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Contract Name:
ProtocolVersions
Compiler Version
v0.8.15+commit.e14f2714
Optimization Enabled:
Yes with 999999 runs
Other Settings:
london EvmVersion
Contract Source Code (Solidity Standard Json-Input format)
// SPDX-License-Identifier: MIT pragma solidity 0.8.15; import { OwnableUpgradeable } from "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol"; import { ISemver } from "src/universal/ISemver.sol"; import { Storage } from "src/libraries/Storage.sol"; import { Constants } from "src/libraries/Constants.sol"; /// @notice ProtocolVersion is a numeric identifier of the protocol version. type ProtocolVersion is uint256; /// @title ProtocolVersions /// @notice The ProtocolVersions contract is used to manage superchain protocol version information. contract ProtocolVersions is OwnableUpgradeable, ISemver { /// @notice Enum representing different types of updates. /// @custom:value REQUIRED_PROTOCOL_VERSION Represents an update to the required protocol version. /// @custom:value RECOMMENDED_PROTOCOL_VERSION Represents an update to the recommended protocol version. enum UpdateType { REQUIRED_PROTOCOL_VERSION, RECOMMENDED_PROTOCOL_VERSION } /// @notice Version identifier, used for upgrades. uint256 public constant VERSION = 0; /// @notice Storage slot that the required protocol version is stored at. bytes32 public constant REQUIRED_SLOT = bytes32(uint256(keccak256("protocolversion.required")) - 1); /// @notice Storage slot that the recommended protocol version is stored at. bytes32 public constant RECOMMENDED_SLOT = bytes32(uint256(keccak256("protocolversion.recommended")) - 1); /// @notice Emitted when configuration is updated. /// @param version ProtocolVersion version. /// @param updateType Type of update. /// @param data Encoded update data. event ConfigUpdate(uint256 indexed version, UpdateType indexed updateType, bytes data); /// @notice Semantic version. /// @custom:semver 1.0.0 string public constant version = "1.0.0"; /// @notice Constructs the ProtocolVersion contract. Cannot set /// the owner to `address(0)` due to the Ownable contract's /// implementation, so set it to `address(0xdEaD)` /// A zero version is considered empty and is ignored by nodes. constructor() { initialize({ _owner: address(0xdEaD), _required: ProtocolVersion.wrap(uint256(0)), _recommended: ProtocolVersion.wrap(uint256(0)) }); } /// @notice Initializer. /// @param _owner Initial owner of the contract. /// @param _required Required protocol version to operate on this chain. /// @param _recommended Recommended protocol version to operate on thi chain. function initialize(address _owner, ProtocolVersion _required, ProtocolVersion _recommended) public initializer { __Ownable_init(); transferOwnership(_owner); _setRequired(_required); _setRecommended(_recommended); } /// @notice High level getter for the required protocol version. /// @return out_ Required protocol version to sync to the head of the chain. function required() external view returns (ProtocolVersion out_) { out_ = ProtocolVersion.wrap(Storage.getUint(REQUIRED_SLOT)); } /// @notice Updates the required protocol version. Can only be called by the owner. /// @param _required New required protocol version. function setRequired(ProtocolVersion _required) external onlyOwner { _setRequired(_required); } /// @notice Internal function for updating the required protocol version. /// @param _required New required protocol version. function _setRequired(ProtocolVersion _required) internal { Storage.setUint(REQUIRED_SLOT, ProtocolVersion.unwrap(_required)); bytes memory data = abi.encode(_required); emit ConfigUpdate(VERSION, UpdateType.REQUIRED_PROTOCOL_VERSION, data); } /// @notice High level getter for the recommended protocol version. /// @return out_ Recommended protocol version to sync to the head of the chain. function recommended() external view returns (ProtocolVersion out_) { out_ = ProtocolVersion.wrap(Storage.getUint(RECOMMENDED_SLOT)); } /// @notice Updates the recommended protocol version. Can only be called by the owner. /// @param _recommended New recommended protocol version. function setRecommended(ProtocolVersion _recommended) external onlyOwner { _setRecommended(_recommended); } /// @notice Internal function for updating the recommended protocol version. /// @param _recommended New recommended protocol version. function _setRecommended(ProtocolVersion _recommended) internal { Storage.setUint(RECOMMENDED_SLOT, ProtocolVersion.unwrap(_recommended)); bytes memory data = abi.encode(_recommended); emit ConfigUpdate(VERSION, UpdateType.RECOMMENDED_PROTOCOL_VERSION, data); } }
// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v4.7.0) (access/Ownable.sol) pragma solidity ^0.8.0; import "../utils/ContextUpgradeable.sol"; import "../proxy/utils/Initializable.sol"; /** * @dev Contract module which provides a basic access control mechanism, where * there is an account (an owner) that can be granted exclusive access to * specific functions. * * By default, the owner account will be the one that deploys the contract. This * can later be changed with {transferOwnership}. * * This module is used through inheritance. It will make available the modifier * `onlyOwner`, which can be applied to your functions to restrict their use to * the owner. */ abstract contract OwnableUpgradeable is Initializable, ContextUpgradeable { address private _owner; event OwnershipTransferred(address indexed previousOwner, address indexed newOwner); /** * @dev Initializes the contract setting the deployer as the initial owner. */ function __Ownable_init() internal onlyInitializing { __Ownable_init_unchained(); } function __Ownable_init_unchained() internal onlyInitializing { _transferOwnership(_msgSender()); } /** * @dev Throws if called by any account other than the owner. */ modifier onlyOwner() { _checkOwner(); _; } /** * @dev Returns the address of the current owner. */ function owner() public view virtual returns (address) { return _owner; } /** * @dev Throws if the sender is not the owner. */ function _checkOwner() internal view virtual { require(owner() == _msgSender(), "Ownable: caller is not the owner"); } /** * @dev Leaves the contract without owner. It will not be possible to call * `onlyOwner` functions anymore. Can only be called by the current owner. * * NOTE: Renouncing ownership will leave the contract without an owner, * thereby removing any functionality that is only available to the owner. */ function renounceOwnership() public virtual onlyOwner { _transferOwnership(address(0)); } /** * @dev Transfers ownership of the contract to a new account (`newOwner`). * Can only be called by the current owner. */ function transferOwnership(address newOwner) public virtual onlyOwner { require(newOwner != address(0), "Ownable: new owner is the zero address"); _transferOwnership(newOwner); } /** * @dev Transfers ownership of the contract to a new account (`newOwner`). * Internal function without access restriction. */ function _transferOwnership(address newOwner) internal virtual { address oldOwner = _owner; _owner = newOwner; emit OwnershipTransferred(oldOwner, newOwner); } /** * @dev This empty reserved space is put in place to allow future versions to add new * variables without shifting down storage in the inheritance chain. * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps */ uint256[49] private __gap; }
