Hawkynt

CMWC (Complementary Multiply-with-Carry)

CMWC is an advanced pseudo-random number generator invented by George Marsaglia. It uses a large state array (4096 values) with multiply-and-carry operations, achieving an extraordinary period of 2^131104. The complementary aspect returns the bitwise complement of computed values, improving randomness quality.

Properties

Property	Value
Category	Random Number Generators
Sub-category	Deterministic PRNG
Security status	🎓 Educational Only
Complexity	Intermediate
Inventor	George Marsaglia
Year	2003
Origin	🇺🇸 United States
Source	algorithms/random/cmwc.js

Parameters

Parameter	Supported values
Seed sizes	1 byte (8 bits) to 8 bytes (64 bits)

Capabilities

Flag	Value
IsDeterministic	Yes
IsCryptographicallySecure	No

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Documentation

• Original Paper: Random Number Generators (Journal of Modern Applied Statistical Methods, 2003)
• Wikipedia: Multiply-with-carry pseudorandom number generator
• Marsaglia’s Post on CMWC4096 (sci.crypt, 2003)
• Logical Intuitions: PRNG 3: Complementary Multiply-with-Carry

References

• TestU01 Statistical Testing Suite
• DieHarder Random Number Test Suite
• Uncommons Maths CMWC4096RNG Java Implementation

Test vectors

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

Vector 1 — Seed 0: First 5 outputs (40 bytes) - verified against C# reference

Source: X:\Coding\Working Copies\Hawkynt.git\Randomizer\RandomNumberGenerators\Deterministic\ComplementaryMultiplyWithCarry.cs

Field	Value
seed	0000000000000000
outputSize	40
input	null
expected	8b912eacca47b64c238592b521f4679e 5aa031f54b2dde8ceaa62edfe6338250 f333513179fbd3ec

Vector 2 — Seed 1: First 5 outputs (40 bytes)

Source: X:\Coding\Working Copies\Hawkynt.git\Randomizer\RandomNumberGenerators\Deterministic\ComplementaryMultiplyWithCarry.cs

Field	Value
seed	0000000000000001
outputSize	40
input	null
expected	c108910a0e5eb78a710077017762a450 17f2258dea636a1960cde049597dfdfe 76dfd35b7206acfd

Vector 3 — Seed 42: First 5 outputs (40 bytes)

Source: X:\Coding\Working Copies\Hawkynt.git\Randomizer\RandomNumberGenerators\Deterministic\ComplementaryMultiplyWithCarry.cs

Field	Value
seed	000000000000002a
outputSize	40
input	null
expected	8211488f4151822e08142692d53eebf4 3ed2ac69afb32196b7937d066ece679c f68f0e03de311c72

Vector 4 — Seed 1234567: First 8 outputs (64 bytes)

Source: X:\Coding\Working Copies\Hawkynt.git\Randomizer\RandomNumberGenerators\Deterministic\ComplementaryMultiplyWithCarry.cs

Field	Value
seed	000000000012d687
outputSize	64
input	null
expected	3e8eecf519743031bedf18e3222799cd eb8f9b725b43854f8a91e2002dedf10b 9eae5ee7c03cad416a6574def1b8840f e939516b2f6a4f743d4da6c4c5b8eb73

Vector 5 — Seed 987654321: First 8 outputs (64 bytes)

Source: X:\Coding\Working Copies\Hawkynt.git\Randomizer\RandomNumberGenerators\Deterministic\ComplementaryMultiplyWithCarry.cs

Field	Value
seed	000000003ade68b1
outputSize	64
input	null
expected	1ac7b2559be4d603ea2c816307a5144a a700d67e836ecb7604e9a7352e91d212 05c4820e5877a6d359613d5949c1e7de 07b44a075e6ceb68c305ea20312d2bca

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