🦊 FoxPi

High-precision terminal π explorer — Chudnovsky, Ramanujan, Machin, and BBP spigot algorithms.

FoxPi is a pure-Python command-line toolkit for computing, exploring, benchmarking, and validating π using several classical and modern algorithms.

It supports arbitrary-precision decimal computation with Chudnovsky, Ramanujan, and Machin, plus direct hexadecimal digit extraction using the Bailey–Borwein–Plouffe (BBP) formula.

The implementation uses integer-scaled arithmetic and includes an independent test suite that checks computed decimal and hexadecimal digits against reference values rather than merely comparing algorithms against themselves.

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✨ Features

• 🧮 Arbitrary-precision decimal computation of π
• ⚡ Chudnovsky computation with binary splitting
• 📜 Ramanujan's rapidly convergent hypergeometric series
• 📐 Classical Machin formula
• 🔢 BBP hexadecimal digit extraction
• 🔬 Term-by-term convergence exploration
• 📊 Built-in algorithm benchmarking
• 🧱 Integer-scaled arithmetic for high-precision calculations
• 🧪 Automated tests against independent reference digits
• 📦 Standard-library implementation with no runtime dependencies
• 🐍 Python package/CLI entry point via pyproject.toml
• 📄 MIT licensed

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📋 Table of Contents

• Installation
• Quick Start
• CLI Reference
  • digits
  • explore
  • compare
  • bbp
• Algorithms
  • Chudnovsky
  • Ramanujan
  • Machin
  • BBP
• Precision and Implementation
• Testing
• Project Structure
• Development
• Performance
• Limitations
• Contributing
• License

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Installation

Requirements

FoxPi requires:

• Python 3.8 or newer
• pip for optional editable/package installation

The project declares no runtime third-party dependencies.

Clone the repository

git clone https://github.com/foxhackerzdevs/foxpi.git
cd foxpi

Run directly

python cli.py digits 100

Example output:

π (100 digits) using Chudnovsky:
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
Time: 0.00xxs

Install the CLI

Install from PyPI

python3 -m pip install foxpi

foxpi digits 100

Install from Source

git clone https://github.com/foxhackerzdevs/foxpi.git
cd foxpi
python -m pip install -e .

Current version: 0.1.4

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Quick Start

# Compute 100 digits
python cli.py digits 100

# Use a specific method
python cli.py digits 1000 --method chudnovsky
python cli.py digits 1000 --method ramanujan
python cli.py digits 1000 --method machin

# Explore convergence
python cli.py explore --method chudnovsky --terms 15

# Benchmark
python cli.py compare

# Extract hexadecimal digits
python cli.py bbp 100

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CLI Reference

FoxPi exposes four commands:

foxpi
├── digits
├── explore
├── compare
└── bbp

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digits

Compute a requested number of decimal digits of π.

python cli.py digits COUNT [--method METHOD]

Argument	Description
COUNT	Number of decimal digits requested
--method	chudnovsky (default), ramanujan, or machin

Examples

python cli.py digits 50
python cli.py digits 1000 --method chudnovsky
python cli.py digits 1000 --method ramanujan
python cli.py digits 1000 --method machin

Negative digit counts are rejected.

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explore

Explore the convergence of the Ramanujan or Chudnovsky series.

python cli.py explore [--method METHOD] [--terms N]

• Default method: ramanujan
• Default terms: 30

python cli.py explore
python cli.py explore --method ramanujan --terms 20
python cli.py explore --method chudnovsky --terms 10

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compare

Benchmark Chudnovsky and Machin at 1000 decimal digits.

python cli.py compare

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bbp

Extract 16 hexadecimal digits of π starting at a given position.

python cli.py bbp POSITION

POSITION=1 is the first hexadecimal digit after the point.

python cli.py bbp 1
python cli.py bbp 25
python cli.py bbp 100

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Algorithms

Algorithm	Output	Primary purpose
Chudnovsky	Decimal	High-precision computation
Ramanujan	Decimal	Rapid convergence / exploration
Machin	Decimal	Classical formula / comparison
BBP	Hexadecimal	Direct digit extraction

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Chudnovsky

Binary-splitting implementation of the Chudnovsky series (~14 digits per term).
This is the default and recommended method for high-precision decimal computation.

python cli.py digits 10000 --method chudnovsky

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Ramanujan

Ramanujan’s 1914 hypergeometric series for 1/π:

1/π = (2√2 / 9801) × Σ [ (4k)! × (1103 + 26390k) / ((k!)⁴ × 396⁴ᵏ) ]

Excellent for studying rapid convergence.

python cli.py digits 1000 --method ramanujan
python cli.py explore --method ramanujan --terms 20

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Machin

Classical Machin formula:

π = 4 × (4 arctan(1/5) − arctan(1/239))

python cli.py digits 500 --method machin

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BBP hexadecimal spigot

Bailey–Borwein–Plouffe formula allowing direct extraction of hexadecimal digits without computing preceding ones.

python cli.py bbp 1
# → 243F6A8885A308D3

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Precision and Implementation

FoxPi uses scaled-integer arithmetic with internal guard digits.
No third-party arbitrary-precision library is required at runtime.

A custom Newton–Raphson isqrt implementation is provided and covered by the test suite.

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Testing

python -m unittest discover -s tests -v

Tests verify results against independently generated reference digits (mpmath, 250 decimal digits of working precision).

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Project Structure

foxpi/
├── core/
│   ├── algorithms.py
│   └── visualize.py
├── tests/
│   ├── test_algorithms.py
│   └── test_cli.py
├── .gitignore
├── LICENSE
├── README.md
├── cli.py
└── pyproject.toml

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Development

git clone https://github.com/foxhackerzdevs/foxpi.git
cd foxpi

# Run directly
python cli.py --help

# Run tests
python -m unittest discover -s tests -v

# Editable install
python -m pip install -e .
foxpi --help

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Performance

Chudnovsky with binary splitting is the recommended high-performance path.
Use python cli.py compare for a quick local benchmark.

Performance depends on Python version, CPU, and requested precision.

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Limitations

• Extremely large precisions consume significant time and memory.
• BBP currently returns a fixed 16 hexadecimal digits.
• The compare command uses a fixed 1000-digit workload.
• Convergence exploration (explore) intentionally recomputes for visualization and is not optimized for speed.

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Contributing

Contributions are welcome. Suggested areas:

• Additional algorithms
• Configurable BBP length
• Expanded benchmarks
• More tests
• Documentation improvements

1. Fork the repository
2. Create a feature branch
3. Add tests where appropriate
4. Open a pull request

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License

FoxPi is released under the MIT License.

Copyright © 2026 Fox Hackerz

See LICENSE for the full text.

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Links

• GitHub: https://github.com/foxhackerzdevs/foxpi
• PyPI: https://pypi.org/project/foxpi/
• Homepage: https://foxhackerzdevs.github.io/foxpi/

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Compute it. Explore it. Benchmark it. Verify it. 🦊