// File: @openzeppelin/contracts/interfaces/draft-IERC1822.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (interfaces/draft-IERC1822.sol)

pragma solidity ^0.8.0;

/**
 * @dev ERC1822: Universal Upgradeable Proxy Standard (UUPS) documents a method for upgradeability through a simplified
 * proxy whose upgrades are fully controlled by the current implementation.
 */
interface IERC1822Proxiable {
    /**
     * @dev Returns the storage slot that the proxiable contract assumes is being used to store the implementation
     * address.
     *
     * IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
     * bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
     * function revert if invoked through a proxy.
     */
    function proxiableUUID() external view returns (bytes32);
}

// File: @openzeppelin/contracts/proxy/beacon/IBeacon.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (proxy/beacon/IBeacon.sol)

pragma solidity ^0.8.0;

/**
 * @dev This is the interface that {BeaconProxy} expects of its beacon.
 */
interface IBeacon {
    /**
     * @dev Must return an address that can be used as a delegate call target.
     *
     * {BeaconProxy} will check that this address is a contract.
     */
    function implementation() external view returns (address);
}

// File: @openzeppelin/contracts/proxy/ERC1967/ERC1967Upgrade.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (proxy/ERC1967/ERC1967Upgrade.sol)

pragma solidity ^0.8.2;

import "../beacon/IBeacon.sol";
import "../../interfaces/draft-IERC1822.sol";
import "../../utils/Address.sol";
import "../../utils/StorageSlot.sol";

/**
 * @dev This abstract contract provides getters and event emitting update functions for
 * https://eips.ethereum.org/EIPS/eip-1967[EIP1967] slots.
 *
 * _Available since v4.1._
 *
 * @custom:oz-upgrades-unsafe-allow delegatecall
 */
abstract contract ERC1967Upgrade {
    // This is the keccak-256 hash of "eip1967.proxy.rollback" subtracted by 1
    bytes32 private constant _ROLLBACK_SLOT = 0x4910fdfa16fed3260ed0e7147f7cc6da11a60208b5b9406d12a635614ffd9143;

    /**
     * @dev Storage slot with the address of the current implementation.
     * This is the keccak-256 hash of "eip1967.proxy.implementation" subtracted by 1, and is
     * validated in the constructor.
     */
    bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;

    /**
     * @dev Emitted when the implementation is upgraded.
     */
    event Upgraded(address indexed implementation);

    /**
     * @dev Returns the current implementation address.
     */
    function _getImplementation() internal view returns (address) {
        return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
    }

    /**
     * @dev Stores a new address in the EIP1967 implementation slot.
     */
    function _setImplementation(address newImplementation) private {
        require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
        StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
    }

    /**
     * @dev Perform implementation upgrade
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeTo(address newImplementation) internal {
        _setImplementation(newImplementation);
        emit Upgraded(newImplementation);
    }

    /**
     * @dev Perform implementation upgrade with additional setup call.
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeToAndCall(
        address newImplementation,
        bytes memory data,
        bool forceCall
    ) internal {
        _upgradeTo(newImplementation);
        if (data.length > 0 || forceCall) {
            Address.functionDelegateCall(newImplementation, data);
        }
    }

    /**
     * @dev Perform implementation upgrade with security checks for UUPS proxies, and additional setup call.
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeToAndCallUUPS(
        address newImplementation,
        bytes memory data,
        bool forceCall
    ) internal {
        // Upgrades from old implementations will perform a rollback test. This test requires the new
        // implementation to upgrade back to the old, non-ERC1822 compliant, implementation. Removing
        // this special case will break upgrade paths from old UUPS implementation to new ones.
        if (StorageSlot.getBooleanSlot(_ROLLBACK_SLOT).value) {
            _setImplementation(newImplementation);
        } else {
            try IERC1822Proxiable(newImplementation).proxiableUUID() returns (bytes32 slot) {
                require(slot == _IMPLEMENTATION_SLOT, "ERC1967Upgrade: unsupported proxiableUUID");
            } catch {
                revert("ERC1967Upgrade: new implementation is not UUPS");
            }
            _upgradeToAndCall(newImplementation, data, forceCall);
        }
    }

    /**
     * @dev Storage slot with the admin of the contract.
     * This is the keccak-256 hash of "eip1967.proxy.admin" subtracted by 1, and is
     * validated in the constructor.
     */
    bytes32 internal constant _ADMIN_SLOT = 0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;

    /**
     * @dev Emitted when the admin account has changed.
     */
    event AdminChanged(address previousAdmin, address newAdmin);

    /**
     * @dev Returns the current admin.
     */
    function _getAdmin() internal view returns (address) {
        return StorageSlot.getAddressSlot(_ADMIN_SLOT).value;
    }

    /**
     * @dev Stores a new address in the EIP1967 admin slot.
     */
    function _setAdmin(address newAdmin) private {
        require(newAdmin != address(0), "ERC1967: new admin is the zero address");
        StorageSlot.getAddressSlot(_ADMIN_SLOT).value = newAdmin;
    }

    /**
     * @dev Changes the admin of the proxy.
     *
     * Emits an {AdminChanged} event.
     */
    function _changeAdmin(address newAdmin) internal {
        emit AdminChanged(_getAdmin(), newAdmin);
        _setAdmin(newAdmin);
    }

    /**
     * @dev The storage slot of the UpgradeableBeacon contract which defines the implementation for this proxy.
     * This is bytes32(uint256(keccak256('eip1967.proxy.beacon')) - 1)) and is validated in the constructor.
     */
    bytes32 internal constant _BEACON_SLOT = 0xa3f0ad74e5423aebfd80d3ef4346578335a9a72aeaee59ff6cb3582b35133d50;

    /**
     * @dev Emitted when the beacon is upgraded.
     */
    event BeaconUpgraded(address indexed beacon);

    /**
     * @dev Returns the current beacon.
     */
    function _getBeacon() internal view returns (address) {
        return StorageSlot.getAddressSlot(_BEACON_SLOT).value;
    }

    /**
     * @dev Stores a new beacon in the EIP1967 beacon slot.
     */
    function _setBeacon(address newBeacon) private {
        require(Address.isContract(newBeacon), "ERC1967: new beacon is not a contract");
        require(
            Address.isContract(IBeacon(newBeacon).implementation()),
            "ERC1967: beacon implementation is not a contract"
        );
        StorageSlot.getAddressSlot(_BEACON_SLOT).value = newBeacon;
    }

    /**
     * @dev Perform beacon upgrade with additional setup call. Note: This upgrades the address of the beacon, it does
     * not upgrade the implementation contained in the beacon (see {UpgradeableBeacon-_setImplementation} for that).
     *
     * Emits a {BeaconUpgraded} event.
     */
    function _upgradeBeaconToAndCall(
        address newBeacon,
        bytes memory data,
        bool forceCall
    ) internal {
        _setBeacon(newBeacon);
        emit BeaconUpgraded(newBeacon);
        if (data.length > 0 || forceCall) {
            Address.functionDelegateCall(IBeacon(newBeacon).implementation(), data);
        }
    }
}

// File: @openzeppelin/contracts/proxy/Proxy.sol



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

pragma solidity ^0.8.0;

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

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

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

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

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

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

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

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

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

// File: @openzeppelin/contracts/proxy/utils/UUPSUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (proxy/utils/UUPSUpgradeable.sol)

pragma solidity ^0.8.0;

import "../../interfaces/draft-IERC1822.sol";
import "../ERC1967/ERC1967Upgrade.sol";

/**
 * @dev An upgradeability mechanism designed for UUPS proxies. The functions included here can perform an upgrade of an
 * {ERC1967Proxy}, when this contract is set as the implementation behind such a proxy.
 *
 * A security mechanism ensures that an upgrade does not turn off upgradeability accidentally, although this risk is
 * reinstated if the upgrade retains upgradeability but removes the security mechanism, e.g. by replacing
 * `UUPSUpgradeable` with a custom implementation of upgrades.
 *
 * The {_authorizeUpgrade} function must be overridden to include access restriction to the upgrade mechanism.
 *
 * _Available since v4.1._
 */
abstract contract UUPSUpgradeable is IERC1822Proxiable, ERC1967Upgrade {
    /// @custom:oz-upgrades-unsafe-allow state-variable-immutable state-variable-assignment
    address private immutable __self = address(this);

    /**
     * @dev Check that the execution is being performed through a delegatecall call and that the execution context is
     * a proxy contract with an implementation (as defined in ERC1967) pointing to self. This should only be the case
     * for UUPS and transparent proxies that are using the current contract as their implementation. Execution of a
     * function through ERC1167 minimal proxies (clones) would not normally pass this test, but is not guaranteed to
     * fail.
     */
    modifier onlyProxy() {
        require(address(this) != __self, "Function must be called through delegatecall");
        require(_getImplementation() == __self, "Function must be called through active proxy");
        _;
    }

