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| Txn Hash | Method |
Block
|
From
|
To
|
Value | [Txn Fee] | |||
|---|---|---|---|---|---|---|---|---|---|
| 0x14d8117f6c260576fb98d93004e70797a7e349f324cda148ac927233e6eb4e83 | 0x61010060 | 25976880 | 137 days 12 hrs ago | 0xa67d0c1180e0e183f482304a9b5436a3478f0674 | IN | Create: Accounting | 0 ETH | 0.00029925 |
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Contract Name:
Accounting
Compiler Version
v0.8.14+commit.80d49f37
Optimization Enabled:
Yes with 200 runs
Other Settings:
default evmVersion
Contract Source Code (Solidity Standard Json-Input format)
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;
import "prb-math/contracts/PRBMathUD60x18.sol";
import "prb-math/contracts/PRBMathSD59x18.sol";
import "./tokens/ERC20.sol";
import "./libraries/OptionsCompute.sol";
import "./interfaces/IAccounting.sol";
import "./interfaces/ILiquidityPool.sol";
/**
* @title Modular contract used by the liquidity pool to conducting accounting logic
*/
contract Accounting is IAccounting {
using PRBMathSD59x18 for int256;
using PRBMathUD60x18 for uint256;
///////////////////////////
/// immutable variables ///
///////////////////////////
// the liquidity pool address
ILiquidityPool public immutable liquidityPool;
// asset that denominates the strike price
address public immutable strikeAsset;
// asset that is used as the reference asset
address public immutable underlyingAsset;
// asset that is used for collateral asset
address public immutable collateralAsset;
// MAX_BPS
uint256 private constant MAX_BPS = 10000;
constructor(address _liquidityPool) {
liquidityPool = ILiquidityPool(_liquidityPool);
strikeAsset = ILiquidityPool(_liquidityPool).strikeAsset();
underlyingAsset = ILiquidityPool(_liquidityPool).underlyingAsset();
collateralAsset = ILiquidityPool(_liquidityPool).collateralAsset();
}
///////////////////////
/// complex getters ///
///////////////////////
/**
* @notice calculates the USDC value of the Liquidity pool's ERC20 vault share token denominated in e6
* @param totalSupply the total supply of the liquidity pool's erc20
* @param assets the value of assets held by the pool
* @param liabilities the value of liabilities held by the pool
* @return tokenPrice the value of the token in e6 terms
*/
function calculateTokenPrice(
uint256 totalSupply,
uint256 assets,
int256 liabilities
) internal view returns (uint256 tokenPrice) {
if (int256(assets) < liabilities) {
revert CustomErrors.LiabilitiesGreaterThanAssets();
}
uint256 NAV = uint256((int256(assets) - liabilities));
tokenPrice = totalSupply > 0
? (1e18 *
(NAV -
OptionsCompute.convertFromDecimals(
liquidityPool.pendingDeposits(),
ERC20(collateralAsset).decimals()
))) / totalSupply
: 1e18;
}
/**
* @notice logic for adding liquidity to the options liquidity pool
* @param depositor the address making the deposit
* @param _amount amount of the collateral asset to deposit
* @return depositAmount the amount to deposit from the round
* @return unredeemedShares number of shares held in the deposit receipt that havent been redeemed
*/
function deposit(address depositor, uint256 _amount)
external
view
returns (uint256 depositAmount, uint256 unredeemedShares)
{
uint256 collateralCap = liquidityPool.collateralCap();
uint256 currentEpoch = liquidityPool.depositEpoch();
// check the total allowed collateral amount isnt surpassed by incrementing the total assets with the amount denominated in e18
uint256 totalAmountWithDeposit = liquidityPool.getAssets() +
OptionsCompute.convertFromDecimals(_amount, ERC20(collateralAsset).decimals());
if (totalAmountWithDeposit > collateralCap) {
revert CustomErrors.TotalSupplyReached();
}
IAccounting.DepositReceipt memory depositReceipt = liquidityPool.depositReceipts(depositor);
// check for any unredeemed shares
unredeemedShares = uint256(depositReceipt.unredeemedShares);
// if there is already a receipt from a previous round then acknowledge and record it
if (depositReceipt.epoch != 0 && depositReceipt.epoch < currentEpoch) {
unredeemedShares += sharesForAmount(
depositReceipt.amount,
liquidityPool.depositEpochPricePerShare(depositReceipt.epoch)
);
}
depositAmount = _amount;
// if there is a second deposit in the same round then increment this amount
if (currentEpoch == depositReceipt.epoch) {
depositAmount += uint256(depositReceipt.amount);
}
require(depositAmount <= type(uint128).max, "overflow");
}
/**
* @notice logic for allowing a user to redeem their shares from a previous epoch
* @param redeemer the address making the deposit
* @param shares amount of the collateral asset to deposit
* @return toRedeem the amount to actually redeem
* @return depositReceipt the updated deposit receipt after the redeem has completed
*/
function redeem(address redeemer, uint256 shares)
external
view
returns (uint256 toRedeem, IAccounting.DepositReceipt memory)
{
IAccounting.DepositReceipt memory depositReceipt = liquidityPool.depositReceipts(redeemer);
uint256 currentEpoch = liquidityPool.depositEpoch();
// check for any unredeemed shares
uint256 unredeemedShares = uint256(depositReceipt.unredeemedShares);
// if there is already a receipt from a previous round then acknowledge and record it
if (depositReceipt.epoch != 0 && depositReceipt.epoch < currentEpoch) {
unredeemedShares += sharesForAmount(
depositReceipt.amount,
liquidityPool.depositEpochPricePerShare(depositReceipt.epoch)
);
}
// if the shares requested are greater than their unredeemedShares then floor to unredeemedShares, otherwise
// use their requested share number
toRedeem = shares > unredeemedShares ? unredeemedShares : shares;
if (toRedeem == 0) {
return (0, depositReceipt);
}
// if the deposit receipt is on this epoch and there are unredeemed shares then we leave amount as is,
// if the epoch has past then we set the amount to 0 and take from the unredeemedShares
if (depositReceipt.epoch < currentEpoch) {
depositReceipt.amount = 0;
}
depositReceipt.unredeemedShares = uint128(unredeemedShares - toRedeem);
return (toRedeem, depositReceipt);
}
/**
* @notice logic for accounting a user to initiate a withdraw request from the pool
* @param withdrawer the address carrying out the withdrawal
* @param shares the amount of shares to withdraw for
* @return withdrawalReceipt the new withdrawal receipt to pass to the liquidityPool
*/
function initiateWithdraw(address withdrawer, uint256 shares)
external
view
returns (IAccounting.WithdrawalReceipt memory withdrawalReceipt)
{
if (liquidityPool.balanceOf(withdrawer) < shares) {
revert CustomErrors.InsufficientShareBalance();
}
uint256 currentEpoch = liquidityPool.withdrawalEpoch();
withdrawalReceipt = liquidityPool.withdrawalReceipts(withdrawer);
uint256 existingShares = withdrawalReceipt.shares;
uint256 withdrawalShares;
// if they already have an initiated withdrawal from this round just increment
if (withdrawalReceipt.epoch == currentEpoch) {
withdrawalShares = existingShares + shares;
} else {
// do 100 wei just in case of any rounding issues
if (existingShares > 100) {
revert CustomErrors.ExistingWithdrawal();
}
withdrawalShares = shares;
withdrawalReceipt.epoch = uint128(currentEpoch);
}
withdrawalReceipt.shares = uint128(withdrawalShares);
}
/**
* @notice logic for accounting a user to complete a withdrawal
* @param withdrawer the address carrying out the withdrawal
* @return withdrawalAmount the amount of collateral to withdraw
* @return withdrawalShares the number of shares to withdraw
* @return withdrawalReceipt the new withdrawal receipt to pass to the liquidityPool
*/
function completeWithdraw(address withdrawer)
external
view
returns (
uint256 withdrawalAmount,
uint256 withdrawalShares,
IAccounting.WithdrawalReceipt memory withdrawalReceipt
)
{
withdrawalReceipt = liquidityPool.withdrawalReceipts(withdrawer);
// cache the storage variables
withdrawalShares = withdrawalReceipt.shares;
uint256 withdrawalEpoch = withdrawalReceipt.epoch;
// make sure there is something to withdraw and make sure the round isnt the current one
if (withdrawalShares == 0) {
revert CustomErrors.NoExistingWithdrawal();
}
if (withdrawalEpoch == liquidityPool.withdrawalEpoch()) {
revert CustomErrors.EpochNotClosed();
}
// reduced the stored share receipt by the shares requested
withdrawalReceipt.shares -= uint128(withdrawalShares);
// get the withdrawal amount based on the shares and pps at the epoch
withdrawalAmount = amountForShares(
withdrawalShares,
liquidityPool.withdrawalEpochPricePerShare(withdrawalEpoch)
);
if (withdrawalAmount == 0) {
revert CustomErrors.InvalidAmount();
}
}
/**
* @notice execute the next epoch
* @param totalSupply the total number of share tokens
* @param assets the amount of collateral assets
* @param liabilities the amount of liabilities of the pool
* @return newPricePerShareDeposit the price per share for deposits
* @return newPricePerShareWithdrawal the price per share for withdrawals
* @return sharesToMint the number of shares to mint this epoch
* @return totalWithdrawAmount the amount of collateral to set aside for partitioning
* @return amountNeeded the amount needed to reach the total withdraw amount if collateral balance of lp is insufficient
*/
function executeEpochCalculation(
uint256 totalSupply,
uint256 assets,
int256 liabilities
)
external
view
returns (
uint256 newPricePerShareDeposit,
uint256 newPricePerShareWithdrawal,
uint256 sharesToMint,
uint256 totalWithdrawAmount,
uint256 amountNeeded
)
{
// get the liquidity that can be withdrawn from the pool without hitting the collateral requirement buffer
int256 bufferRemaining = liquidityPool.checkBuffer();
newPricePerShareDeposit = newPricePerShareWithdrawal = calculateTokenPrice(
totalSupply,
assets,
liabilities
);
sharesToMint = sharesForAmount(liquidityPool.pendingDeposits(), newPricePerShareDeposit);
totalWithdrawAmount = amountForShares(
liquidityPool.pendingWithdrawals(),
newPricePerShareWithdrawal
);
if (bufferRemaining > int256(totalWithdrawAmount)) {
amountNeeded = 0;
} else {
// get the extra liquidity that is needed from hedging reactors
amountNeeded = uint256(int256(totalWithdrawAmount) - bufferRemaining);
}
}
/**
* @notice get the number of shares for a given amount
* @param _amount the amount to convert to shares - assumed in collateral decimals
* @param assetPerShare the amount of assets received per share
* @return shares the number of shares based on the amount - assumed in e18
*/
function sharesForAmount(uint256 _amount, uint256 assetPerShare)
public
view
returns (uint256 shares)
{
uint256 convertedAmount = OptionsCompute.convertFromDecimals(
_amount,
ERC20(collateralAsset).decimals()
);
shares = (convertedAmount * PRBMath.SCALE) / assetPerShare;
}
/**
* @notice get the amount for a given number of shares
* @param _shares the shares to convert to amount in e18
* @param _assetPerShare the amount of assets received per share
* @return amount the number of amount based on shares in collateral decimals
*/
function amountForShares(uint256 _shares, uint256 _assetPerShare)
public
view
returns (uint256 amount)
{
amount = OptionsCompute.convertToDecimals(
(_shares * _assetPerShare) / PRBMath.SCALE,
ERC20(collateralAsset).decimals()
);
}
}// SPDX-License-Identifier: UNLICENSED
pragma solidity >=0.8.9;
import { Types } from "../libraries/Types.sol";
import "../interfaces/IOptionRegistry.sol";
import "../interfaces/IAccounting.sol";
import "../interfaces/I_ERC20.sol";
interface ILiquidityPool is I_ERC20 {
///////////////////////////
/// immutable variables ///
///////////////////////////
function strikeAsset() external view returns (address);
function underlyingAsset() external view returns (address);
function collateralAsset() external view returns (address);
/////////////////////////
/// dynamic variables ///
/////////////////////////
function collateralAllocated() external view returns (uint256);
function ephemeralLiabilities() external view returns (int256);
function ephemeralDelta() external view returns (int256);
function depositEpoch() external view returns (uint256);
function withdrawalEpoch() external view returns (uint256);
function depositEpochPricePerShare(uint256 epoch) external view returns (uint256 price);
function withdrawalEpochPricePerShare(uint256 epoch) external view returns (uint256 price);
function depositReceipts(address depositor)
external
view
returns (IAccounting.DepositReceipt memory);
function withdrawalReceipts(address withdrawer)
external
view
returns (IAccounting.WithdrawalReceipt memory);
function pendingDeposits() external view returns (uint256);
function pendingWithdrawals() external view returns (uint256);
function partitionedFunds() external view returns (uint256);
/////////////////////////////////////
/// governance settable variables ///
/////////////////////////////////////
function bufferPercentage() external view returns (uint256);
function collateralCap() external view returns (uint256);
/////////////////
/// functions ///
/////////////////
function handlerIssue(Types.OptionSeries memory optionSeries) external returns (address);
function resetEphemeralValues() external;
function getAssets() external view returns (uint256);
function redeem(uint256) external returns (uint256);
function handlerWriteOption(
Types.OptionSeries memory optionSeries,
address seriesAddress,
uint256 amount,
IOptionRegistry optionRegistry,
uint256 premium,
int256 delta,
address recipient
) external returns (uint256);
function handlerBuybackOption(
Types.OptionSeries memory optionSeries,
uint256 amount,
IOptionRegistry optionRegistry,
address seriesAddress,
uint256 premium,
int256 delta,
address seller
) external returns (uint256);
function handlerIssueAndWriteOption(
Types.OptionSeries memory optionSeries,
uint256 amount,
uint256 premium,
int256 delta,
address recipient
) external returns (uint256, address);
function getPortfolioDelta() external view returns (int256);
function quotePriceWithUtilizationGreeks(
Types.OptionSeries memory optionSeries,
uint256 amount,
bool toBuy
) external view returns (uint256 quote, int256 delta);
function checkBuffer() external view returns (int256 bufferRemaining);
function getBalance(address asset) external view returns (uint256);
}// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;
/// @notice Modern and gas efficient ERC20 + EIP-2612 implementation.
