// SPDX-License-Identifier: MIT

pragma solidity 0.6.11;

// Common interface for the Pools.
interface IPool {
    
    // --- Events ---
    
    event ETHBalanceUpdated(uint _newBalance);
    event RUBCBalanceUpdated(uint _newBalance);
    event ActivePoolAddressChanged(address _newActivePoolAddress);
    event DefaultPoolAddressChanged(address _newDefaultPoolAddress);
    event StabilityPoolAddressChanged(address _newStabilityPoolAddress);
    event EtherSent(address _to, uint _amount);

    // --- Functions ---
    
    function getETH() external view returns (uint);

    function getRUBCDebt() external view returns (uint);

    function increaseRUBCDebt(uint _amount) external;

    function decreaseRUBCDebt(uint _amount) external;
}

library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");

        return c;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        return sub(a, b, "SafeMath: subtraction overflow");
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     * - Subtraction cannot overflow.
     *
     * _Available since v2.4.0._
     */
    function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        uint256 c = a - b;

        return c;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) {
            return 0;
        }

        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");

        return c;
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        return div(a, b, "SafeMath: division by zero");
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     * - The divisor cannot be zero.
     *
     * _Available since v2.4.0._
     */
    function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        // Solidity only automatically asserts when dividing by 0
        require(b > 0, errorMessage);
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold

        return c;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        return mod(a, b, "SafeMath: modulo by zero");
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts with custom message when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     * - The divisor cannot be zero.
     *
     * _Available since v2.4.0._
     */
    function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b != 0, errorMessage);
        return a % b;
    }
}

interface ILiquityBase {
    function priceFeed() external view returns (IPriceFeed);
}

interface IERC2612 {
    /**
     * @dev Sets `amount` as the allowance of `spender` over `owner`'s tokens,
     * given `owner`'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     */
    function permit(address owner, address spender, uint256 amount, 
                    uint256 deadline, uint8 v, bytes32 r, bytes32 s) external;
    
    /**
     * @dev Returns the current ERC2612 nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases `owner`'s nonce by one. This
     * prevents a signature from being used multiple times.
     *
     * `owner` can limit the time a Permit is valid for by setting `deadline` to 
     * a value in the near future. The deadline argument can be set to uint(-1) to 
     * create Permits that effectively never expire.
     */
    function nonces(address owner) external view returns (uint256);
    
    function version() external view returns (string memory);
    function permitTypeHash() external view returns (bytes32);
    function domainSeparator() external view returns (bytes32);
}

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);
    function increaseAllowance(address spender, uint256 addedValue) external returns (bool);
    function decreaseAllowance(address spender, uint256 subtractedValue) external returns (bool);

    /**
     * @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);

    function name() external view returns (string memory);
    function symbol() external view returns (string memory);
    function decimals() external view returns (uint8);
    
    /**
     * @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);
}

interface IStabilityPool {

    // --- Events ---
    
    event StabilityPoolETHBalanceUpdated(uint _newBalance);
    event StabilityPoolRUBCBalanceUpdated(uint _newBalance);

    event BorrowerOperationsAddressChanged(address _newBorrowerOperationsAddress);
    event TroveManagerAddressChanged(address _newTroveManagerAddress);
    event ActivePoolAddressChanged(address _newActivePoolAddress);
    event DefaultPoolAddressChanged(address _newDefaultPoolAddress);
    event RUBCAddressChanged(address _newRUBCAddress);
    event SortedTrovesAddressChanged(address _newSortedTrovesAddress);
    event PriceFeedAddressChanged(address _newPriceFeedAddress);
    event CommunityIssuanceAddressChanged(address _newCommunityIssuanceAddress);

    event P_Updated(uint _P);
    event S_Updated(uint _S, uint128 _epoch, uint128 _scale);
    event G_Updated(uint _G, uint128 _epoch, uint128 _scale);
    event EpochUpdated(uint128 _currentEpoch);
    event ScaleUpdated(uint128 _currentScale);

    event FrontEndRegistered(address indexed _frontEnd, uint _kickbackRate);
    event FrontEndTagSet(address indexed _depositor, address indexed _frontEnd);

    event DepositSnapshotUpdated(address indexed _depositor, uint _P, uint _S, uint _G);
    event FrontEndSnapshotUpdated(address indexed _frontEnd, uint _P, uint _G);
    event UserDepositChanged(address indexed _depositor, uint _newDeposit);
    event FrontEndStakeChanged(address indexed _frontEnd, uint _newFrontEndStake, address _depositor);

    event ETHGainWithdrawn(address indexed _depositor, uint _ETH, uint _RUBCLoss);
    event RBSTPaidToDepositor(address indexed _depositor, uint _RBST);
    event RBSTPaidToFrontEnd(address indexed _frontEnd, uint _RBST);
    event EtherSent(address _to, uint _amount);

