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

pragma solidity ^0.8.1;

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     *
     * Furthermore, `isContract` will also return true if the target contract within
     * the same transaction is already scheduled for destruction by `SELFDESTRUCT`,
     * which only has an effect at the end of a transaction.
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.8.0/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    function _revert(bytes memory returndata, string memory errorMessage) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            /// @solidity memory-safe-assembly
            assembly {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert(errorMessage);
        }
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

library ArrayLib {
    function sum(uint256[] memory input) internal pure returns (uint256) {
        uint256 value = 0;
        for (uint256 i = 0; i < input.length; ) {
            value += input[i];
            unchecked {
                i++;
            }
        }
        return value;
    }

    /// @notice return index of the element if found, else return uint256.max
    function find(address[] memory array, address element) internal pure returns (uint256 index) {
        uint256 length = array.length;
        for (uint256 i = 0; i < length; ) {
            if (array[i] == element) return i;
            unchecked {
                i++;
            }
        }
        return type(uint256).max;
    }

    function append(address[] memory inp, address element) internal pure returns (address[] memory out) {
        uint256 length = inp.length;
        out = new address[](length + 1);
        for (uint256 i = 0; i < length; ) {
            out[i] = inp[i];
            unchecked {
                i++;
            }
        }
        out[length] = element;
    }

    /**
     * @dev This function assumes a and b each contains unidentical elements
     * @param a array of addresses a
     * @param b array of addresses b
     * @return out Concatenation of a and b containing unidentical elements
     */
    function merge(address[] memory a, address[] memory b) internal pure returns (address[] memory out) {
        unchecked {
            uint256 countUnidenticalB = 0;
            bool[] memory isUnidentical = new bool[](b.length);
            for (uint256 i = 0; i < b.length; ++i) {
                if (!contains(a, b[i])) {
                    countUnidenticalB++;
                    isUnidentical[i] = true;
                }
            }

            out = new address[](a.length + countUnidenticalB);
            for (uint256 i = 0; i < a.length; ++i) {
                out[i] = a[i];
            }
            uint256 id = a.length;
            for (uint256 i = 0; i < b.length; ++i) {
                if (isUnidentical[i]) {
                    out[id++] = b[i];
                }
            }
        }
    }

    // various version of contains
    function contains(address[] memory array, address element) internal pure returns (bool) {
        uint256 length = array.length;
        for (uint256 i = 0; i < length; ) {
            if (array[i] == element) return true;
            unchecked {
                i++;
            }
        }
        return false;
    }

    function contains(bytes4[] memory array, bytes4 element) internal pure returns (bool) {
        uint256 length = array.length;
        for (uint256 i = 0; i < length; ) {
            if (array[i] == element) return true;
            unchecked {
                i++;
            }
        }
        return false;
    }

    function create(address a) internal pure returns (address[] memory res) {
        res = new address[](1);
        res[0] = a;
    }

    function create(address a, address b) internal pure returns (address[] memory res) {
        res = new address[](2);
        res[0] = a;
        res[1] = b;
    }

    function create(uint256 a) internal pure returns (uint256[] memory res) {
        res = new uint256[](1);
        res[0] = a;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (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;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Counters.sol)

pragma solidity ^0.8.0;

/**
 * @title Counters
 * @author Matt Condon (@shrugs)
 * @dev Provides counters that can only be incremented, decremented or reset. This can be used e.g. to track the number
 * of elements in a mapping, issuing ERC721 ids, or counting request ids.
 *
 * Include with `using Counters for Counters.Counter;`
 */
library Counters {
    struct Counter {
        // This variable should never be directly accessed by users of the library: interactions must be restricted to
        // the library's function. As of Solidity v0.5.2, this cannot be enforced, though there is a proposal to add
        // this feature: see https://github.com/ethereum/solidity/issues/4637
        uint256 _value; // default: 0
    }

    function current(Counter storage counter) internal view returns (uint256) {
        return counter._value;
    }

    function increment(Counter storage counter) internal {
        unchecked {
            counter._value += 1;
        }
    }

    function decrement(Counter storage counter) internal {
        uint256 value = counter._value;
        require(value > 0, "Counter: decrement overflow");
        unchecked {
            counter._value = value - 1;
        }
    }

    function reset(Counter storage counter) internal {
        counter._value = 0;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.0;

import "../Strings.sol";

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS,
        InvalidSignatureV // Deprecated in v4.8
    }

    function _throwError(RecoverError error) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert("ECDSA: invalid signature");
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert("ECDSA: invalid signature length");
        } else if (error == RecoverError.InvalidSignatureS) {
            revert("ECDSA: invalid signature 's' value");
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature` or error string. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            /// @solidity memory-safe-assembly
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength);
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address, RecoverError) {
        bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
        uint8 v = uint8((uint256(vs) >> 255) + 27);
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address, RecoverError) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32 message) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, "\x19Ethereum Signed Message:\n32")
            mstore(0x1c, hash)
            message := keccak256(0x00, 0x3c)
        }
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from `s`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n", Strings.toString(s.length), s));
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32 data) {
        /// @solidity memory-safe-assembly
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, "\x19\x01")
            mstore(add(ptr, 0x02), domainSeparator)
            mstore(add(ptr, 0x22), structHash)
            data := keccak256(ptr, 0x42)
        }
    }

    /**
     * @dev Returns an Ethereum Signed Data with intended validator, created from a
     * `validator` and `data` according to the version 0 of EIP-191.
     *
     * See {recover}.
     */
    function toDataWithIntendedValidatorHash(address validator, bytes memory data) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x00", validator, data));
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/cryptography/EIP712.sol)

pragma solidity ^0.8.8;

import "./ECDSA.sol";
import "../ShortStrings.sol";
import "../../interfaces/IERC5267.sol";

/**
 * @dev https://eips.ethereum.org/EIPS/eip-712[EIP 712] is a standard for hashing and signing of typed structured data.
 *
 * The encoding specified in the EIP is very generic, and such a generic implementation in Solidity is not feasible,
 * thus this contract does not implement the encoding itself. Protocols need to implement the type-specific encoding
 * they need in their contracts using a combination of `abi.encode` and `keccak256`.
 *
 * This contract implements the EIP 712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding
 * scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA
 * ({_hashTypedDataV4}).
 *
 * The implementation of the domain separator was designed to be as efficient as possible while still properly updating
 * the chain id to protect against replay attacks on an eventual fork of the chain.
 *
 * NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method
 * https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask].
 *
 * NOTE: In the upgradeable version of this contract, the cached values will correspond to the address, and the domain
 * separator of the implementation contract. This will cause the `_domainSeparatorV4` function to always rebuild the
 * separator from the immutable values, which is cheaper than accessing a cached version in cold storage.
 *
 * _Available since v3.4._
 *
 * @custom:oz-upgrades-unsafe-allow state-variable-immutable state-variable-assignment
 */
abstract contract EIP712 is IERC5267 {
    using ShortStrings for *;

    bytes32 private constant _TYPE_HASH =
        keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)");

    // Cache the domain separator as an immutable value, but also store the chain id that it corresponds to, in order to
    // invalidate the cached domain separator if the chain id changes.
    bytes32 private immutable _cachedDomainSeparator;
    uint256 private immutable _cachedChainId;
    address private immutable _cachedThis;

    bytes32 private immutable _hashedName;
    bytes32 private immutable _hashedVersion;

    ShortString private immutable _name;
    ShortString private immutable _version;
    string private _nameFallback;
    string private _versionFallback;

    /**
     * @dev Initializes the domain separator and parameter caches.
     *
     * The meaning of `name` and `version` is specified in
     * https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP 712]:
     *
     * - `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol.
     * - `version`: the current major version of the signing domain.
     *
     * NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart
     * contract upgrade].
     */
    constructor(string memory name, string memory version) {
        _name = name.toShortStringWithFallback(_nameFallback);
        _version = version.toShortStringWithFallback(_versionFallback);
        _hashedName = keccak256(bytes(name));
        _hashedVersion = keccak256(bytes(version));

        _cachedChainId = block.chainid;
        _cachedDomainSeparator = _buildDomainSeparator();
        _cachedThis = address(this);
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view returns (bytes32) {
        if (address(this) == _cachedThis && block.chainid == _cachedChainId) {
            return _cachedDomainSeparator;
        } else {
            return _buildDomainSeparator();
        }
    }

    function _buildDomainSeparator() private view returns (bytes32) {
        return keccak256(abi.encode(_TYPE_HASH, _hashedName, _hashedVersion, block.chainid, address(this)));
    }

    /**
     * @dev Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this
     * function returns the hash of the fully encoded EIP712 message for this domain.
     *
     * This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example:
     *
     * ```solidity
     * bytes32 digest = _hashTypedDataV4(keccak256(abi.encode(
     *     keccak256("Mail(address to,string contents)"),
     *     mailTo,
     *     keccak256(bytes(mailContents))
     * )));
     * address signer = ECDSA.recover(digest, signature);
     * ```
     */
    function _hashTypedDataV4(bytes32 structHash) internal view virtual returns (bytes32) {
        return ECDSA.toTypedDataHash(_domainSeparatorV4(), structHash);
    }

    /**
     * @dev See {EIP-5267}.
     *
     * _Available since v4.9._
     */
    function eip712Domain()
        public
        view
        virtual
        override
        returns (
            bytes1 fields,
            string memory name,
            string memory version,
            uint256 chainId,
            address verifyingContract,
            bytes32 salt,
            uint256[] memory extensions
        )
    {
        return (
            hex"0f", // 01111
            _name.toStringWithFallback(_nameFallback),
            _version.toStringWithFallback(_versionFallback),
            block.chainid,
            address(this),
            bytes32(0),
            new uint256[](0)
        );
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.0;

import "./IERC20.sol";
import "./extensions/IERC20Metadata.sol";
import "../../utils/Context.sol";

/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 * For a generic mechanism see {ERC20PresetMinterPauser}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.openzeppelin.com/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * The default value of {decimals} is 18. To change this, you should override
 * this function so it returns a different value.
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead returning `false` on failure. This behavior is nonetheless
 * conventional and does not conflict with the expectations of ERC20
 * applications.
 *
 * Additionally, an {Approval} event is emitted on calls to {transferFrom}.
 * This allows applications to reconstruct the allowance for all accounts just
 * by listening to said events. Other implementations of the EIP may not emit
 * these events, as it isn't required by the specification.
 *
 * Finally, the non-standard {decreaseAllowance} and {increaseAllowance}
 * functions have been added to mitigate the well-known issues around setting
 * allowances. See {IERC20-approve}.
 */
contract ERC20 is Context, IERC20, IERC20Metadata {
    mapping(address => uint256) private _balances;

    mapping(address => mapping(address => uint256)) private _allowances;

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * All two of these values are immutable: they can only be set once during
     * construction.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev Returns the name of the token.
     */
    function name() public view virtual override returns (string memory) {
        return _name;
    }

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the default value returned by this function, unless
     * it's overridden.
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual override returns (uint8) {
        return 18;
    }

