Description:
Multi-signature wallet contract requiring multiple confirmations for transaction execution.
Blockchain: Ethereum
Source Code: View Code On The Blockchain
Solidity Source Code:
{{
"language": "Solidity",
"sources": {
"src/NFTAuction.sol": {
"content": "// SPDX-License-Identifier: MIT
pragma solidity ^0.8.26;
import {IERC721} from "@openzeppelin/contracts/token/ERC721/IERC721.sol";
import {IERC20} from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import {ReentrancyGuard} from "@openzeppelin/contracts/utils/ReentrancyGuard.sol";
import {Ownable} from "@openzeppelin/contracts/access/Ownable.sol";
import {FixedPointMathLib} from "solady/utils/FixedPointMathLib.sol";
import {INFTAuction} from "./interfaces/INFTAuction.sol";
contract NFTAuction is INFTAuction, ReentrancyGuard, Ownable {
using FixedPointMathLib for uint256;
// Constants
address public constant DEAD_ADDRESS =
0x000000000000000000000000000000000000dEaD;
uint256 public constant AUCTION_DECAY_RATE = 1e14; // Same as AuctionHouse - exponential decay rate
// State variables
IERC20 public immutable paymentToken;
uint256 public defaultStartPrice;
// Current auction
Auction public currentAuction;
// Queue for NFTs waiting for auction
NFTItem[] public nftQueue;
mapping(address => mapping(uint256 => uint256)) public nftQueueIndex; // nftContract => tokenId => queue index + 1
// Whitelist for NFT contracts
mapping(address => bool) public whitelistedNFTContracts;
// Constructor
constructor(
address _paymentToken,
uint256 _defaultStartPrice
) Ownable(_msgSender()) {
require(_paymentToken != address(0), "Invalid payment token");
paymentToken = IERC20(_paymentToken);
defaultStartPrice = _defaultStartPrice;
}
// Deposit NFT to queue
function depositNFT(
address nftContract,
uint256 tokenId
) external nonReentrant {
require(nftContract != address(0), "Invalid NFT contract");
require(whitelistedNFTContracts[nftContract], "NFT contract not whitelisted");
// Check if NFT is already in queue
require(
nftQueueIndex[nftContract][tokenId] == 0,
"NFT already in queue"
);
// Transfer NFT from depositor to this contract
IERC721(nftContract).transferFrom(_msgSender(), address(this), tokenId);
// Add to queue
nftQueue.push(
NFTItem({
nftContract: nftContract,
tokenId: tokenId,
depositor: _msgSender()
})
);
// Store queue index (1-indexed to differentiate from default 0)
nftQueueIndex[nftContract][tokenId] = nftQueue.length;
emit NFTDeposited(_msgSender(), nftContract, tokenId);
// If no active auction, start one
if (!currentAuction.isActive && nftQueue.length > 0) {
_startNextAuction();
}
}
// Buy current auction NFT
function buy() external nonReentrant {
require(currentAuction.isActive, "No active auction");
uint256 currentPrice = getCurrentPrice();
require(currentPrice > 0, "Invalid price");
// Transfer payment tokens from buyer to DEAD address
require(
paymentToken.transferFrom(_msgSender(), DEAD_ADDRESS, currentPrice),
"Payment transfer failed"
);
// Transfer NFT to buyer
IERC721(currentAuction.nftContract).transferFrom(
address(this),
_msgSender(),
currentAuction.tokenId
);
emit AuctionEnded(
_msgSender(),
currentAuction.nftContract,
currentAuction.tokenId,
currentPrice
);
// End current auction
currentAuction.isActive = false;
// Start next auction if NFTs available
if (nftQueue.length > 0) {
_startNextAuction();
}
}
/**
* @dev Buy NFT with tokens already transferred to contract
* Called by NFTAuctionToken when user transfers tokens to this contract
* @param buyer Address of the buyer
* @param amount Amount of tokens transferred
*/
function buyWithTokens(address buyer, uint256 amount) external returns (bool) {
require(_msgSender() == address(paymentToken), "Only payment token");
require(currentAuction.isActive, "No active auction");
uint256 currentPrice = getCurrentPrice();
require(currentPrice > 0, "Invalid price");
require(amount >= currentPrice, "Insufficient tokens");
// Tokens already transferred to this contract, now send to DEAD address
require(
paymentToken.transfer(DEAD_ADDRESS, currentPrice),
"Payment transfer failed"
);
// If buyer sent more than needed, refund excess
if (amount > currentPrice) {
require(
paymentToken.transfer(buyer, amount - currentPrice),
"Refund transfer failed"
);
}
// Transfer NFT to buyer
IERC721(currentAuction.nftContract).transferFrom(
address(this),
buyer,
currentAuction.tokenId
);
emit AuctionEnded(
buyer,
currentAuction.nftContract,
currentAuction.tokenId,
currentPrice
);
// End current auction
currentAuction.isActive = false;
// Start next auction if NFTs available
if (nftQueue.length > 0) {
_startNextAuction();
}
return true;
}
// Withdraw NFT from queue (only if not in active auction)
function withdrawNFT(uint256 queueIndex) external nonReentrant {
require(queueIndex < nftQueue.length, "Invalid queue index");
NFTItem memory item = nftQueue[queueIndex];
require(item.depositor == _msgSender(), "Not depositor");
// Cannot withdraw if in active auction
require(
!currentAuction.isActive ||
currentAuction.nftContract != item.nftContract ||
currentAuction.tokenId != item.tokenId,
"NFT in active auction"
);
// Remove from queue index mapping
delete nftQueueIndex[item.nftContract][item.tokenId];