/// @author Solmate (https://github.com/Rari-Capital/solmate/blob/main/src/tokens/ERC20.sol)
/// @author Modified from Uniswap (https://github.com/Uniswap/uniswap-v2-core/blob/master/contracts/UniswapV2ERC20.sol)
/// @dev Do not manually set balances without updating totalSupply, as the sum of all user balances must not exceed it.
abstract contract ERC20 {
/*///////////////////////////////////////////////////////////////
EVENTS
//////////////////////////////////////////////////////////////*/
event Transfer(address indexed from, address indexed to, uint256 amount);
event Approval(address indexed owner, address indexed spender, uint256 amount);
/*///////////////////////////////////////////////////////////////
METADATA STORAGE
//////////////////////////////////////////////////////////////*/
string public name;
string public symbol;
uint8 public immutable decimals;
/*///////////////////////////////////////////////////////////////
ERC20 STORAGE
//////////////////////////////////////////////////////////////*/
uint256 public totalSupply;
mapping(address => uint256) public balanceOf;
mapping(address => mapping(address => uint256)) public allowance;
/*///////////////////////////////////////////////////////////////
EIP-2612 STORAGE
//////////////////////////////////////////////////////////////*/
uint256 internal immutable INITIAL_CHAIN_ID;
bytes32 internal immutable INITIAL_DOMAIN_SEPARATOR;
mapping(address => uint256) public nonces;
/*///////////////////////////////////////////////////////////////
CONSTRUCTOR
//////////////////////////////////////////////////////////////*/
constructor(
string memory _name,
string memory _symbol,
uint8 _decimals
) {
name = _name;
symbol = _symbol;
decimals = _decimals;
INITIAL_CHAIN_ID = block.chainid;
INITIAL_DOMAIN_SEPARATOR = computeDomainSeparator();
}
/*///////////////////////////////////////////////////////////////
ERC20 LOGIC
//////////////////////////////////////////////////////////////*/
function approve(address spender, uint256 amount) public virtual returns (bool) {
allowance[msg.sender][spender] = amount;
emit Approval(msg.sender, spender, amount);
return true;
}
function transfer(address to, uint256 amount) public virtual returns (bool) {
balanceOf[msg.sender] -= amount;
// Cannot overflow because the sum of all user
// balances can't exceed the max uint256 value.
unchecked {
balanceOf[to] += amount;
}
emit Transfer(msg.sender, to, amount);
return true;
}
function transferFrom(
address from,
address to,
uint256 amount
) public virtual returns (bool) {
uint256 allowed = allowance[from][msg.sender]; // Saves gas for limited approvals.
if (allowed != type(uint256).max) allowance[from][msg.sender] = allowed - amount;
balanceOf[from] -= amount;
// Cannot overflow because the sum of all user
// balances can't exceed the max uint256 value.
unchecked {
balanceOf[to] += amount;
}
emit Transfer(from, to, amount);
return true;
}
/*///////////////////////////////////////////////////////////////
EIP-2612 LOGIC
//////////////////////////////////////////////////////////////*/
function permit(
address owner,
address spender,
uint256 value,
uint256 deadline,
uint8 v,
bytes32 r,
bytes32 s
) public virtual {
require(deadline >= block.timestamp, "PERMIT_DEADLINE_EXPIRED");
// Unchecked because the only math done is incrementing
// the owner's nonce which cannot realistically overflow.
unchecked {
bytes32 digest = keccak256(
abi.encodePacked(
"\x19\x01",
DOMAIN_SEPARATOR(),
keccak256(
abi.encode(
keccak256(
"Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)"
),
owner,
spender,
value,
nonces[owner]++,
deadline
)
)
)
);
address recoveredAddress = ecrecover(digest, v, r, s);
require(recoveredAddress != address(0) && recoveredAddress == owner, "INVALID_SIGNER");
allowance[recoveredAddress][spender] = value;
}
emit Approval(owner, spender, value);
}
function DOMAIN_SEPARATOR() public view virtual returns (bytes32) {
return block.chainid == INITIAL_CHAIN_ID ? INITIAL_DOMAIN_SEPARATOR : computeDomainSeparator();
}
function computeDomainSeparator() internal view virtual returns (bytes32) {
return
keccak256(
abi.encode(
keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"),
keccak256(bytes(name)),
keccak256("1"),
block.chainid,
address(this)
)
);
}
/*///////////////////////////////////////////////////////////////
INTERNAL MINT/BURN LOGIC
//////////////////////////////////////////////////////////////*/
function _mint(address to, uint256 amount) internal virtual {
totalSupply += amount;
// Cannot overflow because the sum of all user
// balances can't exceed the max uint256 value.
unchecked {
balanceOf[to] += amount;
}
emit Transfer(address(0), to, amount);
}
function _burn(address from, uint256 amount) internal virtual {
balanceOf[from] -= amount;
// Cannot underflow because a user's balance
// will never be larger than the total supply.
unchecked {
totalSupply -= amount;
}
emit Transfer(from, address(0), amount);
}
}// SPDX-License-Identifier: UNLICENSED
pragma solidity >=0.8.9;
/// @title Accounting contract to calculate the dhv token value and handle deposit/withdraw mechanics
interface IAccounting {
struct DepositReceipt {
uint128 epoch;
uint128 amount; // collateral decimals
uint256 unredeemedShares; // e18
}
struct WithdrawalReceipt {
uint128 epoch;
uint128 shares; // e18
}
/**
* @notice logic for adding liquidity to the options liquidity pool
* @param depositor the address making the deposit
* @param _amount amount of the collateral asset to deposit
* @return depositAmount the amount to deposit from the round
* @return unredeemedShares number of shares held in the deposit receipt that havent been redeemed
*/
function deposit(address depositor, uint256 _amount)
external
returns (uint256 depositAmount, uint256 unredeemedShares);
/**
* @notice logic for allowing a user to redeem their shares from a previous epoch
* @param redeemer the address making the deposit
* @param shares amount of the collateral asset to deposit
* @return toRedeem the amount to actually redeem
* @return depositReceipt the updated deposit receipt after the redeem has completed
*/
function redeem(address redeemer, uint256 shares)
external
returns (uint256 toRedeem, DepositReceipt memory depositReceipt);
/**
* @notice logic for accounting a user to initiate a withdraw request from the pool
* @param withdrawer the address carrying out the withdrawal
* @param shares the amount of shares to withdraw for
* @return withdrawalReceipt the new withdrawal receipt to pass to the liquidityPool
*/
function initiateWithdraw(address withdrawer, uint256 shares)
external
returns (WithdrawalReceipt memory withdrawalReceipt);
/**
* @notice logic for accounting a user to complete a withdrawal
* @param withdrawer the address carrying out the withdrawal
* @return withdrawalAmount the amount of collateral to withdraw
* @return withdrawalShares the number of shares to withdraw
* @return withdrawalReceipt the new withdrawal receipt to pass to the liquidityPool
*/
function completeWithdraw(address withdrawer)
external
returns (
uint256 withdrawalAmount,
uint256 withdrawalShares,
WithdrawalReceipt memory withdrawalReceipt
);
/**
* @notice execute the next epoch
* @param totalSupply the total number of share tokens
* @param assets the amount of collateral assets
* @param liabilities the amount of liabilities of the pool
* @return newPricePerShareDeposit the price per share for deposits
* @return newPricePerShareWithdrawal the price per share for withdrawals
* @return sharesToMint the number of shares to mint this epoch
* @return totalWithdrawAmount the amount of collateral to set aside for partitioning
* @return amountNeeded the amount needed to reach the total withdraw amount if collateral balance of lp is insufficient
*/
function executeEpochCalculation(
uint256 totalSupply,
uint256 assets,
int256 liabilities
)
external
view
returns (
uint256 newPricePerShareDeposit,
uint256 newPricePerShareWithdrawal,
uint256 sharesToMint,
uint256 totalWithdrawAmount,
uint256 amountNeeded
);
/**
* @notice get the number of shares for a given amount
* @param _amount the amount to convert to shares - assumed in collateral decimals
* @param assetPerShare the amount of assets received per share
* @return shares the number of shares based on the amount - assumed in e18
*/
function sharesForAmount(uint256 _amount, uint256 assetPerShare)
external
view
returns (uint256 shares);
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;
import "./Types.sol";
import "./CustomErrors.sol";
import "./BlackScholes.sol";
import "prb-math/contracts/PRBMathUD60x18.sol";
import "prb-math/contracts/PRBMathSD59x18.sol";
/**
* @title Library used for various helper functionality for the Liquidity Pool
*/
library OptionsCompute {
using PRBMathUD60x18 for uint256;
using PRBMathSD59x18 for int256;
uint8 private constant SCALE_DECIMALS = 18;
/// @dev assumes decimals are coming in as e18
function convertToDecimals(uint256 value, uint256 decimals) internal pure returns (uint256) {
if (decimals > SCALE_DECIMALS) {
revert();
}
uint256 difference = SCALE_DECIMALS - decimals;
return value / (10**difference);
}
/// @dev converts from specified decimals to e18
function convertFromDecimals(uint256 value, uint256 decimals) internal pure returns (uint256) {
if (decimals > SCALE_DECIMALS) {
revert();
}
uint256 difference = SCALE_DECIMALS - decimals;
return value * (10**difference);
}
// doesnt allow for interest bearing collateral
function convertToCollateralDenominated(
uint256 quote,
uint256 underlyingPrice,
Types.OptionSeries memory optionSeries
) internal pure returns (uint256 convertedQuote) {
if (optionSeries.strikeAsset != optionSeries.collateral) {
// convert value from strike asset to collateral asset
return (quote * 1e18) / underlyingPrice;
} else {
return quote;
}
}
/**
* @dev computes the percentage change between two integers
* @param n new value in e18
* @param o old value in e18
* @return pC uint256 the percentage change in e18
*/
function calculatePercentageChange(uint256 n, uint256 o) internal pure returns (uint256 pC) {
// if new > old then its a percentage increase so do:
// ((new - old) * 1e18) / old
// if new < old then its a percentage decrease so do:
// ((old - new) * 1e18) / old
if (n > o) {
pC = (n - o).div(o);
} else {
pC = (o - n).div(o);
}
}
/**
* @notice get the latest oracle fed portfolio values and check when they were last updated and make sure this is within a reasonable window in
* terms of price and time
*/
function validatePortfolioValues(
uint256 spotPrice,
Types.PortfolioValues memory portfolioValues,
uint256 maxTimeDeviationThreshold,
uint256 maxPriceDeviationThreshold
) public view {
uint256 timeDelta = block.timestamp - portfolioValues.timestamp;
// If too much time has passed we want to prevent a possible oracle attack
if (timeDelta > maxTimeDeviationThreshold) {
revert CustomErrors.TimeDeltaExceedsThreshold(timeDelta);
}
uint256 priceDelta = calculatePercentageChange(spotPrice, portfolioValues.spotPrice);
// If price has deviated too much we want to prevent a possible oracle attack
if (priceDelta > maxPriceDeviationThreshold) {
revert CustomErrors.PriceDeltaExceedsThreshold(priceDelta);
}
}
/**
* @notice calculates the utilization price of an option using the liquidity pool's utilisation skew algorithm
*/
function getUtilizationPrice(
uint256 _utilizationBefore,
uint256 _utilizationAfter,
uint256 _totalOptionPrice,
uint256 _utilizationFunctionThreshold,
uint256 _belowThresholdGradient,
uint256 _aboveThresholdGradient,
uint256 _aboveThresholdYIntercept
) internal pure returns (uint256 utilizationPrice) {
if (
_utilizationBefore <= _utilizationFunctionThreshold &&
_utilizationAfter <= _utilizationFunctionThreshold
) {
// linear function up to threshold utilization
// take average of before and after utilization and multiply the average by belowThresholdGradient
uint256 multiplicationFactor = (_utilizationBefore + _utilizationAfter)
.mul(_belowThresholdGradient)
.div(2e18);
return _totalOptionPrice + _totalOptionPrice.mul(multiplicationFactor);
} else if (
_utilizationBefore >= _utilizationFunctionThreshold &&
_utilizationAfter >= _utilizationFunctionThreshold
) {
// over threshold utilization the skew factor will follow a steeper line
uint256 multiplicationFactor = _aboveThresholdGradient
.mul(_utilizationBefore + _utilizationAfter)
.div(2e18) - _aboveThresholdYIntercept;
return _totalOptionPrice + _totalOptionPrice.mul(multiplicationFactor);
} else {
// in this case the utilization after is above the threshold and
// utilization before is below it.
