// File: github/jackygu2006/ferc20_contracts/InscriptionFactory.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

import "./Inscription.sol";
import "./String.sol";
import "./TransferHelper.sol";
import "@openzeppelin/contracts/utils/Counters.sol";
import "@openzeppelin/contracts/access/Ownable.sol";

contract InscriptionFactory is Ownable{
    using Counters for Counters.Counter;
    Counters.Counter private _inscriptionNumbers;

    uint8 public maxTickSize = 4;                   // tick(symbol) length is 4.
    uint256 public baseFee = 250000000000000;       // Will charge 0.00025 ETH as extra min tip from the second time of mint in the frozen period. And this tip will be double for each mint.
    uint256 public fundingCommission = 100;       // commission rate of fund raising, 100 means 1%

    mapping(uint256 => Token) private inscriptions; // key is inscription id, value is token data
    mapping(string => uint256) private ticks;       // Key is tick, value is inscription id

    event DeployInscription(
        uint256 indexed id, 
        string tick, 
        string name, 
        uint256 cap, 
        uint256 limitPerMint, 
        address inscriptionAddress, 
        uint256 timestamp
    );

    struct Token {
        string tick;            // same as symbol in ERC20
        string name;            // full name of token
        uint256 cap;            // Hard cap of token
        uint256 limitPerMint;   // Limitation per mint
        uint256 maxMintSize;    // // max mint size, that means the max mint quantity is: maxMintSize * limitPerMint
        uint256 inscriptionId;  // Inscription id
        uint256 freezeTime;
        address onlyContractAddress;
        uint256 onlyMinQuantity;
        uint256 crowdFundingRate;
        address crowdfundingAddress;
        address addr;           // Contract address of inscribed token 
        uint256 timestamp;      // Inscribe timestamp
    }

    constructor() {
        // The inscription id will be from 1, not zero.
        _inscriptionNumbers.increment();
    }

    // Let this contract accept ETH as tip
    receive() external payable {}
    
    function deploy(
        string memory _name,
        string memory _tick,
        uint256 _cap,
        uint256 _limitPerMint,
        uint256 _maxMintSize, // The max lots of each mint
        uint256 _freezeTime, // Freeze seconds between two mint, during this freezing period, the mint fee will be increased 
        address _onlyContractAddress, // Only the holder of this asset can mint, optional
        uint256 _onlyMinQuantity, // The min quantity of asset for mint, optional
        uint256 _crowdFundingRate,
        address _crowdFundingAddress
    ) external returns (address _inscriptionAddress) {
        require(String.strlen(_tick) == maxTickSize, "Tick lenght should be 4");
        require(_cap >= _limitPerMint, "Limit per mint exceed cap");

        _tick = String.toLower(_tick);
        require(this.getIncriptionIdByTick(_tick) == 0, "tick is existed");

        // Create inscription contract
        bytes memory bytecode = type(Inscription).creationCode;
        uint256 _id = _inscriptionNumbers.current();
		bytecode = abi.encodePacked(bytecode, abi.encode(
            _name, 
            _tick, 
            _cap, 
            _limitPerMint, 
            _id, 
            _maxMintSize,
            _freezeTime,
            _onlyContractAddress,
            _onlyMinQuantity,
            baseFee,
            fundingCommission,
            _crowdFundingRate,
            _crowdFundingAddress,
            address(this)
        ));
		bytes32 salt = keccak256(abi.encodePacked(_id));
		assembly ("memory-safe") {
			_inscriptionAddress := create2(0, add(bytecode, 32), mload(bytecode), salt)
			if iszero(extcodesize(_inscriptionAddress)) {
				revert(0, 0)
			}
		}
        inscriptions[_id] = Token(
            _tick, 
            _name, 
            _cap, 
            _limitPerMint, 
            _maxMintSize,
            _id,
            _freezeTime,
            _onlyContractAddress,
            _onlyMinQuantity,
            _crowdFundingRate,
            _crowdFundingAddress,
            _inscriptionAddress, 
            block.timestamp
        );
        ticks[_tick] = _id;

