[Python-ideas] PEP 485: A Function for testing approximate equality

[Andrew Barnert]

On Jan 23, 2015, at 17:41, Chris Barker - NOAA Federal <chris.barker at noaa.gov> wrote:

>> One option would be to add a zero_tol argument, which is an absolute
>> tolerance that is only applied if expected == 0.
> 
> Here is where I'm not sure: is there only an issue with comparing to
> exactly zero? Or can vet small numbers under flow and cause the same
> problem?

Of course they can underflow. But I don't think that's a practical problem except in very rare cases. It means you're explicitly asking for better than +/- 2**min_exp, so it shouldn't be surprising that nothing but an exact match qualifies.

Take a concrete example: with a tol of
1e-5, it's only going to underflow if expected is around 1e-320 or below. But since the next smaller and larger numbers (9.95e-321 and 1.0005e-320) aren't within 1e-5, the test gives the right answer despite underflowing.

I'd have to think about it a bit to make sure there's no pathological case that doesn't work out that way--but really, if you're checking subnormal numbers for closeness with a general-purpose function, or checking for relative closeness pushing the bounds of 1 ulp without thinking about what that means, I suspect you're already doing something wrong at a much higher level.

So, just special-casing 0 should be sufficient.

Maybe the answer there is to have an is_close_to_0 function, instead of a parameter that's only useful if expected is 0? But then you might have, say, a comprehension where some of the expected values are 0 and some aren't, so maybe not...