    /**
     * @dev Check that the execution is not being performed through a delegate call. This allows a function to be
     * callable on the implementing contract but not through proxies.
     */
    modifier notDelegated() {
        require(address(this) == __self, "UUPSUpgradeable: must not be called through delegatecall");
        _;
    }

    /**
     * @dev Implementation of the ERC1822 {proxiableUUID} function. This returns the storage slot used by the
     * implementation. It is used to validate that the this implementation remains valid after an upgrade.
     *
     * IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
     * bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
     * function revert if invoked through a proxy. This is guaranteed by the `notDelegated` modifier.
     */
    function proxiableUUID() external view virtual override notDelegated returns (bytes32) {
        return _IMPLEMENTATION_SLOT;
    }

    /**
     * @dev Upgrade the implementation of the proxy to `newImplementation`.
     *
     * Calls {_authorizeUpgrade}.
     *
     * Emits an {Upgraded} event.
     */
    function upgradeTo(address newImplementation) external virtual onlyProxy {
        _authorizeUpgrade(newImplementation);
        _upgradeToAndCallUUPS(newImplementation, new bytes(0), false);
    }

    /**
     * @dev Upgrade the implementation of the proxy to `newImplementation`, and subsequently execute the function call
     * encoded in `data`.
     *
     * Calls {_authorizeUpgrade}.
     *
     * Emits an {Upgraded} event.
     */
    function upgradeToAndCall(address newImplementation, bytes memory data) external payable virtual onlyProxy {
        _authorizeUpgrade(newImplementation);
        _upgradeToAndCallUUPS(newImplementation, data, true);
    }

    /**
     * @dev Function that should revert when `msg.sender` is not authorized to upgrade the contract. Called by
     * {upgradeTo} and {upgradeToAndCall}.
     *
     * Normally, this function will use an xref:access.adoc[access control] modifier such as {Ownable-onlyOwner}.
     *
     * ```solidity
     * function _authorizeUpgrade(address) internal override onlyOwner {}
     * ```
     */
    function _authorizeUpgrade(address newImplementation) internal virtual;
}

// File: @openzeppelin/contracts/token/ERC20/extensions/draft-IERC20Permit.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/draft-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);
}

// File: @openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol



// 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);
}

// File: @openzeppelin/contracts/token/ERC20/IERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (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);
}

// File: @openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";
import "../extensions/draft-IERC20Permit.sol";
import "../../../utils/Address.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    using Address for address;

    function safeTransfer(
        IERC20 token,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transfer.selector, to, value));
    }

    function safeTransferFrom(
        IERC20 token,
        address from,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transferFrom.selector, from, to, value));
    }

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        require(
            (value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

    function safeIncreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        uint256 newAllowance = token.allowance(address(this), spender) + value;
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        unchecked {
            uint256 oldAllowance = token.allowance(address(this), spender);
            require(oldAllowance >= value, "SafeERC20: decreased allowance below zero");
            uint256 newAllowance = oldAllowance - value;
            _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
        }
    }

    function safePermit(
        IERC20Permit token,
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        uint256 nonceBefore = token.nonces(owner);
        token.permit(owner, spender, value, deadline, v, r, s);
        uint256 nonceAfter = token.nonces(owner);
        require(nonceAfter == nonceBefore + 1, "SafeERC20: permit did not succeed");
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We use {Address.functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

        bytes memory returndata = address(token).functionCall(data, "SafeERC20: low-level call failed");
        if (returndata.length > 0) {
            // Return data is optional
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}

// File: @openzeppelin/contracts/utils/Address.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (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
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

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

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

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

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

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

        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

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

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        require(isContract(target), "Address: static call to non-contract");

        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev 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) {
        require(isContract(target), "Address: delegate call to non-contract");

        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly
                /// @solidity memory-safe-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

// File: @openzeppelin/contracts/utils/StorageSlot.sol



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

pragma solidity ^0.8.0;

/**
 * @dev Library for reading and writing primitive types to specific storage slots.
 *
 * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
 * This library helps with reading and writing to such slots without the need for inline assembly.
 *
 * The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
 *
 * Example usage to set ERC1967 implementation slot:
 * ```
 * contract ERC1967 {
 *     bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
 *
 *     function _getImplementation() internal view returns (address) {
 *         return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
 *     }
 *
 *     function _setImplementation(address newImplementation) internal {
 *         require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
 *         StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
 *     }
 * }
 * ```
 *
 * _Available since v4.1 for `address`, `bool`, `bytes32`, and `uint256`._
 */
library StorageSlot {
    struct AddressSlot {
        address value;
    }

    struct BooleanSlot {
        bool value;
    }

    struct Bytes32Slot {
        bytes32 value;
    }

    struct Uint256Slot {
        uint256 value;
    }

    /**
     * @dev Returns an `AddressSlot` with member `value` located at `slot`.
     */
    function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BooleanSlot` with member `value` located at `slot`.
     */
    function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `Bytes32Slot` with member `value` located at `slot`.
     */
    function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `Uint256Slot` with member `value` located at `slot`.
     */
    function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }
}

// File: contracts/pendle/contracts/core/libraries/Errors.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

/// Adapted from UniswapV3's Oracle

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 MarketFactoryReserveFeePercentTooHigh(
        uint8 reserveFeePercent,
        uint8 maxReserveFeePercent
    );
    error MarketFactoryZeroTreasury();
    error MarketFactoryInitialAnchorTooLow(int256 initialAnchor, int256 minInitialAnchor);

    // 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 RouterExceededLimitSyIn(uint256 actualSyIn, uint256 limitSyIn);
    error RouterExceededLimitPtIn(uint256 actualPtIn, uint256 limitPtIn);
    error RouterExceededLimitYtIn(uint256 actualYtIn, uint256 limitYtIn);
    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 RouterKyberSwapDataZero();

    // 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();

    // 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 FDCantFundFutureEpoch();
    error FDFactoryDistributorAlreadyExisted(address pool, address distributor);

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

// File: contracts/pendle/contracts/core/libraries/math/LogExpMath.sol



// 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 0.8.17;

/* 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;
        }
    }
}

// File: contracts/pendle/contracts/core/libraries/math/Math.sol



// 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 0.8.17;

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

library Math {
    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 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 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 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);
    }
}

// File: contracts/pendle/contracts/core/libraries/MiniHelpers.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

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
    }
}

// File: contracts/pendle/contracts/core/libraries/TokenHelper.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;
import "@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";

abstract contract TokenHelper {
    using SafeERC20 for IERC20;
    address internal constant NATIVE = address(0);
    uint256 internal constant LOWER_BOUND_APPROVAL = type(uint96).max / 2; // some tokens use 96 bits for approval

    function _transferIn(
        address token,
        address from,
        uint256 amount
    ) internal {
        if (token == NATIVE) require(msg.value == amount, "eth mismatch");
        else if (amount != 0) IERC20(token).safeTransferFrom(from, address(this), amount);
    }

    function _transferFrom(
        IERC20 token,
        address from,
        address to,
        uint256 amount
    ) internal {
        if (amount != 0) token.safeTransferFrom(from, to, amount);
    }

    function _transferOut(
        address token,
        address to,
        uint256 amount
    ) internal {
        if (amount == 0) return;
        if (token == NATIVE) {
            (bool success, ) = to.call{ value: amount }("");
            require(success, "eth send failed");
        } else {
            IERC20(token).safeTransfer(to, amount);
        }
    }

    function _transferOut(
        address[] memory tokens,
        address to,
        uint256[] memory amounts
    ) internal {
        uint256 numTokens = tokens.length;
        require(numTokens == amounts.length, "length mismatch");
        for (uint256 i = 0; i < numTokens; ) {
            _transferOut(tokens[i], to, amounts[i]);
            unchecked {
                i++;
            }
        }
    }

    function _selfBalance(address token) internal view returns (uint256) {
        return (token == NATIVE) ? address(this).balance : IERC20(token).balanceOf(address(this));
    }

    function _selfBalance(IERC20 token) internal view returns (uint256) {
        return token.balanceOf(address(this));
    }

