# 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:​

NameTypeDescription
sqrtPX96uint160The starting price, i.e. before accounting for the token0 delta
liquidityuint128The amount of usable liquidity
amountuint256How much of token0 to add or remove from virtual reserves
addboolWhether to add or remove the amount of token0

TypeDescription

### 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:​

NameTypeDescription
sqrtPX96uint160The starting price, i.e., before accounting for the token1 delta
liquidityuint128The amount of usable liquidity
amountuint256How much of token1 to add, or remove, from virtual reserves
addboolWhether to add, or remove, the amount of token1

#### Return Values:​

TypeDescription
uint160price 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:​

NameTypeDescription
sqrtPX96uint160The starting price, i.e., before accounting for the input amount
liquidityuint128The amount of usable liquidity
amountInuint256How much of token0, or token1, is being swapped in
zeroForOneboolWhether the amount in is token0 or token1

#### Return Values:​

NameTypeDescription
sqrtQX96uint160The 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:​

NameTypeDescription
sqrtPX96uint160The starting price before accounting for the output amount
liquidityuint128The amount of usable liquidity
amountOutuint256How much of token0, or token1, is being swapped out
zeroForOneboolWhether the amount out is token0 or token1

#### Return Values:​

NameTypeDescription
sqrtQX96uint160The 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:​

NameTypeDescription
sqrtRatioAX96uint160A sqrt price
sqrtRatioBX96uint160Another sqrt price
liquidityuint128The amount of usable liquidity
roundUpboolWhether to round the amount up or down

#### Return Values:​

NameTypeDescription
amount0uint256Amount 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:​

NameTypeDescription
sqrtRatioAX96uint160A sqrt price
sqrtRatioBX96uint160Another sqrt price
liquidityuint128The amount of usable liquidity
roundUpboolWhether to round the amount up, or down

#### Return Values:​

NameTypeDescription
amount1uint256Amount 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:​

NameTypeDescription
sqrtRatioAX96uint160A sqrt price
sqrtRatioBX96uint160Another sqrt price
liquidityint128The change in liquidity for which to compute the amount0 delta

#### Return Values:​

NameTypeDescription
amount0int256Amount 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:​

NameTypeDescription
sqrtRatioAX96uint160A sqrt price
sqrtRatioBX96uint160Another sqrt price
liquidityint128The change in liquidity for which to compute the amount1 delta

#### Return Values:​

NameTypeDescription
amount1int256Amount of token1 corresponding to the passed liquidityDelta between the two prices