creation_sourcecode: # pragma version 0.3.10
  # pragma optimize codesize
  # pragma evm-version shanghai
  """
  @title CurveStableSwapNG
  @author Curve.Fi
  @license Copyright (c) Curve.Fi, 2020-2023 - all rights reserved
  @notice Stableswap implementation for up to 8 coins with no rehypothecation,
          i.e. the AMM does not deposit tokens into other contracts. The Pool contract also
          records exponential moving averages for coins relative to coin 0.
  @dev Asset Types:
          0. Standard ERC20 token with no additional features.
                            Note: Users are advised to do careful due-diligence on
                                  ERC20 tokens that they interact with, as this
                                  contract cannot differentiate between harmless and
                                  malicious ERC20 tokens.
          1. Oracle - token with rate oracle (e.g. wstETH)
                      Note: Oracles may be controlled externally by an EOA. Users
                            are advised to proceed with caution.
          2. Rebasing - token with rebase (e.g. stETH).
                        Note: Users and Integrators are advised to understand how
                              the AMM contract works with rebasing balances.
          3. ERC4626 - token with convertToAssets method (e.g. sDAI).
                       Note: Some ERC4626 implementations may be susceptible to
                             Donation/Inflation attacks. Users are advised to
                             proceed with caution.
          NOTE: Pool Cannot support tokens with multiple asset types: e.g. ERC4626
                with fees are not supported.
       Supports:
          1. ERC20 support for return True/revert, return True/False, return None
          2. ERC20 tokens can have arbitrary decimals (<=18).
          3. ERC20 tokens that rebase (either positive or fee on transfer)
          4. ERC20 tokens that have a rate oracle (e.g. wstETH, cbETH, sDAI, etc.)
             Note: Oracle precision _must_ be 10**18.
          5. ERC4626 tokens with arbitrary precision (<=18) of Vault token and underlying
             asset.
       Additional features include:
          1. Adds price oracles based on AMM State Price (and _not_ last traded price).
          2. Adds TVL oracle based on D.
          3. `exchange_received`: swaps that expect an ERC20 transfer to have occurred
             prior to executing the swap.
             Note: a. If pool contains rebasing tokens and one of the `asset_types` is 2 (Rebasing)
                      then calling `exchange_received` will REVERT.
                   b. If pool contains rebasing token and `asset_types` does not contain 2 (Rebasing)
                      then this is an incorrect implementation and rebases can be
                      stolen.
          4. Adds `get_dx`: Similar to `get_dy` which returns an expected output
             of coin[j] for given `dx` amount of coin[i], `get_dx` returns expected
             input of coin[i] for an output amount of coin[j].
          5. Fees are dynamic: AMM will charge a higher fee if pool depegs. This can cause very
                               slight discrepancies between calculated fees and realised fees.
  """
  
  from vyper.interfaces import ERC20
  from vyper.interfaces import ERC20Detailed
  from vyper.interfaces import ERC4626
  
  implements: ERC20
  
  # ------------------------------- Interfaces ---------------------------------
  
  interface Factory:
      def fee_receiver() -> address: view
      def admin() -> address: view
      def views_implementation() -> address: view
  
  interface ERC1271:
      def isValidSignature(_hash: bytes32, _signature: Bytes[65]) -> bytes32: view
  
  interface StableSwapViews:
      def get_dx(i: int128, j: int128, dy: uint256, pool: address) -> uint256: view
      def get_dy(i: int128, j: int128, dx: uint256, pool: address) -> uint256: view
      def dynamic_fee(i: int128, j: int128, pool: address) -> uint256: view
      def calc_token_amount(
          _amounts: DynArray[uint256, MAX_COINS],
          _is_deposit: bool,
          _pool: address
      ) -> uint256: view
  
  # --------------------------------- Events -----------------------------------
  
  event Transfer:
      sender: indexed(address)
      receiver: indexed(address)
      value: uint256
  
  event Approval:
      owner: indexed(address)
      spender: indexed(address)
      value: uint256
  
  event TokenExchange:
      buyer: indexed(address)
      sold_id: int128
      tokens_sold: uint256
      bought_id: int128
      tokens_bought: uint256
  
  event TokenExchangeUnderlying:
      buyer: indexed(address)
      sold_id: int128
      tokens_sold: uint256
      bought_id: int128
      tokens_bought: uint256
  
  event AddLiquidity:
      provider: indexed(address)
      token_amounts: DynArray[uint256, MAX_COINS]
      fees: DynArray[uint256, MAX_COINS]
      invariant: uint256
      token_supply: uint256
  
  event RemoveLiquidity:
      provider: indexed(address)
      token_amounts: DynArray[uint256, MAX_COINS]
      fees: DynArray[uint256, MAX_COINS]
      token_supply: uint256
  
  event RemoveLiquidityOne:
      provider: indexed(address)
      token_id: int128
      token_amount: uint256
      coin_amount: uint256
      token_supply: uint256
  
  event RemoveLiquidityImbalance:
      provider: indexed(address)
      token_amounts: DynArray[uint256, MAX_COINS]
      fees: DynArray[uint256, MAX_COINS]
      invariant: uint256
      token_supply: uint256
  
  event RampA:
      old_A: uint256
      new_A: uint256
      initial_time: uint256
      future_time: uint256
  
  event StopRampA:
      A: uint256
      t: uint256
  
  event ApplyNewFee:
      fee: uint256
      offpeg_fee_multiplier: uint256
  
  event SetNewMATime:
      ma_exp_time: uint256
      D_ma_time: uint256
  
  
  MAX_COINS: constant(uint256) = 8  # max coins is 8 in the factory
  MAX_COINS_128: constant(int128) = 8
  
  # ---------------------------- Pool Variables --------------------------------
  
  N_COINS: public(immutable(uint256))
  N_COINS_128: immutable(int128)
  PRECISION: constant(uint256) = 10 ** 18
  
  factory: immutable(Factory)
  coins: public(immutable(DynArray[address, MAX_COINS]))
  asset_types: immutable(DynArray[uint8, MAX_COINS])
  pool_contains_rebasing_tokens: immutable(bool)
  stored_balances: DynArray[uint256, MAX_COINS]
  
  # Fee specific vars
  FEE_DENOMINATOR: constant(uint256) = 10 ** 10
  fee: public(uint256)  # fee * 1e10
  offpeg_fee_multiplier: public(uint256)  # * 1e10
  admin_fee: public(constant(uint256)) = 5000000000
  MAX_FEE: constant(uint256) = 5 * 10 ** 9
  
  # ---------------------- Pool Amplification Parameters -----------------------
  
  A_PRECISION: constant(uint256) = 100
  MAX_A: constant(uint256) = 10 ** 6
  MAX_A_CHANGE: constant(uint256) = 10
  
  initial_A: public(uint256)
  future_A: public(uint256)
  initial_A_time: public(uint256)
  future_A_time: public(uint256)
  
  # ---------------------------- Admin Variables -------------------------------
  
  MIN_RAMP_TIME: constant(uint256) = 86400
  admin_balances: public(DynArray[uint256, MAX_COINS])
  
  # ----------------------- Oracle Specific vars -------------------------------
  
  rate_multipliers: immutable(DynArray[uint256, MAX_COINS])
  # [bytes4 method_id][bytes8 <empty>][bytes20 oracle]
  rate_oracles: immutable(DynArray[uint256, MAX_COINS])
  
  # For ERC4626 tokens, we need:
  call_amount: immutable(DynArray[uint256, MAX_COINS])
  scale_factor: immutable(DynArray[uint256, MAX_COINS])
  
  last_prices_packed: DynArray[uint256, MAX_COINS]  #  packing: last_price, ma_price
  last_D_packed: uint256                            #  packing: last_D, ma_D
  ma_exp_time: public(uint256)
  D_ma_time: public(uint256)
  ma_last_time: public(uint256)                     # packing: ma_last_time_p, ma_last_time_D
  # ma_last_time has a distinction for p and D because p is _not_ updated if
  # users remove_liquidity, but D is.
  
