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

// SPDX-License-Identifier: MIT

pragma solidity ^0.6.0;

/**
 * @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: @bancor/token-governance/contracts/IClaimable.sol


pragma solidity 0.6.12;

/// @title Claimable contract interface
interface IClaimable {
    function owner() external view returns (address);

    function transferOwnership(address newOwner) external;

    function acceptOwnership() external;
}

// File: @bancor/token-governance/contracts/IMintableToken.sol


pragma solidity 0.6.12;



/// @title Mintable Token interface
interface IMintableToken is IERC20, IClaimable {
    function issue(address to, uint256 amount) external;

    function destroy(address from, uint256 amount) external;
}

// File: @bancor/token-governance/contracts/ITokenGovernance.sol


pragma solidity 0.6.12;


/// @title The interface for mintable/burnable token governance.
interface ITokenGovernance {
    // The address of the mintable ERC20 token.
    function token() external view returns (IMintableToken);

    /// @dev Mints new tokens.
    ///
    /// @param to Account to receive the new amount.
    /// @param amount Amount to increase the supply by.
    ///
    function mint(address to, uint256 amount) external;

    /// @dev Burns tokens from the caller.
    ///
    /// @param amount Amount to decrease the supply by.
    ///
    function burn(uint256 amount) external;
}

// 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/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 {
    // 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");
    }

    // verifies that the address is different than this contract address
    modifier notThis(address _address) {
        _notThis(_address);
        _;
    }

    // error message binary size optimization
    function _notThis(address _address) internal view {
        require(_address != address(this), "ERR_ADDRESS_IS_SELF");
    }
}

// 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 CHAINLINK_ORACLE_WHITELIST = "ChainlinkOracleWhitelist";

    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/SafeMath.sol


pragma solidity 0.6.12;

/**
 * @dev This library supports basic math operations with overflow/underflow protection.
 */
library SafeMath {
    /**
     * @dev returns the sum of _x and _y, reverts if the calculation overflows
     *
     * @param _x   value 1
     * @param _y   value 2
     *
     * @return sum
     */
    function add(uint256 _x, uint256 _y) internal pure returns (uint256) {
        uint256 z = _x + _y;
        require(z >= _x, "ERR_OVERFLOW");
        return z;
    }

    /**
     * @dev returns the difference of _x minus _y, reverts if the calculation underflows
     *
     * @param _x   minuend
     * @param _y   subtrahend
     *
     * @return difference
     */
    function sub(uint256 _x, uint256 _y) internal pure returns (uint256) {
        require(_x >= _y, "ERR_UNDERFLOW");
        return _x - _y;
    }

    /**
     * @dev returns the product of multiplying _x by _y, reverts if the calculation overflows
     *
     * @param _x   factor 1
     * @param _y   factor 2
     *
     * @return product
     */
    function mul(uint256 _x, uint256 _y) internal pure returns (uint256) {
        // gas optimization
        if (_x == 0) return 0;

        uint256 z = _x * _y;
        require(z / _x == _y, "ERR_OVERFLOW");
        return z;
    }

    /**
     * @dev Integer division of two numbers truncating the quotient, reverts on division by zero.
     *
     * @param _x   dividend
     * @param _y   divisor
     *
     * @return quotient
     */
    function div(uint256 _x, uint256 _y) internal pure returns (uint256) {
        require(_y > 0, "ERR_DIVIDE_BY_ZERO");
        uint256 c = _x / _y;
        return c;
    }
}

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


pragma solidity 0.6.12;


/**
 * @dev This library provides a set of complex math operations.
 */
library Math {
    using SafeMath for uint256;

    /**
     * @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 = _num / 2 + 1;
        uint256 y = (x + _num / x) / 2;
        while (x > y) {
            x = y;
            y = (x + _num / x) / 2;
        }
        return x * x == _num ? x : x + 1;
    }

    /**
     * @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) {
        if (_n > _max || _d > _max) return normalizedRatio(_n, _d, _max);
        return (_n, _d);
    }

    /**
     * @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 (_scale / 2, _scale / 2);
        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;
            _b /= c;
        }
        uint256 x = roundDiv(_a * _scale, _a.add(_b));
        uint256 y = _scale - x;
        return (x, y);
    }

    /**
     * @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;
    }
}

// File: solidity/contracts/token/interfaces/IERC20Token.sol


pragma solidity 0.6.12;

/*
    ERC20 Standard Token interface
*/
interface IERC20Token {
    function name() external view returns (string memory);

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

    function decimals() external view returns (uint8);

    function totalSupply() external view returns (uint256);

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

    function allowance(address _owner, address _spender) external view returns (uint256);

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

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

    function approve(address _spender, uint256 _value) external returns (bool);
}

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


pragma solidity 0.6.12;


contract TokenHandler {
    bytes4 private constant APPROVE_FUNC_SELECTOR = bytes4(keccak256("approve(address,uint256)"));
    bytes4 private constant TRANSFER_FUNC_SELECTOR = bytes4(keccak256("transfer(address,uint256)"));
    bytes4 private constant TRANSFER_FROM_FUNC_SELECTOR = bytes4(keccak256("transferFrom(address,address,uint256)"));

    /**
     * @dev executes the ERC20 token's `approve` function and reverts upon failure
     * the main purpose of this function is to prevent a non standard ERC20 token
     * from failing silently
     *
     * @param _token   ERC20 token address
     * @param _spender approved address
     * @param _value   allowance amount
     */
    function safeApprove(
        IERC20Token _token,
        address _spender,
        uint256 _value
    ) internal {
        (bool success, bytes memory data) = address(_token).call(
            abi.encodeWithSelector(APPROVE_FUNC_SELECTOR, _spender, _value)
        );
        require(success && (data.length == 0 || abi.decode(data, (bool))), "ERR_APPROVE_FAILED");
    }

    /**
     * @dev executes the ERC20 token's `transfer` function and reverts upon failure
     * the main purpose of this function is to prevent a non standard ERC20 token
     * from failing silently
     *
     * @param _token   ERC20 token address
     * @param _to      target address
     * @param _value   transfer amount
     */
    function safeTransfer(
        IERC20Token _token,
        address _to,
        uint256 _value
    ) internal {
        (bool success, bytes memory data) = address(_token).call(
            abi.encodeWithSelector(TRANSFER_FUNC_SELECTOR, _to, _value)
        );
        require(success && (data.length == 0 || abi.decode(data, (bool))), "ERR_TRANSFER_FAILED");
    }

    /**
     * @dev executes the ERC20 token's `transferFrom` function and reverts upon failure
     * the main purpose of this function is to prevent a non standard ERC20 token
     * from failing silently
     *
     * @param _token   ERC20 token address
     * @param _from    source address
     * @param _to      target address
     * @param _value   transfer amount
     */
    function safeTransferFrom(
        IERC20Token _token,
        address _from,
        address _to,
        uint256 _value
    ) internal {
        (bool success, bytes memory data) = address(_token).call(
            abi.encodeWithSelector(TRANSFER_FROM_FUNC_SELECTOR, _from, _to, _value)
        );
        require(success && (data.length == 0 || abi.decode(data, (bool))), "ERR_TRANSFER_FROM_FAILED");
    }
}

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


pragma solidity 0.6.12;

/**
 * @dev This contract provides types which can be used by various contracts.
 */

struct Fraction {
    uint256 n; // numerator
    uint256 d; // denominator
}

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


pragma solidity 0.6.12;


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

}

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


pragma solidity 0.6.12;




/*
    DSToken interface
*/
interface IDSToken is IConverterAnchor, IERC20Token {
    function issue(address _to, uint256 _amount) external;

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

// File: solidity/contracts/liquidity-protection/interfaces/ILiquidityProtectionStore.sol


pragma solidity 0.6.12;





