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https://github.com/nsajko/go-prng-test

Go PRNG experiments
https://github.com/nsajko/go-prng-test

golang prng rng

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Go PRNG experiments

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### Some tests for some properties of the math/rand PRNG which are mainly related to its initialization



The PRNG of the math/rand package is implemented by the rngSource struct, which has the Seed method, whose beginning contains a surprise:



```

	seed = seed % int32max

	if seed < 0 {

		seed += int32max

	}

	if seed == 0 {

		seed = 89482311

	}

```



See https://tip.golang.org/src/math/rand/rng.go



(The constant ```int32max``` defined as ```(1 << 31) - 1``` in the same file.)



The Seed function throws away entropy, even though even the full 64 bits (seed is of type int64) wouldn't be enough to fill the _huge_ 4856-byte state of the PRNG! This is actually partially documented, at least for the default Source, for which the documentation says:



> Seed values that have the same remainder when divided by 2³¹-1 generate the same pseudo-random sequence.



[This](https://www.pcg-random.org/posts/cpp-seeding-surprises.html) blog post prompted me to do some tests to check how the small amount (relative to state size) of input entropy affects certain qualities of the rngSource PRNG.



#### Terminology



I'm not an expert (far from it), so it's possible I'm abusing some terminology myself. I'll give this definition though, it might help someone.



The pseudo-random stream/sequence, mentioned in several places in this repo, refers to the ordered collection of number values generated by a PRNG (pseudo-random number generator). The "pseudo" is because these are deterministic algorithms, as opposed to true randomness.



Sometimes I refer to positions within the stream, position 0 is the first generated value, position 1 is the second one, etc.



#### Results



See [this](go1-init-interesting/README.md) for the results regarding generated values that belong to a small predetermined range.



See [this](go1-init-int63/README.md) for the results of a test that concetrates on math/rand.Rand.Int63, and the first position of its pseudo-random sequences, counting how many distinct generated values exist.



#### Go 2?



Note that the experimental code in golang.org/x/exp/rand, currently the intended replacement for math/rand in Go 2, (apart from implementing a better PRNG algorithm) has the method UnmarshalBinary (on PCGSource), which kind of prevents similar issues there, as it makes it possible to initialize the entire 128-bit state of the PRNG. But PCGSource also has a Seed method, which only takes a single uint64 input value as the seed, and the Source interface in golang.org/x/exp/rand only includes the Seed method. I hope the Source interface gets a redesign before any breaking changes to Go are made, maybe the API could be based on a sponge/duplex construction (which would be quite flexible, enable reseeding, but would perhaps be a better fit to a PRNG that actually is a sponge/duplex, unlike the simpler PCG family).