Contract Source Code (Solidity Multiple files format)

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// SPDX-License-Identifier: MIT

pragma solidity >=0.8.4;

import "./DNTfixedPointMath.sol";


// Interface for IERC20.
interface IERC20 {

    function totalSupply() external view returns (uint256);
    function balanceOf(address account) external view returns (uint256);
    function transfer(address recipient, uint256 amount) external returns (bool);
    function allowance(address owner, address spender) external view returns (uint256);
    function approve(address spender, uint256 amount) external returns (bool);
    function transferFrom(address sender, address recipient, uint256 amount) external returns (bool);
    event Transfer(address indexed from, address indexed to, uint256 value);
    event Approval(address indexed owner, address indexed spender, uint256 value);
}

// Interface for IERC20Metadata.
interface IERC20Metadata is IERC20 {

    function name() external view returns (string memory);

    function symbol() external view returns (string memory);

    function decimals() external view returns (uint8);
}

// Interface for IAccessControl.
interface IAccessControl {

    event RoleAdminChanged(bytes32 indexed role, bytes32 indexed previousAdminRole, bytes32 indexed newAdminRole);

    event RoleGranted(bytes32 indexed role, address indexed account, address indexed sender);

    event RoleRevoked(bytes32 indexed role, address indexed account, address indexed sender);

    function hasRole(bytes32 role, address account) external view returns (bool);

    function getRoleAdmin(bytes32 role) external view returns (bytes32);

    function grantRole(bytes32 role, address account) external;

    function revokeRole(bytes32 role, address account) external;

    function renounceRole(bytes32 role, address account) external;
}


// Interface for IERC165
interface IERC165 {

    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

// Contract for Context.
abstract contract Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

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

// Contract for ERC165
abstract contract ERC165 is IERC165 {

    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// Contract for ERC20.
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;

    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    function name() public view virtual override returns (string memory) {
        return _name;
    }

    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    function decimals() public view virtual override returns (uint8) {
        return 18;
    }

    function totalSupply() public view virtual override returns (uint256) {
        return _totalSupply;
    }

    function balanceOf(address account) public view virtual override returns (uint256) {
        return _balances[account];
    }

    function transfer(address recipient, uint256 amount) public virtual override returns (bool) {
        _transfer(_msgSender(), recipient, amount);
        return true;
    }

    function allowance(address owner, address spender) public view virtual override returns (uint256) {
        return _allowances[owner][spender];
    }

    function approve(address spender, uint256 amount) public virtual override returns (bool) {
        _approve(_msgSender(), spender, amount);
        return true;
    }

    function transferFrom(
        address sender,
        address recipient,
        uint256 amount
    ) public virtual override returns (bool) {
        _transfer(sender, recipient, amount);

        uint256 currentAllowance = _allowances[sender][_msgSender()];
        require(currentAllowance >= amount, "ERC20: transfer amount exceeds allowance");
        unchecked {
    _approve(sender, _msgSender(), currentAllowance - amount);
    }

        return true;
    }

    function increaseAllowance(address spender, uint256 addedValue) public virtual returns (bool) {
        _approve(_msgSender(), spender, _allowances[_msgSender()][spender] + addedValue);
        return true;
    }

    function decreaseAllowance(address spender, uint256 subtractedValue) public virtual returns (bool) {
        uint256 currentAllowance = _allowances[_msgSender()][spender];
        require(currentAllowance >= subtractedValue, "ERC20: decreased allowance below zero");
        unchecked {
    _approve(_msgSender(), spender, currentAllowance - subtractedValue);
    }

        return true;
    }

    function _transfer(
        address sender,
        address recipient,
        uint256 amount
    ) internal virtual {
        require(sender != address(0), "ERC20: transfer from the zero address");
        require(recipient != address(0), "ERC20: transfer to the zero address");

        _beforeTokenTransfer(sender, recipient, amount);

        uint256 senderBalance = _balances[sender];
        require(senderBalance >= amount, "ERC20: transfer amount exceeds balance");
        unchecked {
    _balances[sender] = senderBalance - amount;
    }
        _balances[recipient] += amount;

        emit Transfer(sender, recipient, amount);

        _afterTokenTransfer(sender, recipient, amount);
    }

    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;
        _balances[account] += amount;
        emit Transfer(address(0), account, amount);

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

    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;
    }
        _totalSupply -= amount;