        _inscriptionNumbers.increment();
        emit DeployInscription(_id, _tick, _name, _cap, _limitPerMint, _inscriptionAddress, block.timestamp);
    }

    function getInscriptionAmount() external view returns(uint256) {
        return _inscriptionNumbers.current() - 1;
    }

    function getIncriptionIdByTick(string memory _tick) external view returns(uint256) {
        return ticks[String.toLower(_tick)];
    }

    function getIncriptionById(uint256 _id) external view returns(Token memory, uint256) {
        Token memory token = inscriptions[_id];
        return (inscriptions[_id], Inscription(token.addr).totalSupply());
    }

    function getIncriptionByTick(string memory _tick) external view returns(Token memory tokens, uint256 totalSupplies) {
        Token memory token = inscriptions[this.getIncriptionIdByTick(_tick)];
        uint256 id = this.getIncriptionIdByTick(String.toLower(_tick));
        if(id > 0) {
            tokens = inscriptions[id];
            totalSupplies = Inscription(token.addr).totalSupply();
        }
    }

    function getInscriptionAmountByType(uint256 _type) external view returns(uint256) {
        require(_type < 3, "type is 0-2");
        uint256 totalInscription = this.getInscriptionAmount();
        uint256 count = 0;
        for(uint256 i = 1; i <= totalInscription; i++) {
            (Token memory _token, uint256 _totalSupply) = this.getIncriptionById(i);
            if(_type == 1 && _totalSupply == _token.cap) continue;
            else if(_type == 2 && _totalSupply < _token.cap) continue;
            else count++;
        }
        return count;
    }
    
    // Fetch inscription data by page no, page size, type and search keyword
    function getIncriptions(
        uint256 _pageNo, 
        uint256 _pageSize, 
        uint256 _type // 0- all, 1- in-process, 2- ended
    ) external view returns(
        Token[] memory, 
        uint256[] memory
    ) {
        // if _searchBy is not empty, the _pageNo and _pageSize should be set to 1
        require(_type < 3, "type is 0-2");
        uint256 totalInscription = this.getInscriptionAmount();
        uint256 pages = (totalInscription - 1) / _pageSize + 1;
        require(_pageNo > 0 && _pageSize > 0 && pages > 0 && _pageNo <= pages, "Params wrong");

        Token[] memory inscriptions_ = new Token[](_pageSize);
        uint256[] memory totalSupplies_ = new uint256[](_pageSize);

        Token[] memory _inscriptions = new Token[](totalInscription);
        uint256[] memory _totalSupplies = new uint256[](totalInscription);

        uint256 index = 0;
        for(uint256 i = 1; i <= totalInscription; i++) {
            (Token memory _token, uint256 _totalSupply) = this.getIncriptionById(i);
            if((_type == 1 && _totalSupply == _token.cap) || (_type == 2 && _totalSupply < _token.cap)) continue; 
            else {
                _inscriptions[index] = _token;
                _totalSupplies[index] = _totalSupply;
                index++;
            }
        }

        for(uint256 i = 0; i < _pageSize; i++) {
            uint256 id = (_pageNo - 1) * _pageSize + i;
            if(id < index) {
                inscriptions_[i] = _inscriptions[id];
                totalSupplies_[i] = _totalSupplies[id];
            } else break;
        }

        return (inscriptions_, totalSupplies_);
    }

    // Withdraw the ETH tip from the contract
    function withdraw(address payable _to, uint256 _amount) external onlyOwner {
        require(_amount <= payable(address(this)).balance);
        TransferHelper.safeTransferETH(_to, _amount);
    }

    // Update base fee
    function updateBaseFee(uint256 _fee) external onlyOwner {
        baseFee = _fee;
    }

    // Update funding commission
    function updateFundingCommission(uint256 _rate) external onlyOwner {
        fundingCommission = _rate;
    }

    // Update character's length of tick
    function updateTickSize(uint8 _size) external onlyOwner {
        maxTickSize = _size;
    }
}
// File: @openzeppelin/contracts/access/Ownable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../utils/Context.sol";

/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract Ownable is Context {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor() {
        _transferOwnership(_msgSender());
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _transferOwnership(newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}

// File: @openzeppelin/contracts/utils/Counters.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Counters.sol)

pragma solidity ^0.8.0;

