Plain Pools

Plain pools are liquidity exchange contracts which contain at least 2 and up to 8 coins.

Contract Source & Deployment

Source code available on Github.

The deployment of plain pools is permissionless and can be done via the deploy_plain_pool function within the StableSwap-NG Factory.

Examples

The examples following each code block of the corresponding functions provide a basic illustration of input/output values. When using the function in production, ensure not to set _min_dy, _min_amount, etc., to zero or other arbitrary numbers. Otherwise, MEV bots may frontrun or sandwich your transaction, leading to a potential loss of funds.

The examples are based on the crvUSD-USDV pool: 0xe1e77de32fb301ce55871ba095fd6b8e5d9abad8

Oracle Methods Documentation

Comprehensive documentation for Oracle Methods is available on a dedicated page, accessible here.

The AMM contract utilizes two internal functions to transfer tokens/coins in and out of the pool and then accordingly update stored_balances:

_transfer_in()

_transfer_in(coin_idx: int128, dx: uint256, sender: address, expect_optimistic_transfer: bool) -> uint256:

expect_optimistic_transfer is relevant when using the exchange_received() function.

Input	Type	Description
`coin_idx`	`int128`	Index value of the token to transfer in.
`dx`	`uint256`	Amount to transfer in.
`sender`	`address`	Address to transfer coins from.
`expect_optimistic_transfer`	`bool`	`True` if the contract expects an optimistic coin transfer.

stored_balances: DynArray[uint256, MAX_COINS]

@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 dy amount of `_coin` to transfer out of 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

_transfer_out()

_transfer_out(_coin_idx: int128, _amount: uint256, receiver: address):

Input	Type	Description
`coin_idx`	`int128`	Index value of the token to transfer out.
`_amount`	`uint256`	Amount to transfer out.
`receiver`	`address`	Address to send the tokens to.

stored_balances: DynArray[uint256, MAX_COINS]

@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`, `_exchange` and `_withdraw_admin_fees` 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
    """

    # 'gulp' coin balance of the pool to stored_balances here to account for
    # donations etc.
    coin_balance: uint256 = ERC20(coins[_coin_idx]).balanceOf(self)

    # ------------------------- Handle Transfers -----------------------------

    assert ERC20(coins[_coin_idx]).transfer(
        receiver, _amount, default_return_value=True
    )

    # ----------------------- Update Stored Balances -------------------------

    self.stored_balances[_coin_idx] = coin_balance - _amount

Exchange Methods¶

Two functions for token exchanges:

The regular exchange function.
A novel exchange_received function that executes a token exchange based on the internal balances of the pool.

There is no exchange_underlying function, as this implementation is for plain pools and not for metapools, meaning no tokens are paired against other LP tokens.

`exchange`¶

StableSwap.exchange(i: int128, j: int128, _dx: uint256, _min_dy: uint256, _receiver: address = msg.sender) -> uint256:

Function to exchange _dx amount of coin i for coin j and receive a minimum amount of _min_dy.

Returns: amount of output coin received (uint256).

Emits: TokenExchange

Input	Type	Description
`i`	`int128`	Index value of input coin.
`j`	`int128`	Index value of output coin.
`_dx`	`uint256`	Amount of coin `i` being exchanged.
`_min_dy`	`uint256`	Minimum amount of coin `j` to receive.
`_receiver`	`address`	Receiver of the output tokens; defaults to `msg.sender`.

Source code

event TokenExchange:
    buyer: indexed(address)
    sold_id: int128
    tokens_sold: uint256
    bought_id: int128
    tokens_bought: uint256

@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 recieve
    @param _dx Amount of `i` being exchanged
    @param _min_dy Minimum amount of `j` to receive
    @return Actual amount of `j` received
    """
    return self._exchange(
        msg.sender,
        i,
        j,
        _dx,
        _min_dy,
        _receiver,
        False
    )

@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] + 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

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 = dy * self._dynamic_fee((_xp[i] + x) / 2, (_xp[j] + y) / 2, self.fee) / FEE_DENOMINATOR

    # Convert all to real units
    dy = (dy - dy_fee) * PRECISION / rates[j]

    self.admin_balances[j] += (
        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

Example

>>> expected_dy = pool.get_dy(0, 1, 10**18) * 0.99
>>> StableSwap.exchange(0, 1, 10**18, expected_dy)
999712

Note

This function exchanges one crvUSD for 0.999712 amount of USDV. expected_dy calculates the predicted input amount j to receive dy of coin i. This value can then be used as _min_dy in the exchange function.