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

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

    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);
    }

    function _beforeTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual {}

    function _afterTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual {}
}

// Contract for AccessControl.
abstract contract AccessControl is Context, IAccessControl, ERC165 {
    struct RoleData {
        mapping(address => bool) members;
        bytes32 adminRole;
    }

    mapping(bytes32 => RoleData) private _roles;

    bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;

    modifier onlyRole(bytes32 role) {
        _checkRole(role, _msgSender());
        _;
    }

    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IAccessControl).interfaceId || super.supportsInterface(interfaceId);
    }

    function hasRole(bytes32 role, address account) public view override returns (bool) {
        return _roles[role].members[account];
    }

    function _checkRole(bytes32 role, address account) internal view {
        if (!hasRole(role, account)) {
            revert(
                string(
                    abi.encodePacked(
                        "AccessControl: account ",
                        Strings.toHexString(uint160(account), 20),
                        " is missing role ",
                        Strings.toHexString(uint256(role), 32)
                    )
                )
            );
        }
    }

    function getRoleAdmin(bytes32 role) public view override returns (bytes32) {
        return _roles[role].adminRole;
    }

    function grantRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _grantRole(role, account);
    }

    function revokeRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _revokeRole(role, account);
    }

    function renounceRole(bytes32 role, address account) public virtual override {
        require(account == _msgSender(), "AccessControl: can only renounce roles for self");

        _revokeRole(role, account);
    }

    function _setupRole(bytes32 role, address account) internal virtual {
        _grantRole(role, account);
    }

    function _setRoleAdmin(bytes32 role, bytes32 adminRole) internal virtual {
        bytes32 previousAdminRole = getRoleAdmin(role);
        _roles[role].adminRole = adminRole;
        emit RoleAdminChanged(role, previousAdminRole, adminRole);
    }

    function _grantRole(bytes32 role, address account) private {
        if (!hasRole(role, account)) {
            _roles[role].members[account] = true;
            emit RoleGranted(role, account, _msgSender());
        }
    }

    function _revokeRole(bytes32 role, address account) private {
        if (hasRole(role, account)) {
            _roles[role].members[account] = false;
            emit RoleRevoked(role, account, _msgSender());
        }
    }
}


// Library for SafeCast.
library SafeCast {

    function toUint224(uint256 value) internal pure returns (uint224) {
        require(value <= type(uint224).max, "SafeCast: value doesn't fit in 224 bits");
        return uint224(value);
    }

    function toUint128(uint256 value) internal pure returns (uint128) {
        require(value <= type(uint128).max, "SafeCast: value doesn't fit in 128 bits");
        return uint128(value);
    }

    function toUint96(uint256 value) internal pure returns (uint96) {
        require(value <= type(uint96).max, "SafeCast: value doesn't fit in 96 bits");
        return uint96(value);
    }

    function toUint64(uint256 value) internal pure returns (uint64) {
        require(value <= type(uint64).max, "SafeCast: value doesn't fit in 64 bits");
        return uint64(value);
    }

    function toUint32(uint256 value) internal pure returns (uint32) {
        require(value <= type(uint32).max, "SafeCast: value doesn't fit in 32 bits");
        return uint32(value);
    }

    function toUint16(uint256 value) internal pure returns (uint16) {
        require(value <= type(uint16).max, "SafeCast: value doesn't fit in 16 bits");
        return uint16(value);
    }

    function toUint8(uint256 value) internal pure returns (uint8) {
        require(value <= type(uint8).max, "SafeCast: value doesn't fit in 8 bits");
        return uint8(value);
    }

    function toUint256(int256 value) internal pure returns (uint256) {
        require(value >= 0, "SafeCast: value must be positive");
        return uint256(value);
    }

    function toInt128(int256 value) internal pure returns (int128) {
        require(value >= type(int128).min && value <= type(int128).max, "SafeCast: value doesn't fit in 128 bits");
        return int128(value);
    }

    function toInt64(int256 value) internal pure returns (int64) {
        require(value >= type(int64).min && value <= type(int64).max, "SafeCast: value doesn't fit in 64 bits");
        return int64(value);
    }

    function toInt32(int256 value) internal pure returns (int32) {
        require(value >= type(int32).min && value <= type(int32).max, "SafeCast: value doesn't fit in 32 bits");
        return int32(value);
    }

    function toInt16(int256 value) internal pure returns (int16) {
        require(value >= type(int16).min && value <= type(int16).max, "SafeCast: value doesn't fit in 16 bits");
        return int16(value);
    }

    function toInt8(int256 value) internal pure returns (int8) {
        require(value >= type(int8).min && value <= type(int8).max, "SafeCast: value doesn't fit in 8 bits");
        return int8(value);
    }