  # shift(2**32 - 1, 224)
  ORACLE_BIT_MASK: constant(uint256) = (2**32 - 1) * 256**28
  
  # --------------------------- ERC20 Specific Vars ----------------------------
  
  name: public(immutable(String[64]))
  symbol: public(immutable(String[32]))
  decimals: public(constant(uint8)) = 18
  version: public(constant(String[8])) = "v7.0.0"
  
  balanceOf: public(HashMap[address, uint256])
  allowance: public(HashMap[address, HashMap[address, uint256]])
  total_supply: uint256
  nonces: public(HashMap[address, uint256])
  
  # keccak256("isValidSignature(bytes32,bytes)")[:4] << 224
  ERC1271_MAGIC_VAL: constant(bytes32) = 0x1626ba7e00000000000000000000000000000000000000000000000000000000
  EIP712_TYPEHASH: constant(bytes32) = keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract,bytes32 salt)")
  EIP2612_TYPEHASH: constant(bytes32) = keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)")
  
  VERSION_HASH: constant(bytes32) = keccak256(version)
  NAME_HASH: immutable(bytes32)
  CACHED_CHAIN_ID: immutable(uint256)
  salt: public(immutable(bytes32))
  CACHED_DOMAIN_SEPARATOR: immutable(bytes32)
  
  
  # ------------------------------ AMM Setup -----------------------------------
  
  
  @external
  def __init__(
      _name: String[32],
      _symbol: String[10],
      _A: uint256,
      _fee: uint256,
      _offpeg_fee_multiplier: uint256,
      _ma_exp_time: uint256,
      _coins: DynArray[address, MAX_COINS],
      _rate_multipliers: DynArray[uint256, MAX_COINS],
      _asset_types: DynArray[uint8, MAX_COINS],
      _method_ids: DynArray[bytes4, MAX_COINS],
      _oracles: DynArray[address, MAX_COINS],
  ):
      """
      @notice Initialize the pool contract
      @param _name Name of the new plain pool.
      @param _symbol Symbol for the new plain pool.
      @param _A Amplification co-efficient - a lower value here means
                less tolerance for imbalance within the pool's assets.
                Suggested values include:
                 * Uncollateralized algorithmic stablecoins: 5-10
                 * Non-redeemable, collateralized assets: 100
                 * Redeemable assets: 200-400
      @param _fee Trade fee, given as an integer with 1e10 precision. The
                  the maximum is 1% (100000000).
                  50% of the fee is distributed to veCRV holders.
      @param _offpeg_fee_multiplier A multiplier that determines how much to increase
                                    Fees by when assets in the AMM depeg. Example value: 20000000000
      @param _ma_exp_time Averaging window of oracle. Set as time_in_seconds / ln(2)
                          Example: for 10 minute EMA, _ma_exp_time is 600 / ln(2) ~= 866
      @param _coins List of addresses of the coins being used in the pool.
      @param _rate_multipliers An array of: [10 ** (36 - _coins[n].decimals()), ... for n in range(N_COINS)]
      @param _asset_types Array of uint8 representing tokens in pool
      @param _method_ids Array of first four bytes of the Keccak-256 hash of the function signatures
                         of the oracle addresses that gives rate oracles.
                         Calculated as: keccak(text=event_signature.replace(" ", ""))[:4]
      @param _oracles Array of rate oracle addresses.
      """
  
      coins = _coins
      asset_types = _asset_types
      pool_contains_rebasing_tokens = 2 in asset_types
      __n_coins: uint256 = len(_coins)
      N_COINS = __n_coins
      N_COINS_128 = convert(__n_coins, int128)
  
      rate_multipliers = _rate_multipliers
  
      factory = Factory(msg.sender)
  
      A: uint256 = unsafe_mul(_A, A_PRECISION)
      self.initial_A = A
      self.future_A = A
      self.fee = _fee
      self.offpeg_fee_multiplier = _offpeg_fee_multiplier
  
      assert _ma_exp_time != 0
      self.ma_exp_time = _ma_exp_time
      self.D_ma_time = 62324  # <--------- 12 hours default on contract start.
      self.ma_last_time = self.pack_2(block.timestamp, block.timestamp)
  
      #  ------------------- initialize storage for DynArrays ------------------
  
      _call_amount: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
      _scale_factor: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
      _rate_oracles: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
      for i in range(N_COINS_128, bound=MAX_COINS_128):
  
          if i < N_COINS_128 - 1:
              self.last_prices_packed.append(self.pack_2(10**18, 10**18))
  
          _rate_oracles.append(convert(_method_ids[i], uint256) * 2**224 | convert(_oracles[i], uint256))
          self.stored_balances.append(0)
          self.admin_balances.append(0)
  
          if _asset_types[i] == 3:
  
              _call_amount.append(10**convert(ERC20Detailed(_coins[i]).decimals(), uint256))
              _underlying_asset: address = ERC4626(_coins[i]).asset()
              _scale_factor.append(10**(18 - convert(ERC20Detailed(_underlying_asset).decimals(), uint256)))
  
          else:
  
              _call_amount.append(0)
              _scale_factor.append(0)
  
      call_amount = _call_amount
      scale_factor = _scale_factor
      rate_oracles = _rate_oracles
  
      # ----------------------------- ERC20 stuff ------------------------------
  
      name = _name
      symbol = _symbol
  
      # EIP712 related params -----------------
      NAME_HASH = keccak256(name)
      salt = block.prevhash
      CACHED_CHAIN_ID = chain.id
      CACHED_DOMAIN_SEPARATOR = keccak256(
          _abi_encode(
              EIP712_TYPEHASH,
              NAME_HASH,
              VERSION_HASH,
              chain.id,
              self,
              salt,
          )
      )
  
      # ------------------------ Fire a transfer event -------------------------
  
      log Transfer(empty(address), msg.sender, 0)
  
  
  # ------------------ Token transfers in and out of the AMM -------------------
  
  
  @internal
  def _transfer_in(
      coin_idx: int128,
      dx: uint256,
      sender: address,
      expect_optimistic_transfer: bool,
  ) -> uint256:
      """
      @notice Contains all logic to handle ERC20 token transfers.
      @param coin_idx Index of the coin to transfer in.
      @param dx amount of `_coin` to transfer into the pool.
      @param sender address to transfer `_coin` from.
      @param receiver address to transfer `_coin` to.
      @param expect_optimistic_transfer True if contract expects an optimistic coin transfer
      """
      _dx: uint256 = ERC20(coins[coin_idx]).balanceOf(self)
  
      # ------------------------- Handle Transfers -----------------------------
  
      if expect_optimistic_transfer:
  
          _dx = _dx - self.stored_balances[coin_idx]
          assert _dx >= dx
  
      else:
  
          assert dx > 0  # dev : do not transferFrom 0 tokens into the pool
          assert ERC20(coins[coin_idx]).transferFrom(
              sender, self, dx, default_return_value=True
          )
  
          _dx = ERC20(coins[coin_idx]).balanceOf(self) - _dx
  
      # --------------------------- Store transferred in amount ---------------------------
  
      self.stored_balances[coin_idx] += _dx
  
      return _dx
  
  
  @internal
  def _transfer_out(_coin_idx: int128, _amount: uint256, receiver: address):
      """
      @notice Transfer a single token from the pool to receiver.
      @dev This function is called by `remove_liquidity` and
           `remove_liquidity_one_coin`, `_exchange`, `_withdraw_admin_fees` and
           `remove_liquidity_imbalance` methods.
      @param _coin_idx Index of the token to transfer out
      @param _amount Amount of token to transfer out
      @param receiver Address to send the tokens to
      """
      assert receiver != empty(address)  # dev: do not send tokens to zero_address
  
      if not pool_contains_rebasing_tokens:
  
          # we need not cache balanceOf pool before swap out
          self.stored_balances[_coin_idx] -= _amount
          assert ERC20(coins[_coin_idx]).transfer(
              receiver, _amount, default_return_value=True
          )
  
      else:
  
          # cache balances pre and post to account for fee on transfers etc.
          coin_balance: uint256 = ERC20(coins[_coin_idx]).balanceOf(self)
          assert ERC20(coins[_coin_idx]).transfer(
              receiver, _amount, default_return_value=True
          )
          self.stored_balances[_coin_idx] = coin_balance - _amount
  
  
  # -------------------------- AMM Special Methods -----------------------------
  
  
  @view
  @internal
  def _stored_rates() -> DynArray[uint256, MAX_COINS]:
      """
      @notice Gets rate multipliers for each coin.
      @dev If the coin has a rate oracle that has been properly initialised,
           this method queries that rate by static-calling an external
           contract.
      """
      rates: DynArray[uint256, MAX_COINS] = rate_multipliers
  
      for i in range(N_COINS_128, bound=MAX_COINS_128):
  
          if asset_types[i] == 1 and not rate_oracles[i] == 0:
  