// SPDX-License-Identifier: MIT pragma solidity ^0.8.0; /// @title ISemver /// @notice ISemver is a simple contract for ensuring that contracts are /// versioned using semantic versioning. interface ISemver { /// @notice Getter for the semantic version of the contract. This is not /// meant to be used onchain but instead meant to be used by offchain /// tooling. /// @return Semver contract version as a string. function version() external view returns (string memory); }
// SPDX-License-Identifier: MIT pragma solidity ^0.8.0; /// @title Storage /// @notice Storage handles reading and writing to arbitary storage locations library Storage { /// @notice Returns an address stored in an arbitrary storage slot. /// These storage slots decouple the storage layout from /// solc's automation. /// @param _slot The storage slot to retrieve the address from. function getAddress(bytes32 _slot) internal view returns (address addr_) { assembly { addr_ := sload(_slot) } } /// @notice Stores an address in an arbitrary storage slot, `_slot`. /// @param _slot The storage slot to store the address in. /// @param _address The protocol version to store /// @dev WARNING! This function must be used cautiously, as it allows for overwriting addresses /// in arbitrary storage slots. function setAddress(bytes32 _slot, address _address) internal { assembly { sstore(_slot, _address) } } /// @notice Returns a uint256 stored in an arbitrary storage slot. /// These storage slots decouple the storage layout from /// solc's automation. /// @param _slot The storage slot to retrieve the address from. function getUint(bytes32 _slot) internal view returns (uint256 value_) { assembly { value_ := sload(_slot) } } /// @notice Stores a value in an arbitrary storage slot, `_slot`. /// @param _slot The storage slot to store the address in. /// @param _value The protocol version to store /// @dev WARNING! This function must be used cautiously, as it allows for overwriting values /// in arbitrary storage slots. function setUint(bytes32 _slot, uint256 _value) internal { assembly { sstore(_slot, _value) } } /// @notice Returns a bytes32 stored in an arbitrary storage slot. /// These storage slots decouple the storage layout from /// solc's automation. /// @param _slot The storage slot to retrieve the address from. function getBytes32(bytes32 _slot) internal view returns (bytes32 value_) { assembly { value_ := sload(_slot) } } /// @notice Stores a bytes32 value in an arbitrary storage slot, `_slot`. /// @param _slot The storage slot to store the address in. /// @param _value The protocol version to store /// @dev WARNING! This function must be used cautiously, as it allows for overwriting values /// in arbitrary storage slots. function setBytes32(bytes32 _slot, bytes32 _value) internal { assembly { sstore(_slot, _value) } } }
// SPDX-License-Identifier: MIT pragma solidity ^0.8.0; import { ResourceMetering } from "../L1/ResourceMetering.sol"; /// @title Constants /// @notice Constants is a library for storing constants. Simple! Don't put everything in here, just /// the stuff used in multiple contracts. Constants that only apply to a single contract /// should be defined in that contract instead. library Constants { /// @notice Special address to be used as the tx origin for gas estimation calls in the /// OptimismPortal and CrossDomainMessenger calls. You only need to use this address if /// the minimum gas limit specified by the user is not actually enough to execute the /// given message and you're attempting to estimate the actual necessary gas limit. We /// use address(1) because it's the ecrecover precompile and therefore guaranteed to /// never have any code on any EVM chain. address internal constant ESTIMATION_ADDRESS = address(1); /// @notice Value used for the L2 sender storage slot in both the OptimismPortal and the /// CrossDomainMessenger contracts before an actual sender is set. This value is /// non-zero to reduce the gas cost of message passing transactions. address internal constant DEFAULT_L2_SENDER = 0x000000000000000000000000000000000000dEaD; /// @notice The storage slot that holds the address of a proxy implementation. /// @dev `bytes32(uint256(keccak256('eip1967.proxy.implementation')) - 1)` bytes32 internal constant PROXY_IMPLEMENTATION_ADDRESS = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc; /// @notice The storage slot that holds the address of the owner. /// @dev `bytes32(uint256(keccak256('eip1967.proxy.admin')) - 1)` bytes32 internal constant PROXY_OWNER_ADDRESS = 0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103; /// @notice Returns the default values for the ResourceConfig. These are the recommended values /// for a production network. function DEFAULT_RESOURCE_CONFIG() internal pure returns (ResourceMetering.ResourceConfig memory) { ResourceMetering.ResourceConfig memory config = ResourceMetering.ResourceConfig({ maxResourceLimit: 20_000_000, elasticityMultiplier: 10, baseFeeMaxChangeDenominator: 8, minimumBaseFee: 1 gwei, systemTxMaxGas: 1_000_000, maximumBaseFee: type(uint128).max }); return config; } }
// SPDX-License-Identifier: MIT // OpenZeppelin Contracts v4.4.1 (utils/Context.sol) pragma solidity ^0.8.0; import "../proxy/utils/Initializable.sol"; /** * @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 ContextUpgradeable is Initializable { function __Context_init() internal onlyInitializing { } function __Context_init_unchained() internal onlyInitializing { } function _msgSender() internal view virtual returns (address) { return msg.sender; } function _msgData() internal view virtual returns (bytes calldata) { return msg.data; } /** * @dev This empty reserved space is put in place to allow future versions to add new * variables without shifting down storage in the inheritance chain. * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps */ uint256[50] private __gap; }
// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v4.7.0) (proxy/utils/Initializable.sol) pragma solidity ^0.8.2; import "../../utils/AddressUpgradeable.sol"; /** * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect. * * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in * case an upgrade adds a module that needs to be initialized. * * For example: * * [.hljs-theme-light.nopadding] * ``` * contract MyToken is ERC20Upgradeable { * function initialize() initializer public { * __ERC20_init("MyToken", "MTK"); * } * } * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable { * function initializeV2() reinitializer(2) public { * __ERC20Permit_init("MyToken"); * } * } * ``` * * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}. * * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity. * * [CAUTION] * ==== * Avoid leaving a contract uninitialized. * * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed: * * [.hljs-theme-light.nopadding] * ``` * /// @custom:oz-upgrades-unsafe-allow constructor * constructor() { * _disableInitializers(); * } * ``` * ==== */ abstract contract Initializable { /** * @dev Indicates that the contract has been initialized. * @custom:oz-retyped-from bool */ uint8 private _initialized; /** * @dev Indicates that the contract is in the process of being initialized. */ bool private _initializing; /** * @dev Triggered when the contract has been initialized or reinitialized. */ event Initialized(uint8 version); /** * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope, * `onlyInitializing` functions can be used to initialize parent contracts. Equivalent to `reinitializer(1)`. */ modifier initializer() { bool isTopLevelCall = !_initializing; require( (isTopLevelCall && _initialized < 1) || (!AddressUpgradeable.isContract(address(this)) && _initialized == 1), "Initializable: contract is already initialized" ); _initialized = 1; if (isTopLevelCall) { _initializing = true; } _; if (isTopLevelCall) { _initializing = false; emit Initialized(1); } } /** * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be * used to initialize parent contracts. * * `initializer` is equivalent to `reinitializer(1)`, so a reinitializer may be used after the original * initialization step. This is essential to configure modules that are added through upgrades and that require * initialization. * * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in * a contract, executing them in the right order is up to the developer or operator. */ modifier reinitializer(uint8 version) { require(!_initializing && _initialized < version, "Initializable: contract is already initialized"); _initialized = version; _initializing = true; _; _initializing = false; emit Initialized(version); } /** * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the * {initializer} and {reinitializer} modifiers, directly or indirectly. */ modifier onlyInitializing() { require(_initializing, "Initializable: contract is not initializing"); _; } /** * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call. * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized * to any version. It is recommended to use this to lock implementation contracts that are designed to be called * through proxies. */ function _disableInitializers() internal virtual { require(!_initializing, "Initializable: contract is initializing"); if (_initialized < type(uint8).max) { _initialized = type(uint8).max; emit Initialized(type(uint8).max); } } }
// SPDX-License-Identifier: MIT pragma solidity 0.8.15; import { Initializable } from "@openzeppelin/contracts/proxy/utils/Initializable.sol"; import { Math } from "@openzeppelin/contracts/utils/math/Math.sol"; import { Burn } from "src/libraries/Burn.sol"; import { Arithmetic } from "src/libraries/Arithmetic.sol"; /// @custom:upgradeable /// @title ResourceMetering /// @notice ResourceMetering implements an EIP-1559 style resource metering system where pricing /// updates automatically based on current demand. abstract contract ResourceMetering is Initializable { /// @notice Represents the various parameters that control the way in which resources are /// metered. Corresponds to the EIP-1559 resource metering system. /// @custom:field prevBaseFee Base fee from the previous block(s). /// @custom:field prevBoughtGas Amount of gas bought so far in the current block. /// @custom:field prevBlockNum Last block number that the base fee was updated. struct ResourceParams { uint128 prevBaseFee; uint64 prevBoughtGas; uint64 prevBlockNum; } /// @notice Represents the configuration for the EIP-1559 based curve for the deposit gas /// market. These values should be set with care as it is possible to set them in /// a way that breaks the deposit gas market. The target resource limit is defined as /// maxResourceLimit / elasticityMultiplier. This struct was designed to fit within a /// single word. There is additional space for additions in the future. /// @custom:field maxResourceLimit Represents the maximum amount of deposit gas that /// can be purchased per block. /// @custom:field elasticityMultiplier Determines the target resource limit along with /// the resource limit. /// @custom:field baseFeeMaxChangeDenominator Determines max change on fee per block. /// @custom:field minimumBaseFee The min deposit base fee, it is clamped to this /// value. /// @custom:field systemTxMaxGas The amount of gas supplied to the system /// transaction. This should be set to the same /// number that the op-node sets as the gas limit /// for the system transaction. /// @custom:field maximumBaseFee The max deposit base fee, it is clamped to this /// value. struct ResourceConfig { uint32 maxResourceLimit; uint8 elasticityMultiplier; uint8 baseFeeMaxChangeDenominator; uint32 minimumBaseFee; uint32 systemTxMaxGas; uint128 maximumBaseFee; } /// @notice EIP-1559 style gas parameters. ResourceParams public params; /// @notice Reserve extra slots (to a total of 50) in the storage layout for future upgrades. uint256[48] private __gap; /// @notice Meters access to a function based an amount of a requested resource. /// @param _amount Amount of the resource requested. modifier metered(uint64 _amount) { // Record initial gas amount so we can refund for it later. uint256 initialGas = gasleft(); // Run the underlying function. _; // Run the metering function. _metered(_amount, initialGas); } /// @notice An internal function that holds all of the logic for metering a resource. /// @param _amount Amount of the resource requested. /// @param _initialGas The amount of gas before any modifier execution. function _metered(uint64 _amount, uint256 _initialGas) internal { // Update block number and base fee if necessary. uint256 blockDiff = block.number - params.prevBlockNum; ResourceConfig memory config = _resourceConfig(); int256 targetResourceLimit = int256(uint256(config.maxResourceLimit)) / int256(uint256(config.elasticityMultiplier)); if (blockDiff > 0) { // Handle updating EIP-1559 style gas parameters. We use EIP-1559 to restrict the rate // at which deposits can be created and therefore limit the potential for deposits to // spam the L2 system. Fee scheme is very similar to EIP-1559 with minor changes. int256 gasUsedDelta = int256(uint256(params.prevBoughtGas)) - targetResourceLimit; int256 baseFeeDelta = (int256(uint256(params.prevBaseFee)) * gasUsedDelta) / (targetResourceLimit * int256(uint256(config.baseFeeMaxChangeDenominator))); // Update base fee by adding the base fee delta and clamp the resulting value between // min and max. int256 newBaseFee = Arithmetic.clamp({ _value: int256(uint256(params.prevBaseFee)) + baseFeeDelta, _min: int256(uint256(config.minimumBaseFee)), _max: int256(uint256(config.maximumBaseFee)) }); // If we skipped more than one block, we also need to account for every empty block. // Empty block means there was no demand for deposits in that block, so we should // reflect this lack of demand in the fee. if (blockDiff > 1) { // Update the base fee by repeatedly applying the exponent 1-(1/change_denominator) // blockDiff - 1 times. Simulates multiple empty blocks. Clamp the resulting value // between min and max. newBaseFee = Arithmetic.clamp({ _value: Arithmetic.cdexp({ _coefficient: newBaseFee, _denominator: int256(uint256(config.baseFeeMaxChangeDenominator)), _exponent: int256(blockDiff - 1) }), _min: int256(uint256(config.minimumBaseFee)), _max: int256(uint256(config.maximumBaseFee)) }); } // Update new base fee, reset bought gas, and update block number. params.prevBaseFee = uint128(uint256(newBaseFee)); params.prevBoughtGas = 0; params.prevBlockNum = uint64(block.number); } // Make sure we can actually buy the resource amount requested by the user. params.prevBoughtGas += _amount; require( int256(uint256(params.prevBoughtGas)) <= int256(uint256(config.maxResourceLimit)), "ResourceMetering: cannot buy more gas than available gas limit" ); // Determine the amount of ETH to be paid. uint256 resourceCost = uint256(_amount) * uint256(params.prevBaseFee); // We currently charge for this ETH amount as an L1 gas burn, so we convert the ETH amount // into gas by dividing by the L1 base fee. We assume a minimum base fee of 1 gwei to avoid // division by zero for L1s that don't support 1559 or to avoid excessive gas burns during // periods of extremely low L1 demand. One-day average gas fee hasn't dipped below 1 gwei // during any 1 day period in the last 5 years, so should be fine. uint256 gasCost = resourceCost / Math.max(block.basefee, 1 gwei); // Give the user a refund based on the amount of gas they used to do all of the work up to // this point. Since we're at the end of the modifier, this should be pretty accurate. Acts // effectively like a dynamic stipend (with a minimum value). uint256 usedGas = _initialGas - gasleft(); if (gasCost > usedGas) { Burn.gas(gasCost - usedGas); } } /// @notice Virtual function that returns the resource config. /// Contracts that inherit this contract must implement this function. /// @return ResourceConfig function _resourceConfig() internal virtual returns (ResourceConfig memory); /// @notice Sets initial resource parameter values. /// This function must either be called by the initializer function of an upgradeable /// child contract. // solhint-disable-next-line func-name-mixedcase function __ResourceMetering_init() internal onlyInitializing { params = ResourceParams({ prevBaseFee: 1 gwei, prevBoughtGas: 0, prevBlockNum: uint64(block.number) }); } }
// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v4.7.0) (utils/Address.sol) pragma solidity ^0.8.1; /** * @dev Collection of functions related to the address type */ library AddressUpgradeable { /** * @dev Returns true if `account` is a contract. * * [IMPORTANT] * ==== * It is unsafe to assume that an address for which this function returns * false is an externally-owned account (EOA) and not a contract. * * Among others, `isContract` will return false for the following * types of addresses: * * - an externally-owned account * - a contract in construction * - an address where a contract will be created * - an address where a contract lived, but was destroyed * ==== * * [IMPORTANT] * ==== * You shouldn't rely on `isContract` to protect against flash loan attacks! * * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract * constructor. * ==== */ function isContract(address account) internal view returns (bool) { // This method relies on extcodesize/address.code.length, which returns 0 // for contracts in construction, since the code is only stored at the end // of the constructor execution. return account.code.length > 0; } /** * @dev Replacement for Solidity's `transfer`: sends `amount` wei to * `recipient`, forwarding all available gas and reverting on errors. * * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost * of certain opcodes, possibly making contracts go over the 2300 gas limit * imposed by `transfer`, making them unable to receive funds via * `transfer`. {sendValue} removes this limitation. * * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more]. * * IMPORTANT: because control is transferred to `recipient`, care must be * taken to not create reentrancy vulnerabilities. Consider using * {ReentrancyGuard} or the * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern]. */ function sendValue(address payable recipient, uint256 amount) internal { require(address(this).balance >= amount, "Address: insufficient balance"); (bool success, ) = recipient.call{value: amount}(""); require(success, "Address: unable to send value, recipient may have reverted"); } /** * @dev Performs a Solidity function call using a low level `call`. A * plain `call` is an unsafe replacement for a function call: use this * function instead. * * If `target` reverts with a revert reason, it is bubbled up by this * function (like regular Solidity function calls). * * Returns the raw returned data. To convert to the expected return value, * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`]. * * Requirements: * * - `target` must be a contract. * - calling `target` with `data` must not revert. * * _Available since v3.1._ */ function functionCall(address target, bytes memory data) internal returns (bytes memory) { return functionCall(target, data, "Address: low-level call failed"); } /** * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with * `errorMessage` as a fallback revert reason when `target` reverts. * * _Available since v3.1._ */ function functionCall( address target, bytes memory data, string memory errorMessage ) internal returns (bytes memory) { return functionCallWithValue(target, data, 0, errorMessage); } /** * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], * but also transferring `value` wei to `target`. * * Requirements: * * - the calling contract must have an ETH balance of at least `value`. * - the called Solidity function must be `payable`. * * _Available since v3.1._ */ function functionCallWithValue( address target, bytes memory data, uint256 value ) internal returns (bytes memory) { return functionCallWithValue(target, data, value, "Address: low-level call with value failed"); } /** * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but * with `errorMessage` as a fallback revert reason when `target` reverts. * * _Available since v3.1._ */ function functionCallWithValue( address target, bytes memory data, uint256 value, string memory errorMessage ) internal returns (bytes memory) { require(address(this).balance >= value, "Address: insufficient balance for call"); require(isContract(target), "Address: call to non-contract"); (bool success, bytes memory returndata) = target.call{value: value}(data); return verifyCallResult(success, returndata, errorMessage); } /** * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], * but performing a static call. * * _Available since v3.3._ */ function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) { return functionStaticCall(target, data, "Address: low-level static call failed"); } /** * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`], * but performing a static call. * * _Available since v3.3._ */ function functionStaticCall( address target, bytes memory data, string memory errorMessage ) internal view returns (bytes memory) { require(isContract(target), "Address: static call to non-contract"); (bool success, bytes memory returndata) = target.staticcall(data); return verifyCallResult(success, returndata, errorMessage); } /** * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the * revert reason using the provided one. * * _Available since v4.3._ */ function verifyCallResult( bool success, bytes memory returndata, string memory errorMessage ) internal pure returns (bytes memory) { if (success) { return returndata; } else { // Look for revert reason and bubble it up if present if (returndata.length > 0) { // The easiest way to bubble the revert reason is using memory via assembly /// @solidity memory-safe-assembly assembly { let returndata_size := mload(returndata) revert(add(32, returndata), returndata_size) } } else { revert(errorMessage); } } } }
// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v4.7.0) (proxy/utils/Initializable.sol) pragma solidity ^0.8.2; import "../../utils/Address.sol"; /** * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect. * * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in * case an upgrade adds a module that needs to be initialized. * * For example: * * [.hljs-theme-light.nopadding] * ``` * contract MyToken is ERC20Upgradeable { * function initialize() initializer public { * __ERC20_init("MyToken", "MTK"); * } * } * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable { * function initializeV2() reinitializer(2) public { * __ERC20Permit_init("MyToken"); * } * } * ``` * * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}. * * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity. * * [CAUTION] * ==== * Avoid leaving a contract uninitialized. * * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed: * * [.hljs-theme-light.nopadding] * ``` * /// @custom:oz-upgrades-unsafe-allow constructor * constructor() { * _disableInitializers(); * } * ``` * ==== */ abstract contract Initializable { /** * @dev Indicates that the contract has been initialized. * @custom:oz-retyped-from bool */ uint8 private _initialized; /** * @dev Indicates that the contract is in the process of being initialized. */ bool private _initializing; /** * @dev Triggered when the contract has been initialized or reinitialized. */ event Initialized(uint8 version); /** * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope, * `onlyInitializing` functions can be used to initialize parent contracts. Equivalent to `reinitializer(1)`. */ modifier initializer() { bool isTopLevelCall = !_initializing; require( (isTopLevelCall && _initialized < 1) || (!Address.isContract(address(this)) && _initialized == 1), "Initializable: contract is already initialized" ); _initialized = 1; if (isTopLevelCall) { _initializing = true; } _; if (isTopLevelCall) { _initializing = false; emit Initialized(1); } } /** * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be * used to initialize parent contracts. * * `initializer` is equivalent to `reinitializer(1)`, so a reinitializer may be used after the original * initialization step. This is essential to configure modules that are added through upgrades and that require * initialization. * * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in * a contract, executing them in the right order is up to the developer or operator. */ modifier reinitializer(uint8 version) { require(!_initializing && _initialized < version, "Initializable: contract is already initialized"); _initialized = version; _initializing = true; _; _initializing = false; emit Initialized(version); } /** * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the * {initializer} and {reinitializer} modifiers, directly or indirectly. */ modifier onlyInitializing() { require(_initializing, "Initializable: contract is not initializing"); _; } /** * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call. * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized * to any version. It is recommended to use this to lock implementation contracts that are designed to be called * through proxies. */ function _disableInitializers() internal virtual { require(!_initializing, "Initializable: contract is initializing"); if (_initialized < type(uint8).max) { _initialized = type(uint8).max; emit Initialized(type(uint8).max); } } }
// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v4.7.0) (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. It 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)`. // We also know that `k`, the position of the most significant bit, is such that `msb(a) = 2**k`. // This gives `2**k < a <= 2**(k+1)` → `2**(k/2) <= sqrt(a) < 2 ** (k/2+1)`. // Using an algorithm similar to the msb conmputation, we are able to compute `result = 2**(k/2)` which is a // good first aproximation of `sqrt(a)` with at least 1 correct bit. uint256 result = 1; uint256 x = a; if (x >> 128 > 0) { x >>= 128; result <<= 64; } if (x >> 64 > 0) { x >>= 64; result <<= 32; } if (x >> 32 > 0) { x >>= 32; result <<= 16; } if (x >> 16 > 0) { x >>= 16; result <<= 8; } if (x >> 8 > 0) { x >>= 8; result <<= 4; } if (x >> 4 > 0) { x >>= 4; result <<= 2; } if (x >> 2 > 0) { result <<= 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) { uint256 result = sqrt(a); if (rounding == Rounding.Up && result * result < a) { result += 1; } return result; } }