// Remove from queue by swapping with last element
if (queueIndex < nftQueue.length - 1) {
nftQueue[queueIndex] = nftQueue[nftQueue.length - 1];
// Update index for swapped item
NFTItem memory swappedItem = nftQueue[queueIndex];
nftQueueIndex[swappedItem.nftContract][swappedItem.tokenId] =
queueIndex +
1;
}
nftQueue.pop();
// Transfer NFT back to depositor
IERC721(item.nftContract).transferFrom(
address(this),
_msgSender(),
item.tokenId
);
emit NFTWithdrawn(_msgSender(), item.nftContract, item.tokenId);
}
// Get current auction price using Dutch auction formula
function getCurrentPrice() public view returns (uint256) {
if (!currentAuction.isActive) return 0;
uint256 elapsed = block.timestamp - currentAuction.startTime;
// Use exponential decay formula from AuctionHouse
// Price naturally decays to near 0, minimum price is 1 wei
return _priceAt(elapsed);
}
// Calculate price at time t using exponential decay (same as AuctionHouse)
function _priceAt(uint256 t) internal view returns (uint256 price) {
int256 exp = -int256(AUCTION_DECAY_RATE) * int256(t);
uint256 ratio = uint256(FixedPointMathLib.expWad(exp));
if (ratio == 0) return 1; // Minimum price
price = FixedPointMathLib.mulWadUp(currentAuction.startPrice, ratio);
}
// Internal function to start next auction
function _startNextAuction() private {
require(nftQueue.length > 0, "No NFTs in queue");
// Take first NFT from queue
NFTItem memory nextNFT = nftQueue[0];
// Remove from queue index mapping
delete nftQueueIndex[nextNFT.nftContract][nextNFT.tokenId];
// Remove from queue by swapping with last element
if (nftQueue.length > 1) {
nftQueue[0] = nftQueue[nftQueue.length - 1];
// Update index for swapped item
NFTItem memory swappedItem = nftQueue[0];
nftQueueIndex[swappedItem.nftContract][swappedItem.tokenId] = 1;
}
nftQueue.pop();
// Start new auction
currentAuction = Auction({
nftContract: nextNFT.nftContract,
tokenId: nextNFT.tokenId,
depositor: nextNFT.depositor,
startTime: block.timestamp,
startPrice: defaultStartPrice,
isActive: true
});
emit AuctionStarted(
nextNFT.nftContract,
nextNFT.tokenId,
defaultStartPrice
);
}
// View functions
function getCurrentAuction() external view returns (Auction memory) {
return currentAuction;
}
function getQueueLength() external view returns (uint256) {
return nftQueue.length;
}
function getQueueItem(
uint256 index
) external view returns (NFTItem memory) {
require(index < nftQueue.length, "Invalid index");
return nftQueue[index];
}
function getQueue() external view returns (NFTItem[] memory) {
return nftQueue;
}
// Admin functions
function setDefaultStartPrice(uint256 _startPrice) external onlyOwner {
require(_startPrice > 0, "Invalid start price");
defaultStartPrice = _startPrice;
}
function emergencyPause() external onlyOwner {
currentAuction.isActive = false;
}
function emergencyResume() external onlyOwner {
require(!currentAuction.isActive, "Auction already active");
if (nftQueue.length > 0) {
_startNextAuction();
}
}
// Emergency NFT recovery (only owner, only if stuck)
function emergencyRecoverNFT(
address nftContract,
uint256 tokenId,
address to
) external onlyOwner {
// Can only recover if not in active auction and not in queue
require(
!currentAuction.isActive ||
currentAuction.nftContract != nftContract ||
currentAuction.tokenId != tokenId,
"NFT in active auction"
);
require(nftQueueIndex[nftContract][tokenId] == 0, "NFT in queue");
IERC721(nftContract).transferFrom(address(this), to, tokenId);
}
// Whitelist management function
function updateWhitelist(address nftContract, bool status) external onlyOwner {
require(nftContract != address(0), "Invalid NFT contract");
whitelistedNFTContracts[nftContract] = status;
if (status) {
emit NFTContractWhitelisted(nftContract);
} else {
emit NFTContractRemovedFromWhitelist(nftContract);
}
}
function isWhitelisted(address nftContract) external view returns (bool) {
return whitelistedNFTContracts[nftContract];
}
}
"
},
"lib/openzeppelin-contracts/contracts/token/ERC721/IERC721.sol": {
"content": "// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (token/ERC721/IERC721.sol)
pragma solidity >=0.6.2;
import {IERC165} from "../../utils/introspection/IERC165.sol";
/**
* @dev Required interface of an ERC-721 compliant contract.
*/
interface IERC721 is IERC165 {
/**
* @dev Emitted when `tokenId` token is transferred from `from` to `to`.
*/
event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);
/**
* @dev Emitted when `owner` enables `approved` to manage the `tokenId` token.
*/
event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);
/**
* @dev Emitted when `owner` enables or disables (`approved`) `operator` to manage all of its assets.
*/
event ApprovalForAll(address indexed owner, address indexed operator, bool approved);
/**
* @dev Returns the number of tokens in ``owner``'s account.
*/
function balanceOf(address owner) external view returns (uint256 balance);
/**
* @dev Returns the owner of the `tokenId` token.
*
* Requirements:
*
* - `tokenId` must exist.
*/
function ownerOf(uint256 tokenId) external view returns (address owner);
/**
* @dev Safely transfers `tokenId` token from `from` to `to`.
*
* Requirements:
*
* - `from` cannot be the zero address.
