A powerful, fast Rust implementation of Euler's Totient function φ(n), with optional parallel processing support to handle large numbers more efficiently.

• Euler's Totient function calculations for arbitrary large integers
• Choose between Euclidean or Binary GCD algorithms
• Fast totient using prime factorization (if known or factorable)
• Optional parallel computation mode during brute-force counting
• Compatible with modern Rust (2021 Edition)
• Clean CLI interface

For a positive integer n, Euler's Totient function φ(n) counts how many integers k ≤ n are coprime with n (no common factors besides 1).

Build with:

cargo build --release

This project includes an optional parallel backend for the brute-force totient count.
Parallel counting significantly speeds up computations on multi-core machines ardalis.com, developer.hashicorp.com.

To enable parallel computations, build with:

cargo build --release --features parallel

or run directly:

cargo run --release --features parallel -- <number> <algorithm>

This activates a multithreaded engine (using Rayon) that divides the counting across CPU cores.

Tip: Parallel build is highly recommended for larger inputs as it cuts down execution time drastically (sometimes up to 2-5x faster depending on hardware and input size).

cargo run --release [--features parallel] -- <number> <algorithm>

where <algorithm> is one of:

• euclidean - brute-force counting using Euclidean GCD
• binary - brute-force counting using the Binary GCD algorithm
• factor - use prime factorization formula instead of counting (fastest if factors known)

Example:

cargo run --release --features parallel -- 12345 binary

or

cargo run --release -- 987654 factor

The parallel feature speeds up brute-force totient counting by dividing the range [1, n-1] into parts and processing them simultaneously on all available CPU cores. This approach is similar to how other build or compute tools use task-based concurrency to reduce total execution time ardalis.com, developer.hashicorp.com.

If you work with large integers or want to save time, enabling --features parallel is highly recommended.

• 🚀 Enable the parallel feature at build time (--features parallel) to significantly accelerate totient calculations
• Supports brute-force (Euclidean or Binary GCD)
• Supports fast factorization-based method
• Handles arbitrary precision integers

MIT OR Apache-2.0

• Euler's Totient Function — Wikipedia

Enjoy fast number theory in Rust!