PiEngine

High Precision π Calculator in C

PiEngine is a high-precision π (pi) calculator written in C using the Chudnovsky algorithm with the GMP and MPFR libraries for arbitrary-precision arithmetic.

This project is built as a systems + mathematics project to learn:

• Numerical algorithms
• High precision arithmetic
• Performance optimization
• Large number computation
• Clean C project structure

---

Project Goals

PiEngine is being developed in multiple versions:

Version	Target	Method
V1	100,000 digits	Basic Chudnovsky (factorials)
V2	1,000,000 digits	Recurrence optimization
V3	10,000,000 digits	Binary splitting
V4	100,000,000+ digits	FFT + Multi-threading

Current Version: V1

Goal: Compute 100,000 digits of π correctly and reliably.

This version focuses on correctness, architecture, and understanding the algorithm rather than heavy optimization.

---

How The Algorithm Works

PiEngine uses the Chudnovsky series:

[ \pi = \frac{426880 \sqrt{10005}}{\sum_{k=0}^{\infty} \text{term}_k} ]

Each term of the series adds approximately 14 digits of precision.

The program uses:

• GMP (mpz_t) → big integers (factorials, powers)
• MPFR (mpfr_t) → high precision floating point (division, square root, final π)

Flow of computation:

Compute C = 426880 * sqrt(10005)

sum = 0
for k = 0 to N:
    compute term_k using factorial formula
    sum += term_k

pi = C / sum

---

Project Structure

PiEngine/
├── Makefile
├── README.md
├── src/
│   ├── main.c          → Program entry point
│   ├── chudnovsky.c    → Pi calculation logic
│   ├── chudnovsky.h
│   ├── cli.c           → Command line interface
│   ├── cli.h
│   ├── utils.c         → Timer, progress, helpers
│   ├── bigint.c        → Custom BigInt (future use)
│   ├── bigint.h
│
└── tests/
    └── test_pi.c

---

Build Instructions

Install Dependencies

Arch Linux

sudo pacman -S gmp mpfr

Ubuntu / Debian

sudo apt install libgmp-dev libmpfr-dev

---

Build

make

Run

./piengine

---

Current Limitations (V1)

Version 1 recomputes factorials from scratch for each term, which is slow for very large digit counts.

Because of this, Version 1 is expected to work efficiently up to:

~100,000 digits

Future versions will implement faster algorithms.

---

Future Improvements

Planned upgrades:

• CLI arguments (--digits, --output)
• Save π to file
• Timing / benchmarking
• Progress indicator
• Recurrence formula (faster term calculation)
• Binary splitting algorithm
• Multi-threaded computation

---

Milestones

Milestone	Target
Milestone 1	1,000 digits
Milestone 2	10,000 digits
Milestone 3	100,000 digits
Milestone 4	1,000,000 digits

---

Summary

PiEngine is not just a π calculator. It is a project to explore high-precision computation, numerical methods, and performance optimization in C.

Current Goal: 100,000 digits Next Goal: 1,000,000 digits