    /**
     * @dev See {IERC20-totalSupply}.
     */
    function totalSupply() public view virtual override returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev See {IERC20-balanceOf}.
     */
    function balanceOf(address account) public view virtual override returns (uint256) {
        return _balances[account];
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - the caller must have a balance of at least `amount`.
     */
    function transfer(address to, uint256 amount) public virtual override returns (bool) {
        address owner = _msgSender();
        _transfer(owner, to, amount);
        return true;
    }

    /**
     * @dev See {IERC20-allowance}.
     */
    function allowance(address owner, address spender) public view virtual override returns (uint256) {
        return _allowances[owner][spender];
    }

    /**
     * @dev See {IERC20-approve}.
     *
     * NOTE: If `amount` is the maximum `uint256`, the allowance is not updated on
     * `transferFrom`. This is semantically equivalent to an infinite approval.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 amount) public virtual override returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, amount);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Emits an {Approval} event indicating the updated allowance. This is not
     * required by the EIP. See the note at the beginning of {ERC20}.
     *
     * NOTE: Does not update the allowance if the current allowance
     * is the maximum `uint256`.
     *
     * Requirements:
     *
     * - `from` and `to` cannot be the zero address.
     * - `from` must have a balance of at least `amount`.
     * - the caller must have allowance for ``from``'s tokens of at least
     * `amount`.
     */
    function transferFrom(address from, address to, uint256 amount) public virtual override returns (bool) {
        address spender = _msgSender();
        _spendAllowance(from, spender, amount);
        _transfer(from, to, amount);
        return true;
    }

    /**
     * @dev Atomically increases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function increaseAllowance(address spender, uint256 addedValue) public virtual returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, allowance(owner, spender) + addedValue);
        return true;
    }

    /**
     * @dev Atomically decreases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `spender` must have allowance for the caller of at least
     * `subtractedValue`.
     */
    function decreaseAllowance(address spender, uint256 subtractedValue) public virtual returns (bool) {
        address owner = _msgSender();
        uint256 currentAllowance = allowance(owner, spender);
        require(currentAllowance >= subtractedValue, "ERC20: decreased allowance below zero");
        unchecked {
            _approve(owner, spender, currentAllowance - subtractedValue);
        }

        return true;
    }

    /**
     * @dev Moves `amount` of tokens from `from` to `to`.
     *
     * This internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `from` must have a balance of at least `amount`.
     */
    function _transfer(address from, address to, uint256 amount) internal virtual {
        require(from != address(0), "ERC20: transfer from the zero address");
        require(to != address(0), "ERC20: transfer to the zero address");

        _beforeTokenTransfer(from, to, amount);

        uint256 fromBalance = _balances[from];
        require(fromBalance >= amount, "ERC20: transfer amount exceeds balance");
        unchecked {
            _balances[from] = fromBalance - amount;
            // Overflow not possible: the sum of all balances is capped by totalSupply, and the sum is preserved by
            // decrementing then incrementing.
            _balances[to] += amount;
        }

        emit Transfer(from, to, amount);

        _afterTokenTransfer(from, to, amount);
    }

    /** @dev Creates `amount` tokens and assigns them to `account`, increasing
     * the total supply.
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     */
    function _mint(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: mint to the zero address");

        _beforeTokenTransfer(address(0), account, amount);

        _totalSupply += amount;
        unchecked {
            // Overflow not possible: balance + amount is at most totalSupply + amount, which is checked above.
            _balances[account] += amount;
        }
        emit Transfer(address(0), account, amount);

        _afterTokenTransfer(address(0), account, amount);
    }

    /**
     * @dev Destroys `amount` tokens from `account`, reducing the
     * total supply.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - `account` must have at least `amount` tokens.
     */
    function _burn(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: burn from the zero address");

        _beforeTokenTransfer(account, address(0), amount);

        uint256 accountBalance = _balances[account];
        require(accountBalance >= amount, "ERC20: burn amount exceeds balance");
        unchecked {
            _balances[account] = accountBalance - amount;
            // Overflow not possible: amount <= accountBalance <= totalSupply.
            _totalSupply -= amount;
        }

        emit Transfer(account, address(0), amount);

        _afterTokenTransfer(account, address(0), amount);
    }

    /**
     * @dev Sets `amount` as the allowance of `spender` over the `owner` s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     */
    function _approve(address owner, address spender, uint256 amount) internal virtual {
        require(owner != address(0), "ERC20: approve from the zero address");
        require(spender != address(0), "ERC20: approve to the zero address");

        _allowances[owner][spender] = amount;
        emit Approval(owner, spender, amount);
    }

    /**
     * @dev Updates `owner` s allowance for `spender` based on spent `amount`.
     *
     * Does not update the allowance amount in case of infinite allowance.
     * Revert if not enough allowance is available.
     *
     * Might emit an {Approval} event.
     */
    function _spendAllowance(address owner, address spender, uint256 amount) internal virtual {
        uint256 currentAllowance = allowance(owner, spender);
        if (currentAllowance != type(uint256).max) {
            require(currentAllowance >= amount, "ERC20: insufficient allowance");
            unchecked {
                _approve(owner, spender, currentAllowance - amount);
            }
        }
    }

    /**
     * @dev Hook that is called before any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * will be transferred to `to`.
     * - when `from` is zero, `amount` tokens will be minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens will be burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(address from, address to, uint256 amount) internal virtual {}

    /**
     * @dev Hook that is called after any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * has been transferred to `to`.
     * - when `from` is zero, `amount` tokens have been minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens have been burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _afterTokenTransfer(address from, address to, uint256 amount) internal virtual {}
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC20/extensions/ERC20Permit.sol)

pragma solidity ^0.8.0;

import "./IERC20Permit.sol";
import "../ERC20.sol";
import "../../../utils/cryptography/ECDSA.sol";
import "../../../utils/cryptography/EIP712.sol";
import "../../../utils/Counters.sol";

/**
 * @dev Implementation of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on `{IERC20-approve}`, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 *
 * _Available since v3.4._
 */
abstract contract ERC20Permit is ERC20, IERC20Permit, EIP712 {
    using Counters for Counters.Counter;

    mapping(address => Counters.Counter) private _nonces;

    // solhint-disable-next-line var-name-mixedcase
    bytes32 private constant _PERMIT_TYPEHASH =
        keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)");
    /**
     * @dev In previous versions `_PERMIT_TYPEHASH` was declared as `immutable`.
     * However, to ensure consistency with the upgradeable transpiler, we will continue
     * to reserve a slot.
     * @custom:oz-renamed-from _PERMIT_TYPEHASH
     */
    // solhint-disable-next-line var-name-mixedcase
    bytes32 private _PERMIT_TYPEHASH_DEPRECATED_SLOT;

    /**
     * @dev Initializes the {EIP712} domain separator using the `name` parameter, and setting `version` to `"1"`.
     *
     * It's a good idea to use the same `name` that is defined as the ERC20 token name.
     */
    constructor(string memory name) EIP712(name, "1") {}

    /**
     * @dev See {IERC20Permit-permit}.
     */
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual override {
        require(block.timestamp <= deadline, "ERC20Permit: expired deadline");

        bytes32 structHash = keccak256(abi.encode(_PERMIT_TYPEHASH, owner, spender, value, _useNonce(owner), deadline));

        bytes32 hash = _hashTypedDataV4(structHash);

        address signer = ECDSA.recover(hash, v, r, s);
        require(signer == owner, "ERC20Permit: invalid signature");

        _approve(owner, spender, value);
    }

    /**
     * @dev See {IERC20Permit-nonces}.
     */
    function nonces(address owner) public view virtual override returns (uint256) {
        return _nonces[owner].current();
    }

    /**
     * @dev See {IERC20Permit-DOMAIN_SEPARATOR}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view override returns (bytes32) {
        return _domainSeparatorV4();
    }

    /**
     * @dev "Consume a nonce": return the current value and increment.
     *
     * _Available since v4.1._
     */
    function _useNonce(address owner) internal virtual returns (uint256 current) {
        Counters.Counter storage nonce = _nonces[owner];
        current = nonce.current();
        nonce.increment();
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

library Errors {
    // BulkSeller
    error BulkInsufficientSyForTrade(uint256 currentAmount, uint256 requiredAmount);
    error BulkInsufficientTokenForTrade(uint256 currentAmount, uint256 requiredAmount);
    error BulkInSufficientSyOut(uint256 actualSyOut, uint256 requiredSyOut);
    error BulkInSufficientTokenOut(uint256 actualTokenOut, uint256 requiredTokenOut);
    error BulkInsufficientSyReceived(uint256 actualBalance, uint256 requiredBalance);
    error BulkNotMaintainer();
    error BulkNotAdmin();
    error BulkSellerAlreadyExisted(address token, address SY, address bulk);
    error BulkSellerInvalidToken(address token, address SY);
    error BulkBadRateTokenToSy(uint256 actualRate, uint256 currentRate, uint256 eps);
    error BulkBadRateSyToToken(uint256 actualRate, uint256 currentRate, uint256 eps);

    // APPROX
    error ApproxFail();
    error ApproxParamsInvalid(uint256 guessMin, uint256 guessMax, uint256 eps);
    error ApproxBinarySearchInputInvalid(
        uint256 approxGuessMin,
        uint256 approxGuessMax,
        uint256 minGuessMin,
        uint256 maxGuessMax
    );

    // MARKET + MARKET MATH CORE
    error MarketExpired();
    error MarketZeroAmountsInput();
    error MarketZeroAmountsOutput();
    error MarketZeroLnImpliedRate();
    error MarketInsufficientPtForTrade(int256 currentAmount, int256 requiredAmount);
    error MarketInsufficientPtReceived(uint256 actualBalance, uint256 requiredBalance);
    error MarketInsufficientSyReceived(uint256 actualBalance, uint256 requiredBalance);
    error MarketZeroTotalPtOrTotalAsset(int256 totalPt, int256 totalAsset);
    error MarketExchangeRateBelowOne(int256 exchangeRate);
    error MarketProportionMustNotEqualOne();
    error MarketRateScalarBelowZero(int256 rateScalar);
    error MarketScalarRootBelowZero(int256 scalarRoot);
    error MarketProportionTooHigh(int256 proportion, int256 maxProportion);

    error OracleUninitialized();
    error OracleTargetTooOld(uint32 target, uint32 oldest);
    error OracleZeroCardinality();

    error MarketFactoryExpiredPt();
    error MarketFactoryInvalidPt();
    error MarketFactoryMarketExists();

    error MarketFactoryLnFeeRateRootTooHigh(uint80 lnFeeRateRoot, uint256 maxLnFeeRateRoot);
    error MarketFactoryOverriddenFeeTooHigh(uint80 overriddenFee, uint256 marketLnFeeRateRoot);
    error MarketFactoryReserveFeePercentTooHigh(uint8 reserveFeePercent, uint8 maxReserveFeePercent);
    error MarketFactoryZeroTreasury();
    error MarketFactoryInitialAnchorTooLow(int256 initialAnchor, int256 minInitialAnchor);
    error MFNotPendleMarket(address addr);

