// File: contracts/Fed.sol



pragma solidity ^0.5.16;

import "./SafeMath.sol";
import "./CErc20.sol";
import "./ERC20.sol";
import "./Exponential.sol";

contract Fed {
    using SafeMath for uint;

    CErc20 public ctoken;
    ERC20 public underlying;
    address public chair; // Fed Chair
    address public gov;
    uint public supply;

    event Expansion(uint amount);
    event Contraction(uint amount);

    constructor(CErc20 ctoken_, address gov_) public {
        ctoken = ctoken_;
        underlying = ERC20(ctoken_.underlying());
        underlying.approve(address(ctoken), uint(-1));
        chair = msg.sender;
        gov = gov_;
    }

    function changeGov(address newGov_) public {
        require(msg.sender == gov, "ONLY GOV");
        gov = newGov_;
    }

    function changeChair(address newChair_) public {
        require(msg.sender == gov, "ONLY GOV");
        chair = newChair_;
    }

    function resign() public {
        require(msg.sender == chair, "ONLY CHAIR");
        chair = address(0);
    }

    function expansion(uint amount) public {
        require(msg.sender == chair, "ONLY CHAIR");
        underlying.mint(address(this), amount);
        require(ctoken.mint(amount) == 0, 'Supplying failed');
        supply = supply.add(amount);
        emit Expansion(amount);
    }

    function contraction(uint amount) public {
        require(msg.sender == chair, "ONLY CHAIR");
        require(amount <= supply, "AMOUNT TOO BIG"); // can't burn profits
        require(ctoken.redeemUnderlying(amount) == 0, "Redeem failed");
        underlying.burn(amount);
        supply = supply.sub(amount);
        emit Contraction(amount);
    }

    function takeProfit() public {
        uint underlyingBalance = ctoken.balanceOfUnderlying(address(this));
        uint profit = underlyingBalance.sub(supply);
        if(profit > 0) {
            require(ctoken.redeemUnderlying(profit) == 0, "Redeem failed");
            underlying.transfer(gov, profit);
        }
    }
    
}
// File: contracts/SafeMath.sol



pragma solidity ^0.5.16;

// From https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/math/Math.sol
// Subject to the MIT license.

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

        return c;
    }

    /**
     * @dev Returns the addition of two unsigned integers, reverting with custom message on overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, errorMessage);

        return c;
    }

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

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on underflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     * - Subtraction cannot underflow.
     */
    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 multiplication of two unsigned integers, reverting on overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b, string memory errorMessage) 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, errorMessage);

        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.
     */
    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.
     */
    function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b != 0, errorMessage);
        return a % b;
    }
}

// File: contracts/CErc20.sol



pragma solidity ^0.5.16;

import "./CToken.sol";

/**
 * @title Compound's CErc20 Contract
 * @notice CTokens which wrap an EIP-20 underlying
 * @author Compound
 */
contract CErc20 is CToken, CErc20Interface {
    /**
     * @notice Initialize the new money market
     * @param underlying_ The address of the underlying asset
     * @param comptroller_ The address of the Comptroller
     * @param interestRateModel_ The address of the interest rate model
     * @param initialExchangeRateMantissa_ The initial exchange rate, scaled by 1e18
     * @param name_ ERC-20 name of this token
     * @param symbol_ ERC-20 symbol of this token
     * @param decimals_ ERC-20 decimal precision of this token
     */
    function initialize(address underlying_,
                        ComptrollerInterface comptroller_,
                        InterestRateModel interestRateModel_,
                        uint initialExchangeRateMantissa_,
                        string memory name_,
                        string memory symbol_,
                        uint8 decimals_) public {
        // CToken initialize does the bulk of the work
        super.initialize(comptroller_, interestRateModel_, initialExchangeRateMantissa_, name_, symbol_, decimals_);

        // Set underlying and sanity check it
        underlying = underlying_;
        EIP20Interface(underlying).totalSupply();
    }

    /*** User Interface ***/

    /**
     * @notice Sender supplies assets into the market and receives cTokens in exchange
     * @dev Accrues interest whether or not the operation succeeds, unless reverted
     * @param mintAmount The amount of the underlying asset to supply
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function mint(uint mintAmount) external returns (uint) {
        (uint err,) = mintInternal(mintAmount);
        return err;
    }

    /**
     * @notice Sender redeems cTokens in exchange for the underlying asset
     * @dev Accrues interest whether or not the operation succeeds, unless reverted
     * @param redeemTokens The number of cTokens to redeem into underlying
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function redeem(uint redeemTokens) external returns (uint) {
        return redeemInternal(redeemTokens);
    }

    /**
     * @notice Sender redeems cTokens in exchange for a specified amount of underlying asset
     * @dev Accrues interest whether or not the operation succeeds, unless reverted
     * @param redeemAmount The amount of underlying to redeem
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function redeemUnderlying(uint redeemAmount) external returns (uint) {
        return redeemUnderlyingInternal(redeemAmount);
    }

    /**
      * @notice Sender borrows assets from the protocol to their own address
      * @param borrowAmount The amount of the underlying asset to borrow
      * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
      */
    function borrow(uint borrowAmount) external returns (uint) {
        return borrowInternal(borrowAmount);
    }

    /**
     * @notice Sender repays their own borrow
     * @param repayAmount The amount to repay
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function repayBorrow(uint repayAmount) external returns (uint) {
        (uint err,) = repayBorrowInternal(repayAmount);
        return err;
    }

    /**
     * @notice Sender repays a borrow belonging to borrower
     * @param borrower the account with the debt being payed off
     * @param repayAmount The amount to repay
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function repayBorrowBehalf(address borrower, uint repayAmount) external returns (uint) {
        (uint err,) = repayBorrowBehalfInternal(borrower, repayAmount);
        return err;
    }

    /**
     * @notice The sender liquidates the borrowers collateral.
     *  The collateral seized is transferred to the liquidator.
     * @param borrower The borrower of this cToken to be liquidated
     * @param repayAmount The amount of the underlying borrowed asset to repay
     * @param cTokenCollateral The market in which to seize collateral from the borrower
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function liquidateBorrow(address borrower, uint repayAmount, CTokenInterface cTokenCollateral) external returns (uint) {
        (uint err,) = liquidateBorrowInternal(borrower, repayAmount, cTokenCollateral);
        return err;
    }

    /**
     * @notice The sender adds to reserves.
     * @param addAmount The amount fo underlying token to add as reserves
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function _addReserves(uint addAmount) external returns (uint) {
        return _addReservesInternal(addAmount);
    }

    /*** Safe Token ***/

    /**
     * @notice Gets balance of this contract in terms of the underlying
     * @dev This excludes the value of the current message, if any
     * @return The quantity of underlying tokens owned by this contract
     */
    function getCashPrior() internal view returns (uint) {
        EIP20Interface token = EIP20Interface(underlying);
        return token.balanceOf(address(this));
    }

    /**
     * @dev Similar to EIP20 transfer, except it handles a False result from `transferFrom` and reverts in that case.
     *      This will revert due to insufficient balance or insufficient allowance.
     *      This function returns the actual amount received,
     *      which may be less than `amount` if there is a fee attached to the transfer.
     *
     *      Note: This wrapper safely handles non-standard ERC-20 tokens that do not return a value.
     *            See here: https://medium.com/coinmonks/missing-return-value-bug-at-least-130-tokens-affected-d67bf08521ca
     */
    function doTransferIn(address from, uint amount) internal returns (uint) {
        EIP20NonStandardInterface token = EIP20NonStandardInterface(underlying);
        uint balanceBefore = EIP20Interface(underlying).balanceOf(address(this));
        token.transferFrom(from, address(this), amount);

        bool success;
        assembly {
            switch returndatasize()
                case 0 {                       // This is a non-standard ERC-20
                    success := not(0)          // set success to true
                }
                case 32 {                      // This is a compliant ERC-20
                    returndatacopy(0, 0, 32)
                    success := mload(0)        // Set `success = returndata` of external call
                }
                default {                      // This is an excessively non-compliant ERC-20, revert.
                    revert(0, 0)
                }
        }
        require(success, "TOKEN_TRANSFER_IN_FAILED");

        // Calculate the amount that was *actually* transferred
        uint balanceAfter = EIP20Interface(underlying).balanceOf(address(this));
        require(balanceAfter >= balanceBefore, "TOKEN_TRANSFER_IN_OVERFLOW");
        return balanceAfter - balanceBefore;   // underflow already checked above, just subtract
    }

    /**
     * @dev Similar to EIP20 transfer, except it handles a False success from `transfer` and returns an explanatory
     *      error code rather than reverting. If caller has not called checked protocol's balance, this may revert due to
     *      insufficient cash held in this contract. If caller has checked protocol's balance prior to this call, and verified
     *      it is >= amount, this should not revert in normal conditions.
     *
     *      Note: This wrapper safely handles non-standard ERC-20 tokens that do not return a value.
     *            See here: https://medium.com/coinmonks/missing-return-value-bug-at-least-130-tokens-affected-d67bf08521ca
     */
    function doTransferOut(address payable to, uint amount) internal {
        EIP20NonStandardInterface token = EIP20NonStandardInterface(underlying);
        token.transfer(to, amount);

        bool success;
        assembly {
            switch returndatasize()
                case 0 {                      // This is a non-standard ERC-20
                    success := not(0)          // set success to true
                }
                case 32 {                     // This is a complaint ERC-20
                    returndatacopy(0, 0, 32)
                    success := mload(0)        // Set `success = returndata` of external call
                }
                default {                     // This is an excessively non-compliant ERC-20, revert.
                    revert(0, 0)
                }
        }
        require(success, "TOKEN_TRANSFER_OUT_FAILED");
    }
}

// File: contracts/ERC20.sol



pragma solidity ^0.5.16;

import "./SafeMath.sol";

contract ERC20 {
    using SafeMath for uint;

    string public name;
    string public symbol;
    uint8 public decimals;
    uint  public totalSupply;
    address public operator;
    address public pendingOperator;
    mapping(address => uint) public balanceOf;
    mapping(address => mapping(address => uint)) public allowance;
    mapping (address => bool) public minters;

    bytes32 public DOMAIN_SEPARATOR;
    // keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)");
    bytes32 public constant PERMIT_TYPEHASH = 0x6e71edae12b1b97f4d1f60370fef10105fa2faae0126114a169c64845d6126c9;
    mapping(address => uint) public nonces;

    event Approval(address indexed owner, address indexed spender, uint value);
    event Transfer(address indexed from, address indexed to, uint value);
    event AddMinter(address indexed minter);
    event RemoveMinter(address indexed minter);
    event ChangeOperator(address indexed newOperator);

    modifier onlyOperator {
        require(msg.sender == operator, "ONLY OPERATOR");
        _;
    }

    constructor(string memory name_, string memory symbol_, uint8 decimals_) public {
        name = name_;
        symbol = symbol_;
        decimals = decimals_;
        operator = msg.sender;
        uint chainId;
        assembly {
            chainId := chainid
        }
        DOMAIN_SEPARATOR = keccak256(
            abi.encode(
                keccak256('EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)'),
                keccak256(bytes(name)),
                keccak256(bytes('1')),
                chainId,
                address(this)
            )
        );
    }

    function setPendingOperator(address newOperator_) public onlyOperator {
        pendingOperator = newOperator_;
    }

    function claimOperator() public {
        require(msg.sender == pendingOperator, "ONLY PENDING OPERATOR");
        operator = pendingOperator;
        pendingOperator = address(0);
        emit ChangeOperator(operator);
    }

    function addMinter(address minter_) public onlyOperator {
        minters[minter_] = true;
        emit AddMinter(minter_);
    }

    function removeMinter(address minter_) public onlyOperator {
        minters[minter_] = false;
        emit RemoveMinter(minter_);
    }

    function mint(address to, uint amount) public {
        require(minters[msg.sender] == true || msg.sender == operator, "ONLY MINTERS OR OPERATOR");
        _mint(to, amount);
    }

    function burn(uint amount) public {
        _burn(msg.sender, amount);
    }

    function _mint(address to, uint value) internal {
        totalSupply = totalSupply.add(value);
        balanceOf[to] = balanceOf[to].add(value);
        emit Transfer(address(0), to, value);
    }

    function _burn(address from, uint value) internal {
        balanceOf[from] = balanceOf[from].sub(value);
        totalSupply = totalSupply.sub(value);
        emit Transfer(from, address(0), value);
    }

    function _approve(address owner, address spender, uint value) private {
        allowance[owner][spender] = value;
        emit Approval(owner, spender, value);
    }

    function _transfer(address from, address to, uint value) private {
        balanceOf[from] = balanceOf[from].sub(value);
        balanceOf[to] = balanceOf[to].add(value);
        emit Transfer(from, to, value);
    }

    function approve(address spender, uint value) external returns (bool) {
        _approve(msg.sender, spender, value);
        return true;
    }

    function transfer(address to, uint value) external returns (bool) {
        _transfer(msg.sender, to, value);
        return true;
    }

    function transferFrom(address from, address to, uint value) external returns (bool) {
        if (allowance[from][msg.sender] != uint(-1)) {
            allowance[from][msg.sender] = allowance[from][msg.sender].sub(value);
        }
        _transfer(from, to, value);
        return true;
    }

    function permit(address owner, address spender, uint value, uint deadline, uint8 v, bytes32 r, bytes32 s) external {
        require(deadline >= block.timestamp, 'EXPIRED');
        bytes32 digest = keccak256(
            abi.encodePacked(
                '\x19\x01',
                DOMAIN_SEPARATOR,
                keccak256(abi.encode(PERMIT_TYPEHASH, owner, spender, value, nonces[owner]++, deadline))
            )
        );
        address recoveredAddress = ecrecover(digest, v, r, s);
        require(recoveredAddress != address(0) && recoveredAddress == owner, 'INVALID_SIGNATURE');
        _approve(owner, spender, value);
    }
}
// File: contracts/Exponential.sol



pragma solidity ^0.5.16;

import "./CarefulMath.sol";
import "./ExponentialNoError.sol";

/**
 * @title Exponential module for storing fixed-precision decimals
 * @author Compound
 * @dev Legacy contract for compatibility reasons with existing contracts that still use MathError
 * @notice Exp is a struct which stores decimals with a fixed precision of 18 decimal places.
 *         Thus, if we wanted to store the 5.1, mantissa would store 5.1e18. That is:
 *         `Exp({mantissa: 5100000000000000000})`.
 */
contract Exponential is CarefulMath, ExponentialNoError {
    /**
     * @dev Creates an exponential from numerator and denominator values.
     *      Note: Returns an error if (`num` * 10e18) > MAX_INT,
     *            or if `denom` is zero.
     */
    function getExp(uint num, uint denom) pure internal returns (MathError, Exp memory) {
        (MathError err0, uint scaledNumerator) = mulUInt(num, expScale);
        if (err0 != MathError.NO_ERROR) {
            return (err0, Exp({mantissa: 0}));
        }

