000000000000000000000) >> 245885 - exponent;
        exponent = 0;
      } else {
        significand >>= 124;
        exponent -= 245760;
      }

      uint128 result = uint128 (significand | exponent << 112);
      if (negative) result |= 0x80000000000000000000000000000000;

      return bytes16 (result);
    }
  }

  /**
   * Convert quadruple precision number into octuple precision number.
   *
   * @param x quadruple precision number
   * @return octuple precision number
   */
  function toOctuple (bytes16 x) internal pure returns (bytes32) {
    unchecked {
      uint256 exponent = uint128 (x) >> 112 & 0x7FFF;

      uint256 result = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

      if (exponent == 0x7FFF) exponent = 0x7FFFF; // Infinity or NaN
      else if (exponent == 0) {
        if (result > 0) {
          uint256 msb = mostSignificantBit (result);
          result = result << 236 - msb & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
          exponent = 245649 + msb;
        }
      } else {
        result <<= 124;
        exponent += 245760;
      }

      result |= exponent << 236;
      if (uint128 (x) >= 0x80000000000000000000000000000000)
        result |= 0x8000000000000000000000000000000000000000000000000000000000000000;

      return bytes32 (result);
    }
  }

  /**
   * Convert double precision number into quadruple precision number.
   *
   * @param x double precision number
   * @return quadruple precision number
   */
  function fromDouble (bytes8 x) internal pure returns (bytes16) {
    unchecked {
      uint256 exponent = uint64 (x) >> 52 & 0x7FF;

      uint256 result = uint64 (x) & 0xFFFFFFFFFFFFF;

      if (exponent == 0x7FF) exponent = 0x7FFF; // Infinity or NaN
      else if (exponent == 0) {
        if (result > 0) {
          uint256 msb = mostSignificantBit (result);
          result = result << 112 - msb & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
          exponent = 15309 + msb;
        }
      } else {
        result <<= 60;
        exponent += 15360;
      }

      result |= exponent << 112;
      if (x & 0x8000000000000000 > 0)
        result |= 0x80000000000000000000000000000000;

      return bytes16 (uint128 (result));
    }
  }

  /**
   * Convert quadruple precision number into double precision number.
   *
   * @param x quadruple precision number
   * @return double precision number
   */
  function toDouble (bytes16 x) internal pure returns (bytes8) {
    unchecked {
      bool negative = uint128 (x) >= 0x80000000000000000000000000000000;

      uint256 exponent = uint128 (x) >> 112 & 0x7FFF;
      uint256 significand = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

      if (exponent == 0x7FFF) {
        if (significand > 0) return 0x7FF8000000000000; // NaN
        else return negative ?
            bytes8 (0xFFF0000000000000) : // -Infinity
            bytes8 (0x7FF0000000000000); // Infinity
      }

      if (exponent > 17406)
        return negative ?
            bytes8 (0xFFF0000000000000) : // -Infinity
            bytes8 (0x7FF0000000000000); // Infinity
      else if (exponent < 15309)
        return negative ?
            bytes8 (0x8000000000000000) : // -0
            bytes8 (0x0000000000000000); // 0
      else if (exponent < 15361) {
        significand = (significand | 0x10000000000000000000000000000) >> 15421 - exponent;
        exponent = 0;
      } else {
        significand >>= 60;
        exponent -= 15360;
      }

      uint64 result = uint64 (significand | exponent << 52);
      if (negative) result |= 0x8000000000000000;

      return bytes8 (result);
    }
  }

  /**
   * Test whether given quadruple precision number is NaN.
   *
   * @param x quadruple precision number
   * @return true if x is NaN, false otherwise
   */
  function isNaN (bytes16 x) internal pure returns (bool) {
    unchecked {
      return uint128 (x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF >
        0x7FFF0000000000000000000000000000;
    }
  }

  /**
   * Test whether given quadruple precision number is positive or negative
   * infinity.
   *
   * @param x quadruple precision number
   * @return true if x is positive or negative infinity, false otherwise
   */
  function isInfinity (bytes16 x) internal pure returns (bool) {
    unchecked {
      return uint128 (x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF ==
        0x7FFF0000000000000000000000000000;
    }
  }

  /**
   * Calculate sign of x, i.e. -1 if x is negative, 0 if x if zero, and 1 if x
   * is positive.  Note that sign (-0) is zero.  Revert if x is NaN. 
   *
   * @param x quadruple precision number
   * @return sign of x
   */
  function sign (bytes16 x) internal pure returns (int8) {
    unchecked {
      uint128 absoluteX = uint128 (x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

      require (absoluteX <= 0x7FFF0000000000000000000000000000); // Not NaN

      if (absoluteX == 0) return 0;
      else if (uint128 (x) >= 0x80000000000000000000000000000000) return -1;
      else return 1;
    }
  }

  /**
   * Calculate sign (x - y).  Revert if either argument is NaN, or both
   * arguments are infinities of the same sign. 
   *
   * @param x quadruple precision number
   * @param y quadruple precision number
   * @return sign (x - y)
   */
  function cmp (bytes16 x, bytes16 y) internal pure returns (int8) {
    unchecked {
      uint128 absoluteX = uint128 (x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

      require (absoluteX <= 0x7FFF0000000000000000000000000000); // Not NaN

      uint128 absoluteY = uint128 (y) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

      require (absoluteY <= 0x7FFF0000000000000000000000000000); // Not NaN

      // Not infinities of the same sign
      require (x != y || absoluteX < 0x7FFF0000000000000000000000000000);

      if (x == y) return 0;
      else {
        bool negativeX = uint128 (x) >= 0x80000000000000000000000000000000;
        bool negativeY = uint128 (y) >= 0x80000000000000000000000000000000;

        if (negativeX) {
          if (negativeY) return absoluteX > absoluteY ? -1 : int8 (1);
          else return -1; 
        } else {
          if (negativeY) return 1;
          else return absoluteX > absoluteY ? int8 (1) : -1;
        }
      }
    }
  }

  /**
   * Test whether x equals y.  NaN, infinity, and -infinity are not equal to
   * anything. 
   *
   * @param x quadruple precision number
   * @param y quadruple precision number
   * @return true if x equals to y, false otherwise
   */
  function eq (bytes16 x, bytes16 y) internal pure returns (bool) {
    unchecked {
      if (x == y) {
        return uint128 (x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF <
          0x7FFF0000000000000000000000000000;
      } else return false;
    }
  }

