numpyrge256 1.0.0

NumPy implementation of the RGE-256 ARX-based pseudorandom number generator.

Numpyrge256

A pure NumPy implementation of RGE-256, a 256-bit ARX-based pseudorandom number generator featuring geometric rotation scheduling and structured entropy from Recursive Division Tree (RDT) analysis.

This package provides a lightweight, dependency-free core suitable for research, simulations, Monte Carlo methods, and general-purpose randomness in scientific computing.

Author: Steven Reid ORCID: 0009-0003-9132-3410 Paper: RGE-256: A New ARX-Based Pseudorandom Number Generator With Structured Entropy and Empirical Validation (Nov 2025) Zenodo: https://zenodo.org/records/17713219 PyTorch version: https://github.com/RRG314/torchrge256 Demo: https://github.com/RRG314/RGE-256-app

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Key Features

• Pure NumPy implementation (no external dependencies)
• 256-bit internal state (8 × 32-bit words)
• Deterministic ARX update structure
• Rotation constants derived from structured geometric entropy
• Domain separation for independent streams
• Reproducible sequences for research and simulation
• Batch generation for large datasets

This implementation is focused on simplicity, portability, and reliability for scientific use cases.

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Installation

PyPI:

pip install rge256

Or install directly from GitHub:

pip install git+https://github.com/RRG314/numpyrge256

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Quick Start

from rge256 import RGE256

rng = RGE256(seed=12345)

# Single 32-bit integer
x = rng.next32()

# Float in [0, 1)
f = rng.nextFloat()

# Integer in range [lo, hi]
v = rng.nextRange(1, 100)

# Batch of numbers
batch = rng.next32_batch(1000)

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API Summary

RGE256(seed, rounds=3, zetas=(1.585, 1.926, 1.262), domain="numpy")

Creates a new RGE-256 generator.

Core methods:

• next32() – returns a 32-bit unsigned integer
• nextFloat() – returns a float in [0, 1)
• nextRange(lo, hi) – returns an integer in [lo, hi]
• next32_batch(n) – generates an array of n random uint32 values

All outputs are deterministic given (seed, domain, rounds, zetas).

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Notes on Statistical Behavior

Empirical testing (Dieharder, bit balance analysis, chi-square evaluation) shows:

• Entropy ≈ 7.999–8.000 bits/byte
• Uniform bit distribution (~50% ones per bit position)
• Low serial and lag-1 correlation
• Stable behavior across NumPy and PyTorch implementations

The design inherits rotation structure from geometric entropy constants used in the corresponding RDT entropy framework.

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Disclaimer

RGE-256 is not designed as or intended to serve as a cryptographic random number generator. It has not been formally analyzed for cryptographic security.

Use only for research, simulation, and non-security-critical applications.

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Citation

Please cite the corresponding preprint:

@misc{reid2025rge256,
  author       = {Reid, Steven},
  title        = {RGE-256: A New ARX-Based Pseudorandom Number Generator
                  With Structured Entropy and Empirical Validation},
  year         = {2025},
  howpublished = {\url{https://zenodo.org/records/17713219}},
  note         = {ORCID: 0009-0003-9132-3410}
}

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Related Repositories

• PyTorch implementation: https://github.com/RRG314/torchrge256

• Web-based demonstration: https://github.com/RRG314/RGE-256-app

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License

MIT license.