/*

    Copyright 2020 dYdX Trading Inc.

    Licensed under the Apache License, Version 2.0 (the "License");
    you may not use this file except in compliance with the License.
    You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

    Unless required by applicable law or agreed to in writing, software
    distributed under the License is distributed on an "AS IS" BASIS,
    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    See the License for the specific language governing permissions and
    limitations under the License.

*/

pragma solidity 0.5.16;
pragma experimental ABIEncoderV2;

// File: @openzeppelin/contracts/math/SafeMath.sol

/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when an
 * operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");

        return c;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        return sub(a, b, "SafeMath: subtraction overflow");
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     * - Subtraction cannot overflow.
     *
     * _Available since v2.4.0._
     */
    function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        uint256 c = a - b;

        return c;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) {
            return 0;
        }

        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");

        return c;
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        return div(a, b, "SafeMath: division by zero");
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     * - The divisor cannot be zero.
     *
     * _Available since v2.4.0._
     */
    function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        // Solidity only automatically asserts when dividing by 0
        require(b > 0, errorMessage);
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold

        return c;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        return mod(a, b, "SafeMath: modulo by zero");
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts with custom message when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     * - The divisor cannot be zero.
     *
     * _Available since v2.4.0._
     */
    function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b != 0, errorMessage);
        return a % b;
    }
}

// File: @openzeppelin/contracts/GSN/Context.sol

/*
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with GSN 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.
 */
contract Context {
    // Empty internal constructor, to prevent people from mistakenly deploying
    // an instance of this contract, which should be used via inheritance.
    constructor () internal { }
    // solhint-disable-previous-line no-empty-blocks

    function _msgSender() internal view returns (address payable) {
        return msg.sender;
    }

    function _msgData() internal view returns (bytes memory) {
        this; // silence state mutability warning without generating bytecode - see https://github.com/ethereum/solidity/issues/2691
        return msg.data;
    }
}

// File: @openzeppelin/contracts/ownership/Ownable.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.
 *
 * 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.
 */
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 () internal {
        address msgSender = _msgSender();
        _owner = msgSender;
        emit OwnershipTransferred(address(0), msgSender);
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        require(isOwner(), "Ownable: caller is not the owner");
        _;
    }

    /**
     * @dev Returns true if the caller is the current owner.
     */
    function isOwner() public view returns (bool) {
        return _msgSender() == _owner;
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     */
    function renounceOwnership() public onlyOwner {
        emit OwnershipTransferred(_owner, address(0));
        _owner = 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 onlyOwner {
        _transferOwnership(newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     */
    function _transferOwnership(address newOwner) internal {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        emit OwnershipTransferred(_owner, newOwner);
        _owner = newOwner;
    }
}

// File: contracts/protocol/v1/traders/P1TraderConstants.sol

/**
 * @title P1TraderConstants
 * @author dYdX
 *
 * @notice Constants for traderFlags set by contracts implementing the I_P1Trader interface.
 */
contract P1TraderConstants {
    bytes32 constant internal TRADER_FLAG_ORDERS = bytes32(uint256(1));
    bytes32 constant internal TRADER_FLAG_LIQUIDATION = bytes32(uint256(2));
    bytes32 constant internal TRADER_FLAG_DELEVERAGING = bytes32(uint256(4));
}

// File: contracts/protocol/lib/Math.sol

/**
 * @title Math
 * @author dYdX
 *
 * @dev Library for non-standard Math functions.
 */
library Math {
    using SafeMath for uint256;

    // ============ Library Functions ============

    /**
     * @dev Return target * (numerator / denominator), rounded down.
     */
    function getFraction(
        uint256 target,
        uint256 numerator,
        uint256 denominator
    )
        internal
        pure
        returns (uint256)
    {
        return target.mul(numerator).div(denominator);
    }

    /**
     * @dev Return target * (numerator / denominator), rounded up.
     */
    function getFractionRoundUp(
        uint256 target,
        uint256 numerator,
        uint256 denominator
    )
        internal
        pure
        returns (uint256)
    {
        if (target == 0 || numerator == 0) {
            // SafeMath will check for zero denominator
            return SafeMath.div(0, denominator);
        }
        return target.mul(numerator).sub(1).div(denominator).add(1);
    }