    // --- Functions ---

    /*
     * Called only once on init, to set addresses of other Liquity contracts
     * Callable only by owner, renounces ownership at the end
     */
    function setAddresses(
        address _borrowerOperationsAddress,
        address _troveManagerAddress,
        address _activePoolAddress,
        address _rubcAddress,
        address _sortedTrovesAddress,
        address _priceFeedAddress,
        address _communityIssuanceAddress
    ) external;

    /*
     * Initial checks:
     * - Frontend is registered or zero address
     * - Sender is not a registered frontend
     * - _amount is not zero
     * ---
     * - Triggers a RBST issuance, based on time passed since the last issuance. The RBST issuance is shared between *all* depositors and front ends
     * - Tags the deposit with the provided front end tag param, if it's a new deposit
     * - Sends depositor's accumulated gains (RBST, ETH) to depositor
     * - Sends the tagged front end's accumulated RBST gains to the tagged front end
     * - Increases deposit and tagged front end's stake, and takes new snapshots for each.
     */
    function provideToSP(uint _amount, address _frontEndTag) external;

    /*
     * Initial checks:
     * - _amount is zero or there are no under collateralized troves left in the system
     * - User has a non zero deposit
     * ---
     * - Triggers a RBST issuance, based on time passed since the last issuance. The RBST issuance is shared between *all* depositors and front ends
     * - Removes the deposit's front end tag if it is a full withdrawal
     * - Sends all depositor's accumulated gains (RBST, ETH) to depositor
     * - Sends the tagged front end's accumulated RBST gains to the tagged front end
     * - Decreases deposit and tagged front end's stake, and takes new snapshots for each.
     *
     * If _amount > userDeposit, the user withdraws all of their compounded deposit.
     */
    function withdrawFromSP(uint _amount) external;

    /*
     * Initial checks:
     * - User has a non zero deposit
     * - User has an open trove
     * - User has some ETH gain
     * ---
     * - Triggers a RBST issuance, based on time passed since the last issuance. The RBST issuance is shared between *all* depositors and front ends
     * - Sends all depositor's RBST gain to  depositor
     * - Sends all tagged front end's RBST gain to the tagged front end
     * - Transfers the depositor's entire ETH gain from the Stability Pool to the caller's trove
     * - Leaves their compounded deposit in the Stability Pool
     * - Updates snapshots for deposit and tagged front end stake
     */
    function withdrawETHGainToTrove(address _upperHint, address _lowerHint) external;

    /*
     * Initial checks:
     * - Frontend (sender) not already registered
     * - User (sender) has no deposit
     * - _kickbackRate is in the range [0, 100%]
     * ---
     * Front end makes a one-time selection of kickback rate upon registering
     */
    function registerFrontEnd(uint _kickbackRate) external;

    /*
     * Initial checks:
     * - Caller is TroveManager
     * ---
     * Cancels out the specified debt against the RUBC contained in the Stability Pool (as far as possible)
     * and transfers the Trove's ETH collateral from ActivePool to StabilityPool.
     * Only called by liquidation functions in the TroveManager.
     */
    function offset(uint _debt, uint _coll) external;

    /*
     * Returns the total amount of ETH held by the pool, accounted in an internal variable instead of `balance`,
     * to exclude edge cases like ETH received from a self-destruct.
     */
    function getETH() external view returns (uint);

    /*
     * Returns RUBC held in the pool. Changes when users deposit/withdraw, and when Trove debt is offset.
     */
    function getTotalRUBCDeposits() external view returns (uint);

    /*
     * Calculates the ETH gain earned by the deposit since its last snapshots were taken.
     */
    function getDepositorETHGain(address _depositor) external view returns (uint);