* - `to` cannot be the zero address.
* - `tokenId` token must exist and be owned by `from`.
* - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
* - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon
* a safe transfer.
*
* Emits a {Transfer} event.
*/
function safeTransferFrom(address from, address to, uint256 tokenId, bytes calldata data) external;
/**
* @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
* are aware of the ERC-721 protocol to prevent tokens from being forever locked.
*
* Requirements:
*
* - `from` cannot be the zero address.
* - `to` cannot be the zero address.
* - `tokenId` token must exist and be owned by `from`.
* - If the caller is not `from`, it must have been allowed to move this token by either {approve} or
* {setApprovalForAll}.
* - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon
* a safe transfer.
*
* Emits a {Transfer} event.
*/
function safeTransferFrom(address from, address to, uint256 tokenId) external;
/**
* @dev Transfers `tokenId` token from `from` to `to`.
*
* WARNING: Note that the caller is responsible to confirm that the recipient is capable of receiving ERC-721
* or else they may be permanently lost. Usage of {safeTransferFrom} prevents loss, though the caller must
* understand this adds an external call which potentially creates a reentrancy vulnerability.
*
* Requirements:
*
* - `from` cannot be the zero address.
* - `to` cannot be the zero address.
* - `tokenId` token must be owned by `from`.
* - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
*
* Emits a {Transfer} event.
*/
function transferFrom(address from, address to, uint256 tokenId) external;
/**
* @dev Gives permission to `to` to transfer `tokenId` token to another account.
* The approval is cleared when the token is transferred.
*
* Only a single account can be approved at a time, so approving the zero address clears previous approvals.
*
* Requirements:
*
* - The caller must own the token or be an approved operator.
* - `tokenId` must exist.
*
* Emits an {Approval} event.
*/
function approve(address to, uint256 tokenId) external;
/**
* @dev Approve or remove `operator` as an operator for the caller.
* Operators can call {transferFrom} or {safeTransferFrom} for any token owned by the caller.
*
* Requirements:
*
* - The `operator` cannot be the address zero.
*
* Emits an {ApprovalForAll} event.
*/
function setApprovalForAll(address operator, bool approved) external;
/**
* @dev Returns the account approved for `tokenId` token.
*
* Requirements:
*
* - `tokenId` must exist.
*/
function getApproved(uint256 tokenId) external view returns (address operator);
/**
* @dev Returns if the `operator` is allowed to manage all of the assets of `owner`.
*
* See {setApprovalForAll}
*/
function isApprovedForAll(address owner, address operator) external view returns (bool);
}
"
},
"lib/openzeppelin-contracts/contracts/token/ERC20/IERC20.sol": {
"content": "// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (token/ERC20/IERC20.sol)
pragma solidity >=0.4.16;
/**
* @dev Interface of the ERC-20 standard as defined in the ERC.
*/
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);
}
"
},
"lib/openzeppelin-contracts/contracts/utils/ReentrancyGuard.sol": {
"content": "// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/ReentrancyGuard.sol)
pragma solidity ^0.8.20;
/**
* @dev Contract module that helps prevent reentrant calls to a function.
*
* Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
* available, which can be applied to functions to make sure there are no nested
* (reentrant) calls to them.
*
* Note that because there is a single `nonReentrant` guard, functions marked as
* `nonReentrant` may not call one another. This can be worked around by making
* those functions `private`, and then adding `external` `nonReentrant` entry
* points to them.
*
* TIP: If EIP-1153 (transient storage) is available on the chain you're deploying at,
* consider using {ReentrancyGuardTransient} instead.
*
* TIP: If you would like to learn more about reentrancy and alternative ways
* to protect against it, check out our blog post
* https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
*/
abstract contract ReentrancyGuard {
// Booleans are more expensive than uint256 or any type that takes up a full
// word because each write operation emits an extra SLOAD to first read the
// slot's contents, replace the bits taken up by the boolean, and then write
// back. This is the compiler's defense against contract upgrades and
// pointer aliasing, and it cannot be disabled.
// The values being non-zero value makes deployment a bit more expensive,
// but in exchange the refund on every call to nonReentrant will be lower in
// amount. Since refunds are capped to a percentage of the total
// transaction's gas, it is best to keep them low in cases like this one, to
// increase the likelihood of the full refund coming into effect.
uint256 private constant NOT_ENTERED = 1;
uint256 private constant ENTERED = 2;
uint256 private _status;
/**
* @dev Unauthorized reentrant call.
*/
error ReentrancyGuardReentrantCall();
constructor() {
_status = NOT_ENTERED;
}
/**
* @dev Prevents a contract from calling itself, directly or indirectly.
* Calling a `nonReentrant` function from another `nonReentrant`
* function is not supported. It is possible to prevent this from happening
* by making the `nonReentrant` function external, and making it call a
* `private` function that does the actual work.
*/
modifier nonReentrant() {
_nonReentrantBefore();
_;
_nonReentrantAfter();
}
function _nonReentrantBefore() private {
// On the first call to nonReentrant, _status will be NOT_ENTERED
if (_status == ENTERED) {
revert ReentrancyGuardReentrantCall();
}
// Any calls to nonReentrant after this point will fail
_status = ENTERED;
}
function _nonReentrantAfter() private {
// By storing the original value once again, a refund is triggered (see
// https://eips.ethereum.org/EIPS/eip-2200)
_status = NOT_ENTERED;
}
/**
* @dev Returns true if the reentrancy guard is currently set to "entered", which indicates there is a
* `nonReentrant` function in the call stack.
