Permuted Congruential Generator 2.0 (64-bit Multiplier, DXSM Output)

class randomgen.pcg64.PCG64DXSM(seed=None, inc=None)

Container for the PCG-64 updated with a 64-bit mult using DXSM output func.

Pre-configured alias for PCG64 with variant=”dxsm” and mode=”sequence”. This bit generator will likely become the default in NumPy in the near future ([3]).

Parameters:

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

Random seed initializing the pseudo-random number generator. Can be an integer in [0, 2**128), a SeedSequence instance or None (the default). If seed is None, then PCG64DXSM will used a SeedSequence initialized with system entropy to Seed the generator

inc{None, int}, optional

The increment in the LCG. Can be an integer in [0, 2**128) or None. If inc is None, then it is initialized using the same SeedSeuqnce used for seed.

See also

numpy.random.PCG64

randomgen.pcg64.PCG64

randomgen.pcg64.LCG128Mix

Notes

Random variates are generated by permuting the output of a 128-bit LCG

\[s_{n+1} = m s_{n} + i \mod 2^{128}\]

where \(s\) is the state of the generator, \(m\) is the multipler and \(i\) is the increment. The multipler is a 64-bit unsigned integer with good spectral properties. The output of the LCG is the permuted using the DXSM output function which is similar to an Xorshift ([1], [2]).

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 RNG is represented by a 128-bit unsigned integer.

State and Seeding

The PCG64DXSM state vector consists of 2 unsigned 128-bit values, which are represented externally as Python ints. PCG64DXSM is seeded using a single 128-bit unsigned integer. In addition, a second 128-bit unsigned integer is used as the increment in the LCG.

Compatibility Guarantee

PCG64DXSM 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”, https://www.pcg-random.org/

[2]

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

[3]

NumPy GitHub Repository. 2020. The PCG Implementation Provided By Numpy Has Significant, Dangerous Self-Correlation. [online] Available at: <https://github.com/numpy/numpy/issues/16313> [Accessed 16 June 2020].

Examples

Parallel Features

PCG64DXSM can be used in parallel applications by calling advance with a different value on each instance to produce non-overlapping sequences.

>>> from numpy.random import Generator
>>> from randomgen import PCG64DXSM
>>> rg = [Generator(PCG64DXSM(1234, i + 1)) for i in range(10)]
>>> for i in range(10):
...     rg[i].bit_generator.advance(i * 2**64)

Attributes:

lockthreading.Lock

Lock instance that is shared so that the same bit git generator can be used in multiple Generators without corrupting the state. Code that generates values from a bit generator should hold the bit generator’s lock.

seed_seq{None, SeedSequence}

The SeedSequence instance used to initialize the generator if mode is “sequence” or is seed is a SeedSequence. None if mode is “legacy”.

Seeding and State

seed([seed, inc])	Seed the generator
state	Get or set the PRNG state

Parallel generation

advance(delta)	Advance the underlying RNG as-if delta draws have occurred.
jump(iter)	Not implemented.
jumped([iter])	Returns a new bit generator with the state jumped

Extending

cffi	CFFI interface
ctypes	ctypes interface

Testing

random_raw([size, output])

Return randoms as generated by the underlying BitGenerator