fionn/batch-gcd

DJB's batch GCD algorithm for fast factoring sequences of integers

Batch GCD

Overview

A pure Python implementation of DJB's Batch GCD algorithm.

Installation

Download and install with pip.

Or, download from source and install with make install (standard, user) or make install_dev (editable, system).

Usage

This is a library and cannot be invoked directly.

Test with make test.

The batch_gcd module exposes a batch_gcd function which takes integers and returns a list of their GCDs at the corresponding index.

>>> # Example batch_gcd usage
>>> from batch_gcd import batch_gcd
>>> batch_gcd(1909, 2923, 291, 205, 989, 62, 451, 1943, 1079, 2419)
[1909, 1, 1, 41, 23, 1, 41, 1, 83, 41]

This calculation involves two intermediate steps: creating a product tree and creating a remainder tree. These functions are also exposed, as products and remainders. products take integers and returns a product tree, remainders takes an integer and a product tree and returns a list of remainders.

Resources

• How to Find Smooth Parts of Integers
• FactHacks: Batch GCD
• FactHacks: RSA Factorization in the Real World