`exchange_received`¶

StableSwap.exchange_received(i: int128, j: int128, _dx: uint256, _min_dy: uint256, _receiver: address) -> uint256:

Danger

exchange_received will revert if the pool contains a rebasing asset. A pool that contains a rebasing token should have an asset_type of 2. If this is not the case, the pool is using an incorrect implementation, and rebases can be stolen.

Function to exchange _dx amount of coin i for coin j, receiving a minimum amount of _min_dy. This is done without actually transferring the coins into the pool within the same call. The exchange is based on the change in the balance of coin i, eliminating the need to grant approval to the contract.

A detailed article can be found here: https://blog.curvemonitor.com/posts/exchange-received/.

Returns: amount of output coin received (uint256).

Emits: TokenExchange

Input	Type	Description
`i`	`int128`	Index value of input coin.
`j`	`int128`	Index value of output coin.
`_dx`	`uint256`	Amount of coin `i` being exchanged.
`_min_dy`	`uint256`	Minimum amount of coin `j` to receive.
`_receiver`	`address`	Receiver of the output tokens; defaults to `msg.sender`.

Source code

event TokenExchange:
    buyer: indexed(address)
    sold_id: int128
    tokens_sold: uint256
    bought_id: int128
    tokens_bought: uint256

stored_balances: DynArray[uint256, MAX_COINS]

@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 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
    """
    assert not 2 in asset_types  # dev: exchange_received not supported if pool contains rebasing tokens
    return self._exchange(
        msg.sender,
        i,
        j,
        _dx,
        _min_dy,
        _receiver,
        True,  # <--------------------------------------- swap optimistically.
    )

@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] + 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

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 = dy * self._dynamic_fee((_xp[i] + x) / 2, (_xp[j] + y) / 2, self.fee) / FEE_DENOMINATOR

    # Convert all to real units
    dy = (dy - dy_fee) * PRECISION / rates[j]

    self.admin_balances[j] += (
        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

Example

>>> crvusd.transfer("0xe1e77de32fb301ce55871ba095fd6b8e5d9abad8", 10**18)
>>> pool.exchange_received(0, 1, 10**18, 0)
999712

Note

First, there needs to be a token transfer into the pool. Here, one crvUSD is transferred into the pool. Afterwards, exchange_received can be called to swap one crvUSD for dy USDV.

More information on this method here.

`get_dy`¶

StableSwap.get_dy(i: int128, j: int128, dx: uint256) -> uint256:

Function to calculate the predicted output amount j to receive at the pool's current state given an input of dx amount of coin i. This is just a simple getter method; the calculation logic is within the CurveStableSwapNGViews contract. See here.

Returns: predicted output amount of j (uint256).

Input	Type	Description
`i`	`int128`	Index value of input coin.
`j`	`int128`	Index value of output coin.
`dx`	`uint256`	Amount of input coin being exchanged.

Source code

CurveStableSwapNG.vyCurveStableSwapNGViews.vy

interface Factory:
    def fee_receiver() -> address: view
    def admin() -> address: view
    def views_implementation() -> address: view

@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
    """
    return StableSwapViews(factory.views_implementation()).get_dy(i, j, dx, self)

@view
@external
def get_dy(i: int128, j: int128, dx: uint256, pool: address) -> 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
    """
    N_COINS: uint256 = StableSwapNG(pool).N_COINS()

    rates: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    balances: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    xp: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    rates, balances, xp = self._get_rates_balances_xp(pool, N_COINS)

    amp: uint256 = StableSwapNG(pool).A() * A_PRECISION
    D: uint256 = self.get_D(xp, amp, N_COINS)

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

    base_fee: uint256 = StableSwapNG(pool).fee()
    fee_multiplier: uint256 = StableSwapNG(pool).offpeg_fee_multiplier()
    fee: uint256 = self._dynamic_fee((xp[i] + x) / 2, (xp[j] + y) / 2, base_fee, fee_multiplier) * dy / FEE_DENOMINATOR

    return (dy - fee) * PRECISION / rates[j]

Example

>>> StableSwap.get_dy(0, 1, 10**18)
999712

`get_dx`¶

StableSwap.get_dx(i: int128, j: int128, dy: uint256) -> uint256:

Function to calculate the predicted input amount i to receive dy of coin j at the pool's current state. This is just a simple getter method; the calculation logic is within the CurveStableSwapNGViews contract. See here.

Returns: predicted input amount of i (uint256).

Input	Type	Description
`i`	`int128`	Index value of input coin.
`j`	`int128`	Index value of output coin.
`dy`	`uint256`	Amount of output coin received.

