xevrion-v2/agent-playground: Calculate the exact value of PI

The gap in what exists

The gap is to deliver a functional, arbitrary-precision Pi calculation implementation that can theoretically extend beyond current limits, integrating with an existing repo.

Wedge to win

The wedge is simply delivering a working, high-precision Pi calculation solution as a PR to the existing repo, securing the $1000 bounty.

Reputation value (worth doing free for proof) — 40/100

Solving a public bounty, even if for a mathematically impossible goal, demonstrates coding skills and responsiveness in a public GitHub project, which can serve as a portfolio piece.

Likely monetization

One-off bounty payment

Incumbents to beat

mpmath (Python)decimal (Python)GMP (C/C++)

You are a senior software engineer specializing in numerical algorithms and high-precision computation. The goal is to calculate the value of Pi to an arbitrary, very large number of decimal places, going significantly beyond 100, and integrate this into an existing GitHub repository as a pull request. The bounty explicitly encourages using AI tools and Google. The output should be a PR to the specified repository. Focus on a robust, performant implementation that demonstrates scalability for precision. The target stack for the implementation itself should be Python, leveraging its arbitrary-precision libraries.

Here's the plan:
1. Research and identify the most efficient algorithm for Pi calculation to arbitrary precision (e.g., Chudnovsky or Borwein algorithms). Focus on algorithms known for rapid convergence.
2. Identify and integrate a suitable Python library for arbitrary-precision arithmetic (e.g., `mpmath` or Python's built-in `decimal` module, configuring its precision context).
3. Implement the chosen algorithm to calculate Pi. The function should accept a parameter for the desired number of decimal places and return Pi as a string.
4. Write comprehensive unit tests to verify the correctness of the calculation for various precision levels, comparing against known values (e.g., from Pi-databases for 1000+ digits).
5. Create a command-line interface or a simple script that can be run to demonstrate the calculation for a user-specified precision, outputting the result.
6. Prepare the code for a pull request to `xevrion-v2/agent-playground` issue #17. Ensure the code is clean, well-commented, and includes a README update explaining how to run the calculation and its theoretical limits regarding 'infinite' precision.

Constraints:
- The solution must be in Python.
- It must demonstrate calculation well beyond 100 decimal places.
- The delivered solution must be a PR that merges into the existing project.
- Explicitly clarify in the PR description that while 'infinite' precision is mathematically impossible for irrational numbers like Pi, this implementation achieves arbitrary, user-defined high precision, limited only by computational resources.