# [bytes4 method_id][bytes8 <empty>][bytes20 oracle]

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

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

:::deploy[Contract Source & Deployment]

Source code available on [Github](https://github.com/curvefi/stableswap-ng/blob/bff1522b30819b7b240af17ccfb72b0effbf6c47/contracts/main/CurveStableSwapNG.vy).  

:::

The deployment of plain pools is permissionless and can be done via the [**`deploy_plain_pool`**](../../factory/stableswap-ng/deployer-api.md#deploy_plain_pool) function within the Stableswap-NG Factory.

:::warning[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.

:::

:::info[**Oracle Methods Documentation**]

Comprehensive documentation for Oracle Methods is available on a dedicated page, accessible [here](./oracles.md).

:::

---

*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()`**

<Dropdown title="`_transfer_in(coin_idx: int128, dx: uint256, sender: address, expect_optimistic_transfer: bool) -> uint256:`">

`expect_optimistic_transfer` is relevant when using the [`exchange_received()`](#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. |

```vyper
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
```

</Dropdown>

- **`_transfer_out()`**

<Dropdown title="`_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.            |

```vyper
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
```

</Dropdown>

---

## 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`
::::description[`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`. |

<SourceCode>

```vyper
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
```

</SourceCode>

<Example>

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

</Example>

:::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`
::::description[`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. |

<SourceCode>

```vyper
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,
) -> 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 POOL_IS_REBASING_IMPLEMENTATION  # 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
```

</SourceCode>

<Example>

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

</Example>

:::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](../overview.md#exchange_received).

:::

::::

### `get_dy`
::::description[`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](../utility-contracts/views.md#get_dy).

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.      |

<SourceCode>
```vyper
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)
```
```vyper
@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]
```
</SourceCode>

<Example>

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

</Example>

::::

### `get_dx`
::::description[`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](../utility-contracts/views.md#get_dx).

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.            |

<SourceCode>
```vyper
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)
```
```vyper
@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]
```
</SourceCode>

<Example>

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

</Example>

::::

---

## 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`
::::description[`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`.|

<SourceCode>

```vyper
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
```

</SourceCode>

<Example>

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

</Example>

::::

### `remove_liquidity`
::::description[`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`.|

<SourceCode>

```vyper
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
```

</SourceCode>

<Example>

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

</Example>

:::note

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

:::

::::

### `remove_liquidity_one_coin`
::::description[`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`.  |

<SourceCode>

```vyper
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
```

</SourceCode>

<Example>

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

</Example>

:::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`
::::description[`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`.   |

<SourceCode>

```vyper
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
```

</SourceCode>

<Example>

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

</Example>

::::

### `calc_token_amount`
::::description[`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.             |

<SourceCode>
```vyper
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)
```
```vyper
@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
```
</SourceCode>

<Example>

```shell
>>> 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
```

</Example>

:::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`
::::description[`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.              |

<SourceCode>

```vyper
@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
```

</SourceCode>

<Example>

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

</Example>

::::

---

## Fee Methods

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

<Dropdown title="`_dynamic_fee`">

```vyper
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)
    )
```

</Dropdown>

More on dynamic fees [here](../overview.md#dynamic-fees).

### `fee`
::::description[`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`](#set_new_fee).

Returns: fee (`uint256`).

<SourceCode>

```vyper
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

    ...
```

</SourceCode>

<Example>

```shell
>>> StableSwap.fee()
1000000
```

</Example>

:::note

The method returns an integer with with 1e10 precision.

:::

::::

### `dynamic_fee`
::::description[`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.                |

<SourceCode>
```vyper
@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)
```
```vyper
@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
```
</SourceCode>

<Example>

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

</Example>

:::note

The method returns an integer with with 1e10 precision.

:::

::::

### `admin_fee`
::::description[`StableSwap.admin_fee() -> uint256: view`]

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

Returns: admin fee (`uint256`).

