Contract Name:
MarketManager
Contract Source Code:
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import "./Roles.sol";
import "./Utility.sol";
import "./MarketState.sol";
import "@openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol";
import "@openzeppelin/contracts-upgradeable/proxy/utils/UUPSUpgradeable.sol";
import "./interface/IMarketManager.sol";
/**
* @title MarketManager
* @notice Manages market operations such as creation, updates, and pool management, with role-based access and upgradeability.
*/
contract MarketManager is
IMarketManager,
Initializable,
UUPSUpgradeable,
Roles,
MarketState
{
/// @custom:oz-upgrades-unsafe-allow constructor
constructor() {
_disableInitializers();
}
/**
* @notice Initializes the contract and sets the deployer as the owner.
*/
function initialize() public initializer {
__AccessControl_init();
__UUPSUpgradeable_init();
__Ownable_init();
transferOwnership(_msgSender());
initializeMarketState();
// Set default K-range values
kRange = [1e18, 2e18, 5e18, 10e18];
}
/**
* @notice Authorizes contract upgrades.
* @param newImplementation The address of the new implementation contract.
*/
function _authorizeUpgrade(
address newImplementation
) internal override onlyRole(DEFAULT_ADMIN_ROLE) {}
/**
* @notice Creates a new prediction market.
* @param questionId Unique identifier for the question (off-chain data).
* @param commissionPercentage The commission percentage for the team (0-100%).
* @param endTime Market's end time (UNIX timestamp).
*/
function createMarket(
uint256 questionId,
uint256 commissionPercentage,
uint256 endTime
) external override onlyTeam {
require(questionId > 0, "Invalid questionId");
require(commissionPercentage <= 100, "Commission exceeds 100%");
require(endTime > block.timestamp, "End time must be in the future");
uint256 currentMarketId = marketCount;
marketCount++;
markets[currentMarketId] = Market({
questionId: questionId,
yesVotes: 0,
noVotes: 0,
totalFunds: 0,
commissionPercentage: commissionPercentage,
baseLiquidity: 0,
endTime: endTime,
isResolved: false,
winningOption: 0,
yesPrice: 0,
noPrice: 0
});
emit MarketCreated(currentMarketId, questionId, endTime);
}
/**
* @notice Updates the end time of a market.
* @param marketId The ID of the market.
* @param newEndTime The new end time (UNIX timestamp).
*/
function updateEndTime(
uint256 marketId,
uint256 newEndTime
) external override onlyTeam {
require(marketId < marketCount, "Market does not exist");
Market storage market = markets[marketId];
require(!market.isResolved, "Market already resolved");
require(
newEndTime > block.timestamp,
"New end time must be in the future"
);
require(newEndTime != market.endTime, "End time is already set");
market.endTime = newEndTime;
emit MarketEndTimeUpdated(marketId, newEndTime);
}
/**
* @notice Updates the pool of a market when points are added or removed.
* @param marketId The ID of the market.
* @param isYesVote True if adding to the "Yes" option, false for "No".
* @param points The amount of points to add.
*/
function updateMarketPool(
uint256 marketId,
bool isYesVote,
uint256 points
) external override onlyAuthorized {
require(points > 0, "MarketManager: Points must be greater than zero");
require(marketId < marketCount, "MarketManager: Market does not exist");
Market storage market = markets[marketId];
require(!market.isResolved, "MarketManager: Market already resolved");
require(
block.timestamp < market.endTime,
"MarketManager: Market expired"
);
if (isYesVote) {
market.yesVotes += points;
} else {
market.noVotes += points;
}
market.totalFunds += points;
// Update LMSR prices
updatePrices(marketId);
emit MarketPoolUpdated(
marketId,
market.yesVotes,
market.noVotes,
market.totalFunds
);
}
/**
* @notice Retrieves the price of a specific option in a market.
* @param marketId The ID of the market.
* @param optionId The ID of the option (0 = "No", 1 = "Yes").
* @return The price of the specified option in 18-decimal precision.
*/
function getPrice(
uint256 marketId,
uint256 optionId
) external view override returns (uint256) {
require(marketId < marketCount, "Market does not exist");
require(optionId == 0 || optionId == 1, "Invalid option ID");
Market storage market = markets[marketId];
return optionId == 1 ? market.yesPrice : market.noPrice;
}
/**
* @notice Retrieves details about a specific market.
* @param marketId The ID of the market.
* @return questionId The unique identifier for the question (off-chain data).
* @return yesVotes The total points for the "Yes" option.
* @return noVotes The total points for the "No" option.
* @return isResolved Whether the market has been resolved.
* @return winningOption The ID of the winning option (0 = "No", 1 = "Yes").
*/
function getMarketDetails(
uint256 marketId
)
external
view
override
returns (
uint256 questionId,
uint256 yesVotes,
uint256 noVotes,
bool isResolved,
uint256 winningOption
)
{
require(marketId < marketCount, "Market does not exist");
Market storage market = markets[marketId];
return (
market.questionId,
market.yesVotes,
market.noVotes,
market.isResolved,
market.winningOption
);
}
/**
* @notice Checks if a market is resolved.
* @param marketId ID of the market.
* @return True if the market is resolved, false otherwise.
*/
function isMarketResolved(
uint256 marketId
) external view override returns (bool) {
require(marketId < marketCount, "Market does not exist");
return markets[marketId].isResolved;
}
/**
* @notice Retrieves the end time of a specific market.
* @param marketId ID of the market.
* @return End time of the market (UNIX timestamp).
*/
function getMarketEndTime(
uint256 marketId
) external view override returns (uint256) {
require(marketId < marketCount, "Market does not exist");
return markets[marketId].endTime;
}
/**
* @notice Retrieves all markets with their pool balances.
* @return marketIds Array of market IDs.
* @return questionIds Array of question IDs.
* @return totalPoolBalances Array of total pool balances for each market.
*/
function getAllMarketsWithPools()
external
view
override
onlyTeam
returns (
uint256[] memory marketIds,
uint256[] memory questionIds,
uint256[] memory totalPoolBalances
)
{
uint256 count = marketCount;
require(count > 0, "No markets exist");
marketIds = new uint256[](count);
questionIds = new uint256[](count);
totalPoolBalances = new uint256[](count);
for (uint256 i = 0; i < count; i++) {
Market storage market = markets[i];
marketIds[i] = i;
questionIds[i] = market.questionId;
totalPoolBalances[i] = market.totalFunds;
}
}
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import "@openzeppelin/contracts-upgradeable/access/AccessControlUpgradeable.sol";
/**
* @title Roles
* @dev Provides role-based access control functionality with additional features for managing an authorized caller.
* @notice Includes TEAM_ROLE, DEFAULT_ADMIN_ROLE, and authorized caller management.
* Inherits from OpenZeppelin's `AccessControlUpgradeable` contract.
*/
abstract contract Roles is AccessControlUpgradeable {
// Define role identifiers
bytes32 public constant TEAM_ROLE = keccak256("TEAM_ROLE");
// Address of the authorized contract for restricted cross-contract interactions
address public authorizedCaller;
/**
* @notice Initializes the contract and sets up the default admin and team roles.
* @dev Should be called during contract initialization.
* @param admin The address to be set as the default admin.
*/
function initializeRoles(address admin) internal onlyInitializing {
require(admin != address(0), "Roles: Admin address cannot be zero");
_setupRole(DEFAULT_ADMIN_ROLE, admin);
_setupRole(TEAM_ROLE, admin);
}
// -------------------------
// Existing Functions
// -------------------------
/**
* @notice Ensures that only users with the TEAM_ROLE can call the function.
* @dev Throws if the caller does not have the TEAM_ROLE.
*/
modifier onlyTeam() {
require(
hasRole(TEAM_ROLE, msg.sender),
"Roles: Not authorized - Requires TEAM_ROLE"
);
_;
}
/**
* @notice Ensures that only users with the DEFAULT_ADMIN_ROLE can call the function.
* @dev Throws if the caller does not have the DEFAULT_ADMIN_ROLE.
*/
modifier onlyAdmin() {
require(
hasRole(DEFAULT_ADMIN_ROLE, msg.sender),
"Roles: Not authorized - Requires DEFAULT_ADMIN_ROLE"
);
_;
}
/**
* @notice Adds a new team member by granting them the TEAM_ROLE.
* @dev Can only be called by a user with the TEAM_ROLE.
* @param account The address to be granted the TEAM_ROLE.
*/
function addTeamMember(address account) external onlyTeam {
require(account != address(0), "Roles: Invalid address");
require(
!hasRole(TEAM_ROLE, account),
"Roles: Address already has TEAM_ROLE"
);
grantRole(TEAM_ROLE, account);
}
/**
* @notice Removes an existing team member by revoking their TEAM_ROLE.
* @dev Can only be called by a user with the TEAM_ROLE.
* @param account The address to be revoked from the TEAM_ROLE.
*/
function removeTeamMember(address account) external onlyTeam {
require(account != address(0), "Roles: Invalid address");
require(
hasRole(TEAM_ROLE, account),
"Roles: Address does not have TEAM_ROLE"
);
revokeRole(TEAM_ROLE, account);
}
/**
* @notice Transfers the DEFAULT_ADMIN_ROLE to a new admin.
* @dev Only the current admin can call this function.
* @param newAdmin The address to be granted the DEFAULT_ADMIN_ROLE.
*/
function transferAdminRole(address newAdmin) external onlyAdmin {
require(newAdmin != address(0), "Roles: Invalid new admin address");
require(
!hasRole(DEFAULT_ADMIN_ROLE, newAdmin),
"Roles: Address already has DEFAULT_ADMIN_ROLE"
);
grantRole(DEFAULT_ADMIN_ROLE, newAdmin);
revokeRole(DEFAULT_ADMIN_ROLE, msg.sender);
}
/**
* @notice Checks whether an address has the TEAM_ROLE.
* @param account The address to check.
* @return A boolean indicating whether the address has the TEAM_ROLE.
*/
function isTeamMember(address account) external view returns (bool) {
require(account != address(0), "Roles: Invalid address");
return hasRole(TEAM_ROLE, account);
}
/**
* @notice Checks whether an address has the DEFAULT_ADMIN_ROLE.
* @param account The address to check.
* @return A boolean indicating whether the address has the DEFAULT_ADMIN_ROLE.
