pragma solidity ^0.6.0;

contract DSMath {
    uint constant WAD = 10 ** 18;
    uint constant RAY = 10 ** 27;

    function add(uint x, uint y) internal pure returns (uint z) {
        require((z = x + y) >= x, "math-not-safe");
    }

    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, "math-not-safe");
    }


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

    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;
    }

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

}