🐇 General GG Fibonacci (GGGF) 🐇

Generalized Generator of Gigantic Fibonacci numbers.

🤔 Want to know what the 1,000,000th Fibonacci number is? 🤔

We've got you covered! Not that you can see it with your small eyes, but it makes an impression by overflowing your text buffer.

🧮 Fibonacci with Negative Indices 🧮

Interested in knowing Fibonacci numbers with a negative index, like -1,235,031?

Try our product!

Explaination of Negabonacci

There actually exists a mathematical relation:

∃ GFib(x) ∀ k∈Z ( [k ≥ 0 ⇒ GFib(k) = Fib(k)] ∧ [k < 0 ⇒ GFib(k) = NFib(k)] ∧ [GFib(k+2) = GFib(k+1)+GFib(k)] ), where:

• Fib –– Fibonacci –– Classic Fibonacci function
• GFib –– GeneralFibonacci –– Generalized Fibonacci function
• NFib –– Negabonacci –– Fibonacci accepting Negative indexes

🧩 Usage 🧩

dotnet run <Fibonacci index>

The Fibonacci index can be any integer.

• Positive indices return the corresponding Fibonacci number.
• Negative indices return the corresponding Negabonacci number.

📝 Notes: 📝

1. Negative Indexing: Fibonacci numbers for negative indices follow the pattern: F(-n) = (-1)^(n+1) × F(n) .
   This means:

   • F(-1) = 1
   • F(-2) = -1
   • F(-3) = 2

2. Large Numbers: This implementation uses BigInteger to handle very large Fibonacci numbers. For example, Fibonacci(1,000,000) can be computed without overflow issues.

3. Performance: Matrix exponentiation is used for efficient computation, making it feasible to calculate Fibonacci numbers for very large indices quickly.

🚀 Features 🚀

• Speed: Efficient computation using matrix exponentiation.
• Accuracy: Gives correct output even for integers of very large absolute value.
• Flexibility: Computes Fibonacci numbers for both positive and negative indices.

🤝 Contributing 🤝

Feel free to fork this project, submit issues, and make pull requests. For major changes, please open an issue first to discuss what you would like to change.

📄 License 📄

This project is licensed under the MIT License - see the LICENSE.txt file for details.

💡 Acknowledgments 💡

Inspired by the classical Fibonacci sequence and its mathematical beauty.

🧑‍💻 Contact 🧑‍💻

For any inquiries, please contact tomasz_nehring@outlook.com.