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TickMath ​

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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

Modified from the original UniswapV3 library to support v0.8 From: require(absTick <= uint256(MAX_TICK), 'T'); To: require(absTick <= uint256(int(MAX_TICK)), 'T');

State Variables ​

MIN_TICK ​

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

solidity
int24 internal constant MIN_TICK = -887272;

MAX_TICK ​

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

solidity
int24 internal constant MAX_TICK = -MIN_TICK;

MIN_SQRT_RATIO ​

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

solidity
uint160 internal constant MIN_SQRT_RATIO = 4295128739;

MAX_SQRT_RATIO ​

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

solidity
uint160 internal constant MAX_SQRT_RATIO = 1461446703485210103287273052203988822378723970342;

Functions ​

getSqrtRatioAtTick ​

Calculates sqrt(1.0001^tick) * 2^96

Throws if |tick| > max tick

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

Parameters

NameTypeDescription
tickint24The input tick for the above formula

Returns

NameTypeDescription
sqrtPriceX96uint160A Fixed point Q64.96 number representing the sqrt of the ratio of the two assets (token1/token0) at the given tick

getTickAtSqrtRatio ​

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

This line was modified for v0.8.x

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

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

Parameters

NameTypeDescription
sqrtPriceX96uint160The sqrt ratio for which to compute the tick as a Q64.96

Returns

NameTypeDescription
tickint24The greatest tick for which the ratio is less than or equal to the input ratio