// _utilizationAfter will always be greater than _utilizationBefore
// finds the ratio of the distance below the threshold to the distance above the threshold
uint256 weightingRatio = (_utilizationFunctionThreshold - _utilizationBefore).div(
_utilizationAfter - _utilizationFunctionThreshold
);
// finds the average y value on the part of the function below threshold
uint256 averageFactorBelow = (_utilizationFunctionThreshold + _utilizationBefore).div(2e18).mul(
_belowThresholdGradient
);
// finds average y value on part of the function above threshold
uint256 averageFactorAbove = (_utilizationAfter + _utilizationFunctionThreshold).div(2e18).mul(
_aboveThresholdGradient
) - _aboveThresholdYIntercept;
// finds the weighted average of the two above averaged to find the average utilization skew over the range of utilization
uint256 multiplicationFactor = (weightingRatio.mul(averageFactorBelow) + averageFactorAbove).div(
1e18 + weightingRatio
);
return _totalOptionPrice + _totalOptionPrice.mul(multiplicationFactor);
}
}
/**
* @notice get the greeks of a quotePrice for a given optionSeries
* @param optionSeries Types.OptionSeries struct for describing the option to price greeks - strike in e18
* @return quote Quote price of the option - in e18
* @return delta delta of the option being priced - in e18
*/
function quotePriceGreeks(
Types.OptionSeries memory optionSeries,
bool isBuying,
uint256 bidAskIVSpread,
uint256 riskFreeRate,
uint256 iv,
uint256 underlyingPrice
) internal view returns (uint256 quote, int256 delta) {
if (iv == 0) {
revert CustomErrors.IVNotFound();
}
// reduce IV by a factor of bidAskIVSpread if we are buying the options
if (isBuying) {
iv = (iv * (1e18 - (bidAskIVSpread))) / 1e18;
}
// revert CustomErrors.if the expiry is in the past
if (optionSeries.expiration <= block.timestamp) {
revert CustomErrors.OptionExpiryInvalid();
}
(quote, delta) = BlackScholes.blackScholesCalcGreeks(
underlyingPrice,
optionSeries.strike,
optionSeries.expiration,
iv,
riskFreeRate,
optionSeries.isPut
);
}
}// SPDX-License-Identifier: Unlicense
pragma solidity >=0.8.4;
import "./PRBMath.sol";
/// @title PRBMathSD59x18
/// @author Paul Razvan Berg
/// @notice Smart contract library for advanced fixed-point math that works with int256 numbers considered to have 18
/// trailing decimals. We call this number representation signed 59.18-decimal fixed-point, since the numbers can have
/// a sign and there can be up to 59 digits in the integer part and up to 18 decimals in the fractional part. The numbers
/// are bound by the minimum and the maximum values permitted by the Solidity type int256.
library PRBMathSD59x18 {
/// @dev log2(e) as a signed 59.18-decimal fixed-point number.
int256 internal constant LOG2_E = 1_442695040888963407;
/// @dev Half the SCALE number.
int256 internal constant HALF_SCALE = 5e17;
/// @dev The maximum value a signed 59.18-decimal fixed-point number can have.
int256 internal constant MAX_SD59x18 =
57896044618658097711785492504343953926634992332820282019728_792003956564819967;
/// @dev The maximum whole value a signed 59.18-decimal fixed-point number can have.
int256 internal constant MAX_WHOLE_SD59x18 =
57896044618658097711785492504343953926634992332820282019728_000000000000000000;
/// @dev The minimum value a signed 59.18-decimal fixed-point number can have.
int256 internal constant MIN_SD59x18 =
-57896044618658097711785492504343953926634992332820282019728_792003956564819968;
/// @dev The minimum whole value a signed 59.18-decimal fixed-point number can have.
int256 internal constant MIN_WHOLE_SD59x18 =
-57896044618658097711785492504343953926634992332820282019728_000000000000000000;
/// @dev How many trailing decimals can be represented.
int256 internal constant SCALE = 1e18;
/// INTERNAL FUNCTIONS ///
/// @notice Calculate the absolute value of x.
///
/// @dev Requirements:
/// - x must be greater than MIN_SD59x18.
///
/// @param x The number to calculate the absolute value for.
/// @param result The absolute value of x.
function abs(int256 x) internal pure returns (int256 result) {
unchecked {
if (x == MIN_SD59x18) {
revert PRBMathSD59x18__AbsInputTooSmall();
}
result = x < 0 ? -x : x;
}
}
/// @notice Calculates the arithmetic average of x and y, rounding down.
/// @param x The first operand as a signed 59.18-decimal fixed-point number.
/// @param y The second operand as a signed 59.18-decimal fixed-point number.
/// @return result The arithmetic average as a signed 59.18-decimal fixed-point number.
function avg(int256 x, int256 y) internal pure returns (int256 result) {
// The operations can never overflow.
unchecked {
int256 sum = (x >> 1) + (y >> 1);
if (sum < 0) {
// If at least one of x and y is odd, we add 1 to the result. This is because shifting negative numbers to the
// right rounds down to infinity.
assembly {
result := add(sum, and(or(x, y), 1))
}
} else {
// If both x and y are odd, we add 1 to the result. This is because if both numbers are odd, the 0.5
// remainder gets truncated twice.
result = sum + (x & y & 1);
}
}
}
/// @notice Yields the least greatest signed 59.18 decimal fixed-point number greater than or equal to x.
///
/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x must be less than or equal to MAX_WHOLE_SD59x18.
///
/// @param x The signed 59.18-decimal fixed-point number to ceil.
/// @param result The least integer greater than or equal to x, as a signed 58.18-decimal fixed-point number.
function ceil(int256 x) internal pure returns (int256 result) {
if (x > MAX_WHOLE_SD59x18) {
revert PRBMathSD59x18__CeilOverflow(x);
}
unchecked {
int256 remainder = x % SCALE;
if (remainder == 0) {
result = x;
} else {
// Solidity uses C fmod style, which returns a modulus with the same sign as x.
result = x - remainder;
if (x > 0) {
result += SCALE;
}
}
}
}
/// @notice Divides two signed 59.18-decimal fixed-point numbers, returning a new signed 59.18-decimal fixed-point number.
///
/// @dev Variant of "mulDiv" that works with signed numbers. Works by computing the signs and the absolute values separately.
///
/// Requirements:
/// - All from "PRBMath.mulDiv".
/// - None of the inputs can be MIN_SD59x18.
/// - The denominator cannot be zero.
/// - The result must fit within int256.
///
/// Caveats:
/// - All from "PRBMath.mulDiv".
///
/// @param x The numerator as a signed 59.18-decimal fixed-point number.
/// @param y The denominator as a signed 59.18-decimal fixed-point number.
/// @param result The quotient as a signed 59.18-decimal fixed-point number.
function div(int256 x, int256 y) internal pure returns (int256 result) {
if (x == MIN_SD59x18 || y == MIN_SD59x18) {
revert PRBMathSD59x18__DivInputTooSmall();
}
// Get hold of the absolute values of x and y.
uint256 ax;
uint256 ay;
unchecked {
ax = x < 0 ? uint256(-x) : uint256(x);
ay = y < 0 ? uint256(-y) : uint256(y);
}
// Compute the absolute value of (x*SCALE)÷y. The result must fit within int256.
uint256 rAbs = PRBMath.mulDiv(ax, uint256(SCALE), ay);
if (rAbs > uint256(MAX_SD59x18)) {
revert PRBMathSD59x18__DivOverflow(rAbs);
}
// Get the signs of x and y.
uint256 sx;
uint256 sy;
assembly {
sx := sgt(x, sub(0, 1))
sy := sgt(y, sub(0, 1))
}
// XOR over sx and sy. This is basically checking whether the inputs have the same sign. If yes, the result
// should be positive. Otherwise, it should be negative.
result = sx ^ sy == 1 ? -int256(rAbs) : int256(rAbs);
}
/// @notice Returns Euler's number as a signed 59.18-decimal fixed-point number.
/// @dev See https://en.wikipedia.org/wiki/E_(mathematical_constant).
function e() internal pure returns (int256 result) {
result = 2_718281828459045235;
}
/// @notice Calculates the natural exponent of x.
///
/// @dev Based on the insight that e^x = 2^(x * log2(e)).
///
/// Requirements:
/// - All from "log2".
/// - x must be less than 133.084258667509499441.
///
/// Caveats:
/// - All from "exp2".
/// - For any x less than -41.446531673892822322, the result is zero.
///
/// @param x The exponent as a signed 59.18-decimal fixed-point number.
/// @return result The result as a signed 59.18-decimal fixed-point number.
function exp(int256 x) internal pure returns (int256 result) {
// Without this check, the value passed to "exp2" would be less than -59.794705707972522261.
if (x < -41_446531673892822322) {
return 0;
}
// Without this check, the value passed to "exp2" would be greater than 192.
if (x >= 133_084258667509499441) {
revert PRBMathSD59x18__ExpInputTooBig(x);
}
// Do the fixed-point multiplication inline to save gas.
unchecked {
int256 doubleScaleProduct = x * LOG2_E;
result = exp2((doubleScaleProduct + HALF_SCALE) / SCALE);
}
}
/// @notice Calculates the binary exponent of x using the binary fraction method.
///
/// @dev See https://ethereum.stackexchange.com/q/79903/24693.
///
/// Requirements:
/// - x must be 192 or less.
/// - The result must fit within MAX_SD59x18.
///
/// Caveats:
/// - For any x less than -59.794705707972522261, the result is zero.
///
/// @param x The exponent as a signed 59.18-decimal fixed-point number.
/// @return result The result as a signed 59.18-decimal fixed-point number.
function exp2(int256 x) internal pure returns (int256 result) {
// This works because 2^(-x) = 1/2^x.
if (x < 0) {
// 2^59.794705707972522262 is the maximum number whose inverse does not truncate down to zero.
if (x < -59_794705707972522261) {
return 0;
}
// Do the fixed-point inversion inline to save gas. The numerator is SCALE * SCALE.
unchecked {
result = 1e36 / exp2(-x);
}
} else {
// 2^192 doesn't fit within the 192.64-bit format used internally in this function.
if (x >= 192e18) {
revert PRBMathSD59x18__Exp2InputTooBig(x);
}
unchecked {
// Convert x to the 192.64-bit fixed-point format.
uint256 x192x64 = (uint256(x) << 64) / uint256(SCALE);
// Safe to convert the result to int256 directly because the maximum input allowed is 192.
result = int256(PRBMath.exp2(x192x64));
}
}
}
/// @notice Yields the greatest signed 59.18 decimal fixed-point number less than or equal to x.
///
/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x must be greater than or equal to MIN_WHOLE_SD59x18.
///
/// @param x The signed 59.18-decimal fixed-point number to floor.
/// @param result The greatest integer less than or equal to x, as a signed 58.18-decimal fixed-point number.
function floor(int256 x) internal pure returns (int256 result) {
if (x < MIN_WHOLE_SD59x18) {
revert PRBMathSD59x18__FloorUnderflow(x);
}
unchecked {
int256 remainder = x % SCALE;
if (remainder == 0) {
result = x;
} else {
// Solidity uses C fmod style, which returns a modulus with the same sign as x.
result = x - remainder;
if (x < 0) {
result -= SCALE;
}
}
}
}
/// @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 signed 59.18-decimal fixed-point number to get the fractional part of.
/// @param result The fractional part of x as a signed 59.18-decimal fixed-point number.
function frac(int256 x) internal pure returns (int256 result) {
unchecked {
result = x % SCALE;
}
}
/// @notice Converts a number from basic integer form to signed 59.18-decimal fixed-point representation.
///
/// @dev Requirements:
/// - x must be greater than or equal to MIN_SD59x18 divided by SCALE.
/// - x must be less than or equal to MAX_SD59x18 divided by SCALE.
///
/// @param x The basic integer to convert.
/// @param result The same number in signed 59.18-decimal fixed-point representation.
function fromInt(int256 x) internal pure returns (int256 result) {
unchecked {
if (x < MIN_SD59x18 / SCALE) {
revert PRBMathSD59x18__FromIntUnderflow(x);
}
if (x > MAX_SD59x18 / SCALE) {
revert PRBMathSD59x18__FromIntOverflow(x);
}
result = x * SCALE;
}
}
/// @notice Calculates geometric mean of x and y, i.e. sqrt(x * y), rounding down.
///
/// @dev Requirements:
/// - x * y must fit within MAX_SD59x18, lest it overflows.
/// - x * y cannot be negative.
///
/// @param x The first operand as a signed 59.18-decimal fixed-point number.
/// @param y The second operand as a signed 59.18-decimal fixed-point number.
/// @return result The result as a signed 59.18-decimal fixed-point number.
function gm(int256 x, int256 y) internal pure returns (int256 result) {
if (x == 0) {
return 0;
}
unchecked {
// Checking for overflow this way is faster than letting Solidity do it.
int256 xy = x * y;
if (xy / x != y) {
revert PRBMathSD59x18__GmOverflow(x, y);
}
// The product cannot be negative.
if (xy < 0) {
revert PRBMathSD59x18__GmNegativeProduct(x, y);
}
// We don't need to multiply by the SCALE here because the x*y product had already picked up a factor of SCALE
// during multiplication. See the comments within the "sqrt" function.
result = int256(PRBMath.sqrt(uint256(xy)));
}
}
/// @notice Calculates 1 / x, rounding toward zero.
///
/// @dev Requirements:
/// - x cannot be zero.
