DAMM v1 Formulas

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DAMM v1 is a full-range AMM with two main curve designs: constant-product pools for volatile assets, and stable-swap pools for assets that should trade close together. The formulas below explain how the product behaves without turning this page into an integration guide.

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Constant-product pools

The basic volatile-pool formula is: $$x \times y = k$$ Where:

• x is the amount of token A in the pool.
• y is the amount of token B in the pool.
• k is the pool invariant.

When a trader adds token A and removes token B, x rises and y falls. The pool reprices the trade so the relationship between both reserves stays balanced. For users, this means:

• Larger pools usually create lower price impact.
• Larger trades move price more than smaller trades.
• The pool supports a continuous price range from very low to very high prices.

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Constant-product swap output

Before fees, a simplified output calculation looks like this: $$\text{new source reserve} = \text{source reserve} + \text{input amount}$$ $$\text{new destination reserve} = \frac{k}{\text{new source reserve}}$$ $$\text{output amount} = \text{destination reserve} - \text{new destination reserve}$$ DAMM v1 uses safe on-chain integer math, so tiny rounding differences can happen at the smallest token unit. Product-wise, the idea is straightforward: every buy makes the bought token scarcer in the pool, which raises its price for the next trade.

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Stable pools

Stable pools are designed for assets that should trade near a target relationship, such as USDC/USDT or SOL/LST markets. Instead of using only x × y = k, DAMM v1 stable pools use a StableSwap-style invariant with an amplification factor. A simplified StableSwap invariant can be represented as: $$A \cdot n^n \cdot \sum x_i + D = A \cdot n^n \cdot D + \frac{D^{n+1}}{n^n \cdot \prod x_i}$$ Where:

• A is the amplification factor.
• n is the number of assets in the pool. DAMM v1 pools are two-token pools.
• x_i represents normalized token balances.
• D is the stable pool invariant.

In plain English: amplification makes the pool behave as if it has deeper liquidity near the target price. That helps reduce slippage when both assets are close to their expected relationship.

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Token normalization

Stable pools normalize token amounts before applying the curve. This matters when two tokens have different decimals. $$\text{normalized amount} = \text{raw amount} \times \text{token multiplier}$$ The goal is to compare both assets on a consistent precision scale before calculating swaps, deposits, and withdrawals.

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LST depeg adjustment

For supported LST pools, DAMM v1 can account for the changing value of the staking token relative to SOL. The program stores and updates a base virtual price for the LST side of the pool. Conceptually: $$\text{pegged LST amount} = \text{LST amount} \times \text{LST virtual price}$$ This lets the pool reason about an LST’s value instead of treating one LST as always equal to one SOL. That is important because LSTs generally increase in SOL terms as staking rewards accrue.

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LP share ownership

LP tokens represent a share of the pool. A simplified LP ownership formula is: $$\text{LP ownership share} = \frac{\text{LP tokens held}}{\text{total LP token supply}}$$ The value of that share depends on the pool’s underlying token value: $$\text{LP share value} = \text{ownership share} \times \text{total pool value}$$ DAMM v1 pools route token balances through Dynamic Vaults. That means the pool often measures its token A and token B totals by converting vault LP balances back into underlying token amounts.

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Virtual price

Virtual price is a useful way to understand whether a pool share is becoming more valuable over time. $$\text{virtual price} = \frac{D}{\text{LP token supply}}$$ D is the curve invariant computed from the pool’s vault-backed token amounts. For constant-product pools, DAMM v1 uses sqrt(x * y). For stable pools, it uses the StableSwap invariant. Virtual price can rise when:

• Swaps generate fees that remain in the pool.
• Eligible vault assets earn yield.
• Rewards or yield increase the underlying value backing pool shares.

For LPs, virtual price is the bridge between pool activity and share value.

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Trading fees

DAMM v1 charges trading fees on swaps. A simplified fee calculation is: $$\text{trading fee} = \text{input amount} \times \frac{\text{trade fee numerator}}{\text{trade fee denominator}}$$ DAMM v1 also supports protocol fees: $$\text{protocol fee} = \text{trading fee} \times \frac{\text{protocol fee numerator}}{\text{protocol fee denominator}}$$ The protocol fee is computed from the total trading fee. The remaining fee value benefits LPs because it stays with the pool and increases the value backing LP tokens.

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Base APY from virtual price

DAMM v1 APY can be estimated from virtual price growth over a time window: $$\text{base APY} = \left(\left(\frac{\text{Virtual Price}_{2}}{\text{Virtual Price}_{1}}\right)^{\frac{\text{1 year}}{\text{timeframe}}} - 1\right) \times 100$$ Where:

• Virtual Price 1 is the earlier virtual price.
• Virtual Price 2 is the later virtual price.
• timeframe is the time between the two measurements.

This base APY can include the effect of trading fees and eligible vault yield because both can increase the value backing each LP token.

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365-day fee over TVL

A simple fee efficiency metric annualizes recent swap fees against pool liquidity: $$\text{365d fee / TVL} = \frac{\text{24h fees} \times 365}{\text{pool TVL}}$$ This helps LPs compare how much fee activity a pool is generating relative to the amount of liquidity supplied.

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External farm rewards

External DAMM v1 farms distribute reward tokens to staked LP tokens over time. Farming is a separate reward layer around the AMM LP token, not core swap logic inside the AMM program. A simplified reward rate is: $$\text{reward rate} = \frac{\text{funded reward amount}}{\text{reward duration}}$$ Reward per staked LP token grows as time passes: $$\text{reward per token} = \text{previous reward per token} + \frac{\text{elapsed time} \times \text{reward rate}}{\text{total staked LP tokens}}$$ A user’s pending reward is based on their staked balance: $$\text{user reward} = \text{staked LP tokens} \times \text{reward per token since last update}$$ DAMM v1 farm integrations have historically supported up to two reward tokens. Check the farm program and campaign configuration for exact reward-accounting behavior.

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LM APR

Liquidity mining APR estimates the annualized value of farm emissions relative to farm TVL: $$\text{LM APR} = \left(\left(1 + \frac{\text{farm reward per day}}{\text{farm TVL}}\right)^{365} - 1\right) \times 100$$ Where:

• farm reward per day is the daily token emission value in USD.
• farm TVL is the value of LP tokens staked in the farm.
• pool TVL is the value of all token A and token B liquidity in the pool.