Permuted Congruential Generator (64-bit, PCG64)

class numpy.random.PCG64(seed=None)

BitGenerator for the PCG-64 pseudo-random number generator.

Parameters

seed{None, int, array_like[ints], SeedSequence}, optional

A seed to initialize the BitGenerator. If None, then fresh, unpredictable entropy will be pulled from the OS. If an int or array_like[ints] is passed, then it will be passed to SeedSequence to derive the initial BitGenerator state. One may also pass in a SeedSequence instance.

Notes

PCG-64 is a 128-bit implementation of O’Neill’s permutation congruential generator ([1], [2]). PCG-64 has a period of and supports advancing an arbitrary number of steps as well as streams. The specific member of the PCG family that we use is PCG XSL RR 128/64 as described in the paper ([2]).

PCG64 provides a capsule containing function pointers that produce doubles, and unsigned 32 and 64- bit integers. These are not directly consumable in Python and must be consumed by a Generator or similar object that supports low-level access.

Supports the method advance to advance the RNG an arbitrary number of steps. The state of the PCG-64 RNG is represented by 2 128-bit unsigned integers.

State and Seeding

The PCG64 state vector consists of 2 unsigned 128-bit values, which are represented externally as Python ints. One is the state of the PRNG, which is advanced by a linear congruential generator (LCG). The second is a fixed odd increment used in the LCG.

The input seed is processed by SeedSequence to generate both values. The increment is not independently settable.

Parallel Features

The preferred way to use a BitGenerator in parallel applications is to use the SeedSequence.spawn method to obtain entropy values, and to use these to generate new BitGenerators:

>>> from numpy.random import Generator, PCG64, SeedSequence
>>> sg = SeedSequence(1234)
>>> rg = [Generator(PCG64(s)) for s in sg.spawn(10)]

Compatibility Guarantee

PCG64 makes a guarantee that a fixed seed and will always produce the same random integer stream.

References

1

“PCG, A Family of Better Random Number Generators”

2(1,2)

O’Neill, Melissa E. “PCG: A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation”

State

Parallel generation

Extending