SqrtPriceMath
Contains the math that uses square root of price as a Q64.96 and liquidity to compute deltas
Functions
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).
Parameters:
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
Return Values:
uint160
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
Parameters:
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
Return Values:
uint160
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
Parameters:
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
Return Values:
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
Parameters:
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
Return Values:
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))
Parameters:
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
Return Values:
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))
Parameters:
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
Return Values:
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
Parameters:
sqrtRatioAX96
uint160
A sqrt price
sqrtRatioBX96
uint160
Another sqrt price
liquidity
int128
The change in liquidity for which to compute the amount0 delta
Return Values:
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
Parameters:
sqrtRatioAX96
uint160
A sqrt price
sqrtRatioBX96
uint160
Another sqrt price
liquidity
int128
The change in liquidity for which to compute the amount1 delta
Return Values:
amount1
int256
Amount of token1 corresponding to the passed liquidityDelta between the two prices
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