        (MathError err1, uint rational) = divUInt(scaledNumerator, denom);
        if (err1 != MathError.NO_ERROR) {
            return (err1, Exp({mantissa: 0}));
        }

        return (MathError.NO_ERROR, Exp({mantissa: rational}));
    }

    /**
     * @dev Adds two exponentials, returning a new exponential.
     */
    function addExp(Exp memory a, Exp memory b) pure internal returns (MathError, Exp memory) {
        (MathError error, uint result) = addUInt(a.mantissa, b.mantissa);

        return (error, Exp({mantissa: result}));
    }

    /**
     * @dev Subtracts two exponentials, returning a new exponential.
     */
    function subExp(Exp memory a, Exp memory b) pure internal returns (MathError, Exp memory) {
        (MathError error, uint result) = subUInt(a.mantissa, b.mantissa);

        return (error, Exp({mantissa: result}));
    }

    /**
     * @dev Multiply an Exp by a scalar, returning a new Exp.
     */
    function mulScalar(Exp memory a, uint scalar) pure internal returns (MathError, Exp memory) {
        (MathError err0, uint scaledMantissa) = mulUInt(a.mantissa, scalar);
        if (err0 != MathError.NO_ERROR) {
            return (err0, Exp({mantissa: 0}));
        }

        return (MathError.NO_ERROR, Exp({mantissa: scaledMantissa}));
    }

    /**
     * @dev Multiply an Exp by a scalar, then truncate to return an unsigned integer.
     */
    function mulScalarTruncate(Exp memory a, uint scalar) pure internal returns (MathError, uint) {
        (MathError err, Exp memory product) = mulScalar(a, scalar);
        if (err != MathError.NO_ERROR) {
            return (err, 0);
        }

        return (MathError.NO_ERROR, truncate(product));
    }

    /**
     * @dev Multiply an Exp by a scalar, truncate, then add an to an unsigned integer, returning an unsigned integer.
     */
    function mulScalarTruncateAddUInt(Exp memory a, uint scalar, uint addend) pure internal returns (MathError, uint) {
        (MathError err, Exp memory product) = mulScalar(a, scalar);
        if (err != MathError.NO_ERROR) {
            return (err, 0);
        }

        return addUInt(truncate(product), addend);
    }

    /**
     * @dev Divide an Exp by a scalar, returning a new Exp.
     */
    function divScalar(Exp memory a, uint scalar) pure internal returns (MathError, Exp memory) {
        (MathError err0, uint descaledMantissa) = divUInt(a.mantissa, scalar);
        if (err0 != MathError.NO_ERROR) {
            return (err0, Exp({mantissa: 0}));
        }

        return (MathError.NO_ERROR, Exp({mantissa: descaledMantissa}));
    }

    /**
     * @dev Divide a scalar by an Exp, returning a new Exp.
     */
    function divScalarByExp(uint scalar, Exp memory divisor) pure internal returns (MathError, Exp memory) {
        /*
          We are doing this as:
          getExp(mulUInt(expScale, scalar), divisor.mantissa)

          How it works:
          Exp = a / b;
          Scalar = s;
          `s / (a / b)` = `b * s / a` and since for an Exp `a = mantissa, b = expScale`
        */
        (MathError err0, uint numerator) = mulUInt(expScale, scalar);
        if (err0 != MathError.NO_ERROR) {
            return (err0, Exp({mantissa: 0}));
        }
        return getExp(numerator, divisor.mantissa);
    }

    /**
     * @dev Divide a scalar by an Exp, then truncate to return an unsigned integer.
     */
    function divScalarByExpTruncate(uint scalar, Exp memory divisor) pure internal returns (MathError, uint) {
        (MathError err, Exp memory fraction) = divScalarByExp(scalar, divisor);
        if (err != MathError.NO_ERROR) {
            return (err, 0);
        }

        return (MathError.NO_ERROR, truncate(fraction));
    }

    /**
     * @dev Multiplies two exponentials, returning a new exponential.
     */
    function mulExp(Exp memory a, Exp memory b) pure internal returns (MathError, Exp memory) {

        (MathError err0, uint doubleScaledProduct) = mulUInt(a.mantissa, b.mantissa);
        if (err0 != MathError.NO_ERROR) {
            return (err0, Exp({mantissa: 0}));
        }

        // We add half the scale before dividing so that we get rounding instead of truncation.
        //  See "Listing 6" and text above it at https://accu.org/index.php/journals/1717
        // Without this change, a result like 6.6...e-19 will be truncated to 0 instead of being rounded to 1e-18.
        (MathError err1, uint doubleScaledProductWithHalfScale) = addUInt(halfExpScale, doubleScaledProduct);
        if (err1 != MathError.NO_ERROR) {
            return (err1, Exp({mantissa: 0}));
        }

        (MathError err2, uint product) = divUInt(doubleScaledProductWithHalfScale, expScale);
        // The only error `div` can return is MathError.DIVISION_BY_ZERO but we control `expScale` and it is not zero.
        assert(err2 == MathError.NO_ERROR);

        return (MathError.NO_ERROR, Exp({mantissa: product}));
    }

    /**
     * @dev Multiplies two exponentials given their mantissas, returning a new exponential.
     */
    function mulExp(uint a, uint b) pure internal returns (MathError, Exp memory) {
        return mulExp(Exp({mantissa: a}), Exp({mantissa: b}));
    }

    /**
     * @dev Multiplies three exponentials, returning a new exponential.
     */
    function mulExp3(Exp memory a, Exp memory b, Exp memory c) pure internal returns (MathError, Exp memory) {
        (MathError err, Exp memory ab) = mulExp(a, b);
        if (err != MathError.NO_ERROR) {
            return (err, ab);
        }
        return mulExp(ab, c);
    }

    /**
     * @dev Divides two exponentials, returning a new exponential.
     *     (a/scale) / (b/scale) = (a/scale) * (scale/b) = a/b,
     *  which we can scale as an Exp by calling getExp(a.mantissa, b.mantissa)
     */
    function divExp(Exp memory a, Exp memory b) pure internal returns (MathError, Exp memory) {
        return getExp(a.mantissa, b.mantissa);
    }
}

// File: contracts/CToken.sol



pragma solidity ^0.5.16;

import "./ComptrollerInterface.sol";
import "./CTokenInterfaces.sol";
import "./ErrorReporter.sol";
import "./Exponential.sol";
import "./EIP20Interface.sol";
import "./EIP20NonStandardInterface.sol";
import "./InterestRateModel.sol";

/**
 * @title Compound's CToken Contract
 * @notice Abstract base for CTokens
 * @author Compound
 */
contract CToken is CTokenInterface, Exponential, TokenErrorReporter {
    /**
     * @notice Initialize the money market
     * @param comptroller_ The address of the Comptroller
     * @param interestRateModel_ The address of the interest rate model
     * @param initialExchangeRateMantissa_ The initial exchange rate, scaled by 1e18
     * @param name_ EIP-20 name of this token
     * @param symbol_ EIP-20 symbol of this token
     * @param decimals_ EIP-20 decimal precision of this token
     */
    function initialize(ComptrollerInterface comptroller_,
                        InterestRateModel interestRateModel_,
                        uint initialExchangeRateMantissa_,
                        string memory name_,
                        string memory symbol_,
                        uint8 decimals_) public {
        require(msg.sender == admin, "only admin may initialize the market");
        require(accrualBlockNumber == 0 && borrowIndex == 0, "market may only be initialized once");

        // Set initial exchange rate
        initialExchangeRateMantissa = initialExchangeRateMantissa_;
        require(initialExchangeRateMantissa > 0, "initial exchange rate must be greater than zero.");

        // Set the comptroller
        uint err = _setComptroller(comptroller_);
        require(err == uint(Error.NO_ERROR), "setting comptroller failed");

        // Initialize block number and borrow index (block number mocks depend on comptroller being set)
        accrualBlockNumber = getBlockNumber();
        borrowIndex = mantissaOne;

        // Set the interest rate model (depends on block number / borrow index)
        err = _setInterestRateModelFresh(interestRateModel_);
        require(err == uint(Error.NO_ERROR), "setting interest rate model failed");

        name = name_;
        symbol = symbol_;
        decimals = decimals_;

        // The counter starts true to prevent changing it from zero to non-zero (i.e. smaller cost/refund)
        _notEntered = true;
    }

    /**
     * @notice Transfer `tokens` tokens from `src` to `dst` by `spender`
     * @dev Called by both `transfer` and `transferFrom` internally
     * @param spender The address of the account performing the transfer
     * @param src The address of the source account
     * @param dst The address of the destination account
     * @param tokens The number of tokens to transfer
     * @return Whether or not the transfer succeeded
     */
    function transferTokens(address spender, address src, address dst, uint tokens) internal returns (uint) {
        /* Fail if transfer not allowed */
        uint allowed = comptroller.transferAllowed(address(this), src, dst, tokens);
        if (allowed != 0) {
            return failOpaque(Error.COMPTROLLER_REJECTION, FailureInfo.TRANSFER_COMPTROLLER_REJECTION, allowed);
        }

        /* Do not allow self-transfers */
        if (src == dst) {
            return fail(Error.BAD_INPUT, FailureInfo.TRANSFER_NOT_ALLOWED);
        }

        /* Get the allowance, infinite for the account owner */
        uint startingAllowance = 0;
        if (spender == src) {
            startingAllowance = uint(-1);
        } else {
            startingAllowance = transferAllowances[src][spender];
        }

        /* Do the calculations, checking for {under,over}flow */
        MathError mathErr;
        uint allowanceNew;
        uint srcTokensNew;
        uint dstTokensNew;

        (mathErr, allowanceNew) = subUInt(startingAllowance, tokens);
        if (mathErr != MathError.NO_ERROR) {
            return fail(Error.MATH_ERROR, FailureInfo.TRANSFER_NOT_ALLOWED);
        }

        (mathErr, srcTokensNew) = subUInt(accountTokens[src], tokens);
        if (mathErr != MathError.NO_ERROR) {
            return fail(Error.MATH_ERROR, FailureInfo.TRANSFER_NOT_ENOUGH);
        }

        (mathErr, dstTokensNew) = addUInt(accountTokens[dst], tokens);
        if (mathErr != MathError.NO_ERROR) {
            return fail(Error.MATH_ERROR, FailureInfo.TRANSFER_TOO_MUCH);
        }

        /////////////////////////
        // EFFECTS & INTERACTIONS
        // (No safe failures beyond this point)

        accountTokens[src] = srcTokensNew;
        accountTokens[dst] = dstTokensNew;

        /* Eat some of the allowance (if necessary) */
        if (startingAllowance != uint(-1)) {
            transferAllowances[src][spender] = allowanceNew;
        }

        /* We emit a Transfer event */
        emit Transfer(src, dst, tokens);

        comptroller.transferVerify(address(this), src, dst, tokens);

        return uint(Error.NO_ERROR);
    }

    /**
     * @notice Transfer `amount` tokens from `msg.sender` to `dst`
     * @param dst The address of the destination account
     * @param amount The number of tokens to transfer
     * @return Whether or not the transfer succeeded
     */
    function transfer(address dst, uint256 amount) external nonReentrant returns (bool) {
        return transferTokens(msg.sender, msg.sender, dst, amount) == uint(Error.NO_ERROR);
    }

    /**
     * @notice Transfer `amount` tokens from `src` to `dst`
     * @param src The address of the source account
     * @param dst The address of the destination account
     * @param amount The number of tokens to transfer
     * @return Whether or not the transfer succeeded
     */
    function transferFrom(address src, address dst, uint256 amount) external nonReentrant returns (bool) {
        return transferTokens(msg.sender, src, dst, amount) == uint(Error.NO_ERROR);
    }

    /**
     * @notice Approve `spender` to transfer up to `amount` from `src`
     * @dev This will overwrite the approval amount for `spender`
     *  and is subject to issues noted [here](https://eips.ethereum.org/EIPS/eip-20#approve)
     * @param spender The address of the account which may transfer tokens
     * @param amount The number of tokens that are approved (-1 means infinite)
     * @return Whether or not the approval succeeded
     */
    function approve(address spender, uint256 amount) external returns (bool) {
        address src = msg.sender;
        transferAllowances[src][spender] = amount;
        emit Approval(src, spender, amount);
        return true;
    }

    /**
     * @notice Get the current allowance from `owner` for `spender`
     * @param owner The address of the account which owns the tokens to be spent
     * @param spender The address of the account which may transfer tokens
     * @return The number of tokens allowed to be spent (-1 means infinite)
     */
    function allowance(address owner, address spender) external view returns (uint256) {
        return transferAllowances[owner][spender];
    }

    /**
     * @notice Get the token balance of the `owner`
     * @param owner The address of the account to query
     * @return The number of tokens owned by `owner`
     */
    function balanceOf(address owner) external view returns (uint256) {
        return accountTokens[owner];
    }

    /**
     * @notice Get the underlying balance of the `owner`
     * @dev This also accrues interest in a transaction
     * @param owner The address of the account to query
     * @return The amount of underlying owned by `owner`
     */
    function balanceOfUnderlying(address owner) external returns (uint) {
        Exp memory exchangeRate = Exp({mantissa: exchangeRateCurrent()});
        (MathError mErr, uint balance) = mulScalarTruncate(exchangeRate, accountTokens[owner]);
        require(mErr == MathError.NO_ERROR, "balance could not be calculated");
        return balance;
    }

    /**
     * @notice Get a snapshot of the account's balances, and the cached exchange rate
     * @dev This is used by comptroller to more efficiently perform liquidity checks.
     * @param account Address of the account to snapshot
     * @return (possible error, token balance, borrow balance, exchange rate mantissa)
     */
    function getAccountSnapshot(address account) external view returns (uint, uint, uint, uint) {
        uint cTokenBalance = accountTokens[account];
        uint borrowBalance;
        uint exchangeRateMantissa;

        MathError mErr;

        (mErr, borrowBalance) = borrowBalanceStoredInternal(account);
        if (mErr != MathError.NO_ERROR) {
            return (uint(Error.MATH_ERROR), 0, 0, 0);
        }

        (mErr, exchangeRateMantissa) = exchangeRateStoredInternal();
        if (mErr != MathError.NO_ERROR) {
            return (uint(Error.MATH_ERROR), 0, 0, 0);
        }

        return (uint(Error.NO_ERROR), cTokenBalance, borrowBalance, exchangeRateMantissa);
    }

    /**
     * @dev Function to simply retrieve block number
     *  This exists mainly for inheriting test contracts to stub this result.
     */
    function getBlockNumber() internal view returns (uint) {
        return block.number;
    }

    /**
     * @notice Returns the current per-block borrow interest rate for this cToken
     * @return The borrow interest rate per block, scaled by 1e18
     */
    function borrowRatePerBlock() external view returns (uint) {
        return interestRateModel.getBorrowRate(getCashPrior(), totalBorrows, totalReserves);
    }

