pragma solidity ^0.4.24;


interface PlayerBookReceiverInterface {
    function receivePlayerInfo(uint256 _pID, address _addr, bytes32 _name, uint256 _laff) external;
    function receivePlayerNameList(uint256 _pID, bytes32 _name) external;
}


contract PlayerBook {
    using NameFilter for string;
    using SafeMath for uint256;
    
    address private communityAddr = 0x180A14aF38384dc15Ce96cbcabCfC8F47794AC3E;
    address private activateAddr1 = 0x6C7DFE3c255a098Ea031f334436DD50345cFC737;
    address private activateAddr2 = 0x180A14aF38384dc15Ce96cbcabCfC8F47794AC3E;
//==============================================================================
//     _| _ _|_ _    _ _ _|_    _   .
//    (_|(_| | (_|  _\(/_ | |_||_)  .
//=============================|================================================    
    uint256 public registrationFee_ = 1 finney;            // price to register a name
    mapping(uint256 => PlayerBookReceiverInterface) public games_;  // mapping of our game interfaces for sending your account info to games
    mapping(address => bytes32) public gameNames_;          // lookup a games name
    mapping(address => uint256) public gameIDs_;            // lokup a games ID
    uint256 public gID_;        // total number of games
    uint256 public pID_;        // total number of players
    mapping (address => uint256) public pIDxAddr_;          // (addr => pID) returns player id by address
    mapping (bytes32 => uint256) public pIDxName_;          // (name => pID) returns player id by name
    mapping (uint256 => Player) public plyr_;               // (pID => data) player data
    mapping (uint256 => mapping (bytes32 => bool)) public plyrNames_; // (pID => name => bool) list of names a player owns.  (used so you can change your display name amoungst any name you own)
    mapping (uint256 => mapping (uint256 => bytes32)) public plyrNameList_; // (pID => nameNum => name) list of names a player owns
    struct Player {
        address addr;
        bytes32 name;
        uint256 laff;
        uint256 names;
    }
//==============================================================================
//     _ _  _  __|_ _    __|_ _  _  .
//    (_(_)| |_\ | | |_|(_ | (_)|   .  (initial data setup upon contract deploy)
//==============================================================================    
    constructor()
        public
    {
        // premine the dev names (sorry not sorry)
            // No keys are purchased with this method, it's simply locking our addresses,
            // PID's and names for referral codes.
        plyr_[1].addr = 0x33E161A482C560DCA9180D84706eCDd2D906668B;
        plyr_[1].name = "daddy";
        plyr_[1].names = 1;
        pIDxAddr_[0x33E161A482C560DCA9180D84706eCDd2D906668B] = 1;
        pIDxName_["daddy"] = 1;
        plyrNames_[1]["daddy"] = true;
        plyrNameList_[1][1] = "daddy";
        
        plyr_[2].addr = 0x9eb79e917b9e051A1BEf27f8A6cCDA316F228a7c;
        plyr_[2].name = "suoha";
        plyr_[2].names = 1;
        pIDxAddr_[0x9eb79e917b9e051A1BEf27f8A6cCDA316F228a7c] = 2;
        pIDxName_["suoha"] = 2;
        plyrNames_[2]["suoha"] = true;
        plyrNameList_[2][1] = "suoha";
        
        plyr_[3].addr = 0x261901840C99C914Aa8Cc2f7AEd0d2e09A749c8B;
        plyr_[3].name = "nodumb";
        plyr_[3].names = 1;
        pIDxAddr_[0x261901840C99C914Aa8Cc2f7AEd0d2e09A749c8B] = 3;
        pIDxName_["nodumb"] = 3;
        plyrNames_[3]["nodumb"] = true;
        plyrNameList_[3][1] = "nodumb";
        