    /*
     * Calculate the RBST gain earned by a deposit since its last snapshots were taken.
     * If not tagged with a front end, the depositor gets a 100% cut of what their deposit earned.
     * Otherwise, their cut of the deposit's earnings is equal to the kickbackRate, set by the front end through
     * which they made their deposit.
     */
    function getDepositorRBSTGain(address _depositor) external view returns (uint);

    /*
     * Return the RBST gain earned by the front end.
     */
    function getFrontEndRBSTGain(address _frontEnd) external view returns (uint);

    /*
     * Return the user's compounded deposit.
     */
    function getCompoundedRUBCDeposit(address _depositor) external view returns (uint);

    /*
     * Return the front end's compounded stake.
     *
     * The front end's compounded stake is equal to the sum of its depositors' compounded deposits.
     */
    function getCompoundedFrontEndStake(address _frontEnd) external view returns (uint);

    /*
     * Fallback function
     * Only callable by Active Pool, it just accounts for ETH received
     * receive() external payable;
     */
}

interface IRUBC is IERC20, IERC2612 { 
    
    // --- Events ---

    event TroveManagerAddressChanged(address _troveManagerAddress);
    event StabilityPoolAddressChanged(address _newStabilityPoolAddress);
    event BorrowerOperationsAddressChanged(address _newBorrowerOperationsAddress);

    event RUBCBalanceUpdated(address _user, uint _amount);

    // --- Functions ---

    function mint(address _account, uint256 _amount) external;

    function burn(address _account, uint256 _amount) external;

    function sendToPool(address _sender,  address poolAddress, uint256 _amount) external;

    function returnFromPool(address poolAddress, address user, uint256 _amount ) external;
}

interface IRBST is IERC20, IERC2612 { 
   
    // --- Events ---
    
    event CommunityIssuanceAddressSet(address _communityIssuanceAddress);
    event RBSTStakingAddressSet(address _rbstStakingAddress);
    event LockupContractFactoryAddressSet(address _lockupContractFactoryAddress);

    // --- Functions ---
    
    function sendToRBSTStaking(address _sender, uint256 _amount) external;

    function getDeploymentStartTime() external view returns (uint256);

    function getLpRewardsEntitlement() external view returns (uint256);
}

interface IRBSTStaking {

    // --- Events --
    
    event RBSTAddressSet(address _rbstAddress);
    event RUBCAddressSet(address _rubcAddress);
    event TroveManagerAddressSet(address _troveManager);
    event BorrowerOperationsAddressSet(address _borrowerOperationsAddress);
    event ActivePoolAddressSet(address _activePoolAddress);

    event StakeChanged(address indexed staker, uint newStake);
    event StakingGainsWithdrawn(address indexed staker, uint RUBCGain, uint ETHGain);
    event F_ETHUpdated(uint _F_ETH);
    event F_RUBCUpdated(uint _F_RUBC);
    event TotalRBSTStakedUpdated(uint _totalRBSTStaked);
    event EtherSent(address _account, uint _amount);
    event StakerSnapshotsUpdated(address _staker, uint _F_ETH, uint _F_RUBC);

    // --- Functions ---

    function setAddresses
    (
        address _rbstAddress,
        address _rubcAddress,
        address _troveManagerAddress, 
        address _borrowerOperationsAddress,
        address _activePoolAddress
    )  external;

    function stake(uint _RBSTamount) external;

    function unstake(uint _RBSTamount) external;

    function increaseF_ETH(uint _ETHFee) external; 

    function increaseF_RUBC(uint _RBSTFee) external;  

    function getPendingETHGain(address _user) external view returns (uint);

    function getPendingRUBCGain(address _user) external view returns (uint);
}


// Common interface for the Trove Manager.
interface ITroveManager is ILiquityBase {
    
    // --- Events ---

    event BorrowerOperationsAddressChanged(address _newBorrowerOperationsAddress);
    event PriceFeedAddressChanged(address _newPriceFeedAddress);
    event RUBCAddressChanged(address _newRUBCAddress);
    event ActivePoolAddressChanged(address _activePoolAddress);
    event DefaultPoolAddressChanged(address _defaultPoolAddress);
    event StabilityPoolAddressChanged(address _stabilityPoolAddress);
    event GasPoolAddressChanged(address _gasPoolAddress);
    event CollSurplusPoolAddressChanged(address _collSurplusPoolAddress);
    event SortedTrovesAddressChanged(address _sortedTrovesAddress);
    event RBSTAddressChanged(address _rbstAddress);
    event RBSTStakingAddressChanged(address _rbstStakingAddress);

