Contract Name:
EtherfunSale
Contract Source Code:
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./SaleContract.sol";
import "@openzeppelin/contracts/security/ReentrancyGuard.sol";
interface ISaleContract {
function buy(address user, uint256 minTokensOut) external payable returns (uint256, uint256);
function sell(address user, uint256 tokenAmount, uint256 minEthOut) external returns (uint256, uint256);
function claimTokens(address user) external;
function launchSale(
address _launchContract,
uint8 buyLpFee,
uint8 sellLpFee,
uint8 buyProtocolFee,
uint8 sellProtocolFee,
address firstBuyer,
address saleInitiator
) external;
function takeFee(address lockFactoryOwner) external;
function token() external view returns (address);
}
contract EtherFunFactory is ReentrancyGuard {
address public owner;
address public launchContractAddress = 0xCEDd366065A146a039B92Db35756ecD7688FCC77;
uint256 public saleCounter;
uint256 public totalTokens = 1000000000 * 1e18;
uint256 public defaultSaleGoal = 1.5 ether;
uint8 public creatorshare = 4;
uint8 public feepercent = 2;
uint256 public defaultK = 222 * 1e15;
uint256 public defaultAlpha = 2878 * 1e6;
uint8 public buyLpFee = 5;
uint8 public sellLpFee = 5;
uint8 public buyProtocolFee = 5;
uint8 public sellProtocolFee = 5;
struct Sale {
address creator;
string name;
string symbol;
uint256 totalRaised;
uint256 saleGoal;
bool launched;
uint256 creationNonce;
}
struct SaleMetadata {
string logoUrl;
string websiteUrl;
string twitterUrl;
string telegramUrl;
string description;
}
mapping(address => Sale) public sales;
mapping(address => mapping(address => bool)) public hasClaimed;
mapping(address => SaleMetadata) public saleMetadata;
mapping(address => address[]) public userBoughtTokens;
mapping(address => mapping(address => bool)) public userHasBoughtToken;
mapping(address => uint256) creationNonce;
mapping(address => address) public firstBuyer;
mapping(address => address[]) public creatorTokens;
event SaleCreated(
address indexed tokenAddress,
address indexed creator,
string name,
string symbol,
uint256 saleGoal,
string logoUrl,
string websiteUrl,
string twitterUrl,
string telegramUrl,
string description
);
event SaleLaunched(address indexed tokenAddress, address indexed launcher);
event Claimed(address indexed tokenAddress, address indexed claimant);
event MetaUpdated(address indexed tokenAddress, string logoUrl, string websiteUrl, string twitterUrl, string telegramUrl, string description);
event TokensBought(address indexed tokenAddress, address indexed buyer, uint256 totalRaised, uint256 tokenBalance);
event TokensSold(address indexed tokenAddress, address indexed seller, uint256 totalRaised, uint256 tokenBalance);
modifier onlyOwner() {
require(msg.sender == owner, "Not the owner");
_;
}
modifier onlySaleCreator(address tokenAddress) {
require(msg.sender == sales[tokenAddress].creator, "Not creator");
_;
}
constructor() {
owner = msg.sender;
}
function createSale(
string memory name,
string memory symbol,
string memory logoUrl,
string memory websiteUrl,
string memory twitterUrl,
string memory telegramUrl,
string memory description
) external payable nonReentrant {
creationNonce[msg.sender]++;
uint256 currentNonce = creationNonce[msg.sender];
address tokenAddress = predictTokenAddress(msg.sender, name, symbol, currentNonce);
sales[tokenAddress] = Sale({
creator: msg.sender,
name: name,
symbol: symbol,
totalRaised: 0,
saleGoal: defaultSaleGoal,
launched: false,
creationNonce: currentNonce
});
saleMetadata[tokenAddress] = SaleMetadata({
logoUrl: logoUrl,
websiteUrl: websiteUrl,
twitterUrl: twitterUrl,
telegramUrl: telegramUrl,
description: description
});
creatorTokens[msg.sender].push(tokenAddress);
saleCounter++;
emit SaleCreated(
tokenAddress,
msg.sender,
name,
symbol,
defaultSaleGoal,
logoUrl,
websiteUrl,
twitterUrl,
telegramUrl,
description
);
if (msg.value > 0) {
require(msg.value < 0.2 ether, "Too many tokens bought");
bytes32 salt = keccak256(abi.encodePacked(msg.sender, currentNonce));
bytes memory bytecode = abi.encodePacked(
type(EtherfunSale).creationCode,
abi.encode(
name,
symbol,
msg.sender,
address(this),
totalTokens,
defaultK,
defaultAlpha,
defaultSaleGoal,
creatorshare,
feepercent
)
);
assembly {
tokenAddress := create2(0, add(bytecode, 32), mload(bytecode), salt)
if iszero(extcodesize(tokenAddress)) { revert(0, 0) }
}
firstBuyer[tokenAddress] = msg.sender;
uint256 minTokensOut = 0;
(uint256 totalRaised, uint256 tokenBalance) = ISaleContract(tokenAddress).buy{value: msg.value}(msg.sender, minTokensOut);
sales[tokenAddress].totalRaised = totalRaised;
userBoughtTokens[msg.sender].push(tokenAddress);
userHasBoughtToken[msg.sender][tokenAddress] = true;
emit TokensBought(tokenAddress, msg.sender, totalRaised, tokenBalance);
}
}
function buyToken(address tokenAddress, uint256 minTokensOut) external payable nonReentrant {
Sale storage sale = sales[tokenAddress];
require(!sale.launched, "Sale already launched");
if (firstBuyer[tokenAddress] == address(0)) {
bytes32 salt = keccak256(abi.encodePacked(sale.creator, sale.creationNonce));
bytes memory bytecode = abi.encodePacked(
type(EtherfunSale).creationCode,
abi.encode(
sale.name,
sale.symbol,
sale.creator,
address(this),
totalTokens,
defaultK,
defaultAlpha,
defaultSaleGoal,
creatorshare,
feepercent
)
);
assembly {
tokenAddress := create2(0, add(bytecode, 32), mload(bytecode), salt)
if iszero(extcodesize(tokenAddress)) { revert(0, 0) }
}
firstBuyer[tokenAddress] = msg.sender;
}
(uint256 totalRaised, uint256 tokenBalance) = ISaleContract(tokenAddress).buy{value: msg.value}(msg.sender, minTokensOut);
sale.totalRaised = totalRaised;
if (!userHasBoughtToken[msg.sender][tokenAddress]) {
userBoughtTokens[msg.sender].push(tokenAddress);
userHasBoughtToken[msg.sender][tokenAddress] = true;
}
if (totalRaised >= sale.saleGoal) {
sale.launched = true;
emit SaleLaunched(tokenAddress, msg.sender);
ISaleContract(tokenAddress).launchSale(
launchContractAddress,
buyLpFee,
sellLpFee,
buyProtocolFee,
sellProtocolFee,
firstBuyer[tokenAddress],
msg.sender
);
}
emit TokensBought(tokenAddress, msg.sender, totalRaised, tokenBalance);
}
function sellToken(address tokenAddress, uint256 tokenAmount, uint256 minEthOut) external nonReentrant {
Sale storage sale = sales[tokenAddress];
require(!sale.launched, "Sale already launched");
(uint256 totalRaised, uint256 tokenBalance) = ISaleContract(tokenAddress).sell(msg.sender, tokenAmount, minEthOut);
sale.totalRaised = totalRaised;
emit TokensSold(tokenAddress, msg.sender, totalRaised, tokenBalance);
}
function claim(address tokenAddress) external nonReentrant {
Sale storage sale = sales[tokenAddress];
require(sale.launched, "Sale not launched");
require(!hasClaimed[tokenAddress][msg.sender], "Already claimed");
hasClaimed[tokenAddress][msg.sender] = true;
emit Claimed(tokenAddress, msg.sender);
ISaleContract(tokenAddress).claimTokens(msg.sender);
}
function setSaleMetadata(
address tokenAddress,
string memory logoUrl,
string memory websiteUrl,
string memory twitterUrl,
string memory telegramUrl,
string memory description // New parameter for description
) external onlySaleCreator(tokenAddress) {
SaleMetadata storage metadata = saleMetadata[tokenAddress];
metadata.logoUrl = logoUrl;
metadata.websiteUrl = websiteUrl;
metadata.twitterUrl = twitterUrl;
metadata.telegramUrl = telegramUrl;
metadata.description = description; // Update the description
emit MetaUpdated(tokenAddress, logoUrl, websiteUrl, twitterUrl, telegramUrl, description);
}
function getUserBoughtTokens(address user) external view returns (address[] memory) {
return userBoughtTokens[user];
}
function getUserBoughtTokensLength(address user) external view returns (uint256) {
return userBoughtTokens[user].length;
}
function getCurrentNonce(address user) public view returns (uint256) {
return creationNonce[user];
}
function getCreatorTokens(address creator) external view returns (address[] memory) {
return creatorTokens[creator];
}
function predictTokenAddress(
address creator,
string memory name,
string memory symbol,
uint256 nonce
) public view returns (address) {
bytes32 salt = keccak256(abi.encodePacked(creator, nonce));
bytes32 initCodeHash = keccak256(abi.encodePacked(
type(EtherfunSale).creationCode,
abi.encode(
name,
symbol,
creator,
address(this),
totalTokens,
defaultK,
defaultAlpha,
defaultSaleGoal,
creatorshare,
feepercent
)
));
return address(uint160(uint256(keccak256(abi.encodePacked(
bytes1(0xff),
address(this),
salt,
initCodeHash
)))));
}
//OWNER FUNCTIONS
function takeFeeFrom(address tokenAddress) external nonReentrant {
Sale storage sale = sales[tokenAddress];
require(sale.launched, "Sale not launched");
ISaleContract(tokenAddress).takeFee(owner);
}
function updateParameters(
uint256 _defaultSaleGoal,
uint256 _defaultK,
uint256 _defaultAlpha,
address _launchContractAddress,
uint8 _buyLpFee,
uint8 _sellLpFee,
uint8 _buyProtocolFee,
uint8 _sellProtocolFee
) external onlyOwner {
require(_defaultSaleGoal > 0, "Invalid sale goal");
require(_defaultK > 0, "Invalid K value");
require(_defaultAlpha > 0, "Invalid alpha value");
require(_launchContractAddress != address(0), "Invalid launch contract");
defaultSaleGoal = _defaultSaleGoal;
defaultK = _defaultK;
defaultAlpha = _defaultAlpha;
launchContractAddress = _launchContractAddress;
buyLpFee = _buyLpFee;
sellLpFee = _sellLpFee;
buyProtocolFee = _buyProtocolFee;
sellProtocolFee = _sellProtocolFee;
}
function updateFeeShares(
uint8 _creatorShare,
uint8 _feePercent
) external onlyOwner {
require(_creatorShare > 0 && _creatorShare <= 100, "Invalid creator share");
require(_feePercent > 0 && _feePercent <= 100, "Invalid fee share");
creatorshare = _creatorShare;
feepercent = _feePercent;
}
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (security/ReentrancyGuard.sol)
pragma solidity ^0.8.0;
/**
* @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 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;
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
require(_status != _ENTERED, "ReentrancyGuard: reentrant call");
// 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;
}
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "@openzeppelin/contracts/security/ReentrancyGuard.sol";
import "@openzeppelin/contracts/token/ERC20/ERC20.sol";
import { UD60x18, ud } from "@prb/math/src/UD60x18.sol"; // Use UD60x18 type and ud() constructor
interface IVistaFactory {
function getPair(address tokenA, address tokenB) external view returns (address);
}
interface IPair {
function claimShare() external;
function viewShare() external view returns (uint256 share);
}
interface ILaunchContract {
function launch(
address token,
uint256 amountTokenDesired,
uint256 amountETHMin,
uint256 amountTokenMin,
uint8 buyLpFee,
uint8 sellLpFee,
uint8 buyProtocolFee,
uint8 sellProtocolFee,
address protocolAddress
) external payable;
}
contract EtherfunSale is ReentrancyGuard, ERC20 {
//using UD60x18 for uint256;
//address public token;
address public creator;
address public factory;
uint256 public totalTokens;
uint256 public totalRaised;
uint256 public maxContribution;
uint8 public creatorshare;
bool public launched;
bool public status;
uint256 public k; // Initial price factor
uint256 public alpha; // Steepness factor for bonding curve
uint256 public saleGoal; // Sale goal in ETH
uint256 public tokensSold; // Track the number of tokens sold, initially 0
mapping(address => uint256) public tokenBalances; // Track user token balances (not actual tokens)
address[] public tokenHolders;
mapping(address => bool) public isTokenHolder;
address public wethAddress = 0xC02aaA39b223FE8D0A0e5C4F27eAD9083C756Cc2;
address public vistaFactoryAddress = 0x9a27cb5ae0B2cEe0bb71f9A85C0D60f3920757B4;
uint256 public feePercent;
address public feeWallet = 0xc07DFf4C8c129aA8FA8b91CC67d74AEd77e4feF1;
struct HistoricalData {
uint256 timestamp;
uint256 totalRaised;
}
HistoricalData[] public historicalData;
event TokensPurchased(
address indexed buyer,
uint256 ethAmount,
uint256 tokenAmount,
uint256 timestamp
);
event TokensSold(
address indexed seller,
uint256 tokenAmount,
uint256 ethAmount,
uint256 timestamp
);
modifier onlyFactory() {
require(msg.sender == factory, "Only factory");
_;
}
constructor(
string memory name,
string memory symbol,
address _creator,
address _factory,
uint256 _totalTokens,
uint256 _k, // Initial price factor
uint256 _alpha, // Steepness of bonding curve
uint256 _saleGoal, // ETH goal for sale
uint8 _creatorshare,
uint256 _feePercent
) ERC20(name, symbol) {
creator = _creator;
factory = _factory;
totalTokens = _totalTokens;
k = _k;
alpha = _alpha;
saleGoal = _saleGoal;
creatorshare = _creatorshare;
feePercent = _feePercent;
tokensSold = 0; // Initialize tokensSold to 0
_mint(address(this), _totalTokens);
//EtherfunToken newToken = new EtherfunToken(name, symbol, _totalTokens, address(this));
//token = address(newToken);
}
function getEthIn(uint256 tokenAmount) public view returns (uint256) {
UD60x18 soldTokensFixed = ud(tokensSold);
UD60x18 tokenAmountFixed = ud(tokenAmount);
UD60x18 kFixed = ud(k);
UD60x18 alphaFixed = ud(alpha);
// Calculate ethBefore = k * (exp(alpha * tokensSold) - 1)
UD60x18 ethBefore = kFixed.mul(alphaFixed.mul(soldTokensFixed).exp()).sub(kFixed);
// Calculate ethAfter = k * (exp(alpha * (tokensSold - tokenAmount)) - 1)
UD60x18 ethAfter = kFixed.mul(alphaFixed.mul(soldTokensFixed.sub(tokenAmountFixed)).exp()).sub(kFixed);
// Return the difference in Wei (ETH)
return ethBefore.sub(ethAfter).unwrap();
}
// Function to calculate the number of tokens for a given ETH amount
function getTokenIn(uint256 ethAmount) public view returns (uint256) {
UD60x18 totalRaisedFixed = ud(totalRaised);
UD60x18 ethAmountFixed = ud(ethAmount);
UD60x18 kFixed = ud(k);
UD60x18 alphaFixed = ud(alpha);
// Calculate tokensBefore = ln((totalRaised / k) + 1) / alpha
UD60x18 tokensBefore = totalRaisedFixed.div(kFixed).add(ud(1e18)).ln().div(alphaFixed);
// Calculate tokensAfter = ln(((totalRaised + ethAmount) / k) + 1) / alpha
UD60x18 tokensAfter = totalRaisedFixed.add(ethAmountFixed).div(kFixed).add(ud(1e18)).ln().div(alphaFixed);
// Return the difference in tokens
return tokensAfter.sub(tokensBefore).unwrap();
}
// Optimized buy function with direct fee distribution
function buy(address user, uint256 minTokensOut) external payable onlyFactory nonReentrant returns (uint256, uint256) {
require(!launched, "Sale already launched");
require(totalRaised + msg.value <= saleGoal + 0.1 ether, "Sale goal reached");
require(msg.value > 0, "No ETH sent");
require(!status, "bonded");
// Calculate the fee and amount after fee deduction
uint256 fee = (msg.value * feePercent) / 100;
uint256 amountAfterFee = msg.value - fee;
// Calculate tokens to buy with amountAfterFee
uint256 tokensToBuy = getTokenIn(amountAfterFee);
require(tokensToBuy >= minTokensOut, "Slippage too high, transaction reverted");
tokensSold += tokensToBuy;
totalRaised += amountAfterFee;
