// File: @openzeppelin/contracts/math/SafeMath.sol

// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @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, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        uint256 c = a + b;
        if (c < a) return (false, 0);
        return (true, c);
    }

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

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

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

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

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

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        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, reverting 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) {
        require(b > 0, "SafeMath: division by zero");
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b > 0, "SafeMath: modulo by zero");
        return a % b;
    }

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

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

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

// File: @openzeppelin/contracts/token/ERC20/IERC20.sol



pragma solidity >=0.6.0 <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);
}

// File: @openzeppelin/contracts/utils/Address.sol



pragma solidity >=0.6.2 <0.8.0;

/**
 * @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) {
        // This method relies on extcodesize, which returns 0 for contracts in
        // construction, since the code is only stored at the end of the
        // constructor execution.

        uint256 size;
        // solhint-disable-next-line no-inline-assembly
        assembly { size := extcodesize(account) }
        return size > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://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].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

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

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

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

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

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

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = target.call{ value: value }(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

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

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data, string memory errorMessage) internal view returns (bytes memory) {
        require(isContract(target), "Address: static call to non-contract");

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = target.staticcall(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

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

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data, string memory errorMessage) internal returns (bytes memory) {
        require(isContract(target), "Address: delegate call to non-contract");

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

    function _verifyCallResult(bool success, bytes memory returndata, string memory errorMessage) private pure returns(bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly

                // solhint-disable-next-line no-inline-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

// File: @openzeppelin/contracts/token/ERC20/SafeERC20.sol



pragma solidity >=0.6.0 <0.8.0;




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

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(IERC20 token, address spender, uint256 value) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        // 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. We use {Address.functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

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

// File: solidity/contracts/converter/ConverterVersion.sol


pragma solidity 0.6.12;

contract ConverterVersion {
    uint16 public constant version = 46;
}

// File: solidity/contracts/utility/interfaces/IOwned.sol


pragma solidity 0.6.12;

/*
    Owned contract interface
*/
interface IOwned {
    // this function isn't since the compiler emits automatically generated getter functions as external
    function owner() external view returns (address);

    function transferOwnership(address _newOwner) external;

    function acceptOwnership() external;
}

// File: solidity/contracts/converter/interfaces/IConverterAnchor.sol


pragma solidity 0.6.12;


/*
    Converter Anchor interface
*/
interface IConverterAnchor is IOwned {

}

// File: solidity/contracts/converter/interfaces/IConverter.sol


pragma solidity 0.6.12;




/*
    Converter interface
*/
interface IConverter is IOwned {
    function converterType() external pure returns (uint16);

    function anchor() external view returns (IConverterAnchor);

    function isActive() external view returns (bool);

    function targetAmountAndFee(
        IERC20 _sourceToken,
        IERC20 _targetToken,
        uint256 _amount
    ) external view returns (uint256, uint256);

    function convert(
        IERC20 _sourceToken,
        IERC20 _targetToken,
        uint256 _amount,
        address _trader,
        address payable _beneficiary
    ) external payable returns (uint256);

    function conversionFee() external view returns (uint32);

    function maxConversionFee() external view returns (uint32);

    function reserveBalance(IERC20 _reserveToken) external view returns (uint256);

    receive() external payable;

    function transferAnchorOwnership(address _newOwner) external;

    function acceptAnchorOwnership() external;

    function setConversionFee(uint32 _conversionFee) external;

    function addReserve(IERC20 _token, uint32 _weight) external;

    function transferReservesOnUpgrade(address _newConverter) external;

    function onUpgradeComplete() external;

    // deprecated, backward compatibility
    function token() external view returns (IConverterAnchor);

    function transferTokenOwnership(address _newOwner) external;

    function acceptTokenOwnership() external;

    function connectors(IERC20 _address)
        external
        view
        returns (
            uint256,
            uint32,
            bool,
            bool,
            bool
        );

    function getConnectorBalance(IERC20 _connectorToken) external view returns (uint256);

    function connectorTokens(uint256 _index) external view returns (IERC20);

    function connectorTokenCount() external view returns (uint16);

    /**
     * @dev triggered when the converter is activated
     *
     * @param _type        converter type
     * @param _anchor      converter anchor
     * @param _activated   true if the converter was activated, false if it was deactivated
     */
    event Activation(uint16 indexed _type, IConverterAnchor indexed _anchor, bool indexed _activated);

    /**
     * @dev triggered when a conversion between two tokens occurs
     *
     * @param _fromToken       source ERC20 token
     * @param _toToken         target ERC20 token
     * @param _trader          wallet that initiated the trade
     * @param _amount          input amount in units of the source token
     * @param _return          output amount minus conversion fee in units of the target token
     * @param _conversionFee   conversion fee in units of the target token
     */
    event Conversion(
        IERC20 indexed _fromToken,
        IERC20 indexed _toToken,
        address indexed _trader,
        uint256 _amount,
        uint256 _return,
        int256 _conversionFee
    );

    /**
     * @dev triggered when the rate between two tokens in the converter changes
     * note that the event might be dispatched for rate updates between any two tokens in the converter
     *
     * @param  _token1 address of the first token
     * @param  _token2 address of the second token
     * @param  _rateN  rate of 1 unit of `_token1` in `_token2` (numerator)
     * @param  _rateD  rate of 1 unit of `_token1` in `_token2` (denominator)
     */
    event TokenRateUpdate(IERC20 indexed _token1, IERC20 indexed _token2, uint256 _rateN, uint256 _rateD);

    /**
     * @dev triggered when the conversion fee is updated
     *
     * @param  _prevFee    previous fee percentage, represented in ppm
     * @param  _newFee     new fee percentage, represented in ppm
     */
    event ConversionFeeUpdate(uint32 _prevFee, uint32 _newFee);
}

// File: solidity/contracts/converter/interfaces/IConverterUpgrader.sol


pragma solidity 0.6.12;

/*
    Converter Upgrader interface
*/
interface IConverterUpgrader {
    function upgrade(bytes32 _version) external;

    function upgrade(uint16 _version) external;
}

// File: solidity/contracts/utility/interfaces/ITokenHolder.sol


pragma solidity 0.6.12;



/*
    Token Holder interface
*/
interface ITokenHolder is IOwned {
    receive() external payable;

    function withdrawTokens(
        IERC20 token,
        address payable to,
        uint256 amount
    ) external;

    function withdrawTokensMultiple(
        IERC20[] calldata tokens,
        address payable to,
        uint256[] calldata amounts
    ) external;
}

// File: solidity/contracts/INetworkSettings.sol


pragma solidity 0.6.12;


interface INetworkSettings {
    function networkFeeParams() external view returns (ITokenHolder, uint32);

    function networkFeeWallet() external view returns (ITokenHolder);

    function networkFee() external view returns (uint32);
}

// File: solidity/contracts/token/interfaces/IDSToken.sol


pragma solidity 0.6.12;




/*
    DSToken interface
*/
interface IDSToken is IConverterAnchor, IERC20 {
    function issue(address _to, uint256 _amount) external;

    function destroy(address _from, uint256 _amount) external;
}

// File: solidity/contracts/utility/MathEx.sol


pragma solidity 0.6.12;

/**
 * @dev This library provides a set of complex math operations.
 */
library MathEx {
    uint256 private constant MAX_EXP_BIT_LEN = 4;
    uint256 private constant MAX_EXP = 2**MAX_EXP_BIT_LEN - 1;
    uint256 private constant MAX_UINT128 = 2**128 - 1;

    /**
     * @dev returns the largest integer smaller than or equal to the square root of a positive integer
     *
     * @param _num a positive integer
     *
     * @return the largest integer smaller than or equal to the square root of the positive integer
     */
    function floorSqrt(uint256 _num) internal pure returns (uint256) {
        uint256 x = _num / 2 + 1;
        uint256 y = (x + _num / x) / 2;
        while (x > y) {
            x = y;
            y = (x + _num / x) / 2;
        }
        return x;
    }

    /**
     * @dev returns the smallest integer larger than or equal to the square root of a positive integer
     *
     * @param _num a positive integer
     *
     * @return the smallest integer larger than or equal to the square root of the positive integer
     */
    function ceilSqrt(uint256 _num) internal pure returns (uint256) {
        uint256 x = floorSqrt(_num);
        return x * x == _num ? x : x + 1;
    }

    /**
     * @dev computes a powered ratio
     *
     * @param _n   ratio numerator
     * @param _d   ratio denominator
     * @param _exp ratio exponent
     *
     * @return powered ratio's numerator and denominator
     */
    function poweredRatio(
        uint256 _n,
        uint256 _d,
        uint256 _exp
    ) internal pure returns (uint256, uint256) {
        require(_exp <= MAX_EXP, "ERR_EXP_TOO_LARGE");

        uint256[MAX_EXP_BIT_LEN] memory ns;
        uint256[MAX_EXP_BIT_LEN] memory ds;

