Interest

Git Source

This library is used for calculating and accruing interest.

many calculations are unchecked because we asset values are stored as uint128. We also limit the max amount amount of interest to ensure that it can not overflow when added to the current assets.

State Variables

OPTIMAL_UTILIZATION

uint128 internal constant OPTIMAL_UTILIZATION = 0.8e18;

DANGER_UTILIZATION

uint128 internal constant DANGER_UTILIZATION = 0.925e18;

SLOPE1

uint128 internal constant SLOPE1 = 0.1e18;

SLOPE2

uint128 internal constant SLOPE2 = 2e18;

SLOPE3

uint128 internal constant SLOPE3 = 20e18;

BASE_OPTIMAL_UTILIZATION

uint128 internal constant BASE_OPTIMAL_UTILIZATION = 0.08e18;

BASE_DANGER_UTILIZATION

uint128 internal constant BASE_DANGER_UTILIZATION = 0.33e18;

LENDING_FEE_RATE

uint128 internal constant LENDING_FEE_RATE = 10;

MAX_UINT112

uint256 private constant MAX_UINT112 = type(uint112).max;

LAST_DEPOSIT

uint256 private constant LAST_DEPOSIT = 2;

PENALTY_SATURATION_PERCENT_IN_WAD

Maximum percentage for the penalty saturation allowed. This is used to prevent excessive penalties in case of high utilization.

uint256 private constant PENALTY_SATURATION_PERCENT_IN_WAD = 0.85e18;

SATURATION_PENALTY_BUFFER_IN_WAD

MAX_SATURATION_PERCENT_IN_WAD - PENALTY_SATURATION_PERCENT_IN_WAD

uint256 private constant SATURATION_PENALTY_BUFFER_IN_WAD = 0.1e18;

Functions

accrueInterestAndUpdateReservesWithAssets

function accrueInterestAndUpdateReservesWithAssets(
    uint128[6] storage assets,
    AccrueInterestParams memory accrueInterestParams
) external returns (uint256 interestXForLP, uint256 interestYForLP, uint256[3] memory protocolFeeAssets);

getReservesAtTick

we approximate the reserves based on an average tick value since the last lending state update.

this will never return values greater than uint112 max when used correctly. The reserve values are underestimated due to a tick being an approximate price. We use a smaller value when multiplying and a larger when dividing to ensure that we do not overflow.

function getReservesAtTick(
    uint256 activeLiquidityAssets,
    int16 lendingStateTick
) internal pure returns (uint256 reserveXAssets, uint256 reserveYAssets);

Parameters

Name	Type	Description
activeLiquidityAssets	uint256	active L where $\sqrt(reserveX * reserveY) = L$
lendingStateTick	int16	Average tick value since last lending state update.

Returns

Name	Type	Description
reserveXAssets	uint256	approximate average reserve since last lending state update.
reserveYAssets	uint256	approximate average reserve since last lending state update.

getUtilizationsInWads

function getUtilizationsInWads(
    uint128[6] memory startingAssets,
    uint256 reservesXAssets,
    uint256 reservesYAssets,
    uint256 satPercentageInWads
) internal pure returns (uint256[3] memory utilizationInWads);

accrueInterestWithAssets

function accrueInterestWithAssets(
    uint128[6] memory assets,
    AccrueInterestParams memory params
)
    public
    pure
    returns (
        uint128[6] memory newAssets,
        uint256 interestXPortionForLP,
        uint256 interestYPortionForLP,
        uint256[3] memory protocolFeeAssets
    );

getUtilizationInWads

function getUtilizationInWads(
    uint256 totalBorrowedAssets,
    uint256 totalDepositedAssets
) internal pure returns (uint256 utilization);

mutateUtilizationForSaturation

Adjusts utilization based on saturation to calculate interest penalties

When saturation exceeds PENALTY_SATURATION_PERCENT_IN_WAD, utilization is increased to apply higher interest rates as a penalty for high saturation

function mutateUtilizationForSaturation(uint256 utilization, uint256 maxSatInWads) internal pure returns (uint256);

Parameters

Name	Type	Description
utilization	uint256	Current utilization of L, X, or Y assets
maxSatInWads	uint256	Saturation utilization

Returns

Name	Type	Description
<none>	uint256	The adjusted utilization value

computeInterestAssets

function computeInterestAssets(
    uint256 duration,
    uint256 utilization,
    uint256 borrowedAssets,
    uint256 depositedAssets
) internal pure returns (uint256);

computeInterestAssetsGivenRate

function computeInterestAssetsGivenRate(
    uint256 duration,
    uint256 borrowedAssets,
    uint256 depositedAssets,
    uint256 rateInWads
) internal pure returns (uint256);

addInterestToAssets

function addInterestToAssets(uint256 prevAssets, uint256 interest) internal pure returns (uint128);

getAnnualInterestRatePerSecondInWads

Gets the annual interest rate for a given utilization

Same as getAnnualInterestRatePerSecondInWads but without dividing by SECONDS_IN_YEAR

function getAnnualInterestRatePerSecondInWads(
    uint256 utilizationInWads
) internal pure returns (uint256 interestRate);

Parameters

Name	Type	Description
utilizationInWads	uint256	The utilization rate in WADs

Returns

Name	Type	Description
interestRate	uint256	The annual interest rate in WADs

Events

InterestAccrued

event InterestAccrued(
    uint128 depositLAssets,
    uint128 depositXAssets,
    uint128 depositYAssets,
    uint128 borrowLAssets,
    uint128 borrowXAssets,
    uint128 borrowYAssets
);

Structs

AccrueInterestParams

struct AccrueInterestParams {
    uint256 duration;
    int16 lendingStateTick;
    uint256 adjustedActiveLiquidity;
    uint112[6] shares;
    uint256 satPercentageInWads;
}