HaskellProjects

🧮 Chudnovsky π Calculator (Haskell)

📘 Overview

This Haskell program computes π (pi) to an arbitrary number of digits using the Chudnovsky algorithm, a highly efficient formula based on Ramanujan-type series. It leverages GMP (GNU Multiple Precision Arithmetic Library) for high-precision integer arithmetic via Haskell’s FFI interface.

⚙️ Features

Implements the binary splitting method for efficient term computation.
Uses GMP’s mpz_sqrt for precise square root evaluation.
Prints π to the desired number of digits with correct formatting.
Modular, recursive design reflecting the Chudnovsky formula structure.

🧩 Algorithm

The Chudnovsky formula for π is: $\frac{1}{\pi} = 12 \sum_{k=0}^\infty \frac{(-1)^k (6k)! (13591409 + 545140134k)}{(3k)! (k!)^3 (640320)^{3k + 3/2}}$

This implementation:

Splits the range recursively with bs.
Computes partial products (p, q, t) for each interval.
Combines results efficiently using the binary splitting technique.

💻 Usage

Compile and run using:

gcc -c cbits/wrappers.c -o cbits/wrappers.o
ghc -O2 pi.hs cbits/wrappers.o -o pi
./pi 1000

This will output π to 1000 digits.

📦 Dependencies

GCC
GHC (Glasgow Haskell Compiler)
GMP (GNU Multiple Precision Arithmetic Library)
Numeric.GMP Haskell bindings

🧠 Example Output

π to 100 digits is: 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170

🪪 Author

Abhrankan Chakrabarti

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