    // ROUTER
    error RouterInsufficientLpOut(uint256 actualLpOut, uint256 requiredLpOut);
    error RouterInsufficientSyOut(uint256 actualSyOut, uint256 requiredSyOut);
    error RouterInsufficientPtOut(uint256 actualPtOut, uint256 requiredPtOut);
    error RouterInsufficientYtOut(uint256 actualYtOut, uint256 requiredYtOut);
    error RouterInsufficientPYOut(uint256 actualPYOut, uint256 requiredPYOut);
    error RouterInsufficientTokenOut(uint256 actualTokenOut, uint256 requiredTokenOut);
    error RouterInsufficientSyRepay(uint256 actualSyRepay, uint256 requiredSyRepay);
    error RouterInsufficientPtRepay(uint256 actualPtRepay, uint256 requiredPtRepay);
    error RouterNotAllSyUsed(uint256 netSyDesired, uint256 netSyUsed);

    error RouterTimeRangeZero();
    error RouterCallbackNotPendleMarket(address caller);
    error RouterInvalidAction(bytes4 selector);
    error RouterInvalidFacet(address facet);

    error RouterKyberSwapDataZero();

    error SimulationResults(bool success, bytes res);

    // YIELD CONTRACT
    error YCExpired();
    error YCNotExpired();
    error YieldContractInsufficientSy(uint256 actualSy, uint256 requiredSy);
    error YCNothingToRedeem();
    error YCPostExpiryDataNotSet();
    error YCNoFloatingSy();

    // YieldFactory
    error YCFactoryInvalidExpiry();
    error YCFactoryYieldContractExisted();
    error YCFactoryZeroExpiryDivisor();
    error YCFactoryZeroTreasury();
    error YCFactoryInterestFeeRateTooHigh(uint256 interestFeeRate, uint256 maxInterestFeeRate);
    error YCFactoryRewardFeeRateTooHigh(uint256 newRewardFeeRate, uint256 maxRewardFeeRate);

    // SY
    error SYInvalidTokenIn(address token);
    error SYInvalidTokenOut(address token);
    error SYZeroDeposit();
    error SYZeroRedeem();
    error SYInsufficientSharesOut(uint256 actualSharesOut, uint256 requiredSharesOut);
    error SYInsufficientTokenOut(uint256 actualTokenOut, uint256 requiredTokenOut);

    // SY-specific
    error SYQiTokenMintFailed(uint256 errCode);
    error SYQiTokenRedeemFailed(uint256 errCode);
    error SYQiTokenRedeemRewardsFailed(uint256 rewardAccruedType0, uint256 rewardAccruedType1);
    error SYQiTokenBorrowRateTooHigh(uint256 borrowRate, uint256 borrowRateMax);

    error SYCurveInvalidPid();
    error SYCurve3crvPoolNotFound();

    error SYApeDepositAmountTooSmall(uint256 amountDeposited);
    error SYBalancerInvalidPid();
    error SYInvalidRewardToken(address token);

    error SYStargateRedeemCapExceeded(uint256 amountLpDesired, uint256 amountLpRedeemable);

    error SYBalancerReentrancy();

    error NotFromTrustedRemote(uint16 srcChainId, bytes path);

    // Liquidity Mining
    error VCInactivePool(address pool);
    error VCPoolAlreadyActive(address pool);
    error VCZeroVePendle(address user);
    error VCExceededMaxWeight(uint256 totalWeight, uint256 maxWeight);
    error VCEpochNotFinalized(uint256 wTime);
    error VCPoolAlreadyAddAndRemoved(address pool);

    error VEInvalidNewExpiry(uint256 newExpiry);
    error VEExceededMaxLockTime();
    error VEInsufficientLockTime();
    error VENotAllowedReduceExpiry();
    error VEZeroAmountLocked();
    error VEPositionNotExpired();
    error VEZeroPosition();
    error VEZeroSlope(uint128 bias, uint128 slope);
    error VEReceiveOldSupply(uint256 msgTime);

    error GCNotPendleMarket(address caller);
    error GCNotVotingController(address caller);

    error InvalidWTime(uint256 wTime);
    error ExpiryInThePast(uint256 expiry);
    error ChainNotSupported(uint256 chainId);

    error FDTotalAmountFundedNotMatch(uint256 actualTotalAmount, uint256 expectedTotalAmount);
    error FDEpochLengthMismatch();
    error FDInvalidPool(address pool);
    error FDPoolAlreadyExists(address pool);
    error FDInvalidNewFinishedEpoch(uint256 oldFinishedEpoch, uint256 newFinishedEpoch);
    error FDInvalidStartEpoch(uint256 startEpoch);
    error FDInvalidWTimeFund(uint256 lastFunded, uint256 wTime);
    error FDFutureFunding(uint256 lastFunded, uint256 currentWTime);

    error BDInvalidEpoch(uint256 epoch, uint256 startTime);

    // Cross-Chain
    error MsgNotFromSendEndpoint(uint16 srcChainId, bytes path);
    error MsgNotFromReceiveEndpoint(address sender);
    error InsufficientFeeToSendMsg(uint256 currentFee, uint256 requiredFee);
    error ApproxDstExecutionGasNotSet();
    error InvalidRetryData();

    // GENERIC MSG
    error ArrayLengthMismatch();
    error ArrayEmpty();
    error ArrayOutOfBounds();
    error ZeroAddress();
    error FailedToSendEther();
    error InvalidMerkleProof();

    error OnlyLayerZeroEndpoint();
    error OnlyYT();
    error OnlyYCFactory();
    error OnlyWhitelisted();

    // Swap Aggregator
    error SAInsufficientTokenIn(address tokenIn, uint256 amountExpected, uint256 amountActual);
    error UnsupportedSelector(uint256 aggregatorType, bytes4 selector);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);

    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the amount of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves `amount` tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 amount) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `from` to `to` using the
     * allowance mechanism. `amount` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(address from, address to, uint256 amount) external returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Metadata.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";

/**
 * @dev Interface for the optional metadata functions from the ERC20 standard.
 *
 * _Available since v4.1._
 */
interface IERC20Metadata is IERC20 {
    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

    /**
     * @dev Returns the symbol of the token.
     */
    function symbol() external view returns (string memory);

    /**
     * @dev Returns the decimals places of the token.
     */
    function decimals() external view returns (uint8);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC20/extensions/IERC20Permit.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on {IERC20-approve}, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 */
interface IERC20Permit {
    /**
     * @dev Sets `value` as the allowance of `spender` over ``owner``'s tokens,
     * given ``owner``'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     */
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

    /**
     * @dev Returns the current nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases ``owner``'s nonce by one. This
     * prevents a signature from being used multiple times.
     */
    function nonces(address owner) external view returns (uint256);

    /**
     * @dev Returns the domain separator used in the encoding of the signature for {permit}, as defined by {EIP712}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view returns (bytes32);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (interfaces/IERC5267.sol)

pragma solidity ^0.8.0;

interface IERC5267 {
    /**
     * @dev MAY be emitted to signal that the domain could have changed.
     */
    event EIP712DomainChanged();

    /**
     * @dev returns the fields and values that describe the domain separator used by this contract for EIP-712
     * signature.
     */
    function eip712Domain()
        external
        view
        returns (
            bytes1 fields,
            string memory name,
            string memory version,
            uint256 chainId,
            address verifyingContract,
            bytes32 salt,
            uint256[] memory extensions
        );
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

interface IPGauge {
    function totalActiveSupply() external view returns (uint256);

    function activeBalance(address user) external view returns (uint256);

    // only available for newer factories. please check the verified contracts
    event RedeemRewards(address indexed user, uint256[] rewardsOut);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

interface IPGaugeController {
    event MarketClaimReward(address indexed market, uint256 amount);

    event ReceiveVotingResults(uint128 indexed wTime, address[] markets, uint256[] pendleAmounts);

    event UpdateMarketReward(address indexed market, uint256 pendlePerSec, uint256 incentiveEndsAt);

    function fundPendle(uint256 amount) external;

    function withdrawPendle(uint256 amount) external;

    function pendle() external returns (address);

    function redeemMarketReward() external;

    function rewardData(address pool) external view returns (uint128 pendlePerSec, uint128, uint128, uint128);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

interface IPInterestManagerYT {
    event CollectInterestFee(uint256 amountInterestFee);

    function userInterest(address user) external view returns (uint128 lastPYIndex, uint128 accruedInterest);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

import "@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol";
import "./IPPrincipalToken.sol";
import "./IPYieldToken.sol";
import "./IStandardizedYield.sol";
import "./IPGauge.sol";
import "../core/Market/MarketMathCore.sol";

interface IPMarket is IERC20Metadata, IPGauge {
    event Mint(address indexed receiver, uint256 netLpMinted, uint256 netSyUsed, uint256 netPtUsed);

    event Burn(
        address indexed receiverSy,
        address indexed receiverPt,
        uint256 netLpBurned,
        uint256 netSyOut,
        uint256 netPtOut
    );

    event Swap(
        address indexed caller,
        address indexed receiver,
        int256 netPtOut,
        int256 netSyOut,
        uint256 netSyFee,
        uint256 netSyToReserve
    );

    event UpdateImpliedRate(uint256 indexed timestamp, uint256 lnLastImpliedRate);

    event IncreaseObservationCardinalityNext(
        uint16 observationCardinalityNextOld,
        uint16 observationCardinalityNextNew
    );

    function mint(
        address receiver,
        uint256 netSyDesired,
        uint256 netPtDesired
    ) external returns (uint256 netLpOut, uint256 netSyUsed, uint256 netPtUsed);

    function burn(
        address receiverSy,
        address receiverPt,
        uint256 netLpToBurn
    ) external returns (uint256 netSyOut, uint256 netPtOut);

    function swapExactPtForSy(
        address receiver,
        uint256 exactPtIn,
        bytes calldata data
    ) external returns (uint256 netSyOut, uint256 netSyFee);

    function swapSyForExactPt(
        address receiver,
        uint256 exactPtOut,
        bytes calldata data
    ) external returns (uint256 netSyIn, uint256 netSyFee);

    function redeemRewards(address user) external returns (uint256[] memory);

    function readState(address router) external view returns (MarketState memory market);

    function observe(uint32[] memory secondsAgos) external view returns (uint216[] memory lnImpliedRateCumulative);

    function increaseObservationsCardinalityNext(uint16 cardinalityNext) external;

    function readTokens() external view returns (IStandardizedYield _SY, IPPrincipalToken _PT, IPYieldToken _YT);

    function getRewardTokens() external view returns (address[] memory);

    function isExpired() external view returns (bool);

    function expiry() external view returns (uint256);

    function observations(
        uint256 index
    ) external view returns (uint32 blockTimestamp, uint216 lnImpliedRateCumulative, bool initialized);

    function _storage()
        external
        view
        returns (
            int128 totalPt,
            int128 totalSy,
            uint96 lastLnImpliedRate,
            uint16 observationIndex,
            uint16 observationCardinality,
            uint16 observationCardinalityNext
        );
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

interface IPMarketFactoryV3 {
    event SetOverriddenFee(address indexed router, address indexed market, uint80 lnFeeRateRoot);

    event CreateNewMarket(
        address indexed market,
        address indexed PT,
        int256 scalarRoot,
        int256 initialAnchor,
        uint256 lnFeeRateRoot
    );

    event NewTreasuryAndFeeReserve(address indexed treasury, uint8 reserveFeePercent);

    function isValidMarket(address market) external view returns (bool);