    /// @notice Approves the stipulated contract to spend the given allowance in the given token
    /// @dev PLS PAY ATTENTION to tokens that requires the approval to be set to 0 before changing it
    function _safeApprove(
        address token,
        address to,
        uint256 value
    ) internal {
        (bool success, bytes memory data) = token.call(
            abi.encodeWithSelector(IERC20.approve.selector, to, value)
        );
        require(success && (data.length == 0 || abi.decode(data, (bool))), "Safe Approve");
    }

    function _safeApproveInf(address token, address to) internal {
        if (token == NATIVE) return;
        if (IERC20(token).allowance(address(this), to) < LOWER_BOUND_APPROVAL) {
            _safeApprove(token, to, 0);
            _safeApprove(token, to, type(uint256).max);
        }
    }
}

// File: contracts/pendle/contracts/core/Market/MarketMathCore.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

import "../libraries/math/Math.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 Math for uint256;
    using Math 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 Math for uint256;
    using Math 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 = Math.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 < Math.IONE)
                revert Errors.MarketExchangeRateBelowOne(postFeeExchangeRate);

            fee = preFeeAssetToAccount.mulDown(Math.IONE - fee);
        } else {
            fee = ((preFeeAssetToAccount * (Math.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 < Math.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 < Math.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 < Math.IONE) revert Errors.MarketExchangeRateBelowOne(exchangeRate);
    }

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

        int256 logitP = proportion.divDown(Math.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
        );
    }
}

// File: contracts/pendle/contracts/core/StandardizedYield/PYIndex.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;
import "../../interfaces/IPYieldToken.sol";
import "../../interfaces/IPPrincipalToken.sol";

import "./SYUtils.sol";
import "../libraries/math/Math.sol";

type PYIndex is uint256;

library PYIndexLib {
    using Math for uint256;
    using Math for int256;

    function newIndex(IPYieldToken YT) internal returns (PYIndex) {
        return PYIndex.wrap(YT.pyIndexCurrent());
    }

    function syToAsset(PYIndex index, uint256 syAmount)
        internal
        pure
        returns (uint256)
    {
        return SYUtils.syToAsset(PYIndex.unwrap(index), syAmount);
    }

    function assetToSy(PYIndex index, uint256 assetAmount)
        internal
        pure
        returns (uint256)
    {
        return SYUtils.assetToSy(PYIndex.unwrap(index), assetAmount);
    }

    function assetToSyUp(PYIndex index, uint256 assetAmount)
        internal
        pure
        returns (uint256)
    {
        return SYUtils.assetToSyUp(PYIndex.unwrap(index), assetAmount);
    }

    function syToAssetUp(PYIndex index, uint256 syAmount)
        internal
        pure
        returns (uint256)
    {
        uint256 _index = PYIndex.unwrap(index);
        return SYUtils.syToAssetUp(_index, syAmount);
    }

    function syToAsset(PYIndex index, int256 syAmount)
        internal
        pure
        returns (int256)
    {
        int256 sign = syAmount < 0 ? int256(-1) : int256(1);
        return sign * (SYUtils.syToAsset(PYIndex.unwrap(index), syAmount.abs())).Int();
    }

    function assetToSy(PYIndex index, int256 assetAmount)
        internal
        pure
        returns (int256)
    {
        int256 sign = assetAmount < 0 ? int256(-1) : int256(1);
        return sign * (SYUtils.assetToSy(PYIndex.unwrap(index), assetAmount.abs())).Int();
    }

    function assetToSyUp(PYIndex index, int256 assetAmount)
        internal
        pure
        returns (int256)
    {
        int256 sign = assetAmount < 0 ? int256(-1) : int256(1);
        return sign * (SYUtils.assetToSyUp(PYIndex.unwrap(index), assetAmount.abs())).Int();
    }

}

// File: contracts/pendle/contracts/core/StandardizedYield/SYUtils.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

library SYUtils {
    uint256 internal constant ONE = 1e18;

    function syToAsset(uint256 exchangeRate, uint256 syAmount) internal pure returns (uint256) {
        return (syAmount * exchangeRate) / ONE;
    }

    function syToAssetUp(uint256 exchangeRate, uint256 syAmount) internal pure returns (uint256) {
        return (syAmount * exchangeRate + ONE - 1) / ONE;
    }

    function assetToSy(uint256 exchangeRate, uint256 assetAmount) internal pure returns (uint256) {
        return (assetAmount * ONE) / exchangeRate;
    }

    function assetToSyUp(uint256 exchangeRate, uint256 assetAmount)
        internal
        pure
        returns (uint256)
    {
        return (assetAmount * ONE + exchangeRate - 1) / exchangeRate;
    }
}

// File: contracts/pendle/contracts/interfaces/IPActionAddRemoveLiq.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

import "../router/base/MarketApproxLib.sol";
import "../router/kyberswap/KyberSwapHelper.sol";

interface IPActionAddRemoveLiq {
    event AddLiquidityDualSyAndPt(
        address indexed caller,
        address indexed market,
        address indexed receiver,
        uint256 netSyUsed,
        uint256 netPtUsed,
        uint256 netLpOut
    );

    event AddLiquidityDualTokenAndPt(
        address indexed caller,
        address indexed market,
        address indexed tokenIn,
        address receiver,
        uint256 netTokenUsed,
        uint256 netPtUsed,
        uint256 netLpOut
    );

    event AddLiquiditySinglePt(
        address indexed caller,
        address indexed market,
        address indexed receiver,
        uint256 netPtIn,
        uint256 netLpOut
    );

    event AddLiquiditySingleSy(
        address indexed caller,
        address indexed market,
        address indexed receiver,
        uint256 netSyIn,
        uint256 netLpOut
    );

    event AddLiquiditySingleToken(
        address indexed caller,
        address indexed market,
        address indexed token,
        address receiver,
        uint256 netTokenIn,
        uint256 netLpOut
    );

    event RemoveLiquidityDualSyAndPt(
        address indexed caller,
        address indexed market,
        address indexed receiver,
        uint256 netLpToRemove,
        uint256 netPtOut,
        uint256 netSyOut
    );

    event RemoveLiquidityDualTokenAndPt(
        address indexed caller,
        address indexed market,
        address indexed tokenOut,
        address receiver,
        uint256 netLpToRemove,
        uint256 netPtOut,
        uint256 netTokenOut
    );

    event RemoveLiquiditySinglePt(
        address indexed caller,
        address indexed market,
        address indexed receiver,
        uint256 netLpToRemove,
        uint256 netPtOut
    );

    event RemoveLiquiditySingleSy(
        address indexed caller,
        address indexed market,
        address indexed receiver,
        uint256 netLpToRemove,
        uint256 netSyOut
    );

    event RemoveLiquiditySingleToken(
        address indexed caller,
        address indexed market,
        address indexed token,
        address receiver,
        uint256 netLpToRemove,
        uint256 netTokenOut
    );

    function addLiquidityDualSyAndPt(
        address receiver,
        address market,
        uint256 netSyDesired,
        uint256 netPtDesired,
        uint256 minLpOut
    )
        external
        returns (
            uint256 netLpOut,
            uint256 netSyUsed,
            uint256 netPtUsed
        );

    function addLiquidityDualTokenAndPt(
        address receiver,
        address market,
        TokenInput calldata input,
        uint256 netPtDesired,
        uint256 minLpOut
    )
        external
        payable
        returns (
            uint256 netLpOut,
            uint256 netTokenUsed,
            uint256 netPtUsed
        );

    function addLiquiditySinglePt(
        address receiver,
        address market,
        uint256 netPtIn,
        uint256 minLpOut,
        ApproxParams calldata guessPtSwapToSy
    ) external returns (uint256 netLpOut, uint256 netSyFee);

    function addLiquiditySingleSy(
        address receiver,
        address market,
        uint256 netSyIn,
        uint256 minLpOut,
        ApproxParams calldata guessPtReceivedFromSy
    ) external returns (uint256 netLpOut, uint256 netSyFee);

    function addLiquiditySingleToken(
        address receiver,
        address market,
        uint256 minLpOut,
        ApproxParams calldata guessPtReceivedFromSy,
        TokenInput calldata input
    ) external payable returns (uint256 netLpOut, uint256 netSyFee);

    function removeLiquidityDualSyAndPt(
        address receiver,
        address market,
        uint256 netLpToRemove,
        uint256 minSyOut,
        uint256 minPtOut
    ) external returns (uint256 netSyOut, uint256 netPtOut);

    function removeLiquidityDualTokenAndPt(
        address receiver,
        address market,
        uint256 netLpToRemove,
        TokenOutput calldata output,
        uint256 minPtOut
    ) external returns (uint256 netTokenOut, uint256 netPtOut);

    function removeLiquiditySinglePt(
        address receiver,
        address market,
        uint256 netLpToRemove,
        uint256 minPtOut,
        ApproxParams calldata guessPtOut
    ) external returns (uint256 netPtOut, uint256 netSyFee);

    function removeLiquiditySingleSy(
        address receiver,
        address market,
        uint256 netLpToRemove,
        uint256 minSyOut
    ) external returns (uint256 netSyOut, uint256 netSyFee);

    function removeLiquiditySingleToken(
        address receiver,
        address market,
        uint256 netLpToRemove,
        TokenOutput calldata output
    ) external returns (uint256 netTokenOut, uint256 netSyFee);
}