tokenBalances[user] += tokensToBuy;
if (!isTokenHolder[user]) {
tokenHolders.push(user);
isTokenHolder[user] = true;
}
payable(feeWallet).transfer(fee / 2);
payable(0x4C5fbF8D815379379b3695ba77B5D3f898C1230b).transfer(fee / 2);
if (totalRaised >= saleGoal) {
status = true;
}
updateHistoricalData();
emit TokensPurchased(
user,
amountAfterFee,
tokensToBuy,
block.timestamp
);
return (totalRaised, tokenBalances[user]);
}
// Optimized sell function with direct fee distribution
function sell(address user, uint256 tokenAmount, uint256 minEthOut) external onlyFactory nonReentrant returns (uint256, uint256) {
require(!launched, "Sale already launched");
require(tokenAmount > 0, "Token amount must be greater than 0");
require(tokenBalances[user] >= tokenAmount, "Insufficient token balance");
require(!status, "bonded");
uint256 ethToReturn = getEthIn(tokenAmount);
require(ethToReturn >= minEthOut, "Slippage too high, transaction reverted");
require(ethToReturn <= address(this).balance, "Insufficient contract balance");
// Calculate the fee and amount after fee deduction
uint256 fee = (ethToReturn * feePercent) / 100;
uint256 ethAfterFee = ethToReturn - fee;
tokensSold -= tokenAmount;
totalRaised -= ethToReturn;
tokenBalances[user] -= tokenAmount;
// Transfer ETH after fee to the user
payable(user).transfer(ethAfterFee);
payable(feeWallet).transfer(fee / 2);
payable(0x4C5fbF8D815379379b3695ba77B5D3f898C1230b).transfer(fee / 2);
updateHistoricalData();
emit TokensSold(
user,
tokenAmount,
ethAfterFee,
block.timestamp
);
return (totalRaised, tokenBalances[user]);
}
function updateHistoricalData() internal {
historicalData.push(HistoricalData({
timestamp: block.timestamp,
totalRaised: totalRaised
}));
//emit HistoricalDataUpdated(block.timestamp, totalRaised);
}
// Launch the sale, users can claim their tokens after launch
function launchSale(
address _launchContract,
uint8 buyLpFee,
uint8 sellLpFee,
uint8 buyProtocolFee,
uint8 sellProtocolFee,
address firstBuyer,
address saleInitiator
) external onlyFactory nonReentrant {
require(!launched, "Sale already launched");
require(totalRaised >= saleGoal, "Sale goal not reached");
require(status, "not bonded");
launched = true;
uint256 tokenAmount = (totalTokens - tokensSold);
uint256 ethAmount = totalRaised;
uint256 launchEthAmount = ((100 - creatorshare) * ethAmount) / 100;
_approve(address(this), _launchContract, tokenAmount);
ILaunchContract(_launchContract).launch{value: launchEthAmount}(
address(this),
tokenAmount,
0,
0,
buyLpFee,
sellLpFee,
buyProtocolFee,
sellProtocolFee,
creator
);
uint256 creatorShareAmount = address(this).balance;
require(creatorShareAmount > 0, "No balance for creator share");
payable(firstBuyer).transfer(creatorShareAmount/2);
payable(saleInitiator).transfer(creatorShareAmount/2);
}
// Claim tokens after the sale is launched
function claimTokens(address user) external onlyFactory nonReentrant {
require(launched, "Sale not launched");
uint256 tokenAmount = tokenBalances[user];
require(tokenAmount > 0, "No tokens to claim");
tokenBalances[user] = 0;
_transfer(address(this), user, tokenAmount);
}
function getTokenHoldersCount() external view returns (uint256) {
return tokenHolders.length;
}
function getAllTokenHolders() external view returns (address[] memory) {
return tokenHolders;
}
function getAllHistoricalData() external view returns (HistoricalData[] memory) {
return historicalData;
}
function takeFee(address lockFactoryOwner) external onlyFactory nonReentrant {
IVistaFactory vistaFactory = IVistaFactory(vistaFactoryAddress);
address pairAddress = vistaFactory.getPair(address(this), wethAddress);
require(pairAddress != address(0), "Pair not found");
IPair pair = IPair(pairAddress);
pair.claimShare();
uint256 claimedEth = address(this).balance;
require(claimedEth > 0, "No ETH claimed");
uint256 fee1 = claimedEth/2;
uint256 fee2 = claimedEth-fee1;
payable(lockFactoryOwner).transfer(fee1);
payable(0x4C5fbF8D815379379b3695ba77B5D3f898C1230b).transfer(fee2);
}
function getShare() external view returns (uint256) {
IVistaFactory vistaFactory = IVistaFactory(vistaFactoryAddress);
address pairAddress = vistaFactory.getPair(address(this), wethAddress);
return IPair(pairAddress).viewShare();
}
receive() external payable {}
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
/*
██████╗ ██████╗ ██████╗ ███╗ ███╗ █████╗ ████████╗██╗ ██╗
██╔══██╗██╔══██╗██╔══██╗████╗ ████║██╔══██╗╚══██╔══╝██║ ██║
██████╔╝██████╔╝██████╔╝██╔████╔██║███████║ ██║ ███████║
██╔═══╝ ██╔══██╗██╔══██╗██║╚██╔╝██║██╔══██║ ██║ ██╔══██║
██║ ██║ ██║██████╔╝██║ ╚═╝ ██║██║ ██║ ██║ ██║ ██║
╚═╝ ╚═╝ ╚═╝╚═════╝ ╚═╝ ╚═╝╚═╝ ╚═╝ ╚═╝ ╚═╝ ╚═╝
██╗ ██╗██████╗ ██████╗ ██████╗ ██╗ ██╗ ██╗ █████╗
██║ ██║██╔══██╗██╔════╝ ██╔═████╗╚██╗██╔╝███║██╔══██╗
██║ ██║██║ ██║███████╗ ██║██╔██║ ╚███╔╝ ╚██║╚█████╔╝
██║ ██║██║ ██║██╔═══██╗████╔╝██║ ██╔██╗ ██║██╔══██╗
╚██████╔╝██████╔╝╚██████╔╝╚██████╔╝██╔╝ ██╗ ██║╚█████╔╝
╚═════╝ ╚═════╝ ╚═════╝ ╚═════╝ ╚═╝ ╚═╝ ╚═╝ ╚════╝
*/
import "./ud60x18/Casting.sol";
import "./ud60x18/Constants.sol";
import "./ud60x18/Conversions.sol";
import "./ud60x18/Errors.sol";
import "./ud60x18/Helpers.sol";
import "./ud60x18/Math.sol";
import "./ud60x18/ValueType.sol";
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/ERC20.sol)
pragma solidity ^0.8.20;
import {IERC20} from "./IERC20.sol";
import {IERC20Metadata} from "./extensions/IERC20Metadata.sol";
import {Context} from "../../utils/Context.sol";
import {IERC20Errors} from "../../interfaces/draft-IERC6093.sol";
/**
* @dev Implementation of the {IERC20} interface.
*
* This implementation is agnostic to the way tokens are created. This means
* that a supply mechanism has to be added in a derived contract using {_mint}.
*
* TIP: For a detailed writeup see our guide
* https://forum.openzeppelin.com/t/how-to-implement-erc20-supply-mechanisms/226[How
* to implement supply mechanisms].
*
* The default value of {decimals} is 18. To change this, you should override
* this function so it returns a different value.
*
* We have followed general OpenZeppelin Contracts guidelines: functions revert
* instead returning `false` on failure. This behavior is nonetheless
* conventional and does not conflict with the expectations of ERC20
* applications.
*
* Additionally, an {Approval} event is emitted on calls to {transferFrom}.
* This allows applications to reconstruct the allowance for all accounts just
* by listening to said events. Other implementations of the EIP may not emit
* these events, as it isn't required by the specification.
*/
abstract contract ERC20 is Context, IERC20, IERC20Metadata, IERC20Errors {
mapping(address account => uint256) private _balances;
mapping(address account => mapping(address spender => uint256)) private _allowances;
uint256 private _totalSupply;
string private _name;
string private _symbol;
/**
* @dev Sets the values for {name} and {symbol}.
*
* All two of these values are immutable: they can only be set once during
* construction.
*/
constructor(string memory name_, string memory symbol_) {
_name = name_;
_symbol = symbol_;
}
/**
* @dev Returns the name of the token.
*/
function name() public view virtual returns (string memory) {
return _name;
}
/**
* @dev Returns the symbol of the token, usually a shorter version of the
* name.
*/
function symbol() public view virtual returns (string memory) {
return _symbol;
}
/**
* @dev Returns the number of decimals used to get its user representation.
* For example, if `decimals` equals `2`, a balance of `505` tokens should
* be displayed to a user as `5.05` (`505 / 10 ** 2`).
*
* Tokens usually opt for a value of 18, imitating the relationship between
* Ether and Wei. This is the default value returned by this function, unless
* it's overridden.
*
* NOTE: This information is only used for _display_ purposes: it in
* no way affects any of the arithmetic of the contract, including
* {IERC20-balanceOf} and {IERC20-transfer}.
*/
function decimals() public view virtual returns (uint8) {
return 18;
}
/**
* @dev See {IERC20-totalSupply}.
*/
function totalSupply() public view virtual returns (uint256) {
return _totalSupply;
}
/**
* @dev See {IERC20-balanceOf}.
*/
function balanceOf(address account) public view virtual returns (uint256) {
return _balances[account];
}
/**
* @dev See {IERC20-transfer}.
*
* Requirements:
*
* - `to` cannot be the zero address.
* - the caller must have a balance of at least `value`.
*/
function transfer(address to, uint256 value) public virtual returns (bool) {
address owner = _msgSender();
_transfer(owner, to, value);
return true;
}
/**
* @dev See {IERC20-allowance}.
*/
function allowance(address owner, address spender) public view virtual returns (uint256) {
return _allowances[owner][spender];
}
/**
* @dev See {IERC20-approve}.
*
* NOTE: If `value` is the maximum `uint256`, the allowance is not updated on
* `transferFrom`. This is semantically equivalent to an infinite approval.
*
* Requirements:
*
* - `spender` cannot be the zero address.
*/
function approve(address spender, uint256 value) public virtual returns (bool) {
address owner = _msgSender();
_approve(owner, spender, value);
return true;
}
/**
* @dev See {IERC20-transferFrom}.
*
* Emits an {Approval} event indicating the updated allowance. This is not
* required by the EIP. See the note at the beginning of {ERC20}.
*
* NOTE: Does not update the allowance if the current allowance
* is the maximum `uint256`.
*
* Requirements:
*
* - `from` and `to` cannot be the zero address.
* - `from` must have a balance of at least `value`.
* - the caller must have allowance for ``from``'s tokens of at least
* `value`.
*/
function transferFrom(address from, address to, uint256 value) public virtual returns (bool) {
address spender = _msgSender();
_spendAllowance(from, spender, value);
_transfer(from, to, value);
return true;
}
/**
* @dev Moves a `value` amount of tokens from `from` to `to`.
*
* This internal function is equivalent to {transfer}, and can be used to
* e.g. implement automatic token fees, slashing mechanisms, etc.
*
* Emits a {Transfer} event.
*
* NOTE: This function is not virtual, {_update} should be overridden instead.
*/
function _transfer(address from, address to, uint256 value) internal {
if (from == address(0)) {
revert ERC20InvalidSender(address(0));
}
if (to == address(0)) {
revert ERC20InvalidReceiver(address(0));
}
_update(from, to, value);
}
/**
* @dev Transfers a `value` amount of tokens from `from` to `to`, or alternatively mints (or burns) if `from`
* (or `to`) is the zero address. All customizations to transfers, mints, and burns should be done by overriding
* this function.
*
* Emits a {Transfer} event.
*/
function _update(address from, address to, uint256 value) internal virtual {
if (from == address(0)) {
// Overflow check required: The rest of the code assumes that totalSupply never overflows
_totalSupply += value;
} else {
uint256 fromBalance = _balances[from];
if (fromBalance < value) {
revert ERC20InsufficientBalance(from, fromBalance, value);
}
unchecked {
// Overflow not possible: value <= fromBalance <= totalSupply.
_balances[from] = fromBalance - value;
}
}
if (to == address(0)) {
unchecked {
// Overflow not possible: value <= totalSupply or value <= fromBalance <= totalSupply.
_totalSupply -= value;
}
} else {
unchecked {
// Overflow not possible: balance + value is at most totalSupply, which we know fits into a uint256.
_balances[to] += value;
}
}
emit Transfer(from, to, value);
}
/**
* @dev Creates a `value` amount of tokens and assigns them to `account`, by transferring it from address(0).
* Relies on the `_update` mechanism
*
* Emits a {Transfer} event with `from` set to the zero address.
*
* NOTE: This function is not virtual, {_update} should be overridden instead.
*/
function _mint(address account, uint256 value) internal {
if (account == address(0)) {
revert ERC20InvalidReceiver(address(0));
}
_update(address(0), account, value);
}
/**
* @dev Destroys a `value` amount of tokens from `account`, lowering the total supply.
* Relies on the `_update` mechanism.
*
* Emits a {Transfer} event with `to` set to the zero address.
*
* NOTE: This function is not virtual, {_update} should be overridden instead
*/
function _burn(address account, uint256 value) internal {
if (account == address(0)) {
revert ERC20InvalidSender(address(0));
}
_update(account, address(0), value);
}
/**
* @dev Sets `value` as the allowance of `spender` over the `owner` s tokens.
*
* This internal function is equivalent to `approve`, and can be used to
* e.g. set automatic allowances for certain subsystems, etc.
*
* Emits an {Approval} event.
*
* Requirements:
*
* - `owner` cannot be the zero address.
* - `spender` cannot be the zero address.
*
* Overrides to this logic should be done to the variant with an additional `bool emitEvent` argument.
*/
function _approve(address owner, address spender, uint256 value) internal {
_approve(owner, spender, value, true);
}
/**
* @dev Variant of {_approve} with an optional flag to enable or disable the {Approval} event.
*
* By default (when calling {_approve}) the flag is set to true. On the other hand, approval changes made by
* `_spendAllowance` during the `transferFrom` operation set the flag to false. This saves gas by not emitting any
* `Approval` event during `transferFrom` operations.
*
* Anyone who wishes to continue emitting `Approval` events on the`transferFrom` operation can force the flag to
* true using the following override:
* ```
* function _approve(address owner, address spender, uint256 value, bool) internal virtual override {
* super._approve(owner, spender, value, true);
* }
* ```
*
* Requirements are the same as {_approve}.
*/
function _approve(address owner, address spender, uint256 value, bool emitEvent) internal virtual {
if (owner == address(0)) {
revert ERC20InvalidApprover(address(0));
}
if (spender == address(0)) {
revert ERC20InvalidSpender(address(0));
}
_allowances[owner][spender] = value;
if (emitEvent) {
emit Approval(owner, spender, value);
}
}
/**
* @dev Updates `owner` s allowance for `spender` based on spent `value`.
*
* Does not update the allowance value in case of infinite allowance.
* Revert if not enough allowance is available.
*
* Does not emit an {Approval} event.
*/
function _spendAllowance(address owner, address spender, uint256 value) internal virtual {
uint256 currentAllowance = allowance(owner, spender);
if (currentAllowance != type(uint256).max) {
if (currentAllowance < value) {
revert ERC20InsufficientAllowance(spender, currentAllowance, value);
}
unchecked {
_approve(owner, spender, currentAllowance - value, false);
}
}
}
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Casting.sol" as Casting;
import "./Helpers.sol" as Helpers;
import "./Math.sol" as Math;
/// @notice The unsigned 60.18-decimal fixed-point number representation, which can have up to 60 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the Solidity type uint256.
