Contract

# @version 0.2.15
"""
@title StableSwap
@author Curve.Fi
@license Copyright (c) Curve.Fi, 2020-2021 - all rights reserved
@notice 2 coin pool implementation with no lending
@dev ERC20 support for return True/revert, return True/False, return None
     Support for positive-rebasing and fee-on-transfer tokens
"""

from vyper.interfaces import ERC20

interface Factory:
    def convert_fees() -> bool: nonpayable
    def get_fee_receiver(_pool: address) -> address: view
    def admin() -> address: view


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 AddLiquidity:
    provider: indexed(address)
    token_amounts: uint256[N_COINS]
    fees: uint256[N_COINS]
    invariant: uint256
    token_supply: uint256

event RemoveLiquidity:
    provider: indexed(address)
    token_amounts: uint256[N_COINS]
    fees: uint256[N_COINS]
    token_supply: uint256

event RemoveLiquidityOne:
    provider: indexed(address)
    token_amount: uint256
    coin_amount: uint256
    token_supply: uint256

event RemoveLiquidityImbalance:
    provider: indexed(address)
    token_amounts: uint256[N_COINS]
    fees: uint256[N_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


N_COINS: constant(int128) = 2
PRECISION: constant(uint256) = 10 ** 18

FEE_DENOMINATOR: constant(uint256) = 10 ** 10
ADMIN_FEE: constant(uint256) = 5000000000

A_PRECISION: constant(uint256) = 100
MAX_A: constant(uint256) = 10 ** 6
MAX_A_CHANGE: constant(uint256) = 10
MIN_RAMP_TIME: constant(uint256) = 86400

factory: address

coins: public(address[N_COINS])
admin_balances: public(uint256[N_COINS])
fee: public(uint256)  # fee * 1e10

initial_A: public(uint256)
future_A: public(uint256)
initial_A_time: public(uint256)
future_A_time: public(uint256)

rate_multipliers: uint256[N_COINS]

name: public(String[64])
symbol: public(String[32])

balanceOf: public(HashMap[address, uint256])
allowance: public(HashMap[address, HashMap[address, uint256]])
totalSupply: public(uint256)


@external
def __init__():
    # we do this to prevent the implementation contract from being used as a pool
    self.fee = 31337


@external
def initialize(
    _name: String[32],
    _symbol: String[10],
    _coins: address[4],
    _rate_multipliers: uint256[4],
    _A: uint256,
    _fee: uint256,
):
    """
    @notice Contract constructor
    @param _name Name of the new pool
    @param _symbol Token symbol
    @param _coins List of all ERC20 conract addresses of coins
    @param _rate_multipliers List of number of decimals in coins
    @param _A Amplification coefficient multiplied by n ** (n - 1)
    @param _fee Fee to charge for exchanges
    """
    # check if fee was already set to prevent initializing contract twice
    assert self.fee == 0

    for i in range(N_COINS):
        coin: address = _coins[i]
        if coin == ZERO_ADDRESS:
            break
        self.coins[i] = coin
        self.rate_multipliers[i] = _rate_multipliers[i]

    A: uint256 = _A * A_PRECISION
    self.initial_A = A
    self.future_A = A
    self.fee = _fee
    self.factory = msg.sender

    self.name = concat("Curve.fi Factory Plain Pool: ", _name)
    self.symbol = concat(_symbol, "-f")

    # fire a transfer event so block explorers identify the contract as an ERC20
    log Transfer(ZERO_ADDRESS, self, 0)


### ERC20 Functionality ###

@view
@external
def decimals() -> uint256:
    """
    @notice Get the number of decimals for this token
    @dev Implemented as a view method to reduce gas costs
    @return uint256 decimal places
    """
    return 18


@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)


@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_UINT256:
        self.allowance[_from][msg.sender] = _allowance - _value

    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


### StableSwap Functionality ###

@view
@internal
def _balances() -> uint256[N_COINS]:
    result: uint256[N_COINS] = empty(uint256[N_COINS])
    for i in range(N_COINS):
        result[i] = ERC20(self.coins[i]).balanceOf(self) - self.admin_balances[i]
    return result