    /**
     * @dev Returns the minimum between a and b.
     */
    function min(
        uint256 a,
        uint256 b
    )
        internal
        pure
        returns (uint256)
    {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the maximum between a and b.
     */
    function max(
        uint256 a,
        uint256 b
    )
        internal
        pure
        returns (uint256)
    {
        return a > b ? a : b;
    }
}

// File: contracts/protocol/lib/Storage.sol

/**
 * @title Storage
 * @author dYdX
 *
 * @dev Storage library for reading/writing storage at a low level.
 */
library Storage {

    /**
     * @dev Performs an SLOAD and returns the data in the slot.
     */
    function load(
        bytes32 slot
    )
        internal
        view
        returns (bytes32)
    {
        bytes32 result;
        /* solium-disable-next-line security/no-inline-assembly */
        assembly {
            result := sload(slot)
        }
        return result;
    }

    /**
     * @dev Performs an SSTORE to save the value to the slot.
     */
    function store(
        bytes32 slot,
        bytes32 value
    )
        internal
    {
        /* solium-disable-next-line security/no-inline-assembly */
        assembly {
            sstore(slot, value)
        }
    }
}

// File: contracts/protocol/lib/Adminable.sol

/**
 * @title Adminable
 * @author dYdX
 *
 * @dev EIP-1967 Proxy Admin contract.
 */
contract Adminable {
    /**
     * @dev Storage slot with the admin of the contract.
     *  This is the keccak-256 hash of "eip1967.proxy.admin" subtracted by 1.
     */
    bytes32 internal constant ADMIN_SLOT =
    0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;

    /**
    * @dev Modifier to check whether the `msg.sender` is the admin.
    *  If it is, it will run the function. Otherwise, it will revert.
    */
    modifier onlyAdmin() {
        require(
            msg.sender == getAdmin(),
            "Adminable: caller is not admin"
        );
        _;
    }

    /**
     * @return The EIP-1967 proxy admin
     */
    function getAdmin()
        public
        view
        returns (address)
    {
        return address(uint160(uint256(Storage.load(ADMIN_SLOT))));
    }
}

// File: contracts/protocol/lib/ReentrancyGuard.sol

/**
 * @title ReentrancyGuard
 * @author dYdX
 *
 * @dev Updated ReentrancyGuard library designed to be used with Proxy Contracts.
 */
contract ReentrancyGuard {
    uint256 private constant NOT_ENTERED = 1;
    uint256 private constant ENTERED = uint256(int256(-1));

    uint256 private _STATUS_;

    constructor () internal {
        _STATUS_ = NOT_ENTERED;
    }

    modifier nonReentrant() {
        require(_STATUS_ != ENTERED, "ReentrancyGuard: reentrant call");
        _STATUS_ = ENTERED;
        _;
        _STATUS_ = NOT_ENTERED;
    }
}

// File: contracts/protocol/v1/lib/P1Types.sol

/**
 * @title P1Types
 * @author dYdX
 *
 * @dev Library for common types used in PerpetualV1 contracts.
 */
library P1Types {
    // ============ Structs ============

    /**
     * @dev Used to represent the global index and each account's cached index.
     *  Used to settle funding paymennts on a per-account basis.
     */
    struct Index {
        uint32 timestamp;
        bool isPositive;
        uint128 value;
    }

    /**
     * @dev Used to track the signed margin balance and position balance values for each account.
     */
    struct Balance {
        bool marginIsPositive;
        bool positionIsPositive;
        uint120 margin;
        uint120 position;
    }

    /**
     * @dev Used to cache commonly-used variables that are relatively gas-intensive to obtain.
     */
    struct Context {
        uint256 price;
        uint256 minCollateral;
        Index index;
    }

    /**
     * @dev Used by contracts implementing the I_P1Trader interface to return the result of a trade.
     */
    struct TradeResult {
        uint256 marginAmount;
        uint256 positionAmount;
        bool isBuy; // From taker's perspective.
        bytes32 traderFlags;
    }
}

// File: contracts/protocol/v1/impl/P1Storage.sol

/**
 * @title P1Storage
 * @author dYdX
 *
 * @notice Storage contract. Contains or inherits from all contracts that have ordered storage.
 */
contract P1Storage is
    Adminable,
    ReentrancyGuard
{
    mapping(address => P1Types.Balance) internal _BALANCES_;
    mapping(address => P1Types.Index) internal _LOCAL_INDEXES_;

    mapping(address => bool) internal _GLOBAL_OPERATORS_;
    mapping(address => mapping(address => bool)) internal _LOCAL_OPERATORS_;

    address internal _TOKEN_;
    address internal _ORACLE_;
    address internal _FUNDER_;