/*
    Liquidity Protection Store interface
*/
interface ILiquidityProtectionStore is IOwned {
    function addPoolToWhitelist(IConverterAnchor _anchor) external;

    function removePoolFromWhitelist(IConverterAnchor _anchor) external;

    function isPoolWhitelisted(IConverterAnchor _anchor) external view returns (bool);

    function withdrawTokens(
        IERC20Token _token,
        address _to,
        uint256 _amount
    ) external;

    function protectedLiquidity(uint256 _id)
        external
        view
        returns (
            address,
            IDSToken,
            IERC20Token,
            uint256,
            uint256,
            uint256,
            uint256,
            uint256
        );

    function addProtectedLiquidity(
        address _provider,
        IDSToken _poolToken,
        IERC20Token _reserveToken,
        uint256 _poolAmount,
        uint256 _reserveAmount,
        uint256 _reserveRateN,
        uint256 _reserveRateD,
        uint256 _timestamp
    ) external returns (uint256);

    function updateProtectedLiquidityAmounts(
        uint256 _id,
        uint256 _poolNewAmount,
        uint256 _reserveNewAmount
    ) external;

    function removeProtectedLiquidity(uint256 _id) external;

    function lockedBalance(address _provider, uint256 _index) external view returns (uint256, uint256);

    function lockedBalanceRange(
        address _provider,
        uint256 _startIndex,
        uint256 _endIndex
    ) external view returns (uint256[] memory, uint256[] memory);

    function addLockedBalance(
        address _provider,
        uint256 _reserveAmount,
        uint256 _expirationTime
    ) external returns (uint256);

    function removeLockedBalance(address _provider, uint256 _index) external;

    function systemBalance(IERC20Token _poolToken) external view returns (uint256);

    function incSystemBalance(IERC20Token _poolToken, uint256 _poolAmount) external;

    function decSystemBalance(IERC20Token _poolToken, uint256 _poolAmount) external;
}

// 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(
        IERC20Token _sourceToken,
        IERC20Token _targetToken,
        uint256 _amount
    ) external view returns (uint256, uint256);

    function convert(
        IERC20Token _sourceToken,
        IERC20Token _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(IERC20Token _reserveToken) external view returns (uint256);

    receive() external payable;

    function transferAnchorOwnership(address _newOwner) external;

    function acceptAnchorOwnership() external;

    function setConversionFee(uint32 _conversionFee) external;

    function withdrawTokens(
        IERC20Token _token,
        address _to,
        uint256 _amount
    ) external;

    function withdrawETH(address payable _to) external;

    function addReserve(IERC20Token _token, uint32 _ratio) external;

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

    function transferTokenOwnership(address _newOwner) external;

    function acceptTokenOwnership() external;

    function connectors(IERC20Token _address)
        external
        view
        returns (
            uint256,
            uint32,
            bool,
            bool,
            bool
        );

    function getConnectorBalance(IERC20Token _connectorToken) external view returns (uint256);

    function connectorTokens(uint256 _index) external view returns (IERC20Token);

    function connectorTokenCount() external view returns (uint16);
}

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


pragma solidity 0.6.12;



interface IConverterRegistry {
    function getAnchorCount() external view returns (uint256);

    function getAnchors() external view returns (address[] memory);

    function getAnchor(uint256 _index) external view returns (IConverterAnchor);

    function isAnchor(address _value) external view returns (bool);

    function getLiquidityPoolCount() external view returns (uint256);

    function getLiquidityPools() external view returns (address[] memory);

    function getLiquidityPool(uint256 _index) external view returns (IConverterAnchor);

    function isLiquidityPool(address _value) external view returns (bool);

    function getConvertibleTokenCount() external view returns (uint256);

    function getConvertibleTokens() external view returns (address[] memory);

    function getConvertibleToken(uint256 _index) external view returns (IERC20Token);

    function isConvertibleToken(address _value) external view returns (bool);

    function getConvertibleTokenAnchorCount(IERC20Token _convertibleToken) external view returns (uint256);

    function getConvertibleTokenAnchors(IERC20Token _convertibleToken) external view returns (address[] memory);

    function getConvertibleTokenAnchor(IERC20Token _convertibleToken, uint256 _index)
        external
        view
        returns (IConverterAnchor);

    function isConvertibleTokenAnchor(IERC20Token _convertibleToken, address _value) external view returns (bool);
}

// File: solidity/contracts/liquidity-protection/LiquidityProtection.sol


pragma solidity 0.6.12;















interface ILiquidityPoolV1Converter is IConverter {
    function addLiquidity(
        IERC20Token[] memory _reserveTokens,
        uint256[] memory _reserveAmounts,
        uint256 _minReturn
    ) external payable;

    function removeLiquidity(
        uint256 _amount,
        IERC20Token[] memory _reserveTokens,
        uint256[] memory _reserveMinReturnAmounts
    ) external;

    function recentAverageRate(IERC20Token _reserveToken) external view returns (uint256, uint256);
}

/**
 * @dev This contract implements the liquidity protection mechanism.
 */
contract LiquidityProtection is TokenHandler, ContractRegistryClient, ReentrancyGuard {
    using SafeMath for uint256;
    using Math for *;

    struct ProtectedLiquidity {
        address provider; // liquidity provider
        IDSToken poolToken; // pool token address
        IERC20Token reserveToken; // reserve token address
        uint256 poolAmount; // pool token amount
        uint256 reserveAmount; // reserve token amount
        uint256 reserveRateN; // rate of 1 protected reserve token in units of the other reserve token (numerator)
        uint256 reserveRateD; // rate of 1 protected reserve token in units of the other reserve token (denominator)
        uint256 timestamp; // timestamp
    }

    // various rates between the two reserve tokens. the rate is of 1 unit of the protected reserve token in units of the other reserve token
    struct PackedRates {
        uint128 addSpotRateN; // spot rate of 1 A in units of B when liquidity was added (numerator)
        uint128 addSpotRateD; // spot rate of 1 A in units of B when liquidity was added (denominator)
        uint128 removeSpotRateN; // spot rate of 1 A in units of B when liquidity is removed (numerator)
        uint128 removeSpotRateD; // spot rate of 1 A in units of B when liquidity is removed (denominator)
        uint128 removeAverageRateN; // average rate of 1 A in units of B when liquidity is removed (numerator)
        uint128 removeAverageRateD; // average rate of 1 A in units of B when liquidity is removed (denominator)
    }

    IERC20Token internal constant ETH_RESERVE_ADDRESS = IERC20Token(0xEeeeeEeeeEeEeeEeEeEeeEEEeeeeEeeeeeeeEEeE);
    uint32 internal constant PPM_RESOLUTION = 1000000;
    uint256 internal constant MAX_UINT128 = 2**128 - 1;

    // the address of the whitelist administrator
    address public whitelistAdmin;

    ILiquidityProtectionStore public immutable store;
    IERC20Token public immutable networkToken;
    ITokenGovernance public immutable networkTokenGovernance;
    IERC20Token public immutable govToken;
    ITokenGovernance public immutable govTokenGovernance;

    // system network token balance limits
    uint256 public maxSystemNetworkTokenAmount = 500000e18;
    uint32 public maxSystemNetworkTokenRatio = 500000; // PPM units

    // number of seconds until any protection is in effect
    uint256 public minProtectionDelay = 30 days;

    // number of seconds until full protection is in effect
    uint256 public maxProtectionDelay = 100 days;

    // minimum amount of network tokens the system can mint as compensation for base token losses, default = 0.01 network tokens
    uint256 public minNetworkCompensation = 1e16;

    // number of seconds from liquidation to full network token release
    uint256 public lockDuration = 24 hours;

    // maximum deviation of the average rate from the spot rate
    uint32 public averageRateMaxDeviation = 5000; // PPM units

    // true if the contract is currently adding/removing liquidity from a converter, used for accepting ETH
    bool private updatingLiquidity = false;

    /**
     * @dev triggered when whitelist admin is updated
     *
     * @param _prevWhitelistAdmin  previous whitelist admin
     * @param _newWhitelistAdmin   new whitelist admin
     */
    event WhitelistAdminUpdated(address indexed _prevWhitelistAdmin, address indexed _newWhitelistAdmin);

    /**
     * @dev triggered when the system network token balance limits are updated
     *
     * @param _prevMaxSystemNetworkTokenAmount  previous maximum absolute balance in a pool
     * @param _newMaxSystemNetworkTokenAmount   new maximum absolute balance in a pool
     * @param _prevMaxSystemNetworkTokenRatio   previos maximum balance out of the total balance in a pool
     * @param _newMaxSystemNetworkTokenRatio    new maximum balance out of the total balance in a pool
     */
    event SystemNetworkTokenLimitsUpdated(
        uint256 _prevMaxSystemNetworkTokenAmount,
        uint256 _newMaxSystemNetworkTokenAmount,
        uint256 _prevMaxSystemNetworkTokenRatio,
        uint256 _newMaxSystemNetworkTokenRatio
    );