@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() -> uint256[N_COINS]:
    return self._balances()


@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 + (A1 - A0) * (block.timestamp - t0) / (t1 - t0)
        else:
            return A0 - (A0 - A1) * (block.timestamp - t0) / (t1 - t0)

    else:  # when t1 == 0 or block.timestamp >= t1
        return A1


@view
@external
def admin_fee() -> uint256:
    return ADMIN_FEE


@view
@external
def A() -> uint256:
    return self._A() / A_PRECISION


@view
@external
def A_precise() -> uint256:
    return self._A()


@pure
@internal
def _xp_mem(_rates: uint256[N_COINS], _balances: uint256[N_COINS]) -> uint256[N_COINS]:
    result: uint256[N_COINS] = empty(uint256[N_COINS])
    for i in range(N_COINS):
        result[i] = _rates[i] * _balances[i] / PRECISION
    return result


@pure
@internal
def get_D(_xp: uint256[N_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 * D / _xp[0] * D / _xp[1] / (N_COINS)**2
        Dprev: uint256 = D
        D = (Ann * S / A_PRECISION + D_P * N_COINS) * D / ((Ann - A_PRECISION) * D / A_PRECISION + (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


@view
@internal
def get_D_mem(_rates: uint256[N_COINS], _balances: uint256[N_COINS], _amp: uint256) -> uint256:
    xp: uint256[N_COINS] = self._xp_mem(_rates, _balances)
    return self.get_D(xp, _amp)


@view
@external
def get_virtual_price() -> uint256:
    """
    @notice The current virtual price of the pool LP token
    @dev Useful for calculating profits
    @return LP token virtual price normalized to 1e18
    """
    amp: uint256 = self._A()
    balances: uint256[N_COINS] = self._balances()
    xp: uint256[N_COINS] = self._xp_mem(self.rate_multipliers, 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.totalSupply


@view
@external
def calc_token_amount(_amounts: uint256[N_COINS], _is_deposit: bool) -> uint256:
    """
    @notice Calculate addition or reduction in token supply from a deposit or withdrawal
    @dev This calculation accounts for slippage, but not fees.
         Needed to prevent front-running, not for precise calculations!
    @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
    """
    amp: uint256 = self._A()
    balances: uint256[N_COINS] = self._balances()

    D0: uint256 = self.get_D_mem(self.rate_multipliers, balances, amp)
    for i in range(N_COINS):
        amount: uint256 = _amounts[i]
        if _is_deposit:
            balances[i] += amount
        else:
            balances[i] -= amount
    D1: uint256 = self.get_D_mem(self.rate_multipliers, balances, amp)
    diff: uint256 = 0
    if _is_deposit:
        diff = D1 - D0
    else:
        diff = D0 - D1
    return diff * self.totalSupply / D0


@external
@nonreentrant('lock')
def add_liquidity(
    _amounts: uint256[N_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
    """
    amp: uint256 = self._A()
    old_balances: uint256[N_COINS] = self._balances()
    rates: uint256[N_COINS] = self.rate_multipliers

    # Initial invariant
    D0: uint256 = self.get_D_mem(rates, old_balances, amp)

    total_supply: uint256 = self.totalSupply
    new_balances: uint256[N_COINS] = old_balances
    for i in range(N_COINS):
        amount: uint256 = _amounts[i]
        if amount > 0:
            coin: address = self.coins[i]
            initial: uint256 = ERC20(coin).balanceOf(self)
            response: Bytes[32] = raw_call(
                coin,
                concat(
                    method_id("transferFrom(address,address,uint256)"),
                    convert(msg.sender, bytes32),
                    convert(self, bytes32),
                    convert(amount, bytes32),
                ),
                max_outsize=32,
            )
            if len(response) > 0:
                assert convert(response, bool)  # dev: failed transfer
            new_balances[i] += ERC20(coin).balanceOf(self) - initial
        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: uint256[N_COINS] = empty(uint256[N_COINS])
    mint_amount: uint256 = 0
    if total_supply > 0:
        # Only account for fees if we are not the first to deposit
        base_fee: uint256 = self.fee * N_COINS / (4 * (N_COINS - 1))
        for i in range(N_COINS):
            ideal_balance: uint256 = D1 * old_balances[i] / D0
            difference: uint256 = 0
            new_balance: uint256 = new_balances[i]
            if ideal_balance > new_balance:
                difference = ideal_balance - new_balance
            else:
                difference = new_balance - ideal_balance
            fees[i] = base_fee * difference / FEE_DENOMINATOR
            self.admin_balances[i] += fees[i] * ADMIN_FEE / FEE_DENOMINATOR
            new_balances[i] -= fees[i]
        D2: uint256 = self.get_D_mem(rates, new_balances, amp)
        mint_amount = total_supply * (D2 - D0) / D0
    else:
        mint_amount = D1  # Take the dust if there was any

