library FixedPoint {
    using OpenZeppelinSafeMath_V3_3_0 for uint256;

    // The scale to use for fixed point numbers.  Same as Ether for simplicity.
    uint256 internal constant SCALE = 1e18;

    /**
        * Calculates a Fixed18 mantissa given the numerator and denominator
        *
        * The mantissa = (numerator * 1e18) / denominator
        *
        * @param numerator The mantissa numerator
        * @param denominator The mantissa denominator
        * @return The mantissa of the fraction
        */
    function calculateMantissa(uint256 numerator, uint256 denominator) internal pure returns (uint256) {
        uint256 mantissa = numerator.mul(SCALE);
        mantissa = mantissa.div(denominator);
        return mantissa;
    }

    /**
        * Multiplies a Fixed18 number by an integer.
        *
        * @param b The whole integer to multiply
        * @param mantissa The Fixed18 number
        * @return An integer that is the result of multiplying the params.
        */
    function multiplyUintByMantissa(uint256 b, uint256 mantissa) internal pure returns (uint256) {
        uint256 result = mantissa.mul(b);
        result = result.div(SCALE);
        return result;
    }

    /**
    * Divides an integer by a fixed point 18 mantissa
    *
    * @param dividend The integer to divide
    * @param mantissa The fixed point 18 number to serve as the divisor
    * @return An integer that is the result of dividing an integer by a fixed point 18 mantissa
    */
    function divideUintByMantissa(uint256 dividend, uint256 mantissa) internal pure returns (uint256) {
        uint256 result = SCALE.mul(dividend);
        result = result.div(mantissa);
        return result;
    }
}
/**
 * @author Brendan Asselstine
 * @notice Provides basic fixed point math calculations.
 *
 * This library calculates integer fractions by scaling values by 1e18 then performing standard integer math.
 */
function calculateMantissa(uint256 numerator, uint256 denominator) internal pure returns (uint256) {
    uint256 mantissa = numerator.mul(SCALE);
    mantissa = mantissa.div(denominator);
    return mantissa;
}

/**
 * Calculates a Fixed18 mantissa given the numerator and denominator
 *
 * The mantissa = (numerator * 1e18) / denominator
 *
 * @param numerator The mantissa numerator
 * @param denominator The mantissa denominator
 * @return The mantissa of the fraction
 */