// File: contracts/pendle/contracts/interfaces/IPActionMintRedeem.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

import "../router/base/MarketApproxLib.sol";
import "../router/kyberswap/KyberSwapHelper.sol";

interface IPActionMintRedeem {
    event MintSyFromToken(
        address indexed caller,
        address indexed tokenIn,
        address indexed SY,
        address receiver,
        uint256 netTokenIn,
        uint256 netSyOut
    );

    event RedeemSyToToken(
        address indexed caller,
        address indexed tokenOut,
        address indexed SY,
        address receiver,
        uint256 netSyIn,
        uint256 netTokenOut
    );

    event MintPyFromSy(
        address indexed caller,
        address indexed receiver,
        address indexed YT,
        uint256 netSyIn,
        uint256 netPyOut
    );

    event RedeemPyToSy(
        address indexed caller,
        address indexed receiver,
        address indexed YT,
        uint256 netPyIn,
        uint256 netSyOut
    );

    event MintPyFromToken(
        address indexed caller,
        address indexed tokenIn,
        address indexed YT,
        address receiver,
        uint256 netTokenIn,
        uint256 netPyOut
    );

    event RedeemPyToToken(
        address indexed caller,
        address indexed tokenOut,
        address indexed YT,
        address receiver,
        uint256 netPyIn,
        uint256 netTokenOut
    );

    event RedeemDueInterestAndRewards(
        address indexed user,
        address[] sys,
        address[] yts,
        address[] markets,
        uint256[][] syRewards,
        uint256[] ytInterests,
        uint256[][] ytRewards,
        uint256[][] marketRewards
    );

    event RedeemDueInterestAndRewardsThenSwapAll(
        address indexed user,
        address[] sys,
        address[] yts,
        address[] markets,
        address indexed tokenOut,
        uint256 netTokenOut
    );

    function mintSyFromToken(
        address receiver,
        address SY,
        uint256 minSyOut,
        TokenInput calldata input
    ) external payable returns (uint256 netSyOut);

    function redeemSyToToken(
        address receiver,
        address SY,
        uint256 netSyIn,
        TokenOutput calldata output
    ) external returns (uint256 netTokenOut);

    function mintPyFromToken(
        address receiver,
        address YT,
        uint256 minPyOut,
        TokenInput calldata input
    ) external payable returns (uint256 netPyOut);

    function redeemPyToToken(
        address receiver,
        address YT,
        uint256 netPyIn,
        TokenOutput calldata output
    ) external returns (uint256 netTokenOut);

    function mintPyFromSy(
        address receiver,
        address YT,
        uint256 netSyIn,
        uint256 minPyOut
    ) external returns (uint256 netPyOut);

    function redeemPyToSy(
        address receiver,
        address YT,
        uint256 netPyIn,
        uint256 minSyOut
    ) external returns (uint256 netSyOut);

    function redeemDueInterestAndRewards(
        address user,
        address[] calldata sys,
        address[] calldata yts,
        address[] calldata markets
    )
        external
        returns (
            uint256[][] memory syRewards,
            uint256[] memory ytInterests,
            uint256[][] memory ytRewards,
            uint256[][] memory marketRewards
        );

    struct RouterYtRedeemStruct {
        address[] yts;
        // key-value pair
        address[] syAddrs;
        address[] tokenRedeemSys;
        address[] bulks;
        //
    }

    struct RouterSwapAllStruct {
        // key-value pair
        address[] tokens;
        bytes[] kybercalls;
        //
        address kyberRouter;
        address outputToken;
        uint256 minTokenOut;
    }

    function redeemDueInterestAndRewardsThenSwapAll(
        address[] calldata sys,
        RouterYtRedeemStruct calldata dataYT,
        address[] calldata markets,
        RouterSwapAllStruct calldata dataSwap
    ) external returns (uint256 netTokenOut, uint256[] memory amountsSwapped);
}

// File: contracts/pendle/contracts/interfaces/IPActionMisc.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

interface IPActionMisc {
    function consult(address market, uint32 secondsAgo)
        external
        view
        returns (uint96 lnImpliedRateMean);
}

// File: contracts/pendle/contracts/interfaces/IPActionSwapPT.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

import "../router/base/MarketApproxLib.sol";
import "../router/kyberswap/KyberSwapHelper.sol";

interface IPActionSwapPT {
    event SwapPtAndSy(
        address indexed caller,
        address indexed market,
        address indexed receiver,
        int256 netPtToAccount,
        int256 netSyToAccount
    );

    event SwapPtAndToken(
        address indexed caller,
        address indexed market,
        address indexed token,
        address receiver,
        int256 netPtToAccount,
        int256 netTokenToAccount
    );

    function swapExactPtForSy(
        address receiver,
        address market,
        uint256 exactPtIn,
        uint256 minSyOut
    ) external returns (uint256 netSyOut, uint256 netSyFee);

    function swapPtForExactSy(
        address receiver,
        address market,
        uint256 exactSyOut,
        uint256 maxPtIn,
        ApproxParams calldata guessPtIn
    ) external returns (uint256 netPtIn, uint256 netSyFee);

    function swapSyForExactPt(
        address receiver,
        address market,
        uint256 exactPtOut,
        uint256 maxSyIn
    ) external returns (uint256 netSyIn, uint256 netSyFee);

    function swapExactSyForPt(
        address receiver,
        address market,
        uint256 exactSyIn,
        uint256 minPtOut,
        ApproxParams calldata guessPtOut
    ) external returns (uint256 netPtOut, uint256 netSyFee);

    function swapExactTokenForPt(
        address receiver,
        address market,
        uint256 minPtOut,
        ApproxParams calldata guessPtOut,
        TokenInput calldata input
    ) external payable returns (uint256 netPtOut, uint256 netSyFee);

    function swapExactPtForToken(
        address receiver,
        address market,
        uint256 exactPtIn,
        TokenOutput calldata output
    ) external returns (uint256 netTokenOut, uint256 netSyFee);
}

// File: contracts/pendle/contracts/interfaces/IPActionSwapPTYT.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

import "../router/base/MarketApproxLib.sol";
import "../router/kyberswap/KyberSwapHelper.sol";

interface IPActionSwapPTYT {
    event SwapPtAndYt(
        address indexed caller,
        address indexed market,
        address indexed receiver,
        int256 netPtToAccount,
        int256 netYtToAccount
    );

    function swapExactPtForYt(
        address receiver,
        address market,
        uint256 exactPtIn,
        uint256 minYtOut,
        ApproxParams calldata guessTotalPtToSwap
    ) external returns (uint256 netYtOut, uint256 netSyFee);

    function swapExactYtForPt(
        address receiver,
        address market,
        uint256 exactYtIn,
        uint256 minPtOut,
        ApproxParams calldata guessTotalPtSwapped
    ) external returns (uint256 netPtOut, uint256 netSyFee);
}

// File: contracts/pendle/contracts/interfaces/IPActionSwapYT.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

import "../router/base/MarketApproxLib.sol";
import "../router/kyberswap/KyberSwapHelper.sol";

interface IPActionSwapYT {
    event SwapYtAndSy(
        address indexed caller,
        address indexed market,
        address indexed receiver,
        int256 netYtToAccount,
        int256 netSyToAccount
    );

    event SwapYtAndToken(
        address indexed caller,
        address indexed market,
        address indexed token,
        address receiver,
        int256 netYtToAccount,
        int256 netTokenToAccount
    );

    function swapExactSyForYt(
        address receiver,
        address market,
        uint256 exactSyIn,
        uint256 minYtOut,
        ApproxParams memory guessYtOut
    ) external returns (uint256 netYtOut, uint256 netSyFee);

    function swapExactYtForSy(
        address receiver,
        address market,
        uint256 exactYtIn,
        uint256 minSyOut
    ) external returns (uint256 netSyOut, uint256 netSyFee);

    function swapSyForExactYt(
        address receiver,
        address market,
        uint256 exactYtOut,
        uint256 maxSyIn
    ) external returns (uint256 netSyIn, uint256 netSyFee);

    function swapYtForExactSy(
        address receiver,
        address market,
        uint256 exactSyOut,
        uint256 maxYtIn,
        ApproxParams memory guessYtIn
    ) external returns (uint256 netYtIn, uint256 netSyFee);

    function swapExactTokenForYt(
        address receiver,
        address market,
        uint256 minYtOut,
        ApproxParams memory guessYtOut,
        TokenInput calldata input
    ) external payable returns (uint256 netYtOut, uint256 netSyFee);

    function swapExactYtForToken(
        address receiver,
        address market,
        uint256 netYtIn,
        TokenOutput calldata output
    ) external returns (uint256 netTokenOut, uint256 netSyFee);
}