///
/// @param x The signed 59.18-decimal fixed-point number for which to calculate the inverse.
/// @return result The inverse as a signed 59.18-decimal fixed-point number.
function inv(int256 x) internal pure returns (int256 result) {
unchecked {
// 1e36 is SCALE * SCALE.
result = 1e36 / x;
}
}
/// @notice Calculates the natural logarithm of x.
///
/// @dev Based on the insight that ln(x) = log2(x) / log2(e).
///
/// Requirements:
/// - All from "log2".
///
/// Caveats:
/// - All from "log2".
/// - This doesn't return exactly 1 for 2718281828459045235, for that we would need more fine-grained precision.
///
/// @param x The signed 59.18-decimal fixed-point number for which to calculate the natural logarithm.
/// @return result The natural logarithm as a signed 59.18-decimal fixed-point number.
function ln(int256 x) internal pure returns (int256 result) {
// Do the fixed-point multiplication inline to save gas. This is overflow-safe because the maximum value that log2(x)
// can return is 195205294292027477728.
unchecked {
result = (log2(x) * SCALE) / LOG2_E;
}
}
/// @notice Calculates the common logarithm of x.
///
/// @dev First checks if x is an exact power of ten and it stops if yes. If it's not, calculates the common
/// logarithm based on the insight that log10(x) = log2(x) / log2(10).
///
/// Requirements:
/// - All from "log2".
///
/// Caveats:
/// - All from "log2".
///
/// @param x The signed 59.18-decimal fixed-point number for which to calculate the common logarithm.
/// @return result The common logarithm as a signed 59.18-decimal fixed-point number.
function log10(int256 x) internal pure returns (int256 result) {
if (x <= 0) {
revert PRBMathSD59x18__LogInputTooSmall(x);
}
// Note that the "mul" in this block is the assembly mul operation, not the "mul" function defined in this contract.
// prettier-ignore
assembly {
switch x
case 1 { result := mul(SCALE, sub(0, 18)) }
case 10 { result := mul(SCALE, sub(1, 18)) }
case 100 { result := mul(SCALE, sub(2, 18)) }
case 1000 { result := mul(SCALE, sub(3, 18)) }
case 10000 { result := mul(SCALE, sub(4, 18)) }
case 100000 { result := mul(SCALE, sub(5, 18)) }
case 1000000 { result := mul(SCALE, sub(6, 18)) }
case 10000000 { result := mul(SCALE, sub(7, 18)) }
case 100000000 { result := mul(SCALE, sub(8, 18)) }
case 1000000000 { result := mul(SCALE, sub(9, 18)) }
case 10000000000 { result := mul(SCALE, sub(10, 18)) }
case 100000000000 { result := mul(SCALE, sub(11, 18)) }
case 1000000000000 { result := mul(SCALE, sub(12, 18)) }
case 10000000000000 { result := mul(SCALE, sub(13, 18)) }
case 100000000000000 { result := mul(SCALE, sub(14, 18)) }
case 1000000000000000 { result := mul(SCALE, sub(15, 18)) }
case 10000000000000000 { result := mul(SCALE, sub(16, 18)) }
case 100000000000000000 { result := mul(SCALE, sub(17, 18)) }
case 1000000000000000000 { result := 0 }
case 10000000000000000000 { result := SCALE }
case 100000000000000000000 { result := mul(SCALE, 2) }
case 1000000000000000000000 { result := mul(SCALE, 3) }
case 10000000000000000000000 { result := mul(SCALE, 4) }
case 100000000000000000000000 { result := mul(SCALE, 5) }
case 1000000000000000000000000 { result := mul(SCALE, 6) }
case 10000000000000000000000000 { result := mul(SCALE, 7) }
case 100000000000000000000000000 { result := mul(SCALE, 8) }
case 1000000000000000000000000000 { result := mul(SCALE, 9) }
case 10000000000000000000000000000 { result := mul(SCALE, 10) }
case 100000000000000000000000000000 { result := mul(SCALE, 11) }
case 1000000000000000000000000000000 { result := mul(SCALE, 12) }
case 10000000000000000000000000000000 { result := mul(SCALE, 13) }
case 100000000000000000000000000000000 { result := mul(SCALE, 14) }
case 1000000000000000000000000000000000 { result := mul(SCALE, 15) }
case 10000000000000000000000000000000000 { result := mul(SCALE, 16) }
case 100000000000000000000000000000000000 { result := mul(SCALE, 17) }
case 1000000000000000000000000000000000000 { result := mul(SCALE, 18) }
case 10000000000000000000000000000000000000 { result := mul(SCALE, 19) }
case 100000000000000000000000000000000000000 { result := mul(SCALE, 20) }
case 1000000000000000000000000000000000000000 { result := mul(SCALE, 21) }
case 10000000000000000000000000000000000000000 { result := mul(SCALE, 22) }
case 100000000000000000000000000000000000000000 { result := mul(SCALE, 23) }
case 1000000000000000000000000000000000000000000 { result := mul(SCALE, 24) }
case 10000000000000000000000000000000000000000000 { result := mul(SCALE, 25) }
case 100000000000000000000000000000000000000000000 { result := mul(SCALE, 26) }
case 1000000000000000000000000000000000000000000000 { result := mul(SCALE, 27) }
case 10000000000000000000000000000000000000000000000 { result := mul(SCALE, 28) }
case 100000000000000000000000000000000000000000000000 { result := mul(SCALE, 29) }
case 1000000000000000000000000000000000000000000000000 { result := mul(SCALE, 30) }
case 10000000000000000000000000000000000000000000000000 { result := mul(SCALE, 31) }
case 100000000000000000000000000000000000000000000000000 { result := mul(SCALE, 32) }
case 1000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 33) }
case 10000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 34) }
case 100000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 35) }
case 1000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 36) }
case 10000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 37) }
case 100000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 38) }
case 1000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 39) }
case 10000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 40) }
case 100000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 41) }
case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 42) }
case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 43) }
case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 44) }
case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 45) }
case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 46) }
case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 47) }
case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 48) }
case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 49) }
case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 50) }
case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 51) }
case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 52) }
case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 53) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 54) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 55) }
case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 56) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 57) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 58) }
default {
result := MAX_SD59x18
}
}
if (result == MAX_SD59x18) {
// Do the fixed-point division inline to save gas. The denominator is log2(10).
unchecked {
result = (log2(x) * SCALE) / 3_321928094887362347;
}
}
}
/// @notice Calculates the binary logarithm of x.
///
/// @dev Based on the iterative approximation algorithm.
/// https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
///
/// Requirements:
/// - x must be greater than zero.
///
/// Caveats:
/// - The results are not perfectly accurate to the last decimal, due to the lossy precision of the iterative approximation.
///
/// @param x The signed 59.18-decimal fixed-point number for which to calculate the binary logarithm.
/// @return result The binary logarithm as a signed 59.18-decimal fixed-point number.
function log2(int256 x) internal pure returns (int256 result) {
if (x <= 0) {
revert PRBMathSD59x18__LogInputTooSmall(x);
}
unchecked {
// This works because log2(x) = -log2(1/x).
int256 sign;
if (x >= SCALE) {
sign = 1;
} else {
sign = -1;
// Do the fixed-point inversion inline to save gas. The numerator is SCALE * SCALE.
assembly {
x := div(1000000000000000000000000000000000000, x)
}
}
// Calculate the integer part of the logarithm and add it to the result and finally calculate y = x * 2^(-n).
uint256 n = PRBMath.mostSignificantBit(uint256(x / SCALE));
// The integer part of the logarithm as a signed 59.18-decimal fixed-point number. The operation can't overflow
// because n is maximum 255, SCALE is 1e18 and sign is either 1 or -1.
result = int256(n) * SCALE;
// This is y = x * 2^(-n).
int256 y = x >> n;
// If y = 1, the fractional part is zero.
if (y == SCALE) {
return result * sign;
}
// Calculate the fractional part via the iterative approximation.
// The "delta >>= 1" part is equivalent to "delta /= 2", but shifting bits is faster.
for (int256 delta = int256(HALF_SCALE); delta > 0; delta >>= 1) {
y = (y * y) / SCALE;
// Is y^2 > 2 and so in the range [2,4)?
if (y >= 2 * SCALE) {
// Add the 2^(-m) factor to the logarithm.
result += delta;
// Corresponds to z/2 on Wikipedia.
y >>= 1;
}
}
result *= sign;
}
}
/// @notice Multiplies two signed 59.18-decimal fixed-point numbers together, returning a new signed 59.18-decimal
/// fixed-point number.
///
/// @dev Variant of "mulDiv" that works with signed numbers and employs constant folding, i.e. the denominator is
/// always 1e18.
///
/// Requirements:
/// - All from "PRBMath.mulDivFixedPoint".
/// - None of the inputs can be MIN_SD59x18
/// - The result must fit within MAX_SD59x18.
///
/// Caveats:
/// - The body is purposely left uncommented; see the NatSpec comments in "PRBMath.mulDiv" to understand how this works.
///
/// @param x The multiplicand as a signed 59.18-decimal fixed-point number.
/// @param y The multiplier as a signed 59.18-decimal fixed-point number.
/// @return result The product as a signed 59.18-decimal fixed-point number.
function mul(int256 x, int256 y) internal pure returns (int256 result) {
if (x == MIN_SD59x18 || y == MIN_SD59x18) {
revert PRBMathSD59x18__MulInputTooSmall();
}
unchecked {
uint256 ax;
uint256 ay;
ax = x < 0 ? uint256(-x) : uint256(x);
ay = y < 0 ? uint256(-y) : uint256(y);
uint256 rAbs = PRBMath.mulDivFixedPoint(ax, ay);
if (rAbs > uint256(MAX_SD59x18)) {
revert PRBMathSD59x18__MulOverflow(rAbs);
}
uint256 sx;
uint256 sy;
assembly {
sx := sgt(x, sub(0, 1))
sy := sgt(y, sub(0, 1))
}
result = sx ^ sy == 1 ? -int256(rAbs) : int256(rAbs);
}
}
/// @notice Returns PI as a signed 59.18-decimal fixed-point number.
function pi() internal pure returns (int256 result) {
result = 3_141592653589793238;
}
/// @notice Raises x to the power of y.
///
/// @dev Based on the insight that x^y = 2^(log2(x) * y).
///
/// Requirements:
/// - All from "exp2", "log2" and "mul".
/// - z cannot be zero.
///
/// Caveats:
/// - All from "exp2", "log2" and "mul".
/// - Assumes 0^0 is 1.
///
/// @param x Number to raise to given power y, as a signed 59.18-decimal fixed-point number.
/// @param y Exponent to raise x to, as a signed 59.18-decimal fixed-point number.
/// @return result x raised to power y, as a signed 59.18-decimal fixed-point number.
function pow(int256 x, int256 y) internal pure returns (int256 result) {
if (x == 0) {
result = y == 0 ? SCALE : int256(0);
} else {
result = exp2(mul(log2(x), y));
}
}
/// @notice Raises x (signed 59.18-decimal fixed-point number) to the power of y (basic unsigned integer) using the
/// famous algorithm "exponentiation by squaring".
///
/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring
///
/// Requirements:
/// - All from "abs" and "PRBMath.mulDivFixedPoint".
/// - The result must fit within MAX_SD59x18.
///
/// Caveats:
/// - All from "PRBMath.mulDivFixedPoint".
/// - Assumes 0^0 is 1.
///
/// @param x The base as a signed 59.18-decimal fixed-point number.
/// @param y The exponent as an uint256.
/// @return result The result as a signed 59.18-decimal fixed-point number.
function powu(int256 x, uint256 y) internal pure returns (int256 result) {
uint256 xAbs = uint256(abs(x));
// Calculate the first iteration of the loop in advance.
uint256 rAbs = y & 1 > 0 ? xAbs : uint256(SCALE);
// Equivalent to "for(y /= 2; y > 0; y /= 2)" but faster.
uint256 yAux = y;
for (yAux >>= 1; yAux > 0; yAux >>= 1) {
xAbs = PRBMath.mulDivFixedPoint(xAbs, xAbs);
// Equivalent to "y % 2 == 1" but faster.
if (yAux & 1 > 0) {
rAbs = PRBMath.mulDivFixedPoint(rAbs, xAbs);
}
}
// The result must fit within the 59.18-decimal fixed-point representation.
if (rAbs > uint256(MAX_SD59x18)) {
revert PRBMathSD59x18__PowuOverflow(rAbs);
}
// Is the base negative and the exponent an odd number?
bool isNegative = x < 0 && y & 1 == 1;
result = isNegative ? -int256(rAbs) : int256(rAbs);
}
/// @notice Returns 1 as a signed 59.18-decimal fixed-point number.
function scale() internal pure returns (int256 result) {
result = SCALE;
}
/// @notice Calculates the square root of x, rounding down.
/// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Requirements:
/// - x cannot be negative.
/// - x must be less than MAX_SD59x18 / SCALE.
///
/// @param x The signed 59.18-decimal fixed-point number for which to calculate the square root.
/// @return result The result as a signed 59.18-decimal fixed-point .
function sqrt(int256 x) internal pure returns (int256 result) {
unchecked {
if (x < 0) {
revert PRBMathSD59x18__SqrtNegativeInput(x);
}
if (x > MAX_SD59x18 / SCALE) {
revert PRBMathSD59x18__SqrtOverflow(x);
}
// Multiply x by the SCALE to account for the factor of SCALE that is picked up when multiplying two signed
// 59.18-decimal fixed-point numbers together (in this case, those two numbers are both the square root).
result = int256(PRBMath.sqrt(uint256(x * SCALE)));
}
}
/// @notice Converts a signed 59.18-decimal fixed-point number to basic integer form, rounding down in the process.
