# BitMath

[Git Source](https://github.com/traderjoe-xyz/joe-v2/blob/16f011d25e6bf6d0a0c479974345b623d491104f/src/libraries/math/BitMath.sol)

Helper contract used for bit calculations

## Functions

### closestBitRight

*Returns the index of the closest bit on the right of x that is non null*

```solidity
function closestBitRight(uint256 x, uint8 bit) internal pure returns (uint256 id);
```

**Parameters**

| Name  | Type      | Description                                |
| ----- | --------- | ------------------------------------------ |
| `x`   | `uint256` | The value as a uint256                     |
| `bit` | `uint8`   | The index of the bit to start searching at |

**Returns**

| Name | Type      | Description                                                                                                  |
| ---- | --------- | ------------------------------------------------------------------------------------------------------------ |
| `id` | `uint256` | The index of the closest non null bit on the right of x. If there is no closest bit, it returns max(uint256) |

### closestBitLeft

*Returns the index of the closest bit on the left of x that is non null*

```solidity
function closestBitLeft(uint256 x, uint8 bit) internal pure returns (uint256 id);
```

**Parameters**

| Name  | Type      | Description                                |
| ----- | --------- | ------------------------------------------ |
| `x`   | `uint256` | The value as a uint256                     |
| `bit` | `uint8`   | The index of the bit to start searching at |

**Returns**

| Name | Type      | Description                                                                                                 |
| ---- | --------- | ----------------------------------------------------------------------------------------------------------- |
| `id` | `uint256` | The index of the closest non null bit on the left of x. If there is no closest bit, it returns max(uint256) |

### mostSignificantBit

*Returns the index of the most significant bit of x*\
*This function returns 0 if x is 0*

```solidity
function mostSignificantBit(uint256 x) internal pure returns (uint8 msb);
```

**Parameters**

| Name | Type      | Description            |
| ---- | --------- | ---------------------- |
| `x`  | `uint256` | The value as a uint256 |

**Returns**

| Name  | Type    | Description                                |
| ----- | ------- | ------------------------------------------ |
| `msb` | `uint8` | The index of the most significant bit of x |

### leastSignificantBit

*Returns the index of the least significant bit of x*\
*This function returns 255 if x is 0*

```solidity
function leastSignificantBit(uint256 x) internal pure returns (uint8 lsb);
```

**Parameters**

| Name | Type      | Description            |
| ---- | --------- | ---------------------- |
| `x`  | `uint256` | The value as a uint256 |

**Returns**

| Name  | Type    | Description                                 |
| ----- | ------- | ------------------------------------------- |
| `lsb` | `uint8` | The index of the least significant bit of x |


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