        (ns[0], ds[0]) = reducedRatio(_n, _d, MAX_UINT128);
        for (uint256 i = 0; (_exp >> i) > 1; i++) {
            (ns[i + 1], ds[i + 1]) = reducedRatio(ns[i] ** 2, ds[i] ** 2, MAX_UINT128);
        }

        uint256 n = 1;
        uint256 d = 1;

        for (uint256 i = 0; (_exp >> i) > 0; i++) {
            if (((_exp >> i) & 1) > 0) {
                (n, d) = reducedRatio(n * ns[i], d * ds[i], MAX_UINT128);
            }
        }

        return (n, d);
    }

    /**
     * @dev computes a reduced-scalar ratio
     *
     * @param _n   ratio numerator
     * @param _d   ratio denominator
     * @param _max maximum desired scalar
     *
     * @return ratio's numerator and denominator
     */
    function reducedRatio(
        uint256 _n,
        uint256 _d,
        uint256 _max
    ) internal pure returns (uint256, uint256) {
        (uint256 n, uint256 d) = (_n, _d);
        if (n > _max || d > _max) {
            (n, d) = normalizedRatio(n, d, _max);
        }
        if (n != d) {
            return (n, d);
        }
        return (1, 1);
    }

    /**
     * @dev computes "scale * a / (a + b)" and "scale * b / (a + b)".
     */
    function normalizedRatio(
        uint256 _a,
        uint256 _b,
        uint256 _scale
    ) internal pure returns (uint256, uint256) {
        if (_a <= _b) {
            return accurateRatio(_a, _b, _scale);
        }
        (uint256 y, uint256 x) = accurateRatio(_b, _a, _scale);
        return (x, y);
    }

    /**
     * @dev computes "scale * a / (a + b)" and "scale * b / (a + b)", assuming that "a <= b".
     */
    function accurateRatio(
        uint256 _a,
        uint256 _b,
        uint256 _scale
    ) internal pure returns (uint256, uint256) {
        uint256 maxVal = uint256(-1) / _scale;
        if (_a > maxVal) {
            uint256 c = _a / (maxVal + 1) + 1;
            _a /= c; // we can now safely compute `_a * _scale`
            _b /= c;
        }
        if (_a != _b) {
            uint256 n = _a * _scale;
            uint256 d = _a + _b; // can overflow
            if (d >= _a) {
                // no overflow in `_a + _b`
                uint256 x = roundDiv(n, d); // we can now safely compute `_scale - x`
                uint256 y = _scale - x;
                return (x, y);
            }
            if (n < _b - (_b - _a) / 2) {
                return (0, _scale); // `_a * _scale < (_a + _b) / 2 < MAX_UINT256 < _a + _b`
            }
            return (1, _scale - 1); // `(_a + _b) / 2 < _a * _scale < MAX_UINT256 < _a + _b`
        }
        return (_scale / 2, _scale / 2); // allow reduction to `(1, 1)` in the calling function
    }

    /**
     * @dev computes the nearest integer to a given quotient without overflowing or underflowing.
     */
    function roundDiv(uint256 _n, uint256 _d) internal pure returns (uint256) {
        return _n / _d + (_n % _d) / (_d - _d / 2);
    }

    /**
     * @dev returns the average number of decimal digits in a given list of positive integers
     *
     * @param _values  list of positive integers
     *
     * @return the average number of decimal digits in the given list of positive integers
     */
    function geometricMean(uint256[] memory _values) internal pure returns (uint256) {
        uint256 numOfDigits = 0;
        uint256 length = _values.length;
        for (uint256 i = 0; i < length; i++) {
            numOfDigits += decimalLength(_values[i]);
        }
        return uint256(10)**(roundDivUnsafe(numOfDigits, length) - 1);
    }

    /**
     * @dev returns the number of decimal digits in a given positive integer
     *
     * @param _x   positive integer
     *
     * @return the number of decimal digits in the given positive integer
     */
    function decimalLength(uint256 _x) internal pure returns (uint256) {
        uint256 y = 0;
        for (uint256 x = _x; x > 0; x /= 10) {
            y++;
        }
        return y;
    }

    /**
     * @dev returns the nearest integer to a given quotient
     * the computation is overflow-safe assuming that the input is sufficiently small
     *
     * @param _n   quotient numerator
     * @param _d   quotient denominator
     *
     * @return the nearest integer to the given quotient
     */
    function roundDivUnsafe(uint256 _n, uint256 _d) internal pure returns (uint256) {
        return (_n + _d / 2) / _d;
    }

    /**
     * @dev returns the larger of two values
     *
     * @param _val1 the first value
     * @param _val2 the second value
     */
    function max(uint256 _val1, uint256 _val2) internal pure returns (uint256) {
        return _val1 > _val2 ? _val1 : _val2;
    }
}

// File: solidity/contracts/utility/Owned.sol


pragma solidity 0.6.12;


/**
 * @dev This contract provides support and utilities for contract ownership.
 */
contract Owned is IOwned {
    address public override owner;
    address public newOwner;

    /**
     * @dev triggered when the owner is updated
     *
     * @param _prevOwner previous owner
     * @param _newOwner  new owner
     */
    event OwnerUpdate(address indexed _prevOwner, address indexed _newOwner);

    /**
     * @dev initializes a new Owned instance
     */
    constructor() public {
        owner = msg.sender;
    }

    // allows execution by the owner only
    modifier ownerOnly {
        _ownerOnly();
        _;
    }

    // error message binary size optimization
    function _ownerOnly() internal view {
        require(msg.sender == owner, "ERR_ACCESS_DENIED");
    }

    /**
     * @dev allows transferring the contract ownership
     * the new owner still needs to accept the transfer
     * can only be called by the contract owner
     *
     * @param _newOwner    new contract owner
     */
    function transferOwnership(address _newOwner) public override ownerOnly {
        require(_newOwner != owner, "ERR_SAME_OWNER");
        newOwner = _newOwner;
    }

    /**
     * @dev used by a new owner to accept an ownership transfer
     */
    function acceptOwnership() public override {
        require(msg.sender == newOwner, "ERR_ACCESS_DENIED");
        emit OwnerUpdate(owner, newOwner);
        owner = newOwner;
        newOwner = address(0);
    }
}

// File: solidity/contracts/utility/Utils.sol


pragma solidity 0.6.12;


/**
 * @dev Utilities & Common Modifiers
 */
contract Utils {
    uint32 internal constant PPM_RESOLUTION = 1000000;
    IERC20 internal constant NATIVE_TOKEN_ADDRESS = IERC20(0xEeeeeEeeeEeEeeEeEeEeeEEEeeeeEeeeeeeeEEeE);

    // verifies that a value is greater than zero
    modifier greaterThanZero(uint256 _value) {
        _greaterThanZero(_value);
        _;
    }

    // error message binary size optimization
    function _greaterThanZero(uint256 _value) internal pure {
        require(_value > 0, "ERR_ZERO_VALUE");
    }

    // validates an address - currently only checks that it isn't null
    modifier validAddress(address _address) {
        _validAddress(_address);
        _;
    }

    // error message binary size optimization
    function _validAddress(address _address) internal pure {
        require(_address != address(0), "ERR_INVALID_ADDRESS");
    }

    // ensures that the portion is valid
    modifier validPortion(uint32 _portion) {
        _validPortion(_portion);
        _;
    }

    // error message binary size optimization
    function _validPortion(uint32 _portion) internal pure {
        require(_portion > 0 && _portion <= PPM_RESOLUTION, "ERR_INVALID_PORTION");
    }

    // validates an external address - currently only checks that it isn't null or this
    modifier validExternalAddress(address _address) {
        _validExternalAddress(_address);
        _;
    }

    // error message binary size optimization
    function _validExternalAddress(address _address) internal view {
        require(_address != address(0) && _address != address(this), "ERR_INVALID_EXTERNAL_ADDRESS");
    }

    // ensures that the fee is valid
    modifier validFee(uint32 fee) {
        _validFee(fee);
        _;
    }

    // error message binary size optimization
    function _validFee(uint32 fee) internal pure {
        require(fee <= PPM_RESOLUTION, "ERR_INVALID_FEE");
    }
}

// File: solidity/contracts/utility/interfaces/IContractRegistry.sol


pragma solidity 0.6.12;

/*
    Contract Registry interface
*/
interface IContractRegistry {
    function addressOf(bytes32 _contractName) external view returns (address);
}

// File: solidity/contracts/utility/ContractRegistryClient.sol


pragma solidity 0.6.12;