    /**
     * @dev triggered when the protection delays are updated
     *
     * @param _prevMinProtectionDelay  previous seconds until the protection starts
     * @param _newMinProtectionDelay   new seconds until the protection starts
     * @param _prevMaxProtectionDelay  previos seconds until full protection
     * @param _newMaxProtectionDelay   new seconds until full protection
     */
    event ProtectionDelaysUpdated(
        uint256 _prevMinProtectionDelay,
        uint256 _newMinProtectionDelay,
        uint256 _prevMaxProtectionDelay,
        uint256 _newMaxProtectionDelay
    );

    /**
     * @dev triggered when the minimum network token compensation is updated
     *
     * @param _prevMinNetworkCompensation  previous minimum network token compensation
     * @param _newMinNetworkCompensation   new minimum network token compensation
     */
    event MinNetworkCompensationUpdated(uint256 _prevMinNetworkCompensation, uint256 _newMinNetworkCompensation);

    /**
     * @dev triggered when the network token lock duration is updated
     *
     * @param _prevLockDuration  previous network token lock duration, in seconds
     * @param _newLockDuration   new network token lock duration, in seconds
     */
    event LockDurationUpdated(uint256 _prevLockDuration, uint256 _newLockDuration);

    /**
     * @dev triggered when the maximum deviation of the average rate from the spot rate is updated
     *
     * @param _prevAverageRateMaxDeviation previous maximum deviation of the average rate from the spot rate
     * @param _newAverageRateMaxDeviation  new maximum deviation of the average rate from the spot rate
     */
    event AverageRateMaxDeviationUpdated(uint32 _prevAverageRateMaxDeviation, uint32 _newAverageRateMaxDeviation);

    /**
     * @dev initializes a new LiquidityProtection contract
     *
     * @param _store                    liquidity protection store
     * @param _networkTokenGovernance   network token governance
     * @param _govTokenGovernance       governance token governance
     * @param _registry                 contract registry
     */
    constructor(
        ILiquidityProtectionStore _store,
        ITokenGovernance _networkTokenGovernance,
        ITokenGovernance _govTokenGovernance,
        IContractRegistry _registry
    )
        public
        ContractRegistryClient(_registry)
        validAddress(address(_store))
        validAddress(address(_networkTokenGovernance))
        validAddress(address(_govTokenGovernance))
        validAddress(address(_registry))
        notThis(address(_store))
        notThis(address(_networkTokenGovernance))
        notThis(address(_govTokenGovernance))
        notThis(address(_registry))
    {
        whitelistAdmin = msg.sender;
        store = _store;

        networkTokenGovernance = _networkTokenGovernance;
        networkToken = IERC20Token(address(_networkTokenGovernance.token()));
        govTokenGovernance = _govTokenGovernance;
        govToken = IERC20Token(address(_govTokenGovernance.token()));
    }

    // ensures that the contract is currently removing liquidity from a converter
    modifier updatingLiquidityOnly() {
        _updatingLiquidityOnly();
        _;
    }

    // error message binary size optimization
    function _updatingLiquidityOnly() internal view {
        require(updatingLiquidity, "ERR_NOT_UPDATING_LIQUIDITY");
    }

    // 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");
    }

    // ensures that the pool is supported
    modifier poolSupported(IConverterAnchor _poolAnchor) {
        _poolSupported(_poolAnchor);
        _;
    }

    // error message binary size optimization
    function _poolSupported(IConverterAnchor _poolAnchor) internal view {
        require(isPoolSupported(_poolAnchor), "ERR_POOL_NOT_SUPPORTED");
    }

    // ensures that the pool is supported and whitelisted
    modifier poolSupportedAndWhitelisted(IConverterAnchor _poolAnchor) {
        _poolSupportedAndWhitelisted(_poolAnchor);
        _;
    }

    // error message binary size optimization
    function _poolSupportedAndWhitelisted(IConverterAnchor _poolAnchor) internal view {
        require(isPoolSupported(_poolAnchor), "ERR_POOL_NOT_SUPPORTED");
        require(store.isPoolWhitelisted(_poolAnchor), "ERR_POOL_NOT_WHITELISTED");
    }

    /**
     * @dev accept ETH
     * used when removing liquidity from ETH converters
     */
    receive() external payable updatingLiquidityOnly() {}

    /**
     * @dev transfers the ownership of the store
     * can only be called by the contract owner
     *
     * @param _newOwner    the new owner of the store
     */
    function transferStoreOwnership(address _newOwner) external {
        transferOwnership(store, _newOwner);
    }

    /**
     * @dev accepts the ownership of the store
     * can only be called by the contract owner
     */
    function acceptStoreOwnership() external {
        acceptOwnership(store);
    }

    /**
     * @dev set the address of the whitelist admin
     * can only be called by the contract owner
     *
     * @param _whitelistAdmin  the address of the new whitelist admin
     */
    function setWhitelistAdmin(address _whitelistAdmin) external ownerOnly validAddress(_whitelistAdmin) {
        emit WhitelistAdminUpdated(whitelistAdmin, _whitelistAdmin);

        whitelistAdmin = _whitelistAdmin;
    }

    /**
     * @dev updates the system network token balance limits
     * can only be called by the contract owner
     *
     * @param _maxSystemNetworkTokenAmount  maximum absolute balance in a pool
     * @param _maxSystemNetworkTokenRatio   maximum balance out of the total balance in a pool (in PPM units)
     */
    function setSystemNetworkTokenLimits(uint256 _maxSystemNetworkTokenAmount, uint32 _maxSystemNetworkTokenRatio)
        external
        ownerOnly
        validPortion(_maxSystemNetworkTokenRatio)
    {
        emit SystemNetworkTokenLimitsUpdated(
            maxSystemNetworkTokenAmount,
            _maxSystemNetworkTokenAmount,
            maxSystemNetworkTokenRatio,
            _maxSystemNetworkTokenRatio
        );

        maxSystemNetworkTokenAmount = _maxSystemNetworkTokenAmount;
        maxSystemNetworkTokenRatio = _maxSystemNetworkTokenRatio;
    }

    /**
     * @dev updates the protection delays
     * can only be called by the contract owner
     *
     * @param _minProtectionDelay  seconds until the protection starts
     * @param _maxProtectionDelay  seconds until full protection
     */
    function setProtectionDelays(uint256 _minProtectionDelay, uint256 _maxProtectionDelay) external ownerOnly {
        require(_minProtectionDelay < _maxProtectionDelay, "ERR_INVALID_PROTECTION_DELAY");

        emit ProtectionDelaysUpdated(minProtectionDelay, _minProtectionDelay, maxProtectionDelay, _maxProtectionDelay);

        minProtectionDelay = _minProtectionDelay;
        maxProtectionDelay = _maxProtectionDelay;
    }

    /**
     * @dev updates the minimum network token compensation
     * can only be called by the contract owner
     *
     * @param _minCompensation new minimum compensation
     */
    function setMinNetworkCompensation(uint256 _minCompensation) external ownerOnly {
        emit MinNetworkCompensationUpdated(minNetworkCompensation, _minCompensation);

        minNetworkCompensation = _minCompensation;
    }

    /**
     * @dev updates the network token lock duration
     * can only be called by the contract owner
     *
     * @param _lockDuration    network token lock duration, in seconds
     */
    function setLockDuration(uint256 _lockDuration) external ownerOnly {
        emit LockDurationUpdated(lockDuration, _lockDuration);

        lockDuration = _lockDuration;
    }

    /**
     * @dev sets the maximum deviation of the average rate from the spot rate
     * can only be called by the contract owner
     *
     * @param _averageRateMaxDeviation maximum deviation of the average rate from the spot rate
     */
    function setAverageRateMaxDeviation(uint32 _averageRateMaxDeviation)
        external
        ownerOnly
        validPortion(_averageRateMaxDeviation)
    {
        emit AverageRateMaxDeviationUpdated(averageRateMaxDeviation, _averageRateMaxDeviation);

        averageRateMaxDeviation = _averageRateMaxDeviation;
    }

    /**
     * @dev adds a pool to the whitelist, or removes a pool from the whitelist
     * note that when a pool is whitelisted, it's not possible to remove liquidity anymore
     * removing a pool from the whitelist is an extreme measure in case of a base token compromise etc.
     * can only be called by the whitelist admin
     *
     * @param _poolAnchor  anchor of the pool
     * @param _add         true to add the pool to the whitelist, false to remove it from the whitelist
     */
    function whitelistPool(IConverterAnchor _poolAnchor, bool _add) external poolSupported(_poolAnchor) {
        require(msg.sender == whitelistAdmin || msg.sender == owner, "ERR_ACCESS_DENIED");

