[Python-ideas] Way to check for floating point "closeness"?

[Ron Adam]

On 01/13/2015 09:53 AM, Chris Barker - NOAA Federal wrote:
>> >On Jan 13, 2015, at 1:29 AM, Mark Dickinson<dickinsm at gmail.com>  wrote:
>> >
>> >
>> >Comparing by ulps was what I needed for testing library-quality functions for the math and cmath modules; I doubt that it's what's needed for most comparison tasks.
> That's the conclusion I was coming to. Ulps are likely to be the right
> way to do it if your trying to understand/test the accuracy of an
> algorithm, but not for general "did I get a close enough result". And
> it would be a lot harder to understand for most of us.
>
> As for comparing to zero -- in reading about this, it seems there
> simply is no general solution -- only the user knows what they want.
> So the only thing to do is a big warning in the docs about it, and
> providing an absolute tolerance option.
>
> Should that a separate function or a flag?
>
> This is actually a harder problem for numpy, as it's an array
> function, so you need to have the same function/parameters for every
> value in the array, some of which may be near zero.
>
> I haven't thought it out yet, but maybe we could specify an absolute
> tolerance near zero, and a relative tolerance elsewhere, both at once.
> Tricky to document, even if possible.

Doesn't this problem come up at any boundary comparison, and not just zero?

So isn't the issue about any n distance from any floating point number that 
is less than 1 ulp?  And in that regard, comparison to zero is no different 
than any comparison to any other floating point value?

Just trying to follow along,
   -Ron


>> >   I'd expect the suggested combination of relative error and absolute error to be more appropriate most of the time.
> And most of the time is what we are going for.