/**
 * @dev This is the base contract for ContractRegistry clients.
 */
contract ContractRegistryClient is Owned, Utils {
    bytes32 internal constant CONTRACT_REGISTRY = "ContractRegistry";
    bytes32 internal constant BANCOR_NETWORK = "BancorNetwork";
    bytes32 internal constant BANCOR_FORMULA = "BancorFormula";
    bytes32 internal constant CONVERTER_FACTORY = "ConverterFactory";
    bytes32 internal constant CONVERSION_PATH_FINDER = "ConversionPathFinder";
    bytes32 internal constant CONVERTER_UPGRADER = "BancorConverterUpgrader";
    bytes32 internal constant CONVERTER_REGISTRY = "BancorConverterRegistry";
    bytes32 internal constant CONVERTER_REGISTRY_DATA = "BancorConverterRegistryData";
    bytes32 internal constant BNT_TOKEN = "BNTToken";
    bytes32 internal constant BANCOR_X = "BancorX";
    bytes32 internal constant BANCOR_X_UPGRADER = "BancorXUpgrader";
    bytes32 internal constant LIQUIDITY_PROTECTION = "LiquidityProtection";
    bytes32 internal constant NETWORK_SETTINGS = "NetworkSettings";

    IContractRegistry public registry; // address of the current contract-registry
    IContractRegistry public prevRegistry; // address of the previous contract-registry
    bool public onlyOwnerCanUpdateRegistry; // only an owner can update the contract-registry

    /**
     * @dev verifies that the caller is mapped to the given contract name
     *
     * @param _contractName    contract name
     */
    modifier only(bytes32 _contractName) {
        _only(_contractName);
        _;
    }

    // error message binary size optimization
    function _only(bytes32 _contractName) internal view {
        require(msg.sender == addressOf(_contractName), "ERR_ACCESS_DENIED");
    }

    /**
     * @dev initializes a new ContractRegistryClient instance
     *
     * @param  _registry   address of a contract-registry contract
     */
    constructor(IContractRegistry _registry) internal validAddress(address(_registry)) {
        registry = IContractRegistry(_registry);
        prevRegistry = IContractRegistry(_registry);
    }

    /**
     * @dev updates to the new contract-registry
     */
    function updateRegistry() public {
        // verify that this function is permitted
        require(msg.sender == owner || !onlyOwnerCanUpdateRegistry, "ERR_ACCESS_DENIED");

        // get the new contract-registry
        IContractRegistry newRegistry = IContractRegistry(addressOf(CONTRACT_REGISTRY));

        // verify that the new contract-registry is different and not zero
        require(newRegistry != registry && address(newRegistry) != address(0), "ERR_INVALID_REGISTRY");

        // verify that the new contract-registry is pointing to a non-zero contract-registry
        require(newRegistry.addressOf(CONTRACT_REGISTRY) != address(0), "ERR_INVALID_REGISTRY");

        // save a backup of the current contract-registry before replacing it
        prevRegistry = registry;

        // replace the current contract-registry with the new contract-registry
        registry = newRegistry;
    }

    /**
     * @dev restores the previous contract-registry
     */
    function restoreRegistry() public ownerOnly {
        // restore the previous contract-registry
        registry = prevRegistry;
    }

    /**
     * @dev restricts the permission to update the contract-registry
     *
     * @param _onlyOwnerCanUpdateRegistry  indicates whether or not permission is restricted to owner only
     */
    function restrictRegistryUpdate(bool _onlyOwnerCanUpdateRegistry) public ownerOnly {
        // change the permission to update the contract-registry
        onlyOwnerCanUpdateRegistry = _onlyOwnerCanUpdateRegistry;
    }

    /**
     * @dev returns the address associated with the given contract name
     *
     * @param _contractName    contract name
     *
     * @return contract address
     */
    function addressOf(bytes32 _contractName) internal view returns (address) {
        return registry.addressOf(_contractName);
    }
}

// File: solidity/contracts/utility/ReentrancyGuard.sol


pragma solidity 0.6.12;

/**
 * @dev This contract provides protection against calling a function
 * (directly or indirectly) from within itself.
 */
contract ReentrancyGuard {
    uint256 private constant UNLOCKED = 1;
    uint256 private constant LOCKED = 2;

    // LOCKED while protected code is being executed, UNLOCKED otherwise
    uint256 private state = UNLOCKED;

    /**
     * @dev ensures instantiation only by sub-contracts
     */
    constructor() internal {}

    // protects a function against reentrancy attacks
    modifier protected() {
        _protected();
        state = LOCKED;
        _;
        state = UNLOCKED;
    }

    // error message binary size optimization
    function _protected() internal view {
        require(state == UNLOCKED, "ERR_REENTRANCY");
    }
}

// File: solidity/contracts/utility/Time.sol


pragma solidity 0.6.12;

/*
    Time implementing contract
*/
contract Time {
    /**
     * @dev returns the current time
     */
    function time() internal view virtual returns (uint256) {
        return block.timestamp;
    }
}

// File: solidity/contracts/converter/types/standard-pool/StandardPoolConverter.sol


pragma solidity 0.6.12;













/**
 * @dev This contract is a specialized version of the converter, which is
 * optimized for a liquidity pool that has 2 reserves with 50%/50% weights.
 */
contract StandardPoolConverter is ConverterVersion, IConverter, ContractRegistryClient, ReentrancyGuard, Time {
    using SafeMath for uint256;
    using SafeERC20 for IERC20;
    using MathEx for *;

    uint256 private constant MAX_UINT128 = 2**128 - 1;
    uint256 private constant MAX_UINT112 = 2**112 - 1;
    uint256 private constant MAX_UINT32 = 2**32 - 1;
    uint256 private constant AVERAGE_RATE_PERIOD = 10 minutes;

    uint256 private __reserveBalances;
    uint256 private _reserveBalancesProduct;
    IERC20[] private __reserveTokens;
    mapping(IERC20 => uint256) private __reserveIds;

    IConverterAnchor public override anchor; // converter anchor contract
    uint32 public override maxConversionFee; // maximum conversion fee, represented in ppm, 0...1000000
    uint32 public override conversionFee; // current conversion fee, represented in ppm, 0...maxConversionFee

    // average rate details:
    // bits 0...111 represent the numerator of the rate between reserve token 0 and reserve token 1
    // bits 111...223 represent the denominator of the rate between reserve token 0 and reserve token 1
    // bits 224...255 represent the update-time of the rate between reserve token 0 and reserve token 1
    // where `numerator / denominator` gives the worth of one reserve token 0 in units of reserve token 1
    uint256 public averageRateInfo;

    /**
     * @dev triggered after liquidity is added
     *
     * @param  _provider       liquidity provider
     * @param  _reserveToken   reserve token address
     * @param  _amount         reserve token amount
     * @param  _newBalance     reserve token new balance
     * @param  _newSupply      pool token new supply
     */
    event LiquidityAdded(
        address indexed _provider,
        IERC20 indexed _reserveToken,
        uint256 _amount,
        uint256 _newBalance,
        uint256 _newSupply
    );

    /**
     * @dev triggered after liquidity is removed
     *
     * @param  _provider       liquidity provider
     * @param  _reserveToken   reserve token address
     * @param  _amount         reserve token amount
     * @param  _newBalance     reserve token new balance
     * @param  _newSupply      pool token new supply
     */
    event LiquidityRemoved(
        address indexed _provider,
        IERC20 indexed _reserveToken,
        uint256 _amount,
        uint256 _newBalance,
        uint256 _newSupply
    );

    /**
     * @dev initializes a new StandardPoolConverter instance
     *
     * @param  _anchor             anchor governed by the converter
     * @param  _registry           address of a contract registry contract
     * @param  _maxConversionFee   maximum conversion fee, represented in ppm
     */
    constructor(
        IConverterAnchor _anchor,
        IContractRegistry _registry,
        uint32 _maxConversionFee
    ) public ContractRegistryClient(_registry) validAddress(address(_anchor)) validConversionFee(_maxConversionFee) {
        anchor = _anchor;
        maxConversionFee = _maxConversionFee;
    }

    // ensures that the converter is active
    modifier active() {
        _active();
        _;
    }

    // error message binary size optimization
    function _active() internal view {
        require(isActive(), "ERR_INACTIVE");
    }

    // ensures that the converter is not active
    modifier inactive() {
        _inactive();
        _;
    }

    // error message binary size optimization
    function _inactive() internal view {
        require(!isActive(), "ERR_ACTIVE");
    }

    // validates a reserve token address - verifies that the address belongs to one of the reserve tokens
    modifier validReserve(IERC20 _address) {
        _validReserve(_address);
        _;
    }

    // error message binary size optimization
    function _validReserve(IERC20 _address) internal view {
        require(__reserveIds[_address] != 0, "ERR_INVALID_RESERVE");
    }

    // validates conversion fee
    modifier validConversionFee(uint32 _conversionFee) {
        _validConversionFee(_conversionFee);
        _;
    }

    // error message binary size optimization
    function _validConversionFee(uint32 _conversionFee) internal pure {
        require(_conversionFee <= PPM_RESOLUTION, "ERR_INVALID_CONVERSION_FEE");
    }

    // validates reserve weight
    modifier validReserveWeight(uint32 _weight) {
        _validReserveWeight(_weight);
        _;
    }

    // error message binary size optimization
    function _validReserveWeight(uint32 _weight) internal pure {
        require(_weight == PPM_RESOLUTION / 2, "ERR_INVALID_RESERVE_WEIGHT");
    }

