BigInteger using GMP

This is the second version of the BigInteger library, which is wrapped around the GMP library. The first version of the library was written in a rush and was not very well designed. This version is a complete rewrite and is designed to be more efficient and easier to use.

BigIntegerGMP2 Improvements over BigIntegerGMP

Overview

This document summarizes the key improvements made in the BigIntegerGMP2 library compared to the previous version. It provides an overview of enhanced features, improved usability, and newly added functionalities that make the updated library more robust and easier to use.

Improvements Summary

1. Enhanced Interoperability and Conversion Capabilities

• Explicit and Implicit Conversions: Added support for type conversion operators to convert between BigInteger and common data types (mpz_t, byte arrays, strings, integers, unsigned integers, etc.).
• Intuitive Integration: This allows for more seamless integration with C# types, minimizing code complexity and enabling natural usage.

2. Expanded Arithmetic and Logical Operators

• Added full suite of arithmetic operators (+, -, *, /, %) and logical operators (&, |, ^, ~), along with shift operators (<<, >>).
• Increment (++) and Decrement (--) operators were also added to provide easier iteration over BigInteger values.
• These additions make the library more natural to use, similar to native integer types.

3. Improved Comparison and Equality Functions

• Comprehensive Comparisons: Added comparison functions (<, <=, >, >=) and multiple CompareTo() overloads, allowing comparisons between BigInteger and common data types (int, long, double, etc.).
• Overridden Equals() Method: Enhanced equality checks to ensure consistent behavior regardless of data types.
• Absolute Comparisons: Added methods for absolute value comparison (CompareAbsTo()).

4. Additional Utility Functions

• Conversion Methods: Expanded utility with functions like ToInt32(), ToInt64(), ToDouble(), and ToByteArray().
• Base Conversion: Added ToString(int radix) and ToString(BaseFormat) for conversion to different bases.
• Base-64 Conversion: Added methods for Base-64 encoding and decoding to ease serialization and deserialization.

5. Random Number Generation

• Added random number generation with specific bit lengths and within a given range.
• Utilizes GMP's random number generator, providing enhanced randomness and cryptographic utility.

6. Specialized Mathematical Functions

• Jacobi and Kronecker Symbols: Added methods to compute these symbols, providing important utility for number theory and cryptographic algorithms.
• Fibonacci and Lucas Numbers: Functions to compute Fibonacci and Lucas numbers, including predecessor values.
• Extended Euclidean Algorithm and Modular Inverse: Added these algorithms for use in modular arithmetic and cryptographic applications.

7. Logging and Debugging Enhancements

• Introduced a ShouldLog property to toggle logging capabilities, allowing detailed tracing during development and debugging. (Still not implemented!)

8. Better Memory Management

• Implemented Dispose() method and IDisposable interface for better management of unmanaged resources and to reduce memory leaks.

9. Mathematical Extensions

• Chinese Remainder Theorem (CRT): Added functionality to solve simultaneous congruences.
• Least Common Multiple (LCM): Added methods to compute LCM for BigInteger and standard types.

10. Constants and Predefined Values

• Added constants like Zero, One, Two, Three, and MinusOne to improve readability and reuse of common values.

11. Bitwise Operations and Hamming Distance

• Bitwise Operations: Added &, |, ^, ~ operations, providing the capability for bit-level manipulation.
• Hamming Distance: Added a method to compute the Hamming Distance between two BigInteger values, useful in error detection/correction and cryptography.

Features

• Efficient: The library is wrapped around the GMP library, which is a highly optimized library for arbitrary precision arithmetic.
• Easy to use: The library is designed to be easy to use and understand.
• Well documented: The library is well documented and has a lot of examples.
• Windows only: The library is currently only supported on Windows - and only on x64.

Building

• Requirements: You need to have Visual Studio 2022 installed on your system.
• Steps:
  1. Clone the repository.
  2. Open the solution file in Visual Studio.
  3. Build the solution.
  4. Select 'Debug-MemoryLoad' or 'Release-MemoryLoad' for the experimental build where the native GMP library is loaded from memory.

Dependencies

This project depends on the QuickLog logging library.

Acknowledgements

• GMP: The GNU Multiple Precision Arithmetic Library.
• MpfrDotNet: The original library that is the core of this library.
• Sdcb.Arithmetic: The library that inspired me to start this project anew.