{"file_path":"StableSwap2EMAOracle.vy","creation_status":"success","source_code":"# @version 0.3.7\n\"\"\"\n@title StableSwap2EMAOracle\n@author Curve.Fi\n@license Copyright (c) Curve.Fi, 2020-2021 - all rights reserved\n@notice 2 coin pool implementation with no lending\n@dev ERC20 support for return True/revert, return True/False, return None\n\"\"\"\n\nfrom vyper.interfaces import ERC20\n\ninterface Factory:\n    def convert_fees() -> bool: nonpayable\n    def get_fee_receiver(_pool: address) -> address: view\n    def admin() -> address: view\n\ninterface ERC1271:\n    def isValidSignature(_hash: bytes32, _signature: Bytes[65]) -> bytes32: view\n\n\nevent Transfer:\n    sender: indexed(address)\n    receiver: indexed(address)\n    value: uint256\n\nevent Approval:\n    owner: indexed(address)\n    spender: indexed(address)\n    value: uint256\n\nevent TokenExchange:\n    buyer: indexed(address)\n    sold_id: int128\n    tokens_sold: uint256\n    bought_id: int128\n    tokens_bought: uint256\n\nevent AddLiquidity:\n    provider: indexed(address)\n    token_amounts: uint256[N_COINS]\n    fees: uint256[N_COINS]\n    invariant: uint256\n    token_supply: uint256\n\nevent RemoveLiquidity:\n    provider: indexed(address)\n    token_amounts: uint256[N_COINS]\n    fees: uint256[N_COINS]\n    token_supply: uint256\n\nevent RemoveLiquidityOne:\n    provider: indexed(address)\n    token_amount: uint256\n    coin_amount: uint256\n    token_supply: uint256\n\nevent RemoveLiquidityImbalance:\n    provider: indexed(address)\n    token_amounts: uint256[N_COINS]\n    fees: uint256[N_COINS]\n    invariant: uint256\n    token_supply: uint256\n\nevent RampA:\n    old_A: uint256\n    new_A: uint256\n    initial_time: uint256\n    future_time: uint256\n\nevent StopRampA:\n    A: uint256\n    t: uint256\n\nevent CommitNewFee:\n    new_fee: uint256\n\nevent ApplyNewFee:\n    fee: uint256\n\n\nN_COINS: constant(uint256) = 2\nN_COINS_128: constant(int128) = 2\nPRECISION: constant(uint256) = 10 ** 18\nADMIN_ACTIONS_DEADLINE_DT: constant(uint256) = 86400 * 3\n\nFEE_DENOMINATOR: constant(uint256) = 10 ** 10\nADMIN_FEE: constant(uint256) = 5000000000\n\nA_PRECISION: constant(uint256) = 100\nMAX_FEE: constant(uint256) = 5 * 10 ** 9\nMAX_A: constant(uint256) = 10 ** 6\nMAX_A_CHANGE: constant(uint256) = 10\nMIN_RAMP_TIME: constant(uint256) = 86400\n\nEIP712_TYPEHASH: constant(bytes32) = keccak256(\"EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)\")\nPERMIT_TYPEHASH: constant(bytes32) = keccak256(\"Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)\")\n\n# keccak256(\"isValidSignature(bytes32,bytes)\")[:4] << 224\nERC1271_MAGIC_VAL: constant(bytes32) = 0x1626ba7e00000000000000000000000000000000000000000000000000000000\nVERSION: constant(String[8]) = \"v6.0.0\"\n\n\nfactory: address\n\ncoins: public(address[N_COINS])\nbalances: public(uint256[N_COINS])\nfee: public(uint256)  # fee * 1e10\nfuture_fee: public(uint256)\nadmin_action_deadline: public(uint256)\n\ninitial_A: public(uint256)\nfuture_A: public(uint256)\ninitial_A_time: public(uint256)\nfuture_A_time: public(uint256)\n\nrate_multipliers: uint256[N_COINS]\n\nname: public(String[64])\nsymbol: public(String[32])\n\nbalanceOf: public(HashMap[address, uint256])\nallowance: public(HashMap[address, HashMap[address, uint256]])\ntotalSupply: public(uint256)\n\nDOMAIN_SEPARATOR: public(bytes32)\nnonces: public(HashMap[address, uint256])\n\nlast_prices_packed: uint256  #  [last_price, ma_price]\nma_exp_time: public(uint256)\nma_last_time: public(uint256)\n\n\n@external\ndef __init__():\n    # we do this to prevent the implementation contract from being used as a pool\n    self.factory = 0x0000000000000000000000000000000000000001\n    assert N_COINS == 2\n\n\n@external\ndef initialize(\n    _name: String[32],\n    _symbol: String[10],\n    _coins: address[4],\n    _rate_multipliers: uint256[4],\n    _A: uint256,\n    _fee: uint256,\n):\n    \"\"\"\n    @notice Contract constructor\n    @param _name Name of the new pool\n    @param _symbol Token symbol\n    @param _coins List of all ERC20 conract addresses of coins\n    @param _rate_multipliers List of number of decimals in coins\n    @param _A Amplification coefficient multiplied by n ** (n - 1)\n    @param _fee Fee to charge for exchanges\n    \"\"\"\n    # check if factory was already set to prevent initializing contract twice\n    assert self.factory == empty(address)\n\n    for i in range(N_COINS):\n        coin: address = _coins[i]\n        if coin == empty(address):\n            break\n        self.coins[i] = coin\n        self.rate_multipliers[i] = _rate_multipliers[i]\n\n    A: uint256 = _A * A_PRECISION\n    self.initial_A = A\n    self.future_A = A\n    self.fee = _fee\n    self.factory = msg.sender\n\n    self.ma_exp_time = 866  # = 600 / ln(2)\n    self.last_prices_packed = self.pack_prices(10**18, 10**18)\n    self.ma_last_time = block.timestamp\n\n    name: String[64] = concat(\"Curve.fi Factory Plain Pool: \", _name)\n    self.name = name\n    self.symbol = concat(_symbol, \"-f\")\n\n    self.DOMAIN_SEPARATOR = keccak256(\n        _abi_encode(EIP712_TYPEHASH, keccak256(name), keccak256(VERSION), chain.id, self)\n    )\n\n    # fire a transfer event so block explorers identify the contract as an ERC20\n    log Transfer(empty(address), self, 0)\n\n\n### ERC20 Functionality ###\n\n@view\n@external\ndef decimals() -> uint8:\n    \"\"\"\n    @notice Get the number of decimals for this token\n    @dev Implemented as a view method to reduce gas costs\n    @return uint8 decimal places\n    \"\"\"\n    return 18\n\n\n@internal\ndef _transfer(_from: address, _to: address, _value: uint256):\n    # # NOTE: vyper does not allow underflows\n    # #       so the following subtraction would revert on insufficient balance\n    self.balanceOf[_from] -= _value\n    self.balanceOf[_to] += _value\n\n    log Transfer(_from, _to, _value)\n\n\n@external\ndef transfer(_to : address, _value : uint256) -> bool:\n    \"\"\"\n    @dev Transfer token for a specified address\n    @param _to The address to transfer to.\n    @param _value The amount to be transferred.\n    \"\"\"\n    self._transfer(msg.sender, _to, _value)\n    return True\n\n\n@external\ndef transferFrom(_from : address, _to : address, _value : uint256) -> bool:\n    \"\"\"\n     @dev Transfer tokens from one address to another.\n     @param _from address The address which you want to send tokens from\n     @param _to address The address which you want to transfer to\n     @param _value uint256 the amount of tokens to be transferred\n    \"\"\"\n    self._transfer(_from, _to, _value)\n\n    _allowance: uint256 = self.allowance[_from][msg.sender]\n    if _allowance != max_value(uint256):\n        self.allowance[_from][msg.sender] = _allowance - _value\n\n    return True\n\n\n@external\ndef approve(_spender : address, _value : uint256) -> bool:\n    \"\"\"\n    @notice Approve the passed address to transfer the specified amount of\n            tokens on behalf of msg.sender\n    @dev Beware that changing an allowance via this method brings the risk that\n         someone may use both the old and new allowance by unfortunate transaction\n         ordering: https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729\n    @param _spender The address which will transfer the funds\n    @param _value The amount of tokens that may be transferred\n    @return bool success\n    \"\"\"\n    self.allowance[msg.sender][_spender] = _value\n\n    log Approval(msg.sender, _spender, _value)\n    return True\n\n\n@external\ndef permit(\n    _owner: address,\n    _spender: address,\n    _value: uint256,\n    _deadline: uint256,\n    _v: uint8,\n    _r: bytes32,\n    _s: bytes32\n) -> bool:\n    \"\"\"\n    @notice Approves spender by owner's signature to expend owner's tokens.\n        See https://eips.ethereum.org/EIPS/eip-2612.\n    @dev Inspired by https://github.com/yearn/yearn-vaults/blob/main/contracts/Vault.vy#L753-L793\n    @dev Supports smart contract wallets which implement ERC1271\n        https://eips.ethereum.org/EIPS/eip-1271\n    @param _owner The address which is a source of funds and has signed the Permit.\n    @param _spender The address which is allowed to spend the funds.\n    @param _value The amount of tokens to be spent.\n    @param _deadline The timestamp after which the Permit is no longer valid.