    // If this is changed, change the readState function in market as well
    function getMarketConfig(
        address market,
        address router
    ) external view returns (address treasury, uint80 overriddenFee, uint8 reserveFeePercent);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

interface IPMarketSwapCallback {
    function swapCallback(int256 ptToAccount, int256 syToAccount, bytes calldata data) external;
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

import "./IPMarket.sol";

interface IPMarketV3 is IPMarket {
    function getNonOverrideLnFeeRateRoot() external view returns (uint80);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;
import "@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol";

interface IPPrincipalToken is IERC20Metadata {
    function burnByYT(address user, uint256 amount) external;

    function mintByYT(address user, uint256 amount) external;

    function initialize(address _YT) external;

    function SY() external view returns (address);

    function YT() external view returns (address);

    function factory() external view returns (address);

    function expiry() external view returns (uint256);

    function isExpired() external view returns (bool);
}

// SPDX-License-Identifier: GPL-3.0-or-later

pragma solidity ^0.8.0;

interface IPVeToken {
    // ============= USER INFO =============

    function balanceOf(address user) external view returns (uint128);

    function positionData(address user) external view returns (uint128 amount, uint128 expiry);

    // ============= META DATA =============

    function totalSupplyStored() external view returns (uint128);

    function totalSupplyCurrent() external returns (uint128);

    function totalSupplyAndBalanceCurrent(address user) external returns (uint128, uint128);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;
import "@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol";
import "./IRewardManager.sol";
import "./IPInterestManagerYT.sol";

interface IPYieldToken is IERC20Metadata, IRewardManager, IPInterestManagerYT {
    event NewInterestIndex(uint256 indexed newIndex);

    event Mint(
        address indexed caller,
        address indexed receiverPT,
        address indexed receiverYT,
        uint256 amountSyToMint,
        uint256 amountPYOut
    );

    event Burn(address indexed caller, address indexed receiver, uint256 amountPYToRedeem, uint256 amountSyOut);

    event RedeemRewards(address indexed user, uint256[] amountRewardsOut);

    event RedeemInterest(address indexed user, uint256 interestOut);

    event CollectRewardFee(address indexed rewardToken, uint256 amountRewardFee);

    function mintPY(address receiverPT, address receiverYT) external returns (uint256 amountPYOut);

    function redeemPY(address receiver) external returns (uint256 amountSyOut);

    function redeemPYMulti(
        address[] calldata receivers,
        uint256[] calldata amountPYToRedeems
    ) external returns (uint256[] memory amountSyOuts);

    function redeemDueInterestAndRewards(
        address user,
        bool redeemInterest,
        bool redeemRewards
    ) external returns (uint256 interestOut, uint256[] memory rewardsOut);

    function rewardIndexesCurrent() external returns (uint256[] memory);

    function pyIndexCurrent() external returns (uint256);

    function pyIndexStored() external view returns (uint256);

    function getRewardTokens() external view returns (address[] memory);

    function SY() external view returns (address);

    function PT() external view returns (address);

    function factory() external view returns (address);

    function expiry() external view returns (uint256);

    function isExpired() external view returns (bool);

    function doCacheIndexSameBlock() external view returns (bool);

    function pyIndexLastUpdatedBlock() external view returns (uint128);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

interface IRewardManager {
    function userReward(address token, address user) external view returns (uint128 index, uint128 accrued);
}

// SPDX-License-Identifier: GPL-3.0-or-later
/*
 * MIT License
 * ===========
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in all
 * copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 */

pragma solidity ^0.8.0;
import "@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol";

interface IStandardizedYield is IERC20Metadata {
    /// @dev Emitted when any base tokens is deposited to mint shares
    event Deposit(
        address indexed caller,
        address indexed receiver,
        address indexed tokenIn,
        uint256 amountDeposited,
        uint256 amountSyOut
    );

    /// @dev Emitted when any shares are redeemed for base tokens
    event Redeem(
        address indexed caller,
        address indexed receiver,
        address indexed tokenOut,
        uint256 amountSyToRedeem,
        uint256 amountTokenOut
    );

    /// @dev check `assetInfo()` for more information
    enum AssetType {
        TOKEN,
        LIQUIDITY
    }

    /// @dev Emitted when (`user`) claims their rewards
    event ClaimRewards(address indexed user, address[] rewardTokens, uint256[] rewardAmounts);

    /**
     * @notice mints an amount of shares by depositing a base token.
     * @param receiver shares recipient address
     * @param tokenIn address of the base tokens to mint shares
     * @param amountTokenToDeposit amount of base tokens to be transferred from (`msg.sender`)
     * @param minSharesOut reverts if amount of shares minted is lower than this
     * @return amountSharesOut amount of shares minted
     * @dev Emits a {Deposit} event
     *
     * Requirements:
     * - (`tokenIn`) must be a valid base token.
     */
    function deposit(
        address receiver,
        address tokenIn,
        uint256 amountTokenToDeposit,
        uint256 minSharesOut
    ) external payable returns (uint256 amountSharesOut);

    /**
     * @notice redeems an amount of base tokens by burning some shares
     * @param receiver recipient address
     * @param amountSharesToRedeem amount of shares to be burned
     * @param tokenOut address of the base token to be redeemed
     * @param minTokenOut reverts if amount of base token redeemed is lower than this
     * @param burnFromInternalBalance if true, burns from balance of `address(this)`, otherwise burns from `msg.sender`
     * @return amountTokenOut amount of base tokens redeemed
     * @dev Emits a {Redeem} event
     *
     * Requirements:
     * - (`tokenOut`) must be a valid base token.
     */
    function redeem(
        address receiver,
        uint256 amountSharesToRedeem,
        address tokenOut,
        uint256 minTokenOut,
        bool burnFromInternalBalance
    ) external returns (uint256 amountTokenOut);

    /**
     * @notice exchangeRate * syBalance / 1e18 must return the asset balance of the account
     * @notice vice-versa, if a user uses some amount of tokens equivalent to X asset, the amount of sy
     he can mint must be X * exchangeRate / 1e18
     * @dev SYUtils's assetToSy & syToAsset should be used instead of raw multiplication
     & division
     */
    function exchangeRate() external view returns (uint256 res);

    /**
     * @notice claims reward for (`user`)
     * @param user the user receiving their rewards
     * @return rewardAmounts an array of reward amounts in the same order as `getRewardTokens`
     * @dev
     * Emits a `ClaimRewards` event
     * See {getRewardTokens} for list of reward tokens
     */
    function claimRewards(address user) external returns (uint256[] memory rewardAmounts);

    /**
     * @notice get the amount of unclaimed rewards for (`user`)
     * @param user the user to check for
     * @return rewardAmounts an array of reward amounts in the same order as `getRewardTokens`
     */
    function accruedRewards(address user) external view returns (uint256[] memory rewardAmounts);

    function rewardIndexesCurrent() external returns (uint256[] memory indexes);

    function rewardIndexesStored() external view returns (uint256[] memory indexes);

    /**
     * @notice returns the list of reward token addresses
     */
    function getRewardTokens() external view returns (address[] memory);

    /**
     * @notice returns the address of the underlying yield token
     */
    function yieldToken() external view returns (address);

    /**
     * @notice returns all tokens that can mint this SY
     */
    function getTokensIn() external view returns (address[] memory res);

    /**
     * @notice returns all tokens that can be redeemed by this SY
     */
    function getTokensOut() external view returns (address[] memory res);

    function isValidTokenIn(address token) external view returns (bool);

    function isValidTokenOut(address token) external view returns (bool);

    function previewDeposit(
        address tokenIn,
        uint256 amountTokenToDeposit
    ) external view returns (uint256 amountSharesOut);

    function previewRedeem(
        address tokenOut,
        uint256 amountSharesToRedeem
    ) external view returns (uint256 amountTokenOut);

    /**
     * @notice This function contains information to interpret what the asset is
     * @return assetType the type of the asset (0 for ERC20 tokens, 1 for AMM liquidity tokens,
        2 for bridged yield bearing tokens like wstETH, rETH on Arbi whose the underlying asset doesn't exist on the chain)
     * @return assetAddress the address of the asset
     * @return assetDecimals the decimals of the asset
     */
    function assetInfo() external view returns (AssetType assetType, address assetAddress, uint8 assetDecimals);
}

// SPDX-License-Identifier: GPL-3.0-or-later
/*
 * MIT License
 * ===========
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in all
 * copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 */
pragma solidity ^0.8.0;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";

interface IWETH is IERC20 {
    event Deposit(address indexed dst, uint256 wad);
    event Withdrawal(address indexed src, uint256 wad);

    function deposit() external payable;

    function withdraw(uint256 wad) external;
}

// SPDX-License-Identifier: GPL-3.0-or-later
// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
// documentation files (the “Software”), to deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
// permit persons to whom the Software is furnished to do so, subject to the following conditions:

// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the
// Software.

// THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
// WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
// OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

pragma solidity ^0.8.0;

/* solhint-disable */

/**
 * @dev Exponentiation and logarithm functions for 18 decimal fixed point numbers (both base and exponent/argument).
 *
 * Exponentiation and logarithm with arbitrary bases (x^y and log_x(y)) are implemented by conversion to natural
 * exponentiation and logarithm (where the base is Euler's number).
 *
 * @author Fernando Martinelli - @fernandomartinelli
 * @author Sergio Yuhjtman - @sergioyuhjtman
 * @author Daniel Fernandez - @dmf7z
 */
library LogExpMath {
    // All fixed point multiplications and divisions are inlined. This means we need to divide by ONE when multiplying
    // two numbers, and multiply by ONE when dividing them.

