Karatsuba Multiplication in R

[Erennn7]

PR: Karatsuba Multiplication in R

This PR introduces a fully documented implementation of Karatsuba Multiplication in R, a fast recursive algorithm designed for efficient large integer multiplication using the divide-and-conquer approach.

Overview

The karatsuba function implements the Karatsuba multiplication algorithm, which optimizes the standard multiplication process by reducing the number of recursive multiplications.
Instead of performing four sub-multiplications as in the traditional method, Karatsuba’s algorithm performs only three, significantly improving performance for large numeric values.

This approach is especially beneficial for computations involving big integers or high-precision arithmetic, offering better efficiency without sacrificing accuracy.

Complexity

• Time Complexity: O(n^log₂3) ≈ O(n^1.585)
• Space Complexity: O(n) due to recursion

[Copilot]

Pull Request Overview

Implements Karatsuba multiplication in R with a recursive divide-and-conquer approach and inline usage examples.

• Adds a karatsuba function for integer multiplication.
• Includes inline examples and ad-hoc test cases (currently executed on load).

[Erennn7]

Implemented improvements based on review feedback and Copilot recommendations.

Changes made:
• ✅ Added input validation and sign handling for negative and non-integer inputs
• ✅ Replaced nchar(as.character(...)) with a numeric-based digit counting function to avoid issues with scientific notation
• ✅ Added execution guard (if (sys.nframe() == 0)) so examples only run when the script is executed directly
• ✅ Expanded function documentation to include input expectations, output type, limitations, and dependencies
• ✅ Verified correctness with test cases and standard multiplication comparisons

These updates enhance robustness, numerical reliability, and documentation clarity.

[Erennn7]

@siriak please have a look

[Copilot]

Pull Request Overview

Copilot reviewed 1 out of 1 changed files in this pull request and generated 3 comments.