    event Liquidation(uint _liquidatedDebt, uint _liquidatedColl, uint _collGasCompensation, uint _RUBCGasCompensation);
    event Redemption(uint _attemptedRUBCAmount, uint _actualRUBCAmount, uint _ETHSent, uint _ETHFee);
    event TroveUpdated(address indexed _borrower, uint _debt, uint _coll, uint stake, uint8 operation);
    event TroveLiquidated(address indexed _borrower, uint _debt, uint _coll, uint8 operation);
    event BaseRateUpdated(uint _baseRate);
    event LastFeeOpTimeUpdated(uint _lastFeeOpTime);
    event TotalStakesUpdated(uint _newTotalStakes);
    event SystemSnapshotsUpdated(uint _totalStakesSnapshot, uint _totalCollateralSnapshot);
    event LTermsUpdated(uint _L_ETH, uint _L_RUBCDebt);
    event TroveSnapshotsUpdated(uint _L_ETH, uint _L_RUBCDebt);
    event TroveIndexUpdated(address _borrower, uint _newIndex);

    // --- Functions ---

    function setAddresses(
        address _borrowerOperationsAddress,
        address _activePoolAddress,
        address _defaultPoolAddress,
        address _stabilityPoolAddress,
        address _gasPoolAddress,
        address _collSurplusPoolAddress,
        address _priceFeedAddress,
        address _rubcAddress,
        address _sortedTrovesAddress,
        address _rbstAddress,
        address _rbstStakingAddress
    ) external;

    function stabilityPool() external view returns (IStabilityPool);
    function rubc() external view returns (IRUBC);
    function rbst() external view returns (IRBST);
    function rbstStaking() external view returns (IRBSTStaking);

    function getTroveOwnersCount() external view returns (uint);

    function getTroveFromTroveOwnersArray(uint _index) external view returns (address);

    function getNominalICR(address _borrower) external view returns (uint);
    function getCurrentICR(address _borrower, uint _price) external view returns (uint);

    function liquidate(address _borrower) external;

    function liquidateTroves(uint _n) external;

    function batchLiquidateTroves(address[] calldata _troveArray) external;

    function redeemCollateral(
        uint _RUBCAmount,
        address _firstRedemptionHint,
        address _upperPartialRedemptionHint,
        address _lowerPartialRedemptionHint,
        uint _partialRedemptionHintNICR,
        uint _maxIterations,
        uint _maxFee
    ) external; 

    function updateStakeAndTotalStakes(address _borrower) external returns (uint);

    function updateTroveRewardSnapshots(address _borrower) external;

    function addTroveOwnerToArray(address _borrower) external returns (uint index);

    function applyPendingRewards(address _borrower) external;

    function getPendingETHReward(address _borrower) external view returns (uint);

    function getPendingRUBCDebtReward(address _borrower) external view returns (uint);

     function hasPendingRewards(address _borrower) external view returns (bool);

    function getEntireDebtAndColl(address _borrower) external view returns (
        uint debt, 
        uint coll, 
        uint pendingRUBCDebtReward, 
        uint pendingETHReward
    );

    function closeTrove(address _borrower) external;

    function removeStake(address _borrower) external;

    function getRedemptionRate() external view returns (uint);
    function getRedemptionRateWithDecay() external view returns (uint);

    function getRedemptionFeeWithDecay(uint _ETHDrawn) external view returns (uint);

    function getBorrowingRate() external view returns (uint);
    function getBorrowingRateWithDecay() external view returns (uint);

    function getBorrowingFee(uint RUBCDebt) external view returns (uint);
    function getBorrowingFeeWithDecay(uint _RUBCDebt) external view returns (uint);

    function decayBaseRateFromBorrowing() external;

    function getTroveStatus(address _borrower) external view returns (uint);
    
    function getTroveStake(address _borrower) external view returns (uint);

    function getTroveDebt(address _borrower) external view returns (uint);

    function getTroveColl(address _borrower) external view returns (uint);

    function setTroveStatus(address _borrower, uint num) external;

    function increaseTroveColl(address _borrower, uint _collIncrease) external returns (uint);

    function decreaseTroveColl(address _borrower, uint _collDecrease) external returns (uint); 

    function increaseTroveDebt(address _borrower, uint _debtIncrease) external returns (uint); 

    function decreaseTroveDebt(address _borrower, uint _collDecrease) external returns (uint); 

    function getTCR(uint _price) external view returns (uint);

    function checkRecoveryMode(uint _price) external view returns (bool);
}

// Common interface for the SortedTroves Doubly Linked List.
interface ISortedTroves {