<SourceCode>

```vyper
admin_fee: public(constant(uint256)) = 5000000000
```

</SourceCode>

<Example>

```shell
>>> StableSwap.admin_fee()
5000000000
```

</Example>

:::note

The method returns an integer with with 1e10 precision.

:::

::::

### `offpeg_fee_multiplier`
::::description[`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`](#set_new_fee).

Returns: offpeg fee multiplier (`uint256`)

<SourceCode>

```vyper
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

    ...
```

</SourceCode>

<Example>

```shell
>>> StableSwap.offpeg_fee_multiplier()
50000000000
```

</Example>

:::note

The method returns an integer with with 1e10 precision.

:::

::::

### `stored_rates`
::::description[`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.

:::

<SourceCode>

```vyper
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
```

</SourceCode>

<Example>

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

</Example>

::::

### `admin_balances`
::::description[`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.                   |

<SourceCode>

```vyper
admin_balances: public(DynArray[uint256, MAX_COINS])
```

</SourceCode>

<Example>

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

</Example>

::::

### `withdraw_admin_fees`
::::description[`StableSwap.withdraw_admin_fees():`]

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

<SourceCode>

```vyper
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
```

</SourceCode>

<Example>

```shell
>>> StableSwap.withdraw_admin_fees()
```

</Example>

::::

---

## 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](#ramp_a).

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

### `A`
::::description[`StableSwap.A() -> uint256:`]

Getter for the amplification coefficient A.

Returns: A (`uint256`).

<SourceCode>

```vyper
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
```

</SourceCode>

<Example>

```shell
>>> StableSwap.A()
500
```

</Example>

::::

### `A_precise`
::::description[`StableSwap.A_precise() -> uint256:`]

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

Returns: precise A (`uint256`).

<SourceCode>

```vyper
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
```

</SourceCode>

<Example>

```shell
>>> StableSwap.A_precise()
50000
```

</Example>

::::

### `initial_A`
::::description[`StableSwap.initial_A() -> uint256: view`]

Getter for the initial A value.

Returns: initial A (`uint256`).

<SourceCode>

```vyper
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)
```

</SourceCode>

<Example>

```shell
>>> StableSwap.initial_A()
50000
```

</Example>

::::

### `future_A`
::::description[`StableSwap.future_A() -> uint256: view`]

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

Returns: future A (`uint256`).

<SourceCode>

```vyper
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)
```

</SourceCode>

<Example>

```shell
>>> StableSwap.future_A()
50000
```

</Example>

::::

### `initial_A_time`
::::description[`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`).

<SourceCode>

```vyper
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)
```

</SourceCode>

<Example>

```shell
>>> StableSwap.initial_A_time()
0
```

</Example>

::::

### `future_A_time`
::::description[`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`).

<SourceCode>

```vyper
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)
```

</SourceCode>

<Example>

```shell
>>> StableSwap.future_A_time()
0
```

</Example>

::::

---

## Contract Info Methods

### `coins`
::::description[`StableSwap.coins(arg0: uint256) -> addresss: view`]

Getter for the coin at index `arg0` within the pool.

Returns: coin (`address`).

<SourceCode>

```vyper
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

    ...
```

</SourceCode>

<Example>

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

</Example>

::::

### `balances`
::::description[`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.    |

<SourceCode>

```vyper
@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 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
```

</SourceCode>

<Example>

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

</Example>

::::

### `get_balances`
::::description[`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]`).

<SourceCode>

```vyper
@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
```

</SourceCode>

<Example>

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

</Example>

:::note

The returned values do not take admin fees into account.

:::

::::

### `N_COINS`
::::description[`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`.

:::

<SourceCode>

```vyper
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)
    
    ...
```

</SourceCode>

<Example>

```shell
>>> StableSwap.N_COINS()
2
```

</Example>

::::

### `totalSupply`
::::description[`StableSwap.totalSupply() -> uint256:`]

Getter for the total supply of the LP token.

Returns: total supply (`uint256`).

