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Multiply-with-Carry (MWC)

Multiply-with-Carry is a fast, simple PRNG invented by George Marsaglia. It uses multiply and carry operations to generate high-quality pseudo-random numbers with very long periods. The algorithm maintains a state value and carry, updating them through multiplication and modular arithmetic.

Properties

Property	Value
Category	Random Number Generators
Sub-category	Deterministic PRNG
Security status	🎓 Educational Only
Complexity	Beginner
Inventor	George Marsaglia
Year	1991
Origin	🇺🇸 United States
Source	algorithms/random/mwc.js

Parameters

Parameter	Supported values
Seed sizes	1 byte (8 bits) to 16 bytes (128 bits)

Capabilities

Flag	Value
IsDeterministic	Yes
IsCryptographicallySecure	No

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Documentation

• Original Paper: A new class of random number generators (1991)
• Efficient MWC Random Number Generators with Maximal Period
• Wikipedia: Multiply-with-carry pseudorandom number generator
• Java Implementation Example

References

• Numerical Recipes (3rd ed., p. 348)
• Distribution Properties of MWC Generators

Test vectors

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

Vector 1 — Seed 1: First 5 outputs (40 bytes) - multiplier 0xffffda61

Field	Value
seed	0100000000000000
outputSize	40
multiplier	4294957665
input	null
expected	5fdaffff0000000000a48705c0b4ffff 00240df6ef9f96102133a247671f62e3 ff167521a1c426df

Vector 2 — Seed 12345: First 5 outputs - standard test seed

Field	Value
seed	3930000000000000
outputSize	40
multiplier	4294957665
input	null
expected	5f9fe9f8383000000049dda20270d3f1 37d902ddd2555ae14f70a9434f1180d7 a208e25d4d3b9ee8

Vector 3 — Seed 0xDEADBEEF: First 5 outputs - hex seed value

Source: Self-generated test vector for verification

Field	Value
seed	efbeadde00000000
outputSize	40
multiplier	4294957665
input	null
expected	9f1fd0b6349eadde40612a60753e1d51 bad64c04749ff9c403f35a8a0c093799 a3245db13a84dd6c

Vector 4 — Seed 999999999: First 8 outputs - large seed

Source: Self-generated test vector for verification

Field	Value
seed	ffc99a3b00000000
outputSize	64
multiplier	4294957665
input	null
expected	9fe50f603cc19a3b4067f0093d2704fd b8575e50e735b04ac6eebd6f706e2275 f33f3670ca1665b54c8632ecffd5212a ed969ab4359f40dd9ad14da677f174f2

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