    // --- Events ---
    
    event SortedTrovesAddressChanged(address _sortedDoublyLLAddress);
    event BorrowerOperationsAddressChanged(address _borrowerOperationsAddress);
    event NodeAdded(address _id, uint _NICR);
    event NodeRemoved(address _id);

    // --- Functions ---
    
    function setParams(uint256 _size, address _TroveManagerAddress, address _borrowerOperationsAddress) external;

    function insert(address _id, uint256 _ICR, address _prevId, address _nextId) external;

    function remove(address _id) external;

    function reInsert(address _id, uint256 _newICR, address _prevId, address _nextId) external;

    function contains(address _id) external view returns (bool);

    function isFull() external view returns (bool);

    function isEmpty() external view returns (bool);

    function getSize() external view returns (uint256);

    function getMaxSize() external view returns (uint256);

    function getFirst() external view returns (address);

    function getLast() external view returns (address);

    function getNext(address _id) external view returns (address);

    function getPrev(address _id) external view returns (address);

    function validInsertPosition(uint256 _ICR, address _prevId, address _nextId) external view returns (bool);

    function findInsertPosition(uint256 _ICR, address _prevId, address _nextId) external view returns (address, address);
}

contract BaseMath {
    uint constant public DECIMAL_PRECISION = 1e18;
}

library LiquityMath {
    using SafeMath for uint;

    uint internal constant DECIMAL_PRECISION = 1e18;

    /* Precision for Nominal ICR (independent of price). Rationale for the value:
     *
     * - Making it “too high” could lead to overflows.
     * - Making it “too low” could lead to an ICR equal to zero, due to truncation from Solidity floor division. 
     *
     * This value of 1e20 is chosen for safety: the NICR will only overflow for numerator > ~1e39 ETH,
     * and will only truncate to 0 if the denominator is at least 1e20 times greater than the numerator.
     *
     */
    uint internal constant NICR_PRECISION = 1e20;

    function _min(uint _a, uint _b) internal pure returns (uint) {
        return (_a < _b) ? _a : _b;
    }

    function _max(uint _a, uint _b) internal pure returns (uint) {
        return (_a >= _b) ? _a : _b;
    }

    /* 
    * Multiply two decimal numbers and use normal rounding rules:
    * -round product up if 19'th mantissa digit >= 5
    * -round product down if 19'th mantissa digit < 5
    *
    * Used only inside the exponentiation, _decPow().
    */
    function decMul(uint x, uint y) internal pure returns (uint decProd) {
        uint prod_xy = x.mul(y);

        decProd = prod_xy.add(DECIMAL_PRECISION / 2).div(DECIMAL_PRECISION);
    }

    /* 
    * _decPow: Exponentiation function for 18-digit decimal base, and integer exponent n.
    * 
    * Uses the efficient "exponentiation by squaring" algorithm. O(log(n)) complexity. 
    * 
    * Called by two functions that represent time in units of minutes:
    * 1) TroveManager._calcDecayedBaseRate
    * 2) CommunityIssuance._getCumulativeIssuanceFraction 
    * 
    * The exponent is capped to avoid reverting due to overflow. The cap 525600000 equals
    * "minutes in 1000 years": 60 * 24 * 365 * 1000
    * 
    * If a period of > 1000 years is ever used as an exponent in either of the above functions, the result will be
    * negligibly different from just passing the cap, since: 
    *
    * In function 1), the decayed base rate will be 0 for 1000 years or > 1000 years
    * In function 2), the difference in tokens issued at 1000 years and any time > 1000 years, will be negligible
    */
    function _decPow(uint _base, uint _minutes) internal pure returns (uint) {
       
        if (_minutes > 525600000) {_minutes = 525600000;}  // cap to avoid overflow
    
        if (_minutes == 0) {return DECIMAL_PRECISION;}

        uint y = DECIMAL_PRECISION;
        uint x = _base;
        uint n = _minutes;