    P1Types.Index internal _GLOBAL_INDEX_;
    uint256 internal _MIN_COLLATERAL_;

    bool internal _FINAL_SETTLEMENT_ENABLED_;
    uint256 internal _FINAL_SETTLEMENT_PRICE_;
}

// File: contracts/protocol/v1/intf/I_P1Oracle.sol

/**
 * @title I_P1Oracle
 * @author dYdX
 *
 * @notice Interface that PerpetualV1 Price Oracles must implement.
 */
interface I_P1Oracle {

    /**
     * @notice Returns the price of the underlying asset relative to the margin token.
     *
     * @return The price as a fixed-point number with 18 decimals.
     */
    function getPrice()
        external
        view
        returns (uint256);
}

// File: contracts/protocol/v1/impl/P1Getters.sol

/**
 * @title P1Getters
 * @author dYdX
 *
 * @notice Contract for read-only getters.
 */
contract P1Getters is
    P1Storage
{
    // ============ Account Getters ============

    /**
     * @notice Get the balance of an account, without accounting for changes in the index.
     *
     * @param  account  The address of the account to query the balances of.
     * @return          The balances of the account.
     */
    function getAccountBalance(
        address account
    )
        external
        view
        returns (P1Types.Balance memory)
    {
        return _BALANCES_[account];
    }

    /**
     * @notice Gets the most recently cached index of an account.
     *
     * @param  account  The address of the account to query the index of.
     * @return          The index of the account.
     */
    function getAccountIndex(
        address account
    )
        external
        view
        returns (P1Types.Index memory)
    {
        return _LOCAL_INDEXES_[account];
    }

    /**
     * @notice Gets the local operator status of an operator for a particular account.
     *
     * @param  account   The account to query the operator for.
     * @param  operator  The address of the operator to query the status of.
     * @return           True if the operator is a local operator of the account, false otherwise.
     */
    function getIsLocalOperator(
        address account,
        address operator
    )
        external
        view
        returns (bool)
    {
        return _LOCAL_OPERATORS_[account][operator];
    }

    // ============ Global Getters ============

    /**
     * @notice Gets the global operator status of an address.
     *
     * @param  operator  The address of the operator to query the status of.
     * @return           True if the address is a global operator, false otherwise.
     */
    function getIsGlobalOperator(
        address operator
    )
        external
        view
        returns (bool)
    {
        return _GLOBAL_OPERATORS_[operator];
    }

    /**
     * @notice Gets the address of the ERC20 margin contract used for margin deposits.
     *
     * @return The address of the ERC20 token.
     */
    function getTokenContract()
        external
        view
        returns (address)
    {
        return _TOKEN_;
    }

    /**
     * @notice Gets the current address of the price oracle contract.
     *
     * @return The address of the price oracle contract.
     */
    function getOracleContract()
        external
        view
        returns (address)
    {
        return _ORACLE_;
    }

    /**
     * @notice Gets the current address of the funder contract.
     *
     * @return The address of the funder contract.
     */
    function getFunderContract()
        external
        view
        returns (address)
    {
        return _FUNDER_;
    }

    /**
     * @notice Gets the most recently cached global index.
     *
     * @return The most recently cached global index.
     */
    function getGlobalIndex()
        external
        view
        returns (P1Types.Index memory)
    {
        return _GLOBAL_INDEX_;
    }

    /**
     * @notice Gets minimum collateralization ratio of the protocol.
     *
     * @return The minimum-acceptable collateralization ratio, returned as a fixed-point number with
     *  18 decimals of precision.
     */
    function getMinCollateral()
        external
        view
        returns (uint256)
    {
        return _MIN_COLLATERAL_;
    }

    /**
     * @notice Gets the status of whether final-settlement was initiated by the Admin.
     *
     * @return True if final-settlement was enabled, false otherwise.
     */
    function getFinalSettlementEnabled()
        external
        view
        returns (bool)
    {
        return _FINAL_SETTLEMENT_ENABLED_;
    }

