CASH token

CASH token

pragma solidity ^0.4.15;

/**
 * @title SafeMath
 * @dev Math operations with safety checks that throw on error
 */
library SafeMath {
    function mul(uint256 a, uint256 b) internal constant returns (uint256) {
        uint256 c = a * b;
        assert(a == 0 || c / a == b);
        return c;
    }

    function div(uint256 a, uint256 b) internal constant returns (uint256) {
        // assert(b > 0); // Solidity automatically throws when dividing by 0
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold
        return c;
    }

    function sub(uint256 a, uint256 b) internal constant returns (uint256) {
        assert(b <= a);
        return a - b;
    }

    function add(uint256 a, uint256 b) internal constant returns (uint256) {
        uint256 c = a + b;
        assert(c >= a);
        return c;
    }
}

/**
 * @title ERC20Basic
 * @dev Simpler version of ERC20 interface
 * @dev see https://github.com/ethereum/EIPs/issues/179
 */
contract ERC20Basic {
    uint256 public totalSupply;

    function balanceOf(address who) constant returns (uint256);

    function transfer(address to, uint256 value) returns (bool);

    event Transfer(address indexed from, address indexed to, uint256 value);
}

/**
 * @title Basic token
 * @dev Basic version of StandardToken, with no allowances.
 */
contract BasicToken is ERC20Basic {
    using SafeMath for uint256;

    mapping (address => uint256) balances;

    /**
    * @dev transfer token for a specified address
    * @param _to The address to transfer to.
    * @param _value The amount to be transferred.
    */
    function transfer(address _to, uint256 _value) returns (bool) {
        balances[msg.sender] = balances[msg.sender].sub(_value);
        balances[_to] = balances[_to].add(_value);
        Transfer(msg.sender, _to, _value);
        return true;
    }

    /**
    * @dev Gets the balance of the specified address.
    * @param _owner The address to query the the balance of.
    * @return An uint256 representing the amount owned by the passed address.
    */
    function balanceOf(address _owner) constant returns (uint256 balance) {
        return balances[_owner];
    }

}

/**
 * @title ERC20 interface
 * @dev see https://github.com/ethereum/EIPs/issues/20
 */
contract ERC20 is ERC20Basic {
    function allowance(address owner, address spender) constant returns (uint256);

    function transferFrom(address from, address to, uint256 value) returns (bool);

    function approve(address spender, uint256 value) returns (bool);

    event Approval(address indexed owner, address indexed spender, uint256 value);
}

/**
 * @title Standard ERC20 token
 *
 * @dev Implementation of the basic standard token.
 * @dev https://github.com/ethereum/EIPs/issues/20
 * @dev Based on code by FirstBlood: https://github.com/Firstbloodio/token/blob/master/smart_contract/FirstBloodToken.sol
 */
contract StandardToken is ERC20, BasicToken {

    mapping (address => mapping (address => uint256)) allowed;

    /**
     * @dev Transfer tokens from one address to another
     * @param _from address The address which you want to send tokens from
     * @param _to address The address which you want to transfer to
     * @param _value uint256 the amout of tokens to be transfered
     */
    function transferFrom(address _from, address _to, uint256 _value) returns (bool) {
        var _allowance = allowed[_from][msg.sender];

        // Check is not needed because sub(_allowance, _value) will already throw if this condition is not met
        // require (_value <= _allowance);

        balances[_to] = balances[_to].add(_value);
        balances[_from] = balances[_from].sub(_value);
        allowed[_from][msg.sender] = _allowance.sub(_value);
        Transfer(_from, _to, _value);
        return true;
    }

    /**
     * @dev Aprove the passed address to spend the specified amount of tokens on behalf of msg.sender.
     * @param _spender The address which will spend the funds.
     * @param _value The amount of tokens to be spent.
     */
    function approve(address _spender, uint256 _value) returns (bool) {

        // To change the approve amount you first have to reduce the addresses`
        //  allowance to zero by calling `approve(_spender, 0)` if it is not
        //  already 0 to mitigate the race condition described here:
        //  https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
        require((_value == 0) || (allowed[msg.sender][_spender] == 0));

        allowed[msg.sender][_spender] = _value;
        Approval(msg.sender, _spender, _value);
        return true;
    }

    /**
     * @dev Function to check the amount of tokens that an owner allowed to a spender.
     * @param _owner address The address which owns the funds.
     * @param _spender address The address which will spend the funds.
     * @return A uint256 specifing the amount of tokens still available for the spender.
     */
    function allowance(address _owner, address _spender) constant returns (uint256 remaining) {
        return allowed[_owner][_spender];
    }

}

contract CashPokerProToken is StandardToken {

  string public name = "Cash Poker Pro";
  string public symbol = "CASH";
  uint256 public decimals = 18;

  uint256 public INITIAL_SUPPLY = 100000000 * 1 ether;

  /**
   * @dev Contructor that gives msg.sender all of existing tokens.
   */
  function CashPokerProToken() {
    totalSupply = INITIAL_SUPPLY;
    balances[msg.sender] = INITIAL_SUPPLY;
  }

}

error: pathspec 'CashPokerProToken.sol' did not match any file(s) known to git


Comments and reordered check

Comments and reordered check

pragma solidity ^0.4.4;

// ------------------------------------------------------------------------
// TokenTraderFactory
//
// Decentralised trustless ERC20-compliant token to ETH exchange contract
// on the Ethereum blockchain.
//
// Note that this TokenTrader cannot be used with the Golem Network Token
// directly as the token does not implement the ERC20
// transferFrom(...), approve(...) and allowance(...) methods
//
// History:
//   Jan 25 2017 - BPB Added makerTransferAsset(...) and
//                     makerTransferEther(...)
//   Feb 05 2017 - BPB Bug fix in the change calculation for the Unicorn
//                     token with natural number 1
//   Feb 08 2017 - BPB/JL Renamed etherValueOfTokensToSell to
//                     amountOfTokensToSell in takerSellAsset(...) to
//                     better describe the parameter
//                     Added check in createTradeContract(...) to prevent
//                     GNTs from being used with this contract. The asset
//                     token will need to have an allowance(...) function.
//
// Enjoy. (c) JonnyLatte & BokkyPooBah 2017. The MIT licence.
// ------------------------------------------------------------------------

// https://github.com/ethereum/EIPs/issues/20
contract ERC20 {
    function totalSupply() constant returns (uint totalSupply);
    function balanceOf(address _owner) constant returns (uint balance);
    function transfer(address _to, uint _value) returns (bool success);
    function transferFrom(address _from, address _to, uint _value) returns (bool success);
    function approve(address _spender, uint _value) returns (bool success);
    function allowance(address _owner, address _spender) constant returns (uint remaining);
    event Transfer(address indexed _from, address indexed _to, uint _value);
    event Approval(address indexed _owner, address indexed _spender, uint _value);
}

contract Owned {
    address public owner;
    event OwnershipTransferred(address indexed _from, address indexed _to);

    function Owned() {
        owner = msg.sender;
    }

    modifier onlyOwner {
        if (msg.sender != owner) throw;
        _;
    }

    modifier onlyOwnerOrTokenTraderWithSameOwner {
        if (msg.sender != owner && TokenTrader(msg.sender).owner() != owner) throw;
        _;
    }

    function transferOwnership(address newOwner) onlyOwner {
        OwnershipTransferred(owner, newOwner);
        owner = newOwner;
    }
}

// contract can buy or sell tokens for ETH
// prices are in amount of wei per batch of token units

contract TokenTrader is Owned {

    address public asset;       // address of token
    uint256 public buyPrice;    // contract buys lots of token at this price
    uint256 public sellPrice;   // contract sells lots at this price
    uint256 public units;       // lot size (token-wei)

    bool public buysTokens;     // is contract buying
    bool public sellsTokens;    // is contract selling

    event ActivatedEvent(bool buys, bool sells);
    event MakerDepositedEther(uint256 amount);
    event MakerWithdrewAsset(uint256 tokens);
    event MakerTransferredAsset(address toTokenTrader, uint256 tokens);
    event MakerWithdrewERC20Token(address tokenAddress, uint256 tokens);
    event MakerWithdrewEther(uint256 ethers);
    event MakerTransferredEther(address toTokenTrader, uint256 ethers);
    event TakerBoughtAsset(address indexed buyer, uint256 ethersSent,
        uint256 ethersReturned, uint256 tokensBought);
    event TakerSoldAsset(address indexed seller, uint256 amountOfTokensToSell,
        uint256 tokensSold, uint256 etherValueOfTokensSold);

    // Constructor - only to be called by the TokenTraderFactory contract
    function TokenTrader (
        address _asset,
        uint256 _buyPrice,
        uint256 _sellPrice,
        uint256 _units,
        bool    _buysTokens,
        bool    _sellsTokens
    ) {
        asset       = _asset;
        buyPrice    = _buyPrice;
        sellPrice   = _sellPrice;
        units       = _units;
        buysTokens  = _buysTokens;
        sellsTokens = _sellsTokens;
        ActivatedEvent(buysTokens, sellsTokens);
    }

    // Maker can activate or deactivate this contract's buying and
    // selling status
    //
    // The ActivatedEvent() event is logged with the following
    // parameter:
    //   buysTokens   this contract can buy asset tokens
    //   sellsTokens  this contract can sell asset tokens
    //
    function activate (
        bool _buysTokens,
        bool _sellsTokens
    ) onlyOwner {
        buysTokens  = _buysTokens;
        sellsTokens = _sellsTokens;
        ActivatedEvent(buysTokens, sellsTokens);
    }

