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Xorshift64

Xorshift64 is a very fast pseudo-random number generator invented by George Marsaglia. It uses three xorshift operations on a single 64-bit state to generate random numbers with a period of 2^64-1. Commonly used in game engines and simulations.

Properties

Property	Value
Category	Random Number Generators
Sub-category	Xorshift Family
Security status	🎓 Educational Only
Complexity	Beginner
Inventor	George Marsaglia
Year	2003
Origin	🇺🇸 United States
Source	algorithms/random/xorshift64.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: Xorshift RNGs (Marsaglia, 2003)
• Wikipedia: Xorshift
• Analysis by Sebastiano Vigna
• Reference Implementation (Stack Overflow)

References

• TestU01 Statistical Testing Suite
• Modern PRNG Alternatives (xoshiro/xoroshiro)
• Note on Marsaglia’s Xorshift RNGs (Panneton and L’Ecuyer)

Test vectors

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

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

Field	Value
seed	0000000000000001
outputSize	40
input	null
expected	0000000040822041100041060c011441 9b1e842f6e862629f554f503555d8025 860c1fb090599265

Vector 2 — Seed 88172645463325252: First 3 outputs (24 bytes) - from Marsaglia’s examples

Field	Value
seed	0139408dcbbf7a44
outputSize	24
input	null
expected	79690975fbde15b02a337357ae2cc59b2fef107a27529ad0

Vector 3 — Seed 12345: First 5 outputs (40 bytes) - common test seed

Field	Value
seed	0000000000003039
outputSize	40
input	null
expected	00000c163a391e199c0eb9542f03ca65 a228090ad781f4b120f578d6eaf5fb18 7b76f0b8e8e1d6ee

Vector 4 — Seed 0 (becomes 1): First 5 outputs (40 bytes) - zero seed handling

Field	Value
seed	0000000000000000
outputSize	40
input	null
expected	0000000040822041100041060c011441 9b1e842f6e862629f554f503555d8025 860c1fb090599265

Vector 5 — Seed 9223372036854775807 (max int64): First 5 outputs - large seed value

Field	Value
seed	7fffffffffffffff
outputSize	40
input	null
expected	810000003f801fc08ffdbffe03feefff ce8fc004c67d0de0ba17a467eef88ffb 901172f84eb1e024

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