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// SPDX-License-Identifier: MIT
pragma solidity 0.8.21;

import "@openzeppelin/contracts/proxy/Proxy.sol";
import "./PerpStorage.sol";
import "../interfaces/ILibraryEvents.sol";
import "../interfaces/IFunctionList.sol";
import "../../libraries/EnumerableBytes4Set.sol";
import "../../libraries/Utils.sol";

contract PerpetualManagerProxy is PerpStorage, Proxy, ILibraryEvents {
    using EnumerableBytes4Set for EnumerableBytes4Set.Bytes4Set;

    bytes32 private constant KEY_IMPLEMENTATION = keccak256("key.implementation");
    bytes32 private constant KEY_OWNER = keccak256("key.proxy.owner");

    event ProxyOwnershipTransferred(address indexed _oldOwner, address indexed _newOwner);
    event ImplementationChanged(
        bytes4 _sig,
        address indexed _oldImplementation,
        address indexed _newImplementation
    );

    /**
     * @notice Set sender as an owner.
     */
    constructor() {
        _setProxyOwner(msg.sender);
    }

    /**
     * @notice Throw error if called not by an owner.
     */
    modifier onlyProxyOwner() {
        require(msg.sender == getProxyOwner(), "Proxy:access denied");
        _;
    }

    function _implementation() internal view override returns (address) {
        address implementation = _getImplementation(msg.sig);
        require(implementation != address(0), "Proxy:Implementation not found");
        return implementation;
    }

    function getImplementation(bytes4 _sig) external view returns (address) {
        return _getImplementation(_sig);
    }

    function _getImplementation(bytes4 _sig) internal view returns (address) {
        bytes32 key = keccak256(abi.encode(_sig, KEY_IMPLEMENTATION));
        address implementation;
        // solhint-disable-next-line no-inline-assembly
        assembly {
            implementation := sload(key)
        }
        return implementation;
    }

    /// @dev to delete module deploy a dummy module with the same name in getFunctionList() as being deleted
    /// it will remove all previous implementation functions
    function setImplementation(address _impl) external onlyProxyOwner {
        _setImplementation(_impl, false);
    }

    ///@dev allows replacement of functions from other modules. Use only if you realize consequences.
    function setImplementationCrossModules(address _impl) external onlyProxyOwner {
        _setImplementation(_impl, true);
    }

    ///@param _impl module address
    ///@param replaceOtherModulesFuncs allow to replace functions of other modules, use with caution
    function _setImplementation(address _impl, bool replaceOtherModulesFuncs) internal {
        require(_impl != address(0), "invalid implementation address");

        (bytes4[] memory functions, bytes32 moduleName) = IFunctionList(_impl).getFunctionList();

        require(moduleName != bytes32(0), "Module name cannot be empty");

        EnumerableBytes4Set.Bytes4Set
            storage moduleActiveFunctionsSet = moduleActiveFuncSignatureList[moduleName];
        bool moduleIsBeingUpdated = moduleActiveFunctionsSet.length() > 0;
        uint256 length = functions.length;
        for (uint256 i = 0; i < length; i++) {
            bytes4 funcSig = functions[i];
            if (!moduleActiveFunctionsSet.contains(functions[i])) {
                // if the function registered with another module
                address anotherModuleImplAddress = _getImplementation(funcSig);
                if (anotherModuleImplAddress != address(0)) {
                    require(replaceOtherModulesFuncs, "cant replace modules funcs");
                    moduleActiveFuncSignatureList[
                        moduleAddressToModuleName[anotherModuleImplAddress]
                    ].removeBytes4(funcSig);
                }
                moduleActiveFunctionsSet.addBytes4(functions[i]);
            }
            _setImplementation(functions[i], _impl);
        }

        /// remove functions of the previous module version
        if (moduleIsBeingUpdated) {
            bytes4[] memory moduleActiveFuncsArray = moduleActiveFunctionsSet.enumerate(
                0,
                moduleActiveFunctionsSet.length()
            );
            length = moduleActiveFuncsArray.length;
            for (uint256 i; i < length; i++) {
                bytes4 funcSig = moduleActiveFuncsArray[i];
                if (_getImplementation(funcSig) != _impl) {
                    _setImplementation(funcSig, address(0));
                    moduleActiveFunctionsSet.removeBytes4(funcSig);
                }
            }
        }

        moduleNameToAddress[moduleName] = _impl;
        moduleAddressToModuleName[_impl] = moduleName;
    }

    function getModuleImplementationAddress(string calldata _moduleName)
        external
        view
        returns (address)
    {
        return moduleNameToAddress[Utils.stringToBytes32(_moduleName)];
    }

    function _setImplementation(bytes4 _sig, address _impl) internal {
        _checkClashing(_sig);
        emit ImplementationChanged(_sig, _getImplementation(_sig), _impl);

        bytes32 key = keccak256(abi.encode(_sig, KEY_IMPLEMENTATION));
        // solhint-disable-next-line no-inline-assembly
        assembly {
            sstore(key, _impl)
        }
    }

    /**
     * @notice Set address of the owner.
     * @param _owner Address of the owner.
     * */
    function setProxyOwner(address _owner) external onlyProxyOwner {
        _setProxyOwner(_owner);
    }

    function _setProxyOwner(address _owner) internal {
        require(_owner != address(0), "invalid proxy owner address");
        emit ProxyOwnershipTransferred(getProxyOwner(), _owner);

        bytes32 key = KEY_OWNER;
        // solhint-disable-next-line no-inline-assembly
        assembly {
            sstore(key, _owner)
        }
    }

    /**
     * @notice Return address of the owner.
     * @return _owner Address of the owner.
     */
    function getProxyOwner() public view returns (address _owner) {
        bytes32 key = KEY_OWNER;
        // solhint-disable-next-line no-inline-assembly
        assembly {
            _owner := sload(key)
        }
    }

    function _checkClashing(bytes4 _sig) internal pure {
        bytes4[] memory functionList = _getFunctionList();
        uint256 length = functionList.length;
        for (uint256 i = 0; i < length; i++) {
            require(_sig != functionList[i], "function id already exists");
        }
    }

    /**
     * @dev Triggers stopped state.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    function pause() external whenNotPaused onlyMaintainer {
        _pause();
    }

    /**
     * @dev Returns to normal state.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    function unpause() external virtual whenPaused onlyMaintainer {
        _unpause();
    }

    function _getFunctionList() internal pure returns (bytes4[] memory) {
        bytes4[] memory functionList = new bytes4[](8);
        functionList[0] = this.getImplementation.selector;
        functionList[1] = this.setImplementation.selector;
        functionList[2] = this.setImplementationCrossModules.selector;
        functionList[3] = this.getModuleImplementationAddress.selector;
        functionList[4] = this.setProxyOwner.selector;
        functionList[5] = this.getProxyOwner.selector;
        functionList[6] = this.pause.selector;
        functionList[7] = this.unpause.selector;
        return functionList;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../utils/Context.sol";

/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract Ownable is Context {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor() {
        _transferOwnership(_msgSender());
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby disabling any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _transferOwnership(newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (proxy/Proxy.sol)

pragma solidity ^0.8.0;

/**
 * @dev This abstract contract provides a fallback function that delegates all calls to another contract using the EVM
 * instruction `delegatecall`. We refer to the second contract as the _implementation_ behind the proxy, and it has to
 * be specified by overriding the virtual {_implementation} function.
 *
 * Additionally, delegation to the implementation can be triggered manually through the {_fallback} function, or to a
 * different contract through the {_delegate} function.
 *
 * The success and return data of the delegated call will be returned back to the caller of the proxy.
 */
abstract contract Proxy {
    /**
     * @dev Delegates the current call to `implementation`.
     *
     * This function does not return to its internal call site, it will return directly to the external caller.
     */
    function _delegate(address implementation) internal virtual {
        assembly {
            // Copy msg.data. We take full control of memory in this inline assembly
            // block because it will not return to Solidity code. We overwrite the
            // Solidity scratch pad at memory position 0.
            calldatacopy(0, 0, calldatasize())

            // Call the implementation.
            // out and outsize are 0 because we don't know the size yet.
            let result := delegatecall(gas(), implementation, 0, calldatasize(), 0, 0)

            // Copy the returned data.
            returndatacopy(0, 0, returndatasize())

            switch result
            // delegatecall returns 0 on error.
            case 0 {
                revert(0, returndatasize())
            }
            default {
                return(0, returndatasize())
            }
        }
    }

    /**
     * @dev This is a virtual function that should be overridden so it returns the address to which the fallback function
     * and {_fallback} should delegate.
     */
    function _implementation() internal view virtual returns (address);

    /**
     * @dev Delegates the current call to the address returned by `_implementation()`.
     *
     * This function does not return to its internal call site, it will return directly to the external caller.
     */
    function _fallback() internal virtual {
        _beforeFallback();
        _delegate(_implementation());
    }

    /**
     * @dev Fallback function that delegates calls to the address returned by `_implementation()`. Will run if no other
     * function in the contract matches the call data.
     */
    fallback() external payable virtual {
        _fallback();
    }

    /**
     * @dev Fallback function that delegates calls to the address returned by `_implementation()`. Will run if call data
     * is empty.
     */
    receive() external payable virtual {
        _fallback();
    }

    /**
     * @dev Hook that is called before falling back to the implementation. Can happen as part of a manual `_fallback`
     * call, or as part of the Solidity `fallback` or `receive` functions.
     *
     * If overridden should call `super._beforeFallback()`.
     */
    function _beforeFallback() internal virtual {}
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (security/Pausable.sol)

pragma solidity ^0.8.0;

import "../utils/Context.sol";

/**
 * @dev Contract module which allows children to implement an emergency stop
 * mechanism that can be triggered by an authorized account.
 *
 * This module is used through inheritance. It will make available the
 * modifiers `whenNotPaused` and `whenPaused`, which can be applied to
 * the functions of your contract. Note that they will not be pausable by
 * simply including this module, only once the modifiers are put in place.
 */
abstract contract Pausable is Context {
    /**
     * @dev Emitted when the pause is triggered by `account`.
     */
    event Paused(address account);

    /**
     * @dev Emitted when the pause is lifted by `account`.
     */
    event Unpaused(address account);

    bool private _paused;

    /**
     * @dev Initializes the contract in unpaused state.
     */
    constructor() {
        _paused = false;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is not paused.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    modifier whenNotPaused() {
        _requireNotPaused();
        _;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is paused.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    modifier whenPaused() {
        _requirePaused();
        _;
    }

    /**
     * @dev Returns true if the contract is paused, and false otherwise.
     */
    function paused() public view virtual returns (bool) {
        return _paused;
    }

    /**
     * @dev Throws if the contract is paused.
     */
    function _requireNotPaused() internal view virtual {
        require(!paused(), "Pausable: paused");
    }

    /**
     * @dev Throws if the contract is not paused.
     */
    function _requirePaused() internal view virtual {
        require(paused(), "Pausable: not paused");
    }

    /**
     * @dev Triggers stopped state.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    function _pause() internal virtual whenNotPaused {
        _paused = true;
        emit Paused(_msgSender());
    }

    /**
     * @dev Returns to normal state.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    function _unpause() internal virtual whenPaused {
        _paused = false;
        emit Unpaused(_msgSender());
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (security/ReentrancyGuard.sol)

pragma solidity ^0.8.0;

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuard {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.

