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PCG64-DXSM

PCG variant using 128-bit state with DXSM (Double Xorshift Multiply) output permutation to produce 64-bit values. This is NumPy’s default random number generator, using a cheap 64-bit multiplier for improved performance while maintaining excellent statistical properties.

Properties

Property	Value
Category	Random Number Generators
Sub-category	Permuted Congruential Generator
Security status	🎓 Educational Only
Complexity	Intermediate
Inventor	Melissa E. O’Neill
Year	2019
Origin	🇺🇸 United States
Source	algorithms/random/pcg64-dxsm.js

Parameters

Parameter	Supported values
Seed sizes	16 bytes (128 bits)

Capabilities

Flag	Value
IsDeterministic	Yes
IsCryptographicallySecure	No

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Documentation

• Official PCG Website
• NumPy PCG64DXSM Documentation
• Original Paper: PCG: A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation
• Wikipedia: Permuted Congruential Generator

References

• NumPy PCG64DXSM Implementation
• PCG C Implementation (Official)
• PCG C++ Implementation (Official)
• Tony Finch’s PCG-DXSM Implementation

Test vectors

1 vector ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — PCG64-DXSM state=0, inc=1: first 10 x 64-bit outputs (NumPy verified)

Field	Value
seed	00000000000000010000000000000000
outputSize	80
input	null
expected	00000000000000000000000000000000 00000000000000005238ea76d1f0df4a 1a3c4747022e48a4340b0228e6afc056 81bb52f8baaa203a0fd17a4a4b0a1ce3 55fe9ec2c245a242a2f6d5a82a0704f9

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