*/
function isAdmin(address account) external view returns (bool) {
require(account != address(0), "Roles: Invalid address");
return hasRole(DEFAULT_ADMIN_ROLE, account);
}
// -------------------------
// New Functions
// -------------------------
/**
* @notice Ensures that only the authorized caller can call the function.
* @dev Throws if the caller is not the authorized caller.
*/
modifier onlyAuthorized() {
require(
msg.sender == authorizedCaller,
"Roles: Caller is not authorized"
);
_;
}
/**
* @notice Sets or updates the authorized caller for restricted functions.
* @dev Can only be called by an admin.
* @param caller The address to be set as the authorized caller.
*/
function setAuthorizedCaller(address caller) external onlyAdmin {
require(caller != address(0), "Roles: Invalid caller address");
authorizedCaller = caller;
}
/**
* @notice Checks whether an address is the authorized caller.
* @param account The address to check.
* @return A boolean indicating whether the address is authorized.
*/
function isAuthorized(address account) external view returns (bool) {
require(account != address(0), "Roles: Invalid address");
return account == authorizedCaller;
}
/**
* @notice Revokes the current authorized caller.
* @dev Can only be called by an admin.
*/
function revokeAuthorizedCaller() external onlyAdmin {
require(authorizedCaller != address(0), "Roles: No caller to revoke");
authorizedCaller = address(0);
}
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/**
* @title Utility
* @dev A library of utility functions for mathematical operations used in prediction markets.
* Includes percentage calculations, logarithmic scaling, and LMSR-related computations.
*/
library Utility {
/**
* @notice Calculates a percentage of a given value.
* @param base The base value.
* @param percentage The percentage to calculate (0-100%).
* @return The calculated percentage of the base value.
*/
function calculatePercentage(
uint256 base,
uint256 percentage
) internal pure returns (uint256) {
require(percentage <= 100, "Percentage cannot exceed 100%");
return (base * percentage) / 100;
}
/**
* @notice Calculates the proportional reward for a user based on their holdings and the total votes.
* @param portion The portion value (e.g., user's holdings).
* @param total The total funds in the pool.
* @param votes The total votes for the winning option.
* @return The proportional reward based on the user's holdings.
*/
function calculateProportion(
uint256 portion,
uint256 total,
uint256 votes
) internal pure returns (uint256) {
require(votes > 0, "Votes must be greater than zero");
require(total >= portion, "Total funds must be >= user portion");
return (portion * total) / votes;
}
/**
* @notice Calculates the base liquidity for LMSR using logarithmic scaling.
* @param k The scaling factor.
* @param numUsers The number of users in the market.
* @return The calculated base liquidity.
*/
function calculateBaseLiquidity(
uint256 k,
uint256 numUsers
) internal pure returns (uint256) {
require(k > 0, "Scaling factor must be greater than zero");
require(numUsers > 0, "Number of users must be greater than zero");
return k * ln(numUsers + 1); // Using natural logarithm (ln)
}
/**
* @notice Calculates LMSR prices for "Yes" and "No" options.
* @param yesVotes Total points for "Yes".
* @param noVotes Total points for "No".
* @param baseLiquidity The base liquidity parameter.
* @return yesPrice The price for "Yes".
* @return noPrice The price for "No".
*/
function calculateLMSRPrices(
uint256 yesVotes,
uint256 noVotes,
uint256 baseLiquidity
) internal pure returns (uint256 yesPrice, uint256 noPrice) {
require(baseLiquidity > 0, "Base liquidity must be greater than zero");
uint256 yesExp = expScaled(yesVotes, baseLiquidity);
uint256 noExp = expScaled(noVotes, baseLiquidity);
// Prevent division by zero
uint256 sumExp = yesExp + noExp;
require(sumExp > 0, "Exponential sum must be greater than zero");
yesPrice = (yesExp * 1e18) / sumExp;
noPrice = (noExp * 1e18) / sumExp;
}
/**
* @notice Scales an exponential calculation for LMSR prices.
* @param votes The votes for a specific option.
* @param baseLiquidity The base liquidity parameter.
* @return The scaled exponential value.
*/
function expScaled(
uint256 votes,
uint256 baseLiquidity
) internal pure returns (uint256) {
require(baseLiquidity > 0, "Base liquidity must be greater than zero");
return exp((votes * 1e18) / baseLiquidity);
}
/**
* @notice Approximates the exponential function for small inputs.
* @param x The input value (in 18-decimal precision).
* @return The approximate exponential value.
*/
function exp(uint256 x) internal pure returns (uint256) {
uint256 result = 1e18; // Start with 1 in 18-decimal precision
uint256 term = 1e18;
for (uint8 i = 1; i < 20; i++) {
term = (term * x) / (i * 1e18);
result += term;
// Stop the loop early if the term becomes negligible
if (term < 1) break;
}
return result;
}
/**
* @notice Calculates the natural logarithm of an input value.
* @param x The input value (in 18-decimal precision).
* @return The natural logarithm of the input.
*/
function ln(uint256 x) internal pure returns (uint256) {
require(x > 0, "Input must be greater than zero");
uint256 result = 0;
uint256 y = x;
uint256 precision = 1e18;
// Normalize input to the range [1, 10) by adjusting the result accordingly
while (y < precision) {
y *= 10;
result -= 2302585092994045684; // ln(10) in 18-decimal precision
}
while (y >= precision * 10) {
y /= 10;
result += 2302585092994045684; // ln(10) in 18-decimal precision
}
// Taylor series approximation
uint256 z = ((y - precision) * precision) / (y + precision);
uint256 z2 = (z * z) / precision;
result += z;
uint256 term = z;
for (uint8 i = 3; i < 40; i += 2) {
term = (term * z2) / precision;
result += term / i;
// Stop if the term becomes negligible
if (term < 1) break;
}
return result;
}
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import "./Utility.sol";
import "./Roles.sol";
import "./UserState.sol";
import "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";
import {UD60x18, ud, ln} from "@prb/math/src/UD60x18.sol";
import "@openzeppelin/contracts/security/ReentrancyGuard.sol";
/**
* @title MarketState
* @dev Abstract contract to manage prediction markets using LMSR with Yes/No outcomes in a points-based system.
* Features include market creation, resolution, reward claims, and fund management.
*/
abstract contract MarketState is
Roles,
OwnableUpgradeable,
UserState,
ReentrancyGuard
{
using Utility for uint256;
using Utility for uint256[];
struct Market {
uint256 questionId; // Unique identifier for the question (off-chain data)
uint256 yesVotes; // Total points for "Yes" option
uint256 noVotes; // Total points for "No" option
uint256 totalFunds; // Total points in the market
uint256 commissionPercentage; // Commission percentage for the team
uint256 baseLiquidity; // LMSR `b` parameter
uint256 endTime; // Market's end time
bool isResolved; // Status of market resolution
uint256 winningOption; // Winning option (0 = "No", 1 = "Yes")
uint256 yesPrice; // Cached price for "Yes" (18-decimal precision)
uint256 noPrice; // Cached price for "No" (18-decimal precision)
}
uint256 public marketCount; // Counter for market IDs
mapping(uint256 => Market) public markets; // Mapping of market IDs to Market structs
uint256[] public kRange; // K-range values for LMSR calculations
uint256 public constant POINTS_PER_DOLLAR = 100; // Conversion rate: 1 USD = 100 points
uint256 public gracePeriod; // Default grace period for unclaimed rewards
// Events
event MarketCreated(
uint256 indexed marketId,
uint256 questionId,
uint256 endTime
);
event MarketResolved(uint256 indexed marketId, uint256 winningOption);
event PricesUpdated(
uint256 indexed marketId,
uint256 yesPrice,
uint256 noPrice
);
event MarketPoolUpdated(
uint256 indexed marketId,
uint256 yesVotes,
uint256 noVotes,
uint256 totalFunds
);
event MarketEndTimeUpdated(uint256 indexed marketId, uint256 newEndTime);
event KRangeUpdated(uint256[] newKRange);
event UnclaimedRewardsReclaimed(uint256 indexed marketId, uint256 amount);
event GracePeriodUpdated(uint256 newGracePeriod);
event EmptyMarketResolved(uint256 indexed marketId);
event RewardClaimed(
address indexed user,
uint256 indexed marketId,
uint256 reward
);
mapping(address => uint256[]) private userUnclaimedMarkets; // Tracks unclaimed markets per user
mapping(uint256 => mapping(address => bool)) private hasClaimed; // Tracks claim status per user and market
/**
* @notice Initializes the MarketState variables.
*/
function initializeMarketState() public initializer {
gracePeriod = 30 days; // Default grace period for unclaimed rewards
}
/**
* @notice Updates the K range values.
* @param newKRange Array of new K values.
*/
function updateKRange(uint256[] calldata newKRange) external onlyTeam {
require(newKRange.length > 0, "K range cannot be empty");
require(newKRange.length <= 10, "K range exceeds maximum length");
for (uint256 i = 0; i < newKRange.length; i++) {
require(newKRange[i] > 0, "K values must be greater than zero");
}
kRange = newKRange;
emit KRangeUpdated(newKRange);
}
/**
* @notice Updates the grace period for unclaimed rewards.
* @param newPeriod The new grace period in seconds.
*/
function setGracePeriod(uint256 newPeriod) external onlyOwner {
require(newPeriod > 0, "Grace period must be greater than zero");
require(newPeriod <= 365 days, "Grace period exceeds maximum limit");
gracePeriod = newPeriod;
emit GracePeriodUpdated(newPeriod);
}
/**
* @notice Reclaims unclaimed rewards after the grace period.
* @param marketId The ID of the market to reclaim rewards from.
*/
function reclaimUnclaimedRewards(uint256 marketId) external onlyOwner {
Market storage market = markets[marketId];
require(market.isResolved, "Market not resolved");
require(
block.timestamp > market.endTime + gracePeriod,
"Grace period not ended"
);
require(market.totalFunds > 0, "No unclaimed rewards");
uint256 unclaimedRewards = market.totalFunds;
market.totalFunds = 0;
userPoints[owner()] += unclaimedRewards;
emit UnclaimedRewardsReclaimed(marketId, unclaimedRewards);
}
/**
* @notice Resolves a market by determining the winning option.
* @param marketId The ID of the market to resolve.
* @param winningOption The winning option (0 = "No", 1 = "Yes").