<SourceCode>

```vyper
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
```

</SourceCode>

<Example>

```shell
>>> StableSwap.totalSupply()
2208717767450789394892159
```

</Example>

::::

---

## LP Token

**Pool and LP tokens are the same smart contract.** The pool itself acts as an LP Token. When coins are deposited into a Curve pool, the depositor receives pool LP (liquidity provider) tokens in return. Each Curve pool has its unique ERC20 contract representing these LP tokens, making them transferable. Holding these LP tokens allows for their deposit and staking in the pool's liquidity gauge, earning CRV token rewards. Additionally, if a metapool supports the LP token, it can be deposited there to receive the metapool's distinct LP tokens.

### `transfer`
::::description[`StableSwap.transfer(_to : address, _value : uint256) -> bool:`]

Function to transfer `_value` tokens to `_to`.

Returns: true (`bool`).

Emits: `Transfer`

| Input      | Type   | Description |
| ----------- | -------| ----|
| `_to` |  `address` | address to transfer token to |
| `_value` |  `uint256` | amount of tokens to transfer |

<SourceCode>

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

@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

@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)
```

</SourceCode>

::::

### `transferFrom`
::::description[`StableSwap.transferFrom(_from : address, _to : address, _value : uint256) -> bool:`]

Function to transfer `_value` tokens from `_from` to `_to`.

Returns: true (`bool`).

Emits: `Transfer`

| Input      | Type   | Description |
| ----------- | -------| ----|
| `_from` |  `address` | address to transfer token from |
| `_to` |  `address` | address to transfer token to |
| `_value` |  `uint256` | amount of tokens to transfer |

<SourceCode>

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

@external
def transferFrom(_from : address, _to : address, _value : uint256) -> bool:
    """
    @dev Transfer tokens from one address to another.
    @param _from address The address which you want to send tokens from
    @param _to address The address which you want to transfer to
    @param _value uint256 the amount of tokens to be transferred
    """
    self._transfer(_from, _to, _value)

    _allowance: uint256 = self.allowance[_from][msg.sender]
    if _allowance != max_value(uint256):
        self.allowance[_from][msg.sender] = _allowance - _value

    return True

@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)
```

</SourceCode>

::::

### `allowance`
::::description[`StableSwap.allowance(arg0: address, arg1: address) -> uint256: view`]

Getter method to check the allowance of `arg0` for funds of `arg1`.

Returns: allowed amount (`uint256`).

| Input      | Type   | Description |
| ----------- | -------| ----|
| `arg0` |  `address` | Address of the spender |
| `arg1` |  `address` | Address of the token owner |

<SourceCode>

```vyper
allowance: public(HashMap[address, HashMap[address, uint256]])
```

</SourceCode>

::::

### `approve`
::::description[`StableSwap.approve(_spender : address, _value : uint256) -> bool:`]

Function to approve `_spender` to transfer `_value` of tokens on behalf of `msg.sender`

Returns: true (`bool`).

Emits: `Approval`

| Input       | Type      | Description                     |
|-------------|-----------|---------------------------------|
| `_spender`  | `address` | Address of the approved spender |
| `_value`    | `uint256` | Amount of tokens to approve     |

<SourceCode>

```vyper
event Approval:
    owner: indexed(address)
    spender: indexed(address)
    value: uint256

@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
```

</SourceCode>

::::

### `permit`
::::description[`StableSwap.permit(_owner: address, _spender: address, _value: uint256, _deadline: uint256, _v: uint8, _r: bytes32, _s: bytes32) -> bool:`]

Function to permit `spender` to spend up to `_value` amount of `_owner`'s tokens via a signature.

Returns: true (`bool`).