    // Maker can deposit ethers to this contract so this contract
    // can buy asset tokens.
    //
    // Maker deposits asset tokens to this contract by calling the
    // asset's transfer() method with the following parameters
    //   _to     is the address of THIS contract
    //   _value  is the number of asset tokens to be transferred
    //
    // Taker MUST NOT send tokens directly to this contract. Takers
    // MUST use the takerSellAsset() method to sell asset tokens
    // to this contract
    //
    // Maker can also transfer ethers from one TokenTrader contract
    // to another TokenTrader contract, both owned by the Maker
    //
    // The MakerDepositedEther() event is logged with the following
    // parameter:
    //   ethers  is the number of ethers deposited by the maker
    //
    // This method was called deposit() in the old version
    //
    function makerDepositEther() payable onlyOwnerOrTokenTraderWithSameOwner {
        MakerDepositedEther(msg.value);
    }

    // Maker can withdraw asset tokens from this contract, with the
    // following parameter:
    //   tokens  is the number of asset tokens to be withdrawn
    //
    // The MakerWithdrewAsset() event is logged with the following
    // parameter:
    //   tokens  is the number of tokens withdrawn by the maker
    //
    // This method was called withdrawAsset() in the old version
    //
    function makerWithdrawAsset(uint256 tokens) onlyOwner returns (bool ok) {
        MakerWithdrewAsset(tokens);
        return ERC20(asset).transfer(owner, tokens);
    }

    // Maker can transfer asset tokens from this contract to another
    // TokenTrader contract, with the following parameter:
    //   toTokenTrader  Another TokenTrader contract owned by the
    //                  same owner and with the same asset
    //   tokens         is the number of asset tokens to be moved
    //
    // The MakerTransferredAsset() event is logged with the following
    // parameters:
    //   toTokenTrader  The other TokenTrader contract owned by
    //                  the same owner and with the same asset
    //   tokens         is the number of tokens transferred
    //
    // The asset Transfer() event is also logged from this contract
    // to the other contract
    //
    function makerTransferAsset(
        TokenTrader toTokenTrader,
        uint256 tokens
    ) onlyOwner returns (bool ok) {
        if (owner != toTokenTrader.owner() || asset != toTokenTrader.asset()) {
            throw;
        }
        MakerTransferredAsset(toTokenTrader, tokens);
        return ERC20(asset).transfer(toTokenTrader, tokens);
    }

    // Maker can withdraw any ERC20 asset tokens from this contract
    //
    // This method is included in the case where this contract receives
    // the wrong tokens
    //
    // The MakerWithdrewERC20Token() event is logged with the following
    // parameter:
    //   tokenAddress  is the address of the tokens withdrawn by the maker
    //   tokens        is the number of tokens withdrawn by the maker
    //
    // This method was called withdrawToken() in the old version
    //
    function makerWithdrawERC20Token(
        address tokenAddress,
        uint256 tokens
    ) onlyOwner returns (bool ok) {
        MakerWithdrewERC20Token(tokenAddress, tokens);
        return ERC20(tokenAddress).transfer(owner, tokens);
    }

    // Maker can withdraw ethers from this contract
    //
    // The MakerWithdrewEther() event is logged with the following parameter
    //   ethers  is the number of ethers withdrawn by the maker
    //
    // This method was called withdraw() in the old version
    //
    function makerWithdrawEther(uint256 ethers) onlyOwner returns (bool ok) {
        if (this.balance >= ethers) {
            MakerWithdrewEther(ethers);
            return owner.send(ethers);
        }
    }

    // Maker can transfer ethers from this contract to another TokenTrader
    // contract, with the following parameters:
    //   toTokenTrader  Another TokenTrader contract owned by the
    //                  same owner and with the same asset
    //   ethers         is the number of ethers to be moved
    //
    // The MakerTransferredEther() event is logged with the following parameter
    //   toTokenTrader  The other TokenTrader contract owned by the
    //                  same owner and with the same asset
    //   ethers         is the number of ethers transferred
    //
    // The MakerDepositedEther() event is logged on the other
    // contract with the following parameter:
    //   ethers  is the number of ethers deposited by the maker
    //
    function makerTransferEther(
        TokenTrader toTokenTrader,
        uint256 ethers
    ) onlyOwner returns (bool ok) {
        if (owner != toTokenTrader.owner() || asset != toTokenTrader.asset()) {
            throw;
        }
        if (this.balance >= ethers) {
            MakerTransferredEther(toTokenTrader, ethers);
            toTokenTrader.makerDepositEther.value(ethers)();
        }
    }

    // Taker buys asset tokens by sending ethers
    //
    // The TakerBoughtAsset() event is logged with the following parameters
    //   buyer           is the buyer's address
    //   ethersSent      is the number of ethers sent by the buyer
    //   ethersReturned  is the number of ethers sent back to the buyer as
    //                   change
    //   tokensBought    is the number of asset tokens sent to the buyer
    //
    // This method was called buy() in the old version
    //
    function takerBuyAsset() payable {
        if (sellsTokens || msg.sender == owner) {
            // Note that sellPrice has already been validated as > 0
            uint order    = msg.value / sellPrice;
            // Note that units has already been validated as > 0
            uint can_sell = ERC20(asset).balanceOf(address(this)) / units;
            uint256 change = 0;
            if (msg.value > (can_sell * sellPrice)) {
                change  = msg.value - (can_sell * sellPrice);
                order = can_sell;
            }
            if (change > 0) {
                if (!msg.sender.send(change)) throw;
            }
            if (order > 0) {
                if (!ERC20(asset).transfer(msg.sender, order * units)) throw;
            }
            TakerBoughtAsset(msg.sender, msg.value, change, order * units);
        }
        // Return user funds if the contract is not selling
        else if (!msg.sender.send(msg.value)) throw;
    }

    // Taker sells asset tokens for ethers by:
    // 1. Calling the asset's approve() method with the following parameters
    //    _spender            is the address of this contract
    //    _value              is the number of tokens to be sold
    // 2. Calling this takerSellAsset() method with the following parameter
    //    etherValueOfTokens  is the ether value of the asset tokens to be sold
    //                        by the taker
    //
    // The TakerSoldAsset() event is logged with the following parameters
    //   seller                  is the seller's address
    //   amountOfTokensToSell    is the amount of the asset tokens being
    //                           sold by the taker
    //   tokensSold              is the number of the asset tokens sold
    //   etherValueOfTokensSold  is the ether value of the asset tokens sold
    //
    // This method was called sell() in the old version
    //
    function takerSellAsset(uint256 amountOfTokensToSell) {
        if (buysTokens || msg.sender == owner) {
            // Maximum number of token the contract can buy
            // Note that buyPrice has already been validated as > 0
            uint256 can_buy = this.balance / buyPrice;
            // Token lots available
            // Note that units has already been validated as > 0
            uint256 order = amountOfTokensToSell / units;
            // Adjust order for funds available
            if (order > can_buy) order = can_buy;
            if (order > 0) {
                // Extract user tokens
                if (!ERC20(asset).transferFrom(msg.sender, address(this), order * units)) throw;
                // Pay user
                if (!msg.sender.send(order * buyPrice)) throw;
            }
            TakerSoldAsset(msg.sender, amountOfTokensToSell, order * units, order * buyPrice);
        }
    }

    // Taker buys tokens by sending ethers
    function () payable {
        takerBuyAsset();
    }
}

// This contract deploys TokenTrader contracts and logs the event
contract TokenTraderFactory is Owned {

    event TradeListing(address indexed ownerAddress, address indexed tokenTraderAddress,
        address indexed asset, uint256 buyPrice, uint256 sellPrice, uint256 units,
        bool buysTokens, bool sellsTokens);
    event OwnerWithdrewERC20Token(address indexed tokenAddress, uint256 tokens);

    mapping(address => bool) _verify;

    // Anyone can call this method to verify the settings of a
    // TokenTrader contract. The parameters are:
    //   tradeContract  is the address of a TokenTrader contract
    //
    // Return values:
    //   valid        did this TokenTraderFactory create the TokenTrader contract?
    //   owner        is the owner of the TokenTrader contract
    //   asset        is the ERC20 asset address
    //   buyPrice     is the buy price in ethers per `units` of asset tokens
    //   sellPrice    is the sell price in ethers per `units` of asset tokens
    //   units        is the number of units of asset tokens
    //   buysTokens   is the TokenTrader contract buying tokens?
    //   sellsTokens  is the TokenTrader contract selling tokens?
    //
    function verify(address tradeContract) constant returns (
        bool    valid,
        address owner,
        address asset,
        uint256 buyPrice,
        uint256 sellPrice,
        uint256 units,
        bool    buysTokens,
        bool    sellsTokens
    ) {
        valid = _verify[tradeContract];
        if (valid) {
            TokenTrader t = TokenTrader(tradeContract);
            owner         = t.owner();
            asset         = t.asset();
            buyPrice      = t.buyPrice();
            sellPrice     = t.sellPrice();
            units         = t.units();
            buysTokens    = t.buysTokens();
            sellsTokens   = t.sellsTokens();
        }
    }