    assert mint_amount >= _min_mint_amount, "Slippage screwed you"

    # Mint pool tokens
    total_supply += mint_amount
    self.balanceOf[_receiver] += mint_amount
    self.totalSupply = total_supply
    log Transfer(ZERO_ADDRESS, _receiver, mint_amount)

    log AddLiquidity(msg.sender, _amounts, fees, D1, total_supply)

    return mint_amount


@view
@internal
def get_y(i: int128, j: int128, x: uint256, xp: uint256[N_COINS]) -> 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  # dev: j above N_COINS

    # should be unreachable, but good for safety
    assert i >= 0
    assert i < N_COINS

    amp: uint256 = self._A()
    D: uint256 = self.get_D(xp, amp)
    S_: uint256 = 0
    _x: uint256 = 0
    y_prev: uint256 = 0
    c: uint256 = D
    Ann: uint256 = amp * N_COINS

    for _i in range(N_COINS):
        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


@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 valie of the coin to recieve
    @param dx Amount of `i` being exchanged
    @return Amount of `j` predicted
    """
    rates: uint256[N_COINS] = self.rate_multipliers
    xp: uint256[N_COINS] = self._xp_mem(rates, self._balances())

    x: uint256 = xp[i] + (dx * rates[i] / PRECISION)
    y: uint256 = self.get_y(i, j, x, xp)
    dy: uint256 = xp[j] - y - 1
    fee: uint256 = self.fee * dy / FEE_DENOMINATOR
    return (dy - fee) * PRECISION / rates[j]


@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 valie of the coin to recieve
    @param _dx Amount of `i` being exchanged
    @param _min_dy Minimum amount of `j` to receive
    @return Actual amount of `j` received
    """
    rates: uint256[N_COINS] = self.rate_multipliers
    old_balances: uint256[N_COINS] = self._balances()
    xp: uint256[N_COINS] = self._xp_mem(rates, old_balances)

    coin: address = self.coins[i]
    dx: uint256 = ERC20(coin).balanceOf(self)
    response: Bytes[32] = raw_call(
        coin,
        concat(
            method_id("transferFrom(address,address,uint256)"),
            convert(msg.sender, bytes32),
            convert(self, bytes32),
            convert(_dx, bytes32),
        ),
        max_outsize=32,
    )
    if len(response) > 0:
        assert convert(response, bool)
    dx = ERC20(coin).balanceOf(self) - dx

    x: uint256 = xp[i] + dx * rates[i] / PRECISION
    y: uint256 = self.get_y(i, j, x, xp)

    dy: uint256 = xp[j] - y - 1  # -1 just in case there were some rounding errors
    dy_fee: uint256 = dy * self.fee / FEE_DENOMINATOR