              # NOTE: fetched_rate is assumed to be 10**18 precision
              oracle_response: Bytes[32] = raw_call(
                  convert(rate_oracles[i] % 2**160, address),
                  _abi_encode(rate_oracles[i] & ORACLE_BIT_MASK),
                  max_outsize=32,
                  is_static_call=True,
              )
              assert len(oracle_response) == 32
              fetched_rate: uint256 = convert(oracle_response, uint256)
  
              rates[i] = unsafe_div(rates[i] * fetched_rate, PRECISION)
  
          elif asset_types[i] == 3:  # ERC4626
  
              # fetched_rate: uint256 = ERC4626(coins[i]).convertToAssets(call_amount[i]) * scale_factor[i]
              # here: call_amount has ERC4626 precision, but the returned value is scaled up to 18
              # using scale_factor which is (18 - n) if underlying asset has n decimals.
              rates[i] = unsafe_div(
                  rates[i] * ERC4626(coins[i]).convertToAssets(call_amount[i]) * scale_factor[i],
                  PRECISION
              )  # 1e18 precision
  
      return rates
  
  
  @view
  @internal
  def _balances() -> DynArray[uint256, MAX_COINS]:
      """
      @notice Calculates the pool's balances _excluding_ the admin's balances.
      @dev If the pool contains rebasing tokens, this method ensures LPs keep all
              rebases and admin only claims swap fees. This also means that, since
              admin's balances are stored in an array and not inferred from read balances,
              the fees in the rebasing token that the admin collects is immune to
              slashing events.
      """
      result: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
      balances_i: uint256 = 0
  
      for i in range(N_COINS_128, bound=MAX_COINS_128):
  
          if pool_contains_rebasing_tokens:
              # Read balances by gulping to account for rebases
              balances_i = ERC20(coins[i]).balanceOf(self) - self.admin_balances[i]
          else:
              # Use cached balances
              balances_i = self.stored_balances[i] - self.admin_balances[i]
  
          result.append(balances_i)
  
      return result
  
  
  # -------------------------- AMM Main Functions ------------------------------
  
  
  @external
  @nonreentrant('lock')
  def exchange(
      i: int128,
      j: int128,
      _dx: uint256,
      _min_dy: uint256,
      _receiver: address = msg.sender,
  ) -> uint256:
      """
      @notice Perform an exchange between two coins
      @dev Index values can be found via the `coins` public getter method
      @param i Index value for the coin to send
      @param j Index value of the coin to receive
      @param _dx Amount of `i` being exchanged
      @param _min_dy Minimum amount of `j` to receive
      @param _receiver Address that receives `j`
      @return Actual amount of `j` received
      """
      return self._exchange(
          msg.sender,
          i,
          j,
          _dx,
          _min_dy,
          _receiver,
          False
      )
  
  
  @external
  @nonreentrant('lock')
  def exchange_received(
      i: int128,
      j: int128,
      _dx: uint256,
      _min_dy: uint256,
      _receiver: address = msg.sender,
  ) -> uint256:
      """
      @notice Perform an exchange between two coins without transferring token in
      @dev The contract swaps tokens based on a change in balance of coin[i]. The
           dx = ERC20(coin[i]).balanceOf(self) - self.stored_balances[i]. Users of
           this method are dex aggregators, arbitrageurs, or other users who do not
           wish to grant approvals to the contract: they would instead send tokens
           directly to the contract and call `exchange_received`.
           Note: This is disabled if pool contains rebasing tokens.
      @param i Index value for the coin to send
      @param j Index value of the coin to receive
      @param _dx Amount of `i` being exchanged
      @param _min_dy Minimum amount of `j` to receive
      @param _receiver Address that receives `j`
      @return Actual amount of `j` received
      """
      assert not pool_contains_rebasing_tokens  # dev: exchange_received not supported if pool contains rebasing tokens
      return self._exchange(
          msg.sender,
          i,
          j,
          _dx,
          _min_dy,
          _receiver,
          True,  # <--------------------------------------- swap optimistically.
      )
  
  
  @external
  @nonreentrant('lock')
  def add_liquidity(
      _amounts: DynArray[uint256, MAX_COINS],
      _min_mint_amount: uint256,
      _receiver: address = msg.sender
  ) -> uint256:
      """
      @notice Deposit coins into the pool
      @param _amounts List of amounts of coins to deposit
      @param _min_mint_amount Minimum amount of LP tokens to mint from the deposit
      @param _receiver Address that owns the minted LP tokens
      @return Amount of LP tokens received by depositing
      """
      assert _receiver != empty(address)  # dev: do not send LP tokens to zero_address
  
      amp: uint256 = self._A()
      old_balances: DynArray[uint256, MAX_COINS] = self._balances()
      rates: DynArray[uint256, MAX_COINS] = self._stored_rates()
  
      # Initial invariant
      D0: uint256 = self.get_D_mem(rates, old_balances, amp)
  
      total_supply: uint256 = self.total_supply
      new_balances: DynArray[uint256, MAX_COINS] = old_balances
  
      # -------------------------- Do Transfers In -----------------------------
  
      for i in range(N_COINS_128, bound=MAX_COINS_128):
  
          if _amounts[i] > 0:
  
              new_balances[i] += self._transfer_in(
                  i,
                  _amounts[i],
                  msg.sender,
                  False,  # expect_optimistic_transfer
              )
  
          else:
  
              assert total_supply != 0  # dev: initial deposit requires all coins
  
      # ------------------------------------------------------------------------
  
      # Invariant after change
      D1: uint256 = self.get_D_mem(rates, new_balances, amp)
      assert D1 > D0
  
      # We need to recalculate the invariant accounting for fees
      # to calculate fair user's share
      fees: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
      mint_amount: uint256 = 0
  
      if total_supply > 0:
  
          ideal_balance: uint256 = 0
          difference: uint256 = 0
          new_balance: uint256 = 0
  
          ys: uint256 = unsafe_div(D0 + D1, N_COINS)
          xs: uint256 = 0
          _dynamic_fee_i: uint256 = 0
  
          # Only account for fees if we are not the first to deposit
          base_fee: uint256 = unsafe_div(
              unsafe_mul(self.fee, N_COINS),
              unsafe_mul(4, unsafe_sub(N_COINS, 1))
          )
  
          for i in range(N_COINS_128, bound=MAX_COINS_128):
  
              ideal_balance = D1 * old_balances[i] / D0
              difference = 0
              new_balance = new_balances[i]
  
              if ideal_balance > new_balance:
                  difference = unsafe_sub(ideal_balance, new_balance)
              else:
                  difference = unsafe_sub(new_balance, ideal_balance)
  
              # fee[i] = _dynamic_fee(i, j) * difference / FEE_DENOMINATOR
              xs = unsafe_div(rates[i] * (old_balances[i] + new_balance), PRECISION)
              _dynamic_fee_i = self._dynamic_fee(xs, ys, base_fee)
              fees.append(unsafe_div(_dynamic_fee_i * difference, FEE_DENOMINATOR))
              self.admin_balances[i] += unsafe_div(fees[i] * admin_fee, FEE_DENOMINATOR)
              new_balances[i] -= fees[i]
  
          xp: DynArray[uint256, MAX_COINS] = self._xp_mem(rates, new_balances)
          D1 = self.get_D(xp, amp)  # <--------------- Reuse D1 for new D value.
          mint_amount = unsafe_div(total_supply * (D1 - D0), D0)
          self.upkeep_oracles(xp, amp, D1)
  
      else:
  
          mint_amount = D1  # Take the dust if there was any
  
          # (re)instantiate D oracle if totalSupply is zero.
          self.last_D_packed = self.pack_2(D1, D1)
  
          # Update D ma time:
          ma_last_time_unpacked: uint256[2] = self.unpack_2(self.ma_last_time)
          if ma_last_time_unpacked[1] < block.timestamp:
              ma_last_time_unpacked[1] = block.timestamp
              self.ma_last_time = self.pack_2(ma_last_time_unpacked[0], ma_last_time_unpacked[1])
  
      assert mint_amount >= _min_mint_amount, "Slippage screwed you"
  
