> ## Documentation Index
> Fetch the complete documentation index at: https://tech.ramses.xyz/llms.txt
> Use this file to discover all available pages before exploring further.

# 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

## Functions

### getSqrtRatioAtTick

```solidity theme={null}
  function getSqrtRatioAtTick(
    int24 tick
  ) internal pure returns (uint160 sqrtPriceX96)
```

Calculates sqrt(1.0001^tick) \* 2^96

Throws if |tick| > max tick

#### Parameters:

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

#### Return Values:

| 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

### getTickAtSqrtRatio

```solidity theme={null}
  function getTickAtSqrtRatio(
    uint160 sqrtPriceX96
  ) internal pure returns (int24 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.

#### Parameters:

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

#### Return Values:

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