    /**
     * @dev returns the converter type
     *
     * @return see the converter types in the the main contract doc
     */
    function converterType() public pure virtual override returns (uint16) {
        return 3;
    }

    /**
     * @dev deposits ether
     * can only be called if the converter has an ETH reserve
     */
    receive() external payable override(IConverter) validReserve(NATIVE_TOKEN_ADDRESS) {}

    /**
     * @dev checks whether or not the converter version is 28 or higher
     *
     * @return true, since the converter version is 28 or higher
     */
    function isV28OrHigher() public pure returns (bool) {
        return true;
    }

    /**
     * @dev returns true if the converter is active, false otherwise
     *
     * @return true if the converter is active, false otherwise
     */
    function isActive() public view virtual override returns (bool) {
        return anchor.owner() == address(this);
    }

    /**
     * @dev transfers the anchor ownership
     * the new owner needs to accept the transfer
     * can only be called by the converter upgrader while the upgrader is the owner
     * note that prior to version 28, you should use 'transferAnchorOwnership' instead
     *
     * @param _newOwner    new token owner
     */
    function transferAnchorOwnership(address _newOwner) public override ownerOnly only(CONVERTER_UPGRADER) {
        anchor.transferOwnership(_newOwner);
    }

    /**
     * @dev accepts ownership of the anchor after an ownership transfer
     * most converters are also activated as soon as they accept the anchor ownership
     * can only be called by the contract owner
     * note that prior to version 28, you should use 'acceptTokenOwnership' instead
     */
    function acceptAnchorOwnership() public virtual override ownerOnly {
        // verify the the converter has exactly two reserves
        require(reserveTokenCount() == 2, "ERR_INVALID_RESERVE_COUNT");
        anchor.acceptOwnership();
        syncReserveBalances(0);
        emit Activation(converterType(), anchor, true);
    }

    /**
     * @dev updates the current conversion fee
     * can only be called by the contract owner
     *
     * @param _conversionFee new conversion fee, represented in ppm
     */
    function setConversionFee(uint32 _conversionFee) public override ownerOnly {
        require(_conversionFee <= maxConversionFee, "ERR_INVALID_CONVERSION_FEE");
        emit ConversionFeeUpdate(conversionFee, _conversionFee);
        conversionFee = _conversionFee;
    }

    /**
     * @dev transfers reserve balances to a new converter during an upgrade
     * can only be called by the converter upgraded which should be set at its owner
     *
     * @param _newConverter address of the converter to receive the new amount
     */
    function transferReservesOnUpgrade(address _newConverter)
        external
        override
        protected
        ownerOnly
        only(CONVERTER_UPGRADER)
    {
        uint256 reserveCount = __reserveTokens.length;
        for (uint256 i = 0; i < reserveCount; ++i) {
            IERC20 reserveToken = __reserveTokens[i];

            uint256 amount;
            if (reserveToken == NATIVE_TOKEN_ADDRESS) {
                amount = address(this).balance;
            } else {
                amount = reserveToken.balanceOf(address(this));
            }

            safeTransfer(reserveToken, _newConverter, amount);

            syncReserveBalance(reserveToken);
        }
    }

    /**
     * @dev upgrades the converter to the latest version
     * can only be called by the owner
     * note that the owner needs to call acceptOwnership on the new converter after the upgrade
     */
    function upgrade() public ownerOnly {
        IConverterUpgrader converterUpgrader = IConverterUpgrader(addressOf(CONVERTER_UPGRADER));

        // trigger de-activation event
        emit Activation(converterType(), anchor, false);

        transferOwnership(address(converterUpgrader));
        converterUpgrader.upgrade(version);
        acceptOwnership();
    }

    /**
     * @dev executed by the upgrader at the end of the upgrade process to handle custom pool logic
     */
    function onUpgradeComplete()
        external
        override
        protected
        ownerOnly
        only(CONVERTER_UPGRADER)
    {
        (uint256 reserveBalance0, uint256 reserveBalance1) = reserveBalances(1, 2);
        _reserveBalancesProduct = reserveBalance0 * reserveBalance1;
    }

    /**
     * @dev returns the number of reserve tokens
     * note that prior to version 17, you should use 'connectorTokenCount' instead
     *
     * @return number of reserve tokens
     */
    function reserveTokenCount() public view returns (uint16) {
        return uint16(__reserveTokens.length);
    }

    /**
     * @dev returns the array of reserve tokens
     *
     * @return array of reserve tokens
     */
    function reserveTokens() public view returns (IERC20[] memory) {
        return __reserveTokens;
    }

    /**
     * @dev defines a new reserve token for the converter
     * can only be called by the owner while the converter is inactive
     *
     * @param _token   address of the reserve token
     * @param _weight  reserve weight, represented in ppm, 1-1000000
     */
    function addReserve(IERC20 _token, uint32 _weight)
        public
        virtual
        override
        ownerOnly
        inactive
        validExternalAddress(address(_token))
        validReserveWeight(_weight)
    {
        // validate input
        require(address(_token) != address(anchor) && __reserveIds[_token] == 0, "ERR_INVALID_RESERVE");
        require(reserveTokenCount() < 2, "ERR_INVALID_RESERVE_COUNT");

        __reserveTokens.push(_token);
        __reserveIds[_token] = __reserveTokens.length;
    }

    /**
     * @dev returns the reserve's weight
     * added in version 28
     *
     * @param _reserveToken    reserve token contract address
     *
     * @return reserve weight
     */
    function reserveWeight(IERC20 _reserveToken) public view validReserve(_reserveToken) returns (uint32) {
        return PPM_RESOLUTION / 2;
    }

    /**
     * @dev returns the balance of a given reserve token
     *
     * @param _reserveToken    reserve token contract address
     *
     * @return the balance of the given reserve token
     */
    function reserveBalance(IERC20 _reserveToken) public view override returns (uint256) {
        uint256 reserveId = __reserveIds[_reserveToken];
        require(reserveId != 0, "ERR_INVALID_RESERVE");
        return reserveBalance(reserveId);
    }

    /**
     * @dev returns the balances of both reserve tokens
     *
     * @return the balances of both reserve tokens
     */
    function reserveBalances() public view returns (uint256, uint256) {
        return reserveBalances(1, 2);
    }

    /**
     * @dev syncs all stored reserve balances
     */
    function syncReserveBalances() external {
        syncReserveBalances(0);
    }

    /**
     * @dev calculates the accumulated network fee and transfers it to the network fee wallet
     */
    function processNetworkFees() external protected {
        (uint256 reserveBalance0, uint256 reserveBalance1) = processNetworkFees(0);
        _reserveBalancesProduct = reserveBalance0 * reserveBalance1;
    }

    /**
     * @dev calculates the accumulated network fee and transfers it to the network fee wallet
     *
     * @param _value amount of ether to exclude from the ether reserve balance (if relevant)
     *
     * @return new reserve balances
     */
    function processNetworkFees(uint256 _value) internal returns (uint256, uint256) {
        syncReserveBalances(_value);
        (uint256 reserveBalance0, uint256 reserveBalance1) = reserveBalances(1, 2);
        (ITokenHolder wallet, uint256 fee0, uint256 fee1) = networkWalletAndFees(reserveBalance0, reserveBalance1);
        reserveBalance0 -= fee0;
        reserveBalance1 -= fee1;
        setReserveBalances(1, 2, reserveBalance0, reserveBalance1);
        safeTransfer(__reserveTokens[0], address(wallet), fee0);
        safeTransfer(__reserveTokens[1], address(wallet), fee1);
        return (reserveBalance0, reserveBalance1);
    }

    /**
     * @dev returns the reserve balances of the given reserve tokens minus their corresponding fees
     *
     * @param _reserveTokens reserve tokens
     *
     * @return reserve balances minus their corresponding fees
     */
    function baseReserveBalances(IERC20[] memory _reserveTokens) internal view returns (uint256[2] memory) {
        uint256 reserveId0 = __reserveIds[_reserveTokens[0]];
        uint256 reserveId1 = __reserveIds[_reserveTokens[1]];
        (uint256 reserveBalance0, uint256 reserveBalance1) = reserveBalances(reserveId0, reserveId1);
        (, uint256 fee0, uint256 fee1) = networkWalletAndFees(reserveBalance0, reserveBalance1);
        return [reserveBalance0 - fee0, reserveBalance1 - fee1];
    }

    /**
     * @dev converts a specific amount of source tokens to target tokens
     * can only be called by the bancor network contract
     *
     * @param _sourceToken source ERC20 token
     * @param _targetToken target ERC20 token
     * @param _amount      amount of tokens to convert (in units of the source token)
     * @param _trader      address of the caller who executed the conversion
     * @param _beneficiary wallet to receive the conversion result
     *
     * @return amount of tokens received (in units of the target token)
     */
    function convert(
        IERC20 _sourceToken,
        IERC20 _targetToken,
        uint256 _amount,
        address _trader,
        address payable _beneficiary
    ) public payable override protected only(BANCOR_NETWORK) returns (uint256) {
        // validate input
        require(_sourceToken != _targetToken, "ERR_SAME_SOURCE_TARGET");

        return doConvert(_sourceToken, _targetToken, _amount, _trader, _beneficiary);
    }