      # Mint pool tokens
      total_supply += mint_amount
      self.balanceOf[_receiver] += mint_amount
      self.total_supply = total_supply
      log Transfer(empty(address), _receiver, mint_amount)
  
      log AddLiquidity(msg.sender, _amounts, fees, D1, total_supply)
  
      return mint_amount
  
  
  @external
  @nonreentrant('lock')
  def remove_liquidity_one_coin(
      _burn_amount: uint256,
      i: int128,
      _min_received: uint256,
      _receiver: address = msg.sender,
  ) -> uint256:
      """
      @notice Withdraw a single coin from the pool
      @param _burn_amount Amount of LP tokens to burn in the withdrawal
      @param i Index value of the coin to withdraw
      @param _min_received Minimum amount of coin to receive
      @param _receiver Address that receives the withdrawn coins
      @return Amount of coin received
      """
      assert _burn_amount > 0  # dev: do not remove 0 LP tokens
      dy: uint256 = 0
      fee: uint256 = 0
      xp: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
      amp: uint256 = empty(uint256)
      D: uint256 = empty(uint256)
  
      dy, fee, xp, amp, D = self._calc_withdraw_one_coin(_burn_amount, i)
      assert dy >= _min_received, "Not enough coins removed"
  
      self.admin_balances[i] += unsafe_div(fee * admin_fee, FEE_DENOMINATOR)
  
      self._burnFrom(msg.sender, _burn_amount)
  
      self._transfer_out(i, dy, _receiver)
  
      log RemoveLiquidityOne(msg.sender, i, _burn_amount, dy, self.total_supply)
  
      self.upkeep_oracles(xp, amp, D)
  
      return dy
  
  
  @external
  @nonreentrant('lock')
  def remove_liquidity_imbalance(
      _amounts: DynArray[uint256, MAX_COINS],
      _max_burn_amount: uint256,
      _receiver: address = msg.sender
  ) -> uint256:
      """
      @notice Withdraw coins from the pool in an imbalanced amount
      @param _amounts List of amounts of underlying coins to withdraw
      @param _max_burn_amount Maximum amount of LP token to burn in the withdrawal
      @param _receiver Address that receives the withdrawn coins
      @return Actual amount of the LP token burned in the withdrawal
      """
      amp: uint256 = self._A()
      rates: DynArray[uint256, MAX_COINS] = self._stored_rates()
      old_balances: DynArray[uint256, MAX_COINS] = self._balances()
      D0: uint256 = self.get_D_mem(rates, old_balances, amp)
      new_balances: DynArray[uint256, MAX_COINS] = old_balances
  
      for i in range(N_COINS_128, bound=MAX_COINS_128):
  
          if _amounts[i] != 0:
              new_balances[i] -= _amounts[i]
              self._transfer_out(i, _amounts[i], _receiver)
  
      D1: uint256 = self.get_D_mem(rates, new_balances, amp)
      base_fee: uint256 = unsafe_div(
          unsafe_mul(self.fee, N_COINS),
          unsafe_mul(4, unsafe_sub(N_COINS, 1))
      )
      ys: uint256 = unsafe_div((D0 + D1), N_COINS)
  
      fees: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
      dynamic_fee: uint256 = 0
      xs: uint256 = 0
      ideal_balance: uint256 = 0
      difference: uint256 = 0
      new_balance: uint256 = 0
  
      for i in range(N_COINS_128, bound=MAX_COINS_128):
  
          ideal_balance = D1 * old_balances[i] / D0
          difference = 0
          new_balance = new_balances[i]
  
          if ideal_balance > new_balance:
              difference = unsafe_sub(ideal_balance, new_balance)
          else:
              difference = unsafe_sub(new_balance, ideal_balance)
  
          xs = unsafe_div(rates[i] * (old_balances[i] + new_balance), PRECISION)
          dynamic_fee = self._dynamic_fee(xs, ys, base_fee)
          fees.append(unsafe_div(dynamic_fee * difference, FEE_DENOMINATOR))
  
          self.admin_balances[i] += unsafe_div(fees[i] * admin_fee, FEE_DENOMINATOR)
          new_balances[i] -= fees[i]
  
      D1 = self.get_D_mem(rates, new_balances, amp)  # dev: reuse D1 for new D.
      self.upkeep_oracles(self._xp_mem(rates, new_balances), amp, D1)
  
      total_supply: uint256 = self.total_supply
      burn_amount: uint256 = unsafe_div((D0 - D1) * total_supply, D0) + 1
      assert burn_amount > 1  # dev: zero tokens burned
      assert burn_amount <= _max_burn_amount, "Slippage screwed you"
  
      self._burnFrom(msg.sender, burn_amount)
  
      log RemoveLiquidityImbalance(
          msg.sender,
          _amounts,
          fees,
          D1,
          total_supply - burn_amount
      )
  
      return burn_amount
  
  
  @external
  @nonreentrant('lock')
  def remove_liquidity(
      _burn_amount: uint256,
      _min_amounts: DynArray[uint256, MAX_COINS],
      _receiver: address = msg.sender,
      _claim_admin_fees: bool = True,
  ) -> DynArray[uint256, MAX_COINS]:
      """
      @notice Withdraw coins from the pool
      @dev Withdrawal amounts are based on current deposit ratios
      @param _burn_amount Quantity of LP tokens to burn in the withdrawal
      @param _min_amounts Minimum amounts of underlying coins to receive
      @param _receiver Address that receives the withdrawn coins
      @return List of amounts of coins that were withdrawn
      """
      total_supply: uint256 = self.total_supply
      assert _burn_amount > 0  # dev: invalid burn amount
      assert len(_min_amounts) == N_COINS  # dev: invalid array length for _min_amounts
  
      amounts: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
      balances: DynArray[uint256, MAX_COINS] = self._balances()
  
      value: uint256 = 0
      for i in range(N_COINS_128, bound=MAX_COINS_128):
  
          value = unsafe_div(balances[i] * _burn_amount, total_supply)
          assert value >= _min_amounts[i], "Withdrawal resulted in fewer coins than expected"
          amounts.append(value)
          self._transfer_out(i, value, _receiver)
  
      self._burnFrom(msg.sender, _burn_amount)  # <---- Updates self.total_supply
  
      # --------------------------- Upkeep D_oracle ----------------------------
  
      ma_last_time_unpacked: uint256[2] = self.unpack_2(self.ma_last_time)
      last_D_packed_current: uint256 = self.last_D_packed
      old_D: uint256 = last_D_packed_current & (2**128 - 1)
  
      self.last_D_packed = self.pack_2(
          old_D - unsafe_div(old_D * _burn_amount, total_supply),  # new_D = proportionally reduce D.
          self._calc_moving_average(
              last_D_packed_current,
              self.D_ma_time,
              ma_last_time_unpacked[1]
          )
      )
  
      if ma_last_time_unpacked[1] < block.timestamp:
          ma_last_time_unpacked[1] = block.timestamp
          self.ma_last_time = self.pack_2(ma_last_time_unpacked[0], ma_last_time_unpacked[1])
  
      # ------------------------------- Log event ------------------------------
  
      log RemoveLiquidity(
          msg.sender,
          amounts,
          empty(DynArray[uint256, MAX_COINS]),
          unsafe_sub(total_supply, _burn_amount)
      )
  
      # ------- Withdraw admin fees if _claim_admin_fees is set to True --------
      if _claim_admin_fees:
          self._withdraw_admin_fees()
  
      return amounts
  
  
  @external
  @nonreentrant('lock')
  def withdraw_admin_fees():
      """
      @notice Claim admin fees. Callable by anyone.
      """
      self._withdraw_admin_fees()
  
  
  # ------------------------ AMM Internal Functions ----------------------------
  
  
  @view
  @internal
  def _dynamic_fee(xpi: uint256, xpj: uint256, _fee: uint256) -> uint256:
  
      _offpeg_fee_multiplier: uint256 = self.offpeg_fee_multiplier
      if _offpeg_fee_multiplier <= FEE_DENOMINATOR:
          return _fee
  
      xps2: uint256 = (xpi + xpj) ** 2
      return unsafe_div(
          unsafe_mul(_offpeg_fee_multiplier, _fee),
          unsafe_add(
              unsafe_sub(_offpeg_fee_multiplier, FEE_DENOMINATOR) * 4 * xpi * xpj / xps2,
              FEE_DENOMINATOR
          )
      )
  