        plyr_[4].addr = 0x7649938FAdf6C597F27349D338e3bDC8488c14e6;
        plyr_[4].name = "dddos";
        plyr_[4].names = 1;
        pIDxAddr_[0x7649938FAdf6C597F27349D338e3bDC8488c14e6] = 4;
        pIDxName_["dddos"] = 4;
        plyrNames_[4]["dddos"] = true;
        plyrNameList_[4][1] = "dddos";
        
        pID_ = 4;
    }
//==============================================================================
//     _ _  _  _|. |`. _  _ _  .
//    | | |(_)(_||~|~|(/_| _\  .  (these are safety checks)
//==============================================================================    
    /**
     * @dev prevents contracts from interacting with fomo3d 
     */
    modifier isHuman() {
        address _addr = msg.sender;
        uint256 _codeLength;
        
        assembly {_codeLength := extcodesize(_addr)}
        require(_codeLength == 0, "sorry humans only");
        _;
    }
    
    modifier onlyCommunity() 
    {
        require(msg.sender == activateAddr1 || msg.sender == activateAddr2, "msg sender is not the community");
        _;
    }
    
    modifier isRegisteredGame()
    {
        require(gameIDs_[msg.sender] != 0);
        _;
    }
//==============================================================================
//     _    _  _ _|_ _  .
//    (/_\/(/_| | | _\  .
//==============================================================================    
    // fired whenever a player registers a name
    event onNewName
    (
        uint256 indexed playerID,
        address indexed playerAddress,
        bytes32 indexed playerName,
        bool isNewPlayer,
        uint256 affiliateID,
        address affiliateAddress,
        bytes32 affiliateName,
        uint256 amountPaid,
        uint256 timeStamp
    );
//==============================================================================
//     _  _ _|__|_ _  _ _  .
//    (_|(/_ |  | (/_| _\  . (for UI & viewing things on etherscan)
//=====_|=======================================================================
    function checkIfNameValid(string _nameStr)
        public
        view
        returns(bool)
    {
        bytes32 _name = _nameStr.nameFilter();
        if (pIDxName_[_name] == 0)
            return (true);
        else 
            return (false);
    }
//==============================================================================
//     _    |_ |. _   |`    _  __|_. _  _  _  .
//    |_)|_||_)||(_  ~|~|_|| |(_ | |(_)| |_\  .  (use these to interact with contract)
//====|=========================================================================    
    /**
     * @dev registers a name.  UI will always display the last name you registered.
     * but you will still own all previously registered names to use as affiliate 
     * links.
     * - must pay a registration fee.
     * - name must be unique
     * - names will be converted to lowercase
     * - name cannot start or end with a space 
     * - cannot have more than 1 space in a row
     * - cannot be only numbers
     * - cannot start with 0x 
     * - name must be at least 1 char
     * - max length of 32 characters long
     * - allowed characters: a-z, 0-9, and space
     * -functionhash- 0x921dec21 (using ID for affiliate)
     * -functionhash- 0x3ddd4698 (using address for affiliate)
     * -functionhash- 0x685ffd83 (using name for affiliate)
     * @param _nameString players desired name
     * @param _affCode affiliate ID, address, or name of who refered you
     * @param _all set to true if you want this to push your info to all games 
     * (this might cost a lot of gas)
     */
    function registerNameXID(string _nameString, uint256 _affCode, bool _all)
        isHuman()
        public
        payable 
    {
        // make sure name fees paid
        require (msg.value >= registrationFee_, "umm.....  you have to pay the name fee");
        
        // filter name + condition checks
        bytes32 _name = NameFilter.nameFilter(_nameString);
        
        // set up address 
        address _addr = msg.sender;
        
        // set up our tx event data and determine if player is new or not
        bool _isNewPlayer = determinePID(_addr);
        
        // fetch player id
        uint256 _pID = pIDxAddr_[_addr];
        
