# DiverSqrtPriceMath

## getSTokenDelta

Gets the delta amount of Spear or Shield tokens based on the given sqrt ratios and liquidity. Computes for Spear token delta when the sqrtPrice moves from upper to lower; or Shield token delta when the sqrtPrice moves from lower to upper. For the same sqrt ratio range and liquidity, the computed delta amounts of Spear and Shield are equal.

The formula for this is spear or shield delta amount = liquidity \* (sqrtRatioBX96 - sqrtRatioAX96) \* (1 + 1 /(sqrtRatioAX96 \* sqrtRatioBX96))

```javascript
function getSTokenDelta(uint160 sqrtRatioAX96, uint160 sqrtRatioBX96, uint128 liquidity, bool roundUp) internal pure returns (uint256 amount)
```

**Params:**

| **Name**      | **Type** | **Description**                                                              |
| ------------- | -------- | ---------------------------------------------------------------------------- |
| sqrtRatioAX96 | uint160  | A sqrt ratio                                                                 |
| sqrtRatioBX96 | uint160  | Another sqrt ratio                                                           |
| liquidity     | uint128  | The change in liquidity for which to compute the Spear or Shield token delta |
| roundUp       | bool     | Whether to round the amount up or down                                       |

**Returns:**

| **Name** | **Type** | **Description**                                                                                       |
| -------- | -------- | ----------------------------------------------------------------------------------------------------- |
| amount   | uint256  | The amount of Spear or Shield token corresponding to the passed liquidityDelta between the two prices |

## getSTokenDelta

Helper that gets signed spear or shield token delta

```javascript
function getSTokenDelta(uint160 sqrtPriceAX96, uint160 sqrtPriceBX96, int128 liquidity) internal pure returns (int256 amount)
```

**Params:**

| **Name**      | **Type** | **Description**                                                              |
| ------------- | -------- | ---------------------------------------------------------------------------- |
| sqrtRatioAX96 | uint160  | A sqrt ratio                                                                 |
| sqrtRatioBX96 | uint160  | Another sqrt ratio                                                           |
| liquidity     | int128   | The change in liquidity for which to compute the Spear or Shield token delta |

**Returns:**

| **Name** | **Type** | **Description**                                                                                       |
| -------- | -------- | ----------------------------------------------------------------------------------------------------- |
| amount   | int256   | The amount of Spear or Shield token corresponding to the passed liquidityDelta between the two prices |

## getNextSqrtPriceFromSpear

Gets the next sqrt ratio based on the given the Spear token delta and liquidity.

```javascript
function getNextSqrtPriceFromSpear(
        uint160 sqrtPrice,
        uint128 liquidity,
        uint256 amount,
        uint256 unit
    )
        internal
        pure
        returns (uint160 nextSqrtPrice)
```

**Params:**

| **Name**  | **Type** | **Description**                                                              |
| --------- | -------- | ---------------------------------------------------------------------------- |
| sqrtPrice | uint160  | The starting price, i.e. before accounting for the spear token delta         |
| liquidity | uint128  | The amount of usable liquidity                                               |
| amount    | uint256  | The amount of Spear token delta to mint for the trade                        |
| unit      | uint256  | The token decimal unit, e.g. a token with 18 decimals has a unit of 10\*\*18 |

**Returns:**

| **Name**      | **Type** | **Description**                                                    |
| ------------- | -------- | ------------------------------------------------------------------ |
| nextSqrtPrice | uint160  | The next sqrt ratio after minting the given amount of Spear tokens |

## getNextSqrtPriceFromShield

Gets the next sqrt ratio based on the given the Shield token delta and liquidity.

```javascript
    function getNextSqrtPriceFromShield(
        uint160 sqrtPrice,
        uint128 liquidity,
        uint256 amount,
        uint256 unit
    )
        internal
        pure
        returns (uint160 nextSqrtPrice)
```

**Params:**

| **Name**  | **Type** | **Description**                                                              |
| --------- | -------- | ---------------------------------------------------------------------------- |
| sqrtPrice | uint160  | The starting price, i.e. before accounting for the Shield token delta        |
| liquidity | uint128  | The amount of usable liquidity                                               |
| amount    | uint256  | The amount of Shield token delta to mint for the trade                       |
| unit      | uint256  | The token decimal unit, e.g. a token with 18 decimals has a unit of 10\*\*18 |

**Returns:**

| **Name**      | **Type** | **Description**                                                     |
| ------------- | -------- | ------------------------------------------------------------------- |
| nextSqrtPrice | uint160  | The next sqrt ratio after minting the given amount of Shield tokens |