`advance` and `randint` about ng-numpy-randomstate

[bashtage]

I hope the explanation above is clear. If not, let me know. I'll add to the documentation.

[bashtage]

randint is efficient in that is uses the smallest number of bytes required to produce the values from the PRNG, and so the dtype affects what you get. In the case of int32 it will generate 2 per 64-bit random generated by PCG.

The only generator that is absolutely guaranteed to behave like you see above is random_raw since it never will transform the underlying output of the PRNG. As you have seen, for some distributions this will always work. For others which use fewer bits (randint) or which use rejection sampling (many) then this simple relationship cannot be easily enforced.

g = rs.prng.pcg64.RandomState(0,0)
x = g.random_raw(10)
g = rs.prng.pcg64.RandomState(0,0)
g.advance(5)
y = g.random_raw(10)

import numpy as np
assert np.all(x[5:]==y[:-5])

[mkoerner]

Sorry for not replying earlier. The explanation was very helpful. As is more documentation. Given your description, a colleague and myself expected advance to "work well" with generating 64-bit random integers, but

import randomstate as rs
import numpy as np

g = rs.prng.pcg64.RandomState(0,0)
x = g.randint(256, size=10, dtype=np.uint64)
g = rs.prng.pcg64.RandomState(0,0)
g.advance(5)
y = g.randint(256, size=10, dtype=np.uint64)

assert np.all(x[5:]==y[:-5])

also raised an exception.

PS: Do you happen to know, if all bits of the numbers generated by PCG64 are of equal quality?

[bashtage]

This works as expected:

g = rs.prng.pcg64.RandomState(0,0)
x = g.randint(2**64-1, size=10, dtype=np.uint64)
g = rs.prng.pcg64.RandomState(0,0)
g.advance(5)
y = g.randint(2**64-1, size=10, dtype=np.uint64)

assert np.all(x[5:]==y[:-5])

You are seeing the behavior you see because of this optimization:

https://github.com/bashtage/ng-numpy-randomstate/blob/master/randomstate/distributions.c#L1415

which uses 32-bit integers when the value required is < 2**32.

[bashtage]

As for pcg64, I've never seen any problems when it is run through tests (which test for dependence in high/low bits). This said, If I needed a log of PRNGs I would go with xorshift1024 with jumps.

[mkoerner]

Ah. Thanks again for the clarification.
... and for the library 👍

Mathias