/// @dev The value type is defined here so it can be imported in all other files.
type UD60x18 is uint256;
/*//////////////////////////////////////////////////////////////////////////
CASTING
//////////////////////////////////////////////////////////////////////////*/
using {
Casting.intoSD1x18,
Casting.intoUD2x18,
Casting.intoSD59x18,
Casting.intoUint128,
Casting.intoUint256,
Casting.intoUint40,
Casting.unwrap
} for UD60x18 global;
/*//////////////////////////////////////////////////////////////////////////
MATHEMATICAL FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
// The global "using for" directive makes the functions in this library callable on the UD60x18 type.
using {
Math.avg,
Math.ceil,
Math.div,
Math.exp,
Math.exp2,
Math.floor,
Math.frac,
Math.gm,
Math.inv,
Math.ln,
Math.log10,
Math.log2,
Math.mul,
Math.pow,
Math.powu,
Math.sqrt
} for UD60x18 global;
/*//////////////////////////////////////////////////////////////////////////
HELPER FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
// The global "using for" directive makes the functions in this library callable on the UD60x18 type.
using {
Helpers.add,
Helpers.and,
Helpers.eq,
Helpers.gt,
Helpers.gte,
Helpers.isZero,
Helpers.lshift,
Helpers.lt,
Helpers.lte,
Helpers.mod,
Helpers.neq,
Helpers.not,
Helpers.or,
Helpers.rshift,
Helpers.sub,
Helpers.uncheckedAdd,
Helpers.uncheckedSub,
Helpers.xor
} for UD60x18 global;
/*//////////////////////////////////////////////////////////////////////////
OPERATORS
//////////////////////////////////////////////////////////////////////////*/
// The global "using for" directive makes it possible to use these operators on the UD60x18 type.
using {
Helpers.add as +,
Helpers.and2 as &,
Math.div as /,
Helpers.eq as ==,
Helpers.gt as >,
Helpers.gte as >=,
Helpers.lt as <,
Helpers.lte as <=,
Helpers.or as |,
Helpers.mod as %,
Math.mul as *,
Helpers.neq as !=,
Helpers.not as ~,
Helpers.sub as -,
Helpers.xor as ^
} for UD60x18 global;
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { wrap } from "./Casting.sol";
import {
uEXP_MAX_INPUT,
uEXP2_MAX_INPUT,
uHALF_UNIT,
uLOG2_10,
uLOG2_E,
uMAX_UD60x18,
uMAX_WHOLE_UD60x18,
UNIT,
uUNIT,
uUNIT_SQUARED,
ZERO
} from "./Constants.sol";
import { UD60x18 } from "./ValueType.sol";
/*//////////////////////////////////////////////////////////////////////////
MATHEMATICAL FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Calculates the arithmetic average of x and y using the following formula:
///
/// $$
/// avg(x, y) = (x & y) + ((xUint ^ yUint) / 2)
/// $$
///
/// In English, this is what this formula does:
///
/// 1. AND x and y.
/// 2. Calculate half of XOR x and y.
/// 3. Add the two results together.
///
/// This technique is known as SWAR, which stands for "SIMD within a register". You can read more about it here:
/// https://devblogs.microsoft.com/oldnewthing/20220207-00/?p=106223
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// @param x The first operand as a UD60x18 number.
/// @param y The second operand as a UD60x18 number.
/// @return result The arithmetic average as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function avg(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
uint256 yUint = y.unwrap();
unchecked {
result = wrap((xUint & yUint) + ((xUint ^ yUint) >> 1));
}
}
/// @notice Yields the smallest whole number greater than or equal to x.
///
/// @dev This is optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional
/// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x must be less than or equal to `MAX_WHOLE_UD60x18`.
///
/// @param x The UD60x18 number to ceil.
/// @param result The smallest whole number greater than or equal to x, as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function ceil(UD60x18 x) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
if (xUint > uMAX_WHOLE_UD60x18) {
revert Errors.PRBMath_UD60x18_Ceil_Overflow(x);
}
assembly ("memory-safe") {
// Equivalent to `x % UNIT`.
let remainder := mod(x, uUNIT)
// Equivalent to `UNIT - remainder`.
let delta := sub(uUNIT, remainder)
// Equivalent to `x + remainder > 0 ? delta : 0`.
result := add(x, mul(delta, gt(remainder, 0)))
}
}
/// @notice Divides two UD60x18 numbers, returning a new UD60x18 number.
///
/// @dev Uses {Common.mulDiv} to enable overflow-safe multiplication and division.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv}.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv}.
///
/// @param x The numerator as a UD60x18 number.
/// @param y The denominator as a UD60x18 number.
/// @param result The quotient as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function div(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(Common.mulDiv(x.unwrap(), uUNIT, y.unwrap()));
}
/// @notice Calculates the natural exponent of x using the following formula:
///
/// $$
/// e^x = 2^{x * log_2{e}}
/// $$
///
/// @dev Requirements:
/// - x must be less than 133_084258667509499441.
///
/// @param x The exponent as a UD60x18 number.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp(UD60x18 x) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
// This check prevents values greater than 192e18 from being passed to {exp2}.
if (xUint > uEXP_MAX_INPUT) {
revert Errors.PRBMath_UD60x18_Exp_InputTooBig(x);
}
unchecked {
// Inline the fixed-point multiplication to save gas.
uint256 doubleUnitProduct = xUint * uLOG2_E;
result = exp2(wrap(doubleUnitProduct / uUNIT));
}
}
/// @notice Calculates the binary exponent of x using the binary fraction method.
///
/// @dev See https://ethereum.stackexchange.com/q/79903/24693
///
/// Requirements:
/// - x must be less than 192e18.
/// - The result must fit in UD60x18.
///
/// @param x The exponent as a UD60x18 number.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp2(UD60x18 x) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
// Numbers greater than or equal to 192e18 don't fit in the 192.64-bit format.
if (xUint > uEXP2_MAX_INPUT) {
revert Errors.PRBMath_UD60x18_Exp2_InputTooBig(x);
}
// Convert x to the 192.64-bit fixed-point format.
uint256 x_192x64 = (xUint << 64) / uUNIT;
// Pass x to the {Common.exp2} function, which uses the 192.64-bit fixed-point number representation.
result = wrap(Common.exp2(x_192x64));
}
/// @notice Yields the greatest whole number less than or equal to x.
/// @dev Optimized for fractional value inputs, because every whole value has (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
/// @param x The UD60x18 number to floor.
/// @param result The greatest whole number less than or equal to x, as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function floor(UD60x18 x) pure returns (UD60x18 result) {
assembly ("memory-safe") {
// Equivalent to `x % UNIT`.
let remainder := mod(x, uUNIT)
// Equivalent to `x - remainder > 0 ? remainder : 0)`.
result := sub(x, mul(remainder, gt(remainder, 0)))
}
}
/// @notice Yields the excess beyond the floor of x using the odd function definition.
/// @dev See https://en.wikipedia.org/wiki/Fractional_part.
/// @param x The UD60x18 number to get the fractional part of.
/// @param result The fractional part of x as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function frac(UD60x18 x) pure returns (UD60x18 result) {
assembly ("memory-safe") {
result := mod(x, uUNIT)
}
}
/// @notice Calculates the geometric mean of x and y, i.e. $\sqrt{x * y}$, rounding down.
///
/// @dev Requirements:
/// - x * y must fit in UD60x18.
///
/// @param x The first operand as a UD60x18 number.
/// @param y The second operand as a UD60x18 number.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function gm(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
uint256 yUint = y.unwrap();
if (xUint == 0 || yUint == 0) {
return ZERO;
}
unchecked {
// Checking for overflow this way is faster than letting Solidity do it.
uint256 xyUint = xUint * yUint;
if (xyUint / xUint != yUint) {
revert Errors.PRBMath_UD60x18_Gm_Overflow(x, y);
}
// We don't need to multiply the result by `UNIT` here because the x*y product picked up a factor of `UNIT`
// during multiplication. See the comments in {Common.sqrt}.
result = wrap(Common.sqrt(xyUint));
}
}
/// @notice Calculates the inverse of x.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x must not be zero.
///
/// @param x The UD60x18 number for which to calculate the inverse.
/// @return result The inverse as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function inv(UD60x18 x) pure returns (UD60x18 result) {
unchecked {
result = wrap(uUNIT_SQUARED / x.unwrap());
}
}
/// @notice Calculates the natural logarithm of x using the following formula:
///
/// $$
/// ln{x} = log_2{x} / log_2{e}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
/// - The precision isn't sufficiently fine-grained to return exactly `UNIT` when the input is `E`.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The UD60x18 number for which to calculate the natural logarithm.
/// @return result The natural logarithm as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function ln(UD60x18 x) pure returns (UD60x18 result) {
unchecked {
// Inline the fixed-point multiplication to save gas. This is overflow-safe because the maximum value that
// {log2} can return is ~196_205294292027477728.
result = wrap(log2(x).unwrap() * uUNIT / uLOG2_E);
}
}
/// @notice Calculates the common logarithm of x using the following formula:
///
/// $$
/// log_{10}{x} = log_2{x} / log_2{10}
/// $$
///
/// However, if x is an exact power of ten, a hard coded value is returned.
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The UD60x18 number for which to calculate the common logarithm.
/// @return result The common logarithm as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function log10(UD60x18 x) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
if (xUint < uUNIT) {
revert Errors.PRBMath_UD60x18_Log_InputTooSmall(x);
}
// Note that the `mul` in this assembly block is the standard multiplication operation, not {UD60x18.mul}.
// prettier-ignore
assembly ("memory-safe") {
switch x
case 1 { result := mul(uUNIT, sub(0, 18)) }
case 10 { result := mul(uUNIT, sub(1, 18)) }
case 100 { result := mul(uUNIT, sub(2, 18)) }
case 1000 { result := mul(uUNIT, sub(3, 18)) }
case 10000 { result := mul(uUNIT, sub(4, 18)) }
case 100000 { result := mul(uUNIT, sub(5, 18)) }
case 1000000 { result := mul(uUNIT, sub(6, 18)) }
case 10000000 { result := mul(uUNIT, sub(7, 18)) }
case 100000000 { result := mul(uUNIT, sub(8, 18)) }
case 1000000000 { result := mul(uUNIT, sub(9, 18)) }
case 10000000000 { result := mul(uUNIT, sub(10, 18)) }
case 100000000000 { result := mul(uUNIT, sub(11, 18)) }
case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }
case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }
case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }
case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }
case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }
case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }
case 1000000000000000000 { result := 0 }
case 10000000000000000000 { result := uUNIT }
case 100000000000000000000 { result := mul(uUNIT, 2) }
case 1000000000000000000000 { result := mul(uUNIT, 3) }
case 10000000000000000000000 { result := mul(uUNIT, 4) }
case 100000000000000000000000 { result := mul(uUNIT, 5) }
case 1000000000000000000000000 { result := mul(uUNIT, 6) }
case 10000000000000000000000000 { result := mul(uUNIT, 7) }
case 100000000000000000000000000 { result := mul(uUNIT, 8) }
case 1000000000000000000000000000 { result := mul(uUNIT, 9) }
case 10000000000000000000000000000 { result := mul(uUNIT, 10) }
case 100000000000000000000000000000 { result := mul(uUNIT, 11) }
case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }
case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }
case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }
case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }
case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }
case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }
case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }
case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }
case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }
case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }
case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }
case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }
case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }
case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }
case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }
case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }
case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }
case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }
case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }
case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }
case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }
case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }
case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }
case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }
case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }
case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }
case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }
case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }
case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }
case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }
case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }
case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }
case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }
case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }
case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }
case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }
case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }
case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }
case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }
case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }
case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }
case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }
case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }
case 100000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 59) }
default { result := uMAX_UD60x18 }
}
if (result.unwrap() == uMAX_UD60x18) {
unchecked {
// Inline the fixed-point division to save gas.
result = wrap(log2(x).unwrap() * uUNIT / uLOG2_10);
}
}
}
/// @notice Calculates the binary logarithm of x using the iterative approximation algorithm:
///
/// $$
/// log_2{x} = n + log_2{y}, \text{ where } y = x*2^{-n}, \ y \in [1, 2)
/// $$
///
/// For $0 \leq x \lt 1$, the input is inverted:
///
/// $$
/// log_2{x} = -log_2{\frac{1}{x}}
/// $$
///
/// @dev See https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
///
/// Notes:
/// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.
///
/// Requirements:
/// - x must be greater than zero.
///
/// @param x The UD60x18 number for which to calculate the binary logarithm.
/// @return result The binary logarithm as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function log2(UD60x18 x) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
if (xUint < uUNIT) {
revert Errors.PRBMath_UD60x18_Log_InputTooSmall(x);
}
unchecked {
// Calculate the integer part of the logarithm.
uint256 n = Common.msb(xUint / uUNIT);
// This is the integer part of the logarithm as a UD60x18 number. The operation can't overflow because n
// n is at most 255 and UNIT is 1e18.
uint256 resultUint = n * uUNIT;
// Calculate $y = x * 2^{-n}$.
uint256 y = xUint >> n;
// If y is the unit number, the fractional part is zero.
if (y == uUNIT) {
return wrap(resultUint);
}
// Calculate the fractional part via the iterative approximation.
// The `delta >>= 1` part is equivalent to `delta /= 2`, but shifting bits is more gas efficient.
uint256 DOUBLE_UNIT = 2e18;
for (uint256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {
y = (y * y) / uUNIT;
// Is y^2 >= 2e18 and so in the range [2e18, 4e18)?
if (y >= DOUBLE_UNIT) {
// Add the 2^{-m} factor to the logarithm.
resultUint += delta;
// Halve y, which corresponds to z/2 in the Wikipedia article.
y >>= 1;
}
}
result = wrap(resultUint);
}
}
/// @notice Multiplies two UD60x18 numbers together, returning a new UD60x18 number.
///
/// @dev Uses {Common.mulDiv} to enable overflow-safe multiplication and division.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv}.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv}.
///
/// @dev See the documentation in {Common.mulDiv18}.
/// @param x The multiplicand as a UD60x18 number.
/// @param y The multiplier as a UD60x18 number.
/// @return result The product as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function mul(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(Common.mulDiv18(x.unwrap(), y.unwrap()));
}
/// @notice Raises x to the power of y.
///
/// For $1 \leq x \leq \infty$, the following standard formula is used:
///
/// $$
/// x^y = 2^{log_2{x} * y}
/// $$
///
/// For $0 \leq x \lt 1$, since the unsigned {log2} is undefined, an equivalent formula is used:
///
/// $$
/// i = \frac{1}{x}
/// w = 2^{log_2{i} * y}
/// x^y = \frac{1}{w}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {log2} and {mul}.
/// - Returns `UNIT` for 0^0.
/// - It may not perform well with very small values of x. Consider using SD59x18 as an alternative.
///
/// Requirements:
/// - Refer to the requirements in {exp2}, {log2}, and {mul}.
///
/// @param x The base as a UD60x18 number.
/// @param y The exponent as a UD60x18 number.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function pow(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
uint256 yUint = y.unwrap();
// If both x and y are zero, the result is `UNIT`. If just x is zero, the result is always zero.
if (xUint == 0) {
return yUint == 0 ? UNIT : ZERO;
}
// If x is `UNIT`, the result is always `UNIT`.
else if (xUint == uUNIT) {
return UNIT;
}
// If y is zero, the result is always `UNIT`.
if (yUint == 0) {
return UNIT;
}
// If y is `UNIT`, the result is always x.
else if (yUint == uUNIT) {
return x;
}
// If x is greater than `UNIT`, use the standard formula.
if (xUint > uUNIT) {
result = exp2(mul(log2(x), y));
}
// Conversely, if x is less than `UNIT`, use the equivalent formula.
else {
UD60x18 i = wrap(uUNIT_SQUARED / xUint);
UD60x18 w = exp2(mul(log2(i), y));
result = wrap(uUNIT_SQUARED / w.unwrap());
}
}
/// @notice Raises x (a UD60x18 number) to the power y (an unsigned basic integer) using the well-known
/// algorithm "exponentiation by squaring".
///
/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv18}.
/// - Returns `UNIT` for 0^0.
///
/// Requirements:
/// - The result must fit in UD60x18.
///
/// @param x The base as a UD60x18 number.
/// @param y The exponent as a uint256.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function powu(UD60x18 x, uint256 y) pure returns (UD60x18 result) {
// Calculate the first iteration of the loop in advance.
uint256 xUint = x.unwrap();
uint256 resultUint = y & 1 > 0 ? xUint : uUNIT;
// Equivalent to `for(y /= 2; y > 0; y /= 2)`.
for (y >>= 1; y > 0; y >>= 1) {
xUint = Common.mulDiv18(xUint, xUint);
// Equivalent to `y % 2 == 1`.
if (y & 1 > 0) {
resultUint = Common.mulDiv18(resultUint, xUint);
}
}
result = wrap(resultUint);
}
/// @notice Calculates the square root of x using the Babylonian method.
///
/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x must be less than `MAX_UD60x18 / UNIT`.
///
/// @param x The UD60x18 number for which to calculate the square root.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function sqrt(UD60x18 x) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
unchecked {
if (xUint > uMAX_UD60x18 / uUNIT) {
revert Errors.PRBMath_UD60x18_Sqrt_Overflow(x);
}
// Multiply x by `UNIT` to account for the factor of `UNIT` picked up when multiplying two UD60x18 numbers.