  
  @internal
  def __exchange(
      x: uint256,
      _xp: DynArray[uint256, MAX_COINS],
      rates: DynArray[uint256, MAX_COINS],
      i: int128,
      j: int128,
  ) -> uint256:
  
      amp: uint256 = self._A()
      D: uint256 = self.get_D(_xp, amp)
      y: uint256 = self.get_y(i, j, x, _xp, amp, D)
  
      dy: uint256 = _xp[j] - y - 1  # -1 just in case there were some rounding errors
      dy_fee: uint256 = unsafe_div(
          dy * self._dynamic_fee(
              unsafe_div(_xp[i] + x, 2), unsafe_div(_xp[j] + y, 2), self.fee
          ),
          FEE_DENOMINATOR
      )
  
      # Convert all to real units
      dy = (dy - dy_fee) * PRECISION / rates[j]
  
      self.admin_balances[j] += unsafe_div(
          unsafe_div(dy_fee * admin_fee, FEE_DENOMINATOR) * PRECISION,
          rates[j]
      )
  
      # Calculate and store state prices:
      xp: DynArray[uint256, MAX_COINS] = _xp
      xp[i] = x
      xp[j] = y
      # D is not changed because we did not apply a fee
      self.upkeep_oracles(xp, amp, D)
  
      return dy
  
  
  @internal
  def _exchange(
      sender: address,
      i: int128,
      j: int128,
      _dx: uint256,
      _min_dy: uint256,
      receiver: address,
      expect_optimistic_transfer: bool
  ) -> uint256:
  
      assert i != j  # dev: coin index out of range
      assert _dx > 0  # dev: do not exchange 0 coins
  
      rates: DynArray[uint256, MAX_COINS] = self._stored_rates()
      old_balances: DynArray[uint256, MAX_COINS] = self._balances()
      xp: DynArray[uint256, MAX_COINS] = self._xp_mem(rates, old_balances)
  
      # --------------------------- Do Transfer in -----------------------------
  
      # `dx` is whatever the pool received after ERC20 transfer:
      dx: uint256 = self._transfer_in(
          i,
          _dx,
          sender,
          expect_optimistic_transfer
      )
  
      # ------------------------------- Exchange -------------------------------
  
      x: uint256 = xp[i] + unsafe_div(dx * rates[i], PRECISION)
      dy: uint256 = self.__exchange(x, xp, rates, i, j)
      assert dy >= _min_dy, "Exchange resulted in fewer coins than expected"
  
      # --------------------------- Do Transfer out ----------------------------
  
      self._transfer_out(j, dy, receiver)
  
      # ------------------------------------------------------------------------
  
      log TokenExchange(msg.sender, i, dx, j, dy)
  
      return dy
  
  
  @internal
  def _withdraw_admin_fees():
      fee_receiver: address = factory.fee_receiver()
      if fee_receiver == empty(address):
          return  # Do nothing.
  
      admin_balances: DynArray[uint256, MAX_COINS] = self.admin_balances
      for i in range(N_COINS_128, bound=MAX_COINS_128):
  
          if admin_balances[i] > 0:
  
              self._transfer_out(i, admin_balances[i], fee_receiver)
              admin_balances[i] = 0
  
      self.admin_balances = admin_balances
  
  
  # --------------------------- AMM Math Functions -----------------------------
  
  
  @view
  @internal
  def get_y(
      i: int128,
      j: int128,
      x: uint256,
      xp: DynArray[uint256, MAX_COINS],
      _amp: uint256,
      _D: uint256
  ) -> uint256:
      """
      Calculate x[j] if one makes x[i] = x
  
      Done by solving quadratic equation iteratively.
      x_1**2 + x_1 * (sum' - (A*n**n - 1) * D / (A * n**n)) = D ** (n + 1) / (n ** (2 * n) * prod' * A)
      x_1**2 + b*x_1 = c
  
      x_1 = (x_1**2 + c) / (2*x_1 + b)
      """
      # x in the input is converted to the same price/precision
  
      assert i != j       # dev: same coin
      assert j >= 0       # dev: j below zero
      assert j < N_COINS_128  # dev: j above N_COINS
  
      # should be unreachable, but good for safety
      assert i >= 0
      assert i < N_COINS_128
  
      amp: uint256 = _amp
      D: uint256 = _D
  
      S_: uint256 = 0
      _x: uint256 = 0
      y_prev: uint256 = 0
      c: uint256 = D
      Ann: uint256 = amp * N_COINS
  
      for _i in range(MAX_COINS_128):
  
          if _i == N_COINS_128:
              break
  
          if _i == i:
              _x = x
          elif _i != j:
              _x = xp[_i]
          else:
              continue
  
          S_ += _x
          c = c * D / (_x * N_COINS)
  
      c = c * D * A_PRECISION / (Ann * N_COINS)
      b: uint256 = S_ + D * A_PRECISION / Ann  # - D
      y: uint256 = D
  
      for _i in range(255):
          y_prev = y
          y = (y*y + c) / (2 * y + b - D)
          # Equality with the precision of 1
          if y > y_prev:
              if y - y_prev <= 1:
                  return y
          else:
              if y_prev - y <= 1:
                  return y
      raise
  
  
  @pure
  @internal
  def get_D(_xp: DynArray[uint256, MAX_COINS], _amp: uint256) -> uint256:
      """
      D invariant calculation in non-overflowing integer operations
      iteratively
  
      A * sum(x_i) * n**n + D = A * D * n**n + D**(n+1) / (n**n * prod(x_i))
  
      Converging solution:
      D[j+1] = (A * n**n * sum(x_i) - D[j]**(n+1) / (n**n prod(x_i))) / (A * n**n - 1)
      """
      S: uint256 = 0
      for x in _xp:
          S += x
      if S == 0:
          return 0
  
      D: uint256 = S
      Ann: uint256 = _amp * N_COINS
  
      for i in range(255):
  
          D_P: uint256 = D
          for x in _xp:
              D_P = D_P * D / x
          D_P /= pow_mod256(N_COINS, N_COINS)
          Dprev: uint256 = D
  
          # (Ann * S / A_PRECISION + D_P * N_COINS) * D / ((Ann - A_PRECISION) * D / A_PRECISION + (N_COINS + 1) * D_P)
          D = (
              (unsafe_div(Ann * S, A_PRECISION) + D_P * N_COINS) * D
              /
              (
                  unsafe_div((Ann - A_PRECISION) * D, A_PRECISION) +
                  unsafe_add(N_COINS, 1) * D_P
              )
          )
  
          # Equality with the precision of 1
          if D > Dprev:
              if D - Dprev <= 1:
                  return D
          else:
              if Dprev - D <= 1:
                  return D
      # convergence typically occurs in 4 rounds or less, this should be unreachable!
      # if it does happen the pool is borked and LPs can withdraw via `remove_liquidity`
      raise
  
  
  @pure
  @internal
  def get_y_D(
      A: uint256,
      i: int128,
      xp: DynArray[uint256, MAX_COINS],
      D: uint256
  ) -> uint256:
      """
      Calculate x[i] if one reduces D from being calculated for xp to D
  
      Done by solving quadratic equation iteratively.
      x_1**2 + x_1 * (sum' - (A*n**n - 1) * D / (A * n**n)) = D ** (n + 1) / (n ** (2 * n) * prod' * A)
      x_1**2 + b*x_1 = c
  
      x_1 = (x_1**2 + c) / (2*x_1 + b)
      """
      # x in the input is converted to the same price/precision
  
      assert i >= 0  # dev: i below zero
      assert i < N_COINS_128  # dev: i above N_COINS
  
      S_: uint256 = 0
      _x: uint256 = 0
      y_prev: uint256 = 0
      c: uint256 = D
      Ann: uint256 = A * N_COINS
  
      for _i in range(MAX_COINS_128):
  
          if _i == N_COINS_128:
              break
  
          if _i != i:
              _x = xp[_i]
          else:
              continue
          S_ += _x
          c = c * D / (_x * N_COINS)
  
      c = c * D * A_PRECISION / (Ann * N_COINS)
      b: uint256 = S_ + D * A_PRECISION / Ann
      y: uint256 = D
  
      for _i in range(255):
          y_prev = y
          y = (y*y + c) / (2 * y + b - D)
          # Equality with the precision of 1
          if y > y_prev:
              if y - y_prev <= 1:
                  return y
          else:
              if y_prev - y <= 1:
                  return y
      raise
  