\n    @param _v The bytes[64] of the valid secp256k1 signature of permit by owner\n    @param _r The bytes[0:32] of the valid secp256k1 signature of permit by owner\n    @param _s The bytes[32:64] of the valid secp256k1 signature of permit by owner\n    @return True, if transaction completes successfully\n    \"\"\"\n    assert _owner != empty(address)\n    assert block.timestamp <= _deadline\n\n    nonce: uint256 = self.nonces[_owner]\n    digest: bytes32 = keccak256(\n        concat(\n            b\"\\x19\\x01\",\n            self.DOMAIN_SEPARATOR,\n            keccak256(_abi_encode(PERMIT_TYPEHASH, _owner, _spender, _value, nonce, _deadline))\n        )\n    )\n\n    if _owner.is_contract:\n        sig: Bytes[65] = concat(_abi_encode(_r, _s), slice(convert(_v, bytes32), 31, 1))\n        # reentrancy not a concern since this is a staticcall\n        assert ERC1271(_owner).isValidSignature(digest, sig) == ERC1271_MAGIC_VAL\n    else:\n        assert ecrecover(digest, convert(_v, uint256), convert(_r, uint256), convert(_s, uint256)) == _owner\n\n    self.allowance[_owner][_spender] = _value\n    self.nonces[_owner] = nonce + 1\n\n    log Approval(_owner, _spender, _value)\n    return True\n\n\n### StableSwap Functionality ###\n\n@pure\n@internal\ndef pack_prices(p1: uint256, p2: uint256) -> uint256:\n    assert p1 < 2**128\n    assert p2 < 2**128\n    return p1 | shift(p2, 128)\n\n\n@view\n@external\ndef last_price() -> uint256:\n    return self.last_prices_packed & (2**128 - 1)\n\n\n@view\n@external\ndef ema_price() -> uint256:\n    return shift(self.last_prices_packed, -128)\n\n\n@view\n@external\ndef get_balances() -> uint256[N_COINS]:\n    return self.balances\n\n\n@view\n@internal\ndef _A() -> uint256:\n    \"\"\"\n    Handle ramping A up or down\n    \"\"\"\n    t1: uint256 = self.future_A_time\n    A1: uint256 = self.future_A\n\n    if block.timestamp < t1:\n        A0: uint256 = self.initial_A\n        t0: uint256 = self.initial_A_time\n        # Expressions in uint256 cannot have negative numbers, thus \"if\"\n        if A1 > A0:\n            return A0 + (A1 - A0) * (block.timestamp - t0) / (t1 - t0)\n        else:\n            return A0 - (A0 - A1) * (block.timestamp - t0) / (t1 - t0)\n\n    else:  # when t1 == 0 or block.timestamp >= t1\n        return A1\n\n\n@view\n@external\ndef admin_fee() -> uint256:\n    return ADMIN_FEE\n\n\n@view\n@external\ndef A() -> uint256:\n    return self._A() / A_PRECISION\n\n\n@view\n@external\ndef A_precise() -> uint256:\n    return self._A()\n\n\n@pure\n@internal\ndef _xp_mem(_rates: uint256[N_COINS], _balances: uint256[N_COINS]) -> uint256[N_COINS]:\n    result: uint256[N_COINS] = empty(uint256[N_COINS])\n    for i in range(N_COINS):\n        result[i] = _rates[i] * _balances[i] / PRECISION\n    return result\n\n\n@pure\n@internal\ndef get_D(_xp: uint256[N_COINS], _amp: uint256) -> uint256:\n    \"\"\"\n    D invariant calculation in non-overflowing integer operations\n    iteratively\n\n    A * sum(x_i) * n**n + D = A * D * n**n + D**(n+1) / (n**n * prod(x_i))\n\n    Converging solution:\n    D[j+1] = (A * n**n * sum(x_i) - D[j]**(n+1) / (n**n prod(x_i))) / (A * n**n - 1)\n    \"\"\"\n    S: uint256 = 0\n    for x in _xp:\n        S += x\n    if S == 0:\n        return 0\n\n    D: uint256 = S\n    Ann: uint256 = _amp * N_COINS\n    for i in range(255):\n        D_P: uint256 = D * D / _xp[0] * D / _xp[1] / N_COINS**N_COINS\n        Dprev: uint256 = D\n        D = (Ann * S / A_PRECISION + D_P * N_COINS) * D / ((Ann - A_PRECISION) * D / A_PRECISION + (N_COINS + 1) * D_P)\n        # Equality with the precision of 1\n        if D > Dprev:\n            if D - Dprev <= 1:\n                return D\n        else:\n            if Dprev - D <= 1:\n                return D\n    # convergence typically occurs in 4 rounds or less, this should be unreachable!\n    # if it does happen the pool is borked and LPs can withdraw via `remove_liquidity`\n    raise\n\n\n@view\n@internal\ndef get_D_mem(_rates: uint256[N_COINS], _balances: uint256[N_COINS], _amp: uint256) -> uint256:\n    xp: uint256[N_COINS] = self._xp_mem(_rates, _balances)\n    return self.get_D(xp, _amp)\n\n\n@internal\n@view\ndef _get_p(xp: uint256[N_COINS], amp: uint256, D: uint256) -> uint256:\n    # dx_0 / dx_1 only, however can have any number of coins in pool\n    ANN: uint256 = amp * N_COINS\n    Dr: uint256 = D / (N_COINS**N_COINS)\n    for i in range(N_COINS):\n        Dr = Dr * D / xp[i]\n    return 10**18 * (ANN * xp[0] / A_PRECISION + Dr * xp[0] / xp[1]) / (ANN * xp[0] / A_PRECISION + Dr)\n\n\n@external\n@view\ndef get_p() -> uint256:\n    amp: uint256 = self._A()\n    xp: uint256[N_COINS] = self._xp_mem(self.rate_multipliers, self.balances)\n    D: uint256 = self.get_D(xp, amp)\n    return self._get_p(xp, amp, D)\n\n\n@internal\n@view\ndef exp(power: int256) -> uint256:\n    if power <= -42139678854452767551:\n        return 0\n\n    if power >= 135305999368893231589:\n        raise \"exp overflow\"\n\n    x: int256 = unsafe_div(unsafe_mul(power, 2**96), 10**18)\n\n    k: int256 = unsafe_div(\n        unsafe_add(\n            unsafe_div(unsafe_mul(x, 2**96), 54916777467707473351141471128),\n            2**95),\n        2**96)\n    x = unsafe_sub(x, unsafe_mul(k, 54916777467707473351141471128))\n\n    y: int256 = unsafe_add(x, 1346386616545796478920950773328)\n    y = unsafe_add(unsafe_div(unsafe_mul(y, x), 2**96), 57155421227552351082224309758442)\n    p: int256 = unsafe_sub(unsafe_add(y, x), 94201549194550492254356042504812)\n    p = unsafe_add(unsafe_div(unsafe_mul(p, y), 2**96), 28719021644029726153956944680412240)\n    p = unsafe_add(unsafe_mul(p, x), (4385272521454847904659076985693276 * 2**96))\n\n    q: int256 = x - 2855989394907223263936484059900\n    q = unsafe_add(unsafe_div(unsafe_mul(q, x), 2**96), 50020603652535783019961831881945)\n    q = unsafe_sub(unsafe_div(unsafe_mul(q, x), 2**96), 533845033583426703283633433725380)\n    q = unsafe_add(unsafe_div(unsafe_mul(q, x), 2**96), 3604857256930695427073651918091429)\n    q = unsafe_sub(unsafe_div(unsafe_mul(q, x), 2**96), 14423608567350463180887372962807573)\n    q = unsafe_add(unsafe_div(unsafe_mul(q, x), 2**96), 26449188498355588339934803723976023)\n\n    return shift(\n        unsafe_mul(convert(unsafe_div(p, q), uint256), 3822833074963236453042738258902158003155416615667),\n        unsafe_sub(k, 195))\n\n\n@internal\n@view\ndef _ma_price() -> uint256:\n    ma_last_time: uint256 = self.ma_last_time\n\n    pp: uint256 = self.last_prices_packed\n    last_price: uint256 = pp & (2**128 - 1)\n    last_ema_price: uint256 = shift(pp, -128)\n\n    if ma_last_time < block.timestamp:\n        alpha: uint256 = self.exp(- convert((block.timestamp - ma_last_time) * 10**18 / self.ma_exp_time, int256))\n        return (last_price * (10**18 - alpha) + last_ema_price * alpha) / 10**18\n\n    else:\n        return last_ema_price\n\n\n@external\n@view\n@nonreentrant('lock')\ndef price_oracle() -> uint256:\n    return self._ma_price()\n\n\n@internal\ndef save_p_from_price(last_price: uint256):\n    \"\"\"\n    Saves current price and its EMA\n    \"\"\"\n    if last_price != 0:\n        self.last_prices_packed = self.pack_prices(last_price, self._ma_price())\n        if self.ma_last_time < block.timestamp:\n            self.ma_last_time = block.timestamp\n\n\n@internal\ndef save_p(xp: uint256[N_COINS], amp: uint256, D: uint256):\n    \"\"\"\n    Saves current price and its EMA\n    \"\"\"\n    self.save_p_from_price(self._get_p(xp, amp, D))\n\n\n@view\n@external\n@nonreentrant('lock')\ndef get_virtual_price() -> uint256:\n    \"\"\"\n    @notice The current virtual price of the pool LP token\n    @dev Useful for calculating profits\n    @return LP token virtual price normalized to 1e18\n    \"\"\"\n    amp: uint256 = self._A()\n    xp: uint256[N_COINS] = self._xp_mem(self.rate_multipliers, self.balances)\n    D: uint256 = self.get_D(xp, amp)\n    # D is in the units similar to DAI (e.g. converted to precision 1e18)\n    # When balanced, D = n * x_u - total virtual value of the portfolio\n    return D * PRECISION / self.totalSupply\n\n\n@view\n@external\ndef calc_token_amount(_amounts: uint256[N_COINS], _is_deposit: bool) -> uint256:\n    \"\"\"\n    @notice Calculate addition or reduction in token supply from a deposit or withdrawal\n    @dev This calculation accounts for slippage, but not fees.\n         Needed to prevent front-running, not for precise calculations!\n    @param _amounts Amount of each coin being deposited\n    @param _is_deposit set True for deposits, False for withdrawals\n    @return Expected amount of LP tokens received\n    \"\"\"\n    amp: uint256 = self._A()\n    balances: uint256[N_COINS] = self.balances\n\n    D0: uint256 = self.get_D_mem(self.rate_multipliers, balances, amp)\n    for i in range(N_COINS):\n        amount: uint256 = _amounts[i]\n        if _is_deposit:\n            balances[i] += amount\n        else:\n            balances[i] -= amount\n    D1: uint256 = self.get_D_mem(self.rate_multipliers, balances, amp)\n    diff: uint256 = 0\n    if _is_deposit:\n        diff = D1 - D0\n    else:\n        diff = D0 - D1\n    return diff * self.totalSupply / D0\n\n\n@external\n@nonreentrant('lock')\ndef add_liquidity(\n    _amounts: uint256[N_COINS],\n    _min_mint_amount: uint256,\n    _receiver: address = msg.sender\n) -> uint256:\n    \"\"\"\n    @notice Deposit coins into the pool\n    @param _amounts List of amounts of coins to deposit\n    @param _min_mint_amount Minimum amount of LP tokens to mint from the deposit\n    @param _receiver Address that owns the minted LP tokens\n    @return Amount of LP tokens received by depositing\n    \"\"\"\n    amp: uint256 = self._A()\n    old_balances: uint256[N_COINS] = self.balances\n    rates: uint256[N_COINS] = self.rate_multipliers\n\n    # Initial invariant\n    D0: uint256 = self.get_D_mem(rates, old_balances, amp)\n\n    total_supply: uint256 = self.totalSupply\n    new_balances: uint256[N_COINS] = old_balances\n    for i in range(N_COINS):\n        amount: uint256 = _amounts[i]\n        if amount > 0:\n            assert ERC20(self.coins[i]).transferFrom(msg.sender, self, amount, default_return_value=True)  # dev: failed transfer\n            new_balances[i] += amount\n        else:\n            assert total_supply != 0  # dev: initial deposit requires all coins\n\n    # Invariant after change\n    D1: uint256 = self.get_D_mem(rates, new_balances, amp)\n    assert D1 > D0\n\n    # We need to recalculate the invariant accounting for fees\n    # to calculate fair user's share\n    fees: uint256[N_COINS] = empty(uint256[N_COINS])\n    mint_amount: uint256 = 0\n\n    if total_supply > 0:\n        # Only account for fees if we are not the first to deposit\n        base_fee: uint256 = self.fee * N_COINS / (4 * (N_COINS - 1))\n        for i in range(N_COINS):\n            ideal_balance: uint256 = D1 * old_balances[i] / D0\n            difference: uint256 = 0\n            new_balance: uint256 = new_balances[i]\n            if ideal_balance > new_balance:\n                difference = ideal_balance - new_balance\n            else:\n                difference = new_balance - ideal_balance\n            fees[i] = base_fee * difference / FEE_DENOMINATOR\n            self.balances[i] = new_balance - (fees[i] * ADMIN_FEE / FEE_DENOMINATOR)\n            new_balances[i] -= fees[i]\n        xp: uint256[N_COINS] = self._xp_mem(rates, new_balances)\n        D2: uint256 = self.get_D(xp, amp)\n        mint_amount = total_supply * (D2 - D0) / D0\n        self.save_p(xp, amp, D2)\n\n    else:\n        self.balances = new_balances\n        mint_amount = D1  # Take the dust if there was any\n\n    assert mint_amount >= _min_mint_amount, \"Slippage screwed you\"\n\n    # Mint pool tokens\n    total_supply += mint_amount\n    self.balanceOf[_receiver] += mint_amount\n    self.totalSupply = total_supply\n    log Transfer(empty(address), _receiver, mint_amount)\n\n    log AddLiquidity(msg.sender, _amounts, fees, D1, total_supply)\n\n    return mint_amount\n\n\n@view\n@internal\ndef get_y(i: int128, j: int128, x: uint256, xp: uint256[N_COINS], _amp: uint256, _D: uint256) -> uint256:\n    \"\"\"\n    Calculate x[j] if one makes x[i] = x\n\n    Done by solving quadratic equation iteratively.\n    x_1**2 + x_1 * (sum' - (A*n**n - 1) * D / (A * n**n)) = D ** (n + 1) / (n ** (2 * n) * prod' * A)\n    x_1**2 + b*x_1 = c\n\n    x_1 = (x_1**2 + c) / (2*x_1 + b)\n    \"\"\"\n    # x in the input is converted to the same price/precision\n\n    assert i != j       # dev: same coin\n    assert j >= 0       # dev: j below zero\n    assert j < N_COINS_128  # dev: j above N_COINS\n\n    # should be unreachable, but good for safety\n    assert i >= 0\n    assert i < N_COINS_128\n\n    amp: uint256 = _amp\n    D: uint256 = _D\n    if _D == 0:\n        amp = self._A()\n        D = self.get_D(xp, amp)\n    S_: uint256 = 0\n    _x: uint256 = 0\n    y_prev: uint256 = 0\n    c: uint256 = D\n    Ann: uint256 = amp * N_COINS\n\n    for _i in range(N_COINS_128):\n        if _i == i:\n            _x = x\n        elif _i != j:\n            _x = xp[_i]\n        else:\n            continue\n        S_ += _x\n        c = c * D / (_x * N_COINS)\n\n    c = c * D * A_PRECISION / (Ann * N_COINS)\n    b: uint256 = S_ + D * A_PRECISION / Ann  # - D\n    y: uint256 = D\n\n    for _i in range(255):\n        y_prev = y\n        y = (y*y + c) / (2 * y + b - D)\n        # Equality with the precision of 1\n        if y > y_prev:\n            if y - y_prev <= 1:\n                return y\n        else:\n            if y_prev - y <= 1:\n                return y\n    raise\n\n\n@view\n@external\ndef get_dy(i: int128, j: int128, dx: uint256) -> uint256:\n    \"\"\"\n    @notice Calculate the current output dy given input dx\n    @dev Index values can be found via the `coins` public getter method\n    @param i Index value for the coin to send\n    @param j Index valie of the coin to recieve\n    @param dx Amount of `i` being exchanged\n    @return Amount of `j` predicted\n    \"\"\"\n    rates: uint256[N_COINS] = self.rate_multipliers\n    xp: uint256[N_COINS] = self._xp_mem(rates, self.balances)\n\n    x: uint256 = xp[i] + (dx * rates[i] / PRECISION)\n    y: uint256 = self.get_y(i, j, x, xp, 0, 0)\n    dy: uint256 = xp[j] - y - 1\n    fee: uint256 = self.fee * dy / FEE_DENOMINATOR\n    return (dy - fee) * PRECISION / rates[j]\n\n\n# get_dx XXX\n\n\n@external\n@nonreentrant('lock')\ndef exchange(\n    i: int128,\n    j: int128,\n    _dx: uint256,\n    _min_dy: uint256,\n    _receiver: address = msg.sender,\n) -> uint256:\n    \"\"\"\n    @notice Perform an exchange between two coins\n    @dev Index values can be found via the `coins` public getter method\n    @param i Index value for the coin to send\n    @param j Index valie of the coin to recieve\n    @param _dx Amount of `i` being exchanged\n    @param _min_dy Minimum amount of `j` to receive\n    @return Actual amount of `j` received\n    \"\"\"\n    rates: uint256[N_COINS] = self.rate_multipliers\n    old_balances: uint256[N_COINS] = self.balances\n    xp: uint256[N_COINS] = self._xp_mem(rates, old_balances)\n\n    x: uint256 = xp[i] + _dx * rates[i] / PRECISION\n\n    amp: uint256 = self._A()\n    D: uint256 = self.get_D(xp, amp)\n    y: uint256 = self.get_y(i, j, x, xp, amp, D)\n\n    dy: uint256 = xp[j] - y - 1  # -1 just in case there were some rounding errors\n    dy_fee: uint256 = dy * self.fee / FEE_DENOMINATOR\n\n    # Convert all to real units\n    dy = (dy - dy_fee) * PRECISION / rates[j]\n    assert dy >= _min_dy, \"Exchange resulted in fewer coins than expected\"\n\n    # xp is not used anymore, so we reuse it for price calc\n    xp[i] = x\n    xp[j] = y\n    # D is not changed because we did not apply a fee\n    self.save_p(xp, amp, D)\n\n    dy_admin_fee: uint256 = dy_fee * ADMIN_FEE / FEE_DENOMINATOR\n    dy_admin_fee = dy_admin_fee * PRECISION / rates[j]\n\n    # Change balances exactly in same way as we change actual ERC20 coin amounts\n    self.balances[i] = old_balances[i] + _dx\n    # When rounding errors happen, we undercharge admin fee in favor of LP\n    self.balances[j] = old_balances[j] - dy - dy_admin_fee\n\n    assert ERC20(self.coins[i]).transferFrom(msg.sender, self, _dx, default_return_value=True)  # dev: failed transfer\n    assert ERC20(self.coins[j]).transfer(_receiver, dy, default_return_value=True)  # dev: failed transfer\n\n    log TokenExchange(msg.sender, i, _dx, j, dy)\n\n    return dy\n\n\n@external\n@nonreentrant('lock')\ndef remove_liquidity(\n    _burn_amount: uint256,\n    _min_amounts: uint256[N_COINS],\n    _receiver: address = msg.sender\n) -> uint256[N_COINS]:\n    \"\"\"\n    @notice Withdraw coins from the pool\n    @dev Withdrawal amounts are based on current deposit ratios\n    @param _burn_amount Quantity of LP tokens to burn in the withdrawal\n    @param _min_amounts Minimum amounts of underlying coins to receive\n    @param _receiver Address that receives the withdrawn coins\n    @return List of amounts of coins that were withdrawn\n    \"\"\"\n    total_supply: uint256 = self.totalSupply\n    amounts: uint256[N_COINS] = empty(uint256[N_COINS])\n\n    for i in range(N_COINS):\n        old_balance: uint256 = self.balances[i]\n        value: uint256 = old_balance * _burn_amount / total_supply\n        assert value >= _min_amounts[i], \"Withdrawal resulted in fewer coins than expected\"\n        self.balances[i] = old_balance - value\n        amounts[i] = value\n        assert ERC20(self.coins[i]).transfer(_receiver, value, default_return_value=True)  # dev: failed transfer\n\n    total_supply -= _burn_amount\n    self.balanceOf[msg.sender] -= _burn_amount\n    self.totalSupply = total_supply\n    log Transfer(msg.sender, empty(address), _burn_amount)\n\n    log RemoveLiquidity(msg.sender, amounts, empty(uint256[N_COINS]), total_supply)\n\n    return amounts\n\n\n@external\n@nonreentrant('lock')\ndef remove_liquidity_imbalance(\n    _amounts: uint256[N_COINS],\n    _max_burn_amount: uint256,\n    _receiver: address = msg.sender\n) -> uint256:\n    \"\"\"\n    @notice Withdraw coins from the pool in an imbalanced amount\n    @param _amounts List of amounts of underlying coins to withdraw\n    @param _max_burn_amount Maximum amount of LP token to burn in the withdrawal\n    @param _receiver Address that receives the withdrawn coins\n    @return Actual amount of the LP token burned in the withdrawal\n    \"\"\"\n    amp: uint256 = self._A()\n    rates: uint256[N_COINS] = self.rate_multipliers\n    old_balances: uint256[N_COINS] = self.balances\n    D0: uint256 = self.get_D_mem(rates, old_balances, amp)\n\n    new_balances: uint256[N_COINS] = old_balances\n    for i in range(N_COINS):\n        amount: uint256 = _amounts[i]\n        if amount != 0:\n            new_balances[i] -= amount\n            assert ERC20(self.coins[i]).transfer(_receiver, amount, default_return_value=True)  # dev: failed transfer\n\n    D1: uint256 = self.get_D_mem(rates, new_balances, amp)\n\n    fees: uint256[N_COINS] = empty(uint256[N_COINS])\n    base_fee: uint256 = self.fee * N_COINS / (4 * (N_COINS - 1))\n    for i in range(N_COINS):\n        ideal_balance: uint256 = D1 * old_balances[i] / D0\n        difference: uint256 = 0\n        new_balance: uint256 = new_balances[i]\n        if ideal_balance > new_balance:\n            difference = ideal_balance - new_balance\n        else:\n            difference = new_balance - ideal_balance\n        fees[i] = base_fee * difference / FEE_DENOMINATOR\n        self.balances[i] = new_balance - (fees[i] * ADMIN_FEE / FEE_DENOMINATOR)\n        new_balances[i] -= fees[i]\n    new_balances = self._xp_mem(rates, new_balances)\n    D2: uint256 = self.get_D(new_balances, amp)\n\n    self.save_p(new_balances, amp, D2)\n\n    total_supply: uint256 = self.totalSupply\n    burn_amount: uint256 = ((D0 - D2) * total_supply / D0) + 1\n    assert burn_amount > 1  # dev: zero tokens burned\n    assert burn_amount <= _max_burn_amount, \"Slippage screwed you\"\n\n    total_supply -= burn_amount\n    self.totalSupply = total_supply\n    self.balanceOf[msg.sender] -= burn_amount\n    log Transfer(msg.sender, empty(address), burn_amount)\n    log RemoveLiquidityImbalance(msg.sender, _amounts, fees, D1, total_supply)\n\n    return burn_amount\n\n\n@pure\n@internal\ndef get_y_D(A: uint256, i: int128, xp: uint256[N_COINS], D: uint256) -> uint256:\n    \"\"\"\n    Calculate x[i] if one reduces D from being calculated for xp to D\n\n    Done by solving quadratic equation iteratively.