// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/ERC20.sol) pragma solidity ^0.8.20; import {IERC20} from "./IERC20.sol"; import {IERC20Metadata} from "./extensions/IERC20Metadata.sol"; import {Context} from "../../utils/Context.sol"; import {IERC20Errors} from "../../interfaces/draft-IERC6093.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}. * * TIP: For a detailed writeup see our guide * https://forum.openzeppelin.com/t/how-to-implement-erc20-supply-mechanisms/226[How * to implement supply mechanisms]. * * The default value of {decimals} is 18. To change this, you should override * this function so it returns a different value. * * We have followed general OpenZeppelin Contracts guidelines: functions revert * instead returning `false` on failure. This behavior is nonetheless * conventional and does not conflict with the expectations of ERC20 * applications. * * Additionally, an {Approval} event is emitted on calls to {transferFrom}. * This allows applications to reconstruct the allowance for all accounts just * by listening to said events. Other implementations of the EIP may not emit * these events, as it isn't required by the specification. */ abstract contract ERC20 is Context, IERC20, IERC20Metadata, IERC20Errors { mapping(address account => uint256) private _balances; mapping(address account => mapping(address spender => uint256)) private _allowances; uint256 private _totalSupply; string private _name; string private _symbol; /** * @dev Sets the values for {name} and {symbol}. * * All two of these values are immutable: they can only be set once during * construction. */ constructor(string memory name_, string memory symbol_) { _name = name_; _symbol = symbol_; } /** * @dev Returns the name of the token. */ function name() public view virtual returns (string memory) { return _name; } /** * @dev Returns the symbol of the token, usually a shorter version of the * name. */ function symbol() public view virtual returns (string memory) { return _symbol; } /** * @dev Returns the number of decimals used to get its user representation. * For example, if `decimals` equals `2`, a balance of `505` tokens should * be displayed to a user as `5.05` (`505 / 10 ** 2`). * * Tokens usually opt for a value of 18, imitating the relationship between * Ether and Wei. This is the default value returned by this function, unless * it's overridden. * * NOTE: This information is only used for _display_ purposes: it in * no way affects any of the arithmetic of the contract, including * {IERC20-balanceOf} and {IERC20-transfer}. */ function decimals() public view virtual returns (uint8) { return 18; } /** * @dev See {IERC20-totalSupply}. */ function totalSupply() public view virtual returns (uint256) { return _totalSupply; } /** * @dev See {IERC20-balanceOf}. */ function balanceOf(address account) public view virtual 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 `value`. */ function transfer(address to, uint256 value) public virtual returns (bool) { address owner = _msgSender(); _transfer(owner, to, value); return true; } /** * @dev See {IERC20-allowance}. */ function allowance(address owner, address spender) public view virtual returns (uint256) { return _allowances[owner][spender]; } /** * @dev See {IERC20-approve}. * * NOTE: If `value` 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 value) public virtual returns (bool) { address owner = _msgSender(); _approve(owner, spender, value); 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 `value`. * - the caller must have allowance for ``from``'s tokens of at least * `value`. */ function transferFrom(address from, address to, uint256 value) public virtual returns (bool) { address spender = _msgSender(); _spendAllowance(from, spender, value); _transfer(from, to, value); return true; } /** * @dev Moves a `value` 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. * * NOTE: This function is not virtual, {_update} should be overridden instead. */ function _transfer(address from, address to, uint256 value) internal { if (from == address(0)) { revert ERC20InvalidSender(address(0)); } if (to == address(0)) { revert ERC20InvalidReceiver(address(0)); } _update(from, to, value); } /** * @dev Transfers a `value` amount of tokens from `from` to `to`, or alternatively mints (or burns) if `from` * (or `to`) is the zero address. All customizations to transfers, mints, and burns should be done by overriding * this function. * * Emits a {Transfer} event. */ function _update(address from, address to, uint256 value) internal virtual { if (from == address(0)) { // Overflow check required: The rest of the code assumes that totalSupply never overflows _totalSupply += value; } else { uint256 fromBalance = _balances[from]; if (fromBalance < value) { revert ERC20InsufficientBalance(from, fromBalance, value); } unchecked { // Overflow not possible: value <= fromBalance <= totalSupply. _balances[from] = fromBalance - value; } } if (to == address(0)) { unchecked { // Overflow not possible: value <= totalSupply or value <= fromBalance <= totalSupply. _totalSupply -= value; } } else { unchecked { // Overflow not possible: balance + value is at most totalSupply, which we know fits into a uint256. _balances[to] += value; } } emit Transfer(from, to, value); } /** * @dev Creates a `value` amount of tokens and assigns them to `account`, by transferring it from address(0). * Relies on the `_update` mechanism * * Emits a {Transfer} event with `from` set to the zero address. * * NOTE: This function