    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;

    uint256 private _status;

    constructor() {
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and making it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        _nonReentrantBefore();
        _;
        _nonReentrantAfter();
    }

    function _nonReentrantBefore() private {
        // On the first call to nonReentrant, _status will be _NOT_ENTERED
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

        // Any calls to nonReentrant after this point will fail
        _status = _ENTERED;
    }

    function _nonReentrantAfter() private {
        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Returns true if the reentrancy guard is currently set to "entered", which indicates there is a
     * `nonReentrant` function in the call stack.
     */
    function _reentrancyGuardEntered() internal view returns (bool) {
        return _status == _ENTERED;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.4) (utils/Context.sol)

pragma solidity ^0.8.0;

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }

    function _contextSuffixLength() internal view virtual returns (uint256) {
        return 0;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (access/Ownable.sol)
// D8X, 2022

pragma solidity 0.8.21;

/**
 * This is a modified version of the OpenZeppelin ownable contract
 * Modifications
 * - instead of an owner, we have two actors: maintainer and governance
 * - maintainer can have certain priviledges but cannot transfer maintainer mandate
 * - governance can exchange maintainer and exchange itself
 * - renounceOwnership is removed
 *
 *
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract Maintainable {
    address private _maintainer;
    address private _governance;

    event MaintainerTransferred(address indexed previousMaintainer, address indexed newMaintainer);
    event GovernanceTransferred(address indexed previousGovernance, address indexed newGovernance);

    /**
     * @dev Initializes the contract setting the deployer as the initial maintainer.
     */
    constructor() {
        _transferMaintainer(msg.sender);
        _transferGovernance(msg.sender);
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function maintainer() public view virtual returns (address) {
        return _maintainer;
    }

    /**
     * @dev Returns the address of the governance.
     */
    function governance() public view virtual returns (address) {
        return _governance;
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyMaintainer() {
        require(maintainer() == msg.sender, "only maintainer");
        _;
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyGovernance() {
        require(governance() == msg.sender, "only governance");
        _;
    }

    /**
     * @dev Transfers maintainer mandate of the contract to a new account (`newMaintainer`).
     * Can only be called by the governance.
     */
    function transferMaintainer(address newMaintainer) public virtual {
        require(msg.sender == _governance, "only governance");
        require(newMaintainer != address(0), "zero address");
        _transferMaintainer(newMaintainer);
    }

    /**
     * @dev Transfers governance mandate of the contract to a new account (`newGovernance`).
     * Can only be called by the governance.
     */
    function transferGovernance(address newGovernance) public virtual {
        require(msg.sender == _governance, "only governance");
        require(newGovernance != address(0), "zero address");
        _transferGovernance(newGovernance);
    }

    /**
     * @dev Transfers maintainer of the contract to a new account (`newMaintainer`).
     * Internal function without access restriction.
     */
    function _transferMaintainer(address newMaintainer) internal virtual {
        address oldM = _maintainer;
        _maintainer = newMaintainer;
        emit MaintainerTransferred(oldM, newMaintainer);
    }

    /**
     * @dev Transfers governance of the contract to a new account (`newGovernance`).
     * Internal function without access restriction.
     */
    function _transferGovernance(address newGovernance) internal virtual {
        address oldG = _governance;
        _governance = newGovernance;
        emit GovernanceTransferred(oldG, newGovernance);
    }
}

// SPDX-License-Identifier: MIT

pragma solidity 0.8.21;

interface IShareTokenFactory {
    function createShareToken(uint8 _poolId, address _marginTokenAddr) external returns (address);
}

// SPDX-License-Identifier: BSD-4-Clause
/*
 * ABDK Math 64.64 Smart Contract Library.  Copyright © 2019 by ABDK Consulting.
 * Author: Mikhail Vladimirov <[email protected]>
 */
pragma solidity 0.8.21;

/**
 * Smart contract library of mathematical functions operating with signed
 * 64.64-bit fixed point numbers.  Signed 64.64-bit fixed point number is
 * basically a simple fraction whose numerator is signed 128-bit integer and
 * denominator is 2^64.  As long as denominator is always the same, there is no
 * need to store it, thus in Solidity signed 64.64-bit fixed point numbers are
 * represented by int128 type holding only the numerator.
 */
library ABDKMath64x64 {
    /*
     * Minimum value signed 64.64-bit fixed point number may have.
     */
    int128 private constant MIN_64x64 = -0x80000000000000000000000000000000;

    /*
     * Maximum value signed 64.64-bit fixed point number may have.
     */
    int128 private constant MAX_64x64 = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

    /**
     * Convert signed 256-bit integer number into signed 64.64-bit fixed point
     * number.  Revert on overflow.
     *
     * @param x signed 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function fromInt(int256 x) internal pure returns (int128) {
        require(x >= -0x8000000000000000 && x <= 0x7FFFFFFFFFFFFFFF, "ABDK.fromInt");
        return int128(x << 64);
    }

    /**
     * Convert signed 64.64 fixed point number into signed 64-bit integer number
     * rounding down.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64-bit integer number
     */
    function toInt(int128 x) internal pure returns (int64) {
        return int64(x >> 64);
    }

    /**
     * Convert unsigned 256-bit integer number into signed 64.64-bit fixed point
     * number.  Revert on overflow.
     *
     * @param x unsigned 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function fromUInt(uint256 x) internal pure returns (int128) {
        require(x <= 0x7FFFFFFFFFFFFFFF, "ABDK.fromUInt");
        return int128(int256(x << 64));
    }

    /**
     * Convert signed 64.64 fixed point number into unsigned 64-bit integer
     * number rounding down.  Revert on underflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return unsigned 64-bit integer number
     */
    function toUInt(int128 x) internal pure returns (uint64) {
        require(x >= 0, "ABDK.toUInt");
        return uint64(uint128(x >> 64));
    }

    /**
     * Convert signed 128.128 fixed point number into signed 64.64-bit fixed point
     * number rounding down.  Revert on overflow.
     *
     * @param x signed 128.128-bin fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function from128x128(int256 x) internal pure returns (int128) {
        int256 result = x >> 64;
        require(result >= MIN_64x64 && result <= MAX_64x64, "ABDK.from128x128");
        return int128(result);
    }

    /**
     * Convert signed 64.64 fixed point number into signed 128.128 fixed point
     * number.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 128.128 fixed point number
     */
    function to128x128(int128 x) internal pure returns (int256) {
        return int256(x) << 64;
    }

    /**
     * Calculate x + y.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function add(int128 x, int128 y) internal pure returns (int128) {
        int256 result = int256(x) + y;
        require(result >= MIN_64x64 && result <= MAX_64x64, "ABDK.add");
        return int128(result);
    }

    /**
     * Calculate x - y.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function sub(int128 x, int128 y) internal pure returns (int128) {
        int256 result = int256(x) - y;
        require(result >= MIN_64x64 && result <= MAX_64x64, "ABDK.sub");
        return int128(result);
    }

    /**
     * Calculate x * y rounding down.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function mul(int128 x, int128 y) internal pure returns (int128) {
        int256 result = (int256(x) * y) >> 64;
        require(result >= MIN_64x64 && result <= MAX_64x64, "ABDK.mul");
        return int128(result);
    }

    /**
     * Calculate x * y rounding towards zero, where x is signed 64.64 fixed point
     * number and y is signed 256-bit integer number.  Revert on overflow.
     *
     * @param x signed 64.64 fixed point number
     * @param y signed 256-bit integer number
     * @return signed 256-bit integer number
     */
    function muli(int128 x, int256 y) internal pure returns (int256) {
        if (x == MIN_64x64) {
            require(
                y >= -0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF &&
                    y <= 0x1000000000000000000000000000000000000000000000000,
                "ABDK.muli-1"
            );
            return -y << 63;
        } else {
            bool negativeResult = false;
            if (x < 0) {
                x = -x;
                negativeResult = true;
            }
            if (y < 0) {
                y = -y;
                // We rely on overflow behavior here
                negativeResult = !negativeResult;
            }
            uint256 absoluteResult = mulu(x, uint256(y));
            if (negativeResult) {
                require(
                    absoluteResult <=
                        0x8000000000000000000000000000000000000000000000000000000000000000,
                    "ABDK.muli-2"
                );
                return -int256(absoluteResult);
                // We rely on overflow behavior here
            } else {
                require(
                    absoluteResult <=
                        0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,
                    "ABDK.muli-3"
                );
                return int256(absoluteResult);
            }
        }
    }

    /**
     * Calculate x * y rounding down, where x is signed 64.64 fixed point number
     * and y is unsigned 256-bit integer number.  Revert on overflow.
     *
     * @param x signed 64.64 fixed point number
     * @param y unsigned 256-bit integer number
     * @return unsigned 256-bit integer number
     */
    function mulu(int128 x, uint256 y) internal pure returns (uint256) {
        if (y == 0) return 0;

        require(x >= 0, "ABDK.mulu-1");

        uint256 lo = (uint256(int256(x)) * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)) >> 64;
        uint256 hi = uint256(int256(x)) * (y >> 128);

        require(hi <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF, "ABDK.mulu-2");
        hi <<= 64;

        require(
            hi <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF - lo,
            "ABDK.mulu-3"
        );
        return hi + lo;
    }

    /**
     * Calculate x / y rounding towards zero.  Revert on overflow or when y is
     * zero.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function div(int128 x, int128 y) internal pure returns (int128) {
        require(y != 0, "ABDK.div-1");
        int256 result = (int256(x) << 64) / y;
        require(result >= MIN_64x64 && result <= MAX_64x64, "ABDK.div-2");
        return int128(result);
    }

    /**
     * Calculate x / y rounding towards zero, where x and y are signed 256-bit
     * integer numbers.  Revert on overflow or when y is zero.
     *
     * @param x signed 256-bit integer number
     * @param y signed 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function divi(int256 x, int256 y) internal pure returns (int128) {
        require(y != 0, "ABDK.divi-1");

        bool negativeResult = false;
        if (x < 0) {
            x = -x;
            // We rely on overflow behavior here
            negativeResult = true;
        }
        if (y < 0) {
            y = -y;
            // We rely on overflow behavior here
            negativeResult = !negativeResult;
        }
        uint128 absoluteResult = divuu(uint256(x), uint256(y));
        if (negativeResult) {
            require(absoluteResult <= 0x80000000000000000000000000000000, "ABDK.divi-2");
            return -int128(absoluteResult);
            // We rely on overflow behavior here
        } else {
            require(absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF, "ABDK.divi-3");
            return int128(absoluteResult);
            // We rely on overflow behavior here
        }
    }

    /**
     * Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
     * integer numbers.  Revert on overflow or when y is zero.
     *
     * @param x unsigned 256-bit integer number
     * @param y unsigned 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function divu(uint256 x, uint256 y) internal pure returns (int128) {
        require(y != 0, "ABDK.divu-1");
        uint128 result = divuu(x, y);
        require(result <= uint128(MAX_64x64), "ABDK.divu-2");
        return int128(result);
    }

    /**
     * Calculate -x.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function neg(int128 x) internal pure returns (int128) {
        require(x != MIN_64x64, "ABDK.neg");
        return -x;
    }

    /**
     * Calculate |x|.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function abs(int128 x) internal pure returns (int128) {
        require(x != MIN_64x64, "ABDK.abs");
        return x < 0 ? -x : x;
    }

    /**
     * Calculate 1 / x rounding towards zero.  Revert on overflow or when x is
     * zero.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function inv(int128 x) internal pure returns (int128) {
        require(x != 0, "ABDK.inv-1");
        int256 result = int256(0x100000000000000000000000000000000) / x;
        require(result >= MIN_64x64 && result <= MAX_64x64, "ABDK.inv-2");
        return int128(result);
    }

    /**
     * Calculate arithmetics average of x and y, i.e. (x + y) / 2 rounding down.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function avg(int128 x, int128 y) internal pure returns (int128) {
        return int128((int256(x) + int256(y)) >> 1);
    }

    /**
     * Calculate geometric average of x and y, i.e. sqrt (x * y) rounding down.
     * Revert on overflow or in case x * y is negative.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function gavg(int128 x, int128 y) internal pure returns (int128) {
        int256 m = int256(x) * int256(y);
        require(m >= 0, "ABDK.gavg-1");
        require(
            m < 0x4000000000000000000000000000000000000000000000000000000000000000,
            "ABDK.gavg-2"
        );
        return int128(sqrtu(uint256(m)));
    }

    /**
     * Calculate x^y assuming 0^0 is 1, where x is signed 64.64 fixed point number
     * and y is unsigned 256-bit integer number.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y uint256 value
     * @return signed 64.64-bit fixed point number
     */
    function pow(int128 x, uint256 y) internal pure returns (int128) {
        bool negative = x < 0 && y & 1 == 1;

        uint256 absX = uint128(x < 0 ? -x : x);
        uint256 absResult;
        absResult = 0x100000000000000000000000000000000;

        if (absX <= 0x10000000000000000) {
            absX <<= 63;
            while (y != 0) {
                if (y & 0x1 != 0) {
                    absResult = (absResult * absX) >> 127;
                }
                absX = (absX * absX) >> 127;

                if (y & 0x2 != 0) {
                    absResult = (absResult * absX) >> 127;
                }
                absX = (absX * absX) >> 127;

                if (y & 0x4 != 0) {
                    absResult = (absResult * absX) >> 127;
                }
                absX = (absX * absX) >> 127;

                if (y & 0x8 != 0) {
                    absResult = (absResult * absX) >> 127;
                }
                absX = (absX * absX) >> 127;

                y >>= 4;
            }

            absResult >>= 64;
        } else {
            uint256 absXShift = 63;
            if (absX < 0x1000000000000000000000000) {
                absX <<= 32;
                absXShift -= 32;
            }
            if (absX < 0x10000000000000000000000000000) {
                absX <<= 16;
                absXShift -= 16;
            }
            if (absX < 0x1000000000000000000000000000000) {
                absX <<= 8;
                absXShift -= 8;
            }
            if (absX < 0x10000000000000000000000000000000) {
                absX <<= 4;
                absXShift -= 4;
            }
            if (absX < 0x40000000000000000000000000000000) {
                absX <<= 2;
                absXShift -= 2;
            }
            if (absX < 0x80000000000000000000000000000000) {
                absX <<= 1;
                absXShift -= 1;
            }

            uint256 resultShift;
            while (y != 0) {
                require(absXShift < 64, "ABDK.pow-1");

                if (y & 0x1 != 0) {
                    absResult = (absResult * absX) >> 127;
                    resultShift += absXShift;
                    if (absResult > 0x100000000000000000000000000000000) {
                        absResult >>= 1;
                        resultShift += 1;
                    }
                }
                absX = (absX * absX) >> 127;
                absXShift <<= 1;
                if (absX >= 0x100000000000000000000000000000000) {
                    absX >>= 1;
                    absXShift += 1;
                }

                y >>= 1;
            }

            require(resultShift < 64, "ABDK.pow-2");
            absResult >>= 64 - resultShift;
        }
        int256 result = negative ? -int256(absResult) : int256(absResult);
        require(result >= MIN_64x64 && result <= MAX_64x64, "ABDK.pow-3");
        return int128(result);
    }

