AMM (LLAMMA)

The AMM contract implements LLAMMA — the Lending-Liquidating AMM Algorithm. It holds borrower collateral distributed across discretized price bands and performs soft liquidation: as the collateral price drops into a borrower's band range, the AMM gradually converts their collateral to the borrowed token. If the price recovers, the process reverses (de-liquidation).

The AMM also serves as a regular DEX — arbitrageurs can swap between the collateral and borrowed tokens, which is the mechanism that drives soft liquidation.

Each lending market has its own AMM instance. The associated LendController is the AMM's admin and is the only address allowed to deposit/withdraw collateral.

AMM.vy

The source code for the AMM.vy contract can be found on GitHub. The contract is written in Vyper version 0.4.3.

Deployment addresses will be added once contracts are finalized.

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Swaps

exchange

AMM.exchange(i: uint256, j: uint256, in_amount: uint256, min_amount: uint256, _for: address) -> uint256[2]

Swaps in_amount of token i for token j. Token index 0 is the borrowed token, index 1 is the collateral token.

Input	Type	Description
i	uint256	Input token index (0 = borrowed, 1 = collateral)
j	uint256	Output token index
in_amount	uint256	Amount of input token
min_amount	uint256	Minimum output amount (slippage protection)
_for	address	Address to receive the output tokens

Returns: [in_amount_done, out_amount] (uint256[2]).

Emits: TokenExchange event.

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exchange_dy

AMM.exchange_dy(i: uint256, j: uint256, out_amount: uint256, max_amount: uint256, _for: address) -> uint256[2]

Swaps to receive exactly out_amount of token j, paying at most max_amount of token i.

Input	Type	Description
i	uint256	Input token index
j	uint256	Output token index
out_amount	uint256	Desired output amount
max_amount	uint256	Maximum input amount (slippage protection)
_for	address	Address to receive the output tokens

Returns: [in_amount, out_amount_done] (uint256[2]).

Emits: TokenExchange event.

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get_dy

AMM.get_dy(i: uint256, j: uint256, in_amount: uint256) -> uint256: view

Calculates the output amount for a given input amount (i.e., a swap quote).

Input	Type	Description
i	uint256	Input token index
j	uint256	Output token index
in_amount	uint256	Input amount

Returns: expected output amount (uint256).

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get_dx

AMM.get_dx(i: uint256, j: uint256, out_amount: uint256) -> uint256: view

Calculates the input amount needed to receive a given output amount.

Input	Type	Description
i	uint256	Input token index
j	uint256	Output token index
out_amount	uint256	Desired output amount

Returns: required input amount (uint256).

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get_dxdy

AMM.get_dxdy(i: uint256, j: uint256, in_amount: uint256) -> uint256[2]: view

Returns both the input amount used and the output amount for a given swap.

Input	Type	Description
i	uint256	Input token index
j	uint256	Output token index
in_amount	uint256	Input amount

Returns: [in_amount_done, out_amount] (uint256[2]).

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get_dydx

AMM.get_dydx(i: uint256, j: uint256, out_amount: uint256) -> uint256[2]: view

Returns both the output amount and the input amount needed for a given desired output.

Input	Type	Description
i	uint256	Input token index
j	uint256	Output token index
out_amount	uint256	Desired output amount

Returns: [out_amount_done, in_amount] (uint256[2]).

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get_amount_for_price

AMM.get_amount_for_price(_p: uint256) -> uint256: view

Returns the amount of token 0 (borrowed token) needed to move the AMM price to _p.

Input	Type	Description
_p	uint256	Target price

Returns: amount of token 0 needed (uint256).

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Price and Band Info

price_oracle

AMM.price_oracle() -> uint256: view

Returns the current price from the external price oracle, smoothed by the AMM's internal EMA.

Returns: oracle price (uint256).

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price_oracle_contract

AMM.price_oracle_contract() -> address: view

Returns the address of the external price oracle contract.

Returns: oracle address (address).