        // Exponentiation-by-squaring
        while (n > 1) {
            if (n % 2 == 0) {
                x = decMul(x, x);
                n = n.div(2);
            } else { // if (n % 2 != 0)
                y = decMul(x, y);
                x = decMul(x, x);
                n = (n.sub(1)).div(2);
            }
        }

        return decMul(x, y);
  }

    function _getAbsoluteDifference(uint _a, uint _b) internal pure returns (uint) {
        return (_a >= _b) ? _a.sub(_b) : _b.sub(_a);
    }

    function _computeNominalCR(uint _coll, uint _debt) internal pure returns (uint) {
        if (_debt > 0) {
            return _coll.mul(NICR_PRECISION).div(_debt);
        }
        // Return the maximal value for uint256 if the Trove has a debt of 0. Represents "infinite" CR.
        else { // if (_debt == 0)
            return 2**256 - 1;
        }
    }

    function _computeCR(uint _coll, uint _debt, uint _price) internal pure returns (uint) {
        if (_debt > 0) {
            uint newCollRatio = _coll.mul(_price).div(_debt);

            return newCollRatio;
        }
        // Return the maximal value for uint256 if the Trove has a debt of 0. Represents "infinite" CR.
        else { // if (_debt == 0)
            return 2**256 - 1; 
        }
    }
}

interface IActivePool is IPool {
    // --- Events ---
    event BorrowerOperationsAddressChanged(address _newBorrowerOperationsAddress);
    event TroveManagerAddressChanged(address _newTroveManagerAddress);
    event ActivePoolRUBCDebtUpdated(uint _RUBCDebt);
    event ActivePoolETHBalanceUpdated(uint _ETH);

    // --- Functions ---
    function sendETH(address _account, uint _amount) external;
}

interface IDefaultPool is IPool {
    // --- Events ---
    event TroveManagerAddressChanged(address _newTroveManagerAddress);
    event DefaultPoolRUBCDebtUpdated(uint _RUBCDebt);
    event DefaultPoolETHBalanceUpdated(uint _ETH);

    // --- Functions ---
    function sendETHToActivePool(uint _amount) external;
}

interface IPriceFeed {

    // --- Events ---
    event LastGoodPriceUpdated(uint _lastGoodPrice);
   
    // --- Function ---
    function fetchPrice() external returns (uint);

    function fetchRUBPriceFeedUpdateTimestamp() external returns(uint256);
}

/* 
* Base contract for TroveManager, BorrowerOperations and StabilityPool. Contains global system constants and
* common functions. 
*/
contract LiquityBase is BaseMath, ILiquityBase {
    using SafeMath for uint;

    uint constant public _100pct = 1000000000000000000; // 1e18 == 100%

    // Minimum collateral ratio for individual troves
    uint constant public MCR = 1100000000000000000; // 110%

    // Critical system collateral ratio. If the system's total collateral ratio (TCR) falls below the CCR, Recovery Mode is triggered.
    uint constant public CCR = 1500000000000000000; // 150%

    // Amount of RUBC to be locked in gas pool on opening troves
    uint constant public RUBC_GAS_COMPENSATION = 20_000e18;

    // Minimum amount of net RUBC debt a trove must have
    uint constant public MIN_NET_DEBT = 100_000e18;

    uint constant public PERCENT_DIVISOR = 200; // dividing by 200 yields 0.5%

    uint constant public BORROWING_FEE_FLOOR = DECIMAL_PRECISION / 1000 * 5; // 0.5%

    IActivePool public activePool;

    IDefaultPool public defaultPool;

    IPriceFeed public override priceFeed;

    // --- Gas compensation functions ---

    // Returns the composite debt (drawn debt + gas compensation) of a trove, for the purpose of ICR calculation
    function _getCompositeDebt(uint _debt) internal pure returns (uint) {
        return _debt.add(RUBC_GAS_COMPENSATION);
    }

    function _getNetDebt(uint _debt) internal pure returns (uint) {
        return _debt.sub(RUBC_GAS_COMPENSATION);
    }