/**
 * @title Counters
 * @author Matt Condon (@shrugs)
 * @dev Provides counters that can only be incremented, decremented or reset. This can be used e.g. to track the number
 * of elements in a mapping, issuing ERC721 ids, or counting request ids.
 *
 * Include with `using Counters for Counters.Counter;`
 */
library Counters {
    struct Counter {
        // This variable should never be directly accessed by users of the library: interactions must be restricted to
        // the library's function. As of Solidity v0.5.2, this cannot be enforced, though there is a proposal to add
        // this feature: see https://github.com/ethereum/solidity/issues/4637
        uint256 _value; // default: 0
    }

    function current(Counter storage counter) internal view returns (uint256) {
        return counter._value;
    }

    function increment(Counter storage counter) internal {
        unchecked {
            counter._value += 1;
        }
    }

    function decrement(Counter storage counter) internal {
        uint256 value = counter._value;
        require(value > 0, "Counter: decrement overflow");
        unchecked {
            counter._value = value - 1;
        }
    }

    function reset(Counter storage counter) internal {
        counter._value = 0;
    }
}

// File: github/jackygu2006/ferc20_contracts/TransferHelper.sol



// SPDX-License-Identifier: GPL-3.0-or-later

pragma solidity >=0.6.0;

// helper methods for interacting with ERC20 tokens and sending ETH that do not consistently return true/false
library TransferHelper {
    function safeApprove(
        address token,
        address to,
        uint256 value
    ) internal {
        // bytes4(keccak256(bytes('approve(address,uint256)')));
        (bool success, bytes memory data) = token.call(abi.encodeWithSelector(0x095ea7b3, to, value));
        require(
            success && (data.length == 0 || abi.decode(data, (bool))),
            'TransferHelper::safeApprove: approve failed'
        );
    }

    function safeTransfer(
        address token,
        address to,
        uint256 value
    ) internal {
        // bytes4(keccak256(bytes('transfer(address,uint256)')));
        (bool success, bytes memory data) = token.call(abi.encodeWithSelector(0xa9059cbb, to, value));
        require(
            success && (data.length == 0 || abi.decode(data, (bool))),
            'TransferHelper::safeTransfer: transfer failed'
        );
    }

    function safeTransferFrom(
        address token,
        address from,
        address to,
        uint256 value
    ) internal {
        // bytes4(keccak256(bytes('transferFrom(address,address,uint256)')));
        (bool success, bytes memory data) = token.call(abi.encodeWithSelector(0x23b872dd, from, to, value));
        require(
            success && (data.length == 0 || abi.decode(data, (bool))),
            'TransferHelper::transferFrom: transferFrom failed'
        );
    }

    function safeTransferETH(address to, uint256 value) internal {
        (bool success, ) = to.call{value: value}(new bytes(0));
        require(success, 'TransferHelper::safeTransferETH: ETH transfer failed');
    }
}
// File: github/jackygu2006/ferc20_contracts/String.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

library String {
    function strlen(string memory s) internal pure returns (uint256) {
        uint256 len;
        uint256 i = 0;
        uint256 bytelength = bytes(s).length;

        for (len = 0; i < bytelength; len++) {
            bytes1 b = bytes(s)[i];
            if (b < 0x80) {
                i += 1;
            } else if (b < 0xE0) {
                i += 2;
            } else if (b < 0xF0) {
                i += 3;
            } else if (b < 0xF8) {
                i += 4;
            } else if (b < 0xFC) {
                i += 5;
            } else {
                i += 6;
            }
        }
        return len;
    }

    function toLower(string memory str) internal pure returns (string memory) {
		bytes memory bStr = bytes(str);
		bytes memory bLower = new bytes(bStr.length);
		for (uint i = 0; i < bStr.length; i++) {
			if (uint8(bStr[i]) >= 65 && uint8(bStr[i]) <= 90) {
				bLower[i] = bytes1(uint8(bStr[i]) + 32);
			} else {
				bLower[i] = bStr[i];
			}
		}
		return string(bLower);
	}

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        // Inspired by OraclizeAPI's implementation - MIT licence
        // https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol

        if (value == 0) {
            return "0";
        }
        uint256 temp = value;
        uint256 digits;
        while (temp != 0) {
            digits++;
            temp /= 10;
        }
        bytes memory buffer = new bytes(digits);
        while (value != 0) {
            digits -= 1;
            buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
            value /= 10;
        }
        return string(buffer);
    }

    function compareStrings(string memory a, string memory b) public pure returns (bool) {
        return keccak256(abi.encodePacked(a)) == keccak256(abi.encodePacked(b));
    }
}
// File: github/jackygu2006/ferc20_contracts/Inscription.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

import "@openzeppelin/contracts/token/ERC20/ERC20.sol";
import "./Logarithm.sol";
import "./TransferHelper.sol";