    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        require(value <= uint256(type(int256).max), "SafeCast: value doesn't fit in an int256");
        return int256(value);
    }
}


// Library for SafeMath
library SafeMath {
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");

        return c;
    }
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        return sub(a, b, "SafeMath: subtraction overflow");
    }
    function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        uint256 c = a - b;

        return c;
    }
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");

        return c;
    }
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        return div(a, b, "SafeMath: division by zero");
    }
    function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        uint256 c = a / b;
        return c;
    }
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        return mod(a, b, "SafeMath: modulo by zero");
    }
    function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b != 0, errorMessage);
        return a % b;
    }
}

// Library for Strings.
library Strings {

    bytes16 private constant _HEX_SYMBOLS = "0123456789abcdef";

    function toString(uint256 value) internal pure returns (string memory) {

        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 toHexString(uint256 value) internal pure returns (string memory) {
        if (value == 0) {
            return "0x00";
        }
        uint256 temp = value;
        uint256 length = 0;
        while (temp != 0) {
            length++;
            temp >>= 8;
        }
        return toHexString(value, length);
    }

    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _HEX_SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }
}

// Smart contract for the Dynamic Network Token.
contract DynamicNetworkToken is ERC20, AccessControl
{
    // Declaration of roles in the network.
    bytes32 public constant ADMIN = keccak256("ADMIN");
    bytes32 public constant LIQ_PROVIDER = keccak256("LIQ_PROVIDER");

    // Govern the amount of tokens with a min and a max.
    uint256 private minimumSupply = 21000000 ether;
    uint256 private maximumSupply = 52500000 ether;

    // Keep track of total amount of burned and minted tokens.
    uint256 private totalBurned = 0;
    uint256 private totalMinted = 0;

    // Keep track of previous burn and mint transaction.
    uint256 private prevAmountMint = 0;
    uint256 private prevAmountBurn = 0;

    // Keep track of wallets in the network with balance > 0.
    uint256 private  totalWallets = 0;

    // Network Based Burn.
    uint256 private networkBasedBurn = 1000000 ether;
    uint256 private nextBurn = 100;

    // The reserve address.
    address private reserveAddress;

    // The minimum balance for the reserveAddress.
    uint256 private minimumReserve = 4200000 ether;

    // The initial supply of the token.
    uint256 private _initialSupply  = 42000000 ether;

    // The current supply of the token.
    uint256 private currentSupply  = _initialSupply;

    // Number of decimals for DNT.
    uint256 private _decimals = 18;

    // Booleans for exp burning and minting.
    bool private isExpBurn = false;
    bool private isExpMint = false;

    using SafeMath for uint256;

    constructor() ERC20("Dynamic Network Token", "DNT"){
        _setupRole(DEFAULT_ADMIN_ROLE, _msgSender());
        _setupRole(LIQ_PROVIDER, _msgSender());
        _setupRole(ADMIN, _msgSender());
        _mint(_msgSender(),  _initialSupply);
        reserveAddress = _msgSender();
    }

    // Getter for nextBurn.
    function getNextBurn() public view returns(uint256){
        return(nextBurn);
    }

    // Getter for networkBasedBurn.
    function getNetworkBasedBurn() public view returns(uint256){
        return(networkBasedBurn/(10**18));
    }

    // Getter for currentSupply. Returns currentSupply with two decimals.
    function getCurrentSupply() public view returns(uint256){
        return(currentSupply/(10**16));
    }

    // Getter for totalBurned.
    function getTotalBurned() public view returns(uint256){
        return(totalBurned/(10**18));
    }

    // Getter for totalMinted.
    function getTotalMinted() public view returns(uint256){
        return(totalMinted/(10**18));
    }

    // Getter for totalWallets.
    function getTotalWallets() public view returns(uint256){
        return(totalWallets);
    }

    // Function for calculating mint.
    function calculateMint(uint256 amount) public returns(uint256){
        uint256 toBeMinted = SafeMath.add(prevAmountMint,amount);
        prevAmountMint = amount;
        uint256 uLog = DNTfixedPointMath.ln(toBeMinted);