        // add or remove the pool to/from the whitelist
        if (_add) store.addPoolToWhitelist(_poolAnchor);
        else store.removePoolFromWhitelist(_poolAnchor);
    }

    /**
     * @dev checks if protection is supported for the given pool
     * only standard pools are supported (2 reserves, 50%/50% weights)
     * note that the pool should still be whitelisted
     *
     * @param _poolAnchor  anchor of the pool
     * @return true if the pool is supported, false otherwise
     */
    function isPoolSupported(IConverterAnchor _poolAnchor) public view returns (bool) {
        // save a local copy of `networkToken`
        IERC20Token networkTokenLocal = networkToken;

        // verify that the pool exists in the registry
        IConverterRegistry converterRegistry = IConverterRegistry(addressOf(CONVERTER_REGISTRY));
        require(converterRegistry.isAnchor(address(_poolAnchor)), "ERR_INVALID_ANCHOR");

        // get the converter
        IConverter converter = IConverter(payable(_poolAnchor.owner()));

        // verify that the converter has 2 reserves
        if (converter.connectorTokenCount() != 2) {
            return false;
        }

        // verify that one of the reserves is the network token
        IERC20Token reserve0Token = converter.connectorTokens(0);
        IERC20Token reserve1Token = converter.connectorTokens(1);
        if (reserve0Token != networkTokenLocal && reserve1Token != networkTokenLocal) {
            return false;
        }

        // verify that the reserve weights are exactly 50%/50%
        if (
            converterReserveWeight(converter, reserve0Token) != PPM_RESOLUTION / 2 ||
            converterReserveWeight(converter, reserve1Token) != PPM_RESOLUTION / 2
        ) {
            return false;
        }

        return true;
    }

    /**
     * @dev adds protection to existing pool tokens
     * also mints new governance tokens for the caller
     *
     * @param _poolAnchor  anchor of the pool
     * @param _amount      amount of pool tokens to protect
     */
    function protectLiquidity(IConverterAnchor _poolAnchor, uint256 _amount)
        external
        protected
        poolSupportedAndWhitelisted(_poolAnchor)
        greaterThanZero(_amount)
    {
        // get the converter
        IConverter converter = IConverter(payable(_poolAnchor.owner()));

        // save a local copy of `networkToken`
        IERC20Token networkTokenLocal = networkToken;

        // protect both reserves
        IDSToken poolToken = IDSToken(address(_poolAnchor));
        protectLiquidity(poolToken, converter, networkTokenLocal, 0, _amount / 2);
        protectLiquidity(poolToken, converter, networkTokenLocal, 1, _amount - _amount / 2);

        // transfer the pool tokens from the caller directly to the store
        safeTransferFrom(poolToken, msg.sender, address(store), _amount);
    }

    /**
     * @dev cancels the protection and returns the pool tokens to the caller
     * also burns governance tokens from the caller
     * must be called with the indices of both the base token and the network token protections
     *
     * @param _id1 id in the caller's list of protected liquidity
     * @param _id2 matching id in the caller's list of protected liquidity
     */
    function unprotectLiquidity(uint256 _id1, uint256 _id2) external protected {
        require(_id1 != _id2, "ERR_SAME_ID");

        ProtectedLiquidity memory liquidity1 = protectedLiquidity(_id1, msg.sender);
        ProtectedLiquidity memory liquidity2 = protectedLiquidity(_id2, msg.sender);

        // save a local copy of `networkToken`
        IERC20Token networkTokenLocal = networkToken;

        // verify that the two protections were added together (using `protect`)
        require(
            liquidity1.poolToken == liquidity2.poolToken &&
                liquidity1.reserveToken != liquidity2.reserveToken &&
                (liquidity1.reserveToken == networkTokenLocal || liquidity2.reserveToken == networkTokenLocal) &&
                liquidity1.timestamp == liquidity2.timestamp &&
                liquidity1.poolAmount <= liquidity2.poolAmount.add(1) &&
                liquidity2.poolAmount <= liquidity1.poolAmount.add(1),
            "ERR_PROTECTIONS_MISMATCH"
        );

        // burn the governance tokens from the caller. we need to transfer the tokens to the contract itself, since only
        // token holders can burn their tokens
        uint256 amount = liquidity1.reserveToken == networkTokenLocal ? liquidity1.reserveAmount : liquidity2.reserveAmount;
        safeTransferFrom(govToken, msg.sender, address(this), amount);
        govTokenGovernance.burn(amount);

        // remove the protected liquidities from the store
        store.removeProtectedLiquidity(_id1);
        store.removeProtectedLiquidity(_id2);

        // transfer the pool tokens back to the caller
        store.withdrawTokens(liquidity1.poolToken, msg.sender, liquidity1.poolAmount.add(liquidity2.poolAmount));
    }

    /**
     * @dev adds protected liquidity to a pool
     * also mints new governance tokens for the caller if the caller adds network tokens
     *
     * @param _poolAnchor      anchor of the pool
     * @param _reserveToken    reserve token to add to the pool
     * @param _amount          amount of tokens to add to the pool
     * @return new protected liquidity id
     */
    function addLiquidity(
        IConverterAnchor _poolAnchor,
        IERC20Token _reserveToken,
        uint256 _amount
    ) external payable protected poolSupportedAndWhitelisted(_poolAnchor) greaterThanZero(_amount) returns (uint256) {
        // save a local copy of `networkToken`
        IERC20Token networkTokenLocal = networkToken;

        if (_reserveToken == networkTokenLocal) {
            require(msg.value == 0, "ERR_ETH_AMOUNT_MISMATCH");
            return addNetworkTokenLiquidity(_poolAnchor, networkTokenLocal, _amount);
        }

        // verify that ETH was passed with the call if needed
        uint256 val = _reserveToken == ETH_RESERVE_ADDRESS ? _amount : 0;
        require(msg.value == val, "ERR_ETH_AMOUNT_MISMATCH");
        return addBaseTokenLiquidity(_poolAnchor, _reserveToken, networkTokenLocal, _amount);
    }

    /**
     * @dev adds protected network token liquidity to a pool
     * also mints new governance tokens for the caller
     *
     * @param _poolAnchor   anchor of the pool
     * @param _networkToken the network reserve token of the pool
     * @param _amount       amount of tokens to add to the pool
     * @return new protected liquidity id
     */
    function addNetworkTokenLiquidity(IConverterAnchor _poolAnchor, IERC20Token _networkToken, uint256 _amount) internal returns (uint256) {
        IDSToken poolToken = IDSToken(address(_poolAnchor));

        // get the rate between the pool token and the reserve
        Fraction memory poolRate = poolTokenRate(poolToken, _networkToken);

        // calculate the amount of pool tokens based on the amount of reserve tokens
        uint256 poolTokenAmount = _amount.mul(poolRate.d).div(poolRate.n);

        // remove the pool tokens from the system's ownership (will revert if not enough tokens are available)
        store.decSystemBalance(poolToken, poolTokenAmount);

        // add protected liquidity for the caller
        uint256 id = addProtectedLiquidity(msg.sender, poolToken, _networkToken, poolTokenAmount, _amount);

        // burns the network tokens from the caller. we need to transfer the tokens to the contract itself, since only
        // token holders can burn their tokens
        safeTransferFrom(_networkToken, msg.sender, address(this), _amount);
        networkTokenGovernance.burn(_amount);

        // mint governance tokens to the caller
        govTokenGovernance.mint(msg.sender, _amount);

        return id;
    }

    /**
     * @dev adds protected base token liquidity to a pool
     *
     * @param _poolAnchor   anchor of the pool
     * @param _baseToken    the base reserve token of the pool
     * @param _networkToken the network reserve token of the pool
     * @param _amount       amount of tokens to add to the pool
     * @return new protected liquidity id
     */
    function addBaseTokenLiquidity(
        IConverterAnchor _poolAnchor,
        IERC20Token _baseToken,
        IERC20Token _networkToken,
        uint256 _amount
    ) internal returns (uint256) {
        IDSToken poolToken = IDSToken(address(_poolAnchor));

