Elastic Core Libraries

BaseSplitCodeFactory

Inherited by the Factory contract. Main purpose is to hold the Kyberswap Elastic Pool creation code in a separate address, since its creation code is close to the bytecode size limit of 24kB.

Taken from Balancer Labs's solidity utils repo. The only modification made is the unchecked keyword for sol 0.8 compatibility.

`getCreationCodeContracts()`

Returns the 2 addresses where the creation code of the contract created by this factory is stored.

`getCreationCode()`

Returns the creation code of the contract this factory creates.

CodeDeployer

Taken from Balancer Labs's solidity utils repo. Imported and used by the BaseSplitCodeFactory contract to handle deployment.

FullMath

Taken from Mathemagic finale: muldiv - Remco Bloeman. Facilitates multiplication and division that can have overflow of an intermediate value without any loss of precision. Handles "phantom overflow" i.e., allows multiplication and division where an intermediate value overflows 256 bits.

`mulDivFloor()`

Returns (a * b / denominator) rounded down.

Input	Type	Explanation
`a`	`uint256`	multiplicand
`b`	`uint256`	multiplier
`denominator`	`uint256`	divisor

`mulDivCeiling()`

Similar to mulDivFloor, but rounded up.

LinkedList

A doubly linked list to be used for tick management.

Struct: Data

Field	Type	Explanation
`previous`	`int24`	previous tick
`next`	`int24`	next tick

`init()`

Initializes the LinkedList with the lowestValue and highestValue, where

lowestValue.previous = lowestValue
lowestValue.next = highestValue
highestValue.previous = lowestValue
highestValue.next = highestValue

Field	Type	Explanation
`self`	`mapping(int24 => Data)`	A mapping of `int24` values to the `Data` struct
`lowestValue`	`int24`	lowest value
`highestValue`	`int24`	highest value

`insert()`

Inserts a new value into the LinkedList, given an existing lower value. The new value to be inserted should not be an existing value. Also, the condition lowerValue < newValue < lowerValue.next should be satisfied.

Field	Type	Explanation
`self`	`mapping(int24 => Data)`	A mapping of `int24` values to the `Data` struct
`newValue`	`int24`	value to be inserted
`lowerValue`	`int24`	highest existing value in the linked list that is `< newValue`

`remove()`

Removes an existing value from the LinkedList. Returns the next lowest value (existingValue.previous).

Note that no removal is performed if removedValue happens to be the lowestValue or highestValue passed in init().

Field	Type	Explanation
`self`	`mapping(int24 => Data)`	A mapping of `int24` values to the `Data` struct
`removedValue`	`int24`	value to be removed

LiqDeltaMath

Contains a function to assist with the addition of signed liquidityDelta to unsigned liquidity.

`applyLiquidityDelta()`

Adds or remove uint128 liquidityDelta to uint128 liquidity

Field	Type	Explanation
`liquidity`	`uint128`	Liquidity to be adjusted
`liquidityDelta`	`int128`	quantity change to be applied
`isAddLiquidity`	`bool`	true = add liquidity, false = remove liquidity

MathConstants

Contains constants commonly used by multiple files.

QtyDeltaMath

Contains functions for calculating token0 and token1 quantites from differences in prices or from burning reinvestment tokens

`getQtysForInitialLockup()`

Calculate the token0 and token1 quantities needed for unlocking the pool given an initial price and liquidity.

Input

Input Field	Type	Explanation
`initialSqrtP`	`uint160`	initial sqrt price raised by `2**96`
`liquidity`	`uint128`	initial liquidity. should be `MIN_LIQUIDITY = 100000`

Output

Return Field	Type	Explanation
`qty0`	`uint256`	token0 quantity required
`qty1`	`uint256`	token1 quantity required

`calcRequiredQty0()`

Calculates the token0 quantity between 2 sqrt prices for a given liquidity quantity.

Note that the function assumes that upperSqrtP > lowerSqrtP.

Input

Field	Type	Explanation
`lowerSqrtP`	`uint160`	the lower sqrt price
`upperSqrtP`	`uint128`	the upper sqrt price
`liquidity`	`int128`	liquidity quantity
`isAddLiquidity`	`bool`	true = add liquidity, false = remove liquidity

Output

Type	Explanation
`int256`	token0 qty required for position with liquidity between the 2 sqrt prices

Generally, if the return value > 0, it will be transferred into the pool. Conversely, if the return value < 0, it will be transferred out of the pool.