// This is common token interface, get balance of owner's token by ERC20/ERC721/ERC1155.
interface ICommonToken {
    function balanceOf(address owner) external returns(uint256);
}

// This contract is extended from ERC20
contract Inscription is ERC20 {
    using Logarithm for int256;
    uint256 public cap;                 // Max amount
    uint256 public limitPerMint;        // Limitaion of each mint
    uint256 public inscriptionId;       // Inscription Id
    uint256 public maxMintSize;         // max mint size, that means the max mint quantity is: maxMintSize * limitPerMint
    uint256 public freezeTime;          // The frozen time (interval) between two mints is a fixed number of seconds. You can mint, but you will need to pay an additional mint fee, and this fee will be double for each mint.
    address public onlyContractAddress; // Only addresses that hold these assets can mint
    uint256 public onlyMinQuantity;     // Only addresses that the quantity of assets hold more than this amount can mint
    uint256 public baseFee;             // base fee of the second mint after frozen interval. The first mint after frozen time is free.
    uint256 public fundingCommission;   // commission rate of fund raising, 100 means 1%
    uint256 public crowdFundingRate;    // rate of crowdfunding
    address payable public crowdfundingAddress; // receiving fee of crowdfunding
    address payable public inscriptionFactory;

    mapping(address => uint256) public lastMintTimestamp;   // record the last mint timestamp of account
    mapping(address => uint256) public lastMintFee;           // record the last mint fee

    constructor(
        string memory _name,            // token name
        string memory _tick,            // token tick, same as symbol. must be 4 characters.
        uint256 _cap,                   // Max amount
        uint256 _limitPerMint,          // Limitaion of each mint
        uint256 _inscriptionId,         // Inscription Id
        uint256 _maxMintSize,           // max mint size, that means the max mint quantity is: maxMintSize * limitPerMint. This is only availabe for non-frozen time token.
        uint256 _freezeTime,            // The frozen time (interval) between two mints is a fixed number of seconds. You can mint, but you will need to pay an additional mint fee, and this fee will be double for each mint.
        address _onlyContractAddress,   // Only addresses that hold these assets can mint
        uint256 _onlyMinQuantity,       // Only addresses that the quantity of assets hold more than this amount can mint
        uint256 _baseFee,               // base fee of the second mint after frozen interval. The first mint after frozen time is free.
        uint256 _fundingCommission,     // commission rate of fund raising, 100 means 1%
        uint256 _crowdFundingRate,      // rate of crowdfunding
        address payable _crowdFundingAddress,   // receiving fee of crowdfunding
        address payable _inscriptionFactory
    ) ERC20(_name, _tick) {
        require(_cap >= _limitPerMint, "Limit per mint exceed cap");
        cap = _cap;
        limitPerMint = _limitPerMint;
        inscriptionId = _inscriptionId;
        maxMintSize = _maxMintSize;
        freezeTime = _freezeTime;
        onlyContractAddress = _onlyContractAddress;
        onlyMinQuantity = _onlyMinQuantity;
        baseFee = _baseFee;
        fundingCommission = _fundingCommission;
        crowdFundingRate = _crowdFundingRate;
        crowdfundingAddress = _crowdFundingAddress;
        inscriptionFactory = _inscriptionFactory;
    }

    function mint(address _to) payable public {
        // Check if the quantity after mint will exceed the cap
        require(totalSupply() + limitPerMint <= cap, "Touched cap");
        // Check if the assets in the msg.sender is satisfied
        require(onlyContractAddress == address(0x0) || ICommonToken(onlyContractAddress).balanceOf(msg.sender) >= onlyMinQuantity, "You don't have required assets");
        
        if(lastMintTimestamp[msg.sender] + freezeTime > block.timestamp) {
            // The min extra tip is double of last mint fee
            lastMintFee[msg.sender] = lastMintFee[msg.sender] == 0 ? baseFee : lastMintFee[msg.sender] * 2;
            // Transfer the fee to the crowdfunding address
            if(crowdFundingRate > 0) {
                // Check if the tip is high than the min extra fee
                require(msg.value >= crowdFundingRate + lastMintFee[msg.sender], "Send some ETH as fee and crowdfunding");
                _dispatchFunding(crowdFundingRate);
            }
            // Transfer the tip to InscriptionFactory smart contract
            if(msg.value - crowdFundingRate > 0) TransferHelper.safeTransferETH(inscriptionFactory, msg.value - crowdFundingRate);
        } else {
            // Transfer the fee to the crowdfunding address
            if(crowdFundingRate > 0) {
                require(msg.value >= crowdFundingRate, "Send some ETH as crowdfunding");
                _dispatchFunding(msg.value);
            }
            // Out of frozen time, free mint. Reset the timestamp and mint times.
            lastMintFee[msg.sender] = 0;
            lastMintTimestamp[msg.sender] = block.timestamp;
        }
        // Do mint
        _mint(_to, limitPerMint);
    }