Emits: `Approval`

| Input      | Type   | Description |
| ----------- | -------| ----|
| `_owner` |  `address` | Account which generated the signature and is granting an allowance  |
| `_spender` |  `address` | Account which will be granted an allowance  |
| `_value` |  `uint256` | Amount to approve |
| `_deadline` |  `uint256` | Deadline by which signature must be submitted |
| `_v` |  `uint8` | The last byte of the ECDSA signature |
| `_r` |  `bytes32` | The first 32 bytes of the ECDSA signature |
| `_s` |  `bytes32` | The second 32 bytes of the ECDSA signature |

<SourceCode>

```vyper
event Approval:
    owner: indexed(address)
    spender: indexed(address)
    value: uint256

@external
def permit(
    _owner: address,
    _spender: address,
    _value: uint256,
    _deadline: uint256,
    _v: uint8,
    _r: bytes32,
    _s: bytes32
) -> bool:
    """
    @notice Approves spender by owner's signature to expend owner's tokens.
        See https://eips.ethereum.org/EIPS/eip-2612.
    @dev Inspired by https://github.com/yearn/yearn-vaults/blob/main/contracts/Vault.vy#L753-L793
    @dev Supports smart contract wallets which implement ERC1271
        https://eips.ethereum.org/EIPS/eip-1271
    @param _owner The address which is a source of funds and has signed the Permit.
    @param _spender The address which is allowed to spend the funds.
    @param _value The amount of tokens to be spent.
    @param _deadline The timestamp after which the Permit is no longer valid.
    @param _v The bytes[64] of the valid secp256k1 signature of permit by owner
    @param _r The bytes[0:32] of the valid secp256k1 signature of permit by owner
    @param _s The bytes[32:64] of the valid secp256k1 signature of permit by owner
    @return True, if transaction completes successfully
    """
    assert _owner != empty(address)
    assert block.timestamp <= _deadline

    nonce: uint256 = self.nonces[_owner]
    digest: bytes32 = keccak256(
        concat(
            b"\x19\x01",
            self._domain_separator(),
            keccak256(_abi_encode(EIP2612_TYPEHASH, _owner, _spender, _value, nonce, _deadline))
        )
    )

    if _owner.is_contract:
        sig: Bytes[65] = concat(_abi_encode(_r, _s), slice(convert(_v, bytes32), 31, 1))
        # reentrancy not a concern since this is a staticcall
        assert ERC1271(_owner).isValidSignature(digest, sig) == ERC1271_MAGIC_VAL
    else:
        assert ecrecover(digest, convert(_v, uint256), convert(_r, uint256), convert(_s, uint256)) == _owner

    self.allowance[_owner][_spender] = _value
    self.nonces[_owner] = nonce + 1

    log Approval(_owner, _spender, _value)
    return True
```

</SourceCode>

::::

### `name`
::::description[`StableSwap.name() -> String[64]: view`]

Getter for the name of the LP token.

Returns: name (`String[64]`).

<SourceCode>

```vyper
name: public(immutable(String[64]))

@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],
):
    ...

    name = _name

    ...
```

</SourceCode>

<Example>

```shell
>>> StableSwap.name()
'USDV-crvUSD'
```

</Example>

::::

### `symbol`
::::description[`StableSwap.symbol() -> String[32]: view`]

Getter for the symbol of the LP token.

Returns: symbol (`String[32]`).

<SourceCode>

```vyper
symbol: public(immutable(String[32]))

@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],
):
    ...

    symbol = _symbol

    ...
```

</SourceCode>

<Example>

```shell
>>> StableSwap.symbol()
'USDVcrvUSD'
```

</Example>

::::

### `decimals`
::::description[`StableSwap.decimals() -> uint8: view`]

Getter for the decimals of the LP token.

Returns: decimals (uint8).

<SourceCode>

```vyper
decimals: public(constant(uint8)) = 18
```

</SourceCode>

<Example>

```shell
>>> StableSwap.decimals()
18
```

</Example>

::::

### `version`
::::description[`StableSwap.version() -> String[8]: view`]

Getter for the version of the LP token.

Returns: version (`String[8]`).

<SourceCode>

```vyper
version: public(constant(String[8])) = "v7.0.0"
```

</SourceCode>

<Example>

```shell
>>> StableSwap.version()
"v7.0.0"
```

</Example>

::::

### `balanceOf`
::::description[`StableSwap.balanceOf(arg0: address) -> uint256: view`]

Getter for the LP token balance of `arg0`.

