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Contract Name:
BurnMintTaxableERC20

Contract Source Code:

// SPDX-License-Identifier: MIT
pragma solidity 0.8.24;

import {Pausable} from "@chainlink/contracts/vendor/openzeppelin-solidity/v4.8.3/contracts/security/Pausable.sol";
import {BurnMintERC20} from "@chainlink/contracts/shared/token/ERC20/BurnMintERC20.sol";

/// @notice A basic ERC20 compatible token contract with burn, minting, and tax-on-transfer functionality.
contract BurnMintTaxableERC20 is BurnMintERC20, Pausable {
  struct SetTaxExemptArgs {
    address account;
    bool isTaxExempt;
  }

  event SetTaxBps(uint16 taxBps);
  event SetTreasury(address indexed treasury);
  event SetTaxExempt(address indexed account, bool isTaxExempt);

  error ZeroAddressNotAllowed();

  bytes32 public constant TAXMAN_ROLE = keccak256("TAXMAN_ROLE");
  bytes32 public constant PAUSE_ROLE = keccak256("PAUSE_ROLE");
  uint256 private constant BPS_DIVISION = 10_000;

  /// @dev The tax rate in basis points (1/100 of a percent)
  uint16 internal s_taxBps;

  /// @dev The treasury address to which tax is sent
  address internal s_treasury;

  /// @dev Mapping of accounts to their tax exempt status
  mapping(address account => bool isTaxExempt) internal s_taxExempt;

  /// @dev the underscores in parameter names are used to suppress compiler warnings about shadowing ERC20 functions
  constructor(
    string memory name,
    string memory symbol,
    uint8 decimals_,
    uint16 taxBps
  )
    BurnMintERC20(name, symbol, decimals_, 0, 0)
  {
    s_treasury = msg.sender;
    s_taxBps = taxBps;
  }

  /// @notice Returns the tax rate in basis points
  function getTaxBps() external view returns (uint256) {
    return s_taxBps;
  }

  /// @notice Sets the tax rate in basis points
  function setTaxBps(uint16 taxBps) external onlyRole(TAXMAN_ROLE) {
    s_taxBps = taxBps;

    emit SetTaxBps(taxBps);
  }

  /// @notice Returns the treasury address
  function getTreasury() external view returns (address) {
    return s_treasury;
  }

  /// @notice Sets the treasury address
  function setTreasury(address treasury) external onlyRole(TAXMAN_ROLE) {
    if (treasury == address(0)) {
      revert ZeroAddressNotAllowed();
    }

    s_treasury = treasury;

    emit SetTreasury(treasury);
  }

  /// @notice Set the tax exempt status for a list accounts
  function setTaxExempt(SetTaxExemptArgs[] calldata setTaxExemptArgs) external onlyRole(TAXMAN_ROLE) {
    for (uint256 i = 0; i < setTaxExemptArgs.length; i++) {
      SetTaxExemptArgs memory arg = setTaxExemptArgs[i];
      s_taxExempt[arg.account] = arg.isTaxExempt;

      emit SetTaxExempt(arg.account, arg.isTaxExempt);
    }
  }

  /// @dev Overrides the internal `_transfer` function to apply tax on transfers
  function _transfer(address from, address to, uint256 amount) internal override whenNotPaused {
    /// no tax if transfer is from or to a tax exempt account
    if (s_taxExempt[from] || s_taxExempt[to]) {
      super._transfer(from, to, amount);
      return;
    }

    // We cast the tax to uint256 to avoid overflows.
    // Since Solidity rounds down, the tax amount will also be rounded down. This means that sending an amount smaller
    // than (`BPS_DIVISION`/`s_taxBps`) will result in a tax of zero.
    uint256 taxAmount = amount * uint256(s_taxBps) / BPS_DIVISION;
    super._transfer(from, s_treasury, taxAmount); // collect tax to treasury
    super._transfer(from, to, amount - taxAmount); // transfer remaining amount
  }

  /// @dev Prevents transfers, burns and mints while paused.
  function _beforeTokenTransfer(address, /*from*/ address, /*to*/ uint256 /*amount*/ ) internal view override {
    _requireNotPaused();
  }

  /// @notice Pauses the contract
  function pause() external onlyRole(PAUSE_ROLE) {
    _pause();
  }