Source code

CurveStableSwapNG.vyCurveStableSwapNGViews.vy

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

@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 valie of the coin to recieve
    @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_dx(i: int128, j: int128, dy: uint256, pool: address) -> 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 valie of the coin to recieve
    @param dy Amount of `j` being received after exchange
    @return Amount of `i` predicted
    """
    N_COINS: uint256 = StableSwapNG(pool).N_COINS()
    return self._get_dx(i, j, dy, pool, False, N_COINS)

@view
@internal
def _get_dx(
    i: int128,
    j: int128,
    dy: uint256,
    pool: address,
    static_fee: bool,
    N_COINS: uint256
) -> uint256:

    rates: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    balances: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    xp: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    rates, balances, xp = self._get_rates_balances_xp(pool, N_COINS)

    amp: uint256 = StableSwapNG(pool).A() * A_PRECISION
    D: uint256 = self.get_D(xp, amp, N_COINS)

    base_fee: uint256 = StableSwapNG(pool).fee()
    dy_with_fee: uint256 = dy * rates[j] / PRECISION + 1

    fee: uint256 = base_fee
    if not static_fee:
        fee_multiplier: uint256 = StableSwapNG(pool).offpeg_fee_multiplier()
        fee = self._dynamic_fee(xp[i], xp[j], base_fee, fee_multiplier)

    y: uint256 = xp[j] - dy_with_fee * FEE_DENOMINATOR / (FEE_DENOMINATOR - fee)
    x: uint256 = self.get_y(j, i, y, xp, amp, D, N_COINS)
    return (x - xp[i]) * PRECISION / rates[i]

Example

>>> StableSwap.get_dx(1, 0, 10**18)
999912

Adding and Removing Liquidity¶

There are no restrictions on how liquidity can be added or removed. Liquidity can be provided or removed in any proportion. However, there are fees associated with adding and removing liquidity that depend on the balances within the pool.

`add_liquidity`¶

StableSwap.add_liquidity(_amounts: DynArray[uint256, MAX_COINS], _min_mint_amount: uint256, _receiver: address = msg.sender) -> uint256:

Function to add liquidity into the pool and mint a minimum of _min_mint_amount of the corresponding LP tokens to _receiver. A value for the minimum amount is used to prevent being front-run by MEV bots.

Returns: amount of LP tokens received (uint256).

Emits: Transfer and AddLiquidity

Input	Type	Description
`_amounts`	`DynArray[uint256, MAX_COINS]`	List of coin amounts to deposit.
`_min_amount`	`uint256`	Minimum amount of LP tokens to mint.
`_receiver`	`address`	Receiver of the LP tokens; defaults to `msg.sender`.

Source code

event Transfer:
    sender: indexed(address)
    receiver: indexed(address)
    value: uint256

event AddLiquidity:
    provider: indexed(address)
    token_amounts: DynArray[uint256, MAX_COINS]
    fees: DynArray[uint256, MAX_COINS]
    invariant: uint256
    token_supply: uint256

@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
    """
    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(MAX_COINS_128):

        if i == N_COINS_128:
            break

        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 = (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 = self.fee * N_COINS / (4 * (N_COINS - 1))

        for i in range(MAX_COINS_128):

            if i == N_COINS_128:
                break

            ideal_balance = D1 * old_balances[i] / D0
            difference = 0
            new_balance = new_balances[i]

            if ideal_balance > new_balance:
                difference = ideal_balance - new_balance
            else:
                difference = 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(_dynamic_fee_i * difference / FEE_DENOMINATOR)
            self.admin_balances[i] += 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 = 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)

    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

Example

>>> StableSwap.add_liquidity([10000000000000000000, 0], 0)
9997967030080774869

`remove_liquidity`¶

StableSwap.remove_liquidity(_burn_amount: uint256, _min_amounts: DynArray[uint256, MAX_COINS], _receiver: address = msg.sender, _claim_admin_fees: bool = True) -> DynArray[uint256, MAX_COINS]:

Info

When removing liquidity in a balanced ratio, there is no need to update the price oracle, as this function does not alter the balance ratio within the pool. Calling this function only updates D_oracle.
The calculation of D does not use Newton methods, ensuring that remove_liquidity should always work, even if the pool gets borked.

Function to remove _min_amount coins from the liquidity pool based on the pools current ratios by burning _burn_amount of LP tokens. Admin fees might be claimed after liquidity is removed.

Returns: amount of coins withdrawn (DynArray[uint256, MAX_COINS]).

Emits: RemoveLiquidity

Input	Type	Description
`_burn_amount`	`uint256`	Amount of LP tokens to be burned.
`_min_amounts`	`DynArray[uint256, MAX_COINS]`	Minimum amounts of coins to receive.
`_receiver`	`address`	Receiver of the coins; defaults to `msg.sender`.
`_claim_admin_fees`	`bool`	If admin fees should be claimed; defaults to `true`.