    # Convert all to real units
    dy = (dy - dy_fee) * PRECISION / rates[j]
    assert dy >= _min_dy, "Exchange resulted in fewer coins than expected"

    self.admin_balances[j] += (dy_fee * ADMIN_FEE / FEE_DENOMINATOR) * PRECISION / rates[j]

    response = raw_call(
        self.coins[j],
        concat(
            method_id("transfer(address,uint256)"),
            convert(_receiver, bytes32),
            convert(dy, bytes32),
        ),
        max_outsize=32,
    )
    if len(response) > 0:
        assert convert(response, bool)

    log TokenExchange(msg.sender, i, _dx, j, dy)

    return dy


@external
@nonreentrant('lock')
def remove_liquidity(
    _burn_amount: uint256,
    _min_amounts: uint256[N_COINS],
    _receiver: address = msg.sender
) -> uint256[N_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.totalSupply
    amounts: uint256[N_COINS] = empty(uint256[N_COINS])
    balances: uint256[N_COINS] = self._balances()

    for i in range(N_COINS):
        value: uint256 = balances[i] * _burn_amount / total_supply
        assert value >= _min_amounts[i], "Withdrawal resulted in fewer coins than expected"
        amounts[i] = value

        response: Bytes[32] = raw_call(
            self.coins[i],
            concat(
                method_id("transfer(address,uint256)"),
                convert(_receiver, bytes32),
                convert(value, bytes32),
            ),
            max_outsize=32,
        )
        if len(response) > 0:
            assert convert(response, bool)

    total_supply -= _burn_amount
    self.balanceOf[msg.sender] -= _burn_amount
    self.totalSupply = total_supply
    log Transfer(msg.sender, ZERO_ADDRESS, _burn_amount)

    log RemoveLiquidity(msg.sender, amounts, empty(uint256[N_COINS]), total_supply)

    return amounts


@external
@nonreentrant('lock')
def remove_liquidity_imbalance(
    _amounts: uint256[N_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()
    old_balances: uint256[N_COINS] = self._balances()
    rates: uint256[N_COINS] = self.rate_multipliers
    D0: uint256 = self.get_D_mem(rates, old_balances, amp)

    new_balances: uint256[N_COINS] = old_balances
    for i in range(N_COINS):
        amount: uint256 = _amounts[i]
        if amount != 0:
            new_balances[i] -= amount
            response: Bytes[32] = raw_call(
                self.coins[i],
                concat(
                    method_id("transfer(address,uint256)"),
                    convert(_receiver, bytes32),
                    convert(amount, bytes32),
                ),
                max_outsize=32,
            )
            if len(response) > 0:
                assert convert(response, bool)
    D1: uint256 = self.get_D_mem(rates, new_balances, amp)

    fees: uint256[N_COINS] = empty(uint256[N_COINS])
    base_fee: uint256 = self.fee * N_COINS / (4 * (N_COINS - 1))
    for i in range(N_COINS):
        ideal_balance: uint256 = D1 * old_balances[i] / D0
        difference: uint256 = 0
        new_balance: uint256 = new_balances[i]
        if ideal_balance > new_balance:
            difference = ideal_balance - new_balance
        else:
            difference = new_balance - ideal_balance
        fees[i] = base_fee * difference / FEE_DENOMINATOR
        self.admin_balances[i] += fees[i] * ADMIN_FEE / FEE_DENOMINATOR
        new_balances[i] -= fees[i]
    D2: uint256 = self.get_D_mem(rates, new_balances, amp)

    total_supply: uint256 = self.totalSupply
    burn_amount: uint256 = ((D0 - D2) * total_supply / D0) + 1
    assert burn_amount > 1  # dev: zero tokens burned
    assert burn_amount <= _max_burn_amount, "Slippage screwed you"

    total_supply -= burn_amount
    self.totalSupply = total_supply
    self.balanceOf[msg.sender] -= burn_amount
    log Transfer(msg.sender, ZERO_ADDRESS, burn_amount)
    log RemoveLiquidityImbalance(msg.sender, _amounts, fees, D1, total_supply)

    return burn_amount


@pure
@internal
def get_y_D(A: uint256, i: int128, xp: uint256[N_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  # 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(N_COINS):
        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 _calc_withdraw_one_coin(_burn_amount: uint256, i: int128) -> uint256[2]:
    # First, need to calculate
    # * Get current D
    # * Solve Eqn against y_i for D - _token_amount
    amp: uint256 = self._A()
    rates: uint256[N_COINS] = self.rate_multipliers
    xp: uint256[N_COINS] = self._xp_mem(rates, self._balances())
    D0: uint256 = self.get_D(xp, amp)