    // ============ Authorized External Getters ============

    /**
     * @notice Gets the price returned by the oracle.
     * @dev Only able to be called by global operators.
     *
     * @return The price returned by the current price oracle.
     */
    function getOraclePrice()
        external
        view
        returns (uint256)
    {
        require(
            _GLOBAL_OPERATORS_[msg.sender],
            "Oracle price requester not global operator"
        );
        return I_P1Oracle(_ORACLE_).getPrice();
    }

    // ============ Public Getters ============

    /**
     * @notice Gets whether an address has permissions to operate an account.
     *
     * @param  account   The account to query.
     * @param  operator  The address to query.
     * @return           True if the operator has permission to operate the account,
     *                   and false otherwise.
     */
    function hasAccountPermissions(
        address account,
        address operator
    )
        public
        view
        returns (bool)
    {
        return account == operator
            || _GLOBAL_OPERATORS_[operator]
            || _LOCAL_OPERATORS_[account][operator];
    }
}

// File: contracts/protocol/lib/BaseMath.sol

/**
 * @title BaseMath
 * @author dYdX
 *
 * @dev Arithmetic for fixed-point numbers with 18 decimals of precision.
 */
library BaseMath {
    using SafeMath for uint256;

    // The number One in the BaseMath system.
    uint256 constant internal BASE = 10 ** 18;

    /**
     * @dev Getter function since constants can't be read directly from libraries.
     */
    function base()
        internal
        pure
        returns (uint256)
    {
        return BASE;
    }

    /**
     * @dev Multiplies a value by a base value (result is rounded down).
     */
    function baseMul(
        uint256 value,
        uint256 baseValue
    )
        internal
        pure
        returns (uint256)
    {
        return value.mul(baseValue).div(BASE);
    }

    /**
     * @dev Multiplies a value by a base value (result is rounded down).
     *  Intended as an alternaltive to baseMul to prevent overflow, when `value` is known
     *  to be divisible by `BASE`.
     */
    function baseDivMul(
        uint256 value,
        uint256 baseValue
    )
        internal
        pure
        returns (uint256)
    {
        return value.div(BASE).mul(baseValue);
    }

    /**
     * @dev Multiplies a value by a base value (result is rounded up).
     */
    function baseMulRoundUp(
        uint256 value,
        uint256 baseValue
    )
        internal
        pure
        returns (uint256)
    {
        if (value == 0 || baseValue == 0) {
            return 0;
        }
        return value.mul(baseValue).sub(1).div(BASE).add(1);
    }
}

// File: contracts/protocol/lib/SafeCast.sol

/**
 * @title SafeCast
 * @author dYdX
 *
 * @dev Library for casting uint256 to other types of uint.
 */
library SafeCast {

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     *  overflow (i.e. when the input is greater than largest uint128).
     *
     *  Counterpart to Solidity's `uint128` operator.
     *
     *  Requirements:
     *  - `value` must fit into 128 bits.
     */
    function toUint128(
        uint256 value
    )
        internal
        pure
        returns (uint128)
    {
        require(value < 2**128, "SafeCast: value doesn\'t fit in 128 bits");
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint120 from uint256, reverting on
     *  overflow (i.e. when the input is greater than largest uint120).
     *
     *  Counterpart to Solidity's `uint120` operator.
     *
     *  Requirements:
     *  - `value` must fit into 120 bits.
     */
    function toUint120(
        uint256 value
    )
        internal
        pure
        returns (uint120)
    {
        require(value < 2**120, "SafeCast: value doesn\'t fit in 120 bits");
        return uint120(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     *  overflow (i.e. when the input is greater than largest uint32).
     *
     *  Counterpart to Solidity's `uint32` operator.
     *
     *  Requirements:
     *  - `value` must fit into 32 bits.
     */
    function toUint32(
        uint256 value
    )
        internal
        pure
        returns (uint32)
    {
        require(value < 2**32, "SafeCast: value doesn\'t fit in 32 bits");
        return uint32(value);
    }
}

// File: contracts/protocol/lib/SignedMath.sol

/**
 * @title SignedMath
 * @author dYdX
 *
 * @dev SignedMath library for doing math with signed integers.
 */
library SignedMath {
    using SafeMath for uint256;

