library StableMath {
    using SafeMath for uint256;

    /**
     * @dev Scaling unit for use in specific calculations,
     * where 1 * 10**18, or 1e18 represents a unit '1'
     */
    uint256 private constant FULL_SCALE = 1e18;

    /**
     * @notice Token Ratios are used when converting between units of bAsset, mAsset and MTA
     * Reasoning: Takes into account token decimals, and difference in base unit (i.e. grams to Troy oz for gold)
     * @dev bAsset ratio unit for use in exact calculations,
     * where (1 bAsset unit * bAsset.ratio) / ratioScale == x mAsset unit
     */
    uint256 private constant RATIO_SCALE = 1e8;

    /**
     * @dev Provides an interface to the scaling unit
     * @return Scaling unit (1e18 or 1 * 10**18)
     */
    function getFullScale() internal pure returns (uint256) {
        return FULL_SCALE;
    }

    /**
     * @dev Provides an interface to the ratio unit
     * @return Ratio scale unit (1e8 or 1 * 10**8)
     */
    function getRatioScale() internal pure returns (uint256) {
        return RATIO_SCALE;
    }

    /**
     * @dev Scales a given integer to the power of the full scale.
     * @param x   Simple uint256 to scale
     * @return    Scaled value a to an exact number
     */
    function scaleInteger(uint256 x) internal pure returns (uint256) {
        return x.mul(FULL_SCALE);
    }

    /***************************************
              PRECISE ARITHMETIC
    ****************************************/

    /**
     * @dev Multiplies two precise units, and then truncates by the full scale
     * @param x     Left hand input to multiplication
     * @param y     Right hand input to multiplication
     * @return      Result after multiplying the two inputs and then dividing by the shared
     *              scale unit
     */
    function mulTruncate(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulTruncateScale(x, y, FULL_SCALE);
    }

    /**
     * @dev Multiplies two precise units, and then truncates by the given scale. For example,
     * when calculating 90% of 10e18, (10e18 * 9e17) / 1e18 = (9e36) / 1e18 = 9e18
     * @param x     Left hand input to multiplication
     * @param y     Right hand input to multiplication
     * @param scale Scale unit
     * @return      Result after multiplying the two inputs and then dividing by the shared
     *              scale unit
     */
    function mulTruncateScale(
        uint256 x,
        uint256 y,
        uint256 scale
    ) internal pure returns (uint256) {
        // e.g. assume scale = fullScale
        // z = 10e18 * 9e17 = 9e36
        uint256 z = x.mul(y);
        // return 9e38 / 1e18 = 9e18
        return z.div(scale);
    }

    /**
     * @dev Multiplies two precise units, and then truncates by the full scale, rounding up the result
     * @param x     Left hand input to multiplication
     * @param y     Right hand input to multiplication
     * @return      Result after multiplying the two inputs and then dividing by the shared
     *              scale unit, rounded up to the closest base unit.
     */
    function mulTruncateCeil(uint256 x, uint256 y)
        internal
        pure
        returns (uint256)
    {
        // e.g. 8e17 * 17268172638 = 138145381104e17
        uint256 scaled = x.mul(y);
        // e.g. 138145381104e17 + 9.99...e17 = 138145381113.99...e17
        uint256 ceil = scaled.add(FULL_SCALE.sub(1));
        // e.g. 13814538111.399...e18 / 1e18 = 13814538111
        return ceil.div(FULL_SCALE);
    }

    /**
     * @dev Precisely divides two units, by first scaling the left hand operand. Useful
     *      for finding percentage weightings, i.e. 8e18/10e18 = 80% (or 8e17)
     * @param x     Left hand input to division
     * @param y     Right hand input to division
     * @return      Result after multiplying the left operand by the scale, and
     *              executing the division on the right hand input.
     */
    function divPrecisely(uint256 x, uint256 y)
        internal
        pure
        returns (uint256)
    {
        // e.g. 8e18 * 1e18 = 8e36
        uint256 z = x.mul(FULL_SCALE);
        // e.g. 8e36 / 10e18 = 8e17
        return z.div(y);
    }