Source code

event RemoveLiquidity:
    provider: indexed(address)
    token_amounts: DynArray[uint256, MAX_COINS]
    fees: DynArray[uint256, MAX_COINS]
    token_supply: uint256

@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

    amounts: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    balances: DynArray[uint256, MAX_COINS] = self._balances()

    value: uint256 = 0
    for i in range(MAX_COINS_128):

        if i == N_COINS_128:
            break

        value = 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]),
        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

Example

>>> StableSwap.get_balances()
[1156170050330410764719488, 1052703857490]
>>> StableSwap.remove_liquidity(10**18, [0, 0])
523455207306501616, 476610

Note

remove_liquidity removes liquidity in a balanced proportion according to the balances in the pool.

`remove_liquidity_one_coin`¶

StableSwap.remove_liquidity_one_coin(_burn_amount: uint256, i: int128, _min_received: uint256, _receiver: address = msg.sender) -> uint256:

Function to remove a minimum of _min_received of coin i by burning _burn_amount of LP tokens.

Returns: coins received (uint256).

Emits: RemoveLiquidityOne

Input	Type	Description
`_burn_amount`	`uint256`	Amount of LP tokens to burn/withdraw.
`i`	`int128`	Index value of the coin to withdraw.
`_min_received`	`uint256`	Minimum amount of coin to receive.
`_receiver`	`address`	Receiver of the coins; defaults to `msg.sender`.

Source code

event RemoveLiquidityOne:
    provider: indexed(address)
    token_id: int128
    token_amount: uint256
    coin_amount: uint256
    token_supply: uint256

@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] += 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

@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 = self.fee * N_COINS / (4 * (N_COINS - 1))
    ys: uint256 = (D0 + D1) / (2 * N_COINS)
    xp_reduced: DynArray[uint256, MAX_COINS] = xp

    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 = (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 - 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 = (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

Example

>>> StableSwap.remove_liquidity_one_coin(10**18, 0, 9**18)
1000107995665331176
>>> StableSwap.remove_liquidity_one_coin(10**18, 1, 9**18)
999915

Note

Both examples involve removing one LP token. With remove_liquidity_one_coin targeted at the higher balanced coin of the pool, a small premium is received. Conversely, when removing liquidity in the form of the lower balance token in the pool, slightly less is received. An estimated value of the output can be obtained via calc_withdraw_one_coin.

`remove_liquidity_imbalance`¶

StableSwap.remove_liquidity_imbalance(_amounts: DynArray[uint256, MAX_COINS], _max_burn_amount: uint256, _receiver: address = msg.sender) -> uint256:

Function to burn a maximum of _max_burn_amount of LP tokens in order to receive _amounts of underlying tokens.

Returns: amount of LP tokens burned (uint256).

Emits: RemoveLiquidityImbalance

Input	Type	Description
`_amounts`	`DynArray[uint256, MAX_COINS]`	List of amounts of coins to withdraw.
`_max_burn_amount`	`uint256`	Maximum amount of LP tokens to burn.
`_receiver`	`address`	Receiver of the coins; defaults to `msg.sender`.

Source code

event RemoveLiquidityImbalance:
    provider: indexed(address)
    token_amounts: DynArray[uint256, MAX_COINS]
    fees: DynArray[uint256, MAX_COINS]
    invariant: uint256
    token_supply: uint256

@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(MAX_COINS_128):

        if i == N_COINS_128:
            break

        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 = self.fee * N_COINS / (4 * (N_COINS - 1))
    ys: uint256 = (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(MAX_COINS_128):

        if i == N_COINS_128:
            break

        ideal_balance = D1 * old_balances[i] / D0
        difference = 0
        new_balance = new_balances[i]

        if ideal_balance > new_balance:
            difference = ideal_balance - new_balance
        else:
            difference = 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(dynamic_fee * difference / FEE_DENOMINATOR)

        self.admin_balances[i] += 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 = ((D0 - D1) * 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._burnFrom(msg.sender, burn_amount)

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

    return burn_amount

Example

>>> StableSwap.remove_liquidity_imbalance([10**18, 10**6] 10**19)
1999880816717294817

`calc_token_amount`¶

StableSwap.calc_token_amount(_amounts: DynArray[uint256, MAX_COINS], _is_deposit: bool) -> uint256:

Function to calculate the addition or reduction of token supply from a deposit (add liquidity) or withdrawal (remove liquidity). This function does take fees into consideration.

Returns: amount of LP tokens (uint256).