    /**
     * @notice Returns the current per-block supply interest rate for this cToken
     * @return The supply interest rate per block, scaled by 1e18
     */
    function supplyRatePerBlock() external view returns (uint) {
        return interestRateModel.getSupplyRate(getCashPrior(), totalBorrows, totalReserves, reserveFactorMantissa);
    }

    /**
     * @notice Returns the current total borrows plus accrued interest
     * @return The total borrows with interest
     */
    function totalBorrowsCurrent() external nonReentrant returns (uint) {
        require(accrueInterest() == uint(Error.NO_ERROR), "accrue interest failed");
        return totalBorrows;
    }

    /**
     * @notice Accrue interest to updated borrowIndex and then calculate account's borrow balance using the updated borrowIndex
     * @param account The address whose balance should be calculated after updating borrowIndex
     * @return The calculated balance
     */
    function borrowBalanceCurrent(address account) external nonReentrant returns (uint) {
        require(accrueInterest() == uint(Error.NO_ERROR), "accrue interest failed");
        return borrowBalanceStored(account);
    }

    /**
     * @notice Return the borrow balance of account based on stored data
     * @param account The address whose balance should be calculated
     * @return The calculated balance
     */
    function borrowBalanceStored(address account) public view returns (uint) {
        (MathError err, uint result) = borrowBalanceStoredInternal(account);
        require(err == MathError.NO_ERROR, "borrowBalanceStored: borrowBalanceStoredInternal failed");
        return result;
    }

    /**
     * @notice Return the borrow balance of account based on stored data
     * @param account The address whose balance should be calculated
     * @return (error code, the calculated balance or 0 if error code is non-zero)
     */
    function borrowBalanceStoredInternal(address account) internal view returns (MathError, uint) {
        /* Note: we do not assert that the market is up to date */
        MathError mathErr;
        uint principalTimesIndex;
        uint result;

        /* Get borrowBalance and borrowIndex */
        BorrowSnapshot storage borrowSnapshot = accountBorrows[account];

        /* If borrowBalance = 0 then borrowIndex is likely also 0.
         * Rather than failing the calculation with a division by 0, we immediately return 0 in this case.
         */
        if (borrowSnapshot.principal == 0) {
            return (MathError.NO_ERROR, 0);
        }

        /* Calculate new borrow balance using the interest index:
         *  recentBorrowBalance = borrower.borrowBalance * market.borrowIndex / borrower.borrowIndex
         */
        (mathErr, principalTimesIndex) = mulUInt(borrowSnapshot.principal, borrowIndex);
        if (mathErr != MathError.NO_ERROR) {
            return (mathErr, 0);
        }

        (mathErr, result) = divUInt(principalTimesIndex, borrowSnapshot.interestIndex);
        if (mathErr != MathError.NO_ERROR) {
            return (mathErr, 0);
        }

        return (MathError.NO_ERROR, result);
    }

    /**
     * @notice Accrue interest then return the up-to-date exchange rate
     * @return Calculated exchange rate scaled by 1e18
     */
    function exchangeRateCurrent() public nonReentrant returns (uint) {
        require(accrueInterest() == uint(Error.NO_ERROR), "accrue interest failed");
        return exchangeRateStored();
    }

    /**
     * @notice Calculates the exchange rate from the underlying to the CToken
     * @dev This function does not accrue interest before calculating the exchange rate
     * @return Calculated exchange rate scaled by 1e18
     */
    function exchangeRateStored() public view returns (uint) {
        (MathError err, uint result) = exchangeRateStoredInternal();
        require(err == MathError.NO_ERROR, "exchangeRateStored: exchangeRateStoredInternal failed");
        return result;
    }

    /**
     * @notice Calculates the exchange rate from the underlying to the CToken
     * @dev This function does not accrue interest before calculating the exchange rate
     * @return (error code, calculated exchange rate scaled by 1e18)
     */
    function exchangeRateStoredInternal() internal view returns (MathError, uint) {
        uint _totalSupply = totalSupply;
        if (_totalSupply == 0) {
            /*
             * If there are no tokens minted:
             *  exchangeRate = initialExchangeRate
             */
            return (MathError.NO_ERROR, initialExchangeRateMantissa);
        } else {
            /*
             * Otherwise:
             *  exchangeRate = (totalCash + totalBorrows - totalReserves) / totalSupply
             */
            uint totalCash = getCashPrior();
            uint cashPlusBorrowsMinusReserves;
            Exp memory exchangeRate;
            MathError mathErr;

            (mathErr, cashPlusBorrowsMinusReserves) = addThenSubUInt(totalCash, totalBorrows, totalReserves);
            if (mathErr != MathError.NO_ERROR) {
                return (mathErr, 0);
            }

            (mathErr, exchangeRate) = getExp(cashPlusBorrowsMinusReserves, _totalSupply);
            if (mathErr != MathError.NO_ERROR) {
                return (mathErr, 0);
            }

            return (MathError.NO_ERROR, exchangeRate.mantissa);
        }
    }

    /**
     * @notice Get cash balance of this cToken in the underlying asset
     * @return The quantity of underlying asset owned by this contract
     */
    function getCash() external view returns (uint) {
        return getCashPrior();
    }

    /**
     * @notice Applies accrued interest to total borrows and reserves
     * @dev This calculates interest accrued from the last checkpointed block
     *   up to the current block and writes new checkpoint to storage.
     */
    function accrueInterest() public returns (uint) {
        /* Remember the initial block number */
        uint currentBlockNumber = getBlockNumber();
        uint accrualBlockNumberPrior = accrualBlockNumber;

        /* Short-circuit accumulating 0 interest */
        if (accrualBlockNumberPrior == currentBlockNumber) {
            return uint(Error.NO_ERROR);
        }

        /* Read the previous values out of storage */
        uint cashPrior = getCashPrior();
        uint borrowsPrior = totalBorrows;
        uint reservesPrior = totalReserves;
        uint borrowIndexPrior = borrowIndex;

        /* Calculate the current borrow interest rate */
        uint borrowRateMantissa = interestRateModel.getBorrowRate(cashPrior, borrowsPrior, reservesPrior);
        require(borrowRateMantissa <= borrowRateMaxMantissa, "borrow rate is absurdly high");

        /* Calculate the number of blocks elapsed since the last accrual */
        (MathError mathErr, uint blockDelta) = subUInt(currentBlockNumber, accrualBlockNumberPrior);
        require(mathErr == MathError.NO_ERROR, "could not calculate block delta");

        /*
         * Calculate the interest accumulated into borrows and reserves and the new index:
         *  simpleInterestFactor = borrowRate * blockDelta
         *  interestAccumulated = simpleInterestFactor * totalBorrows
         *  totalBorrowsNew = interestAccumulated + totalBorrows
         *  totalReservesNew = interestAccumulated * reserveFactor + totalReserves
         *  borrowIndexNew = simpleInterestFactor * borrowIndex + borrowIndex
         */

        Exp memory simpleInterestFactor;
        uint interestAccumulated;
        uint totalBorrowsNew;
        uint totalReservesNew;
        uint borrowIndexNew;

        (mathErr, simpleInterestFactor) = mulScalar(Exp({mantissa: borrowRateMantissa}), blockDelta);
        if (mathErr != MathError.NO_ERROR) {
            return failOpaque(Error.MATH_ERROR, FailureInfo.ACCRUE_INTEREST_SIMPLE_INTEREST_FACTOR_CALCULATION_FAILED, uint(mathErr));
        }

        (mathErr, interestAccumulated) = mulScalarTruncate(simpleInterestFactor, borrowsPrior);
        if (mathErr != MathError.NO_ERROR) {
            return failOpaque(Error.MATH_ERROR, FailureInfo.ACCRUE_INTEREST_ACCUMULATED_INTEREST_CALCULATION_FAILED, uint(mathErr));
        }

        (mathErr, totalBorrowsNew) = addUInt(interestAccumulated, borrowsPrior);
        if (mathErr != MathError.NO_ERROR) {
            return failOpaque(Error.MATH_ERROR, FailureInfo.ACCRUE_INTEREST_NEW_TOTAL_BORROWS_CALCULATION_FAILED, uint(mathErr));
        }

        (mathErr, totalReservesNew) = mulScalarTruncateAddUInt(Exp({mantissa: reserveFactorMantissa}), interestAccumulated, reservesPrior);
        if (mathErr != MathError.NO_ERROR) {
            return failOpaque(Error.MATH_ERROR, FailureInfo.ACCRUE_INTEREST_NEW_TOTAL_RESERVES_CALCULATION_FAILED, uint(mathErr));
        }

        (mathErr, borrowIndexNew) = mulScalarTruncateAddUInt(simpleInterestFactor, borrowIndexPrior, borrowIndexPrior);
        if (mathErr != MathError.NO_ERROR) {
            return failOpaque(Error.MATH_ERROR, FailureInfo.ACCRUE_INTEREST_NEW_BORROW_INDEX_CALCULATION_FAILED, uint(mathErr));
        }

        /////////////////////////
        // EFFECTS & INTERACTIONS
        // (No safe failures beyond this point)

        /* We write the previously calculated values into storage */
        accrualBlockNumber = currentBlockNumber;
        borrowIndex = borrowIndexNew;
        totalBorrows = totalBorrowsNew;
        totalReserves = totalReservesNew;

        /* We emit an AccrueInterest event */
        emit AccrueInterest(cashPrior, interestAccumulated, borrowIndexNew, totalBorrowsNew);

        return uint(Error.NO_ERROR);
    }

    /**
     * @notice Sender supplies assets into the market and receives cTokens in exchange
     * @dev Accrues interest whether or not the operation succeeds, unless reverted
     * @param mintAmount The amount of the underlying asset to supply
     * @return (uint, uint) An error code (0=success, otherwise a failure, see ErrorReporter.sol), and the actual mint amount.
     */
    function mintInternal(uint mintAmount) internal nonReentrant returns (uint, uint) {
        uint error = accrueInterest();
        if (error != uint(Error.NO_ERROR)) {
            // accrueInterest emits logs on errors, but we still want to log the fact that an attempted borrow failed
            return (fail(Error(error), FailureInfo.MINT_ACCRUE_INTEREST_FAILED), 0);
        }
        // mintFresh emits the actual Mint event if successful and logs on errors, so we don't need to
        return mintFresh(msg.sender, mintAmount);
    }

    struct MintLocalVars {
        Error err;
        MathError mathErr;
        uint exchangeRateMantissa;
        uint mintTokens;
        uint totalSupplyNew;
        uint accountTokensNew;
        uint actualMintAmount;
    }

    /**
     * @notice User supplies assets into the market and receives cTokens in exchange
     * @dev Assumes interest has already been accrued up to the current block
     * @param minter The address of the account which is supplying the assets
     * @param mintAmount The amount of the underlying asset to supply
     * @return (uint, uint) An error code (0=success, otherwise a failure, see ErrorReporter.sol), and the actual mint amount.
     */
    function mintFresh(address minter, uint mintAmount) internal returns (uint, uint) {
        /* Fail if mint not allowed */
        uint allowed = comptroller.mintAllowed(address(this), minter, mintAmount);
        if (allowed != 0) {
            return (failOpaque(Error.COMPTROLLER_REJECTION, FailureInfo.MINT_COMPTROLLER_REJECTION, allowed), 0);
        }

        /* Verify market's block number equals current block number */
        if (accrualBlockNumber != getBlockNumber()) {
            return (fail(Error.MARKET_NOT_FRESH, FailureInfo.MINT_FRESHNESS_CHECK), 0);
        }

        MintLocalVars memory vars;

        (vars.mathErr, vars.exchangeRateMantissa) = exchangeRateStoredInternal();
        if (vars.mathErr != MathError.NO_ERROR) {
            return (failOpaque(Error.MATH_ERROR, FailureInfo.MINT_EXCHANGE_RATE_READ_FAILED, uint(vars.mathErr)), 0);
        }

        /////////////////////////
        // EFFECTS & INTERACTIONS
        // (No safe failures beyond this point)

        /*
         *  We call `doTransferIn` for the minter and the mintAmount.
         *  Note: The cToken must handle variations between ERC-20 and ETH underlying.
         *  `doTransferIn` reverts if anything goes wrong, since we can't be sure if
         *  side-effects occurred. The function returns the amount actually transferred,
         *  in case of a fee. On success, the cToken holds an additional `actualMintAmount`
         *  of cash.
         */
        vars.actualMintAmount = doTransferIn(minter, mintAmount);

        /*
         * We get the current exchange rate and calculate the number of cTokens to be minted:
         *  mintTokens = actualMintAmount / exchangeRate
         */

        (vars.mathErr, vars.mintTokens) = divScalarByExpTruncate(vars.actualMintAmount, Exp({mantissa: vars.exchangeRateMantissa}));
        require(vars.mathErr == MathError.NO_ERROR, "MINT_EXCHANGE_CALCULATION_FAILED");

        /*
         * We calculate the new total supply of cTokens and minter token balance, checking for overflow:
         *  totalSupplyNew = totalSupply + mintTokens
         *  accountTokensNew = accountTokens[minter] + mintTokens
         */
        (vars.mathErr, vars.totalSupplyNew) = addUInt(totalSupply, vars.mintTokens);
        require(vars.mathErr == MathError.NO_ERROR, "MINT_NEW_TOTAL_SUPPLY_CALCULATION_FAILED");

        (vars.mathErr, vars.accountTokensNew) = addUInt(accountTokens[minter], vars.mintTokens);
        require(vars.mathErr == MathError.NO_ERROR, "MINT_NEW_ACCOUNT_BALANCE_CALCULATION_FAILED");

        /* We write previously calculated values into storage */
        totalSupply = vars.totalSupplyNew;
        accountTokens[minter] = vars.accountTokensNew;

        /* We emit a Mint event, and a Transfer event */
        emit Mint(minter, vars.actualMintAmount, vars.mintTokens);
        emit Transfer(address(this), minter, vars.mintTokens);

        /* We call the defense hook */
        comptroller.mintVerify(address(this), minter, vars.actualMintAmount, vars.mintTokens);

        return (uint(Error.NO_ERROR), vars.actualMintAmount);
    }

    /**
     * @notice Sender redeems cTokens in exchange for the underlying asset
     * @dev Accrues interest whether or not the operation succeeds, unless reverted
     * @param redeemTokens The number of cTokens to redeem into underlying
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function redeemInternal(uint redeemTokens) internal nonReentrant returns (uint) {
        uint error = accrueInterest();
        if (error != uint(Error.NO_ERROR)) {
            // accrueInterest emits logs on errors, but we still want to log the fact that an attempted redeem failed
            return fail(Error(error), FailureInfo.REDEEM_ACCRUE_INTEREST_FAILED);
        }
        // redeemFresh emits redeem-specific logs on errors, so we don't need to
        return redeemFresh(msg.sender, redeemTokens, 0);
    }

