Cryo Explorer Ethereum Mainnet

pragma solidity 0.5.16;

// INTERFACE
interface IERC20Mintable {
    function transfer(address _to, uint256 _value) external returns (bool);

    function transferFrom(
        address _from,
        address _to,
        uint256 _value
    ) external returns (bool);

    function mint(address _to, uint256 _value) external returns (bool);

    function balanceOf(address _account) external view returns (uint256);

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

/**
 * @dev Interface of the ERC20 standard as defined in the EIP. Does not include
 * the optional functions; to access them see {ERC20Detailed}.
 */
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);
}

// LIB

/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when an
 * operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");

        return c;
    }

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

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     * - Subtraction cannot overflow.
     *
     * _Available since v2.4.0._
     */
    function sub(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        uint256 c = a - b;

        return c;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) {
            return 0;
        }

        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");

        return c;
    }

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

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     * - The divisor cannot be zero.
     *
     * _Available since v2.4.0._
     */
    function div(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        // Solidity only automatically asserts when dividing by 0
        require(b > 0, errorMessage);
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold

        return c;
    }

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

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts with custom message when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     * - The divisor cannot be zero.
     *
     * _Available since v2.4.0._
     */
    function mod(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        require(b != 0, errorMessage);
        return a % b;
    }
}

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // According to EIP-1052, 0x0 is the value returned for not-yet created accounts
        // and 0xc5d2460186f7233c927e7db2dcc703c0e500b653ca82273b7bfad8045d85a470 is returned
        // for accounts without code, i.e. `keccak256('')`
        bytes32 codehash;
        bytes32 accountHash = 0xc5d2460186f7233c927e7db2dcc703c0e500b653ca82273b7bfad8045d85a470;
        // solhint-disable-next-line no-inline-assembly
        assembly {
            codehash := extcodehash(account)
        }
        return (codehash != accountHash && codehash != 0x0);
    }

    /**
     * @dev Converts an `address` into `address payable`. Note that this is
     * simply a type cast: the actual underlying value is not changed.
     *
     * _Available since v2.4.0._
     */
    function toPayable(address account) internal pure returns (address payable) {
        return address(uint160(account));
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     *
     * _Available since v2.4.0._
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        // solhint-disable-next-line avoid-call-value
        (bool success, ) = recipient.call.value(amount)("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }
}

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for ERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    using SafeMath for uint256;
    using Address for address;

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

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

    function safeApprove(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        // solhint-disable-next-line max-line-length
        require(
            (value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

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

    function safeDecreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        uint256 newAllowance = token.allowance(address(this), spender).sub(
            value,
            "SafeERC20: decreased allowance below zero"
        );
        callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function callOptionalReturn(IERC20 token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves.

        // A Solidity high level call has three parts:
        //  1. The target address is checked to verify it contains contract code
        //  2. The call itself is made, and success asserted
        //  3. The return value is decoded, which in turn checks the size of the returned data.
        // solhint-disable-next-line max-line-length
        require(address(token).isContract(), "SafeERC20: call to non-contract");

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = address(token).call(data);
        require(success, "SafeERC20: low-level call failed");

        if (returndata.length > 0) {
            // Return data is optional
            // solhint-disable-next-line max-line-length
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}

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

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

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

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

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

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

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

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

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

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

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

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

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

        require(x >= 0);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                y >>= 4;
            }

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

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

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

                y >>= 1;
            }

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

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

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

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

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

        return int128(result);
    }

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

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

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

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

        uint256 result = 0x80000000000000000000000000000000;

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

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

        return int128(result);
    }

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

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

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

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

        uint256 result;

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

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

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

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

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

            assert(xh == hi >> 128);

            result += xl / y;
        }

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

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

/**
 * 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) {
        if (x == 0) return bytes16(0);
        else {
            // We rely on overflow behavior here
            uint256 result = uint256(x > 0 ? x : -x);

            uint256 msb = msb(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) {
        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) {
        if (x == 0) return bytes16(0);
        else {
            uint256 result = x;

            uint256 msb = msb(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) {
        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) {
        if (x == 0) return bytes16(0);
        else {
            // We rely on overflow behavior here
            uint256 result = uint256(x > 0 ? x : -x);

            uint256 msb = msb(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) {
        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) {
        if (x == 0) return bytes16(0);
        else {
            // We rely on overflow behavior here
            uint256 result...

// [truncated — 127947 bytes total]