TickMath

Computes sqrt price for ticks of size 1.0001, i.e. sqrt(1.0001^tick) as fixed point Q64.96 numbers. Supports prices between 2**-128 and 2**128

State Variables

The minimum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2*-128*

int24 internal constant MIN_TICK = -887_272;

The maximum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**128

int24 internal constant MAX_TICK = -MIN_TICK;

The minimum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MIN_TICK)

uint160 internal constant MIN_SQRT_RATIO = 4_295_128_739;

The maximum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MAX_TICK)

uint160 internal constant MAX_SQRT_RATIO = 1_461_446_703_485_210_103_287_273_052_203_988_822_378_723_970_342;

Calculates sqrt(1.0001^tick) * 2^96

Throws if |tick| > max tick

function getSqrtRatioAtTick(int24 tick) internal pure returns (uint160 sqrtPriceX96);

Parameters

Name	Type	Description
`tick`	`int24`	The input tick for the above formula

Returns

Name	Type	Description
`sqrtPriceX96`	`uint160`	A Fixed point Q64.96 number representing the sqrt of the ratio of the two assets (token1/token0) at the given tick

Calculates the greatest tick value such that getRatioAtTick(tick) <= ratio

Throws in case sqrtPriceX96 < MIN_SQRT_RATIO, as MIN_SQRT_RATIO is the lowest value getRatioAtTick may ever return.

function getTickAtSqrtRatio(uint160 sqrtPriceX96) internal pure returns (int24 tick);

Parameters

Name	Type	Description
`sqrtPriceX96`	`uint160`	The sqrt ratio for which to compute the tick as a Q64.96

Returns

Name	Type	Description
`tick`	`int24`	The greatest tick for which the ratio is less than or equal to the input ratio