\n    x_1**2 + x_1 * (sum' - (A*n**n - 1) * D / (A * n**n)) = D ** (n + 1) / (n ** (2 * n) * prod' * A)\n    x_1**2 + b*x_1 = c\n\n    x_1 = (x_1**2 + c) / (2*x_1 + b)\n    \"\"\"\n    # x in the input is converted to the same price/precision\n\n    assert i >= 0  # dev: i below zero\n    assert i < N_COINS_128  # dev: i above N_COINS\n\n    S_: uint256 = 0\n    _x: uint256 = 0\n    y_prev: uint256 = 0\n    c: uint256 = D\n    Ann: uint256 = A * N_COINS\n\n    for _i in range(N_COINS_128):\n        if _i != i:\n            _x = xp[_i]\n        else:\n            continue\n        S_ += _x\n        c = c * D / (_x * N_COINS)\n\n    c = c * D * A_PRECISION / (Ann * N_COINS)\n    b: uint256 = S_ + D * A_PRECISION / Ann\n    y: uint256 = D\n\n    for _i in range(255):\n        y_prev = y\n        y = (y*y + c) / (2 * y + b - D)\n        # Equality with the precision of 1\n        if y > y_prev:\n            if y - y_prev <= 1:\n                return y\n        else:\n            if y_prev - y <= 1:\n                return y\n    raise\n\n\n@view\n@internal\ndef _calc_withdraw_one_coin(_burn_amount: uint256, i: int128) -> uint256[3]:\n    # First, need to calculate\n    # * Get current D\n    # * Solve Eqn against y_i for D - _token_amount\n    amp: uint256 = self._A()\n    rates: uint256[N_COINS] = self.rate_multipliers\n    xp: uint256[N_COINS] = self._xp_mem(rates, self.balances)\n    D0: uint256 = self.get_D(xp, amp)\n\n    total_supply: uint256 = self.totalSupply\n    D1: uint256 = D0 - _burn_amount * D0 / total_supply\n    new_y: uint256 = self.get_y_D(amp, i, xp, D1)\n\n    base_fee: uint256 = self.fee * N_COINS / (4 * (N_COINS - 1))\n    xp_reduced: uint256[N_COINS] = empty(uint256[N_COINS])\n\n    for j in range(N_COINS_128):\n        dx_expected: uint256 = 0\n        xp_j: uint256 = xp[j]\n        if j == i:\n            dx_expected = xp_j * D1 / D0 - new_y\n        else:\n            dx_expected = xp_j - xp_j * D1 / D0\n        xp_reduced[j] = xp_j - base_fee * dx_expected / FEE_DENOMINATOR\n\n    dy: uint256 = xp_reduced[i] - self.get_y_D(amp, i, xp_reduced, D1)\n    dy_0: uint256 = (xp[i] - new_y) * PRECISION / rates[i]  # w/o fees\n    dy = (dy - 1) * PRECISION / rates[i]  # Withdraw less to account for rounding errors\n\n    xp[i] = new_y\n    last_p: uint256 = 0\n    if new_y > 0:\n        last_p = self._get_p(xp, amp, D1)\n\n    return [dy, dy_0 - dy, last_p]\n\n\n@view\n@external\ndef calc_withdraw_one_coin(_burn_amount: uint256, i: int128) -> uint256:\n    \"\"\"\n    @notice Calculate the amount received when withdrawing a single coin\n    @param _burn_amount Amount of LP tokens to burn in the withdrawal\n    @param i Index value of the coin to withdraw\n    @return Amount of coin received\n    \"\"\"\n    return self._calc_withdraw_one_coin(_burn_amount, i)[0]\n\n\n@external\n@nonreentrant('lock')\ndef remove_liquidity_one_coin(\n    _burn_amount: uint256,\n    i: int128,\n    _min_received: uint256,\n    _receiver: address = msg.sender,\n) -> uint256:\n    \"\"\"\n    @notice Withdraw a single coin from the pool\n    @param _burn_amount Amount of LP tokens to burn in the withdrawal\n    @param i Index value of the coin to withdraw\n    @param _min_received Minimum amount of coin to receive\n    @param _receiver Address that receives the withdrawn coins\n    @return Amount of coin received\n    \"\"\"\n    dy: uint256[3] = self._calc_withdraw_one_coin(_burn_amount, i)\n    assert dy[0] >= _min_received, \"Not enough coins removed\"\n\n    self.balances[i] -= (dy[0] + dy[1] * ADMIN_FEE / FEE_DENOMINATOR)\n    total_supply: uint256 = self.totalSupply - _burn_amount\n    self.totalSupply = total_supply\n    self.balanceOf[msg.sender] -= _burn_amount\n    log Transfer(msg.sender, empty(address), _burn_amount)\n\n    assert ERC20(self.coins[i]).transfer(_receiver, dy[0], default_return_value=True)  # dev: failed transfer\n    log RemoveLiquidityOne(msg.sender, _burn_amount, dy[0], total_supply)\n\n    self.save_p_from_price(dy[2])\n\n    return dy[0]\n\n\n@external\ndef ramp_A(_future_A: uint256, _future_time: uint256):\n    assert msg.sender == Factory(self.factory).admin()  # dev: only owner\n    assert block.timestamp >= self.initial_A_time + MIN_RAMP_TIME\n    assert _future_time >= block.timestamp + MIN_RAMP_TIME  # dev: insufficient time\n\n    _initial_A: uint256 = self._A()\n    _future_A_p: uint256 = _future_A * A_PRECISION\n\n    assert _future_A > 0 and _future_A < MAX_A\n    if _future_A_p < _initial_A:\n        assert _future_A_p * MAX_A_CHANGE >= _initial_A\n    else:\n        assert _future_A_p <= _initial_A * MAX_A_CHANGE\n\n    self.initial_A = _initial_A\n    self.future_A = _future_A_p\n    self.initial_A_time = block.timestamp\n    self.future_A_time = _future_time\n\n    log RampA(_initial_A, _future_A_p, block.timestamp, _future_time)\n\n\n@external\ndef stop_ramp_A():\n    assert msg.sender == Factory(self.factory).admin()  # dev: only owner\n\n    current_A: uint256 = self._A()\n    self.initial_A = current_A\n    self.future_A = current_A\n    self.initial_A_time = block.timestamp\n    self.future_A_time = block.timestamp\n    # now (block.timestamp < t1) is always False, so we return saved A\n\n    log StopRampA(current_A, block.timestamp)\n\n\n@external\ndef set_ma_exp_time(_ma_exp_time: uint256):\n    assert msg.sender == Factory(self.factory).admin()  # dev: only owner\n    assert _ma_exp_time != 0\n\n    self.ma_exp_time = _ma_exp_time\n\n\n@view\n@external\ndef admin_balances(i: uint256) -> uint256:\n    return ERC20(self.coins[i]).balanceOf(self) - self.balances[i]\n\n\n@external\ndef commit_new_fee(_new_fee: uint256):\n    assert msg.sender == Factory(self.factory).admin()\n    assert _new_fee <= MAX_FEE\n    assert self.admin_action_deadline == 0\n\n    self.future_fee = _new_fee\n    self.admin_action_deadline = block.timestamp + ADMIN_ACTIONS_DEADLINE_DT\n    log CommitNewFee(_new_fee)\n\n\n@external\ndef apply_new_fee():\n    assert msg.sender == Factory(self.factory).admin()\n    deadline: uint256 = self.admin_action_deadline\n    assert deadline != 0 and block.timestamp >= deadline\n\n    fee: uint256 = self.future_fee\n    self.fee = fee\n    self.admin_action_deadline = 0\n    log ApplyNewFee(fee)\n\n\n@external\ndef withdraw_admin_fees():\n    receiver: address = Factory(self.factory).get_fee_receiver(self)\n\n    for i in range(N_COINS):\n        coin: address = self.coins[i]\n        fees: uint256 = ERC20(coin).balanceOf(self) - self.balances[i]\n        assert ERC20(coin).transfer(receiver, fees, default_return_value=True)\n\n\n@pure\n@external\ndef version() -> String[8]:\n    \"\"\"\n    @notice Get the version of this token contract\n    \"\"\"\n    return 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ueprint":false,"license_type":"none","is_fully_verified":false,"is_verified_via_eth_bytecode_db":true,"language":"vyper","evm_version":null,"can_be_visualized_via_sol2uml":false,"is_verified_via_sourcify":false,"additional_sources":[{"file_path":"Vyper_contract.vy","source_code":"# @version 0.3.7\n\"\"\"\n@title StableSwap\n@author Curve.Fi\n@license Copyright (c) Curve.Fi, 2020-2021 - all rights reserved\n@notice 2 coin pool implementation with no lending\n@dev ERC20 support for return True/revert, return True/False, return None\n\"\"\"\n\nfrom vyper.interfaces import ERC20\n\ninterface Factory:\n    def convert_fees() -> bool: nonpayable\n    def get_fee_receiver(_pool: address) -> address: view\n    def admin() -> address: view\n\ninterface ERC1271:\n    def isValidSignature(_hash: bytes32, _signature: Bytes[65]) -> bytes32: view\n\n\nevent Transfer:\n    sender: indexed(address)\n    receiver: indexed(address)\n    value: uint256\n\nevent Approval:\n    owner: indexed(address)\n    spender: indexed(address)\n    value: uint256\n\nevent TokenExchange:\n    buyer: indexed(address)\n    sold_id: int128\n    tokens_sold: uint256\n    bought_id: int128\n    tokens_bought: uint256\n\nevent AddLiquidity:\n    provider: indexed(address)\n    token_amounts: uint256[N_COINS]\n    fees: uint256[N_COINS]\n    invariant: uint256\n    token_supply: uint256\n\nevent RemoveLiquidity:\n    provider: indexed(address)\n    token_amounts: uint256[N_COINS]\n    fees: uint256[N_COINS]\n    token_supply: uint256\n\nevent RemoveLiquidityOne:\n    provider: indexed(address)\n    token_amount: uint256\n    coin_amount: uint256\n    token_supply: uint256\n\nevent RemoveLiquidityImbalance:\n    provider: indexed(address)\n    token_amounts: uint256[N_COINS]\n    fees: uint256[N_COINS]\n    invariant: uint256\n    token_supply: uint256\n\nevent RampA:\n    old_A: uint256\n    new_A: uint256\n    initial_time: uint256\n    future_time: uint256\n\nevent StopRampA:\n    A: uint256\n    t: uint256\n\nevent CommitNewFee:\n    new_fee: uint256\n\nevent ApplyNewFee:\n    fee: uint256\n\n\nN_COINS: constant(uint256) = 2\nN_COINS_128: constant(int128) = 2\nPRECISION: constant(uint256) = 10 ** 18\nADMIN_ACTIONS_DEADLINE_DT: constant(uint256) = 86400 * 3\n\nFEE_DENOMINATOR: constant(uint256) = 10 ** 10\nADMIN_FEE: constant(uint256) = 5000000000\n\nA_PRECISION: constant(uint256) = 