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# BitMath

This library provides functionality for computing bit properties of an unsigned integer

## Functions

### mostSignificantBit

```solidity theme={null}
  function mostSignificantBit(
    uint256 x
  ) internal pure returns (uint8 r)
```

Returns the index of the most significant bit of the number,
where the least significant bit is at index 0 and the most significant bit is at index 255

The function satisfies the property:
x >= 2**mostSignificantBit(x) and x \< 2**(mostSignificantBit(x)+1)

#### Parameters:

| Name | Type    | Description                                                                     |
| :--- | :------ | :------------------------------------------------------------------------------ |
| `x`  | uint256 | the value for which to compute the most significant bit, must be greater than 0 |

#### Return Values:

| Name | Type  | Description                           |
| :--- | :---- | :------------------------------------ |
| `r`  | uint8 | the index of the most significant bit |

### leastSignificantBit

```solidity theme={null}
  function leastSignificantBit(
    uint256 x
  ) internal pure returns (uint8 r)
```

Returns the index of the least significant bit of the number,
where the least significant bit is at index 0 and the most significant bit is at index 255

The function satisfies the property:
(x & 2**leastSignificantBit(x)) != 0 and (x & (2**(leastSignificantBit(x)) - 1)) == 0)

#### Parameters:

| Name | Type    | Description                                                                      |
| :--- | :------ | :------------------------------------------------------------------------------- |
| `x`  | uint256 | the value for which to compute the least significant bit, must be greater than 0 |

#### Return Values:

| Name | Type  | Description                            |
| :--- | :---- | :------------------------------------- |
| `r`  | uint8 | the index of the least significant bit |