    /**
     * @notice Sender redeems cTokens in exchange for a specified amount of underlying asset
     * @dev Accrues interest whether or not the operation succeeds, unless reverted
     * @param redeemAmount The amount of underlying to receive from redeeming cTokens
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function redeemUnderlyingInternal(uint redeemAmount) internal nonReentrant returns (uint) {
        uint error = accrueInterest();
        if (error != uint(Error.NO_ERROR)) {
            // accrueInterest emits logs on errors, but we still want to log the fact that an attempted redeem failed
            return fail(Error(error), FailureInfo.REDEEM_ACCRUE_INTEREST_FAILED);
        }
        // redeemFresh emits redeem-specific logs on errors, so we don't need to
        return redeemFresh(msg.sender, 0, redeemAmount);
    }

    struct RedeemLocalVars {
        Error err;
        MathError mathErr;
        uint exchangeRateMantissa;
        uint redeemTokens;
        uint redeemAmount;
        uint totalSupplyNew;
        uint accountTokensNew;
    }

    /**
     * @notice User redeems cTokens in exchange for the underlying asset
     * @dev Assumes interest has already been accrued up to the current block
     * @param redeemer The address of the account which is redeeming the tokens
     * @param redeemTokensIn The number of cTokens to redeem into underlying (only one of redeemTokensIn or redeemAmountIn may be non-zero)
     * @param redeemAmountIn The number of underlying tokens to receive from redeeming cTokens (only one of redeemTokensIn or redeemAmountIn may be non-zero)
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function redeemFresh(address payable redeemer, uint redeemTokensIn, uint redeemAmountIn) internal returns (uint) {
        require(redeemTokensIn == 0 || redeemAmountIn == 0, "one of redeemTokensIn or redeemAmountIn must be zero");

        RedeemLocalVars memory vars;

        /* exchangeRate = invoke Exchange Rate Stored() */
        (vars.mathErr, vars.exchangeRateMantissa) = exchangeRateStoredInternal();
        if (vars.mathErr != MathError.NO_ERROR) {
            return failOpaque(Error.MATH_ERROR, FailureInfo.REDEEM_EXCHANGE_RATE_READ_FAILED, uint(vars.mathErr));
        }

        /* If redeemTokensIn > 0: */
        if (redeemTokensIn > 0) {
            /*
             * We calculate the exchange rate and the amount of underlying to be redeemed:
             *  redeemTokens = redeemTokensIn
             *  redeemAmount = redeemTokensIn x exchangeRateCurrent
             */
            vars.redeemTokens = redeemTokensIn;

            (vars.mathErr, vars.redeemAmount) = mulScalarTruncate(Exp({mantissa: vars.exchangeRateMantissa}), redeemTokensIn);
            if (vars.mathErr != MathError.NO_ERROR) {
                return failOpaque(Error.MATH_ERROR, FailureInfo.REDEEM_EXCHANGE_TOKENS_CALCULATION_FAILED, uint(vars.mathErr));
            }
        } else {
            /*
             * We get the current exchange rate and calculate the amount to be redeemed:
             *  redeemTokens = redeemAmountIn / exchangeRate
             *  redeemAmount = redeemAmountIn
             */

            (vars.mathErr, vars.redeemTokens) = divScalarByExpTruncate(redeemAmountIn, Exp({mantissa: vars.exchangeRateMantissa}));
            if (vars.mathErr != MathError.NO_ERROR) {
                return failOpaque(Error.MATH_ERROR, FailureInfo.REDEEM_EXCHANGE_AMOUNT_CALCULATION_FAILED, uint(vars.mathErr));
            }

            vars.redeemAmount = redeemAmountIn;
        }

        /* Fail if redeem not allowed */
        uint allowed = comptroller.redeemAllowed(address(this), redeemer, vars.redeemTokens);
        if (allowed != 0) {
            return failOpaque(Error.COMPTROLLER_REJECTION, FailureInfo.REDEEM_COMPTROLLER_REJECTION, allowed);
        }

        /* Verify market's block number equals current block number */
        if (accrualBlockNumber != getBlockNumber()) {
            return fail(Error.MARKET_NOT_FRESH, FailureInfo.REDEEM_FRESHNESS_CHECK);
        }

        /*
         * We calculate the new total supply and redeemer balance, checking for underflow:
         *  totalSupplyNew = totalSupply - redeemTokens
         *  accountTokensNew = accountTokens[redeemer] - redeemTokens
         */
        (vars.mathErr, vars.totalSupplyNew) = subUInt(totalSupply, vars.redeemTokens);
        if (vars.mathErr != MathError.NO_ERROR) {
            return failOpaque(Error.MATH_ERROR, FailureInfo.REDEEM_NEW_TOTAL_SUPPLY_CALCULATION_FAILED, uint(vars.mathErr));
        }

        (vars.mathErr, vars.accountTokensNew) = subUInt(accountTokens[redeemer], vars.redeemTokens);
        if (vars.mathErr != MathError.NO_ERROR) {
            return failOpaque(Error.MATH_ERROR, FailureInfo.REDEEM_NEW_ACCOUNT_BALANCE_CALCULATION_FAILED, uint(vars.mathErr));
        }

        /* Fail gracefully if protocol has insufficient cash */
        if (getCashPrior() < vars.redeemAmount) {
            return fail(Error.TOKEN_INSUFFICIENT_CASH, FailureInfo.REDEEM_TRANSFER_OUT_NOT_POSSIBLE);
        }

        /////////////////////////
        // EFFECTS & INTERACTIONS
        // (No safe failures beyond this point)

        /*
         * We invoke doTransferOut for the redeemer and the redeemAmount.
         *  Note: The cToken must handle variations between ERC-20 and ETH underlying.
         *  On success, the cToken has redeemAmount less of cash.
         *  doTransferOut reverts if anything goes wrong, since we can't be sure if side effects occurred.
         */
        doTransferOut(redeemer, vars.redeemAmount);

        /* We write previously calculated values into storage */
        totalSupply = vars.totalSupplyNew;
        accountTokens[redeemer] = vars.accountTokensNew;

        /* We emit a Transfer event, and a Redeem event */
        emit Transfer(redeemer, address(this), vars.redeemTokens);
        emit Redeem(redeemer, vars.redeemAmount, vars.redeemTokens);

        /* We call the defense hook */
        comptroller.redeemVerify(address(this), redeemer, vars.redeemAmount, vars.redeemTokens);

        return uint(Error.NO_ERROR);
    }

    /**
      * @notice Sender borrows assets from the protocol to their own address
      * @param borrowAmount The amount of the underlying asset to borrow
      * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
      */
    function borrowInternal(uint borrowAmount) internal nonReentrant returns (uint) {
        uint error = accrueInterest();
        if (error != uint(Error.NO_ERROR)) {
            // accrueInterest emits logs on errors, but we still want to log the fact that an attempted borrow failed
            return fail(Error(error), FailureInfo.BORROW_ACCRUE_INTEREST_FAILED);
        }
        // borrowFresh emits borrow-specific logs on errors, so we don't need to
        return borrowFresh(msg.sender, borrowAmount);
    }

    struct BorrowLocalVars {
        MathError mathErr;
        uint accountBorrows;
        uint accountBorrowsNew;
        uint totalBorrowsNew;
    }

    /**
      * @notice Users borrow assets from the protocol to their own address
      * @param borrowAmount The amount of the underlying asset to borrow
      * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
      */
    function borrowFresh(address payable borrower, uint borrowAmount) internal returns (uint) {
        /* Fail if borrow not allowed */
        uint allowed = comptroller.borrowAllowed(address(this), borrower, borrowAmount);
        if (allowed != 0) {
            return failOpaque(Error.COMPTROLLER_REJECTION, FailureInfo.BORROW_COMPTROLLER_REJECTION, allowed);
        }

        /* Verify market's block number equals current block number */
        if (accrualBlockNumber != getBlockNumber()) {
            return fail(Error.MARKET_NOT_FRESH, FailureInfo.BORROW_FRESHNESS_CHECK);
        }

        /* Fail gracefully if protocol has insufficient underlying cash */
        if (getCashPrior() < borrowAmount) {
            return fail(Error.TOKEN_INSUFFICIENT_CASH, FailureInfo.BORROW_CASH_NOT_AVAILABLE);
        }

        BorrowLocalVars memory vars;

        /*
         * We calculate the new borrower and total borrow balances, failing on overflow:
         *  accountBorrowsNew = accountBorrows + borrowAmount
         *  totalBorrowsNew = totalBorrows + borrowAmount
         */
        (vars.mathErr, vars.accountBorrows) = borrowBalanceStoredInternal(borrower);
        if (vars.mathErr != MathError.NO_ERROR) {
            return failOpaque(Error.MATH_ERROR, FailureInfo.BORROW_ACCUMULATED_BALANCE_CALCULATION_FAILED, uint(vars.mathErr));
        }

        (vars.mathErr, vars.accountBorrowsNew) = addUInt(vars.accountBorrows, borrowAmount);
        if (vars.mathErr != MathError.NO_ERROR) {
            return failOpaque(Error.MATH_ERROR, FailureInfo.BORROW_NEW_ACCOUNT_BORROW_BALANCE_CALCULATION_FAILED, uint(vars.mathErr));
        }

        (vars.mathErr, vars.totalBorrowsNew) = addUInt(totalBorrows, borrowAmount);
        if (vars.mathErr != MathError.NO_ERROR) {
            return failOpaque(Error.MATH_ERROR, FailureInfo.BORROW_NEW_TOTAL_BALANCE_CALCULATION_FAILED, uint(vars.mathErr));
        }

        /////////////////////////
        // EFFECTS & INTERACTIONS
        // (No safe failures beyond this point)

        /*
         * We invoke doTransferOut for the borrower and the borrowAmount.
         *  Note: The cToken must handle variations between ERC-20 and ETH underlying.
         *  On success, the cToken borrowAmount less of cash.
         *  doTransferOut reverts if anything goes wrong, since we can't be sure if side effects occurred.
         */
        doTransferOut(borrower, borrowAmount);

        /* We write the previously calculated values into storage */
        accountBorrows[borrower].principal = vars.accountBorrowsNew;
        accountBorrows[borrower].interestIndex = borrowIndex;
        totalBorrows = vars.totalBorrowsNew;

        /* We emit a Borrow event */
        emit Borrow(borrower, borrowAmount, vars.accountBorrowsNew, vars.totalBorrowsNew);

        /* We call the defense hook */
        comptroller.borrowVerify(address(this), borrower, borrowAmount);

        return uint(Error.NO_ERROR);
    }

    /**
     * @notice Sender repays their own borrow
     * @param repayAmount The amount to repay
     * @return (uint, uint) An error code (0=success, otherwise a failure, see ErrorReporter.sol), and the actual repayment amount.
     */
    function repayBorrowInternal(uint repayAmount) internal nonReentrant returns (uint, uint) {
        uint error = accrueInterest();
        if (error != uint(Error.NO_ERROR)) {
            // accrueInterest emits logs on errors, but we still want to log the fact that an attempted borrow failed
            return (fail(Error(error), FailureInfo.REPAY_BORROW_ACCRUE_INTEREST_FAILED), 0);
        }
        // repayBorrowFresh emits repay-borrow-specific logs on errors, so we don't need to
        return repayBorrowFresh(msg.sender, msg.sender, repayAmount);
    }

    /**
     * @notice Sender repays a borrow belonging to borrower
     * @param borrower the account with the debt being payed off
     * @param repayAmount The amount to repay
     * @return (uint, uint) An error code (0=success, otherwise a failure, see ErrorReporter.sol), and the actual repayment amount.
     */
    function repayBorrowBehalfInternal(address borrower, uint repayAmount) internal nonReentrant returns (uint, uint) {
        uint error = accrueInterest();
        if (error != uint(Error.NO_ERROR)) {
            // accrueInterest emits logs on errors, but we still want to log the fact that an attempted borrow failed
            return (fail(Error(error), FailureInfo.REPAY_BEHALF_ACCRUE_INTEREST_FAILED), 0);
        }
        // repayBorrowFresh emits repay-borrow-specific logs on errors, so we don't need to
        return repayBorrowFresh(msg.sender, borrower, repayAmount);
    }

    struct RepayBorrowLocalVars {
        Error err;
        MathError mathErr;
        uint repayAmount;
        uint borrowerIndex;
        uint accountBorrows;
        uint accountBorrowsNew;
        uint totalBorrowsNew;
        uint actualRepayAmount;
    }

    /**
     * @notice Borrows are repaid by another user (possibly the borrower).
     * @param payer the account paying off the borrow
     * @param borrower the account with the debt being payed off
     * @param repayAmount the amount of undelrying tokens being returned
     * @return (uint, uint) An error code (0=success, otherwise a failure, see ErrorReporter.sol), and the actual repayment amount.
     */
    function repayBorrowFresh(address payer, address borrower, uint repayAmount) internal returns (uint, uint) {
        /* Fail if repayBorrow not allowed */
        uint allowed = comptroller.repayBorrowAllowed(address(this), payer, borrower, repayAmount);
        if (allowed != 0) {
            return (failOpaque(Error.COMPTROLLER_REJECTION, FailureInfo.REPAY_BORROW_COMPTROLLER_REJECTION, allowed), 0);
        }

        /* Verify market's block number equals current block number */
        if (accrualBlockNumber != getBlockNumber()) {
            return (fail(Error.MARKET_NOT_FRESH, FailureInfo.REPAY_BORROW_FRESHNESS_CHECK), 0);
        }

        RepayBorrowLocalVars memory vars;

        /* We remember the original borrowerIndex for verification purposes */
        vars.borrowerIndex = accountBorrows[borrower].interestIndex;

        /* We fetch the amount the borrower owes, with accumulated interest */
        (vars.mathErr, vars.accountBorrows) = borrowBalanceStoredInternal(borrower);
        if (vars.mathErr != MathError.NO_ERROR) {
            return (failOpaque(Error.MATH_ERROR, FailureInfo.REPAY_BORROW_ACCUMULATED_BALANCE_CALCULATION_FAILED, uint(vars.mathErr)), 0);
        }

        /* If repayAmount == -1, repayAmount = accountBorrows */
        if (repayAmount == uint(-1)) {
            vars.repayAmount = vars.accountBorrows;
        } else {
            vars.repayAmount = repayAmount;
        }

        /////////////////////////
        // EFFECTS & INTERACTIONS
        // (No safe failures beyond this point)

        /*
         * We call doTransferIn for the payer and the repayAmount
         *  Note: The cToken must handle variations between ERC-20 and ETH underlying.
         *  On success, the cToken holds an additional repayAmount of cash.
         *  doTransferIn reverts if anything goes wrong, since we can't be sure if side effects occurred.
         *   it returns the amount actually transferred, in case of a fee.
         */
        vars.actualRepayAmount = doTransferIn(payer, vars.repayAmount);

        /*
         * We calculate the new borrower and total borrow balances, failing on underflow:
         *  accountBorrowsNew = accountBorrows - actualRepayAmount
         *  totalBorrowsNew = totalBorrows - actualRepayAmount
         */
        (vars.mathErr, vars.accountBorrowsNew) = subUInt(vars.accountBorrows, vars.actualRepayAmount);
        require(vars.mathErr == MathError.NO_ERROR, "REPAY_BORROW_NEW_ACCOUNT_BORROW_BALANCE_CALCULATION_FAILED");