        // manage affiliate residuals
        // if no affiliate code was given, no new affiliate code was given, or the 
        // player tried to use their own pID as an affiliate code, lolz
        if (_affCode != 0 && _affCode != plyr_[_pID].laff && _affCode != _pID) 
        {
            // update last affiliate 
            plyr_[_pID].laff = _affCode;
        } else if (_affCode == _pID) {
            _affCode = 0;
        }
        
        // register name 
        registerNameCore(_pID, _addr, _affCode, _name, _isNewPlayer, _all);
    }
    
    function registerNameXaddr(string _nameString, address _affCode, bool _all)
        isHuman()
        public
        payable 
    {
        // make sure name fees paid
        require (msg.value >= registrationFee_, "umm.....  you have to pay the name fee");
        
        // filter name + condition checks
        bytes32 _name = NameFilter.nameFilter(_nameString);
        
        // set up address 
        address _addr = msg.sender;
        
        // set up our tx event data and determine if player is new or not
        bool _isNewPlayer = determinePID(_addr);
        
        // fetch player id
        uint256 _pID = pIDxAddr_[_addr];
        
        // manage affiliate residuals
        // if no affiliate code was given or player tried to use their own, lolz
        uint256 _affID;
        if (_affCode != address(0) && _affCode != _addr)
        {
            // get affiliate ID from aff Code 
            _affID = pIDxAddr_[_affCode];
            
            // if affID is not the same as previously stored 
            if (_affID != plyr_[_pID].laff)
            {
                // update last affiliate
                plyr_[_pID].laff = _affID;
            }
        }
        
        // register name 
        registerNameCore(_pID, _addr, _affID, _name, _isNewPlayer, _all);
    }
    
    function registerNameXname(string _nameString, bytes32 _affCode, bool _all)
        isHuman()
        public
        payable 
    {
        // make sure name fees paid
        require (msg.value >= registrationFee_, "umm.....  you have to pay the name fee");
        
        // filter name + condition checks
        bytes32 _name = NameFilter.nameFilter(_nameString);
        
        // set up address 
        address _addr = msg.sender;
        
        // set up our tx event data and determine if player is new or not
        bool _isNewPlayer = determinePID(_addr);
        
        // fetch player id
        uint256 _pID = pIDxAddr_[_addr];
        
        // manage affiliate residuals
        // if no affiliate code was given or player tried to use their own, lolz
        uint256 _affID;
        if (_affCode != "" && _affCode != _name)
        {
            // get affiliate ID from aff Code 
            _affID = pIDxName_[_affCode];
            
            // if affID is not the same as previously stored 
            if (_affID != plyr_[_pID].laff)
            {
                // update last affiliate
                plyr_[_pID].laff = _affID;
            }
        }
        
        // register name 
        registerNameCore(_pID, _addr, _affID, _name, _isNewPlayer, _all);
    }
    
    /**
     * @dev players, if you registered a profile, before a game was released, or
     * set the all bool to false when you registered, use this function to push
     * your profile to a single game.  also, if you've  updated your name, you
     * can use this to push your name to games of your choosing.
     * -functionhash- 0x81c5b206
     * @param _gameID game id 
     */
    function addMeToGame(uint256 _gameID)
        isHuman()
        public
    {
        require(_gameID <= gID_, "silly player, that game doesn't exist yet");
        address _addr = msg.sender;
        uint256 _pID = pIDxAddr_[_addr];
        require(_pID != 0, "hey there buddy, you dont even have an account");
        uint256 _totalNames = plyr_[_pID].names;
        
        // add players profile and most recent name
        games_[_gameID].receivePlayerInfo(_pID, _addr, plyr_[_pID].name, plyr_[_pID].laff);
        
        // add list of all names
        if (_totalNames > 1)
            for (uint256 ii = 1; ii <= _totalNames; ii++)
                games_[_gameID].receivePlayerNameList(_pID, plyrNameList_[_pID][ii]);
    }
    