*/
function _reentrancyGuardEntered() internal view returns (bool) {
return _status == ENTERED;
}
}
"
},
"lib/openzeppelin-contracts/contracts/access/Ownable.sol": {
"content": "// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (access/Ownable.sol)
pragma solidity ^0.8.20;
import {Context} from "../utils/Context.sol";
/**
* @dev Contract module which provides a basic access control mechanism, where
* there is an account (an owner) that can be granted exclusive access to
* specific functions.
*
* The initial owner is set to the address provided by the deployer. This can
* later be changed with {transferOwnership}.
*
* This module is used through inheritance. It will make available the modifier
* `onlyOwner`, which can be applied to your functions to restrict their use to
* the owner.
*/
abstract contract Ownable is Context {
address private _owner;
/**
* @dev The caller account is not authorized to perform an operation.
*/
error OwnableUnauthorizedAccount(address account);
/**
* @dev The owner is not a valid owner account. (eg. `address(0)`)
*/
error OwnableInvalidOwner(address owner);
event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);
/**
* @dev Initializes the contract setting the address provided by the deployer as the initial owner.
*/
constructor(address initialOwner) {
if (initialOwner == address(0)) {
revert OwnableInvalidOwner(address(0));
}
_transferOwnership(initialOwner);
}
/**
* @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 {
if (owner() != _msgSender()) {
revert OwnableUnauthorizedAccount(_msgSender());
}
}
/**
* @dev Leaves the contract without owner. It will not be possible to call
* `onlyOwner` functions. Can only be called by the current owner.
*
* NOTE: Renouncing ownership will leave the contract without an owner,
* thereby disabling 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 {
if (newOwner == address(0)) {
revert OwnableInvalidOwner(address(0));
}
_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);
}
}
"
},
"lib/solady/src/utils/FixedPointMathLib.sol": {
"content": "// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Arithmetic library with operations for fixed-point numbers.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/FixedPointMathLib.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/FixedPointMathLib.sol)
library FixedPointMathLib {
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* CUSTOM ERRORS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev The operation failed, as the output exceeds the maximum value of uint256.
error ExpOverflow();
/// @dev The operation failed, as the output exceeds the maximum value of uint256.
error FactorialOverflow();
/// @dev The operation failed, due to an overflow.
error RPowOverflow();
/// @dev The mantissa is too big to fit.
error MantissaOverflow();
/// @dev The operation failed, due to an multiplication overflow.
error MulWadFailed();
/// @dev The operation failed, due to an multiplication overflow.
error SMulWadFailed();
/// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
error DivWadFailed();
/// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
error SDivWadFailed();
/// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
error MulDivFailed();
/// @dev The division failed, as the denominator is zero.
error DivFailed();
/// @dev The full precision multiply-divide operation failed, either due
/// to the result being larger than 256 bits, or a division by a zero.
error FullMulDivFailed();
/// @dev The output is undefined, as the input is less-than-or-equal to zero.
error LnWadUndefined();
/// @dev The input outside the acceptable domain.
error OutOfDomain();
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* CONSTANTS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev The scalar of ETH and most ERC20s.
uint256 internal constant WAD = 1e18;
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* SIMPLIFIED FIXED POINT OPERATIONS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev Equivalent to `(x * y) / WAD` rounded down.
function mulWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
// Equivalent to `require(y == 0 || x <= type(uint256).max / y)`.
if gt(x, div(not(0), y)) {
if y {
mstore(0x00, 0xbac65e5b) // `MulWadFailed()`.
revert(0x1c, 0x04)
}
}
z := div(mul(x, y), WAD)
}
}
/// @dev Equivalent to `(x * y) / WAD` rounded down.
function sMulWad(int256 x, int256 y) internal pure returns (int256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mul(x, y)
// Equivalent to `require((x == 0 || z / x == y) && !(x == -1 && y == type(int256).min))`.
if iszero(gt(or(iszero(x), eq(sdiv(z, x), y)), lt(not(x), eq(y, shl(255, 1))))) {
mstore(0x00, 0xedcd4dd4) // `SMulWadFailed()`.
revert(0x1c, 0x04)
}
z := sdiv(z, WAD)
}
}
/// @dev Equivalent to `(x * y) / WAD` rounded down, but without overflow checks.
function rawMulWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := div(mul(x, y), WAD)
}
}
/// @dev Equivalent to `(x * y) / WAD` rounded down, but without overflow checks.
function rawSMulWad(int256 x, int256 y) internal pure returns (int256 z) {
/// @solidity memory-safe-assembly
assembly {
z := sdiv(mul(x, y), WAD)
}
}
/// @dev Equivalent to `(x * y) / WAD` rounded up.
function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mul(x, y)
// Equivalent to `require(y == 0 || x <= type(uint256).max / y)`.
if iszero(eq(div(z, y), x)) {
if y {
mstore(0x00, 0xbac65e5b) // `MulWadFailed()`.
revert(0x1c, 0x04)
}
}
z := add(iszero(iszero(mod(z, WAD))), div(z, WAD))
}
}
/// @dev Equivalent to `(x * y) / WAD` rounded up, but without overflow checks.
function rawMulWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := add(iszero(iszero(mod(mul(x, y), WAD))), div(mul(x, y), WAD))
}
}
/// @dev Equivalent to `(x * WAD) / y` rounded down.
function divWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
// Equivalent to `require(y != 0 && x <= type(uint256).max / WAD)`.
if iszero(mul(y, lt(x, add(1, div(not(0), WAD))))) {
mstore(0x00, 0x7c5f487d) // `DivWadFailed()`.