Input	Type	Description
`_amounts`	`DynArray[uint256, MAX_COINS]`	Amount of coins being deposited/withdrawn.
`_is_deposit`	`bool`	`true` = deposit, `false` = withdraw.

Source code

CurveStableSwapNG.vyCurveStableSwapNGViews.vy

interface Factory:
    def fee_receiver() -> address: view
    def admin() -> address: view
    def views_implementation() -> address: view

@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 calc_token_amount(
    _amounts: DynArray[uint256, MAX_COINS],
    _is_deposit: bool,
    pool: address
) -> 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
    """
    amp: uint256 = StableSwapNG(pool).A() * A_PRECISION
    N_COINS: uint256 = StableSwapNG(pool).N_COINS()

    rates: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    old_balances: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    xp: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    rates, old_balances, xp = self._get_rates_balances_xp(pool, N_COINS)

    # Initial invariant
    D0: uint256 = self.get_D(xp, amp, N_COINS)

    total_supply: uint256 = StableSwapNG(pool).totalSupply()
    new_balances: DynArray[uint256, MAX_COINS] = old_balances
    for i in range(MAX_COINS):
        if i == N_COINS:
            break

        amount: uint256 = _amounts[i]
        if _is_deposit:
            new_balances[i] += amount
        else:
            new_balances[i] -= amount

    # Invariant after change
    for idx in range(MAX_COINS):
        if idx == N_COINS:
            break
        xp[idx] = rates[idx] * new_balances[idx] / PRECISION
    D1: uint256 = self.get_D(xp, amp, N_COINS)

    # We need to recalculate the invariant accounting for fees
    # to calculate fair user's share
    D2: uint256 = D1
    if total_supply > 0:

        # Only account for fees if we are not the first to deposit
        base_fee: uint256 = StableSwapNG(pool).fee() * N_COINS / (4 * (N_COINS - 1))
        fee_multiplier: uint256 = StableSwapNG(pool).offpeg_fee_multiplier()
        _dynamic_fee_i: uint256 = 0
        xs: uint256 = 0
        ys: uint256 = (D0 + D1) / N_COINS

        for i in range(MAX_COINS):
            if i == N_COINS:
                break

            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

            xs = old_balances[i] + new_balance
            _dynamic_fee_i = self._dynamic_fee(xs, ys, base_fee, fee_multiplier)
            new_balances[i] -= _dynamic_fee_i * difference / FEE_DENOMINATOR

        for idx in range(MAX_COINS):
            if idx == N_COINS:
                break
            xp[idx] = rates[idx] * new_balances[idx] / PRECISION

        D2 = self.get_D(xp, amp, N_COINS)
    else:
        return D1  # Take the dust if there was any

    diff: uint256 = 0
    if _is_deposit:
        diff = D2 - D0
    else:
        diff = D0 - D2
    return diff * total_supply / D0

Example

>>> StableSwap.calc_token_amount([10**18, 0], True) # deposit (coin[0])
999701503692424994
>>> StableSwap.calc_token_amount([0, 10**6], True) # deposit (coin[1])
999875942505458416
>>> StableSwap.calc_token_amount([10**18, 10**6], True) # deposit (coin[0] and coin[1])
1999863130101592370
>>> StableSwap.calc_token_amount([10**18, 0], False) # withdraw (coin[1])
999987187514411723
>>> StableSwap.calc_token_amount([10**18, 0], False) # withdraw (coin[0])
1000188312578139610
>>> StableSwap.calc_token_amount([10**18, 10**6], False) # withdraw (coin[0] and coin[1])
1999889816188803581

Note

If _is_deposit is True, the method calculates the increase in LP token supply when adding _amounts of tokens to the pool. Conversely, when _is_deposit is False, the method calculates the decrease in LP token supply when removing _amounts of tokens from the pool. This is a view function and does not actually alter any states.

`calc_withdraw_one_coin`¶

StableSwap.calc_withdraw_one_coin(_burn_amount: uint256, i: int128) -> uint256:

Function to calculate the amount of single token i withdrawn when burning _burn_amount LP tokens.

Returns: amount of tokens withdrawn (uint256).

Input	Type	Description
`_burn_amount`	`uint256`	Amount of LP tokens to burn.
`i`	`int128`	Index value of the coin to withdraw.

