🦊 FoxPi

High-precision π explorer and mathematical visualization toolkit for the command line.

FoxPi is a Python-based CLI application for computing and exploring the digits of π using several famous algorithms. It provides fast high-precision computation, convergence visualization, benchmarking tools, and hexadecimal digit extraction via the Bailey–Borwein–Plouffe (BBP) formula.

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Table of Contents

• Features

• Project Structure

• Installation

• Usage

  • Compute Digits
  • Explore Convergence
  • Compare Algorithms
  • BBP Hexadecimal Digits

• Algorithms Implemented

• Examples

• Dependencies

• Configuration

• Troubleshooting

• Contributing

• License

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Features

• Compute π to an arbitrary number of decimal digits.

• Multiple computation algorithms:

  • Chudnovsky Algorithm
  • Ramanujan Series
  • Machin Formula

• Interactive convergence exploration.

• Benchmark algorithm performance.

• Extract hexadecimal digits directly using the BBP formula.

• Pure Python implementation using integer arithmetic for high precision.

• No third-party dependencies.

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Project Structure

foxpi/
│
├── cli.py                # Command-line interface
└── core/
    ├── algorithms.py     # Mathematical algorithms
    └── visualize.py      # CLI visualization utilities

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Installation

Clone the repository:

git clone <repository-url>
cd foxpi

Python 3.9+ is recommended.

No external packages are required.

Run with a subcommand:

python cli.py digits 100

python cli.py alone (with no subcommand) prints usage and exits with an error — a subcommand (digits, explore, compare, or bbp) is required.

or

python -m cli

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Usage

Compute Decimal Digits

Compute π using one of the supported algorithms.

python cli.py digits 1000

Specify the algorithm:

python cli.py digits 5000 --method chudnovsky

python cli.py digits 1000 --method ramanujan

python cli.py digits 1000 --method machin

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Explore Convergence

Watch the approximation converge term by term.

python cli.py explore

Choose an algorithm:

python cli.py explore --method ramanujan

python cli.py explore --method chudnovsky

Limit the number of displayed terms:

python cli.py explore --terms 20

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Compare Algorithms

Benchmark the available implementations.

python cli.py compare

Current benchmark compares:

• Chudnovsky
• Machin

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Extract Hexadecimal Digits (BBP)

Retrieve hexadecimal digits beginning at a specified position without computing previous digits.

python cli.py bbp 1

Example:

python cli.py bbp 1000

Outputs the next 16 hexadecimal digits beginning at that position.

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Algorithms Implemented

Chudnovsky Algorithm

• Modern state-of-the-art series for computing π.
• Approximately 14 decimal digits per term.
• Uses binary splitting for efficient large integer arithmetic.
• Suitable for very high precision.

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Ramanujan Series

• Classic 1914 hypergeometric series.
• Extremely rapid convergence.
• Integer-scaled implementation for numerical stability.

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Machin Formula

Uses

π = 4 × (4 arccot(5) − arccot(239))

Advantages:

• Simple
• Educational
• Useful for comparison against faster modern methods

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Bailey–Borwein–Plouffe (BBP)

Supports direct extraction of hexadecimal digits of π.

Unlike traditional algorithms, BBP allows accessing hexadecimal digits beginning at an arbitrary position without computing all preceding digits.

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Examples

Compute 100 digits:

python cli.py digits 100

Compute 5000 digits using Chudnovsky:

python cli.py digits 5000 --method chudnovsky

Visualize convergence:

python cli.py explore --method chudnovsky --terms 15

Benchmark:

python cli.py compare

Extract hexadecimal digits:

python cli.py bbp 250

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Dependencies

Only Python standard library modules are used:

• argparse
• decimal
• pathlib
• sys
• time
• typing

No external dependencies are required.

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Configuration

There are currently no configuration files.

Precision and algorithm selection are controlled through command-line arguments.

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Troubleshooting

Import errors

Ensure the project directory structure matches the expected layout:

core/
    algorithms.py
    visualize.py

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Slow execution

Very large digit counts require significant CPU time.

For best performance:

• Prefer the Chudnovsky algorithm.
• Use Ramanujan for convergence exploration.
• Use Machin primarily for educational purposes and comparisons.

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Unexpected precision

Higher requested precision naturally requires more computation time and memory due to large integer arithmetic.

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Contributing

Contributions are welcome.

Possible improvements include:

• Additional π algorithms
• Parallel binary splitting
• Progress bars
• Graphical convergence plots
• Export benchmark results
• Automated testing
• Packaging for PyPI

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License

No license information was provided in the source files.

Consider adding a LICENSE file (for example MIT, Apache-2.0, or GPL-3.0) before publishing the project.