  /**
   * Calculate x + y.  Special values behave in the following way:
   *
   * NaN + x = NaN for any x.
   * Infinity + x = Infinity for any finite x.
   * -Infinity + x = -Infinity for any finite x.
   * Infinity + Infinity = Infinity.
   * -Infinity + -Infinity = -Infinity.
   * Infinity + -Infinity = -Infinity + Infinity = NaN.
   *
   * @param x quadruple precision number
   * @param y quadruple precision number
   * @return quadruple precision number
   */
  function add (bytes16 x, bytes16 y) internal pure returns (bytes16) {
    unchecked {
      uint256 xExponent = uint128 (x) >> 112 & 0x7FFF;
      uint256 yExponent = uint128 (y) >> 112 & 0x7FFF;

      if (xExponent == 0x7FFF) {
        if (yExponent == 0x7FFF) { 
          if (x == y) return x;
          else return NaN;
        } else return x; 
      } else if (yExponent == 0x7FFF) return y;
      else {
        bool xSign = uint128 (x) >= 0x80000000000000000000000000000000;
        uint256 xSignifier = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
        if (xExponent == 0) xExponent = 1;
        else xSignifier |= 0x10000000000000000000000000000;

        bool ySign = uint128 (y) >= 0x80000000000000000000000000000000;
        uint256 ySignifier = uint128 (y) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
        if (yExponent == 0) yExponent = 1;
        else ySignifier |= 0x10000000000000000000000000000;

        if (xSignifier == 0) return y == NEGATIVE_ZERO ? POSITIVE_ZERO : y;
        else if (ySignifier == 0) return x == NEGATIVE_ZERO ? POSITIVE_ZERO : x;
        else {
          int256 delta = int256 (xExponent) - int256 (yExponent);
  
          if (xSign == ySign) {
            if (delta > 112) return x;
            else if (delta > 0) ySignifier >>= uint256 (delta);
            else if (delta < -112) return y;
            else if (delta < 0) {
              xSignifier >>= uint256 (-delta);
              xExponent = yExponent;
            }
  
            xSignifier += ySignifier;
  
            if (xSignifier >= 0x20000000000000000000000000000) {
              xSignifier >>= 1;
              xExponent += 1;
            }
  
            if (xExponent == 0x7FFF)
              return xSign ? NEGATIVE_INFINITY : POSITIVE_INFINITY;
            else {
              if (xSignifier < 0x10000000000000000000000000000) xExponent = 0;
              else xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
  
              return bytes16 (uint128 (
                  (xSign ? 0x80000000000000000000000000000000 : 0) |
                  (xExponent << 112) |
                  xSignifier)); 
            }
          } else {
            if (delta > 0) {
              xSignifier <<= 1;
              xExponent -= 1;
            } else if (delta < 0) {
              ySignifier <<= 1;
              xExponent = yExponent - 1;
            }

            if (delta > 112) ySignifier = 1;
            else if (delta > 1) ySignifier = (ySignifier - 1 >> uint256 (delta - 1)) + 1;
            else if (delta < -112) xSignifier = 1;
            else if (delta < -1) xSignifier = (xSignifier - 1 >> uint256 (-delta - 1)) + 1;

            if (xSignifier >= ySignifier) xSignifier -= ySignifier;
            else {
              xSignifier = ySignifier - xSignifier;
              xSign = ySign;
            }

            if (xSignifier == 0)
              return POSITIVE_ZERO;

            uint256 msb = mostSignificantBit (xSignifier);

            if (msb == 113) {
              xSignifier = xSignifier >> 1 & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
              xExponent += 1;
            } else if (msb < 112) {
              uint256 shift = 112 - msb;
              if (xExponent > shift) {
                xSignifier = xSignifier << shift & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                xExponent -= shift;
              } else {
                xSignifier <<= xExponent - 1;
                xExponent = 0;
              }
            } else xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

            if (xExponent == 0x7FFF)
              return xSign ? NEGATIVE_INFINITY : POSITIVE_INFINITY;
            else return bytes16 (uint128 (
                (xSign ? 0x80000000000000000000000000000000 : 0) |
                (xExponent << 112) |
                xSignifier));
          }
        }
      }
    }
  }

  /**
   * Calculate x - y.  Special values behave in the following way:
   *
   * NaN - x = NaN for any x.
   * Infinity - x = Infinity for any finite x.
   * -Infinity - x = -Infinity for any finite x.
   * Infinity - -Infinity = Infinity.
   * -Infinity - Infinity = -Infinity.
   * Infinity - Infinity = -Infinity - -Infinity = NaN.
   *
   * @param x quadruple precision number
   * @param y quadruple precision number
   * @return quadruple precision number
   */
  function sub (bytes16 x, bytes16 y) internal pure returns (bytes16) {
    unchecked {
      return add (x, y ^ 0x80000000000000000000000000000000);
    }
  }

  /**
   * Calculate x * y.  Special values behave in the following way:
   *
   * NaN * x = NaN for any x.
   * Infinity * x = Infinity for any finite positive x.
   * Infinity * x = -Infinity for any finite negative x.
   * -Infinity * x = -Infinity for any finite positive x.
   * -Infinity * x = Infinity for any finite negative x.
   * Infinity * 0 = NaN.
   * -Infinity * 0 = NaN.
   * Infinity * Infinity = Infinity.
   * Infinity * -Infinity = -Infinity.
   * -Infinity * Infinity = -Infinity.
   * -Infinity * -Infinity = Infinity.
   *
   * @param x quadruple precision number
   * @param y quadruple precision number
   * @return quadruple precision number
   */
  function mul (bytes16 x, bytes16 y) internal pure returns (bytes16) {
    unchecked {
      uint256 xExponent = uint128 (x) >> 112 & 0x7FFF;
      uint256 yExponent = uint128 (y) >> 112 & 0x7FFF;

      if (xExponent == 0x7FFF) {
        if (yExponent == 0x7FFF) {
          if (x == y) return x ^ y & 0x80000000000000000000000000000000;
          else if (x ^ y == 0x80000000000000000000000000000000) return x | y;
          else return NaN;
        } else {
          if (y & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) return NaN;
          else return x ^ y & 0x80000000000000000000000000000000;
        }
      } else if (yExponent == 0x7FFF) {
          if (x & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) return NaN;
          else return y ^ x & 0x80000000000000000000000000000000;
      } else {
        uint256 xSignifier = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
        if (xExponent == 0) xExponent = 1;
        else xSignifier |= 0x10000000000000000000000000000;