    // All arguments and return values are 18 decimal fixed point numbers.
    int256 constant ONE_18 = 1e18;

    // Internally, intermediate values are computed with higher precision as 20 decimal fixed point numbers, and in the
    // case of ln36, 36 decimals.
    int256 constant ONE_20 = 1e20;
    int256 constant ONE_36 = 1e36;

    // The domain of natural exponentiation is bound by the word size and number of decimals used.
    //
    // Because internally the result will be stored using 20 decimals, the largest possible result is
    // (2^255 - 1) / 10^20, which makes the largest exponent ln((2^255 - 1) / 10^20) = 130.700829182905140221.
    // The smallest possible result is 10^(-18), which makes largest negative argument
    // ln(10^(-18)) = -41.446531673892822312.
    // We use 130.0 and -41.0 to have some safety margin.
    int256 constant MAX_NATURAL_EXPONENT = 130e18;
    int256 constant MIN_NATURAL_EXPONENT = -41e18;

    // Bounds for ln_36's argument. Both ln(0.9) and ln(1.1) can be represented with 36 decimal places in a fixed point
    // 256 bit integer.
    int256 constant LN_36_LOWER_BOUND = ONE_18 - 1e17;
    int256 constant LN_36_UPPER_BOUND = ONE_18 + 1e17;

    uint256 constant MILD_EXPONENT_BOUND = 2 ** 254 / uint256(ONE_20);

    // 18 decimal constants
    int256 constant x0 = 128000000000000000000; // 2ˆ7
    int256 constant a0 = 38877084059945950922200000000000000000000000000000000000; // eˆ(x0) (no decimals)
    int256 constant x1 = 64000000000000000000; // 2ˆ6
    int256 constant a1 = 6235149080811616882910000000; // eˆ(x1) (no decimals)

    // 20 decimal constants
    int256 constant x2 = 3200000000000000000000; // 2ˆ5
    int256 constant a2 = 7896296018268069516100000000000000; // eˆ(x2)
    int256 constant x3 = 1600000000000000000000; // 2ˆ4
    int256 constant a3 = 888611052050787263676000000; // eˆ(x3)
    int256 constant x4 = 800000000000000000000; // 2ˆ3
    int256 constant a4 = 298095798704172827474000; // eˆ(x4)
    int256 constant x5 = 400000000000000000000; // 2ˆ2
    int256 constant a5 = 5459815003314423907810; // eˆ(x5)
    int256 constant x6 = 200000000000000000000; // 2ˆ1
    int256 constant a6 = 738905609893065022723; // eˆ(x6)
    int256 constant x7 = 100000000000000000000; // 2ˆ0
    int256 constant a7 = 271828182845904523536; // eˆ(x7)
    int256 constant x8 = 50000000000000000000; // 2ˆ-1
    int256 constant a8 = 164872127070012814685; // eˆ(x8)
    int256 constant x9 = 25000000000000000000; // 2ˆ-2
    int256 constant a9 = 128402541668774148407; // eˆ(x9)
    int256 constant x10 = 12500000000000000000; // 2ˆ-3
    int256 constant a10 = 113314845306682631683; // eˆ(x10)
    int256 constant x11 = 6250000000000000000; // 2ˆ-4
    int256 constant a11 = 106449445891785942956; // eˆ(x11)

    /**
     * @dev Natural exponentiation (e^x) with signed 18 decimal fixed point exponent.
     *
     * Reverts if `x` is smaller than MIN_NATURAL_EXPONENT, or larger than `MAX_NATURAL_EXPONENT`.
     */
    function exp(int256 x) internal pure returns (int256) {
        unchecked {
            require(x >= MIN_NATURAL_EXPONENT && x <= MAX_NATURAL_EXPONENT, "Invalid exponent");

            if (x < 0) {
                // We only handle positive exponents: e^(-x) is computed as 1 / e^x. We can safely make x positive since it
                // fits in the signed 256 bit range (as it is larger than MIN_NATURAL_EXPONENT).
                // Fixed point division requires multiplying by ONE_18.
                return ((ONE_18 * ONE_18) / exp(-x));
            }

            // First, we use the fact that e^(x+y) = e^x * e^y to decompose x into a sum of powers of two, which we call x_n,
            // where x_n == 2^(7 - n), and e^x_n = a_n has been precomputed. We choose the first x_n, x0, to equal 2^7
            // because all larger powers are larger than MAX_NATURAL_EXPONENT, and therefore not present in the
            // decomposition.
            // At the end of this process we will have the product of all e^x_n = a_n that apply, and the remainder of this
            // decomposition, which will be lower than the smallest x_n.
            // exp(x) = k_0 * a_0 * k_1 * a_1 * ... + k_n * a_n * exp(remainder), where each k_n equals either 0 or 1.
            // We mutate x by subtracting x_n, making it the remainder of the decomposition.

            // The first two a_n (e^(2^7) and e^(2^6)) are too large if stored as 18 decimal numbers, and could cause
            // intermediate overflows. Instead we store them as plain integers, with 0 decimals.
            // Additionally, x0 + x1 is larger than MAX_NATURAL_EXPONENT, which means they will not both be present in the
            // decomposition.

            // For each x_n, we test if that term is present in the decomposition (if x is larger than it), and if so deduct
            // it and compute the accumulated product.

            int256 firstAN;
            if (x >= x0) {
                x -= x0;
                firstAN = a0;
            } else if (x >= x1) {
                x -= x1;
                firstAN = a1;
            } else {
                firstAN = 1; // One with no decimal places
            }

            // We now transform x into a 20 decimal fixed point number, to have enhanced precision when computing the
            // smaller terms.
            x *= 100;

            // `product` is the accumulated product of all a_n (except a0 and a1), which starts at 20 decimal fixed point
            // one. Recall that fixed point multiplication requires dividing by ONE_20.
            int256 product = ONE_20;

            if (x >= x2) {
                x -= x2;
                product = (product * a2) / ONE_20;
            }
            if (x >= x3) {
                x -= x3;
                product = (product * a3) / ONE_20;
            }
            if (x >= x4) {
                x -= x4;
                product = (product * a4) / ONE_20;
            }
            if (x >= x5) {
                x -= x5;
                product = (product * a5) / ONE_20;
            }
            if (x >= x6) {
                x -= x6;
                product = (product * a6) / ONE_20;
            }
            if (x >= x7) {
                x -= x7;
                product = (product * a7) / ONE_20;
            }
            if (x >= x8) {
                x -= x8;
                product = (product * a8) / ONE_20;
            }
            if (x >= x9) {
                x -= x9;
                product = (product * a9) / ONE_20;
            }

            // x10 and x11 are unnecessary here since we have high enough precision already.

            // Now we need to compute e^x, where x is small (in particular, it is smaller than x9). We use the Taylor series
            // expansion for e^x: 1 + x + (x^2 / 2!) + (x^3 / 3!) + ... + (x^n / n!).

            int256 seriesSum = ONE_20; // The initial one in the sum, with 20 decimal places.
            int256 term; // Each term in the sum, where the nth term is (x^n / n!).

            // The first term is simply x.
            term = x;
            seriesSum += term;

            // Each term (x^n / n!) equals the previous one times x, divided by n. Since x is a fixed point number,
            // multiplying by it requires dividing by ONE_20, but dividing by the non-fixed point n values does not.

            term = ((term * x) / ONE_20) / 2;
            seriesSum += term;

            term = ((term * x) / ONE_20) / 3;
            seriesSum += term;

            term = ((term * x) / ONE_20) / 4;
            seriesSum += term;

            term = ((term * x) / ONE_20) / 5;
            seriesSum += term;

            term = ((term * x) / ONE_20) / 6;
            seriesSum += term;

            term = ((term * x) / ONE_20) / 7;
            seriesSum += term;

            term = ((term * x) / ONE_20) / 8;
            seriesSum += term;

            term = ((term * x) / ONE_20) / 9;
            seriesSum += term;

            term = ((term * x) / ONE_20) / 10;
            seriesSum += term;

            term = ((term * x) / ONE_20) / 11;
            seriesSum += term;

            term = ((term * x) / ONE_20) / 12;
            seriesSum += term;

            // 12 Taylor terms are sufficient for 18 decimal precision.

            // We now have the first a_n (with no decimals), and the product of all other a_n present, and the Taylor
            // approximation of the exponentiation of the remainder (both with 20 decimals). All that remains is to multiply
            // all three (one 20 decimal fixed point multiplication, dividing by ONE_20, and one integer multiplication),
            // and then drop two digits to return an 18 decimal value.

            return (((product * seriesSum) / ONE_20) * firstAN) / 100;
        }
    }

    /**
     * @dev Natural logarithm (ln(a)) with signed 18 decimal fixed point argument.
     */
    function ln(int256 a) internal pure returns (int256) {
        unchecked {
            // The real natural logarithm is not defined for negative numbers or zero.
            require(a > 0, "out of bounds");
            if (LN_36_LOWER_BOUND < a && a < LN_36_UPPER_BOUND) {
                return _ln_36(a) / ONE_18;
            } else {
                return _ln(a);
            }
        }
    }

    /**
     * @dev Exponentiation (x^y) with unsigned 18 decimal fixed point base and exponent.
     *
     * Reverts if ln(x) * y is smaller than `MIN_NATURAL_EXPONENT`, or larger than `MAX_NATURAL_EXPONENT`.
     */
    function pow(uint256 x, uint256 y) internal pure returns (uint256) {
        unchecked {
            if (y == 0) {
                // We solve the 0^0 indetermination by making it equal one.
                return uint256(ONE_18);
            }

            if (x == 0) {
                return 0;
            }

            // Instead of computing x^y directly, we instead rely on the properties of logarithms and exponentiation to
            // arrive at that r`esult. In particular, exp(ln(x)) = x, and ln(x^y) = y * ln(x). This means
            // x^y = exp(y * ln(x)).

            // The ln function takes a signed value, so we need to make sure x fits in the signed 256 bit range.
            require(x < 2 ** 255, "x out of bounds");
            int256 x_int256 = int256(x);

            // We will compute y * ln(x) in a single step. Depending on the value of x, we can either use ln or ln_36. In
            // both cases, we leave the division by ONE_18 (due to fixed point multiplication) to the end.

            // This prevents y * ln(x) from overflowing, and at the same time guarantees y fits in the signed 256 bit range.
            require(y < MILD_EXPONENT_BOUND, "y out of bounds");
            int256 y_int256 = int256(y);

            int256 logx_times_y;
            if (LN_36_LOWER_BOUND < x_int256 && x_int256 < LN_36_UPPER_BOUND) {
                int256 ln_36_x = _ln_36(x_int256);

                // ln_36_x has 36 decimal places, so multiplying by y_int256 isn't as straightforward, since we can't just
                // bring y_int256 to 36 decimal places, as it might overflow. Instead, we perform two 18 decimal
                // multiplications and add the results: one with the first 18 decimals of ln_36_x, and one with the
                // (downscaled) last 18 decimals.
                logx_times_y = ((ln_36_x / ONE_18) * y_int256 + ((ln_36_x % ONE_18) * y_int256) / ONE_18);
            } else {
                logx_times_y = _ln(x_int256) * y_int256;
            }
            logx_times_y /= ONE_18;

            // Finally, we compute exp(y * ln(x)) to arrive at x^y
            require(
                MIN_NATURAL_EXPONENT <= logx_times_y && logx_times_y <= MAX_NATURAL_EXPONENT,
                "product out of bounds"
            );

            return uint256(exp(logx_times_y));
        }
    }

    /**
     * @dev Internal natural logarithm (ln(a)) with signed 18 decimal fixed point argument.
     */
    function _ln(int256 a) private pure returns (int256) {
        unchecked {
            if (a < ONE_18) {
                // Since ln(a^k) = k * ln(a), we can compute ln(a) as ln(a) = ln((1/a)^(-1)) = - ln((1/a)). If a is less
                // than one, 1/a will be greater than one, and this if statement will not be entered in the recursive call.
                // Fixed point division requires multiplying by ONE_18.
                return (-_ln((ONE_18 * ONE_18) / a));
            }

            // First, we use the fact that ln^(a * b) = ln(a) + ln(b) to decompose ln(a) into a sum of powers of two, which
            // we call x_n, where x_n == 2^(7 - n), which are the natural logarithm of precomputed quantities a_n (that is,
            // ln(a_n) = x_n). We choose the first x_n, x0, to equal 2^7 because the exponential of all larger powers cannot
            // be represented as 18 fixed point decimal numbers in 256 bits, and are therefore larger than a.
            // At the end of this process we will have the sum of all x_n = ln(a_n) that apply, and the remainder of this
            // decomposition, which will be lower than the smallest a_n.
            // ln(a) = k_0 * x_0 + k_1 * x_1 + ... + k_n * x_n + ln(remainder), where each k_n equals either 0 or 1.
            // We mutate a by subtracting a_n, making it the remainder of the decomposition.