  
  @view
  @internal
  def _A() -> uint256:
      """
      Handle ramping A up or down
      """
      t1: uint256 = self.future_A_time
      A1: uint256 = self.future_A
  
      if block.timestamp < t1:
          A0: uint256 = self.initial_A
          t0: uint256 = self.initial_A_time
          # Expressions in uint256 cannot have negative numbers, thus "if"
          if A1 > A0:
              return A0 + unsafe_sub(A1, A0) * (block.timestamp - t0) / (t1 - t0)
          else:
              return A0 - unsafe_sub(A0, A1) * (block.timestamp - t0) / (t1 - t0)
  
      else:  # when t1 == 0 or block.timestamp >= t1
          return A1
  
  
  @pure
  @internal
  def _xp_mem(
      _rates: DynArray[uint256, MAX_COINS],
      _balances: DynArray[uint256, MAX_COINS]
  ) -> DynArray[uint256, MAX_COINS]:
  
      result: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
      for i in range(N_COINS_128, bound=MAX_COINS_128):
          result.append(unsafe_div(_rates[i] * _balances[i], PRECISION))
      return result
  
  
  @view
  @internal
  def get_D_mem(
      _rates: DynArray[uint256, MAX_COINS],
      _balances: DynArray[uint256, MAX_COINS],
      _amp: uint256
  ) -> uint256:
      xp: DynArray[uint256, MAX_COINS] = self._xp_mem(_rates, _balances)
      return self.get_D(xp, _amp)
  
  
  @view
  @internal
  def _calc_withdraw_one_coin(
      _burn_amount: uint256,
      i: int128
  ) -> (
      uint256,
      uint256,
      DynArray[uint256, MAX_COINS],
      uint256,
      uint256
  ):
      # First, need to calculate
      # * Get current D
      # * Solve Eqn against y_i for D - _token_amount
      amp: uint256 = self._A()
      rates: DynArray[uint256, MAX_COINS] = self._stored_rates()
      xp: DynArray[uint256, MAX_COINS] = self._xp_mem(rates, self._balances())
      D0: uint256 = self.get_D(xp, amp)
  
      total_supply: uint256 = self.total_supply
      D1: uint256 = D0 - _burn_amount * D0 / total_supply
      new_y: uint256 = self.get_y_D(amp, i, xp, D1)
  
      base_fee: uint256 = unsafe_div(
          unsafe_mul(self.fee, N_COINS),
          unsafe_mul(4, unsafe_sub(N_COINS, 1))
      )
      xp_reduced: DynArray[uint256, MAX_COINS] = xp
      ys: uint256 = unsafe_div((D0 + D1), unsafe_mul(2, N_COINS))
  
      dx_expected: uint256 = 0
      xp_j: uint256 = 0
      xavg: uint256 = 0
      dynamic_fee: uint256 = 0
  
      for j in range(MAX_COINS_128):
  
          if j == N_COINS_128:
              break
  
          dx_expected = 0
          xp_j = xp[j]
  
          if j == i:
              dx_expected = xp_j * D1 / D0 - new_y
              xavg = unsafe_div((xp_j + new_y), 2)
          else:
              dx_expected = xp_j - xp_j * D1 / D0
              xavg = xp_j
  
          dynamic_fee = self._dynamic_fee(xavg, ys, base_fee)
          xp_reduced[j] = xp_j - unsafe_div(dynamic_fee * dx_expected, FEE_DENOMINATOR)
  
      dy: uint256 = xp_reduced[i] - self.get_y_D(amp, i, xp_reduced, D1)
      dy_0: uint256 = (xp[i] - new_y) * PRECISION / rates[i]  # w/o fees
      dy = unsafe_div((dy - 1) * PRECISION, rates[i])  # Withdraw less to account for rounding errors
  
      # update xp with new_y for p calculations.
      xp[i] = new_y
  
      return dy, dy_0 - dy, xp, amp, D1
  
  
  # -------------------------- AMM Price Methods -------------------------------
  
  @pure
  @internal
  def pack_2(p1: uint256, p2: uint256) -> uint256:
      assert p1 < 2**128
      assert p2 < 2**128
      return p1 | (p2 << 128)
  
  
  @pure
  @internal
  def unpack_2(packed: uint256) -> uint256[2]:
      return [packed & (2**128 - 1), packed >> 128]
  
  
  @internal
  @pure
  def _get_p(
      xp: DynArray[uint256, MAX_COINS],
      amp: uint256,
      D: uint256,
  ) -> DynArray[uint256, MAX_COINS]:
  
      # dx_0 / dx_1 only, however can have any number of coins in pool
      ANN: uint256 = unsafe_mul(amp, N_COINS)
      Dr: uint256 = unsafe_div(D, pow_mod256(N_COINS, N_COINS))
  
      for i in range(N_COINS_128, bound=MAX_COINS_128):
          Dr = Dr * D / xp[i]
  
      p: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
      xp0_A: uint256 = unsafe_div(ANN * xp[0], A_PRECISION)
  
      for i in range(1, MAX_COINS):
  
          if i == N_COINS:
              break
  
          p.append(10**18 * (xp0_A + unsafe_div(Dr * xp[0], xp[i])) / (xp0_A + Dr))
  
      return p
  
  
  @internal
  def upkeep_oracles(xp: DynArray[uint256, MAX_COINS], amp: uint256, D: uint256):
      """
      @notice Upkeeps price and D oracles.
      """
      ma_last_time_unpacked: uint256[2] = self.unpack_2(self.ma_last_time)
      last_prices_packed_current: DynArray[uint256, MAX_COINS] = self.last_prices_packed
      last_prices_packed_new: DynArray[uint256, MAX_COINS] = last_prices_packed_current
  
      spot_price: DynArray[uint256, MAX_COINS] = self._get_p(xp, amp, D)
  
      # -------------------------- Upkeep price oracle -------------------------
  
      for i in range(MAX_COINS):
  
          if i == N_COINS - 1:
              break
  
          if spot_price[i] != 0:
  
              # Update packed prices -----------------
              last_prices_packed_new[i] = self.pack_2(
                  min(spot_price[i], 2 * 10**18),  # <----- Cap spot value by 2.
                  self._calc_moving_average(
                      last_prices_packed_current[i],
                      self.ma_exp_time,
                      ma_last_time_unpacked[0],  # index 0 is ma_last_time for prices
                  )
              )
  
      self.last_prices_packed = last_prices_packed_new
  
      # ---------------------------- Upkeep D oracle ---------------------------
  
      last_D_packed_current: uint256 = self.last_D_packed
      self.last_D_packed = self.pack_2(
          D,
          self._calc_moving_average(
              last_D_packed_current,
              self.D_ma_time,
              ma_last_time_unpacked[1],  # index 1 is ma_last_time for D
          )
      )
  
      # Housekeeping: Update ma_last_time for p and D oracles ------------------
      for i in range(2):
          if ma_last_time_unpacked[i] < block.timestamp:
              ma_last_time_unpacked[i] = block.timestamp
  
      self.ma_last_time = self.pack_2(ma_last_time_unpacked[0], ma_last_time_unpacked[1])
  
  
  @internal
  @view
  def _calc_moving_average(
      packed_value: uint256,
      averaging_window: uint256,
      ma_last_time: uint256
  ) -> uint256:
  
      last_spot_value: uint256 = packed_value & (2**128 - 1)
      last_ema_value: uint256 = (packed_value >> 128)
  
      if ma_last_time < block.timestamp:  # calculate new_ema_value and return that.
          alpha: uint256 = self.exp(
              -convert(
                  unsafe_div(unsafe_mul(unsafe_sub(block.timestamp, ma_last_time), 10**18), averaging_window), int256
              )
          )
          return unsafe_div(last_spot_value * (10**18 - alpha) + last_ema_value * alpha, 10**18)
  
      return last_ema_value
  
  
  @view
  @external
  def last_price(i: uint256) -> uint256:
      return self.last_prices_packed[i] & (2**128 - 1)
  
  
  @view
  @external
  def ema_price(i: uint256) -> uint256:
      return (self.last_prices_packed[i] >> 128)
  
  
  @external
  @view
  def get_p(i: uint256) -> uint256:
      """
      @notice Returns the AMM State price of token
      @dev if i = 0, it will return the state price of coin[1].
      @param i index of state price (0 for coin[1], 1 for coin[2], ...)
      @return uint256 The state price quoted by the AMM for coin[i+1]
      """
      amp: uint256 = self._A()
      xp: DynArray[uint256, MAX_COINS] = self._xp_mem(
          self._stored_rates(), self._balances()
      )
      D: uint256 = self.get_D(xp, amp)
      return self._get_p(xp, amp, D)[i]
  