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get_p

AMM.get_p() -> uint256: view

Returns the current AMM price (the marginal price at the active band).

Returns: current price (uint256).

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get_base_price

AMM.get_base_price() -> uint256: view

Returns the base price used to calculate band boundaries, adjusted for accumulated interest rate.

Returns: base price (uint256).

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active_band

AMM.active_band() -> int256: view

Returns the index of the currently active band (the band where trading is happening).

Returns: active band index (int256).

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active_band_with_skip

AMM.active_band_with_skip() -> int256: view

Returns the active band, skipping over empty bands for gas efficiency.

Returns: active band index (int256).

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min_band

AMM.min_band() -> int256: view

Returns the lowest band index that has ever been used.

Returns: minimum band index (int256).

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max_band

AMM.max_band() -> int256: view

Returns the highest band index that has ever been used.

Returns: maximum band index (int256).

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p_current_up

AMM.p_current_up(_n: int256) -> uint256: view

Returns the upper price boundary of band _n, accounting for the current state of the band.

Input	Type	Description
_n	int256	Band index

Returns: upper price boundary (uint256).

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p_current_down

AMM.p_current_down(_n: int256) -> uint256: view

Returns the lower price boundary of band _n, accounting for the current state of the band.

Input	Type	Description
_n	int256	Band index

Returns: lower price boundary (uint256).

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p_oracle_up

AMM.p_oracle_up(_n: int256) -> uint256: view

Returns the upper oracle price boundary of band _n (based on the oracle price, not the current AMM state).

Input	Type	Description
_n	int256	Band index

Returns: upper oracle price (uint256).

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p_oracle_down

AMM.p_oracle_down(_n: int256) -> uint256: view

Returns the lower oracle price boundary of band _n.

Input	Type	Description
_n	int256	Band index

Returns: lower oracle price (uint256).

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dynamic_fee

AMM.dynamic_fee() -> uint256: view

Returns the current dynamic fee, which increases when the AMM price deviates from the oracle price to discourage trades that worsen the deviation.

Returns: dynamic fee (uint256).

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---

User Position Info

get_y_up

AMM.get_y_up(_user: address) -> uint256: view

Returns the amount of collateral token a user would have if the price goes up (full de-liquidation scenario).

Input	Type	Description
_user	address	User address

Returns: collateral amount (uint256).

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get_x_down

AMM.get_x_down(_user: address) -> uint256: view

Returns the amount of borrowed token a user would have if the price goes down (full soft-liquidation scenario).

Input	Type	Description
_user	address	User address

Returns: borrowed token amount (uint256).

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get_sum_xy

AMM.get_sum_xy(_user: address) -> uint256[2]: view

Returns the total amounts of borrowed token and collateral token held in a user's bands.

Input	Type	Description
_user	address	User address

Returns: [sum_x (borrowed), sum_y (collateral)] (uint256[2]).

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get_xy

AMM.get_xy(_user: address) -> IController.UserTicks[]: view

Returns the per-band breakdown of a user's position — the amount of borrowed and collateral tokens in each band.

Input	Type	Description
_user	address	User address

Returns: array of per-band positions (IController.UserTicks[]).

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read_user_tick_numbers

AMM.read_user_tick_numbers(_user: address) -> int256[2]: view

Returns the upper and lower band indices of a user's position.

Input	Type	Description
_user	address	User address

Returns: [n1 (upper), n2 (lower)] (int256[2]).

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has_liquidity

AMM.has_liquidity(_user: address) -> bool: view

Returns whether a user has any liquidity deposited in the AMM.

Input	Type	Description
_user	address	User address

Returns: has liquidity (bool).

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bands_x

AMM.bands_x(_n: int256) -> uint256: view

Returns the total amount of borrowed token in band _n.

Input	Type	Description
_n	int256	Band index

Returns: borrowed token amount in band (uint256).

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bands_y

AMM.bands_y(_n: int256) -> uint256: view

Returns the total amount of collateral token in band _n.

Input	Type	Description
_n	int256	Band index

Returns: collateral token amount in band (uint256).

