Aryabhata

A Python implementation of Aryabhata’s digit‑pair square‑root algorithm — a classical Indian arithmetic method for extracting square roots using only integer operations.

This project provides:

• A mathematically exact square‑root engine
• A modern CLI
• Optional ASCII animation of the digit‑pair extraction
• 100% unit‑test and branch coverage

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Features

• Exact integer arithmetic — no floating point drift
• Arbitrary precision via digit‑pair extension
• Decimal output with proper zero‑padding
• Debug mode exposing the invariant: N = root² + remainder
• Optional ASCII animation showing every digit trial
• Pytest test suite with full coverage

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Installation

Install with pip:

pip install aryabhata

Local development:

git clone https://github.com/djstompzone/aryabhata
cd aryabhata
pip install -e .[dev]

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Usage

Basic

python -m aryabhata 82

Or

aryabhata 82

Output:

9

With decimal precision

aryabhata 82 --digits 3

Output:

9.055

Debug mode

aryabhata 82 --digits 3 --debug

Output:

9.055
[scaled-root] 9055
[remainder]   6975
[identity]    8200000 = 9055^2 + 6975

ASCII animation

aryabhata 82 --digits 3 --animate

This plays a frame‑by‑frame digit‑pair square‑root extraction in your terminal.

Control speed with:

--fps 15

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How the algorithm works

Aryabhata’s method operates by grouping digits into base‑100 pairs and extracting square‑root digits one at a time using this rule:

At each step:

Choose max x such that (20R + x)·x ≤ remainder
R := 10R + x
remainder := remainder − (20R + x)·x

Where R is the root built so far.

This is mathematically equivalent to long‑hand square‑root extraction but works entirely in integers.

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Library API

from aryabhata.sqrt import sqrt_aryabhata

root, remainder = sqrt_aryabhata(82, digits=3)

Returns:

root = floor( sqrt(n) × 10^digits )
remainder = n × 10^(2·digits) − root²

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Testing

Run all tests with coverage:

poetry run coverage run -m pytest
poetry run coverage report -m

All code paths are fully covered.

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Why this exists

Most square‑root implementations hide the math behind floating point hardware.

This project exposes the actual arithmetic behind root extraction — the same logic used by scribes, calculators, and engineers long before digital computers existed.

It’s math you can watch happening.

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License

MIT License