        (vars.mathErr, vars.totalBorrowsNew) = subUInt(totalBorrows, vars.actualRepayAmount);
        require(vars.mathErr == MathError.NO_ERROR, "REPAY_BORROW_NEW_TOTAL_BALANCE_CALCULATION_FAILED");

        /* We write the previously calculated values into storage */
        accountBorrows[borrower].principal = vars.accountBorrowsNew;
        accountBorrows[borrower].interestIndex = borrowIndex;
        totalBorrows = vars.totalBorrowsNew;

        /* We emit a RepayBorrow event */
        emit RepayBorrow(payer, borrower, vars.actualRepayAmount, vars.accountBorrowsNew, vars.totalBorrowsNew);

        /* We call the defense hook */
        comptroller.repayBorrowVerify(address(this), payer, borrower, vars.actualRepayAmount, vars.borrowerIndex);

        return (uint(Error.NO_ERROR), vars.actualRepayAmount);
    }

    /**
     * @notice The sender liquidates the borrowers collateral.
     *  The collateral seized is transferred to the liquidator.
     * @param borrower The borrower of this cToken to be liquidated
     * @param cTokenCollateral The market in which to seize collateral from the borrower
     * @param repayAmount The amount of the underlying borrowed asset to repay
     * @return (uint, uint) An error code (0=success, otherwise a failure, see ErrorReporter.sol), and the actual repayment amount.
     */
    function liquidateBorrowInternal(address borrower, uint repayAmount, CTokenInterface cTokenCollateral) internal nonReentrant returns (uint, uint) {
        uint error = accrueInterest();
        if (error != uint(Error.NO_ERROR)) {
            // accrueInterest emits logs on errors, but we still want to log the fact that an attempted liquidation failed
            return (fail(Error(error), FailureInfo.LIQUIDATE_ACCRUE_BORROW_INTEREST_FAILED), 0);
        }

        error = cTokenCollateral.accrueInterest();
        if (error != uint(Error.NO_ERROR)) {
            // accrueInterest emits logs on errors, but we still want to log the fact that an attempted liquidation failed
            return (fail(Error(error), FailureInfo.LIQUIDATE_ACCRUE_COLLATERAL_INTEREST_FAILED), 0);
        }

        // liquidateBorrowFresh emits borrow-specific logs on errors, so we don't need to
        return liquidateBorrowFresh(msg.sender, borrower, repayAmount, cTokenCollateral);
    }

    /**
     * @notice The liquidator liquidates the borrowers collateral.
     *  The collateral seized is transferred to the liquidator.
     * @param borrower The borrower of this cToken to be liquidated
     * @param liquidator The address repaying the borrow and seizing collateral
     * @param cTokenCollateral The market in which to seize collateral from the borrower
     * @param repayAmount The amount of the underlying borrowed asset to repay
     * @return (uint, uint) An error code (0=success, otherwise a failure, see ErrorReporter.sol), and the actual repayment amount.
     */
    function liquidateBorrowFresh(address liquidator, address borrower, uint repayAmount, CTokenInterface cTokenCollateral) internal returns (uint, uint) {
        /* Fail if liquidate not allowed */
        uint allowed = comptroller.liquidateBorrowAllowed(address(this), address(cTokenCollateral), liquidator, borrower, repayAmount);
        if (allowed != 0) {
            return (failOpaque(Error.COMPTROLLER_REJECTION, FailureInfo.LIQUIDATE_COMPTROLLER_REJECTION, allowed), 0);
        }

        /* Verify market's block number equals current block number */
        if (accrualBlockNumber != getBlockNumber()) {
            return (fail(Error.MARKET_NOT_FRESH, FailureInfo.LIQUIDATE_FRESHNESS_CHECK), 0);
        }

        /* Verify cTokenCollateral market's block number equals current block number */
        if (cTokenCollateral.accrualBlockNumber() != getBlockNumber()) {
            return (fail(Error.MARKET_NOT_FRESH, FailureInfo.LIQUIDATE_COLLATERAL_FRESHNESS_CHECK), 0);
        }

        /* Fail if borrower = liquidator */
        if (borrower == liquidator) {
            return (fail(Error.INVALID_ACCOUNT_PAIR, FailureInfo.LIQUIDATE_LIQUIDATOR_IS_BORROWER), 0);
        }

        /* Fail if repayAmount = 0 */
        if (repayAmount == 0) {
            return (fail(Error.INVALID_CLOSE_AMOUNT_REQUESTED, FailureInfo.LIQUIDATE_CLOSE_AMOUNT_IS_ZERO), 0);
        }

        /* Fail if repayAmount = -1 */
        if (repayAmount == uint(-1)) {
            return (fail(Error.INVALID_CLOSE_AMOUNT_REQUESTED, FailureInfo.LIQUIDATE_CLOSE_AMOUNT_IS_UINT_MAX), 0);
        }


        /* Fail if repayBorrow fails */
        (uint repayBorrowError, uint actualRepayAmount) = repayBorrowFresh(liquidator, borrower, repayAmount);
        if (repayBorrowError != uint(Error.NO_ERROR)) {
            return (fail(Error(repayBorrowError), FailureInfo.LIQUIDATE_REPAY_BORROW_FRESH_FAILED), 0);
        }

        /////////////////////////
        // EFFECTS & INTERACTIONS
        // (No safe failures beyond this point)

        /* We calculate the number of collateral tokens that will be seized */
        (uint amountSeizeError, uint seizeTokens) = comptroller.liquidateCalculateSeizeTokens(address(this), address(cTokenCollateral), actualRepayAmount);
        require(amountSeizeError == uint(Error.NO_ERROR), "LIQUIDATE_COMPTROLLER_CALCULATE_AMOUNT_SEIZE_FAILED");

        /* Revert if borrower collateral token balance < seizeTokens */
        require(cTokenCollateral.balanceOf(borrower) >= seizeTokens, "LIQUIDATE_SEIZE_TOO_MUCH");

        // If this is also the collateral, run seizeInternal to avoid re-entrancy, otherwise make an external call
        uint seizeError;
        if (address(cTokenCollateral) == address(this)) {
            seizeError = seizeInternal(address(this), liquidator, borrower, seizeTokens);
        } else {
            seizeError = cTokenCollateral.seize(liquidator, borrower, seizeTokens);
        }

        /* Revert if seize tokens fails (since we cannot be sure of side effects) */
        require(seizeError == uint(Error.NO_ERROR), "token seizure failed");

        /* We emit a LiquidateBorrow event */
        emit LiquidateBorrow(liquidator, borrower, actualRepayAmount, address(cTokenCollateral), seizeTokens);

        /* We call the defense hook */
        comptroller.liquidateBorrowVerify(address(this), address(cTokenCollateral), liquidator, borrower, actualRepayAmount, seizeTokens);

        return (uint(Error.NO_ERROR), actualRepayAmount);
    }

    /**
     * @notice Transfers collateral tokens (this market) to the liquidator.
     * @dev Will fail unless called by another cToken during the process of liquidation.
     *  Its absolutely critical to use msg.sender as the borrowed cToken and not a parameter.
     * @param liquidator The account receiving seized collateral
     * @param borrower The account having collateral seized
     * @param seizeTokens The number of cTokens to seize
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function seize(address liquidator, address borrower, uint seizeTokens) external nonReentrant returns (uint) {
        return seizeInternal(msg.sender, liquidator, borrower, seizeTokens);
    }

    /**
     * @notice Transfers collateral tokens (this market) to the liquidator.
     * @dev Called only during an in-kind liquidation, or by liquidateBorrow during the liquidation of another CToken.
     *  Its absolutely critical to use msg.sender as the seizer cToken and not a parameter.
     * @param seizerToken The contract seizing the collateral (i.e. borrowed cToken)
     * @param liquidator The account receiving seized collateral
     * @param borrower The account having collateral seized
     * @param seizeTokens The number of cTokens to seize
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function seizeInternal(address seizerToken, address liquidator, address borrower, uint seizeTokens) internal returns (uint) {
        /* Fail if seize not allowed */
        uint allowed = comptroller.seizeAllowed(address(this), seizerToken, liquidator, borrower, seizeTokens);
        if (allowed != 0) {
            return failOpaque(Error.COMPTROLLER_REJECTION, FailureInfo.LIQUIDATE_SEIZE_COMPTROLLER_REJECTION, allowed);
        }

        /* Fail if borrower = liquidator */
        if (borrower == liquidator) {
            return fail(Error.INVALID_ACCOUNT_PAIR, FailureInfo.LIQUIDATE_SEIZE_LIQUIDATOR_IS_BORROWER);
        }

        MathError mathErr;
        uint borrowerTokensNew;
        uint liquidatorTokensNew;

        /*
         * We calculate the new borrower and liquidator token balances, failing on underflow/overflow:
         *  borrowerTokensNew = accountTokens[borrower] - seizeTokens
         *  liquidatorTokensNew = accountTokens[liquidator] + seizeTokens
         */
        (mathErr, borrowerTokensNew) = subUInt(accountTokens[borrower], seizeTokens);
        if (mathErr != MathError.NO_ERROR) {
            return failOpaque(Error.MATH_ERROR, FailureInfo.LIQUIDATE_SEIZE_BALANCE_DECREMENT_FAILED, uint(mathErr));
        }

        (mathErr, liquidatorTokensNew) = addUInt(accountTokens[liquidator], seizeTokens);
        if (mathErr != MathError.NO_ERROR) {
            return failOpaque(Error.MATH_ERROR, FailureInfo.LIQUIDATE_SEIZE_BALANCE_INCREMENT_FAILED, uint(mathErr));
        }

        /////////////////////////
        // EFFECTS & INTERACTIONS
        // (No safe failures beyond this point)

        /* We write the previously calculated values into storage */
        accountTokens[borrower] = borrowerTokensNew;
        accountTokens[liquidator] = liquidatorTokensNew;

        /* Emit a Transfer event */
        emit Transfer(borrower, liquidator, seizeTokens);

        /* We call the defense hook */
        comptroller.seizeVerify(address(this), seizerToken, liquidator, borrower, seizeTokens);

        return uint(Error.NO_ERROR);
    }


    /*** Admin Functions ***/

    /**
      * @notice Begins transfer of admin rights. The newPendingAdmin must call `_acceptAdmin` to finalize the transfer.
      * @dev Admin function to begin change of admin. The newPendingAdmin must call `_acceptAdmin` to finalize the transfer.
      * @param newPendingAdmin New pending admin.
      * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
      */
    function _setPendingAdmin(address payable newPendingAdmin) external returns (uint) {
        // Check caller = admin
        if (msg.sender != admin) {
            return fail(Error.UNAUTHORIZED, FailureInfo.SET_PENDING_ADMIN_OWNER_CHECK);
        }

        // Save current value, if any, for inclusion in log
        address oldPendingAdmin = pendingAdmin;

        // Store pendingAdmin with value newPendingAdmin
        pendingAdmin = newPendingAdmin;

        // Emit NewPendingAdmin(oldPendingAdmin, newPendingAdmin)
        emit NewPendingAdmin(oldPendingAdmin, newPendingAdmin);

        return uint(Error.NO_ERROR);
    }

    /**
      * @notice Accepts transfer of admin rights. msg.sender must be pendingAdmin
      * @dev Admin function for pending admin to accept role and update admin
      * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
      */
    function _acceptAdmin() external returns (uint) {
        // Check caller is pendingAdmin and pendingAdmin ≠ address(0)
        if (msg.sender != pendingAdmin || msg.sender == address(0)) {
            return fail(Error.UNAUTHORIZED, FailureInfo.ACCEPT_ADMIN_PENDING_ADMIN_CHECK);
        }

        // Save current values for inclusion in log
        address oldAdmin = admin;
        address oldPendingAdmin = pendingAdmin;

        // Store admin with value pendingAdmin
        admin = pendingAdmin;

        // Clear the pending value
        pendingAdmin = address(0);

        emit NewAdmin(oldAdmin, admin);
        emit NewPendingAdmin(oldPendingAdmin, pendingAdmin);

        return uint(Error.NO_ERROR);
    }

    /**
      * @notice Sets a new comptroller for the market
      * @dev Admin function to set a new comptroller
      * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
      */
    function _setComptroller(ComptrollerInterface newComptroller) public returns (uint) {
        // Check caller is admin
        if (msg.sender != admin) {
            return fail(Error.UNAUTHORIZED, FailureInfo.SET_COMPTROLLER_OWNER_CHECK);
        }

        ComptrollerInterface oldComptroller = comptroller;
        // Ensure invoke comptroller.isComptroller() returns true
        require(newComptroller.isComptroller(), "marker method returned false");

        // Set market's comptroller to newComptroller
        comptroller = newComptroller;

        // Emit NewComptroller(oldComptroller, newComptroller)
        emit NewComptroller(oldComptroller, newComptroller);

        return uint(Error.NO_ERROR);
    }

    /**
      * @notice accrues interest and sets a new reserve factor for the protocol using _setReserveFactorFresh
      * @dev Admin function to accrue interest and set a new reserve factor
      * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
      */
    function _setReserveFactor(uint newReserveFactorMantissa) external nonReentrant returns (uint) {
        uint error = accrueInterest();
        if (error != uint(Error.NO_ERROR)) {
            // accrueInterest emits logs on errors, but on top of that we want to log the fact that an attempted reserve factor change failed.
            return fail(Error(error), FailureInfo.SET_RESERVE_FACTOR_ACCRUE_INTEREST_FAILED);
        }
        // _setReserveFactorFresh emits reserve-factor-specific logs on errors, so we don't need to.
        return _setReserveFactorFresh(newReserveFactorMantissa);
    }

    /**
      * @notice Sets a new reserve factor for the protocol (*requires fresh interest accrual)
      * @dev Admin function to set a new reserve factor
      * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
      */
    function _setReserveFactorFresh(uint newReserveFactorMantissa) internal returns (uint) {
        // Check caller is admin
        if (msg.sender != admin) {
            return fail(Error.UNAUTHORIZED, FailureInfo.SET_RESERVE_FACTOR_ADMIN_CHECK);
        }

        // Verify market's block number equals current block number
        if (accrualBlockNumber != getBlockNumber()) {
            return fail(Error.MARKET_NOT_FRESH, FailureInfo.SET_RESERVE_FACTOR_FRESH_CHECK);
        }

        // Check newReserveFactor ≤ maxReserveFactor
        if (newReserveFactorMantissa > reserveFactorMaxMantissa) {
            return fail(Error.BAD_INPUT, FailureInfo.SET_RESERVE_FACTOR_BOUNDS_CHECK);
        }

        uint oldReserveFactorMantissa = reserveFactorMantissa;
        reserveFactorMantissa = newReserveFactorMantissa;

        emit NewReserveFactor(oldReserveFactorMantissa, newReserveFactorMantissa);

        return uint(Error.NO_ERROR);
    }

    /**
     * @notice Accrues interest and reduces reserves by transferring from msg.sender
     * @param addAmount Amount of addition to reserves
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function _addReservesInternal(uint addAmount) internal nonReentrant returns (uint) {
        uint error = accrueInterest();
        if (error != uint(Error.NO_ERROR)) {
            // accrueInterest emits logs on errors, but on top of that we want to log the fact that an attempted reduce reserves failed.
            return fail(Error(error), FailureInfo.ADD_RESERVES_ACCRUE_INTEREST_FAILED);
        }

