IShifting

_calcRangeShifting

function _calcRangeShifting(uint256 upperRange_, uint256 lowerRange_, uint256 dexVariables2_) external returns (uint256, uint256, uint256)

Calculates the new upper and lower range values during an active range shift

Parameters

Name	Type	Description
upperRange_	uint256	The target upper range value
lowerRange_	uint256	The target lower range value
dexVariables2_	uint256	needed in case shift is ended and we need to update dexVariables2

Return Values

Name	Type	Description
[0]	uint256	The updated upper range, lower range, and dexVariables2
[1]	uint256
[2]	uint256

_calcThresholdShifting

function _calcThresholdShifting(uint256 upperThreshold_, uint256 lowerThreshold_, uint256 dexVariables2_) external returns (uint256, uint256, uint256)

Calculates the new threshold values during an active threshold shift

Parameters

Name	Type	Description
upperThreshold_	uint256	The target upper threshold value
lowerThreshold_	uint256	The target lower threshold value
dexVariables2_	uint256	needed in case shift is ended and we need to update dexVariables2

Return Values

Name	Type	Description
[0]	uint256	The updated upper threshold, lower threshold, and dexVariables2
[1]	uint256
[2]	uint256

_calcCenterPrice

function _calcCenterPrice(uint256 dexVariables_, uint256 dexVariables2_) external returns (uint256)

Calculates the new center price during an active center price shift

Parameters

Name	Type	Description
dexVariables_	uint256	The current state of dex variables
dexVariables2_	uint256	Additional dex variables

Return Values

Name	Type	Description
[0]	uint256	The updated center price

CoreHelpers

_spell

function _spell(address target_, bytes data_) internal returns (bytes response_)

do any arbitrary call

Parameters

Name	Type	Description
target_	address	Address to which the call needs to be delegated
data_	bytes	Data to execute at the delegated address

_getAmountOut

function _getAmountOut(uint256 amountIn_, uint256 iReserveIn_, uint256 iReserveOut_) internal pure returns (uint256 amountOut_)

Given an input amount of asset and pair reserves, returns the maximum output amount of the other asset

Parameters

Name	Type	Description
amountIn_	uint256	The amount of input asset.
iReserveIn_	uint256	Imaginary token reserve with input amount.
iReserveOut_	uint256	Imaginary token reserve of output amount.

_getAmountIn

function _getAmountIn(uint256 amountOut_, uint256 iReserveIn_, uint256 iReserveOut_) internal pure returns (uint256 amountIn_)

Given an output amount of asset and pair reserves, returns the input amount of the other asset

Parameters

Name	Type	Description
amountOut_	uint256	Desired output amount of the asset.
iReserveIn_	uint256	Imaginary token reserve of input amount.
iReserveOut_	uint256	Imaginary token reserve of output amount.

_swapRoutingIn

function _swapRoutingIn(uint256 t, uint256 x, uint256 y, uint256 x2, uint256 y2) internal pure returns (int256 a_)

Parameters

Name	Type	Description
t	uint256	total amount in
x	uint256	imaginary reserves of token out of collateral
y	uint256	imaginary reserves of token in of collateral
x2	uint256	imaginary reserves of token out of debt
y2	uint256	imaginary reserves of token in of debt

Return Values

Name	Type	Description
a_	int256	how much swap should go through collateral pool. Remaining will go from debt note if a < 0 then entire trade route through debt pool and debt pool arbitrage with col pool note if a > t then entire trade route through col pool and col pool arbitrage with debt pool note if a > 0 & a < t then swap will route through both pools

_swapRoutingOut

function _swapRoutingOut(uint256 t, uint256 x, uint256 y, uint256 x2, uint256 y2) internal pure returns (int256 a_)

Parameters

Name	Type	Description
t	uint256	total amount out
x	uint256	imaginary reserves of token in of collateral
y	uint256	imaginary reserves of token out of collateral
x2	uint256	imaginary reserves of token in of debt
y2	uint256	imaginary reserves of token out of debt

Return Values

Name	Type	Description
a_	int256	how much swap should go through collateral pool. Remaining will go from debt note if a < 0 then entire trade route through debt pool and debt pool arbitrage with col pool note if a > t then entire trade route through col pool and col pool arbitrage with debt pool note if a > 0 & a < t then swap will route through both pools

_utilizationVerify

function _utilizationVerify(uint256 utilizationLimit_, bytes32 exchangePriceSlot_) internal view

_check

function _check(uint256 dexVariables_, uint256 dexVariables2_) internal

_verifyToken0Reserves

function _verifyToken0Reserves(uint256 token0Reserves_, uint256 token1Reserves_, uint256 centerPrice_, uint256 minLiquidity_) internal pure

if token0 reserves are too low w.r.t token1 then revert, this is to avoid edge case scenario and making sure that precision on calculations should be high enough