            // For reasons related to how `exp` works, the first two a_n (e^(2^7) and e^(2^6)) are not stored as fixed point
            // numbers with 18 decimals, but instead as plain integers with 0 decimals, so we need to multiply them by
            // ONE_18 to convert them to fixed point.
            // For each a_n, we test if that term is present in the decomposition (if a is larger than it), and if so divide
            // by it and compute the accumulated sum.

            int256 sum = 0;
            if (a >= a0 * ONE_18) {
                a /= a0; // Integer, not fixed point division
                sum += x0;
            }

            if (a >= a1 * ONE_18) {
                a /= a1; // Integer, not fixed point division
                sum += x1;
            }

            // All other a_n and x_n are stored as 20 digit fixed point numbers, so we convert the sum and a to this format.
            sum *= 100;
            a *= 100;

            // Because further a_n are  20 digit fixed point numbers, we multiply by ONE_20 when dividing by them.

            if (a >= a2) {
                a = (a * ONE_20) / a2;
                sum += x2;
            }

            if (a >= a3) {
                a = (a * ONE_20) / a3;
                sum += x3;
            }

            if (a >= a4) {
                a = (a * ONE_20) / a4;
                sum += x4;
            }

            if (a >= a5) {
                a = (a * ONE_20) / a5;
                sum += x5;
            }

            if (a >= a6) {
                a = (a * ONE_20) / a6;
                sum += x6;
            }

            if (a >= a7) {
                a = (a * ONE_20) / a7;
                sum += x7;
            }

            if (a >= a8) {
                a = (a * ONE_20) / a8;
                sum += x8;
            }

            if (a >= a9) {
                a = (a * ONE_20) / a9;
                sum += x9;
            }

            if (a >= a10) {
                a = (a * ONE_20) / a10;
                sum += x10;
            }

            if (a >= a11) {
                a = (a * ONE_20) / a11;
                sum += x11;
            }

            // a is now a small number (smaller than a_11, which roughly equals 1.06). This means we can use a Taylor series
            // that converges rapidly for values of `a` close to one - the same one used in ln_36.
            // Let z = (a - 1) / (a + 1).
            // ln(a) = 2 * (z + z^3 / 3 + z^5 / 5 + z^7 / 7 + ... + z^(2 * n + 1) / (2 * n + 1))

            // Recall that 20 digit fixed point division requires multiplying by ONE_20, and multiplication requires
            // division by ONE_20.
            int256 z = ((a - ONE_20) * ONE_20) / (a + ONE_20);
            int256 z_squared = (z * z) / ONE_20;

            // num is the numerator of the series: the z^(2 * n + 1) term
            int256 num = z;

            // seriesSum holds the accumulated sum of each term in the series, starting with the initial z
            int256 seriesSum = num;

            // In each step, the numerator is multiplied by z^2
            num = (num * z_squared) / ONE_20;
            seriesSum += num / 3;

            num = (num * z_squared) / ONE_20;
            seriesSum += num / 5;

            num = (num * z_squared) / ONE_20;
            seriesSum += num / 7;

            num = (num * z_squared) / ONE_20;
            seriesSum += num / 9;

            num = (num * z_squared) / ONE_20;
            seriesSum += num / 11;

            // 6 Taylor terms are sufficient for 36 decimal precision.

            // Finally, we multiply by 2 (non fixed point) to compute ln(remainder)
            seriesSum *= 2;

            // We now have the sum of all x_n present, and the Taylor approximation of the logarithm of the remainder (both
            // with 20 decimals). All that remains is to sum these two, and then drop two digits to return a 18 decimal
            // value.

            return (sum + seriesSum) / 100;
        }
    }

    /**
     * @dev Intrnal high precision (36 decimal places) natural logarithm (ln(x)) with signed 18 decimal fixed point argument,
     * for x close to one.
     *
     * Should only be used if x is between LN_36_LOWER_BOUND and LN_36_UPPER_BOUND.
     */
    function _ln_36(int256 x) private pure returns (int256) {
        unchecked {
            // Since ln(1) = 0, a value of x close to one will yield a very small result, which makes using 36 digits
            // worthwhile.

            // First, we transform x to a 36 digit fixed point value.
            x *= ONE_18;

            // We will use the following Taylor expansion, which converges very rapidly. Let z = (x - 1) / (x + 1).
            // ln(x) = 2 * (z + z^3 / 3 + z^5 / 5 + z^7 / 7 + ... + z^(2 * n + 1) / (2 * n + 1))

            // Recall that 36 digit fixed point division requires multiplying by ONE_36, and multiplication requires
            // division by ONE_36.
            int256 z = ((x - ONE_36) * ONE_36) / (x + ONE_36);
            int256 z_squared = (z * z) / ONE_36;

            // num is the numerator of the series: the z^(2 * n + 1) term
            int256 num = z;

            // seriesSum holds the accumulated sum of each term in the series, starting with the initial z
            int256 seriesSum = num;

            // In each step, the numerator is multiplied by z^2
            num = (num * z_squared) / ONE_36;
            seriesSum += num / 3;

            num = (num * z_squared) / ONE_36;
            seriesSum += num / 5;

            num = (num * z_squared) / ONE_36;
            seriesSum += num / 7;

            num = (num * z_squared) / ONE_36;
            seriesSum += num / 9;

            num = (num * z_squared) / ONE_36;
            seriesSum += num / 11;

            num = (num * z_squared) / ONE_36;
            seriesSum += num / 13;

            num = (num * z_squared) / ONE_36;
            seriesSum += num / 15;

            // 8 Taylor terms are sufficient for 36 decimal precision.

            // All that remains is multiplying by 2 (non fixed point).
            return seriesSum * 2;
        }
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

import "../libraries/math/PMath.sol";
import "../libraries/math/LogExpMath.sol";

import "../StandardizedYield/PYIndex.sol";
import "../libraries/MiniHelpers.sol";
import "../libraries/Errors.sol";

struct MarketState {
    int256 totalPt;
    int256 totalSy;
    int256 totalLp;
    address treasury;
    /// immutable variables ///
    int256 scalarRoot;
    uint256 expiry;
    /// fee data ///
    uint256 lnFeeRateRoot;
    uint256 reserveFeePercent; // base 100
    /// last trade data ///
    uint256 lastLnImpliedRate;
}

// params that are expensive to compute, therefore we pre-compute them
struct MarketPreCompute {
    int256 rateScalar;
    int256 totalAsset;
    int256 rateAnchor;
    int256 feeRate;
}

// solhint-disable ordering
library MarketMathCore {
    using PMath for uint256;
    using PMath for int256;
    using LogExpMath for int256;
    using PYIndexLib for PYIndex;

    int256 internal constant MINIMUM_LIQUIDITY = 10 ** 3;
    int256 internal constant PERCENTAGE_DECIMALS = 100;
    uint256 internal constant DAY = 86400;
    uint256 internal constant IMPLIED_RATE_TIME = 365 * DAY;

    int256 internal constant MAX_MARKET_PROPORTION = (1e18 * 96) / 100;

    using PMath for uint256;
    using PMath for int256;

    /*///////////////////////////////////////////////////////////////
                UINT FUNCTIONS TO PROXY TO CORE FUNCTIONS
    //////////////////////////////////////////////////////////////*/

    function addLiquidity(
        MarketState memory market,
        uint256 syDesired,
        uint256 ptDesired,
        uint256 blockTime
    ) internal pure returns (uint256 lpToReserve, uint256 lpToAccount, uint256 syUsed, uint256 ptUsed) {
        (int256 _lpToReserve, int256 _lpToAccount, int256 _syUsed, int256 _ptUsed) = addLiquidityCore(
            market,
            syDesired.Int(),
            ptDesired.Int(),
            blockTime
        );

        lpToReserve = _lpToReserve.Uint();
        lpToAccount = _lpToAccount.Uint();
        syUsed = _syUsed.Uint();
        ptUsed = _ptUsed.Uint();
    }

    function removeLiquidity(
        MarketState memory market,
        uint256 lpToRemove
    ) internal pure returns (uint256 netSyToAccount, uint256 netPtToAccount) {
        (int256 _syToAccount, int256 _ptToAccount) = removeLiquidityCore(market, lpToRemove.Int());

        netSyToAccount = _syToAccount.Uint();
        netPtToAccount = _ptToAccount.Uint();
    }

    function swapExactPtForSy(
        MarketState memory market,
        PYIndex index,
        uint256 exactPtToMarket,
        uint256 blockTime
    ) internal pure returns (uint256 netSyToAccount, uint256 netSyFee, uint256 netSyToReserve) {
        (int256 _netSyToAccount, int256 _netSyFee, int256 _netSyToReserve) = executeTradeCore(
            market,
            index,
            exactPtToMarket.neg(),
            blockTime
        );

        netSyToAccount = _netSyToAccount.Uint();
        netSyFee = _netSyFee.Uint();
        netSyToReserve = _netSyToReserve.Uint();
    }

    function swapSyForExactPt(
        MarketState memory market,
        PYIndex index,
        uint256 exactPtToAccount,
        uint256 blockTime
    ) internal pure returns (uint256 netSyToMarket, uint256 netSyFee, uint256 netSyToReserve) {
        (int256 _netSyToAccount, int256 _netSyFee, int256 _netSyToReserve) = executeTradeCore(
            market,
            index,
            exactPtToAccount.Int(),
            blockTime
        );

        netSyToMarket = _netSyToAccount.neg().Uint();
        netSyFee = _netSyFee.Uint();
        netSyToReserve = _netSyToReserve.Uint();
    }

    /*///////////////////////////////////////////////////////////////
                    CORE FUNCTIONS
    //////////////////////////////////////////////////////////////*/

    function addLiquidityCore(
        MarketState memory market,
        int256 syDesired,
        int256 ptDesired,
        uint256 blockTime
    ) internal pure returns (int256 lpToReserve, int256 lpToAccount, int256 syUsed, int256 ptUsed) {
        /// ------------------------------------------------------------
        /// CHECKS
        /// ------------------------------------------------------------
        if (syDesired == 0 || ptDesired == 0) revert Errors.MarketZeroAmountsInput();
        if (MiniHelpers.isExpired(market.expiry, blockTime)) revert Errors.MarketExpired();

        /// ------------------------------------------------------------
        /// MATH
        /// ------------------------------------------------------------
        if (market.totalLp == 0) {
            lpToAccount = PMath.sqrt((syDesired * ptDesired).Uint()).Int() - MINIMUM_LIQUIDITY;
            lpToReserve = MINIMUM_LIQUIDITY;
            syUsed = syDesired;
            ptUsed = ptDesired;
        } else {
            int256 netLpByPt = (ptDesired * market.totalLp) / market.totalPt;
            int256 netLpBySy = (syDesired * market.totalLp) / market.totalSy;
            if (netLpByPt < netLpBySy) {
                lpToAccount = netLpByPt;
                ptUsed = ptDesired;
                syUsed = (market.totalSy * lpToAccount) / market.totalLp;
            } else {
                lpToAccount = netLpBySy;
                syUsed = syDesired;
                ptUsed = (market.totalPt * lpToAccount) / market.totalLp;
            }
        }

        if (lpToAccount <= 0) revert Errors.MarketZeroAmountsOutput();