    // Return the amount of ETH to be drawn from a trove's collateral and sent as gas compensation.
    function _getCollGasCompensation(uint _entireColl) internal pure returns (uint) {
        return _entireColl / PERCENT_DIVISOR;
    }

    function getEntireSystemColl() public view returns (uint entireSystemColl) {
        uint activeColl = activePool.getETH();
        uint liquidatedColl = defaultPool.getETH();

        return activeColl.add(liquidatedColl);
    }

    function getEntireSystemDebt() public view returns (uint entireSystemDebt) {
        uint activeDebt = activePool.getRUBCDebt();
        uint closedDebt = defaultPool.getRUBCDebt();

        return activeDebt.add(closedDebt);
    }

    function _getTCR(uint _price) internal view returns (uint TCR) {
        uint entireSystemColl = getEntireSystemColl();
        uint entireSystemDebt = getEntireSystemDebt();

        TCR = LiquityMath._computeCR(entireSystemColl, entireSystemDebt, _price);

        return TCR;
    }

    function _checkRecoveryMode(uint _price) internal view returns (bool) {
        uint TCR = _getTCR(_price);

        return TCR < CCR;
    }

    function _requireUserAcceptsFee(uint _fee, uint _amount, uint _maxFeePercentage) internal pure {
        uint feePercentage = _fee.mul(DECIMAL_PRECISION).div(_amount);
        require(feePercentage <= _maxFeePercentage, "Fee exceeded provided maximum");
    }
}

/**
 * Based on OpenZeppelin's Ownable contract:
 * https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/access/Ownable.sol
 *
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
contract Ownable {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor () internal {
        _owner = msg.sender;
        emit OwnershipTransferred(address(0), msg.sender);
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        require(isOwner(), "Ownable: caller is not the owner");
        _;
    }

    /**
     * @dev Returns true if the caller is the current owner.
     */
    function isOwner() public view returns (bool) {
        return msg.sender == _owner;
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     *
     * NOTE: This function is not safe, as it doesn’t check owner is calling it.
     * Make sure you check it before calling it.
     */
    function _renounceOwnership() internal {
        emit OwnershipTransferred(_owner, address(0));
        _owner = address(0);
    }
}

contract CheckContract {
    /**
     * Check that the account is an already deployed non-destroyed contract.
     * See: https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/utils/Address.sol#L12
     */
    function checkContract(address _account) internal view {
        require(_account != address(0), "Account cannot be zero address");

        uint256 size;
        // solhint-disable-next-line no-inline-assembly
        assembly { size := extcodesize(_account) }
        require(size > 0, "Account code size cannot be zero");
    }
}

contract HintHelpers is LiquityBase, Ownable, CheckContract {
    string constant public NAME = "HintHelpers";

    ISortedTroves public sortedTroves;
    ITroveManager public troveManager;

    // --- Events ---

    event SortedTrovesAddressChanged(address _sortedTrovesAddress);
    event TroveManagerAddressChanged(address _troveManagerAddress);

    // --- Dependency setters ---

    function setAddresses(
        address _sortedTrovesAddress,
        address _troveManagerAddress
    )
        external
        onlyOwner
    {
        checkContract(_sortedTrovesAddress);
        checkContract(_troveManagerAddress);

        sortedTroves = ISortedTroves(_sortedTrovesAddress);
        troveManager = ITroveManager(_troveManagerAddress);

        emit SortedTrovesAddressChanged(_sortedTrovesAddress);
        emit TroveManagerAddressChanged(_troveManagerAddress);

        _renounceOwnership();
    }

    // --- Functions ---

    /* getRedemptionHints() - Helper function for finding the right hints to pass to redeemCollateral().
     *
     * It simulates a redemption of `_RUBCamount` to figure out where the redemption sequence will start and what state the final Trove
     * of the sequence will end up in.
     *
     * Returns three hints:
     *  - `firstRedemptionHint` is the address of the first Trove with ICR >= MCR (i.e. the first Trove that will be redeemed).
     *  - `partialRedemptionHintNICR` is the final nominal ICR of the last Trove of the sequence after being hit by partial redemption,
     *     or zero in case of no partial redemption.
     *  - `truncatedRUBCamount` is the maximum amount that can be redeemed out of the the provided `_RUBCamount`. This can be lower than
     *    `_RUBCamount` when redeeming the full amount would leave the last Trove of the redemption sequence with less net debt than the
     *    minimum allowed value (i.e. MIN_NET_DEBT).
     *
     * The number of Troves to consider for redemption can be capped by passing a non-zero value as `_maxIterations`, while passing zero
     * will leave it uncapped.
     */