    // ============ Structs ============

    struct Int {
        uint256 value;
        bool isPositive;
    }

    // ============ Functions ============

    /**
     * @dev Returns a new signed integer equal to a signed integer plus an unsigned integer.
     */
    function add(
        Int memory sint,
        uint256 value
    )
        internal
        pure
        returns (Int memory)
    {
        if (sint.isPositive) {
            return Int({
                value: value.add(sint.value),
                isPositive: true
            });
        }
        if (sint.value < value) {
            return Int({
                value: value.sub(sint.value),
                isPositive: true
            });
        }
        return Int({
            value: sint.value.sub(value),
            isPositive: false
        });
    }

    /**
     * @dev Returns a new signed integer equal to a signed integer minus an unsigned integer.
     */
    function sub(
        Int memory sint,
        uint256 value
    )
        internal
        pure
        returns (Int memory)
    {
        if (!sint.isPositive) {
            return Int({
                value: value.add(sint.value),
                isPositive: false
            });
        }
        if (sint.value > value) {
            return Int({
                value: sint.value.sub(value),
                isPositive: true
            });
        }
        return Int({
            value: value.sub(sint.value),
            isPositive: false
        });
    }

    /**
     * @dev Returns a new signed integer equal to a signed integer plus another signed integer.
     */
    function signedAdd(
        Int memory augend,
        Int memory addend
    )
        internal
        pure
        returns (Int memory)
    {
        return addend.isPositive
            ? add(augend, addend.value)
            : sub(augend, addend.value);
    }

    /**
     * @dev Returns a new signed integer equal to a signed integer minus another signed integer.
     */
    function signedSub(
        Int memory minuend,
        Int memory subtrahend
    )
        internal
        pure
        returns (Int memory)
    {
        return subtrahend.isPositive
            ? sub(minuend, subtrahend.value)
            : add(minuend, subtrahend.value);
    }

    /**
     * @dev Returns true if signed integer `a` is greater than signed integer `b`, false otherwise.
     */
    function gt(
        Int memory a,
        Int memory b
    )
        internal
        pure
        returns (bool)
    {
        if (a.isPositive) {
            if (b.isPositive) {
                return a.value > b.value;
            } else {
                // True, unless both values are zero.
                return a.value != 0 || b.value != 0;
            }
        } else {
            if (b.isPositive) {
                return false;
            } else {
                return a.value < b.value;
            }
        }
    }

    /**
     * @dev Returns the minimum of signed integers `a` and `b`.
     */
    function min(
        Int memory a,
        Int memory b
    )
        internal
        pure
        returns (Int memory)
    {
        return gt(b, a) ? a : b;
    }

    /**
     * @dev Returns the maximum of signed integers `a` and `b`.
     */
    function max(
        Int memory a,
        Int memory b
    )
        internal
        pure
        returns (Int memory)
    {
        return gt(a, b) ? a : b;
    }
}

// File: contracts/protocol/v1/lib/P1BalanceMath.sol

/**
 * @title P1BalanceMath
 * @author dYdX
 *
 * @dev Library for manipulating P1Types.Balance structs.
 */
library P1BalanceMath {
    using BaseMath for uint256;
    using SafeCast for uint256;
    using SafeMath for uint256;
    using SignedMath for SignedMath.Int;
    using P1BalanceMath for P1Types.Balance;

    // ============ Constants ============

    uint256 private constant FLAG_MARGIN_IS_POSITIVE = 1 << (8 * 31);
    uint256 private constant FLAG_POSITION_IS_POSITIVE = 1 << (8 * 15);

    // ============ Functions ============

    /**
     * @dev Create a copy of the balance struct.
     */
    function copy(
        P1Types.Balance memory balance
    )
        internal
        pure
        returns (P1Types.Balance memory)
    {
        return P1Types.Balance({
            marginIsPositive: balance.marginIsPositive,
            positionIsPositive: balance.positionIsPositive,
            margin: balance.margin,
            position: balance.position
        });
    }

    /**
     * @dev In-place add amount to balance.margin.
     */
    function addToMargin(
        P1Types.Balance memory balance,
        uint256 amount
    )
        internal
        pure
    {
        SignedMath.Int memory signedMargin = balance.getMargin();
        signedMargin = signedMargin.add(amount);
        balance.setMargin(signedMargin);
    }