    total_supply: uint256 = self.totalSupply
    D1: uint256 = D0 - _burn_amount * D0 / total_supply
    new_y: uint256 = self.get_y_D(amp, i, xp, D1)

    base_fee: uint256 = self.fee * N_COINS / (4 * (N_COINS - 1))
    xp_reduced: uint256[N_COINS] = empty(uint256[N_COINS])

    for j in range(N_COINS):
        dx_expected: uint256 = 0
        xp_j: uint256 = xp[j]
        if j == i:
            dx_expected = xp_j * D1 / D0 - new_y
        else:
            dx_expected = xp_j - xp_j * D1 / D0
        xp_reduced[j] = xp_j - base_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 = (dy - 1) * PRECISION / rates[i]  # Withdraw less to account for rounding errors

    return [dy, dy_0 - dy]


@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]


@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
    """
    dy: uint256[2] = self._calc_withdraw_one_coin(_burn_amount, i)
    assert dy[0] >= _min_received, "Not enough coins removed"

    self.admin_balances[i] += dy[1] * ADMIN_FEE / FEE_DENOMINATOR
    total_supply: uint256 = self.totalSupply - _burn_amount
    self.totalSupply = total_supply
    self.balanceOf[msg.sender] -= _burn_amount
    log Transfer(msg.sender, ZERO_ADDRESS, _burn_amount)

    response: Bytes[32] = raw_call(
        self.coins[i],
        concat(
            method_id("transfer(address,uint256)"),
            convert(_receiver, bytes32),
            convert(dy[0], bytes32),
        ),
        max_outsize=32,
    )
    if len(response) > 0:
        assert convert(response, bool)

    log RemoveLiquidityOne(msg.sender, _burn_amount, dy[0], total_supply)

    return dy[0]


@external
def ramp_A(_future_A: uint256, _future_time: uint256):
    assert msg.sender == Factory(self.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(self.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 withdraw_admin_fees():
    receiver: address = Factory(self.factory).get_fee_receiver(self)

    for i in range(N_COINS):
        amount: uint256 = self.admin_balances[i]
        if amount != 0:
            coin: address = self.coins[i]
            raw_call(
                coin,
                concat(
                    method_id("transfer(address,uint256)"),
                    convert(receiver, bytes32),
                    convert(amount, bytes32)
                )
            )
            self.admin_balances[i] = 0