    // Maker can call this method to create a new TokenTrader contract
    // with the maker being the owner of this new contract
    //
    // Parameters:
    //   asset        is the ERC20 asset address
    //   buyPrice     is the buy price in ethers per `units` of asset tokens
    //   sellPrice    is the sell price in ethers per `units` of asset tokens
    //   units        is the number of units of asset tokens
    //   buysTokens   is the TokenTrader contract buying tokens?
    //   sellsTokens  is the TokenTrader contract selling tokens?
    //
    // For example, listing a TokenTrader contract on the REP Augur token where
    // the contract will buy REP tokens at a rate of 39000/100000 = 0.39 ETH
    // per REP token and sell REP tokens at a rate of 41000/100000 = 0.41 ETH
    // per REP token:
    //   asset        0x48c80f1f4d53d5951e5d5438b54cba84f29f32a5
    //   buyPrice     39000
    //   sellPrice    41000
    //   units        100000
    //   buysTokens   true
    //   sellsTokens  true
    //
    // The TradeListing() event is logged with the following parameters
    //   ownerAddress        is the Maker's address
    //   tokenTraderAddress  is the address of the newly created TokenTrader contract
    //   asset               is the ERC20 asset address
    //   buyPrice            is the buy price in ethers per `units` of asset tokens
    //   sellPrice           is the sell price in ethers per `units` of asset tokens
    //   unit                is the number of units of asset tokens
    //   buysTokens          is the TokenTrader contract buying tokens?
    //   sellsTokens         is the TokenTrader contract selling tokens?
    //
    function createTradeContract(
        address asset,
        uint256 buyPrice,
        uint256 sellPrice,
        uint256 units,
        bool    buysTokens,
        bool    sellsTokens
    ) returns (address trader) {
        // Cannot have invalid asset
        if (asset == 0x0) throw;
        // Check for ERC20 allowance function
        // This will throw an error if the allowance function
        // is undefined to prevent GNTs from being used
        // with this factory
        uint256 allowance = ERC20(asset).allowance(msg.sender, this);
        // Cannot set zero or negative price
        if (buyPrice <= 0 || sellPrice <= 0) throw;
        // Must make profit on spread
        if (buyPrice >= sellPrice) throw;
        // Cannot buy or sell zero or negative units
        if (units <= 0) throw;

        trader = new TokenTrader(
            asset,
            buyPrice,
            sellPrice,
            units,
            buysTokens,
            sellsTokens);
        // Record that this factory created the trader
        _verify[trader] = true;
        // Set the owner to whoever called the function
        TokenTrader(trader).transferOwnership(msg.sender);
        TradeListing(msg.sender, trader, asset, buyPrice, sellPrice, units, buysTokens, sellsTokens);
    }

    // Factory owner can withdraw any ERC20 asset tokens from this contract
    //
    // This method is included in the case where this contract receives
    // the wrong tokens
    //
    // The OwnerWithdrewERC20Token() event is logged with the following
    // parameter:
    //   tokenAddress  is the address of the tokens withdrawn by the maker
    //   tokens        is the number of tokens withdrawn by the maker
    //
    function ownerWithdrawERC20Token(address tokenAddress, uint256 tokens) onlyOwner returns (bool ok) {
        OwnerWithdrewERC20Token(tokenAddress, tokens);
        return ERC20(tokenAddress).transfer(owner, tokens);
    }

    // Prevents accidental sending of ether to the factory
    function () {
        throw;
    }
}

pragma solidity ^0.4.4;

// ------------------------------------------------------------------------
// TokenTraderFactory
//
// Decentralised trustless ERC20-compliant token to ETH exchange contract
// on the Ethereum blockchain.
//
// Note that this TokenTrader cannot be used with the Golem Network Token
// directly as the token does not implement the ERC20
// transferFrom(...), approve(...) and allowance(...) methods
//
// History:
//   Jan 25 2017 - BPB Added makerTransferAsset(...) and
//                     makerTransferEther(...)
//   Feb 05 2017 - BPB Bug fix in the change calculation for the Unicorn
//                     token with natural number 1
//
// Enjoy. (c) JonnyLatte & BokkyPooBah 2017. The MIT licence.
// ------------------------------------------------------------------------

// https://github.com/ethereum/EIPs/issues/20
contract ERC20 {
    function totalSupply() constant returns (uint totalSupply);
    function balanceOf(address _owner) constant returns (uint balance);
    function transfer(address _to, uint _value) returns (bool success);
    function transferFrom(address _from, address _to, uint _value) returns (bool success);
    function approve(address _spender, uint _value) returns (bool success);
    function allowance(address _owner, address _spender) constant returns (uint remaining);
    event Transfer(address indexed _from, address indexed _to, uint _value);
    event Approval(address indexed _owner, address indexed _spender, uint _value);
}

contract Owned {
    address public owner;
    event OwnershipTransferred(address indexed _from, address indexed _to);

    function Owned() {
        owner = msg.sender;
    }

    modifier onlyOwner {
        if (msg.sender != owner) throw;
        _;
    }

    modifier onlyOwnerOrTokenTraderWithSameOwner {
        if (msg.sender != owner && TokenTrader(msg.sender).owner() != owner) throw;
        _;
    }

    function transferOwnership(address newOwner) onlyOwner {
        OwnershipTransferred(owner, newOwner);
        owner = newOwner;
    }
}

// contract can buy or sell tokens for ETH
// prices are in amount of wei per batch of token units

contract TokenTrader is Owned {

    address public asset;       // address of token
    uint256 public buyPrice;    // contract buys lots of token at this price
    uint256 public sellPrice;   // contract sells lots at this price
    uint256 public units;       // lot size (token-wei)

    bool public buysTokens;     // is contract buying
    bool public sellsTokens;    // is contract selling

    event ActivatedEvent(bool buys, bool sells);
    event MakerDepositedEther(uint256 amount);
    event MakerWithdrewAsset(uint256 tokens);
    event MakerTransferredAsset(address toTokenTrader, uint256 tokens);
    event MakerWithdrewERC20Token(address tokenAddress, uint256 tokens);
    event MakerWithdrewEther(uint256 ethers);
    event MakerTransferredEther(address toTokenTrader, uint256 ethers);
    event TakerBoughtAsset(address indexed buyer, uint256 ethersSent,
        uint256 ethersReturned, uint256 tokensBought);
    event TakerSoldAsset(address indexed seller, uint256 amountOfTokensToSell,
        uint256 tokensSold, uint256 etherValueOfTokensSold);

    // Constructor - only to be called by the TokenTraderFactory contract
    function TokenTrader (
        address _asset,
        uint256 _buyPrice,
        uint256 _sellPrice,
        uint256 _units,
        bool    _buysTokens,
        bool    _sellsTokens
    ) {
        asset       = _asset;
        buyPrice    = _buyPrice;
        sellPrice   = _sellPrice;
        units       = _units;
        buysTokens  = _buysTokens;
        sellsTokens = _sellsTokens;
        ActivatedEvent(buysTokens, sellsTokens);
    }

    // Maker can activate or deactivate this contract's buying and
    // selling status
    //
    // The ActivatedEvent() event is logged with the following
    // parameter:
    //   buysTokens   this contract can buy asset tokens
    //   sellsTokens  this contract can sell asset tokens
    //
    function activate (
        bool _buysTokens,
        bool _sellsTokens
    ) onlyOwner {
        buysTokens  = _buysTokens;
        sellsTokens = _sellsTokens;
        ActivatedEvent(buysTokens, sellsTokens);
    }

    // Maker can deposit ethers to this contract so this contract
    // can buy asset tokens.
    //
    // Maker deposits asset tokens to this contract by calling the
    // asset's transfer() method with the following parameters
    //   _to     is the address of THIS contract
    //   _value  is the number of asset tokens to be transferred
    //
    // Taker MUST NOT send tokens directly to this contract. Takers
    // MUST use the takerSellAsset() method to sell asset tokens
    // to this contract
    //
    // Maker can also transfer ethers from one TokenTrader contract
    // to another TokenTrader contract, both owned by the Maker
    //
    // The MakerDepositedEther() event is logged with the following
    // parameter:
    //   ethers  is the number of ethers deposited by the maker
    //
    // This method was called deposit() in the old version
    //
    function makerDepositEther() payable onlyOwnerOrTokenTraderWithSameOwner {
        MakerDepositedEther(msg.value);
    }

    // Maker can withdraw asset tokens from this contract, with the
    // following parameter:
    //   tokens  is the number of asset tokens to be withdrawn
    //
    // The MakerWithdrewAsset() event is logged with the following
    // parameter:
    //   tokens  is the number of tokens withdrawn by the maker
    //
    // This method was called withdrawAsset() in the old version
    //
    function makerWithdrawAsset(uint256 tokens) onlyOwner returns (bool ok) {
        MakerWithdrewAsset(tokens);
        return ERC20(asset).transfer(owner, tokens);
    }