// SPDX-License-Identifier: MIT pragma solidity 0.8.15; /// @title Burn /// @notice Utilities for burning stuff. library Burn { /// @notice Burns a given amount of ETH. /// @param _amount Amount of ETH to burn. function eth(uint256 _amount) internal { new Burner{ value: _amount }(); } /// @notice Burns a given amount of gas. /// @param _amount Amount of gas to burn. function gas(uint256 _amount) internal view { uint256 i = 0; uint256 initialGas = gasleft(); while (initialGas - gasleft() < _amount) { ++i; } } } /// @title Burner /// @notice Burner self-destructs on creation and sends all ETH to itself, removing all ETH given to /// the contract from the circulating supply. Self-destructing is the only way to remove ETH /// from the circulating supply. contract Burner { constructor() payable { selfdestruct(payable(address(this))); } }
// SPDX-License-Identifier: MIT pragma solidity 0.8.15; import { SignedMath } from "@openzeppelin/contracts/utils/math/SignedMath.sol"; import { FixedPointMathLib } from "@rari-capital/solmate/src/utils/FixedPointMathLib.sol"; /// @title Arithmetic /// @notice Even more math than before. library Arithmetic { /// @notice Clamps a value between a minimum and maximum. /// @param _value The value to clamp. /// @param _min The minimum value. /// @param _max The maximum value. /// @return The clamped value. function clamp(int256 _value, int256 _min, int256 _max) internal pure returns (int256) { return SignedMath.min(SignedMath.max(_value, _min), _max); } /// @notice (c)oefficient (d)enominator (exp)onentiation function. /// Returns the result of: c * (1 - 1/d)^exp. /// @param _coefficient Coefficient of the function. /// @param _denominator Fractional denominator. /// @param _exponent Power function exponent. /// @return Result of c * (1 - 1/d)^exp. function cdexp(int256 _coefficient, int256 _denominator, int256 _exponent) internal pure returns (int256) { return (_coefficient * (FixedPointMathLib.powWad(1e18 - (1e18 / _denominator), _exponent * 1e18))) / 1e18; } }
// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v4.7.0) (utils/Address.sol) pragma solidity ^0.8.1; /** * @dev Collection of functions related to the address type */ library Address { /** * @dev Returns true if `account` is a contract. * * [IMPORTANT] * ==== * It is unsafe to assume that an address for which this function returns * false is an externally-owned account (EOA) and not a contract. * * Among others, `isContract` will return false for the following * types of addresses: * * - an externally-owned account * - a contract in construction * - an address where a contract will be created * - an address where a contract lived, but was destroyed * ==== * * [IMPORTANT] * ==== * You shouldn't rely on `isContract` to protect against flash loan attacks! * * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract * constructor. * ==== */ function isContract(address account) internal view returns (bool) { // This method relies on extcodesize/address.code.length, which returns 0 // for contracts in construction, since the code is only stored at the end // of the constructor execution. return account.code.length > 0; } /** * @dev Replacement for Solidity's `transfer`: sends `amount` wei to * `recipient`, forwarding all available gas and reverting on errors. * * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost * of certain opcodes, possibly making contracts go over the 2300 gas limit * imposed by `transfer`, making them unable to receive funds via * `transfer`. {sendValue} removes this limitation. * * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more]. * * IMPORTANT: because control is transferred to `recipient`, care must be * taken to not create reentrancy vulnerabilities. Consider using * {ReentrancyGuard} or the * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern]. */ function sendValue(address payable recipient, uint256 amount) internal { require(address(this).balance >= amount, "Address: insufficient balance"); (bool success, ) = recipient.call{value: amount}(""); require(success, "Address: unable to send value, recipient may have reverted"); } /** * @dev Performs a Solidity function call using a low level `call`. A * plain `call` is an unsafe replacement for a function call: use this * function instead. * * If `target` reverts with a revert reason, it is bubbled up by this * function (like regular Solidity function calls). * * Returns the raw returned data. To convert to the expected return value, * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`]. * * Requirements: * * - `target` must be a contract. * - calling `target` with `data` must not revert. * * _Available since v3.1._ */ function functionCall(address target, bytes memory data) internal returns (bytes memory) { return functionCall(target, data, "Address: low-level call failed"); } /** * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with * `errorMessage` as a fallback revert reason when `target` reverts. * * _Available since v3.1._ */ function functionCall( address target, bytes memory data, string memory errorMessage ) internal returns (bytes memory) { return functionCallWithValue(target, data, 0, errorMessage); } /** * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], * but also transferring `value` wei to `target`. * * Requirements: * * - the calling contract must have an ETH balance of at least `value`. * - the called Solidity function must be `payable`. * * _Available since v3.1._ */ function functionCallWithValue( address target, bytes memory data, uint256 value ) internal returns (bytes memory) { return functionCallWithValue(target, data, value, "Address: low-level call with value failed"); } /** * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but * with `errorMessage` as a fallback revert reason when `target` reverts. * * _Available since v3.1._ */ function functionCallWithValue( address target, bytes memory data, uint256 value, string memory errorMessage ) internal returns (bytes memory) { require(address(this).balance >= value, "Address: insufficient balance for call"); require(isContract(target), "Address: call to non-contract"); (bool success, bytes memory returndata) = target.call{value: value}(data); return verifyCallResult(success, returndata, errorMessage); } /** * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], * but performing a static call. * * _Available since v3.3._ */ function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) { return functionStaticCall(target, data, "Address: low-level static call failed"); } /** * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`], * but performing a static call. * * _Available since v3.3._ */ function functionStaticCall( address target, bytes memory data, string memory errorMessage ) internal view returns (bytes memory) { require(isContract(target), "Address: static call to non-contract"); (bool success, bytes memory returndata) = target.staticcall(data); return verifyCallResult(success, returndata, errorMessage); } /** * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], * but performing a delegate call. * * _Available since v3.4._ */ function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) { return