        // Check if log < 1, if so calculate exp for minting.
        if(uLog<1)
        {
            isExpMint = true;
            int256 iExp = DNTfixedPointMath.exp(SafeCast.toInt256(toBeMinted));
            iExp = iExp * 8;
            iExp =  DNTfixedPointMath.div(SafeCast.toInt256(toBeMinted),iExp);
            uint256 uExp = SafeCast.toUint256(iExp);
            uExp = uExp * 10**4;
            return  uExp;
        }
        uint256 log = SafeMath.mul(uLog,8);
        uint256 logMint = SafeMath.div(toBeMinted,log);
        logMint = logMint * 10 ** _decimals;
        return logMint;
    }

    // Function for calculating burn.
    function calculateBurn(uint256 amount) public returns(uint256){
        uint256 toBeBurned = SafeMath.add(prevAmountBurn,amount);
        prevAmountBurn = amount;
        uint256 uLog = DNTfixedPointMath.ln(toBeBurned);

        // Check if log < 1, if so calculate exp for burning.
        if(uLog<1)
        {
            isExpBurn = true;
            int256 iExp = DNTfixedPointMath.exp(SafeCast.toInt256(toBeBurned));
            iExp = iExp * 4;
            iExp =  DNTfixedPointMath.div(SafeCast.toInt256(toBeBurned),iExp);
            uint256 uExp = SafeCast.toUint256(iExp);
            uExp = uExp * 10**4;
            return  uExp;
        }
        uint256 log = SafeMath.mul(uLog,4);
        uint256 logBurn = SafeMath.div(toBeBurned,log);
        logBurn = logBurn * 10 ** _decimals;
        return logBurn;
    }

    function transfer(address recipient, uint256 amount) public virtual override returns (bool) {
        // Calculate burn and mint.
        uint256 toBeBurned = calculateBurn(amount);
        uint256 toBeMinted = calculateMint(amount);
        uint256 currentSupplyAfterBurn = SafeMath.sub(currentSupply,toBeBurned);
        uint256 currentSupplyAfterMint = SafeMath.add(currentSupply,toBeMinted);
        // Add to totalWalelts if balance is 0.
        if(balanceOf(recipient)==0)
        {
            totalWallets += 1;
        }
        // Check if Network Based Burn.
        if(totalWallets>=nextBurn && SafeMath.sub(currentSupply,amount)>=minimumSupply && SafeMath.sub(balanceOf(reserveAddress),networkBasedBurn)>=minimumReserve)
        {
            _burn(reserveAddress,networkBasedBurn);
            currentSupply = SafeMath.sub(currentSupply,networkBasedBurn);
            totalBurned = SafeMath.add(totalBurned,networkBasedBurn);
            nextBurn = nextBurn*2;
            networkBasedBurn = networkBasedBurn/2;
        }
        if(hasRole(LIQ_PROVIDER, _msgSender()))
        {
            if(currentSupplyAfterMint<=maximumSupply && isExpMint)
            {
                _mint(reserveAddress,SafeMath.div(toBeMinted,10**4));
                isExpMint = false;
                currentSupply = SafeMath.add(currentSupply,SafeMath.div(toBeMinted,10**4));
                totalMinted = SafeMath.add(totalMinted,SafeMath.div(toBeMinted,10**4));
            }
            else if(currentSupplyAfterMint<=maximumSupply && toBeMinted > 0)
            {
                _mint(reserveAddress,toBeMinted);
                currentSupply = SafeMath.add(currentSupply,toBeMinted);
                totalMinted = SafeMath.add(totalMinted,toBeMinted);
            }
        }
        if(hasRole(LIQ_PROVIDER, recipient))
        {
            if(isExpBurn && currentSupplyAfterBurn>=minimumSupply)
            {
                if(SafeMath.sub(balanceOf(reserveAddress),SafeMath.div(toBeBurned,10**4))>= minimumReserve)
                {
                    _burn(reserveAddress,SafeMath.div(toBeBurned,10**4));
                    isExpBurn= false;
                    currentSupply = SafeMath.sub(currentSupply,SafeMath.div(toBeBurned,10**4));
                    totalBurned = SafeMath.add(totalBurned,SafeMath.div(toBeBurned,10**4));
                }
            }
            else if(currentSupplyAfterBurn>=minimumSupply && toBeBurned > 0)
            {
                if(SafeMath.sub(balanceOf(reserveAddress),toBeBurned)>= minimumReserve)
                {
                    _burn(reserveAddress,toBeBurned);
                    currentSupply = SafeMath.sub(currentSupply,toBeBurned);
                    totalBurned = SafeMath.add(totalBurned,toBeBurned);
                }
            }
        }
        _transfer(_msgSender(), recipient, amount);
        return true;
    }