is not virtual, {_update} should be overridden instead. */ function _mint(address account, uint256 value) internal { if (account == address(0)) { revert ERC20InvalidReceiver(address(0)); } _update(address(0), account, value); } /** * @dev Destroys a `value` amount of tokens from `account`, lowering the total supply. * Relies on the `_update` mechanism. * * Emits a {Transfer} event with `to` set to the zero address. * * NOTE: This function is not virtual, {_update} should be overridden instead */ function _burn(address account, uint256 value) internal { if (account == address(0)) { revert ERC20InvalidSender(address(0)); } _update(account, address(0), value); } /** * @dev Sets `value` 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. * * Overrides to this logic should be done to the variant with an additional `bool emitEvent` argument. */ function _approve(address owner, address spender, uint256 value) internal { _approve(owner, spender, value, true); } /** * @dev Variant of {_approve} with an optional flag to enable or disable the {Approval} event. * * By default (when calling {_approve}) the flag is set to true. On the other hand, approval changes made by * `_spendAllowance` during the `transferFrom` operation set the flag to false. This saves gas by not emitting any * `Approval` event during `transferFrom` operations. * * Anyone who wishes to continue emitting `Approval` events on the`transferFrom` operation can force the flag to * true using the following override: * ``` * function _approve(address owner, address spender, uint256 value, bool) internal virtual override { * super._approve(owner, spender, value, true); * } * ``` * * Requirements are the same as {_approve}. */ function _approve(address owner, address spender, uint256 value, bool emitEvent) internal virtual { if (owner == address(0)) { revert ERC20InvalidApprover(address(0)); } if (spender == address(0)) { revert ERC20InvalidSpender(address(0)); } _allowances[owner][spender] = value; if (emitEvent) { emit Approval(owner, spender, value); } } /** * @dev Updates `owner` s allowance for `spender` based on spent `value`. * * Does not update the allowance value in case of infinite allowance. * Revert if not enough allowance is available. * * Does not emit an {Approval} event. */ function _spendAllowance(address owner, address spender, uint256 value) internal virtual { uint256 currentAllowance = allowance(owner, spender); if (currentAllowance != type(uint256).max) { if (currentAllowance < value) { revert ERC20InsufficientAllowance(spender, currentAllowance, value); } unchecked { _approve(owner, spender, currentAllowance - value, false); } } } }

// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/IERC20.sol) pragma solidity ^0.8.20; /** * @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 value of tokens in existence. */ function totalSupply() external view returns (uint256); /** * @dev Returns the value of tokens owned by `account`. */ function balanceOf(address account) external view returns (uint256); /** * @dev Moves a `value` amount of 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 value) 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 a `value` amount of tokens 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 value) external returns (bool); /** * @dev Moves a `value` amount of tokens from `from` to `to` using the * allowance mechanism. `value` 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 value) external returns (bool); }

// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/extensions/ERC20Permit.sol) pragma solidity ^0.8.20; import {IERC20Permit} from "./IERC20Permit.sol"; import {ERC20} from "../ERC20.sol"; import {ECDSA} from "../../../utils/cryptography/ECDSA.sol"; import {EIP712} from "../../../utils/cryptography/EIP712.sol"; import {Nonces} from "../../../utils/Nonces.sol"; /** * @dev Implementation of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612]. * * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by * presenting a message signed by the account. By not relying on `{IERC20-approve}`, the token holder account doesn't * need to send a transaction, and thus is not required to hold Ether at all. */ abstract contract ERC20Permit is ERC20, IERC20Permit, EIP712, Nonces { bytes32 private constant PERMIT_TYPEHASH = keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)"); /** * @dev Permit deadline has expired. */ error ERC2612ExpiredSignature(uint256 deadline); /** * @dev Mismatched signature. */ error ERC2612InvalidSigner(address signer, address owner); /** * @dev Initializes the {EIP712} domain separator using the `name` parameter, and setting `version` to `"1"`. * * It's a good idea to use the same `name` that is defined as the ERC20 token name. */ constructor(string memory name) EIP712(name, "1") {} /** * @inheritdoc IERC20Permit */ function permit( address owner, address spender, uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s ) public virtual { if (block.timestamp > deadline) { revert ERC2612ExpiredSignature(deadline); } bytes32 structHash = keccak256(abi.encode(PERMIT_TYPEHASH, owner, spender, value, _useNonce(owner), deadline)); bytes32 hash = _hashTypedDataV4(structHash); address signer = ECDSA.recover(hash, v, r, s); if (signer != owner) { revert ERC2612InvalidSigner(signer, owner); } _approve(owner, spender, value); } /** * @inheritdoc IERC20Permit */ function nonces(address owner) public view virtual override(IERC20Permit, Nonces) returns (uint256) { return super.nonces(owner); } /** * @inheritdoc IERC20Permit */ // solhint-disable-next-line func-name-mixedcase function DOMAIN_SEPARATOR() external view virtual returns (bytes32) { return _domainSeparatorV4(); } }

// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/extensions/IERC20Metadata.sol) pragma solidity ^0.8.20; import {IERC20} from "../IERC20.sol"; /** * @dev Interface for the optional metadata functions from the ERC20 standard. */ 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 v5.0.0) (token/ERC20/extensions/IERC20Permit.sol) pragma solidity ^0.8.20; /** * @dev Interface of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612]. * * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by * presenting a message signed by the account. By not relying on {IERC20-approve}, the token holder account doesn't * need to send a transaction, and thus is not required to hold Ether at all. * * ==== Security Considerations * * There are two important considerations concerning the use of `permit`. The first is that a valid permit signature * expresses an allowance, and it should not be assumed to convey additional meaning. In particular, it should not be * considered as an intention to spend the allowance in any specific way. The second is that because permits have * built-in replay protection and can be submitted by anyone, they can be frontrun. A protocol that uses permits should * take this into consideration and allow a `permit` call to fail. Combining these two aspects, a pattern that may be * generally recommended is: * * ```solidity * function doThingWithPermit(..., uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s) public { * try token.permit(msg.sender, address(this), value, deadline, v, r, s) {} catch {} * doThing(..., value); * } * * function doThing(..., uint256 value) public { * token.safeTransferFrom(msg.sender, address(this), value); * ... * } * ``` * * Observe that: 1) `msg.sender` is used as the owner, leaving no ambiguity as to the signer intent, and 2) the use of * `try/catch` allows the permit to fail and makes the code tolerant to frontrunning. (See also * {SafeERC20-safeTransferFrom}). * * Additionally, note that smart contract wallets (such as Argent or Safe) are not able to produce permit signatures, so * contracts should have entry points that don't rely on permit. */ interface IERC20Permit { /** * @dev Sets `value` as the allowance of `spender` over ``owner``'s tokens, * given ``owner``'s signed approval. * * IMPORTANT: The same issues {IERC20-approve} has related to transaction * ordering also apply here. * * Emits an {Approval} event. * * Requirements: * * - `spender` cannot be the zero address. * - `deadline` must be a timestamp in the future. * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner` * over the EIP712-formatted function arguments. * - the signature must use ``owner``'s current nonce (see {nonces}). * * For more information on the signature format, see the * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP * section]. * * CAUTION: See Security Considerations above. */ function permit( address owner, address spender, uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s ) external; /** * @dev Returns the current nonce for `owner`. This value must be * included whenever a signature is generated for {permit}. * * Every successful call to {permit} increases ``owner``'s nonce by one. This * prevents a signature from being used multiple times. */ function nonces(address owner) external view returns (uint256); /** * @dev Returns the domain separator used in the encoding of the signature for {permit}, as defined by {EIP712}. */ // solhint-disable-next-line func-name-mixedcase function DOMAIN_SEPARATOR() external view returns (bytes32); }

// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.1) (utils/Context.sol) pragma solidity ^0.8.20; /** * @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; } function _contextSuffixLength() internal view virtual returns (uint256) { return 0; } }

// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.0) (utils/Nonces.sol) pragma solidity ^0.8.20; /** * @dev Provides tracking nonces for addresses. Nonces will only increment. */ abstract contract Nonces { /** * @dev The nonce used for an `account` is not the expected current nonce. */ error InvalidAccountNonce(address account, uint256 currentNonce); mapping(address account => uint256) private _nonces; /** * @dev Returns the next unused nonce for an address. */ function nonces(address owner) public view virtual returns (uint256) { return _nonces[owner]; } /** * @dev Consumes a nonce. * * Returns the current value and increments nonce. */ function _useNonce(address owner) internal virtual returns (uint256) { // For each account, the nonce has an initial value of 0, can only be incremented by one, and cannot be // decremented or reset. This guarantees that the nonce never overflows. unchecked { // It is important to do x++ and not ++x here. return _nonces[owner]++; } } /** * @dev Same as {_useNonce} but checking that `nonce` is the next valid for `owner`. */ function _useCheckedNonce(address owner, uint256 nonce) internal virtual { uint256 current = _useNonce(owner); if (nonce != current) { revert InvalidAccountNonce(owner, current); } } }

// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.0) (utils/ShortStrings.sol) pragma solidity ^0.8.20; import {StorageSlot} from "./StorageSlot.sol"; // | string | 0xAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA | // | length | 0x BB | type ShortString is bytes32; /** * @dev This library provides functions to convert short memory strings * into a `ShortString` type that can be used as an immutable variable. * * Strings of arbitrary length can be optimized using this library if * they are short enough (up to 31 bytes) by packing them with their * length (1 byte) in a single EVM word (32 bytes). Additionally, a * fallback mechanism can be used for every other case. * * Usage example: * * ```solidity * contract Named { * using ShortStrings for *; * * ShortString private immutable _name; * string private _nameFallback; * * constructor(string memory contractName) { * _name = contractName.toShortStringWithFallback(_nameFallback); * } * * function name() external view returns (string memory) { * return _name.toStringWithFallback(_nameFallback); * } * } * ``` */ library ShortStrings { // Used as an identifier for strings longer than 31 bytes. bytes32 private constant FALLBACK_SENTINEL = 0x00000000000000000000000000000000000000000000000000000000000000FF; error StringTooLong(string str); error InvalidShortString(); /** * @dev Encode a string of at most 31 chars into a `ShortString`. * * This will trigger a `StringTooLong` error is the input string is too long. */ function toShortString(string memory str) internal pure returns (ShortString) { bytes memory bstr = bytes(str); if (bstr.length > 31) { revert StringTooLong(str); } return ShortString.wrap(bytes32(uint256(bytes32(bstr)) | bstr.length)); } /** * @dev Decode a `ShortString` back to a "normal" string. */ function toString(ShortString sstr) internal pure returns (string memory) { uint256 len = byteLength(sstr); // using `new string(len)` would work locally but is not memory safe. string memory str = new string(32); /// @solidity memory-safe-assembly assembly { mstore(str, len) mstore(add(str, 0x20), sstr) } return str; } /** * @dev Return the length of a `ShortString`. */ function byteLength(ShortString sstr) internal pure returns (uint256) { uint256 result = uint256(ShortString.unwrap(sstr)) & 0xFF; if (result > 31) { revert InvalidShortString(); } return result; } /** * @dev Encode a string into a `ShortString`, or write it to storage if it is too long. */ function toShortStringWithFallback(string memory value, string storage store) internal returns (ShortString) { if (bytes(value).length < 32) { return toShortString(value); } else { StorageSlot.getStringSlot(store).value = value; return ShortString.wrap(FALLBACK_SENTINEL); } } /** * @dev Decode a string that was encoded to `ShortString` or written to storage using {setWithFallback}. */ function toStringWithFallback(ShortString value, string storage store) internal pure returns (string memory) { if (ShortString.unwrap(value) != FALLBACK_SENTINEL) { return toString(value); } else { return store; } } /** * @dev Return the length of a string that was encoded to `ShortString` or written to storage using * {setWithFallback}. * * WARNING: This will return the "byte length" of the string. This may not reflect the actual length in terms of * actual characters as the UTF-8 encoding of a single character can span over multiple bytes. */ function byteLengthWithFallback(ShortString value, string storage store) internal view returns (uint256) { if (ShortString.unwrap(value) != FALLBACK_SENTINEL) { return byteLength(value); } else { return bytes(store).length; } } }

// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.0) (utils/StorageSlot.sol) // This file was procedurally generated from scripts/generate/templates/StorageSlot.js. pragma solidity ^0.8.20; /** * @dev Library for reading and writing primitive types to specific storage slots. * * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts. * This library helps with reading and writing to such slots without the need for inline assembly. * * The functions in this library return Slot structs that contain a `value` member that can be used to read or write. * * Example usage to set ERC1967 implementation slot: * ```solidity * contract ERC1967 { * bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc; * * function _getImplementation() internal view returns (address) { * return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value; * } * * function _setImplementation(address newImplementation) internal { * require(newImplementation.code.length > 0); * StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation; * } * } * ``` */ library StorageSlot { struct AddressSlot { address value; } struct BooleanSlot { bool value; } struct Bytes32Slot { bytes32 value; } struct Uint256Slot { uint256 value; } struct StringSlot { string value; } struct BytesSlot { bytes value; } /** * @dev Returns an `AddressSlot` with member `value` located at `slot`. */ function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) { /// @solidity memory-safe-assembly assembly { r.slot := slot } } /** * @dev Returns an `BooleanSlot` with member `value` located at `slot`. */ function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) { /// @solidity memory-safe-assembly assembly { r.slot := slot } } /** * @dev Returns an `Bytes32Slot` with member `value` located at `slot`. */ function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) { /// @solidity memory-safe-assembly assembly { r.slot := slot } } /** * @dev Returns an `Uint256Slot` with member `value` located at `slot`. */ function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) { /// @solidity memory-safe-assembly assembly { r.slot := slot } } /** * @dev Returns an `StringSlot` with member `value` located at `slot`. */ function getStringSlot(bytes32 slot) internal pure returns (StringSlot storage r) { /// @solidity memory-safe-assembly assembly { r.slot := slot } } /** * @dev Returns an `StringSlot` representation of the string storage pointer `store`. */ function getStringSlot(string storage store) internal pure returns (StringSlot storage r) { /// @solidity memory-safe-assembly assembly { r.slot := store.slot } } /** * @dev Returns an `BytesSlot` with member `value` located at `slot`. */ function getBytesSlot(bytes32 slot) internal pure returns (BytesSlot storage r) { /// @solidity memory-safe-assembly assembly { r.slot := slot } } /** * @dev Returns an `BytesSlot` representation of the bytes storage pointer `store`. */ function getBytesSlot(bytes storage store) internal pure returns (BytesSlot storage r) { /// @solidity memory-safe-assembly assembly { r.slot := store.slot } } }

// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.0) (utils/Strings.sol) pragma solidity ^0.8.20; import {Math} from "./math/Math.sol"; import {SignedMath} from "./math/SignedMath.sol"; /** * @dev String operations. */ library Strings { bytes16 private constant HEX_DIGITS = "0123456789abcdef"; uint8 private constant ADDRESS_LENGTH = 20; /** * @dev The `value` string doesn't fit in the specified `length`. */ error StringsInsufficientHexLength(uint256 value, uint256 length); /** * @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), HEX_DIGITS)) } value /= 10; if (value == 0) break; } return buffer; } } /** * @dev Converts a `int256` to its ASCII `string` decimal representation. */ function toStringSigned(int256 value) internal pure returns (string memory) { return string.concat(value < 0 ? "-" : "", toString(SignedMath.abs(value))); } /** * @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) { uint256 localValue = value; 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_DIGITS[localValue & 0xf]; localValue >>= 4; } if (localValue != 0) { revert StringsInsufficientHexLength(value, length); } 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); } /** * @dev Returns true if the two strings are equal. */ function equal(string memory a, string memory b) internal pure returns (bool) { return bytes(a).length == bytes(b).length && keccak256(bytes(a)) == keccak256(bytes(b)); } }

// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.0) (utils/cryptography/ECDSA.sol) pragma solidity ^0.8.20; /** * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations. * * These functions can be used to verify that a message was signed by the holder * of the private keys of a given address. */ library ECDSA { enum RecoverError { NoError, InvalidSignature, InvalidSignatureLength, InvalidSignatureS } /** * @dev The signature derives the `address(0)`. */ error ECDSAInvalidSignature(); /** * @dev The signature has an invalid length. */ error ECDSAInvalidSignatureLength(uint256 length); /** * @dev The signature has an S value that is in the upper half order. */ error ECDSAInvalidSignatureS(bytes32 s); /** * @dev Returns the address that signed a hashed message (`hash`) with `signature` or an error. This will not * return address(0) without also returning an error description. Errors are documented using an enum (error type) * and a bytes32 providing additional information about the error. * * If no error is returned, then the address can be used for verification purposes. * * The `ecrecover` EVM precompile allows for malleable (non-unique) signatures: * this function rejects them by requiring the `s` value to be in the lower * half order, and the `v` value to be either 27 or 28. * * IMPORTANT: `hash` _must_ be the result of a hash operation for the * verification to be secure: it is possible to craft signatures that * recover to arbitrary addresses for non-hashed data. A safe way to ensure * this is by receiving a hash of the original message (which may otherwise * be too long), and then calling {MessageHashUtils-toEthSignedMessageHash} on it. * * Documentation for signature generation: * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js] * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers] */ function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError, bytes32) { if (signature.length == 65) { bytes32 r; bytes32 s; uint8 v; // ecrecover takes the signature parameters, and the only way to get them // currently is to use assembly. /// @solidity memory-safe-assembly assembly { r := mload(add(signature, 0x20)) s := mload(add(signature, 0x40)) v := byte(0, mload(add(signature, 0x60))) } return tryRecover(hash, v, r, s); } else { return (address(0), RecoverError.InvalidSignatureLength, bytes32(signature.length)); } } /** * @dev Returns the address that signed a hashed message (`hash`) with * `signature`. This address can then be used for verification purposes. * * The `ecrecover` EVM precompile allows for malleable (non-unique) signatures: * this function rejects them by requiring the `s` value to be in the lower * half order, and the `v` value to be either 27 or 28. * * IMPORTANT: `hash` _must_ be the result of a hash operation for the * verification to be secure: it is possible to craft signatures that * recover to arbitrary addresses for non-hashed data. A safe way to ensure * this is by receiving a hash of the original message (which may otherwise * be too long), and then calling {MessageHashUtils-toEthSignedMessageHash} on it. */ function recover(bytes32 hash, bytes memory signature) internal