BinaryGcd

An efficient Elixir implementation of the binary GCD algorithm (Stein's algorithm) for computing the greatest common divisor (GCD) of two or more 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, "~> 1.1"}
  ]
end

Then run:

mix deps.get

Usage

You can use the module directly in your code or in IEx:

Computing GCD of two numbers

iex> BinaryGcd.of(48, 18)
6

iex> BinaryGcd.of(0, 5)
5

iex> BinaryGcd.of(54, 24)
6

iex> BinaryGcd.of(17, 13)
1

Computing GCD of multiple numbers

iex> BinaryGcd.of([48, 18, 12])
6

iex> BinaryGcd.of([0, 5, 10])
5

iex> BinaryGcd.of([54, 24, 36])
6

iex> BinaryGcd.of([100, 200, 300, 400])
100

iex> BinaryGcd.of([17, 13, 19])
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:

1. If either number is zero, return the other number.
2. If both numbers are even, divide both by 2 and multiply the result by 2.
3. If one number is even, divide it by 2.
4. If both numbers are odd, subtract the smaller from the larger.
5. 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.