        // get the reserve balances
        ILiquidityPoolV1Converter converter = ILiquidityPoolV1Converter(payable(_poolAnchor.owner()));
        (uint256 reserveBalanceBase, uint256 reserveBalanceNetwork) = converterReserveBalances(
            converter,
            _baseToken,
            _networkToken
        );

        // calculate and mint the required amount of network tokens for adding liquidity
        uint256 networkLiquidityAmount = _amount.mul(reserveBalanceNetwork).div(reserveBalanceBase);

        // verify network token limits
        // note that the amount is divided by 2 since it's not possible to liquidate one reserve only
        Fraction memory poolRate = poolTokenRate(poolToken, _networkToken);
        uint256 newSystemBalance = store.systemBalance(poolToken);
        newSystemBalance = (newSystemBalance.mul(poolRate.n / 2).div(poolRate.d)).add(networkLiquidityAmount);

        require(newSystemBalance <= maxSystemNetworkTokenAmount, "ERR_MAX_AMOUNT_REACHED");
        require(
            newSystemBalance.mul(PPM_RESOLUTION) <=
                newSystemBalance.add(reserveBalanceNetwork).mul(maxSystemNetworkTokenRatio),
            "ERR_MAX_RATIO_REACHED"
        );

        // issue new network tokens to the system
        networkTokenGovernance.mint(address(this), networkLiquidityAmount);

        // transfer the base tokens from the caller and approve the converter
        ensureAllowance(_networkToken, address(converter), networkLiquidityAmount);
        if (_baseToken != ETH_RESERVE_ADDRESS) {
            safeTransferFrom(_baseToken, msg.sender, address(this), _amount);
            ensureAllowance(_baseToken, address(converter), _amount);
        }

        // add liquidity
        addLiquidity(converter, _baseToken, _networkToken, _amount, networkLiquidityAmount, msg.value);

        // transfer the new pool tokens to the store
        uint256 poolTokenAmount = poolToken.balanceOf(address(this));
        safeTransfer(poolToken, address(store), poolTokenAmount);

        // the system splits the pool tokens with the caller
        // increase the system's pool token balance and add protected liquidity for the caller
        store.incSystemBalance(poolToken, poolTokenAmount - poolTokenAmount / 2); // account for rounding errors
        return addProtectedLiquidity(msg.sender, poolToken, _baseToken, poolTokenAmount / 2, _amount);
    }

    /**
     * @dev transfers protected liquidity to a new provider
     *
     * @param _id          protected liquidity id
     * @param _newProvider new provider
     * @return new protected liquidity id
     */
    function transferLiquidity(uint256 _id, address _newProvider)
        external
        protected
        validAddress(_newProvider)
        notThis(_newProvider)
        returns (uint256)
    {
        ProtectedLiquidity memory liquidity = protectedLiquidity(_id, msg.sender);

        // remove the protected liquidity from the current provider
        store.removeProtectedLiquidity(_id);

        // add the protected liquidity to the new provider
        return
            store.addProtectedLiquidity(
                _newProvider,
                liquidity.poolToken,
                liquidity.reserveToken,
                liquidity.poolAmount,
                liquidity.reserveAmount,
                liquidity.reserveRateN,
                liquidity.reserveRateD,
                liquidity.timestamp
            );
    }

    /**
     * @dev returns the expected/actual amounts the provider will receive for removing liquidity
     * it's also possible to provide the remove liquidity time to get an estimation
     * for the return at that given point
     *
     * @param _id              protected liquidity id
     * @param _portion         portion of liquidity to remove, in PPM
     * @param _removeTimestamp time at which the liquidity is removed
     * @return expected return amount in the reserve token
     * @return actual return amount in the reserve token
     * @return compensation in the network token
     */
    function removeLiquidityReturn(
        uint256 _id,
        uint32 _portion,
        uint256 _removeTimestamp
    )
        external
        view
        validPortion(_portion)
        returns (
            uint256,
            uint256,
            uint256
        )
    {
        ProtectedLiquidity memory liquidity = protectedLiquidity(_id);

        // verify input
        require(liquidity.provider != address(0), "ERR_INVALID_ID");
        require(_removeTimestamp >= liquidity.timestamp, "ERR_INVALID_TIMESTAMP");

        // calculate the portion of the liquidity to remove
        if (_portion != PPM_RESOLUTION) {
            liquidity.poolAmount = liquidity.poolAmount.mul(_portion) / PPM_RESOLUTION;
            liquidity.reserveAmount = liquidity.reserveAmount.mul(_portion) / PPM_RESOLUTION;
        }

        // get the various rates between the reserves upon adding liquidity and now
        PackedRates memory packedRates = packRates(
            liquidity.poolToken,
            liquidity.reserveToken,
            liquidity.reserveRateN,
            liquidity.reserveRateD
        );

        uint256 targetAmount = removeLiquidityTargetAmount(
            liquidity.poolToken,
            liquidity.reserveToken,
            liquidity.poolAmount,
            liquidity.reserveAmount,
            packedRates,
            liquidity.timestamp,
            _removeTimestamp
        );

        // for network token, the return amount is identical to the target amount
        if (liquidity.reserveToken == networkToken) {
            return (targetAmount, targetAmount, 0);
        }

        // handle base token return

        // calculate the amount of pool tokens required for liquidation
        // note that the amount is doubled since it's not possible to liquidate one reserve only
        Fraction memory poolRate = poolTokenRate(liquidity.poolToken, liquidity.reserveToken);
        uint256 poolAmount = targetAmount.mul(poolRate.d).div(poolRate.n / 2);

        // limit the amount of pool tokens by the amount the system/caller holds
        uint256 availableBalance = store.systemBalance(liquidity.poolToken).add(liquidity.poolAmount);
        poolAmount = poolAmount > availableBalance ? availableBalance : poolAmount;

        // calculate the base token amount received by liquidating the pool tokens
        // note that the amount is divided by 2 since the pool amount represents both reserves
        uint256 baseAmount = poolAmount.mul(poolRate.n / 2).div(poolRate.d);
        uint256 networkAmount = getNetworkCompensation(targetAmount, baseAmount, packedRates);

        return (targetAmount, baseAmount, networkAmount);
    }

    /**
     * @dev removes protected liquidity from a pool
     * also burns governance tokens from the caller if the caller removes network tokens
     *
     * @param _id      id in the caller's list of protected liquidity
     * @param _portion portion of liquidity to remove, in PPM
     */
    function removeLiquidity(uint256 _id, uint32 _portion) external validPortion(_portion) protected {
        ProtectedLiquidity memory liquidity = protectedLiquidity(_id, msg.sender);

        // save a local copy of `networkToken`
        IERC20Token networkTokenLocal = networkToken;

        // verify that the pool is whitelisted
        require(store.isPoolWhitelisted(liquidity.poolToken), "ERR_POOL_NOT_WHITELISTED");

        if (_portion == PPM_RESOLUTION) {
            // remove the pool tokens from the provider
            store.removeProtectedLiquidity(_id);
        } else {
            // remove portion of the pool tokens from the provider
            uint256 fullPoolAmount = liquidity.poolAmount;
            uint256 fullReserveAmount = liquidity.reserveAmount;
            liquidity.poolAmount = liquidity.poolAmount.mul(_portion) / PPM_RESOLUTION;
            liquidity.reserveAmount = liquidity.reserveAmount.mul(_portion) / PPM_RESOLUTION;

            store.updateProtectedLiquidityAmounts(
                _id,
                fullPoolAmount - liquidity.poolAmount,
                fullReserveAmount - liquidity.reserveAmount
            );
        }

        // add the pool tokens to the system
        store.incSystemBalance(liquidity.poolToken, liquidity.poolAmount);

        // if removing network token liquidity, burn the governance tokens from the caller. we need to transfer the
        // tokens to the contract itself, since only token holders can burn their tokens
        if (liquidity.reserveToken == networkTokenLocal) {
            safeTransferFrom(govToken, msg.sender, address(this), liquidity.reserveAmount);
            govTokenGovernance.burn(liquidity.reserveAmount);
        }

        // get the various rates between the reserves upon adding liquidity and now
        PackedRates memory packedRates = packRates(
            liquidity.poolToken,
            liquidity.reserveToken,
            liquidity.reserveRateN,
            liquidity.reserveRateD
        );