revert(0x1c, 0x04)
}
z := div(mul(x, WAD), y)
}
}
/// @dev Equivalent to `(x * WAD) / y` rounded down.
function sDivWad(int256 x, int256 y) internal pure returns (int256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mul(x, WAD)
// Equivalent to `require(y != 0 && ((x * WAD) / WAD == x))`.
if iszero(mul(y, eq(sdiv(z, WAD), x))) {
mstore(0x00, 0x5c43740d) // `SDivWadFailed()`.
revert(0x1c, 0x04)
}
z := sdiv(z, y)
}
}
/// @dev Equivalent to `(x * WAD) / y` rounded down, but without overflow and divide by zero checks.
function rawDivWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := div(mul(x, WAD), y)
}
}
/// @dev Equivalent to `(x * WAD) / y` rounded down, but without overflow and divide by zero checks.
function rawSDivWad(int256 x, int256 y) internal pure returns (int256 z) {
/// @solidity memory-safe-assembly
assembly {
z := sdiv(mul(x, WAD), y)
}
}
/// @dev Equivalent to `(x * WAD) / y` rounded up.
function divWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
// Equivalent to `require(y != 0 && x <= type(uint256).max / WAD)`.
if iszero(mul(y, lt(x, add(1, div(not(0), WAD))))) {
mstore(0x00, 0x7c5f487d) // `DivWadFailed()`.
revert(0x1c, 0x04)
}
z := add(iszero(iszero(mod(mul(x, WAD), y))), div(mul(x, WAD), y))
}
}
/// @dev Equivalent to `(x * WAD) / y` rounded up, but without overflow and divide by zero checks.
function rawDivWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := add(iszero(iszero(mod(mul(x, WAD), y))), div(mul(x, WAD), y))
}
}
/// @dev Equivalent to `x` to the power of `y`.
/// because `x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y)`.
/// Note: This function is an approximation.
function powWad(int256 x, int256 y) internal pure returns (int256) {
// Using `ln(x)` means `x` must be greater than 0.
return expWad((lnWad(x) * y) / int256(WAD));
}
/// @dev Returns `exp(x)`, denominated in `WAD`.
/// Credit to Remco Bloemen under MIT license: https://2π.com/22/exp-ln
/// Note: This function is an approximation. Monotonically increasing.
function expWad(int256 x) internal pure returns (int256 r) {
unchecked {
// When the result is less than 0.5 we return zero.
// This happens when `x <= (log(1e-18) * 1e18) ~ -4.15e19`.
if (x <= -41446531673892822313) return r;
/// @solidity memory-safe-assembly
assembly {
// When the result is greater than `(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 iszero(slt(x, 135305999368893231589)) {
mstore(0x00, 0xa37bfec9) // `ExpOverflow()`.
revert(0x1c, 0x04)
}
}
// `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;
/// @solidity memory-safe-assembly
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)
);
}
}
/// @dev Returns `ln(x)`, denominated in `WAD`.
/// Credit to Remco Bloemen under MIT license: https://2π.com/22/exp-ln
/// Note: This function is an approximation. Monotonically increasing.
function lnWad(int256 x) internal pure returns (int256 r) {
/// @solidity memory-safe-assembly
assembly {
// 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.
// Compute `k = log2(x) - 96`, `r = 159 - k = 255 - log2(x) = 255 ^ log2(x)`.
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))))
// We place the check here for more optimal stack operations.
if iszero(sgt(x, 0)) {
mstore(0x00, 0x1615e638) // `LnWadUndefined()`.
revert(0x1c, 0x04)
}
// forgefmt: disable-next-item
r := xor(r, byte(and(0x1f, shr(shr(r, x), 0x8421084210842108cc6318c6db6d54be)),
0xf8f9f9faf9fdfafbf9fdfcfdfafbfcfef9fafdfafcfcfbfefafafcfbffffffff))
// Reduce range of x to (1, 2) * 2**96
// ln(2^k * x) = k * ln(2) + ln(x)
x := shr(159, shl(r, x))
// Evaluate using a (8, 8)-term rational approximation.
// `p` is made monic, we will multiply by a scale factor later.
// forgefmt: disable-next-item
let p := sub( // This heavily nested expression is to avoid stack-too-deep for via-ir.
sar(96, mul(add(43456485725739037958740375743393,
sar(96, mul(add(24828157081833163892658089445524,
sar(96, mul(add(3273285459638523848632254066296,
x), x))), x))), x)), 11111509109440967052023855526967)
p := sub(sar(96, mul(p, x)), 45023709667254063763336534515857)
p := sub(sar(96, mul(p, x)), 14706773417378608786704636184526)
p := sub(mul(p, x), shl(96, 795164235651350426258249787498))
// 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.
let q := add(5573035233440673466300451813936, x)
q := add(71694874799317883764090561454958, sar(96, mul(x, q)))
q := add(283447036172924575727196451306956, sar(96, mul(x, q)))
q := add(401686690394027663651624208769553, sar(96, mul(x, q)))
q := add(204048457590392012362485061816622, sar(96, mul(x, q)))
q := add(31853899698501571402653359427138, sar(96, mul(x, q)))
q := add(909429971244387300277376558375, sar(96, mul(x, q)))
// `p / q` 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`.
// The q polynomial is known not to have zeros in the domain.
// No scaling required because p is already `2**96` too large.
p := sdiv(p, q)
// Multiply by the scaling factor: `s * 5**18 * 2**96`, base is now `5**18 * 2**192`.
p := mul(1677202110996718588342820967067443963516166, p)
// Add `ln(2) * k * 5**18 * 2**192`.
