Stable Pools

Stable pools are designed to facilitate low-slippage swaps between assets that are expected to have a similar value, such as different stablecoins (e.g. USDC ↔ USDT) or derivatives of the same token.

They use a different mathematical model than constant product pools, one that allows for flatter pricing curves near equilibrium. This results in better capital efficiency and reduced slippage when swapping similarly priced tokens.

The Amplified Invariant

Stable pools follow a generalized StableSwap invariant. Instead of:

$$x \cdot y = k$$

They maintain a more complex function based on a virtual price curve and an amplification coefficient (A).

The invariant balances the two reserves using:

$$D = \text{Invariant}(A, x, y)$$

Where:

• $D$ is the invariant
• $A$ is the amplification factor
• $x$ and $y$ are token reserves

This invariant flattens the price curve around the target 1:1 ratio, allowing large volume swaps with minimal price impact — something constant product pools can't do efficiently.

Amplification Factor (A)

The amplification factor $A$ determines how flat the curve is near equilibrium:

• A higher A makes the pool behave more like a constant sum (ideal 1:1 ratio)
• A lower A behaves more like a constant product pool

This lets protocols tune the trade-off between slippage and pool stability.

Swap Calculation Logic

Given two reserves and the amount of one token being offered, the pool uses Newton's method to solve the invariant and compute the return amount for the other token. The actual formula for calculating output is complex but conceptually aims to maintain the invariant $D$ before and after the swap.

In simplified terms:

$$\text{New state still satisfies the same invariant: } D = f(x + \Delta x, y - \Delta y, A)$$

This is done with high-precision arithmetic (e.g., using libraries like shopspring/decimal) to avoid rounding errors.

When to Use

Stable pools are ideal for:

• Swapping pegged assets (e.g. USDT/USDC, stETH/wstETH)
• Minimizing slippage near 1:1 ratio
• Reducing impermanent loss when token prices are tightly correlated