    /**
     * @dev returns the conversion fee for a given target amount
     *
     * @param _targetAmount  target amount
     *
     * @return conversion fee
     */
    function calculateFee(uint256 _targetAmount) internal view returns (uint256) {
        return _targetAmount.mul(conversionFee) / PPM_RESOLUTION;
    }

    /**
     * @dev returns the conversion fee taken from a given target amount
     *
     * @param _targetAmount  target amount
     *
     * @return conversion fee
     */
    function calculateFeeInv(uint256 _targetAmount) internal view returns (uint256) {
        return _targetAmount.mul(conversionFee).div(PPM_RESOLUTION - conversionFee);
    }

    /**
     * @dev loads the stored reserve balance for a given reserve id
     *
     * @param _reserveId   reserve id
     */
    function reserveBalance(uint256 _reserveId) internal view returns (uint256) {
        return decodeReserveBalance(__reserveBalances, _reserveId);
    }

    /**
     * @dev loads the stored reserve balances
     *
     * @param _sourceId    source reserve id
     * @param _targetId    target reserve id
     */
    function reserveBalances(uint256 _sourceId, uint256 _targetId) internal view returns (uint256, uint256) {
        require((_sourceId == 1 && _targetId == 2) || (_sourceId == 2 && _targetId == 1), "ERR_INVALID_RESERVES");
        return decodeReserveBalances(__reserveBalances, _sourceId, _targetId);
    }

    /**
     * @dev stores the stored reserve balance for a given reserve id
     *
     * @param _reserveId       reserve id
     * @param _reserveBalance  reserve balance
     */
    function setReserveBalance(uint256 _reserveId, uint256 _reserveBalance) internal {
        require(_reserveBalance <= MAX_UINT128, "ERR_RESERVE_BALANCE_OVERFLOW");
        uint256 otherBalance = decodeReserveBalance(__reserveBalances, 3 - _reserveId);
        __reserveBalances = encodeReserveBalances(_reserveBalance, _reserveId, otherBalance, 3 - _reserveId);
    }

    /**
     * @dev stores the stored reserve balances
     *
     * @param _sourceId        source reserve id
     * @param _targetId        target reserve id
     * @param _sourceBalance   source reserve balance
     * @param _targetBalance   target reserve balance
     */
    function setReserveBalances(
        uint256 _sourceId,
        uint256 _targetId,
        uint256 _sourceBalance,
        uint256 _targetBalance
    ) internal {
        require(_sourceBalance <= MAX_UINT128 && _targetBalance <= MAX_UINT128, "ERR_RESERVE_BALANCE_OVERFLOW");
        __reserveBalances = encodeReserveBalances(_sourceBalance, _sourceId, _targetBalance, _targetId);
    }

    /**
     * @dev syncs the stored reserve balance for a given reserve with the real reserve balance
     *
     * @param _reserveToken    address of the reserve token
     */
    function syncReserveBalance(IERC20 _reserveToken) internal {
        uint256 reserveId = __reserveIds[_reserveToken];
        uint256 balance =
            _reserveToken == NATIVE_TOKEN_ADDRESS ? address(this).balance : _reserveToken.balanceOf(address(this));
        setReserveBalance(reserveId, balance);
    }

    /**
     * @dev syncs all stored reserve balances, excluding a given amount of ether from the ether reserve balance (if relevant)
     *
     * @param _value   amount of ether to exclude from the ether reserve balance (if relevant)
     */
    function syncReserveBalances(uint256 _value) internal {
        IERC20 _reserveToken0 = __reserveTokens[0];
        IERC20 _reserveToken1 = __reserveTokens[1];
        uint256 balance0 =
            _reserveToken0 == NATIVE_TOKEN_ADDRESS
                ? address(this).balance - _value
                : _reserveToken0.balanceOf(address(this));
        uint256 balance1 =
            _reserveToken1 == NATIVE_TOKEN_ADDRESS
                ? address(this).balance - _value
                : _reserveToken1.balanceOf(address(this));
        setReserveBalances(1, 2, balance0, balance1);
    }

    /**
     * @dev helper, dispatches the Conversion event
     *
     * @param _sourceToken     source ERC20 token
     * @param _targetToken     target ERC20 token
     * @param _trader          address of the caller who executed the conversion
     * @param _amount          amount purchased/sold (in the source token)
     * @param _returnAmount    amount returned (in the target token)
     */
    function dispatchConversionEvent(
        IERC20 _sourceToken,
        IERC20 _targetToken,
        address _trader,
        uint256 _amount,
        uint256 _returnAmount,
        uint256 _feeAmount
    ) internal {
        emit Conversion(_sourceToken, _targetToken, _trader, _amount, _returnAmount, int256(_feeAmount));
    }

    /**
     * @dev returns the expected amount and expected fee for converting one reserve to another
     *
     * @param _sourceToken address of the source reserve token contract
     * @param _targetToken address of the target reserve token contract
     * @param _amount      amount of source reserve tokens converted
     *
     * @return expected amount in units of the target reserve token
     * @return expected fee in units of the target reserve token
     */
    function targetAmountAndFee(
        IERC20 _sourceToken,
        IERC20 _targetToken,
        uint256 _amount
    ) public view virtual override active returns (uint256, uint256) {
        uint256 sourceId = __reserveIds[_sourceToken];
        uint256 targetId = __reserveIds[_targetToken];

        (uint256 sourceBalance, uint256 targetBalance) = reserveBalances(sourceId, targetId);

        return targetAmountAndFee(_sourceToken, _targetToken, sourceBalance, targetBalance, _amount);
    }

    /**
     * @dev returns the expected amount and expected fee for converting one reserve to another
     *
     * @param _sourceBalance    balance in the source reserve token contract
     * @param _targetBalance    balance in the target reserve token contract
     * @param _amount           amount of source reserve tokens converted
     *
     * @return expected amount in units of the target reserve token
     * @return expected fee in units of the target reserve token
     */
    function targetAmountAndFee(
        IERC20, /* _sourceToken */
        IERC20, /* _targetToken */
        uint256 _sourceBalance,
        uint256 _targetBalance,
        uint256 _amount
    ) internal view virtual returns (uint256, uint256) {
        uint256 amount = crossReserveTargetAmount(_sourceBalance, _targetBalance, _amount);

        uint256 fee = calculateFee(amount);

        return (amount - fee, fee);
    }

    /**
     * @dev returns the required amount and expected fee for converting one reserve to another
     *
     * @param _sourceToken address of the source reserve token contract
     * @param _targetToken address of the target reserve token contract
     * @param _amount      amount of target reserve tokens desired
     *
     * @return required amount in units of the source reserve token
     * @return expected fee in units of the target reserve token
     */
    function sourceAmountAndFee(
        IERC20 _sourceToken,
        IERC20 _targetToken,
        uint256 _amount
    ) public view virtual active returns (uint256, uint256) {
        uint256 sourceId = __reserveIds[_sourceToken];
        uint256 targetId = __reserveIds[_targetToken];

        (uint256 sourceBalance, uint256 targetBalance) = reserveBalances(sourceId, targetId);

        uint256 fee = calculateFeeInv(_amount);

        uint256 amount = crossReserveSourceAmount(sourceBalance, targetBalance, _amount.add(fee));

        return (amount, fee);
    }

    /**
     * @dev converts a specific amount of source tokens to target tokens
     *
     * @param _sourceToken source ERC20 token
     * @param _targetToken target ERC20 token
     * @param _amount      amount of tokens to convert (in units of the source token)
     * @param _trader      address of the caller who executed the conversion
     * @param _beneficiary wallet to receive the conversion result
     *
     * @return amount of tokens received (in units of the target token)
     */
    function doConvert(
        IERC20 _sourceToken,
        IERC20 _targetToken,
        uint256 _amount,
        address _trader,
        address payable _beneficiary
    ) internal returns (uint256) {
        // update the recent average rate
        updateRecentAverageRate();

        uint256 sourceId = __reserveIds[_sourceToken];
        uint256 targetId = __reserveIds[_targetToken];

        (uint256 sourceBalance, uint256 targetBalance) = reserveBalances(sourceId, targetId);

        // get the target amount minus the conversion fee and the conversion fee
        (uint256 amount, uint256 fee) =
            targetAmountAndFee(_sourceToken, _targetToken, sourceBalance, targetBalance, _amount);

        // ensure that the trade gives something in return
        require(amount != 0, "ERR_ZERO_TARGET_AMOUNT");

        // ensure that the trade won't deplete the reserve balance
        assert(amount < targetBalance);