    // batch mint is only available for non-frozen-time tokens
    function batchMint(address _to, uint256 _num) payable public {
        require(_num <= maxMintSize, "exceed max mint size");
        require(totalSupply() + _num * limitPerMint <= cap, "Touch cap");
        require(freezeTime == 0, "Batch mint only for non-frozen token");
        require(onlyContractAddress == address(0x0) || ICommonToken(onlyContractAddress).balanceOf(msg.sender) >= onlyMinQuantity, "You don't have required assets");
        if(crowdFundingRate > 0) {
            require(msg.value >= crowdFundingRate * _num, "Crowdfunding ETH not enough");
            _dispatchFunding(msg.value);
        }
        for(uint256 i = 0; i < _num; i++) _mint(_to, limitPerMint);
    }

    function getMintFee(address _addr) public view returns(uint256 mintedTimes, uint256 nextMintFee) {
        if(lastMintTimestamp[_addr] + freezeTime > block.timestamp) {
            int256 scale = 1e18;
            int256 halfScale = 5e17;
            // times = log_2(lastMintFee / baseFee) + 1 (if lastMintFee > 0)
            nextMintFee = lastMintFee[_addr] == 0 ? baseFee : lastMintFee[_addr] * 2;
            mintedTimes = uint256((Logarithm.log2(int256(nextMintFee / baseFee) * scale, scale, halfScale) + 1) / scale) + 1;
        }
    }

    function _dispatchFunding(uint256 _amount) private {
        uint256 commission = _amount * fundingCommission / 10000;
        TransferHelper.safeTransferETH(crowdfundingAddress, _amount - commission);
        if(commission > 0) TransferHelper.safeTransferETH(inscriptionFactory, commission);
    }
}

// File: github/jackygu2006/ferc20_contracts/Logarithm.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

library Logarithm {
    /// @notice Finds the zero-based index of the first one in the binary representation of x.
    /// @dev See the note on msb in the "Find First Set" Wikipedia article https://en.wikipedia.org/wiki/Find_first_set
    /// @param x The uint256 number for which to find the index of the most significant bit.
    /// @return msb The index of the most significant bit as an uint256.
    function mostSignificantBit(uint256 x) internal pure returns (uint256 msb) {
        if (x >= 2**128) {
            x >>= 128;
            msb += 128;
        }
        if (x >= 2**64) {
            x >>= 64;
            msb += 64;
        }
        if (x >= 2**32) {
            x >>= 32;
            msb += 32;
        }
        if (x >= 2**16) {
            x >>= 16;
            msb += 16;
        }
        if (x >= 2**8) {
            x >>= 8;
            msb += 8;
        }
        if (x >= 2**4) {
            x >>= 4;
            msb += 4;
        }
        if (x >= 2**2) {
            x >>= 2;
            msb += 2;
        }
        if (x >= 2**1) {
            // No need to shift x any more.
            msb += 1;
        }
    }
    /// @notice Calculates the binary logarithm of x.
    ///
    /// @dev Based on the iterative approximation algorithm.
    /// https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
    ///
    /// Requirements:
    /// - x must be greater than zero.
    ///
    /// Caveats:
    /// - The results are nor perfectly accurate to the last digit, due to the lossy precision of the iterative approximation.
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the binary logarithm.
    /// @return result The binary logarithm as a signed 59.18-decimal fixed-point number.
    function log2(int256 x, int256 scale, int256 halfScale) internal pure returns (int256 result) {
        require(x > 0);
        unchecked {
            // This works because log2(x) = -log2(1/x).
            int256 sign;
            if (x >= scale) {
                sign = 1;
            } else {
                sign = -1;
                // Do the fixed-point inversion inline to save gas. The numerator is SCALE * SCALE.
                assembly {
                    x := div(1000000000000000000000000000000000000, x)
                }
            }

            // Calculate the integer part of the logarithm and add it to the result and finally calculate y = x * 2^(-n).
            uint256 n = mostSignificantBit(uint256(x / scale));