        uint256 ySignifier = uint128 (y) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
        if (yExponent == 0) yExponent = 1;
        else ySignifier |= 0x10000000000000000000000000000;

        xSignifier *= ySignifier;
        if (xSignifier == 0)
          return (x ^ y) & 0x80000000000000000000000000000000 > 0 ?
              NEGATIVE_ZERO : POSITIVE_ZERO;

        xExponent += yExponent;

        uint256 msb =
          xSignifier >= 0x200000000000000000000000000000000000000000000000000000000 ? 225 :
          xSignifier >= 0x100000000000000000000000000000000000000000000000000000000 ? 224 :
          mostSignificantBit (xSignifier);

        if (xExponent + msb < 16496) { // Underflow
          xExponent = 0;
          xSignifier = 0;
        } else if (xExponent + msb < 16608) { // Subnormal
          if (xExponent < 16496)
            xSignifier >>= 16496 - xExponent;
          else if (xExponent > 16496)
            xSignifier <<= xExponent - 16496;
          xExponent = 0;
        } else if (xExponent + msb > 49373) {
          xExponent = 0x7FFF;
          xSignifier = 0;
        } else {
          if (msb > 112)
            xSignifier >>= msb - 112;
          else if (msb < 112)
            xSignifier <<= 112 - msb;

          xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

          xExponent = xExponent + msb - 16607;
        }

        return bytes16 (uint128 (uint128 ((x ^ y) & 0x80000000000000000000000000000000) |
            xExponent << 112 | xSignifier));
      }
    }
  }

  /**
   * Calculate x / y.  Special values behave in the following way:
   *
   * NaN / x = NaN for any x.
   * x / NaN = NaN for any x.
   * Infinity / x = Infinity for any finite non-negative x.
   * Infinity / x = -Infinity for any finite negative x including -0.
   * -Infinity / x = -Infinity for any finite non-negative x.
   * -Infinity / x = Infinity for any finite negative x including -0.
   * x / Infinity = 0 for any finite non-negative x.
   * x / -Infinity = -0 for any finite non-negative x.
   * x / Infinity = -0 for any finite non-negative x including -0.
   * x / -Infinity = 0 for any finite non-negative x including -0.
   * 
   * Infinity / Infinity = NaN.
   * Infinity / -Infinity = -NaN.
   * -Infinity / Infinity = -NaN.
   * -Infinity / -Infinity = NaN.
   *
   * Division by zero behaves in the following way:
   *
   * x / 0 = Infinity for any finite positive x.
   * x / -0 = -Infinity for any finite positive x.
   * x / 0 = -Infinity for any finite negative x.
   * x / -0 = Infinity for any finite negative x.
   * 0 / 0 = NaN.
   * 0 / -0 = NaN.
   * -0 / 0 = NaN.
   * -0 / -0 = NaN.
   *
   * @param x quadruple precision number
   * @param y quadruple precision number
   * @return quadruple precision number
   */
  function div (bytes16 x, bytes16 y) internal pure returns (bytes16) {
    unchecked {
      uint256 xExponent = uint128 (x) >> 112 & 0x7FFF;
      uint256 yExponent = uint128 (y) >> 112 & 0x7FFF;

      if (xExponent == 0x7FFF) {
        if (yExponent == 0x7FFF) return NaN;
        else return x ^ y & 0x80000000000000000000000000000000;
      } else if (yExponent == 0x7FFF) {
        if (y & 0x0000FFFFFFFFFFFFFFFFFFFFFFFFFFFF != 0) return NaN;
        else return POSITIVE_ZERO | (x ^ y) & 0x80000000000000000000000000000000;
      } else if (y & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) {
        if (x & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) return NaN;
        else return POSITIVE_INFINITY | (x ^ y) & 0x80000000000000000000000000000000;
      } else {
        uint256 ySignifier = uint128 (y) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
        if (yExponent == 0) yExponent = 1;
        else ySignifier |= 0x10000000000000000000000000000;

        uint256 xSignifier = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
        if (xExponent == 0) {
          if (xSignifier != 0) {
            uint shift = 226 - mostSignificantBit (xSignifier);

            xSignifier <<= shift;

            xExponent = 1;
            yExponent += shift - 114;
          }
        }
        else {
          xSignifier = (xSignifier | 0x10000000000000000000000000000) << 114;
        }

        xSignifier = xSignifier / ySignifier;
        if (xSignifier == 0)
          return (x ^ y) & 0x80000000000000000000000000000000 > 0 ?
              NEGATIVE_ZERO : POSITIVE_ZERO;

        assert (xSignifier >= 0x1000000000000000000000000000);

        uint256 msb =
          xSignifier >= 0x80000000000000000000000000000 ? mostSignificantBit (xSignifier) :
          xSignifier >= 0x40000000000000000000000000000 ? 114 :
          xSignifier >= 0x20000000000000000000000000000 ? 113 : 112;

        if (xExponent + msb > yExponent + 16497) { // Overflow
          xExponent = 0x7FFF;
          xSignifier = 0;
        } else if (xExponent + msb + 16380  < yExponent) { // Underflow
          xExponent = 0;
          xSignifier = 0;
        } else if (xExponent + msb + 16268  < yExponent) { // Subnormal
          if (xExponent + 16380 > yExponent)
            xSignifier <<= xExponent + 16380 - yExponent;
          else if (xExponent + 16380 < yExponent)
            xSignifier >>= yExponent - xExponent - 16380;

          xExponent = 0;
        } else { // Normal
          if (msb > 112)
            xSignifier >>= msb - 112;

          xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

          xExponent = xExponent + msb + 16269 - yExponent;
        }

        return bytes16 (uint128 (uint128 ((x ^ y) & 0x80000000000000000000000000000000) |
            xExponent << 112 | xSignifier));
      }
    }
  }

  /**
   * Calculate -x.
   *
   * @param x quadruple precision number
   * @return quadruple precision number
   */
  function neg (bytes16 x) internal pure returns (bytes16) {
    unchecked {
      return x ^ 0x80000000000000000000000000000000;
    }
  }

  /**
   * Calculate |x|.
   *
   * @param x quadruple precision number
   * @return quadruple precision number
   */
  function abs (bytes16 x) internal pure returns (bytes16) {
    unchecked {
      return x & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
    }
  }