*/
function resolveMarket(
uint256 marketId,
uint256 winningOption
) external onlyTeam {
Market storage market = markets[marketId];
require(!market.isResolved, "Market already resolved");
require(
winningOption == 0 || winningOption == 1,
"Invalid winning option"
);
// If both "Yes" and "No" votes are zero, resolve as empty market
if (market.yesVotes == 0 && market.noVotes == 0) {
market.isResolved = true;
emit EmptyMarketResolved(marketId);
return;
}
// Check if either "Yes" or "No" votes are zero, no commission applies
if (market.yesVotes == 0 || market.noVotes == 0) {
market.isResolved = true;
market.winningOption = market.yesVotes > 0 ? 1 : 0; // Winning option is the one with non-zero votes
emit MarketResolved(marketId, market.winningOption);
return;
}
// Calculate team commission only if both "Yes" and "No" have votes
uint256 teamCommission = market.totalFunds.calculatePercentage(
market.commissionPercentage
);
market.totalFunds -= teamCommission;
userPoints[owner()] += teamCommission;
market.isResolved = true;
market.winningOption = winningOption;
emit MarketResolved(marketId, winningOption);
}
/**
* @notice Claims rewards for a resolved market.
* @param marketId The ID of the market to claim rewards from.
*/
function claimReward(uint256 marketId) external nonReentrant {
Market storage market = markets[marketId];
require(market.isResolved, "Market not resolved");
uint256 activeOption = market.yesVotes > 0 ? 1 : 0;
uint256 userHolding = userHoldings[msg.sender][marketId][activeOption];
require(userHolding > 0, "No rewards to claim");
uint256 activeReward = userHolding.calculateProportion(
market.totalFunds,
activeOption == 1 ? market.yesVotes : market.noVotes
);
market.totalFunds -= activeReward; // Update total funds after rewards are claimed
userPoints[msg.sender] += activeReward;
userHoldings[msg.sender][marketId][activeOption] = 0;
emit RewardClaimed(msg.sender, marketId, activeReward);
}
/**
* @notice Updates prices for "Yes" and "No" options in a market.
* @param marketId The ID of the market.
*/
function updatePrices(uint256 marketId) internal {
Market storage market = markets[marketId];
require(!market.isResolved, "Market already resolved");
require(kRange.length > 0, "K range not initialized");
uint256 k = kRange[market.totalFunds % kRange.length];
require(k > 0, "Invalid k value");
market.baseLiquidity = Utility.calculateBaseLiquidity(
k,
market.yesVotes + market.noVotes
);
(market.yesPrice, market.noPrice) = Utility.calculateLMSRPrices(
market.yesVotes,
market.noVotes,
market.baseLiquidity
);
emit PricesUpdated(marketId, market.yesPrice, market.noPrice);
}
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/**
* @title IMarketManager
* @notice Interface defining core functionalities for managing prediction markets.
*/
interface IMarketManager {
/**
* @notice Creates a new prediction market.
* @param questionId The unique identifier for the question (off-chain data).
* @param commissionPercentage The commission percentage for the team (0-100%).
* @param endTime The timestamp (in seconds) when the market ends.
*/
function createMarket(
uint256 questionId,
uint256 commissionPercentage,
uint256 endTime
) external;
/**
* @notice Updates the end time of an existing market.
* @param marketId The ID of the market to update.
* @param newEndTime The new end time (in seconds) for the market.
*/
function updateEndTime(uint256 marketId, uint256 newEndTime) external;
/**
* @notice Retrieves the price of a specific option in a market.
* @param marketId The ID of the market.
* @param optionId The ID of the option (0 = "No", 1 = "Yes").
* @return The price of the specified option in 18-decimal precision.
*/
function getPrice(
uint256 marketId,
uint256 optionId
) external view returns (uint256);
/**
* @notice Updates the market pool balances when points are added or removed.
* @param marketId The ID of the market.
* @param isYesVote True if adding points to "Yes" option, false for "No" option.
* @param amount The amount of points to add or subtract from the pool.
*/
function updateMarketPool(
uint256 marketId,
bool isYesVote,
uint256 amount
) external;
/**
* @notice Retrieves details about a specific market.
* @param marketId The ID of the market.
* @return questionId The unique identifier for the question (off-chain data).
* @return yesVotes The total points for the "Yes" option.
* @return noVotes The total points for the "No" option.
* @return isResolved Whether the market has been resolved.
* @return winningOption The ID of the winning option (0 = "No", 1 = "Yes").
*/
function getMarketDetails(
uint256 marketId
)
external
view
returns (
uint256 questionId,
uint256 yesVotes,
uint256 noVotes,
bool isResolved,
uint256 winningOption
);
/**
* @notice Checks if a specific market has been resolved.
* @param marketId The ID of the market.
* @return True if the market is resolved, false otherwise.
*/
function isMarketResolved(uint256 marketId) external view returns (bool);
/**
* @notice Retrieves the end time of a specific market.
* @param marketId The ID of the market.
* @return The end time of the market in UNIX timestamp.
*/
function getMarketEndTime(uint256 marketId) external view returns (uint256);
/**
* @notice Retrieves details of all markets with their pool balances.
* @return marketIds An array of market IDs.
* @return questionIds An array of question IDs for the markets.
* @return totalPoolBalances An array of total pool balances for each market.
*/
function getAllMarketsWithPools()
external
view
returns (
uint256[] memory marketIds,
uint256[] memory questionIds,
uint256[] memory totalPoolBalances
);
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/**
* @title UserState
* @dev Abstract contract to manage user points and token holdings in prediction markets.
*/
abstract contract UserState {
// State Variables
mapping(address => uint256) public userPoints; // Maps user addresses to their points balance
mapping(address => mapping(uint256 => uint256[2])) public userHoldings; // User holdings for "Yes" (index 1) and "No" (index 0) options in each market
mapping(uint256 => address[]) public marketParticipants; // List of participants per market
mapping(uint256 => mapping(address => bool)) private isMarketParticipant;
// Events
event UserDeposited(address indexed user, uint256 points);
event UserWithdrawn(address indexed user, uint256 stablecoins);
uint8 public stablecoinCount; // Total number of supported stablecoins
uint256 public constant CONVERSION_RATE = 100; // $1 = 100 points
// Events
event StablecoinAdded(
uint8 indexed stablecoinIndex,
address stablecoinAddress
);
event StablecoinUpdated(
uint8 indexed stablecoinIndex,
address oldStablecoinAddress,
address newStablecoinAddress
);
event TokensBought(
address indexed user,
uint256 indexed marketId,
uint256 optionId,
uint256 amount
);
/**
* @notice Internal function to update user holdings when buying tokens.
* @dev Adds the specified amount of tokens to the user's holdings for a given market option.
* Emits the TokensBought event in the calling function for logging purposes.
* @param user The address of the user buying tokens.
* @param marketId The ID of the market in which tokens are bought.
* @param optionId The ID of the market option being bought (0 = "No", 1 = "Yes").
* @param amount The number of tokens being bought.
*/
function _updateHoldingsOnBuy(
address user,
uint256 marketId,
uint256 optionId,
uint256 amount
) internal {
// Validate the option ID
require(optionId == 0 || optionId == 1, "UserState: Invalid option ID");
// Ensure a valid user address
require(user != address(0), "UserState: User address cannot be zero");
// Ensure a valid market ID
require(marketId > 0, "UserState: Invalid market ID");
// Ensure a valid token amount
require(amount > 0, "UserState: Amount must be greater than zero");
// Update user holdings
userHoldings[user][marketId][optionId] += amount;
}
/**
* @notice Internal function to validate if the user has sufficient balance for an action.
* @dev Reverts with a specific message if the user's balance is insufficient.
* @param user The address of the user to check.
* @param pointsRequired The number of points required for the action.
*/
function _validateUserBalance(
address user,
uint256 pointsRequired
) internal view {
require(user != address(0), "UserState: User address cannot be zero");
require(
userPoints[user] >= pointsRequired,
"UserState: Insufficient balance"
);
}
/**
* @notice Internal function to add a participant to a market if not already added.
* @param user The address of the participant.
* @param marketId The ID of the market.
*/
function _addParticipantIfNotExists(
address user,
uint256 marketId
) internal {
require(user != address(0), "UserState: User address cannot be zero");
require(marketId > 0, "UserState: Invalid market ID");
// Add user to participant list only if not already added
if (!isMarketParticipant[marketId][user]) {
marketParticipants[marketId].push(user);
isMarketParticipant[marketId][user] = true;
}
}
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (proxy/utils/UUPSUpgradeable.sol)
pragma solidity ^0.8.0;
import "../../interfaces/draft-IERC1822Upgradeable.sol";
import "../ERC1967/ERC1967UpgradeUpgradeable.sol";
import "./Initializable.sol";
/**
* @dev An upgradeability mechanism designed for UUPS proxies. The functions included here can perform an upgrade of an
* {ERC1967Proxy}, when this contract is set as the implementation behind such a proxy.
*
* A security mechanism ensures that an upgrade does not turn off upgradeability accidentally, although this risk is
* reinstated if the upgrade retains upgradeability but removes the security mechanism, e.g. by replacing
* `UUPSUpgradeable` with a custom implementation of upgrades.
*
* The {_authorizeUpgrade} function must be overridden to include access restriction to the upgrade mechanism.
*
* _Available since v4.1._
*/
abstract contract UUPSUpgradeable is Initializable, IERC1822ProxiableUpgradeable, ERC1967UpgradeUpgradeable {
function __UUPSUpgradeable_init() internal onlyInitializing {
}
function __UUPSUpgradeable_init_unchained() internal onlyInitializing {
}
/// @custom:oz-upgrades-unsafe-allow state-variable-immutable state-variable-assignment
address private immutable __self = address(this);
/**
* @dev Check that the execution is being performed through a delegatecall call and that the execution context is
* a proxy contract with an implementation (as defined in ERC1967) pointing to self. This should only be the case
* for UUPS and transparent proxies that are using the current contract as their implementation. Execution of a
* function through ERC1167 minimal proxies (clones) would not normally pass this test, but is not guaranteed to
* fail.
*/
modifier onlyProxy() {
require(address(this) != __self, "Function must be called through delegatecall");
require(_getImplementation() == __self, "Function must be called through active proxy");
_;
}
/**
* @dev Check that the execution is not being performed through a delegate call. This allows a function to be
* callable on the implementing contract but not through proxies.