        // _addReservesFresh emits reserve-addition-specific logs on errors, so we don't need to.
        (error, ) = _addReservesFresh(addAmount);
        return error;
    }

    /**
     * @notice Add reserves by transferring from caller
     * @dev Requires fresh interest accrual
     * @param addAmount Amount of addition to reserves
     * @return (uint, uint) An error code (0=success, otherwise a failure (see ErrorReporter.sol for details)) and the actual amount added, net token fees
     */
    function _addReservesFresh(uint addAmount) internal returns (uint, uint) {
        // totalReserves + actualAddAmount
        uint totalReservesNew;
        uint actualAddAmount;

        // We fail gracefully unless market's block number equals current block number
        if (accrualBlockNumber != getBlockNumber()) {
            return (fail(Error.MARKET_NOT_FRESH, FailureInfo.ADD_RESERVES_FRESH_CHECK), actualAddAmount);
        }

        /////////////////////////
        // EFFECTS & INTERACTIONS
        // (No safe failures beyond this point)

        /*
         * We call doTransferIn for the caller and the addAmount
         *  Note: The cToken must handle variations between ERC-20 and ETH underlying.
         *  On success, the cToken holds an additional addAmount of cash.
         *  doTransferIn reverts if anything goes wrong, since we can't be sure if side effects occurred.
         *  it returns the amount actually transferred, in case of a fee.
         */

        actualAddAmount = doTransferIn(msg.sender, addAmount);

        totalReservesNew = totalReserves + actualAddAmount;

        /* Revert on overflow */
        require(totalReservesNew >= totalReserves, "add reserves unexpected overflow");

        // Store reserves[n+1] = reserves[n] + actualAddAmount
        totalReserves = totalReservesNew;

        /* Emit NewReserves(admin, actualAddAmount, reserves[n+1]) */
        emit ReservesAdded(msg.sender, actualAddAmount, totalReservesNew);

        /* Return (NO_ERROR, actualAddAmount) */
        return (uint(Error.NO_ERROR), actualAddAmount);
    }


    /**
     * @notice Accrues interest and reduces reserves by transferring to admin
     * @param reduceAmount Amount of reduction to reserves
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function _reduceReserves(uint reduceAmount) external nonReentrant returns (uint) {
        uint error = accrueInterest();
        if (error != uint(Error.NO_ERROR)) {
            // accrueInterest emits logs on errors, but on top of that we want to log the fact that an attempted reduce reserves failed.
            return fail(Error(error), FailureInfo.REDUCE_RESERVES_ACCRUE_INTEREST_FAILED);
        }
        // _reduceReservesFresh emits reserve-reduction-specific logs on errors, so we don't need to.
        return _reduceReservesFresh(reduceAmount);
    }

    /**
     * @notice Reduces reserves by transferring to admin
     * @dev Requires fresh interest accrual
     * @param reduceAmount Amount of reduction to reserves
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function _reduceReservesFresh(uint reduceAmount) internal returns (uint) {
        // totalReserves - reduceAmount
        uint totalReservesNew;

        // Check caller is admin
        if (msg.sender != admin) {
            return fail(Error.UNAUTHORIZED, FailureInfo.REDUCE_RESERVES_ADMIN_CHECK);
        }

        // We fail gracefully unless market's block number equals current block number
        if (accrualBlockNumber != getBlockNumber()) {
            return fail(Error.MARKET_NOT_FRESH, FailureInfo.REDUCE_RESERVES_FRESH_CHECK);
        }

        // Fail gracefully if protocol has insufficient underlying cash
        if (getCashPrior() < reduceAmount) {
            return fail(Error.TOKEN_INSUFFICIENT_CASH, FailureInfo.REDUCE_RESERVES_CASH_NOT_AVAILABLE);
        }

        // Check reduceAmount ≤ reserves[n] (totalReserves)
        if (reduceAmount > totalReserves) {
            return fail(Error.BAD_INPUT, FailureInfo.REDUCE_RESERVES_VALIDATION);
        }

        /////////////////////////
        // EFFECTS & INTERACTIONS
        // (No safe failures beyond this point)

        totalReservesNew = totalReserves - reduceAmount;
        // We checked reduceAmount <= totalReserves above, so this should never revert.
        require(totalReservesNew <= totalReserves, "reduce reserves unexpected underflow");

        // Store reserves[n+1] = reserves[n] - reduceAmount
        totalReserves = totalReservesNew;

        // doTransferOut reverts if anything goes wrong, since we can't be sure if side effects occurred.
        doTransferOut(admin, reduceAmount);

        emit ReservesReduced(admin, reduceAmount, totalReservesNew);

        return uint(Error.NO_ERROR);
    }

    /**
     * @notice accrues interest and updates the interest rate model using _setInterestRateModelFresh
     * @dev Admin function to accrue interest and update the interest rate model
     * @param newInterestRateModel the new interest rate model to use
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function _setInterestRateModel(InterestRateModel newInterestRateModel) public returns (uint) {
        uint error = accrueInterest();
        if (error != uint(Error.NO_ERROR)) {
            // accrueInterest emits logs on errors, but on top of that we want to log the fact that an attempted change of interest rate model failed
            return fail(Error(error), FailureInfo.SET_INTEREST_RATE_MODEL_ACCRUE_INTEREST_FAILED);
        }
        // _setInterestRateModelFresh emits interest-rate-model-update-specific logs on errors, so we don't need to.
        return _setInterestRateModelFresh(newInterestRateModel);
    }

    /**
     * @notice updates the interest rate model (*requires fresh interest accrual)
     * @dev Admin function to update the interest rate model
     * @param newInterestRateModel the new interest rate model to use
     * @return uint 0=success, otherwise a failure (see ErrorReporter.sol for details)
     */
    function _setInterestRateModelFresh(InterestRateModel newInterestRateModel) internal returns (uint) {

        // Used to store old model for use in the event that is emitted on success
        InterestRateModel oldInterestRateModel;

        // Check caller is admin
        if (msg.sender != admin) {
            return fail(Error.UNAUTHORIZED, FailureInfo.SET_INTEREST_RATE_MODEL_OWNER_CHECK);
        }

        // We fail gracefully unless market's block number equals current block number
        if (accrualBlockNumber != getBlockNumber()) {
            return fail(Error.MARKET_NOT_FRESH, FailureInfo.SET_INTEREST_RATE_MODEL_FRESH_CHECK);
        }

        // Track the market's current interest rate model
        oldInterestRateModel = interestRateModel;

        // Ensure invoke newInterestRateModel.isInterestRateModel() returns true
        require(newInterestRateModel.isInterestRateModel(), "marker method returned false");

        // Set the interest rate model to newInterestRateModel
        interestRateModel = newInterestRateModel;

        // Emit NewMarketInterestRateModel(oldInterestRateModel, newInterestRateModel)
        emit NewMarketInterestRateModel(oldInterestRateModel, newInterestRateModel);

        return uint(Error.NO_ERROR);
    }

    /*** Safe Token ***/

    /**
     * @notice Gets balance of this contract in terms of the underlying
     * @dev This excludes the value of the current message, if any
     * @return The quantity of underlying owned by this contract
     */
    function getCashPrior() internal view returns (uint);

    /**
     * @dev Performs a transfer in, reverting upon failure. Returns the amount actually transferred to the protocol, in case of a fee.
     *  This may revert due to insufficient balance or insufficient allowance.
     */
    function doTransferIn(address from, uint amount) internal returns (uint);

    /**
     * @dev Performs a transfer out, ideally returning an explanatory error code upon failure tather than reverting.
     *  If caller has not called checked protocol's balance, may revert due to insufficient cash held in the contract.
     *  If caller has checked protocol's balance, and verified it is >= amount, this should not revert in normal conditions.
     */
    function doTransferOut(address payable to, uint amount) internal;


    /*** Reentrancy Guard ***/

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     */
    modifier nonReentrant() {
        require(_notEntered, "re-entered");
        _notEntered = false;
        _;
        _notEntered = true; // get a gas-refund post-Istanbul
    }
}

// File: contracts/ComptrollerInterface.sol



pragma solidity ^0.5.16;

contract ComptrollerInterface {
    /// @notice Indicator that this is a Comptroller contract (for inspection)
    bool public constant isComptroller = true;

    /*** Assets You Are In ***/

    function enterMarkets(address[] calldata cTokens) external returns (uint[] memory);
    function exitMarket(address cToken) external returns (uint);

    /*** Policy Hooks ***/

    function mintAllowed(address cToken, address minter, uint mintAmount) external returns (uint);
    function mintVerify(address cToken, address minter, uint mintAmount, uint mintTokens) external;

    function redeemAllowed(address cToken, address redeemer, uint redeemTokens) external returns (uint);
    function redeemVerify(address cToken, address redeemer, uint redeemAmount, uint redeemTokens) external;

    function borrowAllowed(address cToken, address borrower, uint borrowAmount) external returns (uint);
    function borrowVerify(address cToken, address borrower, uint borrowAmount) external;

    function repayBorrowAllowed(
        address cToken,
        address payer,
        address borrower,
        uint repayAmount) external returns (uint);
    function repayBorrowVerify(
        address cToken,
        address payer,
        address borrower,
        uint repayAmount,
        uint borrowerIndex) external;

    function liquidateBorrowAllowed(
        address cTokenBorrowed,
        address cTokenCollateral,
        address liquidator,
        address borrower,
        uint repayAmount) external returns (uint);
    function liquidateBorrowVerify(
        address cTokenBorrowed,
        address cTokenCollateral,
        address liquidator,
        address borrower,
        uint repayAmount,
        uint seizeTokens) external;

    function seizeAllowed(
        address cTokenCollateral,
        address cTokenBorrowed,
        address liquidator,
        address borrower,
        uint seizeTokens) external returns (uint);
    function seizeVerify(
        address cTokenCollateral,
        address cTokenBorrowed,
        address liquidator,
        address borrower,
        uint seizeTokens) external;

    function transferAllowed(address cToken, address src, address dst, uint transferTokens) external returns (uint);
    function transferVerify(address cToken, address src, address dst, uint transferTokens) external;

    /*** Liquidity/Liquidation Calculations ***/

    function liquidateCalculateSeizeTokens(
        address cTokenBorrowed,
        address cTokenCollateral,
        uint repayAmount) external view returns (uint, uint);
}

// File: contracts/CTokenInterfaces.sol



pragma solidity ^0.5.16;

import "./ComptrollerInterface.sol";
import "./InterestRateModel.sol";

contract CTokenStorage {
    /**
     * @dev Guard variable for re-entrancy checks
     */
    bool internal _notEntered;

    /**
     * @notice EIP-20 token name for this token
     */
    string public name;

    /**
     * @notice EIP-20 token symbol for this token
     */
    string public symbol;

    /**
     * @notice EIP-20 token decimals for this token
     */
    uint8 public decimals;

    /**
     * @notice Maximum borrow rate that can ever be applied (.0005% / block)
     */

    uint internal constant borrowRateMaxMantissa = 0.0005e16;

    /**
     * @notice Maximum fraction of interest that can be set aside for reserves
     */
    uint internal constant reserveFactorMaxMantissa = 1e18;

    /**
     * @notice Administrator for this contract
     */
    address payable public admin;

    /**
     * @notice Pending administrator for this contract
     */
    address payable public pendingAdmin;

    /**
     * @notice Contract which oversees inter-cToken operations
     */
    ComptrollerInterface public comptroller;

    /**
     * @notice Model which tells what the current interest rate should be
     */
    InterestRateModel public interestRateModel;

    /**
     * @notice Initial exchange rate used when minting the first CTokens (used when totalSupply = 0)
     */
    uint internal initialExchangeRateMantissa;

    /**
     * @notice Fraction of interest currently set aside for reserves
     */
    uint public reserveFactorMantissa;

    /**
     * @notice Block number that interest was last accrued at
     */
    uint public accrualBlockNumber;

    /**
     * @notice Accumulator of the total earned interest rate since the opening of the market
     */
    uint public borrowIndex;

    /**
     * @notice Total amount of outstanding borrows of the underlying in this market
     */
    uint public totalBorrows;

    /**
     * @notice Total amount of reserves of the underlying held in this market
     */
    uint public totalReserves;

    /**
     * @notice Total number of tokens in circulation
     */
    uint public totalSupply;

    /**
     * @notice Official record of token balances for each account
     */
    mapping (address => uint) internal accountTokens;

    /**
     * @notice Approved token transfer amounts on behalf of others
     */
    mapping (address => mapping (address => uint)) internal transferAllowances;

    /**
     * @notice Container for borrow balance information
     * @member principal Total balance (with accrued interest), after applying the most recent balance-changing action
     * @member interestIndex Global borrowIndex as of the most recent balance-changing action
     */
    struct BorrowSnapshot {
        uint principal;
        uint interestIndex;
    }

    /**
     * @notice Mapping of account addresses to outstanding borrow balances
     */
    mapping(address => BorrowSnapshot) internal accountBorrows;
}

contract CTokenInterface is CTokenStorage {
    /**
     * @notice Indicator that this is a CToken contract (for inspection)
     */
    bool public constant isCToken = true;


    /*** Market Events ***/

    /**
     * @notice Event emitted when interest is accrued
     */
    event AccrueInterest(uint cashPrior, uint interestAccumulated, uint borrowIndex, uint totalBorrows);

    /**
     * @notice Event emitted when tokens are minted
     */
    event Mint(address minter, uint mintAmount, uint mintTokens);

    /**
     * @notice Event emitted when tokens are redeemed
     */
    event Redeem(address redeemer, uint redeemAmount, uint redeemTokens);

    /**
     * @notice Event emitted when underlying is borrowed
     */
    event Borrow(address borrower, uint borrowAmount, uint accountBorrows, uint totalBorrows);

    /**
     * @notice Event emitted when a borrow is repaid
     */
    event RepayBorrow(address payer, address borrower, uint repayAmount, uint accountBorrows, uint totalBorrows);

    /**
     * @notice Event emitted when a borrow is liquidated
     */
    event LiquidateBorrow(address liquidator, address borrower, uint repayAmount, address cTokenCollateral, uint seizeTokens);


    /*** Admin Events ***/

    /**
     * @notice Event emitted when pendingAdmin is changed
     */
    event NewPendingAdmin(address oldPendingAdmin, address newPendingAdmin);

    /**
     * @notice Event emitted when pendingAdmin is accepted, which means admin is updated
     */
    event NewAdmin(address oldAdmin, address newAdmin);