    /**
     * @dev In-place subtract amount from balance.margin.
     */
    function subFromMargin(
        P1Types.Balance memory balance,
        uint256 amount
    )
        internal
        pure
    {
        SignedMath.Int memory signedMargin = balance.getMargin();
        signedMargin = signedMargin.sub(amount);
        balance.setMargin(signedMargin);
    }

    /**
     * @dev In-place add amount to balance.position.
     */
    function addToPosition(
        P1Types.Balance memory balance,
        uint256 amount
    )
        internal
        pure
    {
        SignedMath.Int memory signedPosition = balance.getPosition();
        signedPosition = signedPosition.add(amount);
        balance.setPosition(signedPosition);
    }

    /**
     * @dev In-place subtract amount from balance.position.
     */
    function subFromPosition(
        P1Types.Balance memory balance,
        uint256 amount
    )
        internal
        pure
    {
        SignedMath.Int memory signedPosition = balance.getPosition();
        signedPosition = signedPosition.sub(amount);
        balance.setPosition(signedPosition);
    }

    /**
     * @dev Returns the positive and negative values of the margin and position together, given a
     *  price, which is used as a conversion rate between the two currencies.
     *
     *  No rounding occurs here--the returned values are "base values" with extra precision.
     */
    function getPositiveAndNegativeValue(
        P1Types.Balance memory balance,
        uint256 price
    )
        internal
        pure
        returns (uint256, uint256)
    {
        uint256 positiveValue = 0;
        uint256 negativeValue = 0;

        // add value of margin
        if (balance.marginIsPositive) {
            positiveValue = uint256(balance.margin).mul(BaseMath.base());
        } else {
            negativeValue = uint256(balance.margin).mul(BaseMath.base());
        }

        // add value of position
        uint256 positionValue = uint256(balance.position).mul(price);
        if (balance.positionIsPositive) {
            positiveValue = positiveValue.add(positionValue);
        } else {
            negativeValue = negativeValue.add(positionValue);
        }

        return (positiveValue, negativeValue);
    }

    /**
     * @dev Returns a compressed bytes32 representation of the balance for logging.
     */
    function toBytes32(
        P1Types.Balance memory balance
    )
        internal
        pure
        returns (bytes32)
    {
        uint256 result =
            uint256(balance.position)
            | (uint256(balance.margin) << 128)
            | (balance.marginIsPositive ? FLAG_MARGIN_IS_POSITIVE : 0)
            | (balance.positionIsPositive ? FLAG_POSITION_IS_POSITIVE : 0);
        return bytes32(result);
    }

    // ============ Helper Functions ============

    /**
     * @dev Returns a SignedMath.Int version of the margin in balance.
     */
    function getMargin(
        P1Types.Balance memory balance
    )
        internal
        pure
        returns (SignedMath.Int memory)
    {
        return SignedMath.Int({
            value: balance.margin,
            isPositive: balance.marginIsPositive
        });
    }

    /**
     * @dev Returns a SignedMath.Int version of the position in balance.
     */
    function getPosition(
        P1Types.Balance memory balance
    )
        internal
        pure
        returns (SignedMath.Int memory)
    {
        return SignedMath.Int({
            value: balance.position,
            isPositive: balance.positionIsPositive
        });
    }

    /**
     * @dev In-place modify the signed margin value of a balance.
     */
    function setMargin(
        P1Types.Balance memory balance,
        SignedMath.Int memory newMargin
    )
        internal
        pure
    {
        balance.margin = newMargin.value.toUint120();
        balance.marginIsPositive = newMargin.isPositive;
    }

    /**
     * @dev In-place modify the signed position value of a balance.
     */
    function setPosition(
        P1Types.Balance memory balance,
        SignedMath.Int memory newPosition
    )
        internal
        pure
    {
        balance.position = newPosition.value.toUint120();
        balance.positionIsPositive = newPosition.isPositive;
    }
}

// File: contracts/protocol/v1/traders/P1Deleveraging.sol

/**
 * @title P1Deleveraging
 * @author dYdX
 *
 * @notice Contract allowing underwater accounts to be deleveraged against offsetting accounts.
 */
contract P1Deleveraging is
    Ownable,
    P1TraderConstants
{
    using SafeMath for uint256;
    using Math for uint256;
    using P1BalanceMath for P1Types.Balance;

    // ============ Structs ============

    struct TradeData {
        uint256 amount;
        bool isBuy; // from taker's perspective
        bool allOrNothing; // if true, will revert if maker's position is less than the amount
    }