`calcRequiredQty1()`

Calculates the token1 quantity between 2 sqrt prices for a given liquidity quantity.

Note that the function assumes that upperSqrtP > lowerSqrtP.

Input

Field	Type	Explanation
`lowerSqrtP`	`uint160`	the lower sqrt price
`upperSqrtP`	`uint128`	the upper sqrt price
`liquidity`	`int128`	liquidity quantity
`isAddLiquidity`	`bool`	true = add liquidity, false = remove liquidity

Output

Type	Explanation
`int256`	token0 qty required for position with liquidity between the 2 sqrt prices

Generally, if the return value > 0, it will be transferred into the pool. Conversely, if the return value < 0, it will be transferred out of the pool.

`getQty0FromBurnRTokens()`

Calculates the token0 quantity to be sent to the user for a given amount of reinvestment tokens to be burnt.

Input Field	Type	Explanation
`sqrtP`	`uint160`	the current sqrt price
`liquidity`	`uint128`	expected change in reinvestment liquidity due to the burning of reinvestment tokens

`getQty1FromBurnRTokens()`

Calculates the token1 quantity to be sent to the user for a given amount of reinvestment tokens to be burnt.

Input Field	Type	Explanation
`sqrtP`	`uint160`	the current sqrt price
`liquidity`	`uint128`	expected change in reinvestment liquidity due to the burning of reinvestment tokens

`divCeiling()`

Returns ceil(x / y). y should not be zero.

QuadMath

`getSmallerRootOfQuadEqn()`

Given a variant of the quadratic equation $$ax^2 - 2bx + c - 0$$ where $$a$$, $$b$$ and $$c > 0$$, calculate the smaller root via the quadratic formula.

Returns $$\frac{b - \sqrt{b^2 - ac}}{a}$$

Input Field	Type	Explanation
`a`	`uint256`
`b`	`uint256`
`c`	`uint256`

`sqrt()`

Unchanged from DMMv1. Calculates the square root of a value using the Babylonian method.

ReinvestmentMath

Contains a helper function to calculate reinvestment tokens to be minted given an increase in reinvestment liquidity.

`calcRMintQty()`

Given the difference between reinvestL and reinvestLLast, calculate how many reinvestment tokens are to be minted.

$$rMintQty = rTotalSupply * \frac{reinvestL - reinvestL_{Last}}{reinvestL_{Last}} * \frac{baseL}{baseL + reinvestL}$$

Input Field	Type	Explanation
`reinvestL`	`uint256`	latest reinvestment liquidity value. Should be `>= reinvestLLast`
`reinvestLLast`	`uint256`	reinvestmentLiquidityLast value
`baseL`	`uint256`	active base liquidity
`rTotalSupply`	`uint256`	total supply of reinvestment token

SafeCast

Contains methods for safely casting between different types.

`toUint32()`

Casts a uint256 to a uint32. Reverts on overflow.

`toInt128()`

Casts a uint128 to a int128. Reverts on overflow.

`toUint128()`

Casts a uint256 to a uint128. Reverts on overflow.

`revToUint128()`

Given int128 y, returns uint128 z = -y.

`toUint160()`

Casts a uint256 to a uint160. Reverts on overflow.

`toInt256()`

Casts a uint256 to a int256. Reverts on overflow.

`revToInt256()`

Cast a uint256 to a int256 and reverses the sign. Reverts on overflow.

`revToUint256()`

Given int256 y, returns uint256 z = -y.

SwapMath

Contains the logic needed for computing swap input / output amounts and fees. The primary function to look at is computeSwapStep, as it is where the bulk of the swap flow logic is in, and where calls to the other functions in the library are made.

`computeSwapStep()`

Computes the actual swap input / output amounts to be deducted or added, the swap fee to be collected and the resulting price.