        // get the target token amount
        uint256 targetAmount = removeLiquidityTargetAmount(
            liquidity.poolToken,
            liquidity.reserveToken,
            liquidity.poolAmount,
            liquidity.reserveAmount,
            packedRates,
            liquidity.timestamp,
            time()
        );

        // remove network token liquidity
        if (liquidity.reserveToken == networkTokenLocal) {
            // mint network tokens for the caller and lock them
            networkTokenGovernance.mint(address(store), targetAmount);
            lockTokens(msg.sender, targetAmount);
            return;
        }

        // remove base token liquidity

        // calculate the amount of pool tokens required for liquidation
        // note that the amount is doubled since it's not possible to liquidate one reserve only
        Fraction memory poolRate = poolTokenRate(liquidity.poolToken, liquidity.reserveToken);
        uint256 poolAmount = targetAmount.mul(poolRate.d).div(poolRate.n / 2);

        // limit the amount of pool tokens by the amount the system holds
        uint256 systemBalance = store.systemBalance(liquidity.poolToken);
        poolAmount = poolAmount > systemBalance ? systemBalance : poolAmount;

        // withdraw the pool tokens from the store
        store.decSystemBalance(liquidity.poolToken, poolAmount);
        store.withdrawTokens(liquidity.poolToken, address(this), poolAmount);

        // remove liquidity
        removeLiquidity(liquidity.poolToken, poolAmount, liquidity.reserveToken, networkTokenLocal);

        // transfer the base tokens to the caller
        uint256 baseBalance;
        if (liquidity.reserveToken == ETH_RESERVE_ADDRESS) {
            baseBalance = address(this).balance;
            msg.sender.transfer(baseBalance);
        } else {
            baseBalance = liquidity.reserveToken.balanceOf(address(this));
            safeTransfer(liquidity.reserveToken, msg.sender, baseBalance);
        }

        // compensate the caller with network tokens if still needed
        uint256 delta = getNetworkCompensation(targetAmount, baseBalance, packedRates);
        if (delta > 0) {
            // check if there's enough network token balance, otherwise mint more
            uint256 networkBalance = networkTokenLocal.balanceOf(address(this));
            if (networkBalance < delta) {
                networkTokenGovernance.mint(address(this), delta - networkBalance);
            }

            // lock network tokens for the caller
            safeTransfer(networkTokenLocal, address(store), delta);
            lockTokens(msg.sender, delta);
        }

        // if the contract still holds network token, burn them
        uint256 networkBalance = networkTokenLocal.balanceOf(address(this));
        if (networkBalance > 0) {
            networkTokenGovernance.burn(networkBalance);
        }
    }

    /**
     * @dev returns the amount the provider will receive for removing liquidity
     * it's also possible to provide the remove liquidity rate & time to get an estimation
     * for the return at that given point
     *
     * @param _poolToken       pool token
     * @param _reserveToken    reserve token
     * @param _poolAmount      pool token amount when the liquidity was added
     * @param _reserveAmount   reserve token amount that was added
     * @param _packedRates     see `struct PackedRates`
     * @param _addTimestamp    time at which the liquidity was added
     * @param _removeTimestamp time at which the liquidity is removed
     * @return amount received for removing liquidity
     */
    function removeLiquidityTargetAmount(
        IDSToken _poolToken,
        IERC20Token _reserveToken,
        uint256 _poolAmount,
        uint256 _reserveAmount,
        PackedRates memory _packedRates,
        uint256 _addTimestamp,
        uint256 _removeTimestamp
    ) internal view returns (uint256) {
        // get the rate between the reserves upon adding liquidity and now
        Fraction memory addSpotRate = Fraction({ n: _packedRates.addSpotRateN, d: _packedRates.addSpotRateD });
        Fraction memory removeSpotRate = Fraction({ n: _packedRates.removeSpotRateN, d: _packedRates.removeSpotRateD });
        Fraction memory removeAverageRate = Fraction({
            n: _packedRates.removeAverageRateN,
            d: _packedRates.removeAverageRateD
        });

        // calculate the protected amount of reserve tokens plus accumulated fee before compensation
        uint256 total = protectedAmountPlusFee(_poolToken, _reserveToken, _poolAmount, addSpotRate, removeSpotRate);
        if (total < _reserveAmount) {
            total = _reserveAmount;
        }

        // calculate the impermanent loss
        Fraction memory loss = impLoss(addSpotRate, removeAverageRate);

        // calculate the protection level
        Fraction memory level = protectionLevel(_addTimestamp, _removeTimestamp);

        // calculate the compensation amount
        return compensationAmount(_reserveAmount, total, loss, level);
    }

    /**
     * @dev allows the caller to claim network token balance that is no longer locked
     * note that the function can revert if the range is too large
     *
     * @param _startIndex  start index in the caller's list of locked balances
     * @param _endIndex    end index in the caller's list of locked balances (exclusive)
     */
    function claimBalance(uint256 _startIndex, uint256 _endIndex) external protected {
        // get the locked balances from the store
        (uint256[] memory amounts, uint256[] memory expirationTimes) = store.lockedBalanceRange(
            msg.sender,
            _startIndex,
            _endIndex
        );

        uint256 totalAmount = 0;
        uint256 length = amounts.length;
        assert(length == expirationTimes.length);

        // reverse iteration since we're removing from the list
        for (uint256 i = length; i > 0; i--) {
            uint256 index = i - 1;
            if (expirationTimes[index] > time()) {
                continue;
            }

            // remove the locked balance item
            store.removeLockedBalance(msg.sender, _startIndex + index);
            totalAmount = totalAmount.add(amounts[index]);
        }

        if (totalAmount > 0) {
            // transfer the tokens to the caller in a single call
            store.withdrawTokens(networkToken, msg.sender, totalAmount);
        }
    }

    /**
     * @dev returns the ROI for removing liquidity in the current state after providing liquidity with the given args
     * the function assumes full protection is in effect
     * return value is in PPM and can be larger than PPM_RESOLUTION for positive ROI, 1M = 0% ROI
     *
     * @param _poolToken       pool token
     * @param _reserveToken    reserve token
     * @param _reserveAmount   reserve token amount that was added
     * @param _poolRateN       rate of 1 pool token in reserve token units when the liquidity was added (numerator)
     * @param _poolRateD       rate of 1 pool token in reserve token units when the liquidity was added (denominator)
     * @param _reserveRateN    rate of 1 reserve token in the other reserve token units when the liquidity was added (numerator)
     * @param _reserveRateD    rate of 1 reserve token in the other reserve token units when the liquidity was added (denominator)
     * @return ROI in PPM
     */
    function poolROI(
        IDSToken _poolToken,
        IERC20Token _reserveToken,
        uint256 _reserveAmount,
        uint256 _poolRateN,
        uint256 _poolRateD,
        uint256 _reserveRateN,
        uint256 _reserveRateD
    ) external view returns (uint256) {
        // calculate the amount of pool tokens based on the amount of reserve tokens
        uint256 poolAmount = _reserveAmount.mul(_poolRateD).div(_poolRateN);

        // get the various rates between the reserves upon adding liquidity and now
        PackedRates memory packedRates = packRates(_poolToken, _reserveToken, _reserveRateN, _reserveRateD);

        // get the current return
        uint256 protectedReturn = removeLiquidityTargetAmount(
            _poolToken,
            _reserveToken,
            poolAmount,
            _reserveAmount,
            packedRates,
            time().sub(maxProtectionDelay),
            time()
        );

        // calculate the ROI as the ratio between the current fully protected return and the initial amount
        return protectedReturn.mul(PPM_RESOLUTION).div(_reserveAmount);
    }

    /**
     * @dev utility to protect existing liquidity
     * also mints new governance tokens for the caller when protecting the network token reserve
     *
     * @param _poolAnchor      pool anchor
     * @param _converter       pool converter
     * @param _networkToken    the network reserve token of the pool
     * @param _reserveIndex    index of the reserve to protect
     * @param _poolAmount      amount of pool tokens to protect
     */
    function protectLiquidity(
        IDSToken _poolAnchor,
        IConverter _converter,
        IERC20Token _networkToken,
        uint256 _reserveIndex,
        uint256 _poolAmount
    ) internal {
        // get the reserves token
        IERC20Token reserveToken = _converter.connectorTokens(_reserveIndex);

        // get the pool token rate
        IDSToken poolToken = IDSToken(address(_poolAnchor));
        Fraction memory poolRate = poolTokenRate(poolToken, reserveToken);