  
  @external
  @view
  @nonreentrant('lock')
  def price_oracle(i: uint256) -> uint256:
      return self._calc_moving_average(
          self.last_prices_packed[i],
          self.ma_exp_time,
          self.ma_last_time & (2**128 - 1)
      )
  
  
  @external
  @view
  @nonreentrant('lock')
  def D_oracle() -> uint256:
      return self._calc_moving_average(
          self.last_D_packed,
          self.D_ma_time,
          self.ma_last_time >> 128
      )
  
  
  # ----------------------------- Math Utils -----------------------------------
  
  
  @internal
  @pure
  def exp(x: int256) -> uint256:
      """
      @dev Calculates the natural exponential function of a signed integer with
           a precision of 1e18.
      @notice Note that this function consumes about 810 gas units. The implementation
              is inspired by Remco Bloemen's implementation under the MIT license here:
              https://xn--2-umb.com/22/exp-ln.
      @dev This implementation is derived from Snekmate, which is authored
           by pcaversaccio (Snekmate), distributed under the AGPL-3.0 license.
           https://github.com/pcaversaccio/snekmate
      @param x The 32-byte variable.
      @return int256 The 32-byte calculation result.
      """
      value: int256 = x
  
      # If the result is `< 0.5`, we return zero. This happens when we have the following:
      # "x <= floor(log(0.5e18) * 1e18) ~ -42e18".
      if (x <= -41446531673892822313):
          return empty(uint256)
  
      # When the result is "> (2 ** 255 - 1) / 1e18" we cannot represent it as a signed integer.
      # This happens when "x >= floor(log((2 ** 255 - 1) / 1e18) * 1e18) ~ 135".
      assert x < 135305999368893231589, "wad_exp overflow"
  
      # `x` is now in the range "(-42, 136) * 1e18". Convert to "(-42, 136) * 2 ** 96" for higher
      # intermediate precision and a binary base. This base conversion is a multiplication with
      # "1e18 / 2 ** 96 = 5 ** 18 / 2 ** 78".
      value = unsafe_div(x << 78, 5 ** 18)
  
      # Reduce the range of `x` to "(-½ ln 2, ½ ln 2) * 2 ** 96" by factoring out powers of two
      # so that "exp(x) = exp(x') * 2 ** k", where `k` is a signer integer. Solving this gives
      # "k = round(x / log(2))" and "x' = x - k * log(2)". Thus, `k` is in the range "[-61, 195]".
      k: int256 = unsafe_add(unsafe_div(value << 96, 54916777467707473351141471128), 2 ** 95) >> 96
      value = unsafe_sub(value, unsafe_mul(k, 54916777467707473351141471128))
  
      # Evaluate using a "(6, 7)"-term rational approximation. Since `p` is monic,
      # we will multiply by a scaling factor later.
      y: int256 = unsafe_add(unsafe_mul(unsafe_add(value, 1346386616545796478920950773328), value) >> 96, 57155421227552351082224309758442)
      p: int256 = unsafe_add(unsafe_mul(unsafe_add(unsafe_mul(unsafe_sub(unsafe_add(y, value), 94201549194550492254356042504812), y) >> 96,\
                             28719021644029726153956944680412240), value), 4385272521454847904659076985693276 << 96)
  
      # We leave `p` in the "2 ** 192" base so that we do not have to scale it up
      # again for the division.
      q: int256 = unsafe_add(unsafe_mul(unsafe_sub(value, 2855989394907223263936484059900), value) >> 96, 50020603652535783019961831881945)
      q = unsafe_sub(unsafe_mul(q, value) >> 96, 533845033583426703283633433725380)
      q = unsafe_add(unsafe_mul(q, value) >> 96, 3604857256930695427073651918091429)
      q = unsafe_sub(unsafe_mul(q, value) >> 96, 14423608567350463180887372962807573)
      q = unsafe_add(unsafe_mul(q, value) >> 96, 26449188498355588339934803723976023)
  
      # The polynomial `q` has no zeros in the range because all its roots are complex.
      # No scaling is required, as `p` is already "2 ** 96" too large. Also,
      # `r` is in the range "(0.09, 0.25) * 2**96" after the division.
      r: int256 = unsafe_div(p, q)
  
      # To finalise the calculation, we have to multiply `r` by:
      #   - the scale factor "s = ~6.031367120",
      #   - the factor "2 ** k" from the range reduction, and
      #   - the factor "1e18 / 2 ** 96" for the base conversion.
      # We do this all at once, with an intermediate result in "2**213" base,
      # so that the final right shift always gives a positive value.
  
      # Note that to circumvent Vyper's safecast feature for the potentially
      # negative parameter value `r`, we first convert `r` to `bytes32` and
      # subsequently to `uint256`. Remember that the EVM default behaviour is
      # to use two's complement representation to handle signed integers.
      return unsafe_mul(convert(convert(r, bytes32), uint256), 3822833074963236453042738258902158003155416615667) >> convert(unsafe_sub(195, k), uint256)
  
  
  # ---------------------------- ERC20 Utils -----------------------------------
  
  @view
  @internal
  def _domain_separator() -> bytes32:
      if chain.id != CACHED_CHAIN_ID:
          return keccak256(
              _abi_encode(
                  EIP712_TYPEHASH,
                  NAME_HASH,
                  VERSION_HASH,
                  chain.id,
                  self,
                  salt,
              )
          )
      return CACHED_DOMAIN_SEPARATOR
  
  
  @internal
  def _transfer(_from: address, _to: address, _value: uint256):
      # # NOTE: vyper does not allow underflows
      # #       so the following subtraction would revert on insufficient balance
      self.balanceOf[_from] -= _value
      self.balanceOf[_to] += _value
  
      log Transfer(_from, _to, _value)
  
  
  @internal
  def _burnFrom(_from: address, _burn_amount: uint256):
  
      self.total_supply -= _burn_amount
      self.balanceOf[_from] -= _burn_amount
      log Transfer(_from, empty(address), _burn_amount)
  
  
  @external
  def transfer(_to : address, _value : uint256) -> bool:
      """
      @dev Transfer token for a specified address
      @param _to The address to transfer to.
      @param _value The amount to be transferred.
      """
      self._transfer(msg.sender, _to, _value)
      return True
  
  
  @external
  def transferFrom(_from : address, _to : address, _value : uint256) -> bool:
      """
       @dev Transfer tokens from one address to another.
       @param _from address The address which you want to send tokens from
       @param _to address The address which you want to transfer to
       @param _value uint256 the amount of tokens to be transferred
      """
      self._transfer(_from, _to, _value)
  
      _allowance: uint256 = self.allowance[_from][msg.sender]
      if _allowance != max_value(uint256):
          _new_allowance: uint256 = _allowance - _value
          self.allowance[_from][msg.sender] = _new_allowance
          log Approval(_from, msg.sender, _new_allowance)
  
      return True
  
  
  @external
  def approve(_spender : address, _value : uint256) -> bool:
      """
      @notice Approve the passed address to transfer the specified amount of
              tokens on behalf of msg.sender
      @dev Beware that changing an allowance via this method brings the risk that
           someone may use both the old and new allowance by unfortunate transaction
           ordering: https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
      @param _spender The address which will transfer the funds
      @param _value The amount of tokens that may be transferred
      @return bool success
      """
      self.allowance[msg.sender][_spender] = _value
  
      log Approval(msg.sender, _spender, _value)
      return True
  
  
  @external
  def permit(
      _owner: address,
      _spender: address,
      _value: uint256,
      _deadline: uint256,
      _v: uint8,
      _r: bytes32,
      _s: bytes32
  ) -> bool:
      """
      @notice Approves spender by owner's signature to expend owner's tokens.
          See https://eips.ethereum.org/EIPS/eip-2612.
      @dev Inspired by https://github.com/yearn/yearn-vaults/blob/main/contracts/Vault.vy#L753-L793
      @dev Supports smart contract wallets which implement ERC1271
          https://eips.ethereum.org/EIPS/eip-1271
      @param _owner The address which is a source of funds and has signed the Permit.
      @param _spender The address which is allowed to spend the funds.
      @param _value The amount of tokens to be spent.
      @param _deadline The timestamp after which the Permit is no longer valid.
      @param _v The bytes[64] of the valid secp256k1 signature of permit by owner
      @param _r The bytes[0:32] of the valid secp256k1 signature of permit by owner
      @param _s The bytes[32:64] of the valid secp256k1 signature of permit by owner
      @return True, if transaction completes successfully
      """
      assert _owner != empty(address)
      assert block.timestamp <= _deadline
  