        // ensure that the input amount was already deposited
        uint256 actualSourceBalance;
        if (_sourceToken == NATIVE_TOKEN_ADDRESS) {
            actualSourceBalance = address(this).balance;
            require(msg.value == _amount, "ERR_ETH_AMOUNT_MISMATCH");
        } else {
            actualSourceBalance = _sourceToken.balanceOf(address(this));
            require(msg.value == 0 && actualSourceBalance.sub(sourceBalance) >= _amount, "ERR_INVALID_AMOUNT");
        }

        // sync the reserve balances
        setReserveBalances(sourceId, targetId, actualSourceBalance, targetBalance - amount);

        // transfer funds to the beneficiary in the to reserve token
        safeTransfer(_targetToken, _beneficiary, amount);

        // dispatch the conversion event
        dispatchConversionEvent(_sourceToken, _targetToken, _trader, _amount, amount, fee);

        // dispatch rate updates
        dispatchTokenRateUpdateEvents(_sourceToken, _targetToken, actualSourceBalance, targetBalance - amount);

        return amount;
    }

    /**
     * @dev returns the recent average rate of 1 `_token` in the other reserve token units
     *
     * @param _token   token to get the rate for
     *
     * @return recent average rate between the reserves (numerator)
     * @return recent average rate between the reserves (denominator)
     */
    function recentAverageRate(IERC20 _token) external view validReserve(_token) returns (uint256, uint256) {
        // get the recent average rate of reserve 0
        uint256 rate = calcRecentAverageRate(averageRateInfo);

        uint256 rateN = decodeAverageRateN(rate);
        uint256 rateD = decodeAverageRateD(rate);

        if (_token == __reserveTokens[0]) {
            return (rateN, rateD);
        }

        return (rateD, rateN);
    }

    /**
     * @dev updates the recent average rate if needed
     */
    function updateRecentAverageRate() internal {
        uint256 averageRateInfo1 = averageRateInfo;
        uint256 averageRateInfo2 = calcRecentAverageRate(averageRateInfo1);
        if (averageRateInfo1 != averageRateInfo2) {
            averageRateInfo = averageRateInfo2;
        }
    }

    /**
     * @dev returns the recent average rate of 1 reserve token 0 in reserve token 1 units
     *
     * @param _averageRateInfo a local copy of the `averageRateInfo` state-variable
     *
     * @return recent average rate between the reserves
     */
    function calcRecentAverageRate(uint256 _averageRateInfo) internal view returns (uint256) {
        // get the previous average rate and its update-time
        uint256 prevAverageRateT = decodeAverageRateT(_averageRateInfo);
        uint256 prevAverageRateN = decodeAverageRateN(_averageRateInfo);
        uint256 prevAverageRateD = decodeAverageRateD(_averageRateInfo);

        // get the elapsed time since the previous average rate was calculated
        uint256 currentTime = time();
        uint256 timeElapsed = currentTime - prevAverageRateT;

        // if the previous average rate was calculated in the current block, the average rate remains unchanged
        if (timeElapsed == 0) {
            return _averageRateInfo;
        }

        // get the current rate between the reserves
        (uint256 currentRateD, uint256 currentRateN) = reserveBalances();

        // if the previous average rate was calculated a while ago or never, the average rate is equal to the current rate
        if (timeElapsed >= AVERAGE_RATE_PERIOD || prevAverageRateT == 0) {
            (currentRateN, currentRateD) = MathEx.reducedRatio(currentRateN, currentRateD, MAX_UINT112);
            return encodeAverageRateInfo(currentTime, currentRateN, currentRateD);
        }

        uint256 x = prevAverageRateD.mul(currentRateN);
        uint256 y = prevAverageRateN.mul(currentRateD);

        // since we know that timeElapsed < AVERAGE_RATE_PERIOD, we can avoid using SafeMath:
        uint256 newRateN = y.mul(AVERAGE_RATE_PERIOD - timeElapsed).add(x.mul(timeElapsed));
        uint256 newRateD = prevAverageRateD.mul(currentRateD).mul(AVERAGE_RATE_PERIOD);

        (newRateN, newRateD) = MathEx.reducedRatio(newRateN, newRateD, MAX_UINT112);
        return encodeAverageRateInfo(currentTime, newRateN, newRateD);
    }

    /**
     * @dev increases the pool's liquidity and mints new shares in the pool to the caller
     *
     * @param _reserveTokens   address of each reserve token
     * @param _reserveAmounts  amount of each reserve token
     * @param _minReturn       token minimum return-amount
     *
     * @return amount of pool tokens issued
     */
    function addLiquidity(
        IERC20[] memory _reserveTokens,
        uint256[] memory _reserveAmounts,
        uint256 _minReturn
    ) public payable protected active returns (uint256) {
        // verify the user input
        verifyLiquidityInput(_reserveTokens, _reserveAmounts, _minReturn);

        // if one of the reserves is ETH, then verify that the input amount of ETH is equal to the input value of ETH
        for (uint256 i = 0; i < 2; i++) {
            if (_reserveTokens[i] == NATIVE_TOKEN_ADDRESS) {
                require(_reserveAmounts[i] == msg.value, "ERR_ETH_AMOUNT_MISMATCH");
            }
        }

        // if the input value of ETH is larger than zero, then verify that one of the reserves is ETH
        if (msg.value > 0) {
            require(__reserveIds[NATIVE_TOKEN_ADDRESS] != 0, "ERR_NO_ETH_RESERVE");
        }

        // save a local copy of the pool token
        IDSToken poolToken = IDSToken(address(anchor));

        // get the total supply
        uint256 totalSupply = poolToken.totalSupply();

        uint256[2] memory prevReserveBalances;
        uint256[2] memory newReserveBalances;

        // process the network fees and get the reserve balances
        (prevReserveBalances[0], prevReserveBalances[1]) = processNetworkFees(msg.value);

        uint256 amount;
        uint256[2] memory reserveAmounts;

        // calculate the amount of pool tokens to mint for the caller
        // and the amount of reserve tokens to transfer from the caller
        if (totalSupply == 0) {
            amount = MathEx.geometricMean(_reserveAmounts);
            reserveAmounts[0] = _reserveAmounts[0];
            reserveAmounts[1] = _reserveAmounts[1];
        } else {
            (amount, reserveAmounts) = addLiquidityAmounts(
                _reserveTokens,
                _reserveAmounts,
                prevReserveBalances,
                totalSupply
            );
        }

        uint256 newPoolTokenSupply = totalSupply.add(amount);
        for (uint256 i = 0; i < 2; i++) {
            IERC20 reserveToken = _reserveTokens[i];
            uint256 reserveAmount = reserveAmounts[i];
            require(reserveAmount > 0, "ERR_ZERO_TARGET_AMOUNT");
            assert(reserveAmount <= _reserveAmounts[i]);

            // transfer each one of the reserve amounts from the user to the pool
            if (reserveToken != NATIVE_TOKEN_ADDRESS) {
                // ETH has already been transferred as part of the transaction
                reserveToken.safeTransferFrom(msg.sender, address(this), reserveAmount);
            } else if (_reserveAmounts[i] > reserveAmount) {
                // transfer the extra amount of ETH back to the user
                msg.sender.transfer(_reserveAmounts[i] - reserveAmount);
            }

            // save the new reserve balance
            newReserveBalances[i] = prevReserveBalances[i].add(reserveAmount);

            emit LiquidityAdded(msg.sender, reserveToken, reserveAmount, newReserveBalances[i], newPoolTokenSupply);

            // dispatch the `TokenRateUpdate` event for the pool token
            emit TokenRateUpdate(poolToken, reserveToken, newReserveBalances[i], newPoolTokenSupply);
        }

        // set the reserve balances
        setReserveBalances(1, 2, newReserveBalances[0], newReserveBalances[1]);

        // set the reserve balances product
        _reserveBalancesProduct = newReserveBalances[0] * newReserveBalances[1];

        // verify that the equivalent amount of tokens is equal to or larger than the user's expectation
        require(amount >= _minReturn, "ERR_RETURN_TOO_LOW");

        // issue the tokens to the user
        poolToken.issue(msg.sender, amount);