Source code

@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
@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 = self.fee * N_COINS / (4 * (N_COINS - 1))
    ys: uint256 = (D0 + D1) / (2 * N_COINS)
    xp_reduced: DynArray[uint256, MAX_COINS] = xp

    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 = (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 - 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 = (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

Example

>>> StableSwap.calc_withdraw_one_coin(10**18, 0)
1000107987022361129
>>> StableSwap.calc_withdraw_one_coin(10**18, 1)
999915
>>> StableSwap.get_balances()
[1156160050449617680048138, 1052703857609]

Fee Methods¶

Stableswap-ng introduces a dynamic fee based on the imbalance of the coins within the pool and their pegs:

_dynamic_fee

offpeg_fee_multiplier: public(uint256)  # * 1e10

@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 (
        (_offpeg_fee_multiplier * _fee) /
        ((_offpeg_fee_multiplier - FEE_DENOMINATOR) * 4 * xpi * xpj / xps2 + FEE_DENOMINATOR)
    )

`fee`¶

StableSwap.fee() -> uint256: view

Getter method for the fee of the pool. This is the value set when initializing the contract and can be changed via set_new_fee.

Returns: fee (uint256).

Source code

fee: public(uint256)  # fee * 1e10

@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],
):
    ...

    self.fee = _fee

    ...

Example

>>> StableSwap.fee()
1000000

Note

The method returns an integer with with 1e10 precision.

`dynamic_fee`¶

StableSwap.dynamic_fee(i: int128, j: int128) -> uint256:

Getter for the swap fee when exchanging between i and j. The swap fee is expressed as an integer with a 1e10 precision.

Returns: dynamic fee (uint256).

Input	Type	Description
`i`	`int128`	Index value of input coin.
`j`	`int128`	Index value of output coin.

Source code

CurveStableSwapNG.vyCurveStableSwapNGViews.vy

@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 recieve
    @return Swap fee expressed as an integer with 1e10 precision
    """
    return StableSwapViews(factory.views_implementation()).dynamic_fee(i, j, self)

@view
@external
def dynamic_fee(i: int128, j: int128, pool:address) -> 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 recieve
    @return Swap fee expressed as an integer with 1e10 precision
    """
    N_COINS: uint256 = StableSwapNG(pool).N_COINS()
    fee: uint256 = StableSwapNG(pool).fee()
    fee_multiplier: uint256 = StableSwapNG(pool).offpeg_fee_multiplier()

    rates: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    balances: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    xp: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    rates, balances, xp = self._get_rates_balances_xp(pool, N_COINS)

    return self._dynamic_fee(xp[i], xp[j], fee, fee_multiplier)

@view
@internal
def _dynamic_fee(xpi: uint256, xpj: uint256, _fee: uint256, _fee_multiplier: uint256) -> uint256:

    if _fee_multiplier <= FEE_DENOMINATOR:
        return _fee

    xps2: uint256 = (xpi + xpj) ** 2
    return (
        (_fee_multiplier * _fee) /
        ((_fee_multiplier - FEE_DENOMINATOR) * 4 * xpi * xpj / xps2 + FEE_DENOMINATOR)
    )

@view
@internal
def _get_rates_balances_xp(pool: address, N_COINS: uint256) -> (
    DynArray[uint256, MAX_COINS],
    DynArray[uint256, MAX_COINS],
    DynArray[uint256, MAX_COINS],
):

    rates: DynArray[uint256, MAX_COINS] = StableSwapNG(pool).stored_rates()
    balances: DynArray[uint256, MAX_COINS] = StableSwapNG(pool).get_balances()
    xp: DynArray[uint256, MAX_COINS] = empty(DynArray[uint256, MAX_COINS])
    for idx in range(MAX_COINS):
        if idx == N_COINS:
            break
        xp.append(rates[idx] * balances[idx] / PRECISION)

    return rates, balances, xp

Example

>>> StableSwap.dynamic_fee(0, 1)
1001758

Note

The method returns an integer with with 1e10 precision.

`admin_fee`¶

StableSwap.admin_fee() -> uint256: view

Getter for the admin fee. It is a constant and is set to 50% (5000000000).

Returns: admin fee (uint256).

Source code

admin_fee: public(constant(uint256)) = 5000000000

Example

>>> StableSwap.admin_fee()
5000000000

Note

The method returns an integer with with 1e10 precision.

`offpeg_fee_multiplier`¶

StableSwap.offpeg_fee_multiplier() -> uint256: view

Getter method for the off-peg fee multiplier. This value determines how much the fee increases when assets within the AMM depeg. This value can be changed via set_new_fee.

Returns: offpeg fee multiplier (uint256)

Source code

offpeg_fee_multiplier: public(uint256)  # * 1e10

@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],
):
    ...

    self.offpeg_fee_multiplier = _offpeg_fee_multiplier

    ...

Example

>>> StableSwap.offpeg_fee_multiplier()
50000000000

Note

The method returns an integer with with 1e10 precision.