// In this case, the two numbers are both the square root.
result = wrap(Common.sqrt(xUint * uUNIT));
}
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { wrap } from "./Casting.sol";
import { UD60x18 } from "./ValueType.sol";
/// @notice Implements the checked addition operation (+) in the UD60x18 type.
function add(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(x.unwrap() + y.unwrap());
}
/// @notice Implements the AND (&) bitwise operation in the UD60x18 type.
function and(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {
result = wrap(x.unwrap() & bits);
}
/// @notice Implements the AND (&) bitwise operation in the UD60x18 type.
function and2(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(x.unwrap() & y.unwrap());
}
/// @notice Implements the equal operation (==) in the UD60x18 type.
function eq(UD60x18 x, UD60x18 y) pure returns (bool result) {
result = x.unwrap() == y.unwrap();
}
/// @notice Implements the greater than operation (>) in the UD60x18 type.
function gt(UD60x18 x, UD60x18 y) pure returns (bool result) {
result = x.unwrap() > y.unwrap();
}
/// @notice Implements the greater than or equal to operation (>=) in the UD60x18 type.
function gte(UD60x18 x, UD60x18 y) pure returns (bool result) {
result = x.unwrap() >= y.unwrap();
}
/// @notice Implements a zero comparison check function in the UD60x18 type.
function isZero(UD60x18 x) pure returns (bool result) {
// This wouldn't work if x could be negative.
result = x.unwrap() == 0;
}
/// @notice Implements the left shift operation (<<) in the UD60x18 type.
function lshift(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {
result = wrap(x.unwrap() << bits);
}
/// @notice Implements the lower than operation (<) in the UD60x18 type.
function lt(UD60x18 x, UD60x18 y) pure returns (bool result) {
result = x.unwrap() < y.unwrap();
}
/// @notice Implements the lower than or equal to operation (<=) in the UD60x18 type.
function lte(UD60x18 x, UD60x18 y) pure returns (bool result) {
result = x.unwrap() <= y.unwrap();
}
/// @notice Implements the checked modulo operation (%) in the UD60x18 type.
function mod(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(x.unwrap() % y.unwrap());
}
/// @notice Implements the not equal operation (!=) in the UD60x18 type.
function neq(UD60x18 x, UD60x18 y) pure returns (bool result) {
result = x.unwrap() != y.unwrap();
}
/// @notice Implements the NOT (~) bitwise operation in the UD60x18 type.
function not(UD60x18 x) pure returns (UD60x18 result) {
result = wrap(~x.unwrap());
}
/// @notice Implements the OR (|) bitwise operation in the UD60x18 type.
function or(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(x.unwrap() | y.unwrap());
}
/// @notice Implements the right shift operation (>>) in the UD60x18 type.
function rshift(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {
result = wrap(x.unwrap() >> bits);
}
/// @notice Implements the checked subtraction operation (-) in the UD60x18 type.
function sub(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(x.unwrap() - y.unwrap());
}
/// @notice Implements the unchecked addition operation (+) in the UD60x18 type.
function uncheckedAdd(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
unchecked {
result = wrap(x.unwrap() + y.unwrap());
}
}
/// @notice Implements the unchecked subtraction operation (-) in the UD60x18 type.
function uncheckedSub(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
unchecked {
result = wrap(x.unwrap() - y.unwrap());
}
}
/// @notice Implements the XOR (^) bitwise operation in the UD60x18 type.
function xor(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(x.unwrap() ^ y.unwrap());
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { UD60x18 } from "./ValueType.sol";
/// @notice Thrown when ceiling a number overflows UD60x18.
error PRBMath_UD60x18_Ceil_Overflow(UD60x18 x);
/// @notice Thrown when converting a basic integer to the fixed-point format overflows UD60x18.
error PRBMath_UD60x18_Convert_Overflow(uint256 x);
/// @notice Thrown when taking the natural exponent of a base greater than 133_084258667509499441.
error PRBMath_UD60x18_Exp_InputTooBig(UD60x18 x);
/// @notice Thrown when taking the binary exponent of a base greater than 192e18.
error PRBMath_UD60x18_Exp2_InputTooBig(UD60x18 x);
/// @notice Thrown when taking the geometric mean of two numbers and multiplying them overflows UD60x18.
error PRBMath_UD60x18_Gm_Overflow(UD60x18 x, UD60x18 y);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.
error PRBMath_UD60x18_IntoSD1x18_Overflow(UD60x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD59x18.
error PRBMath_UD60x18_IntoSD59x18_Overflow(UD60x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.
error PRBMath_UD60x18_IntoUD2x18_Overflow(UD60x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.
error PRBMath_UD60x18_IntoUint128_Overflow(UD60x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.
error PRBMath_UD60x18_IntoUint40_Overflow(UD60x18 x);
/// @notice Thrown when taking the logarithm of a number less than 1.
error PRBMath_UD60x18_Log_InputTooSmall(UD60x18 x);
/// @notice Thrown when calculating the square root overflows UD60x18.
error PRBMath_UD60x18_Sqrt_Overflow(UD60x18 x);
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { uMAX_UD60x18, uUNIT } from "./Constants.sol";
import { PRBMath_UD60x18_Convert_Overflow } from "./Errors.sol";
import { UD60x18 } from "./ValueType.sol";
/// @notice Converts a UD60x18 number to a simple integer by dividing it by `UNIT`.
/// @dev The result is rounded toward zero.
/// @param x The UD60x18 number to convert.
/// @return result The same number in basic integer form.
function convert(UD60x18 x) pure returns (uint256 result) {
result = UD60x18.unwrap(x) / uUNIT;
}
/// @notice Converts a simple integer to UD60x18 by multiplying it by `UNIT`.
///
/// @dev Requirements:
/// - x must be less than or equal to `MAX_UD60x18 / UNIT`.
///
/// @param x The basic integer to convert.
/// @param result The same number converted to UD60x18.
function convert(uint256 x) pure returns (UD60x18 result) {
if (x > uMAX_UD60x18 / uUNIT) {
revert PRBMath_UD60x18_Convert_Overflow(x);
}
unchecked {
result = UD60x18.wrap(x * uUNIT);
}
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { UD60x18 } from "./ValueType.sol";
// NOTICE: the "u" prefix stands for "unwrapped".
/// @dev Euler's number as a UD60x18 number.
UD60x18 constant E = UD60x18.wrap(2_718281828459045235);
/// @dev The maximum input permitted in {exp}.
uint256 constant uEXP_MAX_INPUT = 133_084258667509499440;
UD60x18 constant EXP_MAX_INPUT = UD60x18.wrap(uEXP_MAX_INPUT);
/// @dev The maximum input permitted in {exp2}.
uint256 constant uEXP2_MAX_INPUT = 192e18 - 1;
UD60x18 constant EXP2_MAX_INPUT = UD60x18.wrap(uEXP2_MAX_INPUT);
/// @dev Half the UNIT number.
uint256 constant uHALF_UNIT = 0.5e18;
UD60x18 constant HALF_UNIT = UD60x18.wrap(uHALF_UNIT);
/// @dev $log_2(10)$ as a UD60x18 number.
uint256 constant uLOG2_10 = 3_321928094887362347;
UD60x18 constant LOG2_10 = UD60x18.wrap(uLOG2_10);
/// @dev $log_2(e)$ as a UD60x18 number.
uint256 constant uLOG2_E = 1_442695040888963407;
UD60x18 constant LOG2_E = UD60x18.wrap(uLOG2_E);
/// @dev The maximum value a UD60x18 number can have.
uint256 constant uMAX_UD60x18 = 115792089237316195423570985008687907853269984665640564039457_584007913129639935;
UD60x18 constant MAX_UD60x18 = UD60x18.wrap(uMAX_UD60x18);
/// @dev The maximum whole value a UD60x18 number can have.
uint256 constant uMAX_WHOLE_UD60x18 = 115792089237316195423570985008687907853269984665640564039457_000000000000000000;
UD60x18 constant MAX_WHOLE_UD60x18 = UD60x18.wrap(uMAX_WHOLE_UD60x18);
/// @dev PI as a UD60x18 number.
UD60x18 constant PI = UD60x18.wrap(3_141592653589793238);
/// @dev The unit number, which gives the decimal precision of UD60x18.
uint256 constant uUNIT = 1e18;
UD60x18 constant UNIT = UD60x18.wrap(uUNIT);
/// @dev The unit number squared.
uint256 constant uUNIT_SQUARED = 1e36;
UD60x18 constant UNIT_SQUARED = UD60x18.wrap(uUNIT_SQUARED);
/// @dev Zero as a UD60x18 number.
UD60x18 constant ZERO = UD60x18.wrap(0);
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Errors.sol" as CastingErrors;
import { MAX_UINT128, MAX_UINT40 } from "../Common.sol";
import { uMAX_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { uMAX_SD59x18 } from "../sd59x18/Constants.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD60x18 } from "./ValueType.sol";
/// @notice Casts a UD60x18 number into SD1x18.
/// @dev Requirements:
/// - x must be less than or equal to `uMAX_SD1x18`.
function intoSD1x18(UD60x18 x) pure returns (SD1x18 result) {
uint256 xUint = UD60x18.unwrap(x);
if (xUint > uint256(int256(uMAX_SD1x18))) {
revert CastingErrors.PRBMath_UD60x18_IntoSD1x18_Overflow(x);
}
result = SD1x18.wrap(int64(uint64(xUint)));
}
/// @notice Casts a UD60x18 number into UD2x18.
/// @dev Requirements:
/// - x must be less than or equal to `uMAX_UD2x18`.
function intoUD2x18(UD60x18 x) pure returns (UD2x18 result) {
uint256 xUint = UD60x18.unwrap(x);
if (xUint > uMAX_UD2x18) {
revert CastingErrors.PRBMath_UD60x18_IntoUD2x18_Overflow(x);
}
result = UD2x18.wrap(uint64(xUint));
}
/// @notice Casts a UD60x18 number into SD59x18.
/// @dev Requirements:
/// - x must be less than or equal to `uMAX_SD59x18`.
function intoSD59x18(UD60x18 x) pure returns (SD59x18 result) {
uint256 xUint = UD60x18.unwrap(x);
if (xUint > uint256(uMAX_SD59x18)) {
revert CastingErrors.PRBMath_UD60x18_IntoSD59x18_Overflow(x);
}
result = SD59x18.wrap(int256(xUint));
}
/// @notice Casts a UD60x18 number into uint128.
/// @dev This is basically an alias for {unwrap}.
function intoUint256(UD60x18 x) pure returns (uint256 result) {
result = UD60x18.unwrap(x);
}
/// @notice Casts a UD60x18 number into uint128.
/// @dev Requirements:
/// - x must be less than or equal to `MAX_UINT128`.
function intoUint128(UD60x18 x) pure returns (uint128 result) {
uint256 xUint = UD60x18.unwrap(x);
if (xUint > MAX_UINT128) {
revert CastingErrors.PRBMath_UD60x18_IntoUint128_Overflow(x);
}
result = uint128(xUint);
}
/// @notice Casts a UD60x18 number into uint40.
/// @dev Requirements:
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(UD60x18 x) pure returns (uint40 result) {
uint256 xUint = UD60x18.unwrap(x);
if (xUint > MAX_UINT40) {
revert CastingErrors.PRBMath_UD60x18_IntoUint40_Overflow(x);
}
result = uint40(xUint);
}
/// @notice Alias for {wrap}.
function ud(uint256 x) pure returns (UD60x18 result) {
result = UD60x18.wrap(x);
}
/// @notice Alias for {wrap}.
function ud60x18(uint256 x) pure returns (UD60x18 result) {
result = UD60x18.wrap(x);
}
/// @notice Unwraps a UD60x18 number into uint256.
function unwrap(UD60x18 x) pure returns (uint256 result) {
result = UD60x18.unwrap(x);
}
/// @notice Wraps a uint256 number into the UD60x18 value type.
function wrap(uint256 x) pure returns (UD60x18 result) {
result = UD60x18.wrap(x);
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/draft-IERC6093.sol)
pragma solidity ^0.8.20;
/**
* @dev Standard ERC20 Errors
* Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC20 tokens.
*/
interface IERC20Errors {
/**
* @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
* @param sender Address whose tokens are being transferred.
* @param balance Current balance for the interacting account.
* @param needed Minimum amount required to perform a transfer.
*/
error ERC20InsufficientBalance(address sender, uint256 balance, uint256 needed);
/**
* @dev Indicates a failure with the token `sender`. Used in transfers.
* @param sender Address whose tokens are being transferred.
*/
error ERC20InvalidSender(address sender);
/**
* @dev Indicates a failure with the token `receiver`. Used in transfers.
* @param receiver Address to which tokens are being transferred.
*/
error ERC20InvalidReceiver(address receiver);
/**
* @dev Indicates a failure with the `spender`’s `allowance`. Used in transfers.
* @param spender Address that may be allowed to operate on tokens without being their owner.
* @param allowance Amount of tokens a `spender` is allowed to operate with.
* @param needed Minimum amount required to perform a transfer.
*/
error ERC20InsufficientAllowance(address spender, uint256 allowance, uint256 needed);
/**
* @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
* @param approver Address initiating an approval operation.
*/
error ERC20InvalidApprover(address approver);
/**
* @dev Indicates a failure with the `spender` to be approved. Used in approvals.
* @param spender Address that may be allowed to operate on tokens without being their owner.
*/
error ERC20InvalidSpender(address spender);
}
/**
* @dev Standard ERC721 Errors
* Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC721 tokens.
*/
interface IERC721Errors {
/**
* @dev Indicates that an address can't be an owner. For example, `address(0)` is a forbidden owner in EIP-20.
* Used in balance queries.
* @param owner Address of the current owner of a token.
*/
error ERC721InvalidOwner(address owner);
/**
* @dev Indicates a `tokenId` whose `owner` is the zero address.
* @param tokenId Identifier number of a token.
*/
error ERC721NonexistentToken(uint256 tokenId);
/**
* @dev Indicates an error related to the ownership over a particular token. Used in transfers.
* @param sender Address whose tokens are being transferred.
* @param tokenId Identifier number of a token.
* @param owner Address of the current owner of a token.
*/
error ERC721IncorrectOwner(address sender, uint256 tokenId, address owner);
/**
* @dev Indicates a failure with the token `sender`. Used in transfers.
* @param sender Address whose tokens are being transferred.
*/
error ERC721InvalidSender(address sender);
/**
* @dev Indicates a failure with the token `receiver`. Used in transfers.
* @param receiver Address to which tokens are being transferred.
*/
error ERC721InvalidReceiver(address receiver);
/**
* @dev Indicates a failure with the `operator`’s approval. Used in transfers.
* @param operator Address that may be allowed to operate on tokens without being their owner.
* @param tokenId Identifier number of a token.
*/
error ERC721InsufficientApproval(address operator, uint256 tokenId);
/**
* @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
* @param approver Address initiating an approval operation.
*/
error ERC721InvalidApprover(address approver);
/**
* @dev Indicates a failure with the `operator` to be approved. Used in approvals.
* @param operator Address that may be allowed to operate on tokens without being their owner.
*/
error ERC721InvalidOperator(address operator);
}
/**
* @dev Standard ERC1155 Errors
* Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC1155 tokens.
*/
interface IERC1155Errors {
/**
* @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
* @param sender Address whose tokens are being transferred.
* @param balance Current balance for the interacting account.
* @param needed Minimum amount required to perform a transfer.
* @param tokenId Identifier number of a token.
*/
error ERC1155InsufficientBalance(address sender, uint256 balance, uint256 needed, uint256 tokenId);
/**
* @dev Indicates a failure with the token `sender`. Used in transfers.
* @param sender Address whose tokens are being transferred.
*/
error ERC1155InvalidSender(address sender);
/**
* @dev Indicates a failure with the token `receiver`. Used in transfers.
* @param receiver Address to which tokens are being transferred.
*/
error ERC1155InvalidReceiver(address receiver);
/**
* @dev Indicates a failure with the `operator`’s approval. Used in transfers.
* @param operator Address that may be allowed to operate on tokens without being their owner.
* @param owner Address of the current owner of a token.
*/
error ERC1155MissingApprovalForAll(address operator, address owner);
/**
* @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
* @param approver Address initiating an approval operation.
*/
error ERC1155InvalidApprover(address approver);
/**
* @dev Indicates a failure with the `operator` to be approved. Used in approvals.
* @param operator Address that may be allowed to operate on tokens without being their owner.
*/
error ERC1155InvalidOperator(address operator);
/**
* @dev Indicates an array length mismatch between ids and values in a safeBatchTransferFrom operation.
* Used in batch transfers.
* @param idsLength Length of the array of token identifiers
* @param valuesLength Length of the array of token amounts
*/
error ERC1155InvalidArrayLength(uint256 idsLength, uint256 valuesLength);
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.1) (utils/Context.sol)
pragma solidity ^0.8.20;
/**
* @dev Provides information about the current execution context, including the
* sender of the transaction and its data. While these are generally available
* via msg.sender and msg.data, they should not be accessed in such a direct
* manner, since when dealing with meta-transactions the account sending and
* paying for execution may not be the actual sender (as far as an application
* is concerned).
*
* This contract is only required for intermediate, library-like contracts.