*/
modifier notDelegated() {
require(address(this) == __self, "UUPSUpgradeable: must not be called through delegatecall");
_;
}
/**
* @dev Implementation of the ERC1822 {proxiableUUID} function. This returns the storage slot used by the
* implementation. It is used to validate that the this implementation remains valid after an upgrade.
*
* IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
* bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
* function revert if invoked through a proxy. This is guaranteed by the `notDelegated` modifier.
*/
function proxiableUUID() external view virtual override notDelegated returns (bytes32) {
return _IMPLEMENTATION_SLOT;
}
/**
* @dev Upgrade the implementation of the proxy to `newImplementation`.
*
* Calls {_authorizeUpgrade}.
*
* Emits an {Upgraded} event.
*/
function upgradeTo(address newImplementation) external virtual onlyProxy {
_authorizeUpgrade(newImplementation);
_upgradeToAndCallUUPS(newImplementation, new bytes(0), false);
}
/**
* @dev Upgrade the implementation of the proxy to `newImplementation`, and subsequently execute the function call
* encoded in `data`.
*
* Calls {_authorizeUpgrade}.
*
* Emits an {Upgraded} event.
*/
function upgradeToAndCall(address newImplementation, bytes memory data) external payable virtual onlyProxy {
_authorizeUpgrade(newImplementation);
_upgradeToAndCallUUPS(newImplementation, data, true);
}
/**
* @dev Function that should revert when `msg.sender` is not authorized to upgrade the contract. Called by
* {upgradeTo} and {upgradeToAndCall}.
*
* Normally, this function will use an xref:access.adoc[access control] modifier such as {Ownable-onlyOwner}.
*
* ```solidity
* function _authorizeUpgrade(address) internal override onlyOwner {}
* ```
*/
function _authorizeUpgrade(address newImplementation) internal virtual;
/**
* @dev This empty reserved space is put in place to allow future versions to add new
* variables without shifting down storage in the inheritance chain.
* See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
*/
uint256[50] private __gap;
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (proxy/utils/Initializable.sol)
pragma solidity ^0.8.2;
import "../../utils/AddressUpgradeable.sol";
/**
* @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
* behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
* external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
* function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
*
* The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
* reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
* case an upgrade adds a module that needs to be initialized.
*
* For example:
*
* [.hljs-theme-light.nopadding]
* ```
* contract MyToken is ERC20Upgradeable {
* function initialize() initializer public {
* __ERC20_init("MyToken", "MTK");
* }
* }
* contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
* function initializeV2() reinitializer(2) public {
* __ERC20Permit_init("MyToken");
* }
* }
* ```
*
* TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
* possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
*
* CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
* that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
*
* [CAUTION]
* ====
* Avoid leaving a contract uninitialized.
*
* An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
* contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
* the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
*
* [.hljs-theme-light.nopadding]
* ```
* /// @custom:oz-upgrades-unsafe-allow constructor
* constructor() {
* _disableInitializers();
* }
* ```
* ====
*/
abstract contract Initializable {
/**
* @dev Indicates that the contract has been initialized.
* @custom:oz-retyped-from bool
*/
uint8 private _initialized;
/**
* @dev Indicates that the contract is in the process of being initialized.
*/
bool private _initializing;
/**
* @dev Triggered when the contract has been initialized or reinitialized.
*/
event Initialized(uint8 version);
/**
* @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
* `onlyInitializing` functions can be used to initialize parent contracts. Equivalent to `reinitializer(1)`.
*/
modifier initializer() {
bool isTopLevelCall = _setInitializedVersion(1);
if (isTopLevelCall) {
_initializing = true;
}
_;
if (isTopLevelCall) {
_initializing = false;
emit Initialized(1);
}
}
/**
* @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
* contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
* used to initialize parent contracts.
*
* `initializer` is equivalent to `reinitializer(1)`, so a reinitializer may be used after the original
* initialization step. This is essential to configure modules that are added through upgrades and that require
* initialization.
*
* Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
* a contract, executing them in the right order is up to the developer or operator.
*/
modifier reinitializer(uint8 version) {
bool isTopLevelCall = _setInitializedVersion(version);
if (isTopLevelCall) {
_initializing = true;
}
_;
if (isTopLevelCall) {
_initializing = false;
emit Initialized(version);
}
}
/**
* @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
* {initializer} and {reinitializer} modifiers, directly or indirectly.
*/
modifier onlyInitializing() {
require(_initializing, "Initializable: contract is not initializing");
_;
}
/**
* @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
* Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
* to any version. It is recommended to use this to lock implementation contracts that are designed to be called
* through proxies.
*/
function _disableInitializers() internal virtual {
_setInitializedVersion(type(uint8).max);
}
function _setInitializedVersion(uint8 version) private returns (bool) {
// If the contract is initializing we ignore whether _initialized is set in order to support multiple
// inheritance patterns, but we only do this in the context of a constructor, and for the lowest level
// of initializers, because in other contexts the contract may have been reentered.
if (_initializing) {
require(
version == 1 && !AddressUpgradeable.isContract(address(this)),
"Initializable: contract is already initialized"
);
return false;
} else {
require(_initialized < version, "Initializable: contract is already initialized");
_initialized = version;
return true;
}
}
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (access/AccessControl.sol)
pragma solidity ^0.8.0;
import "./IAccessControlUpgradeable.sol";
import "../utils/ContextUpgradeable.sol";
import "../utils/StringsUpgradeable.sol";
import "../utils/introspection/ERC165Upgradeable.sol";
import "../proxy/utils/Initializable.sol";
/**
* @dev Contract module that allows children to implement role-based access
* control mechanisms. This is a lightweight version that doesn't allow enumerating role
* members except through off-chain means by accessing the contract event logs. Some
* applications may benefit from on-chain enumerability, for those cases see
* {AccessControlEnumerable}.
*
* Roles are referred to by their `bytes32` identifier. These should be exposed
* in the external API and be unique. The best way to achieve this is by
* using `public constant` hash digests:
*
* ```
* bytes32 public constant MY_ROLE = keccak256("MY_ROLE");
* ```
*
* Roles can be used to represent a set of permissions. To restrict access to a
* function call, use {hasRole}:
*
* ```
* function foo() public {
* require(hasRole(MY_ROLE, msg.sender));
* ...
* }
* ```
*
* Roles can be granted and revoked dynamically via the {grantRole} and
* {revokeRole} functions. Each role has an associated admin role, and only
* accounts that have a role's admin role can call {grantRole} and {revokeRole}.
*
* By default, the admin role for all roles is `DEFAULT_ADMIN_ROLE`, which means
* that only accounts with this role will be able to grant or revoke other
* roles. More complex role relationships can be created by using
* {_setRoleAdmin}.
*
* WARNING: The `DEFAULT_ADMIN_ROLE` is also its own admin: it has permission to
* grant and revoke this role. Extra precautions should be taken to secure
* accounts that have been granted it.
*/
abstract contract AccessControlUpgradeable is Initializable, ContextUpgradeable, IAccessControlUpgradeable, ERC165Upgradeable {
function __AccessControl_init() internal onlyInitializing {
}
function __AccessControl_init_unchained() internal onlyInitializing {
}
struct RoleData {
mapping(address => bool) members;
bytes32 adminRole;
}
mapping(bytes32 => RoleData) private _roles;
bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;
/**
* @dev Modifier that checks that an account has a specific role. Reverts
* with a standardized message including the required role.
*
* The format of the revert reason is given by the following regular expression:
*
* /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
*
* _Available since v4.1._
*/
modifier onlyRole(bytes32 role) {
_checkRole(role);
_;
}
/**
* @dev See {IERC165-supportsInterface}.
*/
function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
return interfaceId == type(IAccessControlUpgradeable).interfaceId || super.supportsInterface(interfaceId);
}
/**
* @dev Returns `true` if `account` has been granted `role`.
*/
function hasRole(bytes32 role, address account) public view virtual override returns (bool) {
return _roles[role].members[account];
}
/**
* @dev Revert with a standard message if `_msgSender()` is missing `role`.
* Overriding this function changes the behavior of the {onlyRole} modifier.
*
* Format of the revert message is described in {_checkRole}.
*
* _Available since v4.6._
*/
function _checkRole(bytes32 role) internal view virtual {
_checkRole(role, _msgSender());
}
/**
* @dev Revert with a standard message if `account` is missing `role`.
*
* The format of the revert reason is given by the following regular expression:
*
* /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
*/
function _checkRole(bytes32 role, address account) internal view virtual {
if (!hasRole(role, account)) {
revert(
string(
abi.encodePacked(
"AccessControl: account ",
StringsUpgradeable.toHexString(uint160(account), 20),
" is missing role ",
StringsUpgradeable.toHexString(uint256(role), 32)
)
)
);
}
}
/**
* @dev Returns the admin role that controls `role`. See {grantRole} and
* {revokeRole}.
*
* To change a role's admin, use {_setRoleAdmin}.
*/
function getRoleAdmin(bytes32 role) public view virtual override returns (bytes32) {
return _roles[role].adminRole;
}
/**
* @dev Grants `role` to `account`.
*
* If `account` had not been already granted `role`, emits a {RoleGranted}
* event.
*
* Requirements:
*
* - the caller must have ``role``'s admin role.
*/
function grantRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
_grantRole(role, account);
}
/**
* @dev Revokes `role` from `account`.
*
* If `account` had been granted `role`, emits a {RoleRevoked} event.
*
* Requirements:
*
* - the caller must have ``role``'s admin role.
*/
function revokeRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
_revokeRole(role, account);
}
/**
* @dev Revokes `role` from the calling account.
*
* Roles are often managed via {grantRole} and {revokeRole}: this function's
* purpose is to provide a mechanism for accounts to lose their privileges
* if they are compromised (such as when a trusted device is misplaced).
*
* If the calling account had been revoked `role`, emits a {RoleRevoked}
* event.
*
* Requirements:
*
* - the caller must be `account`.
*/
function renounceRole(bytes32 role, address account) public virtual override {
require(account == _msgSender(), "AccessControl: can only renounce roles for self");
_revokeRole(role, account);
}
/**
* @dev Grants `role` to `account`.
