contract DSMath {
    function add(uint x, uint y) internal pure returns (uint z) {
        require((z = x + y) >= x, "ds-math-add-overflow");
    }
    function sub(uint x, uint y) internal pure returns (uint z) {
        require((z = x - y) <= x, "ds-math-sub-underflow");
    }
    function mul(uint x, uint y) internal pure returns (uint z) {
        require(y == 0 || (z = x * y) / y == x, "ds-math-mul-overflow");
    }

    function div(uint x, uint y) internal pure returns (uint z) {
        require(y > 0, "ds-math-div-overflow");
        z = x / y;
    }

    function min(uint x, uint y) internal pure returns (uint z) {
        return x <= y ? x : y;
    }
    function max(uint x, uint y) internal pure returns (uint z) {
        return x >= y ? x : y;
    }
    // function imin(int x, int y) internal pure returns (int z) {
    //     return x <= y ? x : y;
    // }
    // function imax(int x, int y) internal pure returns (int z) {
    //     return x >= y ? x : y;
    // }

    uint constant WAD = 10 ** 18;
    // uint constant RAY = 10 ** 27;

    // function wmul(uint x, uint y) internal pure returns (uint z) {
    //     z = add(mul(x, y), WAD / 2) / WAD;
    // }
    // function rmul(uint x, uint y) internal pure returns (uint z) {
    //     z = add(mul(x, y), RAY / 2) / RAY;
    // }
    function wdiv(uint x, uint y) internal pure returns (uint z) {
        z = add(mul(x, WAD), y / 2) / y;
    }
    // function rdiv(uint x, uint y) internal pure returns (uint z) {
    //     z = add(mul(x, RAY), y / 2) / y;
    // }

    // This famous algorithm is called "exponentiation by squaring"
    // and calculates x^n with x as fixed-point and n as regular unsigned.
    //
    // It's O(log n), instead of O(n) for naive repeated multiplication.
    //
    // These facts are why it works:
    //
    //  If n is even, then x^n = (x^2)^(n/2).
    //  If n is odd,  then x^n = x * x^(n-1),
    //   and applying the equation for even x gives
    //    x^n = x * (x^2)^((n-1) / 2).
    //
    //  Also, EVM division is flooring and
    //    floor[(n-1) / 2] = floor[n / 2].
    //
    // function rpow(uint _x, uint n) internal pure returns (uint z) {
    //     uint x = _x;
    //     z = n % 2 != 0 ? x : RAY;

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

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

    /**
     * @dev x to the power of y power(base, exponent)
     */
    function pow(uint256 base, uint256 exponent) public pure returns (uint256) {
        if (exponent == 0) {
            return 1;
        }
        else if (exponent == 1) {
            return base;
        }
        else if (base == 0 && exponent != 0) {
            return 0;
        }
        else {
            uint256 z = base;
            for (uint256 i = 1; i < exponent; i++)
                z = mul(z, base);
            return z;
        }
    }
}
function wdiv(uint x, uint y) internal pure returns (uint z) {
    z = add(mul(x, WAD), y / 2) / y;
}

// uint constant RAY = 10 ** 27;
// function wmul(uint x, uint y) internal pure returns (uint z) {
//     z = add(mul(x, y), WAD / 2) / WAD;
// }
// function rmul(uint x, uint y) internal pure returns (uint z) {
//     z = add(mul(x, y), RAY / 2) / RAY;
// }