  /// @notice Unpauses the contract
  function unpause() external onlyRole(PAUSE_ROLE) {
    _unpause();
  }
}

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

pragma solidity ^0.8.0;

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

/**
 * @dev Contract module which allows children to implement an emergency stop
 * mechanism that can be triggered by an authorized account.
 *
 * This module is used through inheritance. It will make available the
 * modifiers `whenNotPaused` and `whenPaused`, which can be applied to
 * the functions of your contract. Note that they will not be pausable by
 * simply including this module, only once the modifiers are put in place.
 */
abstract contract Pausable is Context {
  /**
   * @dev Emitted when the pause is triggered by `account`.
   */
  event Paused(address account);

  /**
   * @dev Emitted when the pause is lifted by `account`.
   */
  event Unpaused(address account);

  bool private _paused;

  /**
   * @dev Initializes the contract in unpaused state.
   */
  constructor() {
    _paused = false;
  }

  /**
   * @dev Modifier to make a function callable only when the contract is not paused.
   *
   * Requirements:
   *
   * - The contract must not be paused.
   */
  modifier whenNotPaused() {
    _requireNotPaused();
    _;
  }

  /**
   * @dev Modifier to make a function callable only when the contract is paused.
   *
   * Requirements:
   *
   * - The contract must be paused.
   */
  modifier whenPaused() {
    _requirePaused();
    _;
  }

  /**
   * @dev Returns true if the contract is paused, and false otherwise.
   */
  function paused() public view virtual returns (bool) {
    return _paused;
  }

  /**
   * @dev Throws if the contract is paused.
   */
  function _requireNotPaused() internal view virtual {
    require(!paused(), "Pausable: paused");
  }

  /**
   * @dev Throws if the contract is not paused.
   */
  function _requirePaused() internal view virtual {
    require(paused(), "Pausable: not paused");
  }

  /**
   * @dev Triggers stopped state.
   *
   * Requirements:
   *
   * - The contract must not be paused.
   */
  function _pause() internal virtual whenNotPaused {
    _paused = true;
    emit Paused(_msgSender());
  }

  /**
   * @dev Returns to normal state.
   *
   * Requirements:
   *
   * - The contract must be paused.
   */
  function _unpause() internal virtual whenPaused {
    _paused = false;
    emit Unpaused(_msgSender());
  }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

import {IGetCCIPAdmin} from "../../../ccip/interfaces/IGetCCIPAdmin.sol";
import {IBurnMintERC20} from "../../../shared/token/ERC20/IBurnMintERC20.sol";

import {AccessControl} from "../../../vendor/openzeppelin-solidity/v4.8.3/contracts/access/AccessControl.sol";
import {IAccessControl} from "../../../vendor/openzeppelin-solidity/v4.8.3/contracts/access/IAccessControl.sol";
import {ERC20} from "../../../vendor/openzeppelin-solidity/v4.8.3/contracts/token/ERC20/ERC20.sol";
import {IERC20} from "../../../vendor/openzeppelin-solidity/v4.8.3/contracts/token/ERC20/IERC20.sol";
import {ERC20Burnable} from "../../../vendor/openzeppelin-solidity/v4.8.3/contracts/token/ERC20/extensions/ERC20Burnable.sol";
import {IERC165} from "../../../vendor/openzeppelin-solidity/v4.8.3/contracts/utils/introspection/IERC165.sol";

/// @notice A basic ERC20 compatible token contract with burn and minting roles.
/// @dev The total supply can be limited during deployment.
/// @dev This contract has not been audited and is not yet approved for production use.
contract BurnMintERC20 is IBurnMintERC20, IGetCCIPAdmin, IERC165, ERC20Burnable, AccessControl {
  error MaxSupplyExceeded(uint256 supplyAfterMint);
  error InvalidRecipient(address recipient);

  event CCIPAdminTransferred(address indexed previousAdmin, address indexed newAdmin);

  /// @dev The number of decimals for the token
  uint8 internal immutable i_decimals;

  /// @dev The maximum supply of the token, 0 if unlimited
  uint256 internal immutable i_maxSupply;