`stored_rates`¶

StableSwap.stored_rates() -> DynArray[uint256, MAX_COINS]:

Getter for the rate multiplier of each coin.

Returns: stored rates (DynArray[uint256, MAX_COINS]).

Info

If the coin has a rate oracle that has been properly initialized, this method queries that rate by static-calling an external contract.

Source code

rate_multipliers: immutable(DynArray[uint256, MAX_COINS])
# [bytes4 method_id][bytes8 <empty>][bytes20 oracle]
oracles: DynArray[uint256, MAX_COINS]

@view
@external
def stored_rates() -> DynArray[uint256, MAX_COINS]:
    return self._stored_rates()

@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
    oracles: DynArray[uint256, MAX_COINS] = self.oracles

    for i in range(MAX_COINS_128):

        if i == N_COINS_128:
            break

        if asset_types[i] == 1 and not oracles[i] == 0:

            # NOTE: fetched_rate is assumed to be 10**18 precision
            fetched_rate: uint256 = convert(
                raw_call(
                    convert(oracles[i] % 2**160, address),
                    _abi_encode(oracles[i] & ORACLE_BIT_MASK),
                    max_outsize=32,
                    is_static_call=True,
                ),
                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

Example

>>> StableSwap.stored_rates()
[1000000000000000000, 1000000000000000000000000000000]

`admin_balances`¶

StableSwap.admin_balances(arg0: uint256) -> uint256: view

Getter for the accumulated admin balance of the pool for a coin. These values essentially represent the claimable admin fee.

Returns: admin balances (uint256).

Input	Type	Description
`arg0`	`uint256`	Index value of the coin.

Source code

admin_balances: public(DynArray[uint256, MAX_COINS])

Example

>>> StableSwap.admin_balances(0)
38117658162246205676
>>> StableSwap.admin_balances(1)
10683574

`withdraw_admin_fees`¶

StableSwap.withdraw_admin_fees():

Function to withdraw accumulated admin fees from the pool and send them to the fee_receiver set in the Factory.

Source code

interface Factory:
    def fee_receiver() -> address: view
    def admin() -> address: view
    def views_implementation() -> address: view

admin_balances: public(DynArray[uint256, MAX_COINS])

@external
def withdraw_admin_fees():
    """
    @notice Claim admin fees. Callable by anyone.
    """
    self._withdraw_admin_fees()

@internal
def _withdraw_admin_fees():
    fee_receiver: address = factory.fee_receiver()
    assert fee_receiver != empty(address)  # dev: fee receiver not set

    admin_balances: DynArray[uint256, MAX_COINS] = self.admin_balances
    for i in range(MAX_COINS_128):

        if i == N_COINS_128:
            break

        if admin_balances[i] > 0:

            self._transfer_out(i, admin_balances[i], fee_receiver)
            admin_balances[i] = 0

    self.admin_balances = admin_balances

Example

>>> StableSwap.withdraw_admin_fees()

Amplification Coefficient¶

The amplification coefficient A determines a pool’s tolerance for imbalance between the assets within it. A higher value means that trades will incur slippage sooner as the assets within the pool become imbalanced.

The appropriate value for A is dependent upon the type of coin being used within the pool, and is subject to optimisation and pool-parameter update based on the market history of the trading pair. It is possible to modify the amplification coefficient for a pool after it has been deployed. This can be done via the ramp_A function. See admin controls.

When a ramping of A has been initialized, the process can be stopped by calling the function stop_ramp_A().

`A`¶

StableSwap.A() -> uint256:

Getter for the amplification coefficient A.

Returns: A (uint256).

Source code

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)

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

@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

Example

>>> StableSwap.A()
500

`A_precise`¶

StableSwap.A_precise() -> uint256:

Getter for the precise A value, which is not divided by A_PRECISION unlike A().

Returns: precise A (uint256).

Source code

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)

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

@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

Example

>>> StableSwap.A_precise()
50000

`initial_A`¶

StableSwap.initial_A() -> uint256: view

Getter for the initial A value.

Returns: initial A (uint256).

Source code

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)

@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)

Example

>>> StableSwap.initial_A()
50000

`future_A`¶

StableSwap.future_A() -> uint256: view

Getter for the future A value. This value is adjusted when ramping A.

Returns: future A (uint256).

Source code

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)

@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)

Example

>>> StableSwap.future_A()
50000

`initial_A_time`¶

StableSwap.initial_A_time() -> uint256: view

Getter for the initial A time. This is the timestamp when ramping A was initialized.

Returns: initial A time (uint256).

Source code

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)

@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)

Example

>>> StableSwap.initial_A_time()
0

`future_A_time`¶

StableSwap.future_A_time() -> uint256: view

Getter for the future A time. This is the timestamp when ramping A should be finished.