    /**
     * Calculate sqrt (x) rounding down.  Revert if x < 0.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function sqrt(int128 x) internal pure returns (int128) {
        require(x >= 0, "ABDK.sqrt");
        return int128(sqrtu(uint256(int256(x)) << 64));
    }

    /**
     * Calculate binary logarithm of x.  Revert if x <= 0.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function log_2(int128 x) internal pure returns (int128) {
        require(x > 0, "ABDK.log_2");

        int256 msb;
        int256 xc = x;
        if (xc >= 0x10000000000000000) {
            xc >>= 64;
            msb += 64;
        }
        if (xc >= 0x100000000) {
            xc >>= 32;
            msb += 32;
        }
        if (xc >= 0x10000) {
            xc >>= 16;
            msb += 16;
        }
        if (xc >= 0x100) {
            xc >>= 8;
            msb += 8;
        }
        if (xc >= 0x10) {
            xc >>= 4;
            msb += 4;
        }
        if (xc >= 0x4) {
            xc >>= 2;
            msb += 2;
        }
        if (xc >= 0x2) msb += 1;
        // No need to shift xc anymore

        int256 result = (msb - 64) << 64;
        uint256 ux = uint256(int256(x)) << uint256(127 - msb);
        for (int256 bit = 0x8000000000000000; bit > 0; bit >>= 1) {
            ux *= ux;
            uint256 b = ux >> 255;
            ux >>= 127 + b;
            result += bit * int256(b);
        }

        return int128(result);
    }

    /**
     * Calculate natural logarithm of x.  Revert if x <= 0.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function ln(int128 x) internal pure returns (int128) {
        unchecked {
            require(x > 0, "ABDK.ln");

            return
                int128(
                    int256((uint256(int256(log_2(x))) * 0xB17217F7D1CF79ABC9E3B39803F2F6AF) >> 128)
                );
        }
    }

    /**
     * Calculate binary exponent of x.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function exp_2(int128 x) internal pure returns (int128) {
        require(x < 0x400000000000000000, "ABDK.exp_2-1");
        // Overflow

        if (x < -0x400000000000000000) return 0;
        // Underflow

        uint256 result = 0x80000000000000000000000000000000;

        if (x & 0x8000000000000000 > 0)
            result = (result * 0x16A09E667F3BCC908B2FB1366EA957D3E) >> 128;
        if (x & 0x4000000000000000 > 0)
            result = (result * 0x1306FE0A31B7152DE8D5A46305C85EDEC) >> 128;
        if (x & 0x2000000000000000 > 0)
            result = (result * 0x1172B83C7D517ADCDF7C8C50EB14A791F) >> 128;
        if (x & 0x1000000000000000 > 0)
            result = (result * 0x10B5586CF9890F6298B92B71842A98363) >> 128;
        if (x & 0x800000000000000 > 0)
            result = (result * 0x1059B0D31585743AE7C548EB68CA417FD) >> 128;
        if (x & 0x400000000000000 > 0)
            result = (result * 0x102C9A3E778060EE6F7CACA4F7A29BDE8) >> 128;
        if (x & 0x200000000000000 > 0)
            result = (result * 0x10163DA9FB33356D84A66AE336DCDFA3F) >> 128;
        if (x & 0x100000000000000 > 0)
            result = (result * 0x100B1AFA5ABCBED6129AB13EC11DC9543) >> 128;
        if (x & 0x80000000000000 > 0)
            result = (result * 0x10058C86DA1C09EA1FF19D294CF2F679B) >> 128;
        if (x & 0x40000000000000 > 0)
            result = (result * 0x1002C605E2E8CEC506D21BFC89A23A00F) >> 128;
        if (x & 0x20000000000000 > 0)
            result = (result * 0x100162F3904051FA128BCA9C55C31E5DF) >> 128;
        if (x & 0x10000000000000 > 0)
            result = (result * 0x1000B175EFFDC76BA38E31671CA939725) >> 128;
        if (x & 0x8000000000000 > 0)
            result = (result * 0x100058BA01FB9F96D6CACD4B180917C3D) >> 128;
        if (x & 0x4000000000000 > 0)
            result = (result * 0x10002C5CC37DA9491D0985C348C68E7B3) >> 128;
        if (x & 0x2000000000000 > 0)
            result = (result * 0x1000162E525EE054754457D5995292026) >> 128;
        if (x & 0x1000000000000 > 0)
            result = (result * 0x10000B17255775C040618BF4A4ADE83FC) >> 128;
        if (x & 0x800000000000 > 0) result = (result * 0x1000058B91B5BC9AE2EED81E9B7D4CFAB) >> 128;
        if (x & 0x400000000000 > 0) result = (result * 0x100002C5C89D5EC6CA4D7C8ACC017B7C9) >> 128;
        if (x & 0x200000000000 > 0) result = (result * 0x10000162E43F4F831060E02D839A9D16D) >> 128;
        if (x & 0x100000000000 > 0) result = (result * 0x100000B1721BCFC99D9F890EA06911763) >> 128;
        if (x & 0x80000000000 > 0) result = (result * 0x10000058B90CF1E6D97F9CA14DBCC1628) >> 128;
        if (x & 0x40000000000 > 0) result = (result * 0x1000002C5C863B73F016468F6BAC5CA2B) >> 128;
        if (x & 0x20000000000 > 0) result = (result * 0x100000162E430E5A18F6119E3C02282A5) >> 128;
        if (x & 0x10000000000 > 0) result = (result * 0x1000000B1721835514B86E6D96EFD1BFE) >> 128;
        if (x & 0x8000000000 > 0) result = (result * 0x100000058B90C0B48C6BE5DF846C5B2EF) >> 128;
        if (x & 0x4000000000 > 0) result = (result * 0x10000002C5C8601CC6B9E94213C72737A) >> 128;
        if (x & 0x2000000000 > 0) result = (result * 0x1000000162E42FFF037DF38AA2B219F06) >> 128;
        if (x & 0x1000000000 > 0) result = (result * 0x10000000B17217FBA9C739AA5819F44F9) >> 128;
        if (x & 0x800000000 > 0) result = (result * 0x1000000058B90BFCDEE5ACD3C1CEDC823) >> 128;
        if (x & 0x400000000 > 0) result = (result * 0x100000002C5C85FE31F35A6A30DA1BE50) >> 128;
        if (x & 0x200000000 > 0) result = (result * 0x10000000162E42FF0999CE3541B9FFFCF) >> 128;
        if (x & 0x100000000 > 0) result = (result * 0x100000000B17217F80F4EF5AADDA45554) >> 128;
        if (x & 0x80000000 > 0) result = (result * 0x10000000058B90BFBF8479BD5A81B51AD) >> 128;
        if (x & 0x40000000 > 0) result = (result * 0x1000000002C5C85FDF84BD62AE30A74CC) >> 128;
        if (x & 0x20000000 > 0) result = (result * 0x100000000162E42FEFB2FED257559BDAA) >> 128;
        if (x & 0x10000000 > 0) result = (result * 0x1000000000B17217F7D5A7716BBA4A9AE) >> 128;
        if (x & 0x8000000 > 0) result = (result * 0x100000000058B90BFBE9DDBAC5E109CCE) >> 128;
        if (x & 0x4000000 > 0) result = (result * 0x10000000002C5C85FDF4B15DE6F17EB0D) >> 128;
        if (x & 0x2000000 > 0) result = (result * 0x1000000000162E42FEFA494F1478FDE05) >> 128;
        if (x & 0x1000000 > 0) result = (result * 0x10000000000B17217F7D20CF927C8E94C) >> 128;
        if (x & 0x800000 > 0) result = (result * 0x1000000000058B90BFBE8F71CB4E4B33D) >> 128;
        if (x & 0x400000 > 0) result = (result * 0x100000000002C5C85FDF477B662B26945) >> 128;
        if (x & 0x200000 > 0) result = (result * 0x10000000000162E42FEFA3AE53369388C) >> 128;
        if (x & 0x100000 > 0) result = (result * 0x100000000000B17217F7D1D351A389D40) >> 128;
        if (x & 0x80000 > 0) result = (result * 0x10000000000058B90BFBE8E8B2D3D4EDE) >> 128;
        if (x & 0x40000 > 0) result = (result * 0x1000000000002C5C85FDF4741BEA6E77E) >> 128;
        if (x & 0x20000 > 0) result = (result * 0x100000000000162E42FEFA39FE95583C2) >> 128;
        if (x & 0x10000 > 0) result = (result * 0x1000000000000B17217F7D1CFB72B45E1) >> 128;
        if (x & 0x8000 > 0) result = (result * 0x100000000000058B90BFBE8E7CC35C3F0) >> 128;
        if (x & 0x4000 > 0) result = (result * 0x10000000000002C5C85FDF473E242EA38) >> 128;
        if (x & 0x2000 > 0) result = (result * 0x1000000000000162E42FEFA39F02B772C) >> 128;
        if (x & 0x1000 > 0) result = (result * 0x10000000000000B17217F7D1CF7D83C1A) >> 128;
        if (x & 0x800 > 0) result = (result * 0x1000000000000058B90BFBE8E7BDCBE2E) >> 128;
        if (x & 0x400 > 0) result = (result * 0x100000000000002C5C85FDF473DEA871F) >> 128;
        if (x & 0x200 > 0) result = (result * 0x10000000000000162E42FEFA39EF44D91) >> 128;
        if (x & 0x100 > 0) result = (result * 0x100000000000000B17217F7D1CF79E949) >> 128;
        if (x & 0x80 > 0) result = (result * 0x10000000000000058B90BFBE8E7BCE544) >> 128;
        if (x & 0x40 > 0) result = (result * 0x1000000000000002C5C85FDF473DE6ECA) >> 128;
        if (x & 0x20 > 0) result = (result * 0x100000000000000162E42FEFA39EF366F) >> 128;
        if (x & 0x10 > 0) result = (result * 0x1000000000000000B17217F7D1CF79AFA) >> 128;
        if (x & 0x8 > 0) result = (result * 0x100000000000000058B90BFBE8E7BCD6D) >> 128;
        if (x & 0x4 > 0) result = (result * 0x10000000000000002C5C85FDF473DE6B2) >> 128;
        if (x & 0x2 > 0) result = (result * 0x1000000000000000162E42FEFA39EF358) >> 128;
        if (x & 0x1 > 0) result = (result * 0x10000000000000000B17217F7D1CF79AB) >> 128;

        result >>= uint256(int256(63 - (x >> 64)));
        require(result <= uint256(int256(MAX_64x64)), "ABDK.exp_2-2");

        return int128(int256(result));
    }

    /**
     * Calculate natural exponent of x.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function exp(int128 x) internal pure returns (int128) {
        require(x < 0x400000000000000000, "ABDK.exp");
        // Overflow

        if (x < -0x400000000000000000) return 0;
        // Underflow

        return exp_2(int128((int256(x) * 0x171547652B82FE1777D0FFDA0D23A7D12) >> 128));
    }

    /**
     * Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
     * integer numbers.  Revert on overflow or when y is zero.
     *
     * @param x unsigned 256-bit integer number
     * @param y unsigned 256-bit integer number
     * @return unsigned 64.64-bit fixed point number
     */
    function divuu(uint256 x, uint256 y) private pure returns (uint128) {
        require(y != 0, "ABDK.divuu-1");

        uint256 result;

        if (x <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF) result = (x << 64) / y;
        else {
            uint256 msb = 192;
            uint256 xc = x >> 192;
            if (xc >= 0x100000000) {
                xc >>= 32;
                msb += 32;
            }
            if (xc >= 0x10000) {
                xc >>= 16;
                msb += 16;
            }
            if (xc >= 0x100) {
                xc >>= 8;
                msb += 8;
            }
            if (xc >= 0x10) {
                xc >>= 4;
                msb += 4;
            }
            if (xc >= 0x4) {
                xc >>= 2;
                msb += 2;
            }
            if (xc >= 0x2) msb += 1;
            // No need to shift xc anymore

            result = (x << (255 - msb)) / (((y - 1) >> (msb - 191)) + 1);
            require(result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF, "ABDK.divuu-2");

            uint256 hi = result * (y >> 128);
            uint256 lo = result * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);

            uint256 xh = x >> 192;
            uint256 xl = x << 64;

            if (xl < lo) xh -= 1;
            xl -= lo;
            // We rely on overflow behavior here
            lo = hi << 128;
            if (xl < lo) xh -= 1;
            xl -= lo;
            // We rely on overflow behavior here

            assert(xh == hi >> 128);

            result += xl / y;
        }

        require(result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF, "ABDK.divuu-3");
        return uint128(result);
    }