// forgefmt: disable-next-item
p := add(mul(16597577552685614221487285958193947469193820559219878177908093499208371, sub(159, r)), p)
// Add `ln(2**96 / 10**18) * 5**18 * 2**192`.
p := add(600920179829731861736702779321621459595472258049074101567377883020018308, p)
// Base conversion: mul `2**18 / 2**192`.
r := sar(174, p)
}
}
/// @dev Returns `W_0(x)`, denominated in `WAD`.
/// See: https://en.wikipedia.org/wiki/Lambert_W_function
/// a.k.a. Product log function. This is an approximation of the principal branch.
/// Note: This function is an approximation. Monotonically increasing.
function lambertW0Wad(int256 x) internal pure returns (int256 w) {
// forgefmt: disable-next-item
unchecked {
if ((w = x) <= -367879441171442322) revert OutOfDomain(); // `x` less than `-1/e`.
(int256 wad, int256 p) = (int256(WAD), x);
uint256 c; // Whether we need to avoid catastrophic cancellation.
uint256 i = 4; // Number of iterations.
if (w <= 0x1ffffffffffff) {
if (-0x4000000000000 <= w) {
i = 1; // Inputs near zero only take one step to converge.
} else if (w <= -0x3ffffffffffffff) {
i = 32; // Inputs near `-1/e` take very long to converge.
}
} else if (uint256(w >> 63) == uint256(0)) {
/// @solidity memory-safe-assembly
assembly {
// Inline log2 for more performance, since the range is small.
let v := shr(49, w)
let l := shl(3, lt(0xff, v))
l := add(or(l, byte(and(0x1f, shr(shr(l, v), 0x8421084210842108cc6318c6db6d54be)),
0x0706060506020504060203020504030106050205030304010505030400000000)), 49)
w := sdiv(shl(l, 7), byte(sub(l, 31), 0x0303030303030303040506080c13))
c := gt(l, 60)
i := add(2, add(gt(l, 53), c))
}
} else {
int256 ll = lnWad(w = lnWad(w));
/// @solidity memory-safe-assembly
assembly {
// `w = ln(x) - ln(ln(x)) + b * ln(ln(x)) / ln(x)`.
w := add(sdiv(mul(ll, 1023715080943847266), w), sub(w, ll))
i := add(3, iszero(shr(68, x)))
c := iszero(shr(143, x))
}
if (c == uint256(0)) {
do { // If `x` is big, use Newton's so that intermediate values won't overflow.
int256 e = expWad(w);
/// @solidity memory-safe-assembly
assembly {
let t := mul(w, div(e, wad))
w := sub(w, sdiv(sub(t, x), div(add(e, t), wad)))
}
if (p <= w) break;
p = w;
} while (--i != uint256(0));
/// @solidity memory-safe-assembly
assembly {
w := sub(w, sgt(w, 2))
}
return w;
}
}
do { // Otherwise, use Halley's for faster convergence.
int256 e = expWad(w);
/// @solidity memory-safe-assembly
assembly {
let t := add(w, wad)
let s := sub(mul(w, e), mul(x, wad))
w := sub(w, sdiv(mul(s, wad), sub(mul(e, t), sdiv(mul(add(t, wad), s), add(t, t)))))
}
if (p <= w) break;
p = w;
} while (--i != c);
/// @solidity memory-safe-assembly
assembly {
w := sub(w, sgt(w, 2))
}
// For certain ranges of `x`, we'll use the quadratic-rate recursive formula of
// R. Iacono and J.P. Boyd for the last iteration, to avoid catastrophic cancellation.
if (c == uint256(0)) return w;
int256 t = w | 1;
/// @solidity memory-safe-assembly
assembly {
x := sdiv(mul(x, wad), t)
}
x = (t * (wad + lnWad(x)));
/// @solidity memory-safe-assembly
assembly {
w := sdiv(x, add(wad, t))
}
}
}
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* GENERAL NUMBER UTILITIES */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev Returns `a * b == x * y`, with full precision.
function fullMulEq(uint256 a, uint256 b, uint256 x, uint256 y)
internal
pure
returns (bool result)
{
/// @solidity memory-safe-assembly
assembly {
result := and(eq(mul(a, b), mul(x, y)), eq(mulmod(x, y, not(0)), mulmod(a, b, not(0))))
}
}
/// @dev Calculates `floor(x * y / d)` with full precision.
/// Throws if result overflows a uint256 or when `d` is zero.
/// Credit to Remco Bloemen under MIT license: https://2π.com/21/muldiv
function fullMulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
// 512-bit multiply `[p1 p0] = x * y`.
// Compute the product mod `2**256` and mod `2**256 - 1`
// then use the Chinese Remainder Theorem to reconstruct
// the 512 bit result. The result is stored in two 256
// variables such that `product = p1 * 2**256 + p0`.
// Temporarily use `z` as `p0` to save gas.
z := mul(x, y) // Lower 256 bits of `x * y`.
for {} 1 {} {
// If overflows.
if iszero(mul(or(iszero(x), eq(div(z, x), y)), d)) {
let mm := mulmod(x, y, not(0))
let p1 := sub(mm, add(z, lt(mm, z))) // Upper 256 bits of `x * y`.
/*------------------- 512 by 256 division --------------------*/
// Make division exact by subtracting the remainder from `[p1 p0]`.
let r := mulmod(x, y, d) // Compute remainder using mulmod.
let t := and(d, sub(0, d)) // The least significant bit of `d`. `t >= 1`.
// Make sure `z` is less than `2**256`. Also prevents `d == 0`.