_verifyToken1Reserves

function _verifyToken1Reserves(uint256 token0Reserves_, uint256 token1Reserves_, uint256 centerPrice_, uint256 minLiquidity_) internal pure

if token1 reserves are too low w.r.t token0 then revert, this is to avoid edge case scenario and making sure that precision on calculations should be high enough

_verifySwapAndNonPerfectActions

function _verifySwapAndNonPerfectActions(uint256 amountAdjusted_, uint256 amount_) internal pure

_calcRangeShifting

function _calcRangeShifting(uint256 upperRange_, uint256 lowerRange_, uint256 dexVariables2_) internal returns (uint256, uint256, uint256)

This function handles the gradual shifting of range values over time If the shift is complete, it updates the state and clears the shift data

Calculates the new upper and lower range values during an active range shift

Parameters

Name	Type	Description
upperRange_	uint256	The target upper range value
lowerRange_	uint256	The target lower range value
dexVariables2_	uint256	needed in case shift is ended and we need to update dexVariables2

Return Values

Name	Type	Description
[0]	uint256	The updated upper range, lower range, and dexVariables2
[1]	uint256
[2]	uint256

_calcThresholdShifting

function _calcThresholdShifting(uint256 upperThreshold_, uint256 lowerThreshold_, uint256 thresholdTime_) internal returns (uint256, uint256, uint256)

This function handles the gradual shifting of threshold values over time If the shift is complete, it updates the state and clears the shift data

Calculates the new upper and lower threshold values during an active threshold shift

Parameters

Name	Type	Description
upperThreshold_	uint256	The target upper threshold value
lowerThreshold_	uint256	The target lower threshold value
thresholdTime_	uint256	The time passed since shifting started

Return Values

Name	Type	Description
[0]	uint256	The updated upper threshold, lower threshold, and threshold time
[1]	uint256
[2]	uint256

_calcCenterPrice

function _calcCenterPrice(uint256 dexVariables_, uint256 dexVariables2_) internal returns (uint256 newCenterPrice_)

This function gradually shifts the center price towards a new target price over time It uses an external price source (via ICenterPrice) to determine the target price The shift continues until the current price reaches the target, or the shift duration ends Once the shift is complete, it updates the state and clears the shift data The shift rate is dynamic and depends on:

• Time remaining in the shift duration
• The new center price (fetched externally, which may change)
• The current (old) center price This results in a fuzzy shifting mechanism where the rate can change as these parameters evolve The externally fetched new center price is expected to not differ significantly from the last externally fetched center price

Calculates the new center price during an active price shift

Parameters

Name	Type	Description
dexVariables_	uint256	The current state of dex variables
dexVariables2_	uint256	Additional dex variables

Return Values

Name	Type	Description
newCenterPrice_	uint256	The updated center price

_getPricesAndExchangePrices

function _getPricesAndExchangePrices(uint256 dexVariables_, uint256 dexVariables2_) internal returns (struct Structs.PricesAndExchangePrice pex_)

Calculates and returns the current prices and exchange prices for the pool

This function performs the following operations: 1. Determines the center price (either from storage, external source, or calculated) 2. Retrieves the last stored price from dexVariables 3. Calculates the upper and lower range prices based on the center price and range percentages 4. Checks if rebalancing is needed based on threshold settings 5. Adjusts prices if necessary based on the time elapsed and threshold conditions 6. Update the dexVariables2* if changes were made 7. Returns the calculated prices and exchange prices in the PricesAndExchangePrice struct*

Parameters

Name	Type	Description
dexVariables_	uint256	The first set of DEX variables containing various pool parameters
dexVariables2_	uint256	The second set of DEX variables containing additional pool parameters

Return Values

Name	Type	Description
pex_	struct Structs.PricesAndExchangePrice	A struct containing the calculated prices and exchange prices: - pex*.lastStoredPrice: The last stored price in 1e27 decimals - pex*.centerPrice: The calculated or fetched center price in 1e27 decimals - pex*.upperRange: The upper range price limit in 1e27 decimals - pex*.lowerRange: The lower range price limit in 1e27 decimals - pex*.geometricMean: The geometric mean of upper range & lower range in 1e27 decimals - pex*.supplyToken0ExchangePrice: The current exchange price for supplying token0 - pex*.borrowToken0ExchangePrice: The current exchange price for borrowing token0 - pex*.supplyToken1ExchangePrice: The current exchange price for supplying token1 - pex_.borrowToken1ExchangePrice: The current exchange price for borrowing token1

_calculateReservesOutsideRange

function _calculateReservesOutsideRange(uint256 gp_, uint256 pa_, uint256 rx_, uint256 ry_) internal pure returns (uint256 xa_, uint256 yb_)

getting reserves outside range.

