library WadRayMath {
    using SafeMath for uint256;

    uint256 internal constant WAD = 1e18;
    uint256 internal constant halfWAD = WAD / 2;

    uint256 internal constant RAY = 1e27;
    uint256 internal constant halfRAY = RAY / 2;

    uint256 internal constant WAD_RAY_RATIO = 1e9;

    /**
    * @return one ray, 1e27
    **/
    function ray() internal pure returns (uint256) {
        return RAY;
    }

    /**
    * @return one wad, 1e18
    **/

    function wad() internal pure returns (uint256) {
        return WAD;
    }

    /**
    * @return half ray, 1e27/2
    **/
    function halfRay() internal pure returns (uint256) {
        return halfRAY;
    }

    /**
    * @return half ray, 1e18/2
    **/
    function halfWad() internal pure returns (uint256) {
        return halfWAD;
    }

    /**
    * @dev multiplies two wad, rounding half up to the nearest wad
    * @param a wad
    * @param b wad
    * @return the result of a*b, in wad
    **/
    function wadMul(uint256 a, uint256 b) internal pure returns (uint256) {
        return halfWAD.add(a.mul(b)).div(WAD);
    }

    /**
    * @dev divides two wad, rounding half up to the nearest wad
    * @param a wad
    * @param b wad
    * @return the result of a/b, in wad
    **/
    function wadDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 halfB = b / 2;

        return halfB.add(a.mul(WAD)).div(b);
    }

    /**
    * @dev multiplies two ray, rounding half up to the nearest ray
    * @param a ray
    * @param b ray
    * @return the result of a*b, in ray
    **/
    function rayMul(uint256 a, uint256 b) internal pure returns (uint256) {
        return halfRAY.add(a.mul(b)).div(RAY);
    }

    /**
    * @dev divides two ray, rounding half up to the nearest ray
    * @param a ray
    * @param b ray
    * @return the result of a/b, in ray
    **/
    function rayDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 halfB = b / 2;

        return halfB.add(a.mul(RAY)).div(b);
    }

    /**
    * @dev casts ray down to wad
    * @param a ray
    * @return a casted to wad, rounded half up to the nearest wad
    **/
    function rayToWad(uint256 a) internal pure returns (uint256) {
        uint256 halfRatio = WAD_RAY_RATIO / 2;

        return halfRatio.add(a).div(WAD_RAY_RATIO);
    }

    /**
    * @dev convert wad up to ray
    * @param a wad
    * @return a converted in ray
    **/
    function wadToRay(uint256 a) internal pure returns (uint256) {
        return a.mul(WAD_RAY_RATIO);
    }

    /**
    * @dev calculates base^exp. The code uses the ModExp precompile
    * @return base^exp, in ray
    */
    //solium-disable-next-line
    function rayPow(uint256 x, uint256 n) internal pure returns (uint256 z) {

        z = n % 2 != 0 ? x : RAY;

        for (n /= 2; n != 0; n /= 2) {
            x = rayMul(x, x);

            if (n % 2 != 0) {
                z = rayMul(z, x);
            }
        }
    }

}
/**
 * @title WadRayMath library
 * @author Aave
 * @dev Provides mul and div function for wads (decimal numbers with 18 digits precision) and rays (decimals with 27 digits)
 **/
function rayDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 halfB = b / 2;

        return halfB.add(a.mul(RAY)).div(b);
    }
/**
 * @dev divides two ray, rounding half up to the nearest ray
 * @param a ray
 * @param b ray
 * @return the result of a/b, in ray
 **/