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XorShift128

XorShift128 is a very fast pseudo-random number generator invented by George Marsaglia. It uses three xorshift operations on a 128-bit state to generate high-quality random numbers with a period of 2^128-1. Widely used in simulations and gaming.

Properties

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

References

• TestU01 Statistical Testing Suite
• Modern PRNG Alternatives (xoshiro/xoroshiro)

Test vectors

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

Vector 1 — Seed (1,2,3,4): First 5 outputs (20 bytes) - verified against reference C implementation

Field	Value
seed	00000001000000020000000300000004
outputSize	20
input	null
expected	0000080d0000181f00000004000020200040004d

Vector 2 — Seed (123456789, 362436069, 521288629, 88675123): First 10 outputs - Marsaglia’s standard test seed

Field	Value
seed	075bcd15159a55e51f123bb505491333
outputSize	40
input	null
expected	dca345ea1b5116e6951049aad88d00b0 1ec7825e8db241469af814432ac00f2c 0837ad5817906569

Vector 3 — Seed (1,1,1,1): First 8 outputs - all identical seed values

Field	Value
seed	00000001000000010000000100000001
outputSize	32
input	null
expected	0000080800000001000008080000000100400841004000400000080800000001

Vector 4 — Seed (1000000, 2000000, 3000000, 4000000): First 5 outputs - large seed values

Field	Value
seed	000f4240001e8480002dc6c0003d0900
outputSize	20
input	null
expected	7a5a56058e94e74ae0e12b9e087c4b8ba03edeff

Vector 5 — Seed (1,2,3,4): Outputs 11-15 - verifies long-term state progression

Field	Value
seed	00000001000000020000000300000004
outputSize	20
skip	10
input	null
expected	00c28a0f004ed75811c11a8922431ffe36c57b4b

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