Inputs

Field	Type	Explanation
`liquidity`	`uint256`	active base liquidity + reinvestment liquidity
`currentSqrtP`	`uint160`	current sqrt price
`targetSqrtP`	`uint160`	sqrt price limit `nextSqrtP` can take
`feeInBps`	`uint256`	swap fee in basis points
`specifiedAmount`	`int256`	amount remaining to be used for the swap
`isExactInput`	`bool`	true if `specifiedAmount` refers to input amount, false if `specifiedAmount` refers to output amount
`isToken0`	`bool`	true if `specifiedAmount` is in token0, false if `specifiedAmount` is in token1

Outputs

Field	Type	Explanation
`usedAmount`	`int256`	actual amount to be used for the swap. >= 0 if `isExactInput` = true, <= 0 if `isExactInput` = false
`returnedAmount`	`int256`	output qty (<= 0) to be accumulated if `isExactInput` = true, input qty (>= 0) if `isExactInput` = false
`deltaL`	`uint256`	collected swap fee, to be incremented to reinvest liquidity
`nextSqrtP`	`uint160`	new sqrt price after the computed swap step

Note

nextSqrtP should not exceed targetSqrtP.

`calcReachAmount()`

Calculates the amount needed to reach targetSqrtP from currentSqrtP. Note that currentSqrtP and targetSqrtP are casted from uint160 to uint256 as they are multiplied by TWO_BPS (20_000) or feeInBps.

The mathematical formulas are provided below for reference.

isExactInput	isToken0	Formula
`true`	`true`	\frac{2BPSL(\sqrt{p_c} - \sqrt{p_n})}{\sqrt{p_c}(2BPS\sqrt{p_n} - fee\sqrt{p_c})} (>0)
`true`	`false`	\frac{2BPS\sqrt{p_c}L(\sqrt{p_n} - \sqrt{p_c})}{(2BPS*\sqrt{p_c} - fee\sqrt{p_n})} (>0)
`false`	`true`	-\frac{2BPSL(\sqrt{p_n} - \sqrt{p_c})}{\sqrt{p_c}(2BPS\sqrt{p_n} - fee\sqrt{p_c})} (<0)
`false`	`false`	-\frac{2BPS\sqrt{p_c}L(\sqrt{p_c} - \sqrt{p_n})}{(2BPS*\sqrt{p_c} - fee\sqrt{p_n})} (<0)

Note that while cases 1 and 3 and cases 2 and 4 are mathematically equivalent, the implementation differs by performing a double negation for the exact output cases. It takes the difference of $$\sqrt{p_n}$$ and $$\sqrt{p_c}$$ in the numerator (>0), then performing a second negation.

Input Field	Type	Formula Variable	Explanation
`liquidity`	`uint256`	$$L$$	active base liquidity + reinvestment liquidity
`currentSqrtP`	`uint160`	$$\sqrt{p_c}$$	current sqrt price
`targetSqrtP`	`uint160`	$$\sqrt{p_n}$$	sqrt price limit `nextSqrtP` can take
`feeInBps`	`uint256`	$$fee$$	swap fee in basis points
`isExactInput`	`bool`	N.A.	true / false if specified swap amount refers to input / output amount respectively
`isToken0`	`bool`	N.A.	true / false if specified swap amount is in token0 / token1 respectively

`estimateIncrementalLiquidity()`

Estimates deltaL, the swap fee to be collected based on amountSpecified. This is called only for the final swap step, where the next (temporary) tick will not be crossed.

In the case where exact input is specified, the formula is rather straightforward.

isToken0	Formula
`true`	\frac{deltafee\sqrt{p_c}}{2*BPS}
`false`	\frac{deltafee}{2BPS*\sqrt{p_c}}

In the case where exact output is specified, a quadratic equation has to be solved. The desired result is the smaller root of the quadratic equation.

isToken0	Formula
`true`	fee(\Delta{L})^2-2[(BPS-fee)L-BPSdelta\sqrt{p_c}]\Delta{L}+feeLdelta*\sqrt{p_c}=0
`false`	fee(\Delta{L})^2-2[(BPS-fee)L-\frac{BPSdelta}{\sqrt{p_c}}]\Delta{L}+\frac{feeL*delta}{\sqrt{p_c}}=0

Input Field	Type	Formula Variable	Explanation
`absDelta`	`uint256`	delta	∥∥`usedAmount`∥∥, absolute value of `usedAmount` (actual amount used for swap)
`liquidity`	`uint256`	L	active base liquidity + reinvestment liquidity
`currentSqrtP`	`uint160`	\sqrt{p_c}	current sqrt price
`feeInBps`	`uint256`	fee	swap fee in basis points
`isExactInput`	`bool`	N.A.	true / false if specified swap amount refers to input / output amount respectively
`isToken0`	`bool`	N.A.	true / false if specified swap amount is in token0 / token1 respectively

`calcIncrementalLiquidity()`

Calculates deltaL, the swap fee to be collected based on amountSpecified. This is called for an intermediate swap step, where the next (temporary) tick will be crossed.

