ndigits(big(0), 1) does not raise an error

[yuyichao]

I'm not sure if it should but it is in the test and I've just triggered it once while stress testing #13995 .

Either way, the test needs to be fixed with explicit test for this case added. The implementation possibly needs fixing too if an error is desired.

[Keno]

Also ndigits(1, 1) hangs for me.

[dpsanders]

Shouldn't bases -1, 0 and 1 all give errors?

[Keno]

There may be an argument to be made that ndigits(x, 1) = x. I believe 0 and negative numbers are already errors.

[yuyichao]

iiuc base 1 can really only represent 0 so returning 1 in that case (ndigits(0, 1)) makes some sense (I'd be quite surprised if anyone really relies on that behavior though) all other cases should be error, which is what the failing test is testing (at least for BigInt).

[rfourquet]

cf. https://en.wikipedia.org/wiki/Non-standard_positional_numeral_systems for an idea why ndigits(x, 1) = x can make sense, but it may be too non-standard to be implemented in base. I think I would also favor erroring on bases -1, 1, and 0, even when x==0.

[TotalVerb]

We would need to have a bijective_ndigits for that to make sense, and I think that's outside the scope of Base.

[simonbyrne]

What does a negative base mean?

[StefanKarpinski]

Negative bases are a real thing, e.g. negabinary. Since I believe there's only one thing they can mean, we might want to just support them correctly. But clearly it's not a high priority.

[simonbyrne]

Okay, but that isn't documented anywhere, nor are they supported by the base function.