library BMKeyCalc {
    using SafeMath for *;
    
    /// @dev calculates number of keys received given X eth 
    /// @param _curEth current amount of eth in contract 
    /// @param _newEth eth being spent
    /// @return amount of ticket purchased
    function keysRec(uint256 _curEth, uint256 _newEth)
        internal
        pure
        returns (uint256)
    {
        return(keys((_curEth).add(_newEth)).sub(keys(_curEth)));
    }


    /// @dev calculates amount of eth received if you sold X keys 
    /// @param _curKeys current amount of keys that exist 
    /// @param _sellKeys amount of keys you wish to sell
    /// @return amount of eth received
    function ethRec(uint256 _curKeys, uint256 _sellKeys)
        internal
        pure
        returns (uint256)
    {
        return((eth(_curKeys)).sub(eth(_curKeys.sub(_sellKeys))));
    }

    /// @dev calculates how many keys would exist with given an amount of eth
    /// @param _eth eth "in contract"
    /// @return number of keys that would exist
    function keys(uint256 _eth) 
        internal
        pure
        returns(uint256)
    {
        return ((((((_eth).mul(1000000000000000000)).mul(3125000000000000000000000000)).add(562498828125610351562500000000000000000000000000000000000000000000)).sqrt()).sub(749999218750000000000000000000000)) / (1562500000);
    }
    
    /// @dev calculates how much eth would be in contract given a number of keys
    /// @param _keys number of keys "in contract" 
    /// @return eth that would exists
    function eth(uint256 _keys) 
        internal
        pure
        returns(uint256)
    {
        return ((781250000).mul(_keys.sq()).add(((1499998437500000).mul(_keys.mul(1000000000000000000))) / (2))) / ((1000000000000000000).sq());
    }
}
// key calculation
function keys(uint256 _eth) 
        internal
        pure
        returns(uint256)
    {
        return ((((((_eth).mul(1000000000000000000)).mul(3125000000000000000000000000)).add(562498828125610351562500000000000000000000000000000000000000000000)).sqrt()).sub(749999218750000000000000000000000)) / (1562500000);
    }
/// @dev calculates how many keys would exist with given an amount of eth
/// @param _eth eth "in contract"
/// @return number of keys that would exist