// File: contracts/pendle/contracts/interfaces/IPAllAction.sol



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

pragma solidity 0.8.17;

import "./IPActionAddRemoveLiq.sol";
import "./IPActionSwapPT.sol";
import "./IPActionSwapYT.sol";
import "./IPActionSwapPTYT.sol";
import "./IPActionMintRedeem.sol";
import "./IPActionMisc.sol";

interface IPAllAction is
    IPActionAddRemoveLiq,
    IPActionSwapPT,
    IPActionSwapYT,
    IPActionSwapPTYT,
    IPActionMintRedeem,
    IPActionMisc
{}

// File: contracts/pendle/contracts/interfaces/IPInterestManagerYT.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

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

// File: contracts/pendle/contracts/interfaces/IPMarketSwapCallback.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

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

// File: contracts/pendle/contracts/interfaces/IPPrincipalToken.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;
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);
}

// File: contracts/pendle/contracts/interfaces/IPYieldToken.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;
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 WithdrawFeeToTreasury(uint256[] amountRewardsOut, uint256 syOut);

    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);
}

// File: contracts/pendle/contracts/interfaces/IRewardManager.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

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

// File: contracts/pendle/contracts/router/base/MarketApproxLib.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

import "../../core/libraries/math/Math.sol";
import "../../core/Market/MarketMathCore.sol";

struct ApproxParams {
    uint256 guessMin;
    uint256 guessMax;
    uint256 guessOffchain; // pass 0 in to skip this variable
    uint256 maxIteration; // every iteration, the diff between guessMin and guessMax will be divided by 2
    uint256 eps; // the max eps between the returned result & the correct result, base 1e18. Normally this number will be set
    // to 1e15 (1e18/1000 = 0.1%)

    /// Further explanation of the eps. Take swapExactSyForPt for example. To calc the corresponding amount of Pt to swap out,
    /// it's necessary to run an approximation algorithm, because by default there only exists the Pt to Sy formula
    /// To approx, the 5 values above will have to be provided, and the approx process will run as follows:
    /// mid = (guessMin + guessMax) / 2 // mid here is the current guess of the amount of Pt out
    /// netSyNeed = calcSwapSyForExactPt(mid)
    /// if (netSyNeed > exactSyIn) guessMax = mid - 1 // since the maximum Sy in can't exceed the exactSyIn
    /// else guessMin = mid (1)
    /// For the (1), since netSyNeed <= exactSyIn, the result might be usable. If the netSyNeed is within eps of
    /// exactSyIn (ex eps=0.1% => we have used 99.9% the amount of Sy specified), mid will be chosen as the final guess result

    /// for guessOffchain, this is to provide a shortcut to guessing. The offchain SDK can precalculate the exact result
    /// before the tx is sent. When the tx reaches the contract, the guessOffchain will be checked first, and if it satisfies the
    /// approximation, it will be used (and save all the guessing). It's expected that this shortcut will be used in most cases
    /// except in cases that there is a trade in the same market right before the tx
}

library MarketApproxPtInLib {
    using MarketMathCore for MarketState;
    using PYIndexLib for PYIndex;
    using Math for uint256;
    using Math for int256;
    using LogExpMath for int256;

    struct ApproxParamsPtIn {
        uint256 guessMin;
        uint256 guessMax;
        uint256 guessOffchain;
        uint256 maxIteration;
        uint256 eps;
        //
        uint256 biggestGoodGuess;
    }

    struct Args1 {
        MarketState market;
        PYIndex index;
        uint256 minSyOut;
        uint256 blockTime;
    }

    /**
     * @dev algorithm:
        - Bin search the amount of PT to swap in
        - Try swapping & get netSyOut
        - Stop when netSyOut greater & approx minSyOut
        - guess & approx is for netPtIn
     */
    function approxSwapPtForExactSy(
        MarketState memory _market,
        PYIndex _index,
        uint256 _minSyOut,
        uint256 _blockTime,
        ApproxParams memory _approx
    )
        internal
        pure
        returns (
            uint256, /*netPtIn*/
            uint256, /*netSyOut*/
            uint256 /*netSyFee*/
        )
    {
        Args1 memory a = Args1(_market, _index, _minSyOut, _blockTime);
        MarketPreCompute memory comp = a.market.getMarketPreCompute(a.index, a.blockTime);
        ApproxParamsPtIn memory p = newApproxParamsPtIn(_approx, 0, calcMaxPtIn(comp.totalAsset));

        for (uint256 iter = 0; iter < p.maxIteration; ++iter) {
            (bool isGoodSlope, uint256 guess) = nextGuess(p, comp, a.market.totalPt, iter);
            if (!isGoodSlope) {
                p.guessMax = guess;
                continue;
            }

            (uint256 netSyOut, uint256 netSyFee, ) = calcSyOut(a.market, comp, a.index, guess);

            if (netSyOut >= a.minSyOut) {
                p.guessMax = guess;
                bool isAnswerAccepted = Math.isAGreaterApproxB(netSyOut, a.minSyOut, p.eps);
                if (isAnswerAccepted) {
                    return (guess, netSyOut, netSyFee);
                }
            } else {
                p.guessMin = guess;
            }
        }
        revert Errors.ApproxFail();
    }

    struct Args2 {
        MarketState market;
        PYIndex index;
        uint256 exactSyIn;
        uint256 blockTime;
    }

    /**
     * @dev algorithm:
        - Bin search the amount of PT to swap in
        - Flashswap the corresponding amount of SY out
        - Pair those amount with exactSyIn SY to tokenize into PT & YT
        - PT to repay the flashswap, YT transferred to user
        - Stop when the amount of SY to be pulled to tokenize PT to repay loan approx the exactSyIn
        - guess & approx is for netYtOut (also netPtIn)
     */
    function approxSwapExactSyForYt(
        MarketState memory _market,
        PYIndex _index,
        uint256 _exactSyIn,
        uint256 _blockTime,
        ApproxParams memory _approx
    )
        internal
        pure
        returns (
            uint256, /*netYtOut*/
            uint256 /*netSyFee*/
        )
    {
        Args2 memory a = Args2(_market, _index, _exactSyIn, _blockTime);
        MarketPreCompute memory comp = a.market.getMarketPreCompute(a.index, a.blockTime);

        // at minimum we will flashswap exactSyIn since we have enough SY to payback the PT loan
        ApproxParamsPtIn memory p = newApproxParamsPtIn(
            _approx,
            a.index.syToAsset(a.exactSyIn),
            calcMaxPtIn(comp.totalAsset)
        );

        for (uint256 iter = 0; iter < p.maxIteration; ++iter) {
            (bool isGoodSlope, uint256 guess) = nextGuess(p, comp, a.market.totalPt, iter);
            if (!isGoodSlope) {
                p.guessMax = guess;
                continue;
            }

            (uint256 netSyOut, uint256 netSyFee, ) = calcSyOut(a.market, comp, a.index, guess);

            uint256 netSyToTokenizePt = a.index.assetToSyUp(guess);

            // for sure netSyToTokenizePt >= netSyOut since we are swapping PT to SY
            uint256 netSyToPull = netSyToTokenizePt - netSyOut;

            if (netSyToPull <= a.exactSyIn) {
                p.guessMin = guess;
                bool isAnswerAccepted = Math.isASmallerApproxB(netSyToPull, a.exactSyIn, p.eps);
                if (isAnswerAccepted) return (guess, netSyFee);
            } else {
                p.guessMax = guess - 1;
            }
        }
        revert Errors.ApproxFail();
    }

    struct Args6 {
        MarketState market;
        PYIndex index;
        uint256 totalPtIn;
        uint256 blockTime;
    }

    /**
     * @dev algorithm:
        - Bin search the amount of PT to swap to SY
        - Swap PT to SY
        - Pair the remaining PT with the SY to add liquidity
        - Stop when the ratio of PT / totalPt & SY / totalSy is approx
        - guess & approx is for netPtSwap
     */
    function approxSwapPtToAddLiquidity(
        MarketState memory _market,
        PYIndex _index,
        uint256 _totalPtIn,
        uint256 _blockTime,
        ApproxParams memory _approx
    )
        internal
        pure
        returns (
            uint256, /*netPtSwap*/
            uint256, /*netSyFromSwap*/
            uint256 /*netSyFee*/
        )
    {
        Args6 memory a = Args6(_market, _index, _totalPtIn, _blockTime);
        require(a.market.totalLp != 0, "no existing lp");