    /**
     * @notice Event emitted when comptroller is changed
     */
    event NewComptroller(ComptrollerInterface oldComptroller, ComptrollerInterface newComptroller);

    /**
     * @notice Event emitted when interestRateModel is changed
     */
    event NewMarketInterestRateModel(InterestRateModel oldInterestRateModel, InterestRateModel newInterestRateModel);

    /**
     * @notice Event emitted when the reserve factor is changed
     */
    event NewReserveFactor(uint oldReserveFactorMantissa, uint newReserveFactorMantissa);

    /**
     * @notice Event emitted when the reserves are added
     */
    event ReservesAdded(address benefactor, uint addAmount, uint newTotalReserves);

    /**
     * @notice Event emitted when the reserves are reduced
     */
    event ReservesReduced(address admin, uint reduceAmount, uint newTotalReserves);

    /**
     * @notice EIP20 Transfer event
     */
    event Transfer(address indexed from, address indexed to, uint amount);

    /**
     * @notice EIP20 Approval event
     */
    event Approval(address indexed owner, address indexed spender, uint amount);

    /**
     * @notice Failure event
     */
    event Failure(uint error, uint info, uint detail);


    /*** User Interface ***/

    function transfer(address dst, uint amount) external returns (bool);
    function transferFrom(address src, address dst, uint amount) external returns (bool);
    function approve(address spender, uint amount) external returns (bool);
    function allowance(address owner, address spender) external view returns (uint);
    function balanceOf(address owner) external view returns (uint);
    function balanceOfUnderlying(address owner) external returns (uint);
    function getAccountSnapshot(address account) external view returns (uint, uint, uint, uint);
    function borrowRatePerBlock() external view returns (uint);
    function supplyRatePerBlock() external view returns (uint);
    function totalBorrowsCurrent() external returns (uint);
    function borrowBalanceCurrent(address account) external returns (uint);
    function borrowBalanceStored(address account) public view returns (uint);
    function exchangeRateCurrent() public returns (uint);
    function exchangeRateStored() public view returns (uint);
    function getCash() external view returns (uint);
    function accrueInterest() public returns (uint);
    function seize(address liquidator, address borrower, uint seizeTokens) external returns (uint);


    /*** Admin Functions ***/

    function _setPendingAdmin(address payable newPendingAdmin) external returns (uint);
    function _acceptAdmin() external returns (uint);
    function _setComptroller(ComptrollerInterface newComptroller) public returns (uint);
    function _setReserveFactor(uint newReserveFactorMantissa) external returns (uint);
    function _reduceReserves(uint reduceAmount) external returns (uint);
    function _setInterestRateModel(InterestRateModel newInterestRateModel) public returns (uint);
}

contract CErc20Storage {
    /**
     * @notice Underlying asset for this CToken
     */
    address public underlying;
}

contract CErc20Interface is CErc20Storage {

    /*** User Interface ***/

    function mint(uint mintAmount) external returns (uint);
    function redeem(uint redeemTokens) external returns (uint);
    function redeemUnderlying(uint redeemAmount) external returns (uint);
    function borrow(uint borrowAmount) external returns (uint);
    function repayBorrow(uint repayAmount) external returns (uint);
    function repayBorrowBehalf(address borrower, uint repayAmount) external returns (uint);
    function liquidateBorrow(address borrower, uint repayAmount, CTokenInterface cTokenCollateral) external returns (uint);


    /*** Admin Functions ***/

    function _addReserves(uint addAmount) external returns (uint);
}

contract CDelegationStorage {
    /**
     * @notice Implementation address for this contract
     */
    address public implementation;
}

contract CDelegatorInterface is CDelegationStorage {
    /**
     * @notice Emitted when implementation is changed
     */
    event NewImplementation(address oldImplementation, address newImplementation);

    /**
     * @notice Called by the admin to update the implementation of the delegator
     * @param implementation_ The address of the new implementation for delegation
     * @param allowResign Flag to indicate whether to call _resignImplementation on the old implementation
     * @param becomeImplementationData The encoded bytes data to be passed to _becomeImplementation
     */
    function _setImplementation(address implementation_, bool allowResign, bytes memory becomeImplementationData) public;
}

contract CDelegateInterface is CDelegationStorage {
    /**
     * @notice Called by the delegator on a delegate to initialize it for duty
     * @dev Should revert if any issues arise which make it unfit for delegation
     * @param data The encoded bytes data for any initialization
     */
    function _becomeImplementation(bytes memory data) public;

    /**
     * @notice Called by the delegator on a delegate to forfeit its responsibility
     */
    function _resignImplementation() public;
}

// File: contracts/ErrorReporter.sol



pragma solidity ^0.5.16;

contract ComptrollerErrorReporter {
    enum Error {
        NO_ERROR,
        UNAUTHORIZED,
        COMPTROLLER_MISMATCH,
        INSUFFICIENT_SHORTFALL,
        INSUFFICIENT_LIQUIDITY,
        INVALID_CLOSE_FACTOR,
        INVALID_COLLATERAL_FACTOR,
        INVALID_LIQUIDATION_INCENTIVE,
        MARKET_NOT_ENTERED, // no longer possible
        MARKET_NOT_LISTED,
        MARKET_ALREADY_LISTED,
        MATH_ERROR,
        NONZERO_BORROW_BALANCE,
        PRICE_ERROR,
        REJECTION,
        SNAPSHOT_ERROR,
        TOO_MANY_ASSETS,
        TOO_MUCH_REPAY
    }

    enum FailureInfo {
        ACCEPT_ADMIN_PENDING_ADMIN_CHECK,
        ACCEPT_PENDING_IMPLEMENTATION_ADDRESS_CHECK,
        EXIT_MARKET_BALANCE_OWED,
        EXIT_MARKET_REJECTION,
        SET_CLOSE_FACTOR_OWNER_CHECK,
        SET_CLOSE_FACTOR_VALIDATION,
        SET_COLLATERAL_FACTOR_OWNER_CHECK,
        SET_COLLATERAL_FACTOR_NO_EXISTS,
        SET_COLLATERAL_FACTOR_VALIDATION,
        SET_COLLATERAL_FACTOR_WITHOUT_PRICE,
        SET_IMPLEMENTATION_OWNER_CHECK,
        SET_LIQUIDATION_INCENTIVE_OWNER_CHECK,
        SET_LIQUIDATION_INCENTIVE_VALIDATION,
        SET_MAX_ASSETS_OWNER_CHECK,
        SET_PENDING_ADMIN_OWNER_CHECK,
        SET_PENDING_IMPLEMENTATION_OWNER_CHECK,
        SET_PRICE_ORACLE_OWNER_CHECK,
        SUPPORT_MARKET_EXISTS,
        SUPPORT_MARKET_OWNER_CHECK,
        SET_PAUSE_GUARDIAN_OWNER_CHECK
    }

    /**
      * @dev `error` corresponds to enum Error; `info` corresponds to enum FailureInfo, and `detail` is an arbitrary
      * contract-specific code that enables us to report opaque error codes from upgradeable contracts.
      **/
    event Failure(uint error, uint info, uint detail);

    /**
      * @dev use this when reporting a known error from the money market or a non-upgradeable collaborator
      */
    function fail(Error err, FailureInfo info) internal returns (uint) {
        emit Failure(uint(err), uint(info), 0);

        return uint(err);
    }

    /**
      * @dev use this when reporting an opaque error from an upgradeable collaborator contract
      */
    function failOpaque(Error err, FailureInfo info, uint opaqueError) internal returns (uint) {
        emit Failure(uint(err), uint(info), opaqueError);

        return uint(err);
    }
}

contract TokenErrorReporter {
    enum Error {
        NO_ERROR,
        UNAUTHORIZED,
        BAD_INPUT,
        COMPTROLLER_REJECTION,
        COMPTROLLER_CALCULATION_ERROR,
        INTEREST_RATE_MODEL_ERROR,
        INVALID_ACCOUNT_PAIR,
        INVALID_CLOSE_AMOUNT_REQUESTED,
        INVALID_COLLATERAL_FACTOR,
        MATH_ERROR,
        MARKET_NOT_FRESH,
        MARKET_NOT_LISTED,
        TOKEN_INSUFFICIENT_ALLOWANCE,
        TOKEN_INSUFFICIENT_BALANCE,
        TOKEN_INSUFFICIENT_CASH,
        TOKEN_TRANSFER_IN_FAILED,
        TOKEN_TRANSFER_OUT_FAILED
    }

    /*
     * Note: FailureInfo (but not Error) is kept in alphabetical order
     *       This is because FailureInfo grows significantly faster, and
     *       the order of Error has some meaning, while the order of FailureInfo
     *       is entirely arbitrary.
     */
    enum FailureInfo {
        ACCEPT_ADMIN_PENDING_ADMIN_CHECK,
        ACCRUE_INTEREST_ACCUMULATED_INTEREST_CALCULATION_FAILED,
        ACCRUE_INTEREST_BORROW_RATE_CALCULATION_FAILED,
        ACCRUE_INTEREST_NEW_BORROW_INDEX_CALCULATION_FAILED,
        ACCRUE_INTEREST_NEW_TOTAL_BORROWS_CALCULATION_FAILED,
        ACCRUE_INTEREST_NEW_TOTAL_RESERVES_CALCULATION_FAILED,
        ACCRUE_INTEREST_SIMPLE_INTEREST_FACTOR_CALCULATION_FAILED,
        BORROW_ACCUMULATED_BALANCE_CALCULATION_FAILED,
        BORROW_ACCRUE_INTEREST_FAILED,
        BORROW_CASH_NOT_AVAILABLE,
        BORROW_FRESHNESS_CHECK,
        BORROW_NEW_TOTAL_BALANCE_CALCULATION_FAILED,
        BORROW_NEW_ACCOUNT_BORROW_BALANCE_CALCULATION_FAILED,
        BORROW_MARKET_NOT_LISTED,
        BORROW_COMPTROLLER_REJECTION,
        LIQUIDATE_ACCRUE_BORROW_INTEREST_FAILED,
        LIQUIDATE_ACCRUE_COLLATERAL_INTEREST_FAILED,
        LIQUIDATE_COLLATERAL_FRESHNESS_CHECK,
        LIQUIDATE_COMPTROLLER_REJECTION,
        LIQUIDATE_COMPTROLLER_CALCULATE_AMOUNT_SEIZE_FAILED,
        LIQUIDATE_CLOSE_AMOUNT_IS_UINT_MAX,
        LIQUIDATE_CLOSE_AMOUNT_IS_ZERO,
        LIQUIDATE_FRESHNESS_CHECK,
        LIQUIDATE_LIQUIDATOR_IS_BORROWER,
        LIQUIDATE_REPAY_BORROW_FRESH_FAILED,
        LIQUIDATE_SEIZE_BALANCE_INCREMENT_FAILED,
        LIQUIDATE_SEIZE_BALANCE_DECREMENT_FAILED,
        LIQUIDATE_SEIZE_COMPTROLLER_REJECTION,
        LIQUIDATE_SEIZE_LIQUIDATOR_IS_BORROWER,
        LIQUIDATE_SEIZE_TOO_MUCH,
        MINT_ACCRUE_INTEREST_FAILED,
        MINT_COMPTROLLER_REJECTION,
        MINT_EXCHANGE_CALCULATION_FAILED,
        MINT_EXCHANGE_RATE_READ_FAILED,
        MINT_FRESHNESS_CHECK,
        MINT_NEW_ACCOUNT_BALANCE_CALCULATION_FAILED,
        MINT_NEW_TOTAL_SUPPLY_CALCULATION_FAILED,
        MINT_TRANSFER_IN_FAILED,
        MINT_TRANSFER_IN_NOT_POSSIBLE,
        REDEEM_ACCRUE_INTEREST_FAILED,
        REDEEM_COMPTROLLER_REJECTION,
        REDEEM_EXCHANGE_TOKENS_CALCULATION_FAILED,
        REDEEM_EXCHANGE_AMOUNT_CALCULATION_FAILED,
        REDEEM_EXCHANGE_RATE_READ_FAILED,
        REDEEM_FRESHNESS_CHECK,
        REDEEM_NEW_ACCOUNT_BALANCE_CALCULATION_FAILED,
        REDEEM_NEW_TOTAL_SUPPLY_CALCULATION_FAILED,
        REDEEM_TRANSFER_OUT_NOT_POSSIBLE,
        REDUCE_RESERVES_ACCRUE_INTEREST_FAILED,
        REDUCE_RESERVES_ADMIN_CHECK,
        REDUCE_RESERVES_CASH_NOT_AVAILABLE,
        REDUCE_RESERVES_FRESH_CHECK,
        REDUCE_RESERVES_VALIDATION,
        REPAY_BEHALF_ACCRUE_INTEREST_FAILED,
        REPAY_BORROW_ACCRUE_INTEREST_FAILED,
        REPAY_BORROW_ACCUMULATED_BALANCE_CALCULATION_FAILED,
        REPAY_BORROW_COMPTROLLER_REJECTION,
        REPAY_BORROW_FRESHNESS_CHECK,
        REPAY_BORROW_NEW_ACCOUNT_BORROW_BALANCE_CALCULATION_FAILED,
        REPAY_BORROW_NEW_TOTAL_BALANCE_CALCULATION_FAILED,
        REPAY_BORROW_TRANSFER_IN_NOT_POSSIBLE,
        SET_COLLATERAL_FACTOR_OWNER_CHECK,
        SET_COLLATERAL_FACTOR_VALIDATION,
        SET_COMPTROLLER_OWNER_CHECK,
        SET_INTEREST_RATE_MODEL_ACCRUE_INTEREST_FAILED,
        SET_INTEREST_RATE_MODEL_FRESH_CHECK,
        SET_INTEREST_RATE_MODEL_OWNER_CHECK,
        SET_MAX_ASSETS_OWNER_CHECK,
        SET_ORACLE_MARKET_NOT_LISTED,
        SET_PENDING_ADMIN_OWNER_CHECK,
        SET_RESERVE_FACTOR_ACCRUE_INTEREST_FAILED,
        SET_RESERVE_FACTOR_ADMIN_CHECK,
        SET_RESERVE_FACTOR_FRESH_CHECK,
        SET_RESERVE_FACTOR_BOUNDS_CHECK,
        TRANSFER_COMPTROLLER_REJECTION,
        TRANSFER_NOT_ALLOWED,
        TRANSFER_NOT_ENOUGH,
        TRANSFER_TOO_MUCH,
        ADD_RESERVES_ACCRUE_INTEREST_FAILED,
        ADD_RESERVES_FRESH_CHECK,
        ADD_RESERVES_TRANSFER_IN_NOT_POSSIBLE
    }

    /**
      * @dev `error` corresponds to enum Error; `info` corresponds to enum FailureInfo, and `detail` is an arbitrary
      * contract-specific code that enables us to report opaque error codes from upgradeable contracts.
      **/
    event Failure(uint error, uint info, uint detail);

