BinaryGcd
An efficient Elixir implementation of the binary GCD algorithm (Stein's algorithm) for computing the greatest common divisor (GCD) of two non-negative integers using only bitwise operations and subtraction.
Features
- Fast GCD computation using Stein's algorithm
- Pure Elixir, no dependencies for core logic
- Well-documented and tested
- Suitable for large integers
Installation
From Hex (Recommended)
Add binary_gcd
to your list of dependencies in mix.exs
:
def deps do
[
{:binary_gcd, "~> 1.0"}
]
end
Then run:
mix deps.get
Usage
You can use the module directly in your code or in IEx:
iex> BinaryGcd.of(48, 18)
6
iex> BinaryGcd.of(0, 5)
5
iex> BinaryGcd.of(54, 24)
6
iex> BinaryGcd.of(17, 13)
1
Algorithm
This library implements the binary GCD algorithm, also known as Stein's algorithm. It is generally faster than the classical Euclidean algorithm for large numbers because it avoids division and uses only subtraction and bitwise operations.
Algorithm steps:
- If either number is zero, return the other number.
- If both numbers are even, divide both by 2 and multiply the result by 2.
- If one number is even, divide it by 2.
- If both numbers are odd, subtract the smaller from the larger.
- Repeat until one number becomes zero.
Tested Platforms
- Ubuntu 22.04 / Elixir 1.18 / Erlang/OTP 28
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
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.