# BitLength
[](https://hex.pm/packages/bit_length)
[](https://hex.pm/packages/bit_length)
[](https://hex.pm/packages/bit_length)
A utility library for calculating the bit length of integers in Elixir.
## What is Bit Length?
The bit length of an integer is the minimum number of bits required to represent that integer in binary form, excluding leading zeros. For example:
- `0` requires 0 bits (special case)
- `1` requires 1 bit (binary: `1`)
- `2` requires 2 bits (binary: `10`)
- `3` requires 2 bits (binary: `11`)
- `255` requires 8 bits (binary: `11111111`)
- `256` requires 9 bits (binary: `100000000`)
## Installation
The package can be installed by adding `bit_length` to your list of dependencies in `mix.exs`:
```elixir
def deps do
[
{:bit_length, "~> 1.0"}
]
end
```
## Usage
```elixir
# Calculate bit length of various integers
BitLength.of(0) # Returns: 0
BitLength.of(1) # Returns: 1
BitLength.of(2) # Returns: 2
BitLength.of(3) # Returns: 2
BitLength.of(7) # Returns: 3
BitLength.of(8) # Returns: 4
BitLength.of(255) # Returns: 8
BitLength.of(256) # Returns: 9
BitLength.of(1023) # Returns: 10
BitLength.of(1024) # Returns: 11
```
## Algorithm
The function uses the mathematical relationship between bit length and logarithms:
- For a positive integer `n`, the bit length is $\lfloor \log_2{n} \rfloor + 1$
- For `n = 0`, the bit length is `0` (special case)
This is equivalent to finding the position of the most significant bit (MSB) in the binary representation of the number.
## Performance
The function uses `:math.log2/1` which provides O(1) performance for calculating the base-2 logarithm of the input integer.
## Documentation
Documentation is available on [HexDocs](https://hexdocs.pm/bit_length).
## License
Copyright (c) 2025 University of Kitakyushu
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at [http://www.apache.org/licenses/LICENSE-2.0](http://www.apache.org/licenses/LICENSE-2.0)
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
## Changelog
See [CHANGELOG.md](CHANGELOG.md) for a list of changes and version history.
