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

[Stephen J. Turnbull]

Guido van Rossum writes:

 > the point of the [Newton's method] example is to show how you would
 > use is_close_to().

Except that this clearly is a Cauchy test, the algorithm doesn't know
the limit.  In principle, the appropriate computation would be
symmetric.  I don't think this is a problem in practice[1], but Skip's
"straddling the tick" example is much stronger for an asymmetric
comparison function.  On the other hand, Skip's case requires an
absolute comparison, not a relative one.

The whole discussion has been really fast and loose about use cases.
People with strong preferences can't seem to wrap their heads around
others' use cases, examples poorly matched to the proposals are
common, the expertise of the numerical experts seems irrelevant
because we *don't* want accuracy even in corner cases, we just want to
make it easier for naive users to avoid writing "x == y".  ISTM that
this PEP can be reduced to

    We need a floating comparison function that's good enough for
    government work, to help naive users avoid writing "x == y" for
    floating point comparisons.  There are use cases where one of the
    values is a known accurate value, so the comparison function is
    asymmetric.  This generally won't get things "too wrong" for
    symmetric comparisons, except where a relative comparison involves
    true values near zero.  Unfortunately, not much can be done in
    that case because it requires enough domain knowledge to realize
    that true values near zero occur and that this is a problem, so
    use of this function is covered by "consenting adults".[2]

    And oh yeah, IANAEINA.[3]  But for this PEP, I don't need to be.

<wink/>

Footnotes: 
[1]  I've reconsidered.  A priori, I still like symmetric errors
better in general, but the target audience for this function isn't
going to be reasoning about equivalence classes of IEEE 754 floats.

[2]  As is all use of floating point.

[3]  I am not an expert in numerical analysis.  Which IIUC applies to
the PEP author as well as to this poster.