/// @param x The signed 59.18-decimal fixed-point number to convert.
/// @return result The same number in basic integer form.
function toInt(int256 x) internal pure returns (int256 result) {
unchecked {
result = x / SCALE;
}
}
}// SPDX-License-Identifier: Unlicense
pragma solidity >=0.8.4;
import "./PRBMath.sol";
/// @title PRBMathUD60x18
/// @author Paul Razvan Berg
/// @notice Smart contract library for advanced fixed-point math that works with uint256 numbers considered to have 18
/// trailing decimals. We call this number representation unsigned 60.18-decimal fixed-point, since there can be up to 60
/// digits in the integer part and up to 18 decimals in the fractional part. The numbers are bound by the minimum and the
/// maximum values permitted by the Solidity type uint256.
library PRBMathUD60x18 {
/// @dev Half the SCALE number.
uint256 internal constant HALF_SCALE = 5e17;
/// @dev log2(e) as an unsigned 60.18-decimal fixed-point number.
uint256 internal constant LOG2_E = 1_442695040888963407;
/// @dev The maximum value an unsigned 60.18-decimal fixed-point number can have.
uint256 internal constant MAX_UD60x18 =
115792089237316195423570985008687907853269984665640564039457_584007913129639935;
/// @dev The maximum whole value an unsigned 60.18-decimal fixed-point number can have.
uint256 internal constant MAX_WHOLE_UD60x18 =
115792089237316195423570985008687907853269984665640564039457_000000000000000000;
/// @dev How many trailing decimals can be represented.
uint256 internal constant SCALE = 1e18;
/// @notice Calculates the arithmetic average of x and y, rounding down.
/// @param x The first operand as an unsigned 60.18-decimal fixed-point number.
/// @param y The second operand as an unsigned 60.18-decimal fixed-point number.
/// @return result The arithmetic average as an unsigned 60.18-decimal fixed-point number.
function avg(uint256 x, uint256 y) internal pure returns (uint256 result) {
// The operations can never overflow.
unchecked {
// The last operand checks if both x and y are odd and if that is the case, we add 1 to the result. We need
// to do this because if both numbers are odd, the 0.5 remainder gets truncated twice.
result = (x >> 1) + (y >> 1) + (x & y & 1);
}
}
/// @notice Yields the least unsigned 60.18 decimal fixed-point number greater than or equal to x.
///
/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x must be less than or equal to MAX_WHOLE_UD60x18.
///
/// @param x The unsigned 60.18-decimal fixed-point number to ceil.
/// @param result The least integer greater than or equal to x, as an unsigned 60.18-decimal fixed-point number.
function ceil(uint256 x) internal pure returns (uint256 result) {
if (x > MAX_WHOLE_UD60x18) {
revert PRBMathUD60x18__CeilOverflow(x);
}
assembly {
// Equivalent to "x % SCALE" but faster.
let remainder := mod(x, SCALE)
// Equivalent to "SCALE - remainder" but faster.
let delta := sub(SCALE, remainder)
// Equivalent to "x + delta * (remainder > 0 ? 1 : 0)" but faster.
result := add(x, mul(delta, gt(remainder, 0)))
}
}
/// @notice Divides two unsigned 60.18-decimal fixed-point numbers, returning a new unsigned 60.18-decimal fixed-point number.
///
/// @dev Uses mulDiv to enable overflow-safe multiplication and division.
///
/// Requirements:
/// - The denominator cannot be zero.
///
/// @param x The numerator as an unsigned 60.18-decimal fixed-point number.
/// @param y The denominator as an unsigned 60.18-decimal fixed-point number.
/// @param result The quotient as an unsigned 60.18-decimal fixed-point number.
function div(uint256 x, uint256 y) internal pure returns (uint256 result) {
result = PRBMath.mulDiv(x, SCALE, y);
}
/// @notice Returns Euler's number as an unsigned 60.18-decimal fixed-point number.
/// @dev See https://en.wikipedia.org/wiki/E_(mathematical_constant).
function e() internal pure returns (uint256 result) {
result = 2_718281828459045235;
}
/// @notice Calculates the natural exponent of x.
///
/// @dev Based on the insight that e^x = 2^(x * log2(e)).
///
/// Requirements:
/// - All from "log2".
/// - x must be less than 133.084258667509499441.
///
/// @param x The exponent as an unsigned 60.18-decimal fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
function exp(uint256 x) internal pure returns (uint256 result) {
// Without this check, the value passed to "exp2" would be greater than 192.
if (x >= 133_084258667509499441) {
revert PRBMathUD60x18__ExpInputTooBig(x);
}
// Do the fixed-point multiplication inline to save gas.
unchecked {
uint256 doubleScaleProduct = x * LOG2_E;
result = exp2((doubleScaleProduct + HALF_SCALE) / SCALE);
}
}
/// @notice Calculates the binary exponent of x using the binary fraction method.
///
/// @dev See https://ethereum.stackexchange.com/q/79903/24693.
///
/// Requirements:
/// - x must be 192 or less.
/// - The result must fit within MAX_UD60x18.
///
/// @param x The exponent as an unsigned 60.18-decimal fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
function exp2(uint256 x) internal pure returns (uint256 result) {
// 2^192 doesn't fit within the 192.64-bit format used internally in this function.
if (x >= 192e18) {
revert PRBMathUD60x18__Exp2InputTooBig(x);
}
unchecked {
// Convert x to the 192.64-bit fixed-point format.
uint256 x192x64 = (x << 64) / SCALE;
// Pass x to the PRBMath.exp2 function, which uses the 192.64-bit fixed-point number representation.
result = PRBMath.exp2(x192x64);
}
}
/// @notice Yields the greatest unsigned 60.18 decimal fixed-point 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.
/// @param x The unsigned 60.18-decimal fixed-point number to floor.
/// @param result The greatest integer less than or equal to x, as an unsigned 60.18-decimal fixed-point number.
function floor(uint256 x) internal pure returns (uint256 result) {
assembly {
// Equivalent to "x % SCALE" but faster.
let remainder := mod(x, SCALE)
// Equivalent to "x - remainder * (remainder > 0 ? 1 : 0)" but faster.
result := sub(x, mul(remainder, gt(remainder, 0)))
}
}
/// @notice Yields the excess beyond the floor of x.
/// @dev Based on the odd function definition https://en.wikipedia.org/wiki/Fractional_part.
/// @param x The unsigned 60.18-decimal fixed-point number to get the fractional part of.
/// @param result The fractional part of x as an unsigned 60.18-decimal fixed-point number.
function frac(uint256 x) internal pure returns (uint256 result) {
assembly {
result := mod(x, SCALE)
}
}
/// @notice Converts a number from basic integer form to unsigned 60.18-decimal fixed-point representation.
///
/// @dev Requirements:
/// - x must be less than or equal to MAX_UD60x18 divided by SCALE.
///
/// @param x The basic integer to convert.
/// @param result The same number in unsigned 60.18-decimal fixed-point representation.
function fromUint(uint256 x) internal pure returns (uint256 result) {
unchecked {
if (x > MAX_UD60x18 / SCALE) {
revert PRBMathUD60x18__FromUintOverflow(x);
}
result = x * SCALE;
}
}
/// @notice Calculates geometric mean of x and y, i.e. sqrt(x * y), rounding down.
///
/// @dev Requirements:
/// - x * y must fit within MAX_UD60x18, lest it overflows.
///
/// @param x The first operand as an unsigned 60.18-decimal fixed-point number.
/// @param y The second operand as an unsigned 60.18-decimal fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
function gm(uint256 x, uint256 y) internal pure returns (uint256 result) {
if (x == 0) {
return 0;
}
unchecked {
// Checking for overflow this way is faster than letting Solidity do it.
uint256 xy = x * y;
if (xy / x != y) {
revert PRBMathUD60x18__GmOverflow(x, y);
}
// We don't need to multiply by the SCALE here because the x*y product had already picked up a factor of SCALE
// during multiplication. See the comments within the "sqrt" function.
result = PRBMath.sqrt(xy);
}
}
/// @notice Calculates 1 / x, rounding toward zero.
///
/// @dev Requirements:
/// - x cannot be zero.
///
/// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the inverse.
/// @return result The inverse as an unsigned 60.18-decimal fixed-point number.
function inv(uint256 x) internal pure returns (uint256 result) {
unchecked {
// 1e36 is SCALE * SCALE.
result = 1e36 / x;
}
}
/// @notice Calculates the natural logarithm of x.
///
/// @dev Based on the insight that ln(x) = log2(x) / log2(e).
///
/// Requirements:
/// - All from "log2".
///
/// Caveats:
/// - All from "log2".
/// - This doesn't return exactly 1 for 2.718281828459045235, for that we would need more fine-grained precision.
///
/// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the natural logarithm.
/// @return result The natural logarithm as an unsigned 60.18-decimal fixed-point number.
function ln(uint256 x) internal pure returns (uint256 result) {
// Do the fixed-point multiplication inline to save gas. This is overflow-safe because the maximum value that log2(x)
// can return is 196205294292027477728.
unchecked {
result = (log2(x) * SCALE) / LOG2_E;
}
}
/// @notice Calculates the common logarithm of x.
///
/// @dev First checks if x is an exact power of ten and it stops if yes. If it's not, calculates the common
/// logarithm based on the insight that log10(x) = log2(x) / log2(10).
///
/// Requirements:
/// - All from "log2".
///
/// Caveats:
/// - All from "log2".
///
/// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the common logarithm.
/// @return result The common logarithm as an unsigned 60.18-decimal fixed-point number.
function log10(uint256 x) internal pure returns (uint256 result) {
if (x < SCALE) {
revert PRBMathUD60x18__LogInputTooSmall(x);
}
// Note that the "mul" in this block is the assembly multiplication operation, not the "mul" function defined
// in this contract.
// prettier-ignore
assembly {
switch x
case 1 { result := mul(SCALE, sub(0, 18)) }
case 10 { result := mul(SCALE, sub(1, 18)) }
case 100 { result := mul(SCALE, sub(2, 18)) }
case 1000 { result := mul(SCALE, sub(3, 18)) }
case 10000 { result := mul(SCALE, sub(4, 18)) }
case 100000 { result := mul(SCALE, sub(5, 18)) }
case 1000000 { result := mul(SCALE, sub(6, 18)) }
case 10000000 { result := mul(SCALE, sub(7, 18)) }
case 100000000 { result := mul(SCALE, sub(8, 18)) }
case 1000000000 { result := mul(SCALE, sub(9, 18)) }
case 10000000000 { result := mul(SCALE, sub(10, 18)) }
case 100000000000 { result := mul(SCALE, sub(11, 18)) }
case 1000000000000 { result := mul(SCALE, sub(12, 18)) }
case 10000000000000 { result := mul(SCALE, sub(13, 18)) }
case 100000000000000 { result := mul(SCALE, sub(14, 18)) }
case 1000000000000000 { result := mul(SCALE, sub(15, 18)) }
case 10000000000000000 { result := mul(SCALE, sub(16, 18)) }
case 100000000000000000 { result := mul(SCALE, sub(17, 18)) }
case 1000000000000000000 { result := 0 }
case 10000000000000000000 { result := SCALE }
case 100000000000000000000 { result := mul(SCALE, 2) }
case 1000000000000000000000 { result := mul(SCALE, 3) }
case 10000000000000000000000 { result := mul(SCALE, 4) }
case 100000000000000000000000 { result := mul(SCALE, 5) }
case 1000000000000000000000000 { result := mul(SCALE, 6) }
case 10000000000000000000000000 { result := mul(SCALE, 7) }
case 100000000000000000000000000 { result := mul(SCALE, 8) }
case 1000000000000000000000000000 { result := mul(SCALE, 9) }
case 10000000000000000000000000000 { result := mul(SCALE, 10) }
case 100000000000000000000000000000 { result := mul(SCALE, 11) }
case 1000000000000000000000000000000 { result := mul(SCALE, 12) }
case 10000000000000000000000000000000 { result := mul(SCALE, 13) }
case 100000000000000000000000000000000 { result := mul(SCALE, 14) }
case 1000000000000000000000000000000000 { result := mul(SCALE, 15) }
case 10000000000000000000000000000000000 { result := mul(SCALE, 16) }
case 100000000000000000000000000000000000 { result := mul(SCALE, 17) }
case 1000000000000000000000000000000000000 { result := mul(SCALE, 18) }
case 10000000000000000000000000000000000000 { result := mul(SCALE, 19) }
case 100000000000000000000000000000000000000 { result := mul(SCALE, 20) }
case 1000000000000000000000000000000000000000 { result := mul(SCALE, 21) }
case 10000000000000000000000000000000000000000 { result := mul(SCALE, 22) }
case 100000000000000000000000000000000000000000 { result := mul(SCALE, 23) }
case 1000000000000000000000000000000000000000000 { result := mul(SCALE, 24) }
case 10000000000000000000000000000000000000000000 { result := mul(SCALE, 25) }
case 100000000000000000000000000000000000000000000 { result := mul(SCALE, 26) }
case 1000000000000000000000000000000000000000000000 { result := mul(SCALE, 27) }
case 10000000000000000000000000000000000000000000000 { result := mul(SCALE, 28) }
case 100000000000000000000000000000000000000000000000 { result := mul(SCALE, 29) }
case 1000000000000000000000000000000000000000000000000 { result := mul(SCALE, 30) }
case 10000000000000000000000000000000000000000000000000 { result := mul(SCALE, 31) }
case 100000000000000000000000000000000000000000000000000 { result := mul(SCALE, 32) }
case 1000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 33) }
case 10000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 34) }
case 100000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 35) }
case 1000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 36) }
case 10000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 37) }
case 100000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 38) }
case 1000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 39) }
case 10000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 40) }
case 100000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 41) }
case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 42) }
case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 43) }
case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 44) }
case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 45) }
case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 46) }
case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 47) }
case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 48) }
case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 49) }
case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 50) }
case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 51) }
case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 52) }
case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 53) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 54) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 55) }
case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 56) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 57) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 58) }
case 100000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 59) }
default {
result := MAX_UD60x18
}
}
if (result == MAX_UD60x18) {
// Do the fixed-point division inline to save gas. The denominator is log2(10).
unchecked {
result = (log2(x) * SCALE) / 3_321928094887362347;
}
}
}
/// @notice Calculates the binary logarithm of x.