  /**
   * Calculate square root of x.  Return NaN on negative x excluding -0.
   *
   * @param x quadruple precision number
   * @return quadruple precision number
   */
  function sqrt (bytes16 x) internal pure returns (bytes16) {
    unchecked {
      if (uint128 (x) >  0x80000000000000000000000000000000) return NaN;
      else {
        uint256 xExponent = uint128 (x) >> 112 & 0x7FFF;
        if (xExponent == 0x7FFF) return x;
        else {
          uint256 xSignifier = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
          if (xExponent == 0) xExponent = 1;
          else xSignifier |= 0x10000000000000000000000000000;

          if (xSignifier == 0) return POSITIVE_ZERO;

          bool oddExponent = xExponent & 0x1 == 0;
          xExponent = xExponent + 16383 >> 1;

          if (oddExponent) {
            if (xSignifier >= 0x10000000000000000000000000000)
              xSignifier <<= 113;
            else {
              uint256 msb = mostSignificantBit (xSignifier);
              uint256 shift = (226 - msb) & 0xFE;
              xSignifier <<= shift;
              xExponent -= shift - 112 >> 1;
            }
          } else {
            if (xSignifier >= 0x10000000000000000000000000000)
              xSignifier <<= 112;
            else {
              uint256 msb = mostSignificantBit (xSignifier);
              uint256 shift = (225 - msb) & 0xFE;
              xSignifier <<= shift;
              xExponent -= shift - 112 >> 1;
            }
          }

          uint256 r = 0x10000000000000000000000000000;
          r = (r + xSignifier / r) >> 1;
          r = (r + xSignifier / r) >> 1;
          r = (r + xSignifier / r) >> 1;
          r = (r + xSignifier / r) >> 1;
          r = (r + xSignifier / r) >> 1;
          r = (r + xSignifier / r) >> 1;
          r = (r + xSignifier / r) >> 1; // Seven iterations should be enough
          uint256 r1 = xSignifier / r;
          if (r1 < r) r = r1;

          return bytes16 (uint128 (xExponent << 112 | r & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF));
        }
      }
    }
  }

  /**
   * Calculate binary logarithm of x.  Return NaN on negative x excluding -0.
   *
   * @param x quadruple precision number
   * @return quadruple precision number
   */
  function log_2 (bytes16 x) internal pure returns (bytes16) {
    unchecked {
      if (uint128 (x) > 0x80000000000000000000000000000000) return NaN;
      else if (x == 0x3FFF0000000000000000000000000000) return POSITIVE_ZERO; 
      else {
        uint256 xExponent = uint128 (x) >> 112 & 0x7FFF;
        if (xExponent == 0x7FFF) return x;
        else {
          uint256 xSignifier = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
          if (xExponent == 0) xExponent = 1;
          else xSignifier |= 0x10000000000000000000000000000;

          if (xSignifier == 0) return NEGATIVE_INFINITY;

          bool resultNegative;
          uint256 resultExponent = 16495;
          uint256 resultSignifier;

          if (xExponent >= 0x3FFF) {
            resultNegative = false;
            resultSignifier = xExponent - 0x3FFF;
            xSignifier <<= 15;
          } else {
            resultNegative = true;
            if (xSignifier >= 0x10000000000000000000000000000) {
              resultSignifier = 0x3FFE - xExponent;
              xSignifier <<= 15;
            } else {
              uint256 msb = mostSignificantBit (xSignifier);
              resultSignifier = 16493 - msb;
              xSignifier <<= 127 - msb;
            }
          }

          if (xSignifier == 0x80000000000000000000000000000000) {
            if (resultNegative) resultSignifier += 1;
            uint256 shift = 112 - mostSignificantBit (resultSignifier);
            resultSignifier <<= shift;
            resultExponent -= shift;
          } else {
            uint256 bb = resultNegative ? 1 : 0;
            while (resultSignifier < 0x10000000000000000000000000000) {
              resultSignifier <<= 1;
              resultExponent -= 1;
  
              xSignifier *= xSignifier;
              uint256 b = xSignifier >> 255;
              resultSignifier += b ^ bb;
              xSignifier >>= 127 + b;
            }
          }

          return bytes16 (uint128 ((resultNegative ? 0x80000000000000000000000000000000 : 0) |
              resultExponent << 112 | resultSignifier & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF));
        }
      }
    }
  }

  /**
   * Calculate natural logarithm of x.  Return NaN on negative x excluding -0.
   *
   * @param x quadruple precision number
   * @return quadruple precision number
   */
  function ln (bytes16 x) internal pure returns (bytes16) {
    unchecked {
      return mul (log_2 (x), 0x3FFE62E42FEFA39EF35793C7673007E5);
    }
  }

  /**
   * Calculate 2^x.
   *
   * @param x quadruple precision number
   * @return quadruple precision number
   */
  function pow_2 (bytes16 x) internal pure returns (bytes16) {
    unchecked {
      bool xNegative = uint128 (x) > 0x80000000000000000000000000000000;
      uint256 xExponent = uint128 (x) >> 112 & 0x7FFF;
      uint256 xSignifier = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

      if (xExponent == 0x7FFF && xSignifier != 0) return NaN;
      else if (xExponent > 16397)
        return xNegative ? POSITIVE_ZERO : POSITIVE_INFINITY;
      else if (xExponent < 16255)
        return 0x3FFF0000000000000000000000000000;
      else {
        if (xExponent == 0) xExponent = 1;
        else xSignifier |= 0x10000000000000000000000000000;

        if (xExponent > 16367)
          xSignifier <<= xExponent - 16367;
        else if (xExponent < 16367)
          xSignifier >>= 16367 - xExponent;

        if (xNegative && xSignifier > 0x406E00000000000000000000000000000000)
          return POSITIVE_ZERO;

        if (!xNegative && xSignifier > 0x3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
          return POSITIVE_INFINITY;

        uint256 resultExponent = xSignifier >> 128;
        xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
        if (xNegative && xSignifier != 0) {
          xSignifier = ~xSignifier;
          resultExponent += 1;
        }

