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StableSwap-NG Pools: Overview

A Curve pool is essentially a smart contract that implements the StableSwap invariant, housing the logic for exchanging stable tokens. While all Curve pools share this core implementation, they come in various pool flavors.

In its simplest form, a Curve pool is an implementation of the StableSwap invariant involving two or more tokens, often referred to as a 'plain pool.' Alternatively, Curve offers more complex pool variants, including pools with rebasing tokens and metapools. Metapools facilitate the exchange of one or more tokens with those from one or more underlying tokens.

New features:

Supported Assets

Stableswap-NG pools supports the following asset types:

Asset Type Description
0 Standard ERC20 token with no additional features
1 Oracle - token with rate oracle (e.g. wstETH)
2 Rebasing - token with rebase (e.g. stETH)
3 ERC4626 - token with convertToAssets method (e.g. sDAI)

Consequently, supported tokens include:

  • ERC20 support for return True/revert, return True/False, return None
  • ERC20 tokens can have arbitrary decimals (<=18)
  • ERC20 tokens that rebase (either positive or fee on transfer)
  • ERC20 tokens that have a rate oracle (e.g. wstETH, cbETH, sDAI, etc.) Oracle precision must be 10^18
  • ERC4626 tokens with arbitrary percision (<=18) of Vault token and underlying asset

Rebasing Tokens

Rebasing Tokens

Pools including rebasing tokens work a bit differently compared to others. The internal **_balance()** function - which is used to calculate the coin balances within the pool - makes sure that LP's keep all rebases.

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:

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


    return result

Dynamic Fees

Stableswap-NG introduces dynamic fees. The use of the offpeg_fee_multiplier allows the system to dynamically adjust fees based on the pool's state.

The internal _dynamic_fee() function calculates the fee based on the balances and rates of the tokens being exchanged. If the balances of the tokens being exchanged are highly imbalanced or significantly differ from its peg, the fee is adjusted using the offpeg_fee_multiplier.

Dynamic Fee Formula


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Let's define some terms and variables for clarity:

  • Let \(fee\) represent the fee, as retrieved by the method StableSwap.fee()
  • Let \(fee_m\) denote the off-peg fee multiplier, sourced from StableSwap.offpeg_fee_multiplier()
  • FEE_DENOMINATOR is a constant with a value of \(10^{10}\), representing the precision of the fee
  • The terms \(rate_{i}\) and \(balance{i}\) refer to the specific rate and balance for coin \(i\), respectively, and similarly, \(rate_j\) and \(balance_j\) for coin \(j\)
  • \(PRECISION_{i}\) and \(PRECISION_{j}\) are the precision constants for the respective coins

Given these, we define:

\(xp_{i} = \frac{{rate_{i} \times balance_{i}}}{{PRECISION_{i}}}\)

\(xp_{j} = \frac{{rate_{j} \times balance_{j}}}{{PRECISION_{j}}}\)

\(xp_{i}\) and \(xp_{j}\) are the token balances of the pool adjusted for decimals and the pool's internal rates (stored in stored_rates).

And we also have:

\(xps2 = (xp_{i} + xp_{j})^2\)

The dynamic fee is calculated by the following formula:

\[\text{dynamic fee} = \frac{{fee_{m} \times fee}}{\frac{(fee_{m} - 10^{10}) \times 4 \times xp_{i} \times xp_{j}}{xps2}+ 10^{10}}\]
dynamic_fee method
A_PRECISION: constant(uint256) = 100
MAX_COINS: constant(uint256) = 8
PRECISION: constant(uint256) = 10 ** 18
FEE_DENOMINATOR: constant(uint256) = 10 ** 10

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)

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)

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:
        xp.append(rates[idx] * balances[idx] / PRECISION)

    return rates, balances, xp

Interactive Graph

The embedded graph has limited features, such as the inability to modify the axis. However, by clicking the "edit graph on desmos" button at the bottom right, one is redirected to the main Desmos site. There, a wider range of functionalities is available, allowing for further adjustments and detailed exploration of the graph.


The new generation (NG) of stableswap introduces two new pool-built-in oracles:

  • price oracle (spot and moving-average price)
  • moving average D oracle

More on oracles here.


This new function allows the exchange of tokens without actually transfering tokens in, as the exchange is based on the change of the coins balances within the pool.

Users of this method are dex aggregators, arbitrageurs, or other users who do not wish to grant approvals to the contract. They can instead send tokens directly to the contract and call exchange_received().


Explore the exchange_received function's role in streamlining swaps without approvals, its efficiency benefits, and security considerations in a succinct article. Learn more about this innovative feature for cost-effective, secure trading through Curve pools: How to Do Cheaper, Approval-Free Swaps.