    /**
     * @dev players, use this to push your player profile to all registered games.
     * -functionhash- 0x0c6940ea
     */
    function addMeToAllGames()
        isHuman()
        public
    {
        address _addr = msg.sender;
        uint256 _pID = pIDxAddr_[_addr];
        require(_pID != 0, "hey there buddy, you dont even have an account");
        uint256 _laff = plyr_[_pID].laff;
        uint256 _totalNames = plyr_[_pID].names;
        bytes32 _name = plyr_[_pID].name;
        
        for (uint256 i = 1; i <= gID_; i++)
        {
            games_[i].receivePlayerInfo(_pID, _addr, _name, _laff);
            if (_totalNames > 1)
                for (uint256 ii = 1; ii <= _totalNames; ii++)
                    games_[i].receivePlayerNameList(_pID, plyrNameList_[_pID][ii]);
        }
                
    }
    
    /**
     * @dev players use this to change back to one of your old names.  tip, you'll
     * still need to push that info to existing games.
     * -functionhash- 0xb9291296
     * @param _nameString the name you want to use 
     */
    function useMyOldName(string _nameString)
        isHuman()
        public 
    {
        // filter name, and get pID
        bytes32 _name = _nameString.nameFilter();
        uint256 _pID = pIDxAddr_[msg.sender];
        
        // make sure they own the name 
        require(plyrNames_[_pID][_name] == true, "umm... thats not a name you own");
        
        // update their current name 
        plyr_[_pID].name = _name;
    }
    
//==============================================================================
//     _ _  _ _   | _  _ . _  .
//    (_(_)| (/_  |(_)(_||(_  . 
//=====================_|=======================================================    
    function registerNameCore(uint256 _pID, address _addr, uint256 _affID, bytes32 _name, bool _isNewPlayer, bool _all)
        private
    {
        // if names already has been used, require that current msg sender owns the name
        if (pIDxName_[_name] != 0)
            require(plyrNames_[_pID][_name] == true, "sorry that names already taken");
        
        // add name to player profile, registry, and name book
        plyr_[_pID].name = _name;
        pIDxName_[_name] = _pID;
        if (plyrNames_[_pID][_name] == false)
        {
            plyrNames_[_pID][_name] = true;
            plyr_[_pID].names++;
            plyrNameList_[_pID][plyr_[_pID].names] = _name;
        }
        
        // registration fee goes directly to community rewards
        communityAddr.transfer(address(this).balance);
        
        // push player info to games
        if (_all == true)
            for (uint256 i = 1; i <= gID_; i++)
                games_[i].receivePlayerInfo(_pID, _addr, _name, _affID);
        
        // fire event
        emit onNewName(_pID, _addr, _name, _isNewPlayer, _affID, plyr_[_affID].addr, plyr_[_affID].name, msg.value, now);
    }
//==============================================================================
//    _|_ _  _ | _  .
//     | (_)(_)|_\  .
//==============================================================================    
    function determinePID(address _addr)
        private
        returns (bool)
    {
        if (pIDxAddr_[_addr] == 0)
        {
            pID_++;
            pIDxAddr_[_addr] = pID_;
            plyr_[pID_].addr = _addr;
            
            // set the new player bool to true
            return (true);
        } else {
            return (false);
        }
    }
//==============================================================================
//   _   _|_ _  _ _  _ |   _ _ || _  .
//  (/_>< | (/_| | |(_||  (_(_|||_\  .
//==============================================================================
    function getPlayerID(address _addr)
        isRegisteredGame()
        external
        returns (uint256)
    {
        determinePID(_addr);
        return (pIDxAddr_[_addr]);
    }
    function getPlayerName(uint256 _pID)
        external
        view
        returns (bytes32)
    {
        return (plyr_[_pID].name);
    }
    function getPlayerLAff(uint256 _pID)
        external
        view
        returns (uint256)
    {
        return (plyr_[_pID].laff);
    }
    function getPlayerAddr(uint256 _pID)
        external
        view
        returns (address)
    {
        return (plyr_[_pID].addr);
    }
    function getNameFee()
        external
        view
        returns (uint256)
    {
        return(registrationFee_);
    }
    function registerNameXIDFromDapp(address _addr, bytes32 _name, uint256 _affCode, bool _all)
        isRegisteredGame()
        external
        payable
        returns(bool, uint256)
    {
        // make sure name fees paid
        require (msg.value >= registrationFee_, "umm.....  you have to pay the name fee");
        
