Permuted Congruential Generator (64-bit, PCG64 DXSM)

class numpy.random.PCG64DXSM(seed=None)

BitGenerator for the PCG-64 DXSM 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 DXSM is a 128-bit implementation of O’Neill’s permutation congruential generator ([1], [2]). PCG-64 DXSM has a period of \(2^{128}\) and supports advancing an arbitrary number of steps as well as \(2^{127}\) streams. The specific member of the PCG family that we use is PCG CM DXSM 128/64. It differs from PCG64 in that it uses the stronger DXSM output function, a 64-bit “cheap multiplier” in the LCG, and outputs from the state before advancing it rather than advance-then-output.

PCG64DXSM 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 DXSM RNG is represented by 2 128-bit unsigned integers.

State and Seeding

The PCG64DXSM 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, PCG64DXSM, SeedSequence
>>> sg = SeedSequence(1234)
>>> rg = [Generator(PCG64DXSM(s)) for s in sg.spawn(10)]

Compatibility Guarantee

PCG64DXSM makes a guarantee that a fixed seed will always produce the same random integer stream.

References

1

“PCG, A Family of Better Random Number Generators”

2

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

State

state

Get or set the PRNG state

Parallel generation

advance(delta)	Advance the underlying RNG as-if delta draws have occurred.
jumped([jumps])	Returns a new bit generator with the state jumped.

Extending

cffi	CFFI interface
ctypes	ctypes interface

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