contract DharmaDaiImplementationV1 is DharmaTokenV1 {
  string internal constant _NAME = "Dharma Dai";
  string internal constant _SYMBOL = "dDai";
  string internal constant _UNDERLYING_NAME = "Dai";
  string internal constant _CTOKEN_SYMBOL = "cDai";

  CTokenInterface internal constant _CDAI = CTokenInterface(
    0x5d3a536E4D6DbD6114cc1Ead35777bAB948E3643 // mainnet
  );

  ERC20Interface internal constant _DAI = ERC20Interface(
    0x6B175474E89094C44Da98b954EedeAC495271d0F // mainnet
  );

  PotInterface internal constant _POT = PotInterface(
    0x197E90f9FAD81970bA7976f33CbD77088E5D7cf7 // mainnet
  );

  address internal constant _VAULT = 0x7e4A8391C728fEd9069B2962699AB416628B19Fa;

  /**
   * @notice Internal view function to get the current cDai exchange rate and
   * supply rate per block.
   * @return The current cDai exchange rate, or amount of Dai that is redeemable
   * for each cDai, and the cDai supply rate per block (with 18 decimal places
   * added to each returned rate).
   */
  function _getCurrentCTokenRates() internal view returns (
    uint256 exchangeRate, uint256 supplyRate
  ) {
    // Determine the number of blocks that have elapsed since last cDai accrual.
    uint256 blockDelta = block.number.sub(_CDAI.accrualBlockNumber());

    // Return stored values if accrual has already been performed this block.
    if (blockDelta == 0) return (
      _CDAI.exchangeRateStored(), _CDAI.supplyRatePerBlock()
    );
    
    // Determine total "cash" held by cDai contract by calculating DSR interest.
    uint256 cash = ( // solhint-disable-next-line not-rely-on-time
      _rpow(_POT.dsr(), now.sub(_POT.rho()), 1e27).mul(_POT.chi()) / 1e27 // chi
    ).mul(_POT.pie(address(_CDAI))) / 1e27;

    // Get the latest interest rate model from the cDai contract.
    CDaiInterestRateModelInterface interestRateModel = (
      CDaiInterestRateModelInterface(_CDAI.interestRateModel())
    );

    // Get the current stored total borrows, reserves, and reserve factor.
    uint256 borrows = _CDAI.totalBorrows();
    uint256 reserves = _CDAI.totalReserves();
    uint256 reserveFactor = _CDAI.reserveFactorMantissa();

    // Get accumulated borrow interest via interest rate model and block delta.
    uint256 interest = interestRateModel.getBorrowRate(
      cash, borrows, reserves
    ).mul(blockDelta).mul(borrows) / _SCALING_FACTOR;

    // Update total borrows and reserves using calculated accumulated interest.
    borrows = borrows.add(interest);
    reserves = reserves.add(reserveFactor.mul(interest) / _SCALING_FACTOR);

    // Determine cDai exchange rate: (cash + borrows - reserves) / total supply
    exchangeRate = (
      ((cash.add(borrows)).sub(reserves)).mul(_SCALING_FACTOR)
    ).div(_CDAI.totalSupply());

    // Get supply rate via interest rate model and calculated parameters.
    supplyRate = interestRateModel.getSupplyRate(
      cash, borrows, reserves, reserveFactor
    );
  }

  /**
   * @notice Internal pure function to supply the name of the underlying token.
   * @return The name of the underlying token.
   */
  function _getUnderlyingName() internal pure returns (string memory underlyingName) {
    underlyingName = _UNDERLYING_NAME;
  }

  /**
   * @notice Internal pure function to supply the address of the underlying
   * token.
   * @return The address of the underlying token.
   */
  function _getUnderlying() internal pure returns (address underlying) {
    underlying = address(_DAI);
  }

  /**
   * @notice Internal pure function to supply the symbol of the backing cToken.
   * @return The symbol of the backing cToken.
   */
  function _getCTokenSymbol() internal pure returns (string memory cTokenSymbol) {
    cTokenSymbol = _CTOKEN_SYMBOL;
  }

  /**
   * @notice Internal pure function to supply the address of the backing cToken.
   * @return The address of the backing cToken.
   */
  function _getCToken() internal pure returns (address cToken) {
    cToken = address(_CDAI);
  }

  /**
   * @notice Internal pure function to supply the name of the dToken.
   * @return The name of the dToken.
   */
  function _getDTokenName() internal pure returns (string memory dTokenName) {
    dTokenName = _NAME;
  }

  /**
   * @notice Internal pure function to supply the symbol of the dToken.
   * @return The symbol of the dToken.
   */
  function _getDTokenSymbol() internal pure returns (string memory dTokenSymbol) {
    dTokenSymbol = _SYMBOL;
  }

  /**
   * @notice Internal pure function to supply the address of the vault that
   * receives surplus cTokens whenever the surplus is pulled.
   * @return The address of the vault.
   */
  function _getVault() internal pure returns (address vault) {
    vault = _VAULT;
  }

  /**
   * @notice Internal pure function to directly emulate exponentiation performed
   * by the Dai Savings Rate contract.
   * @param x uint256 The number that will be raised to the given power.
   * @param n uint256 The power to raise that number by.
   * @param base uint256 The scaling factor that will be applied to n and z.
   * @return The number raised to the given power.
   */
  function _rpow(
    uint256 x, uint256 n, uint256 base
  ) internal pure returns (uint256 z) {
    assembly {
      switch x case 0 {switch n case 0 {z := base} default {z := 0}}
      default {
        switch mod(n, 2) case 0 { z := base } default { z := x }
        let half := div(base, 2)  // for rounding.
        for { n := div(n, 2) } n { n := div(n, 2) } {
          let xx := mul(x, x)
          if iszero(eq(div(xx, x), x)) { revert(0, 0) }
          let xxRound := add(xx, half)
          if lt(xxRound, xx) { revert(0, 0) }
          x := div(xxRound, base)
          if mod(n, 2) {
            let zx := mul(z, x)
            if and(iszero(iszero(x)), iszero(eq(div(zx, x), z))) { revert(0, 0) }
            let zxRound := add(zx, half)
            if lt(zxRound, zx) { revert(0, 0) }
            z := div(zxRound, base)
          }
        }
      }
    }
  }
}
/**
 * @title DharmaDaiImplementationV1
 * @author 0age (dToken mechanics derived from Compound cTokens, ERC20 methods
 * derived from Open Zeppelin's ERC20 contract)
 * @notice This contract provides the V1 implementation of Dharma Dai (or dDai),
 * an upgradeable, interest-bearing ERC20 token with cDai as the backing token
 * and Dai as the underlying token. The V1 dDai exchange rate will grow at 90%
 * the rate of the backing cDai exchange rate. Dharma Dai also supports
 * meta-transactions originating from externally-owned accounts, as well as from
 * contract accounts via ERC-1271.
 */
function _getCToken() internal pure returns (address cToken) {
    cToken = address(_CDAI);
  }
/**
 * @notice Internal pure function to supply the address of the backing cToken.
 * @return The address of the backing cToken.
 */