        // set up our tx event data and determine if player is new or not
        bool _isNewPlayer = determinePID(_addr);
        
        // fetch player id
        uint256 _pID = pIDxAddr_[_addr];
        
        // manage affiliate residuals
        // if no affiliate code was given, no new affiliate code was given, or the 
        // player tried to use their own pID as an affiliate code, lolz
        uint256 _affID = _affCode;
        if (_affID != 0 && _affID != plyr_[_pID].laff && _affID != _pID) 
        {
            // update last affiliate 
            plyr_[_pID].laff = _affID;
        } else if (_affID == _pID) {
            _affID = 0;
        }
        
        // register name 
        registerNameCore(_pID, _addr, _affID, _name, _isNewPlayer, _all);
        
        return(_isNewPlayer, _affID);
    }
    function registerNameXaddrFromDapp(address _addr, bytes32 _name, address _affCode, bool _all)
        isRegisteredGame()
        external
        payable
        returns(bool, uint256)
    {
        // make sure name fees paid
        require (msg.value >= registrationFee_, "umm.....  you have to pay the name fee");
        
        // set up our tx event data and determine if player is new or not
        bool _isNewPlayer = determinePID(_addr);
        
        // fetch player id
        uint256 _pID = pIDxAddr_[_addr];
        
        // manage affiliate residuals
        // if no affiliate code was given or player tried to use their own, lolz
        uint256 _affID;
        if (_affCode != address(0) && _affCode != _addr)
        {
            // get affiliate ID from aff Code 
            _affID = pIDxAddr_[_affCode];
            
            // if affID is not the same as previously stored 
            if (_affID != plyr_[_pID].laff)
            {
                // update last affiliate
                plyr_[_pID].laff = _affID;
            }
        }
        
        // register name 
        registerNameCore(_pID, _addr, _affID, _name, _isNewPlayer, _all);
        
        return(_isNewPlayer, _affID);
    }
    function registerNameXnameFromDapp(address _addr, bytes32 _name, bytes32 _affCode, bool _all)
        isRegisteredGame()
        external
        payable
        returns(bool, uint256)
    {
        // make sure name fees paid
        require (msg.value >= registrationFee_, "umm.....  you have to pay the name fee");
        
        // set up our tx event data and determine if player is new or not
        bool _isNewPlayer = determinePID(_addr);
        
        // fetch player id
        uint256 _pID = pIDxAddr_[_addr];
        
        // manage affiliate residuals
        // if no affiliate code was given or player tried to use their own, lolz
        uint256 _affID;
        if (_affCode != "" && _affCode != _name)
        {
            // get affiliate ID from aff Code 
            _affID = pIDxName_[_affCode];
            
            // if affID is not the same as previously stored 
            if (_affID != plyr_[_pID].laff)
            {
                // update last affiliate
                plyr_[_pID].laff = _affID;
            }
        }
        