*
* If `account` had not been already granted `role`, emits a {RoleGranted}
* event. Note that unlike {grantRole}, this function doesn't perform any
* checks on the calling account.
*
* [WARNING]
* ====
* This function should only be called from the constructor when setting
* up the initial roles for the system.
*
* Using this function in any other way is effectively circumventing the admin
* system imposed by {AccessControl}.
* ====
*
* NOTE: This function is deprecated in favor of {_grantRole}.
*/
function _setupRole(bytes32 role, address account) internal virtual {
_grantRole(role, account);
}
/**
* @dev Sets `adminRole` as ``role``'s admin role.
*
* Emits a {RoleAdminChanged} event.
*/
function _setRoleAdmin(bytes32 role, bytes32 adminRole) internal virtual {
bytes32 previousAdminRole = getRoleAdmin(role);
_roles[role].adminRole = adminRole;
emit RoleAdminChanged(role, previousAdminRole, adminRole);
}
/**
* @dev Grants `role` to `account`.
*
* Internal function without access restriction.
*/
function _grantRole(bytes32 role, address account) internal virtual {
if (!hasRole(role, account)) {
_roles[role].members[account] = true;
emit RoleGranted(role, account, _msgSender());
}
}
/**
* @dev Revokes `role` from `account`.
*
* Internal function without access restriction.
*/
function _revokeRole(bytes32 role, address account) internal virtual {
if (hasRole(role, account)) {
_roles[role].members[account] = false;
emit RoleRevoked(role, account, _msgSender());
}
}
/**
* @dev This empty reserved space is put in place to allow future versions to add new
* variables without shifting down storage in the inheritance chain.
* See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
*/
uint256[49] private __gap;
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (access/Ownable.sol)
pragma solidity ^0.8.0;
import "../utils/ContextUpgradeable.sol";
import "../proxy/utils/Initializable.sol";
/**
* @dev Contract module which provides a basic access control mechanism, where
* there is an account (an owner) that can be granted exclusive access to
* specific functions.
*
* By default, the owner account will be the one that deploys the contract. This
* can later be changed with {transferOwnership}.
*
* This module is used through inheritance. It will make available the modifier
* `onlyOwner`, which can be applied to your functions to restrict their use to
* the owner.
*/
abstract contract OwnableUpgradeable is Initializable, ContextUpgradeable {
address private _owner;
event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);
/**
* @dev Initializes the contract setting the deployer as the initial owner.
*/
function __Ownable_init() internal onlyInitializing {
__Ownable_init_unchained();
}
function __Ownable_init_unchained() internal onlyInitializing {
_transferOwnership(_msgSender());
}
/**
* @dev Returns the address of the current owner.
*/
function owner() public view virtual returns (address) {
return _owner;
}
/**
* @dev Throws if called by any account other than the owner.
*/
modifier onlyOwner() {
require(owner() == _msgSender(), "Ownable: caller is not the owner");
_;
}
/**
* @dev Leaves the contract without owner. It will not be possible to call
* `onlyOwner` functions anymore. Can only be called by the current owner.
*
* NOTE: Renouncing ownership will leave the contract without an owner,
* thereby removing any functionality that is only available to the owner.
*/
function renounceOwnership() public virtual onlyOwner {
_transferOwnership(address(0));
}
/**
* @dev Transfers ownership of the contract to a new account (`newOwner`).
* Can only be called by the current owner.
*/
function transferOwnership(address newOwner) public virtual onlyOwner {
require(newOwner != address(0), "Ownable: new owner is the zero address");
_transferOwnership(newOwner);
}
/**
* @dev Transfers ownership of the contract to a new account (`newOwner`).
* Internal function without access restriction.
*/
function _transferOwnership(address newOwner) internal virtual {
address oldOwner = _owner;
_owner = newOwner;
emit OwnershipTransferred(oldOwner, newOwner);
}
/**
* @dev This empty reserved space is put in place to allow future versions to add new
* variables without shifting down storage in the inheritance chain.
* See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
*/
uint256[49] private __gap;
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
/*
██████╗ ██████╗ ██████╗ ███╗ ███╗ █████╗ ████████╗██╗ ██╗
██╔══██╗██╔══██╗██╔══██╗████╗ ████║██╔══██╗╚══██╔══╝██║ ██║
██████╔╝██████╔╝██████╔╝██╔████╔██║███████║ ██║ ███████║
██╔═══╝ ██╔══██╗██╔══██╗██║╚██╔╝██║██╔══██║ ██║ ██╔══██║
██║ ██║ ██║██████╔╝██║ ╚═╝ ██║██║ ██║ ██║ ██║ ██║
╚═╝ ╚═╝ ╚═╝╚═════╝ ╚═╝ ╚═╝╚═╝ ╚═╝ ╚═╝ ╚═╝ ╚═╝
██╗ ██╗██████╗ ██████╗ ██████╗ ██╗ ██╗ ██╗ █████╗
██║ ██║██╔══██╗██╔════╝ ██╔═████╗╚██╗██╔╝███║██╔══██╗
██║ ██║██║ ██║███████╗ ██║██╔██║ ╚███╔╝ ╚██║╚█████╔╝
██║ ██║██║ ██║██╔═══██╗████╔╝██║ ██╔██╗ ██║██╔══██╗
╚██████╔╝██████╔╝╚██████╔╝╚██████╔╝██╔╝ ██╗ ██║╚█████╔╝
╚═════╝ ╚═════╝ ╚═════╝ ╚═════╝ ╚═╝ ╚═╝ ╚═╝ ╚════╝
*/
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 v4.4.1 (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() {
// On the first call to nonReentrant, _notEntered will be true
require(_status != _ENTERED, "ReentrancyGuard: reentrant call");
// Any calls to nonReentrant after this point will fail
_status = _ENTERED;
_;
// By storing the original value once again, a refund is triggered (see
// https://eips.ethereum.org/EIPS/eip-2200)
_status = _NOT_ENTERED;
}
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (interfaces/draft-IERC1822.sol)
pragma solidity ^0.8.0;
/**
* @dev ERC1822: Universal Upgradeable Proxy Standard (UUPS) documents a method for upgradeability through a simplified
* proxy whose upgrades are fully controlled by the current implementation.
*/
interface IERC1822ProxiableUpgradeable {
/**
* @dev Returns the storage slot that the proxiable contract assumes is being used to store the implementation
* address.
*
* IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
* bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
* function revert if invoked through a proxy.
*/
function proxiableUUID() external view returns (bytes32);
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (utils/Address.sol)
pragma solidity ^0.8.1;
/**
* @dev Collection of functions related to the address type
*/
library AddressUpgradeable {
/**
* @dev Returns true if `account` is a contract.
*
* [IMPORTANT]
* ====
* It is unsafe to assume that an address for which this function returns
* false is an externally-owned account (EOA) and not a contract.
*
* Among others, `isContract` will return false for the following
* types of addresses:
*
* - an externally-owned account
* - a contract in construction
* - an address where a contract will be created
* - an address where a contract lived, but was destroyed
* ====
*
* [IMPORTANT]
* ====
* You shouldn't rely on `isContract` to protect against flash loan attacks!
*
* Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
* like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
* constructor.
* ====
*/
function isContract(address account) internal view returns (bool) {
// This method relies on extcodesize/address.code.length, which returns 0
// for contracts in construction, since the code is only stored at the end
// of the constructor execution.
return account.code.length > 0;
}
/**
* @dev Replacement for Solidity's `transfer`: sends `amount` wei to
* `recipient`, forwarding all available gas and reverting on errors.
*
* https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
* of certain opcodes, possibly making contracts go over the 2300 gas limit
* imposed by `transfer`, making them unable to receive funds via
* `transfer`. {sendValue} removes this limitation.
*
* https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
*
* IMPORTANT: because control is transferred to `recipient`, care must be
* taken to not create reentrancy vulnerabilities. Consider using
* {ReentrancyGuard} or the
* https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
*/
function sendValue(address payable recipient, uint256 amount) internal {
require(address(this).balance >= amount, "Address: insufficient balance");
(bool success, ) = recipient.call{value: amount}("");
require(success, "Address: unable to send value, recipient may have reverted");
}
/**
* @dev Performs a Solidity function call using a low level `call`. A
* plain `call` is an unsafe replacement for a function call: use this
* function instead.
*
* If `target` reverts with a revert reason, it is bubbled up by this
* function (like regular Solidity function calls).
*
* Returns the raw returned data. To convert to the expected return value,
* use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
*
* Requirements:
*
* - `target` must be a contract.
* - calling `target` with `data` must not revert.
*
* _Available since v3.1._
*/
function functionCall(address target, bytes memory data) internal returns (bytes memory) {
return functionCall(target, data, "Address: low-level call failed");
}
/**
* @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
* `errorMessage` as a fallback revert reason when `target` reverts.
*
* _Available since v3.1._
*/
function functionCall(
address target,
bytes memory data,
string memory errorMessage
) internal returns (bytes memory) {
return functionCallWithValue(target, data, 0, errorMessage);
}
/**
* @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
* but also transferring `value` wei to `target`.
*
* Requirements:
*
* - the calling contract must have an ETH balance of at least `value`.
* - the called Solidity function must be `payable`.
*
* _Available since v3.1._
*/
function functionCallWithValue(
address target,
bytes memory data,
uint256 value
) internal returns (bytes memory) {
return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
}
/**
* @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
* with `errorMessage` as a fallback revert reason when `target` reverts.
*
* _Available since v3.1._
*/
function functionCallWithValue(
address target,
bytes memory data,
uint256 value,
string memory errorMessage
) internal returns (bytes memory) {
require(address(this).balance >= value, "Address: insufficient balance for call");
require(isContract(target), "Address: call to non-contract");
(bool success, bytes memory returndata) = target.call{value: value}(data);
return verifyCallResult(success, returndata, errorMessage);
}
/**
* @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
* but performing a static call.
*
* _Available since v3.3._
*/
function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
return functionStaticCall(target, data, "Address: low-level static call failed");
}
/**
* @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
* but performing a static call.
*
* _Available since v3.3._
*/
function functionStaticCall(
address target,
bytes memory data,
string memory errorMessage
) internal view returns (bytes memory) {
require(isContract(target), "Address: static call to non-contract");
(bool success, bytes memory returndata) = target.staticcall(data);
return verifyCallResult(success, returndata, errorMessage);
}
/**
* @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
* revert reason using the provided one.