100\nMAX_FEE: constant(uint256) = 5 * 10 ** 9\nMAX_A: constant(uint256) = 10 ** 6\nMAX_A_CHANGE: constant(uint256) = 10\nMIN_RAMP_TIME: constant(uint256) = 86400\n\nEIP712_TYPEHASH: constant(bytes32) = keccak256(\"EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)\")\nPERMIT_TYPEHASH: constant(bytes32) = keccak256(\"Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)\")\n\n# keccak256(\"isValidSignature(bytes32,bytes)\")[:4] << 224\nERC1271_MAGIC_VAL: constant(bytes32) = 0x1626ba7e00000000000000000000000000000000000000000000000000000000\nVERSION: constant(String[8]) = \"v6.0.0\"\n\n\nfactory: address\n\ncoins: public(address[N_COINS])\nbalances: public(uint256[N_COINS])\nfee: public(uint256)  # fee * 1e10\nfuture_fee: public(uint256)\nadmin_action_deadline: public(uint256)\n\ninitial_A: public(uint256)\nfuture_A: public(uint256)\ninitial_A_time: public(uint256)\nfuture_A_time: public(uint256)\n\nrate_multipliers: uint256[N_COINS]\n\nname: public(String[64])\nsymbol: public(String[32])\n\nbalanceOf: public(HashMap[address, uint256])\nallowance: public(HashMap[address, HashMap[address, uint256]])\ntotalSupply: public(uint256)\n\nDOMAIN_SEPARATOR: public(bytes32)\nnonces: public(HashMap[address, uint256])\n\nlast_prices_packed: uint256  #  [last_price, ma_price]\nma_exp_time: public(uint256)\nma_last_time: public(uint256)\n\n\n@external\ndef __init__():\n    # we do this to prevent the implementation contract from being used as a pool\n    self.factory = 0x0000000000000000000000000000000000000001\n    assert N_COINS == 2\n\n\n@external\ndef initialize(\n    _name: String[32],\n    _symbol: String[10],\n    _coins: address[4],\n    _rate_multipliers: uint256[4],\n    _A: uint256,\n    _fee: uint256,\n):\n    \"\"\"\n    @notice Contract constructor\n    @param _name Name of the new pool\n    @param _symbol Token symbol\n    @param _coins List of all ERC20 conract addresses of coins\n    @param _rate_multipliers List of number of decimals in coins\n    @param _A Amplification coefficient multiplied by n ** (n - 1)\n    @param _fee Fee to charge for exchanges\n    \"\"\"\n    # check if factory was already set to prevent initializing contract twice\n    assert self.factory == empty(address)\n\n    for i in range(N_COINS):\n        coin: address = _coins[i]\n        if coin == empty(address):\n            break\n        self.coins[i] = coin\n        self.rate_multipliers[i] = _rate_multipliers[i]\n\n    A: uint256 = _A * A_PRECISION\n    self.initial_A = A\n    self.future_A = A\n    self.fee = _fee\n    self.factory = msg.sender\n\n    self.ma_exp_time = 866  # = 600 / ln(2)\n    self.last_prices_packed = self.pack_prices(10**18, 10**18)\n    self.ma_last_time = block.timestamp\n\n    name: String[64] = concat(\"Curve.fi Factory Plain Pool: \", _name)\n    self.name = name\n    self.symbol = concat(_symbol, \"-f\")\n\n    self.DOMAIN_SEPARATOR = keccak256(\n        _abi_encode(EIP712_TYPEHASH, keccak256(name), keccak256(VERSION), chain.id, self)\n    )\n\n    # fire a transfer event so block explorers identify the contract as an ERC20\n    log Transfer(empty(address), self, 0)\n\n\n### ERC20 Functionality ###\n\n@view\n@external\ndef decimals() -> uint8:\n    \"\"\"\n    @notice Get the number of decimals for this token\n    @dev Implemented as a view method to reduce gas costs\n    @return uint8 decimal places\n    \"\"\"\n    return 18\n\n\n@internal\ndef _transfer(_from: address, _to: address, _value: uint256):\n    # # NOTE: vyper does not allow underflows\n    # #       so the following subtraction would revert on insufficient balance\n    self.balanceOf[_from] -= _value\n    self.balanceOf[_to] += _value\n\n    log Transfer(_from, _to, _value)\n\n\n@external\ndef transfer(_to : address, _value : uint256) -> bool:\n    \"\"\"\n    @dev Transfer token for a specified address\n    @param _to The address to transfer to.\n    @param _value The amount to be transferred.\n    \"\"\"\n    self._transfer(msg.sender, _to, _value)\n    return True\n\n\n@external\ndef transferFrom(_from : address, _to : address, _value : uint256) -> bool:\n    \"\"\"\n     @dev Transfer tokens from one address to another.\n     @param _from address The address which you want to send tokens from\n     @param _to address The address which you want to transfer to\n     @param _value uint256 the amount of tokens to be transferred\n    \"\"\"\n    self._transfer(_from, _to, _value)\n\n    _allowance: uint256 = self.allowance[_from][msg.sender]\n    if _allowance != max_value(uint256):\n        self.allowance[_from][msg.sender] = _allowance - _value\n\n    return True\n\n\n@external\ndef approve(_spender : address, _value : uint256) -> bool:\n    \"\"\"\n    @notice Approve the passed address to transfer the specified amount of\n            tokens on behalf of msg.sender\n    @dev Beware that changing an allowance via this method brings the risk that\n         someone may use both the old and new allowance by unfortunate transaction\n         ordering: https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729\n    @param _spender The address which will transfer the funds\n    @param _value The amount of tokens that may be transferred\n    @return bool success\n    \"\"\"\n    self.allowance[msg.sender][_spender] = _value\n\n    log Approval(msg.sender, _spender, _value)\n    return True\n\n\n@external\ndef permit(\n    _owner: address,\n    _spender: address,\n    _value: uint256,\n    _deadline: uint256,\n    _v: uint8,\n    _r: bytes32,\n    _s: bytes32\n) -> bool:\n    \"\"\"\n    @notice Approves spender by owner's signature to expend owner's tokens.\n        See https://eips.ethereum.org/EIPS/eip-2612.\n    @dev Inspired by https://github.com/yearn/yearn-vaults/blob/main/contracts/Vault.vy#L753-L793\n    @dev Supports smart contract wallets which implement ERC1271\n        https://eips.ethereum.org/EIPS/eip-1271\n    @param _owner The address which is a source of funds and has signed the Permit.\n    @param _spender The address which is allowed to spend the funds.\n    @param _value The amount of tokens to be spent.\n    @param _deadline The timestamp after which the Permit is no longer valid.\n    @param _v The bytes[64] of the valid secp256k1 signature of permit by owner\n    @param _r The bytes[0:32] of the valid secp256k1 signature of permit by owner\n    @param _s The bytes[32:64] of the valid secp256k1 signature of permit by owner\n    @return True, if transaction completes successfully\n    \"\"\"\n    assert _owner != empty(address)\n    assert block.timestamp <= _deadline\n\n    nonce: uint256 = self.nonces[_owner]\n    digest: bytes32 = keccak256(\n        concat(\n            b\"\\x19\\x01\",\n            self.DOMAIN_SEPARATOR,\n            keccak256(_abi_encode(PERMIT_TYPEHASH, _owner, _spender, _value, nonce, _deadline))\n        )\n    )\n\n    if _owner.is_contract:\n        sig: Bytes[65] = concat(_abi_encode(_r, _s), slice(convert(_v, bytes32), 31, 1))\n        # reentrancy not a concern since this is a staticcall\n        assert ERC1271(_owner).isValidSignature(digest, sig) == ERC1271_MAGIC_VAL\n    else:\n        assert ecrecover(digest, convert(_v, uint256), convert(_r, uint256), convert(_s, uint256)) == _owner\n\n    self.allowance[_owner][_spender] = _value\n    self.nonces[_owner] = nonce + 1\n\n    log Approval(_owner, _spender, _value)\n    return True\n\n\n### StableSwap Functionality ###\n\n@pure\n@internal\ndef pack_prices(p1: uint256, p2: uint256) -> uint256:\n    assert p1 < 2**128\n    assert p2 < 2**128\n    return p1 | shift(p2, 128)\n\n\n@view\n@external\ndef last_price() -> uint256:\n    return self.last_prices_packed & (2**128 - 1)\n\n\n@view\n@external\ndef ema_price() -> uint256:\n    return shift(self.last_prices_packed, -128)\n\n\n@view\n@external\ndef get_balances() -> uint256[N_COINS]:\n    return self.balances\n\n\n@view\n@internal\ndef _A() -> uint256:\n    \"\"\"\n    Handle ramping A up or down\n    \"\"\"\n    t1: uint256 = self.future_A_time\n    A1: uint256 = self.future_A\n\n    if block.timestamp < t1:\n        A0: uint256 = self.initial_A\n        t0: uint256 = self.initial_A_time\n        # Expressions in uint256 cannot have negative numbers, thus \"if\"\n        if A1 > A0:\n            return A0 + (A1 - A0) * (block.timestamp - t0) / (t1 - t0)\n        else:\n            return A0 - (A0 - A1) * (block.timestamp - t0) / (t1 - t0)\n\n    else:  # when t1 == 0 or block.timestamp >= t1\n        return A1\n\n\n@view\n@external\ndef admin_fee() -> uint256:\n    return ADMIN_FEE\n\n\n@view\n@external\ndef A() -> uint256:\n    return self._A() / A_PRECISION\n\n\n@view\n@external\ndef A_precise() -> uint256:\n    return self._A()\n\n\n@pure\n@internal\ndef _xp_mem(_rates: uint256[N_COINS], _balances: uint256[N_COINS]) -> uint256[N_COINS]:\n    result: uint256[N_COINS] = empty(uint256[N_COINS])\n    for i in range(N_COINS):\n        result[i] = _rates[i] * _balances[i] / PRECISION\n    return result\n\n\n@pure\n@internal\ndef get_D(_xp: uint256[N_COINS], _amp: uint256) -> uint256:\n    \"\"\"\n    D invariant calculation in non-overflowing integer operations\n    iteratively\n\n    A * sum(x_i) * n**n + D = A * D * n**n + D**(n+1) / (n**n * prod(x_i))\n\n    Converging solution:\n    D[j+1] = (A * n**n * sum(x_i) - D[j]**(n+1) / (n**n prod(x_i))) / (A * n**n - 1)\n    \"\"\"\n    S: uint256 = 0\n    for x in _xp:\n        S += x\n    if S == 0:\n        return 0\n\n    D: uint256 = S\n    Ann: uint256 = _amp * N_COINS\n    for i in range(255):\n        D_P: uint256 = D * D / _xp[0] * D / _xp[1] / N_COINS**N_COINS\n        Dprev: uint256 = D\n        D = (Ann * S / A_PRECISION + D_P * N_COINS) * D / ((Ann - A_PRECISION) * D / A_PRECISION + (N_COINS + 1) * D_P)\n        # Equality with the precision of 1\n        if D > Dprev:\n            if D - Dprev <= 1:\n                return D\n        else:\n            if Dprev - D <= 1:\n                return D\n    # convergence typically occurs in 4 rounds or less, this should be unreachable!