This project is part of the "Praktikum Grundlagen Rechnerarchitektur" course at TUM. It involves approximating the mathematical constant π using efficient algorithms. The goal is to calculate π with configurable precision and evaluate the solution's quality scientifically.
The task is to implement an efficient algorithm to approximate the mathematical constant π with arbitrary precision. The algorithm will utilize the Karatsuba multiplication and Binary Splitting techniques.
The Karatsuba algorithm allows efficient multiplication of large numbers by recursively dividing them into smaller parts. It reduces the number of required multiplications and improves performance.
Binary Splitting is a technique used to efficiently calculate mathematical sequences. It utilizes polynomials and integer arithmetic operations to perform calculations. The approach avoids division operations except for the final step.
The framework program supports the following command-line options:
-d <int>: Output n decimal places after the decimal point. Overrides the-hoption.-h <int>: Output n hexadecimal places after the decimal point.-B <int>: Print running time with an optional argument for the number of function call repeats.-h: Print the description of all options and exit.--help: Print the description of all options and exit.-V <int>: Choose the implementation:V0: Main implementation (default).V1: Comparison implementation.
To begin working on this project, follow these steps:
- Clone the project repository from Git.
- Compile the program with
make. - Run the program as
./main.