    /**
     * Calculate sqrt (x) rounding down, where x is unsigned 256-bit integer
     * number.
     *
     * @param x unsigned 256-bit integer number
     * @return unsigned 128-bit integer number
     */
    function sqrtu(uint256 x) private pure returns (uint128) {
        if (x == 0) return 0;
        else {
            uint256 xx = x;
            uint256 r = 1;
            if (xx >= 0x100000000000000000000000000000000) {
                xx >>= 128;
                r <<= 64;
            }
            if (xx >= 0x10000000000000000) {
                xx >>= 64;
                r <<= 32;
            }
            if (xx >= 0x100000000) {
                xx >>= 32;
                r <<= 16;
            }
            if (xx >= 0x10000) {
                xx >>= 16;
                r <<= 8;
            }
            if (xx >= 0x100) {
                xx >>= 8;
                r <<= 4;
            }
            if (xx >= 0x10) {
                xx >>= 4;
                r <<= 2;
            }
            if (xx >= 0x8) {
                r <<= 1;
            }
            r = (r + x / r) >> 1;
            r = (r + x / r) >> 1;
            r = (r + x / r) >> 1;
            r = (r + x / r) >> 1;
            r = (r + x / r) >> 1;
            r = (r + x / r) >> 1;
            r = (r + x / r) >> 1;
            // Seven iterations should be enough
            uint256 r1 = x / r;
            return uint128(r < r1 ? r : r1);
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.21;

import "./ABDKMath64x64.sol";

library ConverterDec18 {
    using ABDKMath64x64 for int128;
    /*
     * Minimum value signed 64.64-bit fixed point number may have.
     */
    int128 private constant MIN_64x64 = -0x80000000000000000000000000000000;

    /*
     * Maximum value signed 64.64-bit fixed point number may have.
     */
    int128 private constant MAX_64x64 = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

    int256 private constant DECIMALS = 10**18;

    int128 private constant ONE_64x64 = 0x010000000000000000;

    int128 public constant HALF_TBPS = 92233720368548; //1e-5 * 0.5 * 2**64

    // convert tenth of basis point to dec 18:
    uint256 public constant TBPSTODEC18 = 0x9184e72a000; // hex(10^18 * 10^-5)=(10^13)
    // convert tenth of basis point to ABDK 64x64:
    int128 public constant TBPSTOABDK = 0xa7c5ac471b48; // hex(2^64 * 10^-5)
    // convert two-digit integer reprentation to ABDK
    int128 public constant TDRTOABDK = 0x28f5c28f5c28f5c; // hex(2^64 * 10^-2)

    function tbpsToDec18(uint16 Vtbps) internal pure returns (uint256) {
        return TBPSTODEC18 * uint256(Vtbps);
    }

    function tbpsToABDK(uint16 Vtbps) internal pure returns (int128) {
        return int128(uint128(TBPSTOABDK) * uint128(Vtbps));
    }

    function TDRToABDK(uint16 V2Tdr) internal pure returns (int128) {
        return int128(uint128(TDRTOABDK) * uint128(V2Tdr));
    }

    function ABDKToTbps(int128 Vabdk) internal pure returns (uint16) {
        // add 0.5 * 1e-5 to ensure correct rounding to tenth of bps
        return uint16(uint128(Vabdk.add(HALF_TBPS) / TBPSTOABDK));
    }

    function fromDec18(int256 x) internal pure returns (int128) {
        int256 result = (x * ONE_64x64) / DECIMALS;
        require(x >= MIN_64x64 && x <= MAX_64x64, "result out of range");
        return int128(result);
    }

    function toDec18(int128 x) internal pure returns (int256) {
        return (int256(x) * DECIMALS) / ONE_64x64;
    }

    function toUDec18(int128 x) internal pure returns (uint256) {
        require(x >= 0, "negative value");
        return uint256(toDec18(x));
    }

    function toUDecN(int128 x, uint8 decimals) internal pure returns (uint256) {
        require(x >= 0, "negative value");
        return uint256((int256(x) * int256(10**decimals)) / ONE_64x64);
    }

    function fromDecN(int256 x, uint8 decimals) internal pure returns (int128) {
        int256 result = (x * ONE_64x64) / int256(10**decimals);
        require(x >= MIN_64x64 && x <= MAX_64x64, "result out of range");
        return int128(result);
    }
}

// SPDX-License-Identifier: MIT

pragma solidity 0.8.21;

/**
 * @title Library for managing loan sets.
 *
 * @notice Sets have the following properties:
 *
 * - Elements are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Elements are enumerated in O(n). No guarantees are made on the ordering.
 *
 * Include with `using EnumerableBytes4Set for EnumerableBytes4Set.Bytes4Set;`.
 * */
library EnumerableBytes4Set {
    struct Bytes4Set {
        // Position of the value in the `values` array, plus 1 because index 0
        // means a value is not in the set.
        mapping(bytes4 => uint256) index;
        bytes4[] values;
    }

    /**
     * @notice Add a value to a set. O(1).
     *
     * @param set The set of values.
     * @param value The new value to add.
     *
     * @return False if the value was already in the set.
     */
    function addBytes4(Bytes4Set storage set, bytes4 value) internal returns (bool) {
        if (!contains(set, value)) {
            set.values.push(value);
            set.index[value] = set.values.length;
            return true;
        } else {
            return false;
        }
    }

    /**
     * @notice Remove a value from a set. O(1).
     *
     * @param set The set of values.
     * @param value The value to remove.
     *
     * @return False if the value was not present in the set.
     */
    function removeBytes4(Bytes4Set storage set, bytes4 value) internal returns (bool) {
        if (contains(set, value)) {
            uint256 toDeleteIndex = set.index[value] - 1;
            uint256 lastIndex = set.values.length - 1;

            /// If the element we're deleting is the last one,
            /// we can just remove it without doing a swap.
            if (lastIndex != toDeleteIndex) {
                bytes4 lastValue = set.values[lastIndex];

                /// Move the last value to the index where the deleted value is.
                set.values[toDeleteIndex] = lastValue;

                /// Update the index for the moved value.
                set.index[lastValue] = toDeleteIndex + 1; // All indexes are 1-based
            }

            /// Delete the index entry for the deleted value.
            delete set.index[value];

            /// Delete the old entry for the moved value.
            set.values.pop();

            return true;
        } else {
            return false;
        }
    }

    /**
     * @notice Find out whether a value exists in the set.
     *
     * @param set The set of values.
     * @param value The value to find.
     *
     * @return True if the value is in the set. O(1).
     */
    function contains(Bytes4Set storage set, bytes4 value) internal view returns (bool) {
        return set.index[value] != 0;
    }

    /**
     * @notice Get all set values.
     *
     * @param set The set of values.
     * @param start The offset of the returning set.
     * @param count The limit of number of values to return.
     *
     * @return output An array with all values in the set. O(N).
     *
     * @dev Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * WARNING: This function may run out of gas on large sets: use {length} and
     * {get} instead in these cases.
     */
    function enumerate(
        Bytes4Set storage set,
        uint256 start,
        uint256 count
    ) internal view returns (bytes4[] memory output) {
        uint256 end = start + count;
        require(end >= start, "addition overflow");
        end = set.values.length < end ? set.values.length : end;
        if (end == 0 || start >= end) {
            return output;
        }

        output = new bytes4[](end - start);
        for (uint256 i; i < end - start; i++) {
            output[i] = set.values[i + start];
        }
        return output;
    }

    /**
     * @notice Get the legth of the set.
     *
     * @param set The set of values.
     *
     * @return the number of elements on the set. O(1).
     */
    function length(Bytes4Set storage set) internal view returns (uint256) {
        return set.values.length;
    }

    /**
     * @notice Get an item from the set by its index.
     *
     * @dev Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     *
     * @param set The set of values.
     * @param index The index of the value to return.
     *
     * @return the element stored at position `index` in the set. O(1).
     */
    function get(Bytes4Set storage set, uint256 index) internal view returns (bytes4) {
        return set.values[index];
    }
}

// SPDX-License-Identifier: MIT

pragma solidity 0.8.21;

/**
 * @dev Library for managing
 * https://en.wikipedia.org/wiki/Set_(abstract_data_type)[sets] of primitive
 * types.
 *
 * Sets have the following properties:
 *
 * - Elements are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Elements are enumerated in O(n). No guarantees are made on the ordering.
 *
 * ```
 * contract Example {
 *     // Add the library methods
 *     using EnumerableSet for EnumerableSet.AddressSet;
 *
 *     // Declare a set state variable
 *     EnumerableSet.AddressSet private mySet;
 * }
 * ```
 *
 * As of v3.3.0, sets of type `bytes32` (`Bytes32Set`), `address` (`AddressSet`)
 * and `uint256` (`UintSet`) are supported.
 */
library EnumerableSetUpgradeable {
    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Set type with
    // bytes32 values.
    // The Set implementation uses private functions, and user-facing
    // implementations (such as AddressSet) are just wrappers around the
    // underlying Set.
    // This means that we can only create new EnumerableSets for types that fit
    // in bytes32.

    struct Set {
        // Storage of set values
        bytes32[] _values;
        // Position of the value in the `values` array, plus 1 because index 0
        // means a value is not in the set.
        mapping(bytes32 => uint256) _indexes;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function _add(Set storage set, bytes32 value) private returns (bool) {
        if (!_contains(set, value)) {
            set._values.push(value);
            // The value is stored at length-1, but we add 1 to all indexes
            // and use 0 as a sentinel value
            set._indexes[value] = set._values.length;
            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function _remove(Set storage set, bytes32 value) private returns (bool) {
        // We read and store the value's index to prevent multiple reads from the same storage slot
        uint256 valueIndex = set._indexes[value];

        if (valueIndex != 0) {
            // Equivalent to contains(set, value)
            // To delete an element from the _values array in O(1), we swap the element to delete with the last one in
            // the array, and then remove the last element (sometimes called as 'swap and pop').
            // This modifies the order of the array, as noted in {at}.

            uint256 toDeleteIndex = valueIndex - 1;
            uint256 lastIndex = set._values.length - 1;

            // When the value to delete is the last one, the swap operation is unnecessary. However, since this occurs
            // so rarely, we still do the swap anyway to avoid the gas cost of adding an 'if' statement.

            bytes32 lastvalue = set._values[lastIndex];

            // Move the last value to the index where the value to delete is
            set._values[toDeleteIndex] = lastvalue;
            // Update the index for the moved value
            set._indexes[lastvalue] = toDeleteIndex + 1; // All indexes are 1-based

            // Delete the slot where the moved value was stored
            set._values.pop();

            // Delete the index for the deleted slot
            delete set._indexes[value];

            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function _contains(Set storage set, bytes32 value) private view returns (bool) {
        return set._indexes[value] != 0;
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function _length(Set storage set) private view returns (uint256) {
        return set._values.length;
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function _at(Set storage set, uint256 index) private view returns (bytes32) {
        require(set._values.length > index, "EnumerableSet: idx out of bounds");
        return set._values[index];
    }

    // Bytes32Set

    struct Bytes32Set {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _add(set._inner, value);
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _remove(set._inner, value);
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(Bytes32Set storage set, bytes32 value) internal view returns (bool) {
        return _contains(set._inner, value);
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(Bytes32Set storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(Bytes32Set storage set, uint256 index) internal view returns (bytes32) {
        return _at(set._inner, index);
    }

    // AddressSet

    struct AddressSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(AddressSet storage set, address value) internal returns (bool) {
        return _add(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(AddressSet storage set, address value) internal returns (bool) {
        return _remove(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(AddressSet storage set, address value) internal view returns (bool) {
        return _contains(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(AddressSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(AddressSet storage set, uint256 index) internal view returns (address) {
        return address(uint160(uint256(_at(set._inner, index))));
    }

    function enumerate(
        AddressSet storage set,
        uint256 start,
        uint256 count
    ) internal view returns (address[] memory output) {
        uint256 end = start + count;
        require(end >= start, "addition overflow");
        uint256 len = length(set);
        end = len < end ? len : end;
        if (end == 0 || start >= end) {
            return output;
        }

        output = new address[](end - start);
        for (uint256 i; i < end - start; i++) {
            output[i] = at(set, i + start);
        }
        return output;
    }

    function enumerateAll(AddressSet storage set) internal view returns (address[] memory output) {
        return enumerate(set, 0, length(set));
    }