        /// ------------------------------------------------------------
        /// WRITE
        /// ------------------------------------------------------------
        market.totalSy += syUsed;
        market.totalPt += ptUsed;
        market.totalLp += lpToAccount + lpToReserve;
    }

    function removeLiquidityCore(
        MarketState memory market,
        int256 lpToRemove
    ) internal pure returns (int256 netSyToAccount, int256 netPtToAccount) {
        /// ------------------------------------------------------------
        /// CHECKS
        /// ------------------------------------------------------------
        if (lpToRemove == 0) revert Errors.MarketZeroAmountsInput();

        /// ------------------------------------------------------------
        /// MATH
        /// ------------------------------------------------------------
        netSyToAccount = (lpToRemove * market.totalSy) / market.totalLp;
        netPtToAccount = (lpToRemove * market.totalPt) / market.totalLp;

        if (netSyToAccount == 0 && netPtToAccount == 0) revert Errors.MarketZeroAmountsOutput();

        /// ------------------------------------------------------------
        /// WRITE
        /// ------------------------------------------------------------
        market.totalLp = market.totalLp.subNoNeg(lpToRemove);
        market.totalPt = market.totalPt.subNoNeg(netPtToAccount);
        market.totalSy = market.totalSy.subNoNeg(netSyToAccount);
    }

    function executeTradeCore(
        MarketState memory market,
        PYIndex index,
        int256 netPtToAccount,
        uint256 blockTime
    ) internal pure returns (int256 netSyToAccount, int256 netSyFee, int256 netSyToReserve) {
        /// ------------------------------------------------------------
        /// CHECKS
        /// ------------------------------------------------------------
        if (MiniHelpers.isExpired(market.expiry, blockTime)) revert Errors.MarketExpired();
        if (market.totalPt <= netPtToAccount)
            revert Errors.MarketInsufficientPtForTrade(market.totalPt, netPtToAccount);

        /// ------------------------------------------------------------
        /// MATH
        /// ------------------------------------------------------------
        MarketPreCompute memory comp = getMarketPreCompute(market, index, blockTime);

        (netSyToAccount, netSyFee, netSyToReserve) = calcTrade(market, comp, index, netPtToAccount);

        /// ------------------------------------------------------------
        /// WRITE
        /// ------------------------------------------------------------
        _setNewMarketStateTrade(market, comp, index, netPtToAccount, netSyToAccount, netSyToReserve, blockTime);
    }

    function getMarketPreCompute(
        MarketState memory market,
        PYIndex index,
        uint256 blockTime
    ) internal pure returns (MarketPreCompute memory res) {
        if (MiniHelpers.isExpired(market.expiry, blockTime)) revert Errors.MarketExpired();

        uint256 timeToExpiry = market.expiry - blockTime;

        res.rateScalar = _getRateScalar(market, timeToExpiry);
        res.totalAsset = index.syToAsset(market.totalSy);

        if (market.totalPt == 0 || res.totalAsset == 0)
            revert Errors.MarketZeroTotalPtOrTotalAsset(market.totalPt, res.totalAsset);

        res.rateAnchor = _getRateAnchor(
            market.totalPt,
            market.lastLnImpliedRate,
            res.totalAsset,
            res.rateScalar,
            timeToExpiry
        );
        res.feeRate = _getExchangeRateFromImpliedRate(market.lnFeeRateRoot, timeToExpiry);
    }

    function calcTrade(
        MarketState memory market,
        MarketPreCompute memory comp,
        PYIndex index,
        int256 netPtToAccount
    ) internal pure returns (int256 netSyToAccount, int256 netSyFee, int256 netSyToReserve) {
        int256 preFeeExchangeRate = _getExchangeRate(
            market.totalPt,
            comp.totalAsset,
            comp.rateScalar,
            comp.rateAnchor,
            netPtToAccount
        );

        int256 preFeeAssetToAccount = netPtToAccount.divDown(preFeeExchangeRate).neg();
        int256 fee = comp.feeRate;

        if (netPtToAccount > 0) {
            int256 postFeeExchangeRate = preFeeExchangeRate.divDown(fee);
            if (postFeeExchangeRate < PMath.IONE) revert Errors.MarketExchangeRateBelowOne(postFeeExchangeRate);

            fee = preFeeAssetToAccount.mulDown(PMath.IONE - fee);
        } else {
            fee = ((preFeeAssetToAccount * (PMath.IONE - fee)) / fee).neg();
        }

        int256 netAssetToReserve = (fee * market.reserveFeePercent.Int()) / PERCENTAGE_DECIMALS;
        int256 netAssetToAccount = preFeeAssetToAccount - fee;

        netSyToAccount = netAssetToAccount < 0
            ? index.assetToSyUp(netAssetToAccount)
            : index.assetToSy(netAssetToAccount);
        netSyFee = index.assetToSy(fee);
        netSyToReserve = index.assetToSy(netAssetToReserve);
    }

    function _setNewMarketStateTrade(
        MarketState memory market,
        MarketPreCompute memory comp,
        PYIndex index,
        int256 netPtToAccount,
        int256 netSyToAccount,
        int256 netSyToReserve,
        uint256 blockTime
    ) internal pure {
        uint256 timeToExpiry = market.expiry - blockTime;

        market.totalPt = market.totalPt.subNoNeg(netPtToAccount);
        market.totalSy = market.totalSy.subNoNeg(netSyToAccount + netSyToReserve);

        market.lastLnImpliedRate = _getLnImpliedRate(
            market.totalPt,
            index.syToAsset(market.totalSy),
            comp.rateScalar,
            comp.rateAnchor,
            timeToExpiry
        );

        if (market.lastLnImpliedRate == 0) revert Errors.MarketZeroLnImpliedRate();
    }

    function _getRateAnchor(
        int256 totalPt,
        uint256 lastLnImpliedRate,
        int256 totalAsset,
        int256 rateScalar,
        uint256 timeToExpiry
    ) internal pure returns (int256 rateAnchor) {
        int256 newExchangeRate = _getExchangeRateFromImpliedRate(lastLnImpliedRate, timeToExpiry);

        if (newExchangeRate < PMath.IONE) revert Errors.MarketExchangeRateBelowOne(newExchangeRate);

        {
            int256 proportion = totalPt.divDown(totalPt + totalAsset);

            int256 lnProportion = _logProportion(proportion);

            rateAnchor = newExchangeRate - lnProportion.divDown(rateScalar);
        }
    }

    /// @notice Calculates the current market implied rate.
    /// @return lnImpliedRate the implied rate
    function _getLnImpliedRate(
        int256 totalPt,
        int256 totalAsset,
        int256 rateScalar,
        int256 rateAnchor,
        uint256 timeToExpiry
    ) internal pure returns (uint256 lnImpliedRate) {
        // This will check for exchange rates < PMath.IONE
        int256 exchangeRate = _getExchangeRate(totalPt, totalAsset, rateScalar, rateAnchor, 0);

        // exchangeRate >= 1 so its ln >= 0
        uint256 lnRate = exchangeRate.ln().Uint();

        lnImpliedRate = (lnRate * IMPLIED_RATE_TIME) / timeToExpiry;
    }

    /// @notice Converts an implied rate to an exchange rate given a time to expiry. The
    /// formula is E = e^rt
    function _getExchangeRateFromImpliedRate(
        uint256 lnImpliedRate,
        uint256 timeToExpiry
    ) internal pure returns (int256 exchangeRate) {
        uint256 rt = (lnImpliedRate * timeToExpiry) / IMPLIED_RATE_TIME;

        exchangeRate = LogExpMath.exp(rt.Int());
    }

    function _getExchangeRate(
        int256 totalPt,
        int256 totalAsset,
        int256 rateScalar,
        int256 rateAnchor,
        int256 netPtToAccount
    ) internal pure returns (int256 exchangeRate) {
        int256 numerator = totalPt.subNoNeg(netPtToAccount);

        int256 proportion = (numerator.divDown(totalPt + totalAsset));

        if (proportion > MAX_MARKET_PROPORTION)
            revert Errors.MarketProportionTooHigh(proportion, MAX_MARKET_PROPORTION);

        int256 lnProportion = _logProportion(proportion);

        exchangeRate = lnProportion.divDown(rateScalar) + rateAnchor;

        if (exchangeRate < PMath.IONE) revert Errors.MarketExchangeRateBelowOne(exchangeRate);
    }

    function _logProportion(int256 proportion) internal pure returns (int256 res) {
        if (proportion == PMath.IONE) revert Errors.MarketProportionMustNotEqualOne();

        int256 logitP = proportion.divDown(PMath.IONE - proportion);

        res = logitP.ln();
    }

    function _getRateScalar(MarketState memory market, uint256 timeToExpiry) internal pure returns (int256 rateScalar) {
        rateScalar = (market.scalarRoot * IMPLIED_RATE_TIME.Int()) / timeToExpiry.Int();
        if (rateScalar <= 0) revert Errors.MarketRateScalarBelowZero(rateScalar);
    }

    function setInitialLnImpliedRate(
        MarketState memory market,
        PYIndex index,
        int256 initialAnchor,
        uint256 blockTime
    ) internal pure {
        /// ------------------------------------------------------------
        /// CHECKS
        /// ------------------------------------------------------------
        if (MiniHelpers.isExpired(market.expiry, blockTime)) revert Errors.MarketExpired();

        /// ------------------------------------------------------------
        /// MATH
        /// ------------------------------------------------------------
        int256 totalAsset = index.syToAsset(market.totalSy);
        uint256 timeToExpiry = market.expiry - blockTime;
        int256 rateScalar = _getRateScalar(market, timeToExpiry);

        /// ------------------------------------------------------------
        /// WRITE
        /// ------------------------------------------------------------
        market.lastLnImpliedRate = _getLnImpliedRate(
            market.totalPt,
            totalAsset,
            rateScalar,
            initialAnchor,
            timeToExpiry
        );
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                // The surrounding unchecked block does not change this fact.
                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1, "Math: mulDiv overflow");

            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10 ** 64) {
                value /= 10 ** 64;
                result += 64;
            }
            if (value >= 10 ** 32) {
                value /= 10 ** 32;
                result += 32;
            }
            if (value >= 10 ** 16) {
                value /= 10 ** 16;
                result += 16;
            }
            if (value >= 10 ** 8) {
                value /= 10 ** 8;
                result += 8;
            }
            if (value >= 10 ** 4) {
                value /= 10 ** 4;
                result += 4;
            }
            if (value >= 10 ** 2) {
                value /= 10 ** 2;
                result += 2;
            }
            if (value >= 10 ** 1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);
        }
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

library MiniHelpers {
    function isCurrentlyExpired(uint256 expiry) internal view returns (bool) {
        return (expiry <= block.timestamp);
    }

    function isExpired(uint256 expiry, uint256 blockTime) internal pure returns (bool) {
        return (expiry <= blockTime);
    }

    function isTimeInThePast(uint256 timestamp) internal view returns (bool) {
        return (timestamp <= block.timestamp); // same definition as isCurrentlyExpired
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

import "../libraries/Errors.sol";