///
/// @dev Based on the iterative approximation algorithm.
/// https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
///
/// Requirements:
/// - x must be greater than or equal to SCALE, otherwise the result would be negative.
///
/// Caveats:
/// - The results are nor perfectly accurate to the last decimal, due to the lossy precision of the iterative approximation.
///
/// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the binary logarithm.
/// @return result The binary logarithm as an unsigned 60.18-decimal fixed-point number.
function log2(uint256 x) internal pure returns (uint256 result) {
if (x < SCALE) {
revert PRBMathUD60x18__LogInputTooSmall(x);
}
unchecked {
// Calculate the integer part of the logarithm and add it to the result and finally calculate y = x * 2^(-n).
uint256 n = PRBMath.mostSignificantBit(x / SCALE);
// The integer part of the logarithm as an unsigned 60.18-decimal fixed-point number. The operation can't overflow
// because n is maximum 255 and SCALE is 1e18.
result = n * SCALE;
// This is y = x * 2^(-n).
uint256 y = x >> n;
// If y = 1, the fractional part is zero.
if (y == SCALE) {
return result;
}
// Calculate the fractional part via the iterative approximation.
// The "delta >>= 1" part is equivalent to "delta /= 2", but shifting bits is faster.
for (uint256 delta = HALF_SCALE; delta > 0; delta >>= 1) {
y = (y * y) / SCALE;
// Is y^2 > 2 and so in the range [2,4)?
if (y >= 2 * SCALE) {
// Add the 2^(-m) factor to the logarithm.
result += delta;
// Corresponds to z/2 on Wikipedia.
y >>= 1;
}
}
}
}
/// @notice Multiplies two unsigned 60.18-decimal fixed-point numbers together, returning a new unsigned 60.18-decimal
/// fixed-point number.
/// @dev See the documentation for the "PRBMath.mulDivFixedPoint" function.
/// @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 product as an unsigned 60.18-decimal fixed-point number.
function mul(uint256 x, uint256 y) internal pure returns (uint256 result) {
result = PRBMath.mulDivFixedPoint(x, y);
}
/// @notice Returns PI as an unsigned 60.18-decimal fixed-point number.
function pi() internal pure returns (uint256 result) {
result = 3_141592653589793238;
}
/// @notice Raises x to the power of y.
///
/// @dev Based on the insight that x^y = 2^(log2(x) * y).
///
/// Requirements:
/// - All from "exp2", "log2" and "mul".
///
/// Caveats:
/// - All from "exp2", "log2" and "mul".
/// - Assumes 0^0 is 1.
///
/// @param x Number to raise to given power y, as an unsigned 60.18-decimal fixed-point number.
/// @param y Exponent to raise x to, as an unsigned 60.18-decimal fixed-point number.
/// @return result x raised to power y, as an unsigned 60.18-decimal fixed-point number.
function pow(uint256 x, uint256 y) internal pure returns (uint256 result) {
if (x == 0) {
result = y == 0 ? SCALE : uint256(0);
} else {
result = exp2(mul(log2(x), y));
}
}
/// @notice Raises x (unsigned 60.18-decimal fixed-point number) to the power of y (basic unsigned integer) using the
/// famous algorithm "exponentiation by squaring".
///
/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring
///
/// Requirements:
/// - The result must fit within MAX_UD60x18.
///
/// Caveats:
/// - All from "mul".
/// - Assumes 0^0 is 1.
///
/// @param x The base as an unsigned 60.18-decimal fixed-point number.
/// @param y The exponent as an uint256.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
function powu(uint256 x, uint256 y) internal pure returns (uint256 result) {
// Calculate the first iteration of the loop in advance.
result = y & 1 > 0 ? x : SCALE;
// Equivalent to "for(y /= 2; y > 0; y /= 2)" but faster.
for (y >>= 1; y > 0; y >>= 1) {
x = PRBMath.mulDivFixedPoint(x, x);
// Equivalent to "y % 2 == 1" but faster.
if (y & 1 > 0) {
result = PRBMath.mulDivFixedPoint(result, x);
}
}
}
/// @notice Returns 1 as an unsigned 60.18-decimal fixed-point number.
function scale() internal pure returns (uint256 result) {
result = SCALE;
}
/// @notice Calculates the square root of x, rounding down.
/// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Requirements:
/// - x must be less than MAX_UD60x18 / SCALE.
///
/// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the square root.
/// @return result The result as an unsigned 60.18-decimal fixed-point .
function sqrt(uint256 x) internal pure returns (uint256 result) {
unchecked {
if (x > MAX_UD60x18 / SCALE) {
revert PRBMathUD60x18__SqrtOverflow(x);
}
// Multiply x by the SCALE to account for the factor of SCALE that is picked up when multiplying two unsigned
// 60.18-decimal fixed-point numbers together (in this case, those two numbers are both the square root).
result = PRBMath.sqrt(x * SCALE);
}
}
/// @notice Converts a unsigned 60.18-decimal fixed-point number to basic integer form, rounding down in the process.
/// @param x The unsigned 60.18-decimal fixed-point number to convert.
/// @return result The same number in basic integer form.
function toUint(uint256 x) internal pure returns (uint256 result) {
unchecked {
result = x / SCALE;
}
}
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;
library Types {
struct OptionSeries {
uint64 expiration;
uint128 strike;
bool isPut;
address underlying;
address strikeAsset;
address collateral;
}
struct PortfolioValues {
int256 delta;
int256 gamma;
int256 vega;
int256 theta;
int256 callPutsValue;
uint256 timestamp;
uint256 spotPrice;
}
struct Order {
OptionSeries optionSeries;
uint256 amount;
uint256 price;
uint256 orderExpiry;
address buyer;
address seriesAddress;
uint128 lowerSpotMovementRange;
uint128 upperSpotMovementRange;
bool isBuyBack;
}
// strike and expiry date range for options
struct OptionParams {
uint128 minCallStrikePrice;
uint128 maxCallStrikePrice;
uint128 minPutStrikePrice;
uint128 maxPutStrikePrice;
uint128 minExpiry;
uint128 maxExpiry;
}
struct UtilizationState {
uint256 totalOptionPrice; //e18
int256 totalDelta; // e18
uint256 collateralToAllocate; //collateral decimals
uint256 utilizationBefore; // e18
uint256 utilizationAfter; //e18
uint256 utilizationPrice; //e18
bool isDecreased;
uint256 deltaTiltAmount; //e18
uint256 underlyingPrice; // strike asset decimals
uint256 iv; // e18
}
}// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/IERC20.sol)
pragma solidity ^0.8.0;
/**
* @dev Interface of the ERC20 standard as defined in the EIP.
*/
interface I_ERC20 {
/**
* @dev Returns the amount of tokens in existence.
*/
function totalSupply() external view returns (uint256);
/**
* @dev Returns the amount of tokens owned by `account`.
*/
function balanceOf(address account) external view returns (uint256);
/**
* @dev Moves `amount` tokens from the caller's account to `recipient`.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* Emits a {Transfer} event.
*/
function transfer(address recipient, uint256 amount) external returns (bool);
/**
* @dev Returns the remaining number of tokens that `spender` will be
* allowed to spend on behalf of `owner` through {transferFrom}. This is
* zero by default.
*
* This value changes when {approve} or {transferFrom} are called.
*/
function allowance(address owner, address spender) external view returns (uint256);
/**
* @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* IMPORTANT: Beware that changing an allowance with this method brings the risk
* that someone may use both the old and the new allowance by unfortunate
* transaction ordering. One possible solution to mitigate this race
* condition is to first reduce the spender's allowance to 0 and set the
* desired value afterwards:
* https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
*
* Emits an {Approval} event.
*/
function approve(address spender, uint256 amount) external returns (bool);
/**
* @dev Moves `amount` tokens from `sender` to `recipient` using the
* allowance mechanism. `amount` is then deducted from the caller's
* allowance.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* Emits a {Transfer} event.
*/
function transferFrom(
address sender,
address recipient,
uint256 amount
) external returns (bool);
/**
* @dev Emitted when `value` tokens are moved from one account (`from`) to
* another (`to`).
*
* Note that `value` may be zero.
*/
event Transfer(address indexed from, address indexed to, uint256 value);
/**
* @dev Emitted when the allowance of a `spender` for an `owner` is set by
* a call to {approve}. `value` is the new allowance.
*/
event Approval(address indexed owner, address indexed spender, uint256 value);
}// SPDX-License-Identifier: UNLICENSED
pragma solidity >=0.8.9;
import { Types } from "../libraries/Types.sol";
interface IOptionRegistry {
//////////////////////////////////////////////////////
/// access-controlled state changing functionality ///
//////////////////////////////////////////////////////
/**
* @notice Either retrieves the option token if it already exists, or deploy it
* @param optionSeries option series to issue
* @return the address of the option
*/
function issue(Types.OptionSeries memory optionSeries) external returns (address);
/**
* @notice Open an options contract using collateral from the liquidity pool
* @param _series the address of the option token to be created
* @param amount the amount of options to deploy
* @param collateralAmount the collateral required for the option
* @dev only callable by the liquidityPool
* @return if the transaction succeeded
* @return the amount of collateral taken from the liquidityPool
*/
function open(
address _series,
uint256 amount,
uint256 collateralAmount
) external returns (bool, uint256);
/**
* @notice Close an options contract (oToken) before it has expired
* @param _series the address of the option token to be burnt
* @param amount the amount of options to burn
* @dev only callable by the liquidityPool
* @return if the transaction succeeded
*/
function close(address _series, uint256 amount) external returns (bool, uint256);
/////////////////////////////////////////////
/// external state changing functionality ///
/////////////////////////////////////////////
/**
* @notice Settle an options vault
* @param _series the address of the option token to be burnt
* @return success if the transaction succeeded
* @return collatReturned the amount of collateral returned from the vault
* @return collatLost the amount of collateral used to pay ITM options on vault settle
* @return amountShort number of oTokens that the vault was short
* @dev callable by anyone but returns funds to the liquidityPool
*/
function settle(address _series)
external
returns (
bool success,
uint256 collatReturned,
uint256 collatLost,
uint256 amountShort
);
///////////////////////
/// complex getters ///
///////////////////////
/**
* @notice Send collateral funds for an option to be minted
* @dev series.strike should be scaled by 1e8.