Returns: token balance (`uint256`).

| Input      | Type   | Description |
| ----------- | -------| ----|
| `arg0` |  `address` | address to check the balance of |

<SourceCode>

```vyper
balanceOf: public(HashMap[address, uint256])
```

</SourceCode>

<Example>

```shell
>>> StableSwap.balanceOf("0x7a16fF8270133F063aAb6C9977183D9e72835428")
999808484451757093697730
```

</Example>

::::

### `nonces`
::::description[`StableSwap.nonces(arg0: address) -> uint256: view`]

Getter for the nonce.

Returns: nonces (`uint256`).

| Input      | Type   | Description |
| ----------- | -------| ----|
| `arg0` |  `address` | address |

<SourceCode>

```vyper
nonces: public(HashMap[address, uint256])
```

</SourceCode>

::::

### `salt`
::::description[`StableSwap.salt() -> bytes32: view`]

Getter for the salt of the LP token.

Returns: salt (`bytes32`).

<SourceCode>

```vyper
salt: public(immutable(bytes32))

@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],
):
    ...

    # EIP712 related params -----------------
    NAME_HASH = keccak256(name)
    salt = block.prevhash
    CACHED_CHAIN_ID = chain.id
    CACHED_DOMAIN_SEPARATOR = keccak256(
        _abi_encode(
            EIP712_TYPEHASH,
            NAME_HASH,
            VERSION_HASH,
            chain.id,
            self,
            salt,
        )
    )

    ...
```

</SourceCode>

<Example>

```shell
>>> StableSwap.salt()
HexBytes('0x814188b56f08130fe7b283343b64baa08f4d207229dc52776968b62b977c8f46')
```

</Example>

::::

### `DOMAIN_SEPARATOR`
::::description[`StableSwap.DOMAIN_SEPARATOR() -> bytes32: view`]

Getter for the domain separator.

Returns: domain separator (`bytes32`).

<SourceCode>

```vyper
CACHED_DOMAIN_SEPARATOR: immutable(bytes32)

@view
@external
def DOMAIN_SEPARATOR() -> bytes32:
    """
    @notice EIP712 domain separator.
    @return bytes32 Domain Separator set for the current chain.
    """
    return self._domain_separator()

@view
@internal
def _domain_separator() -> bytes32:
    if chain.id != CACHED_CHAIN_ID:
        return keccak256(
            _abi_encode(
                EIP712_TYPEHASH,
                NAME_HASH,
                VERSION_HASH,
                chain.id,
                self,
                salt,
            )
        )
    return CACHED_DOMAIN_SEPARATOR
```

</SourceCode>

<Example>

```shell
>>> StableSwap.DOMAIN_SEPARATOR()
HexBytes('0xf60903716a331f2ad023b28477aceee88e5180cab4694c497f4f9cefac657989')
```

</Example>

::::

---

## Admin Controls

The following methods are guarded and may only be called by the **`admin`** of the Stableswap-NG Factory.

### `ramp_A`
::::description[`StableSwap.ramp_A(_future_A: uint256, _future_time: uint256):`]

:::guard[Guarded Method]

This function is only callable by the `admin` of the Factory.

:::

Function to ramp amplification coefficient A. Minimum ramp time is 86400 (24h).

*Limitations when ramping A:*

- `block.timestamp` >= `initial_A_time` + `MIN_RAMP_TIME`
- `_future_time` >= `block.timestamp` + `MIN_RAMP_TIME`
- `future_A` > 0
- `future_A` < `MAX_A (1000000)`

Emits: `RampA`

| Input      | Type   | Description |
| ----------- | -------| ----|
| `_future_A` |  `uint256` | future A value |
| `_future_time` |  `uint256` | timestamp until ramping should occur; needs to be at least 24h (`MIN_RAMP_TIME`) |

<SourceCode>

```vyper
A_PRECISION: constant(uint256) = 100
MAX_A: constant(uint256) = 10 **6
MAX_A_CHANGE: constant(uint256) = 10

MIN_RAMP_TIME: constant(uint256) = 86400

event RampA:
    old_A: uint256
    new_A: uint256
    initial_time: uint256
    future_time: 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)
```

</SourceCode>

::::

### `stop_ramp_A`
::::description[`StableSwap.stop_ramp_A():`]

:::guard[Guarded Method]

This function is only callable by the `admin` of the Factory.