/// Adapted from UniswapV3's Oracle

library OracleLib {
    struct Observation {
        uint32 blockTimestamp;
        uint216 lnImpliedRateCumulative;
        bool initialized;
        // 1 SLOT = 256 bits
    }

    function transform(
        Observation memory last,
        uint32 blockTimestamp,
        uint96 lnImpliedRate
    ) public pure returns (Observation memory) {
        return
            Observation({
                blockTimestamp: blockTimestamp,
                lnImpliedRateCumulative: last.lnImpliedRateCumulative +
                    uint216(lnImpliedRate) *
                    (blockTimestamp - last.blockTimestamp),
                initialized: true
            });
    }

    function initialize(
        Observation[65535] storage self,
        uint32 time
    ) public returns (uint16 cardinality, uint16 cardinalityNext) {
        self[0] = Observation({blockTimestamp: time, lnImpliedRateCumulative: 0, initialized: true});
        return (1, 1);
    }

    function write(
        Observation[65535] storage self,
        uint16 index,
        uint32 blockTimestamp,
        uint96 lnImpliedRate,
        uint16 cardinality,
        uint16 cardinalityNext
    ) public returns (uint16 indexUpdated, uint16 cardinalityUpdated) {
        Observation memory last = self[index];

        // early return if we've already written an observation this block
        if (last.blockTimestamp == blockTimestamp) return (index, cardinality);

        // if the conditions are right, we can bump the cardinality
        if (cardinalityNext > cardinality && index == (cardinality - 1)) {
            cardinalityUpdated = cardinalityNext;
        } else {
            cardinalityUpdated = cardinality;
        }

        indexUpdated = (index + 1) % cardinalityUpdated;
        self[indexUpdated] = transform(last, blockTimestamp, lnImpliedRate);
    }

    function grow(Observation[65535] storage self, uint16 current, uint16 next) public returns (uint16) {
        if (current == 0) revert Errors.OracleUninitialized();
        // no-op if the passed next value isn't greater than the current next value
        if (next <= current) return current;
        // store in each slot to prevent fresh SSTOREs in swaps
        // this data will not be used because the initialized boolean is still false
        for (uint16 i = current; i != next; ) {
            self[i].blockTimestamp = 1;
            unchecked {
                ++i;
            }
        }
        return next;
    }

    function binarySearch(
        Observation[65535] storage self,
        uint32 target,
        uint16 index,
        uint16 cardinality
    ) public view returns (Observation memory beforeOrAt, Observation memory atOrAfter) {
        uint256 l = (index + 1) % cardinality; // oldest observation
        uint256 r = l + cardinality - 1; // newest observation
        uint256 i;
        while (true) {
            i = (l + r) / 2;

            beforeOrAt = self[i % cardinality];

            // we've landed on an uninitialized observation, keep searching higher (more recently)
            if (!beforeOrAt.initialized) {
                l = i + 1;
                continue;
            }

            atOrAfter = self[(i + 1) % cardinality];

            bool targetAtOrAfter = beforeOrAt.blockTimestamp <= target;

            // check if we've found the answer!
            if (targetAtOrAfter && target <= atOrAfter.blockTimestamp) break;

            if (!targetAtOrAfter) r = i - 1;
            else l = i + 1;
        }
    }

    function getSurroundingObservations(
        Observation[65535] storage self,
        uint32 target,
        uint96 lnImpliedRate,
        uint16 index,
        uint16 cardinality
    ) public view returns (Observation memory beforeOrAt, Observation memory atOrAfter) {
        // optimistically set before to the newest observation
        beforeOrAt = self[index];

        // if the target is chronologically at or after the newest observation, we can early return
        if (beforeOrAt.blockTimestamp <= target) {
            if (beforeOrAt.blockTimestamp == target) {
                // if newest observation equals target, we're in the same block, so we can ignore atOrAfter
                return (beforeOrAt, atOrAfter);
            } else {
                // otherwise, we need to transform
                return (beforeOrAt, transform(beforeOrAt, target, lnImpliedRate));
            }
        }

        // now, set beforeOrAt to the oldest observation
        beforeOrAt = self[(index + 1) % cardinality];
        if (!beforeOrAt.initialized) beforeOrAt = self[0];

        // ensure that the target is chronologically at or after the oldest observation
        if (target < beforeOrAt.blockTimestamp) revert Errors.OracleTargetTooOld(target, beforeOrAt.blockTimestamp);

        // if we've reached this point, we have to binary search
        return binarySearch(self, target, index, cardinality);
    }

    function observeSingle(
        Observation[65535] storage self,
        uint32 time,
        uint32 secondsAgo,
        uint96 lnImpliedRate,
        uint16 index,
        uint16 cardinality
    ) public view returns (uint216 lnImpliedRateCumulative) {
        if (secondsAgo == 0) {
            Observation memory last = self[index];
            if (last.blockTimestamp != time) {
                return transform(last, time, lnImpliedRate).lnImpliedRateCumulative;
            }
            return last.lnImpliedRateCumulative;
        }

        uint32 target = time - secondsAgo;

        (Observation memory beforeOrAt, Observation memory atOrAfter) = getSurroundingObservations(
            self,
            target,
            lnImpliedRate,
            index,
            cardinality
        );

        if (target == beforeOrAt.blockTimestamp) {
            // we're at the left boundary
            return beforeOrAt.lnImpliedRateCumulative;
        } else if (target == atOrAfter.blockTimestamp) {
            // we're at the right boundary
            return atOrAfter.lnImpliedRateCumulative;
        } else {
            // we're in the middle
            return (beforeOrAt.lnImpliedRateCumulative +
                uint216(
                    (uint256(atOrAfter.lnImpliedRateCumulative - beforeOrAt.lnImpliedRateCumulative) *
                        (target - beforeOrAt.blockTimestamp)) / (atOrAfter.blockTimestamp - beforeOrAt.blockTimestamp)
                ));
        }
    }

    function observe(
        Observation[65535] storage self,
        uint32 time,
        uint32[] memory secondsAgos,
        uint96 lnImpliedRate,
        uint16 index,
        uint16 cardinality
    ) public view returns (uint216[] memory lnImpliedRateCumulative) {
        if (cardinality == 0) revert Errors.OracleZeroCardinality();

        lnImpliedRateCumulative = new uint216[](secondsAgos.length);
        for (uint256 i = 0; i < lnImpliedRateCumulative.length; ++i) {
            lnImpliedRateCumulative[i] = observeSingle(self, time, secondsAgos[i], lnImpliedRate, index, cardinality);
        }
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.8.0;

/* solhint-disable private-vars-leading-underscore, reason-string */

library PMath {
    uint256 internal constant ONE = 1e18; // 18 decimal places
    int256 internal constant IONE = 1e18; // 18 decimal places

    function subMax0(uint256 a, uint256 b) internal pure returns (uint256) {
        unchecked {
            return (a >= b ? a - b : 0);
        }
    }

    function subNoNeg(int256 a, int256 b) internal pure returns (int256) {
        require(a >= b, "negative");
        return a - b; // no unchecked since if b is very negative, a - b might overflow
    }

    function mulDown(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 product = a * b;
        unchecked {
            return product / ONE;
        }
    }

    function mulDown(int256 a, int256 b) internal pure returns (int256) {
        int256 product = a * b;
        unchecked {
            return product / IONE;
        }
    }

    function divDown(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 aInflated = a * ONE;
        unchecked {
            return aInflated / b;
        }
    }

    function divDown(int256 a, int256 b) internal pure returns (int256) {
        int256 aInflated = a * IONE;
        unchecked {
            return aInflated / b;
        }
    }

    function rawDivUp(uint256 a, uint256 b) internal pure returns (uint256) {
        return (a + b - 1) / b;
    }

    // @author Uniswap
    function sqrt(uint256 y) internal pure returns (uint256 z) {
        if (y > 3) {
            z = y;
            uint256 x = y / 2 + 1;
            while (x < z) {
                z = x;
                x = (y / x + x) / 2;
            }
        } else if (y != 0) {
            z = 1;
        }
    }

    function square(uint256 x) internal pure returns (uint256) {
        return x * x;
    }

    function squareDown(uint256 x) internal pure returns (uint256) {
        return mulDown(x, x);
    }

    function abs(int256 x) internal pure returns (uint256) {
        return uint256(x > 0 ? x : -x);
    }

    function neg(int256 x) internal pure returns (int256) {
        return x * (-1);
    }

    function neg(uint256 x) internal pure returns (int256) {
        return Int(x) * (-1);
    }

    function max(uint256 x, uint256 y) internal pure returns (uint256) {
        return (x > y ? x : y);
    }

    function max(int256 x, int256 y) internal pure returns (int256) {
        return (x > y ? x : y);
    }

    function min(uint256 x, uint256 y) internal pure returns (uint256) {
        return (x < y ? x : y);
    }

    function min(int256 x, int256 y) internal pure returns (int256) {
        return (x < y ? x : y);
    }

    /*///////////////////////////////////////////////////////////////
                               SIGNED CASTS
    //////////////////////////////////////////////////////////////*/

    function Int(uint256 x) internal pure returns (int256) {
        require(x <= uint256(type(int256).max));
        return int256(x);
    }

    function Int128(int256 x) internal pure returns (int128) {
        require(type(int128).min <= x && x <= type(int128).max);
        return int128(x);
    }

    function Int128(uint256 x) internal pure returns (int128) {
        return Int128(Int(x));
    }

    /*///////////////////////////////////////////////////////////////
                               UNSIGNED CASTS
    //////////////////////////////////////////////////////////////*/

    function Uint(int256 x) internal pure returns (uint256) {
        require(x >= 0);
        return uint256(x);
    }

    function Uint32(uint256 x) internal pure returns (uint32) {
        require(x <= type(uint32).max);
        return uint32(x);
    }

    function Uint64(uint256 x) internal pure returns (uint64) {
        require(x <= type(uint64).max);
        return uint64(x);
    }

    function Uint112(uint256 x) internal pure returns (uint112) {
        require(x <= type(uint112).max);
        return uint112(x);
    }

    function Uint96(uint256 x) internal pure returns (uint96) {
        require(x <= type(uint96).max);
        return uint96(x);
    }

    function Uint128(uint256 x) internal pure returns (uint128) {
        require(x <= type(uint128).max);
        return uint128(x);
    }

    function Uint192(uint256 x) internal pure returns (uint192) {
        require(x <= type(uint192).max);
        return uint192(x);
    }

    function isAApproxB(uint256 a, uint256 b, uint256 eps) internal pure returns (bool) {
        return mulDown(b, ONE - eps) <= a && a <= mulDown(b, ONE + eps);
    }

    function isAGreaterApproxB(uint256 a, uint256 b, uint256 eps) internal pure returns (bool) {
        return a >= b && a <= mulDown(b, ONE + eps);
    }

    function isASmallerApproxB(uint256 a, uint256 b, uint256 eps) internal pure returns (bool) {
        return a <= b && a >= mulDown(b, ONE - eps);
    }
}