        // calculate the reserve balance based on the amount provided and the pool token rate
        uint256 reserveAmount = _poolAmount.mul(poolRate.n).div(poolRate.d);

        // protect the liquidity
        addProtectedLiquidity(msg.sender, poolToken, reserveToken, _poolAmount, reserveAmount);

        // for network token liquidity, mint governance tokens to the caller
        if (reserveToken == _networkToken) {
            govTokenGovernance.mint(msg.sender, reserveAmount);
        }
    }

    /**
     * @dev adds protected liquidity for the caller to the store
     *
     * @param _provider        protected liquidity provider
     * @param _poolToken       pool token
     * @param _reserveToken    reserve token
     * @param _poolAmount      amount of pool tokens to protect
     * @param _reserveAmount   amount of reserve tokens to protect
     * @return new protected liquidity id
     */
    function addProtectedLiquidity(
        address _provider,
        IDSToken _poolToken,
        IERC20Token _reserveToken,
        uint256 _poolAmount,
        uint256 _reserveAmount
    ) internal returns (uint256) {
        Fraction memory rate = reserveTokenAverageRate(_poolToken, _reserveToken);
        return
            store.addProtectedLiquidity(
                _provider,
                _poolToken,
                _reserveToken,
                _poolAmount,
                _reserveAmount,
                rate.n,
                rate.d,
                time()
            );
    }

    /**
     * @dev locks network tokens for the provider and emits the tokens locked event
     *
     * @param _provider    tokens provider
     * @param _amount      amount of network tokens
     */
    function lockTokens(address _provider, uint256 _amount) internal {
        uint256 expirationTime = time().add(lockDuration);
        store.addLockedBalance(_provider, _amount, expirationTime);
    }

    /**
     * @dev returns the rate of 1 pool token in reserve token units
     *
     * @param _poolToken       pool token
     * @param _reserveToken    reserve token
     */
    function poolTokenRate(IDSToken _poolToken, IERC20Token _reserveToken) internal view returns (Fraction memory) {
        // get the pool token supply
        uint256 poolTokenSupply = _poolToken.totalSupply();

        // get the reserve balance
        IConverter converter = IConverter(payable(_poolToken.owner()));
        uint256 reserveBalance = converter.getConnectorBalance(_reserveToken);

        // for standard pools, 50% of the pool supply value equals the value of each reserve
        return Fraction({ n: reserveBalance.mul(2), d: poolTokenSupply });
    }

    /**
     * @dev returns the average rate of 1 reserve token in the other reserve token units
     *
     * @param _poolToken       pool token
     * @param _reserveToken    reserve token
     */
    function reserveTokenAverageRate(IDSToken _poolToken, IERC20Token _reserveToken)
        internal
        view
        returns (Fraction memory)
    {
        (, , uint256 averageRateN, uint256 averageRateD) = reserveTokenRates(_poolToken, _reserveToken);
        return Fraction(averageRateN, averageRateD);
    }

    /**
     * @dev returns the spot rate and average rate of 1 reserve token in the other reserve token units
     *
     * @param _poolToken       pool token
     * @param _reserveToken    reserve token
     */
    function reserveTokenRates(IDSToken _poolToken, IERC20Token _reserveToken)
        internal
        view
        returns (
            uint256,
            uint256,
            uint256,
            uint256
        )
    {
        ILiquidityPoolV1Converter converter = ILiquidityPoolV1Converter(payable(_poolToken.owner()));

        IERC20Token otherReserve = converter.connectorTokens(0);
        if (otherReserve == _reserveToken) {
            otherReserve = converter.connectorTokens(1);
        }

        (uint256 spotRateN, uint256 spotRateD) = converterReserveBalances(converter, otherReserve, _reserveToken);
        (uint256 averageRateN, uint256 averageRateD) = converter.recentAverageRate(_reserveToken);

        require(
            averageRateInRange(spotRateN, spotRateD, averageRateN, averageRateD, averageRateMaxDeviation),
            "ERR_INVALID_RATE"
        );

        return (spotRateN, spotRateD, averageRateN, averageRateD);
    }

    /**
     * @dev returns the various rates between the reserves
     *
     * @param _poolToken       pool token
     * @param _reserveToken    reserve token
     * @param _addSpotRateN    add spot rate numerator
     * @param _addSpotRateD    add spot rate denominator
     * @return see `struct PackedRates`
     */
    function packRates(
        IDSToken _poolToken,
        IERC20Token _reserveToken,
        uint256 _addSpotRateN,
        uint256 _addSpotRateD
    ) internal view returns (PackedRates memory) {
        (
            uint256 removeSpotRateN,
            uint256 removeSpotRateD,
            uint256 removeAverageRateN,
            uint256 removeAverageRateD
        ) = reserveTokenRates(_poolToken, _reserveToken);

        require(
            (_addSpotRateN <= MAX_UINT128 && _addSpotRateD <= MAX_UINT128) &&
                (removeSpotRateN <= MAX_UINT128 && removeSpotRateD <= MAX_UINT128) &&
                (removeAverageRateN <= MAX_UINT128 && removeAverageRateD <= MAX_UINT128),
            "ERR_INVALID_RATE"
        );

        return
            PackedRates({
                addSpotRateN: uint128(_addSpotRateN),
                addSpotRateD: uint128(_addSpotRateD),
                removeSpotRateN: uint128(removeSpotRateN),
                removeSpotRateD: uint128(removeSpotRateD),
                removeAverageRateN: uint128(removeAverageRateN),
                removeAverageRateD: uint128(removeAverageRateD)
            });
    }

    /**
     * @dev returns whether or not the deviation of the average rate from the spot rate is within range
     * for example, if the maximum permitted deviation is 5%, then return `95/100 <= average/spot <= 100/95`
     *
     * @param _spotRateN       spot rate numerator
     * @param _spotRateD       spot rate denominator
     * @param _averageRateN    average rate numerator
     * @param _averageRateD    average rate denominator
     * @param _maxDeviation    the maximum permitted deviation of the average rate from the spot rate
     */
    function averageRateInRange(
        uint256 _spotRateN,
        uint256 _spotRateD,
        uint256 _averageRateN,
        uint256 _averageRateD,
        uint32 _maxDeviation
    ) internal pure returns (bool) {
        uint256 min = _spotRateN.mul(_averageRateD).mul(PPM_RESOLUTION - _maxDeviation).mul(
            PPM_RESOLUTION - _maxDeviation
        );
        uint256 mid = _spotRateD.mul(_averageRateN).mul(PPM_RESOLUTION - _maxDeviation).mul(PPM_RESOLUTION);
        uint256 max = _spotRateN.mul(_averageRateD).mul(PPM_RESOLUTION).mul(PPM_RESOLUTION);
        return min <= mid && mid <= max;
    }

    /**
     * @dev utility to add liquidity to a converter
     *
     * @param _converter       converter
     * @param _reserveToken1   reserve token 1
     * @param _reserveToken2   reserve token 2
     * @param _reserveAmount1  reserve amount 1
     * @param _reserveAmount2  reserve amount 2
     * @param _value           ETH amount to add
     */
    function addLiquidity(
        ILiquidityPoolV1Converter _converter,
        IERC20Token _reserveToken1,
        IERC20Token _reserveToken2,
        uint256 _reserveAmount1,
        uint256 _reserveAmount2,
        uint256 _value
    ) internal {
        IERC20Token[] memory reserveTokens = new IERC20Token[](2);
        uint256[] memory amounts = new uint256[](2);
        reserveTokens[0] = _reserveToken1;
        reserveTokens[1] = _reserveToken2;
        amounts[0] = _reserveAmount1;
        amounts[1] = _reserveAmount2;

        // ensure that the contract can receive ETH
        updatingLiquidity = true;
        _converter.addLiquidity{ value: _value }(reserveTokens, amounts, 1);
        updatingLiquidity = false;
    }

    /**
     * @dev utility to remove liquidity from a converter
     *
     * @param _poolToken       pool token of the converter
     * @param _poolAmount      amount of pool tokens to remove
     * @param _reserveToken1   reserve token 1
     * @param _reserveToken2   reserve token 2
     */
    function removeLiquidity(
        IDSToken _poolToken,
        uint256 _poolAmount,
        IERC20Token _reserveToken1,
        IERC20Token _reserveToken2
    ) internal {
        ILiquidityPoolV1Converter converter = ILiquidityPoolV1Converter(payable(_poolToken.owner()));