*/
abstract contract Context {
function _msgSender() internal view virtual returns (address) {
return msg.sender;
}
function _msgData() internal view virtual returns (bytes calldata) {
return msg.data;
}
function _contextSuffixLength() internal view virtual returns (uint256) {
return 0;
}
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/extensions/IERC20Metadata.sol)
pragma solidity ^0.8.20;
import {IERC20} from "../IERC20.sol";
/**
* @dev Interface for the optional metadata functions from the ERC20 standard.
*/
interface IERC20Metadata is IERC20 {
/**
* @dev Returns the name of the token.
*/
function name() external view returns (string memory);
/**
* @dev Returns the symbol of the token.
*/
function symbol() external view returns (string memory);
/**
* @dev Returns the decimals places of the token.
*/
function decimals() external view returns (uint8);
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/IERC20.sol)
pragma solidity ^0.8.20;
/**
* @dev Interface of the ERC20 standard as defined in the EIP.
*/
interface IERC20 {
/**
* @dev Emitted when `value` tokens are moved from one account (`from`) to
* another (`to`).
*
* Note that `value` may be zero.
*/
event Transfer(address indexed from, address indexed to, uint256 value);
/**
* @dev Emitted when the allowance of a `spender` for an `owner` is set by
* a call to {approve}. `value` is the new allowance.
*/
event Approval(address indexed owner, address indexed spender, uint256 value);
/**
* @dev Returns the value of tokens in existence.
*/
function totalSupply() external view returns (uint256);
/**
* @dev Returns the value of tokens owned by `account`.
*/
function balanceOf(address account) external view returns (uint256);
/**
* @dev Moves a `value` amount of tokens from the caller's account to `to`.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* Emits a {Transfer} event.
*/
function transfer(address to, uint256 value) external returns (bool);
/**
* @dev Returns the remaining number of tokens that `spender` will be
* allowed to spend on behalf of `owner` through {transferFrom}. This is
* zero by default.
*
* This value changes when {approve} or {transferFrom} are called.
*/
function allowance(address owner, address spender) external view returns (uint256);
/**
* @dev Sets a `value` amount of tokens as the allowance of `spender` over the
* caller's tokens.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* IMPORTANT: Beware that changing an allowance with this method brings the risk
* that someone may use both the old and the new allowance by unfortunate
* transaction ordering. One possible solution to mitigate this race
* condition is to first reduce the spender's allowance to 0 and set the
* desired value afterwards:
* https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
*
* Emits an {Approval} event.
*/
function approve(address spender, uint256 value) external returns (bool);
/**
* @dev Moves a `value` amount of tokens from `from` to `to` using the
* allowance mechanism. `value` is then deducted from the caller's
* allowance.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* Emits a {Transfer} event.
*/
function transferFrom(address from, address to, uint256 value) external returns (bool);
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
// Common.sol
//
// Common mathematical functions used in both SD59x18 and UD60x18. Note that these global functions do not
// always operate with SD59x18 and UD60x18 numbers.
/*//////////////////////////////////////////////////////////////////////////
CUSTOM ERRORS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Thrown when the resultant value in {mulDiv} overflows uint256.
error PRBMath_MulDiv_Overflow(uint256 x, uint256 y, uint256 denominator);
/// @notice Thrown when the resultant value in {mulDiv18} overflows uint256.
error PRBMath_MulDiv18_Overflow(uint256 x, uint256 y);
/// @notice Thrown when one of the inputs passed to {mulDivSigned} is `type(int256).min`.
error PRBMath_MulDivSigned_InputTooSmall();
/// @notice Thrown when the resultant value in {mulDivSigned} overflows int256.
error PRBMath_MulDivSigned_Overflow(int256 x, int256 y);
/*//////////////////////////////////////////////////////////////////////////
CONSTANTS
//////////////////////////////////////////////////////////////////////////*/
/// @dev The maximum value a uint128 number can have.
uint128 constant MAX_UINT128 = type(uint128).max;
/// @dev The maximum value a uint40 number can have.
uint40 constant MAX_UINT40 = type(uint40).max;
/// @dev The unit number, which the decimal precision of the fixed-point types.
uint256 constant UNIT = 1e18;
/// @dev The unit number inverted mod 2^256.
uint256 constant UNIT_INVERSE = 78156646155174841979727994598816262306175212592076161876661_508869554232690281;
/// @dev The the largest power of two that divides the decimal value of `UNIT`. The logarithm of this value is the least significant
/// bit in the binary representation of `UNIT`.
uint256 constant UNIT_LPOTD = 262144;
/*//////////////////////////////////////////////////////////////////////////
FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Calculates the binary exponent of x using the binary fraction method.
/// @dev Has to use 192.64-bit fixed-point numbers. See https://ethereum.stackexchange.com/a/96594/24693.
/// @param x The exponent as an unsigned 192.64-bit fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
/// @custom:smtchecker abstract-function-nondet
function exp2(uint256 x) pure returns (uint256 result) {
unchecked {
// Start from 0.5 in the 192.64-bit fixed-point format.
result = 0x800000000000000000000000000000000000000000000000;
// The following logic multiplies the result by $\sqrt{2^{-i}}$ when the bit at position i is 1. Key points:
//
// 1. Intermediate results will not overflow, as the starting point is 2^191 and all magic factors are under 2^65.
// 2. The rationale for organizing the if statements into groups of 8 is gas savings. If the result of performing
// a bitwise AND operation between x and any value in the array [0x80; 0x40; 0x20; 0x10; 0x08; 0x04; 0x02; 0x01] is 1,
// we know that `x & 0xFF` is also 1.
if (x & 0xFF00000000000000 > 0) {
if (x & 0x8000000000000000 > 0) {
result = (result * 0x16A09E667F3BCC909) >> 64;
}
if (x & 0x4000000000000000 > 0) {
result = (result * 0x1306FE0A31B7152DF) >> 64;
}
if (x & 0x2000000000000000 > 0) {
result = (result * 0x1172B83C7D517ADCE) >> 64;
}
if (x & 0x1000000000000000 > 0) {
result = (result * 0x10B5586CF9890F62A) >> 64;
}
if (x & 0x800000000000000 > 0) {
result = (result * 0x1059B0D31585743AE) >> 64;
}
if (x & 0x400000000000000 > 0) {
result = (result * 0x102C9A3E778060EE7) >> 64;
}
if (x & 0x200000000000000 > 0) {
result = (result * 0x10163DA9FB33356D8) >> 64;
}
if (x & 0x100000000000000 > 0) {
result = (result * 0x100B1AFA5ABCBED61) >> 64;
}
}
if (x & 0xFF000000000000 > 0) {
if (x & 0x80000000000000 > 0) {
result = (result * 0x10058C86DA1C09EA2) >> 64;
}
if (x & 0x40000000000000 > 0) {
result = (result * 0x1002C605E2E8CEC50) >> 64;
}
if (x & 0x20000000000000 > 0) {
result = (result * 0x100162F3904051FA1) >> 64;
}
if (x & 0x10000000000000 > 0) {
result = (result * 0x1000B175EFFDC76BA) >> 64;
}
if (x & 0x8000000000000 > 0) {
result = (result * 0x100058BA01FB9F96D) >> 64;
}
if (x & 0x4000000000000 > 0) {
result = (result * 0x10002C5CC37DA9492) >> 64;
}
if (x & 0x2000000000000 > 0) {
result = (result * 0x1000162E525EE0547) >> 64;
}
if (x & 0x1000000000000 > 0) {
result = (result * 0x10000B17255775C04) >> 64;
}
}
if (x & 0xFF0000000000 > 0) {
if (x & 0x800000000000 > 0) {
result = (result * 0x1000058B91B5BC9AE) >> 64;
}
if (x & 0x400000000000 > 0) {
result = (result * 0x100002C5C89D5EC6D) >> 64;
}
if (x & 0x200000000000 > 0) {
result = (result * 0x10000162E43F4F831) >> 64;
}
if (x & 0x100000000000 > 0) {
result = (result * 0x100000B1721BCFC9A) >> 64;
}
if (x & 0x80000000000 > 0) {
result = (result * 0x10000058B90CF1E6E) >> 64;
}
if (x & 0x40000000000 > 0) {
result = (result * 0x1000002C5C863B73F) >> 64;
}
if (x & 0x20000000000 > 0) {
result = (result * 0x100000162E430E5A2) >> 64;
}
if (x & 0x10000000000 > 0) {
result = (result * 0x1000000B172183551) >> 64;
}
}
if (x & 0xFF00000000 > 0) {
if (x & 0x8000000000 > 0) {
result = (result * 0x100000058B90C0B49) >> 64;
}
if (x & 0x4000000000 > 0) {
result = (result * 0x10000002C5C8601CC) >> 64;
}
if (x & 0x2000000000 > 0) {
result = (result * 0x1000000162E42FFF0) >> 64;
}
if (x & 0x1000000000 > 0) {
result = (result * 0x10000000B17217FBB) >> 64;
}
if (x & 0x800000000 > 0) {
result = (result * 0x1000000058B90BFCE) >> 64;
}
if (x & 0x400000000 > 0) {
result = (result * 0x100000002C5C85FE3) >> 64;
}
if (x & 0x200000000 > 0) {
result = (result * 0x10000000162E42FF1) >> 64;
}
if (x & 0x100000000 > 0) {
result = (result * 0x100000000B17217F8) >> 64;
}
}
if (x & 0xFF000000 > 0) {
if (x & 0x80000000 > 0) {
result = (result * 0x10000000058B90BFC) >> 64;
}
if (x & 0x40000000 > 0) {
result = (result * 0x1000000002C5C85FE) >> 64;
}
if (x & 0x20000000 > 0) {
result = (result * 0x100000000162E42FF) >> 64;
}
if (x & 0x10000000 > 0) {
result = (result * 0x1000000000B17217F) >> 64;
}
if (x & 0x8000000 > 0) {
result = (result * 0x100000000058B90C0) >> 64;
}
if (x & 0x4000000 > 0) {
result = (result * 0x10000000002C5C860) >> 64;
}
if (x & 0x2000000 > 0) {
result = (result * 0x1000000000162E430) >> 64;
}
if (x & 0x1000000 > 0) {
result = (result * 0x10000000000B17218) >> 64;
}
}
if (x & 0xFF0000 > 0) {
if (x & 0x800000 > 0) {
result = (result * 0x1000000000058B90C) >> 64;
}
if (x & 0x400000 > 0) {
result = (result * 0x100000000002C5C86) >> 64;
}
if (x & 0x200000 > 0) {
result = (result * 0x10000000000162E43) >> 64;
}
if (x & 0x100000 > 0) {
result = (result * 0x100000000000B1721) >> 64;
}
if (x & 0x80000 > 0) {
result = (result * 0x10000000000058B91) >> 64;
}
if (x & 0x40000 > 0) {
result = (result * 0x1000000000002C5C8) >> 64;
}
if (x & 0x20000 > 0) {
result = (result * 0x100000000000162E4) >> 64;
}
if (x & 0x10000 > 0) {
result = (result * 0x1000000000000B172) >> 64;
}
}
if (x & 0xFF00 > 0) {
if (x & 0x8000 > 0) {
result = (result * 0x100000000000058B9) >> 64;
}
if (x & 0x4000 > 0) {
result = (result * 0x10000000000002C5D) >> 64;
}
if (x & 0x2000 > 0) {
result = (result * 0x1000000000000162E) >> 64;
}
if (x & 0x1000 > 0) {
result = (result * 0x10000000000000B17) >> 64;
}
if (x & 0x800 > 0) {
result = (result * 0x1000000000000058C) >> 64;
}
if (x & 0x400 > 0) {
result = (result * 0x100000000000002C6) >> 64;
}
if (x & 0x200 > 0) {
result = (result * 0x10000000000000163) >> 64;
}
if (x & 0x100 > 0) {
result = (result * 0x100000000000000B1) >> 64;
}
}
if (x & 0xFF > 0) {
if (x & 0x80 > 0) {
result = (result * 0x10000000000000059) >> 64;
}
if (x & 0x40 > 0) {
result = (result * 0x1000000000000002C) >> 64;
}
if (x & 0x20 > 0) {
result = (result * 0x10000000000000016) >> 64;
}
if (x & 0x10 > 0) {
result = (result * 0x1000000000000000B) >> 64;
}
if (x & 0x8 > 0) {
result = (result * 0x10000000000000006) >> 64;
}
if (x & 0x4 > 0) {
result = (result * 0x10000000000000003) >> 64;
}
if (x & 0x2 > 0) {
result = (result * 0x10000000000000001) >> 64;
}
if (x & 0x1 > 0) {
result = (result * 0x10000000000000001) >> 64;
}
}
// In the code snippet below, two operations are executed simultaneously:
//
// 1. The result is multiplied by $(2^n + 1)$, where $2^n$ represents the integer part, and the additional 1
// accounts for the initial guess of 0.5. This is achieved by subtracting from 191 instead of 192.
// 2. The result is then converted to an unsigned 60.18-decimal fixed-point format.
//
// The underlying logic is based on the relationship $2^{191-ip} = 2^{ip} / 2^{191}$, where $ip$ denotes the,
// integer part, $2^n$.
result *= UNIT;
result >>= (191 - (x >> 64));
}
}
/// @notice Finds the zero-based index of the first 1 in the binary representation of x.
///
/// @dev See the note on "msb" in this Wikipedia article: https://en.wikipedia.org/wiki/Find_first_set
///
/// Each step in this implementation is equivalent to this high-level code:
///
/// ```solidity
/// if (x >= 2 ** 128) {
/// x >>= 128;
/// result += 128;
/// }
/// ```
///
/// Where 128 is replaced with each respective power of two factor. See the full high-level implementation here:
/// https://gist.github.com/PaulRBerg/f932f8693f2733e30c4d479e8e980948
///
/// The Yul instructions used below are:
///
/// - "gt" is "greater than"
/// - "or" is the OR bitwise operator
/// - "shl" is "shift left"
/// - "shr" is "shift right"
///
/// @param x The uint256 number for which to find the index of the most significant bit.
/// @return result The index of the most significant bit as a uint256.
/// @custom:smtchecker abstract-function-nondet
function msb(uint256 x) pure returns (uint256 result) {
// 2^128
assembly ("memory-safe") {
let factor := shl(7, gt(x, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
x := shr(factor, x)
result := or(result, factor)
}
// 2^64
assembly ("memory-safe") {
let factor := shl(6, gt(x, 0xFFFFFFFFFFFFFFFF))
x := shr(factor, x)
result := or(result, factor)
}
// 2^32
assembly ("memory-safe") {
let factor := shl(5, gt(x, 0xFFFFFFFF))
x := shr(factor, x)
result := or(result, factor)
}
// 2^16
assembly ("memory-safe") {
let factor := shl(4, gt(x, 0xFFFF))
x := shr(factor, x)
result := or(result, factor)
}
// 2^8
assembly ("memory-safe") {
let factor := shl(3, gt(x, 0xFF))
x := shr(factor, x)
result := or(result, factor)
}
// 2^4
assembly ("memory-safe") {
let factor := shl(2, gt(x, 0xF))
x := shr(factor, x)
result := or(result, factor)
}
// 2^2
assembly ("memory-safe") {
let factor := shl(1, gt(x, 0x3))
x := shr(factor, x)
result := or(result, factor)
}
// 2^1
// No need to shift x any more.
assembly ("memory-safe") {
let factor := gt(x, 0x1)
result := or(result, factor)
}
}
/// @notice Calculates x*y÷denominator with 512-bit precision.
///
/// @dev Credits to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
///
/// Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - The denominator must not be zero.
/// - The result must fit in uint256.
///
/// @param x The multiplicand as a uint256.
/// @param y The multiplier as a uint256.
/// @param denominator The divisor as a uint256.
/// @return result The result as a uint256.
/// @custom:smtchecker abstract-function-nondet
function mulDiv(uint256 x, uint256 y, uint256 denominator) pure returns (uint256 result) {
// 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
// use the Chinese Remainder Theorem to reconstruct the 512-bit result. The result is stored in two 256
// variables such that product = prod1 * 2^256 + prod0.
uint256 prod0; // Least significant 256 bits of the product
uint256 prod1; // Most significant 256 bits of the product
assembly ("memory-safe") {
let mm := mulmod(x, y, not(0))
prod0 := mul(x, y)
prod1 := sub(sub(mm, prod0), lt(mm, prod0))
}
// Handle non-overflow cases, 256 by 256 division.
if (prod1 == 0) {
unchecked {
return prod0 / denominator;
}
}
// Make sure the result is less than 2^256. Also prevents denominator == 0.
if (prod1 >= denominator) {
revert PRBMath_MulDiv_Overflow(x, y, denominator);
}
////////////////////////////////////////////////////////////////////////////
// 512 by 256 division
////////////////////////////////////////////////////////////////////////////
// Make division exact by subtracting the remainder from [prod1 prod0].
uint256 remainder;
assembly ("memory-safe") {
// Compute remainder using the mulmod Yul instruction.
remainder := mulmod(x, y, denominator)
// Subtract 256 bit number from 512-bit number.
prod1 := sub(prod1, gt(remainder, prod0))
prod0 := sub(prod0, remainder)
}
unchecked {
// Calculate the largest power of two divisor of the denominator using the unary operator ~. This operation cannot overflow
// because the denominator cannot be zero at this point in the function execution. The result is always >= 1.
