# SwapMath

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

#### \_amountToBinNetOfProtocolFee <a href="#amounttobinnetofprotocolfee" id="amounttobinnetofprotocolfee"></a>

Internal function to calculate the amount after deducting the protocol fee.

```
```

```solidity
function _amountToBinNetOfProtocolFee(uint256 deltaInErc, uint256 feeBasis, uint256 protocolFeeD3)
    private
    pure
    returns (uint256 amount);
```

**Parameters**

| Name            | Type      | Description                                                                                                        |
| --------------- | --------- | ------------------------------------------------------------------------------------------------------------------ |
| `deltaInErc`    | `uint256` | Input delta in ERC token.                                                                                          |
| `feeBasis`      | `uint256` | Fee basis for calculating the fee amount.                                                                          |
| `protocolFeeD3` | `uint256` | Proportion of the fee that goes to the protocol in three-decimal format. e.g. fee of 100 is 10% protocol fee rate. |

**Returns**

| Name     | Type      | Description                                  |
| -------- | --------- | -------------------------------------------- |
| `amount` | `uint256` | The amount after deducting the protocol fee. |

#### \_remainingBinInputSpaceGivenOutput <a href="#remainingbininputspacegivenoutput" id="remainingbininputspacegivenoutput"></a>

Internal function to calculate the remaining input space given the output.

```solidity
function _remainingBinInputSpaceGivenOutput(uint256 binLiquidity, uint256 output, uint256 sqrtPrice, bool tokenAIn)
    private
    pure
    returns (uint256 binAmountIn);
```

**Parameters**

| Name           | Type      | Description                        |
| -------------- | --------- | ---------------------------------- |
| `binLiquidity` | `uint256` | The current liquidity in the bin.  |
| `output`       | `uint256` | The desired output amount.         |
| `sqrtPrice`    | `uint256` | The current square root price.     |
| `tokenAIn`     | `bool`    | True if the swap input is token A. |

**Returns**

| Name          | Type      | Description                                           |
| ------------- | --------- | ----------------------------------------------------- |
| `binAmountIn` | `uint256` | The input amount that can be accommodated in the bin. |

#### computeEndPrice <a href="#computeendprice" id="computeendprice"></a>

Compute end price of a swap as well as the approximate end price in the tick domain. The resulting output fraction tick part is written to the input newDelta object.

Ain: `endSqrtP = in / L + sqrtP`

Bin: `endSqrtP = 1 / (in / L + 1 / sqrtP) = L / (in + L / sqrtP)`

fractional Tick: `(endSqrtP - lowerSqrtP) / (upperSqrtP - lowerSqrtP)`

```solidity
function computeEndPrice(
    Delta.Instance memory delta,
    Delta.Instance memory newDelta,
    IMaverickV2Pool.TickData memory tickData
) internal pure;
```

#### computeSwapExactIn <a href="#computeswapexactin" id="computeswapexactin"></a>

Calculate swap data for an exact input swap.

```solidity
function computeSwapExactIn(
    uint256 sqrtPrice,
    IMaverickV2Pool.TickData memory tickData,
    uint256 amountIn,
    bool tokenAIn,
    uint256 fee,
    uint256 protocolFeeD3
) internal pure returns (Delta.Instance memory delta);
```

**Parameters**

| Name            | Type                       | Description                                      |
| --------------- | -------------------------- | ------------------------------------------------ |
| `sqrtPrice`     | `uint256`                  | Current price.                                   |
| `tickData`      | `IMaverickV2Pool.TickData` | Reserve and liquidity values of the bin.         |
| `amountIn`      | `uint256`                  | Desired input amount.                            |
| `tokenAIn`      | `bool`                     | True if the swap input is token A.               |
| `fee`           | `uint256`                  | Ratio that the swapper pays in D18 format.       |
| `protocolFeeD3` | `uint256`                  | Proportion of the fee that goes to the protocol. |

**Returns**

| Name    | Type             | Description                               |
| ------- | ---------------- | ----------------------------------------- |
| `delta` | `Delta.Instance` | Swap data delta for the exact input swap. |

#### computeSwapExactOut <a href="#computeswapexactout" id="computeswapexactout"></a>

Calculate swap data for an exact output swap.

```solidity
function computeSwapExactOut(
    uint256 sqrtPrice,
    IMaverickV2Pool.TickData memory tickData,
    uint256 amountOut,
    bool tokenAIn,
    uint256 fee,
    uint256 protocolFeeD3
) internal pure returns (Delta.Instance memory delta);
```

**Parameters**

| Name            | Type                       | Description                                      |
| --------------- | -------------------------- | ------------------------------------------------ |
| `sqrtPrice`     | `uint256`                  | Current price.                                   |
| `tickData`      | `IMaverickV2Pool.TickData` | Reserve and liquidity values of the bin.         |
| `amountOut`     | `uint256`                  | Desired output amount.                           |
| `tokenAIn`      | `bool`                     | True if the swap input is token A.               |
| `fee`           | `uint256`                  | Ratio that the swapper pays in D18 format.       |
| `protocolFeeD3` | `uint256`                  | Proportion of the fee that goes to the protocol. |

**Returns**

| Name    | Type             | Description                                |
| ------- | ---------------- | ------------------------------------------ |
| `delta` | `Delta.Instance` | Swap data delta for the exact output swap. |


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