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user_shares

AMM.user_shares(_user: address) -> UserTicks: view

Returns a user's share information across their deposited bands.

Input	Type	Description
_user	address	User address

Returns: user tick/share info (UserTicks).

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Rate and Fee

rate

AMM.rate() -> uint256: view

Returns the current interest rate stored in the AMM, set by the controller from the monetary policy.

Returns: current rate (uint256).

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get_rate_mul

AMM.get_rate_mul() -> uint256: view

Returns the current rate multiplier — a cumulative value that tracks how much the base price has shifted due to interest accrual.

Returns: rate multiplier (uint256).

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fee

AMM.fee() -> uint256: view

Returns the current swap fee.

Returns: fee (uint256).

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Admin Methods

These functions are restricted to the AMM's admin, which is the LendController.

set_admin

AMM.set_admin(_admin: address)

Guarded Method

This function is only callable by the current admin (the LendController).

Transfers AMM admin to a new address.

Input	Type	Description
_admin	address	New admin address

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deposit_range

AMM.deposit_range(_user: address, _amount: uint256, _n1: int256, _n2: int256)

Guarded Method

This function is only callable by the admin (LendController). It is called internally when a loan is created or collateral is added.

Deposits collateral for a user across bands _n1 to _n2.

Input	Type	Description
_user	address	User address
_amount	uint256	Collateral amount
_n1	int256	Upper band index
_n2	int256	Lower band index

Emits: Deposit event.

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withdraw

AMM.withdraw(_user: address, _frac: uint256) -> uint256[2]

Guarded Method

This function is only callable by the admin (LendController). It is called internally during repayment and liquidation.

Withdraws a fraction of a user's position from the AMM. A _frac of 10**18 means full withdrawal.

Input	Type	Description
_user	address	User address
_frac	uint256	Fraction to withdraw (scaled by 1e18)

Returns: [withdrawn_borrowed, withdrawn_collateral] (uint256[2]).

Emits: Withdraw event.

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set_rate

AMM.set_rate(_rate: uint256) -> uint256

Guarded Method

This function is only callable by the admin (LendController).

Sets the interest rate in the AMM and returns the updated rate multiplier.

Input	Type	Description
_rate	uint256	New rate value

Returns: updated rate multiplier (uint256).

Emits: SetRate event.

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set_fee

AMM.set_fee(_fee: uint256)

Guarded Method

This function is only callable by the admin (LendController).

Sets the swap fee.

Input	Type	Description
_fee	uint256	New fee value

Emits: SetFee event.

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set_price_oracle

AMM.set_price_oracle(_price_oracle: address)

Guarded Method

This function is only callable by the admin (LendController).

Sets the external price oracle contract.

Input	Type	Description
_price_oracle	address	New oracle address

Emits: SetPriceOracle event.

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set_callback

AMM.set_callback(_liquidity_mining_callback: address)

Guarded Method

This function is only callable by the admin (LendController).

Sets the liquidity mining callback (gauge) address.

Input	Type	Description
_liquidity_mining_callback	address	Callback address

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Other Methods

coins

AMM.coins(_i: uint256) -> address: view

Returns the token address at index _i (0 = borrowed token, 1 = collateral token).

Input	Type	Description
_i	uint256	Token index (0 or 1)

Returns: token address (address).

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A

AMM.A() -> uint256: view

Returns the amplification coefficient. Band width is approximately 1/A.

Returns: amplification coefficient (uint256).

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admin

AMM.admin() -> address: view

Returns the admin address (the LendController).

Returns: admin address (address).

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can_skip_bands

AMM.can_skip_bands(_n_end: int256) -> bool: view

Returns whether bands up to _n_end can be skipped (are empty) during traversal.

Input	Type	Description
_n_end	int256	Target band index

Returns: whether bands can be skipped (bool).

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liquidity_mining_callback

AMM.liquidity_mining_callback() -> address: view

Returns the liquidity mining callback (gauge) address.

Returns: callback address (address).

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