[{"name":"Transfer","inputs":[{"name":"sender","type":"address","indexed":true},{"name":"receiver","type":"address","indexed":true},{"name":"value","type":"uint256","indexed":false}],"anonymous":false,"type":"event"},{"name":"Approval","inputs":[{"name":"owner","type":"address","indexed":true},{"name":"spender","type":"address","indexed":true},{"name":"value","type":"uint256","indexed":false}],"anonymous":false,"type":"event"},{"name":"TokenExchange","inputs":[{"name":"buyer","type":"address","indexed":true},{"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","indexed":false}],"anonymous":false,"type":"event"},{"name":"AddLiquidity","inputs":[{"name":"provider","type":"address","indexed":true},{"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","indexed":false}],"anonymous":false,"type":"event"},{"name":"RemoveLiquidity","inputs":[{"name":"provider","type":"address","indexed":true},{"name":"token_amounts","type":"uint256[2]","indexed":false},{"name":"fees","type":"uint256[2]","indexed":false},{"name":"token_supply","type":"uint256","indexed":false}],"anonymous":false,"type":"event"},{"name":"RemoveLiquidityOne","inputs":[{"name":"provider","type":"address","indexed":true},{"name":"token_amount","type":"uint256","indexed":false},{"name":"coin_amount","type":"uint256","indexed":false},{"name":"token_supply","type":"uint256","indexed":false}],"anonymous":false,"type":"event"},{"name":"RemoveLiquidityImbalance","inputs":[{"name":"provider","type":"address","indexed":true},{"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","indexed":false}],"anonymous":false,"type":"event"},{"name":"RampA","inputs":[{"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","indexed":false}],"anonymous":false,"type":"event"},{"name":"StopRampA","inputs":[{"name":"A","type":"uint256","indexed":false},{"name":"t","type":"uint256","indexed":false}],"anonymous":false,"type":"event"},{"stateMutability":"nonpayable","type":"constructor","inputs":[],"outputs":[]},{"stateMutability":"nonpayable","type":"function","name":"initialize","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"}],"outputs":[],"gas":471502},{"stateMutability":"view","type":"function","name":"decimals","inputs":[],"outputs":[{"name":"","type":"uint256"}],"gas":318},{"stateMutability":"nonpayable","type":"function","name":"transfer","inputs":[{"name":"_to","type":"address"},{"name":"_value","type":"uint256"}],"outputs":[{"name":"","type":"bool"}],"gas":77977},{"stateMutability":"nonpayable","type":"function","name":"transferFrom","inputs":[{"name":"_from","type":"address"},{"name":"_to","type":"address"},{"name":"_value","type":"uint256"}],"outputs":[{"name":"","type":"bool"}],"gas":115912},{"stateMutability":"nonpayable","type":"function","name":"approve","inputs":[{"name":"_spender","type":"address"},{"name":"_value","type":"uint256"}],"outputs":[{"name":"","type":"bool"}],"gas":37851},{"stateMutability":"view","type":"function","name":"balances","inputs":[{"name":"i","type":"uint256"}],"outputs":[{"name":"","type":"uint256"}],"gas":15163},{"stateMutability":"view","type":"function","name":"get_balances","inputs":[],"outputs":[{"name":"","type":"uint256[2]"}],"gas":15139},{"stateMutability":"view","type":"function","name":"admin_fee","inputs":[],"outputs":[{"name":"","type":"uint256"}],"gas":498},{"stateMutability":"view","type":"function","name":"A","inputs":[],"outputs":[{"name":"","type":"uint256"}],"gas":10824},{"stateMutability":"view","type":"function","name":"A_precise","inputs":[],"outputs":[{"name":"","type":"uint256"}],"gas":10786},{"stateMutability":"view","type":"function","name":"get_virtual_price","inputs":[],"outputs":[{"name":"","type":"uint256"}],"gas":859368},{"stateMutability":"view","type":"function","name":"calc_token_amount","inputs":[{"name":"_amounts","type":"uint256[2]"},{"name":"_is_deposit","type":"bool"}],"outputs":[{"name":"","type":"uint256"}],"gas":3347181},{"stateMutability":"nonpayable","type":"function","name":"add_liquidity","inputs":[{"name":"_amounts","type":"uint256[2]"},{"name":"_min_mint_amount","type":"uint256"}],"outputs":[{"name":"","type":"uint256"}]},{"stateMutability":"nonpayable","type":"function","name":"add_liquidity","inputs":[{"name":"_amounts","type":"uint256[2]"},{"name":"_min_mint_amount","type":"uint256"},{"name":"_receiver","type":"address"}],"outputs":[{"name":"","type":"uint256"}]},{"stateMutability":"view","type":"function","name":"get_dy","inputs":[{"name":"i","type":