    /***************************************
                  RATIO FUNCS
    ****************************************/

    /**
     * @dev Multiplies and truncates a token ratio, essentially flooring the result
     *      i.e. How much mAsset is this bAsset worth?
     * @param x     Left hand operand to multiplication (i.e Exact quantity)
     * @param ratio bAsset ratio
     * @return c    Result after multiplying the two inputs and then dividing by the ratio scale
     */
    function mulRatioTruncate(uint256 x, uint256 ratio)
        internal
        pure
        returns (uint256 c)
    {
        return mulTruncateScale(x, ratio, RATIO_SCALE);
    }

    /**
     * @dev Multiplies and truncates a token ratio, rounding up the result
     *      i.e. How much mAsset is this bAsset worth?
     * @param x     Left hand input to multiplication (i.e Exact quantity)
     * @param ratio bAsset ratio
     * @return      Result after multiplying the two inputs and then dividing by the shared
     *              ratio scale, rounded up to the closest base unit.
     */
    function mulRatioTruncateCeil(uint256 x, uint256 ratio)
        internal
        pure
        returns (uint256)
    {
        // e.g. How much mAsset should I burn for this bAsset (x)?
        // 1e18 * 1e8 = 1e26
        uint256 scaled = x.mul(ratio);
        // 1e26 + 9.99e7 = 100..00.999e8
        uint256 ceil = scaled.add(RATIO_SCALE.sub(1));
        // return 100..00.999e8 / 1e8 = 1e18
        return ceil.div(RATIO_SCALE);
    }

    /**
     * @dev Precisely divides two ratioed units, by first scaling the left hand operand
     *      i.e. How much bAsset is this mAsset worth?
     * @param x     Left hand operand in division
     * @param ratio bAsset ratio
     * @return c    Result after multiplying the left operand by the scale, and
     *              executing the division on the right hand input.
     */
    function divRatioPrecisely(uint256 x, uint256 ratio)
        internal
        pure
        returns (uint256 c)
    {
        // e.g. 1e14 * 1e8 = 1e22
        uint256 y = x.mul(RATIO_SCALE);
        // return 1e22 / 1e12 = 1e10
        return y.div(ratio);
    }

    /***************************************
                    HELPERS
    ****************************************/

    /**
     * @dev Calculates minimum of two numbers
     * @param x     Left hand input
     * @param y     Right hand input
     * @return      Minimum of the two inputs
     */
    function min(uint256 x, uint256 y) internal pure returns (uint256) {
        return x > y ? y : x;
    }

    /**
     * @dev Calculated maximum of two numbers
     * @param x     Left hand input
     * @param y     Right hand input
     * @return      Maximum of the two inputs
     */
    function max(uint256 x, uint256 y) internal pure returns (uint256) {
        return x > y ? x : y;
    }

    /**
     * @dev Clamps a value to an upper bound
     * @param x           Left hand input
     * @param upperBound  Maximum possible value to return
     * @return            Input x clamped to a maximum value, upperBound
     */
    function clamp(uint256 x, uint256 upperBound)
        internal
        pure
        returns (uint256)
    {
        return x > upperBound ? upperBound : x;
    }
}
function mulTruncateScale(
    uint256 x,
    uint256 y,
    uint256 scale
) internal pure returns (uint256) {
    // e.g. assume scale = fullScale
    // z = 10e18 * 9e17 = 9e36
    uint256 z = x.mul(y);
    // return 9e38 / 1e18 = 9e18
    return z.div(scale);
}

/**
 * @dev Multiplies two precise units, and then truncates by the given scale. For example,
 * when calculating 90% of 10e18, (10e18 * 9e17) / 1e18 = (9e36) / 1e18 = 9e18
 * @param x     Left hand input to multiplication
 * @param y     Right hand input to multiplication
 * @param scale Scale unit
 * @return      Result after multiplying the two inputs and then dividing by the shared
 *              scale unit
 */