Parameters

Name	Type	Description
gp_	uint256	is geometric mean pricing of upper percent & lower percent
pa_	uint256	price of upper range or lower range
rx_	uint256	real reserves of token0 or token1
ry_	uint256	whatever is rx* the other will be ry*

_getLiquidityCollateral

function _getLiquidityCollateral(bytes32 supplyTokenSlot_, uint256 tokenExchangePrice_, bool isToken0_) internal view returns (uint256 tokenSupply_)

Retrieves collateral amount from liquidity layer for a given token

Parameters

Name	Type	Description
supplyTokenSlot_	bytes32	The storage slot for the supply token data
tokenExchangePrice_	uint256	The exchange price of the token
isToken0_	bool	Boolean indicating if the token is token0 (true) or token1 (false)

Return Values

Name	Type	Description
tokenSupply_	uint256	The calculated liquidity collateral amount

_getCollateralReserves

function _getCollateralReserves(uint256 geometricMean_, uint256 upperRange_, uint256 lowerRange_, uint256 token0SupplyExchangePrice_, uint256 token1SupplyExchangePrice_) internal view returns (struct Structs.CollateralReserves c_)

Calculates the real and imaginary reserves for collateral tokens

This function retrieves the supply of both tokens from the liquidity layer, adjusts them based on exchange prices, and calculates imaginary reserves based on the geometric mean and price range

Parameters

Name	Type	Description
geometricMean_	uint256	The geometric mean of the token prices
upperRange_	uint256	The upper price range
lowerRange_	uint256	The lower price range
token0SupplyExchangePrice_	uint256	The exchange price for token0 from liquidity layer
token1SupplyExchangePrice_	uint256	The exchange price for token1 from liquidity layer

Return Values

Name	Type	Description
c_	struct Structs.CollateralReserves	A struct containing the calculated real and imaginary reserves for both tokens: - token0RealReserves: The real reserves of token0 - token1RealReserves: The real reserves of token1 - token0ImaginaryReserves: The imaginary reserves of token0 - token1ImaginaryReserves: The imaginary reserves of token1

_calculateDebtReserves

function _calculateDebtReserves(uint256 gp_, uint256 pb_, uint256 dx_, uint256 dy_) internal pure returns (uint256 rx_, uint256 ry_, uint256 irx_, uint256 iry_)

Calculates the real and imaginary debt reserves for both tokens

This function uses a quadratic equation to determine the debt reserves based on the geometric mean price and the current debt amounts

Parameters

Name	Type	Description
gp_	uint256	The geometric mean price of upper range & lower range
pb_	uint256	The price of lower range
dx_	uint256	The debt amount of one token
dy_	uint256	The debt amount of the other token

Return Values

Name	Type	Description
rx_	uint256	The real debt reserve of the first token
ry_	uint256	The real debt reserve of the second token
irx_	uint256	The imaginary debt reserve of the first token
iry_	uint256	The imaginary debt reserve of the second token

_getLiquidityDebt

function _getLiquidityDebt(bytes32 borrowTokenSlot_, uint256 tokenExchangePrice_, bool isToken0_) internal view returns (uint256 tokenDebt_)

Calculates the debt amount for a given token from liquidity layer

Parameters

Name	Type	Description
borrowTokenSlot_	bytes32	The storage slot for the token's borrow data
tokenExchangePrice_	uint256	The current exchange price of the token
isToken0_	bool	Boolean indicating if this is for token0 (true) or token1 (false)

Return Values

Name	Type	Description
tokenDebt_	uint256	The calculated debt amount for the token

_getDebtReserves

function _getDebtReserves(uint256 geometricMean_, uint256 upperRange_, uint256 lowerRange_, uint256 token0BorrowExchangePrice_, uint256 token1BorrowExchangePrice_) internal view returns (struct Structs.DebtReserves d_)

Calculates the debt reserves for both tokens

Parameters

Name	Type	Description
geometricMean_	uint256	The geometric mean of the upper and lower price ranges
upperRange_	uint256	The upper price range
lowerRange_	uint256	The lower price range
token0BorrowExchangePrice_	uint256	The exchange price of token0 from liquidity layer
token1BorrowExchangePrice_	uint256	The exchange price of token1 from liquidity layer

Return Values

Name	Type	Description
d_	struct Structs.DebtReserves	The calculated debt reserves for both tokens, containing: - token0Debt: The debt amount of token0 - token1Debt: The debt amount of token1 - token0RealReserves: The real reserves of token0 derived from token1 debt - token1RealReserves: The real reserves of token1 derived from token0 debt - token0ImaginaryReserves: The imaginary debt reserves of token0 - token1ImaginaryReserves: The imaginary debt reserves of token1

_priceDiffCheck

function _priceDiffCheck(uint256 oldPrice_, uint256 newPrice_) internal pure returns (int256 priceDiff_)

_updateOracle

function _updateOracle(uint256 newPrice_, uint256 centerPrice_, uint256 dexVariables_) internal returns (uint256)

_hookVerify

function _hookVerify(uint256 hookAddress_, uint256 mode_, bool swap0to1_, uint256 price_) internal

_updateSupplyShares

function _updateSupplyShares(uint256 newTotalShares_) internal

_updateBorrowShares

function _updateBorrowShares(uint256 newTotalShares_) internal

constructor

constructor(struct Structs.ConstantViews constantViews_) internal