functionDelegateCall(target, data, "Address: low-level delegate call failed"); } /** * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`], * but performing a delegate call. * * _Available since v3.4._ */ function functionDelegateCall( address target, bytes memory data, string memory errorMessage ) internal returns (bytes memory) { require(isContract(target), "Address: delegate call to non-contract"); (bool success, bytes memory returndata) = target.delegatecall(data); return verifyCallResult(success, returndata, errorMessage); } /** * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the * revert reason using the provided one. * * _Available since v4.3._ */ function verifyCallResult( bool success, bytes memory returndata, string memory errorMessage ) internal pure returns (bytes memory) { if (success) { return returndata; } else { // Look for revert reason and bubble it up if present if (returndata.length > 0) { // The easiest way to bubble the revert reason is using memory via assembly /// @solidity memory-safe-assembly assembly { let returndata_size := mload(returndata) revert(add(32, returndata), returndata_size) } } else { revert(errorMessage); } } } }
// SPDX-License-Identifier: MIT // OpenZeppelin Contracts (last updated v4.5.0) (utils/math/SignedMath.sol) pragma solidity ^0.8.0; /** * @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); } } }
// SPDX-License-Identifier: MIT pragma solidity >=0.8.0; /// @notice Arithmetic library with operations for fixed-point numbers. /// @author Solmate (https://github.com/Rari-Capital/solmate/blob/main/src/utils/FixedPointMathLib.sol) library FixedPointMathLib { /*////////////////////////////////////////////////////////////// SIMPLIFIED FIXED POINT OPERATIONS //////////////////////////////////////////////////////////////*/ uint256 internal constant WAD = 1e18; // The scalar of ETH and most ERC20s. function mulWadDown(uint256 x, uint256 y) internal pure returns (uint256) { return mulDivDown(x, y, WAD); // Equivalent to (x * y) / WAD rounded down. } function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256) { return mulDivUp(x, y, WAD); // Equivalent to (x * y) / WAD rounded up. } function divWadDown(uint256 x, uint256 y) internal pure returns (uint256) { return mulDivDown(x, WAD, y); // Equivalent to (x * WAD) / y rounded down. } function divWadUp(uint256 x, uint256 y) internal pure returns (uint256) { return mulDivUp(x, WAD, y); // Equivalent to (x * WAD) / y rounded up. } function powWad(int256 x, int256 y) internal pure returns (int256) { // Equivalent to x to the power of y because x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y) return expWad((lnWad(x) * y) / int256(WAD)); // Using ln(x) means x must be greater than 0. } function expWad(int256 x) internal pure returns (int256 r) { unchecked { // When the result is < 0.5 we return zero. This happens when // x <= floor(log(0.5e18) * 1e18) ~ -42e18 if (x <= -42139678854452767551) return 0; // When the result is > (2**255 - 1) / 1e18 we can not represent it as an // int. This happens when x >= floor(log((2**255 - 1) / 1e18) * 1e18) ~ 135. if (x >= 135305999368893231589) revert("EXP_OVERFLOW"); // x is now in the range (-42, 136) * 1e18. Convert to (-42, 136) * 2**96 // for more intermediate precision and a binary basis. This base conversion // is a multiplication by 1e18 / 2**96 = 5**18 / 2**78. x = (x << 78) / 5**18; // Reduce range of x to (-½ ln 2, ½ ln 2) * 2**96 by factoring out powers // of two such that exp(x) = exp(x') * 2**k, where k is an integer. // Solving this gives k = round(x / log(2)) and x' = x - k * log(2). int256 k = ((x << 96) / 54916777467707473351141471128 + 2**95) >> 96; x = x - k * 54916777467707473351141471128; // k is in the range [-61, 195]. // Evaluate using a (6, 7)-term rational approximation. // p is made monic, we'll multiply by a scale factor later. int256 y = x + 1346386616545796478920950773328; y = ((y * x) >> 96) + 57155421227552351082224309758442; int256 p = y + x - 94201549194550492254356042504812; p = ((p * y) >> 96) + 28719021644029726153956944680412240; p = p * x + (4385272521454847904659076985693276 << 96); // We leave p in 2**192 basis so we don't need to scale it back up for the division. int256 q = x - 2855989394907223263936484059900; q = ((q * x) >> 96) + 50020603652535783019961831881945; q = ((q * x) >> 96) - 533845033583426703283633433725380; q = ((q * x) >> 96) + 3604857256930695427073651918091429; q = ((q * x) >> 96) - 14423608567350463180887372962807573; q = ((q * x) >> 96) + 26449188498355588339934803723976023; assembly { // Div in assembly because solidity adds a zero check despite the unchecked. // The q polynomial won't have zeros in the domain as all its roots are complex. // No scaling is necessary because p is already 2**96 too large. r := sdiv(p, q) } // r should be in the range (0.09, 0.25) * 2**96. // We now need to multiply r by: // * the scale factor s = ~6.031367120. // * the 2**k factor from the range reduction. // * the 1e18 / 2**96 factor for base conversion. // We do this all at once, with an intermediate result in 2**213 // basis, so the final right shift is always by a positive amount. r = int256((uint256(r) * 3822833074963236453042738258902158003155416615667) >> uint256(195 - k)); } } function lnWad(int256 x) internal pure returns (int256 r) { unchecked { require(x > 0, "UNDEFINED"); // We want to convert x from 10**18 fixed point to 2**96 fixed point. // We do this by multiplying by 2**96 / 10**18. But since // ln(x * C) = ln(x) + ln(C), we can simply do nothing here // and add ln(2**96 / 10**18) at the end. // Reduce range of x to (1, 2) * 2**96 // ln(2^k * x) = k * ln(2) + ln(x) int256 k = int256(log2(uint256(x))) - 96; x <<= uint256(159 - k); x = int256(uint256(x) >> 159); // Evaluate using a (8, 8)-term rational approximation. // p is made monic, we will multiply by a scale factor later. int256 p = x + 3273285459638523848632254066296; p = ((p * x) >> 96) + 24828157081833163892658089445524; p = ((p * x) >> 96) + 43456485725739037958740375743393; p = ((p * x) >> 96) - 11111509109440967052023855526967; p = ((p * x) >> 96) - 45023709667254063763336534515857; p = ((p * x) >> 96) - 14706773417378608786704636184526; p = p * x - (795164235651350426258249787498 << 96); // We leave p in 2**192 basis so we don't need to scale it back up for the division. // q is monic by convention. int256 q = x + 5573035233440673466300451813936; q = ((q * x) >> 96) + 71694874799317883764090561454958; q = ((q * x) >> 96) + 283447036172924575727196451306956; q = ((q * x) >> 96) + 401686690394027663651624208769553; q = ((q * x) >> 96) + 204048457590392012362485061816622; q = ((q * x) >> 96) + 31853899698501571402653359427138; q = ((q * x) >> 96) + 909429971244387300277376558375; assembly { // Div in assembly because solidity adds a zero check