        MarketPreCompute memory comp = a.market.getMarketPreCompute(a.index, a.blockTime);
        ApproxParamsPtIn memory p = newApproxParamsPtIn(
            _approx,
            0,
            Math.min(a.totalPtIn, calcMaxPtIn(comp.totalAsset))
        );

        p.guessMax = Math.min(p.guessMax, a.totalPtIn);

        for (uint256 iter = 0; iter < p.maxIteration; ++iter) {
            (bool isGoodSlope, uint256 guess) = nextGuess(p, comp, a.market.totalPt, iter);

            if (!isGoodSlope) {
                p.guessMax = guess;
                continue;
            }

            (uint256 netSyOut, uint256 netSyFee, uint256 netSyToReserve) = calcSyOut(
                a.market,
                comp,
                a.index,
                guess
            );

            uint256 syNumerator;
            uint256 ptNumerator;
            {
                uint256 newTotalPt = a.market.totalPt.Uint() + guess;
                uint256 newTotalSy = (a.market.totalSy.Uint() - netSyOut - netSyToReserve);

                // it is desired that
                // netSyOut / newTotalSy = netPtRemaining / newTotalPt
                // which is equivalent to
                // netSyOut * newTotalPt = netPtRemaining * newTotalSy

                syNumerator = netSyOut * newTotalPt;
                ptNumerator = (a.totalPtIn - guess) * newTotalSy;
            }

            if (Math.isAApproxB(syNumerator, ptNumerator, p.eps)) {
                return (guess, netSyOut, netSyFee);
            }

            if (syNumerator <= ptNumerator) {
                // needs more SY --> swap more PT
                p.guessMin = guess + 1;
            } else {
                // needs less SY --> swap less PT
                p.guessMax = guess - 1;
            }
        }
        revert Errors.ApproxFail();
    }

    struct Args7 {
        MarketState market;
        PYIndex index;
        uint256 exactPtIn;
        uint256 blockTime;
    }

    /**
     * @dev algorithm:
        - Bin search the amount of PT to swap to SY
        - Flashswap the corresponding amount of SY out
        - Tokenize all the SY into PT + YT
        - PT to repay the flashswap, YT transferred to user
        - Stop when the additional amount of PT to pull to repay the loan approx the exactPtIn
        - guess & approx is for totalPtToSwap
     */
    function approxSwapExactPtForYt(
        MarketState memory _market,
        PYIndex _index,
        uint256 _exactPtIn,
        uint256 _blockTime,
        ApproxParams memory _approx
    )
        internal
        pure
        returns (
            uint256, /*netYtOut*/
            uint256, /*totalPtToSwap*/
            uint256 /*netSyFee*/
        )
    {
        Args7 memory a = Args7(_market, _index, _exactPtIn, _blockTime);

        MarketPreCompute memory comp = a.market.getMarketPreCompute(a.index, a.blockTime);
        ApproxParamsPtIn memory p = newApproxParamsPtIn(
            _approx,
            a.exactPtIn,
            calcMaxPtIn(comp.totalAsset)
        );

        for (uint256 iter = 0; iter < p.maxIteration; ++iter) {
            (bool isGoodSlope, uint256 guess) = nextGuess(p, comp, a.market.totalPt, iter);

            if (!isGoodSlope) {
                p.guessMax = guess;
                continue;
            }

            (uint256 netSyOut, uint256 netSyFee, ) = calcSyOut(a.market, comp, a.index, guess);

            uint256 netAssetOut = a.index.syToAsset(netSyOut);

            // guess >= netAssetOut since we are swapping PT to SY
            uint256 netPtToPull = guess - netAssetOut;

            if (netPtToPull <= a.exactPtIn) {
                p.guessMin = guess;
                if (Math.isASmallerApproxB(netPtToPull, a.exactPtIn, p.eps)) {
                    return (netAssetOut, guess, netSyFee);
                }
            } else {
                p.guessMax = guess - 1;
            }
        }
        revert Errors.ApproxFail();
    }

    ////////////////////////////////////////////////////////////////////////////////

    function calcSyOut(
        MarketState memory market,
        MarketPreCompute memory comp,
        PYIndex index,
        uint256 netPtIn
    )
        internal
        pure
        returns (
            uint256 netSyOut,
            uint256 netSyFee,
            uint256 netSyToReserve
        )
    {
        (int256 _netSyOut, int256 _netSyFee, int256 _netSyToReserve) = market.calcTrade(
            comp,
            index,
            netPtIn.neg()
        );
        netSyOut = _netSyOut.Uint();
        netSyFee = _netSyFee.Uint();
        netSyToReserve = _netSyToReserve.Uint();
    }

    function newApproxParamsPtIn(
        ApproxParams memory _approx,
        uint256 minGuessMin,
        uint256 maxGuessMax
    ) internal pure returns (ApproxParamsPtIn memory res) {
        res.guessMin = Math.max(_approx.guessMin, minGuessMin);
        res.guessMax = Math.min(_approx.guessMax, maxGuessMax);

        if (res.guessMin > res.guessMax || _approx.eps > Math.ONE)
            revert Errors.ApproxParamsInvalid(_approx.guessMin, _approx.guessMax, _approx.eps);

        res.guessOffchain = _approx.guessOffchain;
        res.maxIteration = _approx.maxIteration;
        res.eps = _approx.eps;
    }

    function calcMaxPtIn(int256 totalAsset) internal pure returns (uint256) {
        return totalAsset.Uint() - 1;
    }

    function nextGuess(
        ApproxParamsPtIn memory p,
        MarketPreCompute memory comp,
        int256 totalPt,
        uint256 iter
    ) internal pure returns (bool, uint256) {
        uint256 guess = _nextGuessPrivate(p, iter);
        if (guess <= p.biggestGoodGuess) return (true, guess);

        int256 slope = calcSlope(comp, totalPt, guess.Int());
        if (slope < 0) return (false, guess);

        p.biggestGoodGuess = guess;
        return (true, guess);
    }

    /**
     * @dev it is safe to assume that p.guessMin <= p.guessMax from the initialization of p
     * So once guessMin becomes larger, it should always be the case of ApproxFail
     */
    function _nextGuessPrivate(ApproxParamsPtIn memory p, uint256 iter)
        private
        pure
        returns (uint256)
    {
        if (iter == 0 && p.guessOffchain != 0) return p.guessOffchain;
        if (p.guessMin <= p.guessMax) return (p.guessMin + p.guessMax) / 2;
        revert Errors.ApproxFail();
    }

    function calcSlope(
        MarketPreCompute memory comp,
        int256 totalPt,
        int256 ptToMarket //
    ) internal pure returns (int256) {
        int256 diffAssetPtToMarket = comp.totalAsset - ptToMarket;
        int256 sumPt = ptToMarket + totalPt; // probably can skip sumPt check

        require(diffAssetPtToMarket > 0 && sumPt > 0, "invalid ptToMarket");

        int256 part1 = (ptToMarket * (totalPt + comp.totalAsset)).divDown(
            sumPt * diffAssetPtToMarket
        );

        int256 part2 = sumPt.divDown(diffAssetPtToMarket).ln();
        int256 part3 = Math.IONE.divDown(comp.rateScalar);

        return comp.rateAnchor - (part1 - part2).mulDown(part3);
    }
}

library MarketApproxPtOutLib {
    using MarketMathCore for MarketState;
    using PYIndexLib for PYIndex;
    using Math for uint256;
    using Math for int256;
    using LogExpMath for int256;

    struct ApproxParamsPtOut {
        uint256 guessMin;
        uint256 guessMax;
        uint256 guessOffchain;
        uint256 maxIteration;
        uint256 eps;
    }

    struct Args4 {
        MarketState market;
        PYIndex index;
        uint256 exactSyIn;
        uint256 blockTime;
    }