\n    # if it does happen the pool is borked and LPs can withdraw via `remove_liquidity`\n    raise\n\n\n@view\n@internal\ndef get_D_mem(_rates: uint256[N_COINS], _balances: uint256[N_COINS], _amp: uint256) -> uint256:\n    xp: uint256[N_COINS] = self._xp_mem(_rates, _balances)\n    return self.get_D(xp, _amp)\n\n\n@internal\n@view\ndef _get_p(xp: uint256[N_COINS], amp: uint256, D: uint256) -> uint256:\n    # dx_0 / dx_1 only, however can have any number of coins in pool\n    ANN: uint256 = amp * N_COINS\n    Dr: uint256 = D / (N_COINS**N_COINS)\n    for i in range(N_COINS):\n        Dr = Dr * D / xp[i]\n    return 10**18 * (ANN * xp[0] / A_PRECISION + Dr * xp[0] / xp[1]) / (ANN * xp[0] / A_PRECISION + Dr)\n\n\n@external\n@view\ndef get_p() -> uint256:\n    amp: uint256 = self._A()\n    xp: uint256[N_COINS] = self._xp_mem(self.rate_multipliers, self.balances)\n    D: uint256 = self.get_D(xp, amp)\n    return self._get_p(xp, amp, D)\n\n\n@internal\n@view\ndef exp(power: int256) -> uint256:\n    if power <= -42139678854452767551:\n        return 0\n\n    if power >= 135305999368893231589:\n        raise \"exp overflow\"\n\n    x: int256 = unsafe_div(unsafe_mul(power, 2**96), 10**18)\n\n    k: int256 = unsafe_div(\n        unsafe_add(\n            unsafe_div(unsafe_mul(x, 2**96), 54916777467707473351141471128),\n            2**95),\n        2**96)\n    x = unsafe_sub(x, unsafe_mul(k, 54916777467707473351141471128))\n\n    y: int256 = unsafe_add(x, 1346386616545796478920950773328)\n    y = unsafe_add(unsafe_div(unsafe_mul(y, x), 2**96), 57155421227552351082224309758442)\n    p: int256 = unsafe_sub(unsafe_add(y, x), 94201549194550492254356042504812)\n    p = unsafe_add(unsafe_div(unsafe_mul(p, y), 2**96), 28719021644029726153956944680412240)\n    p = unsafe_add(unsafe_mul(p, x), (4385272521454847904659076985693276 * 2**96))\n\n    q: int256 = x - 2855989394907223263936484059900\n    q = unsafe_add(unsafe_div(unsafe_mul(q, x), 2**96), 50020603652535783019961831881945)\n    q = unsafe_sub(unsafe_div(unsafe_mul(q, x), 2**96), 533845033583426703283633433725380)\n    q = unsafe_add(unsafe_div(unsafe_mul(q, x), 2**96), 3604857256930695427073651918091429)\n    q = unsafe_sub(unsafe_div(unsafe_mul(q, x), 2**96), 14423608567350463180887372962807573)\n    q = unsafe_add(unsafe_div(unsafe_mul(q, x), 2**96), 26449188498355588339934803723976023)\n\n    return shift(\n        unsafe_mul(convert(unsafe_div(p, q), uint256), 3822833074963236453042738258902158003155416615667),\n        unsafe_sub(k, 195))\n\n\n@internal\n@view\ndef _ma_price() -> uint256:\n    ma_last_time: uint256 = self.ma_last_time\n\n    pp: uint256 = self.last_prices_packed\n    last_price: uint256 = pp & (2**128 - 1)\n    last_ema_price: uint256 = shift(pp, -128)\n\n    if ma_last_time < block.timestamp:\n        alpha: uint256 = self.exp(- convert((block.timestamp - ma_last_time) * 10**18 / self.ma_exp_time, int256))\n        return (last_price * (10**18 - alpha) + last_ema_price * alpha) / 10**18\n\n    else:\n        return last_ema_price\n\n\n@external\n@view\n@nonreentrant('lock')\ndef price_oracle() -> uint256:\n    return self._ma_price()\n\n\n@internal\ndef save_p_from_price(last_price: uint256):\n    \"\"\"\n    Saves current price and its EMA\n    \"\"\"\n    if last_price != 0:\n        self.last_prices_packed = self.pack_prices(last_price, self._ma_price())\n        if self.ma_last_time < block.timestamp:\n            self.ma_last_time = block.timestamp\n\n\n@internal\ndef save_p(xp: uint256[N_COINS], amp: uint256, D: uint256):\n    \"\"\"\n    Saves current price and its EMA\n    \"\"\"\n    self.save_p_from_price(self._get_p(xp, amp, D))\n\n\n@view\n@external\n@nonreentrant('lock')\ndef get_virtual_price() -> uint256:\n    \"\"\"\n    @notice The current virtual price of the pool LP token\n    @dev Useful for calculating profits\n    @return LP token virtual price normalized to 1e18\n    \"\"\"\n    amp: uint256 = self._A()\n    xp: uint256[N_COINS] = self._xp_mem(self.rate_multipliers, self.balances)\n    D: uint256 = self.get_D(xp, amp)\n    # D is in the units similar to DAI (e.g. converted to precision 1e18)\n    # When balanced, D = n * x_u - total virtual value of the portfolio\n    return D * PRECISION / self.totalSupply\n\n\n@view\n@external\ndef calc_token_amount(_amounts: uint256[N_COINS], _is_deposit: bool) -> uint256:\n    \"\"\"\n    @notice Calculate addition or reduction in token supply from a deposit or withdrawal\n    @dev This calculation accounts for slippage, but not fees.\n         Needed to prevent front-running, not for precise calculations!\n    @param _amounts Amount of each coin being deposited\n    @param _is_deposit set True for deposits, False for withdrawals\n    @return Expected amount of LP tokens received\n    \"\"\"\n    amp: uint256 = self._A()\n    balances: uint256[N_COINS] = self.balances\n\n    D0: uint256 = self.get_D_mem(self.rate_multipliers, balances, amp)\n    for i in range(N_COINS):\n        amount: uint256 = _amounts[i]\n        if _is_deposit:\n            balances[i] += amount\n        else:\n            balances[i] -= amount\n    D1: uint256 = self.get_D_mem(self.rate_multipliers, balances, amp)\n    diff: uint256 = 0\n    if _is_deposit:\n        diff = D1 - D0\n    else:\n        diff = D0 - D1\n    return diff * self.totalSupply / D0\n\n\n@external\n@nonreentrant('lock')\ndef add_liquidity(\n    _amounts: uint256[N_COINS],\n    _min_mint_amount: uint256,\n    _receiver: address = msg.sender\n) -> uint256:\n    \"\"\"\n    @notice Deposit coins into the pool\n    @param _amounts List of amounts of coins to deposit\n    @param _min_mint_amount Minimum amount of LP tokens to mint from the deposit\n    @param _receiver Address that owns the minted LP tokens\n    @return Amount of LP tokens received by depositing\n    \"\"\"\n    amp: uint256 = self._A()\n    old_balances: uint256[N_COINS] = self.balances\n    rates: uint256[N_COINS] = self.rate_multipliers\n\n    # Initial invariant\n    D0: uint256 = self.get_D_mem(rates, old_balances, amp)\n\n    total_supply: uint256 = self.totalSupply\n    new_balances: uint256[N_COINS] = old_balances\n    for i in range(N_COINS):\n        amount: uint256 = _amounts[i]\n        if amount > 0:\n            assert ERC20(self.coins[i]).transferFrom(msg.sender, self, amount, default_return_value=True)  # dev: failed transfer\n            new_balances[i] += amount\n        else:\n            assert total_supply != 0  # dev: initial deposit requires all coins\n\n    # Invariant after change\n    D1: uint256 = self.get_D_mem(rates, new_balances, amp)\n    assert D1 > D0\n\n    # We need to recalculate the invariant accounting for fees\n    # to calculate fair user's share\n    fees: uint256[N_COINS] = empty(uint256[N_COINS])\n    mint_amount: uint256 = 0\n\n    if total_supply > 0:\n        # Only account for fees if we are not the first to deposit\n        base_fee: uint256 = self.fee * N_COINS / (4 * (N_COINS - 1))\n        for i in range(N_COINS):\n            ideal_balance: uint256 = D1 * old_balances[i] / D0\n            difference: uint256 = 0\n            new_balance: uint256 = new_balances[i]\n            if ideal_balance > new_balance:\n                difference = ideal_balance - new_balance\n            else:\n                difference = new_balance - ideal_balance\n            fees[i] = base_fee * difference / FEE_DENOMINATOR\n            self.balances[i] = new_balance - (fees[i] * ADMIN_FEE / FEE_DENOMINATOR)\n            new_balances[i] -= fees[i]\n        xp: uint256[N_COINS] = self._xp_mem(rates, new_balances)\n        D2: uint256 = self.get_D(xp, amp)\n        mint_amount = total_supply * (D2 - D0) / D0\n        self.save_p(xp, amp, D2)\n\n    else:\n        self.balances = new_balances\n        mint_amount = D1  # Take the dust if there was any\n\n    assert mint_amount >= _min_mint_amount, \"Slippage screwed you\"\n\n    # Mint pool tokens\n    total_supply += mint_amount\n    self.balanceOf[_receiver] += mint_amount\n    self.totalSupply = total_supply\n    log Transfer(empty(address), _receiver, mint_amount)\n\n    log AddLiquidity(msg.sender, _amounts, fees, D1, total_supply)\n\n    return mint_amount\n\n\n@view\n@internal\ndef get_y(i: int128, j: int128, x: uint256, xp: uint256[N_COINS], _amp: uint256, _D: uint256) -> uint256:\n    \"\"\"\n    Calculate x[j] if one makes x[i] = x\n\n    Done by solving quadratic equation iteratively.