  /// @dev the CCIPAdmin can be used to register with the CCIP token admin registry, but has no other special powers,
  /// and can only be transferred by the owner.
  address internal s_ccipAdmin;

  bytes32 public constant MINTER_ROLE = keccak256("MINTER_ROLE");
  bytes32 public constant BURNER_ROLE = keccak256("BURNER_ROLE");

  /// @dev the underscores in parameter names are used to suppress compiler warnings about shadowing ERC20 functions
  constructor(
    string memory name,
    string memory symbol,
    uint8 decimals_,
    uint256 maxSupply_,
    uint256 preMint
  ) ERC20(name, symbol) {
    i_decimals = decimals_;
    i_maxSupply = maxSupply_;

    s_ccipAdmin = msg.sender;

    // Mint the initial supply to the new Owner, saving gas by not calling if the mint amount is zero
    if (preMint != 0) _mint(msg.sender, preMint);

    // Set up the owner as the initial minter and burner
    _grantRole(DEFAULT_ADMIN_ROLE, msg.sender);
  }

  /// @inheritdoc IERC165
  function supportsInterface(bytes4 interfaceId) public pure virtual override(AccessControl, IERC165) returns (bool) {
    return
      interfaceId == type(IERC20).interfaceId ||
      interfaceId == type(IBurnMintERC20).interfaceId ||
      interfaceId == type(IERC165).interfaceId ||
      interfaceId == type(IAccessControl).interfaceId ||
      interfaceId == type(IGetCCIPAdmin).interfaceId;
  }

  // ================================================================
  // │                            ERC20                             │
  // ================================================================

  /// @dev Returns the number of decimals used in its user representation.
  function decimals() public view virtual override returns (uint8) {
    return i_decimals;
  }

  /// @dev Returns the max supply of the token, 0 if unlimited.
  function maxSupply() public view virtual returns (uint256) {
    return i_maxSupply;
  }

  /// @dev Uses OZ ERC20 _transfer to disallow sending to address(0).
  /// @dev Disallows sending to address(this)
  function _transfer(address from, address to, uint256 amount) internal virtual override {
    if (to == address(this)) revert InvalidRecipient(to);

    super._transfer(from, to, amount);
  }

  /// @dev Uses OZ ERC20 _approve to disallow approving for address(0).
  /// @dev Disallows approving for address(this)
  function _approve(address owner, address spender, uint256 amount) internal virtual override {
    if (spender == address(this)) revert InvalidRecipient(spender);

    super._approve(owner, spender, amount);
  }

  // ================================================================
  // │                      Burning & minting                       │
  // ================================================================

  /// @inheritdoc ERC20Burnable
  /// @dev Uses OZ ERC20 _burn to disallow burning from address(0).
  /// @dev Decreases the total supply.
  function burn(uint256 amount) public override(IBurnMintERC20, ERC20Burnable) onlyRole(BURNER_ROLE) {
    super.burn(amount);
  }

  /// @inheritdoc IBurnMintERC20
  /// @dev Alias for BurnFrom for compatibility with the older naming convention.
  /// @dev Uses burnFrom for all validation & logic.
  function burn(address account, uint256 amount) public virtual override {
    burnFrom(account, amount);
  }

  /// @inheritdoc ERC20Burnable
  /// @dev Uses OZ ERC20 _burn to disallow burning from address(0).
  /// @dev Decreases the total supply.
  function burnFrom(
    address account,
    uint256 amount
  ) public override(IBurnMintERC20, ERC20Burnable) onlyRole(BURNER_ROLE) {
    super.burnFrom(account, amount);
  }

  /// @inheritdoc IBurnMintERC20
  /// @dev Uses OZ ERC20 _mint to disallow minting to address(0).
  /// @dev Disallows minting to address(this)
  /// @dev Increases the total supply.
  function mint(address account, uint256 amount) external override onlyRole(MINTER_ROLE) {
    if (account == address(this)) revert InvalidRecipient(account);
    if (i_maxSupply != 0 && totalSupply() + amount > i_maxSupply) revert MaxSupplyExceeded(totalSupply() + amount);

    _mint(account, amount);
  }

  // ================================================================
  // │                            Roles                             │
  // ================================================================

  /// @notice grants both mint and burn roles to `burnAndMinter`.
  /// @dev calls public functions so this function does not require
  /// access controls. This is handled in the inner functions.
  function grantMintAndBurnRoles(address burnAndMinter) external {
    grantRole(MINTER_ROLE, burnAndMinter);
    grantRole(BURNER_ROLE, burnAndMinter);
  }