    /**
      * @dev use this when reporting a known error from the money market or a non-upgradeable collaborator
      */
    function fail(Error err, FailureInfo info) internal returns (uint) {
        emit Failure(uint(err), uint(info), 0);

        return uint(err);
    }

    /**
      * @dev use this when reporting an opaque error from an upgradeable collaborator contract
      */
    function failOpaque(Error err, FailureInfo info, uint opaqueError) internal returns (uint) {
        emit Failure(uint(err), uint(info), opaqueError);

        return uint(err);
    }
}
// File: contracts/EIP20Interface.sol



pragma solidity ^0.5.16;

/**
 * @title ERC 20 Token Standard Interface
 *  https://eips.ethereum.org/EIPS/eip-20
 */
interface EIP20Interface {
    function name() external view returns (string memory);
    function symbol() external view returns (string memory);
    function decimals() external view returns (uint8);

    /**
      * @notice Get the total number of tokens in circulation
      * @return The supply of tokens
      */
    function totalSupply() external view returns (uint256);

    /**
     * @notice Gets the balance of the specified address
     * @param owner The address from which the balance will be retrieved
     * @return The balance
     */
    function balanceOf(address owner) external view returns (uint256 balance);

    /**
      * @notice Transfer `amount` tokens from `msg.sender` to `dst`
      * @param dst The address of the destination account
      * @param amount The number of tokens to transfer
      * @return Whether or not the transfer succeeded
      */
    function transfer(address dst, uint256 amount) external returns (bool success);

    /**
      * @notice Transfer `amount` tokens from `src` to `dst`
      * @param src The address of the source account
      * @param dst The address of the destination account
      * @param amount The number of tokens to transfer
      * @return Whether or not the transfer succeeded
      */
    function transferFrom(address src, address dst, uint256 amount) external returns (bool success);

    /**
      * @notice Approve `spender` to transfer up to `amount` from `src`
      * @dev This will overwrite the approval amount for `spender`
      *  and is subject to issues noted [here](https://eips.ethereum.org/EIPS/eip-20#approve)
      * @param spender The address of the account which may transfer tokens
      * @param amount The number of tokens that are approved (-1 means infinite)
      * @return Whether or not the approval succeeded
      */
    function approve(address spender, uint256 amount) external returns (bool success);

    /**
      * @notice Get the current allowance from `owner` for `spender`
      * @param owner The address of the account which owns the tokens to be spent
      * @param spender The address of the account which may transfer tokens
      * @return The number of tokens allowed to be spent (-1 means infinite)
      */
    function allowance(address owner, address spender) external view returns (uint256 remaining);

    event Transfer(address indexed from, address indexed to, uint256 amount);
    event Approval(address indexed owner, address indexed spender, uint256 amount);
}

// File: contracts/EIP20NonStandardInterface.sol



pragma solidity ^0.5.16;

/**
 * @title EIP20NonStandardInterface
 * @dev Version of ERC20 with no return values for `transfer` and `transferFrom`
 *  See https://medium.com/coinmonks/missing-return-value-bug-at-least-130-tokens-affected-d67bf08521ca
 */
interface EIP20NonStandardInterface {

    /**
     * @notice Get the total number of tokens in circulation
     * @return The supply of tokens
     */
    function totalSupply() external view returns (uint256);

    /**
     * @notice Gets the balance of the specified address
     * @param owner The address from which the balance will be retrieved
     * @return The balance
     */
    function balanceOf(address owner) external view returns (uint256 balance);

    ///
    /// !!!!!!!!!!!!!!
    /// !!! NOTICE !!! `transfer` does not return a value, in violation of the ERC-20 specification
    /// !!!!!!!!!!!!!!
    ///

    /**
      * @notice Transfer `amount` tokens from `msg.sender` to `dst`
      * @param dst The address of the destination account
      * @param amount The number of tokens to transfer
      */
    function transfer(address dst, uint256 amount) external;

    ///
    /// !!!!!!!!!!!!!!
    /// !!! NOTICE !!! `transferFrom` does not return a value, in violation of the ERC-20 specification
    /// !!!!!!!!!!!!!!
    ///

    /**
      * @notice Transfer `amount` tokens from `src` to `dst`
      * @param src The address of the source account
      * @param dst The address of the destination account
      * @param amount The number of tokens to transfer
      */
    function transferFrom(address src, address dst, uint256 amount) external;

    /**
      * @notice Approve `spender` to transfer up to `amount` from `src`
      * @dev This will overwrite the approval amount for `spender`
      *  and is subject to issues noted [here](https://eips.ethereum.org/EIPS/eip-20#approve)
      * @param spender The address of the account which may transfer tokens
      * @param amount The number of tokens that are approved
      * @return Whether or not the approval succeeded
      */
    function approve(address spender, uint256 amount) external returns (bool success);

    /**
      * @notice Get the current allowance from `owner` for `spender`
      * @param owner The address of the account which owns the tokens to be spent
      * @param spender The address of the account which may transfer tokens
      * @return The number of tokens allowed to be spent
      */
    function allowance(address owner, address spender) external view returns (uint256 remaining);

    event Transfer(address indexed from, address indexed to, uint256 amount);
    event Approval(address indexed owner, address indexed spender, uint256 amount);
}

// File: contracts/InterestRateModel.sol



pragma solidity ^0.5.16;

/**
  * @title Compound's InterestRateModel Interface
  * @author Compound
  */
contract InterestRateModel {
    /// @notice Indicator that this is an InterestRateModel contract (for inspection)
    bool public constant isInterestRateModel = true;

    /**
      * @notice Calculates the current borrow interest rate per block
      * @param cash The total amount of cash the market has
      * @param borrows The total amount of borrows the market has outstanding
      * @param reserves The total amount of reserves the market has
      * @return The borrow rate per block (as a percentage, and scaled by 1e18)
      */
    function getBorrowRate(uint cash, uint borrows, uint reserves) external view returns (uint);

    /**
      * @notice Calculates the current supply interest rate per block
      * @param cash The total amount of cash the market has
      * @param borrows The total amount of borrows the market has outstanding
      * @param reserves The total amount of reserves the market has
      * @param reserveFactorMantissa The current reserve factor the market has
      * @return The supply rate per block (as a percentage, and scaled by 1e18)
      */
    function getSupplyRate(uint cash, uint borrows, uint reserves, uint reserveFactorMantissa) external view returns (uint);

}

// File: contracts/CarefulMath.sol



pragma solidity ^0.5.16;

/**
  * @title Careful Math
  * @author Compound
  * @notice Derived from OpenZeppelin's SafeMath library
  *         https://github.com/OpenZeppelin/openzeppelin-solidity/blob/master/contracts/math/SafeMath.sol
  */
contract CarefulMath {

    /**
     * @dev Possible error codes that we can return
     */
    enum MathError {
        NO_ERROR,
        DIVISION_BY_ZERO,
        INTEGER_OVERFLOW,
        INTEGER_UNDERFLOW
    }

    /**
    * @dev Multiplies two numbers, returns an error on overflow.
    */
    function mulUInt(uint a, uint b) internal pure returns (MathError, uint) {
        if (a == 0) {
            return (MathError.NO_ERROR, 0);
        }

        uint c = a * b;

        if (c / a != b) {
            return (MathError.INTEGER_OVERFLOW, 0);
        } else {
            return (MathError.NO_ERROR, c);
        }
    }

    /**
    * @dev Integer division of two numbers, truncating the quotient.
    */
    function divUInt(uint a, uint b) internal pure returns (MathError, uint) {
        if (b == 0) {
            return (MathError.DIVISION_BY_ZERO, 0);
        }

        return (MathError.NO_ERROR, a / b);
    }

    /**
    * @dev Subtracts two numbers, returns an error on overflow (i.e. if subtrahend is greater than minuend).
    */
    function subUInt(uint a, uint b) internal pure returns (MathError, uint) {
        if (b <= a) {
            return (MathError.NO_ERROR, a - b);
        } else {
            return (MathError.INTEGER_UNDERFLOW, 0);
        }
    }

    /**
    * @dev Adds two numbers, returns an error on overflow.
    */
    function addUInt(uint a, uint b) internal pure returns (MathError, uint) {
        uint c = a + b;

        if (c >= a) {
            return (MathError.NO_ERROR, c);
        } else {
            return (MathError.INTEGER_OVERFLOW, 0);
        }
    }

    /**
    * @dev add a and b and then subtract c
    */
    function addThenSubUInt(uint a, uint b, uint c) internal pure returns (MathError, uint) {
        (MathError err0, uint sum) = addUInt(a, b);

        if (err0 != MathError.NO_ERROR) {
            return (err0, 0);
        }

        return subUInt(sum, c);
    }
}
// File: contracts/ExponentialNoError.sol



pragma solidity ^0.5.16;

/**
 * @title Exponential module for storing fixed-precision decimals
 * @author Compound
 * @notice Exp is a struct which stores decimals with a fixed precision of 18 decimal places.
 *         Thus, if we wanted to store the 5.1, mantissa would store 5.1e18. That is:
 *         `Exp({mantissa: 5100000000000000000})`.
 */
contract ExponentialNoError {
    uint constant expScale = 1e18;
    uint constant doubleScale = 1e36;
    uint constant halfExpScale = expScale/2;
    uint constant mantissaOne = expScale;

    struct Exp {
        uint mantissa;
    }

    struct Double {
        uint mantissa;
    }

    /**
     * @dev Truncates the given exp to a whole number value.
     *      For example, truncate(Exp{mantissa: 15 * expScale}) = 15
     */
    function truncate(Exp memory exp) pure internal returns (uint) {
        // Note: We are not using careful math here as we're performing a division that cannot fail
        return exp.mantissa / expScale;
    }

    /**
     * @dev Multiply an Exp by a scalar, then truncate to return an unsigned integer.
     */
    function mul_ScalarTruncate(Exp memory a, uint scalar) pure internal returns (uint) {
        Exp memory product = mul_(a, scalar);
        return truncate(product);
    }

    /**
     * @dev Multiply an Exp by a scalar, truncate, then add an to an unsigned integer, returning an unsigned integer.
     */
    function mul_ScalarTruncateAddUInt(Exp memory a, uint scalar, uint addend) pure internal returns (uint) {
        Exp memory product = mul_(a, scalar);
        return add_(truncate(product), addend);
    }

    /**
     * @dev Checks if first Exp is less than second Exp.
     */
    function lessThanExp(Exp memory left, Exp memory right) pure internal returns (bool) {
        return left.mantissa < right.mantissa;
    }

    /**
     * @dev Checks if left Exp <= right Exp.
     */
    function lessThanOrEqualExp(Exp memory left, Exp memory right) pure internal returns (bool) {
        return left.mantissa <= right.mantissa;
    }

    /**
     * @dev Checks if left Exp > right Exp.
     */
    function greaterThanExp(Exp memory left, Exp memory right) pure internal returns (bool) {
        return left.mantissa > right.mantissa;
    }

    /**
     * @dev returns true if Exp is exactly zero
     */
    function isZeroExp(Exp memory value) pure internal returns (bool) {
        return value.mantissa == 0;
    }

    function safe224(uint n, string memory errorMessage) pure internal returns (uint224) {
        require(n < 2**224, errorMessage);
        return uint224(n);
    }

    function safe32(uint n, string memory errorMessage) pure internal returns (uint32) {
        require(n < 2**32, errorMessage);
        return uint32(n);
    }

    function add_(Exp memory a, Exp memory b) pure internal returns (Exp memory) {
        return Exp({mantissa: add_(a.mantissa, b.mantissa)});
    }

    function add_(Double memory a, Double memory b) pure internal returns (Double memory) {
        return Double({mantissa: add_(a.mantissa, b.mantissa)});
    }

    function add_(uint a, uint b) pure internal returns (uint) {
        return add_(a, b, "addition overflow");
    }

    function add_(uint a, uint b, string memory errorMessage) pure internal returns (uint) {
        uint c = a + b;
        require(c >= a, errorMessage);
        return c;
    }

    function sub_(Exp memory a, Exp memory b) pure internal returns (Exp memory) {
        return Exp({mantissa: sub_(a.mantissa, b.mantissa)});
    }

    function sub_(Double memory a, Double memory b) pure internal returns (Double memory) {
        return Double({mantissa: sub_(a.mantissa, b.mantissa)});
    }

    function sub_(uint a, uint b) pure internal returns (uint) {
        return sub_(a, b, "subtraction underflow");
    }

    function sub_(uint a, uint b, string memory errorMessage) pure internal returns (uint) {
        require(b <= a, errorMessage);
        return a - b;
    }

    function mul_(Exp memory a, Exp memory b) pure internal returns (Exp memory) {
        return Exp({mantissa: mul_(a.mantissa, b.mantissa) / expScale});
    }

    function mul_(Exp memory a, uint b) pure internal returns (Exp memory) {
        return Exp({mantissa: mul_(a.mantissa, b)});
    }

    function mul_(uint a, Exp memory b) pure internal returns (uint) {
        return mul_(a, b.mantissa) / expScale;
    }

    function mul_(Double memory a, Double memory b) pure internal returns (Double memory) {
        return Double({mantissa: mul_(a.mantissa, b.mantissa) / doubleScale});
    }

    function mul_(Double memory a, uint b) pure internal returns (Double memory) {
        return Double({mantissa: mul_(a.mantissa, b)});
    }

    function mul_(uint a, Double memory b) pure internal returns (uint) {
        return mul_(a, b.mantissa) / doubleScale;
    }

    function mul_(uint a, uint b) pure internal returns (uint) {
        return mul_(a, b, "multiplication overflow");
    }

    function mul_(uint a, uint b, string memory errorMessage) pure internal returns (uint) {
        if (a == 0 || b == 0) {
            return 0;
        }
        uint c = a * b;
        require(c / a == b, errorMessage);
        return c;
    }

    function div_(Exp memory a, Exp memory b) pure internal returns (Exp memory) {
        return Exp({mantissa: div_(mul_(a.mantissa, expScale), b.mantissa)});
    }

    function div_(Exp memory a, uint b) pure internal returns (Exp memory) {
        return Exp({mantissa: div_(a.mantissa, b)});
    }

    function div_(uint a, Exp memory b) pure internal returns (uint) {
        return div_(mul_(a, expScale), b.mantissa);
    }

    function div_(Double memory a, Double memory b) pure internal returns (Double memory) {
        return Double({mantissa: div_(mul_(a.mantissa, doubleScale), b.mantissa)});
    }

    function div_(Double memory a, uint b) pure internal returns (Double memory) {
        return Double({mantissa: div_(a.mantissa, b)});
    }

    function div_(uint a, Double memory b) pure internal returns (uint) {
        return div_(mul_(a, doubleScale), b.mantissa);
    }

    function div_(uint a, uint b) pure internal returns (uint) {
        return div_(a, b, "divide by zero");
    }

    function div_(uint a, uint b, string memory errorMessage) pure internal returns (uint) {
        require(b > 0, errorMessage);
        return a / b;
    }

    function fraction(uint a, uint b) pure internal returns (Double memory) {
        return Double({mantissa: div_(mul_(a, doubleScale), b)});
    }
}