            // The integer part of the logarithm as a signed 59.18-decimal fixed-point number. The operation can't overflow
            // because n is maximum 255, SCALE is 1e18 and sign is either 1 or -1.
            result = int256(n) * scale;

            // This is y = x * 2^(-n).
            int256 y = x >> n;

            // If y = 1, the fractional part is zero.
            if (y == scale) {
                return result * sign;
            }

            // Calculate the fractional part via the iterative approximation.
            // The "delta >>= 1" part is equivalent to "delta /= 2", but shifting bits is faster.
            for (int256 delta = int256(halfScale); delta > 0; delta >>= 1) {
                y = (y * y) / scale;

                // Is y^2 > 2 and so in the range [2,4)?
                if (y >= 2 * scale) {
                    // Add the 2^(-m) factor to the logarithm.
                    result += delta;

                    // Corresponds to z/2 on Wikipedia.
                    y >>= 1;
                }
            }
            result *= sign;
        }
    }
}
// File: @openzeppelin/contracts/token/ERC20/ERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.0;

import "./IERC20.sol";
import "./extensions/IERC20Metadata.sol";
import "../../utils/Context.sol";

/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 * For a generic mechanism see {ERC20PresetMinterPauser}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.openzeppelin.com/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * The default value of {decimals} is 18. To change this, you should override
 * this function so it returns a different value.
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead returning `false` on failure. This behavior is nonetheless
 * conventional and does not conflict with the expectations of ERC20
 * applications.
 *
 * Additionally, an {Approval} event is emitted on calls to {transferFrom}.
 * This allows applications to reconstruct the allowance for all accounts just
 * by listening to said events. Other implementations of the EIP may not emit
 * these events, as it isn't required by the specification.
 *
 * Finally, the non-standard {decreaseAllowance} and {increaseAllowance}
 * functions have been added to mitigate the well-known issues around setting
 * allowances. See {IERC20-approve}.
 */
contract ERC20 is Context, IERC20, IERC20Metadata {
    mapping(address => uint256) private _balances;

    mapping(address => mapping(address => uint256)) private _allowances;

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * All two of these values are immutable: they can only be set once during
     * construction.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev Returns the name of the token.
     */
    function name() public view virtual override returns (string memory) {
        return _name;
    }

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the default value returned by this function, unless
     * it's overridden.
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual override returns (uint8) {
        return 18;
    }

    /**
     * @dev See {IERC20-totalSupply}.
     */
    function totalSupply() public view virtual override returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev See {IERC20-balanceOf}.
     */
    function balanceOf(address account) public view virtual override returns (uint256) {
        return _balances[account];
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - the caller must have a balance of at least `amount`.
     */
    function transfer(address to, uint256 amount) public virtual override returns (bool) {
        address owner = _msgSender();
        _transfer(owner, to, amount);
        return true;
    }

    /**
     * @dev See {IERC20-allowance}.
     */
    function allowance(address owner, address spender) public view virtual override returns (uint256) {
        return _allowances[owner][spender];
    }

    /**
     * @dev See {IERC20-approve}.
     *
     * NOTE: If `amount` is the maximum `uint256`, the allowance is not updated on
     * `transferFrom`. This is semantically equivalent to an infinite approval.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 amount) public virtual override returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, amount);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Emits an {Approval} event indicating the updated allowance. This is not
     * required by the EIP. See the note at the beginning of {ERC20}.
     *
     * NOTE: Does not update the allowance if the current allowance
     * is the maximum `uint256`.
     *
     * Requirements:
     *
     * - `from` and `to` cannot be the zero address.
     * - `from` must have a balance of at least `amount`.
     * - the caller must have allowance for ``from``'s tokens of at least
     * `amount`.
     */
    function transferFrom(address from, address to, uint256 amount) public virtual override returns (bool) {
        address spender = _msgSender();
        _spendAllowance(from, spender, amount);
        _transfer(from, to, amount);
        return true;
    }

    /**
     * @dev Atomically increases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function increaseAllowance(address spender, uint256 addedValue) public virtual returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, allowance(owner, spender) + addedValue);
        return true;
    }