\n    x_1**2 + x_1 * (sum' - (A*n**n - 1) * D / (A * n**n)) = D ** (n + 1) / (n ** (2 * n) * prod' * A)\n    x_1**2 + b*x_1 = c\n\n    x_1 = (x_1**2 + c) / (2*x_1 + b)\n    \"\"\"\n    # x in the input is converted to the same price/precision\n\n    assert i != j       # dev: same coin\n    assert j >= 0       # dev: j below zero\n    assert j < N_COINS_128  # dev: j above N_COINS\n\n    # should be unreachable, but good for safety\n    assert i >= 0\n    assert i < N_COINS_128\n\n    amp: uint256 = _amp\n    D: uint256 = _D\n    if _D == 0:\n        amp = self._A()\n        D = self.get_D(xp, amp)\n    S_: uint256 = 0\n    _x: uint256 = 0\n    y_prev: uint256 = 0\n    c: uint256 = D\n    Ann: uint256 = amp * N_COINS\n\n    for _i in range(N_COINS_128):\n        if _i == i:\n            _x = x\n        elif _i != j:\n            _x = xp[_i]\n        else:\n            continue\n        S_ += _x\n        c = c * D / (_x * N_COINS)\n\n    c = c * D * A_PRECISION / (Ann * N_COINS)\n    b: uint256 = S_ + D * A_PRECISION / Ann  # - D\n    y: uint256 = D\n\n    for _i in range(255):\n        y_prev = y\n        y = (y*y + c) / (2 * y + b - D)\n        # Equality with the precision of 1\n        if y > y_prev:\n            if y - y_prev <= 1:\n                return y\n        else:\n            if y_prev - y <= 1:\n                return y\n    raise\n\n\n@view\n@external\ndef get_dy(i: int128, j: int128, dx: uint256) -> uint256:\n    \"\"\"\n    @notice Calculate the current output dy given input dx\n    @dev Index values can be found via the `coins` public getter method\n    @param i Index value for the coin to send\n    @param j Index valie of the coin to recieve\n    @param dx Amount of `i` being exchanged\n    @return Amount of `j` predicted\n    \"\"\"\n    rates: uint256[N_COINS] = self.rate_multipliers\n    xp: uint256[N_COINS] = self._xp_mem(rates, self.balances)\n\n    x: uint256 = xp[i] + (dx * rates[i] / PRECISION)\n    y: uint256 = self.get_y(i, j, x, xp, 0, 0)\n    dy: uint256 = xp[j] - y - 1\n    fee: uint256 = self.fee * dy / FEE_DENOMINATOR\n    return (dy - fee) * PRECISION / rates[j]\n\n\n# get_dx XXX\n\n\n@external\n@nonreentrant('lock')\ndef exchange(\n    i: int128,\n    j: int128,\n    _dx: uint256,\n    _min_dy: uint256,\n    _receiver: address = msg.sender,\n) -> uint256:\n    \"\"\"\n    @notice Perform an exchange between two coins\n    @dev Index values can be found via the `coins` public getter method\n    @param i Index value for the coin to send\n    @param j Index valie of the coin to recieve\n    @param _dx Amount of `i` being exchanged\n    @param _min_dy Minimum amount of `j` to receive\n    @return Actual amount of `j` received\n    \"\"\"\n    rates: uint256[N_COINS] = self.rate_multipliers\n    old_balances: uint256[N_COINS] = self.balances\n    xp: uint256[N_COINS] = self._xp_mem(rates, old_balances)\n\n    x: uint256 = xp[i] + _dx * rates[i] / PRECISION\n\n    amp: uint256 = self._A()\n    D: uint256 = self.get_D(xp, amp)\n    y: uint256 = self.get_y(i, j, x, xp, amp, D)\n\n    dy: uint256 = xp[j] - y - 1  # -1 just in case there were some rounding errors\n    dy_fee: uint256 = dy * self.fee / FEE_DENOMINATOR\n\n    # Convert all to real units\n    dy = (dy - dy_fee) * PRECISION / rates[j]\n    assert dy >= _min_dy, \"Exchange resulted in fewer coins than expected\"\n\n    # xp is not used anymore, so we reuse it for price calc\n    xp[i] = x\n    xp[j] = y\n    # D is not changed because we did not apply a fee\n    self.save_p(xp, amp, D)\n\n    dy_admin_fee: uint256 = dy_fee * ADMIN_FEE / FEE_DENOMINATOR\n    dy_admin_fee = dy_admin_fee * PRECISION / rates[j]\n\n    # Change balances exactly in same way as we change actual ERC20 coin amounts\n    self.balances[i] = old_balances[i] + _dx\n    # When rounding errors happen, we undercharge admin fee in favor of LP\n    self.balances[j] = old_balances[j] - dy - dy_admin_fee\n\n    assert ERC20(self.coins[i]).transferFrom(msg.sender, self, _dx, default_return_value=True)  # dev: failed transfer\n    assert ERC20(self.coins[j]).transfer(_receiver, dy, default_return_value=True)  # dev: failed transfer\n\n    log TokenExchange(msg.sender, i, _dx, j, dy)\n\n    return dy\n\n\n@external\n@nonreentrant('lock')\ndef remove_liquidity(\n    _burn_amount: uint256,\n    _min_amounts: uint256[N_COINS],\n    _receiver: address = msg.sender\n) -> uint256[N_COINS]:\n    \"\"\"\n    @notice Withdraw coins from the pool\n    @dev Withdrawal amounts are based on current deposit ratios\n    @param _burn_amount Quantity of LP tokens to burn in the withdrawal\n    @param _min_amounts Minimum amounts of underlying coins to receive\n    @param _receiver Address that receives the withdrawn coins\n    @return List of amounts of coins that were withdrawn\n    \"\"\"\n    total_supply: uint256 = self.totalSupply\n    amounts: uint256[N_COINS] = empty(uint256[N_COINS])\n\n    for i in range(N_COINS):\n        old_balance: uint256 = self.balances[i]\n        value: uint256 = old_balance * _burn_amount / total_supply\n        assert value >= _min_amounts[i], \"Withdrawal resulted in fewer coins than expected\"\n        self.balances[i] = old_balance - value\n        amounts[i] = value\n        assert ERC20(self.coins[i]).transfer(_receiver, value, default_return_value=True)  # dev: failed transfer\n\n    total_supply -= _burn_amount\n    self.balanceOf[msg.sender] -= _burn_amount\n    self.totalSupply = total_supply\n    log Transfer(msg.sender, empty(address), _burn_amount)\n\n    log RemoveLiquidity(msg.sender, amounts, empty(uint256[N_COINS]), total_supply)\n\n    return amounts\n\n\n@external\n@nonreentrant('lock')\ndef remove_liquidity_imbalance(\n    _amounts: uint256[N_COINS],\n    _max_burn_amount: uint256,\n    _receiver: address = msg.sender\n) -> uint256:\n    \"\"\"\n    @notice Withdraw coins from the pool in an imbalanced amount\n    @param _amounts List of amounts of underlying coins to withdraw\n    @param _max_burn_amount Maximum amount of LP token to burn in the withdrawal\n    @param _receiver Address that receives the withdrawn coins\n    @return Actual amount of the LP token burned in the withdrawal\n    \"\"\"\n    amp: uint256 = self._A()\n    rates: uint256[N_COINS] = self.rate_multipliers\n    old_balances: uint256[N_COINS] = self.balances\n    D0: uint256 = self.get_D_mem(rates, old_balances, amp)\n\n    new_balances: uint256[N_COINS] = old_balances\n    for i in range(N_COINS):\n        amount: uint256 = _amounts[i]\n        if amount != 0:\n            new_balances[i] -= amount\n            assert ERC20(self.coins[i]).transfer(_receiver, amount, default_return_value=True)  # dev: failed transfer\n\n    D1: uint256 = self.get_D_mem(rates, new_balances, amp)\n\n    fees: uint256[N_COINS] = empty(uint256[N_COINS])\n    base_fee: uint256 = self.fee * N_COINS / (4 * (N_COINS - 1))\n    for i in range(N_COINS):\n        ideal_balance: uint256 = D1 * old_balances[i] / D0\n        difference: uint256 = 0\n        new_balance: uint256 = new_balances[i]\n        if ideal_balance > new_balance:\n            difference = ideal_balance - new_balance\n        else:\n            difference = new_balance - ideal_balance\n        fees[i] = base_fee * difference / FEE_DENOMINATOR\n        self.balances[i] = new_balance - (fees[i] * ADMIN_FEE / FEE_DENOMINATOR)\n        new_balances[i] -= fees[i]\n    new_balances = self._xp_mem(rates, new_balances)\n    D2: uint256 = self.get_D(new_balances, amp)\n\n    self.save_p(new_balances, amp, D2)\n\n    total_supply: uint256 = self.totalSupply\n    burn_amount: uint256 = ((D0 - D2) * total_supply / D0) + 1\n    assert burn_amount > 1  # dev: zero tokens burned\n    assert burn_amount <= _max_burn_amount, \"Slippage screwed you\"\n\n    total_supply -= burn_amount\n    self.totalSupply = total_supply\n    self.balanceOf[msg.sender] -= burn_amount\n    log Transfer(msg.sender, empty(address), burn_amount)\n    log RemoveLiquidityImbalance(msg.sender, _amounts, fees, D1, total_supply)\n\n    return burn_amount\n\n\n@pure\n@internal\ndef get_y_D(A: uint256, i: int128, xp: uint256[N_COINS], D: uint256) -> uint256:\n    \"\"\"\n    Calculate x[i] if one reduces D from being calculated for xp to D\n\n    Done by solving quadratic equation iteratively.\n    x_1**2 + x_1 * (sum' - (A*n**n - 1) * D / (A * n**n)) = D ** (n + 1) / (n ** (2 * n) * prod' * A)\n    x_1**2 + b*x_1 = c\n\n    x_1 = (x_1**2 + c) / (2*x_1 + b)\n    \"\"\"\n    # x in the input is converted to the same price/precision\n\n    assert i >= 0  # dev: i below zero\n    assert i < N_COINS_128  # dev: i above N_COINS\n\n    S_: uint256 = 0\n    _x: uint256 = 0\n    y_prev: uint256 = 0\n    c: uint256 = D\n    Ann: uint256 = A * N_COINS\n\n    for _i in range(N_COINS_128):\n        if _i != i:\n            _x = xp[_i]\n        else:\n            continue\n        S_ += _x\n        c = c * D / (_x * N_COINS)\n\n    c = c * D * A_PRECISION / (Ann * N_COINS)\n    b: uint256 = S_ + D * A_PRECISION / Ann\n    y: uint256 = D\n\n    for _i in range(255):\n        y_prev = y\n        y = (y*y + c) / (2 * y + b - D)\n        # Equality with the precision of 1\n        if y > y_prev:\n            if y - y_prev <= 1:\n                return y\n        else:\n            if y_prev - y <= 1:\n                return y\n    raise\n\n\n@view\n@internal\ndef _calc_withdraw_one_coin(_burn_amount: uint256, i: int128) -> uint256[3]:\n    # First, need to calculate\n    # * Get current D\n    # * Solve Eqn against y_i for D - _token_amount\n    amp: uint256 = self._A()\n    rates: uint256[N_COINS] = self.rate_multipliers\n    xp: uint256[N_COINS] = self._xp_mem(rates, self.balances)\n    D0: uint256 = self.get_D(xp, amp)\n\n    total_supply: uint256 = self.totalSupply\n    D1: uint256 = D0 - _burn_amount * D0 / total_supply\n    new_y: uint256 = self.get_y_D(amp, i, xp, D1)\n\n    base_fee: uint256 = self.fee * N_COINS / (4 * (N_COINS - 1))\n    xp_reduced: uint256[N_COINS] = empty(uint256[N_COINS])\n\n    for j in range(N_COINS_128):\n        dx_expected: uint256 = 0\n        xp_j: uint256 = xp[j]\n        