[matklad]

It is much better than this. You can _directly_ enumerate all the objects, without any probabilities involved. There's nothing about probabilities in the interface of a PRNG, it's just non-determinism!

You could _implement_ non-determinism via probabilistic sampling, but you could also implement the same interface as exhaustive search.

[pfdietz]

Well, yes. But the point is that random sampling lets you do it without thinking. Even better, it can sample over multiple spaces at the same time, and over spaces we haven't even yet formalized. "Civilization advances by extending the number of important operations which we can perform without thinking of them." (Whitehead)

An example is something like "pairwise testing" of arguments to a function. Just randomly generating values will hit all possible pairs of values to arguments, again with a logarithmic penalty.

[AlotOfReading]

The point is that you can exhaustively explore the space without logarithmic overhead. There's no benefits to doing it with random sampling and it doesn't even save thought.

[pfdietz]

I already explained what the benefit is. What is it with this focus on offloading work from computers to people? Let people do things more easily without thinking, even if it burns more increasingly cheap cycles.

[AlotOfReading]

You haven't explained what the benefit is. There aren't "spaces we haven't formalized" because of the pigeonhole principle. There are M bits. You can generate every one of those 2^M values with any max cycle permutation.

What work is being offloaded from computers to people? It's exactly the same thing with more determinism and no logarithmic overhead.

[pfdietz]

> There aren't any "spaces we haven't formalized"

Suppose that space of N points is partitioned into M relevant subsets, for now we assume of the same size. Then random sampling hits each of those subsets in O(M log M) time, even if we don't know what they are.

This sort of partitioning is long talked about in the testing literature, with the idea you should do it manually.

> what work is being offloaded

The need to write that program for explicitly enumerating the space.

[matklad]

Just to avoid potential confusion, the claim is that this is a function that generates a random permutation:

    pub fn shuffle(g: *Gen, T: type, slice: []T) void {
        if (slice.len <= 1) return;

        for (0..slice.len - 1) |i| {
            const j = g.range_inclusive(u64, i, slice.len - 1);
            std.mem.swap(T, &slice[i], &slice[j]);
        }
    }

And this is a function that enumerates all permutations, in order, exactly once:

    pub fn shuffle(g: *Gen, T: type, slice: []T) void {
        if (slice.len <= 1) return;

        for (0..slice.len - 1) |i| {
            const j = g.range_inclusive(u64, i, slice.len - 1);
            std.mem.swap(T, &slice[i], &slice[j]);
        }
    }

Yes, they are exactly the same function. What matters is Gen. If it looks like this

https://github.com/tigerbeetle/tigerbeetle/blob/809fe06a2ffc...

then you get a random permutation. If it rather looks like this

https://github.com/tigerbeetle/tigerbeetle/blob/809fe06a2ffc...

you enumerate all permutations.

[AlotOfReading]

What's being suggested also has the m log m partition behavior in the limit where N >> M. It might be easier to see why these are actually the same things with slightly different limits, imagine a huge N enumerated by an LFSR. We'll call our enumeration function rand() for tradition's sake. Now we're back to sampling.