* @param series details of the option series
* @param amount amount of options to mint
* @return amount transferred
*/
function getCollateral(Types.OptionSeries memory series, uint256 amount)
external
view
returns (uint256);
/**
* @notice Retrieves the option token if it exists
* @param underlying is the address of the underlying asset of the option
* @param strikeAsset is the address of the collateral asset of the option
* @param expiration is the expiry timestamp of the option
* @param isPut the type of option
* @param strike is the strike price of the option - 1e18 format
* @param collateral is the address of the asset to collateralize the option with
* @return the address of the option
*/
function getOtoken(
address underlying,
address strikeAsset,
uint256 expiration,
bool isPut,
uint256 strike,
address collateral
) external view returns (address);
///////////////////////////
/// non-complex getters ///
///////////////////////////
function getSeriesInfo(address series) external view returns (Types.OptionSeries memory);
function vaultIds(address series) external view returns (uint256);
function gammaController() external view returns (address);
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;
interface CustomErrors {
error NotKeeper();
error IVNotFound();
error NotHandler();
error VaultExpired();
error InvalidInput();
error InvalidPrice();
error InvalidBuyer();
error InvalidOrder();
error OrderExpired();
error InvalidAmount();
error TradingPaused();
error InvalidAddress();
error IssuanceFailed();
error EpochNotClosed();
error InvalidDecimals();
error TradingNotPaused();
error NotLiquidityPool();
error DeltaNotDecreased();
error NonExistentOtoken();
error OrderExpiryTooLong();
error InvalidShareAmount();
error ExistingWithdrawal();
error TotalSupplyReached();
error StrikeAssetInvalid();
error OptionStrikeInvalid();
error OptionExpiryInvalid();
error NoExistingWithdrawal();
error SpotMovedBeyondRange();
error ReactorAlreadyExists();
error CollateralAssetInvalid();
error UnderlyingAssetInvalid();
error CollateralAmountInvalid();
error WithdrawExceedsLiquidity();
error InsufficientShareBalance();
error MaxLiquidityBufferReached();
error LiabilitiesGreaterThanAssets();
error CustomOrderInsufficientPrice();
error CustomOrderInvalidDeltaValue();
error DeltaQuoteError(uint256 quote, int256 delta);
error TimeDeltaExceedsThreshold(uint256 timeDelta);
error PriceDeltaExceedsThreshold(uint256 priceDelta);
error StrikeAmountExceedsLiquidity(uint256 strikeAmount, uint256 strikeLiquidity);
error MinStrikeAmountExceedsLiquidity(uint256 strikeAmount, uint256 strikeAmountMin);
error UnderlyingAmountExceedsLiquidity(uint256 underlyingAmount, uint256 underlyingLiquidity);
error MinUnderlyingAmountExceedsLiquidity(uint256 underlyingAmount, uint256 underlyingAmountMin);
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;
import "prb-math/contracts/PRBMathSD59x18.sol";
import "prb-math/contracts/PRBMathUD60x18.sol";
import { NormalDist } from "./NormalDist.sol";
/**
* @title Library used to calculate an option price using Black Scholes
*/
library BlackScholes {
using PRBMathSD59x18 for int256;
using PRBMathSD59x18 for int8;
using PRBMathUD60x18 for uint256;
uint256 private constant ONE_YEAR_SECONDS = 31557600;
uint256 private constant ONE = 1000000000000000000;
uint256 private constant TWO = 2000000000000000000;
struct Intermediates {
uint256 d1Denominator;
int256 d1;
int256 eToNegRT;
}
function callOptionPrice(
int256 d1,
int256 d1Denominator,
int256 price,
int256 strike,
int256 eToNegRT
) public pure returns (uint256) {
int256 d2 = d1 - d1Denominator;
int256 cdfD1 = NormalDist.cdf(d1);
int256 cdfD2 = NormalDist.cdf(d2);
int256 priceCdf = price.mul(cdfD1);
int256 strikeBy = strike.mul(eToNegRT).mul(cdfD2);
assert(priceCdf >= strikeBy);
return uint256(priceCdf - strikeBy);
}
function callOptionPriceGreeks(
int256 d1,
int256 d1Denominator,
int256 price,
int256 strike,
int256 eToNegRT
) public pure returns (uint256 quote, int256 delta) {
int256 d2 = d1 - d1Denominator;
int256 cdfD1 = NormalDist.cdf(d1);
int256 cdfD2 = NormalDist.cdf(d2);
int256 priceCdf = price.mul(cdfD1);
int256 strikeBy = strike.mul(eToNegRT).mul(cdfD2);
assert(priceCdf >= strikeBy);
quote = uint256(priceCdf - strikeBy);
delta = cdfD1;
}
function putOptionPriceGreeks(
int256 d1,
int256 d1Denominator,
int256 price,
int256 strike,
int256 eToNegRT
) public pure returns (uint256 quote, int256 delta) {
int256 d2 = d1Denominator - d1;
int256 cdfD1 = NormalDist.cdf(-d1);
int256 cdfD2 = NormalDist.cdf(d2);
int256 priceCdf = price.mul(cdfD1);
int256 strikeBy = strike.mul(eToNegRT).mul(cdfD2);
assert(strikeBy >= priceCdf);
quote = uint256(strikeBy - priceCdf);
delta = -cdfD1;
}
function putOptionPrice(
int256 d1,
int256 d1Denominator,
int256 price,
int256 strike,
int256 eToNegRT
) public pure returns (uint256) {
int256 d2 = d1Denominator - d1;
int256 cdfD1 = NormalDist.cdf(-d1);
int256 cdfD2 = NormalDist.cdf(d2);
int256 priceCdf = price.mul(cdfD1);
int256 strikeBy = strike.mul(eToNegRT).mul(cdfD2);
assert(strikeBy >= priceCdf);
return uint256(strikeBy - priceCdf);
}
function getTimeStamp() private view returns (uint256) {
return block.timestamp;
}
function getD1(
uint256 price,
uint256 strike,
uint256 time,
uint256 vol,
uint256 rfr
) private pure returns (int256 d1, uint256 d1Denominator) {
uint256 d1Right = (vol.mul(vol).div(TWO) + rfr).mul(time);
int256 d1Left = int256(price.div(strike)).ln();
int256 d1Numerator = d1Left + int256(d1Right);
d1Denominator = vol.mul(time.sqrt());
d1 = d1Numerator.div(int256(d1Denominator));
}
function getIntermediates(
uint256 price,
uint256 strike,
uint256 time,
uint256 vol,
uint256 rfr
) private pure returns (Intermediates memory) {
(int256 d1, uint256 d1Denominator) = getD1(price, strike, time, vol, rfr);
return
Intermediates({
d1Denominator: d1Denominator,
d1: d1,
eToNegRT: (int256(rfr).mul(int256(time)).mul(-int256(ONE))).exp()
});
}
function blackScholesCalc(
uint256 price,
uint256 strike,
uint256 expiration,
uint256 vol,
uint256 rfr,
bool isPut
) public view returns (uint256) {
uint256 time = (expiration - getTimeStamp()).div(ONE_YEAR_SECONDS);
Intermediates memory i = getIntermediates(price, strike, time, vol, rfr);
if (!isPut) {
return
callOptionPrice(
int256(i.d1),
int256(i.d1Denominator),
int256(price),
int256(strike),
i.eToNegRT
);
} else {
return
putOptionPrice(
int256(i.d1),
int256(i.d1Denominator),
int256(price),
int256(strike),
i.eToNegRT
);
}
}
function blackScholesCalcGreeks(
uint256 price,
uint256 strike,
uint256 expiration,
uint256 vol,
uint256 rfr,
bool isPut
) public view returns (uint256 quote, int256 delta) {
uint256 time = (expiration - getTimeStamp()).div(ONE_YEAR_SECONDS);
Intermediates memory i = getIntermediates(price, strike, time, vol, rfr);
if (!isPut) {
return
callOptionPriceGreeks(
int256(i.d1),
int256(i.d1Denominator),
int256(price),
int256(strike),
i.eToNegRT
);
} else {
return
putOptionPriceGreeks(
int256(i.d1),
int256(i.d1Denominator),
int256(price),
int256(strike),
i.eToNegRT
);
}
}
function getDelta(
uint256 price,
uint256 strike,
uint256 expiration,
uint256 vol,
uint256 rfr,
bool isPut
) public view returns (int256) {
uint256 time = (expiration - getTimeStamp()).div(ONE_YEAR_SECONDS);
(int256 d1, ) = getD1(price, strike, time, vol, rfr);
if (!isPut) {
return NormalDist.cdf(d1);
} else {
return -NormalDist.cdf(-d1);
}
}
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;
import "prb-math/contracts/PRBMathSD59x18.sol";
/**
* @title Library used for approximating a normal distribution
*/
library NormalDist {
using PRBMathSD59x18 for int256;
int256 private constant ONE = 1000000000000000000;
int256 private constant ONE_HALF = 500000000000000000;
int256 private constant SQRT_TWO = 1414213562373095048;
// z-scores
// A1 0.254829592
int256 private constant A1 = 254829592000000000;
// A2 -0.284496736
int256 private constant A2 = -284496736000000000;
// A3 1.421413741
int256 private constant A3 = 1421413741000000000;
// A4 -1.453152027
int256 private constant A4 = -1453152027000000000;
// A5 1.061405429
int256 private constant A5 = 1061405429000000000;
// P 0.3275911
int256 private constant P = 327591100000000000;
function cdf(int256 x) public pure returns (int256) {
int256 phiParam = x.div(SQRT_TWO);
int256 onePlusPhi = ONE + (phi(phiParam));
return ONE_HALF.mul(onePlusPhi);
}
function phi(int256 x) public pure returns (int256) {
int256 sign = x >= 0 ? ONE : -ONE;
int256 abs = x.abs();
// A&S formula 7.1.26
int256 t = ONE.div(ONE + (P.mul(abs)));
int256 scoresByT = getScoresFromT(t);
int256 eToXs = abs.mul(-ONE).mul(abs).exp();
int256 y = ONE - (scoresByT.mul(eToXs));
return sign.mul(y);
}
function getScoresFromT(int256 t) public pure returns (int256) {
int256 byA5T = A5.mul(t);
int256 byA4T = (byA5T + A4).mul(t);
int256 byA3T = (byA4T + A3).mul(t);
int256 byA2T = (byA3T + A2).mul(t);
int256 byA1T = (byA2T + A1).mul(t);
return byA1T;
}
}// SPDX-License-Identifier: Unlicense
pragma solidity >=0.8.4;
/// @notice Emitted when the result overflows uint256.
error PRBMath__MulDivFixedPointOverflow(uint256 prod1);
/// @notice Emitted when the result overflows uint256.
error PRBMath__MulDivOverflow(uint256 prod1, uint256 denominator);
/// @notice Emitted when one of the inputs is type(int256).min.
error PRBMath__MulDivSignedInputTooSmall();
/// @notice Emitted when the intermediary absolute result overflows int256.
error PRBMath__MulDivSignedOverflow(uint256 rAbs);
/// @notice Emitted when the input is MIN_SD59x18.
error PRBMathSD59x18__AbsInputTooSmall();
/// @notice Emitted when ceiling a number overflows SD59x18.
error PRBMathSD59x18__CeilOverflow(int256 x);
/// @notice Emitted when one of the inputs is MIN_SD59x18.
error PRBMathSD59x18__DivInputTooSmall();
/// @notice Emitted when one of the intermediary unsigned results overflows SD59x18.
error PRBMathSD59x18__DivOverflow(uint256 rAbs);
/// @notice Emitted when the input is greater than 133.084258667509499441.
error PRBMathSD59x18__ExpInputTooBig(int256 x);
/// @notice Emitted when the input is greater than 192.
error PRBMathSD59x18__Exp2InputTooBig(int256 x);
/// @notice Emitted when flooring a number underflows SD59x18.
error PRBMathSD59x18__FloorUnderflow(int256 x);
/// @notice Emitted when converting a basic integer to the fixed-point format overflows SD59x18.
error PRBMathSD59x18__FromIntOverflow(int256 x);
/// @notice Emitted when converting a basic integer to the fixed-point format underflows SD59x18.
error PRBMathSD59x18__FromIntUnderflow(int256 x);
/// @notice Emitted when the product of the inputs is negative.
error PRBMathSD59x18__GmNegativeProduct(int256 x, int256 y);
/// @notice Emitted when multiplying the inputs overflows SD59x18.
error PRBMathSD59x18__GmOverflow(int256 x, int256 y);
/// @notice Emitted when the input is less than or equal to zero.
error PRBMathSD59x18__LogInputTooSmall(int256 x);
/// @notice Emitted when one of the inputs is MIN_SD59x18.
error PRBMathSD59x18__MulInputTooSmall();
/// @notice Emitted when the intermediary absolute result overflows SD59x18.
error PRBMathSD59x18__MulOverflow(uint256 rAbs);
/// @notice Emitted when the intermediary absolute result overflows SD59x18.
error PRBMathSD59x18__PowuOverflow(uint256 rAbs);
/// @notice Emitted when the input is negative.
error PRBMathSD59x18__SqrtNegativeInput(int256 x);
/// @notice Emitted when the calculating the square root overflows SD59x18.
error PRBMathSD59x18__SqrtOverflow(int256 x);
/// @notice Emitted when addition overflows UD60x18.
error PRBMathUD60x18__AddOverflow(uint256 x, uint256 y);
/// @notice Emitted when ceiling a number overflows UD60x18.
error PRBMathUD60x18__CeilOverflow(uint256 x);
/// @notice Emitted when the input is greater than 133.084258667509499441.
error PRBMathUD60x18__ExpInputTooBig(uint256 x);
/// @notice Emitted when the input is greater than 192.
error PRBMathUD60x18__Exp2InputTooBig(uint256 x);
/// @notice Emitted when converting a basic integer to the fixed-point format format overflows UD60x18.
error PRBMathUD60x18__FromUintOverflow(uint256 x);
/// @notice Emitted when multiplying the inputs overflows UD60x18.
error PRBMathUD60x18__GmOverflow(uint256 x, uint256 y);
/// @notice Emitted when the input is less than 1.
error PRBMathUD60x18__LogInputTooSmall(uint256 x);
/// @notice Emitted when the calculating the square root overflows UD60x18.
error PRBMathUD60x18__SqrtOverflow(uint256 x);
/// @notice Emitted when subtraction underflows UD60x18.
error PRBMathUD60x18__SubUnderflow(uint256 x, uint256 y);
/// @dev Common mathematical functions used in both PRBMathSD59x18 and PRBMathUD60x18. Note that this shared library
/// does not always assume the signed 59.18-decimal fixed-point or the unsigned 60.18-decimal fixed-point
/// representation. When it does not, it is explicitly mentioned in the NatSpec documentation.
library PRBMath {
/// STRUCTS ///
struct SD59x18 {
int256 value;
}
struct UD60x18 {
uint256 value;
}
/// STORAGE ///
/// @dev How many trailing decimals can be represented.
uint256 internal constant SCALE = 1e18;
/// @dev Largest power of two divisor of SCALE.
uint256 internal constant SCALE_LPOTD = 262144;
/// @dev SCALE inverted mod 2^256.
uint256 internal constant SCALE_INVERSE =
78156646155174841979727994598816262306175212592076161876661_508869554232690281;
/// 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.
function exp2(uint256 x) internal pure returns (uint256 result) {
unchecked {
// Start from 0.5 in the 192.64-bit fixed-point format.
result = 0x800000000000000000000000000000000000000000000000;
// Multiply the result by root(2, 2^-i) when the bit at position i is 1. None of the intermediary results overflows
// because the initial result is 2^191 and all magic factors are less than 2^65.