        uint256 resultSignifier = 0x80000000000000000000000000000000;
        if (xSignifier & 0x80000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x16A09E667F3BCC908B2FB1366EA957D3E >> 128;
        if (xSignifier & 0x40000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1306FE0A31B7152DE8D5A46305C85EDEC >> 128;
        if (xSignifier & 0x20000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1172B83C7D517ADCDF7C8C50EB14A791F >> 128;
        if (xSignifier & 0x10000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10B5586CF9890F6298B92B71842A98363 >> 128;
        if (xSignifier & 0x8000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1059B0D31585743AE7C548EB68CA417FD >> 128;
        if (xSignifier & 0x4000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x102C9A3E778060EE6F7CACA4F7A29BDE8 >> 128;
        if (xSignifier & 0x2000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10163DA9FB33356D84A66AE336DCDFA3F >> 128;
        if (xSignifier & 0x1000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100B1AFA5ABCBED6129AB13EC11DC9543 >> 128;
        if (xSignifier & 0x800000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10058C86DA1C09EA1FF19D294CF2F679B >> 128;
        if (xSignifier & 0x400000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1002C605E2E8CEC506D21BFC89A23A00F >> 128;
        if (xSignifier & 0x200000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100162F3904051FA128BCA9C55C31E5DF >> 128;
        if (xSignifier & 0x100000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000B175EFFDC76BA38E31671CA939725 >> 128;
        if (xSignifier & 0x80000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100058BA01FB9F96D6CACD4B180917C3D >> 128;
        if (xSignifier & 0x40000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10002C5CC37DA9491D0985C348C68E7B3 >> 128;
        if (xSignifier & 0x20000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000162E525EE054754457D5995292026 >> 128;
        if (xSignifier & 0x10000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000B17255775C040618BF4A4ADE83FC >> 128;
        if (xSignifier & 0x8000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000058B91B5BC9AE2EED81E9B7D4CFAB >> 128;
        if (xSignifier & 0x4000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100002C5C89D5EC6CA4D7C8ACC017B7C9 >> 128;
        if (xSignifier & 0x2000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000162E43F4F831060E02D839A9D16D >> 128;
        if (xSignifier & 0x1000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000B1721BCFC99D9F890EA06911763 >> 128;
        if (xSignifier & 0x800000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000058B90CF1E6D97F9CA14DBCC1628 >> 128;
        if (xSignifier & 0x400000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000002C5C863B73F016468F6BAC5CA2B >> 128;
        if (xSignifier & 0x200000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000162E430E5A18F6119E3C02282A5 >> 128;
        if (xSignifier & 0x100000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000B1721835514B86E6D96EFD1BFE >> 128;
        if (xSignifier & 0x80000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000058B90C0B48C6BE5DF846C5B2EF >> 128;
        if (xSignifier & 0x40000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000002C5C8601CC6B9E94213C72737A >> 128;
        if (xSignifier & 0x20000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000162E42FFF037DF38AA2B219F06 >> 128;
        if (xSignifier & 0x10000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000B17217FBA9C739AA5819F44F9 >> 128;
        if (xSignifier & 0x8000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000058B90BFCDEE5ACD3C1CEDC823 >> 128;
        if (xSignifier & 0x4000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000002C5C85FE31F35A6A30DA1BE50 >> 128;
        if (xSignifier & 0x2000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000162E42FF0999CE3541B9FFFCF >> 128;
        if (xSignifier & 0x1000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000B17217F80F4EF5AADDA45554 >> 128;
        if (xSignifier & 0x800000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000058B90BFBF8479BD5A81B51AD >> 128;
        if (xSignifier & 0x400000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000002C5C85FDF84BD62AE30A74CC >> 128;
        if (xSignifier & 0x200000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000162E42FEFB2FED257559BDAA >> 128;
        if (xSignifier & 0x100000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000B17217F7D5A7716BBA4A9AE >> 128;
        if (xSignifier & 0x80000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000058B90BFBE9DDBAC5E109CCE >> 128;
        if (xSignifier & 0x40000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000002C5C85FDF4B15DE6F17EB0D >> 128;
        if (xSignifier & 0x20000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000162E42FEFA494F1478FDE05 >> 128;
        if (xSignifier & 0x10000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000B17217F7D20CF927C8E94C >> 128;
        if (xSignifier & 0x8000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000058B90BFBE8F71CB4E4B33D >> 128;
        if (xSignifier & 0x4000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000002C5C85FDF477B662B26945 >> 128;
        if (xSignifier & 0x2000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000162E42FEFA3AE53369388C >> 128;
        if (xSignifier & 0x1000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000B17217F7D1D351A389D40 >> 128;
        if (xSignifier & 0x800000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000058B90BFBE8E8B2D3D4EDE >> 128;
        if (xSignifier & 0x400000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000002C5C85FDF4741BEA6E77E >> 128;
        if (xSignifier & 0x200000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000162E42FEFA39FE95583C2 >> 128;
        if (xSignifier & 0x100000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000B17217F7D1CFB72B45E1 >> 128;
        if (xSignifier & 0x80000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000058B90BFBE8E7CC35C3F0 >> 128;
        if (xSignifier & 0x40000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000002C5C85FDF473E242EA38 >> 128;
        if (xSignifier & 0x20000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000162E42FEFA39F02B772C >> 128;
        if (xSignifier & 0x10000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000B17217F7D1CF7D83C1A >> 128;
        if (xSignifier & 0x8000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000058B90BFBE8E7BDCBE2E >> 128;
        if (xSignifier & 0x4000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000002C5C85FDF473DEA871F >> 128;
        if (xSignifier & 0x2000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000162E42FEFA39EF44D91 >> 128;
        if (xSignifier & 0x1000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000B17217F7D1CF79E949 >> 128;
        if (xSignifier & 0x800000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000058B90BFBE8E7BCE544 >> 128;
        if (xSignifier & 0x400000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000002C5C85FDF473DE6ECA >> 128;
        if (xSignifier & 0x200000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000162E42FEFA39EF366F >> 128;
        if (xSignifier & 0x100000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000B17217F7D1CF79AFA >> 128;
        if (xSignifier & 0x80000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000058B90BFBE8E7BCD6D >> 128;
        if (xSignifier & 0x40000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000002C5C85FDF473DE6B2 >> 128;
        if (xSignifier & 0x20000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000162E42FEFA39EF358 >> 128;
        if (xSignifier & 0x10000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000B17217F7D1CF79AB >> 128;
        if (xSignifier & 0x8000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000058B90BFBE8E7BCD5 >> 128;
        if (xSignifier & 0x4000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000002C5C85FDF473DE6A >> 128;
        if (xSignifier & 0x2000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000162E42FEFA39EF34 >> 128;
        if (xSignifier & 0x1000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000B17217F7D1CF799 >> 128;
        if (xSignifier & 0x800000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000058B90BFBE8E7BCC >> 128;
        if (xSignifier & 0x400000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000002C5C85FDF473DE5 >> 128;
        if (xSignifier & 0x200000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000162E42FEFA39EF2 >> 128;
        if (xSignifier & 0x100000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000B17217F7D1CF78 >> 128;
        if (xSignifier & 0x80000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000058B90BFBE8E7BB >> 128;
        if (xSignifier & 0x40000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000002C5C85FDF473DD >> 128;
        if (xSignifier & 0x20000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000162E42FEFA39EE >> 128;
        if (xSignifier & 0x10000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000B17217F7D1CF6 >> 128;
        if (xSignifier & 0x8000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000058B90BFBE8E7A >> 128;
        if (xSignifier & 0x4000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000002C5C85FDF473C >> 128;
        if (xSignifier & 0x2000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000162E42FEFA39D >> 128;
        if (xSignifier & 0x1000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000B17217F7D1CE >> 128;
        if (xSignifier & 0x800000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000058B90BFBE8E6 >> 128;
        if (xSignifier & 0x400000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000002C5C85FDF472 >> 128;
        if (xSignifier & 0x200000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000162E42FEFA38 >> 128;
        if (xSignifier & 0x100000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000B17217F7D1B >> 128;
        if (xSignifier & 0x80000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000058B90BFBE8D >> 128;
        if (xSignifier & 0x40000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000002C5C85FDF46 >> 128;
        if (xSignifier & 0x20000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000162E42FEFA2 >> 128;
        if (xSignifier & 0x10000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000B17217F7D0 >> 128;
        if (xSignifier & 0x8000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000058B90BFBE7 >> 128;
        if (xSignifier & 0x4000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000002C5C85FDF3 >> 128;
        if (xSignifier & 0x2000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000162E42FEF9 >> 128;
        if (xSignifier & 0x1000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000B17217F7C >> 128;
        if (xSignifier & 0x800000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000058B90BFBD >> 128;
        if (xSignifier & 0x400000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000002C5C85FDE >> 128;
        if (xSignifier & 0x200000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000162E42FEE >> 128;
        if (xSignifier & 0x100000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000B17217F6 >> 128;
        if (xSignifier & 0x80000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000058B90BFA >> 128;
        if (xSignifier & 0x40000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000002C5C85FC >> 128;
        if (xSignifier & 0x20000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000162E42FD >> 128;
        if (xSignifier & 0x10000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000B17217E >> 128;
        if (xSignifier & 0x8000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000058B90BE >> 128;
        if (xSignifier & 0x4000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000002C5C85E >> 128;
        if (xSignifier & 0x2000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000162E42E >> 128;
        if (xSignifier & 0x1000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000B17216 >> 128;
        if (xSignifier & 0x800000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000058B90A >> 128;
        if (xSignifier & 0x400000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000002C5C84 >> 128;
        if (xSignifier & 0x200000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000162E41 >> 128;
        if (xSignifier & 0x100000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000000B1720 >> 128;
        if (xSignifier & 0x80000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000058B8F >> 128;
        if (xSignifier & 0x40000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000002C5C7 >> 128;
        if (xSignifier & 0x20000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000000162E3 >> 128;
        if (xSignifier & 0x10000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000000B171 >> 128;
        if (xSignifier & 0x8000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000000058B8 >> 128;
        if (xSignifier & 0x4000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000002C5B >> 128;
        if (xSignifier & 0x2000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000000162D >> 128;
        if (xSignifier & 0x1000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000000B16 >> 128;
        if (xSignifier & 0x800 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000000058A >> 128;
        if (xSignifier & 0x400 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000000002C4 >> 128;
        if (xSignifier & 0x200 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000000161 >> 128;
        if (xSignifier & 0x100 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000000000B0 >> 128;
        if (xSignifier & 0x80 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000000057 >> 128;
        if (xSignifier & 0x40 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000000002B >> 128;
        if (xSignifier & 0x20 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000000015 >> 128;
        if (xSignifier & 0x10 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000000000A >> 128;
        if (xSignifier & 0x8 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000000004 >> 128;
        if (xSignifier & 0x4 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000000001 >> 128;