    // UintSet

    struct UintSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(UintSet storage set, uint256 value) internal returns (bool) {
        return _add(set._inner, bytes32(value));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(UintSet storage set, uint256 value) internal returns (bool) {
        return _remove(set._inner, bytes32(value));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(UintSet storage set, uint256 value) internal view returns (bool) {
        return _contains(set._inner, bytes32(value));
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function length(UintSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(UintSet storage set, uint256 index) internal view returns (uint256) {
        return uint256(_at(set._inner, index));
    }
}

// SPDX-License-Identifier: MIT

pragma solidity 0.8.21;

library Utils {
    function stringToBytes32(string memory source) internal pure returns (bytes32 result) {
        bytes memory tempEmptyStringTest = bytes(source);
        if (tempEmptyStringTest.length == 0) {
            return 0x0;
        }

        assembly {
            result := mload(add(source, 32))
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.21;

import "@openzeppelin/contracts/security/ReentrancyGuard.sol";
import "@openzeppelin/contracts/security/Pausable.sol";

import "../../interface/IShareTokenFactory.sol";
import "../../libraries/ABDKMath64x64.sol";
import "./../functions/AMMPerpLogic.sol";
import "../../libraries/EnumerableSetUpgradeable.sol";
import "../../libraries/EnumerableBytes4Set.sol";
import "../../governance/Maintainable.sol";

/* solhint-disable max-states-count */
contract PerpStorage is Maintainable, Pausable, ReentrancyGuard {
    using ABDKMath64x64 for int128;
    using EnumerableSetUpgradeable for EnumerableSetUpgradeable.AddressSet;
    using EnumerableBytes4Set for EnumerableBytes4Set.Bytes4Set; // enumerable map of bytes4 or addresses
    /**
     * @notice  Perpetual state:
     *          - INVALID:      Uninitialized or not non-existent perpetual.
     *          - INITIALIZING: Only when LiquidityPoolData.isRunning == false. Traders cannot perform operations.
     *          - NORMAL:       Full functional state. Traders are able to perform all operations.
     *          - EMERGENCY:    Perpetual is unsafe and the perpetual needs to be settled.
     *          - SETTLE:       Perpetual ready to be settled
     *          - CLEARED:      All margin accounts are cleared. Traders can withdraw remaining margin balance.
     */
    enum PerpetualState {
        INVALID,
        INITIALIZING,
        NORMAL,
        EMERGENCY,
        SETTLE,
        CLEARED
    }

    // margin and liquidity pool are held in 'collateral currency' which can be either of
    // quote currency, base currency, or quanto currency
    // solhint-disable-next-line const-name-snakecase
    int128 internal constant ONE_64x64 = 0x10000000000000000; // 2^64
    int128 internal constant FUNDING_INTERVAL_SEC = 0x70800000000000000000; //3600 * 8 * 0x10000000000000000 = 8h in seconds scaled by 2^64 for ABDKMath64x64
    int128 internal constant MIN_NUM_LOTS_PER_POSITION = 0x0a0000000000000000; // 10, minimal position size in number of lots
    uint8 internal constant MASK_ORDER_CANCELLED = 0x1;
    uint8 internal constant MASK_ORDER_EXECUTED = 0x2;
    // at target, 1% of missing amount is transferred
    // at every rebalance
    uint8 internal iPoolCount;
    // delay required for trades to mitigate oracle front-running in seconds
    uint8 internal iTradeDelaySec;
    address internal ammPerpLogic;

    IShareTokenFactory internal shareTokenFactory;

    //pool id (incremental index, starts from 1) => pool data
    mapping(uint8 => LiquidityPoolData) internal liquidityPools;

    //perpetual id  => pool id
    mapping(uint24 => uint8) internal perpetualPoolIds;

    address internal orderBookFactory;

    /**
     * @notice  Data structure to store oracle price data.
     */
    struct PriceTimeData {
        int128 fPrice;
        uint64 time;
    }

    /**
     * @notice  Data structure to store user margin information.
     */
    struct MarginAccount {
        int128 fLockedInValueQC; // unrealized value locked-in when trade occurs
        int128 fCashCC; // cash in collateral currency (base, quote, or quanto)
        int128 fPositionBC; // position in base currency (e.g., 1 BTC for BTCUSD)
        int128 fUnitAccumulatedFundingStart; // accumulated funding rate
    }

    /**
     * @notice  Store information for a given perpetual market.
     */
    struct PerpetualData {
        // ------ 0
        uint8 poolId;
        uint24 id;
        int32 fInitialMarginRate; //parameter: initial margin
        int32 fSigma2; // parameter: volatility of base-quote pair
        uint32 iLastFundingTime; //timestamp since last funding rate payment
        int32 fDFCoverNRate; // parameter: cover-n rule for default fund. E.g., fDFCoverNRate=0.05 -> we try to cover 5% of active accounts with default fund
        int32 fMaintenanceMarginRate; // parameter: maintenance margin
        PerpetualState state; // Perpetual AMM state
        AMMPerpLogic.CollateralCurrency eCollateralCurrency; //parameter: in what currency is the collateral held?
        // uint16 minimalSpreadTbps; //parameter: minimal spread between long and short perpetual price
        // ------ 1
        bytes4 S2BaseCCY; //base currency of S2
        bytes4 S2QuoteCCY; //quote currency of S2
        uint16 incentiveSpreadTbps; //parameter: maximum spread added to the PD
        uint16 minimalSpreadTbps; //parameter: minimal spread between long and short perpetual price
        bytes4 S3BaseCCY; //base currency of S3
        bytes4 S3QuoteCCY; //quote currency of S3
        int32 fSigma3; // parameter: volatility of quanto-quote pair
        int32 fRho23; // parameter: correlation of quanto/base returns
        uint16 liquidationPenaltyRateTbps; //parameter: penalty if AMM closes the position and not the trader
        //------- 2
        PriceTimeData currentMarkPremiumRate; //relative diff to index price EMA, used for markprice.
        //------- 3
        int128 premiumRatesEMA; // EMA of premium rate
        int128 fUnitAccumulatedFunding; //accumulated funding in collateral currency
        //------- 4
        int128 fOpenInterest; //open interest is the larger of the amount of long and short positions in base currency
        int128 fTargetAMMFundSize; //target liquidity pool funds to allocate to the AMM
        //------- 5
        int128 fCurrentTraderExposureEMA; // trade amounts (storing absolute value)
        int128 fCurrentFundingRate; // current instantaneous funding rate
        //------- 6
        int128 fLotSizeBC; //parameter: minimal trade unit (in base currency) to avoid dust positions
        int128 fReferralRebateCC; //parameter: referall rebate in collateral currency
        //------- 7
        int128 fTargetDFSize; // target default fund size
        int128 fkStar; // signed trade size that minimizes the AMM risk
        //------- 8
        int128 fAMMTargetDD; // parameter: target distance to default (=inverse of default probability)
        int128 fAMMMinSizeCC; // parameter: minimal size of AMM pool, regardless of current exposure
        //------- 9
        int128 fMinimalTraderExposureEMA; // parameter: minimal value for fCurrentTraderExposureEMA that we don't want to undershoot
        int128 fMinimalAMMExposureEMA; // parameter: minimal abs value for fCurrentAMMExposureEMA that we don't want to undershoot
        //------- 10
        int128 fSettlementS3PriceData; //quanto index
        int128 fSettlementS2PriceData; //base-quote pair. Used as last price in normal state.
        //------- 11
        int128 fTotalMarginBalance; //calculated for settlement, in collateral currency
        int32 fMarkPriceEMALambda; // parameter: Lambda parameter for EMA used in mark-price for funding rates
        int32 fFundingRateClamp; // parameter: funding rate clamp between which we charge 1bps
        int32 fMaximalTradeSizeBumpUp; // parameter: >1, users can create a maximal position of size fMaximalTradeSizeBumpUp*fCurrentAMMExposureEMA
        uint32 iLastTargetPoolSizeTime; //timestamp (seconds) since last update of fTargetDFSize and fTargetAMMFundSize
        //------- 12

        //-------
        int128[2] fStressReturnS3; // parameter: negative and positive stress returns for quanto-quote asset
        int128[2] fDFLambda; // parameter: EMA lambda for AMM and trader exposure K,k: EMA*lambda + (1-lambda)*K. 0 regular lambda, 1 if current value exceeds past
        int128[2] fCurrentAMMExposureEMA; // 0: negative aggregated exposure (storing negative value), 1: positive
        int128[2] fStressReturnS2; // parameter: negative and positive stress returns for base-quote asset
        // -----
    }

    address internal oracleFactoryAddress;

    // users
    mapping(uint24 => EnumerableSetUpgradeable.AddressSet) internal activeAccounts; //perpetualId => traderAddressSet
    // accounts
    mapping(uint24 => mapping(address => MarginAccount)) internal marginAccounts;
    // delegates
    mapping(address => address) internal delegates;

    // broker maps: poolId -> brokeraddress-> lots contributed
    // contains non-zero entries for brokers. Brokers pay default fund contributions.
    mapping(uint8 => mapping(address => uint32)) internal brokerMap;

    struct LiquidityPoolData {
        bool isRunning; // state
        uint8 iPerpetualCount; // state
        uint8 id; // parameter: index, starts from 1
        int32 fCeilPnLShare; // parameter: cap on the share of PnL allocated to liquidity providers
        uint8 marginTokenDecimals; // parameter: decimals of margin token, inferred from token contract
        uint16 iTargetPoolSizeUpdateTime; //parameter: timestamp in seconds. How often we update the pool's target size
        address marginTokenAddress; //parameter: address of the margin token
        // -----
        uint64 prevAnchor; // state: keep track of timestamp since last withdrawal was initiated
        int128 fRedemptionRate; // state: used for settlement in case of AMM default
        address shareTokenAddress; // parameter
        // -----
        int128 fPnLparticipantsCashCC; // state: addLiquidity/withdrawLiquidity + profit/loss - rebalance
        int128 fTargetAMMFundSize; // state: target liquidity for all perpetuals in pool (sum)
        // -----
        int128 fDefaultFundCashCC; // state: profit/loss
        int128 fTargetDFSize; // state: target default fund size for all perpetuals in pool
        // -----
        int128 fBrokerCollateralLotSize; // param:how much collateral do brokers deposit when providing "1 lot" (not trading lot)
        uint128 prevTokenAmount; // state
        // -----
        uint128 nextTokenAmount; // state
        uint128 totalSupplyShareToken; // state
        // -----
        int128 fBrokerFundCashCC; // state: amount of cash in broker fund
    }

    address internal treasuryAddress; // address for the protocol treasury

    //pool id => perpetual id list
    mapping(uint8 => uint24[]) internal perpetualIds;

    //pool id => perpetual id => data
    mapping(uint8 => mapping(uint24 => PerpetualData)) internal perpetuals;

    /// @dev flag whether MarginTradeOrder was already executed or cancelled
    mapping(bytes32 => uint8) internal executedOrCancelledOrders;

    //proxy
    mapping(bytes32 => EnumerableBytes4Set.Bytes4Set) internal moduleActiveFuncSignatureList;
    mapping(bytes32 => address) internal moduleNameToAddress;
    mapping(address => bytes32) internal moduleAddressToModuleName;

    // fee structure
    struct VolumeEMA {
        int128 fTradingVolumeEMAusd; //trading volume EMA in usd
        uint64 timestamp; // timestamp of last trade
    }

    uint256[] public traderVolumeTiers; // dec18, regardless of token
    uint256[] public brokerVolumeTiers; // dec18, regardless of token
    uint16[] public traderVolumeFeesTbps;
    uint16[] public brokerVolumeFeesTbps;
    mapping(uint24 => address) public perpBaseToUSDOracle;
    mapping(uint24 => int128) public perpToLastBaseToUSD;
    mapping(uint8 => mapping(address => VolumeEMA)) public traderVolumeEMA;
    mapping(uint8 => mapping(address => VolumeEMA)) public brokerVolumeEMA;
    uint64 public lastBaseToUSDUpdateTs;

    // liquidity withdrawals
    struct WithdrawRequest {
        address lp;
        uint256 shareTokens;
        uint64 withdrawTimestamp;
    }

    mapping(address => mapping(uint8 => WithdrawRequest)) internal lpWithdrawMap;

    // users who initiated withdrawals are registered here
    mapping(uint8 => EnumerableSetUpgradeable.AddressSet) internal activeWithdrawals; //poolId => lpAddressSet

    mapping(uint8 => bool) public liquidityProvisionIsPaused;
}
/* solhint-enable max-states-count */