// For more detail, see https://cs.stackexchange.com/q/138556/92363.
uint256 lpotdod = denominator & (~denominator + 1);
uint256 flippedLpotdod;
assembly ("memory-safe") {
// Factor powers of two out of denominator.
denominator := div(denominator, lpotdod)
// Divide [prod1 prod0] by lpotdod.
prod0 := div(prod0, lpotdod)
// Get the flipped value `2^256 / lpotdod`. If the `lpotdod` is zero, the flipped value is one.
// `sub(0, lpotdod)` produces the two's complement version of `lpotdod`, which is equivalent to flipping all the bits.
// However, `div` interprets this value as an unsigned value: https://ethereum.stackexchange.com/q/147168/24693
flippedLpotdod := add(div(sub(0, lpotdod), lpotdod), 1)
}
// Shift in bits from prod1 into prod0.
prod0 |= prod1 * flippedLpotdod;
// 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;
}
}
/// @notice Calculates x*y÷1e18 with 512-bit precision.
///
/// @dev A variant of {mulDiv} with constant folding, i.e. in which the denominator is hard coded to 1e18.
///
/// Notes:
/// - The body is purposely left uncommented; to understand how this works, see the documentation in {mulDiv}.
/// - The result is rounded toward zero.
/// - We take as an axiom that the result cannot be `MAX_UINT256` when x and y solve the following system of equations:
///
/// $$
/// \begin{cases}
/// x * y = MAX\_UINT256 * UNIT \\
/// (x * y) \% UNIT \geq \frac{UNIT}{2}
/// \end{cases}
/// $$
///
/// Requirements:
/// - Refer to the requirements in {mulDiv}.
/// - The result must fit in uint256.
///
/// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.
/// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
/// @custom:smtchecker abstract-function-nondet
function mulDiv18(uint256 x, uint256 y) pure returns (uint256 result) {
uint256 prod0;
uint256 prod1;
assembly ("memory-safe") {
let mm := mulmod(x, y, not(0))
prod0 := mul(x, y)
prod1 := sub(sub(mm, prod0), lt(mm, prod0))
}
if (prod1 == 0) {
unchecked {
return prod0 / UNIT;
}
}
if (prod1 >= UNIT) {
revert PRBMath_MulDiv18_Overflow(x, y);
}
uint256 remainder;
assembly ("memory-safe") {
remainder := mulmod(x, y, UNIT)
result :=
mul(
or(
div(sub(prod0, remainder), UNIT_LPOTD),
mul(sub(prod1, gt(remainder, prod0)), add(div(sub(0, UNIT_LPOTD), UNIT_LPOTD), 1))
),
UNIT_INVERSE
)
}
}
/// @notice Calculates x*y÷denominator with 512-bit precision.
///
/// @dev This is an extension of {mulDiv} for signed numbers, which works by computing the signs and the absolute values separately.
///
/// Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - Refer to the requirements in {mulDiv}.
/// - None of the inputs can be `type(int256).min`.
/// - The result must fit in int256.
///
/// @param x The multiplicand as an int256.
/// @param y The multiplier as an int256.
/// @param denominator The divisor as an int256.
/// @return result The result as an int256.
/// @custom:smtchecker abstract-function-nondet
function mulDivSigned(int256 x, int256 y, int256 denominator) pure returns (int256 result) {
if (x == type(int256).min || y == type(int256).min || denominator == type(int256).min) {
revert PRBMath_MulDivSigned_InputTooSmall();
}
// Get hold of the absolute values of x, y and the denominator.
uint256 xAbs;
uint256 yAbs;
uint256 dAbs;
unchecked {
xAbs = x < 0 ? uint256(-x) : uint256(x);
yAbs = y < 0 ? uint256(-y) : uint256(y);
dAbs = denominator < 0 ? uint256(-denominator) : uint256(denominator);
}
// Compute the absolute value of x*y÷denominator. The result must fit in int256.
uint256 resultAbs = mulDiv(xAbs, yAbs, dAbs);
if (resultAbs > uint256(type(int256).max)) {
revert PRBMath_MulDivSigned_Overflow(x, y);
}
// Get the signs of x, y and the denominator.
uint256 sx;
uint256 sy;
uint256 sd;
assembly ("memory-safe") {
// "sgt" is the "signed greater than" assembly instruction and "sub(0,1)" is -1 in two's complement.
sx := sgt(x, sub(0, 1))
sy := sgt(y, sub(0, 1))
sd := sgt(denominator, sub(0, 1))
}
// XOR over sx, sy and sd. What this does is to check whether there are 1 or 3 negative signs in the inputs.
// If there are, the result should be negative. Otherwise, it should be positive.
unchecked {
result = sx ^ sy ^ sd == 0 ? -int256(resultAbs) : int256(resultAbs);
}
}
/// @notice Calculates the square root of x using the Babylonian method.
///
/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Notes:
/// - If x is not a perfect square, the result is rounded down.
/// - Credits to OpenZeppelin for the explanations in comments below.
///
/// @param x The uint256 number for which to calculate the square root.
/// @return result The result as a uint256.
/// @custom:smtchecker abstract-function-nondet
function sqrt(uint256 x) pure returns (uint256 result) {
if (x == 0) {
return 0;
}
// For our first guess, we calculate the biggest power of 2 which is smaller than the square root of x.
//
// We know that the "msb" (most significant bit) of x is a power of 2 such that we have:
//
// $$
// msb(x) <= x <= 2*msb(x)$
// $$
//
// We write $msb(x)$ as $2^k$, and we get:
//
// $$
// k = log_2(x)
// $$
//
// Thus, we can write the initial inequality as:
//
// $$
// 2^{log_2(x)} <= x <= 2*2^{log_2(x)+1} \\
// sqrt(2^k) <= sqrt(x) < sqrt(2^{k+1}) \\
// 2^{k/2} <= sqrt(x) < 2^{(k+1)/2} <= 2^{(k/2)+1}
// $$
//
// Consequently, $2^{log_2(x) /2} is a good first approximation of sqrt(x) with at least one correct bit.
uint256 xAux = uint256(x);
result = 1;
if (xAux >= 2 ** 128) {
xAux >>= 128;
result <<= 64;
}
if (xAux >= 2 ** 64) {
xAux >>= 64;
result <<= 32;
}
if (xAux >= 2 ** 32) {
xAux >>= 32;
result <<= 16;
}
if (xAux >= 2 ** 16) {
xAux >>= 16;
result <<= 8;
}
if (xAux >= 2 ** 8) {
xAux >>= 8;
result <<= 4;
}
if (xAux >= 2 ** 4) {
xAux >>= 4;
result <<= 2;
}
if (xAux >= 2 ** 2) {
result <<= 1;
}
// At this point, `result` is an estimation with at least one bit of precision. We know the true value has at
// most 128 bits, 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 + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
// If x is not a perfect square, round the result toward zero.
uint256 roundedResult = x / result;
if (result >= roundedResult) {
result = roundedResult;
}
}
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Casting.sol" as Casting;
/// @notice The unsigned 2.18-decimal fixed-point number representation, which can have up to 2 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type uint64. This is useful when end users want to use uint64 to save gas, e.g. with tight variable packing in contract
/// storage.
type UD2x18 is uint64;
/*//////////////////////////////////////////////////////////////////////////
CASTING
//////////////////////////////////////////////////////////////////////////*/
using {
Casting.intoSD1x18,
Casting.intoSD59x18,
Casting.intoUD60x18,
Casting.intoUint256,
Casting.intoUint128,
Casting.intoUint40,
Casting.unwrap
} for UD2x18 global;
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { UD2x18 } from "./ValueType.sol";
/// @dev Euler's number as a UD2x18 number.
UD2x18 constant E = UD2x18.wrap(2_718281828459045235);
/// @dev The maximum value a UD2x18 number can have.
uint64 constant uMAX_UD2x18 = 18_446744073709551615;
UD2x18 constant MAX_UD2x18 = UD2x18.wrap(uMAX_UD2x18);
/// @dev PI as a UD2x18 number.
UD2x18 constant PI = UD2x18.wrap(3_141592653589793238);
/// @dev The unit number, which gives the decimal precision of UD2x18.
UD2x18 constant UNIT = UD2x18.wrap(1e18);
uint64 constant uUNIT = 1e18;
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Casting.sol" as Casting;
import "./Helpers.sol" as Helpers;
import "./Math.sol" as Math;
/// @notice The signed 59.18-decimal fixed-point number representation, which can have up to 59 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type int256.
type SD59x18 is int256;
/*//////////////////////////////////////////////////////////////////////////
CASTING
//////////////////////////////////////////////////////////////////////////*/
using {
Casting.intoInt256,
Casting.intoSD1x18,
Casting.intoUD2x18,
Casting.intoUD60x18,
Casting.intoUint256,
Casting.intoUint128,
Casting.intoUint40,
Casting.unwrap
} for SD59x18 global;
/*//////////////////////////////////////////////////////////////////////////
MATHEMATICAL FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
using {
Math.abs,
Math.avg,
Math.ceil,
Math.div,
Math.exp,
Math.exp2,
Math.floor,
Math.frac,
Math.gm,
Math.inv,
Math.log10,
Math.log2,
Math.ln,
Math.mul,
Math.pow,
Math.powu,
Math.sqrt
} for SD59x18 global;
/*//////////////////////////////////////////////////////////////////////////
HELPER FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
using {
Helpers.add,
Helpers.and,
Helpers.eq,
Helpers.gt,
Helpers.gte,
Helpers.isZero,
Helpers.lshift,
Helpers.lt,
Helpers.lte,
Helpers.mod,
Helpers.neq,
Helpers.not,
Helpers.or,
Helpers.rshift,
Helpers.sub,
Helpers.uncheckedAdd,
Helpers.uncheckedSub,
Helpers.uncheckedUnary,
Helpers.xor
} for SD59x18 global;
/*//////////////////////////////////////////////////////////////////////////
OPERATORS
//////////////////////////////////////////////////////////////////////////*/
// The global "using for" directive makes it possible to use these operators on the SD59x18 type.
using {
Helpers.add as +,
Helpers.and2 as &,
Math.div as /,
Helpers.eq as ==,
Helpers.gt as >,
Helpers.gte as >=,
Helpers.lt as <,
Helpers.lte as <=,
Helpers.mod as %,
Math.mul as *,
Helpers.neq as !=,
Helpers.not as ~,
Helpers.or as |,
Helpers.sub as -,
Helpers.unary as -,
Helpers.xor as ^
} for SD59x18 global;
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { SD59x18 } from "./ValueType.sol";
// NOTICE: the "u" prefix stands for "unwrapped".
/// @dev Euler's number as an SD59x18 number.
SD59x18 constant E = SD59x18.wrap(2_718281828459045235);
/// @dev The maximum input permitted in {exp}.
int256 constant uEXP_MAX_INPUT = 133_084258667509499440;
SD59x18 constant EXP_MAX_INPUT = SD59x18.wrap(uEXP_MAX_INPUT);
/// @dev Any value less than this returns 0 in {exp}.
int256 constant uEXP_MIN_THRESHOLD = -41_446531673892822322;
SD59x18 constant EXP_MIN_THRESHOLD = SD59x18.wrap(uEXP_MIN_THRESHOLD);
/// @dev The maximum input permitted in {exp2}.
int256 constant uEXP2_MAX_INPUT = 192e18 - 1;
SD59x18 constant EXP2_MAX_INPUT = SD59x18.wrap(uEXP2_MAX_INPUT);
/// @dev Any value less than this returns 0 in {exp2}.
int256 constant uEXP2_MIN_THRESHOLD = -59_794705707972522261;
SD59x18 constant EXP2_MIN_THRESHOLD = SD59x18.wrap(uEXP2_MIN_THRESHOLD);
/// @dev Half the UNIT number.
int256 constant uHALF_UNIT = 0.5e18;
SD59x18 constant HALF_UNIT = SD59x18.wrap(uHALF_UNIT);
/// @dev $log_2(10)$ as an SD59x18 number.
int256 constant uLOG2_10 = 3_321928094887362347;
SD59x18 constant LOG2_10 = SD59x18.wrap(uLOG2_10);
/// @dev $log_2(e)$ as an SD59x18 number.
int256 constant uLOG2_E = 1_442695040888963407;
SD59x18 constant LOG2_E = SD59x18.wrap(uLOG2_E);
/// @dev The maximum value an SD59x18 number can have.
int256 constant uMAX_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_792003956564819967;
SD59x18 constant MAX_SD59x18 = SD59x18.wrap(uMAX_SD59x18);
/// @dev The maximum whole value an SD59x18 number can have.
int256 constant uMAX_WHOLE_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_000000000000000000;
SD59x18 constant MAX_WHOLE_SD59x18 = SD59x18.wrap(uMAX_WHOLE_SD59x18);
/// @dev The minimum value an SD59x18 number can have.
int256 constant uMIN_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_792003956564819968;
SD59x18 constant MIN_SD59x18 = SD59x18.wrap(uMIN_SD59x18);
/// @dev The minimum whole value an SD59x18 number can have.
int256 constant uMIN_WHOLE_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_000000000000000000;
SD59x18 constant MIN_WHOLE_SD59x18 = SD59x18.wrap(uMIN_WHOLE_SD59x18);
/// @dev PI as an SD59x18 number.
SD59x18 constant PI = SD59x18.wrap(3_141592653589793238);
/// @dev The unit number, which gives the decimal precision of SD59x18.
int256 constant uUNIT = 1e18;
SD59x18 constant UNIT = SD59x18.wrap(1e18);
/// @dev The unit number squared.
int256 constant uUNIT_SQUARED = 1e36;
SD59x18 constant UNIT_SQUARED = SD59x18.wrap(uUNIT_SQUARED);
/// @dev Zero as an SD59x18 number.
SD59x18 constant ZERO = SD59x18.wrap(0);
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Casting.sol" as Casting;
/// @notice The signed 1.18-decimal fixed-point number representation, which can have up to 1 digit and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type int64. This is useful when end users want to use int64 to save gas, e.g. with tight variable packing in contract
/// storage.
type SD1x18 is int64;
/*//////////////////////////////////////////////////////////////////////////
CASTING
//////////////////////////////////////////////////////////////////////////*/
using {
Casting.intoSD59x18,
Casting.intoUD2x18,
Casting.intoUD60x18,
Casting.intoUint256,
Casting.intoUint128,
Casting.intoUint40,
Casting.unwrap
} for SD1x18 global;
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { SD1x18 } from "./ValueType.sol";
/// @dev Euler's number as an SD1x18 number.
SD1x18 constant E = SD1x18.wrap(2_718281828459045235);
/// @dev The maximum value an SD1x18 number can have.
int64 constant uMAX_SD1x18 = 9_223372036854775807;
SD1x18 constant MAX_SD1x18 = SD1x18.wrap(uMAX_SD1x18);
/// @dev The maximum value an SD1x18 number can have.
int64 constant uMIN_SD1x18 = -9_223372036854775808;
SD1x18 constant MIN_SD1x18 = SD1x18.wrap(uMIN_SD1x18);
/// @dev PI as an SD1x18 number.
SD1x18 constant PI = SD1x18.wrap(3_141592653589793238);
/// @dev The unit number, which gives the decimal precision of SD1x18.
SD1x18 constant UNIT = SD1x18.wrap(1e18);
int64 constant uUNIT = 1e18;
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { uMAX_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { UD2x18 } from "./ValueType.sol";
/// @notice Casts a UD2x18 number into SD1x18.
/// - x must be less than or equal to `uMAX_SD1x18`.
function intoSD1x18(UD2x18 x) pure returns (SD1x18 result) {
uint64 xUint = UD2x18.unwrap(x);
if (xUint > uint64(uMAX_SD1x18)) {
revert Errors.PRBMath_UD2x18_IntoSD1x18_Overflow(x);
}
result = SD1x18.wrap(int64(xUint));
}
/// @notice Casts a UD2x18 number into SD59x18.
/// @dev There is no overflow check because the domain of UD2x18 is a subset of SD59x18.
function intoSD59x18(UD2x18 x) pure returns (SD59x18 result) {
result = SD59x18.wrap(int256(uint256(UD2x18.unwrap(x))));
}
/// @notice Casts a UD2x18 number into UD60x18.
/// @dev There is no overflow check because the domain of UD2x18 is a subset of UD60x18.
function intoUD60x18(UD2x18 x) pure returns (UD60x18 result) {
result = UD60x18.wrap(UD2x18.unwrap(x));
}
/// @notice Casts a UD2x18 number into uint128.
