# TickMath

### Functions <a href="#functions" id="functions"></a>

#### tickSqrtPrices <a href="#ticksqrtprices" id="ticksqrtprices"></a>

Compute the lower and upper sqrtPrice of a tick.

```solidity
function tickSqrtPrices(uint256 tickSpacing, int32 _tick)
    internal
    pure
    returns (uint256 sqrtLowerPrice, uint256 sqrtUpperPrice);
```

**Parameters**

| Name          | Type      | Description                             |
| ------------- | --------- | --------------------------------------- |
| `tickSpacing` | `uint256` | The tick spacing used for calculations. |
| `_tick`       | `int32`   | The input tick value.                   |

#### subTickIndex <a href="#subtickindex" id="subtickindex"></a>

Compute the base tick value from the pool tick and the tickSpacing. Revert if base tick is beyond the max tick boundary.

```solidity
function subTickIndex(uint256 tickSpacing, int32 _tick) internal pure returns (uint32 subTick);
```

**Parameters**

| Name          | Type      | Description                             |
| ------------- | --------- | --------------------------------------- |
| `tickSpacing` | `uint256` | The tick spacing used for calculations. |
| `_tick`       | `int32`   | The input tick value.                   |

#### tickSqrtPrice <a href="#ticksqrtprice" id="ticksqrtprice"></a>

Calculate the square root price for a given tick and tick spacing.

```solidity
function tickSqrtPrice(uint256 tickSpacing, int32 _tick) internal pure returns (uint256 _result);
```

**Parameters**

| Name          | Type      | Description                             |
| ------------- | --------- | --------------------------------------- |
| `tickSpacing` | `uint256` | The tick spacing used for calculations. |
| `_tick`       | `int32`   | The input tick value.                   |

**Returns**

| Name      | Type      | Description            |
| --------- | --------- | ---------------------- |
| `_result` | `uint256` | The square root price. |

#### getTickL <a href="#gettickl" id="gettickl"></a>

Calculate liquidity of a tick.

```solidity
function getTickL(uint256 reserveA, uint256 reserveB, uint256 sqrtLowerTickPrice, uint256 sqrtUpperTickPrice)
    internal
    pure
    returns (uint256 liquidity);
```

**Parameters**

| Name                 | Type      | Description                                   |
| -------------------- | --------- | --------------------------------------------- |
| `reserveA`           | `uint256` | Tick reserve of token A.                      |
| `reserveB`           | `uint256` | Tick reserve of token B.                      |
| `sqrtLowerTickPrice` | `uint256` | The square root price of the lower tick edge. |
| `sqrtUpperTickPrice` | `uint256` | The square root price of the upper tick edge. |

#### getSqrtPrice <a href="#getsqrtprice" id="getsqrtprice"></a>

Calculate square root price of a tick. Returns left edge of the tick if the tick has no reserves.

```solidity
function getSqrtPrice(
    uint256 reserveA,
    uint256 reserveB,
    uint256 sqrtLowerTickPrice,
    uint256 sqrtUpperTickPrice,
    uint256 liquidity
) internal pure returns (uint256 sqrtPrice);
```

**Parameters**

| Name                 | Type      | Description                                   |
| -------------------- | --------- | --------------------------------------------- |
| `reserveA`           | `uint256` | Tick reserve of token A.                      |
| `reserveB`           | `uint256` | Tick reserve of token B.                      |
| `sqrtLowerTickPrice` | `uint256` | The square root price of the lower tick edge. |
| `sqrtUpperTickPrice` | `uint256` | The square root price of the upper tick edge. |
| `liquidity`          | `uint256` |                                               |

**Returns**

| Name        | Type      | Description                       |
| ----------- | --------- | --------------------------------- |
| `sqrtPrice` | `uint256` | The calculated square root price. |

#### getTickSqrtPriceAndL <a href="#getticksqrtpriceandl" id="getticksqrtpriceandl"></a>

Calculate square root price of a tick. Returns left edge of the tick if the tick has no reserves.

```solidity
function getTickSqrtPriceAndL(
    uint256 reserveA,
    uint256 reserveB,
    uint256 sqrtLowerTickPrice,
    uint256 sqrtUpperTickPrice
) internal pure returns (uint256 sqrtPrice, uint256 liquidity);
```

**Parameters**

| Name                 | Type      | Description                                   |
| -------------------- | --------- | --------------------------------------------- |
| `reserveA`           | `uint256` | Tick reserve of token A.                      |
| `reserveB`           | `uint256` | Tick reserve of token B.                      |
| `sqrtLowerTickPrice` | `uint256` | The square root price of the lower tick edge. |
| `sqrtUpperTickPrice` | `uint256` | The square root price of the upper tick edge. |

**Returns**

| Name        | Type      | Description                       |
| ----------- | --------- | --------------------------------- |
| `sqrtPrice` | `uint256` | The calculated square root price. |
| `liquidity` | `uint256` | The calculated liquidity.         |

### Errors <a href="#errors" id="errors"></a>

#### TickMaxExceeded <a href="#tickmaxexceeded" id="tickmaxexceeded"></a>

```solidity
error TickMaxExceeded(int256 tick);
```