  /// @notice Returns the current CCIPAdmin
  function getCCIPAdmin() external view returns (address) {
    return s_ccipAdmin;
  }

  /// @notice Transfers the CCIPAdmin role to a new address
  /// @dev only the owner can call this function, NOT the current ccipAdmin, and 1-step ownership transfer is used.
  /// @param newAdmin The address to transfer the CCIPAdmin role to. Setting to address(0) is a valid way to revoke
  /// the role
  function setCCIPAdmin(address newAdmin) public onlyRole(DEFAULT_ADMIN_ROLE) {
    address currentAdmin = s_ccipAdmin;

    s_ccipAdmin = newAdmin;

    emit CCIPAdminTransferred(currentAdmin, newAdmin);
  }
}

// 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;
  }
}

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

interface IGetCCIPAdmin {
  /// @notice Returns the admin of the token.
  /// @dev This method is named to never conflict with existing methods.
  function getCCIPAdmin() external view returns (address);
}

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

import {IERC20} from "../../../vendor/openzeppelin-solidity/v4.8.3/contracts/token/ERC20/IERC20.sol";

interface IBurnMintERC20 is IERC20 {
  /// @notice Mints new tokens for a given address.
  /// @param account The address to mint the new tokens to.
  /// @param amount The number of tokens to be minted.
  /// @dev this function increases the total supply.
  function mint(address account, uint256 amount) external;

  /// @notice Burns tokens from the sender.
  /// @param amount The number of tokens to be burned.
  /// @dev this function decreases the total supply.
  function burn(uint256 amount) external;

  /// @notice Burns tokens from a given address..
  /// @param account The address to burn tokens from.
  /// @param amount The number of tokens to be burned.
  /// @dev this function decreases the total supply.
  function burn(address account, uint256 amount) external;

  /// @notice Burns tokens from a given address..
  /// @param account The address to burn tokens from.
  /// @param amount The number of tokens to be burned.
  /// @dev this function decreases the total supply.
  function burnFrom(address account, uint256 amount) external;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (access/AccessControl.sol)

pragma solidity ^0.8.0;

import "./IAccessControl.sol";
import "../utils/Context.sol";
import "../utils/Strings.sol";
import "../utils/introspection/ERC165.sol";

/**
 * @dev Contract module that allows children to implement role-based access
 * control mechanisms. This is a lightweight version that doesn't allow enumerating role
 * members except through off-chain means by accessing the contract event logs. Some
 * applications may benefit from on-chain enumerability, for those cases see
 * {AccessControlEnumerable}.
 *
 * Roles are referred to by their `bytes32` identifier. These should be exposed
 * in the external API and be unique. The best way to achieve this is by
 * using `public constant` hash digests:
 *
 * ```
 * bytes32 public constant MY_ROLE = keccak256("MY_ROLE");
 * ```
 *
 * Roles can be used to represent a set of permissions. To restrict access to a
 * function call, use {hasRole}:
 *
 * ```
 * function foo() public {
 *     require(hasRole(MY_ROLE, msg.sender));
 *     ...
 * }
 * ```
 *
 * Roles can be granted and revoked dynamically via the {grantRole} and
 * {revokeRole} functions. Each role has an associated admin role, and only
 * accounts that have a role's admin role can call {grantRole} and {revokeRole}.
 *
 * By default, the admin role for all roles is `DEFAULT_ADMIN_ROLE`, which means
 * that only accounts with this role will be able to grant or revoke other
 * roles. More complex role relationships can be created by using
 * {_setRoleAdmin}.
 *
 * WARNING: The `DEFAULT_ADMIN_ROLE` is also its own admin: it has permission to
 * grant and revoke this role. Extra precautions should be taken to secure
 * accounts that have been granted it.
 */
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;

    /**
     * @dev Modifier that checks that an account has a specific role. Reverts
     * with a standardized message including the required role.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     *
     * _Available since v4.1._
     */
    modifier onlyRole(bytes32 role) {
        _checkRole(role);
        _;
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IAccessControl).interfaceId || super.supportsInterface(interfaceId);
    }

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) public view virtual override returns (bool) {
        return _roles[role].members[account];
    }

