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 anint
orarray_like[ints]
is passed, then it will be passed toSeedSequence
to derive the initialBitGenerator
state. One may also pass in aSeedSequence
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 aGenerator
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 and will always produce the same random integer stream.References