:::

Function to immediately stop the ramping A. The current value during the ramping process will be finalized as `A`.

Emits: `StopRampA`

<SourceCode>

```vyper
event StopRampA:
    A: uint256
    t: uint256

@external
def stop_ramp_A():
    assert msg.sender == factory.admin()  # dev: only owner

    current_A: uint256 = self._A()
    self.initial_A = current_A
    self.future_A = current_A
    self.initial_A_time = block.timestamp
    self.future_A_time = block.timestamp
    # now (block.timestamp < t1) is always False, so we return saved A

    log StopRampA(current_A, block.timestamp)
```

</SourceCode>

::::

### `set_new_fee`
::::description[`StableSwap.set_new_fee(_new_fee: uint256, _new_offpeg_fee_multiplier: uint256):`]

:::guard[Guarded Method]

This function is only callable by the `admin` of the Factory.

:::

Function to set new values for `fee` and `offpeg_fee_multiplier`.

*Limitations when setting new parameters:*

- `_new_fee` &lt;= `MAX_FEE` (5000000000)
- `_new_offpeg_fee_multiplier` * `_new_fee` &lt;= `MAX_FEE` * `FEE_DENOMINATOR`

Emits: `ApplyNewFee`

| Input      | Type   | Description |
| ----------- | -------| ----|
| `_new_fee` |  `uint256` | new fee |
| `_new_offpeg_fee_multiplier` |  `uint256` | new off-peg fee multiplier |

<SourceCode>

```vyper
MAX_FEE: constant(uint256) = 5 * 10 **9
FEE_DENOMINATOR: constant(uint256) = 10 **10

event ApplyNewFee:
    fee: uint256
    offpeg_fee_multiplier: uint256

@external
def set_new_fee(_new_fee: uint256, _new_offpeg_fee_multiplier: uint256):

    assert msg.sender == factory.admin()

    # set new fee:
    assert _new_fee <= MAX_FEE
    self.fee = _new_fee

    # set new offpeg_fee_multiplier:
    assert _new_offpeg_fee_multiplier * _new_fee <= MAX_FEE * FEE_DENOMINATOR  # dev: offpeg multiplier exceeds maximum
    self.offpeg_fee_multiplier = _new_offpeg_fee_multiplier

    log ApplyNewFee(_new_fee, _new_offpeg_fee_multiplier)
```

</SourceCode>

::::

### `set_ma_exp_time`
::::description[`StableSwap.set_ma_exp_time(_ma_exp_time: uint256, _D_ma_time: uint256):`]

:::guard[Guarded Method]

This function is only callable by the `admin` of the Factory.

:::

Function to set the moving average window for `ma_exp_time` and `D_ma_time`.

*Limitations when setting new fee parameters:*

- `_ma_exp_time` and `_D_ma_time` > 0

| Input      | Type   | Description |
| ----------- | -------| ----|
| `_ma_exp_time` |  `uint256` | new ma exp time |
| `_D_ma_time` |  `uint256` | new D ma time |

<SourceCode>

```vyper
@external
def set_ma_exp_time(_ma_exp_time: uint256, _D_ma_time: uint256):
    """
    @notice Set the moving average window of the price oracles.
    @param _ma_exp_time Moving average window. It is time_in_seconds / ln(2)
    """
    assert msg.sender == factory.admin()  # dev: only owner
    assert 0 not in [_ma_exp_time, _D_ma_time]

    self.ma_exp_time = _ma_exp_time
    self.D_ma_time = _D_ma_time
```

</SourceCode>

::::