[Cuis-dev] testing Float results

[Andres Valloud]

Indeed, it all depends on what is being done.  Sometimes a few ulps off 
is fine (because numerical analysis often cannot guarantee exact results 
for arbitrary inputs), and some other times even one ulp off is 
definitely wrong.

On 6/3/24 8:46 PM, Martin McClure via Cuis-dev wrote:
> Hi Mark,
> 
> Welcome to the list -- good to see you diving into Cuis!
> 
> As Andres says, there are messages to do this kind of test on Floats.
> 
> I find myself compelled, however, to warn about using such 
> "approximately equal" tests when inappropriate. I recently discovered 
> this kind of usage in an ancient test framework, and it was allowing 
> tests to pass that should not have. Those tests are being replaced with 
> equality tests.
> 
> As I commented to a co-worker just this morning, accepting as correct a 
> Float result that is one ULP different from the correct Float is really 
> no different than accepting 5 as a correct answer to 2 + 2.
> 
> There are, of course, times when figuring out the exact rounding 
> expected in a sequence of floating-point operations is impractical, and 
> accepting a certain amount of cumulative error is OK. Floats are often 
> used in applications where accuracy is only required to some specific 
> precision, but it's also good to keep in mind that each Float precisely 
> represents one value, and each operation on a Float has only one correct 
> answer.
> 
> Regards,
> -Martin
> 
> On 6/3/24 19:49, Andres Valloud via Cuis-dev wrote:
>> Look at Float>>isWithin:floatsFrom:, and see also Float>>ulp.
>>
>> On 6/3/24 4:36 PM, Mark Volkmann via Cuis-dev wrote:
>>> Is there a function that tests whether two Float values are "close" 
>>> (within some delta)?
>>> I can write it, but I thought that might be provided.
>>> I looked at all the methods in the Float class, but didn't find one 
>>> like that.
>>>
>>> -- 
>>> R. Mark Volkmann
>>> Object Computing, Inc.
>>>
>