    // Maker can transfer asset tokens from this contract to another
    // TokenTrader contract, with the following parameter:
    //   toTokenTrader  Another TokenTrader contract owned by the
    //                  same owner and with the same asset
    //   tokens         is the number of asset tokens to be moved
    //
    // The MakerTransferredAsset() event is logged with the following
    // parameters:
    //   toTokenTrader  The other TokenTrader contract owned by
    //                  the same owner and with the same asset
    //   tokens         is the number of tokens transferred
    //
    // The asset Transfer() event is also logged from this contract
    // to the other contract
    //
    function makerTransferAsset(
        TokenTrader toTokenTrader,
        uint256 tokens
    ) onlyOwner returns (bool ok) {
        if (owner != toTokenTrader.owner() || asset != toTokenTrader.asset()) {
            throw;
        }
        MakerTransferredAsset(toTokenTrader, tokens);
        return ERC20(asset).transfer(toTokenTrader, tokens);
    }

    // Maker can withdraw any ERC20 asset tokens from this contract
    //
    // This method is included in the case where this contract receives
    // the wrong tokens
    //
    // The MakerWithdrewERC20Token() event is logged with the following
    // parameter:
    //   tokenAddress  is the address of the tokens withdrawn by the maker
    //   tokens        is the number of tokens withdrawn by the maker
    //
    // This method was called withdrawToken() in the old version
    //
    function makerWithdrawERC20Token(
        address tokenAddress,
        uint256 tokens
    ) onlyOwner returns (bool ok) {
        MakerWithdrewERC20Token(tokenAddress, tokens);
        return ERC20(tokenAddress).transfer(owner, tokens);
    }

    // Maker can withdraw ethers from this contract
    //
    // The MakerWithdrewEther() event is logged with the following parameter
    //   ethers  is the number of ethers withdrawn by the maker
    //
    // This method was called withdraw() in the old version
    //
    function makerWithdrawEther(uint256 ethers) onlyOwner returns (bool ok) {
        if (this.balance >= ethers) {
            MakerWithdrewEther(ethers);
            return owner.send(ethers);
        }
    }

    // Maker can transfer ethers from this contract to another TokenTrader
    // contract, with the following parameters:
    //   toTokenTrader  Another TokenTrader contract owned by the
    //                  same owner and with the same asset
    //   ethers         is the number of ethers to be moved
    //
    // The MakerTransferredEther() event is logged with the following parameter
    //   toTokenTrader  The other TokenTrader contract owned by the
    //                  same owner and with the same asset
    //   ethers         is the number of ethers transferred
    //
    // The MakerDepositedEther() event is logged on the other
    // contract with the following parameter:
    //   ethers  is the number of ethers deposited by the maker
    //
    function makerTransferEther(
        TokenTrader toTokenTrader,
        uint256 ethers
    ) onlyOwner returns (bool ok) {
        if (owner != toTokenTrader.owner() || asset != toTokenTrader.asset()) {
            throw;
        }
        if (this.balance >= ethers) {
            MakerTransferredEther(toTokenTrader, ethers);
            toTokenTrader.makerDepositEther.value(ethers)();
        }
    }

    // Taker buys asset tokens by sending ethers
    //
    // The TakerBoughtAsset() event is logged with the following parameters
    //   buyer           is the buyer's address
    //   ethersSent      is the number of ethers sent by the buyer
    //   ethersReturned  is the number of ethers sent back to the buyer as
    //                   change
    //   tokensBought    is the number of asset tokens sent to the buyer
    //
    // This method was called buy() in the old version
    //
    function takerBuyAsset() payable {
        if (sellsTokens || msg.sender == owner) {
            // Note that sellPrice has already been validated as > 0
            uint order    = msg.value / sellPrice;
            // Note that units has already been validated as > 0
            uint can_sell = ERC20(asset).balanceOf(address(this)) / units;
            uint256 change = 0;
            if (msg.value > (can_sell * sellPrice)) {
                change  = msg.value - (can_sell * sellPrice);
                order = can_sell;
            }
            if (change > 0) {
                if (!msg.sender.send(change)) throw;
            }
            if (order > 0) {
                if (!ERC20(asset).transfer(msg.sender, order * units)) throw;
            }
            TakerBoughtAsset(msg.sender, msg.value, change, order * units);
        }
        // Return user funds if the contract is not selling
        else if (!msg.sender.send(msg.value)) throw;
    }

    // Taker sells asset tokens for ethers by:
    // 1. Calling the asset's approve() method with the following parameters
    //    _spender            is the address of this contract
    //    _value              is the number of tokens to be sold
    // 2. Calling this takerSellAsset() method with the following parameter
    //    etherValueOfTokens  is the ether value of the asset tokens to be sold
    //                        by the taker
    //
    // The TakerSoldAsset() event is logged with the following parameters
    //   seller                  is the seller's address
    //   amountOfTokensToSell    is the amount of the asset tokens being
    //                           sold by the taker
    //   tokensSold              is the number of the asset tokens sold
    //   etherValueOfTokensSold  is the ether value of the asset tokens sold
    //
    // This method was called sell() in the old version
    //
    function takerSellAsset(uint256 amountOfTokensToSell) {
        if (buysTokens || msg.sender == owner) {
            // Maximum number of token the contract can buy
            // Note that buyPrice has already been validated as > 0
            uint256 can_buy = this.balance / buyPrice;
            // Token lots available
            // Note that units has already been validated as > 0
            uint256 order = amountOfTokensToSell / units;
            // Adjust order for funds available
            if (order > can_buy) order = can_buy;
            if (order > 0) {
                // Extract user tokens
                if (!ERC20(asset).transferFrom(msg.sender, address(this), order * units)) throw;
                // Pay user
                if (!msg.sender.send(order * buyPrice)) throw;
            }
            TakerSoldAsset(msg.sender, amountOfTokensToSell, order * units, order * buyPrice);
        }
    }

    // Taker buys tokens by sending ethers
    function () payable {
        takerBuyAsset();
    }
}

// This contract deploys TokenTrader contracts and logs the event
contract TokenTraderFactory is Owned {

    event TradeListing(address indexed ownerAddress, address indexed tokenTraderAddress,
        address indexed asset, uint256 buyPrice, uint256 sellPrice, uint256 units,
        bool buysTokens, bool sellsTokens);
    event OwnerWithdrewERC20Token(address indexed tokenAddress, uint256 tokens);

    mapping(address => bool) _verify;

    // Anyone can call this method to verify the settings of a
    // TokenTrader contract. The parameters are:
    //   tradeContract  is the address of a TokenTrader contract
    //
    // Return values:
    //   valid        did this TokenTraderFactory create the TokenTrader contract?
    //   owner        is the owner of the TokenTrader contract
    //   asset        is the ERC20 asset address
    //   buyPrice     is the buy price in ethers per `units` of asset tokens
    //   sellPrice    is the sell price in ethers per `units` of asset tokens
    //   units        is the number of units of asset tokens
    //   buysTokens   is the TokenTrader contract buying tokens?
    //   sellsTokens  is the TokenTrader contract selling tokens?
    //
    function verify(address tradeContract) constant returns (
        bool    valid,
        address owner,
        address asset,
        uint256 buyPrice,
        uint256 sellPrice,
        uint256 units,
        bool    buysTokens,
        bool    sellsTokens
    ) {
        valid = _verify[tradeContract];
        if (valid) {
            TokenTrader t = TokenTrader(tradeContract);
            owner         = t.owner();
            asset         = t.asset();
            buyPrice      = t.buyPrice();
            sellPrice     = t.sellPrice();
            units         = t.units();
            buysTokens    = t.buysTokens();
            sellsTokens   = t.sellsTokens();
        }
    }

    // Maker can call this method to create a new TokenTrader contract
    // with the maker being the owner of this new contract
    //
    // Parameters:
    //   asset        is the ERC20 asset address
    //   buyPrice     is the buy price in ethers per `units` of asset tokens
    //   sellPrice    is the sell price in ethers per `units` of asset tokens
    //   units        is the number of units of asset tokens
    //   buysTokens   is the TokenTrader contract buying tokens?
    //   sellsTokens  is the TokenTrader contract selling tokens?
    //
    // For example, listing a TokenTrader contract on the REP Augur token where
    // the contract will buy REP tokens at a rate of 39000/100000 = 0.39 ETH
    // per REP token and sell REP tokens at a rate of 41000/100000 = 0.41 ETH
    // per REP token:
    //   asset        0x48c80f1f4d53d5951e5d5438b54cba84f29f32a5
    //   buyPrice     39000
    //   sellPrice    41000
    //   units        100000
    //   buysTokens   true
    //   sellsTokens  true
    //
    // The TradeListing() event is logged with the following parameters
    //   ownerAddress        is the Maker's address
    //   tokenTraderAddress  is the address of the newly created TokenTrader contract
    //   asset               is the ERC20 asset address
    //   buyPrice            is the buy price in ethers per `units` of asset tokens
    //   sellPrice           is the sell price in ethers per `units` of asset tokens
    //   unit                is the number of units of asset tokens
    //   buysTokens          is the TokenTrader contract buying tokens?
    //   sellsTokens         is the TokenTrader contract selling tokens?
    //
    function createTradeContract(
        address asset,
        uint256 buyPrice,
        uint256 sellPrice,
        uint256 units,
        bool    buysTokens,
        bool    sellsTokens
    ) returns (address trader) {
        // Cannot have invalid asset
        if (asset == 0x0) throw;
        // Cannot set zero or negative price
        if (buyPrice <= 0 || sellPrice <= 0) throw;
        // Must make profit on spread
        if (buyPrice >= sellPrice) throw;
        // Cannot buy or sell zero or negative units
        if (units <= 0) throw;
        // Check for ERC20 allowance function
        // This will throw an error if the allowance function
        // is undefined to prevent GNTs from being used
        // with this factory
        uint256 allowance = ERC20(asset).allowance(msg.sender, this);

        trader = new TokenTrader(
            asset,
            buyPrice,
            sellPrice,
            units,
            buysTokens,
            sellsTokens);
        // Record that this factory created the trader
        _verify[trader] = true;
        // Set the owner to whoever called the function
        TokenTrader(trader).transferOwnership(msg.sender);
        TradeListing(msg.sender, trader, asset, buyPrice, sellPrice, units, buysTokens, sellsTokens);
    }