// Placing the check here seems to give more optimal stack operations.
if iszero(gt(d, p1)) {
mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
revert(0x1c, 0x04)
}
d := div(d, t) // Divide `d` by `t`, which is a power of two.
// Invert `d mod 2**256`
// Now that `d` is an odd number, it has an inverse
// modulo `2**256` such that `d * inv = 1 mod 2**256`.
// Compute the inverse by starting with a seed that is correct
// correct for four bits. That is, `d * inv = 1 mod 2**4`.
let inv := xor(2, mul(3, d))
// Now use Newton-Raphson iteration to improve the precision.
// Thanks to Hensel's lifting lemma, this also works in modular
// arithmetic, doubling the correct bits in each step.
inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**8
inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**16
inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**32
inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**64
inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**128
z :=
mul(
// Divide [p1 p0] by the factors of two.
// Shift in bits from `p1` into `p0`. For this we need
// to flip `t` such that it is `2**256 / t`.
or(mul(sub(p1, gt(r, z)), add(div(sub(0, t), t), 1)), div(sub(z, r), t)),
mul(sub(2, mul(d, inv)), inv) // inverse mod 2**256
)
break
}
z := div(z, d)
break
}
}
}
/// @dev Calculates `floor(x * y / d)` with full precision.
/// Behavior is undefined if `d` is zero or the final result cannot fit in 256 bits.
/// Performs the full 512 bit calculation regardless.
function fullMulDivUnchecked(uint256 x, uint256 y, uint256 d)
internal
pure
returns (uint256 z)
{
/// @solidity memory-safe-assembly
assembly {
z := mul(x, y)
let mm := mulmod(x, y, not(0))
let p1 := sub(mm, add(z, lt(mm, z)))
let t := and(d, sub(0, d))
let r := mulmod(x, y, d)
d := div(d, t)
let inv := xor(2, mul(3, d))
inv := mul(inv, sub(2, mul(d, inv)))
inv := mul(inv, sub(2, mul(d, inv)))
inv := mul(inv, sub(2, mul(d, inv)))
inv := mul(inv, sub(2, mul(d, inv)))
inv := mul(inv, sub(2, mul(d, inv)))
z :=
mul(
or(mul(sub(p1, gt(r, z)), add(div(sub(0, t), t), 1)), div(sub(z, r), t)),
mul(sub(2, mul(d, inv)), inv)
)
}
}
/// @dev Calculates `floor(x * y / d)` with full precision, rounded up.
/// Throws if result overflows a uint256 or when `d` is zero.
/// Credit to Uniswap-v3-core under MIT license:
/// https://github.com/Uniswap/v3-core/blob/main/contracts/libraries/FullMath.sol
function fullMulDivUp(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
z = fullMulDiv(x, y, d);
/// @solidity memory-safe-assembly
assembly {
if mulmod(x, y, d) {
z := add(z, 1)
if iszero(z) {
mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
revert(0x1c, 0x04)
}
}
}
}
/// @dev Calculates `floor(x * y / 2 ** n)` with full precision.
/// Throws if result overflows a uint256.
/// Credit to Philogy under MIT license:
/// https://github.com/SorellaLabs/angstrom/blob/main/contracts/src/libraries/X128MathLib.sol
function fullMulDivN(uint256 x, uint256 y, uint8 n) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
// Temporarily use `z` as `p0` to save gas.
z := mul(x, y) // Lower 256 bits of `x * y`. We'll call this `z`.
for {} 1 {} {
if iszero(or(iszero(x), eq(div(z, x), y))) {
let k := and(n, 0xff) // `n`, cleaned.
let mm := mulmod(x, y, not(0))
let p1 := sub(mm, add(z, lt(mm, z))) // Upper 256 bits of `x * y`.
// | p1 | z |
// Before: | p1_0 ¦ p1_1 | z_0 ¦ z_1 |
// Final: | 0 ¦ p1_0 | p1_1 ¦ z_0 |
// Check that final `z` doesn't overflow by checking that p1_0 = 0.
if iszero(shr(k, p1)) {
z := add(shl(sub(256, k), p1), shr(k, z))
break
}
mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
revert(0x1c, 0x04)
}
z := shr(and(n, 0xff), z)
break
}
}
}
/// @dev Returns `floor(x * y / d)`.
/// Reverts if `x * y` overflows, or `d` is zero.
function mulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mul(x, y)
// Equivalent to `require(d != 0 && (y == 0 || x <= type(uint256).max / y))`.
if iszero(mul(or(iszero(x), eq(div(z, x), y)), d)) {
mstore(0x00, 0xad251c27) // `MulDivFailed()`.
revert(0x1c, 0x04)
}
z := div(z, d)
}
}
/// @dev Returns `ceil(x * y / d)`.
/// Reverts if `x * y` overflows, or `d` is zero.
function mulDivUp(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mul(x, y)
// Equivalent to `require(d != 0 && (y == 0 || x <= type(uint256).max / y))`.
if iszero(mul(or(iszero(x), eq(div(z, x), y)), d)) {
mstore(0x00, 0xad251c27) // `MulDivFailed()`.
revert(0x1c, 0x04)
}
z := add(iszero(iszero(mod(z, d))), div(z, d))
}
}
/// @dev Returns `x`, the modular multiplicative inverse of `a`, such that `(a * x) % n == 1`.
function invMod(uint256 a, uint256 n) internal pure returns (uint256 x) {
/// @solidity memory-safe-assembly
assembly {
let g := n
let r := mod(a, n)
for { let y := 1 } 1 {} {
let q := div(g, r)
let t := g
g := r
r := sub(t, mul(r, q))
let u := x
x := y
y := sub(u, mul(y, q))
if iszero(r) { break }
}
x := mul(eq(g, 1), add(x, mul(slt(x, 0), n)))
}
}
/// @dev Returns `ceil(x / d)`.