// SPDX-License-Identifier: MIT
pragma solidity 0.8.21;

import "../../libraries/ABDKMath64x64.sol";
import "../../libraries/ConverterDec18.sol";
import "../../perpetual/interfaces/IAMMPerpLogic.sol";
import "@openzeppelin/contracts/access/Ownable.sol";

contract AMMPerpLogic is Ownable, IAMMPerpLogic {
    using ABDKMath64x64 for int128;
    /* solhint-disable const-name-snakecase */
    int128 internal constant ONE_64x64 = 0x10000000000000000; // 2^64
    int128 internal constant TWO_64x64 = 0x20000000000000000; // 2*2^64
    int128 internal constant FOUR_64x64 = 0x40000000000000000; //4*2^64
    int128 internal constant HALF_64x64 = 0x8000000000000000; //0.5*2^64
    int128 internal constant TWENTY_64x64 = 0x140000000000000000; //20*2^64
    int128 private constant CDF_CONST_0 = 0x023a6ce358298c;
    int128 private constant CDF_CONST_1 = -0x216c61522a6f3f;
    int128 private constant CDF_CONST_2 = 0xc9320d9945b6c3;
    int128 private constant CDF_CONST_3 = -0x01bcfd4bf0995aaf;
    int128 private constant CDF_CONST_4 = -0x086de76427c7c501;
    int128 private constant CDF_CONST_5 = 0x749741d084e83004;
    int128 private constant CDF_CONST_6 = 0xcc42299ea1b28805;
    int128 private constant CDF_CONST_7 = 0x0281b263fec4e0a007;
    int128 private constant EXPM1_Q0 = 0x0a26c00000000000000000;
    int128 private constant EXPM1_Q1 = 0x0127500000000000000000;
    int128 private constant EXPM1_P0 = 0x0513600000000000000000;
    int128 private constant EXPM1_P1 = 0x27600000000000000000;
    int128 private constant MAX_64x64 = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

    /* solhint-enable const-name-snakecase */

    enum CollateralCurrency {
        QUOTE,
        BASE,
        QUANTO
    }

    struct AMMVariables {
        // all variables are
        // signed 64.64-bit fixed point number
        int128 fLockedValue1; // L1 in quote currency
        int128 fPoolM1; // M1 in quote currency
        int128 fPoolM2; // M2 in base currency
        int128 fPoolM3; // M3 in quanto currency
        int128 fAMM_K2; // AMM exposure (positive if trader long)
        int128 fCurrentTraderExposureEMA; // current average unsigned trader exposure
    }

    struct MarketVariables {
        int128 fIndexPriceS2; // base index
        int128 fIndexPriceS3; // quanto index
        int128 fSigma2; // standard dev of base currency
        int128 fSigma3; // standard dev of quanto currency
        int128 fRho23; // correlation base/quanto currency
    }

    /**
     * Calculate a EWMA when the last observation happened n periods ago
     * @dev Given is x_t = (1 - lambda) * mean + lambda * x_t-1, and x_0 = _newObs
     * it returns the value of x_deltaTime
     * @param _mean long term mean
     * @param _newObs observation deltaTime periods ago
     * @param _fLambda lambda of the EWMA
     * @param _deltaTime number of periods elapsed
     * @return result EWMA at deltaPeriods
     */
    function _emaWithTimeJumps(
        uint16 _mean,
        uint16 _newObs,
        int128 _fLambda,
        uint256 _deltaTime
    ) internal pure returns (int128 result) {
        _fLambda = _fLambda.pow(_deltaTime);
        result = ConverterDec18.tbpsToABDK(_mean).mul(ONE_64x64.sub(_fLambda));
        result = result.add(_fLambda.mul(ConverterDec18.tbpsToABDK(_newObs)));
    }

    /**
     *  Calculate the normal CDF value of _fX, i.e.,
     *  k=P(X<=_fX), for X~normal(0,1)
     *  The approximation is of the form
     *  Phi(x) = 1 - phi(x) / (x + exp(p(x))),
     *  where p(x) is a polynomial of degree 6
     *  @param _fX signed 64.64-bit fixed point number
     *  @return fY approximated normal-cdf evaluated at X
     */
    function _normalCDF(int128 _fX) internal pure returns (int128 fY) {
        bool isNegative = _fX < 0;
        if (isNegative) {
            _fX = _fX.neg();
        }
        if (_fX > FOUR_64x64) {
            fY = int128(0);
        } else {
            fY = _fX.mul(CDF_CONST_0).add(CDF_CONST_1);
            fY = _fX.mul(fY).add(CDF_CONST_2);
            fY = _fX.mul(fY).add(CDF_CONST_3);
            fY = _fX.mul(fY).add(CDF_CONST_4);
            fY = _fX.mul(fY).add(CDF_CONST_5).mul(_fX).neg().exp();
            fY = fY.mul(CDF_CONST_6).add(_fX);
            fY = _fX.mul(_fX).mul(HALF_64x64).neg().exp().div(CDF_CONST_7).div(fY);
        }
        if (!isNegative) {
            fY = ONE_64x64.sub(fY);
        }
        return fY;
    }

    /**
     *  Calculate the target size for the default fund
     *
     *  @param _fK2AMM       signed 64.64-bit fixed point number, Conservative negative[0]/positive[1] AMM exposure
     *  @param _fk2Trader    signed 64.64-bit fixed point number, Conservative (absolute) trader exposure
     *  @param _fCoverN      signed 64.64-bit fixed point number, cover-n rule for default fund parameter
     *  @param fStressRet2   signed 64.64-bit fixed point number, negative[0]/positive[1] stress returns for base/quote pair
     *  @param fStressRet3   signed 64.64-bit fixed point number, negative[0]/positive[1] stress returns for quanto/quote currency
     *  @param fIndexPrices  signed 64.64-bit fixed point number, spot price for base/quote[0] and quanto/quote[1] pairs
     *  @param _eCCY         enum that specifies in which currency the collateral is held: QUOTE, BASE, QUANTO
     *  @return approximated normal-cdf evaluated at X
     */
    function calculateDefaultFundSize(
        int128[2] memory _fK2AMM,
        int128 _fk2Trader,
        int128 _fCoverN,
        int128[2] memory fStressRet2,
        int128[2] memory fStressRet3,
        int128[2] memory fIndexPrices,
        AMMPerpLogic.CollateralCurrency _eCCY
    ) external pure override returns (int128) {
        require(_fK2AMM[0] < 0, "_fK2AMM[0] must be negative");
        require(_fK2AMM[1] > 0, "_fK2AMM[1] must be positive");
        require(_fk2Trader > 0, "_fk2Trader must be positive");

        int128[2] memory fEll;
        // downward stress scenario
        fEll[0] = (_fK2AMM[0].abs().add(_fk2Trader.mul(_fCoverN))).mul(
            ONE_64x64.sub((fStressRet2[0].exp()))
        );
        // upward stress scenario
        fEll[1] = (_fK2AMM[1].abs().add(_fk2Trader.mul(_fCoverN))).mul(
            (fStressRet2[1].exp().sub(ONE_64x64))
        );
        int128 fIstar;
        if (_eCCY == AMMPerpLogic.CollateralCurrency.BASE) {
            fIstar = fEll[0].div(fStressRet2[0].exp());
            int128 fI2 = fEll[1].div(fStressRet2[1].exp());
            if (fI2 > fIstar) {
                fIstar = fI2;
            }
        } else if (_eCCY == AMMPerpLogic.CollateralCurrency.QUANTO) {
            fIstar = fEll[0].div(fStressRet3[0].exp());
            int128 fI2 = fEll[1].div(fStressRet3[1].exp());
            if (fI2 > fIstar) {
                fIstar = fI2;
            }
            fIstar = fIstar.mul(fIndexPrices[0].div(fIndexPrices[1]));
        } else {
            assert(_eCCY == AMMPerpLogic.CollateralCurrency.QUOTE);
            if (fEll[0] > fEll[1]) {
                fIstar = fEll[0].mul(fIndexPrices[0]);
            } else {
                fIstar = fEll[1].mul(fIndexPrices[0]);
            }
        }
        return fIstar;
    }

    /**
     *  Calculate the risk neutral Distance to Default (Phi(DD)=default probability) when
     *  there is no quanto currency collateral.
     *  We assume r=0 everywhere.
     *  The underlying distribution is log-normal, hence the log below.
     *  All variables are 64.64-bit fixed point number (or struct thereof)
     *  @param fSigma2 current Market variables (price&params)
     *  @param _fSign signed 64.64-bit fixed point number, sign of denominator of distance to default
     *  @return _fThresh signed 64.64-bit fixed point number, number for which the log is the unnormalized distance to default
     */
    function _calculateRiskNeutralDDNoQuanto(
        int128 fSigma2,
        int128 _fSign,
        int128 _fThresh
    ) internal pure returns (int128) {
        require(_fThresh > 0, "argument to log must be >0");
        int128 _fLogTresh = _fThresh.ln();
        int128 fSigma2_2 = fSigma2.mul(fSigma2);
        int128 fMean = fSigma2_2.div(TWO_64x64).neg();
        int128 fDistanceToDefault = ABDKMath64x64.sub(_fLogTresh, fMean).div(fSigma2);
        // because 1-Phi(x) = Phi(-x) we change the sign if _fSign<0
        // now we would like to get the normal cdf of that beast
        if (_fSign < 0) {
            fDistanceToDefault = fDistanceToDefault.neg();
        }
        return fDistanceToDefault;
    }

    /**
     *  Calculate the standard deviation for the random variable
     *  evolving when quanto currencies are involved.
     *  We assume r=0 everywhere.
     *  All variables are 64.64-bit fixed point number (or struct thereof)
     *  @param _mktVars current Market variables (price&params)
     *  @param _fC3 signed 64.64-bit fixed point number current AMM/Market variables
     *  @param _fC3_2 signed 64.64-bit fixed point number, squared fC3
     *  @return fSigmaZ standard deviation, 64.64-bit fixed point number
     */
    function _calculateStandardDeviationQuanto(
        MarketVariables memory _mktVars,
        int128 _fC3,
        int128 _fC3_2
    ) internal pure returns (int128 fSigmaZ) {
        // fVarA = (exp(sigma2^2) - 1)
        int128 fVarA = _mktVars.fSigma2.mul(_mktVars.fSigma2);

        // fVarB = 2*(exp(sigma2*sigma3*rho) - 1)
        int128 fVarB = _mktVars.fSigma2.mul(_mktVars.fSigma3).mul(_mktVars.fRho23).mul(TWO_64x64);

        // fVarC = exp(sigma3^2) - 1
        int128 fVarC = _mktVars.fSigma3.mul(_mktVars.fSigma3);

        // sigmaZ = fVarA*C^2 + fVarB*C + fVarC
        fSigmaZ = fVarA.mul(_fC3_2).add(fVarB.mul(_fC3)).add(fVarC).sqrt();
    }

    /**
     *  Calculate the risk neutral Distance to Default (Phi(DD)=default probability) when
     *  presence of quanto currency collateral.
     *
     *  We approximate the distribution with a normal distribution
     *  We assume r=0 everywhere.
     *  All variables are 64.64-bit fixed point number
     *  @param _ammVars current AMM/Market variables
     *  @param _mktVars current Market variables (price&params)
     *  @param _fSign 64.64-bit fixed point number, current AMM/Market variables
     *  @return fDistanceToDefault signed 64.64-bit fixed point number
     */
    function _calculateRiskNeutralDDWithQuanto(
        AMMVariables memory _ammVars,
        MarketVariables memory _mktVars,
        int128 _fSign,
        int128 _fThresh
    ) internal pure returns (int128 fDistanceToDefault) {
        require(_fSign > 0, "no sign in quanto case");
        // 1) Calculate C3
        int128 fC3 = _mktVars.fIndexPriceS2.mul(_ammVars.fPoolM2.sub(_ammVars.fAMM_K2)).div(
            _ammVars.fPoolM3.mul(_mktVars.fIndexPriceS3)
        );
        int128 fC3_2 = fC3.mul(fC3);

        // 2) Calculate Variance
        int128 fSigmaZ = _calculateStandardDeviationQuanto(_mktVars, fC3, fC3_2);

        // 3) Calculate mean
        int128 fMean = fC3.add(ONE_64x64);
        // 4) Distance to default
        fDistanceToDefault = _fThresh.sub(fMean).div(fSigmaZ);
    }

    function calculateRiskNeutralPD(
        AMMVariables memory _ammVars,
        MarketVariables memory _mktVars,
        int128 _fTradeAmount,
        bool _withCDF
    ) external view virtual override returns (int128, int128) {
        return _calculateRiskNeutralPD(_ammVars, _mktVars, _fTradeAmount, _withCDF);
    }