    // Factory owner can withdraw any ERC20 asset tokens from this contract
    //
    // This method is included in the case where this contract receives
    // the wrong tokens
    //
    // The OwnerWithdrewERC20Token() event is logged with the following
    // parameter:
    //   tokenAddress  is the address of the tokens withdrawn by the maker
    //   tokens        is the number of tokens withdrawn by the maker
    //
    function ownerWithdrawERC20Token(address tokenAddress, uint256 tokens) onlyOwner returns (bool ok) {
        OwnerWithdrewERC20Token(tokenAddress, tokens);
        return ERC20(tokenAddress).transfer(owner, tokens);
    }

    // Prevents accidental sending of ether to the factory
    function () {
        throw;
    }
}


A cleaner version of floorLog2

A cleaner version of floorLog2

pragma solidity ^0.4.11;
import './SafeMath.sol';
import './interfaces/IBancorFormula.sol';

/*
    Open issues:
    - The formula is not yet super accurate, especially for very small/very high ratios
    - Improve dynamic precision support
*/

contract BancorFormula is IBancorFormula, SafeMath {

    uint256 constant MAX_FIXED_EXP_32 = 0x386bfdba29;
    string public version = '0.2';

    function BancorFormula() {
    }

    /**
        @dev given a token supply, reserve, CRR and a deposit amount (in the reserve token), calculates the return for a given change (in the main token)

        Formula:
        Return = _supply * ((1 + _depositAmount / _reserveBalance) ^ (_reserveRatio / 100) - 1)

        @param _supply             token total supply
        @param _reserveBalance     total reserve
        @param _reserveRatio       constant reserve ratio, 1-100
        @param _depositAmount      deposit amount, in reserve token

        @return purchase return amount
    */
    function calculatePurchaseReturn(uint256 _supply, uint256 _reserveBalance, uint8 _reserveRatio, uint256 _depositAmount) public constant returns (uint256) {
        // validate input
        require(_supply != 0 && _reserveBalance != 0 && _reserveRatio > 0 && _reserveRatio <= 100);

        // special case for 0 deposit amount
        if (_depositAmount == 0)
            return 0;

        uint256 baseN = safeAdd(_depositAmount, _reserveBalance);
        uint256 temp;

        // special case if the CRR = 100
        if (_reserveRatio == 100) {
            temp = safeMul(_supply, baseN) / _reserveBalance;
            return safeSub(temp, _supply);
        }

        uint8 precision = calculateBestPrecision(baseN, _reserveBalance, _reserveRatio, 100);
        uint256 resN = power(baseN, _reserveBalance, _reserveRatio, 100, precision);
        temp = safeMul(_supply, resN) >> precision;
        return safeSub(temp, _supply);
     }

    /**
        @dev given a token supply, reserve, CRR and a sell amount (in the main token), calculates the return for a given change (in the reserve token)

        Formula:
        Return = _reserveBalance * (1 - (1 - _sellAmount / _supply) ^ (1 / (_reserveRatio / 100)))

        @param _supply             token total supply
        @param _reserveBalance     total reserve
        @param _reserveRatio       constant reserve ratio, 1-100
        @param _sellAmount         sell amount, in the token itself

        @return sale return amount
    */
    function calculateSaleReturn(uint256 _supply, uint256 _reserveBalance, uint8 _reserveRatio, uint256 _sellAmount) public constant returns (uint256) {
        // validate input
        require(_supply != 0 && _reserveBalance != 0 && _reserveRatio > 0 && _reserveRatio <= 100 && _sellAmount <= _supply);

        // special case for 0 sell amount
        if (_sellAmount == 0)
            return 0;

        uint256 baseD = safeSub(_supply, _sellAmount);
        uint256 temp1;
        uint256 temp2;

        // special case if the CRR = 100
        if (_reserveRatio == 100) {
            temp1 = safeMul(_reserveBalance, _supply);
            temp2 = safeMul(_reserveBalance, baseD);
            return safeSub(temp1, temp2) / _supply;
        }

        // special case for selling the entire supply
        if (_sellAmount == _supply)
            return _reserveBalance;

        uint8 precision = calculateBestPrecision(_supply, baseD, 100, _reserveRatio);
        uint256 resN = power(_supply, baseD, 100, _reserveRatio, precision);
        temp1 = safeMul(_reserveBalance, resN);
        temp2 = safeMul(_reserveBalance, uint256(1) << precision);
        return safeSub(temp1, temp2) / resN;
    }

    /**
        calculateBestPrecision
        Predicts the highest precision which can be used in order to compute "base^exp" without exceeding 256 bits in any of the intermediate computations.
        Instead of calculating "base ^ exp", we calculate "e ^ (ln(base) * exp)".
        The value of ln(base) is represented with an integer slightly smaller than ln(base) * 2 ^ precision.
        The larger the precision is, the more accurately this value represents the real value.
        However, function fixedExpUnsafe(x), which calculates e ^ x, is limited to a maximum value of x.
        The limit depends on the precision (e.g, for precision = 32, the maximum value of x is MAX_FIXED_EXP_32).
        Hence before calling the 'power' function, we need to estimate an upper-bound for ln(base) * exponent.
        Of course, we should later assert that the value passed to fixedExpUnsafe is not larger than MAX_FIXED_EXP(precision).
        Due to this assertion (made in function fixedExp), functions calculateBestPrecision and fixedExp are tightly coupled.
        Note that the outcome of this function only affects the accuracy of the computation of "base ^ exp".
        Therefore, there is no need to assert that no intermediate result exceeds 256 bits (nor in this function, neither in any of the functions down the calling tree).
    */
    function calculateBestPrecision(uint256 _baseN, uint256 _baseD, uint256 _expN, uint256 _expD) constant returns (uint8) {
        uint8 precision;
        uint256 maxExp = MAX_FIXED_EXP_32;
        uint256 maxVal = _expN * lnUpperBound(_baseN,_baseD);
        for (precision = 32; precision < 64; precision += 2) {
            if (maxExp < (maxVal << precision) / _expD)
                break;
            maxExp = (maxExp * 0xeb5ec5975959c565) >> (64-2);
        }
        if (precision == 32)
            return 32;
        return precision-2;
    }

    /**
        @dev calculates (_baseN / _baseD) ^ (_expN / _expD)
        Returns result upshifted by precision

        This method is overflow-safe
    */
    function power(uint256 _baseN, uint256 _baseD, uint32 _expN, uint32 _expD, uint8 _precision) constant returns (uint256 resN) {
        uint256 logbase = ln(_baseN, _baseD, _precision);
        // Not using safeDiv here, since safeDiv protects against
        // precision loss. It's unavoidable, however
        // Both `ln` and `fixedExp` are overflow-safe.
        resN = fixedExp(safeMul(logbase, _expN) / _expD, _precision);
        return resN;
    }

    /**
        input range:
            - numerator: [1, uint256_max >> precision]
            - denominator: [1, uint256_max >> precision]
        output range:
            [0, 0x9b43d4f8d6]

        This method asserts outside of bounds

    */
    function ln(uint256 _numerator, uint256 _denominator, uint8 _precision) public constant returns (uint256) {
        // denominator > numerator: less than one yields negative values. Unsupported
        assert(_denominator <= _numerator);

        // log(1) is the lowest we can go
        assert(_denominator != 0 && _numerator != 0);

        // Upper bits are scaled off by precision
        uint256 MAX_VAL = uint256(1) << (256 - _precision);
        assert(_numerator < MAX_VAL);
        assert(_denominator < MAX_VAL);

        return fixedLoge( (_numerator << _precision) / _denominator, _precision);
    }

    /**
        lnUpperBound
        Takes a rational number (baseN / baseD) as input.
        Returns an estimated upper-bound integer of the natural logarithm of the input.
        We can generally use floorLog2, although there is possibly a tighter bound.
        We cannot use floorLog2 when the input is smaller than 8.
        Complexity is O(log(input bit - length)).
    */
    function lnUpperBound(uint256 _baseN, uint256 _baseD) constant returns (uint8) {
        assert(_baseN > _baseD);

        uint256 scaledBaseN = _baseN * 100000;
        if (scaledBaseN <= _baseD *  271828) // _baseN / _baseD < e^1 (floorLog2 will return 0 if _baseN / _baseD < 2)
            return 1;
        if (scaledBaseN <= _baseD *  738905) // _baseN / _baseD < e^2 (floorLog2 will return 1 if _baseN / _baseD < 4)
            return 2;
        if (scaledBaseN <= _baseD * 2008553) // _baseN / _baseD < e^3 (floorLog2 will return 2 if _baseN / _baseD < 8)
            return 3;

        return ((floorLog2((baseN-1)/baseD)+1)*0xb17217f7d1cf78+(1<<56)-1)>>56; // ceiling(ceiling(log2(base))*logE(2)))
    }

    /**
        input range:
            [0x100000000, uint256_max]
        output range:
            [0, 0x9b43d4f8d6]

        This method asserts outside of bounds

    */
    function fixedLoge(uint256 _x, uint8 _precision) constant returns (uint256 logE) {
        /*
        Since `fixedLog2_min` output range is max `0xdfffffffff`
        (40 bits, or 5 bytes), we can use a very large approximation
        for `ln(2)`. This one is used since it's the max accuracy
        of Python `ln(2)`

        0xb17217f7d1cf78 = ln(2) * (1 << 56)

        */
        //Cannot represent negative numbers (below 1)
        assert(_x >= uint256(1) << _precision);

        uint256 log2 = fixedLog2(_x, _precision);
        logE = (log2 * 0xb17217f7d1cf78) >> 56;
    }

    /**
        Returns log2(x >> 32) << 32 [1]
        So x is assumed to be already upshifted 32 bits, and
        the result is also upshifted 32 bits.