pure returns (address) { (address recovered, RecoverError error, bytes32 errorArg) = tryRecover(hash, signature); _throwError(error, errorArg); return recovered; } /** * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately. * * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures] */ function tryRecover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address, RecoverError, bytes32) { unchecked { bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff); // We do not check for an overflow here since the shift operation results in 0 or 1. uint8 v = uint8((uint256(vs) >> 255) + 27); return tryRecover(hash, v, r, s); } } /** * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately. */ function recover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address) { (address recovered, RecoverError error, bytes32 errorArg) = tryRecover(hash, r, vs); _throwError(error, errorArg); return recovered; } /** * @dev Overload of {ECDSA-tryRecover} that receives the `v`, * `r` and `s` signature fields separately. */ function tryRecover( bytes32 hash, uint8 v, bytes32 r, bytes32 s ) internal pure returns (address, RecoverError, bytes32) { // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most // signatures from current libraries generate a unique signature with an s-value in the lower half order. // // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept // these malleable signatures as well. if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) { return (address(0), RecoverError.InvalidSignatureS, s); } // If the signature is valid (and not malleable), return the signer address address signer = ecrecover(hash, v, r, s); if (signer == address(0)) { return (address(0), RecoverError.InvalidSignature, bytes32(0)); } return (signer, RecoverError.NoError, bytes32(0)); } /** * @dev Overload of {ECDSA-recover} that receives the `v`, * `r` and `s` signature fields separately. */ function recover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address) { (address recovered, RecoverError error, bytes32 errorArg) = tryRecover(hash, v, r, s); _throwError(error, errorArg); return recovered; } /** * @dev Optionally reverts with the corresponding custom error according to the `error` argument provided. */ function _throwError(RecoverError error, bytes32 errorArg) private pure { if (error == RecoverError.NoError) { return; // no error: do nothing } else if (error == RecoverError.InvalidSignature) { revert ECDSAInvalidSignature(); } else if (error == RecoverError.InvalidSignatureLength) { revert ECDSAInvalidSignatureLength(uint256(errorArg)); } else if (error == RecoverError.InvalidSignatureS) { revert ECDSAInvalidSignatureS(errorArg); } } }

// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.0) (utils/cryptography/EIP712.sol) pragma solidity ^0.8.20; import {MessageHashUtils} from "./MessageHashUtils.sol"; import {ShortStrings, ShortString} from "../ShortStrings.sol"; import {IERC5267} from "../../interfaces/IERC5267.sol"; /** * @dev https://eips.ethereum.org/EIPS/eip-712[EIP 712] is a standard for hashing and signing of typed structured data. * * The encoding scheme specified in the EIP requires a domain separator and a hash of the typed structured data, whose * encoding is very generic and therefore its implementation in Solidity is not feasible, thus this contract * does not implement the encoding itself. Protocols need to implement the type-specific encoding they need in order to * produce the hash of their typed data using a combination of `abi.encode` and `keccak256`. * * This contract implements the EIP 712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding * scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA * ({_hashTypedDataV4}). * * The implementation of the domain separator was designed to be as efficient as possible while still properly updating * the chain id to protect against replay attacks on an eventual fork of the chain. * * NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method * https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask]. * * NOTE: In the upgradeable version of this contract, the cached values will correspond to the address, and the domain * separator of the implementation contract. This will cause the {_domainSeparatorV4} function to always rebuild the * separator from the immutable values, which is cheaper than accessing a cached version in cold storage. * * @custom:oz-upgrades-unsafe-allow state-variable-immutable */ abstract contract EIP712 is IERC5267 { using ShortStrings for *; bytes32 private constant TYPE_HASH = keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"); // Cache the domain separator as an immutable value, but also store the chain id that it corresponds to, in order to // invalidate the cached domain separator if the chain id changes. bytes32 private immutable _cachedDomainSeparator; uint256 private immutable _cachedChainId; address private immutable _cachedThis; bytes32 private immutable _hashedName; bytes32 private immutable _hashedVersion; ShortString private immutable _name; ShortString private immutable _version; string private _nameFallback; string private _versionFallback; /** * @dev Initializes the domain separator and parameter caches. * * The meaning of `name` and `version` is specified in * https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP 712]: * * - `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol. * - `version`: the current major version of the signing domain. * * NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart * contract upgrade]. */ constructor(string memory name, string memory version) { _name = name.toShortStringWithFallback(_nameFallback); _version = version.toShortStringWithFallback(_versionFallback); _hashedName = keccak256(bytes(name)); _hashedVersion = keccak256(bytes(version)); _cachedChainId = block.chainid; _cachedDomainSeparator = _buildDomainSeparator(); _cachedThis = address(this); } /** * @dev Returns the domain separator for the current chain. */ function _domainSeparatorV4() internal view returns (bytes32) { if (address(this) == _cachedThis && block.chainid == _cachedChainId) { return _cachedDomainSeparator; } else { return _buildDomainSeparator(); } } function _buildDomainSeparator() private view returns (bytes32) { return keccak256(abi.encode(TYPE_HASH, _hashedName, _hashedVersion, block.chainid, address(this))); } /** * @dev Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this * function returns the hash of the fully encoded EIP712 message for this domain. * * This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example: * * ```solidity * bytes32 digest = _hashTypedDataV4(keccak256(abi.encode( * keccak256("Mail(address to,string contents)"), * mailTo, * keccak256(bytes(mailContents)) * ))); * address signer = ECDSA.recover(digest, signature); * ``` */ function _hashTypedDataV4(bytes32 structHash) internal view virtual returns (bytes32) { return MessageHashUtils.toTypedDataHash(_domainSeparatorV4(), structHash); } /** * @dev See {IERC-5267}. */ function eip712Domain() public view virtual returns ( bytes1 fields, string memory name, string memory version, uint256 chainId, address verifyingContract, bytes32 salt, uint256[] memory extensions ) { return ( hex"0f", // 01111 _EIP712Name(), _EIP712Version(), block.chainid, address(this), bytes32(0), new uint256[](0) ); } /** * @dev The name parameter for the EIP712 domain. * * NOTE: By default this function reads _name which is an immutable value. * It only reads from storage if necessary (in case the value is too large to fit in a ShortString). */ // solhint-disable-next-line func-name-mixedcase function _EIP712Name() internal view returns (string memory) { return _name.toStringWithFallback(_nameFallback); } /** * @dev The version parameter for the EIP712 domain. * * NOTE: By default this function reads _version which is an immutable value. * It only reads from storage if necessary (in case the value is too large to fit in a ShortString). */ // solhint-disable-next-line func-name-mixedcase function _EIP712Version() internal view returns (string memory) { return _version.toStringWithFallback(_versionFallback); } }

// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.0) (utils/cryptography/MessageHashUtils.sol) pragma solidity ^0.8.20; import {Strings} from "../Strings.sol"; /** * @dev Signature message hash utilities for producing digests to be consumed by {ECDSA} recovery or signing. * * The library provides methods for generating a hash of a message that conforms to the * https://eips.ethereum.org/EIPS/eip-191[EIP 191] and https://eips.ethereum.org/EIPS/eip-712[EIP 712] * specifications. */ library MessageHashUtils { /** * @dev Returns the keccak256 digest of an EIP-191 signed data with version * `0x45` (`personal_sign` messages). * * The digest is calculated by prefixing a bytes32 `messageHash` with * `"\x19Ethereum Signed Message:\n32"` and hashing the result. It corresponds with the * hash signed when using the https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`] JSON-RPC method. * * NOTE: The `messageHash` parameter is intended to be the result of hashing a raw message with * keccak256, although any bytes32 value can be safely used because the final digest will * be re-hashed. * * See {ECDSA-recover}. */ function toEthSignedMessageHash(bytes32 messageHash) internal pure returns (bytes32 digest) { /// @solidity memory-safe-assembly assembly { mstore(0x00, "\x19Ethereum Signed Message:\n32") // 32 is the bytes-length of messageHash mstore(0x1c, messageHash) // 0x1c (28) is the length of the prefix digest := keccak256(0x00, 0x3c) // 0x3c is the length of the prefix (0x1c) + messageHash (0x20) } } /** * @dev Returns the keccak256 digest of an EIP-191 signed data with version * `0x45` (`personal_sign` messages). * * The digest is calculated by prefixing an arbitrary `message` with * `"\x19Ethereum Signed Message:\n" + len(message)` and hashing the result. It corresponds with the * hash signed when using the https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`] JSON-RPC method. * * See {ECDSA-recover}. */ function toEthSignedMessageHash(bytes memory message) internal pure returns (bytes32) { return keccak256(bytes.concat("\x19Ethereum Signed Message:\n", bytes(Strings.toString(message.length)), message)); } /** * @dev Returns the keccak256 digest of an EIP-191 signed data with version * `0x00` (data with intended validator). * * The digest is calculated by prefixing an arbitrary `data` with `"\x19\x00"` and the intended * `validator` address. Then hashing the result. * * See {ECDSA-recover}. */ function toDataWithIntendedValidatorHash(address validator, bytes memory data) internal pure returns (bytes32) { return keccak256(abi.encodePacked(hex"19_00", validator, data)); } /** * @dev Returns the keccak256 digest of an EIP-712 typed data (EIP-191 version `0x01`). * * The digest is calculated from a `domainSeparator` and a `structHash`, by prefixing them with * `\x19\x01` and hashing the result. It corresponds to the hash signed by the * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`] JSON-RPC method as part of EIP-712. * * See {ECDSA-recover}. */ function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32 digest) { /// @solidity memory-safe-assembly assembly { let ptr := mload(0x40) mstore(ptr, hex"19_01") mstore(add(ptr, 0x02), domainSeparator) mstore(add(ptr, 0x22), structHash) digest := keccak256(ptr, 0x42) } } }

// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.0) (utils/math/Math.sol) pragma solidity ^0.8.20; /** * @dev Standard math utilities missing in the Solidity language. */ library Math { /** * @dev Muldiv operation overflow. */ error MathOverflowedMulDiv(); enum Rounding { Floor, // Toward negative infinity Ceil, // Toward positive infinity Trunc, // Toward zero Expand // Away from zero } /** * @dev Returns the addition of two unsigned integers, with an overflow flag. */ function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) { unchecked { uint256 c = a + b; if (c < a) return (false, 0); return (true, c); } } /** * @dev Returns the subtraction of two unsigned integers, with an overflow flag. */ function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) { unchecked { if (b > a) return (false, 0); return (true, a - b); } } /** * @dev Returns the multiplication of two unsigned integers, with an overflow flag. */ function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) { unchecked { // Gas optimization: this is cheaper than requiring 'a' not being zero, but the // benefit is lost if 'b' is also tested. // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522 if (a == 0) return (true, 0); uint256 c = a * b; if (c / a != b) return (false, 0); return (true, c); } } /** * @dev Returns the division of two unsigned integers, with a division by zero flag. */ function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) { unchecked { if (b == 0) return (false, 0); return (true, a / b); } } /** * @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag. */ function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) { unchecked { if (b == 0) return (false, 0); return (true, a % b); } } /** * @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 towards infinity instead * of rounding towards zero. */ function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) { if (b == 0) { // Guarantee the same behavior as in a regular Solidity division. return a / b; } // (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 = x * y; // Least significant 256 bits of the product uint256 prod1; // Most significant 256 bits of the product assembly { let mm := mulmod(x, y, not(0)) prod1 := sub(sub(mm, prod0), lt(mm, prod0)) } // Handle non-overflow cases, 256 by 256 division. if (prod1 == 0) { // Solidity will revert if denominator == 0, unlike the div opcode on its own. // The surrounding unchecked block does not change this fact. // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic. return prod0 / denominator; } // Make sure the result is less than 2^256. Also prevents denominator == 0. if (denominator <= prod1) { revert MathOverflowedMulDiv(); } /////////////////////////////////////////////// // 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. uint256 twos = denominator & (0 - denominator); 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 (unsignedRoundsUp(rounding) && 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 * towards zero. * * 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 + (unsignedRoundsUp(rounding) && result * result < a ? 1 : 0); } } /** * @dev Return the log in base 2 of a positive value rounded towards zero. * 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 + (unsignedRoundsUp(rounding) && 1 << result < value ? 1 : 0); } } /** * @dev Return the log in base 10 of a positive value rounded towards zero. * 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 + (unsignedRoundsUp(rounding) && 10 ** result < value ? 1 : 0); } } /** * @dev Return the log in base 256 of a positive value rounded towards zero. * 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 256, 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 + (unsignedRoundsUp(rounding) && 1 << (result << 3) < value ? 1 : 0); } } /** * @dev Returns whether a provided rounding mode is considered rounding up for unsigned integers. */ function unsignedRoundsUp(Rounding rounding) internal pure returns (bool) { return uint8(rounding) % 2 == 1; } }

// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v5.0.0) (utils/math/SignedMath.sol) pragma solidity ^0.8.20; /** * @dev Standard signed math utilities missing in the Solidity language. */ library SignedMath { /** * @dev Returns the largest of two signed numbers. */ function max(int256 a, int256 b) internal pure returns (int256) { return a > b ? a : b; } /** * @dev Returns the smallest of two signed numbers. */ function min(int256 a, int256 b) internal pure returns (int256) { return a < b ? a : b; } /** * @dev Returns the average of two signed numbers without overflow. * The result is rounded towards zero. */ function average(int256 a, int256 b) internal pure returns (int256) { // Formula from the book "Hacker's Delight" int256 x = (a & b) + ((a ^ b) >> 1); return x + (int256(uint256(x) >> 255) & (a ^ b)); } /** * @dev Returns the absolute unsigned value of a signed value. */ function abs(int256 n) internal pure returns (uint256) { unchecked { // must be unchecked in order to support `n = type(int256).min` return uint256(n >= 0 ? n : -n); } } }