SqrtPriceMath

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

Functions

getNextSqrtPriceFromAmount0RoundingUp

Gets the next sqrt price given a delta of currency0

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).

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

Parameters

Name	Type	Description
sqrtPX96	uint160	The starting price, i.e. before accounting for the currency0 delta
liquidity	uint128	The amount of usable liquidity
amount	uint256	How much of currency0 to add or remove from virtual reserves
add	bool	Whether to add or remove the amount of currency0

Returns

Name	Type	Description
<none>	uint160	The price after adding or removing amount, depending on add

getNextSqrtPriceFromAmount1RoundingDown

Gets the next sqrt price given a delta of currency1

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

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

Parameters

Name	Type	Description
sqrtPX96	uint160	The starting price, i.e., before accounting for the currency1 delta
liquidity	uint128	The amount of usable liquidity
amount	uint256	How much of currency1 to add, or remove, from virtual reserves
add	bool	Whether to add, or remove, the amount of currency1

Returns

Name	Type	Description
<none>	uint160	The price after adding or removing amount

getNextSqrtPriceFromInput

Gets the next sqrt price given an input amount of currency0 or currency1

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

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

Parameters

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 currency0, or currency1, is being swapped in
zeroForOne	bool	Whether the amount in is currency0 or currency1

Returns

Name	Type	Description
<none>	uint160	uint160 The price after adding the input amount to currency0 or currency1

getNextSqrtPriceFromOutput

Gets the next sqrt price given an output amount of currency0 or currency1

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

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

Parameters

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 currency0, or currency1, is being swapped out
zeroForOne	bool	Whether the amount out is currency1 or currency0

Returns

Name	Type	Description
<none>	uint160	uint160 The price after removing the output amount of currency0 or currency1

getAmount0Delta

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))

function getAmount0Delta(uint160 sqrtPriceAX96, uint160 sqrtPriceBX96, uint128 liquidity, bool roundUp)
    internal
    pure
    returns (uint256);

Parameters

Name	Type	Description
sqrtPriceAX96	uint160	A sqrt price
sqrtPriceBX96	uint160	Another sqrt price
liquidity	uint128	The amount of usable liquidity
roundUp	bool	Whether to round the amount up or down

Returns

Name	Type	Description
<none>	uint256	uint256 Amount of currency0 required to cover a position of size liquidity between the two passed prices

absDiff

Equivalent to: a >= b ? a - b : b - a

function absDiff(uint160 a, uint160 b) internal pure returns (uint256 res);

getAmount1Delta

Gets the amount1 delta between two prices

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

function getAmount1Delta(uint160 sqrtPriceAX96, uint160 sqrtPriceBX96, uint128 liquidity, bool roundUp)
    internal
    pure
    returns (uint256 amount1);

Parameters

Name	Type	Description
sqrtPriceAX96	uint160	A sqrt price
sqrtPriceBX96	uint160	Another sqrt price
liquidity	uint128	The amount of usable liquidity
roundUp	bool	Whether to round the amount up, or down

Returns

Name	Type	Description
amount1	uint256	Amount of currency1 required to cover a position of size liquidity between the two passed prices

getAmount0Delta

Equivalent to: amount1 = roundUp ? FullMath.mulDivRoundingUp(liquidity, sqrtPriceBX96 - sqrtPriceAX96, FixedPoint96.Q96) : FullMath.mulDiv(liquidity, sqrtPriceBX96 - sqrtPriceAX96, FixedPoint96.Q96); Cannot overflow because type(uint128).max * type(uint160).max >> 96 < (1 << 192).

Helper that gets signed currency0 delta

function getAmount0Delta(uint160 sqrtPriceAX96, uint160 sqrtPriceBX96, int128 liquidity)
    internal
    pure
    returns (int256);

Parameters

Name	Type	Description
sqrtPriceAX96	uint160	A sqrt price
sqrtPriceBX96	uint160	Another sqrt price
liquidity	int128	The change in liquidity for which to compute the amount0 delta

Returns

Name	Type	Description
<none>	int256	int256 Amount of currency0 corresponding to the passed liquidityDelta between the two prices

getAmount1Delta

Helper that gets signed currency1 delta

function getAmount1Delta(uint160 sqrtPriceAX96, uint160 sqrtPriceBX96, int128 liquidity)
    internal
    pure
    returns (int256);

Parameters

Name	Type	Description
sqrtPriceAX96	uint160	A sqrt price
sqrtPriceBX96	uint160	Another sqrt price
liquidity	int128	The change in liquidity for which to compute the amount1 delta

Returns

Name	Type	Description
<none>	int256	int256 Amount of currency1 corresponding to the passed liquidityDelta between the two prices

Errors

InvalidPriceOrLiquidity

error InvalidPriceOrLiquidity();

InvalidPrice

error InvalidPrice();

NotEnoughLiquidity

error NotEnoughLiquidity();

PriceOverflow

error PriceOverflow();