        if (!xNegative) {
          resultSignifier = resultSignifier >> 15 & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
          resultExponent += 0x3FFF;
        } else if (resultExponent <= 0x3FFE) {
          resultSignifier = resultSignifier >> 15 & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
          resultExponent = 0x3FFF - resultExponent;
        } else {
          resultSignifier = resultSignifier >> resultExponent - 16367;
          resultExponent = 0;
        }

        return bytes16 (uint128 (resultExponent << 112 | resultSignifier));
      }
    }
  }

  /**
   * Calculate e^x.
   *
   * @param x quadruple precision number
   * @return quadruple precision number
   */
  function exp (bytes16 x) internal pure returns (bytes16) {
    unchecked {
      return pow_2 (mul (x, 0x3FFF71547652B82FE1777D0FFDA0D23A));
    }
  }

  /**
   * Get index of the most significant non-zero bit in binary representation of
   * x.  Reverts if x is zero.
   *
   * @return index of the most significant non-zero bit in binary representation
   *         of x
   */
  function mostSignificantBit (uint256 x) private pure returns (uint256) {
    unchecked {
      require (x > 0);

      uint256 result = 0;

      if (x >= 0x100000000000000000000000000000000) { x >>= 128; result += 128; }
      if (x >= 0x10000000000000000) { x >>= 64; result += 64; }
      if (x >= 0x100000000) { x >>= 32; result += 32; }
      if (x >= 0x10000) { x >>= 16; result += 16; }
      if (x >= 0x100) { x >>= 8; result += 8; }
      if (x >= 0x10) { x >>= 4; result += 4; }
      if (x >= 0x4) { x >>= 2; result += 2; }
      if (x >= 0x2) result += 1; // No need to shift x anymore

      return result;
    }
  }
}

// SPDX-License-Identifier: GPL-3.0

/// @title Interface for Noun Auction Houses

/*********************************
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 * ░░░░░░█████████░░█████████░░░ *
 * ░░░░░░██░░░████░░██░░░████░░░ *
 * ░░██████░░░████████░░░████░░░ *
 * ░░██░░██░░░████░░██░░░████░░░ *
 * ░░██░░██░░░████░░██░░░████░░░ *
 * ░░░░░░█████████░░█████████░░░ *
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 *********************************/