    /**
     * @dev algorithm:
        - Bin search the amount of PT to swapExactOut
        - Calculate the amount of SY needed
        - Stop when the netSyIn is smaller approx exactSyIn
        - guess & approx is for netSyIn
     */
    function approxSwapExactSyForPt(
        MarketState memory _market,
        PYIndex _index,
        uint256 _exactSyIn,
        uint256 _blockTime,
        ApproxParams memory _approx
    )
        internal
        pure
        returns (
            uint256, /*netPtOut*/
            uint256 /*netSyFee*/
        )
    {
        Args4 memory a = Args4(_market, _index, _exactSyIn, _blockTime);
        MarketPreCompute memory comp = a.market.getMarketPreCompute(a.index, a.blockTime);
        ApproxParamsPtOut memory p = newApproxParamsPtOut(
            _approx,
            0,
            calcMaxPtOut(comp, a.market.totalPt)
        );

        for (uint256 iter = 0; iter < p.maxIteration; ++iter) {
            uint256 guess = nextGuess(p, iter);

            (uint256 netSyIn, uint256 netSyFee, ) = calcSyIn(a.market, comp, a.index, guess);

            if (netSyIn <= a.exactSyIn) {
                p.guessMin = guess;
                bool isAnswerAccepted = Math.isASmallerApproxB(netSyIn, a.exactSyIn, p.eps);
                if (isAnswerAccepted) return (guess, netSyFee);
            } else {
                p.guessMax = guess - 1;
            }
        }

        revert Errors.ApproxFail();
    }

    struct Args5 {
        MarketState market;
        PYIndex index;
        uint256 minSyOut;
        uint256 blockTime;
    }

    /**
     * @dev algorithm:
        - Bin search the amount of PT to swapExactOut
        - Flashswap that amount of PT & pair with YT to redeem SY
        - Use the SY to repay the flashswap debt and the remaining is transferred to user
        - Stop when the netSyOut is greater approx the minSyOut
        - guess & approx is for netSyOut
     */
    function approxSwapYtForExactSy(
        MarketState memory _market,
        PYIndex _index,
        uint256 _minSyOut,
        uint256 _blockTime,
        ApproxParams memory _approx
    )
        internal
        pure
        returns (
            uint256, /*netYtIn*/
            uint256, /*netSyOut*/
            uint256 /*netSyFee*/
        )
    {
        Args5 memory a = Args5(_market, _index, _minSyOut, _blockTime);
        MarketPreCompute memory comp = a.market.getMarketPreCompute(a.index, a.blockTime);
        ApproxParamsPtOut memory p = newApproxParamsPtOut(
            _approx,
            0,
            calcMaxPtOut(comp, a.market.totalPt)
        );

        for (uint256 iter = 0; iter < p.maxIteration; ++iter) {
            uint256 guess = nextGuess(p, iter);

            (uint256 netSyOwed, uint256 netSyFee, ) = calcSyIn(a.market, comp, a.index, guess);

            uint256 netAssetToRepay = a.index.syToAssetUp(netSyOwed);
            uint256 netSyOut = a.index.assetToSy(guess - netAssetToRepay);

            if (netSyOut >= a.minSyOut) {
                p.guessMax = guess;
                if (Math.isAGreaterApproxB(netSyOut, a.minSyOut, p.eps)) {
                    return (guess, netSyOut, netSyFee);
                }
            } else {
                p.guessMin = guess + 1;
            }
        }
        revert Errors.ApproxFail();
    }

    struct Args6 {
        MarketState market;
        PYIndex index;
        uint256 totalSyIn;
        uint256 blockTime;
    }

    /**
     * @dev algorithm:
        - Bin search the amount of PT to swapExactOut
        - Swap that amount of PT out
        - Pair the remaining PT with the SY to add liquidity
        - Stop when the ratio of PT / totalPt & SY / totalSy is approx
        - guess & approx is for netPtFromSwap
     */
    function approxSwapSyToAddLiquidity(
        MarketState memory _market,
        PYIndex _index,
        uint256 _totalSyIn,
        uint256 _blockTime,
        ApproxParams memory _approx
    )
        internal
        pure
        returns (
            uint256, /*netPtFromSwap*/
            uint256, /*netSySwap*/
            uint256 /*netSyFee*/
        )
    {
        Args6 memory a = Args6(_market, _index, _totalSyIn, _blockTime);
        require(a.market.totalLp != 0, "no existing lp");

        MarketPreCompute memory comp = a.market.getMarketPreCompute(a.index, a.blockTime);
        ApproxParamsPtOut memory p = newApproxParamsPtOut(
            _approx,
            0,
            calcMaxPtOut(comp, a.market.totalPt)
        );

        for (uint256 iter = 0; iter < p.maxIteration; ++iter) {
            uint256 guess = nextGuess(p, iter);

            (uint256 netSyIn, uint256 netSyFee, uint256 netSyToReserve) = calcSyIn(
                a.market,
                comp,
                a.index,
                guess
            );

            if (netSyIn > a.totalSyIn) {
                p.guessMax = guess - 1;
                continue;
            }

            uint256 syNumerator;
            uint256 ptNumerator;

            {
                uint256 newTotalPt = a.market.totalPt.Uint() - guess;
                uint256 netTotalSy = a.market.totalSy.Uint() + netSyIn - netSyToReserve;

                // it is desired that
                // netPtFromSwap / newTotalPt = netSyRemaining / netTotalSy
                // which is equivalent to
                // netPtFromSwap * netTotalSy = netSyRemaining * newTotalPt

                ptNumerator = guess * netTotalSy;
                syNumerator = (a.totalSyIn - netSyIn) * newTotalPt;
            }

            if (Math.isAApproxB(ptNumerator, syNumerator, p.eps)) {
                return (guess, netSyIn, netSyFee);
            }

            if (ptNumerator <= syNumerator) {
                // needs more PT
                p.guessMin = guess + 1;
            } else {
                // needs less PT
                p.guessMax = guess - 1;
            }
        }
        revert Errors.ApproxFail();
    }

    struct Args8 {
        MarketState market;
        PYIndex index;
        uint256 exactYtIn;
        uint256 blockTime;
        uint256 maxSyPayable;
    }

    /**
     * @dev algorithm:
        - Bin search the amount of PT to swapExactOut
        - Flashswap that amount of PT out
        - Pair all the PT with the YT to redeem SY
        - Use the SY to repay the flashswap debt
        - Stop when the amount of SY owed is smaller approx the amount of SY to repay the flashswap
        - guess & approx is for netPtFromSwap
     */
    function approxSwapExactYtForPt(
        MarketState memory _market,
        PYIndex _index,
        uint256 _exactYtIn,
        uint256 _blockTime,
        ApproxParams memory _approx
    )
        internal
        pure
        returns (
            uint256, /*netPtOut*/
            uint256, /*totalPtSwapped*/
            uint256 /*netSyFee*/
        )
    {
        Args8 memory a = Args8(
            _market,
            _index,
            _exactYtIn,
            _blockTime,
            _index.assetToSy(_exactYtIn)
        );
        MarketPreCompute memory comp = a.market.getMarketPreCompute(a.index, a.blockTime);
        ApproxParamsPtOut memory p = newApproxParamsPtOut(
            _approx,
            a.exactYtIn,
            calcMaxPtOut(comp, a.market.totalPt)
        );

        for (uint256 iter = 0; iter < p.maxIteration; ++iter) {
            uint256 guess = nextGuess(p, iter);

            (uint256 netSyOwed, uint256 netSyFee, ) = calcSyIn(a.market, comp, a.index, guess);

            if (netSyOwed <= a.maxSyPayable) {
                p.guessMin = guess;

                if (Math.isASmallerApproxB(netSyOwed, a.maxSyPayable, p.eps)) {
                    return (guess - a.exactYtIn, guess, netSyFee);
                }
            } else {
                p.guessMax = guess - 1;
            }
        }
        revert Errors.ApproxFail();
    }

    ////////////////////////////////////////////////////////////////////////////////

    function calcSyIn(
        MarketState memory market,
        MarketPreCompute memory comp,
        PYIndex index,
        uint256 netPtOut
    )
        internal
        pure
        returns (
            uint256 netSyIn,
            uint256 netSyFee,
            uint256 netSyToReserve
        )
    {
        (int256 _netSyIn, int256 _netSyFee, int256 _netSyToReserve) = market.calcTrade(
            comp,
            index,
            netPtOut.Int()
        );

        netSyIn = _netSyIn.abs();
        netSyFee = _netSyFee.Uint();
        netSyToReserve = _netSyToReserve.Uint();
    }

    function newApproxParamsPtOut(
        ApproxParams memory _approx,
        uint256 minGuessMin,
        uint256 maxGuessMax
    ) internal pure returns (ApproxParamsPtOut memory res) {
        if (_approx.guessMin > _approx.guessMax || _approx.eps > Math.ONE)
            revert Errors.ApproxParamsInvalid(_approx.guessMin, _approx.guessMax, _approx.eps);

        res.guessMin = Math.max(_approx.guessMin, minGuessMin);
        res.guessMax = Math.min(_approx.guessMax, maxGuessMax);

        if (res.guessMin > res.guessMax)
            revert Errors.ApproxBinarySearchInputInvalid(
                _approx.guessMin,
                _approx.guessMax,
                minGuessMin,
                maxGuessMax
            );

        res.guessOffchain = _approx.guessOffchain;
        res.maxIteration = _approx.maxIteration;
        res.eps = _approx.eps;
    }

    function calcMaxPtOut(MarketPreCompute memory comp, int256 totalPt)
        internal
        pure
        returns (uint256)
    {
        int256 logitP = (comp.feeRate - comp.rateAnchor).mulDown(comp.rateScalar).exp();
        int256 proportion = logitP.divDown(logitP + Math.IONE);
        int256 numerator = proportion.mulDown(totalPt + comp.totalAsset);
        int256 maxPtOut = totalPt - numerator;
        // only get 99.9% of the theoretical max to accommodate some precision issues
        return (maxPtOut.Uint() * 999) / 1000;
    }