    /**
     * @dev Revert with a standard message if `_msgSender()` is missing `role`.
     * Overriding this function changes the behavior of the {onlyRole} modifier.
     *
     * Format of the revert message is described in {_checkRole}.
     *
     * _Available since v4.6._
     */
    function _checkRole(bytes32 role) internal view virtual {
        _checkRole(role, _msgSender());
    }

    /**
     * @dev Revert with a standard message if `account` is missing `role`.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     */
    function _checkRole(bytes32 role, address account) internal view virtual {
        if (!hasRole(role, account)) {
            revert(
                string(
                    abi.encodePacked(
                        "AccessControl: account ",
                        Strings.toHexString(account),
                        " is missing role ",
                        Strings.toHexString(uint256(role), 32)
                    )
                )
            );
        }
    }

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) public view virtual override returns (bytes32) {
        return _roles[role].adminRole;
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     *
     * May emit a {RoleGranted} event.
     */
    function grantRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _grantRole(role, account);
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     *
     * May emit a {RoleRevoked} event.
     */
    function revokeRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _revokeRole(role, account);
    }

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been revoked `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     *
     * May emit a {RoleRevoked} event.
     */
    function renounceRole(bytes32 role, address account) public virtual override {
        require(account == _msgSender(), "AccessControl: can only renounce roles for self");

        _revokeRole(role, account);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event. Note that unlike {grantRole}, this function doesn't perform any
     * checks on the calling account.
     *
     * May emit a {RoleGranted} event.
     *
     * [WARNING]
     * ====
     * This function should only be called from the constructor when setting
     * up the initial roles for the system.
     *
     * Using this function in any other way is effectively circumventing the admin
     * system imposed by {AccessControl}.
     * ====
     *
     * NOTE: This function is deprecated in favor of {_grantRole}.
     */
    function _setupRole(bytes32 role, address account) internal virtual {
        _grantRole(role, account);
    }

    /**
     * @dev Sets `adminRole` as ``role``'s admin role.
     *
     * Emits a {RoleAdminChanged} event.
     */
    function _setRoleAdmin(bytes32 role, bytes32 adminRole) internal virtual {
        bytes32 previousAdminRole = getRoleAdmin(role);
        _roles[role].adminRole = adminRole;
        emit RoleAdminChanged(role, previousAdminRole, adminRole);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleGranted} event.
     */
    function _grantRole(bytes32 role, address account) internal virtual {
        if (!hasRole(role, account)) {
            _roles[role].members[account] = true;
            emit RoleGranted(role, account, _msgSender());
        }
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleRevoked} event.
     */
    function _revokeRole(bytes32 role, address account) internal virtual {
        if (hasRole(role, account)) {
            _roles[role].members[account] = false;
            emit RoleRevoked(role, account, _msgSender());
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (access/IAccessControl.sol)

pragma solidity ^0.8.0;

/**
 * @dev External interface of AccessControl declared to support ERC165 detection.
 */
interface IAccessControl {
    /**
     * @dev Emitted when `newAdminRole` is set as ``role``'s admin role, replacing `previousAdminRole`
     *
     * `DEFAULT_ADMIN_ROLE` is the starting admin for all roles, despite
     * {RoleAdminChanged} not being emitted signaling this.
     *
     * _Available since v3.1._
     */
    event RoleAdminChanged(bytes32 indexed role, bytes32 indexed previousAdminRole, bytes32 indexed newAdminRole);

    /**
     * @dev Emitted when `account` is granted `role`.
     *
     * `sender` is the account that originated the contract call, an admin role
     * bearer except when using {AccessControl-_setupRole}.
     */
    event RoleGranted(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Emitted when `account` is revoked `role`.
     *
     * `sender` is the account that originated the contract call:
     *   - if using `revokeRole`, it is the admin role bearer
     *   - if using `renounceRole`, it is the role bearer (i.e. `account`)
     */
    event RoleRevoked(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) external view returns (bool);

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {AccessControl-_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) external view returns (bytes32);

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function grantRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function revokeRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been granted `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     */
    function renounceRole(bytes32 role, address account) external;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (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].
 *
 * 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}.
   *
   * The default value of {decimals} is 18. To select a different value for
   * {decimals} you should overload it.
   *
   * 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 value {ERC20} uses, unless this function is
   * 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 {}
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (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);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (token/ERC20/extensions/ERC20Burnable.sol)

pragma solidity ^0.8.0;

import "../ERC20.sol";
import "../../../utils/Context.sol";