*
* _Available since v4.3._
*/
function verifyCallResult(
bool success,
bytes memory returndata,
string memory errorMessage
) internal pure returns (bytes memory) {
if (success) {
return returndata;
} else {
// Look for revert reason and bubble it up if present
if (returndata.length > 0) {
// The easiest way to bubble the revert reason is using memory via assembly
assembly {
let returndata_size := mload(returndata)
revert(add(32, returndata), returndata_size)
}
} else {
revert(errorMessage);
}
}
}
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (proxy/ERC1967/ERC1967Upgrade.sol)
pragma solidity ^0.8.2;
import "../beacon/IBeaconUpgradeable.sol";
import "../../interfaces/draft-IERC1822Upgradeable.sol";
import "../../utils/AddressUpgradeable.sol";
import "../../utils/StorageSlotUpgradeable.sol";
import "../utils/Initializable.sol";
/**
* @dev This abstract contract provides getters and event emitting update functions for
* https://eips.ethereum.org/EIPS/eip-1967[EIP1967] slots.
*
* _Available since v4.1._
*
* @custom:oz-upgrades-unsafe-allow delegatecall
*/
abstract contract ERC1967UpgradeUpgradeable is Initializable {
function __ERC1967Upgrade_init() internal onlyInitializing {
}
function __ERC1967Upgrade_init_unchained() internal onlyInitializing {
}
// This is the keccak-256 hash of "eip1967.proxy.rollback" subtracted by 1
bytes32 private constant _ROLLBACK_SLOT = 0x4910fdfa16fed3260ed0e7147f7cc6da11a60208b5b9406d12a635614ffd9143;
/**
* @dev Storage slot with the address of the current implementation.
* This is the keccak-256 hash of "eip1967.proxy.implementation" subtracted by 1, and is
* validated in the constructor.
*/
bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
/**
* @dev Emitted when the implementation is upgraded.
*/
event Upgraded(address indexed implementation);
/**
* @dev Returns the current implementation address.
*/
function _getImplementation() internal view returns (address) {
return StorageSlotUpgradeable.getAddressSlot(_IMPLEMENTATION_SLOT).value;
}
/**
* @dev Stores a new address in the EIP1967 implementation slot.
*/
function _setImplementation(address newImplementation) private {
require(AddressUpgradeable.isContract(newImplementation), "ERC1967: new implementation is not a contract");
StorageSlotUpgradeable.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
}
/**
* @dev Perform implementation upgrade
*
* Emits an {Upgraded} event.
*/
function _upgradeTo(address newImplementation) internal {
_setImplementation(newImplementation);
emit Upgraded(newImplementation);
}
/**
* @dev Perform implementation upgrade with additional setup call.
*
* Emits an {Upgraded} event.
*/
function _upgradeToAndCall(
address newImplementation,
bytes memory data,
bool forceCall
) internal {
_upgradeTo(newImplementation);
if (data.length > 0 || forceCall) {
_functionDelegateCall(newImplementation, data);
}
}
/**
* @dev Perform implementation upgrade with security checks for UUPS proxies, and additional setup call.
*
* Emits an {Upgraded} event.
*/
function _upgradeToAndCallUUPS(
address newImplementation,
bytes memory data,
bool forceCall
) internal {
// Upgrades from old implementations will perform a rollback test. This test requires the new
// implementation to upgrade back to the old, non-ERC1822 compliant, implementation. Removing
// this special case will break upgrade paths from old UUPS implementation to new ones.
if (StorageSlotUpgradeable.getBooleanSlot(_ROLLBACK_SLOT).value) {
_setImplementation(newImplementation);
} else {
try IERC1822ProxiableUpgradeable(newImplementation).proxiableUUID() returns (bytes32 slot) {
require(slot == _IMPLEMENTATION_SLOT, "ERC1967Upgrade: unsupported proxiableUUID");
} catch {
revert("ERC1967Upgrade: new implementation is not UUPS");
}
_upgradeToAndCall(newImplementation, data, forceCall);
}
}
/**
* @dev Storage slot with the admin of the contract.
* This is the keccak-256 hash of "eip1967.proxy.admin" subtracted by 1, and is
* validated in the constructor.
*/
bytes32 internal constant _ADMIN_SLOT = 0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;
/**
* @dev Emitted when the admin account has changed.
*/
event AdminChanged(address previousAdmin, address newAdmin);
/**
* @dev Returns the current admin.
*/
function _getAdmin() internal view returns (address) {
return StorageSlotUpgradeable.getAddressSlot(_ADMIN_SLOT).value;
}
/**
* @dev Stores a new address in the EIP1967 admin slot.
*/
function _setAdmin(address newAdmin) private {
require(newAdmin != address(0), "ERC1967: new admin is the zero address");
StorageSlotUpgradeable.getAddressSlot(_ADMIN_SLOT).value = newAdmin;
}
/**
* @dev Changes the admin of the proxy.
*
* Emits an {AdminChanged} event.
*/
function _changeAdmin(address newAdmin) internal {
emit AdminChanged(_getAdmin(), newAdmin);
_setAdmin(newAdmin);
}
/**
* @dev The storage slot of the UpgradeableBeacon contract which defines the implementation for this proxy.
* This is bytes32(uint256(keccak256('eip1967.proxy.beacon')) - 1)) and is validated in the constructor.
*/
bytes32 internal constant _BEACON_SLOT = 0xa3f0ad74e5423aebfd80d3ef4346578335a9a72aeaee59ff6cb3582b35133d50;
/**
* @dev Emitted when the beacon is upgraded.
*/
event BeaconUpgraded(address indexed beacon);
/**
* @dev Returns the current beacon.
*/
function _getBeacon() internal view returns (address) {
return StorageSlotUpgradeable.getAddressSlot(_BEACON_SLOT).value;
}
/**
* @dev Stores a new beacon in the EIP1967 beacon slot.
*/
function _setBeacon(address newBeacon) private {
require(AddressUpgradeable.isContract(newBeacon), "ERC1967: new beacon is not a contract");
require(
AddressUpgradeable.isContract(IBeaconUpgradeable(newBeacon).implementation()),
"ERC1967: beacon implementation is not a contract"
);
StorageSlotUpgradeable.getAddressSlot(_BEACON_SLOT).value = newBeacon;
}
/**
* @dev Perform beacon upgrade with additional setup call. Note: This upgrades the address of the beacon, it does
* not upgrade the implementation contained in the beacon (see {UpgradeableBeacon-_setImplementation} for that).
*
* Emits a {BeaconUpgraded} event.
*/
function _upgradeBeaconToAndCall(
address newBeacon,
bytes memory data,
bool forceCall
) internal {
_setBeacon(newBeacon);
emit BeaconUpgraded(newBeacon);
if (data.length > 0 || forceCall) {
_functionDelegateCall(IBeaconUpgradeable(newBeacon).implementation(), data);
}
}
/**
* @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
* but performing a delegate call.
*
* _Available since v3.4._
*/
function _functionDelegateCall(address target, bytes memory data) private returns (bytes memory) {
require(AddressUpgradeable.isContract(target), "Address: delegate call to non-contract");
// solhint-disable-next-line avoid-low-level-calls
(bool success, bytes memory returndata) = target.delegatecall(data);
return AddressUpgradeable.verifyCallResult(success, returndata, "Address: low-level delegate call failed");
}
/**
* @dev This empty reserved space is put in place to allow future versions to add new
* variables without shifting down storage in the inheritance chain.
* See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
*/
uint256[50] private __gap;
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)
pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";
/**
* @dev Provides information about the current execution context, including the
* sender of the transaction and its data. While these are generally available
* via msg.sender and msg.data, they should not be accessed in such a direct
* manner, since when dealing with meta-transactions the account sending and
* paying for execution may not be the actual sender (as far as an application
* is concerned).
*
* This contract is only required for intermediate, library-like contracts.
*/
abstract contract ContextUpgradeable is Initializable {
function __Context_init() internal onlyInitializing {
}
function __Context_init_unchained() internal onlyInitializing {
}
function _msgSender() internal view virtual returns (address) {
return msg.sender;
}
function _msgData() internal view virtual returns (bytes calldata) {
return msg.data;
}
/**
* @dev This empty reserved space is put in place to allow future versions to add new
* variables without shifting down storage in the inheritance chain.
* See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
*/
uint256[50] private __gap;
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (access/IAccessControl.sol)
pragma solidity ^0.8.0;
/**
* @dev External interface of AccessControl declared to support ERC165 detection.
*/
interface IAccessControlUpgradeable {
/**
* @dev Emitted when `newAdminRole` is set as ``role``'s admin role, replacing `previousAdminRole`
*
* `DEFAULT_ADMIN_ROLE` is the starting admin for all roles, despite
* {RoleAdminChanged} not being emitted signaling this.
*
* _Available since v3.1._
*/
event RoleAdminChanged(bytes32 indexed role, bytes32 indexed previousAdminRole, bytes32 indexed newAdminRole);
/**
* @dev Emitted when `account` is granted `role`.
*
* `sender` is the account that originated the contract call, an admin role
* bearer except when using {AccessControl-_setupRole}.
*/
event RoleGranted(bytes32 indexed role, address indexed account, address indexed sender);
/**
* @dev Emitted when `account` is revoked `role`.
*
* `sender` is the account that originated the contract call:
* - if using `revokeRole`, it is the admin role bearer
* - if using `renounceRole`, it is the role bearer (i.e. `account`)
*/
event RoleRevoked(bytes32 indexed role, address indexed account, address indexed sender);
/**
* @dev Returns `true` if `account` has been granted `role`.
*/
function hasRole(bytes32 role, address account) external view returns (bool);
/**
* @dev Returns the admin role that controls `role`. See {grantRole} and
* {revokeRole}.
*
* To change a role's admin, use {AccessControl-_setRoleAdmin}.
*/
function getRoleAdmin(bytes32 role) external view returns (bytes32);
/**
* @dev Grants `role` to `account`.
*
* If `account` had not been already granted `role`, emits a {RoleGranted}
* event.
*
* Requirements:
*
* - the caller must have ``role``'s admin role.
*/
function grantRole(bytes32 role, address account) external;
/**
* @dev Revokes `role` from `account`.
*
* If `account` had been granted `role`, emits a {RoleRevoked} event.