        // return the amount of pool tokens issued
        return amount;
    }

    /**
     * @dev get the amount of pool tokens to mint for the caller
     * and the amount of reserve tokens to transfer from the caller
     *
     * @param _reserveAmounts   amount of each reserve token
     * @param _reserveBalances  balance of each reserve token
     * @param _totalSupply      total supply of pool tokens
     *
     * @return amount of pool tokens to mint for the caller
     * @return amount of reserve tokens to transfer from the caller
     */
    function addLiquidityAmounts(
        IERC20[] memory, /* _reserveTokens */
        uint256[] memory _reserveAmounts,
        uint256[2] memory _reserveBalances,
        uint256 _totalSupply
    ) internal view virtual returns (uint256, uint256[2] memory) {
        this;

        uint256 index =
            _reserveAmounts[0].mul(_reserveBalances[1]) < _reserveAmounts[1].mul(_reserveBalances[0]) ? 0 : 1;
        uint256 amount = fundSupplyAmount(_totalSupply, _reserveBalances[index], _reserveAmounts[index]);

        uint256[2] memory reserveAmounts =
            [fundCost(_totalSupply, _reserveBalances[0], amount), fundCost(_totalSupply, _reserveBalances[1], amount)];

        return (amount, reserveAmounts);
    }

    /**
     * @dev decreases the pool's liquidity and burns the caller's shares in the pool
     *
     * @param _amount                  token amount
     * @param _reserveTokens           address of each reserve token
     * @param _reserveMinReturnAmounts minimum return-amount of each reserve token
     *
     * @return the amount of each reserve token granted for the given amount of pool tokens
     */
    function removeLiquidity(
        uint256 _amount,
        IERC20[] memory _reserveTokens,
        uint256[] memory _reserveMinReturnAmounts
    ) public protected active returns (uint256[] memory) {
        // verify the user input
        bool inputRearranged = verifyLiquidityInput(_reserveTokens, _reserveMinReturnAmounts, _amount);

        // save a local copy of the pool token
        IDSToken poolToken = IDSToken(address(anchor));

        // get the total supply BEFORE destroying the user tokens
        uint256 totalSupply = poolToken.totalSupply();

        // destroy the user tokens
        poolToken.destroy(msg.sender, _amount);

        uint256 newPoolTokenSupply = totalSupply.sub(_amount);

        uint256[2] memory prevReserveBalances;
        uint256[2] memory newReserveBalances;

        // process the network fees and get the reserve balances
        (prevReserveBalances[0], prevReserveBalances[1]) = processNetworkFees(0);

        uint256[] memory reserveAmounts = removeLiquidityReserveAmounts(_amount, totalSupply, prevReserveBalances);

        for (uint256 i = 0; i < 2; i++) {
            IERC20 reserveToken = _reserveTokens[i];
            uint256 reserveAmount = reserveAmounts[i];
            require(reserveAmount >= _reserveMinReturnAmounts[i], "ERR_ZERO_TARGET_AMOUNT");

            // save the new reserve balance
            newReserveBalances[i] = prevReserveBalances[i].sub(reserveAmount);

            // transfer each one of the reserve amounts from the pool to the user
            safeTransfer(reserveToken, msg.sender, reserveAmount);

            emit LiquidityRemoved(msg.sender, reserveToken, reserveAmount, newReserveBalances[i], newPoolTokenSupply);

            // dispatch the `TokenRateUpdate` event for the pool token
            emit TokenRateUpdate(poolToken, reserveToken, newReserveBalances[i], newPoolTokenSupply);
        }

        // set the reserve balances
        setReserveBalances(1, 2, newReserveBalances[0], newReserveBalances[1]);

        // set the reserve balances product
        _reserveBalancesProduct = newReserveBalances[0] * newReserveBalances[1];

        if (inputRearranged) {
            uint256 tempReserveAmount = reserveAmounts[0];
            reserveAmounts[0] = reserveAmounts[1];
            reserveAmounts[1] = tempReserveAmount;
        }

        // return the amount of each reserve token granted for the given amount of pool tokens
        return reserveAmounts;
    }

    /**
     * @dev given the amount of one of the reserve tokens to add liquidity of,
     * returns the required amount of each one of the other reserve tokens
     * since an empty pool can be funded with any list of non-zero input amounts,
     * this function assumes that the pool is not empty (has already been funded)
     *
     * @param _reserveTokens       address of each reserve token
     * @param _reserveTokenIndex   index of the relevant reserve token
     * @param _reserveAmount       amount of the relevant reserve token
     *
     * @return the required amount of each one of the reserve tokens
     */
    function addLiquidityCost(
        IERC20[] memory _reserveTokens,
        uint256 _reserveTokenIndex,
        uint256 _reserveAmount
    ) public view returns (uint256[] memory) {
        uint256 totalSupply = IDSToken(address(anchor)).totalSupply();
        uint256[2] memory baseBalances = baseReserveBalances(_reserveTokens);
        uint256 amount = fundSupplyAmount(totalSupply, baseBalances[_reserveTokenIndex], _reserveAmount);

        uint256[] memory reserveAmounts = new uint256[](2);
        reserveAmounts[0] = fundCost(totalSupply, baseBalances[0], amount);
        reserveAmounts[1] = fundCost(totalSupply, baseBalances[1], amount);
        return reserveAmounts;
    }

    /**
     * @dev returns the amount of pool tokens entitled for given amounts of reserve tokens
     * since an empty pool can be funded with any list of non-zero input amounts,
     * this function assumes that the pool is not empty (has already been funded)
     *
     * @param _reserveTokens   address of each reserve token
     * @param _reserveAmounts  amount of each reserve token
     *
     * @return the amount of pool tokens entitled for the given amounts of reserve tokens
     */
    function addLiquidityReturn(IERC20[] memory _reserveTokens, uint256[] memory _reserveAmounts)
        public
        view
        returns (uint256)
    {
        uint256 totalSupply = IDSToken(address(anchor)).totalSupply();
        uint256[2] memory baseBalances = baseReserveBalances(_reserveTokens);
        (uint256 amount, ) = addLiquidityAmounts(_reserveTokens, _reserveAmounts, baseBalances, totalSupply);
        return amount;
    }

    /**
     * @dev returns the amount of each reserve token entitled for a given amount of pool tokens
     *
     * @param _amount          amount of pool tokens
     * @param _reserveTokens   address of each reserve token
     *
     * @return the amount of each reserve token entitled for the given amount of pool tokens
     */
    function removeLiquidityReturn(uint256 _amount, IERC20[] memory _reserveTokens)
        public
        view
        returns (uint256[] memory)
    {
        uint256 totalSupply = IDSToken(address(anchor)).totalSupply();
        uint256[2] memory baseBalances = baseReserveBalances(_reserveTokens);
        return removeLiquidityReserveAmounts(_amount, totalSupply, baseBalances);
    }

    /**
     * @dev verifies that a given array of tokens is identical to the converter's array of reserve tokens
     * we take this input in order to allow specifying the corresponding reserve amounts in any order
     * this function rearranges the input arrays according to the converter's array of reserve tokens
     *
     * @param _reserveTokens   array of reserve tokens
     * @param _reserveAmounts  array of reserve amounts
     * @param _amount          token amount
     *
     * @return true if the function has rearranged the input arrays; false otherwise
     */
    function verifyLiquidityInput(
        IERC20[] memory _reserveTokens,
        uint256[] memory _reserveAmounts,
        uint256 _amount
    ) private view returns (bool) {
        require(validReserveAmounts(_reserveAmounts) && _amount > 0, "ERR_ZERO_AMOUNT");

        uint256 reserve0Id = __reserveIds[_reserveTokens[0]];
        uint256 reserve1Id = __reserveIds[_reserveTokens[1]];

        if (reserve0Id == 2 && reserve1Id == 1) {
            IERC20 tempReserveToken = _reserveTokens[0];
            _reserveTokens[0] = _reserveTokens[1];
            _reserveTokens[1] = tempReserveToken;
            uint256 tempReserveAmount = _reserveAmounts[0];
            _reserveAmounts[0] = _reserveAmounts[1];
            _reserveAmounts[1] = tempReserveAmount;
            return true;
        }

        require(reserve0Id == 1 && reserve1Id == 2, "ERR_INVALID_RESERVE");
        return false;
    }

    /**
     * @dev checks whether or not both reserve amounts are larger than zero
     *
     * @param _reserveAmounts  array of reserve amounts
     *
     * @return true if both reserve amounts are larger than zero; false otherwise
     */
    function validReserveAmounts(uint256[] memory _reserveAmounts) internal pure virtual returns (bool) {
        return _reserveAmounts[0] > 0 && _reserveAmounts[1] > 0;
    }

    /**
     * @dev returns the amount of each reserve token entitled for a given amount of pool tokens
     *
     * @param _amount          amount of pool tokens
     * @param _totalSupply     total supply of pool tokens
     * @param _reserveBalances balance of each reserve token
     *
     * @return the amount of each reserve token entitled for the given amount of pool tokens
     */
    function removeLiquidityReserveAmounts(
        uint256 _amount,
        uint256 _totalSupply,
        uint256[2] memory _reserveBalances
    ) private pure returns (uint256[] memory) {
        uint256[] memory reserveAmounts = new uint256[](2);
        reserveAmounts[0] = liquidateReserveAmount(_totalSupply, _reserveBalances[0], _amount);
        reserveAmounts[1] = liquidateReserveAmount(_totalSupply, _reserveBalances[1], _amount);
        return reserveAmounts;
    }

    /**
     * @dev dispatches token rate update events for the reserve tokens and the pool token
     *
     * @param _sourceToken     address of the source reserve token
     * @param _targetToken     address of the target reserve token
     * @param _sourceBalance   balance of the source reserve token
     * @param _targetBalance   balance of the target reserve token
     */
    function dispatchTokenRateUpdateEvents(
        IERC20 _sourceToken,
        IERC20 _targetToken,
        uint256 _sourceBalance,
        uint256 _targetBalance
    ) private {
        // save a local copy of the pool token
        IDSToken poolToken = IDSToken(address(anchor));