    /**
     *  Calculate the risk neutral default probability (>=0).
     *  Function decides whether pricing with or without quanto CCY is chosen.
     *  We assume r=0 everywhere.
     *  All variables are 64.64-bit fixed point number (or struct thereof)
     *  @param _ammVars         current AMM variables.
     *  @param _mktVars         current Market variables (price&params)
     *  @param _fTradeAmount    Trade amount (can be 0), hence amounts k2 are not already factored in
     *                          that is, function will set K2:=K2+k2, L1:=L1+k2*s2 (k2=_fTradeAmount)
     *  @param _withCDF         bool. If false, the normal-cdf is not evaluated (in case the caller is only
     *                          interested in the distance-to-default, this saves calculations)
     *  @return (default probabilit, distance to default) ; 64.64-bit fixed point numbers
     */
    function _calculateRiskNeutralPD(
        AMMVariables memory _ammVars,
        MarketVariables memory _mktVars,
        int128 _fTradeAmount,
        bool _withCDF
    ) internal pure returns (int128, int128) {
        int128 dL = _fTradeAmount.mul(_mktVars.fIndexPriceS2);
        int128 dK = _fTradeAmount;
        _ammVars.fLockedValue1 = _ammVars.fLockedValue1.add(dL);
        _ammVars.fAMM_K2 = _ammVars.fAMM_K2.add(dK);
        // -L1 - k*s2 - M1
        int128 fNumerator = (_ammVars.fLockedValue1.neg()).sub(_ammVars.fPoolM1);
        // s2*(M2-k2-K2) if no quanto, else M3 * s3
        int128 fDenominator = _ammVars.fPoolM3 == 0
            ? (_ammVars.fPoolM2.sub(_ammVars.fAMM_K2)).mul(_mktVars.fIndexPriceS2)
            : _ammVars.fPoolM3.mul(_mktVars.fIndexPriceS3);
        // handle edge sign cases first
        int128 fThresh;
        if (_ammVars.fPoolM3 == 0) {
            if (fNumerator < 0) {
                if (fDenominator >= 0) {
                    // P( den * exp(x) < 0) = 0
                    return (int128(0), TWENTY_64x64.neg());
                } else {
                    // num < 0 and den < 0, and P(exp(x) > infty) = 0
                    int256 result = (int256(fNumerator) << 64) / fDenominator;
                    if (result > MAX_64x64) {
                        return (int128(0), TWENTY_64x64.neg());
                    }
                    fThresh = int128(result);
                }
            } else if (fNumerator > 0) {
                if (fDenominator <= 0) {
                    // P( exp(x) >= 0) = 1
                    return (int128(ONE_64x64), TWENTY_64x64);
                } else {
                    // num > 0 and den > 0, and P(exp(x) < infty) = 1
                    int256 result = (int256(fNumerator) << 64) / fDenominator;
                    if (result > MAX_64x64) {
                        return (int128(ONE_64x64), TWENTY_64x64);
                    }
                    fThresh = int128(result);
                }
            } else {
                return
                    fDenominator >= 0
                        ? (int128(0), TWENTY_64x64.neg())
                        : (int128(ONE_64x64), TWENTY_64x64);
            }
        } else {
            // denom is O(M3 * S3), div should not overflow
            fThresh = fNumerator.div(fDenominator);
        }
        // if we're here fDenominator !=0 and fThresh did not overflow
        // sign tells us whether we consider norm.cdf(f(threshold)) or 1-norm.cdf(f(threshold))
        // we recycle fDenominator to store the sign since it's no longer used
        fDenominator = fDenominator < 0 ? ONE_64x64.neg() : ONE_64x64;
        int128 dd = _ammVars.fPoolM3 == 0
            ? _calculateRiskNeutralDDNoQuanto(_mktVars.fSigma2, fDenominator, fThresh)
            : _calculateRiskNeutralDDWithQuanto(_ammVars, _mktVars, fDenominator, fThresh);

        int128 q;
        if (_withCDF) {
            q = _normalCDF(dd);
        }
        return (q, dd);
    }

    /**
     *  Calculate additional/non-risk based slippage.
     *  Ensures slippage is bounded away from zero for small trades,
     *  and plateaus for larger-than-average trades, so that price becomes risk based.
     *
     *  All variables are 64.64-bit fixed point number (or struct thereof)
     *  @param _ammVars current AMM variables - we need the current average exposure per trader
     *  @param _fTradeAmount 64.64-bit fixed point number, signed size of trade
     *  @return 64.64-bit fixed point number, a number between minus one and one
     */
    function _calculateBoundedSlippage(
        AMMVariables memory _ammVars,
        int128 _fTradeAmount
    ) internal pure returns (int128) {
        int128 fTradeSizeEMA = _ammVars.fCurrentTraderExposureEMA;
        int128 fSlippageSize = ONE_64x64;
        if (_fTradeAmount.abs() < fTradeSizeEMA) {
            fSlippageSize = fSlippageSize.sub(_fTradeAmount.abs().div(fTradeSizeEMA));
            fSlippageSize = ONE_64x64.sub(fSlippageSize.mul(fSlippageSize));
        }
        return _fTradeAmount > 0 ? fSlippageSize : fSlippageSize.neg();
    }

    /**
     *  Calculate AMM price.
     *
     *  All variables are 64.64-bit fixed point number (or struct thereof)
     *  @param _ammVars current AMM variables.
     *  @param _mktVars current Market variables (price&params)
     *                 Trader amounts k2 must already be factored in
     *                 that is, K2:=K2+k2, L1:=L1+k2*s2
     *  @param _fTradeAmount 64.64-bit fixed point number, signed size of trade
     *  @param _fHBidAskSpread half bid-ask spread, 64.64-bit fixed point number
     *  @return 64.64-bit fixed point number, AMM price
     */
    function calculatePerpetualPrice(
        AMMVariables memory _ammVars,
        MarketVariables memory _mktVars,
        int128 _fTradeAmount,
        int128 _fHBidAskSpread,
        int128 _fIncentiveSpread
    ) external view virtual override returns (int128) {
        // add minimal spread in quote currency
        _fHBidAskSpread = _fTradeAmount > 0 ? _fHBidAskSpread : _fHBidAskSpread.neg();
        if (_fTradeAmount == 0) {
            _fHBidAskSpread = 0;
        }
        // get risk-neutral default probability (always >0)
        {
            int128 fQ;
            int128 dd;
            int128 fkStar = _ammVars.fPoolM2.sub(_ammVars.fAMM_K2);
            (fQ, dd) = _calculateRiskNeutralPD(_ammVars, _mktVars, _fTradeAmount, true);
            if (_ammVars.fPoolM3 != 0) {
                // amend K* (see whitepaper)
                int128 nominator = _mktVars.fRho23.mul(_mktVars.fSigma2.mul(_mktVars.fSigma3));
                int128 denom = _mktVars.fSigma2.mul(_mktVars.fSigma2);
                int128 h = nominator.div(denom).mul(_ammVars.fPoolM3);
                h = h.mul(_mktVars.fIndexPriceS3).div(_mktVars.fIndexPriceS2);
                fkStar = fkStar.add(h);
            }
            // decide on sign of premium
            if (_fTradeAmount < fkStar) {
                fQ = fQ.neg();
            }
            // no rebate if exposure increases
            if (_fTradeAmount > 0 && _ammVars.fAMM_K2 > 0) {
                fQ = fQ > 0 ? fQ : int128(0);
            } else if (_fTradeAmount < 0 && _ammVars.fAMM_K2 < 0) {
                fQ = fQ < 0 ? fQ : int128(0);
            }
            // handle discontinuity at zero
            if (
                _fTradeAmount == 0 &&
                ((fQ < 0 && _ammVars.fAMM_K2 > 0) || (fQ > 0 && _ammVars.fAMM_K2 < 0))
            ) {
                fQ = fQ.div(TWO_64x64);
            }
            _fHBidAskSpread = _fHBidAskSpread.add(fQ);
        }
        // get additional slippage
        if (_fTradeAmount != 0) {
            _fIncentiveSpread = _fIncentiveSpread.mul(
                _calculateBoundedSlippage(_ammVars, _fTradeAmount)
            );
            _fHBidAskSpread = _fHBidAskSpread.add(_fIncentiveSpread);
        }
        // s2*(1 + sign(qp-q)*q + sign(k)*minSpread)
        return _mktVars.fIndexPriceS2.mul(ONE_64x64.add(_fHBidAskSpread));
    }

    /**
     *  Calculate target collateral M1 (Quote Currency), when no M2, M3 is present
     *  The targeted default probability is expressed using the inverse
     *  _fTargetDD = Phi^(-1)(targetPD)
     *  _fK2 in absolute terms must be 'reasonably large'
     *  sigma3, rho23, IndexpriceS3 not relevant.
     *  @param _fK2 signed 64.64-bit fixed point number, !=0, EWMA of actual K.
     *  @param _fL1 signed 64.64-bit fixed point number, >0, EWMA of actual L.
     *  @param  _mktVars contains 64.64 values for fIndexPriceS2*, fIndexPriceS3, fSigma2*, fSigma3, fRho23
     *  @param _fTargetDD signed 64.64-bit fixed point number
     *  @return M1Star signed 64.64-bit fixed point number, >0
     */
    function getTargetCollateralM1(
        int128 _fK2,
        int128 _fL1,
        MarketVariables memory _mktVars,
        int128 _fTargetDD
    ) external pure virtual override returns (int128) {
        assert(_fK2 != 0);
        assert(_mktVars.fSigma3 == 0);
        assert(_mktVars.fIndexPriceS3 == 0);
        assert(_mktVars.fRho23 == 0);
        int128 fMu2 = HALF_64x64.neg().mul(_mktVars.fSigma2).mul(_mktVars.fSigma2);
        int128 ddScaled = _fK2 < 0
            ? _mktVars.fSigma2.mul(_fTargetDD)
            : _mktVars.fSigma2.mul(_fTargetDD).neg();
        int128 A1 = ABDKMath64x64.exp(fMu2.add(ddScaled));
        return _fK2.mul(_mktVars.fIndexPriceS2).mul(A1).sub(_fL1);
    }

    /**
     *  Calculate target collateral *M2* (Base Currency), when no M1, M3 is present
     *  The targeted default probability is expressed using the inverse
     *  _fTargetDD = Phi^(-1)(targetPD)
     *  _fK2 in absolute terms must be 'reasonably large'
     *  sigma3, rho23, IndexpriceS3 not relevant.
     *  @param _fK2 signed 64.64-bit fixed point number, EWMA of actual K.
     *  @param _fL1 signed 64.64-bit fixed point number, EWMA of actual L.
     *  @param _mktVars contains 64.64 values for fIndexPriceS2, fIndexPriceS3, fSigma2, fSigma3, fRho23
     *  @param _fTargetDD signed 64.64-bit fixed point number
     *  @return M2Star signed 64.64-bit fixed point number
     */
    function getTargetCollateralM2(
        int128 _fK2,
        int128 _fL1,
        MarketVariables memory _mktVars,
        int128 _fTargetDD
    ) external pure virtual override returns (int128) {
        assert(_fK2 != 0);
        assert(_mktVars.fSigma3 == 0);
        assert(_mktVars.fIndexPriceS3 == 0);
        assert(_mktVars.fRho23 == 0);
        int128 fMu2 = HALF_64x64.mul(_mktVars.fSigma2).mul(_mktVars.fSigma2).neg();
        int128 ddScaled = _fL1 < 0
            ? _mktVars.fSigma2.mul(_fTargetDD)
            : _mktVars.fSigma2.mul(_fTargetDD).neg();
        int128 A1 = ABDKMath64x64.exp(fMu2.add(ddScaled)).mul(_mktVars.fIndexPriceS2);
        return _fK2.sub(_fL1.div(A1));
    }