The mathematical formulas are provided below for reference.

isExactInput	isToken0	Formula
`true`	`true`	\sqrt{p_n}*(\frac{L}{\sqrt{p_c}}+\\|delta\\|)-L
`true`	`false`	\frac{(L*\sqrt{p_c})+\\|delta\\|}{\sqrt{p_n}}-L
`false`	`true`	\sqrt{p_n}*(\frac{L}{\sqrt{p_c}}-\\|delta\\|)-L
`false`	`false`	\frac{(L*\sqrt{p_c})-\\|delta\\|}{\sqrt{p_n}}-L

Inputs

Input Field	Type	Formula Variable	Explanation
`absDelta`	`uint256`	\|delta\|	∥∥`usedAmount`∥∥, absolute value of `usedAmount` (actual amount used for swap)
`liquidity`	`uint256`	L	active base liquidity + reinvestment liquidity
`currentSqrtP`	`uint160`	\sqrt{p_c}	current sqrt price
`nextSqrtP`	`uint160`	\sqrt{p_n}	next sqrt price
`isExactInput`	`bool`	N.A.	true / false if specified swap amount refers to input / output amount respectively
`isToken0`	`bool`	N.A.	true / false if specified swap amount is in token0 / token1 respectively

`calcFinalPrice()`

Calculates the sqrt price of the final swap step where the next (temporary) tick will not be crossed.

The mathematical formulas are provided below for reference.

isExactInput	isToken0	Formula
`true`	`true`	\frac{(L+\Delta{L})\sqrt{p_c}}{L+\\|delta\\|\sqrt{p_c}}
`true`	`false`	\frac{L\sqrt{p_c}+\\|delta\\|}{L+\Delta{L}}
`false`	`true`	\frac{(L+\Delta{L})\sqrt{p_c}}{L-\\|delta\\|\sqrt{p_c}}
`false`	`false`	\frac{L\sqrt{p_c}-\\|delta\\|}{L+\Delta{L}}

Input

Input Field	Type	Formula Variable	Explanation
`absDelta`	`uint256`	\|$$delta$$\|	$$∥∥$$usedAmount$$∥∥$$, absolute value of `usedAmount` (actual amount used for swap)
`liquidity`	`uint256`	$$L$$	active base liquidity + reinvestment liquidity
`deltaL`	`uint256`	$$ΔL$$	collected swap fee
`currentSqrtP`	`uint160`	$$\sqrt{p_c}$$	current sqrt price
`isExactInput`	`bool`	N.A.	true / false if specified swap amount refers to input / output amount respectively
`isToken0`	`bool`	N.A.	true / false if specified swap amount is in token0 / token1 respectively

`calcReturnedAmount()`

Calculates returnedAmount for the computeSwapStep function. Rounds down when isExactInput = true (calculating output < 0) so that we avoid sending too much. Conversely, rounds up when isExactInput = false to ensure sufficient input > 0 will be received.

The mathematical formulas are provided below for reference.

isToken0 = true

The formula is actually the same, with the difference being made to the operands to ensure the price difference is non-negative.

isExactInput	Formula
`true`	$$\Delta{L}\sqrt{p_n}-L(\sqrt{p_c}-\sqrt{p_n})$$
`false`	$$\Delta{L}\sqrt{p_n}+L(\sqrt{p_n}-\sqrt{p_c})$$

isToken0 = false

$$\frac{L+\Delta{L}}{\sqrt{p_n}} - \frac{L}{\sqrt{p_c}}$$

Input Field	Type	Formula Variable	Explanation
`liquidity`	`uint256`	L	active base liquidity + reinvestment liquidity
`currentSqrtP`	`uint160`	\sqrt{p_c}	current sqrt price
`nextSqrtP`	`uint160`	\sqrt{p_n}	next sqrt price
`deltaL`	`uint256`	ΔL	collected swap fee
`isExactInput`	`bool`	N.A.	true / false if specified swap amount refers to input / output amount respectively
`isToken0`	`bool`	N.A.	true / false if specified swap amount is in token0 / token1 respectively

TickMath

Contains functions for computing square root prices from ticks and vice versa. Adapted from Uniswap V3's TickMath library.