/// @dev There is no overflow check because the domain of UD2x18 is a subset of uint128.
function intoUint128(UD2x18 x) pure returns (uint128 result) {
result = uint128(UD2x18.unwrap(x));
}
/// @notice Casts a UD2x18 number into uint256.
/// @dev There is no overflow check because the domain of UD2x18 is a subset of uint256.
function intoUint256(UD2x18 x) pure returns (uint256 result) {
result = uint256(UD2x18.unwrap(x));
}
/// @notice Casts a UD2x18 number into uint40.
/// @dev Requirements:
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(UD2x18 x) pure returns (uint40 result) {
uint64 xUint = UD2x18.unwrap(x);
if (xUint > uint64(Common.MAX_UINT40)) {
revert Errors.PRBMath_UD2x18_IntoUint40_Overflow(x);
}
result = uint40(xUint);
}
/// @notice Alias for {wrap}.
function ud2x18(uint64 x) pure returns (UD2x18 result) {
result = UD2x18.wrap(x);
}
/// @notice Unwrap a UD2x18 number into uint64.
function unwrap(UD2x18 x) pure returns (uint64 result) {
result = UD2x18.unwrap(x);
}
/// @notice Wraps a uint64 number into UD2x18.
function wrap(uint64 x) pure returns (UD2x18 result) {
result = UD2x18.wrap(x);
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import {
uEXP_MAX_INPUT,
uEXP2_MAX_INPUT,
uEXP_MIN_THRESHOLD,
uEXP2_MIN_THRESHOLD,
uHALF_UNIT,
uLOG2_10,
uLOG2_E,
uMAX_SD59x18,
uMAX_WHOLE_SD59x18,
uMIN_SD59x18,
uMIN_WHOLE_SD59x18,
UNIT,
uUNIT,
uUNIT_SQUARED,
ZERO
} from "./Constants.sol";
import { wrap } from "./Helpers.sol";
import { SD59x18 } from "./ValueType.sol";
/// @notice Calculates the absolute value of x.
///
/// @dev Requirements:
/// - x must be greater than `MIN_SD59x18`.
///
/// @param x The SD59x18 number for which to calculate the absolute value.
/// @param result The absolute value of x as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function abs(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt == uMIN_SD59x18) {
revert Errors.PRBMath_SD59x18_Abs_MinSD59x18();
}
result = xInt < 0 ? wrap(-xInt) : x;
}
/// @notice Calculates the arithmetic average of x and y.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// @param x The first operand as an SD59x18 number.
/// @param y The second operand as an SD59x18 number.
/// @return result The arithmetic average as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function avg(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
int256 yInt = y.unwrap();
unchecked {
// This operation is equivalent to `x / 2 + y / 2`, and it can never overflow.
int256 sum = (xInt >> 1) + (yInt >> 1);
if (sum < 0) {
// If at least one of x and y is odd, add 1 to the result, because shifting negative numbers to the right
// rounds toward negative infinity. The right part is equivalent to `sum + (x % 2 == 1 || y % 2 == 1)`.
assembly ("memory-safe") {
result := add(sum, and(or(xInt, yInt), 1))
}
} else {
// Add 1 if both x and y are odd to account for the double 0.5 remainder truncated after shifting.
result = wrap(sum + (xInt & yInt & 1));
}
}
}
/// @notice Yields the smallest whole number greater than or equal to x.
///
/// @dev Optimized for fractional value inputs, because every whole value has (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x must be less than or equal to `MAX_WHOLE_SD59x18`.
///
/// @param x The SD59x18 number to ceil.
/// @param result The smallest whole number greater than or equal to x, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function ceil(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt > uMAX_WHOLE_SD59x18) {
revert Errors.PRBMath_SD59x18_Ceil_Overflow(x);
}
int256 remainder = xInt % uUNIT;
if (remainder == 0) {
result = x;
} else {
unchecked {
// Solidity uses C fmod style, which returns a modulus with the same sign as x.
int256 resultInt = xInt - remainder;
if (xInt > 0) {
resultInt += uUNIT;
}
result = wrap(resultInt);
}
}
}
/// @notice Divides two SD59x18 numbers, returning a new SD59x18 number.
///
/// @dev This is an extension of {Common.mulDiv} for signed numbers, which works by computing the signs and the absolute
/// values separately.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv}.
/// - The result is rounded toward zero.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv}.
/// - None of the inputs can be `MIN_SD59x18`.
/// - The denominator must not be zero.
/// - The result must fit in SD59x18.
///
/// @param x The numerator as an SD59x18 number.
/// @param y The denominator as an SD59x18 number.
/// @param result The quotient as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function div(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
int256 yInt = y.unwrap();
if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {
revert Errors.PRBMath_SD59x18_Div_InputTooSmall();
}
// Get hold of the absolute values of x and y.
uint256 xAbs;
uint256 yAbs;
unchecked {
xAbs = xInt < 0 ? uint256(-xInt) : uint256(xInt);
yAbs = yInt < 0 ? uint256(-yInt) : uint256(yInt);
}
// Compute the absolute value (x*UNIT÷y). The resulting value must fit in SD59x18.
uint256 resultAbs = Common.mulDiv(xAbs, uint256(uUNIT), yAbs);
if (resultAbs > uint256(uMAX_SD59x18)) {
revert Errors.PRBMath_SD59x18_Div_Overflow(x, y);
}
// Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for
// negative, 0 for positive or zero).
bool sameSign = (xInt ^ yInt) > -1;
// If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.
unchecked {
result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));
}
}
/// @notice Calculates the natural exponent of x using the following formula:
///
/// $$
/// e^x = 2^{x * log_2{e}}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {exp2}.
///
/// Requirements:
/// - Refer to the requirements in {exp2}.
/// - x must be less than 133_084258667509499441.
///
/// @param x The exponent as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
// Any input less than the threshold returns zero.
// This check also prevents an overflow for very small numbers.
if (xInt < uEXP_MIN_THRESHOLD) {
return ZERO;
}
// This check prevents values greater than 192e18 from being passed to {exp2}.
if (xInt > uEXP_MAX_INPUT) {
revert Errors.PRBMath_SD59x18_Exp_InputTooBig(x);
}
unchecked {
// Inline the fixed-point multiplication to save gas.
int256 doubleUnitProduct = xInt * uLOG2_E;
result = exp2(wrap(doubleUnitProduct / uUNIT));
}
}
/// @notice Calculates the binary exponent of x using the binary fraction method using the following formula:
///
/// $$
/// 2^{-x} = \frac{1}{2^x}
/// $$
///
/// @dev See https://ethereum.stackexchange.com/q/79903/24693.
///
/// Notes:
/// - If x is less than -59_794705707972522261, the result is zero.
///
/// Requirements:
/// - x must be less than 192e18.
/// - The result must fit in SD59x18.
///
/// @param x The exponent as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp2(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt < 0) {
// The inverse of any number less than the threshold is truncated to zero.
if (xInt < uEXP2_MIN_THRESHOLD) {
return ZERO;
}
unchecked {
// Inline the fixed-point inversion to save gas.
result = wrap(uUNIT_SQUARED / exp2(wrap(-xInt)).unwrap());
}
} else {
// Numbers greater than or equal to 192e18 don't fit in the 192.64-bit format.
if (xInt > uEXP2_MAX_INPUT) {
revert Errors.PRBMath_SD59x18_Exp2_InputTooBig(x);
}
unchecked {
// Convert x to the 192.64-bit fixed-point format.
uint256 x_192x64 = uint256((xInt << 64) / uUNIT);
// It is safe to cast the result to int256 due to the checks above.
result = wrap(int256(Common.exp2(x_192x64)));
}
}
}
/// @notice Yields the greatest whole number less than or equal to x.
///
/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional
/// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x must be greater than or equal to `MIN_WHOLE_SD59x18`.
///
/// @param x The SD59x18 number to floor.
/// @param result The greatest whole number less than or equal to x, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function floor(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt < uMIN_WHOLE_SD59x18) {
revert Errors.PRBMath_SD59x18_Floor_Underflow(x);
}
int256 remainder = xInt % uUNIT;
if (remainder == 0) {
result = x;
} else {
unchecked {
// Solidity uses C fmod style, which returns a modulus with the same sign as x.
int256 resultInt = xInt - remainder;
if (xInt < 0) {
resultInt -= uUNIT;
}
result = wrap(resultInt);
}
}
}
/// @notice Yields the excess beyond the floor of x for positive numbers and the part of the number to the right.
/// of the radix point for negative numbers.
/// @dev Based on the odd function definition. https://en.wikipedia.org/wiki/Fractional_part
/// @param x The SD59x18 number to get the fractional part of.
/// @param result The fractional part of x as an SD59x18 number.
function frac(SD59x18 x) pure returns (SD59x18 result) {
result = wrap(x.unwrap() % uUNIT);
}
/// @notice Calculates the geometric mean of x and y, i.e. $\sqrt{x * y}$.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x * y must fit in SD59x18.
/// - x * y must not be negative, since complex numbers are not supported.
///
/// @param x The first operand as an SD59x18 number.
/// @param y The second operand as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function gm(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
int256 yInt = y.unwrap();
if (xInt == 0 || yInt == 0) {
return ZERO;
}
unchecked {
// Equivalent to `xy / x != y`. Checking for overflow this way is faster than letting Solidity do it.
int256 xyInt = xInt * yInt;
if (xyInt / xInt != yInt) {
revert Errors.PRBMath_SD59x18_Gm_Overflow(x, y);
}
// The product must not be negative, since complex numbers are not supported.
if (xyInt < 0) {
revert Errors.PRBMath_SD59x18_Gm_NegativeProduct(x, y);
}
// We don't need to multiply the result by `UNIT` here because the x*y product picked up a factor of `UNIT`
// during multiplication. See the comments in {Common.sqrt}.
uint256 resultUint = Common.sqrt(uint256(xyInt));
result = wrap(int256(resultUint));
}
}
/// @notice Calculates the inverse of x.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x must not be zero.
///
/// @param x The SD59x18 number for which to calculate the inverse.
/// @return result The inverse as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function inv(SD59x18 x) pure returns (SD59x18 result) {
result = wrap(uUNIT_SQUARED / x.unwrap());
}
/// @notice Calculates the natural logarithm of x using the following formula:
///
/// $$
/// ln{x} = log_2{x} / log_2{e}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
/// - The precision isn't sufficiently fine-grained to return exactly `UNIT` when the input is `E`.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The SD59x18 number for which to calculate the natural logarithm.
/// @return result The natural logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function ln(SD59x18 x) pure returns (SD59x18 result) {
// Inline the fixed-point multiplication to save gas. This is overflow-safe because the maximum value that
// {log2} can return is ~195_205294292027477728.
result = wrap(log2(x).unwrap() * uUNIT / uLOG2_E);
}
/// @notice Calculates the common logarithm of x using the following formula:
///
/// $$
/// log_{10}{x} = log_2{x} / log_2{10}
/// $$
///
/// However, if x is an exact power of ten, a hard coded value is returned.
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The SD59x18 number for which to calculate the common logarithm.
/// @return result The common logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function log10(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt < 0) {
revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);
}
// Note that the `mul` in this block is the standard multiplication operation, not {SD59x18.mul}.
// prettier-ignore
assembly ("memory-safe") {
switch x
case 1 { result := mul(uUNIT, sub(0, 18)) }
case 10 { result := mul(uUNIT, sub(1, 18)) }
case 100 { result := mul(uUNIT, sub(2, 18)) }
case 1000 { result := mul(uUNIT, sub(3, 18)) }
case 10000 { result := mul(uUNIT, sub(4, 18)) }
case 100000 { result := mul(uUNIT, sub(5, 18)) }
case 1000000 { result := mul(uUNIT, sub(6, 18)) }
case 10000000 { result := mul(uUNIT, sub(7, 18)) }
case 100000000 { result := mul(uUNIT, sub(8, 18)) }
case 1000000000 { result := mul(uUNIT, sub(9, 18)) }
case 10000000000 { result := mul(uUNIT, sub(10, 18)) }
case 100000000000 { result := mul(uUNIT, sub(11, 18)) }
case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }
case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }
case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }
case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }
case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }
case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }
case 1000000000000000000 { result := 0 }
case 10000000000000000000 { result := uUNIT }
case 100000000000000000000 { result := mul(uUNIT, 2) }
case 1000000000000000000000 { result := mul(uUNIT, 3) }
case 10000000000000000000000 { result := mul(uUNIT, 4) }
case 100000000000000000000000 { result := mul(uUNIT, 5) }
case 1000000000000000000000000 { result := mul(uUNIT, 6) }
case 10000000000000000000000000 { result := mul(uUNIT, 7) }
case 100000000000000000000000000 { result := mul(uUNIT, 8) }
case 1000000000000000000000000000 { result := mul(uUNIT, 9) }
case 10000000000000000000000000000 { result := mul(uUNIT, 10) }
case 100000000000000000000000000000 { result := mul(uUNIT, 11) }
case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }
case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }
case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }
case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }
case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }
case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }
case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }
case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }
case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }
case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }
case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }
case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }
case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }
case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }
case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }
case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }
case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }
case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }
case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }
case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }
case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }
case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }
case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }
case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }
case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }
case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }
case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }
case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }
case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }
case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }
case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }
case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }
case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }
case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }
case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }
case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }
case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }
case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }
case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }
case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }
case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }
case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }
case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }
default { result := uMAX_SD59x18 }
}
if (result.unwrap() == uMAX_SD59x18) {
unchecked {
// Inline the fixed-point division to save gas.
result = wrap(log2(x).unwrap() * uUNIT / uLOG2_10);
}
}
}
/// @notice Calculates the binary logarithm of x using the iterative approximation algorithm:
///
/// $$
/// log_2{x} = n + log_2{y}, \text{ where } y = x*2^{-n}, \ y \in [1, 2)
/// $$
///
/// For $0 \leq x \lt 1$, the input is inverted:
///
/// $$
/// log_2{x} = -log_2{\frac{1}{x}}
/// $$
///
/// @dev See https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation.
///
/// Notes:
/// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.
///
/// Requirements:
/// - x must be greater than zero.
///
/// @param x The SD59x18 number for which to calculate the binary logarithm.
/// @return result The binary logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function log2(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt <= 0) {
revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);
}
unchecked {
int256 sign;
if (xInt >= uUNIT) {
sign = 1;
} else {
sign = -1;
// Inline the fixed-point inversion to save gas.
xInt = uUNIT_SQUARED / xInt;
}
// Calculate the integer part of the logarithm.
uint256 n = Common.msb(uint256(xInt / uUNIT));
// This is the integer part of the logarithm as an SD59x18 number. The operation can't overflow
// because n is at most 255, `UNIT` is 1e18, and the sign is either 1 or -1.
int256 resultInt = int256(n) * uUNIT;
// Calculate $y = x * 2^{-n}$.
int256 y = xInt >> n;
// If y is the unit number, the fractional part is zero.
if (y == uUNIT) {
return wrap(resultInt * sign);
}
// Calculate the fractional part via the iterative approximation.
// The `delta >>= 1` part is equivalent to `delta /= 2`, but shifting bits is more gas efficient.
int256 DOUBLE_UNIT = 2e18;
for (int256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {
y = (y * y) / uUNIT;
// Is y^2 >= 2e18 and so in the range [2e18, 4e18)?
if (y >= DOUBLE_UNIT) {
// Add the 2^{-m} factor to the logarithm.
resultInt = resultInt + delta;
// Halve y, which corresponds to z/2 in the Wikipedia article.
y >>= 1;
}
}
resultInt *= sign;
result = wrap(resultInt);
}
}
/// @notice Multiplies two SD59x18 numbers together, returning a new SD59x18 number.
///
/// @dev Notes:
/// - Refer to the notes in {Common.mulDiv18}.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv18}.
/// - None of the inputs can be `MIN_SD59x18`.
/// - The result must fit in SD59x18.
///
/// @param x The multiplicand as an SD59x18 number.
/// @param y The multiplier as an SD59x18 number.
/// @return result The product as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function mul(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
int256 yInt = y.unwrap();
if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {
revert Errors.PRBMath_SD59x18_Mul_InputTooSmall();
}
// Get hold of the absolute values of x and y.
uint256 xAbs;
uint256 yAbs;
unchecked {
xAbs = xInt < 0 ? uint256(-xInt) : uint256(xInt);
yAbs = yInt < 0 ? uint256(-yInt) : uint256(yInt);
}
// Compute the absolute value (x*y÷UNIT). The resulting value must fit in SD59x18.
uint256 resultAbs = Common.mulDiv18(xAbs, yAbs);
if (resultAbs > uint256(uMAX_SD59x18)) {
revert Errors.PRBMath_SD59x18_Mul_Overflow(x, y);
}
// Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for
// negative, 0 for positive or zero).
bool sameSign = (xInt ^ yInt) > -1;
// If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.
unchecked {
result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));
}
}
/// @notice Raises x to the power of y using the following formula:
///
/// $$
/// x^y = 2^{log_2{x} * y}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {exp2}, {log2}, and {mul}.