    function transferFrom(address sender,address recipient, uint256 amount) public virtual override returns (bool) {
        uint256 toBeBurned = calculateBurn(amount);
        uint256 currentSupplyAfterBurn = SafeMath.sub(currentSupply,toBeBurned);
        if(hasRole(LIQ_PROVIDER, recipient))
        {
            if(isExpBurn && currentSupplyAfterBurn>=minimumSupply)
            {
                if(SafeMath.sub(balanceOf(reserveAddress),SafeMath.div(toBeBurned,10**4))>= minimumReserve)
                {
                    _burn(reserveAddress,SafeMath.div(toBeBurned,10**4));
                    isExpBurn= false;
                    currentSupply = SafeMath.sub(currentSupply,SafeMath.div(toBeBurned,10**4));
                    totalBurned = SafeMath.add(totalBurned,SafeMath.div(toBeBurned,10**4));
                }
            }
            else if(currentSupplyAfterBurn>=minimumSupply && toBeBurned > 0)
            {
                if(SafeMath.sub(balanceOf(reserveAddress), amount) >= minimumReserve)
                {
                    _burn(reserveAddress,toBeBurned);
                    currentSupply = SafeMath.sub(currentSupply,toBeBurned);
                    totalBurned = SafeMath.add(totalBurned,toBeBurned);
                }
            }
        }
        _transfer(sender, recipient, amount);
        uint256 currentAllowance = allowance(sender,_msgSender());
        require(currentAllowance >= amount, "ERC20: transfer amount exceeds allowance");
        unchecked {
    _approve(sender, _msgSender(), currentAllowance - amount);
    }
        return true;
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.4;

/// @notice Emitted when the input is greater than 133.084258667509499441.
error _ExpInputTooBig(int256 x);

/// @notice Emitted when the input is greater than 192.
error _Exp2InputTooBig(int256 x);

/// @notice Emitted when one of the inputs is MIN_SD59x18.
error _DivInputTooSmall();

/// @notice Emitted when one of the intermediary unsigned results overflows SD59x18.
error _DivOverflow(uint256 rAbs);

/// @notice Emitted when the result overflows uint256.
error _MulDivOverflow(uint256 prod1, uint256 denominator);

/// @notice Emitted when the input is less than or equal to zero.
error _LogInputTooSmall(uint256 x);

// Lib for fixed-point math in the Dynamic Network Token.
// Thanks to PRBMath.

library DNTfixedPointMath{

// int256s for fixed-point math.

int256 internal constant MAX_SD59x18 = 57896044618658097711785492504343953926634992332820282019728792003956564819967;
int256 internal constant MIN_SD59x18 = - 57896044618658097711785492504343953926634992332820282019728792003956564819968;
int256 internal constant LOG2_E = 1442695040888963407;
int256 internal constant SCALE = 1e18;
int256 internal constant HALF_SCALE = 5e17;

// uint256s for fixed-point math.

uint256 internal constant uSCALE = 1e18;
uint256 internal constant uLOG2_E = 1442695040888963407;
uint256 internal constant uHALF_SCALE = 5e17;

function ln(uint256 x) internal pure returns (uint256 result) {

// Do the fixed-point multiplication inline to save gas. This is overflow-safe because the maximum value that log2(x)
// can return is 195205294292027477728.
    unchecked {
        result = (log2(x) * uSCALE) / uLOG2_E;
    }
}

function log2(uint256 x) internal pure returns (uint256 result) {

    if (x <= 0) {
        revert _LogInputTooSmall(x);
    }
        unchecked {
        // This works because log2(x) = -log2(1/x).
        uint256 sign;
        if (x >= uSCALE) {
            sign = 1;
        }
        else {

            // 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 / uSCALE));

    // 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 = uint256(n) * uSCALE;

    // This is y = x * 2^(-n).
    uint256 y = x >> n;

    // If y = 1, the fractional part is zero.
    if (y == uSCALE) {
        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 (uint256 delta = uint256(HALF_SCALE); delta > 0; delta >>= 1) {
        y = (y * y) / uSCALE;

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

    // Corresponds to z/2 on Wikipedia.
            y >>= 1;
        }
    }
        result *= sign;
    }
}


/// @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;
    }
}

/// @param x The exponent as a signed 59.18-decimal fixed-point number.
/// @return result The result as a signed 59.18-decimal fixed-point number.