despite the unchecked. // The q polynomial is known not to have zeros in the domain. // No scaling required because p is already 2**96 too large. r := sdiv(p, q) } // r is in the range (0, 0.125) * 2**96 // Finalization, we need to: // * multiply by the scale factor s = 5.549… // * add ln(2**96 / 10**18) // * add k * ln(2) // * multiply by 10**18 / 2**96 = 5**18 >> 78 // mul s * 5e18 * 2**96, base is now 5**18 * 2**192 r *= 1677202110996718588342820967067443963516166; // add ln(2) * k * 5e18 * 2**192 r += 16597577552685614221487285958193947469193820559219878177908093499208371 * k; // add ln(2**96 / 10**18) * 5e18 * 2**192 r += 600920179829731861736702779321621459595472258049074101567377883020018308; // base conversion: mul 2**18 / 2**192 r >>= 174; } } /*////////////////////////////////////////////////////////////// LOW LEVEL FIXED POINT OPERATIONS //////////////////////////////////////////////////////////////*/ function mulDivDown( uint256 x, uint256 y, uint256 denominator ) internal pure returns (uint256 z) { assembly { // Store x * y in z for now. z := mul(x, y) // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y)) if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) { revert(0, 0) } // Divide z by the denominator. z := div(z, denominator) } } function mulDivUp( uint256 x, uint256 y, uint256 denominator ) internal pure returns (uint256 z) { assembly { // Store x * y in z for now. z := mul(x, y) // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y)) if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) { revert(0, 0) } // First, divide z - 1 by the denominator and add 1. // We allow z - 1 to underflow if z is 0, because we multiply the // end result by 0 if z is zero, ensuring we return 0 if z is zero. z := mul(iszero(iszero(z)), add(div(sub(z, 1), denominator), 1)) } } function rpow( uint256 x, uint256 n, uint256 scalar ) internal pure returns (uint256 z) { assembly { switch x case 0 { switch n case 0 { // 0 ** 0 = 1 z := scalar } default { // 0 ** n = 0 z := 0 } } default { switch mod(n, 2) case 0 { // If n is even, store scalar in z for now. z := scalar } default { // If n is odd, store x in z for now. z := x } // Shifting right by 1 is like dividing by 2. let half := shr(1, scalar) for { // Shift n right by 1 before looping to halve it. n := shr(1, n) } n { // Shift n right by 1 each iteration to halve it. n := shr(1, n) } { // Revert immediately if x ** 2 would overflow. // Equivalent to iszero(eq(div(xx, x), x)) here. if shr(128, x) { revert(0, 0) } // Store x squared. let xx := mul(x, x) // Round to the nearest number. let xxRound := add(xx, half) // Revert if xx + half overflowed. if lt(xxRound, xx) { revert(0, 0) } // Set x to scaled xxRound. x := div(xxRound, scalar) // If n is even: if mod(n, 2) { // Compute z * x. let zx := mul(z, x) // If z * x overflowed: if iszero(eq(div(zx, x), z)) { // Revert if x is non-zero. if iszero(iszero(x)) { revert(0, 0) } } // Round to the nearest number. let zxRound := add(zx, half) // Revert if zx + half overflowed. if lt(zxRound, zx) { revert(0, 0) } // Return properly scaled zxRound. z := div(zxRound, scalar) } } } } } /*////////////////////////////////////////////////////////////// GENERAL NUMBER UTILITIES //////////////////////////////////////////////////////////////*/ function sqrt(uint256 x) internal pure returns (uint256 z) { assembly { let y := x // We start y at x, which will help us make our initial estimate. z := 181 // The "correct" value is 1, but this saves a multiplication later. // This segment is to get a reasonable initial estimate for the Babylonian method. With a bad // start, the correct # of bits increases ~linearly each iteration instead of ~quadratically. // We check y >= 2^(k + 8) but shift right by k bits // each branch to ensure that if x >= 256, then y >= 256. if iszero(lt(y, 0x10000000000000000000000000000000000)) { y := shr(128, y) z := shl(64, z) } if iszero(lt(y, 0x1000000000000000000)) { y := shr(64, y) z := shl(32, z) } if iszero(lt(y, 0x10000000000)) { y := shr(32, y) z := shl(16, z) } if iszero(lt(y, 0x1000000)) { y := shr(16, y) z := shl(8, z) } // Goal was to get z*z*y within a small factor of x. More iterations could // get y in a tighter range. Currently, we will have y in [256, 256*2^16). // We ensured y >= 256 so that the relative difference between y and y+1 is small. // That's not possible if x < 256 but we can just verify those cases exhaustively. // Now, z*z*y <= x < z*z*(y+1), and y <= 2^(16+8), and either y >= 256, or x < 256. // Correctness can be checked exhaustively for x < 256, so we assume y >= 256. // Then z*sqrt(y) is within sqrt(257)/sqrt(256) of sqrt(x), or about 20bps. // For s in the range [1/256, 256], the estimate f(s) = (181/1024) * (s+1) is in the range // (1/2.84 * sqrt(s), 2.84 * sqrt(s)), with largest error when s = 1 and when s = 256 or 1/256. // Since y is in [256, 256*2^16), let a = y/65536, so that a is in [1/256, 256). Then we can estimate // sqrt(y) using sqrt(65536) * 181/1024 * (a + 1) = 181/4 * (y + 65536)/65536 = 181 * (y + 65536)/2^18. // There is no overflow risk here since y < 2^136 after the first branch above. z := shr(18, mul(z, add(y, 65536))) // A mul() is saved from starting z at 181. // Given the worst case multiplicative error of 2.84 above, 7 iterations should be enough. z := shr(1, add(z, div(x, z))) z := shr(1, add(z, div(x, z))) z := shr(1, add(z, div(x, z))) z := shr(1, add(z, div(x, z))) z := shr(1, add(z, div(x, z))) z := shr(1, add(z, div(x, z))) z := shr(1, add(z, div(x, z))) // If x+1 is a perfect square, the Babylonian method cycles between // floor(sqrt(x)) and ceil(sqrt(x)). This statement ensures we return floor. // See: https://en.wikipedia.org/wiki/Integer_square_root#Using_only_integer_division // Since the ceil is rare, we save gas on the assignment and repeat division in the rare case. // If you don't care whether the floor or ceil square root is returned, you can remove this statement. z := sub(z, lt(div(x, z), z)) } } function log2(uint256 x) internal pure returns (uint256 r) { require(x > 0, "UNDEFINED"); assembly { r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x)) r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x)))) r := or(r, shl(5, lt(0xffffffff, shr(r, x)))) r := or(r, shl(4, lt(0xffff, shr(r, x)))) r := or(r, shl(3, lt(0xff, shr(r, x)))) r := or(r, shl(2, lt(0xf, shr(r, x)))) r := or(r, shl(1, lt(0x3, shr(r, x)))) r := or(r, lt(0x1, shr(r, x))) } } }
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Contract Creation Code
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Deployed Bytecode
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A contract address hosts a smart contract, which is a set of code stored on the blockchain that runs when predetermined conditions are met. Learn more about addresses in our Knowledge Base.