/**
 * @dev Extension of {ERC20} that allows token holders to destroy both their own
 * tokens and those that they have an allowance for, in a way that can be
 * recognized off-chain (via event analysis).
 */
abstract contract ERC20Burnable is Context, ERC20 {
  /**
   * @dev Destroys `amount` tokens from the caller.
   *
   * See {ERC20-_burn}.
   */
  function burn(uint256 amount) public virtual {
    _burn(_msgSender(), amount);
  }

  /**
   * @dev Destroys `amount` tokens from `account`, deducting from the caller's
   * allowance.
   *
   * See {ERC20-_burn} and {ERC20-allowance}.
   *
   * Requirements:
   *
   * - the caller must have allowance for ``accounts``'s tokens of at least
   * `amount`.
   */
  function burnFrom(address account, uint256 amount) public virtual {
    _spendAllowance(account, _msgSender(), amount);
    _burn(account, amount);
  }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165 {
    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/Strings.sol)

pragma solidity ^0.8.0;

import "./math/Math.sol";

/**
 * @dev String operations.
 */
library Strings {
  bytes16 private constant _SYMBOLS = "0123456789abcdef";
  uint8 private constant _ADDRESS_LENGTH = 20;

  /**
   * @dev Converts a `uint256` to its ASCII `string` decimal representation.
   */
  function toString(uint256 value) internal pure returns (string memory) {
    unchecked {
      uint256 length = Math.log10(value) + 1;
      string memory buffer = new string(length);
      uint256 ptr;
      /// @solidity memory-safe-assembly
      assembly {
        ptr := add(buffer, add(32, length))
      }
      while (true) {
        ptr--;
        /// @solidity memory-safe-assembly
        assembly {
          mstore8(ptr, byte(mod(value, 10), _SYMBOLS))
        }
        value /= 10;
        if (value == 0) break;
      }
      return buffer;
    }
  }

  /**
   * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
   */
  function toHexString(uint256 value) internal pure returns (string memory) {
    unchecked {
      return toHexString(value, Math.log256(value) + 1);
    }
  }

  /**
   * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed 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] = _SYMBOLS[value & 0xf];
      value >>= 4;
    }
    require(value == 0, "Strings: hex length insufficient");
    return string(buffer);
  }

  /**
   * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.
   */
  function toHexString(address addr) internal pure returns (string memory) {
    return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);
  }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/ERC165.sol)

pragma solidity ^0.8.0;

import "./IERC165.sol";

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 *
 * Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
 */
abstract contract ERC165 is IERC165 {
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// 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);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
  enum Rounding {
    Down, // Toward negative infinity
    Up, // Toward infinity
    Zero // Toward zero
  }

  /**
   * @dev Returns the largest of two numbers.
   */
  function max(uint256 a, uint256 b) internal pure returns (uint256) {
    return a > b ? a : b;
  }

  /**
   * @dev Returns the smallest of two numbers.
   */
  function min(uint256 a, uint256 b) internal pure returns (uint256) {
    return a < b ? a : b;
  }

  /**
   * @dev Returns the average of two numbers. The result is rounded towards
   * zero.
   */
  function average(uint256 a, uint256 b) internal pure returns (uint256) {
    // (a + b) / 2 can overflow.
    return (a & b) + (a ^ b) / 2;
  }

  /**
   * @dev Returns the ceiling of the division of two numbers.
   *
   * This differs from standard division with `/` in that it rounds up instead
   * of rounding down.
   */
  function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
    // (a + b - 1) / b can overflow on addition, so we distribute.
    return a == 0 ? 0 : (a - 1) / b + 1;
  }

  /**
   * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
   * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
   * with further edits by Uniswap Labs also under MIT license.
   */
  function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
    unchecked {
      // 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) {
        return prod0 / denominator;
      }

      // Make sure the result is less than 2^256. Also prevents denominator == 0.
      require(denominator > prod1);

      ///////////////////////////////////////////////
      // 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.