function exp(int256 x) internal pure returns (int256 result) {

    // Without this check, the value passed to "exp2" would be less than -59.794705707972522261.
    if (x < - 41446531673892822322) {
         return 0;
    }

    // Without this check, the value passed to "exp2" would be greater than 192.
    if (x >= 133084258667509499441) {
        revert _ExpInputTooBig(x);
    }

    // Do the fixed-point multiplication inline to save gas.
    unchecked {
        int256 doubleScaleProduct = x * LOG2_E;
        result = exp2((doubleScaleProduct + HALF_SCALE) / SCALE);
    }
}

/// @param x The exponent as a signed 59.18-decimal fixed-point number.
/// @return result The result as a signed 59.18-decimal fixed-point number.

function exp2(int256 x) internal pure returns (int256 result) {
    // This works because 2^(-x) = 1/2^x.
    if (x < 0) {
    // 2^59.794705707972522262 is the maximum number whose inverse does not truncate down to zero.
        if (x < - 59794705707972522261) {
            return 0;
        }

    // Do the fixed-point inversion inline to save gas. The numerator is SCALE * SCALE.
        unchecked {
            result = 1e36 / exp2(- x);
        }
    }
    else {
    // 2^192 doesn't fit within the 192.64-bit format used internally in this function.
    if (x >= 192e18) {
        revert _Exp2InputTooBig(x);
    }

        unchecked {
            // Convert x to the 192.64-bit fixed-point format.
            uint256 x192x64 = (uint256(x) << 64) / uint256(SCALE);
            // Safe to convert the result to int256 directly because the maximum input allowed is 192.
            result = int256(uExp2(x192x64));
        }
    }
}


/// @notice Calculates the binary exponent of x using the binary fraction method.
/// @dev Has to use 192.64-bit fixed-point numbers.
/// See https://ethereum.stackexchange.com/a/96594/24693.
/// @param x The exponent as an unsigned 192.64-bit fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
function uExp2(uint256 x) internal pure returns (uint256 result) {

    unchecked {
        // Start from 0.5 in the 192.64-bit fixed-point format.
        result = 0x800000000000000000000000000000000000000000000000;