*
* Requirements:
*
* - the caller must have ``role``'s admin role.
*/
function revokeRole(bytes32 role, address account) external;
/**
* @dev Revokes `role` from the calling account.
*
* Roles are often managed via {grantRole} and {revokeRole}: this function's
* purpose is to provide a mechanism for accounts to lose their privileges
* if they are compromised (such as when a trusted device is misplaced).
*
* If the calling account had been granted `role`, emits a {RoleRevoked}
* event.
*
* Requirements:
*
* - the caller must be `account`.
*/
function renounceRole(bytes32 role, address account) external;
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Strings.sol)
pragma solidity ^0.8.0;
/**
* @dev String operations.
*/
library StringsUpgradeable {
bytes16 private constant _HEX_SYMBOLS = "0123456789abcdef";
/**
* @dev Converts a `uint256` to its ASCII `string` decimal representation.
*/
function toString(uint256 value) internal pure returns (string memory) {
// Inspired by OraclizeAPI's implementation - MIT licence
// https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol
if (value == 0) {
return "0";
}
uint256 temp = value;
uint256 digits;
while (temp != 0) {
digits++;
temp /= 10;
}
bytes memory buffer = new bytes(digits);
while (value != 0) {
digits -= 1;
buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
value /= 10;
}
return string(buffer);
}
/**
* @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
*/
function toHexString(uint256 value) internal pure returns (string memory) {
if (value == 0) {
return "0x00";
}
uint256 temp = value;
uint256 length = 0;
while (temp != 0) {
length++;
temp >>= 8;
}
return toHexString(value, length);
}
/**
* @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
*/
function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
bytes memory buffer = new bytes(2 * length + 2);
buffer[0] = "0";
buffer[1] = "x";
for (uint256 i = 2 * length + 1; i > 1; --i) {
buffer[i] = _HEX_SYMBOLS[value & 0xf];
value >>= 4;
}
require(value == 0, "Strings: hex length insufficient");
return string(buffer);
}
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/ERC165.sol)
pragma solidity ^0.8.0;
import "./IERC165Upgradeable.sol";
import "../../proxy/utils/Initializable.sol";
/**
* @dev Implementation of the {IERC165} interface.
*
* Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
* for the additional interface id that will be supported. For example:
*
* ```solidity
* function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
* return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
* }
* ```
*
* Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
*/
abstract contract ERC165Upgradeable is Initializable, IERC165Upgradeable {
function __ERC165_init() internal onlyInitializing {
}
function __ERC165_init_unchained() internal onlyInitializing {
}
/**
* @dev See {IERC165-supportsInterface}.
*/
function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
return interfaceId == type(IERC165Upgradeable).interfaceId;
}
/**
* @dev This empty reserved space is put in place to allow future versions to add new
* variables without shifting down storage in the inheritance chain.
* See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
*/
uint256[50] private __gap;
}
// SPDX-License-Identifier: MIT
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_SD21x18 } from "../sd21x18/Constants.sol";
import { SD21x18 } from "../sd21x18/ValueType.sol";
import { uMAX_SD59x18 } from "../sd59x18/Constants.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { uMAX_UD21x18 } from "../ud21x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD21x18 } from "../ud21x18/ValueType.sol";
import { UD60x18 } from "./ValueType.sol";
/// @notice Casts a UD60x18 number into SD1x18.
/// @dev Requirements:
/// - x ≤ 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 SD21x18.
/// @dev Requirements:
/// - x ≤ uMAX_SD21x18
function intoSD21x18(UD60x18 x) pure returns (SD21x18 result) {
uint256 xUint = UD60x18.unwrap(x);
if (xUint > uint256(int256(uMAX_SD21x18))) {
revert CastingErrors.PRBMath_UD60x18_IntoSD21x18_Overflow(x);
}
result = SD21x18.wrap(int128(uint128(xUint)));
}
/// @notice Casts a UD60x18 number into UD2x18.
/// @dev Requirements:
/// - x ≤ 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 UD21x18.
/// @dev Requirements:
/// - x ≤ uMAX_UD21x18
function intoUD21x18(UD60x18 x) pure returns (UD21x18 result) {
uint256 xUint = UD60x18.unwrap(x);
if (xUint > uMAX_UD21x18) {
revert CastingErrors.PRBMath_UD60x18_IntoUD21x18_Overflow(x);
}
result = UD21x18.wrap(uint128(xUint));
}
/// @notice Casts a UD60x18 number into SD59x18.
/// @dev Requirements:
/// - x ≤ 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 ≤ 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 ≤ 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
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 { 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 SD21x18.
error PRBMath_UD60x18_IntoSD21x18_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 UD21x18.
error PRBMath_UD60x18_IntoUD21x18_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 UNIT.
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 ≤ MAX_UD60x18 / UNIT
///
/// @param x The basic integer to convert.
/// @return 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 "./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.intoSD21x18,
Casting.intoSD59x18,
Casting.intoUD2x18,
Casting.intoUD21x18,
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 ≤ MAX_WHOLE_UD60x18
///
/// @param x The UD60x18 number to ceil.
/// @return 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.
/// @return 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 ≤ 133_084258667509499440
///
/// @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 < 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.
/// @return 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.
/// @return 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 ≥ UNIT
///
/// @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 > UNIT, use the standard formula.
if (xUint > uUNIT) {
result = exp2(mul(log2(x), y));
}
// Conversely, if x < 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 ≤ 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
// OpenZeppelin Contracts v4.4.1 (utils/StorageSlot.sol)
pragma solidity ^0.8.0;
/**
* @dev Library for reading and writing primitive types to specific storage slots.
*
* Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
* This library helps with reading and writing to such slots without the need for inline assembly.
*
* The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
*
* Example usage to set ERC1967 implementation slot:
* ```
* contract ERC1967 {
* bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
*
* function _getImplementation() internal view returns (address) {
* return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
* }
*
* function _setImplementation(address newImplementation) internal {
* require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
* StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
* }
* }
* ```
*
* _Available since v4.1 for `address`, `bool`, `bytes32`, and `uint256`._
*/
library StorageSlotUpgradeable {
struct AddressSlot {
address value;
}
struct BooleanSlot {
bool value;
}
struct Bytes32Slot {
bytes32 value;
}
struct Uint256Slot {
uint256 value;
}
/**
* @dev Returns an `AddressSlot` with member `value` located at `slot`.
*/
function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) {
assembly {
r.slot := slot
}
}
/**
* @dev Returns an `BooleanSlot` with member `value` located at `slot`.
*/
function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) {
assembly {
r.slot := slot
}
}
/**
* @dev Returns an `Bytes32Slot` with member `value` located at `slot`.
*/
function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) {
assembly {
r.slot := slot
}
}
/**
* @dev Returns an `Uint256Slot` with member `value` located at `slot`.
*/
function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) {
assembly {
r.slot := slot
}
}
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (proxy/beacon/IBeacon.sol)
pragma solidity ^0.8.0;
/**
* @dev This is the interface that {BeaconProxy} expects of its beacon.
*/
interface IBeaconUpgradeable {
/**
* @dev Must return an address that can be used as a delegate call target.
*
* {BeaconProxy} will check that this address is a contract.
*/
function implementation() external view returns (address);
}
// 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 maximum value a uint64 number can have.
uint64 constant MAX_UINT64 = type(uint64).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
// OpenZeppelin Contracts v4.4.1 (utils/introspection/IERC165.sol)
pragma solidity ^0.8.0;
/**
* @dev Interface of the ERC165 standard, as defined in the
* https://eips.ethereum.org/EIPS/eip-165[EIP].
*
* Implementers can declare support of contract interfaces, which can then be
* queried by others ({ERC165Checker}).
*
* For an implementation, see {ERC165}.
*/
interface IERC165Upgradeable {
/**
* @dev Returns true if this contract implements the interface defined by
* `interfaceId`. See the corresponding
* https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
* to learn more about how these ids are created.
*
* This function call must use less than 30 000 gas.
*/
function supportsInterface(bytes4 interfaceId) external view returns (bool);
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { SD21x18 } from "./ValueType.sol";
/// @dev Euler's number as an SD21x18 number.
SD21x18 constant E = SD21x18.wrap(2_718281828459045235);
/// @dev The maximum value an SD21x18 number can have.
int128 constant uMAX_SD21x18 = 170141183460469231731_687303715884105727;
SD21x18 constant MAX_SD21x18 = SD21x18.wrap(uMAX_SD21x18);
/// @dev The minimum value an SD21x18 number can have.
int128 constant uMIN_SD21x18 = -170141183460469231731_687303715884105728;
SD21x18 constant MIN_SD21x18 = SD21x18.wrap(uMIN_SD21x18);
/// @dev PI as an SD21x18 number.
SD21x18 constant PI = SD21x18.wrap(3_141592653589793238);
/// @dev The unit number, which gives the decimal precision of SD21x18.
SD21x18 constant UNIT = SD21x18.wrap(1e18);
int128 constant uUNIT = 1e18;
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Casting.sol" as Casting;
/// @notice The signed 21.18-decimal fixed-point number representation, which can have up to 21 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 int128. This is useful when end users want to use int128 to save gas, e.g. with tight variable packing in contract
/// storage.
type SD21x18 is int128;
/*//////////////////////////////////////////////////////////////////////////
CASTING
//////////////////////////////////////////////////////////////////////////*/
using {
Casting.intoSD59x18,
Casting.intoUD60x18,
Casting.intoUint128,
Casting.intoUint256,
Casting.intoUint40,
Casting.unwrap
} for SD21x18 global;
// 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.intoUD60x18,
Casting.intoUint128,
Casting.intoUint256,
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 minimum 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 { 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 { 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 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.intoSD59x18,
Casting.intoUD60x18,
Casting.intoUint128,
Casting.intoUint256,
Casting.intoUint40,
Casting.unwrap
} for UD2x18 global;
// 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.intoSD21x18,
Casting.intoUD2x18,
Casting.intoUD21x18,
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 { UD21x18 } from "./ValueType.sol";
/// @dev Euler's number as a UD21x18 number.
UD21x18 constant E = UD21x18.wrap(2_718281828459045235);
/// @dev The maximum value a UD21x18 number can have.
uint128 constant uMAX_UD21x18 = 340282366920938463463_374607431768211455;
UD21x18 constant MAX_UD21x18 = UD21x18.wrap(uMAX_UD21x18);
/// @dev PI as a UD21x18 number.