pragma solidity ^0.8.6;

interface INounsAuctionHouse {
    struct Auction {
        // ID for the Noun (ERC721 token ID)
        uint256 nounId;
        // The current highest bid amount
        uint256 amount;
        // The time that the auction started
        uint256 startTime;
        // The time that the auction is scheduled to end
        uint256 endTime;
        // The address of the current highest bid
        address payable bidder;
        // Whether or not the auction has been settled
        bool settled;
    }

    event AuctionCreated(uint256 indexed nounId, uint256 startTime, uint256 endTime);

    event AuctionBid(uint256 indexed nounId, address sender, uint256 value, bool extended);

    event AuctionExtended(uint256 indexed nounId, uint256 endTime);

    event AuctionSettled(uint256 indexed nounId, address winner, uint256 amount);

    event AuctionTimeBufferUpdated(uint256 timeBuffer);

    event AuctionReservePriceUpdated(uint256 reservePrice);

    event AuctionMinBidIncrementPercentageUpdated(uint256 minBidIncrementPercentage);

    function settleAuction() external;

    function settleCurrentAndCreateNewAuction() external;

    function createBid(uint256 nounId) external payable;

    function pause() external;

    function unpause() external;

    function setTimeBuffer(uint256 timeBuffer) external;

    function setReservePrice(uint256 reservePrice) external;

    function setMinBidIncrementPercentage(uint8 minBidIncrementPercentage) external;
}

// SPDX-License-Identifier: GPL-3.0

/// @title Interface for NounsToken

/*********************************
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 * ░░░░░░█████████░░█████████░░░ *
 * ░░░░░░██░░░████░░██░░░████░░░ *
 * ░░██████░░░████████░░░████░░░ *
 * ░░██░░██░░░████░░██░░░████░░░ *
 * ░░██░░██░░░████░░██░░░████░░░ *
 * ░░░░░░█████████░░█████████░░░ *
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 *********************************/

pragma solidity ^0.8.6;

import { IERC721 } from '@openzeppelin/contracts/token/ERC721/IERC721.sol';
import { INounsDescriptorMinimal } from './INounsDescriptorMinimal.sol';
import { INounsSeeder } from './INounsSeeder.sol';

interface INounsToken is IERC721 {
    event NounCreated(uint256 indexed tokenId, INounsSeeder.Seed seed);

    event NounBurned(uint256 indexed tokenId);

    event NoundersDAOUpdated(address noundersDAO);

    event MinterUpdated(address minter);

    event MinterLocked();

    event DescriptorUpdated(INounsDescriptorMinimal descriptor);

    event DescriptorLocked();

    event SeederUpdated(INounsSeeder seeder);

    event SeederLocked();

    function mint() external returns (uint256);

    function burn(uint256 tokenId) external;

    function dataURI(uint256 tokenId) external returns (string memory);

    function setNoundersDAO(address noundersDAO) external;

    function setMinter(address minter) external;

    function lockMinter() external;

    function setDescriptor(INounsDescriptorMinimal descriptor) external;

    function lockDescriptor() external;

    function setSeeder(INounsSeeder seeder) external;

    function lockSeeder() external;
}

// SPDX-License-Identifier: GPL-3.0

pragma solidity ^0.8.6;

interface IWETH {
    function deposit() external payable;

    function withdraw(uint256 wad) external;

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/Context.sol)

pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract ContextUpgradeable is Initializable {
    function __Context_init() internal initializer {
        __Context_init_unchained();
    }

    function __Context_init_unchained() internal initializer {
    }
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
    uint256[50] private __gap;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (proxy/utils/Initializable.sol)

pragma solidity ^0.8.0;

/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since a proxied contract can't have a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To initialize the implementation contract, you can either invoke the
 * initializer manually, or you can include a constructor to automatically mark it as initialized when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() initializer {}
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     */
    bool private _initialized;

    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;

    /**
     * @dev Modifier to protect an initializer function from being invoked twice.
     */
    modifier initializer() {
        require(_initializing || !_initialized, "Initializable: contract is already initialized");

        bool isTopLevelCall = !_initializing;
        if (isTopLevelCall) {
            _initializing = true;
            _initialized = true;
        }

        _;

        if (isTopLevelCall) {
            _initializing = false;
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (token/ERC721/IERC721.sol)

pragma solidity ^0.8.0;

import "../../utils/introspection/IERC165.sol";

/**
 * @dev Required interface of an ERC721 compliant contract.
 */
interface IERC721 is IERC165 {
    /**
     * @dev Emitted when `tokenId` token is transferred from `from` to `to`.
     */
    event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables `approved` to manage the `tokenId` token.
     */
    event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables or disables (`approved`) `operator` to manage all of its assets.
     */
    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

    /**
     * @dev Returns the number of tokens in ``owner``'s account.
     */
    function balanceOf(address owner) external view returns (uint256 balance);

    /**
     * @dev Returns the owner of the `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function ownerOf(uint256 tokenId) external view returns (address owner);

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
     * are aware of the ERC721 protocol to prevent tokens from being forever locked.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If the caller is not `from`, it must be have been allowed to move this token by either {approve} or {setApprovalForAll}.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId
    ) external;

    /**
     * @dev Transfers `tokenId` token from `from` to `to`.
     *
     * WARNING: Usage of this method is discouraged, use {safeTransferFrom} whenever possible.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(
        address from,
        address to,
        uint256 tokenId
    ) external;

    /**
     * @dev Gives permission to `to` to transfer `tokenId` token to another account.
     * The approval is cleared when the token is transferred.
     *
     * Only a single account can be approved at a time, so approving the zero address clears previous approvals.
     *
     * Requirements:
     *
     * - The caller must own the token or be an approved operator.
     * - `tokenId` must exist.
     *
     * Emits an {Approval} event.
     */
    function approve(address to, uint256 tokenId) external;

    /**
     * @dev Returns the account approved for `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function getApproved(uint256 tokenId) external view returns (address operator);

    /**
     * @dev Approve or remove `operator` as an operator for the caller.
     * Operators can call {transferFrom} or {safeTransferFrom} for any token owned by the caller.
     *
     * Requirements:
     *
     * - The `operator` cannot be the caller.
     *
     * Emits an {ApprovalForAll} event.
     */
    function setApprovalForAll(address operator, bool _approved) external;

    /**
     * @dev Returns if the `operator` is allowed to manage all of the assets of `owner`.
     *
     * See {setApprovalForAll}
     */
    function isApprovedForAll(address owner, address operator) external view returns (bool);

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId,
        bytes calldata data
    ) external;
}

// SPDX-License-Identifier: GPL-3.0

/// @title Common interface for NounsDescriptor versions, as used by NounsToken and NounsSeeder.