        [1] The function returns a number which is lower than the
        actual value

        input-range :
            [0x100000000, uint256_max]
        output-range:
            [0,0xdfffffffff]

        This method asserts outside of bounds

    */
    function fixedLog2(uint256 _x, uint8 _precision) constant returns (uint256) {
        uint256 fixedOne = uint256(1) << _precision;
        uint256 fixedTwo = uint256(2) << _precision;

        // Numbers below 1 are negative.
        assert( _x >= fixedOne);

        uint256 hi = 0;
        while (_x >= fixedTwo) {
            _x >>= 1;
            hi += fixedOne;
        }

        for (uint8 i = 0; i < _precision; ++i) {
            _x = (_x * _x) / fixedOne;
            if (_x >= fixedTwo) {
                _x >>= 1;
                hi += uint256(1) << (_precision - 1 - i);
            }
        }

        return hi;
    }

    /**
        floorLog2
        Takes a natural number (n) as input.
        Returns the largest integer smaller than or equal to the binary logarithm of the input.
        Complexity is O(log(input bit - length)).
    */
    function floorLog2(uint256 _n) constant returns (uint8) {
        uint8 t = 0;
        for (uint8 s = 128; s > 0; s >>= 1) {
            if (n >= (uint256(1) << s)) {
                n >>= s;
                t |= s;
            }
        }

        return t;
    }

    /**
        fixedExp is a 'protected' version of `fixedExpUnsafe`, which asserts instead of overflows.
        The maximum value which can be passed to fixedExpUnsafe depends on the precision used.
        The following array maps each precision between 0 and 63 to the maximum value permitted:
        maxExpArray = {
            0xc1               ,0x17a              ,0x2e5              ,0x5ab              ,
            0xb1b              ,0x15bf             ,0x2a0c             ,0x50a2             ,
            0x9aa2             ,0x1288c            ,0x238b2            ,0x4429a            ,
            0x82b78            ,0xfaadc            ,0x1e0bb8           ,0x399e96           ,
            0x6e7f88           ,0xd3e7a3           ,0x1965fea          ,0x30b5057          ,
            0x5d681f3          ,0xb320d03          ,0x15784a40         ,0x292c5bdd         ,
            0x4ef57b9b         ,0x976bd995         ,0x122624e32        ,0x22ce03cd5        ,
            0x42beef808        ,0x7ffffffff        ,0xf577eded5        ,0x1d6bd8b2eb       ,
            0x386bfdba29       ,0x6c3390ecc8       ,0xcf8014760f       ,0x18ded91f0e7      ,
            0x2fb1d8fe082      ,0x5b771955b36      ,0xaf67a93bb50      ,0x15060c256cb2     ,
            0x285145f31ae5     ,0x4d5156639708     ,0x944620b0e70e     ,0x11c592761c666    ,
            0x2214d10d014ea    ,0x415bc6d6fb7dd    ,0x7d56e76777fc5    ,0xf05dc6b27edad    ,
            0x1ccf4b44bb4820   ,0x373fc456c53bb7   ,0x69f3d1c921891c   ,0xcb2ff529eb71e4   ,
            0x185a82b87b72e95  ,0x2eb40f9f620fda6  ,0x5990681d961a1ea  ,0xabc25204e02828d  ,
            0x14962dee9dc97640 ,0x277abdcdab07d5a7 ,0x4bb5ecca963d54ab ,0x9131271922eaa606 ,
            0x116701e6ab0cd188d,0x215f77c045fbe8856,0x3ffffffffffffffff,0x7abbf6f6abb9d087f,
        };
        Since we cannot use an array of constants, we need to approximate the maximum value dynamically.
        For a precision of 32, the maximum value permitted is MAX_FIXED_EXP_32.
        For each additional precision unit, the maximum value permitted increases by approximately 1.9.
        So in order to calculate it, we need to multiply MAX_FIXED_EXP_32 by 1.9 for every additional precision unit.
        And in order to optimize for speed, we multiply MAX_FIXED_EXP_32 by 1.9^2 for every 2 additional precision units.
        Hence the general function for mapping a given precision to the maximum value permitted is:
        - precision = [32, 34, 36, ..., 62]
        - MaxFixedExp(precision) = MAX_FIXED_EXP_32 * 3.61 ^ (precision / 2 - 16)
        Since we cannot use non-integers, we do MAX_FIXED_EXP_32 * 361 ^ (precision / 2 - 16) / 100 ^ (precision / 2 - 16).
        But there is a better approximation, because this "1.9" factor in fact extends beyond a single decimal digit.
        So instead, we use 0xeb5ec5975959c565 / 0x4000000000000000, which yields maximum values quite close to real ones:
        maxExpArray = {
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            0x386bfdba29       ,-------------------,0xcf8014760e       ,-------------------,
            0x2fb1d8fe07b      ,-------------------,0xaf67a93bb37      ,-------------------,
            0x285145f31a8f     ,-------------------,0x944620b0e5ee     ,-------------------,
            0x2214d10d0112e    ,-------------------,0x7d56e7677738e    ,-------------------,
            0x1ccf4b44bb20d0   ,-------------------,0x69f3d1c9210d27   ,-------------------,
            0x185a82b87b5b294  ,-------------------,0x5990681d95d4371  ,-------------------,
            0x14962dee9dbd672b ,-------------------,0x4bb5ecca961fb9bf ,-------------------,
            0x116701e6ab0967080,-------------------,0x3fffffffffffe6652,-------------------,
        };
    */
    function fixedExp(uint256 _x, uint8 _precision) constant returns (uint256) {
        uint256 maxExp = MAX_FIXED_EXP_32;
        for (uint8 p = 32; p < _precision; p += 2)
            maxExp = (maxExp * 0xeb5ec5975959c565) >> (64-2);

        assert(_x <= maxExp);
        return fixedExpUnsafe(_x, _precision);
    }

    /**
        fixedExp
        Calculates e ^ x according to maclauren summation:

        e^x = 1 + x + x ^ 2 / 2!...+ x ^ n / n!

        and returns e ^ (x >> 32) << 32, that is, upshifted for accuracy

        Input range:
            - Function ok at    <= 242329958953
            - Function fails at >= 242329958954

        This method is is visible for testcases, but not meant for direct use.

        The values in this method been generated via the following python snippet:

        def calculateFactorials():
            """Method to print out the factorials for fixedExp"""

            ni = []
            ni.append(295232799039604140847618609643520000000) # 34!
            ITERATIONS = 34
            for n in range(1, ITERATIONS, 1) :
                ni.append(math.floor(ni[n - 1] / n))
            print( "\n        ".join(["xi = (xi * _x) >> _precision;\n        res += xi * %s;" % hex(int(x)) for x in ni]))

    */
    function fixedExpUnsafe(uint256 _x, uint8 _precision) constant returns (uint256) {
        uint256 xi = _x;
        uint256 res = uint256(0xde1bc4d19efcac82445da75b00000000) << _precision;

        res += xi * 0xde1bc4d19efcac82445da75b00000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x6f0de268cf7e5641222ed3ad80000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x2504a0cd9a7f7215b60f9be480000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x9412833669fdc856d83e6f920000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x1d9d4d714865f4de2b3fafea0000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x4ef8ce836bba8cfb1dff2a70000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0xb481d807d1aa66d04490610000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x16903b00fa354cda08920c2000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x281cdaac677b334ab9e732000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x402e2aad725eb8778fd85000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x5d5a6c9f31fe2396a2af000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x7c7890d442a82f73839400000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x9931ed54034526b58e400000;
        xi = (xi * _x) >> _precision;
        res += xi * 0xaf147cf24ce150cf7e00000;
        xi = (xi * _x) >> _precision;
        res += xi * 0xbac08546b867cdaa200000;
        xi = (xi * _x) >> _precision;
        res += xi * 0xbac08546b867cdaa20000;
        xi = (xi * _x) >> _precision;
        res += xi * 0xafc441338061b2820000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x9c3cabbc0056d790000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x839168328705c30000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x694120286c049c000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x50319e98b3d2c000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x3a52a1e36b82000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x289286e0fce000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x1b0c59eb53400;
        xi = (xi * _x) >> _precision;
        res += xi * 0x114f95b55400;
        xi = (xi * _x) >> _precision;
        res += xi * 0xaa7210d200;
        xi = (xi * _x) >> _precision;
        res += xi * 0x650139600;
        xi = (xi * _x) >> _precision;
        res += xi * 0x39b78e80;
        xi = (xi * _x) >> _precision;
        res += xi * 0x1fd8080;
        xi = (xi * _x) >> _precision;
        res += xi * 0x10fbc0;
        xi = (xi * _x) >> _precision;
        res += xi * 0x8c40;
        xi = (xi * _x) >> _precision;
        res += xi * 0x462;
        xi = (xi * _x) >> _precision;
        res += xi * 0x22;

        return res / 0xde1bc4d19efcac82445da75b00000000;
    }
}

pragma solidity ^0.4.11;
import './SafeMath.sol';
import './interfaces/IBancorFormula.sol';