UD21x18 constant PI = UD21x18.wrap(3_141592653589793238);
/// @dev The unit number, which gives the decimal precision of UD21x18.
uint256 constant uUNIT = 1e18;
UD21x18 constant UNIT = UD21x18.wrap(1e18);
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Casting.sol" as Casting;
/// @notice The unsigned 21.18-decimal fixed-point number representation, which can have up to 21 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 uint128. This is useful when end users want to use uint128 to save gas, e.g. with tight variable packing in contract
/// storage.
type UD21x18 is uint128;
/*//////////////////////////////////////////////////////////////////////////
CASTING
//////////////////////////////////////////////////////////////////////////*/
using {
Casting.intoSD59x18,
Casting.intoUD60x18,
Casting.intoUint128,
Casting.intoUint256,
Casting.intoUint40,
Casting.unwrap
} for UD21x18 global;
// 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 { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD1x18 } from "./ValueType.sol";
/// @notice Casts an SD1x18 number into SD59x18.
/// @dev There is no overflow check because SD1x18 ⊆ SD59x18.
function intoSD59x18(SD1x18 x) pure returns (SD59x18 result) {
result = SD59x18.wrap(int256(SD1x18.unwrap(x)));
}
/// @notice Casts an SD1x18 number into UD60x18.
/// @dev Requirements:
/// - x ≥ 0
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 uint128.
/// @dev Requirements:
/// - x ≥ 0
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 uint256.
/// @dev Requirements:
/// - x ≥ 0
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 uint40.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ 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 "../Common.sol" as Common;
import "./Errors.sol" as CastingErrors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD21x18 } from "./ValueType.sol";
/// @notice Casts an SD21x18 number into SD59x18.
/// @dev There is no overflow check because SD21x18 ⊆ SD59x18.
function intoSD59x18(SD21x18 x) pure returns (SD59x18 result) {
result = SD59x18.wrap(int256(SD21x18.unwrap(x)));
}
/// @notice Casts an SD21x18 number into UD60x18.
/// @dev Requirements:
/// - x ≥ 0
function intoUD60x18(SD21x18 x) pure returns (UD60x18 result) {
int128 xInt = SD21x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD21x18_ToUD60x18_Underflow(x);
}
result = UD60x18.wrap(uint128(xInt));
}
/// @notice Casts an SD21x18 number into uint128.
/// @dev Requirements:
/// - x ≥ 0
function intoUint128(SD21x18 x) pure returns (uint128 result) {
int128 xInt = SD21x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD21x18_ToUint128_Underflow(x);
}
result = uint128(xInt);
}
/// @notice Casts an SD21x18 number into uint256.
/// @dev Requirements:
/// - x ≥ 0
function intoUint256(SD21x18 x) pure returns (uint256 result) {
int128 xInt = SD21x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD21x18_ToUint256_Underflow(x);
}
result = uint256(uint128(xInt));
}
/// @notice Casts an SD21x18 number into uint40.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ MAX_UINT40
function intoUint40(SD21x18 x) pure returns (uint40 result) {
int128 xInt = SD21x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD21x18_ToUint40_Underflow(x);
}
if (xInt > int128(uint128(Common.MAX_UINT40))) {
revert CastingErrors.PRBMath_SD21x18_ToUint40_Overflow(x);
}
result = uint40(uint128(xInt));
}
/// @notice Alias for {wrap}.
function sd21x18(int128 x) pure returns (SD21x18 result) {
result = SD21x18.wrap(x);
}
/// @notice Unwraps an SD21x18 number into int128.
function unwrap(SD21x18 x) pure returns (int128 result) {
result = SD21x18.unwrap(x);
}
/// @notice Wraps an int128 number into SD21x18.
function wrap(int128 x) pure returns (SD21x18 result) {
result = SD21x18.wrap(x);
}
// 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_SD21x18, uMIN_SD21x18 } from "../sd21x18/Constants.sol";
import { SD21x18 } from "../sd21x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { uMAX_UD21x18 } from "../ud21x18/Constants.sol";
import { UD21x18 } from "../ud21x18/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 ≥ uMIN_SD1x18
/// - x ≤ 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 SD21x18.
/// @dev Requirements:
/// - x ≥ uMIN_SD21x18
/// - x ≤ uMAX_SD21x18
function intoSD21x18(SD59x18 x) pure returns (SD21x18 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < uMIN_SD21x18) {
revert CastingErrors.PRBMath_SD59x18_IntoSD21x18_Underflow(x);
}
if (xInt > uMAX_SD21x18) {
revert CastingErrors.PRBMath_SD59x18_IntoSD21x18_Overflow(x);
}
result = SD21x18.wrap(int128(xInt));
}
/// @notice Casts an SD59x18 number into UD2x18.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ 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 UD21x18.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ uMAX_UD21x18
function intoUD21x18(SD59x18 x) pure returns (UD21x18 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD59x18_IntoUD21x18_Underflow(x);
}
if (xInt > int256(uint256(uMAX_UD21x18))) {
revert CastingErrors.PRBMath_SD59x18_IntoUD21x18_Overflow(x);
}
result = UD21x18.wrap(uint128(uint256(xInt)));
}
/// @notice Casts an SD59x18 number into UD60x18.
/// @dev Requirements:
/// - x ≥ 0
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 ≥ 0
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 ≥ 0
/// - x ≤ 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 ≥ 0
/// - x ≤ 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 Errors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { UD2x18 } from "./ValueType.sol";
/// @notice Casts a UD2x18 number into SD59x18.
/// @dev There is no overflow check because UD2x18 ⊆ 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 UD2x18 ⊆ 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 UD2x18 ⊆ 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 UD2x18 ⊆ uint256.
function intoUint256(UD2x18 x) pure returns (uint256 result) {
result = uint256(UD2x18.unwrap(x));
}
/// @notice Casts a UD2x18 number into uint40.
/// @dev Requirements:
/// - x ≤ 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 > MIN_SD59x18.
///
/// @param x The SD59x18 number for which to calculate the absolute value.
/// @return 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 ≤ MAX_WHOLE_SD59x18
///
/// @param x The SD59x18 number to ceil.
/// @return 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.
/// @return 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 < 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 < -59_794705707972522261, the result is zero.
///
/// Requirements:
/// - x < 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 ≥ MIN_WHOLE_SD59x18
///
/// @param x The SD59x18 number to floor.
/// @return 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.
/// @return 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 > 0
///
/// @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 ≥ 0, since complex numbers are not supported.
/// - x ≤ 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 "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { UD21x18 } from "./ValueType.sol";
/// @notice Casts a UD21x18 number into SD59x18.
/// @dev There is no overflow check because UD21x18 ⊆ SD59x18.
function intoSD59x18(UD21x18 x) pure returns (SD59x18 result) {
result = SD59x18.wrap(int256(uint256(UD21x18.unwrap(x))));
}
/// @notice Casts a UD21x18 number into UD60x18.
/// @dev There is no overflow check because UD21x18 ⊆ UD60x18.
function intoUD60x18(UD21x18 x) pure returns (UD60x18 result) {
result = UD60x18.wrap(UD21x18.unwrap(x));
}
/// @notice Casts a UD21x18 number into uint128.
/// @dev This is basically an alias for {unwrap}.
function intoUint128(UD21x18 x) pure returns (uint128 result) {
result = UD21x18.unwrap(x);
}
/// @notice Casts a UD21x18 number into uint256.
/// @dev There is no overflow check because UD21x18 ⊆ uint256.
function intoUint256(UD21x18 x) pure returns (uint256 result) {
result = uint256(UD21x18.unwrap(x));
}
/// @notice Casts a UD21x18 number into uint40.
/// @dev Requirements:
/// - x ≤ MAX_UINT40
function intoUint40(UD21x18 x) pure returns (uint40 result) {
uint128 xUint = UD21x18.unwrap(x);
if (xUint > uint128(Common.MAX_UINT40)) {
revert Errors.PRBMath_UD21x18_IntoUint40_Overflow(x);
}
result = uint40(xUint);
}
/// @notice Alias for {wrap}.
function ud21x18(uint128 x) pure returns (UD21x18 result) {
result = UD21x18.wrap(x);
}
/// @notice Unwrap a UD21x18 number into uint128.
function unwrap(UD21x18 x) pure returns (uint128 result) {
result = UD21x18.unwrap(x);
}
/// @notice Wraps a uint128 number into UD21x18.
function wrap(uint128 x) pure returns (UD21x18 result) {
result = UD21x18.wrap(x);
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { SD1x18 } from "./ValueType.sol";
/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in UD60x18.
error PRBMath_SD1x18_ToUD60x18_Underflow(SD1x18 x);
/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint128.
error PRBMath_SD1x18_ToUint128_Underflow(SD1x18 x);
/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint256.
error PRBMath_SD1x18_ToUint256_Underflow(SD1x18 x);
/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Overflow(SD1x18 x);
/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Underflow(SD1x18 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 an SD59x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD21x18.
error PRBMath_SD59x18_IntoSD21x18_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD21x18.
error PRBMath_SD59x18_IntoSD21x18_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD21x18.
error PRBMath_SD59x18_IntoUD21x18_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD21x18.
error PRBMath_SD59x18_IntoUD21x18_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD60x18.
error PRBMath_SD59x18_IntoUD60x18_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint256.
error PRBMath_SD59x18_IntoUint256_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast an SD59x18 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 { UD2x18 } from "./ValueType.sol";
/// @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 { SD21x18 } from "./ValueType.sol";
/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint128.
error PRBMath_SD21x18_ToUint128_Underflow(SD21x18 x);
/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in UD60x18.
error PRBMath_SD21x18_ToUD60x18_Underflow(SD21x18 x);
/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint256.
error PRBMath_SD21x18_ToUint256_Underflow(SD21x18 x);
/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint40.
error PRBMath_SD21x18_ToUint40_Overflow(SD21x18 x);
/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint40.
error PRBMath_SD21x18_ToUint40_Underflow(SD21x18 x);
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { UD21x18 } from "./ValueType.sol";
/// @notice Thrown when trying to cast a UD21x18 number that doesn't fit in uint40.
error PRBMath_UD21x18_IntoUint40_Overflow(UD21x18 x);