      nonce: uint256 = self.nonces[_owner]
      digest: bytes32 = keccak256(
          concat(
              b"\x19\x01",
              self._domain_separator(),
              keccak256(_abi_encode(EIP2612_TYPEHASH, _owner, _spender, _value, nonce, _deadline))
          )
      )
  
      if _owner.is_contract:
          sig: Bytes[65] = concat(_abi_encode(_r, _s), slice(convert(_v, bytes32), 31, 1))
          # reentrancy not a concern since this is a staticcall
          assert ERC1271(_owner).isValidSignature(digest, sig) == ERC1271_MAGIC_VAL
      else:
          assert ecrecover(digest, convert(_v, uint256), convert(_r, uint256), convert(_s, uint256)) == _owner
  
      self.allowance[_owner][_spender] = _value
      self.nonces[_owner] = unsafe_add(nonce, 1)
  
      log Approval(_owner, _spender, _value)
      return True
  
  
  @view
  @external
  def DOMAIN_SEPARATOR() -> bytes32:
      """
      @notice EIP712 domain separator.
      @return bytes32 Domain Separator set for the current chain.
      """
      return self._domain_separator()
  
  
  # ------------------------- AMM View Functions -------------------------------
  
  
  @view
  @external
  def get_dx(i: int128, j: int128, dy: uint256) -> uint256:
      """
      @notice Calculate the current input dx given output dy
      @dev Index values can be found via the `coins` public getter method
      @param i Index value for the coin to send
      @param j Index value of the coin to receive
      @param dy Amount of `j` being received after exchange
      @return Amount of `i` predicted
      """
      return StableSwapViews(factory.views_implementation()).get_dx(i, j, dy, self)
  
  
  @view
  @external
  def get_dy(i: int128, j: int128, dx: uint256) -> uint256:
      """
      @notice Calculate the current output dy given input dx
      @dev Index values can be found via the `coins` public getter method
      @param i Index value for the coin to send
      @param j Index value of the coin to receive
      @param dx Amount of `i` being exchanged
      @return Amount of `j` predicted
      """
      return StableSwapViews(factory.views_implementation()).get_dy(i, j, dx, self)
  
  
  @view
  @external
  def calc_withdraw_one_coin(_burn_amount: uint256, i: int128) -> uint256:
      """
      @notice Calculate the amount received when withdrawing a single coin
      @param _burn_amount Amount of LP tokens to burn in the withdrawal
      @param i Index value of the coin to withdraw
      @return Amount of coin received
      """
      return self._calc_withdraw_one_coin(_burn_amount, i)[0]
  
  
  @view
  @external
  @nonreentrant('lock')
  def totalSupply() -> uint256:
      """
      @notice The total supply of pool LP tokens
      @return self.total_supply, 18 decimals.
      """
      return self.total_supply
  
  
  @view
  @external
  @nonreentrant('lock')
  def get_virtual_price() -> uint256:
      """
      @notice The current virtual price of the pool LP token
      @dev Useful for calculating profits.
           The method may be vulnerable to donation-style attacks if implementation
           contains rebasing tokens. For integrators, caution is advised.
      @return LP token virtual price normalized to 1e18
      """
      amp: uint256 = self._A()
      xp: DynArray[uint256, MAX_COINS] = self._xp_mem(
          self._stored_rates(), self._balances()
      )
      D: uint256 = self.get_D(xp, amp)
      # D is in the units similar to DAI (e.g. converted to precision 1e18)
      # When balanced, D = n * x_u - total virtual value of the portfolio
      return D * PRECISION / self.total_supply
  
  
  @view
  @external
  def calc_token_amount(
      _amounts: DynArray[uint256, MAX_COINS],
      _is_deposit: bool
  ) -> uint256:
      """
      @notice Calculate addition or reduction in token supply from a deposit or withdrawal
      @param _amounts Amount of each coin being deposited
      @param _is_deposit set True for deposits, False for withdrawals
      @return Expected amount of LP tokens received
      """
      return StableSwapViews(factory.views_implementation()).calc_token_amount(_amounts, _is_deposit, self)
  
  
  @view
  @external
  def A() -> uint256:
      return unsafe_div(self._A(), A_PRECISION)
  
  
  @view
  @external
  def A_precise() -> uint256:
      return self._A()
  
  
  @view
  @external
  def balances(i: uint256) -> uint256:
      """
      @notice Get the current balance of a coin within the
              pool, less the accrued admin fees
      @param i Index value for the coin to query balance of
      @return Token balance
      """
      return self._balances()[i]
  
  
  @view
  @external
  def get_balances() -> DynArray[uint256, MAX_COINS]:
      return self._balances()
  
  
  @view
  @external
  def stored_rates() -> DynArray[uint256, MAX_COINS]:
      return self._stored_rates()
  
  
  @view
  @external
  def dynamic_fee(i: int128, j: int128) -> uint256:
      """
      @notice Return the fee for swapping between `i` and `j`
      @param i Index value for the coin to send
      @param j Index value of the coin to receive
      @return Swap fee expressed as an integer with 1e10 precision
      """
      return StableSwapViews(factory.views_implementation()).dynamic_fee(i, j, self)
  
  
  # --------------------------- AMM Admin Functions ----------------------------
  
  
  @external
  def ramp_A(_future_A: uint256, _future_time: uint256):
      assert msg.sender == factory.admin()  # dev: only owner
      assert block.timestamp >= self.initial_A_time + MIN_RAMP_TIME
      assert _future_time >= block.timestamp + MIN_RAMP_TIME  # dev: insufficient time
  
      _initial_A: uint256 = self._A()
      _future_A_p: uint256 = _future_A * A_PRECISION
  
      assert _future_A > 0 and _future_A < MAX_A
      if _future_A_p < _initial_A:
          assert _future_A_p * MAX_A_CHANGE >= _initial_A
      else:
          assert _future_A_p <= _initial_A * MAX_A_CHANGE
  
      self.initial_A = _initial_A
      self.future_A = _future_A_p
      self.initial_A_time = block.timestamp
      self.future_A_time = _future_time
  
      log RampA(_initial_A, _future_A_p, block.timestamp, _future_time)
  
  
  @external
  def stop_ramp_A():
      assert msg.sender == factory.admin()  # dev: only owner
  
      current_A: uint256 = self._A()
      self.initial_A = current_A
      self.future_A = current_A
      self.initial_A_time = block.timestamp
      self.future_A_time = block.timestamp
      # now (block.timestamp < t1) is always False, so we return saved A
  
      log StopRampA(current_A, block.timestamp)
  
  
  @external
  def set_new_fee(_new_fee: uint256, _new_offpeg_fee_multiplier: uint256):
  
      assert msg.sender == factory.admin()
  
      # set new fee:
      assert _new_fee <= MAX_FEE
      self.fee = _new_fee
  
      # set new offpeg_fee_multiplier:
      assert _new_offpeg_fee_multiplier * _new_fee <= MAX_FEE * FEE_DENOMINATOR  # dev: offpeg multiplier exceeds maximum
      self.offpeg_fee_multiplier = _new_offpeg_fee_multiplier
  
      log ApplyNewFee(_new_fee, _new_offpeg_fee_multiplier)
  
  
  @external
  def set_ma_exp_time(_ma_exp_time: uint256, _D_ma_time: uint256):
      """
      @notice Set the moving average window of the price oracles.
      @param _ma_exp_time Moving average window for the price oracle. It is time_in_seconds / ln(2).
      @param _D_ma_time Moving average window for the D oracle. It is time_in_seconds / ln(2).
      """
      assert msg.sender == factory.admin()  # dev: only owner
      assert unsafe_mul(_ma_exp_time, _D_ma_time) > 0  # dev: 0 in input values
  
      self.ma_exp_time = _ma_exp_time
      self.D_ma_time = _D_ma_time
  
      log SetNewMATime(_ma_exp_time, _D_ma_time)