    /**
     * @dev it is safe to assume that p.guessMin <= p.guessMax from the initialization of p
     * So once guessMin becomes larger, it should always be the case of ApproxFail
     */
    function nextGuess(ApproxParamsPtOut memory p, uint256 iter) private pure returns (uint256) {
        if (iter == 0 && p.guessOffchain != 0) return p.guessOffchain;
        if (p.guessMin <= p.guessMax) return (p.guessMin + p.guessMax) / 2;
        revert Errors.ApproxFail();
    }
}

// File: contracts/pendle/contracts/router/kyberswap/IAggregatorRouterHelper.sol



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

pragma solidity 0.8.17;

interface IAggregationRouterHelper {
    function getScaledInputData(bytes calldata kybercall, uint256 newAmount)
        external
        pure
        returns (bytes memory);
}

// File: contracts/pendle/contracts/router/kyberswap/KyberSwapHelper.sol



// 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 0.8.17;

import "@openzeppelin/contracts/utils/Address.sol";
import "../../core/libraries/TokenHelper.sol";
import "./IAggregatorRouterHelper.sol";
import "../../core/libraries/Errors.sol";

struct TokenInput {
    // Token/Sy data
    address tokenIn;
    uint256 netTokenIn;
    address tokenMintSy;
    address bulk;
    // Kyber data
    address kyberRouter;
    bytes kybercall;
}

struct TokenOutput {
    // Token/Sy data
    address tokenOut;
    uint256 minTokenOut;
    address tokenRedeemSy;
    address bulk;
    // Kyber data
    address kyberRouter;
    bytes kybercall;
}

abstract contract KyberSwapHelper is TokenHelper {
    using Address for address;

    address public immutable kyberScalingLib;

    constructor(address _kyberScalingLib) {
        kyberScalingLib = _kyberScalingLib;
    }

    function _kyberswap(
        address tokenIn,
        uint256 amountIn,
        address kyberRouter,
        bytes memory rawKybercall
    ) internal {
        if (kyberRouter == address(0) || rawKybercall.length == 0)
            revert Errors.RouterKyberSwapDataZero();

        _safeApproveInf(tokenIn, kyberRouter);

        bytes memory kybercall = IAggregationRouterHelper(kyberScalingLib).getScaledInputData(
            rawKybercall,
            amountIn
        );
        kyberRouter.functionCallWithValue(kybercall, tokenIn == NATIVE ? amountIn : 0);
    }
}

// File: contracts/pendle/contracts/router/PendleRouter.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.17;

import "@openzeppelin/contracts/proxy/utils/UUPSUpgradeable.sol";
import "@openzeppelin/contracts/proxy/Proxy.sol";
import "../interfaces/IPAllAction.sol";
import "../interfaces/IPMarketSwapCallback.sol";
import "../core/libraries/Errors.sol";

/// @dev this contract will be deployed behind an ERC1967 proxy
/// calls to the ERC1967 proxy will be resolved at this contract, and proxied again to the
/// corresponding implementation contracts

// solhint-disable no-empty-blocks
contract PendleRouter is Proxy {
    address public immutable ACTION_MINT_REDEEM;
    address public immutable ACTION_ADD_REMOVE_LIQ;
    address public immutable ACTION_SWAP_PT;
    address public immutable ACTION_SWAP_YT;
    address public immutable ACTION_SWAP_PTYT;
    address public immutable ACTION_CALLBACK;
    address public immutable ACTION_MISC;

    constructor(
        address _ACTION_MINT_REDEEM,
        address _ACTION_ADD_REMOVE_LIQ,
        address _ACTION_SWAP_PT,
        address _ACTION_SWAP_YT,
        address _ACTION_SWAP_PTYT,
        address _ACTION_CALLBACK,
        address _ACTION_MISC
    ) {
        ACTION_MINT_REDEEM = _ACTION_MINT_REDEEM;
        ACTION_ADD_REMOVE_LIQ = _ACTION_ADD_REMOVE_LIQ;
        ACTION_SWAP_PT = _ACTION_SWAP_PT;
        ACTION_SWAP_YT = _ACTION_SWAP_YT;
        ACTION_SWAP_PTYT = _ACTION_SWAP_PTYT;
        ACTION_CALLBACK = _ACTION_CALLBACK;
        ACTION_MISC = _ACTION_MISC;
    }

    receive() external payable virtual override {}

    function getRouterImplementation(bytes4 sig) public view returns (address) {
        if (
            sig == IPActionMintRedeem.mintSyFromToken.selector ||
            sig == IPActionMintRedeem.redeemSyToToken.selector ||
            sig == IPActionMintRedeem.mintPyFromToken.selector ||
            sig == IPActionMintRedeem.redeemPyToToken.selector ||
            sig == IPActionMintRedeem.mintPyFromSy.selector ||
            sig == IPActionMintRedeem.redeemPyToSy.selector ||
            sig == IPActionMintRedeem.redeemDueInterestAndRewards.selector ||
            sig == IPActionMintRedeem.redeemDueInterestAndRewardsThenSwapAll.selector
        ) {
            return ACTION_MINT_REDEEM;
        } else if (
            sig == IPActionAddRemoveLiq.addLiquidityDualSyAndPt.selector ||
            sig == IPActionAddRemoveLiq.addLiquidityDualTokenAndPt.selector ||
            sig == IPActionAddRemoveLiq.addLiquiditySinglePt.selector ||
            sig == IPActionAddRemoveLiq.addLiquiditySingleSy.selector ||
            sig == IPActionAddRemoveLiq.addLiquiditySingleToken.selector ||
            sig == IPActionAddRemoveLiq.removeLiquidityDualSyAndPt.selector ||
            sig == IPActionAddRemoveLiq.removeLiquidityDualTokenAndPt.selector ||
            sig == IPActionAddRemoveLiq.removeLiquiditySinglePt.selector ||
            sig == IPActionAddRemoveLiq.removeLiquiditySingleSy.selector ||
            sig == IPActionAddRemoveLiq.removeLiquiditySingleToken.selector
        ) {
            return ACTION_ADD_REMOVE_LIQ;
        } else if (
            sig == IPActionSwapPT.swapExactPtForSy.selector ||
            sig == IPActionSwapPT.swapPtForExactSy.selector ||
            sig == IPActionSwapPT.swapSyForExactPt.selector ||
            sig == IPActionSwapPT.swapExactSyForPt.selector ||
            sig == IPActionSwapPT.swapExactTokenForPt.selector ||
            sig == IPActionSwapPT.swapExactPtForToken.selector
        ) {
            return ACTION_SWAP_PT;
        } else if (
            sig == IPActionSwapYT.swapExactYtForSy.selector ||
            sig == IPActionSwapYT.swapSyForExactYt.selector ||
            sig == IPActionSwapYT.swapExactSyForYt.selector ||
            sig == IPActionSwapYT.swapExactTokenForYt.selector ||
            sig == IPActionSwapYT.swapExactYtForToken.selector ||
            sig == IPActionSwapYT.swapYtForExactSy.selector
        ) {
            return ACTION_SWAP_YT;
        } else if (
            sig == IPActionSwapPTYT.swapExactPtForYt.selector ||
            sig == IPActionSwapPTYT.swapExactYtForPt.selector
        ) {
            return ACTION_SWAP_PTYT;
        } else if (sig == IPMarketSwapCallback.swapCallback.selector) {
            return ACTION_CALLBACK;
        } else if (sig == IPActionMisc.consult.selector) {
            return ACTION_MISC;
        }
        revert Errors.RouterInvalidAction(sig);
    }

    function _implementation() internal view override returns (address) {
        return getRouterImplementation(msg.sig);
    }
}