[Python-Dev] math.areclose ...?

[Alex Martelli]

On 2/6/06, Aahz <aahz at pythoncraft.com> wrote:
   ...
> > def areclose(x, y, relative_err = 1.e-5, absolute_err=1.e-8):
> >   diff = abs(x - y)
> >   ave = (abs(x) + abs(y))/2
> >   return diff < absolute_err or diff/ave < relative_err
> >
> > Also, separating the two terms with 'or' rather than '+' makes the
> > two error terms mean more what they are named. The '+' mixes the two
> > effects and even though the result is basically the same, it makes it
> > difficult to explain when the test will be true.
>
> Yes, that's a big help.  I was a bit concerned that this would have no
> utility for numbers with large magnitude.  Alex, given your focus on
> Python readability, I'm a bit surprised you didn't write this to start
> with!

As I said, I was just copying the definition in Numeric, which is
well-tried by long use.  Besides, this "clear expression" could
present problems, such as possible overflows or divisions by zero when
ave is 0 or very small; much as I care about readability, I care about
correctness even more.

Once it comes to readability, I prefer Numeric's choice to call the
two terms "tolerances", rather than (as here) "errors"; maybe that
depends on my roots being in engineering, where an error means a
mistake (like it does in real life), while tolerance's a good and
useful thing to have (ditto), rather than some scientific discipline
where terms carry different nuances.


Alex