Hawkynt

Multiply-with-Carry (MWC)

George Marsaglia’s lag-1 multiply-with-carry generator with base 2^32: a 64-bit state holds the current value and the carry, and each step computes x = a * (x mod 2^32) + floor(x / 2^32), returning the low 32 bits. The default multiplier 0xFFFFDA61 is the one used by javamex and Numerical Recipes.

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 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: A new class of random number generators (1991)
• javamex: Multiply-with-carry generator in Java
• Wikipedia: Multiply-with-carry pseudorandom number generator

References

• Numerical Recipes (3rd ed., p. 348)
• Efficient MWC Random Number Generators with Maximal Period

Test vectors

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

Vector 1 — Seed 1, multiplier 0xFFFFDA61: first 10 outputs

Field	Value
seed	01000000
outputSize	40
multiplier	4294957665
input	null
expected	61daffffc1588705e3af1b01f54ae954 8eb8608c48182a2a3527b9462b0f807a 1b7afeae653fcc02

Vector 2 — Seed 12345: first 10 outputs

Field	Value
seed	39300000
outputSize	40
input	null
expected	99cfe9f83123c79b95ba2470c2a0ffa5 9cc723647902ed47beb29376e57d5b49 16578ead732e5deb

Vector 3 — Seed 0xDEADBEEF: first 10 outputs

Field	Value
seed	efbeadde
outputSize	40
input	null
expected	8fde7d9564b855d47bce9950cb93f689 8ea017fd524115ee6e0f730b04a36330 443a0197ab973439

Vector 4 — Seed 999999999: first 16 outputs

Field	Value
seed	ffc99a3b
outputSize	64
input	null
expected	9fafaa9b7bb235e159f784f81b14e04e 0f6f709833e3fd60fbdce9a80d4ecdaa 15691ee7e8e7b9b906b622aee3e0db8d 722011cb3c2b88f4567c3e3ce35fc081

Vector 5 — Value 0xDEADBEEF with carry 0x12345678: first 8 outputs

Field	Value
seed	efbeadde78563412
outputSize	32
input	null
expected	0735b2a7dcab54f5be92440bcded870cc43d799d393b4db83821f2fb5b661d3e

Vector 6 — Fixed point: value 2^32 - 1 with carry a - 1 (largest carry) repeats

Field	Value
seed	ffffffff60daffff
outputSize	16
input	null
expected	ffffffffffffffffffffffffffffffff

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