        // register name 
        registerNameCore(_pID, _addr, _affID, _name, _isNewPlayer, _all);
        
        return(_isNewPlayer, _affID);
    }
    
//==============================================================================
//   _ _ _|_    _   .
//  _\(/_ | |_||_)  .
//=============|================================================================
    function addGame(address _gameAddress, string _gameNameStr)
     onlyCommunity()
        public
    {
        require(gameIDs_[_gameAddress] == 0, "derp, that games already been registered");

            gID_++;
            bytes32 _name = _gameNameStr.nameFilter();
            gameIDs_[_gameAddress] = gID_;
            gameNames_[_gameAddress] = _name;
            games_[gID_] = PlayerBookReceiverInterface(_gameAddress);
        
            games_[gID_].receivePlayerInfo(1, plyr_[1].addr, plyr_[1].name, 0);
            games_[gID_].receivePlayerInfo(2, plyr_[2].addr, plyr_[2].name, 0);
            games_[gID_].receivePlayerInfo(3, plyr_[3].addr, plyr_[3].name, 0);
            games_[gID_].receivePlayerInfo(4, plyr_[4].addr, plyr_[4].name, 0);
    }
    
    function setRegistrationFee(uint256 _fee)
     onlyCommunity()
        public
    {
            registrationFee_ = _fee;
    }
        
} 

/**
* @title -Name Filter- v0.1.9
* ┌┬┐┌─┐┌─┐┌┬┐   ╦╦ ╦╔═╗╔╦╗  ┌─┐┬─┐┌─┐┌─┐┌─┐┌┐┌┌┬┐┌─┐
*  │ ├┤ ├─┤│││   ║║ ║╚═╗ ║   ├─┘├┬┘├┤ └─┐├┤ │││ │ └─┐
*  ┴ └─┘┴ ┴┴ ┴  ╚╝╚═╝╚═╝ ╩   ┴  ┴└─└─┘└─┘└─┘┘└┘ ┴ └─┘
*                                  _____                      _____
*                                 (, /     /)       /) /)    (, /      /)          /)
*          ┌─┐                      /   _ (/_      // //       /  _   // _   __  _(/
*          ├─┤                  ___/___(/_/(__(_/_(/_(/_   ___/__/_)_(/_(_(_/ (_(_(_
*          ┴ ┴                /   /          .-/ _____   (__ /                               
*                            (__ /          (_/ (, /                                      /)? 
*                                                 /  __  __ __ __  _   __ __  _  _/_ _  _(/
* ┌─┐┬─┐┌─┐┌┬┐┬ ┬┌─┐┌┬┐                          /__/ (_(__(_)/ (_/_)_(_)/ (_(_(_(__(/_(_(_
* ├─┘├┬┘│ │ │││ ││   │                      (__ /              .-/  ? Jekyll Island Inc. 2018
* ┴  ┴└─└─┘─┴┘└─┘└─┘ ┴                                        (_/
*              _       __    _      ____      ____  _   _    _____  ____  ___  
*=============| |\ |  / /\  | |\/| | |_ =====| |_  | | | |    | |  | |_  | |_)==============*
*=============|_| \| /_/--\ |_|  | |_|__=====|_|   |_| |_|__  |_|  |_|__ |_| \==============*
*
* ╔═╗┌─┐┌┐┌┌┬┐┬─┐┌─┐┌─┐┌┬┐  ╔═╗┌─┐┌┬┐┌─┐ ┌──────────┐
* ║  │ ││││ │ ├┬┘├─┤│   │   ║  │ │ ││├┤  │ dddos │
* ╚═╝└─┘┘└┘ ┴ ┴└─┴ ┴└─┘ ┴   ╚═╝└─┘─┴┘└─┘ └──────────┘
*/
library NameFilter {
    
    /**
     * @dev filters name strings
     * -converts uppercase to lower case.  
     * -makes sure it does not start/end with a space
     * -makes sure it does not contain multiple spaces in a row
     * -cannot be only numbers
     * -cannot start with 0x 
     * -restricts characters to A-Z, a-z, 0-9, and space.
     * @return reprocessed string in bytes32 format
     */
    function nameFilter(string _input)
        internal
        pure
        returns(bytes32)
    {
        bytes memory _temp = bytes(_input);
        uint256 _length = _temp.length;
        
