R30R2

High-performance pseudo-random number generator based on Rule 30 (radius-2) cellular automaton.

• 2× faster than Go's math/rand/v2
• 160/160 BigCrush tests pass perfectly.

Quick Start

Installation

# As a command-line tool
go install github.com/vrypan/r30r2@latest

# As a library
go get github.com/vrypan/r30r2

Command Line Usage

# Generate random data
./r30r2 --bytes=1048576 > random.bin

# Generate specific size with dd
./r30r2 --bytes=1073741824 | dd of=test.data bs=1m

# Unlimited streaming (use with head, pv, or Ctrl+C)
./r30r2 --bytes=0 | head -c 1073741824 > test.data

# Reproducible output with seed
./r30r2 --seed=12345 --bytes=1024 > random.bin

Library Usage

Drop-in replacement for math/rand:

import "github.com/vrypan/r30r2/rand"

rng := rand.New(12345)

// Full math/rand interface
rng.Uint64()           // Random uint64
rng.Intn(100)          // Random int in [0, 100)
rng.Float64()          // Random float64 in [0.0, 1.0)
rng.NormFloat64()      // Normal distribution (mean=0, stddev=1)

// Also implements io.Reader
buf := make([]byte, 1024)
rng.Read(buf)

API: Compatible with math/rand - all methods supported (Uint32/64, Int/Intn, Float32/64, NormFloat64, ExpFloat64, Read).

Performance

Benchmarks on Apple M4, verified 2026-01-01 (run make bench to reproduce):

Throughput Comparison

Algorithm	Read() 32KB	Read() 1KB	Uint64()
math/rand	21316.00 ns	674.30 ns	1.81 ns
math/rand/v2	13369.00 ns	423.50 ns	3.22 ns
R30R2	5516.00 ns	183.90 ns	1.75 ns
crypto/rand	7009.00 ns	367.90 ns	56.29 ns

Relative to math/rand:

Algorithm	Read() 32KB	Read() 1KB	Uint64()
math/rand	1.00x	1.00x	1.00x
math/rand/v2	1.59x	1.59x	0.56x
R30R2	3.86x	3.67x	1.03x
crypto/rand	3.04x	1.83x	0.03x

Randomness Quality

Perfect scores on complete TestU01 test suite - exceptional statistical quality verified through rigorous testing:

Test Battery	Tests	R30R2	Pass Rate	Status
SmallCrush	15	15/15 ✓	100%	✅ Verified 2026-01-01
Crush	144	144/144 ✓	100%	✅ Verified 2026-01-01
BigCrush	160	160/160 ✓	100%	✅ Verified 2026-01-01

Historic Achievement: The implementation demonstrates exceptional quality across all test categories: serial correlation, birthday spacing, collision, permutation, matrix rank, spectral, string, compression, random walk, Fourier analysis, linear complexity, and autocorrelation tests.

Comparison with Go Standard Library

BigCrush results comparing Rule 30 with Go's stdlib RNGs (verified 2026-01-01):

Generator	BigCrush Score	Performance vs math/rand
math/rand	159/160*	1.00× (baseline)
math/rand/v2	160/160 ✓	0.56×
Rule 30	160/160 ✓	1.03×

*math/rand fails test #37 (Gap, r = 20) with p-value 5.6e-16

Key insight: Rule 30 delivers equivalent statistical quality to math/rand/v2 (both perfect 160/160) while being 2x faster.

To run TestU01 tests:

cd testu01
make smallcrush   # Quick test (15 tests, 2 min)
make crush        # Medium test (144 tests, 10 min)
make bigcrush     # Comprehensive test (160 tests, 1 hour)

How It Works

Algorithm:

• Radius-2 cellular automaton based on Rule 30 on a circular 256-bit strip.

  new_bit = (left2 XOR left1) XOR ((center OR right1) OR right2)

• Hybrid rotation + multiply mixing applied on output

Implementation:

• 256-bit state as 4 × 64-bit words
• Radius-2 neighborhood: each bit depends on 5 neighboring cells
• Processes 64 bits in parallel per word (bitwise operations)
• Fully unrolled loop - all 4 words updated simultaneously
• Pure CA evolution stored in state
• Hybrid rotation + multiply mixing applied at output time for diffusion
  • Combines rotation, golden ratio multiplication, and shift-XOR
  • Provides strong avalanche effect and non-linearity
  • Verified through rigorous TestU01 testing (144/144 Crush tests)
• Each iteration generates 256 bits (4 × 64-bit words)

Building & Testing

# Build all binaries
make all

# Run Go benchmarks
make bench

# Run comparison tools
make compare-run
./misc/compare-urandom.sh

# Run TestU01 statistical tests
cd testu01
make smallcrush

Use Cases

Good for:

• Monte Carlo simulations
• Procedural generation (games, graphics)
• High-throughput random sampling
• Reproducible sequences (deterministic from seed)

Not for:

• Cryptographic applications (use crypto/rand)
• Security-critical randomness

Background

Rule 30 is a Class III cellular automaton discovered by Stephen Wolfram in 1983. Despite its simple definition, it exhibits chaotic behavior and generates high-quality randomness. Wolfram Research used it as the basis for Mathematica's random number generator.

License

MIT License - See LICENSE file for details

References

• Wolfram, Stephen (1983). "Statistical mechanics of cellular automata"
• Wolfram, Stephen (2002). "A New Kind of Science"
• Rule 30 on Wikipedia