Returns: future A time (uint256).

Source code

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)

@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)

Example

>>> StableSwap.future_A_time()
0

Contract Info Methods¶

`coins`¶

StableSwap.coins(arg0: uint256) -> addresss: view

Getter for the coin at index arg0 within the pool.

Returns: coin (address).

Source code

coins: public(immutable(DynArray[address, MAX_COINS]))

@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],
):
    ...

    coins = _coins

    ...

Example

>>> StableSwap.coins(0)
'0xf939E0A03FB07F59A73314E73794Be0E57ac1b4E'
>>> StableSwap.coins(1)
'0x0E573Ce2736Dd9637A0b21058352e1667925C7a8'

`balances`¶

StableSwap.balances(i: uint256) -> uint256:

Getter for the current balance of coin i within the pool.

Returns: coin balance (uint256).

Input	Type	Description
`i`	`uint256`	Index value of the coin.

Source code

@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
@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(MAX_COINS_128):

        if i == N_COINS_128:
            break

        if 2 in asset_types:
            balances_i = ERC20(coins[i]).balanceOf(self) - self.admin_balances[i]
        else:
            balances_i = self.stored_balances[i] - self.admin_balances[i]

        result.append(balances_i)

    return result

Example

>>> StableSwap.balances(0)
1156160050449617680048138
>>> StableSwap.balances(1)
1052703857609

`get_balances`¶

StableSwap.get_balances() -> DynArray[uint256, MAX_COINS]:

Getter for an array with all coin balances in the pool.

Returns: coin balances (DynArray[uint256, MAX_COINS]).

Source code

@view
@external
def get_balances() -> DynArray[uint256, MAX_COINS]:
    return self._balances()

@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(MAX_COINS_128):

        if i == N_COINS_128:
            break

        if POOL_IS_REBASING_IMPLEMENTATION:
            balances_i = ERC20(coins[i]).balanceOf(self) - self.admin_balances[i]
        else:
            balances_i = self.stored_balances[i] - self.admin_balances[i]

        result.append(balances_i)

    return result

Example

>>> StableSwap.get_balances()
[1156160050449617680048138, 1052703857609]

Note

The returned values do not take admin fees into account.

`N_COINS`¶

StableSwap.N_COINS() -> uint256: view

Getter for the total number of coins in the pool.

Returns: number of coins (uint256).

Info

There can be a maximum of 8 coins per pool due to MAX_COINS = 8.

Source code

MAX_COINS: constant(uint256) = 8  # max coins is 8 in the factory

N_COINS: public(immutable(uint256))

@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],
):
    ...

    coins = _coins
    __n_coins: uint256 = len(_coins)
    N_COINS = __n_coins
    N_COINS_128 = convert(__n_coins, int128)

    ...

Example

>>> StableSwap.N_COINS()
2

`totalSupply`¶

StableSwap.totalSupply() -> uint256:

Getter for the total supply of the LP token.

Returns: total supply (uint256).

Source code

total_supply: uint256

@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

Example

>>> StableSwap.totalSupply()
2208717767450789394892159

Plain Pools

Exchange Methods¶

exchange¶

exchange_received¶

get_dy¶

get_dx¶

Adding and Removing Liquidity¶

add_liquidity¶

remove_liquidity¶

remove_liquidity_one_coin¶

remove_liquidity_imbalance¶

calc_token_amount¶

calc_withdraw_one_coin¶

Fee Methods¶

fee¶

dynamic_fee¶

admin_fee¶

offpeg_fee_multiplier¶

stored_rates¶

admin_balances¶

withdraw_admin_fees¶

Amplification Coefficient¶

A¶

A_precise¶

initial_A¶

future_A¶

initial_A_time¶

future_A_time¶

Contract Info Methods¶

coins¶

balances¶

get_balances¶

N_COINS¶

totalSupply¶

`exchange`¶

`exchange_received`¶

`get_dy`¶

`get_dx`¶

`add_liquidity`¶

`remove_liquidity`¶

`remove_liquidity_one_coin`¶

`remove_liquidity_imbalance`¶

`calc_token_amount`¶

`calc_withdraw_one_coin`¶

`fee`¶

`dynamic_fee`¶

`admin_fee`¶

`offpeg_fee_multiplier`¶

`stored_rates`¶

`admin_balances`¶

`withdraw_admin_fees`¶

`A`¶

`A_precise`¶

`initial_A`¶

`future_A`¶

`initial_A_time`¶

`future_A_time`¶

`coins`¶

`balances`¶

`get_balances`¶

`N_COINS`¶

`totalSupply`¶