/*********************************
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 * ░░░░░░█████████░░█████████░░░ *
 * ░░░░░░██░░░████░░██░░░████░░░ *
 * ░░██████░░░████████░░░████░░░ *
 * ░░██░░██░░░████░░██░░░████░░░ *
 * ░░██░░██░░░████░░██░░░████░░░ *
 * ░░░░░░█████████░░█████████░░░ *
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 *********************************/

pragma solidity ^0.8.6;

// LICENSE
// This file is a modified version of nounsDAO's INounsDescriptorMinimal.sol:
// https://github.com/nounsDAO/nouns-monorepo/blob/854b9b64770401da71503972c65c4f9eda060ba6/packages/nouns-contracts/contracts/interfaces/INounsDescriptorMinimal.sol
//
// INounsDescriptorMinimal.sol licensed under the GPL-3.0 license.
// With modifications by CNNouns DAO.

import { INounsSeeder } from './INounsSeeder.sol';

interface INounsDescriptorMinimal {
    ///
    /// USED BY TOKEN
    ///

    function tokenURI(uint256 tokenId, INounsSeeder.Seed memory seed) external view returns (string memory);

    function dataURI(uint256 tokenId, INounsSeeder.Seed memory seed) external view returns (string memory);

    ///
    /// USED BY SEEDER
    ///

    function backgroundCount() external view returns (uint256);

    function bodyCount() external view returns (uint256);

    function headCount() external view returns (uint256);

    function glassesCount() external view returns (uint256);

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

// SPDX-License-Identifier: GPL-3.0

/// @title Interface for NounsSeeder

/*********************************
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 * ░░░░░░█████████░░█████████░░░ *
 * ░░░░░░██░░░████░░██░░░████░░░ *
 * ░░██████░░░████████░░░████░░░ *
 * ░░██░░██░░░████░░██░░░████░░░ *
 * ░░██░░██░░░████░░██░░░████░░░ *
 * ░░░░░░█████████░░█████████░░░ *
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 * ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ *
 *********************************/

pragma solidity ^0.8.6;

// LICENSE
// This file is a modified version of nounsDAO's INounsSeeder.sol:
// https://github.com/nounsDAO/nouns-monorepo/blob/854b9b64770401da71503972c65c4f9eda060ba6/packages/nouns-contracts/contracts/interfaces/INounsSeeder.sol
//
// INounsSeeder.sol licensed under the GPL-3.0 license.
// With modifications by CNNouns DAO.

import { INounsDescriptorMinimal } from './INounsDescriptorMinimal.sol';

interface INounsSeeder {
    struct Seed {
        uint48 background;
        uint48 body;
        uint48 head;
        uint48 glasses;
        uint48 skill;
    }

    function generateSeed(uint256 nounId, INounsDescriptorMinimal descriptor) external view returns (Seed memory);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165 {
    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

{
  "optimizer": {
    "enabled": true,
    "runs": 10000
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "libraries": {}
}

• No Contract Security Audit Submitted- Submit Audit Here

[{"anonymous":false,"inputs":[{"indexed":true,"internalType":"uint256","name":"nounId","type":"uint256"},{"indexed":false,"internalType":"address","name":"sender","type":"address"},{"indexed":false,"internalType":"uint256","name":"value","type":"uint256"},{"indexed":false,"internalType":"bool","name":"extended","type":"bool"}],"name":"AuctionBid","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"uint256","name":"nounId","type":"uint256"},{"indexed":false,"internalType":"uint256","name":"startTime","type":"uint256"},{"indexed":false,"internalType":"uint256","name":"endTime","type":"uint256"}],"name":"AuctionCreated","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"uint256","name":"nounId","type":"uint256"},{"indexed":false,"internalType":"uint256","name":"endTime","type":"uint256"}],"name":"AuctionExtended","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"internalType":"uint256","name":"minBidIncrementPercentage","type":"uint256"}],"name":"AuctionMinBidIncrementPercentageUpdated","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"internalType":"uint256","name":"reservePrice","type":"uint256"}],"name":"AuctionReservePriceUpdated","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"uint256","name":"nounId","type":"uint256"},{"indexed":false,"internalType":"address","name":"winner","type":"address"},{"indexed":false,"internalType":"uint256","name":"amount","type":"uint256"}],"name":"AuctionSettled","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"internalType":"uint256","name":"timeBuffer","type":"uint256"}],"name":"AuctionTimeBufferUpdated","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"address","name":"previousOwner","type":"address"},{"indexed":true,"internalType":"address","name":"newOwner","type":"address"}],"name":"OwnershipTransferred","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"internalType":"address","name":"account","type":"address"}],"name":"Paused","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"internalType":"address","name":"account","type":"address"}],"name":"Unpaused","type":"event"},{"inputs":[],"name":"auction","outputs":[{"internalType":"uint256","name":"nounId","type":"uint256"},{"internalType":"uint256","name":"amount","type":"uint256"},{"internalType":"uint256","name":"startTime","type":"uint256"},{"internalType":"uint256","name":"endTime","type":"uint256"},{"internalType":"address payable","name":"bidder","type":"address"},{"internalType":"bool","name":"settled","type":"bool"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"baseDuration","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"nounId","type":"uint256"}],"name":"createBid","outputs":[],"stateMutability":"payable","type":"function"},{"inputs":[{"internalType":"contract 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INounsToken","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"origin","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"owner","outputs":[{"internalType":"address","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"pause","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"paused","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"renounceOwnership","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"reservePrice","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint8","name":"_minBidIncrementPercentage","type":"uint8"}],"name":"setMinBidIncrementPercentage","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"uint256","name":"_reservePrice","type":"uint256"}],"name":"setReservePrice","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"uint256","name":"_timeBuffer","type":"uint256"}],"name":"setTimeBuffer","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"settleAuction","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"settleCurrentAndCreateNewAuction","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"timeBuffer","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"newOwner","type":"address"}],"name":"transferOwnership","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"unpause","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"weth","outputs":[{"internalType":"address","name":"","type":"address"}],"stateMutability":"view","type":"function"}]

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