    // ============ Events ============

    event LogDeleveraged(
        address indexed maker,
        address indexed taker,
        uint256 amount,
        bool isBuy, // from taker's perspective
        uint256 oraclePrice
    );

    event LogMarkedForDeleveraging(
        address indexed account
    );

    event LogUnmarkedForDeleveraging(
        address indexed account
    );

    event LogDeleveragingOperatorSet(
        address deleveragingOperator
    );

    // ============ Immutable Storage ============

    // address of the perpetual contract
    address public _PERPETUAL_V1_;

    // Waiting period for non-admin to deleverage an account after marking it.
    uint256 constant public DELEVERAGING_TIMELOCK_S = 1800; // 30 minutes

    // ============ Mutable Storage ============

    // account => timestamp at which an account was marked as underwater
    //
    // After an account has been marked for the timelock period, it can be deleveraged by anybody.
    // The contract admin can deleverage underwater accounts at any time.
    mapping (address => uint256) public _MARKED_TIMESTAMP_;

    // Address which has the ability to deleverage accounts without marking them first.
    address public _DELEVERAGING_OPERATOR_;

    // ============ Constructor ============

    constructor (
        address perpetualV1,
        address deleveragingOperator
    )
        public
    {
        _PERPETUAL_V1_ = perpetualV1;
        _DELEVERAGING_OPERATOR_ = deleveragingOperator;

        emit LogDeleveragingOperatorSet(deleveragingOperator);
    }

    // ============ External Functions ============

    /**
     * @notice Allows an underwater (less than 100% collateralization) account to be subsumed by any
     *  other account with an offsetting position (a position of opposite sign). The sender must be
     *  the privileged deleveraging operator unless the account has been marked as underwater for
     *  the timelock period.
     * @dev Emits the LogDeleveraged event. May emit the LogUnmarkedForDeleveraging event.
     *
     * @param  sender  The address that called the trade() function on PerpetualV1.
     * @param  maker   The underwater account.
     * @param  taker   The offsetting account.
     * @param  price   The current oracle price of the underlying asset.
     * @param  data    A struct of type TradeData.
     * @return         The amounts to be traded, and flags indicating that deleveraging occurred.
     */
    function trade(
        address sender,
        address maker,
        address taker,
        uint256 price,
        bytes calldata data,
        bytes32 traderFlags
    )
        external
        returns (P1Types.TradeResult memory)
    {
        address perpetual = _PERPETUAL_V1_;
        require(
            msg.sender == perpetual,
            "msg.sender must be PerpetualV1"
        );
        require(
            traderFlags == 0,
            "cannot deleverage after other trade operations, in the same tx"
        );

        _verifyPermissions(
            sender,
            maker
        );

        TradeData memory tradeData = abi.decode(data, (TradeData));
        P1Types.Balance memory makerBalance = P1Getters(perpetual).getAccountBalance(maker);
        P1Types.Balance memory takerBalance = P1Getters(perpetual).getAccountBalance(taker);

        _verifyTrade(
            tradeData,
            makerBalance,
            takerBalance,
            price
        );

        // Bound the execution amount by the size of the maker and taker positions.
        uint256 amount = Math.min(
            tradeData.amount,
            Math.min(makerBalance.position, takerBalance.position)
        );

        // When partially deleveraging the maker, maintain the same position/margin ratio.
        // Ensure the collateralization of the maker does not decrease.
        uint256 marginAmount;
        if (tradeData.isBuy) {
            marginAmount = uint256(makerBalance.margin).getFractionRoundUp(
                amount,
                makerBalance.position
            );
        } else {
            marginAmount = uint256(makerBalance.margin).getFraction(amount, makerBalance.position);
        }

        if (amount == makerBalance.position && _isMarked(maker)) {
            _unmark(maker);
        }

        emit LogDeleveraged(
            maker,
            taker,
            amount,
            tradeData.isBuy,
            price
        );

        return P1Types.TradeResult({
            marginAmount: marginAmount,
            positionAmount: amount,
            isBuy: tradeData.isBuy,
            traderFlags: TRADER_FLAG_DELEVERAGING
        });
    }