if j == i:\n            dx_expected = xp_j * D1 / D0 - new_y\n        else:\n            dx_expected = xp_j - xp_j * D1 / D0\n        xp_reduced[j] = xp_j - base_fee * dx_expected / FEE_DENOMINATOR\n\n    dy: uint256 = xp_reduced[i] - self.get_y_D(amp, i, xp_reduced, D1)\n    dy_0: uint256 = (xp[i] - new_y) * PRECISION / rates[i]  # w/o fees\n    dy = (dy - 1) * PRECISION / rates[i]  # Withdraw less to account for rounding errors\n\n    xp[i] = new_y\n    last_p: uint256 = 0\n    if new_y > 0:\n        last_p = self._get_p(xp, amp, D1)\n\n    return [dy, dy_0 - dy, last_p]\n\n\n@view\n@external\ndef calc_withdraw_one_coin(_burn_amount: uint256, i: int128) -> uint256:\n    \"\"\"\n    @notice Calculate the amount received when withdrawing a single coin\n    @param _burn_amount Amount of LP tokens to burn in the withdrawal\n    @param i Index value of the coin to withdraw\n    @return Amount of coin received\n    \"\"\"\n    return self._calc_withdraw_one_coin(_burn_amount, i)[0]\n\n\n@external\n@nonreentrant('lock')\ndef remove_liquidity_one_coin(\n    _burn_amount: uint256,\n    i: int128,\n    _min_received: uint256,\n    _receiver: address = msg.sender,\n) -> uint256:\n    \"\"\"\n    @notice Withdraw a single coin from the pool\n    @param _burn_amount Amount of LP tokens to burn in the withdrawal\n    @param i Index value of the coin to withdraw\n    @param _min_received Minimum amount of coin to receive\n    @param _receiver Address that receives the withdrawn coins\n    @return Amount of coin received\n    \"\"\"\n    dy: uint256[3] = self._calc_withdraw_one_coin(_burn_amount, i)\n    assert dy[0] >= _min_received, \"Not enough coins removed\"\n\n    self.balances[i] -= (dy[0] + dy[1] * ADMIN_FEE / FEE_DENOMINATOR)\n    total_supply: uint256 = self.totalSupply - _burn_amount\n    self.totalSupply = total_supply\n    self.balanceOf[msg.sender] -= _burn_amount\n    log Transfer(msg.sender, empty(address), _burn_amount)\n\n    assert ERC20(self.coins[i]).transfer(_receiver, dy[0], default_return_value=True)  # dev: failed transfer\n    log RemoveLiquidityOne(msg.sender, _burn_amount, dy[0], total_supply)\n\n    self.save_p_from_price(dy[2])\n\n    return dy[0]\n\n\n@external\ndef ramp_A(_future_A: uint256, _future_time: uint256):\n    assert msg.sender == Factory(self.factory).admin()  # dev: only owner\n    assert block.timestamp >= self.initial_A_time + MIN_RAMP_TIME\n    assert _future_time >= block.timestamp + MIN_RAMP_TIME  # dev: insufficient time\n\n    _initial_A: uint256 = self._A()\n    _future_A_p: uint256 = _future_A * A_PRECISION\n\n    assert _future_A > 0 and _future_A < MAX_A\n    if _future_A_p < _initial_A:\n        assert _future_A_p * MAX_A_CHANGE >= _initial_A\n    else:\n        assert _future_A_p <= _initial_A * MAX_A_CHANGE\n\n    self.initial_A = _initial_A\n    self.future_A = _future_A_p\n    self.initial_A_time = block.timestamp\n    self.future_A_time = _future_time\n\n    log RampA(_initial_A, _future_A_p, block.timestamp, _future_time)\n\n\n@external\ndef stop_ramp_A():\n    assert msg.sender == Factory(self.factory).admin()  # dev: only owner\n\n    current_A: uint256 = self._A()\n    self.initial_A = current_A\n    self.future_A = current_A\n    self.initial_A_time = block.timestamp\n    self.future_A_time = block.timestamp\n    # now (block.timestamp < t1) is always False, so we return saved A\n\n    log StopRampA(current_A, block.timestamp)\n\n\n@external\ndef set_ma_exp_time(_ma_exp_time: uint256):\n    assert msg.sender == Factory(self.factory).admin()  # dev: only owner\n    assert _ma_exp_time != 0\n\n    self.ma_exp_time = _ma_exp_time\n\n\n@view\n@external\ndef admin_balances(i: uint256) -> uint256:\n    return ERC20(self.coins[i]).balanceOf(self) - self.balances[i]\n\n\n@external\ndef commit_new_fee(_new_fee: uint256):\n    assert msg.sender == Factory(self.factory).admin()\n    assert _new_fee <= MAX_FEE\n    assert self.admin_action_deadline == 0\n\n    self.future_fee = _new_fee\n    self.admin_action_deadline = block.timestamp + ADMIN_ACTIONS_DEADLINE_DT\n    log CommitNewFee(_new_fee)\n\n\n@external\ndef apply_new_fee():\n    assert msg.sender == Factory(self.factory).admin()\n    deadline: uint256 = self.admin_action_deadline\n    assert deadline != 0 and block.timestamp >= deadline\n    \n    fee: uint256 = self.future_fee\n    self.fee = fee\n    self.admin_action_deadline = 0\n    log ApplyNewFee(fee)\n\n\n@external\ndef withdraw_admin_fees():\n    receiver: address = Factory(self.factory).get_fee_receiver(self)\n\n    for i in range(N_COINS):\n        coin: address = self.coins[i]\n        fees: uint256 = ERC20(coin).balanceOf(self) - self.balances[i]\n        assert ERC20(coin).transfer(receiver, fees, default_return_value=True)\n\n\n@pure\n@external\ndef version() -> String[8]:\n    \"\"\"\n    @notice Get the version of this token contract\n    \"\"\"\n    return VERSION"}],"certified":false,"conflicting_implementations":null,"abi":[{"anonymous":false,"inputs":[{"indexed":true,"name":"sender","type":"address"},{"indexed":true,"name":"receiver","type":"address"},{"indexed":false,"name":"value","type":"uint256"}],"name":"Transfer","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"name":"owner","type":"address"},{"indexed":true,"name":"spender","type":"address"},{"indexed":false,"name":"value","type":"uint256"}],"name":"Approval","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"name":"buyer","type":"address"},{"indexed":false,"name":"sold_id","type":"int128"},{"indexed":false,"name":"tokens_sold","type":"uint256"},{"indexed":false,"name":"bought_id","type":"int128"},{"indexed":false,"name":"tokens_bought","type":"uint256"}],"name":"TokenExchange","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"name":"provider","type":"address"},{"indexed":false,"name":"token_amounts","type":"uint256[2]"},{"indexed":false,"name":"fees","type":"uint256[2]"},{"indexed":false,"name":"invariant","type":"uint256"},{"indexed":false,"name":"token_supply","type":"uint256"}],"name":"AddLiquidity","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"name":"provider","type":"address"},{"indexed":false,"name":"token_amounts","type":"uint256[2]"},{"indexed":false,"name":"fees","type":"uint256[2]"},{"indexed":false,"name":"token_supply","type":"uint256"}],"name":"RemoveLiquidity","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"name":"provider","type":"address"},{"indexed":false,"name":"token_amount","type":"uint256"},{"indexed":false,"name":"coin_amount","type":"uint256"},{"indexed":false,"name":"token_supply","type":"uint256"}],"name":"RemoveLiquidityOne","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"name":"provider","type":"address"},{"indexed":false,"name":"token_amounts","type":"uint256[2]"},{"indexed":false,"name":"fees","type":"uint256[2]"},{"indexed":false,"name":"invariant","type":"uint256"},{"indexed":false,"name":"token_supply","type":"uint256"}],"name":"RemoveLiquidityImbalance","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"name":"old_A","type":"uint256"},{"indexed":false,"name":"new_A","type":"uint256"},{"indexed":false,"name":"initial_time","type":"uint256"},{"indexed":false,"name":"future_time","type":"uint256"}],"name":"RampA","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"name":"A","type":"uint256"},{"indexed":false,"name":"t","type":"uint256"}],"name":"StopRampA","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"name":"new_fee","type":"uint256"}],"name":"CommitNewFee","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"name":"fee","type":"uint256"}],"name":"ApplyNewFee","type":"event"},{"inputs":[],"outputs":[],"stateMutability":"nonpayable","type":"constructor"},{"inputs":[{"name":"_name","type":"string"},{"name":"_symbol","type":"string"},{"name":"_coins","type":"address[4]"},{"name":"_rate_multipliers","type":"uint256[4]"},{"name":"_A","type":"uint256"},{"name":"_fee","type":"uint256"}],"name":"initialize","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"decimals","outputs":[{"name":"","type":"uint8"}],"stateMutability":"view","type":"function"},{"inputs":[{"name":"_to","type":"address"},{"name":"_value","type":"uint256"}],"name":"transfer","outputs":[{"name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"name":"_from","type":"address"},{"name":"_to","type":"address"},{"name":"_value","type":"uint256"}],"name":"transferFrom","outputs":[{"name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"name":"_spender","type":"address"},{"name":"_value","type":"uint256"}],"name":"approve","outputs":[{"name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"name":"_owner","type":"address"},{"name":"_spender","type":"address"},{"name":"_value","type":"uint256"},{"name":"_deadline","type":"uint256"},{"name":"_v","type":"uint8"},{"name":"_r","type":"bytes32"},{"name":"_s","type":"bytes32"}],"name":"permit","outputs":[{"name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"last_price","outputs":[{"name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"ema_price","outputs":[{"name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"get_balances","outputs":[{"name":"","type":"uint256[2]"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"admin_fee","outputs":[{"name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"A","outputs":[{"name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"A_precise","outputs":[{"name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"get_p","outputs":[{"name":"","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