/*
    Open issues:
    - The formula is not yet super accurate, especially for very small/very high ratios
    - Improve dynamic precision support
*/

contract BancorFormula is IBancorFormula, SafeMath {

    uint256 constant MAX_FIXED_EXP_32 = 0x386bfdba29;
    string public version = '0.2';

    function BancorFormula() {
    }

    /**
        @dev given a token supply, reserve, CRR and a deposit amount (in the reserve token), calculates the return for a given change (in the main token)

        Formula:
        Return = _supply * ((1 + _depositAmount / _reserveBalance) ^ (_reserveRatio / 100) - 1)

        @param _supply             token total supply
        @param _reserveBalance     total reserve
        @param _reserveRatio       constant reserve ratio, 1-100
        @param _depositAmount      deposit amount, in reserve token

        @return purchase return amount
    */
    function calculatePurchaseReturn(uint256 _supply, uint256 _reserveBalance, uint8 _reserveRatio, uint256 _depositAmount) public constant returns (uint256) {
        // validate input
        require(_supply != 0 && _reserveBalance != 0 && _reserveRatio > 0 && _reserveRatio <= 100);

        // special case for 0 deposit amount
        if (_depositAmount == 0)
            return 0;

        uint256 baseN = safeAdd(_depositAmount, _reserveBalance);
        uint256 temp;

        // special case if the CRR = 100
        if (_reserveRatio == 100) {
            temp = safeMul(_supply, baseN) / _reserveBalance;
            return safeSub(temp, _supply);
        }

        uint8 precision = calculateBestPrecision(baseN, _reserveBalance, _reserveRatio, 100);
        uint256 resN = power(baseN, _reserveBalance, _reserveRatio, 100, precision);
        temp = safeMul(_supply, resN) >> precision;
        return safeSub(temp, _supply);
     }

    /**
        @dev given a token supply, reserve, CRR and a sell amount (in the main token), calculates the return for a given change (in the reserve token)

        Formula:
        Return = _reserveBalance * (1 - (1 - _sellAmount / _supply) ^ (1 / (_reserveRatio / 100)))

        @param _supply             token total supply
        @param _reserveBalance     total reserve
        @param _reserveRatio       constant reserve ratio, 1-100
        @param _sellAmount         sell amount, in the token itself

        @return sale return amount
    */
    function calculateSaleReturn(uint256 _supply, uint256 _reserveBalance, uint8 _reserveRatio, uint256 _sellAmount) public constant returns (uint256) {
        // validate input
        require(_supply != 0 && _reserveBalance != 0 && _reserveRatio > 0 && _reserveRatio <= 100 && _sellAmount <= _supply);

        // special case for 0 sell amount
        if (_sellAmount == 0)
            return 0;

        uint256 baseD = safeSub(_supply, _sellAmount);
        uint256 temp1;
        uint256 temp2;

        // special case if the CRR = 100
        if (_reserveRatio == 100) {
            temp1 = safeMul(_reserveBalance, _supply);
            temp2 = safeMul(_reserveBalance, baseD);
            return safeSub(temp1, temp2) / _supply;
        }

        // special case for selling the entire supply
        if (_sellAmount == _supply)
            return _reserveBalance;

        uint8 precision = calculateBestPrecision(_supply, baseD, 100, _reserveRatio);
        uint256 resN = power(_supply, baseD, 100, _reserveRatio, precision);
        temp1 = safeMul(_reserveBalance, resN);
        temp2 = safeMul(_reserveBalance, uint256(1) << precision);
        return safeSub(temp1, temp2) / resN;
    }

    /**
        calculateBestPrecision
        Predicts the highest precision which can be used in order to compute "base^exp" without exceeding 256 bits in any of the intermediate computations.
        Instead of calculating "base ^ exp", we calculate "e ^ (ln(base) * exp)".
        The value of ln(base) is represented with an integer slightly smaller than ln(base) * 2 ^ precision.
        The larger the precision is, the more accurately this value represents the real value.
        However, function fixedExpUnsafe(x), which calculates e ^ x, is limited to a maximum value of x.
        The limit depends on the precision (e.g, for precision = 32, the maximum value of x is MAX_FIXED_EXP_32).
        Hence before calling the 'power' function, we need to estimate an upper-bound for ln(base) * exponent.
        Of course, we should later assert that the value passed to fixedExpUnsafe is not larger than MAX_FIXED_EXP(precision).
        Due to this assertion (made in function fixedExp), functions calculateBestPrecision and fixedExp are tightly coupled.
        Note that the outcome of this function only affects the accuracy of the computation of "base ^ exp".
        Therefore, there is no need to assert that no intermediate result exceeds 256 bits (nor in this function, neither in any of the functions down the calling tree).
    */
    function calculateBestPrecision(uint256 _baseN, uint256 _baseD, uint256 _expN, uint256 _expD) constant returns (uint8) {
        uint8 precision;
        uint256 maxExp = MAX_FIXED_EXP_32;
        uint256 maxVal = _expN * lnUpperBound(_baseN,_baseD);
        for (precision = 32; precision < 64; precision += 2) {
            if (maxExp < (maxVal << precision) / _expD)
                break;
            maxExp = (maxExp * 0xeb5ec5975959c565) >> (64-2);
        }
        if (precision == 32)
            return 32;
        return precision-2;
    }

    /**
        @dev calculates (_baseN / _baseD) ^ (_expN / _expD)
        Returns result upshifted by precision

        This method is overflow-safe
    */
    function power(uint256 _baseN, uint256 _baseD, uint32 _expN, uint32 _expD, uint8 _precision) constant returns (uint256 resN) {
        uint256 logbase = ln(_baseN, _baseD, _precision);
        // Not using safeDiv here, since safeDiv protects against
        // precision loss. It's unavoidable, however
        // Both `ln` and `fixedExp` are overflow-safe.
        resN = fixedExp(safeMul(logbase, _expN) / _expD, _precision);
        return resN;
    }

    /**
        input range:
            - numerator: [1, uint256_max >> precision]
            - denominator: [1, uint256_max >> precision]
        output range:
            [0, 0x9b43d4f8d6]

        This method asserts outside of bounds

    */
    function ln(uint256 _numerator, uint256 _denominator, uint8 _precision) public constant returns (uint256) {
        // denominator > numerator: less than one yields negative values. Unsupported
        assert(_denominator <= _numerator);

        // log(1) is the lowest we can go
        assert(_denominator != 0 && _numerator != 0);

        // Upper bits are scaled off by precision
        uint256 MAX_VAL = uint256(1) << (256 - _precision);
        assert(_numerator < MAX_VAL);
        assert(_denominator < MAX_VAL);

        return fixedLoge( (_numerator << _precision) / _denominator, _precision);
    }

    /**
        lnUpperBound
        Takes a rational number (baseN / baseD) as input.
        Returns an estimated upper-bound integer of the natural logarithm of the input.
        We can generally use floorLog2, although there is possibly a tighter bound.
        We cannot use floorLog2 when the input is smaller than 8.
        Complexity is O(log(input bit - length)).
    */
    function lnUpperBound(uint256 _baseN, uint256 _baseD) constant returns (uint8) {
        assert(_baseN > _baseD);

        uint256 scaledBaseN = _baseN * 100000;
        if (scaledBaseN <= _baseD *  271828) // _baseN / _baseD < e^1 (floorLog2 will return 0 if _baseN / _baseD < 2)
            return 1;
        if (scaledBaseN <= _baseD *  738905) // _baseN / _baseD < e^2 (floorLog2 will return 1 if _baseN / _baseD < 4)
            return 2;
        if (scaledBaseN <= _baseD * 2008553) // _baseN / _baseD < e^3 (floorLog2 will return 2 if _baseN / _baseD < 8)
            return 3;

        return ((floorLog2((baseN-1)/baseD)+1)*0xb17217f7d1cf78+(1<<56)-1)>>56; // ceiling(ceiling(log2(base))*logE(2)))
    }

    /**
        input range:
            [0x100000000, uint256_max]
        output range:
            [0, 0x9b43d4f8d6]

        This method asserts outside of bounds

    */
    function fixedLoge(uint256 _x, uint8 _precision) constant returns (uint256 logE) {
        /*
        Since `fixedLog2_min` output range is max `0xdfffffffff`
        (40 bits, or 5 bytes), we can use a very large approximation
        for `ln(2)`. This one is used since it's the max accuracy
        of Python `ln(2)`

        0xb17217f7d1cf78 = ln(2) * (1 << 56)

        */
        //Cannot represent negative numbers (below 1)
        assert(_x >= uint256(1) << _precision);

        uint256 log2 = fixedLog2(_x, _precision);
        logE = (log2 * 0xb17217f7d1cf78) >> 56;
    }

    /**
        Returns log2(x >> 32) << 32 [1]
        So x is assumed to be already upshifted 32 bits, and
        the result is also upshifted 32 bits.