"int128"},{"name":"j","type":"int128"},{"name":"dx","type":"uint256"}],"outputs":[{"name":"","type":"uint256"}],"gas":2128404},{"stateMutability":"nonpayable","type":"function","name":"exchange","inputs":[{"name":"i","type":"int128"},{"name":"j","type":"int128"},{"name":"_dx","type":"uint256"},{"name":"_min_dy","type":"uint256"}],"outputs":[{"name":"","type":"uint256"}]},{"stateMutability":"nonpayable","type":"function","name":"exchange","inputs":[{"name":"i","type":"int128"},{"name":"j","type":"int128"},{"name":"_dx","type":"uint256"},{"name":"_min_dy","type":"uint256"},{"name":"_receiver","type":"address"}],"outputs":[{"name":"","type":"uint256"}]},{"stateMutability":"nonpayable","type":"function","name":"remove_liquidity","inputs":[{"name":"_burn_amount","type":"uint256"},{"name":"_min_amounts","type":"uint256[2]"}],"outputs":[{"name":"","type":"uint256[2]"}]},{"stateMutability":"nonpayable","type":"function","name":"remove_liquidity","inputs":[{"name":"_burn_amount","type":"uint256"},{"name":"_min_amounts","type":"uint256[2]"},{"name":"_receiver","type":"address"}],"outputs":[{"name":"","type":"uint256[2]"}]},{"stateMutability":"nonpayable","type":"function","name":"remove_liquidity_imbalance","inputs":[{"name":"_amounts","type":"uint256[2]"},{"name":"_max_burn_amount","type":"uint256"}],"outputs":[{"name":"","type":"uint256"}]},{"stateMutability":"nonpayable","type":"function","name":"remove_liquidity_imbalance","inputs":[{"name":"_amounts","type":"uint256[2]"},{"name":"_max_burn_amount","type":"uint256"},{"name":"_receiver","type":"address"}],"outputs":[{"name":"","type":"uint256"}]},{"stateMutability":"view","type":"function","name":"calc_withdraw_one_coin","inputs":[{"name":"_burn_amount","type":"uint256"},{"name":"i","type":"int128"}],"outputs":[{"name":"","type":"uint256"}],"gas":1130},{"stateMutability":"nonpayable","type":"function","name":"remove_liquidity_one_coin","inputs":[{"name":"_burn_amount","type":"uint256"},{"name":"i","type":"int128"},{"name":"_min_received","type":"uint256"}],"outputs":[{"name":"","type":"uint256"}]},{"stateMutability":"nonpayable","type":"function","name":"remove_liquidity_one_coin","inputs":[{"name":"_burn_amount","type":"uint256"},{"name":"i","type":"int128"},{"name":"_min_received","type":"uint256"},{"name":"_receiver","type":"address"}],"outputs":[{"name":"","type":"uint256"}]},{"stateMutability":"nonpayable","type":"function","name":"ramp_A","inputs":[{"name":"_future_A","type":"uint256"},{"name":"_future_time","type":"uint256"}],"outputs":[],"gas":162161},{"stateMutability":"nonpayable","type":"function","name":"stop_ramp_A","inputs":[],"outputs":[],"gas":157625},{"stateMutability":"nonpayable","type":"function","name":"withdraw_admin_fees","inputs":[],"outputs":[],"gas":68306},{"stateMutability":"view","type":"function","name":"coins","inputs":[{"name":"arg0","type":"uint256"}],"outputs":[{"name":"","type":"address"}],"gas":3093},{"stateMutability":"view","type":"function","name":"admin_balances","inputs":[{"name":"arg0","type":"uint256"}],"outputs":[{"name":"","type":"uint256"}],"gas":3123},{"stateMutability":"view","type":"function","name":"fee","inputs":[],"outputs":[{"name":"","type":"uint256"}],"gas":3108},{"stateMutability":"view","type":"function","name":"initial_A","inputs":[],"outputs":[{"name":"","type":"uint256"}],"gas":3138},{"stateMutability":"view","type":"function","name":"future_A","inputs":[],"outputs":[{"name":"","type":"uint256"}],"gas":3168},{"stateMutability":"view","type":"function","name":"initial_A_time","inputs":[],"outputs":[{"name":"","type":"uint256"}],"gas":3198},{"stateMutability":"view","type":"function","name":"future_A_time","inputs":[],"outputs":[{"name":"","type":"uint256"}],"gas":3228},{"stateMutability":"view","type":"function","name":"name","inputs":[],"outputs":[{"name":"","type":"string"}],"gas":13488},{"stateMutability":"view","type":"function","name":"symbol","inputs":[],"outputs":[{"name":"","type":"string"}],"gas":11241},{"stateMutability":"view","type":"function","name":"balanceOf","inputs":[{"name":"arg0","type":"address"}],"outputs":[{"name":"","type":"uint256"}],"gas":3533},{"stateMutability":"view","type":"function","name":"allowance","inputs":[{"name":"arg0","type":"address"},{"name":"arg1","type":"address"}],"outputs":[{"name":"","type":"uint256"}],"gas":3778},{"stateMutability":"view","type":"function","name":"totalSupply","inputs":[],"outputs":[{"name":"","type":"uint256"}],"gas":3378}]