        //sorry limited to 32 characters
        require (_length <= 32 && _length > 0, "string must be between 1 and 32 characters");
        // make sure it doesnt start with or end with space
        require(_temp[0] != 0x20 && _temp[_length-1] != 0x20, "string cannot start or end with space");
        // make sure first two characters are not 0x
        if (_temp[0] == 0x30)
        {
            require(_temp[1] != 0x78, "string cannot start with 0x");
            require(_temp[1] != 0x58, "string cannot start with 0X");
        }
        
        // create a bool to track if we have a non number character
        bool _hasNonNumber;
        
        // convert & check
        for (uint256 i = 0; i < _length; i++)
        {
            // if its uppercase A-Z
            if (_temp[i] > 0x40 && _temp[i] < 0x5b)
            {
                // convert to lower case a-z
                _temp[i] = byte(uint(_temp[i]) + 32);
                
                // we have a non number
                if (_hasNonNumber == false)
                    _hasNonNumber = true;
            } else {
                require
                (
                    // require character is a space
                    _temp[i] == 0x20 || 
                    // OR lowercase a-z
                    (_temp[i] > 0x60 && _temp[i] < 0x7b) ||
                    // or 0-9
                    (_temp[i] > 0x2f && _temp[i] < 0x3a),
                    "string contains invalid characters"
                );
                // make sure theres not 2x spaces in a row
                if (_temp[i] == 0x20)
                    require( _temp[i+1] != 0x20, "string cannot contain consecutive spaces");
                
                // see if we have a character other than a number
                if (_hasNonNumber == false && (_temp[i] < 0x30 || _temp[i] > 0x39))
                    _hasNonNumber = true;    
            }
        }
        
        require(_hasNonNumber == true, "string cannot be only numbers");
        
        bytes32 _ret;
        assembly {
            _ret := mload(add(_temp, 32))
        }
        return (_ret);
    }
}

/**
 * @title SafeMath v0.1.9
 * @dev Math operations with safety checks that throw on error
 * change notes:  original SafeMath library from OpenZeppelin modified by dddos
 * - added sqrt
 * - added sq
 * - added pwr 
 * - changed asserts to requires with error log outputs
 * - removed div, its useless
 */
library SafeMath {
    
    /**
    * @dev Multiplies two numbers, throws on overflow.
    */
    function mul(uint256 a, uint256 b) 
        internal 
        pure 
        returns (uint256 c) 
    {
        if (a == 0) {
            return 0;
        }
        c = a * b;
        require(c / a == b, "SafeMath mul failed");
        return c;
    }

    /**
    * @dev Subtracts two numbers, throws on overflow (i.e. if subtrahend is greater than minuend).
    */
    function sub(uint256 a, uint256 b)
        internal
        pure
        returns (uint256) 
    {
        require(b <= a, "SafeMath sub failed");
        return a - b;
    }

    /**
    * @dev Adds two numbers, throws on overflow.
    */
    function add(uint256 a, uint256 b)
        internal
        pure
        returns (uint256 c) 
    {
        c = a + b;
        require(c >= a, "SafeMath add failed");
        return c;
    }
    
    /**
     * @dev gives square root of given x.
     */
    function sqrt(uint256 x)
        internal
        pure
        returns (uint256 y) 
    {
        uint256 z = ((add(x,1)) / 2);
        y = x;
        while (z < y) 
        {
            y = z;
            z = ((add((x / z),z)) / 2);
        }
    }
    
    /**
     * @dev gives square. multiplies x by x
     */
    function sq(uint256 x)
        internal
        pure
        returns (uint256)
    {
        return (mul(x,x));
    }
    
    /**
     * @dev x to the power of y 
     */
    function pwr(uint256 x, uint256 y)
        internal 
        pure 
        returns (uint256)
    {
        if (x==0)
            return (0);
        else if (y==0)
            return (1);
        else 
        {
            uint256 z = x;
            for (uint256 i=1; i < y; i++)
                z = mul(z,x);
            return (z);
        }
    }
}