        // Multiply the result by root(2, 2^-i) when the bit at position i is 1. None of the intermediary results overflows
        // because the initial result is 2^191 and all magic factors are less than 2^65.
        if (x & 0x8000000000000000 > 0) {
            result = (result * 0x16A09E667F3BCC909) >> 64;
        }
        if (x & 0x4000000000000000 > 0) {
            result = (result * 0x1306FE0A31B7152DF) >> 64;
        }
        if (x & 0x2000000000000000 > 0) {
            result = (result * 0x1172B83C7D517ADCE) >> 64;
        }
        if (x & 0x1000000000000000 > 0) {
            result = (result * 0x10B5586CF9890F62A) >> 64;
        }
        if (x & 0x800000000000000 > 0) {
            result = (result * 0x1059B0D31585743AE) >> 64;
        }
        if (x & 0x400000000000000 > 0) {
            result = (result * 0x102C9A3E778060EE7) >> 64;
        }
        if (x & 0x200000000000000 > 0) {
            result = (result * 0x10163DA9FB33356D8) >> 64;
        }
        if (x & 0x100000000000000 > 0) {
            result = (result * 0x100B1AFA5ABCBED61) >> 64;
        }
        if (x & 0x80000000000000 > 0) {
            result = (result * 0x10058C86DA1C09EA2) >> 64;
        }
        if (x & 0x40000000000000 > 0) {
            result = (result * 0x1002C605E2E8CEC50) >> 64;
        }
        if (x & 0x20000000000000 > 0) {
            result = (result * 0x100162F3904051FA1) >> 64;
        }
        if (x & 0x10000000000000 > 0) {
            result = (result * 0x1000B175EFFDC76BA) >> 64;
        }
        if (x & 0x8000000000000 > 0) {
            result = (result * 0x100058BA01FB9F96D) >> 64;
        }
        if (x & 0x4000000000000 > 0) {
            result = (result * 0x10002C5CC37DA9492) >> 64;
        }
        if (x & 0x2000000000000 > 0) {
            result = (result * 0x1000162E525EE0547) >> 64;
        }
        if (x & 0x1000000000000 > 0) {
            result = (result * 0x10000B17255775C04) >> 64;
        }
        if (x & 0x800000000000 > 0) {
            result = (result * 0x1000058B91B5BC9AE) >> 64;
        }
        if (x & 0x400000000000 > 0) {
            result = (result * 0x100002C5C89D5EC6D) >> 64;
        }
        if (x & 0x200000000000 > 0) {
            result = (result * 0x10000162E43F4F831) >> 64;
        }
        if (x & 0x100000000000 > 0) {
            result = (result * 0x100000B1721BCFC9A) >> 64;
        }
        if (x & 0x80000000000 > 0) {
            result = (result * 0x10000058B90CF1E6E) >> 64;
        }
        if (x & 0x40000000000 > 0) {
            result = (result * 0x1000002C5C863B73F) >> 64;
        }
        if (x & 0x20000000000 > 0) {
            result = (result * 0x100000162E430E5A2) >> 64;
        }
        if (x & 0x10000000000 > 0) {
            result = (result * 0x1000000B172183551) >> 64;
        }
        if (x & 0x8000000000 > 0) {
            result = (result * 0x100000058B90C0B49) >> 64;
        }
        if (x & 0x4000000000 > 0) {
            result = (result * 0x10000002C5C8601CC) >> 64;
        }
        if (x & 0x2000000000 > 0) {
            result = (result * 0x1000000162E42FFF0) >> 64;
        }
        if (x & 0x1000000000 > 0) {
            result = (result * 0x10000000B17217FBB) >> 64;
        }
        if (x & 0x800000000 > 0) {
            result = (result * 0x1000000058B90BFCE) >> 64;
        }
        if (x & 0x400000000 > 0) {
            result = (result * 0x100000002C5C85FE3) >> 64;
        }
        if (x & 0x200000000 > 0) {
            result = (result * 0x10000000162E42FF1) >> 64;
        }
        if (x & 0x100000000 > 0) {
            result = (result * 0x100000000B17217F8) >> 64;
        }
        if (x & 0x80000000 > 0) {
            result = (result * 0x10000000058B90BFC) >> 64;
        }
        if (x & 0x40000000 > 0) {
            result = (result * 0x1000000002C5C85FE) >> 64;
        }
        if (x & 0x20000000 > 0) {
            result = (result * 0x100000000162E42FF) >> 64;
        }
        if (x & 0x10000000 > 0) {
            result = (result * 0x1000000000B17217F) >> 64;
        }
        if (x & 0x8000000 > 0) {
            result = (result * 0x100000000058B90C0) >> 64;
        }
        if (x & 0x4000000 > 0) {
            result = (result * 0x10000000002C5C860) >> 64;
        }
        if (x & 0x2000000 > 0) {
            result = (result * 0x1000000000162E430) >> 64;
        }
        if (x & 0x1000000 > 0) {
            result = (result * 0x10000000000B17218) >> 64;
        }
        if (x & 0x800000 > 0) {
            result = (result * 0x1000000000058B90C) >> 64;
        }
        if (x & 0x400000 > 0) {
            result = (result * 0x100000000002C5C86) >> 64;
        }
        if (x & 0x200000 > 0) {
            result = (result * 0x10000000000162E43) >> 64;
        }
        if (x & 0x100000 > 0) {
            result = (result * 0x100000000000B1721) >> 64;
        }
        if (x & 0x80000 > 0) {
            result = (result * 0x10000000000058B91) >> 64;
        }
        if (x & 0x40000 > 0) {
            result = (result * 0x1000000000002C5C8) >> 64;
        }
        if (x & 0x20000 > 0) {
            result = (result * 0x100000000000162E4) >> 64;
        }
        if (x & 0x10000 > 0) {
            result = (result * 0x1000000000000B172) >> 64;
        }
        if (x & 0x8000 > 0) {
            result = (result * 0x100000000000058B9) >> 64;
        }
        if (x & 0x4000 > 0) {
            result = (result * 0x10000000000002C5D) >> 64;
        }
        if (x & 0x2000 > 0) {
            result = (result * 0x1000000000000162E) >> 64;
        }
        if (x & 0x1000 > 0) {
            result = (result * 0x10000000000000B17) >> 64;
        }
        if (x & 0x800 > 0) {
            result = (result * 0x1000000000000058C) >> 64;
        }
        if (x & 0x400 > 0) {
            result = (result * 0x100000000000002C6) >> 64;
        }
        if (x & 0x200 > 0) {
            result = (result * 0x10000000000000163) >> 64;
        }
        if (x & 0x100 > 0) {
            result = (result * 0x100000000000000B1) >> 64;
        }
        if (x & 0x80 > 0) {
            result = (result * 0x10000000000000059) >> 64;
        }
        if (x & 0x40 > 0) {
            result = (result * 0x1000000000000002C) >> 64;
        }
        if (x & 0x20 > 0) {
            result = (result * 0x10000000000000016) >> 64;
        }
        if (x & 0x10 > 0) {
            result = (result * 0x1000000000000000B) >> 64;
        }
        if (x & 0x8 > 0) {
            result = (result * 0x10000000000000006) >> 64;
        }
        if (x & 0x4 > 0) {
            result = (result * 0x10000000000000003) >> 64;
        }
        if (x & 0x2 > 0) {
            result = (result * 0x10000000000000001) >> 64;
        }
        if (x & 0x1 > 0) {
            result = (result * 0x10000000000000001) >> 64;
        }