/// - Returns `UNIT` for 0^0.
///
/// Requirements:
/// - Refer to the requirements in {exp2}, {log2}, and {mul}.
///
/// @param x The base as an SD59x18 number.
/// @param y Exponent to raise x to, as an SD59x18 number
/// @return result x raised to power y, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function pow(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
int256 yInt = y.unwrap();
// If both x and y are zero, the result is `UNIT`. If just x is zero, the result is always zero.
if (xInt == 0) {
return yInt == 0 ? UNIT : ZERO;
}
// If x is `UNIT`, the result is always `UNIT`.
else if (xInt == uUNIT) {
return UNIT;
}
// If y is zero, the result is always `UNIT`.
if (yInt == 0) {
return UNIT;
}
// If y is `UNIT`, the result is always x.
else if (yInt == uUNIT) {
return x;
}
// Calculate the result using the formula.
result = exp2(mul(log2(x), y));
}
/// @notice Raises x (an SD59x18 number) to the power y (an unsigned basic integer) using the well-known
/// algorithm "exponentiation by squaring".
///
/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv18}.
/// - Returns `UNIT` for 0^0.
///
/// Requirements:
/// - Refer to the requirements in {abs} and {Common.mulDiv18}.
/// - The result must fit in SD59x18.
///
/// @param x The base as an SD59x18 number.
/// @param y The exponent as a uint256.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function powu(SD59x18 x, uint256 y) pure returns (SD59x18 result) {
uint256 xAbs = uint256(abs(x).unwrap());
// Calculate the first iteration of the loop in advance.
uint256 resultAbs = y & 1 > 0 ? xAbs : uint256(uUNIT);
// Equivalent to `for(y /= 2; y > 0; y /= 2)`.
uint256 yAux = y;
for (yAux >>= 1; yAux > 0; yAux >>= 1) {
xAbs = Common.mulDiv18(xAbs, xAbs);
// Equivalent to `y % 2 == 1`.
if (yAux & 1 > 0) {
resultAbs = Common.mulDiv18(resultAbs, xAbs);
}
}
// The result must fit in SD59x18.
if (resultAbs > uint256(uMAX_SD59x18)) {
revert Errors.PRBMath_SD59x18_Powu_Overflow(x, y);
}
unchecked {
// Is the base negative and the exponent odd? If yes, the result should be negative.
int256 resultInt = int256(resultAbs);
bool isNegative = x.unwrap() < 0 && y & 1 == 1;
if (isNegative) {
resultInt = -resultInt;
}
result = wrap(resultInt);
}
}
/// @notice Calculates the square root of x using the Babylonian method.
///
/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Notes:
/// - Only the positive root is returned.
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x cannot be negative, since complex numbers are not supported.
/// - x must be less than `MAX_SD59x18 / UNIT`.
///
/// @param x The SD59x18 number for which to calculate the square root.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function sqrt(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt < 0) {
revert Errors.PRBMath_SD59x18_Sqrt_NegativeInput(x);
}
if (xInt > uMAX_SD59x18 / uUNIT) {
revert Errors.PRBMath_SD59x18_Sqrt_Overflow(x);
}
unchecked {
// Multiply x by `UNIT` to account for the factor of `UNIT` picked up when multiplying two SD59x18 numbers.
// In this case, the two numbers are both the square root.
uint256 resultUint = Common.sqrt(uint256(xInt * uUNIT));
result = wrap(int256(resultUint));
}
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { wrap } from "./Casting.sol";
import { SD59x18 } from "./ValueType.sol";
/// @notice Implements the checked addition operation (+) in the SD59x18 type.
function add(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
return wrap(x.unwrap() + y.unwrap());
}
/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.
function and(SD59x18 x, int256 bits) pure returns (SD59x18 result) {
return wrap(x.unwrap() & bits);
}
/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.
function and2(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
return wrap(x.unwrap() & y.unwrap());
}
/// @notice Implements the equal (=) operation in the SD59x18 type.
function eq(SD59x18 x, SD59x18 y) pure returns (bool result) {
result = x.unwrap() == y.unwrap();
}
/// @notice Implements the greater than operation (>) in the SD59x18 type.
function gt(SD59x18 x, SD59x18 y) pure returns (bool result) {
result = x.unwrap() > y.unwrap();
}
/// @notice Implements the greater than or equal to operation (>=) in the SD59x18 type.
function gte(SD59x18 x, SD59x18 y) pure returns (bool result) {
result = x.unwrap() >= y.unwrap();
}
/// @notice Implements a zero comparison check function in the SD59x18 type.
function isZero(SD59x18 x) pure returns (bool result) {
result = x.unwrap() == 0;
}
/// @notice Implements the left shift operation (<<) in the SD59x18 type.
function lshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {
result = wrap(x.unwrap() << bits);
}
/// @notice Implements the lower than operation (<) in the SD59x18 type.
function lt(SD59x18 x, SD59x18 y) pure returns (bool result) {
result = x.unwrap() < y.unwrap();
}
/// @notice Implements the lower than or equal to operation (<=) in the SD59x18 type.
function lte(SD59x18 x, SD59x18 y) pure returns (bool result) {
result = x.unwrap() <= y.unwrap();
}
/// @notice Implements the unchecked modulo operation (%) in the SD59x18 type.
function mod(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
result = wrap(x.unwrap() % y.unwrap());
}
/// @notice Implements the not equal operation (!=) in the SD59x18 type.
function neq(SD59x18 x, SD59x18 y) pure returns (bool result) {
result = x.unwrap() != y.unwrap();
}
/// @notice Implements the NOT (~) bitwise operation in the SD59x18 type.
function not(SD59x18 x) pure returns (SD59x18 result) {
result = wrap(~x.unwrap());
}
/// @notice Implements the OR (|) bitwise operation in the SD59x18 type.
function or(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
result = wrap(x.unwrap() | y.unwrap());
}
/// @notice Implements the right shift operation (>>) in the SD59x18 type.
function rshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {
result = wrap(x.unwrap() >> bits);
}
/// @notice Implements the checked subtraction operation (-) in the SD59x18 type.
function sub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
result = wrap(x.unwrap() - y.unwrap());
}
/// @notice Implements the checked unary minus operation (-) in the SD59x18 type.
function unary(SD59x18 x) pure returns (SD59x18 result) {
result = wrap(-x.unwrap());
}
/// @notice Implements the unchecked addition operation (+) in the SD59x18 type.
function uncheckedAdd(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
unchecked {
result = wrap(x.unwrap() + y.unwrap());
}
}
/// @notice Implements the unchecked subtraction operation (-) in the SD59x18 type.
function uncheckedSub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
unchecked {
result = wrap(x.unwrap() - y.unwrap());
}
}
/// @notice Implements the unchecked unary minus operation (-) in the SD59x18 type.
function uncheckedUnary(SD59x18 x) pure returns (SD59x18 result) {
unchecked {
result = wrap(-x.unwrap());
}
}
/// @notice Implements the XOR (^) bitwise operation in the SD59x18 type.
function xor(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
result = wrap(x.unwrap() ^ y.unwrap());
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Errors.sol" as CastingErrors;
import { MAX_UINT128, MAX_UINT40 } from "../Common.sol";
import { uMAX_SD1x18, uMIN_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD59x18 } from "./ValueType.sol";
/// @notice Casts an SD59x18 number into int256.
/// @dev This is basically a functional alias for {unwrap}.
function intoInt256(SD59x18 x) pure returns (int256 result) {
result = SD59x18.unwrap(x);
}
/// @notice Casts an SD59x18 number into SD1x18.
/// @dev Requirements:
/// - x must be greater than or equal to `uMIN_SD1x18`.
/// - x must be less than or equal to `uMAX_SD1x18`.
function intoSD1x18(SD59x18 x) pure returns (SD1x18 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < uMIN_SD1x18) {
revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Underflow(x);
}
if (xInt > uMAX_SD1x18) {
revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Overflow(x);
}
result = SD1x18.wrap(int64(xInt));
}
/// @notice Casts an SD59x18 number into UD2x18.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `uMAX_UD2x18`.
function intoUD2x18(SD59x18 x) pure returns (UD2x18 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Underflow(x);
}
if (xInt > int256(uint256(uMAX_UD2x18))) {
revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Overflow(x);
}
result = UD2x18.wrap(uint64(uint256(xInt)));
}
/// @notice Casts an SD59x18 number into UD60x18.
/// @dev Requirements:
/// - x must be positive.
function intoUD60x18(SD59x18 x) pure returns (UD60x18 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD59x18_IntoUD60x18_Underflow(x);
}
result = UD60x18.wrap(uint256(xInt));
}
/// @notice Casts an SD59x18 number into uint256.
/// @dev Requirements:
/// - x must be positive.
function intoUint256(SD59x18 x) pure returns (uint256 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD59x18_IntoUint256_Underflow(x);
}
result = uint256(xInt);
}
/// @notice Casts an SD59x18 number into uint128.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `uMAX_UINT128`.
function intoUint128(SD59x18 x) pure returns (uint128 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD59x18_IntoUint128_Underflow(x);
}
if (xInt > int256(uint256(MAX_UINT128))) {
revert CastingErrors.PRBMath_SD59x18_IntoUint128_Overflow(x);
}
result = uint128(uint256(xInt));
}
/// @notice Casts an SD59x18 number into uint40.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(SD59x18 x) pure returns (uint40 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD59x18_IntoUint40_Underflow(x);
}
if (xInt > int256(uint256(MAX_UINT40))) {
revert CastingErrors.PRBMath_SD59x18_IntoUint40_Overflow(x);
}
result = uint40(uint256(xInt));
}
/// @notice Alias for {wrap}.
function sd(int256 x) pure returns (SD59x18 result) {
result = SD59x18.wrap(x);
}
/// @notice Alias for {wrap}.
function sd59x18(int256 x) pure returns (SD59x18 result) {
result = SD59x18.wrap(x);
}
/// @notice Unwraps an SD59x18 number into int256.
function unwrap(SD59x18 x) pure returns (int256 result) {
result = SD59x18.unwrap(x);
}
/// @notice Wraps an int256 number into SD59x18.
function wrap(int256 x) pure returns (SD59x18 result) {
result = SD59x18.wrap(x);
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "../Common.sol" as Common;
import "./Errors.sol" as CastingErrors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD1x18 } from "./ValueType.sol";
/// @notice Casts an SD1x18 number into SD59x18.
/// @dev There is no overflow check because the domain of SD1x18 is a subset of SD59x18.
function intoSD59x18(SD1x18 x) pure returns (SD59x18 result) {
result = SD59x18.wrap(int256(SD1x18.unwrap(x)));
}
/// @notice Casts an SD1x18 number into UD2x18.
/// - x must be positive.
function intoUD2x18(SD1x18 x) pure returns (UD2x18 result) {
int64 xInt = SD1x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD1x18_ToUD2x18_Underflow(x);
}
result = UD2x18.wrap(uint64(xInt));
}
/// @notice Casts an SD1x18 number into UD60x18.
/// @dev Requirements:
/// - x must be positive.
function intoUD60x18(SD1x18 x) pure returns (UD60x18 result) {
int64 xInt = SD1x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD1x18_ToUD60x18_Underflow(x);
}
result = UD60x18.wrap(uint64(xInt));
}
/// @notice Casts an SD1x18 number into uint256.
/// @dev Requirements:
/// - x must be positive.
function intoUint256(SD1x18 x) pure returns (uint256 result) {
int64 xInt = SD1x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD1x18_ToUint256_Underflow(x);
}
result = uint256(uint64(xInt));
}
/// @notice Casts an SD1x18 number into uint128.
/// @dev Requirements:
/// - x must be positive.
function intoUint128(SD1x18 x) pure returns (uint128 result) {
int64 xInt = SD1x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD1x18_ToUint128_Underflow(x);
}
result = uint128(uint64(xInt));
}
/// @notice Casts an SD1x18 number into uint40.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(SD1x18 x) pure returns (uint40 result) {
int64 xInt = SD1x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD1x18_ToUint40_Underflow(x);
}
if (xInt > int64(uint64(Common.MAX_UINT40))) {
revert CastingErrors.PRBMath_SD1x18_ToUint40_Overflow(x);
}
result = uint40(uint64(xInt));
}
/// @notice Alias for {wrap}.
function sd1x18(int64 x) pure returns (SD1x18 result) {
result = SD1x18.wrap(x);
}
/// @notice Unwraps an SD1x18 number into int64.
function unwrap(SD1x18 x) pure returns (int64 result) {
result = SD1x18.unwrap(x);
}
/// @notice Wraps an int64 number into SD1x18.
function wrap(int64 x) pure returns (SD1x18 result) {
result = SD1x18.wrap(x);
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { UD2x18 } from "./ValueType.sol";
/// @notice Thrown when trying to cast a UD2x18 number that doesn't fit in SD1x18.
error PRBMath_UD2x18_IntoSD1x18_Overflow(UD2x18 x);
/// @notice Thrown when trying to cast a UD2x18 number that doesn't fit in uint40.
error PRBMath_UD2x18_IntoUint40_Overflow(UD2x18 x);
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { SD59x18 } from "./ValueType.sol";
/// @notice Thrown when taking the absolute value of `MIN_SD59x18`.
error PRBMath_SD59x18_Abs_MinSD59x18();
/// @notice Thrown when ceiling a number overflows SD59x18.
error PRBMath_SD59x18_Ceil_Overflow(SD59x18 x);
/// @notice Thrown when converting a basic integer to the fixed-point format overflows SD59x18.
error PRBMath_SD59x18_Convert_Overflow(int256 x);
/// @notice Thrown when converting a basic integer to the fixed-point format underflows SD59x18.
error PRBMath_SD59x18_Convert_Underflow(int256 x);
/// @notice Thrown when dividing two numbers and one of them is `MIN_SD59x18`.
error PRBMath_SD59x18_Div_InputTooSmall();
/// @notice Thrown when dividing two numbers and one of the intermediary unsigned results overflows SD59x18.
error PRBMath_SD59x18_Div_Overflow(SD59x18 x, SD59x18 y);
/// @notice Thrown when taking the natural exponent of a base greater than 133_084258667509499441.
error PRBMath_SD59x18_Exp_InputTooBig(SD59x18 x);
/// @notice Thrown when taking the binary exponent of a base greater than 192e18.
error PRBMath_SD59x18_Exp2_InputTooBig(SD59x18 x);
/// @notice Thrown when flooring a number underflows SD59x18.
error PRBMath_SD59x18_Floor_Underflow(SD59x18 x);
/// @notice Thrown when taking the geometric mean of two numbers and their product is negative.
error PRBMath_SD59x18_Gm_NegativeProduct(SD59x18 x, SD59x18 y);
/// @notice Thrown when taking the geometric mean of two numbers and multiplying them overflows SD59x18.
error PRBMath_SD59x18_Gm_Overflow(SD59x18 x, SD59x18 y);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD60x18.
error PRBMath_SD59x18_IntoUD60x18_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint256.
error PRBMath_SD59x18_IntoUint256_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Underflow(SD59x18 x);
/// @notice Thrown when taking the logarithm of a number less than or equal to zero.
error PRBMath_SD59x18_Log_InputTooSmall(SD59x18 x);
/// @notice Thrown when multiplying two numbers and one of the inputs is `MIN_SD59x18`.
error PRBMath_SD59x18_Mul_InputTooSmall();
/// @notice Thrown when multiplying two numbers and the intermediary absolute result overflows SD59x18.
error PRBMath_SD59x18_Mul_Overflow(SD59x18 x, SD59x18 y);
/// @notice Thrown when raising a number to a power and the intermediary absolute result overflows SD59x18.
error PRBMath_SD59x18_Powu_Overflow(SD59x18 x, uint256 y);
/// @notice Thrown when taking the square root of a negative number.
error PRBMath_SD59x18_Sqrt_NegativeInput(SD59x18 x);
/// @notice Thrown when the calculating the square root overflows SD59x18.
error PRBMath_SD59x18_Sqrt_Overflow(SD59x18 x);
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { SD1x18 } from "./ValueType.sol";
/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in UD2x18.
error PRBMath_SD1x18_ToUD2x18_Underflow(SD1x18 x);
/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in UD60x18.
error PRBMath_SD1x18_ToUD60x18_Underflow(SD1x18 x);
/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint128.
error PRBMath_SD1x18_ToUint128_Underflow(SD1x18 x);
/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint256.
error PRBMath_SD1x18_ToUint256_Underflow(SD1x18 x);
/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Overflow(SD1x18 x);
/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Underflow(SD1x18 x);