    /**
     * @notice Mark an account as underwater. An account must be marked for a period of time before
     *  any non-admin is allowed to deleverage that account.
     * @dev Emits the LogMarkedForDeleveraging event.
     *
     * @param  account  The account to mark.
     */
    function mark(
        address account
    )
        external
    {
        require(
            _isAccountUnderwater(account),
            "Cannot mark since account is not underwater"
        );
        _MARKED_TIMESTAMP_[account] = block.timestamp;
        emit LogMarkedForDeleveraging(account);
    }

    /**
     * @notice Un-mark an account which is no longer underwater.
     * @dev Emits the LogUnmarkedForDeleveraging event.
     *
     * @param  account  The account to unmark.
     */
    function unmark(
        address account
    )
        external
    {
        require(
            !_isAccountUnderwater(account),
            "Cannot unmark since account is underwater"
        );
        _unmark(account);
    }

    /**
     * @notice Set the privileged deleveraging operator. Can only be called by the admin.
     * @dev Emits the LogFundingRateProviderSet event.
     *
     * @param  newOperator  The new operator, who will have the ability to deleverage accounts
     *                      without first marking them and waiting the timelock period.
     */
    function setDeleveragingOperator(
        address newOperator
    )
        external
        onlyOwner
    {
        _DELEVERAGING_OPERATOR_ = newOperator;
        emit LogDeleveragingOperatorSet(newOperator);
    }

    // ============ Helper Functions ============

    function _unmark(
        address account
    )
        private
    {
        _MARKED_TIMESTAMP_[account] = 0;
        emit LogUnmarkedForDeleveraging(account);
    }

    function _isMarked(
        address account
    )
        private
        view
        returns (bool)
    {
        return _MARKED_TIMESTAMP_[account] != 0;
    }

    function _verifyPermissions(
        address sender,
        address maker
    )
        private
        view
    {
        // The privileged deleveraging operator may deleverage underwater accounts at any time.
        if (sender != _DELEVERAGING_OPERATOR_) {
            uint256 markedTimestamp = _MARKED_TIMESTAMP_[maker];
            require(
                markedTimestamp != 0,
                "Cannot deleverage since account is not marked"
            );
            uint256 timeDelta = block.timestamp.sub(markedTimestamp);
            require(
                timeDelta >= DELEVERAGING_TIMELOCK_S,
                "Cannot deleverage since account has not been marked for the timelock period"
            );
        }
    }

    function _verifyTrade(
        TradeData memory tradeData,
        P1Types.Balance memory makerBalance,
        P1Types.Balance memory takerBalance,
        uint256 price
    )
        private
        pure
    {
        require(
            _isUnderwater(makerBalance, price),
            "Cannot deleverage since maker is not underwater"
        );
        require(
            !tradeData.allOrNothing || makerBalance.position >= tradeData.amount,
            "allOrNothing is set and maker position is less than amount"
        );
        require(
            takerBalance.positionIsPositive != makerBalance.positionIsPositive,
            "Taker position has wrong sign to deleverage this maker"
        );
        require(
            !tradeData.allOrNothing || takerBalance.position >= tradeData.amount,
            "allOrNothing is set and taker position is less than amount"
        );
        require(
            tradeData.isBuy == makerBalance.positionIsPositive,
            "deleveraging must not increase maker's position size"
        );

        // Disallow deleveraging in the edge case where both the position and margin are negative.
        //
        // This case is not handled correctly by P1Trade. If an account is in this situation, the
        // margin should first be set to zero via a deposit, then the account should be deleveraged.
        require(
            makerBalance.marginIsPositive || makerBalance.margin == 0 ||
                makerBalance.positionIsPositive || makerBalance.position == 0,
            "Cannot liquidate when maker position and margin are both negative"
        );
    }

    function _isUnderwater(
        P1Types.Balance memory balance,
        uint256 price
    )
        private
        pure
        returns (bool)
    {
        (uint256 positive, uint256 negative) = balance.getPositiveAndNegativeValue(price);
        return positive < negative;
    }

    function _isAccountUnderwater(
        address account
    )
        private
        view
        returns (bool)
    {
        address perpetual = _PERPETUAL_V1_;
        P1Types.Balance memory balance = P1Getters(perpetual).getAccountBalance(account);
        address oracle = P1Getters(perpetual).getOracleContract();
        uint256 price = I_P1Oracle(oracle).getPrice();
        return _isUnderwater(balance, price);
    }
}