SFC64 Generator¶
- class randomgen.sfc.SFC64(seed=None, w=1, k=1, *, mode='sequence')¶
Chris Doty-Humphrey’s Small Fast Chaotic PRNG with optional Weyl Sequence
- 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
orarray_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.- w{uint64, None}, default 1
The starting value of the Weyl sequence. If None, then the initial value is generated from the SeedSequence.
- k{uint64, None}, default 1
The increment to the Weyl sequence. Must be odd, and if even, 1 is added. If None, then k is generated from the `SeedSequence.
- mode{“sequence”, “numpy”}
The default uses a seed sequence to initialize all unspecified values. When using “numpy” uses the seed sequence to initialize three values and checks that both w and k are 1.
Notes
SFC64
is a 256-bit implementation of Chris Doty-Humphrey’s Small Fast Chaotic PRNG ([1]).SFC64
has a few different cycles that one might be on, depending on the seed; the expected period will be about \(2^{255}\) ([2]).SFC64
incorporates a 64-bit counter which means that the absolute minimum cycle length is \(2^{64}\) and that distinct seeds will not run into each other for at least \(2^{64}\) iterations.SFC64
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.State and Seeding
The
SFC64
state vector consists of 4 unsigned 64-bit values. The last is a 64-bit counter that increments by 1 each iteration. The input seed is processed by SeedSequence to generate the first 3 values, then theSFC64
algorithm is iterated a small number of times to mix.Compatibility Guarantee
SFC64
makes a guarantee that a fixed seed will always produce the same random integer stream.References
- 1
“PractRand”. http://pracrand.sourceforge.net/RNG_engines.txt.
- 2
“Random Invertible Mapping Statistics”. https://www.pcg-random.org/posts/random-invertible-mapping-statistics.html.
Examples
SFC64
supports generating distinct streams using different Weyl increments. The recommend practice is to chose a set of distinct odd coefficients that have 32 or fewer bits set of 1 (i.e., <= 50%).>>> import numpy as np >>> from randomgen import SFC64, SeedSequence >>> NUM_STREAMS = 8196 >>> seed_seq = SeedSequence(325874985469) >>> bit_gen = SFC64(seed_seq) >>> weyl_inc = bit_gen.weyl_increments(NUM_STREAMS) >>> streams = [SFC64(seed_seq, k=k) for k in list(weyl_inc)] >>> [stream.random_raw() for stream in streams[:3]] [13020151409549081939, 8062752282355435850, 13933250373249421220]
Seeding and State¶
| Seed the generator |
Get or set the PRNG state |
Extending¶
CFFI interface | |
ctypes interface |
Testing¶
| Return randoms as generated by the underlying BitGenerator |
Parallelization¶
| Generate distinct Weyl increments to construct multiple streams |