    function getRedemptionHints(
        uint _RUBCamount, 
        uint _price,
        uint _maxIterations
    )
        external
        view
        returns (
            address firstRedemptionHint,
            uint partialRedemptionHintNICR,
            uint truncatedRUBCamount
        )
    {
        ISortedTroves sortedTrovesCached = sortedTroves;

        uint remainingRUBC = _RUBCamount;
        address currentTroveuser = sortedTrovesCached.getLast();

        while (currentTroveuser != address(0) && troveManager.getCurrentICR(currentTroveuser, _price) < MCR) {
            currentTroveuser = sortedTrovesCached.getPrev(currentTroveuser);
        }

        firstRedemptionHint = currentTroveuser;

        if (_maxIterations == 0) {
            _maxIterations = uint(-1);
        }

        while (currentTroveuser != address(0) && remainingRUBC > 0 && _maxIterations-- > 0) {
            uint netRUBCDebt = _getNetDebt(troveManager.getTroveDebt(currentTroveuser))
                .add(troveManager.getPendingRUBCDebtReward(currentTroveuser));

            if (netRUBCDebt > remainingRUBC) {
                if (netRUBCDebt > MIN_NET_DEBT) {
                    uint maxRedeemableRUBC = LiquityMath._min(remainingRUBC, netRUBCDebt.sub(MIN_NET_DEBT));

                    uint ETH = troveManager.getTroveColl(currentTroveuser)
                        .add(troveManager.getPendingETHReward(currentTroveuser));

                    uint newColl = ETH.sub(maxRedeemableRUBC.mul(DECIMAL_PRECISION).div(_price));
                    uint newDebt = netRUBCDebt.sub(maxRedeemableRUBC);

                    uint compositeDebt = _getCompositeDebt(newDebt);
                    partialRedemptionHintNICR = LiquityMath._computeNominalCR(newColl, compositeDebt);

                    remainingRUBC = remainingRUBC.sub(maxRedeemableRUBC);
                }
                break;
            } else {
                remainingRUBC = remainingRUBC.sub(netRUBCDebt);
            }

            currentTroveuser = sortedTrovesCached.getPrev(currentTroveuser);
        }

        truncatedRUBCamount = _RUBCamount.sub(remainingRUBC);
    }

    /* getApproxHint() - return address of a Trove that is, on average, (length / numTrials) positions away in the 
    sortedTroves list from the correct insert position of the Trove to be inserted. 
    
    Note: The output address is worst-case O(n) positions away from the correct insert position, however, the function 
    is probabilistic. Input can be tuned to guarantee results to a high degree of confidence, e.g:

    Submitting numTrials = k * sqrt(length), with k = 15 makes it very, very likely that the ouput address will 
    be <= sqrt(length) positions away from the correct insert position.
    */
    function getApproxHint(uint _CR, uint _numTrials, uint _inputRandomSeed)
        external
        view
        returns (address hintAddress, uint diff, uint latestRandomSeed)
    {
        uint arrayLength = troveManager.getTroveOwnersCount();

        if (arrayLength == 0) {
            return (address(0), 0, _inputRandomSeed);
        }

        hintAddress = sortedTroves.getLast();
        diff = LiquityMath._getAbsoluteDifference(_CR, troveManager.getNominalICR(hintAddress));
        latestRandomSeed = _inputRandomSeed;

        uint i = 1;

        while (i < _numTrials) {
            latestRandomSeed = uint(keccak256(abi.encodePacked(latestRandomSeed)));

            uint arrayIndex = latestRandomSeed % arrayLength;
            address currentAddress = troveManager.getTroveFromTroveOwnersArray(arrayIndex);
            uint currentNICR = troveManager.getNominalICR(currentAddress);

            // check if abs(current - CR) > abs(closest - CR), and update closest if current is closer
            uint currentDiff = LiquityMath._getAbsoluteDifference(currentNICR, _CR);

            if (currentDiff < diff) {
                diff = currentDiff;
                hintAddress = currentAddress;
            }
            i++;
        }
    }

    function computeNominalCR(uint _coll, uint _debt) external pure returns (uint) {
        return LiquityMath._computeNominalCR(_coll, _debt);
    }

    function computeCR(uint _coll, uint _debt, uint _price) external pure returns (uint) {
        return LiquityMath._computeCR(_coll, _debt, _price);
    }
}