SqrtPriceMath

Contains the math that uses square root of price as a Q64.96 and liquidity to compute deltas

getNextSqrtPriceFromAmount0RoundingUp

function getNextSqrtPriceFromAmount0RoundingUp(uint160 sqrtPX96, uint128 liquidity, uint256 amount, bool add) internal pure returns (uint160)

Gets the next sqrt price given a delta of token0

Always rounds up, because in the exact output case (increasing price) we need to move the price at least far enough to get the desired output amount, and in the exact input case (decreasing price) we need to move the price less in order to not send too much output. The most precise formula for this is liquidity * sqrtPX96 / (liquidity +- amount * sqrtPX96), if this is impossible because of overflow, we calculate liquidity / (liquidity / sqrtPX96 +- amount).

Name Type Description
sqrtPX96 uint160 The starting price, i.e. before accounting for the token0 delta
liquidity uint128 The amount of usable liquidity
amount uint256 How much of token0 to add or remove from virtual reserves
add bool Whether to add or remove the amount of token0
Name Type Description
[0] uint160 The price after adding or removing amount, depending on add

getNextSqrtPriceFromAmount1RoundingDown

function getNextSqrtPriceFromAmount1RoundingDown(uint160 sqrtPX96, uint128 liquidity, uint256 amount, bool add) internal pure returns (uint160)

Gets the next sqrt price given a delta of token1

Always rounds down, because in the exact output case (decreasing price) we need to move the price at least far enough to get the desired output amount, and in the exact input case (increasing price) we need to move the price less in order to not send too much output. The formula we compute is within <1 wei of the lossless version: sqrtPX96 +- amount / liquidity

Name Type Description
sqrtPX96 uint160 The starting price, i.e., before accounting for the token1 delta
liquidity uint128 The amount of usable liquidity
amount uint256 How much of token1 to add, or remove, from virtual reserves
add bool Whether to add, or remove, the amount of token1
Name Type Description
[0] uint160 The price after adding or removing amount

getNextSqrtPriceFromInput

function getNextSqrtPriceFromInput(uint160 sqrtPX96, uint128 liquidity, uint256 amountIn, bool zeroForOne) internal pure returns (uint160 sqrtQX96)

Gets the next sqrt price given an input amount of token0 or token1

Throws if price or liquidity are 0, or if the next price is out of bounds

Name Type Description
sqrtPX96 uint160 The starting price, i.e., before accounting for the input amount
liquidity uint128 The amount of usable liquidity
amountIn uint256 How much of token0, or token1, is being swapped in
zeroForOne bool Whether the amount in is token0 or token1
Name Type Description
sqrtQX96 uint160 The price after adding the input amount to token0 or token1

getNextSqrtPriceFromOutput

function getNextSqrtPriceFromOutput(uint160 sqrtPX96, uint128 liquidity, uint256 amountOut, bool zeroForOne) internal pure returns (uint160 sqrtQX96)

Gets the next sqrt price given an output amount of token0 or token1

Throws if price or liquidity are 0 or the next price is out of bounds

Name Type Description
sqrtPX96 uint160 The starting price before accounting for the output amount
liquidity uint128 The amount of usable liquidity
amountOut uint256 How much of token0, or token1, is being swapped out
zeroForOne bool Whether the amount out is token0 or token1
Name Type Description
sqrtQX96 uint160 The price after removing the output amount of token0 or token1

getAmount0Delta

function getAmount0Delta(uint160 sqrtRatioAX96, uint160 sqrtRatioBX96, uint128 liquidity, bool roundUp) internal pure returns (uint256 amount0)

Gets the amount0 delta between two prices

Calculates liquidity / sqrt(lower) - liquidity / sqrt(upper), i.e. liquidity * (sqrt(upper) - sqrt(lower)) / (sqrt(upper) * sqrt(lower))

Name Type Description
sqrtRatioAX96 uint160 A sqrt price
sqrtRatioBX96 uint160 Another sqrt price
liquidity uint128 The amount of usable liquidity
roundUp bool Whether to round the amount up or down
Name Type Description
amount0 uint256 Amount of token0 required to cover a position of size liquidity between the two passed prices

getAmount1Delta

function getAmount1Delta(uint160 sqrtRatioAX96, uint160 sqrtRatioBX96, uint128 liquidity, bool roundUp) internal pure returns (uint256 amount1)

Gets the amount1 delta between two prices

Calculates liquidity * (sqrt(upper) - sqrt(lower))

Name Type Description
sqrtRatioAX96 uint160 A sqrt price
sqrtRatioBX96 uint160 Another sqrt price
liquidity uint128 The amount of usable liquidity
roundUp bool Whether to round the amount up, or down
Name Type Description
amount1 uint256 Amount of token1 required to cover a position of size liquidity between the two passed prices

getAmount0Delta

function getAmount0Delta(uint160 sqrtRatioAX96, uint160 sqrtRatioBX96, int128 liquidity) internal pure returns (int256 amount0)

Helper that gets signed token0 delta

Name Type Description
sqrtRatioAX96 uint160 A sqrt price
sqrtRatioBX96 uint160 Another sqrt price
liquidity int128 The change in liquidity for which to compute the amount0 delta
Name Type Description
amount0 int256 Amount of token0 corresponding to the passed liquidityDelta between the two prices

getAmount1Delta

function getAmount1Delta(uint160 sqrtRatioAX96, uint160 sqrtRatioBX96, int128 liquidity) internal pure returns (int256 amount1)

Helper that gets signed token1 delta

Name Type Description
sqrtRatioAX96 uint160 A sqrt price
sqrtRatioBX96 uint160 Another sqrt price
liquidity int128 The change in liquidity for which to compute the amount1 delta
Name Type Description
amount1 int256 Amount of token1 corresponding to the passed liquidityDelta between the two prices