    /**
     * @dev Atomically decreases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `spender` must have allowance for the caller of at least
     * `subtractedValue`.
     */
    function decreaseAllowance(address spender, uint256 subtractedValue) public virtual returns (bool) {
        address owner = _msgSender();
        uint256 currentAllowance = allowance(owner, spender);
        require(currentAllowance >= subtractedValue, "ERC20: decreased allowance below zero");
        unchecked {
            _approve(owner, spender, currentAllowance - subtractedValue);
        }

        return true;
    }

    /**
     * @dev Moves `amount` of tokens from `from` to `to`.
     *
     * This internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `from` must have a balance of at least `amount`.
     */
    function _transfer(address from, address to, uint256 amount) internal virtual {
        require(from != address(0), "ERC20: transfer from the zero address");
        require(to != address(0), "ERC20: transfer to the zero address");

        _beforeTokenTransfer(from, to, amount);

        uint256 fromBalance = _balances[from];
        require(fromBalance >= amount, "ERC20: transfer amount exceeds balance");
        unchecked {
            _balances[from] = fromBalance - amount;
            // Overflow not possible: the sum of all balances is capped by totalSupply, and the sum is preserved by
            // decrementing then incrementing.
            _balances[to] += amount;
        }

        emit Transfer(from, to, amount);

        _afterTokenTransfer(from, to, amount);
    }

    /** @dev Creates `amount` tokens and assigns them to `account`, increasing
     * the total supply.
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     */
    function _mint(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: mint to the zero address");

        _beforeTokenTransfer(address(0), account, amount);

        _totalSupply += amount;
        unchecked {
            // Overflow not possible: balance + amount is at most totalSupply + amount, which is checked above.
            _balances[account] += amount;
        }
        emit Transfer(address(0), account, amount);

        _afterTokenTransfer(address(0), account, amount);
    }

    /**
     * @dev Destroys `amount` tokens from `account`, reducing the
     * total supply.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - `account` must have at least `amount` tokens.
     */
    function _burn(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: burn from the zero address");

        _beforeTokenTransfer(account, address(0), amount);

        uint256 accountBalance = _balances[account];
        require(accountBalance >= amount, "ERC20: burn amount exceeds balance");
        unchecked {
            _balances[account] = accountBalance - amount;
            // Overflow not possible: amount <= accountBalance <= totalSupply.
            _totalSupply -= amount;
        }

        emit Transfer(account, address(0), amount);

        _afterTokenTransfer(account, address(0), amount);
    }

    /**
     * @dev Sets `amount` as the allowance of `spender` over the `owner` s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     */
    function _approve(address owner, address spender, uint256 amount) internal virtual {
        require(owner != address(0), "ERC20: approve from the zero address");
        require(spender != address(0), "ERC20: approve to the zero address");

        _allowances[owner][spender] = amount;
        emit Approval(owner, spender, amount);
    }

    /**
     * @dev Updates `owner` s allowance for `spender` based on spent `amount`.
     *
     * Does not update the allowance amount in case of infinite allowance.
     * Revert if not enough allowance is available.
     *
     * Might emit an {Approval} event.
     */
    function _spendAllowance(address owner, address spender, uint256 amount) internal virtual {
        uint256 currentAllowance = allowance(owner, spender);
        if (currentAllowance != type(uint256).max) {
            require(currentAllowance >= amount, "ERC20: insufficient allowance");
            unchecked {
                _approve(owner, spender, currentAllowance - amount);
            }
        }
    }

    /**
     * @dev Hook that is called before any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * will be transferred to `to`.
     * - when `from` is zero, `amount` tokens will be minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens will be burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(address from, address to, uint256 amount) internal virtual {}

    /**
     * @dev Hook that is called after any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * has been transferred to `to`.
     * - when `from` is zero, `amount` tokens have been minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens have been burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _afterTokenTransfer(address from, address to, uint256 amount) internal virtual {}
}

// File: @openzeppelin/contracts/utils/Context.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
}

// File: @openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Metadata.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";

/**
 * @dev Interface for the optional metadata functions from the ERC20 standard.
 *
 * _Available since v4.1._
 */
interface IERC20Metadata is IERC20 {
    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

    /**
     * @dev Returns the symbol of the token.
     */
    function symbol() external view returns (string memory);

    /**
     * @dev Returns the decimals places of the token.
     */
    function decimals() external view returns (uint8);
}

// File: @openzeppelin/contracts/token/ERC20/IERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);

    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the amount of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves `amount` tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 amount) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `from` to `to` using the
     * allowance mechanism. `amount` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(address from, address to, uint256 amount) external returns (bool);
}