// We're doing two things at the same time:
//
//   1. Multiply the result by 2^n + 1, where "2^n" is the integer part and the one is added to account for
//      the fact that we initially set the result to 0.5. This is accomplished by subtracting from 191
//      rather than 192.
//   2. Convert the result to the unsigned 60.18-decimal fixed-point format.
//
// This works because 2^(191-ip) = 2^ip / 2^191, where "ip" is the integer part "2^n".
            result *= uSCALE;
            result >>= (191 - (x >> 64));
        }
    }


function div(int256 x, int256 y) internal pure returns (int256 result) {

    if (x == MIN_SD59x18 || y == MIN_SD59x18) {
        revert _DivInputTooSmall();
    }

    // Get hold of the absolute values of x and y.
    uint256 ax;
    uint256 ay;

    unchecked {
        ax = x < 0 ? uint256(- x) : uint256(x);
        ay = y < 0 ? uint256(- y) : uint256(y);
    }

    // Compute the absolute value of (x*SCALE)÷y. The result must fit within int256.
    uint256 rAbs = mulDiv(ax, uint256(SCALE), ay);
    if (rAbs > uint256(MAX_SD59x18)) {
        revert _DivOverflow(rAbs);
    }

    // Get the signs of x and y.
    uint256 sx;
    uint256 sy;

    assembly {
        sx := sgt(x, sub(0, 1))
        sy := sgt(y, sub(0, 1))
    }

        // XOR over sx and sy. This is basically checking whether the inputs have the same sign. If yes, the result
        // should be positive. Otherwise, it should be negative.
        result = sx ^ sy == 1 ? - int256(rAbs) : int256(rAbs);
    }


/// @param x The multiplicand as an uint256.
/// @param y The multiplier as an uint256.
/// @param denominator The divisor as an uint256.
/// @return result The result as an uint256.

function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {

    // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
    // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
    // variables such that product = prod1 * 2^256 + prod0.
    uint256 prod0; // Least significant 256 bits of the product
    uint256 prod1; // Most significant 256 bits of the product
    assembly {
        let mm := mulmod(x, y, not(0))
        prod0 := mul(x, y)
        prod1 := sub(sub(mm, prod0), lt(mm, prod0))
    }

    // Handle non-overflow cases, 256 by 256 division.
    if (prod1 == 0) {
        unchecked {
        result = prod0 / denominator;
    }
        return result;
    }

    // Make sure the result is less than 2^256. Also prevents denominator == 0.
    if (prod1 >= denominator) {
        revert _MulDivOverflow(prod1, denominator);
    }

    ///////////////////////////////////////////////
    // 512 by 256 division.
    ///////////////////////////////////////////////

    // Make division exact by subtracting the remainder from [prod1 prod0].
    uint256 remainder;

    assembly {
        // Compute remainder using mulmod.
        remainder := mulmod(x, y, denominator)

        // Subtract 256 bit number from 512 bit number.
        prod1 := sub(prod1, gt(remainder, prod0))
        prod0 := sub(prod0, remainder)
    }

    // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
    // See https://cs.stackexchange.com/q/138556/92363.
    unchecked {
        // Does not overflow because the denominator cannot be zero at this stage in the function.
        uint256 lpotdod = denominator & (~denominator + 1);

    assembly {
            // Divide denominator by lpotdod.
            denominator := div(denominator, lpotdod)

            // Divide [prod1 prod0] by lpotdod.
            prod0 := div(prod0, lpotdod)

            // Flip lpotdod such that it is 2^256 / lpotdod. If lpotdod is zero, then it becomes one.
            lpotdod := add(div(sub(0, lpotdod), lpotdod), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * lpotdod;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Now use Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

}

• No Contract Security Audit Submitted- Submit Audit Here

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