ring30mix

High-performance pseudo-random number generator based on Rule 30 cellular automaton with golden ratio mixing.

• ~2× faster than Go's math/rand/v2 PCG
• Perfect BigCrush score (254/254 p-values) with superior distribution

See ALGORITHM.md for details.

Quick Start

Installation

# As a command-line tool
go install github.com/vrypan/ring30mix@latest

# As a library
go get github.com/vrypan/ring30mix

Command Line Usage

# Generate random data
./ring30mix --bytes=1048576 > random.bin

# Generate specific size with dd
./ring30mix --bytes=1073741824 | dd of=test.data bs=1m

# Unlimited streaming (use with head, pv, or Ctrl+C)
./ring30mix --bytes=0 | head -c 1073741824 > test.data

# Reproducible output with seed
./ring30mix --seed=12345 --bytes=1024 > random.bin

Library Usage

Drop-in replacement for math/rand:

import "github.com/vrypan/ring30mix/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 2026-01-03 (run make bench to reproduce):

Absolute Performance

Algorithm	Read() 32KB	Read() 1KB	Uint64()
math/rand/v2 PCG	13249.00 ns	413.30 ns	3.23 ns
math/rand/v2 ChaCha8	11478.00 ns	360.70 ns	2.77 ns
ring30mix	6721.00 ns	214.90 ns	1.62 ns
math/rand	21409.00 ns	683.50 ns	1.80 ns
crypto/rand	7448.00 ns	365.10 ns	54.58 ns

Speed vs math/rand/v2 PCG (baseline = 1.00×)

Algorithm	Read() 32KB	Read() 1KB	Uint64()
math/rand/v2 PCG	1.00x	1.00x	1.00x
math/rand/v2 ChaCha8	1.15x	1.15x	1.16x
ring30mix	1.97x	1.92x	1.99x
math/rand	0.62x	0.60x	1.79x
crypto/rand	1.78x	1.13x	0.06x

Randomness Quality

Perfect BigCrush score - verified 2026-01-04:

Test Suite	P-values	Passed	Status
SmallCrush	15	15/15 ✅	100%
Crush	186	186/186 ✅	100%
BigCrush	254	254/254 ✅	100%

Superior to math/rand/v2 PCG:

• ring30mix: 4 borderline p-values (2 low + 2 high, all safe)
• math/rand/v2 PCG: 5 borderline p-values (3 low + 2 high)
• math/rand: 10 borderline + 1 FAIL ❌

Run tests yourself:

cd testu01
make smallcrush   # 15 p-values, ~2 min
make crush        # 186 p-values, ~10 min
make bigcrush     # 254 p-values, ~1 hour

How It Works

Core algorithm:

• Rule 30 cellular automaton: new_bit = left XOR (center OR right)
• 256-bit ring (4 × 64-bit words)
• Golden ratio mixing on output (rotation + φ multiply + shift-XOR)

Key optimizations:

• Bit-parallel processing (64 bits per operation)
• Fully unrolled loops
• Pre-computed border bits
• Amortized state evolution (1 step per 4 outputs)

See ALGORITHM.md for complete technical details, optimizations, and analysis.

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