        [1] The function returns a number which is lower than the
        actual value

        input-range :
            [0x100000000, uint256_max]
        output-range:
            [0,0xdfffffffff]

        This method asserts outside of bounds

    */
    function fixedLog2(uint256 _x, uint8 _precision) constant returns (uint256) {
        uint256 fixedOne = uint256(1) << _precision;
        uint256 fixedTwo = uint256(2) << _precision;

        // Numbers below 1 are negative.
        assert( _x >= fixedOne);

        uint256 hi = 0;
        while (_x >= fixedTwo) {
            _x >>= 1;
            hi += fixedOne;
        }

        for (uint8 i = 0; i < _precision; ++i) {
            _x = (_x * _x) / fixedOne;
            if (_x >= fixedTwo) {
                _x >>= 1;
                hi += uint256(1) << (_precision - 1 - i);
            }
        }

        return hi;
    }

    /**
        floorLog2
        Takes a natural number (n) as input.
        Returns the largest integer smaller than or equal to the binary logarithm of the input.
        Complexity is O(log(input bit - length)).
    */
    function floorLog2(uint256 _n) constant returns (uint8) {
        uint8 t = 0;
        for (int k = 7; k >= 0; k--) {
            if (_n >= (uint256(1) << (1 << k))) {
                uint8 s = 1 << k;
                _n >>= s;
                t |= s;
            }
        }

        return t;
    }

    /**
        fixedExp is a 'protected' version of `fixedExpUnsafe`, which asserts instead of overflows.
        The maximum value which can be passed to fixedExpUnsafe depends on the precision used.
        The following array maps each precision between 0 and 63 to the maximum value permitted:
        maxExpArray = {
            0xc1               ,0x17a              ,0x2e5              ,0x5ab              ,
            0xb1b              ,0x15bf             ,0x2a0c             ,0x50a2             ,
            0x9aa2             ,0x1288c            ,0x238b2            ,0x4429a            ,
            0x82b78            ,0xfaadc            ,0x1e0bb8           ,0x399e96           ,
            0x6e7f88           ,0xd3e7a3           ,0x1965fea          ,0x30b5057          ,
            0x5d681f3          ,0xb320d03          ,0x15784a40         ,0x292c5bdd         ,
            0x4ef57b9b         ,0x976bd995         ,0x122624e32        ,0x22ce03cd5        ,
            0x42beef808        ,0x7ffffffff        ,0xf577eded5        ,0x1d6bd8b2eb       ,
            0x386bfdba29       ,0x6c3390ecc8       ,0xcf8014760f       ,0x18ded91f0e7      ,
            0x2fb1d8fe082      ,0x5b771955b36      ,0xaf67a93bb50      ,0x15060c256cb2     ,
            0x285145f31ae5     ,0x4d5156639708     ,0x944620b0e70e     ,0x11c592761c666    ,
            0x2214d10d014ea    ,0x415bc6d6fb7dd    ,0x7d56e76777fc5    ,0xf05dc6b27edad    ,
            0x1ccf4b44bb4820   ,0x373fc456c53bb7   ,0x69f3d1c921891c   ,0xcb2ff529eb71e4   ,
            0x185a82b87b72e95  ,0x2eb40f9f620fda6  ,0x5990681d961a1ea  ,0xabc25204e02828d  ,
            0x14962dee9dc97640 ,0x277abdcdab07d5a7 ,0x4bb5ecca963d54ab ,0x9131271922eaa606 ,
            0x116701e6ab0cd188d,0x215f77c045fbe8856,0x3ffffffffffffffff,0x7abbf6f6abb9d087f,
        };
        Since we cannot use an array of constants, we need to approximate the maximum value dynamically.
        For a precision of 32, the maximum value permitted is MAX_FIXED_EXP_32.
        For each additional precision unit, the maximum value permitted increases by approximately 1.9.
        So in order to calculate it, we need to multiply MAX_FIXED_EXP_32 by 1.9 for every additional precision unit.
        And in order to optimize for speed, we multiply MAX_FIXED_EXP_32 by 1.9^2 for every 2 additional precision units.
        Hence the general function for mapping a given precision to the maximum value permitted is:
        - precision = [32, 34, 36, ..., 62]
        - MaxFixedExp(precision) = MAX_FIXED_EXP_32 * 3.61 ^ (precision / 2 - 16)
        Since we cannot use non-integers, we do MAX_FIXED_EXP_32 * 361 ^ (precision / 2 - 16) / 100 ^ (precision / 2 - 16).
        But there is a better approximation, because this "1.9" factor in fact extends beyond a single decimal digit.
        So instead, we use 0xeb5ec5975959c565 / 0x4000000000000000, which yields maximum values quite close to real ones:
        maxExpArray = {
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            -------------------,-------------------,-------------------,-------------------,
            0x386bfdba29       ,-------------------,0xcf8014760e       ,-------------------,
            0x2fb1d8fe07b      ,-------------------,0xaf67a93bb37      ,-------------------,
            0x285145f31a8f     ,-------------------,0x944620b0e5ee     ,-------------------,
            0x2214d10d0112e    ,-------------------,0x7d56e7677738e    ,-------------------,
            0x1ccf4b44bb20d0   ,-------------------,0x69f3d1c9210d27   ,-------------------,
            0x185a82b87b5b294  ,-------------------,0x5990681d95d4371  ,-------------------,
            0x14962dee9dbd672b ,-------------------,0x4bb5ecca961fb9bf ,-------------------,
            0x116701e6ab0967080,-------------------,0x3fffffffffffe6652,-------------------,
        };
    */
    function fixedExp(uint256 _x, uint8 _precision) constant returns (uint256) {
        uint256 maxExp = MAX_FIXED_EXP_32;
        for (uint8 p = 32; p < _precision; p += 2)
            maxExp = (maxExp * 0xeb5ec5975959c565) >> (64-2);

        assert(_x <= maxExp);
        return fixedExpUnsafe(_x, _precision);
    }

    /**
        fixedExp
        Calculates e ^ x according to maclauren summation:

        e^x = 1 + x + x ^ 2 / 2!...+ x ^ n / n!

        and returns e ^ (x >> 32) << 32, that is, upshifted for accuracy

        Input range:
            - Function ok at    <= 242329958953
            - Function fails at >= 242329958954

        This method is is visible for testcases, but not meant for direct use.

        The values in this method been generated via the following python snippet:

        def calculateFactorials():
            """Method to print out the factorials for fixedExp"""

            ni = []
            ni.append(295232799039604140847618609643520000000) # 34!
            ITERATIONS = 34
            for n in range(1, ITERATIONS, 1) :
                ni.append(math.floor(ni[n - 1] / n))
            print( "\n        ".join(["xi = (xi * _x) >> _precision;\n        res += xi * %s;" % hex(int(x)) for x in ni]))

    */
    function fixedExpUnsafe(uint256 _x, uint8 _precision) constant returns (uint256) {
        uint256 xi = _x;
        uint256 res = uint256(0xde1bc4d19efcac82445da75b00000000) << _precision;

        res += xi * 0xde1bc4d19efcac82445da75b00000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x6f0de268cf7e5641222ed3ad80000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x2504a0cd9a7f7215b60f9be480000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x9412833669fdc856d83e6f920000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x1d9d4d714865f4de2b3fafea0000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x4ef8ce836bba8cfb1dff2a70000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0xb481d807d1aa66d04490610000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x16903b00fa354cda08920c2000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x281cdaac677b334ab9e732000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x402e2aad725eb8778fd85000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x5d5a6c9f31fe2396a2af000000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x7c7890d442a82f73839400000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x9931ed54034526b58e400000;
        xi = (xi * _x) >> _precision;
        res += xi * 0xaf147cf24ce150cf7e00000;
        xi = (xi * _x) >> _precision;
        res += xi * 0xbac08546b867cdaa200000;
        xi = (xi * _x) >> _precision;
        res += xi * 0xbac08546b867cdaa20000;
        xi = (xi * _x) >> _precision;
        res += xi * 0xafc441338061b2820000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x9c3cabbc0056d790000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x839168328705c30000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x694120286c049c000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x50319e98b3d2c000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x3a52a1e36b82000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x289286e0fce000;
        xi = (xi * _x) >> _precision;
        res += xi * 0x1b0c59eb53400;
        xi = (xi * _x) >> _precision;
        res += xi * 0x114f95b55400;
        xi = (xi * _x) >> _precision;
        res += xi * 0xaa7210d200;
        xi = (xi * _x) >> _precision;
        res += xi * 0x650139600;
        xi = (xi * _x) >> _precision;
        res += xi * 0x39b78e80;
        xi = (xi * _x) >> _precision;
        res += xi * 0x1fd8080;
        xi = (xi * _x) >> _precision;
        res += xi * 0x10fbc0;
        xi = (xi * _x) >> _precision;
        res += xi * 0x8c40;
        xi = (xi * _x) >> _precision;
        res += xi * 0x462;
        xi = (xi * _x) >> _precision;
        res += xi * 0x22;

        return res / 0xde1bc4d19efcac82445da75b00000000;
    }
}