/// Reverts if `d` is zero.
function divUp(uint256 x, uint256 d) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
if iszero(d) {
mstore(0x00, 0x65244e4e) // `DivFailed()`.
revert(0x1c, 0x04)
}
z := add(iszero(iszero(mod(x, d))), div(x, d))
}
}
/// @dev Returns `max(0, x - y)`. Alias for `saturatingSub`.
function zeroFloorSub(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mul(gt(x, y), sub(x, y))
}
}
/// @dev Returns `max(0, x - y)`.
function saturatingSub(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mul(gt(x, y), sub(x, y))
}
}
/// @dev Returns `min(2 ** 256 - 1, x + y)`.
function saturatingAdd(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := or(sub(0, lt(add(x, y), x)), add(x, y))
}
}
/// @dev Returns `min(2 ** 256 - 1, x * y)`.
function saturatingMul(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := or(sub(or(iszero(x), eq(div(mul(x, y), x), y)), 1), mul(x, y))
}
}
/// @dev Returns `condition ? x : y`, without branching.
function ternary(bool condition, uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := xor(x, mul(xor(x, y), iszero(condition)))
}
}
/// @dev Returns `condition ? x : y`, without branching.
function ternary(bool condition, bytes32 x, bytes32 y) internal pure returns (bytes32 z) {
/// @solidity memory-safe-assembly
assembly {
z := xor(x, mul(xor(x, y), iszero(condition)))
}
}
/// @dev Returns `condition ? x : y`, without branching.
function ternary(bool condition, address x, address y) internal pure returns (address z) {
/// @solidity memory-safe-assembly
assembly {
z := xor(x, mul(xor(x, y), iszero(condition)))
}
}
/// @dev Returns `x != 0 ? x : y`, without branching.
function coalesce(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := or(x, mul(y, iszero(x)))
}
}
/// @dev Returns `x != bytes32(0) ? x : y`, without branching.
function coalesce(bytes32 x, bytes32 y) internal pure returns (bytes32 z) {
/// @solidity memory-safe-assembly
assembly {
z := or(x, mul(y, iszero(x)))
}
}
/// @dev Returns `x != address(0) ? x : y`, without branching.
function coalesce(address x, address y) internal pure returns (address z) {
/// @solidity memory-safe-assembly
assembly {
z := or(x, mul(y, iszero(shl(96, x))))
}
}
/// @dev Exponentiate `x` to `y` by squaring, denominated in base `b`.
/// Reverts if the computation overflows.
function rpow(uint256 x, uint256 y, uint256 b) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mul(b, iszero(y)) // `0 ** 0 = 1`. Otherwise, `0 ** n = 0`.
if x {
z := xor(b, mul(xor(b, x), and(y, 1))) // `z = isEven(y) ? scale : x`
let half := shr(1, b) // Divide `b` by 2.
// Divide `y` by 2 every iteration.
for { y := shr(1, y) } y { y := shr(1, y) } {
let xx := mul(x, x) // Store x squared.
let xxRound := add(xx, half) // Round to the nearest number.
// Revert if `xx + half` overflowed, or if `x ** 2` overflows.
if or(lt(xxRound, xx), shr(128, x)) {
mstore(0x00, 0x49f7642b) // `RPowOverflow()`.
revert(0x1c, 0x04)
}
x := div(xxRound, b) // Set `x` to scaled `xxRound`.
// If `y` is odd:
if and(y, 1) {
let zx := mul(z, x) // Compute `z * x`.
let zxRound := add(zx, half) // Round to the nearest number.
// If `z * x` overflowed or `zx + half` overflowed:
if or(xor(div(zx, x), z), lt(zxRound, zx)) {
// Revert if `x` is non-zero.
if x {
mstore(0x00, 0x49f7642b) // `RPowOverflow()`.
revert(0x1c, 0x04)
}
}
z := div(zxRound, b) // Return properly scaled `zxRound`.
}
}
}
}
}
/// @dev Returns the square root of `x`, rounded down.
function sqrt(uint256 x) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
// `floor(sqrt(2**15)) = 181`. `sqrt(2**15) - 181 = 2.84`.
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.
// Let `y = x / 2**r`. We check `y >= 2**(k + 8)`
// but shift right by `k` bits to ensure that if `x >= 256`, then `y >= 256`.
let r := shl(7, lt(0xffffffffffffffffffffffffffffffffff, x))
r := or(r, shl(6, lt(0xffffffffffffffffff, shr(r, x))))
r := or(r, shl(5, lt(0xffffffffff, shr(r, x))))
r := or(r, shl(4, lt(0xffffff, shr(r, x))))
z := shl(shr(1, r), 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(shr(r, x), 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
z := sub(z, lt(div(x, z), z))
}
}
/// @dev Returns the cube root of `x`, rounded down.
/// Credit to bout3fiddy and pcaversaccio under AGPLv3 license:
/// https://github.com/pcaversaccio/snekmate/blob/main/src/snekmate/utils/math.vy
/// Formally verified by xuwinnie:
/// https://github.com/vectorized/solady/blob/main/audits/xuwinnie-solady-cbrt-proof.pdf
function cbrt(uint256 x) internal pure returns (uint256 z) {
/// @solidity memory-safe-Submitted on: 2025-10-07 11:44:59
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