      // Does not overflow because the denominator cannot be zero at this stage in the function.
      uint256 twos = denominator & (~denominator + 1);
      assembly {
        // Divide denominator by twos.
        denominator := div(denominator, twos)

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

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

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

      // 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;

      // Use the 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;
    }
  }

  /**
   * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
   */
  function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
    uint256 result = mulDiv(x, y, denominator);
    if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
      result += 1;
    }
    return result;
  }

  /**
   * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
   *
   * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
   */
  function sqrt(uint256 a) internal pure returns (uint256) {
    if (a == 0) {
      return 0;
    }

    // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
    //
    // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
    // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
    //
    // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
    // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
    // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
    //
    // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
    uint256 result = 1 << (log2(a) >> 1);

    // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
    // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
    // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
    // into the expected uint128 result.
    unchecked {
      result = (result + a / result) >> 1;
      result = (result + a / result) >> 1;
      result = (result + a / result) >> 1;
      result = (result + a / result) >> 1;
      result = (result + a / result) >> 1;
      result = (result + a / result) >> 1;
      result = (result + a / result) >> 1;
      return min(result, a / result);
    }
  }

  /**
   * @notice Calculates sqrt(a), following the selected rounding direction.
   */
  function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
    unchecked {
      uint256 result = sqrt(a);
      return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
    }
  }

  /**
   * @dev Return the log in base 2, rounded down, of a positive value.
   * Returns 0 if given 0.
   */
  function log2(uint256 value) internal pure returns (uint256) {
    uint256 result = 0;
    unchecked {
      if (value >> 128 > 0) {
        value >>= 128;
        result += 128;
      }
      if (value >> 64 > 0) {
        value >>= 64;
        result += 64;
      }
      if (value >> 32 > 0) {
        value >>= 32;
        result += 32;
      }
      if (value >> 16 > 0) {
        value >>= 16;
        result += 16;
      }
      if (value >> 8 > 0) {
        value >>= 8;
        result += 8;
      }
      if (value >> 4 > 0) {
        value >>= 4;
        result += 4;
      }
      if (value >> 2 > 0) {
        value >>= 2;
        result += 2;
      }
      if (value >> 1 > 0) {
        result += 1;
      }
    }
    return result;
  }

  /**
   * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
   * Returns 0 if given 0.
   */
  function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
    unchecked {
      uint256 result = log2(value);
      return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
    }
  }

  /**
   * @dev Return the log in base 10, rounded down, of a positive value.
   * Returns 0 if given 0.
   */
  function log10(uint256 value) internal pure returns (uint256) {
    uint256 result = 0;
    unchecked {
      if (value >= 10 ** 64) {
        value /= 10 ** 64;
        result += 64;
      }
      if (value >= 10 ** 32) {
        value /= 10 ** 32;
        result += 32;
      }
      if (value >= 10 ** 16) {
        value /= 10 ** 16;
        result += 16;
      }
      if (value >= 10 ** 8) {
        value /= 10 ** 8;
        result += 8;
      }
      if (value >= 10 ** 4) {
        value /= 10 ** 4;
        result += 4;
      }
      if (value >= 10 ** 2) {
        value /= 10 ** 2;
        result += 2;
      }
      if (value >= 10 ** 1) {
        result += 1;
      }
    }
    return result;
  }

  /**
   * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
   * Returns 0 if given 0.
   */
  function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
    unchecked {
      uint256 result = log10(value);
      return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);
    }
  }

  /**
   * @dev Return the log in base 256, rounded down, of a positive value.
   * Returns 0 if given 0.
   *
   * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
   */
  function log256(uint256 value) internal pure returns (uint256) {
    uint256 result = 0;
    unchecked {
      if (value >> 128 > 0) {
        value >>= 128;
        result += 16;
      }
      if (value >> 64 > 0) {
        value >>= 64;
        result += 8;
      }
      if (value >> 32 > 0) {
        value >>= 32;
        result += 4;
      }
      if (value >> 16 > 0) {
        value >>= 16;
        result += 2;
      }
      if (value >> 8 > 0) {
        result += 1;
      }
    }
    return result;
  }

  /**
   * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
   * Returns 0 if given 0.
   */
  function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
    unchecked {
      uint256 result = log256(value);
      return result + (rounding == Rounding.Up && 1 << (result * 8) < value ? 1 : 0);
    }
  }
}

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