        IERC20Token[] memory reserveTokens = new IERC20Token[](2);
        uint256[] memory minReturns = new uint256[](2);
        reserveTokens[0] = _reserveToken1;
        reserveTokens[1] = _reserveToken2;
        minReturns[0] = 1;
        minReturns[1] = 1;

        // ensure that the contract can receive ETH
        updatingLiquidity = true;
        converter.removeLiquidity(_poolAmount, reserveTokens, minReturns);
        updatingLiquidity = false;
    }

    /**
     * @dev returns a protected liquidity from the store
     *
     * @param _id  protected liquidity id
     * @return protected liquidity
     */
    function protectedLiquidity(uint256 _id) internal view returns (ProtectedLiquidity memory) {
        ProtectedLiquidity memory liquidity;
        (
            liquidity.provider,
            liquidity.poolToken,
            liquidity.reserveToken,
            liquidity.poolAmount,
            liquidity.reserveAmount,
            liquidity.reserveRateN,
            liquidity.reserveRateD,
            liquidity.timestamp
        ) = store.protectedLiquidity(_id);

        return liquidity;
    }

    /**
     * @dev returns a protected liquidity from the store
     *
     * @param _id          protected liquidity id
     * @param _provider    authorized provider
     * @return protected liquidity
     */
    function protectedLiquidity(uint256 _id, address _provider) internal view returns (ProtectedLiquidity memory) {
        ProtectedLiquidity memory liquidity = protectedLiquidity(_id);
        require(liquidity.provider == _provider, "ERR_ACCESS_DENIED");
        return liquidity;
    }

    /**
     * @dev returns the protected amount of reserve tokens plus accumulated fee before compensation
     *
     * @param _poolToken       pool token
     * @param _reserveToken    reserve token
     * @param _poolAmount      pool token amount when the liquidity was added
     * @param _addRate         rate of 1 reserve token in the other reserve token units when the liquidity was added
     * @param _removeRate      rate of 1 reserve token in the other reserve token units when the liquidity is removed
     * @return protected amount of reserve tokens plus accumulated fee = sqrt(_removeRate / _addRate) * poolRate * _poolAmount
     */
    function protectedAmountPlusFee(
        IDSToken _poolToken,
        IERC20Token _reserveToken,
        uint256 _poolAmount,
        Fraction memory _addRate,
        Fraction memory _removeRate
    ) internal view returns (uint256) {
        Fraction memory poolRate = poolTokenRate(_poolToken, _reserveToken);
        uint256 n = Math.ceilSqrt(_addRate.d.mul(_removeRate.n)).mul(poolRate.n);
        uint256 d = Math.floorSqrt(_addRate.n.mul(_removeRate.d)).mul(poolRate.d);

        uint256 x = n * _poolAmount;
        if (x / n == _poolAmount) {
            return x / d;
        }

        (uint256 hi, uint256 lo) = n > _poolAmount ? (n, _poolAmount) : (_poolAmount, n);
        (uint256 p, uint256 q) = Math.reducedRatio(hi, d, uint256(-1) / lo);
        return (p * lo) / q;
    }

    /**
     * @dev returns the impermanent loss incurred due to the change in rates between the reserve tokens
     *
     * @param _prevRate    previous rate between the reserves
     * @param _newRate     new rate between the reserves
     * @return impermanent loss (as a ratio)
     */
    function impLoss(Fraction memory _prevRate, Fraction memory _newRate) internal pure returns (Fraction memory) {
        uint256 ratioN = _newRate.n.mul(_prevRate.d);
        uint256 ratioD = _newRate.d.mul(_prevRate.n);

        // no need for SafeMath - can't overflow
        uint256 prod = ratioN * ratioD;
        uint256 root = prod / ratioN == ratioD ? Math.floorSqrt(prod) : Math.floorSqrt(ratioN) * Math.floorSqrt(ratioD);
        uint256 sum = ratioN.add(ratioD);
        return Fraction({ n: sum.sub(root.mul(2)), d: sum });
    }

    /**
     * @dev returns the protection level based on the timestamp and protection delays
     *
     * @param _addTimestamp    time at which the liquidity was added
     * @param _removeTimestamp time at which the liquidity is removed
     * @return protection level (as a ratio)
     */
    function protectionLevel(uint256 _addTimestamp, uint256 _removeTimestamp) internal view returns (Fraction memory) {
        uint256 timeElapsed = _removeTimestamp.sub(_addTimestamp);
        if (timeElapsed < minProtectionDelay) {
            return Fraction({ n: 0, d: 1 });
        }

        if (timeElapsed >= maxProtectionDelay) {
            return Fraction({ n: 1, d: 1 });
        }

        return Fraction({ n: timeElapsed, d: maxProtectionDelay });
    }

    /**
     * @dev returns the compensation amount based on the impermanent loss and the protection level
     *
     * @param _amount  protected amount in units of the reserve token
     * @param _total   amount plus fee in units of the reserve token
     * @param _loss    protection level (as a ratio between 0 and 1)
     * @param _level   impermanent loss (as a ratio between 0 and 1)
     * @return compensation amount
     */
    function compensationAmount(
        uint256 _amount,
        uint256 _total,
        Fraction memory _loss,
        Fraction memory _level
    ) internal pure returns (uint256) {
        (uint256 lossN, uint256 lossD) = Math.reducedRatio(_loss.n, _loss.d, MAX_UINT128);
        return _total.mul(lossD.sub(lossN)).div(lossD).add(_amount.mul(lossN.mul(_level.n)).div(lossD.mul(_level.d)));
    }

    function getNetworkCompensation(
        uint256 _targetAmount,
        uint256 _baseAmount,
        PackedRates memory _packedRates
    ) internal view returns (uint256) {
        if (_targetAmount <= _baseAmount) {
            return 0;
        }

        // calculate the delta in network tokens
        uint256 delta = (_targetAmount - _baseAmount).mul(_packedRates.removeAverageRateN).div(
            _packedRates.removeAverageRateD
        );

        // the delta might be very small due to precision loss
        // in which case no compensation will take place (gas optimization)
        if (delta >= _minNetworkCompensation()) {
            return delta;
        }

        return 0;
    }

    /**
     * @dev transfers the ownership of a contract
     * can only be called by the contract owner
     *
     * @param _owned       the owned contract
     * @param _newOwner    the new owner of the contract
     */
    function transferOwnership(IOwned _owned, address _newOwner) internal ownerOnly {
        _owned.transferOwnership(_newOwner);
    }

    /**
     * @dev accepts the ownership of a contract
     * can only be called by the contract owner
     */
    function acceptOwnership(IOwned _owned) internal ownerOnly {
        _owned.acceptOwnership();
    }

    /**
     * @dev utility, checks whether allowance for the given spender exists and approves one if it doesn't.
     * note that we use the non standard erc-20 interface in which `approve` has no return value so that
     * this function will work for both standard and non standard tokens
     *
     * @param _token   token to check the allowance in
     * @param _spender approved address
     * @param _value   allowance amount
     */
    function ensureAllowance(
        IERC20Token _token,
        address _spender,
        uint256 _value
    ) private {
        uint256 allowance = _token.allowance(address(this), _spender);
        if (allowance < _value) {
            if (allowance > 0) safeApprove(_token, _spender, 0);
            safeApprove(_token, _spender, _value);
        }
    }

    // utility to get the reserve balances
    function converterReserveBalances(
        IConverter _converter,
        IERC20Token _reserveToken1,
        IERC20Token _reserveToken2
    ) private view returns (uint256, uint256) {
        return (_converter.getConnectorBalance(_reserveToken1), _converter.getConnectorBalance(_reserveToken2));
    }

    // utility to get the reserve weight (including from older converters that don't support the new converterReserveWeight function)
    function converterReserveWeight(IConverter _converter, IERC20Token _reserveToken) private view returns (uint32) {
        (, uint32 weight, , , ) = _converter.connectors(_reserveToken);
        return weight;
    }

    /**
     * @dev returns minimum network tokens compensation
     * utility to allow overrides for tests
     */
    function _minNetworkCompensation() internal view virtual returns (uint256) {
        return minNetworkCompensation;
    }

    /**
     * @dev returns the current time
     * utility to allow overrides for tests
     */
    function time() internal view virtual returns (uint256) {
        return block.timestamp;
    }
}