        // get the total supply of pool tokens
        uint256 poolTokenSupply = poolToken.totalSupply();

        // dispatch token rate update event for the reserve tokens
        emit TokenRateUpdate(_sourceToken, _targetToken, _targetBalance, _sourceBalance);

        // dispatch token rate update events for the pool token
        emit TokenRateUpdate(poolToken, _sourceToken, _sourceBalance, poolTokenSupply);
        emit TokenRateUpdate(poolToken, _targetToken, _targetBalance, poolTokenSupply);
    }

    function encodeReserveBalance(uint256 _balance, uint256 _id) private pure returns (uint256) {
        assert(_balance <= MAX_UINT128 && (_id == 1 || _id == 2));
        return _balance << ((_id - 1) * 128);
    }

    function decodeReserveBalance(uint256 _balances, uint256 _id) private pure returns (uint256) {
        assert(_id == 1 || _id == 2);
        return (_balances >> ((_id - 1) * 128)) & MAX_UINT128;
    }

    function encodeReserveBalances(
        uint256 _balance0,
        uint256 _id0,
        uint256 _balance1,
        uint256 _id1
    ) private pure returns (uint256) {
        return encodeReserveBalance(_balance0, _id0) | encodeReserveBalance(_balance1, _id1);
    }

    function decodeReserveBalances(
        uint256 _balances,
        uint256 _id0,
        uint256 _id1
    ) private pure returns (uint256, uint256) {
        return (decodeReserveBalance(_balances, _id0), decodeReserveBalance(_balances, _id1));
    }

    function encodeAverageRateInfo(
        uint256 _averageRateT,
        uint256 _averageRateN,
        uint256 _averageRateD
    ) private pure returns (uint256) {
        assert(_averageRateT <= MAX_UINT32 && _averageRateN <= MAX_UINT112 && _averageRateD <= MAX_UINT112);
        return (_averageRateT << 224) | (_averageRateN << 112) | _averageRateD;
    }

    function decodeAverageRateT(uint256 _averageRateInfo) private pure returns (uint256) {
        return _averageRateInfo >> 224;
    }

    function decodeAverageRateN(uint256 _averageRateInfo) private pure returns (uint256) {
        return (_averageRateInfo >> 112) & MAX_UINT112;
    }

    function decodeAverageRateD(uint256 _averageRateInfo) private pure returns (uint256) {
        return _averageRateInfo & MAX_UINT112;
    }

    /**
     * @dev returns the largest integer smaller than or equal to the square root of a given value
     *
     * @param x the given value
     *
     * @return the largest integer smaller than or equal to the square root of the given value
     */
    function floorSqrt(uint256 x) private pure returns (uint256) {
        return x > 0 ? MathEx.floorSqrt(x) : 0;
    }

    function crossReserveTargetAmount(
        uint256 _sourceReserveBalance,
        uint256 _targetReserveBalance,
        uint256 _amount
    ) private pure returns (uint256) {
        // validate input
        require(_sourceReserveBalance > 0 && _targetReserveBalance > 0, "ERR_INVALID_RESERVE_BALANCE");

        return _targetReserveBalance.mul(_amount) / _sourceReserveBalance.add(_amount);
    }

    function crossReserveSourceAmount(
        uint256 _sourceReserveBalance,
        uint256 _targetReserveBalance,
        uint256 _amount
    ) private pure returns (uint256) {
        // validate input
        require(_sourceReserveBalance > 0, "ERR_INVALID_RESERVE_BALANCE");
        require(_amount < _targetReserveBalance, "ERR_INVALID_AMOUNT");

        if (_amount == 0) {
            return 0;
        }

        return (_sourceReserveBalance.mul(_amount) - 1) / (_targetReserveBalance - _amount) + 1;
    }

    function fundCost(
        uint256 _supply,
        uint256 _reserveBalance,
        uint256 _amount
    ) private pure returns (uint256) {
        // validate input
        require(_supply > 0, "ERR_INVALID_SUPPLY");
        require(_reserveBalance > 0, "ERR_INVALID_RESERVE_BALANCE");

        // special case for 0 amount
        if (_amount == 0) {
            return 0;
        }

        return (_amount.mul(_reserveBalance) - 1) / _supply + 1;
    }

    function fundSupplyAmount(
        uint256 _supply,
        uint256 _reserveBalance,
        uint256 _amount
    ) private pure returns (uint256) {
        // validate input
        require(_supply > 0, "ERR_INVALID_SUPPLY");
        require(_reserveBalance > 0, "ERR_INVALID_RESERVE_BALANCE");

        // special case for 0 amount
        if (_amount == 0) {
            return 0;
        }

        return _amount.mul(_supply) / _reserveBalance;
    }

    function liquidateReserveAmount(
        uint256 _supply,
        uint256 _reserveBalance,
        uint256 _amount
    ) private pure returns (uint256) {
        // validate input
        require(_supply > 0, "ERR_INVALID_SUPPLY");
        require(_reserveBalance > 0, "ERR_INVALID_RESERVE_BALANCE");
        require(_amount <= _supply, "ERR_INVALID_AMOUNT");

        // special case for 0 amount
        if (_amount == 0) {
            return 0;
        }

        // special case for liquidating the entire supply
        if (_amount == _supply) {
            return _reserveBalance;
        }

        return _amount.mul(_reserveBalance) / _supply;
    }

    /**
     * @dev returns the network wallet and fees
     *
     * @param reserveBalance0 1st reserve balance
     * @param reserveBalance1 2nd reserve balance
     *
     * @return the network wallet
     * @return the network fee on the 1st reserve
     * @return the network fee on the 2nd reserve
     */
    function networkWalletAndFees(uint256 reserveBalance0, uint256 reserveBalance1)
        private
        view
        returns (
            ITokenHolder,
            uint256,
            uint256
        )
    {
        uint256 prevPoint = floorSqrt(_reserveBalancesProduct);
        uint256 currPoint = floorSqrt(reserveBalance0 * reserveBalance1);

        if (prevPoint >= currPoint) {
            return (ITokenHolder(address(0)), 0, 0);
        }

        (ITokenHolder networkFeeWallet, uint32 networkFee) =
            INetworkSettings(addressOf(NETWORK_SETTINGS)).networkFeeParams();
        uint256 n = (currPoint - prevPoint) * networkFee;
        uint256 d = currPoint * PPM_RESOLUTION;
        return (networkFeeWallet, reserveBalance0.mul(n).div(d), reserveBalance1.mul(n).div(d));
    }

    /**
     * @dev transfers funds held by the contract and sends them to an account
     *
     * @param token ERC20 token contract address
     * @param to account to receive the new amount
     * @param amount amount to withdraw
     */
    function safeTransfer(
        IERC20 token,
        address to,
        uint256 amount
    ) private {
        if (amount == 0) {
            return;
        }

        if (token == NATIVE_TOKEN_ADDRESS) {
            payable(to).transfer(amount);
        } else {
            token.safeTransfer(to, amount);
        }
    }

    /**
     * @dev deprecated since version 28, backward compatibility - use only for earlier versions
     */
    function token() public view override returns (IConverterAnchor) {
        return anchor;
    }

    /**
     * @dev deprecated, backward compatibility
     */
    function transferTokenOwnership(address _newOwner) public override ownerOnly {
        transferAnchorOwnership(_newOwner);
    }

    /**
     * @dev deprecated, backward compatibility
     */
    function acceptTokenOwnership() public override ownerOnly {
        acceptAnchorOwnership();
    }

    /**
     * @dev deprecated, backward compatibility
     */
    function connectors(IERC20 _address)
        public
        view
        override
        returns (
            uint256,
            uint32,
            bool,
            bool,
            bool
        )
    {
        uint256 reserveId = __reserveIds[_address];
        if (reserveId != 0) {
            return (reserveBalance(reserveId), PPM_RESOLUTION / 2, false, false, true);
        }
        return (0, 0, false, false, false);
    }

    /**
     * @dev deprecated, backward compatibility
     */
    function connectorTokens(uint256 _index) public view override returns (IERC20) {
        return __reserveTokens[_index];
    }

    /**
     * @dev deprecated, backward compatibility
     */
    function connectorTokenCount() public view override returns (uint16) {
        return reserveTokenCount();
    }

    /**
     * @dev deprecated, backward compatibility
     */
    function getConnectorBalance(IERC20 _connectorToken) public view override returns (uint256) {
        return reserveBalance(_connectorToken);
    }

    /**
     * @dev deprecated, backward compatibility
     */
    function getReturn(
        IERC20 _sourceToken,
        IERC20 _targetToken,
        uint256 _amount
    ) public view returns (uint256, uint256) {
        return targetAmountAndFee(_sourceToken, _targetToken, _amount);
    }
}