numpy.random._pcg64:PCG64DXSM

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.