Constants

Field	Type	Value	Explanation
`MIN_TICK`	`int24`	`-887272`	Minimum possible tick = {log_{1.0001}2^{-128}}
`MAX_TICK`	`int24`	`887272`	Minimum possible tick = {log_{1.0001}2^{128}}
`MIN_SQRT_RATIO`	`uint160`	`4295128739`	`getSqrtRatioAtTick(MIN_TICK)`
`MAX_SQRT_RATIO`	`uint160`	`1461446703485210103287273052203988822378723970342`	`getSqrtRatioAtTick(MAX_TICK)`

`getSqrtRatioAtTick()`

Given a int24 tick, calculates $${\sqrt{1.0001^{tick}} * 2^{96}}$$.

`getTickAtSqrtRatio()`

Given a square root price ratio uint160 sqrtP, calculates the greatest tick such that getSqrtRatioAtTick(tick) <= sqrtP.

Note that MIN_SQRT_RATIO <= sqrtP <= MAX_SQRT_RATIO, otherwise the function will revert.

`getMaxNumberTicks()`

Used to calculate the maximum liquidity allowable per tick. This function calculates the maximum number of ticks that can be inserted into the LinkedList, given a tickDistance.

Field	Type	Explanation
`_tickDistance`	`int24`	Ticks can only be initialized at multiples of this value.

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Elastic Core Libraries

BaseSplitCodeFactory​

getCreationCodeContracts()​

getCreationCode()​

CodeDeployer​

FullMath​

mulDivFloor()​

mulDivCeiling()​

LinkedList​

Struct: Data​

init()​

insert()​

remove()​

LiqDeltaMath​

applyLiquidityDelta()​

MathConstants​

QtyDeltaMath​

getQtysForInitialLockup()​

calcRequiredQty0()​

calcRequiredQty1()​

getQty0FromBurnRTokens()​

getQty1FromBurnRTokens()​

divCeiling()​

QuadMath​

getSmallerRootOfQuadEqn()​

sqrt()​

ReinvestmentMath​

calcRMintQty()​

SafeCast​

toUint32()​

toInt128()​

toUint128()​

revToUint128()​

toUint160()​

toInt256()​

revToInt256()​

revToUint256()​

SwapMath​

computeSwapStep()​

calcReachAmount()​

estimateIncrementalLiquidity()​

calcIncrementalLiquidity()​

calcFinalPrice()​

calcReturnedAmount()​

TickMath​

Constants​

getSqrtRatioAtTick()​

getTickAtSqrtRatio()​

getMaxNumberTicks()​

BaseSplitCodeFactory

`getCreationCodeContracts()`

`getCreationCode()`

CodeDeployer

FullMath

`mulDivFloor()`

`mulDivCeiling()`

LinkedList

Struct: Data

`init()`

`insert()`

`remove()`

LiqDeltaMath

`applyLiquidityDelta()`

MathConstants

QtyDeltaMath

`getQtysForInitialLockup()`

`calcRequiredQty0()`

`calcRequiredQty1()`

`getQty0FromBurnRTokens()`

`getQty1FromBurnRTokens()`

`divCeiling()`

QuadMath

`getSmallerRootOfQuadEqn()`

`sqrt()`

ReinvestmentMath

`calcRMintQty()`

SafeCast

`toUint32()`

`toInt128()`

`toUint128()`

`revToUint128()`

`toUint160()`

`toInt256()`

`revToInt256()`

`revToUint256()`

SwapMath

`computeSwapStep()`

`calcReachAmount()`

`estimateIncrementalLiquidity()`

`calcIncrementalLiquidity()`

`calcFinalPrice()`

`calcReturnedAmount()`

TickMath

Constants

`getSqrtRatioAtTick()`

`getTickAtSqrtRatio()`

`getMaxNumberTicks()`