Hawkynt

MRG32k3a

MRG32k3a is a combined multiple recursive generator with period approximately 2^191. It combines two MRG components using carefully chosen parameters for excellent statistical properties and is recommended for Monte Carlo simulations.

Properties

Property	Value
Category	Random Number Generators
Sub-category	Pseudo-Random Number Generator
Security status	🎓 Educational Only
Complexity	Intermediate
Inventor	Pierre L’Ecuyer
Year	1999
Origin	🇨🇦 Canada
Source	algorithms/random/mrg32k3a.js

Parameters

Parameter	Supported values
Seed sizes	4 bytes (32 bits); 24 bytes (192 bits)

Capabilities

Flag	Value
IsDeterministic	Yes
IsCryptographicallySecure	No

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Documentation

• Original Paper: Good Parameters and Implementations for Combined MRGs (Operations Research 1999)
• L’Ecuyer’s MRG32k3a Reference Implementation
• TestU01: Statistical Test Suite
• Wikipedia: Combined Linear Congruential Generator

References

• Rosetta Code: MRG32k3a Implementation Examples
• RngStreams Library (multiple independent streams)

Test vectors

3 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — MRG32k3a with seed 1234567 (first 5 outputs - Rosetta Code verification)

Field	Value
seed	87d61200
outputSize	20
input	null
expected	99d6f9569a6e8ba895cd0ffdd59c1fe71ff2b09a

Vector 2 — MRG32k3a with seed 987654321 (first 5 outputs)

Field	Value
seed	b168de3a
outputSize	20
input	null
expected	44775cb5c8b3f5b8a93488c320e06f2fee99fc5f

Vector 3 — MRG32k3a with seed 12345 (first 5 outputs)

Field	Value
seed	39300000
outputSize	20
input	null
expected	cf81c57ba22715c3768957e45edb6ac52b06432c

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