    /**
     *  Calculate target collateral M3 (Quanto Currency), when no M1, M2 not present
     *  @param _fK2 signed 64.64-bit fixed point number. EWMA of actual K.
     *  @param _fL1 signed 64.64-bit fixed point number.  EWMA of actual L.
     *  @param  _mktVars contains 64.64 values for
     *           fIndexPriceS2, fIndexPriceS3, fSigma2, fSigma3, fRho23 - all required
     *  @param _fTargetDD signed 64.64-bit fixed point number
     *  @return M2Star signed 64.64-bit fixed point number
     */
    function getTargetCollateralM3(
        int128 _fK2,
        int128 _fL1,
        MarketVariables memory _mktVars,
        int128 _fTargetDD
    ) external pure override returns (int128) {
        assert(_fK2 != 0);
        assert(_mktVars.fSigma3 != 0);
        assert(_mktVars.fIndexPriceS3 != 0);
        // we solve the quadratic equation A x^2 + Bx + C = 0
        // B = 2 * [X + Y * target_dd^2 * (exp(rho*sigma2*sigma3) - 1) ]
        // C = X^2  - Y^2 * target_dd^2 * (exp(sigma2^2) - 1)
        // where:
        // X = L1 / S3 - Y and Y = K2 * S2 / S3
        // we re-use L1 for X and K2 for Y to save memory since they don't enter the equations otherwise
        _fK2 = _fK2.mul(_mktVars.fIndexPriceS2).div(_mktVars.fIndexPriceS3); // Y
        _fL1 = _fL1.div(_mktVars.fIndexPriceS3).sub(_fK2); // X
        // we only need the square of the target DD
        _fTargetDD = _fTargetDD.mul(_fTargetDD);
        // and we only need B/2
        int128 fHalfB = _fL1.add(
            _fK2.mul(_fTargetDD.mul(_mktVars.fRho23.mul(_mktVars.fSigma2.mul(_mktVars.fSigma3))))
        );
        int128 fC = _fL1.mul(_fL1).sub(
            _fK2.mul(_fK2).mul(_fTargetDD).mul(_mktVars.fSigma2.mul(_mktVars.fSigma2))
        );
        // A = 1 - (exp(sigma3^2) - 1) * target_dd^2
        int128 fA = ONE_64x64.sub(_mktVars.fSigma3.mul(_mktVars.fSigma3).mul(_fTargetDD));
        // we re-use C to store the discriminant: D = (B/2)^2 - A * C
        fC = fHalfB.mul(fHalfB).sub(fA.mul(fC));
        if (fC < 0) {
            // no solutions -> AMM is in profit, probability is smaller than target regardless of capital
            return int128(0);
        }
        // we want the larger of (-B/2 + sqrt((B/2)^2-A*C)) / A and (-B/2 - sqrt((B/2)^2-A*C)) / A
        // so it depends on the sign of A, or, equivalently, the sign of sqrt(...)/A
        fC = ABDKMath64x64.sqrt(fC).div(fA);
        fHalfB = fHalfB.div(fA);
        return fC > 0 ? fC.sub(fHalfB) : fC.neg().sub(fHalfB);
    }

    /**
     *  Calculate the required deposit for a new position
     *  of size _fPosition+_fTradeAmount and leverage _fTargetLeverage,
     *  having an existing position with balance fBalance0 and size _fPosition.
     *  This is the amount to be added to the margin collateral and can be negative (hence remove).
     *  Fees not factored-in.
     *  @param _fPosition0   signed 64.64-bit fixed point number. Position in base currency
     *  @param _fBalance0   signed 64.64-bit fixed point number. Current balance.
     *  @param _fTradeAmount signed 64.64-bit fixed point number. Trade amt in base currency
     *  @param _fTargetLeverage signed 64.64-bit fixed point number. Desired leverage
     *  @param _fPrice signed 64.64-bit fixed point number. Price for the trade of size _fTradeAmount
     *  @param _fS2Mark signed 64.64-bit fixed point number. Mark-price
     *  @param _fS3 signed 64.64-bit fixed point number. Collateral 2 quote conversion
     *  @return signed 64.64-bit fixed point number. Required cash_cc
     */
    function getDepositAmountForLvgPosition(
        int128 _fPosition0,
        int128 _fBalance0,
        int128 _fTradeAmount,
        int128 _fTargetLeverage,
        int128 _fPrice,
        int128 _fS2Mark,
        int128 _fS3,
        int128 _fS2
    ) external pure override returns (int128) {
        // calculation has to be aligned with _getAvailableMargin and _executeTrade
        // calculation
        // otherwise the calculated deposit might not be enough to declare
        // the margin to be enough
        // aligned with get available margin balance
        int128 fPremiumCash = _fTradeAmount.mul(_fPrice.sub(_fS2));
        int128 fDeltaLockedValue = _fTradeAmount.mul(_fS2);
        int128 fPnL = _fTradeAmount.mul(_fS2Mark);
        // we replace _fTradeAmount * price/S3 by
        // fDeltaLockedValue + fPremiumCash to be in line with
        // _executeTrade
        fPnL = fPnL.sub(fDeltaLockedValue).sub(fPremiumCash);
        int128 fLvgFrac = _fPosition0.add(_fTradeAmount).abs();
        fLvgFrac = fLvgFrac.mul(_fS2Mark).div(_fTargetLeverage);
        fPnL = fPnL.sub(fLvgFrac).div(_fS3);
        _fBalance0 = _fBalance0.add(fPnL);
        return _fBalance0.neg();
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.21;

import "../functions/AMMPerpLogic.sol";

interface IAMMPerpLogic {
    function calculateDefaultFundSize(
        int128[2] memory _fK2AMM,
        int128 _fk2Trader,
        int128 _fCoverN,
        int128[2] memory fStressRet2,
        int128[2] memory fStressRet3,
        int128[2] memory fIndexPrices,
        AMMPerpLogic.CollateralCurrency _eCCY
    ) external pure returns (int128);

    function calculateRiskNeutralPD(
        AMMPerpLogic.AMMVariables memory _ammVars,
        AMMPerpLogic.MarketVariables memory _mktVars,
        int128 _fTradeAmount,
        bool _withCDF
    ) external view returns (int128, int128);

    function calculatePerpetualPrice(
        AMMPerpLogic.AMMVariables memory _ammVars,
        AMMPerpLogic.MarketVariables memory _mktVars,
        int128 _fTradeAmount,
        int128 _fBidAskSpread,
        int128 _fIncentiveSpread
    ) external view returns (int128);

    function getTargetCollateralM1(
        int128 _fK2,
        int128 _fL1,
        AMMPerpLogic.MarketVariables memory _mktVars,
        int128 _fTargetDD
    ) external pure returns (int128);

    function getTargetCollateralM2(
        int128 _fK2,
        int128 _fL1,
        AMMPerpLogic.MarketVariables memory _mktVars,
        int128 _fTargetDD
    ) external pure returns (int128);

    function getTargetCollateralM3(
        int128 _fK2,
        int128 _fL1,
        AMMPerpLogic.MarketVariables memory _mktVars,
        int128 _fTargetDD
    ) external pure returns (int128);

    function getDepositAmountForLvgPosition(
        int128 _fPosition0,
        int128 _fBalance0,
        int128 _fTradeAmount,
        int128 _fTargetLeverage,
        int128 _fPrice,
        int128 _fS2Mark,
        int128 _fS3,
        int128 _fS2
    ) external pure returns (int128);
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.21;

interface IFunctionList {
    function getFunctionList()
        external
        pure
        returns (bytes4[] memory functionSignatures, bytes32 moduleName);
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.21;
import "./IPerpetualOrder.sol";

/**
 * @notice  The libraryEvents defines events that will be raised from modules (contract/modules).
 * @dev     DO REMEMBER to add new events in modules here.
 */
interface ILibraryEvents {
    // PerpetualModule
    event Clear(uint24 indexed perpetualId, address indexed trader);
    event Settle(uint24 indexed perpetualId, address indexed trader, int256 amount);
    event SettlementComplete(uint24 indexed perpetualId);
    event SetNormalState(uint24 indexed perpetualId);
    event SetEmergencyState(
        uint24 indexed perpetualId,
        int128 fSettlementMarkPremiumRate,
        int128 fSettlementS2Price,
        int128 fSettlementS3Price
    );
    event SettleState(uint24 indexed perpetualId);
    event SetClearedState(uint24 indexed perpetualId);

    // Participation pool
    event LiquidityAdded(
        uint8 indexed poolId,
        address indexed user,
        uint256 tokenAmount,
        uint256 shareAmount
    );
    event LiquidityProvisionPaused(bool pauseOn, uint8 poolId);
    event LiquidityRemoved(
        uint8 indexed poolId,
        address indexed user,
        uint256 tokenAmount,
        uint256 shareAmount
    );
    event LiquidityWithdrawalInitiated(
        uint8 indexed poolId,
        address indexed user,
        uint256 shareAmount
    );

    // setters
    // oracles
    event SetOracles(uint24 indexed perpetualId, bytes4[2] baseQuoteS2, bytes4[2] baseQuoteS3);
    // perp parameters
    event SetPerpetualBaseParameters(uint24 indexed perpetualId, int128[7] baseParams);
    event SetPerpetualRiskParameters(
        uint24 indexed perpetualId,
        int128[5] underlyingRiskParams,
        int128[12] defaultFundRiskParams
    );
    event SetParameter(uint24 indexed perpetualId, string name, int128 value);
    event SetParameterPair(uint24 indexed perpetualId, string name, int128 value1, int128 value2);
    // pool parameters
    event SetPoolParameter(uint8 indexed poolId, string name, int128 value);

    event TransferAddressTo(string name, address oldOBFactory, address newOBFactory); // only governance
    event SetBlockDelay(uint8 delay);

    // fee structure parameters
    event SetBrokerDesignations(uint32[] designations, uint16[] fees);
    event SetBrokerTiers(uint256[] tiers, uint16[] feesTbps);
    event SetTraderTiers(uint256[] tiers, uint16[] feesTbps);
    event SetTraderVolumeTiers(uint256[] tiers, uint16[] feesTbps);
    event SetBrokerVolumeTiers(uint256[] tiers, uint16[] feesTbps);
    event SetUtilityToken(address tokenAddr);

    event BrokerLotsTransferred(
        uint8 indexed poolId,
        address oldOwner,
        address newOwner,
        uint32 numLots
    );
    event BrokerVolumeTransferred(
        uint8 indexed poolId,
        address oldOwner,
        address newOwner,
        int128 fVolume
    );

    // brokers
    event UpdateBrokerAddedCash(uint8 indexed poolId, uint32 iLots, uint32 iNewBrokerLots);

    // TradeModule

    event Trade(
        uint24 indexed perpetualId,
        address indexed trader,
        IPerpetualOrder.Order order,
        bytes32 orderDigest,
        int128 newPositionSizeBC,
        int128 price,
        int128 fFeeCC,
        int128 fPnlCC,
        int128 fB2C
    );

    event UpdateMarginAccount(
        uint24 indexed perpetualId,
        address indexed trader,
        int128 fFundingPaymentCC
    );

    event Liquidate(
        uint24 perpetualId,
        address indexed liquidator,
        address indexed trader,
        int128 amountLiquidatedBC,
        int128 liquidationPrice,
        int128 newPositionSizeBC,
        int128 fFeeCC,
        int128 fPnlCC
    );

    event PerpetualLimitOrderCancelled(uint24 indexed perpetualId, bytes32 indexed orderHash);
    event DistributeFees(
        uint8 indexed poolId,
        uint24 indexed perpetualId,
        address indexed trader,
        int128 protocolFeeCC,
        int128 participationFundFeeCC
    );

    // PerpetualManager/factory
    event RunLiquidityPool(uint8 _liqPoolID);
    event LiquidityPoolCreated(
        uint8 id,
        address marginTokenAddress,
        address shareTokenAddress,
        uint16 iTargetPoolSizeUpdateTime,
        int128 fBrokerCollateralLotSize
    );
    event PerpetualCreated(
        uint8 poolId,
        uint24 id,
        int128[7] baseParams,
        int128[5] underlyingRiskParams,
        int128[12] defaultFundRiskParams,
        uint256 eCollateralCurrency
    );

    // emit tokenAddr==0x0 if the token paid is the aggregated token, otherwise the address of the token
    event TokensDeposited(uint24 indexed perpetualId, address indexed trader, int128 amount);
    event TokensWithdrawn(uint24 indexed perpetualId, address indexed trader, int128 amount);

    event UpdateMarkPrice(
        uint24 indexed perpetualId,
        int128 fMidPricePremium,
        int128 fMarkPricePremium,
        int128 fSpotIndexPrice
    );

    event UpdateFundingRate(uint24 indexed perpetualId, int128 fFundingRate);

    event SetDelegate(address indexed trader, address indexed delegate, uint256 index);
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.21;

interface IPerpetualOrder {
    struct Order {
        uint16 leverageTDR; // 12.43x leverage is represented by 1243 (two-digit integer representation); 0 if deposit and trade separate
        uint16 brokerFeeTbps; // broker can set their own fee
        uint24 iPerpetualId; // global id for perpetual
        address traderAddr; // address of trader
        uint32 executionTimestamp; // normally set to current timestamp; order will not be executed prior to this timestamp.
        address brokerAddr; // address of the broker or zero
        uint32 submittedTimestamp;
        uint32 flags; // order flags
        uint32 iDeadline; //deadline for price (seconds timestamp)
        address executorAddr; // address of the executor set by contract
        int128 fAmount; // amount in base currency to be traded
        int128 fLimitPrice; // limit price
        int128 fTriggerPrice; //trigger price. Non-zero for stop orders.
        bytes brokerSignature; //signature of broker (or 0)
    }
}

{
  "optimizer": {
    "enabled": true,
    "runs": 10000000
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "evmVersion": "paris",
  "metadata": {
    "useLiteralContent": true
  },
  "libraries": {}
}

• No Contract Security Audit Submitted- Submit Audit Here

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