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 & 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 & 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 & 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 & 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 & 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 & 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 & 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;
}
// We're doing two things at the same time:
//
// 1. Multiply the result by 2^n + 1, where "2^n" is the integer part and the one is added to account for
// the fact that we initially set the result to 0.5. This is accomplished by subtracting from 191
// rather than 192.
// 2. Convert the result to the unsigned 60.18-decimal fixed-point format.
//
// This works because 2^(191-ip) = 2^ip / 2^191, where "ip" is the integer part "2^n".
result *= SCALE;
result >>= (191 - (x >> 64));
}
}
/// @notice Finds the zero-based index of the first one in the binary representation of x.
/// @dev See the note on msb in the "Find First Set" Wikipedia article https://en.wikipedia.org/wiki/Find_first_set
/// @param x The uint256 number for which to find the index of the most significant bit.
/// @return msb The index of the most significant bit as an uint256.
function mostSignificantBit(uint256 x) internal pure returns (uint256 msb) {
if (x >= 2**128) {
x >>= 128;
msb += 128;
}
if (x >= 2**64) {
x >>= 64;
msb += 64;
}
if (x >= 2**32) {
x >>= 32;
msb += 32;
}
if (x >= 2**16) {
x >>= 16;
msb += 16;
}
if (x >= 2**8) {
x >>= 8;
msb += 8;
}
if (x >= 2**4) {
x >>= 4;
msb += 4;
}
if (x >= 2**2) {
x >>= 2;
msb += 2;
}
if (x >= 2**1) {
// No need to shift x any more.
msb += 1;
}
}
/// @notice Calculates floor(x*y÷denominator) with full precision.
///
/// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
///
/// Requirements:
/// - The denominator cannot be zero.
/// - The result must fit within uint256.
///
/// Caveats:
/// - This function does not work with fixed-point numbers.
///
/// @param x The multiplicand as an uint256.
/// @param y The multiplier as an uint256.
/// @param denominator The divisor as an uint256.
/// @return result The result as an uint256.
function mulDiv(
uint256 x,
uint256 y,
uint256 denominator
) internal 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 {
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 {
result = prod0 / denominator;
}
return result;
}
// Make sure the result is less than 2^256. Also prevents denominator == 0.
if (prod1 >= denominator) {
revert PRBMath__MulDivOverflow(prod1, denominator);
}
///////////////////////////////////////////////
// 512 by 256 division.
///////////////////////////////////////////////
// Make division exact by subtracting the remainder from [prod1 prod0].
uint256 remainder;
assembly {
// Compute remainder using mulmod.
remainder := mulmod(x, y, denominator)
// Subtract 256 bit number from 512 bit number.
prod1 := sub(prod1, gt(remainder, prod0))
prod0 := sub(prod0, remainder)
}
// Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
// See https://cs.stackexchange.com/q/138556/92363.
unchecked {
// Does not overflow because the denominator cannot be zero at this stage in the function.
uint256 lpotdod = denominator & (~denominator + 1);
assembly {
// Divide denominator by lpotdod.
denominator := div(denominator, lpotdod)
// Divide [prod1 prod0] by lpotdod.
prod0 := div(prod0, lpotdod)
// Flip lpotdod such that it is 2^256 / lpotdod. If lpotdod is zero, then it becomes one.
lpotdod := add(div(sub(0, lpotdod), lpotdod), 1)
}
// Shift in bits from prod1 into prod0.
prod0 |= prod1 * lpotdod;
// Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
// that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
// four bits. That is, denominator * inv = 1 mod 2^4.
uint256 inverse = (3 * denominator) ^ 2;
// Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
// in modular arithmetic, doubling the correct bits in each step.
inverse *= 2 - denominator * inverse; // inverse mod 2^8
inverse *= 2 - denominator * inverse; // inverse mod 2^16
inverse *= 2 - denominator * inverse; // inverse mod 2^32
inverse *= 2 - denominator * inverse; // inverse mod 2^64
inverse *= 2 - denominator * inverse; // inverse mod 2^128
inverse *= 2 - denominator * inverse; // inverse mod 2^256
// Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
// This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
// less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
// is no longer required.
result = prod0 * inverse;
return result;
}
}
/// @notice Calculates floor(x*y÷1e18) with full precision.
///
/// @dev Variant of "mulDiv" with constant folding, i.e. in which the denominator is always 1e18. Before returning the
/// final result, we add 1 if (x * y) % SCALE >= HALF_SCALE. Without this, 6.6e-19 would be truncated to 0 instead of
/// being rounded to 1e-18. See "Listing 6" and text above it at https://accu.org/index.php/journals/1717.
///
/// Requirements:
/// - The result must fit within uint256.
///
/// Caveats:
/// - The body is purposely left uncommented; see the NatSpec comments in "PRBMath.mulDiv" to understand how this works.
/// - It is assumed that the result can never be type(uint256).max when x and y solve the following two equations:
/// 1. x * y = type(uint256).max * SCALE
/// 2. (x * y) % SCALE >= SCALE / 2
///
/// @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.
function mulDivFixedPoint(uint256 x, uint256 y) internal pure returns (uint256 result) {
uint256 prod0;
uint256 prod1;
assembly {
let mm := mulmod(x, y, not(0))
prod0 := mul(x, y)
prod1 := sub(sub(mm, prod0), lt(mm, prod0))
}
if (prod1 >= SCALE) {
revert PRBMath__MulDivFixedPointOverflow(prod1);
}
uint256 remainder;
uint256 roundUpUnit;
assembly {
remainder := mulmod(x, y, SCALE)
roundUpUnit := gt(remainder, 499999999999999999)
}
if (prod1 == 0) {
unchecked {
result = (prod0 / SCALE) + roundUpUnit;
return result;
}
}
assembly {
result := add(
mul(
or(
div(sub(prod0, remainder), SCALE_LPOTD),
mul(sub(prod1, gt(remainder, prod0)), add(div(sub(0, SCALE_LPOTD), SCALE_LPOTD), 1))
),
SCALE_INVERSE
),
roundUpUnit
)
}
}
/// @notice Calculates floor(x*y÷denominator) with full precision.
///
/// @dev An extension of "mulDiv" for signed numbers. Works by computing the signs and the absolute values separately.
///
/// Requirements:
/// - None of the inputs can be type(int256).min.
/// - The result must fit within 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.
function mulDivSigned(
int256 x,
int256 y,
int256 denominator
) internal pure returns (int256 result) {
if (x == type(int256).min || y == type(int256).min || denominator == type(int256).min) {
revert PRBMath__MulDivSignedInputTooSmall();
}
// Get hold of the absolute values of x, y and the denominator.
uint256 ax;
uint256 ay;
uint256 ad;
unchecked {
ax = x < 0 ? uint256(-x) : uint256(x);
ay = y < 0 ? uint256(-y) : uint256(y);
ad = denominator < 0 ? uint256(-denominator) : uint256(denominator);
}
// Compute the absolute value of (x*y)÷denominator. The result must fit within int256.
uint256 rAbs = mulDiv(ax, ay, ad);
if (rAbs > uint256(type(int256).max)) {
revert PRBMath__MulDivSignedOverflow(rAbs);
}
// Get the signs of x, y and the denominator.
uint256 sx;
uint256 sy;
uint256 sd;
assembly {
sx := sgt(x, sub(0, 1))
sy := sgt(y, sub(0, 1))
sd := sgt(denominator, sub(0, 1))
}
// XOR over sx, sy and sd. This is checking whether there are one or three negative signs in the inputs.
// If yes, the result should be negative.
result = sx ^ sy ^ sd == 0 ? -int256(rAbs) : int256(rAbs);
}
/// @notice Calculates the square root of x, rounding down.
/// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Caveats:
/// - This function does not work with fixed-point numbers.
///
/// @param x The uint256 number for which to calculate the square root.
/// @return result The result as an uint256.
function sqrt(uint256 x) internal pure returns (uint256 result) {
if (x == 0) {
return 0;
}
// Set the initial guess to the least power of two that is greater than or equal to sqrt(x).
uint256 xAux = uint256(x);
result = 1;
if (xAux >= 0x100000000000000000000000000000000) {
xAux >>= 128;
result <<= 64;
}
if (xAux >= 0x10000000000000000) {
xAux >>= 64;
result <<= 32;
}
if (xAux >= 0x100000000) {
xAux >>= 32;
result <<= 16;
}
if (xAux >= 0x10000) {
xAux >>= 16;
result <<= 8;
}
if (xAux >= 0x100) {
xAux >>= 8;
result <<= 4;
}
if (xAux >= 0x10) {
xAux >>= 4;
result <<= 2;
}
if (xAux >= 0x8) {
result <<= 1;
}
// The operations can never overflow because the result is max 2^127 when it enters this block.
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; // Seven iterations should be enough
uint256 roundedDownResult = x / result;
return result >= roundedDownResult ? roundedDownResult : result;
}
}
}{
"optimizer": {
"enabled": true,
"runs": 200
},
"outputSelection": {
"*": {
"*": [
"evm.bytecode",
"evm.deployedBytecode",
"devdoc",
"userdoc",
"metadata",
"abi"
]
}
},
"metadata": {
"useLiteralContent": true
},
"libraries": {}
}[{"inputs":[{"internalType":"address","name":"_liquidityPool","type":"address"}],"stateMutability":"nonpayable","type":"constructor"},{"inputs":[],"name":"EpochNotClosed","type":"error"},{"inputs":[],"name":"ExistingWithdrawal","type":"error"},{"inputs":[],"name":"InsufficientShareBalance","type":"error"},{"inputs":[],"name":"InvalidAmount","type":"error"},{"inputs":[],"name":"LiabilitiesGreaterThanAssets","type":"error"},{"inputs":[],"name":"NoExistingWithdrawal","type":"error"},{"inputs":[],"name":"TotalSupplyReached","type":"error"},{"inputs":[{"internalType":"uint256","name":"_shares","type":"uint256"},{"internalType":"uint256","name":"_assetPerShare","type":"uint256"}],"name":"amountForShares","outputs":[{"internalType":"uint256","name":"amount","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"collateralAsset","outputs":[{"internalType":"address","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"withdrawer","type":"address"}],"name":"completeWithdraw","outputs":[{"internalType":"uint256","name":"withdrawalAmount","type":"uint256"},{"internalType":"uint256","name":"withdrawalShares","type":"uint256"},{"components":[{"internalType":"uint128","name":"epoch","type":"uint128"},{"internalType":"uint128","name":"shares","type":"uint128"}],"internalType":"struct IAccounting.WithdrawalReceipt","name":"withdrawalReceipt","type":"tuple"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"depositor","type":"address"},{"internalType":"uint256","name":"_amount","type":"uint256"}],"name":"deposit","outputs":[{"internalType":"uint256","name":"depositAmount","type":"uint256"},{"internalType":"uint256","name":"unredeemedShares","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"totalSupply","type":"uint256"},{"internalType":"uint256","name":"assets","type":"uint256"},{"internalType":"int256","name":"liabilities","type":"int256"}],"name":"executeEpochCalculation","outputs":[{"internalType":"uint256","name":"newPricePerShareDeposit","type":"uint256"},{"internalType":"uint256","name":"newPricePerShareWithdrawal","type":"uint256"},{"internalType":"uint256","name":"sharesToMint","type":"uint256"},{"internalType":"uint256","name":"totalWithdrawAmount","type":"uint256"},{"internalType":"uint256","name":"amountNeeded","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"withdrawer","type":"address"},{"internalType":"uint256","name":"shares","type":"uint256"}],"name":"initiateWithdraw","outputs":[{"components":[{"internalType":"uint128","name":"epoch","type":"uint128"},{"internalType":"uint128","name":"shares","type":"uint128"}],"internalType":"struct IAccounting.WithdrawalReceipt","name":"withdrawalReceipt","type":"tuple"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"liquidityPool","outputs":[{"internalType":"contract ILiquidityPool","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"redeemer","type":"address"},{"internalType":"uint256","name":"shares","type":"uint256"}],"name":"redeem","outputs":[{"internalType":"uint256","name":"toRedeem","type":"uint256"},{"components":[{"internalType":"uint128","name":"epoch","type":"uint128"},{"internalType":"uint128","name":"amount","type":"uint128"},{"internalType":"uint256","name":"unredeemedShares","type":"uint256"}],"internalType":"struct IAccounting.DepositReceipt","name":"","type":"tuple"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"_amount","type":"uint256"},{"internalType":"uint256","name":"assetPerShare","type":"uint256"}],"name":"sharesForAmount","outputs":[{"internalType":"uint256","name":"shares","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"strikeAsset","outputs":[{"internalType":"address","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"underlyingAsset","outputs":[{"internalType":"address","name":"","type":"address"}],"stateMutability":"view","type":"function"}]Contract Creation Code
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Constructor Arguments (ABI-Encoded and is the last bytes of the Contract Creation Code above)
000000000000000000000000c10b976c671ce9bff0723611f01422acbae100a5
-----Decoded View---------------
Arg [0] : _liquidityPool (address): 0xc10b976c671ce9bff0723611f01422acbae100a5
-----Encoded View---------------
1 Constructor Arguments found :
Arg [0] : 000000000000000000000000c10b976c671ce9bff0723611f01422acbae100a5
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